Properties

Label 546.2.q.d.251.1
Level $546$
Weight $2$
Character 546.251
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(251,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.q (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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 251.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.251
Dual form 546.2.q.d.335.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(1.50000 - 0.866025i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(1.50000 - 0.866025i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{10} +(-1.50000 + 2.59808i) q^{11} -1.73205i q^{12} +(3.50000 - 0.866025i) q^{13} +(2.00000 - 1.73205i) q^{14} +(3.00000 - 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +3.00000 q^{18} +(-3.50000 - 6.06218i) q^{19} +(-3.00000 + 1.73205i) q^{20} +(3.00000 + 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{22} +(6.00000 + 3.46410i) q^{23} +(-1.50000 - 0.866025i) q^{24} -7.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +5.19615i q^{27} +(-0.500000 - 2.59808i) q^{28} +(-1.50000 - 0.866025i) q^{29} +(-3.00000 - 5.19615i) q^{30} -4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} -3.00000 q^{34} +(3.00000 - 8.66025i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-6.00000 - 3.46410i) q^{37} -7.00000 q^{38} +(6.00000 + 1.73205i) q^{39} +3.46410i q^{40} +(-4.50000 - 2.59808i) q^{41} +(4.50000 - 0.866025i) q^{42} +(4.00000 + 6.92820i) q^{43} +3.00000 q^{44} +(9.00000 - 5.19615i) q^{45} +(6.00000 - 3.46410i) q^{46} +8.66025i q^{47} +(-1.50000 + 0.866025i) q^{48} +(5.50000 + 4.33013i) q^{49} +(-3.50000 + 6.06218i) q^{50} -5.19615i q^{51} +(-2.50000 - 2.59808i) q^{52} +8.66025i q^{53} +(4.50000 + 2.59808i) q^{54} +(9.00000 + 5.19615i) q^{55} +(-2.50000 - 0.866025i) q^{56} -12.1244i q^{57} +(-1.50000 + 0.866025i) q^{58} +(9.00000 - 5.19615i) q^{59} -6.00000 q^{60} +(4.50000 - 2.59808i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.50000 + 7.79423i) q^{63} +1.00000 q^{64} +(-3.00000 - 12.1244i) q^{65} +5.19615i q^{66} +(-1.50000 + 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{69} +(-6.00000 - 6.92820i) q^{70} +(3.00000 + 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} -4.00000 q^{73} +(-6.00000 + 3.46410i) q^{74} +(-10.5000 - 6.06218i) q^{75} +(-3.50000 + 6.06218i) q^{76} +(-6.00000 + 5.19615i) q^{77} +(4.50000 - 4.33013i) q^{78} -11.0000 q^{79} +(3.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 2.59808i) q^{82} +13.8564i q^{83} +(1.50000 - 4.33013i) q^{84} +(-9.00000 + 5.19615i) q^{85} +8.00000 q^{86} +(-1.50000 - 2.59808i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-7.50000 - 4.33013i) q^{89} -10.3923i q^{90} +(9.50000 + 0.866025i) q^{91} -6.92820i q^{92} +(-6.00000 - 3.46410i) q^{93} +(7.50000 + 4.33013i) q^{94} +(-21.0000 + 12.1244i) q^{95} +1.73205i q^{96} +(1.00000 + 1.73205i) q^{97} +(6.50000 - 2.59808i) q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{6} + 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{6} + 5 q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{10} - 3 