Properties

Label 966.2.l.b.185.2
Level $966$
Weight $2$
Character 966.185
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 185.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 966.185
Dual form 966.2.l.b.47.2

$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

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

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 0.935021 + 0.354593i \(0.115380\pi\)
−0.160424 + 0.987048i \(0.551286\pi\)
\(6\) 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 0.0542666 0.998526i \(-0.482718\pi\)
−0.837616 + 0.546259i \(0.816051\pi\)
\(12\) 1.50000 0.866025i 0.433013 0.250000i
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) −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 −0.741685 0.670748i \(-0.765973\pi\)
0.951727 + 0.306944i \(0.0993066\pi\)
\(18\) 2.59808 + 1.50000i 0.612372 + 0.353553i
\(19\) 6.00000 3.46410i 1.37649 0.794719i 0.384759 0.923017i \(-0.374285\pi\)
0.991736 + 0.128298i \(0.0409513\pi\)
\(20\) 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 \(0.0898515\pi\)
−0.960424 + 0.278543i \(0.910149\pi\)
\(30\) 3.00000 + 5.19615i 0.547723 + 0.948683i
\(31\) 3.00000 + 1.73205i 0.538816 + 0.311086i 0.744599 0.667512i \(-0.232641\pi\)
−0.205783 + 0.978598i \(0.565974\pi\)
\(32\) −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 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 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 −0.987222 0.159352i \(-0.949059\pi\)
0.355608 0.934635i \(-0.384274\pi\)
\(48\) 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 −0.430570 0.902557i \(-0.641688\pi\)
−0.996922 + 0.0783936i \(0.975021\pi\)
\(54\) 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 0.0770484 0.997027i \(-0.475450\pi\)
0.824927 0.565240i \(-0.191216\pi\)
\(60\) 5.19615 + 3.00000i 0.670820 + 0.387298i
\(61\) −12.0000 + 6.92820i −1.53644 + 0.887066i −0.537400 + 0.843328i \(0.680593\pi\)
−0.999043 + 0.0437377i \(0.986073\pi\)
\(62\) 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 −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) −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 \(0.179331\pi\)
−0.845452 + 0.534052i \(0.820669\pi\)
\(72\) 2.59808 1.50000i 0.306186 0.176777i
\(73\) 7.50000 + 4.33013i 0.877809 + 0.506803i 0.869935 0.493166i \(-0.164160\pi\)
0.00787336 + 0.999969i \(0.497494\pi\)
\(74\) 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 −0.989705 0.143120i \(-0.954286\pi\)
0.370907 0.928670i \(-0.379047\pi\)
\(80\) 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 0.621932 0.783072i \(-0.286348\pi\)
−0.989126 + 0.147073i \(0.953015\pi\)
\(90\) 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 \(-0.943728\pi\)
0.984415 0.175863i \(-0.0562716\pi\)
\(98\) 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 −0.158927 0.987290i \(-0.550804\pi\)
0.934482 0.356010i \(-0.115863\pi\)
\(102\) 1.50000 2.59808i 0.148522 0.257248i
\(103\) 7.50000 4.33013i 0.738997 0.426660i −0.0827075 0.996574i \(-0.526357\pi\)
0.821705 + 0.569914i \(0.193023\pi\)
\(104\) 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 0.0950377 0.995474i \(-0.469703\pi\)
0.909624 + 0.415432i \(0.136370\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) 8.50000 14.7224i 0.814152 1.41015i −0.0957826 0.995402i \(-0.530535\pi\)
0.909935 0.414751i \(-0.136131\pi\)
\(110\) −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 \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 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 0.992001 + 0.126231i \(0.0402882\pi\)
−0.386681 + 0.922214i \(0.626379\pi\)
\(132\) −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 0.128618 0.991694i \(-0.458946\pi\)
−0.794524 + 0.607233i \(0.792279\pi\)
\(138\) −1.50000 + 0.866025i −0.127688 + 0.0737210i
\(139\) 1.73205i 0.146911i −0.997299 0.0734553i \(-0.976597\pi\)
