Properties

Label 966.2.l.b.47.2
Level $966$
Weight $2$
Character 966.47
Analytic conductor $7.714$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(47,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.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: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 47.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 966.47
Dual form 966.2.l.b.185.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.73205 - 3.00000i) q^{5} +1.73205 q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.73205 - 3.00000i) q^{5} +1.73205 q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(1.50000 + 0.866025i) q^{12} -3.46410i q^{13} +(-1.73205 - 2.00000i) q^{14} -6.00000i q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.866025 + 1.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(6.00000 + 3.46410i) q^{19} +3.46410 q^{20} +(-4.50000 + 0.866025i) q^{21} -3.00000 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.866025 + 1.50000i) q^{24} +(-3.50000 - 6.06218i) q^{25} +(1.73205 - 3.00000i) q^{26} -5.19615i q^{27} +(-0.500000 - 2.59808i) q^{28} -3.00000i q^{29} +(3.00000 - 5.19615i) q^{30} +(3.00000 - 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.59808 + 4.50000i) q^{33} +1.73205i q^{34} +(-6.92820 + 6.00000i) q^{35} +3.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(3.46410 + 6.00000i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(3.00000 + 1.73205i) q^{40} -3.46410 q^{41} +(-4.33013 - 1.50000i) q^{42} +10.0000 q^{43} +(-2.59808 - 1.50000i) q^{44} +(-5.19615 - 9.00000i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-4.33013 + 7.50000i) q^{47} +1.73205i q^{48} +(5.50000 + 4.33013i) q^{49} -7.00000i q^{50} +(2.59808 + 1.50000i) q^{51} +(3.00000 - 1.73205i) q^{52} +(-10.3923 + 6.00000i) q^{53} +(2.59808 - 4.50000i) q^{54} +10.3923i q^{55} +(0.866025 - 2.50000i) q^{56} +12.0000 q^{57} +(1.50000 - 2.59808i) q^{58} +(6.92820 + 12.0000i) q^{59} +(5.19615 - 3.00000i) q^{60} +(-12.0000 - 6.92820i) q^{61} +3.46410 q^{62} +(-6.00000 + 5.19615i) q^{63} -1.00000 q^{64} +(-10.3923 - 6.00000i) q^{65} +(-4.50000 + 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-0.866025 + 1.50000i) q^{68} -1.73205 q^{69} +(-9.00000 + 1.73205i) q^{70} -9.00000i q^{71} +(2.59808 + 1.50000i) q^{72} +(7.50000 - 4.33013i) q^{73} +(1.73205 - 1.00000i) q^{74} +(-10.5000 - 6.06218i) q^{75} +6.92820i q^{76} +(7.79423 - 1.50000i) q^{77} -6.00000i q^{78} +(-5.50000 + 9.52628i) q^{79} +(1.73205 + 3.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 - 1.73205i) q^{82} +3.46410 q^{83} +(-3.00000 - 3.46410i) q^{84} +6.00000 q^{85} +(8.66025 + 5.00000i) q^{86} +(-2.59808 - 4.50000i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-3.46410 + 6.00000i) q^{89} -10.3923i q^{90} +(-3.00000 + 8.66025i) q^{91} -1.00000i q^{92} +(3.00000 - 5.19615i) q^{93} +(-7.50000 + 4.33013i) q^{94} +(20.7846 - 12.0000i) q^{95} +(-0.866025 + 1.50000i) q^{96} +3.46410i q^{97} +(2.59808 + 6.50000i) q^{98} +9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} + 2 q^{4} - 10 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{3} + 2 q^{4} - 10 q^{7} + 6 q^{9} + 12 q^{10} + 6 q^{12} - 2 q^{16} + 24 q^{19} - 18 q^{21} - 12 q^{22} - 14 q^{25} - 2 q^{28} + 12 q^{30} + 12 q^{31} + 12 q^{36} + 4 q^{37} - 12 q^{39} + 12 q^{40} + 40 q^{43} - 2 q^{46} + 22 q^{49} + 12 q^{52} + 48 q^{57} + 6 q^{58} - 48 q^{61} - 24 q^{63} - 4 q^{64} - 18 q^{66} + 8 q^{67} - 36 q^{70} + 30 q^{73} - 42 q^{75} - 22 q^{79} - 18 q^{81} - 12 q^{82} - 12 q^{84} + 24 q^{85} - 6 q^{88} - 12 q^{91} + 12 q^{93} - 30 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 1.50000 0.866025i 0.866025 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.73205 3.00000i 0.774597 1.34164i −0.160424 0.987048i \(-0.551286\pi\)
0.935021 0.354593i \(-0.115380\pi\)
\(6\) 1.73205 0.707107
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 1.00000i 0.353553i
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 3.00000 1.73205i 0.948683 0.547723i
\(11\) −2.59808 + 1.50000i −0.783349 + 0.452267i −0.837616 0.546259i \(-0.816051\pi\)
0.0542666 + 0.998526i \(0.482718\pi\)
\(12\) 1.50000 + 0.866025i 0.433013 + 0.250000i
\(13\) 3.46410i 0.960769i −0.877058 0.480384i \(-0.840497\pi\)
0.877058 0.480384i \(-0.159503\pi\)
\(14\) −1.73205 2.00000i −0.462910 0.534522i
\(15\) 6.00000i 1.54919i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.866025 + 1.50000i 0.210042 + 0.363803i 0.951727 0.306944i \(-0.0993066\pi\)
−0.741685 + 0.670748i \(0.765973\pi\)
\(18\) 2.59808 1.50000i 0.612372 0.353553i
\(19\) 6.00000 + 3.46410i 1.37649 + 0.794719i 0.991736 0.128298i \(-0.0409513\pi\)
0.384759 + 0.923017i \(0.374285\pi\)
\(20\) 3.46410 0.774597
\(21\) −4.50000 + 0.866025i −0.981981 + 0.188982i
\(22\) −3.00000 −0.639602
\(23\) −0.866025 0.500000i −0.180579 0.104257i
\(24\) 0.866025 + 1.50000i 0.176777 + 0.306186i
\(25\) −3.50000 6.06218i −0.700000 1.21244i
\(26\) 1.73205 3.00000i 0.339683 0.588348i
\(27\) 5.19615i 1.00000i
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) 3.00000i 0.557086i −0.960424 0.278543i \(-0.910149\pi\)
0.960424 0.278543i \(-0.0898515\pi\)
\(30\) 3.00000 5.19615i 0.547723 0.948683i
\(31\) 3.00000 1.73205i 0.538816 0.311086i −0.205783 0.978598i \(-0.565974\pi\)
0.744599 + 0.667512i \(0.232641\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −2.59808 + 4.50000i −0.452267 + 0.783349i
\(34\) 1.73205i 0.297044i
\(35\) −6.92820 + 6.00000i −1.17108 + 1.01419i