q^{11} + 7 q^{13} + 4 q^{14} + 6 q^{15} - q^{16} - 3 q^{17} + 6 q^{18} - 7 q^{19} - 6 q^{20} + 6 q^{21} + 3 q^{22} + 12 q^{23} - 3 q^{24} - 14 q^{25} + 2 q^{26} - q^{28} - 3 q^{29} - 6 q^{30} - 8 q^{31} + q^{32} - 9 q^{33} - 6 q^{34} + 6 q^{35} + 3 q^{36} - 12 q^{37} - 14 q^{38} + 12 q^{39} - 9 q^{41} + 9 q^{42} + 8 q^{43} + 6 q^{44} + 18 q^{45} + 12 q^{46} - 3 q^{48} + 11 q^{49} - 7 q^{50} - 5 q^{52} + 9 q^{54} + 18 q^{55} - 5 q^{56} - 3 q^{58} + 18 q^{59} - 12 q^{60} + 9 q^{61} - 4 q^{62} + 3 q^{63} + 2 q^{64} - 6 q^{65} - 3 q^{68} + 12 q^{69} - 12 q^{70} + 6 q^{71} - 3 q^{72} - 8 q^{73} - 12 q^{74} - 21 q^{75} - 7 q^{76} - 12 q^{77} + 9 q^{78} - 22 q^{79} + 6 q^{80} - 9 q^{81} - 9 q^{82} + 3 q^{84} - 18 q^{85} + 16 q^{86} - 3 q^{87} + 3 q^{88} - 15 q^{89} + 19 q^{91} - 12 q^{93} + 15 q^{94} - 42 q^{95} + 2 q^{97} + 13 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 3.46410i 1.54919i −0.632456 0.774597i \(-0.717953\pi\)
0.632456 0.774597i \(-0.282047\pi\)
\(6\) 1.50000 0.866025i 0.612372 0.353553i
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) −3.00000 1.73205i −0.948683 0.547723i
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 1.73205i 0.500000i
\(13\) 3.50000 0.866025i 0.970725 0.240192i
\(14\) 2.00000 1.73205i 0.534522 0.462910i
\(15\) 3.00000 5.19615i 0.774597 1.34164i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 3.00000 0.707107
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) −3.00000 + 1.73205i −0.670820 + 0.387298i
\(21\) 3.00000 + 3.46410i 0.654654 + 0.755929i
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) 6.00000 + 3.46410i 1.25109 + 0.722315i 0.971325 0.237754i \(-0.0764114\pi\)
0.279761 + 0.960070i \(0.409745\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) −7.00000 −1.40000
\(26\) 1.00000 3.46410i 0.196116 0.679366i
\(27\) 5.19615i 1.00000i
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) −1.50000 0.866025i −0.278543 0.160817i 0.354221 0.935162i \(-0.384746\pi\)
−0.632764 + 0.774345i \(0.718080\pi\)
\(30\) −3.00000 5.19615i −0.547723 0.948683i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −4.50000 + 2.59808i −0.783349 + 0.452267i
\(34\) −3.00000 −0.514496
\(35\) 3.00000 8.66025i 0.507093 1.46385i
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) −6.00000 3.46410i −0.986394 0.569495i −0.0821995 0.996616i \(-0.526194\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) −7.00000 −1.13555
\(39\) 6.00000 + 1.73205i 0.960769 + 0.277350i
\(40\) 3.46410i 0.547723i
\(41\) −4.50000 2.59808i −0.702782 0.405751i 0.105601 0.994409i \(-0.466323\pi\)
−0.808383 + 0.588657i \(0.799657\pi\)
\(42\) 4.50000 0.866025i 0.694365 0.133631i
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 3.00000 0.452267
\(45\) 9.00000 5.19615i 1.34164 0.774597i
\(46\) 6.00000 3.46410i 0.884652 0.510754i
\(47\) 8.66025i 1.26323i 0.775283 + 0.631614i \(0.217607\pi\)
−0.775283 + 0.631614i \(0.782393\pi\)
\(48\) −1.50000 + 0.866025i −0.216506 + 0.125000i
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −3.50000 + 6.06218i −0.494975 + 0.857321i
\(51\) 5.19615i 0.727607i