0.997299 0.0734553i \(-0.0234026\pi\)
\(140\) −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 −0.697507 0.716578i \(-0.745707\pi\)
0.271821 + 0.962348i \(0.412374\pi\)
\(150\) −6.06218 + 10.5000i −0.494975 + 0.857321i
\(151\) −8.00000 + 13.8564i −0.651031 + 1.12762i 0.331842 + 0.943335i \(0.392330\pi\)
−0.982873 + 0.184284i \(0.941004\pi\)
\(152\) −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 0.309564 0.950879i \(-0.399817\pi\)
−0.668703 + 0.743530i \(0.733150\pi\)
\(158\) −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 0.969918 0.243432i \(-0.0782731\pi\)
−0.695777 + 0.718258i \(0.744940\pi\)
\(164\) −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 0.959274 + 0.282477i \(0.0911562\pi\)
−0.235004 + 0.971994i \(0.575510\pi\)
\(174\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 5.19615 + 9.00000i 0.387298 + 0.670820i
\(181\) 12.1244i 0.901196i −0.892727 0.450598i \(-0.851211\pi\)
0.892727 0.450598i \(-0.148789\pi\)
\(182\) −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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −1.50000 0.866025i −0.108253 0.0625000i
\(193\) 1.00000 1.73205i 0.0719816 0.124676i −0.827788 0.561041i \(-0.810401\pi\)
0.899770 + 0.436365i \(0.143734\pi\)
\(194\) −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 \(-0.896112\pi\)
0.947211 0.320612i \(-0.103888\pi\)
\(198\) −4.50000 7.79423i −0.319801 0.553912i
\(199\) −22.5000 12.9904i −1.59498 0.920864i −0.992434 0.122782i \(-0.960818\pi\)
−0.602549 0.798082i \(-0.705848\pi\)
\(200\) 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 \(0.0745182\pi\)
−0.972722 + 0.231973i \(0.925482\pi\)
\(224\) 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 −0.766832 0.641848i \(-0.778168\pi\)
0.939272 + 0.343172i \(0.111501\pi\)
\(228\) 6.00000 10.3923i 0.397360 0.688247i
\(229\) −10.5000 + 6.06218i −0.693860 + 0.400600i −0.805056 0.593198i \(-0.797865\pi\)
0.111197 + 0.993798i \(0.464532\pi\)
\(230\) −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 −0.119342 0.992853i \(-0.538079\pi\)
0.800165 + 0.599780i \(0.204745\pi\)
\(234\) −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 \(0.161229\pi\)
−0.874439 + 0.485135i \(0.838771\pi\)
\(240\) 5.19615 3.00000i 0.335410 0.193649i
\(241\) 12.0000 + 6.92820i 0.772988 + 0.446285i 0.833939 0.551856i \(-0.186080\pi\)
−0.0609515 + 0.998141i \(0.519414\pi\)
\(242\) −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 0.953608 0.301052i \(-0.0973379\pi\)
−0.737523 + 0.675322i \(0.764005\pi\)
\(258\) 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 0.784929 0.619586i \(-0.212699\pi\)
−0.144112 + 0.989561i \(0.546033\pi\)
\(264\) −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 −0.989506 0.144494i \(-0.953845\pi\)
0.619888 + 0.784690i \(0.287178\pi\)
\(270\) −9.00000 + 15.5885i −0.547723 + 0.948683i
\(271\) −6.00000 + 3.46410i −0.364474 + 0.210429i −0.671042 0.741420i \(-0.734153\pi\)
0.306568 + 0.951849i \(0.400819\pi\)
\(272\) −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 −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) −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 \(-0.913489\pi\)
0.963294 0.268447i \(-0.0865106\pi\)
\(282\) −7.50000 12.9904i −0.446619 0.773566i
\(283\) −15.0000 8.66025i −0.891657 0.514799i −0.0171732 0.999853i \(-0.505467\pi\)
−0.874484 + 0.485054i \(0.838800\pi\)
\(284\) 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 \(0.146740\pi\)
−0.895610 + 0.444840i \(0.853260\pi\)
\(308\) 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 −0.782914 0.622130i \(-0.786268\pi\)
0.930237 + 0.366958i \(0.119601\pi\)
\(312\) 5.19615 + 3.00000i 0.294174 + 0.169842i
\(313\) −27.0000 + 15.5885i −1.52613 + 0.881112i −0.526611 + 0.850106i \(0.676538\pi\)
−0.999519 + 0.0310053i \(0.990129\pi\)
\(314\) −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 −0.869184 0.494489i \(-0.835355\pi\)