\(36\) 3.00000 0.500000
\(37\) 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 3.46410 + 6.00000i 0.561951 + 0.973329i
\(39\) −3.00000 5.19615i −0.480384 0.832050i
\(40\) 3.00000 + 1.73205i 0.474342 + 0.273861i
\(41\) −3.46410 −0.541002 −0.270501 0.962720i \(-0.587189\pi\)
−0.270501 + 0.962720i \(0.587189\pi\)
\(42\) −4.33013 1.50000i −0.668153 0.231455i
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) −2.59808 1.50000i −0.391675 0.226134i
\(45\) −5.19615 9.00000i −0.774597 1.34164i
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) −4.33013 + 7.50000i −0.631614 + 1.09399i 0.355608 + 0.934635i \(0.384274\pi\)
−0.987222 + 0.159352i \(0.949059\pi\)
\(48\) 1.73205i 0.250000i
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 7.00000i 0.989949i
\(51\) 2.59808 + 1.50000i 0.363803 + 0.210042i
\(52\) 3.00000 1.73205i 0.416025 0.240192i
\(53\) −10.3923 + 6.00000i −1.42749 + 0.824163i −0.996922 0.0783936i \(-0.975021\pi\)
−0.430570 + 0.902557i \(0.641688\pi\)
\(54\) 2.59808 4.50000i 0.353553 0.612372i
\(55\) 10.3923i 1.40130i
\(56\) 0.866025 2.50000i 0.115728 0.334077i
\(57\) 12.0000 1.58944
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 6.92820 + 12.0000i 0.901975 + 1.56227i 0.824927 + 0.565240i \(0.191216\pi\)
0.0770484 + 0.997027i \(0.475450\pi\)
\(60\) 5.19615 3.00000i 0.670820 0.387298i
\(61\) −12.0000 6.92820i −1.53644 0.887066i −0.999043 0.0437377i \(-0.986073\pi\)
−0.537400 0.843328i \(-0.680593\pi\)
\(62\) 3.46410 0.439941
\(63\) −6.00000 + 5.19615i −0.755929 + 0.654654i
\(64\) −1.00000 −0.125000
\(65\) −10.3923 6.00000i −1.28901 0.744208i
\(66\) −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 \(0.754762\pi\)
\(68\) −0.866025 + 1.50000i −0.105021 + 0.181902i
\(69\) −1.73205 −0.208514
\(70\) −9.00000 + 1.73205i −1.07571 + 0.207020i
\(71\) 9.00000i 1.06810i −0.845452 0.534052i \(-0.820669\pi\)
0.845452 0.534052i \(-0.179331\pi\)
\(72\) 2.59808 + 1.50000i 0.306186 + 0.176777i
\(73\) 7.50000 4.33013i 0.877809 0.506803i 0.00787336 0.999969i \(-0.497494\pi\)
0.869935 + 0.493166i \(0.164160\pi\)
\(74\) 1.73205 1.00000i 0.201347 0.116248i
\(75\) −10.5000 6.06218i −1.21244 0.700000i
\(76\) 6.92820i 0.794719i
\(77\) 7.79423 1.50000i 0.888235 0.170941i
\(78\) 6.00000i 0.679366i
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 1.73205 + 3.00000i 0.193649 + 0.335410i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −3.00000 1.73205i −0.331295 0.191273i
\(83\) 3.46410 0.380235 0.190117 0.981761i \(-0.439113\pi\)
0.190117 + 0.981761i \(0.439113\pi\)
\(84\) −3.00000 3.46410i −0.327327 0.377964i
\(85\) 6.00000 0.650791
\(86\) 8.66025 + 5.00000i 0.933859 + 0.539164i
\(87\) −2.59808 4.50000i −0.278543 0.482451i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) −3.46410 + 6.00000i −0.367194 + 0.635999i −0.989126 0.147073i \(-0.953015\pi\)
0.621932 + 0.783072i \(0.286348\pi\)
\(90\) 10.3923i 1.09545i
\(91\) −3.00000 + 8.66025i −0.314485 + 0.907841i
\(92\) 1.00000i 0.104257i
\(93\) 3.00000 5.19615i 0.311086 0.538816i
\(94\) −7.50000 + 4.33013i −0.773566 + 0.446619i
\(95\) 20.7846 12.0000i 2.13246 1.23117i
\(96\) −0.866025 + 1.50000i −0.0883883 + 0.153093i
\(97\) 3.46410i 0.351726i 0.984415 + 0.175863i \(0.0562716\pi\)
−0.984415 + 0.175863i \(0.943728\pi\)
\(98\) 2.59808 + 6.50000i 0.262445 + 0.656599i
\(99\) 9.00000i 0.904534i
\(100\) 3.50000 6.06218i 0.350000 0.606218i
\(101\) 7.79423 + 13.5000i 0.775555 + 1.34330i 0.934482 + 0.356010i \(0.115863\pi\)
−0.158927 + 0.987290i \(0.550804\pi\)
\(102\) 1.50000 + 2.59808i 0.148522 + 0.257248i
\(103\) 7.50000 + 4.33013i 0.738997 + 0.426660i 0.821705 0.569914i \(-0.193023\pi\)
−0.0827075 + 0.996574i \(0.526357\pi\)
\(104\) 3.46410 0.339683
\(105\) −5.19615 + 15.0000i −0.507093 + 1.46385i
\(106\) −12.0000 −1.16554
\(107\) 10.3923 + 6.00000i 1.00466 + 0.580042i 0.909624 0.415432i \(-0.136370\pi\)
0.0950377 + 0.995474i \(0.469703\pi\)
\(108\) 4.50000 2.59808i 0.433013 0.250000i
\(109\) 8.50000 + 14.7224i 0.814152 + 1.41015i 0.909935 + 0.414751i \(0.136131\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −5.19615 + 9.00000i −0.495434 + 0.858116i
\(111\) 3.46410i 0.328798i
\(112\) 2.00000 1.73205i 0.188982 0.163663i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 10.3923 + 6.00000i 0.973329 + 0.561951i
\(115\) −3.00000 + 1.73205i −0.279751 + 0.161515i
\(116\) 2.59808 1.50000i 0.241225 0.139272i
\(117\) −9.00000 5.19615i −0.832050 0.480384i
\(118\) 13.8564i 1.27559i
\(119\) −0.866025 4.50000i −0.0793884 0.412514i
\(120\) 6.00000 0.547723
\(121\) −1.00000 + 1.73205i −0.0909091 + 0.157459i
\(122\) −6.92820 12.0000i −0.627250 1.08643i
\(123\) −5.19615 + 3.00000i −0.468521 + 0.270501i
\(124\) 3.00000 + 1.73205i 0.269408 + 0.155543i
\(125\) −6.92820 −0.619677
\(126\) −7.79423 + 1.50000i −0.694365 + 0.133631i
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 15.0000 8.66025i 1.32068 0.762493i
\(130\) −6.00000 10.3923i −0.526235 0.911465i
\(131\) 6.92820 12.0000i 0.605320 1.04844i −0.386681 0.922214i \(-0.626379\pi\)
0.992001 0.126231i \(-0.0402882\pi\)
\(132\) −5.19615 −0.452267
\(133\) −12.0000 13.8564i −1.04053 1.20150i
\(134\) 4.00000i 0.345547i
\(135\) −15.5885 9.00000i −1.34164 0.774597i
\(136\) −1.50000 + 0.866025i −0.128624 + 0.0742611i
\(137\) −7.79423 + 4.50000i −0.665906 + 0.384461i −0.794524 0.607233i \(-0.792279\pi\)
0.128618 + 0.991694i \(0.458946\pi\)
\(138\) −1.50000 0.866025i −0.127688 0.0737210i
\(139\) 1.73205i 0.146911i 0.997299 + 0.0734553i \(0.0234026\pi\)