\(52\) −2.50000 2.59808i −0.346688 0.360288i
\(53\) 8.66025i 1.18958i 0.803882 + 0.594789i \(0.202764\pi\)
−0.803882 + 0.594789i \(0.797236\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) 9.00000 + 5.19615i 1.21356 + 0.700649i
\(56\) −2.50000 0.866025i −0.334077 0.115728i
\(57\) 12.1244i 1.60591i
\(58\) −1.50000 + 0.866025i −0.196960 + 0.113715i
\(59\) 9.00000 5.19615i 1.17170 0.676481i 0.217620 0.976034i \(-0.430171\pi\)
0.954080 + 0.299552i \(0.0968372\pi\)
\(60\) −6.00000 −0.774597
\(61\) 4.50000 2.59808i 0.576166 0.332650i −0.183442 0.983030i \(-0.558724\pi\)
0.759608 + 0.650381i \(0.225391\pi\)
\(62\) −2.00000 + 3.46410i −0.254000 + 0.439941i
\(63\) 1.50000 + 7.79423i 0.188982 + 0.981981i
\(64\) 1.00000 0.125000
\(65\) −3.00000 12.1244i −0.372104 1.50384i
\(66\) 5.19615i 0.639602i
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) 6.00000 + 10.3923i 0.722315 + 1.25109i
\(70\) −6.00000 6.92820i −0.717137 0.828079i
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) −1.50000 2.59808i −0.176777 0.306186i
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −6.00000 + 3.46410i −0.697486 + 0.402694i
\(75\) −10.5000 6.06218i −1.21244 0.700000i
\(76\) −3.50000 + 6.06218i −0.401478 + 0.695379i
\(77\) −6.00000 + 5.19615i −0.683763 + 0.592157i
\(78\) 4.50000 4.33013i 0.509525 0.490290i
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 3.00000 + 1.73205i 0.335410 + 0.193649i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −4.50000 + 2.59808i −0.496942 + 0.286910i
\(83\) 13.8564i 1.52094i 0.649374 + 0.760469i \(0.275031\pi\)
−0.649374 + 0.760469i \(0.724969\pi\)
\(84\) 1.50000 4.33013i 0.163663 0.472456i
\(85\) −9.00000 + 5.19615i −0.976187 + 0.563602i
\(86\) 8.00000 0.862662
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −7.50000 4.33013i −0.794998 0.458993i 0.0467209 0.998908i \(-0.485123\pi\)
−0.841719 + 0.539915i \(0.818456\pi\)
\(90\) 10.3923i 1.09545i
\(91\) 9.50000 + 0.866025i 0.995871 + 0.0907841i
\(92\) 6.92820i 0.722315i
\(93\) −6.00000 3.46410i −0.622171 0.359211i
\(94\) 7.50000 + 4.33013i 0.773566 + 0.446619i
\(95\) −21.0000 + 12.1244i −2.15455 + 1.24393i
\(96\) 1.73205i 0.176777i
\(97\) 1.00000 + 1.73205i 0.101535 + 0.175863i 0.912317 0.409484i \(-0.134291\pi\)
−0.810782 + 0.585348i \(0.800958\pi\)
\(98\) 6.50000 2.59808i 0.656599 0.262445i
\(99\) −9.00000 −0.904534
\(100\) 3.50000 + 6.06218i 0.350000 + 0.606218i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) −4.50000 2.59808i −0.445566 0.257248i
\(103\) 3.46410i 0.341328i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) −3.50000 + 0.866025i −0.343203 + 0.0849208i
\(105\) 12.0000 10.3923i 1.17108 1.01419i
\(106\) 7.50000 + 4.33013i 0.728464 + 0.420579i
\(107\) −4.50000 2.59808i −0.435031 0.251166i 0.266456 0.963847i \(-0.414147\pi\)
−0.701488 + 0.712681i \(0.747481\pi\)
\(108\) 4.50000 2.59808i 0.433013 0.250000i
\(109\) 3.46410i 0.331801i 0.986143 + 0.165900i \(0.0530530\pi\)
−0.986143 + 0.165900i \(0.946947\pi\)
\(110\) 9.00000 5.19615i 0.858116 0.495434i
\(111\) −6.00000 10.3923i −0.569495 0.986394i