−0.00635137 + 0.999980i \(0.502022\pi\)
\(318\) −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 −0.937829 0.347097i \(-0.887167\pi\)
0.168320 0.985732i \(-0.446166\pi\)
\(332\) 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 0.856186 0.516667i \(-0.172828\pi\)
−0.0193540 + 0.999813i \(0.506161\pi\)
\(348\) 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 −0.970528 0.240987i \(-0.922529\pi\)
0.693965 + 0.720009i \(0.255862\pi\)
\(354\) 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 −0.666608 + 0.745409i \(0.732254\pi\)
−0.978847 + 0.204595i \(0.934412\pi\)
\(360\) 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 0.837490 0.546452i \(-0.184022\pi\)
−0.0544966 + 0.998514i \(0.517355\pi\)
\(368\) 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 0.878680 0.477412i \(-0.158425\pi\)
−0.852791 + 0.522253i \(0.825092\pi\)
\(374\) −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 0.818375 0.574684i \(-0.194875\pi\)
−0.906879 + 0.421392i \(0.861542\pi\)
\(384\) −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 0.212847 0.977086i \(-0.431726\pi\)
−0.739758 + 0.672874i \(0.765060\pi\)
\(390\) −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 −0.256850 0.966451i \(-0.582685\pi\)
0.708547 + 0.705664i \(0.249351\pi\)
\(398\) −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 −0.787961 0.615725i \(-0.788863\pi\)
0.139253 + 0.990257i \(0.455530\pi\)
\(402\) 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 0.462456 0.886642i \(-0.346968\pi\)
−0.536626 + 0.843820i \(0.680302\pi\)
\(410\) −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 0.908591 0.417687i \(-0.137159\pi\)
0.0925683 + 0.995706i \(0.470492\pi\)
\(432\) 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 0.197681 0.980266i \(-0.436659\pi\)
0.947776 + 0.318936i \(0.103326\pi\)
\(440\) −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 −0.904528 0.426414i \(-0.859777\pi\)
−0.0829786 + 0.996551i \(0.526443\pi\)
\(444\) 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 \(0.191631\pi\)
−0.824189 + 0.566315i \(0.808369\pi\)
\(450\) −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 0.948566 + 0.316579i \(0.102534\pi\)
−0.200118 + 0.979772i \(0.564132\pi\)
\(458\) −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 0.748275 0.663389i \(-0.230883\pi\)
−0.948649 + 0.316330i \(0.897549\pi\)
\(468\) 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 −0.133710 0.991021i \(-0.542689\pi\)
0.925104 0.379714i \(-0.123978\pi\)
\(480\) 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 −0.545436 0.838152i \(-0.683636\pi\)
0.998579 + 0.0532853i \(0.0169693\pi\)
\(488\) 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 \(-0.763305\pi\)
0.736038 0.676941i \(-0.236695\pi\)
\(492\) −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 0.916542 0.399937i \(-0.130968\pi\)
−0.804627 + 0.593780i \(0.797635\pi\)
\(500\) −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 0.699825 0.714314i \(-0.253261\pi\)
−0.968527 + 0.248910i \(0.919928\pi\)
\(510\) 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 −0.0973580 + 0.995249i \(0.531039\pi\)
−0.813232 + 0.581939i \(0.802294\pi\)
\(522\) −4.50000 + 7.79423i −0.196960 + 0.341144i
\(523\) 9.00000 5.19615i 0.393543 0.227212i −0.290151 0.956981i \(-0.593706\pi\)
0.683694 + 0.729769i \(0.260372\pi\)
\(524\) 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 0.956504 + 0.291718i \(0.0942267\pi\)
−0.225617 + 0.974216i \(0.572440\pi\)
\(542\) −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 0.998765 + 0.0496855i \(0.0158219\pi\)
0.542411 + 0.840113i \(0.317511\pi\)
\(558\) 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 −0.847199 0.531276i \(-0.821713\pi\)
0.883698 + 0.468058i \(0.155046\pi\)
\(564\) −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 −0.933355 0.358954i \(-0.883134\pi\)