−0.997299 + 0.0734553i \(0.976597\pi\)
\(140\) −8.66025 3.00000i −0.731925 0.253546i
\(141\) 15.0000i 1.26323i
\(142\) 4.50000 7.79423i 0.377632 0.654077i
\(143\) 5.19615 + 9.00000i 0.434524 + 0.752618i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) −9.00000 5.19615i −0.747409 0.431517i
\(146\) 8.66025 0.716728
\(147\) 12.0000 + 1.73205i 0.989743 + 0.142857i
\(148\) 2.00000 0.164399
\(149\) −5.19615 3.00000i −0.425685 0.245770i 0.271821 0.962348i \(-0.412374\pi\)
−0.697507 + 0.716578i \(0.745707\pi\)
\(150\) −6.06218 10.5000i −0.494975 0.857321i
\(151\) −8.00000 13.8564i −0.651031 1.12762i −0.982873 0.184284i \(-0.941004\pi\)
0.331842 0.943335i \(-0.392330\pi\)
\(152\) −3.46410 + 6.00000i −0.280976 + 0.486664i
\(153\) 5.19615 0.420084
\(154\) 7.50000 + 2.59808i 0.604367 + 0.209359i
\(155\) 12.0000i 0.963863i
\(156\) 3.00000 5.19615i 0.240192 0.416025i
\(157\) −4.50000 + 2.59808i −0.359139 + 0.207349i −0.668703 0.743530i \(-0.733150\pi\)
0.309564 + 0.950879i \(0.399817\pi\)
\(158\) −9.52628 + 5.50000i −0.757870 + 0.437557i
\(159\) −10.3923 + 18.0000i −0.824163 + 1.42749i
\(160\) 3.46410i 0.273861i
\(161\) 1.73205 + 2.00000i 0.136505 + 0.157622i
\(162\) 9.00000i 0.707107i
\(163\) 3.50000 6.06218i 0.274141 0.474826i −0.695777 0.718258i \(-0.744940\pi\)
0.969918 + 0.243432i \(0.0782731\pi\)
\(164\) −1.73205 3.00000i −0.135250 0.234261i
\(165\) 9.00000 + 15.5885i 0.700649 + 1.21356i
\(166\) 3.00000 + 1.73205i 0.232845 + 0.134433i
\(167\) −3.46410 −0.268060 −0.134030 0.990977i \(-0.542792\pi\)
−0.134030 + 0.990977i \(0.542792\pi\)
\(168\) −0.866025 4.50000i −0.0668153 0.347183i
\(169\) 1.00000 0.0769231
\(170\) 5.19615 + 3.00000i 0.398527 + 0.230089i
\(171\) 18.0000 10.3923i 1.37649 0.794719i
\(172\) 5.00000 + 8.66025i 0.381246 + 0.660338i
\(173\) 9.52628 16.5000i 0.724270 1.25447i −0.235004 0.971994i \(-0.575510\pi\)
0.959274 0.282477i \(-0.0911562\pi\)
\(174\) 5.19615i 0.393919i
\(175\) 3.50000 + 18.1865i 0.264575 + 1.37477i
\(176\) 3.00000i 0.226134i
\(177\) 20.7846 + 12.0000i 1.56227 + 0.901975i
\(178\) −6.00000 + 3.46410i −0.449719 + 0.259645i
\(179\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) 5.19615 9.00000i 0.387298 0.670820i
\(181\) 12.1244i 0.901196i 0.892727 + 0.450598i \(0.148789\pi\)
−0.892727 + 0.450598i \(0.851211\pi\)
\(182\) −6.92820 + 6.00000i −0.513553 + 0.444750i
\(183\) −24.0000 −1.77413
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −3.46410 6.00000i −0.254686 0.441129i
\(186\) 5.19615 3.00000i 0.381000 0.219971i
\(187\) −4.50000 2.59808i −0.329073 0.189990i
\(188\) −8.66025 −0.631614
\(189\) −4.50000 + 12.9904i −0.327327 + 0.944911i
\(190\) 24.0000 1.74114
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) −1.50000 + 0.866025i −0.108253 + 0.0625000i
\(193\) 1.00000 + 1.73205i 0.0719816 + 0.124676i 0.899770 0.436365i \(-0.143734\pi\)
−0.827788 + 0.561041i \(0.810401\pi\)
\(194\) −1.73205 + 3.00000i −0.124354 + 0.215387i
\(195\) −20.7846 −1.48842
\(196\) −1.00000 + 6.92820i −0.0714286 + 0.494872i
\(197\) 9.00000i 0.641223i 0.947211 + 0.320612i \(0.103888\pi\)
−0.947211 + 0.320612i \(0.896112\pi\)
\(198\) −4.50000 + 7.79423i −0.319801 + 0.553912i
\(199\) −22.5000 + 12.9904i −1.59498 + 0.920864i −0.602549 + 0.798082i \(0.705848\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) 6.06218 3.50000i 0.428661 0.247487i
\(201\) 6.00000 + 3.46410i 0.423207 + 0.244339i
\(202\) 15.5885i 1.09680i
\(203\) −2.59808 + 7.50000i −0.182349 + 0.526397i
\(204\) 3.00000i 0.210042i
\(205\) −6.00000 + 10.3923i −0.419058 + 0.725830i
\(206\) 4.33013 + 7.50000i 0.301694 + 0.522550i
\(207\) −2.59808 + 1.50000i −0.180579 + 0.104257i
\(208\) 3.00000 + 1.73205i 0.208013 + 0.120096i
\(209\) −20.7846 −1.43770
\(210\) −12.0000 + 10.3923i −0.828079 + 0.717137i
\(211\) −23.0000 −1.58339 −0.791693 0.610920i \(-0.790800\pi\)
−0.791693 + 0.610920i \(0.790800\pi\)
\(212\) −10.3923 6.00000i −0.713746 0.412082i
\(213\) −7.79423 13.5000i −0.534052 0.925005i
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 17.3205 30.0000i 1.18125 2.04598i
\(216\) 5.19615 0.353553
\(217\) −9.00000 + 1.73205i −0.610960 + 0.117579i
\(218\) 17.0000i 1.15139i
\(219\) 7.50000 12.9904i 0.506803 0.877809i
\(220\) −9.00000 + 5.19615i −0.606780 + 0.350325i
\(221\) 5.19615 3.00000i 0.349531 0.201802i
\(222\) 1.73205 3.00000i 0.116248 0.201347i
\(223\) 6.92820i 0.463947i −0.972722 0.231973i \(-0.925482\pi\)
0.972722 0.231973i \(-0.0745182\pi\)
\(224\) 2.59808 0.500000i 0.173591 0.0334077i
\(225\) −21.0000 −1.40000
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) 2.59808 + 4.50000i 0.172440 + 0.298675i 0.939272 0.343172i \(-0.111501\pi\)
−0.766832 + 0.641848i \(0.778168\pi\)
\(228\) 6.00000 + 10.3923i 0.397360 + 0.688247i
\(229\) −10.5000 6.06218i −0.693860 0.400600i 0.111197 0.993798i \(-0.464532\pi\)
−0.805056 + 0.593198i \(0.797865\pi\)
\(230\) −3.46410 −0.228416
\(231\) 10.3923 9.00000i 0.683763 0.592157i
\(232\) 3.00000 0.196960
\(233\) 10.3923 + 6.00000i 0.680823 + 0.393073i 0.800165 0.599780i \(-0.204745\pi\)
−0.119342 + 0.992853i \(0.538079\pi\)
\(234\) −5.19615 9.00000i −0.339683 0.588348i
\(235\) 15.0000 + 25.9808i 0.978492 + 1.69480i
\(236\) −6.92820 + 12.0000i −0.450988 + 0.781133i
\(237\) 19.0526i 1.23760i
\(238\) 1.50000 4.33013i 0.0972306 0.280680i
\(239\) 15.0000i 0.970269i −0.874439 0.485135i \(-0.838771\pi\)
0.874439 0.485135i \(-0.161229\pi\)
\(240\) 5.19615 + 3.00000i 0.335410 + 0.193649i
\(241\) 12.0000 6.92820i 0.772988 0.446285i −0.0609515 0.998141i \(-0.519414\pi\)