\(112\) −2.00000 + 1.73205i −0.188982 + 0.163663i
\(113\) −12.0000 + 6.92820i −1.12887 + 0.651751i −0.943649 0.330947i \(-0.892632\pi\)
−0.185216 + 0.982698i \(0.559298\pi\)
\(114\) −10.5000 6.06218i −0.983415 0.567775i
\(115\) 12.0000 20.7846i 1.11901 1.93817i
\(116\) 1.73205i 0.160817i
\(117\) 7.50000 + 7.79423i 0.693375 + 0.720577i
\(118\) 10.3923i 0.956689i
\(119\) −1.50000 7.79423i −0.137505 0.714496i
\(120\) −3.00000 + 5.19615i −0.273861 + 0.474342i
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 5.19615i 0.470438i
\(123\) −4.50000 7.79423i −0.405751 0.702782i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 6.92820i 0.619677i
\(126\) 7.50000 + 2.59808i 0.668153 + 0.231455i
\(127\) 4.00000 6.92820i 0.354943 0.614779i −0.632166 0.774833i \(-0.717834\pi\)
0.987108 + 0.160055i \(0.0511671\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 13.8564i 1.21999i
\(130\) −12.0000 3.46410i −1.05247 0.303822i
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 4.50000 + 2.59808i 0.391675 + 0.226134i
\(133\) −3.50000 18.1865i −0.303488 1.57697i
\(134\) 0 0
\(135\) 18.0000 1.54919
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 12.0000 1.02151
\(139\) −4.50000 + 2.59808i −0.381685 + 0.220366i −0.678551 0.734553i \(-0.737392\pi\)
0.296866 + 0.954919i \(0.404058\pi\)
\(140\) −9.00000 + 1.73205i −0.760639 + 0.146385i
\(141\) −7.50000 + 12.9904i −0.631614 + 1.09399i
\(142\) 6.00000 0.503509
\(143\) −3.00000 + 10.3923i −0.250873 + 0.869048i
\(144\) −3.00000 −0.250000
\(145\) −3.00000 + 5.19615i −0.249136 + 0.431517i
\(146\) −2.00000 + 3.46410i −0.165521 + 0.286691i
\(147\) 4.50000 + 11.2583i 0.371154 + 0.928571i
\(148\) 6.92820i 0.569495i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) −10.5000 + 6.06218i −0.857321 + 0.494975i
\(151\) 8.66025i 0.704761i −0.935857 0.352381i \(-0.885372\pi\)
0.935857 0.352381i \(-0.114628\pi\)
\(152\) 3.50000 + 6.06218i 0.283887 + 0.491708i
\(153\) 4.50000 7.79423i 0.363803 0.630126i
\(154\) 1.50000 + 7.79423i 0.120873 + 0.628077i
\(155\) 13.8564i 1.11297i
\(156\) −1.50000 6.06218i −0.120096 0.485363i
\(157\) 13.8564i 1.10586i 0.833227 + 0.552931i \(0.186491\pi\)
−0.833227 + 0.552931i \(0.813509\pi\)
\(158\) −5.50000 + 9.52628i −0.437557 + 0.757870i
\(159\) −7.50000 + 12.9904i −0.594789 + 1.03020i
\(160\) 3.00000 1.73205i 0.237171 0.136931i
\(161\) 12.0000 + 13.8564i 0.945732 + 1.09204i
\(162\) 4.50000 + 7.79423i 0.353553 + 0.612372i
\(163\) 21.0000 12.1244i 1.64485 0.949653i 0.665771 0.746156i \(-0.268103\pi\)
0.979076 0.203497i \(-0.0652307\pi\)
\(164\) 5.19615i 0.405751i
\(165\) 9.00000 + 15.5885i 0.700649 + 1.21356i
\(166\) 12.0000 + 6.92820i 0.931381 + 0.537733i
\(167\) −15.0000 8.66025i −1.16073 0.670151i −0.209255 0.977861i \(-0.567104\pi\)
−0.951480 + 0.307711i \(0.900437\pi\)
\(168\) −3.00000 3.46410i −0.231455 0.267261i
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) 10.3923i 0.797053i
\(171\) 10.5000 18.1865i 0.802955 1.39076i
\(172\) 4.00000 6.92820i 0.304997 0.528271i
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) −3.00000 −0.227429