−0.155815 + 0.987786i \(0.549800\pi\)
\(570\) 36.0000 + 20.7846i 1.50787 + 0.870572i
\(571\) −4.00000 + 6.92820i −0.167395 + 0.289936i −0.937503 0.347977i \(-0.886869\pi\)
0.770108 + 0.637913i \(0.220202\pi\)
\(572\) −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 0.191940 0.981407i \(-0.438522\pi\)
−0.753953 + 0.656929i \(0.771855\pi\)
\(578\) 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 0.878010 + 0.478643i \(0.158871\pi\)
−0.0244882 + 0.999700i \(0.507796\pi\)
\(594\) 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 −0.387849 0.921723i \(-0.626782\pi\)
−0.992160 + 0.124975i \(0.960115\pi\)
\(600\) 6.06218 + 10.5000i 0.247487 + 0.428661i
\(601\) 20.7846i 0.847822i −0.905704 0.423911i \(-0.860657\pi\)
0.905704 0.423911i \(-0.139343\pi\)
\(602\) −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 −0.588537 + 0.808470i \(0.700296\pi\)
−0.994424 + 0.105453i \(0.966371\pi\)
\(608\) −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 −0.955458 0.295126i \(-0.904638\pi\)
0.733316 + 0.679888i \(0.237972\pi\)
\(614\) 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 \(-0.817103\pi\)
0.839416 0.543490i \(-0.182897\pi\)
\(618\) 12.9904 7.50000i 0.522550 0.301694i
\(619\) −30.0000 17.3205i −1.20580 0.696170i −0.243962 0.969785i \(-0.578447\pi\)
−0.961839 + 0.273615i \(0.911781\pi\)
\(620\) 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 0.734103 0.679039i \(-0.237603\pi\)
−0.221013 + 0.975271i \(0.570936\pi\)
\(642\) 18.0000 10.3923i 0.710403 0.410152i
\(643\) 13.8564i 0.546443i −0.961951 0.273222i \(-0.911911\pi\)
0.961951 0.273222i \(-0.0880892\pi\)
\(644\) −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 −0.416819 0.908990i \(-0.636855\pi\)
0.995618 0.0935189i \(-0.0298116\pi\)
\(648\) 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 −0.549973 0.835182i \(-0.685362\pi\)
0.448303 + 0.893882i \(0.352029\pi\)
\(654\) 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 \(-0.943912\pi\)
0.984516 0.175295i \(-0.0560880\pi\)
\(660\) −9.00000 15.5885i −0.350325 0.606780i
\(661\) 1.50000 + 0.866025i 0.0583432 + 0.0336845i 0.528888 0.848692i \(-0.322609\pi\)
−0.470545 + 0.882376i \(0.655943\pi\)
\(662\) −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 0.650227 0.759740i \(-0.274674\pi\)
−0.983068 + 0.183243i \(0.941340\pi\)
\(678\) 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 0.596107 0.802905i \(-0.296713\pi\)
−0.397282 + 0.917697i \(0.630047\pi\)
\(684\) 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 −0.411958 0.911203i \(-0.635155\pi\)
0.583146 + 0.812367i \(0.301822\pi\)
\(692\) 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 \(0.291565\pi\)
−0.609015 + 0.793159i \(0.708435\pi\)
\(702\) −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 0.630641 0.776075i \(-0.282792\pi\)
−0.987421 + 0.158114i \(0.949459\pi\)
\(710\) −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 −0.890121 0.455725i \(-0.849380\pi\)
0.0503909 0.998730i \(-0.483953\pi\)
\(720\) 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 \(-0.529556\pi\)
0.0927199 0.995692i \(-0.470444\pi\)
\(728\) −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 −0.0231578 0.999732i \(-0.507372\pi\)
0.854214 + 0.519921i \(0.174039\pi\)
\(734\) 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 −0.426371 0.904549i \(-0.640208\pi\)
0.996547 0.0830265i \(-0.0264586\pi\)
\(740\) 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 \(-0.964896\pi\)
0.993925 0.110059i \(-0.0351041\pi\)
\(744\) 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 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) −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 0.712695 0.701474i \(-0.247474\pi\)
−0.963842 + 0.266475i \(0.914141\pi\)
\(762\) 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 \(-0.898902\pi\)
0.949985 0.312297i