0.833939 + 0.551856i \(0.186080\pi\)
\(242\) −1.73205 + 1.00000i −0.111340 + 0.0642824i
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) 13.8564i 0.887066i
\(245\) 22.5167 9.00000i 1.43854 0.574989i
\(246\) −6.00000 −0.382546
\(247\) 12.0000 20.7846i 0.763542 1.32249i
\(248\) 1.73205 + 3.00000i 0.109985 + 0.190500i
\(249\) 5.19615 3.00000i 0.329293 0.190117i
\(250\) −6.00000 3.46410i −0.379473 0.219089i
\(251\) −29.4449 −1.85854 −0.929272 0.369397i \(-0.879564\pi\)
−0.929272 + 0.369397i \(0.879564\pi\)
\(252\) −7.50000 2.59808i −0.472456 0.163663i
\(253\) 3.00000 0.188608
\(254\) 1.73205 + 1.00000i 0.108679 + 0.0627456i
\(255\) 9.00000 5.19615i 0.563602 0.325396i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.46410 6.00000i 0.216085 0.374270i −0.737523 0.675322i \(-0.764005\pi\)
0.953608 + 0.301052i \(0.0973379\pi\)
\(258\) 17.3205 1.07833
\(259\) −4.00000 + 3.46410i −0.248548 + 0.215249i
\(260\) 12.0000i 0.744208i
\(261\) −7.79423 4.50000i −0.482451 0.278543i
\(262\) 12.0000 6.92820i 0.741362 0.428026i
\(263\) 10.3923 6.00000i 0.640817 0.369976i −0.144112 0.989561i \(-0.546033\pi\)
0.784929 + 0.619586i \(0.212699\pi\)
\(264\) −4.50000 2.59808i −0.276956 0.159901i
\(265\) 41.5692i 2.55358i
\(266\) −3.46410 18.0000i −0.212398 1.10365i
\(267\) 12.0000i 0.734388i
\(268\) −2.00000 + 3.46410i −0.122169 + 0.211604i
\(269\) −6.06218 10.5000i −0.369618 0.640196i 0.619888 0.784690i \(-0.287178\pi\)
−0.989506 + 0.144494i \(0.953845\pi\)
\(270\) −9.00000 15.5885i −0.547723 0.948683i
\(271\) −6.00000 3.46410i −0.364474 0.210429i 0.306568 0.951849i \(-0.400819\pi\)
−0.671042 + 0.741420i \(0.734153\pi\)
\(272\) −1.73205 −0.105021
\(273\) 3.00000 + 15.5885i 0.181568 + 0.943456i
\(274\) −9.00000 −0.543710
\(275\) 18.1865 + 10.5000i 1.09669 + 0.633174i
\(276\) −0.866025 1.50000i −0.0521286 0.0902894i
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) −0.866025 + 1.50000i −0.0519408 + 0.0899640i
\(279\) 10.3923i 0.622171i
\(280\) −6.00000 6.92820i −0.358569 0.414039i
\(281\) 9.00000i 0.536895i 0.963294 + 0.268447i \(0.0865106\pi\)
−0.963294 + 0.268447i \(0.913489\pi\)
\(282\) −7.50000 + 12.9904i −0.446619 + 0.773566i
\(283\) −15.0000 + 8.66025i −0.891657 + 0.514799i −0.874484 0.485054i \(-0.838800\pi\)
−0.0171732 + 0.999853i \(0.505467\pi\)
\(284\) 7.79423 4.50000i 0.462502 0.267026i
\(285\) 20.7846 36.0000i 1.23117 2.13246i
\(286\) 10.3923i 0.614510i
\(287\) 8.66025 + 3.00000i 0.511199 + 0.177084i
\(288\) 3.00000i 0.176777i
\(289\) 7.00000 12.1244i 0.411765 0.713197i
\(290\) −5.19615 9.00000i −0.305129 0.528498i
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) 7.50000 + 4.33013i 0.438904 + 0.253402i
\(293\) −31.1769 −1.82137 −0.910687 0.413096i \(-0.864447\pi\)
−0.910687 + 0.413096i \(0.864447\pi\)
\(294\) 9.52628 + 7.50000i 0.555584 + 0.437409i
\(295\) 48.0000 2.79467
\(296\) 1.73205 + 1.00000i 0.100673 + 0.0581238i
\(297\) 7.79423 + 13.5000i 0.452267 + 0.783349i
\(298\) −3.00000 5.19615i −0.173785 0.301005i
\(299\) −1.73205 + 3.00000i −0.100167 + 0.173494i
\(300\) 12.1244i 0.700000i
\(301\) −25.0000 8.66025i −1.44098 0.499169i
\(302\) 16.0000i 0.920697i
\(303\) 23.3827 + 13.5000i 1.34330 + 0.775555i
\(304\) −6.00000 + 3.46410i −0.344124 + 0.198680i
\(305\) −41.5692 + 24.0000i −2.38025 + 1.37424i
\(306\) 4.50000 + 2.59808i 0.257248 + 0.148522i
\(307\) 15.5885i 0.889680i −0.895610 0.444840i \(-0.853260\pi\)
0.895610 0.444840i \(-0.146740\pi\)
\(308\) 5.19615 + 6.00000i 0.296078 + 0.341882i
\(309\) 15.0000 0.853320
\(310\) 6.00000 10.3923i 0.340777 0.590243i
\(311\) 2.59808 + 4.50000i 0.147323 + 0.255172i 0.930237 0.366958i \(-0.119601\pi\)
−0.782914 + 0.622130i \(0.786268\pi\)
\(312\) 5.19615 3.00000i 0.294174 0.169842i
\(313\) −27.0000 15.5885i −1.52613 0.881112i −0.999519 0.0310053i \(-0.990129\pi\)
−0.526611 0.850106i \(-0.676538\pi\)
\(314\) −5.19615 −0.293236
\(315\) 5.19615 + 27.0000i 0.292770 + 1.52128i
\(316\) −11.0000 −0.618798
\(317\) −15.5885 9.00000i −0.875535 0.505490i −0.00635137 0.999980i \(-0.502022\pi\)
−0.869184 + 0.494489i \(0.835355\pi\)
\(318\) −18.0000 + 10.3923i −1.00939 + 0.582772i
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) −1.73205 + 3.00000i −0.0968246 + 0.167705i
\(321\) 20.7846 1.16008
\(322\) 0.500000 + 2.59808i 0.0278639 + 0.144785i
\(323\) 12.0000i 0.667698i
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) −21.0000 + 12.1244i −1.16487 + 0.672538i
\(326\) 6.06218 3.50000i 0.335753 0.193847i
\(327\) 25.5000 + 14.7224i 1.41015 + 0.814152i
\(328\) 3.46410i 0.191273i
\(329\) 17.3205 15.0000i 0.954911 0.826977i
\(330\) 18.0000i 0.990867i
\(331\) −14.0000 + 24.2487i −0.769510 + 1.33283i 0.168320 + 0.985732i \(0.446166\pi\)
−0.937829 + 0.347097i \(0.887167\pi\)
\(332\) 1.73205 + 3.00000i 0.0950586 + 0.164646i
\(333\) −3.00000 5.19615i −0.164399 0.284747i
\(334\) −3.00000 1.73205i −0.164153 0.0947736i
\(335\) 13.8564 0.757056
\(336\) 1.50000 4.33013i 0.0818317 0.236228i
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) 0.866025 + 0.500000i 0.0471056 + 0.0271964i
\(339\) −5.19615 9.00000i −0.282216 0.488813i
\(340\) 3.00000 + 5.19615i 0.162698 + 0.281801i
\(341\) −5.19615 + 9.00000i −0.281387 + 0.487377i
\(342\) 20.7846 1.12390
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 10.0000i 0.539164i
\(345\) −3.00000 + 5.19615i −0.161515 + 0.279751i
\(346\) 16.5000 9.52628i 0.887045 0.512136i
\(347\) 15.5885 9.00000i 0.836832 0.483145i −0.0193540 0.999813i \(-0.506161\pi\)
0.856186 + 0.516667i \(0.172828\pi\)
\(348\) 2.59808 4.50000i 0.139272 0.241225i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) −6.06218 + 17.5000i −0.324037 + 0.935414i
\(351\) −18.0000 −0.960769
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) −5.19615 9.00000i −0.276563 0.479022i 0.693965 0.720009i \(-0.255862\pi\)
−0.970528 + 0.240987i \(0.922529\pi\)
\(354\) 12.0000 + 20.7846i 0.637793 + 1.10469i
\(355\) −27.0000 15.5885i −1.43301 0.827349i
\(356\) −6.92820 −0.367194
\(357\) −5.19615 6.00000i −0.275010 0.317554i
\(358\) 0 0
\(359\) −31.1769 18.0000i −1.64545 0.950004i −0.978847 0.204595i \(-0.934412\pi\)
−0.666608 0.745409i \(-0.732254\pi\)
\(360\) 9.00000 5.19615i 0.474342 0.273861i
\(361\) 14.5000 + 25.1147i 0.763158 + 1.32183i
\(362\) −6.06218 + 10.5000i −0.318621 + 0.551868i
\(363\) 3.46410i 0.181818i
\(364\) −9.00000 + 1.73205i −0.471728 + 0.0907841i
\(365\) 30.0000i 1.57027i
\(366\) −20.7846 12.0000i −1.08643 0.627250i
\(367\) 15.0000 8.66025i 0.782994 0.452062i −0.0544966 0.998514i \(-0.517355\pi\)
0.837490 + 0.546452i \(0.184022\pi\)
\(368\) 0.866025 0.500000i 0.0451447 0.0260643i
\(369\) −5.19615 + 9.00000i −0.270501 + 0.468521i
\(370\) 6.92820i 0.360180i
\(371\) 31.1769 6.00000i 1.61862 0.311504i
\(372\) 6.00000 0.311086
\(373\) 0.500000 0.866025i 0.0258890 0.0448411i −0.852791 0.522253i \(-0.825092\pi\)
0.878680 + 0.477412i \(0.158425\pi\)
\(374\) −2.59808 4.50000i −0.134343 0.232689i
\(375\) −10.3923 + 6.00000i −0.536656 + 0.309839i
\(376\) −7.50000 4.33013i −0.386783 0.223309i
\(377\) −10.3923 −0.535231
\(378\) −10.3923 + 9.00000i −0.534522 + 0.462910i
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) 20.7846 + 12.0000i 1.06623 + 0.615587i
\(381\) 3.00000 1.73205i 0.153695 0.0887357i
\(382\) 0 0
\(383\) −1.73205 + 3.00000i −0.0885037 + 0.153293i −0.906879 0.421392i \(-0.861542\pi\)
0.818375 + 0.574684i \(0.194875\pi\)
\(384\) −1.73205 −0.0883883
\(385\) 9.00000 25.9808i 0.458682 1.32410i
\(386\) 2.00000i 0.101797i
\(387\) 15.0000 25.9808i 0.762493 1.32068i
\(388\) −3.00000 + 1.73205i −0.152302 + 0.0879316i
\(389\) −10.3923 + 6.00000i −0.526911 + 0.304212i −0.739758 0.672874i \(-0.765060\pi\)
0.212847 + 0.977086i \(0.431726\pi\)
\(390\) −18.0000 10.3923i −0.911465 0.526235i
\(391\) 1.73205i 0.0875936i
\(392\) −4.33013 + 5.50000i −0.218704 + 0.277792i
\(393\) 24.0000i 1.21064i
\(394\) −4.50000 + 7.79423i −0.226707 + 0.392668i
\(395\) 19.0526 + 33.0000i 0.958638 + 1.66041i
\(396\) −7.79423 + 4.50000i −0.391675 + 0.226134i
\(397\) 9.00000 + 5.19615i 0.451697 + 0.260787i 0.708547 0.705664i \(-0.249351\pi\)
−0.256850 + 0.966451i \(0.582685\pi\)
\(398\) −25.9808 −1.30230
\(399\) −30.0000 10.3923i −1.50188 0.520266i
\(400\) 7.00000 0.350000
\(401\) −12.9904 7.50000i −0.648709 0.374532i 0.139253 0.990257i \(-0.455530\pi\)
−0.787961 + 0.615725i \(0.788863\pi\)
\(402\) 3.46410 + 6.00000i 0.172774 + 0.299253i
\(403\) −6.00000 10.3923i −0.298881 0.517678i
\(404\) −7.79423 + 13.5000i −0.387777 + 0.671650i
\(405\) −31.1769 −1.54919
\(406\) −6.00000 + 5.19615i −0.297775 + 0.257881i
\(407\) 6.00000i 0.297409i
\(408\) −1.50000 + 2.59808i −0.0742611 + 0.128624i
\(409\) −1.50000 + 0.866025i −0.0741702 + 0.0428222i −0.536626 0.843820i \(-0.680302\pi\)
0.462456 + 0.886642i \(0.346968\pi\)
\(410\) −10.3923 + 6.00000i −0.513239 + 0.296319i
\(411\) −7.79423 + 13.5000i −0.384461 + 0.665906i
\(412\) 8.66025i 0.426660i
\(413\) −6.92820 36.0000i −0.340915 1.77144i
\(414\) −3.00000 −0.147442
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 1.73205 + 3.00000i 0.0849208 + 0.147087i
\(417\) 1.50000 + 2.59808i 0.0734553 + 0.127228i
\(418\) −18.0000 10.3923i −0.880409 0.508304i
\(419\) −1.73205 −0.0846162 −0.0423081 0.999105i \(-0.513471\pi\)
−0.0423081 + 0.999105i \(0.513471\pi\)
\(420\) −15.5885 + 3.00000i −0.760639 + 0.146385i
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) −19.9186 11.5000i −0.969622 0.559811i
\(423\) 12.9904 + 22.5000i 0.631614 + 1.09399i
\(424\) −6.00000 10.3923i −0.291386 0.504695i
\(425\) 6.06218 10.5000i 0.294059 0.509325i
\(426\) 15.5885i 0.755263i
\(427\) 24.0000 + 27.7128i 1.16144 + 1.34112i
\(428\) 12.0000i 0.580042i
\(429\) 15.5885 + 9.00000i 0.752618 + 0.434524i
\(430\) 30.0000 17.3205i 1.44673 0.835269i
\(431\) 20.7846 12.0000i 1.00116 0.578020i 0.0925683 0.995706i \(-0.470492\pi\)
0.908591 + 0.417687i \(0.137159\pi\)
\(432\) 4.50000 + 2.59808i 0.216506 + 0.125000i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) −8.66025 3.00000i −0.415705 0.144005i
\(435\) −18.0000 −0.863034
\(436\) −8.50000 + 14.7224i −0.407076 + 0.705077i
\(437\) −3.46410 6.00000i −0.165710 0.287019i
\(438\) 12.9904 7.50000i 0.620704 0.358364i
\(439\) 24.0000 + 13.8564i 1.14546 + 0.661330i 0.947776 0.318936i \(-0.103326\pi\)
0.197681 + 0.980266i \(0.436659\pi\)
\(440\) −10.3923 −0.495434
\(441\) 19.5000 7.79423i 0.928571 0.371154i
\(442\) 6.00000 0.285391
\(443\) −20.7846 12.0000i −0.987507 0.570137i −0.0829786 0.996551i \(-0.526443\pi\)
−0.904528 + 0.426414i \(0.859777\pi\)
\(444\) 3.00000 1.73205i 0.142374 0.0821995i
\(445\) 12.0000 + 20.7846i 0.568855 + 0.985285i
\(446\) 3.46410 6.00000i 0.164030 0.284108i
\(447\) −10.3923 −0.491539
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) 24.0000i 1.13263i −0.824189 0.566315i \(-0.808369\pi\)
0.824189 0.566315i \(-0.191631\pi\)
\(450\) −18.1865 10.5000i −0.857321 0.494975i
\(451\) 9.00000 5.19615i 0.423793 0.244677i
\(452\) 5.19615 3.00000i 0.244406 0.141108i
\(453\) −24.0000 13.8564i −1.12762 0.651031i
\(454\) 5.19615i 0.243868i
\(455\) 20.7846 + 24.0000i 0.974398 + 1.12514i
\(456\) 12.0000i 0.561951i
\(457\) 16.0000 27.7128i 0.748448 1.29635i −0.200118 0.979772i \(-0.564132\pi\)
0.948566 0.316579i \(-0.102534\pi\)
\(458\) −6.06218 10.5000i −0.283267 0.490633i
\(459\) 7.79423 4.50000i 0.363803 0.210042i
\(460\) −3.00000 1.73205i −0.139876 0.0807573i
\(461\) 41.5692 1.93607 0.968036 0.250812i \(-0.0806976\pi\)
0.968036 + 0.250812i \(0.0806976\pi\)
\(462\) 13.5000 2.59808i 0.628077 0.120873i
\(463\) −10.0000 −0.464739 −0.232370 0.972628i \(-0.574648\pi\)
−0.232370 + 0.972628i \(0.574648\pi\)
\(464\) 2.59808 + 1.50000i 0.120613 + 0.0696358i
\(465\) −10.3923 18.0000i −0.481932 0.834730i
\(466\) 6.00000 + 10.3923i 0.277945 + 0.481414i
\(467\) −4.33013 + 7.50000i −0.200374 + 0.347059i −0.948649 0.316330i \(-0.897549\pi\)
0.748275 + 0.663389i \(0.230883\pi\)
\(468\) 10.3923i 0.480384i
\(469\) −2.00000 10.3923i −0.0923514 0.479872i
\(470\) 30.0000i 1.38380i
\(471\) −4.50000 + 7.79423i −0.207349 + 0.359139i
\(472\) −12.0000 + 6.92820i −0.552345 + 0.318896i
\(473\) −25.9808 + 15.0000i −1.19460 + 0.689701i
\(474\) −9.52628 + 16.5000i −0.437557 + 0.757870i
\(475\) 48.4974i 2.22521i
\(476\) 3.46410 3.00000i 0.158777 0.137505i
\(477\) 36.0000i 1.64833i
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) 17.3205 + 30.0000i 0.791394 + 1.37073i 0.925104 + 0.379714i \(0.123978\pi\)
−0.133710 + 0.991021i \(0.542689\pi\)
\(480\) 3.00000 + 5.19615i 0.136931 + 0.237171i
\(481\) −6.00000 3.46410i −0.273576 0.157949i
\(482\) 13.8564 0.631142
\(483\) 4.33013 + 1.50000i 0.197028 + 0.0682524i
\(484\) −2.00000 −0.0909091
\(485\) 10.3923 + 6.00000i 0.471890 + 0.272446i
\(486\) −7.79423 13.5000i −0.353553 0.612372i
\(487\) 10.0000 + 17.3205i 0.453143 + 0.784867i 0.998579 0.0532853i \(-0.0169693\pi\)
−0.545436 + 0.838152i \(0.683636\pi\)
\(488\) 6.92820 12.0000i 0.313625 0.543214i
\(489\) 12.1244i 0.548282i
\(490\) 24.0000 + 3.46410i 1.08421 + 0.156492i
\(491\) 30.0000i 1.35388i 0.736038 + 0.676941i \(0.236695\pi\)
−0.736038 + 0.676941i \(0.763305\pi\)
\(492\) −5.19615 3.00000i −0.234261 0.135250i
\(493\) 4.50000 2.59808i 0.202670 0.117011i
\(494\) 20.7846 12.0000i 0.935144 0.539906i
\(495\) 27.0000 + 15.5885i 1.21356 + 0.700649i
\(496\) 3.46410i 0.155543i
\(497\) −7.79423 + 22.5000i −0.349619 + 1.00926i
\(498\) 6.00000 0.268866
\(499\) 2.50000 4.33013i 0.111915 0.193843i −0.804627 0.593780i \(-0.797635\pi\)
0.916542 + 0.399937i \(0.130968\pi\)
\(500\) −3.46410 6.00000i −0.154919 0.268328i
\(501\) −5.19615 + 3.00000i −0.232147 + 0.134030i
\(502\) −25.5000 14.7224i −1.13812 0.657094i
\(503\) 41.5692 1.85348 0.926740 0.375703i \(-0.122599\pi\)
0.926740 + 0.375703i \(0.122599\pi\)
\(504\) −5.19615 6.00000i −0.231455 0.267261i
\(505\) 54.0000 2.40297
\(506\) 2.59808 + 1.50000i 0.115499 + 0.0666831i
\(507\) 1.50000 0.866025i 0.0666173 0.0384615i
\(508\) 1.00000 + 1.73205i 0.0443678 + 0.0768473i
\(509\) −6.06218 + 10.5000i −0.268701 + 0.465404i −0.968527 0.248910i \(-0.919928\pi\)
0.699825 + 0.714314i \(0.253261\pi\)
\(510\) 10.3923 0.460179
\(511\) −22.5000 + 4.33013i −0.995341 + 0.191554i
\(512\) 1.00000i 0.0441942i
\(513\) 18.0000 31.1769i 0.794719 1.37649i
\(514\) 6.00000 3.46410i 0.264649 0.152795i
\(515\) 25.9808 15.0000i 1.14485 0.660979i
\(516\) 15.0000 + 8.66025i 0.660338 + 0.381246i
\(517\) 25.9808i 1.14263i
\(518\) −5.19615 + 1.00000i −0.228306 + 0.0439375i
\(519\) 33.0000i 1.44854i
\(520\) 6.00000 10.3923i 0.263117 0.455733i
\(521\) −20.7846 36.0000i −0.910590 1.57719i −0.813232 0.581939i \(-0.802294\pi\)
−0.0973580 0.995249i \(-0.531039\pi\)
\(522\) −4.50000 7.79423i −0.196960 0.341144i
\(523\) 9.00000 + 5.19615i 0.393543 + 0.227212i 0.683694 0.729769i \(-0.260372\pi\)
−0.290151 + 0.956981i \(0.593706\pi\)
\(524\) 13.8564 0.605320
\(525\) 21.0000 + 24.2487i 0.916515 + 1.05830i
\(526\) 12.0000 0.523225
\(527\) 5.19615 + 3.00000i 0.226348 + 0.130682i
\(528\) −2.59808 4.50000i −0.113067 0.195837i
\(529\) 0.500000 + 0.866025i 0.0217391 + 0.0376533i
\(530\) −20.7846 + 36.0000i −0.902826 + 1.56374i
\(531\) 41.5692 1.80395
\(532\) 6.00000 17.3205i 0.260133 0.750939i
\(533\) 12.0000i 0.519778i
\(534\) −6.00000 + 10.3923i −0.259645 + 0.449719i
\(535\) 36.0000 20.7846i 1.55642 0.898597i
\(536\) −3.46410 + 2.00000i −0.149626 + 0.0863868i
\(537\) 0 0
\(538\) 12.1244i 0.522718i
\(539\) −20.7846 3.00000i −0.895257 0.129219i
\(540\) 18.0000i 0.774597i
\(541\) 17.0000 29.4449i 0.730887 1.26593i −0.225617 0.974216i \(-0.572440\pi\)
0.956504 0.291718i \(-0.0942267\pi\)
\(542\) −3.46410 6.00000i −0.148796 0.257722i
\(543\) 10.5000 + 18.1865i 0.450598 + 0.780459i
\(544\) −1.50000 0.866025i −0.0643120 0.0371305i
\(545\) 58.8897 2.52256
\(546\) −5.19615 + 15.0000i −0.222375 + 0.641941i
\(547\) −19.0000 −0.812381 −0.406191 0.913788i \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(548\) −7.79423 4.50000i −0.332953 0.192230i
\(549\) −36.0000 + 20.7846i −1.53644 + 0.887066i
\(550\) 10.5000 + 18.1865i 0.447722 + 0.775476i
\(551\) 10.3923 18.0000i 0.442727 0.766826i
\(552\) 1.73205i 0.0737210i
\(553\) 22.0000 19.0526i 0.935535 0.810197i
\(554\) 2.00000i 0.0849719i
\(555\) −10.3923 6.00000i −0.441129 0.254686i
\(556\) −1.50000 + 0.866025i −0.0636142 + 0.0367277i
\(557\) 36.3731 21.0000i 1.54118 0.889799i 0.542411 0.840113i \(-0.317511\pi\)
0.998765 0.0496855i \(-0.0158219\pi\)
\(558\) 5.19615 9.00000i 0.219971 0.381000i
\(559\) 34.6410i 1.46516i
\(560\) −1.73205 9.00000i −0.0731925 0.380319i
\(561\) −9.00000 −0.379980
\(562\) −4.50000 + 7.79423i −0.189821 + 0.328780i
\(563\) 0.866025 + 1.50000i 0.0364986 + 0.0632175i 0.883698 0.468058i \(-0.155046\pi\)
−0.847199 + 0.531276i \(0.821713\pi\)
\(564\) −12.9904 + 7.50000i −0.546994 + 0.315807i
\(565\) −18.0000 10.3923i −0.757266 0.437208i
\(566\) −17.3205 −0.728035
\(567\) 4.50000 + 23.3827i 0.188982 + 0.981981i
\(568\) 9.00000 0.377632
\(569\) −25.9808 15.0000i −1.08917 0.628833i −0.155815 0.987786i \(-0.549800\pi\)
−0.933355 + 0.358954i \(0.883134\pi\)
\(570\) 36.0000 20.7846i 1.50787 0.870572i
\(571\) −4.00000 6.92820i −0.167395 0.289936i 0.770108 0.637913i \(-0.220202\pi\)
−0.937503 + 0.347977i \(0.886869\pi\)
\(572\) −5.19615 + 9.00000i −0.217262 + 0.376309i
\(573\) 0 0
\(574\) 6.00000 + 6.92820i 0.250435 + 0.289178i
\(575\) 7.00000i 0.291920i
\(576\) −1.50000 + 2.59808i −0.0625000 + 0.108253i
\(577\) −13.5000 + 7.79423i −0.562012 + 0.324478i −0.753953 0.656929i \(-0.771855\pi\)
0.191940 + 0.981407i \(0.438522\pi\)
\(578\) 12.1244 7.00000i 0.504307 0.291162i
\(579\) 3.00000 + 1.73205i 0.124676 + 0.0719816i
\(580\) 10.3923i 0.431517i
\(581\) −8.66025 3.00000i −0.359288 0.124461i
\(582\) 6.00000i 0.248708i
\(583\) 18.0000 31.1769i 0.745484 1.29122i
\(584\) 4.33013 + 7.50000i 0.179182 + 0.310352i
\(585\) −31.1769 + 18.0000i −1.28901 + 0.744208i
\(586\) −27.0000 15.5885i −1.11536 0.643953i
\(587\) −17.3205 −0.714894 −0.357447 0.933933i \(-0.616353\pi\)
−0.357447 + 0.933933i \(0.616353\pi\)
\(588\) 4.50000 + 11.2583i 0.185577 + 0.464286i
\(589\) 24.0000 0.988903
\(590\) 41.5692 + 24.0000i 1.71138 + 0.988064i
\(591\) 7.79423 + 13.5000i 0.320612 + 0.555316i
\(592\) 1.00000 + 1.73205i 0.0410997 + 0.0711868i
\(593\) 20.7846 36.0000i 0.853522 1.47834i −0.0244882 0.999700i \(-0.507796\pi\)
0.878010 0.478643i \(-0.158871\pi\)
\(594\) 15.5885i 0.639602i
\(595\) −15.0000 5.19615i −0.614940 0.213021i
\(596\) 6.00000i 0.245770i
\(597\) −22.5000 + 38.9711i −0.920864 + 1.59498i
\(598\) −3.00000 + 1.73205i −0.122679 + 0.0708288i
\(599\) −33.7750 + 19.5000i −1.38001 + 0.796748i −0.992160 0.124975i \(-0.960115\pi\)
−0.387849 + 0.921723i \(0.626782\pi\)
\(600\) 6.06218 10.5000i 0.247487 0.428661i
\(601\) 20.7846i 0.847822i 0.905704 + 0.423911i \(0.139343\pi\)
−0.905704 + 0.423911i \(0.860657\pi\)
\(602\) −17.3205 20.0000i −0.705931 0.815139i
\(603\) 12.0000 0.488678
\(604\) 8.00000 13.8564i 0.325515 0.563809i
\(605\) 3.46410 + 6.00000i 0.140836 + 0.243935i
\(606\) 13.5000 + 23.3827i 0.548400 + 0.949857i
\(607\) −39.0000 22.5167i −1.58296 0.913923i −0.994424 0.105453i \(-0.966371\pi\)
−0.588537 0.808470i \(-0.700296\pi\)
\(608\) −6.92820 −0.280976
\(609\) 2.59808 + 13.5000i 0.105279 + 0.547048i
\(610\) −48.0000 −1.94346
\(611\) 25.9808 + 15.0000i 1.05107 + 0.606835i
\(612\) 2.59808 + 4.50000i 0.105021 + 0.181902i
\(613\) −5.50000 9.52628i −0.222143 0.384763i 0.733316 0.679888i \(-0.237972\pi\)
−0.955458 + 0.295126i \(0.904638\pi\)
\(614\) 7.79423 13.5000i 0.314549 0.544816i
\(615\) 20.7846i 0.838116i
\(616\) 1.50000 + 7.79423i 0.0604367 + 0.314038i
\(617\) 27.0000i 1.08698i 0.839416 + 0.543490i \(0.182897\pi\)
−0.839416 + 0.543490i \(0.817103\pi\)
\(618\) 12.9904 + 7.50000i 0.522550 + 0.301694i
\(619\) −30.0000 + 17.3205i −1.20580 + 0.696170i −0.961839 0.273615i \(-0.911781\pi\)
−0.243962 + 0.969785i \(0.578447\pi\)
\(620\) 10.3923 6.00000i 0.417365 0.240966i
\(621\) −2.59808 + 4.50000i −0.104257 + 0.180579i
\(622\) 5.19615i 0.208347i
\(623\) 13.8564 12.0000i 0.555145 0.480770i
\(624\) 6.00000 0.240192
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −15.5885 27.0000i −0.623040 1.07914i
\(627\) −31.1769 + 18.0000i −1.24509 + 0.718851i
\(628\) −4.50000 2.59808i −0.179570 0.103675i
\(629\) 3.46410 0.138123
\(630\) −9.00000 + 25.9808i −0.358569 + 1.03510i
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) −9.52628 5.50000i −0.378935 0.218778i
\(633\) −34.5000 + 19.9186i −1.37125 + 0.791693i
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) 3.46410 6.00000i 0.137469 0.238103i
\(636\) −20.7846 −0.824163
\(637\) 15.0000 19.0526i 0.594322 0.754890i
\(638\) 9.00000i 0.356313i
\(639\) −23.3827 13.5000i −0.925005 0.534052i
\(640\) −3.00000 + 1.73205i −0.118585 + 0.0684653i
\(641\) 12.9904 7.50000i 0.513089 0.296232i −0.221013 0.975271i \(-0.570936\pi\)
0.734103 + 0.679039i \(0.237603\pi\)
\(642\) 18.0000 + 10.3923i 0.710403 + 0.410152i
\(643\) 13.8564i 0.546443i 0.961951 + 0.273222i \(0.0880892\pi\)
−0.961951 + 0.273222i \(0.911911\pi\)
\(644\) −0.866025 + 2.50000i −0.0341262 + 0.0985138i
\(645\) 60.0000i 2.36250i
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) 14.7224 + 25.5000i 0.578799 + 1.00251i 0.995618 + 0.0935189i \(0.0298116\pi\)
−0.416819 + 0.908990i \(0.636855\pi\)
\(648\) 7.79423 4.50000i 0.306186 0.176777i
\(649\) −36.0000 20.7846i −1.41312 0.815867i
\(650\) −24.2487 −0.951113
\(651\) −12.0000 + 10.3923i −0.470317 + 0.407307i
\(652\) 7.00000 0.274141
\(653\) −2.59808 1.50000i −0.101671 0.0586995i 0.448303 0.893882i \(-0.352029\pi\)
−0.549973 + 0.835182i \(0.685362\pi\)
\(654\) 14.7224 + 25.5000i 0.575693 + 0.997129i
\(655\) −24.0000 41.5692i −0.937758 1.62424i
\(656\) 1.73205 3.00000i 0.0676252 0.117130i
\(657\) 25.9808i 1.01361i
\(658\) 22.5000 4.33013i 0.877141 0.168806i
\(659\) 9.00000i 0.350590i 0.984516 + 0.175295i \(0.0560880\pi\)
−0.984516 + 0.175295i \(0.943912\pi\)
\(660\) −9.00000 + 15.5885i −0.350325 + 0.606780i
\(661\) 1.50000 0.866025i 0.0583432 0.0336845i −0.470545 0.882376i \(-0.655943\pi\)
0.528888 + 0.848692i \(0.322609\pi\)
\(662\) −24.2487 + 14.0000i −0.942453 + 0.544125i
\(663\) 5.19615 9.00000i 0.201802 0.349531i
\(664\) 3.46410i 0.134433i
\(665\) −62.3538 + 12.0000i −2.41798 + 0.465340i
\(666\) 6.00000i 0.232495i
\(667\) −1.50000 + 2.59808i −0.0580802 + 0.100598i
\(668\) −1.73205 3.00000i −0.0670151 0.116073i
\(669\) −6.00000 10.3923i −0.231973 0.401790i
\(670\) 12.0000 + 6.92820i 0.463600 + 0.267660i
\(671\) 41.5692 1.60476
\(672\) 3.46410 3.00000i 0.133631 0.115728i
\(673\) −47.0000 −1.81172 −0.905858 0.423581i \(-0.860773\pi\)
−0.905858 + 0.423581i \(0.860773\pi\)
\(674\) 19.0526 + 11.0000i 0.733877 + 0.423704i
\(675\) −31.5000 + 18.1865i −1.21244 + 0.700000i
\(676\) 0.500000 + 0.866025i 0.0192308 + 0.0333087i
\(677\) −8.66025 + 15.0000i −0.332841 + 0.576497i −0.983068 0.183243i \(-0.941340\pi\)
0.650227 + 0.759740i \(0.274674\pi\)
\(678\) 10.3923i 0.399114i
\(679\) 3.00000 8.66025i 0.115129 0.332350i
\(680\) 6.00000i 0.230089i
\(681\) 7.79423 + 4.50000i 0.298675 + 0.172440i
\(682\) −9.00000 + 5.19615i −0.344628 + 0.198971i
\(683\) 5.19615 3.00000i 0.198825 0.114792i −0.397282 0.917697i \(-0.630047\pi\)
0.596107 + 0.802905i \(0.296713\pi\)
\(684\) 18.0000 + 10.3923i 0.688247 + 0.397360i
\(685\) 31.1769i 1.19121i
\(686\) −0.866025 18.5000i −0.0330650 0.706333i
\(687\) −21.0000 −0.801200
\(688\) −5.00000 + 8.66025i −0.190623 + 0.330169i
\(689\) 20.7846 + 36.0000i 0.791831 + 1.37149i
\(690\) −5.19615 + 3.00000i −0.197814 + 0.114208i
\(691\) 4.50000 + 2.59808i 0.171188 + 0.0988355i 0.583146 0.812367i \(-0.301822\pi\)
−0.411958 + 0.911203i \(0.635155\pi\)
\(692\) 19.0526 0.724270
\(693\) 7.79423 22.5000i 0.296078 0.854704i
\(694\) 18.0000 0.683271
\(695\) 5.19615 + 3.00000i 0.197101 + 0.113796i
\(696\) 4.50000 2.59808i 0.170572 0.0984798i
\(697\) −3.00000 5.19615i −0.113633 0.196818i
\(698\) 0 0
\(699\) 20.7846 0.786146
\(700\) −14.0000 + 12.1244i −0.529150 + 0.458258i
\(701\) 42.0000i 1.58632i −0.609015 0.793159i \(-0.708435\pi\)
0.609015 0.793159i \(-0.291565\pi\)
\(702\) −15.5885 9.00000i −0.588348 0.339683i
\(703\) 12.0000 6.92820i 0.452589 0.261302i
\(704\) 2.59808 1.50000i 0.0979187 0.0565334i
\(705\) 45.0000 + 25.9808i 1.69480 + 0.978492i
\(706\) 10.3923i 0.391120i
\(707\) −7.79423 40.5000i −0.293132 1.52316i
\(708\) 24.0000i 0.901975i
\(709\) −9.50000 + 16.4545i −0.356780 + 0.617961i −0.987421 0.158114i \(-0.949459\pi\)
0.630641 + 0.776075i \(0.282792\pi\)
\(710\) −15.5885 27.0000i −0.585024 1.01329i
\(711\) 16.5000 + 28.5788i 0.618798 + 1.07179i
\(712\) −6.00000 3.46410i −0.224860 0.129823i
\(713\) −3.46410 −0.129732
\(714\) −1.50000 7.79423i −0.0561361 0.291692i
\(715\) 36.0000 1.34632
\(716\) 0 0
\(717\) −12.9904 22.5000i −0.485135 0.840278i
\(718\) −18.0000 31.1769i −0.671754 1.16351i
\(719\) −22.5167 + 39.0000i −0.839730 + 1.45445i 0.0503909 + 0.998730i \(0.483953\pi\)
−0.890121 + 0.455725i \(0.849380\pi\)
\(720\) 10.3923 0.387298
\(721\) −15.0000 17.3205i −0.558629 0.645049i
\(722\) 29.0000i 1.07927i
\(723\) 12.0000 20.7846i 0.446285 0.772988i
\(724\) −10.5000 + 6.06218i −0.390229 + 0.225299i
\(725\) −18.1865 + 10.5000i −0.675431 + 0.389960i
\(726\) −1.73205 + 3.00000i −0.0642824 + 0.111340i
\(727\) 53.6936i 1.99138i 0.0927199 + 0.995692i \(0.470444\pi\)
−0.0927199 + 0.995692i \(0.529556\pi\)
\(728\) −8.66025 3.00000i −0.320970 0.111187i
\(729\) −27.0000 −1.00000
\(730\) 15.0000 25.9808i 0.555175 0.961591i
\(731\) 8.66025 + 15.0000i 0.320311 + 0.554795i
\(732\) −12.0000 20.7846i −0.443533 0.768221i
\(733\) 22.5000 + 12.9904i 0.831056 + 0.479811i 0.854214 0.519921i \(-0.174039\pi\)
−0.0231578 + 0.999732i \(0.507372\pi\)
\(734\) 17.3205 0.639312
\(735\) 25.9808 33.0000i 0.958315 1.21722i
\(736\) 1.00000 0.0368605
\(737\) −10.3923 6.00000i −0.382805 0.221013i
\(738\) −9.00000 + 5.19615i −0.331295 + 0.191273i
\(739\) 15.5000 + 26.8468i 0.570177 + 0.987575i 0.996547 + 0.0830265i \(0.0264586\pi\)
−0.426371 + 0.904549i \(0.640208\pi\)
\(740\) 3.46410 6.00000i 0.127343 0.220564i
\(741\) 41.5692i 1.52708i
\(742\) 30.0000 + 10.3923i 1.10133 + 0.381514i
\(743\) 6.00000i 0.220119i 0.993925 + 0.110059i \(0.0351041\pi\)
−0.993925 + 0.110059i \(0.964896\pi\)
\(744\) 5.19615 + 3.00000i 0.190500 + 0.109985i
\(745\) −18.0000 + 10.3923i −0.659469 + 0.380745i
\(746\) 0.866025 0.500000i 0.0317074 0.0183063i
\(747\) 5.19615 9.00000i 0.190117 0.329293i
\(748\) 5.19615i 0.189990i
\(749\) −20.7846 24.0000i −0.759453 0.876941i
\(750\) −12.0000 −0.438178
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) −4.33013 7.50000i −0.157903 0.273497i
\(753\) −44.1673 + 25.5000i −1.60955 + 0.929272i
\(754\) −9.00000 5.19615i −0.327761 0.189233i
\(755\) −55.4256 −2.01715
\(756\) −13.5000 + 2.59808i −0.490990 + 0.0944911i
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 8.66025 + 5.00000i 0.314555 + 0.181608i
\(759\) 4.50000 2.59808i 0.163340 0.0943042i
\(760\) 12.0000 + 20.7846i 0.435286 + 0.753937i
\(761\) −6.92820 + 12.0000i −0.251147 + 0.435000i −0.963842 0.266475i \(-0.914141\pi\)
0.712695 + 0.701474i \(0.247474\pi\)
\(762\) 3.46410 0.125491
\(763\) −8.50000 44.1673i −0.307721 1.59896i
\(764\) 0 0
\(765\) 9.00000 15.5885i 0.325396 0.563602i
\(766\) −3.00000 + 1.73205i −0.108394 + 0.0625815i
\(767\) 41.5692 24.0000i 1.50098 0.866590i
\(768\) −1.50000 0.866025i −0.0541266 0.0312500i
\(769\) 17.3205i 0.624593i 0.949985 + 0.312297i \(0.101098\pi\)
−0.949985 + 0.312297i