\(175\) −17.5000 6.06218i −1.32288 0.458258i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 18.0000 1.35296
\(178\) −7.50000 + 4.33013i −0.562149 + 0.324557i
\(179\) −21.0000 12.1244i −1.56961 0.906217i −0.996213 0.0869415i \(-0.972291\pi\)
−0.573400 0.819275i \(-0.694376\pi\)
\(180\) −9.00000 5.19615i −0.670820 0.387298i
\(181\) 1.73205i 0.128742i −0.997926 0.0643712i \(-0.979496\pi\)
0.997926 0.0643712i \(-0.0205042\pi\)
\(182\) 5.50000 7.79423i 0.407687 0.577747i
\(183\) 9.00000 0.665299
\(184\) −6.00000 3.46410i −0.442326 0.255377i
\(185\) −12.0000 + 20.7846i −0.882258 + 1.52811i
\(186\) −6.00000 + 3.46410i −0.439941 + 0.254000i
\(187\) 9.00000 0.658145
\(188\) 7.50000 4.33013i 0.546994 0.315807i
\(189\) −4.50000 + 12.9904i −0.327327 + 0.944911i
\(190\) 24.2487i 1.75919i
\(191\) 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
\(193\) −10.5000 6.06218i −0.755807 0.436365i 0.0719816 0.997406i \(-0.477068\pi\)
−0.827788 + 0.561041i \(0.810401\pi\)
\(194\) 2.00000 0.143592
\(195\) 6.00000 20.7846i 0.429669 1.48842i
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 13.5000 23.3827i 0.961835 1.66595i 0.243947 0.969788i \(-0.421558\pi\)
0.717888 0.696159i \(-0.245109\pi\)
\(198\) −4.50000 + 7.79423i −0.319801 + 0.553912i
\(199\) −9.00000 + 5.19615i −0.637993 + 0.368345i −0.783841 0.620962i \(-0.786742\pi\)
0.145848 + 0.989307i \(0.453409\pi\)
\(200\) 7.00000 0.494975
\(201\) 0 0
\(202\) 0 0
\(203\) −3.00000 3.46410i −0.210559 0.243132i
\(204\) −4.50000 + 2.59808i −0.315063 + 0.181902i
\(205\) −9.00000 + 15.5885i −0.628587 + 1.08875i
\(206\) 3.00000 + 1.73205i 0.209020 + 0.120678i
\(207\) 20.7846i 1.44463i
\(208\) −1.00000 + 3.46410i −0.0693375 + 0.240192i
\(209\) 21.0000 1.45260
\(210\) −3.00000 15.5885i −0.207020 1.07571i
\(211\) 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i \(-0.559865\pi\)
0.944237 0.329266i \(-0.106801\pi\)
\(212\) 7.50000 4.33013i 0.515102 0.297394i
\(213\) 10.3923i 0.712069i
\(214\) −4.50000 + 2.59808i −0.307614 + 0.177601i
\(215\) 24.0000 13.8564i 1.63679 0.944999i
\(216\) 5.19615i 0.353553i
\(217\) −10.0000 3.46410i −0.678844 0.235159i
\(218\) 3.00000 + 1.73205i 0.203186 + 0.117309i
\(219\) −6.00000 3.46410i −0.405442 0.234082i
\(220\) 10.3923i 0.700649i
\(221\) −7.50000 7.79423i −0.504505 0.524297i
\(222\) −12.0000 −0.805387
\(223\) −8.00000 + 13.8564i −0.535720 + 0.927894i 0.463409 + 0.886145i \(0.346626\pi\)
−0.999128 + 0.0417488i \(0.986707\pi\)
\(224\) 0.500000 + 2.59808i 0.0334077 + 0.173591i
\(225\) −10.5000 18.1865i −0.700000 1.21244i
\(226\) 13.8564i 0.921714i
\(227\) 9.00000 5.19615i 0.597351 0.344881i −0.170648 0.985332i \(-0.554586\pi\)
0.767999 + 0.640451i \(0.221253\pi\)
\(228\) −10.5000 + 6.06218i −0.695379 + 0.401478i
\(229\) −13.0000 −0.859064 −0.429532 0.903052i \(-0.641321\pi\)
−0.429532 + 0.903052i \(0.641321\pi\)
\(230\) −12.0000 20.7846i −0.791257 1.37050i
\(231\) −13.5000 + 2.59808i −0.888235 + 0.170941i
\(232\) 1.50000 + 0.866025i 0.0984798 + 0.0568574i
\(233\) 6.92820i 0.453882i 0.973909 + 0.226941i \(0.0728724\pi\)
−0.973909 + 0.226941i \(0.927128\pi\)
\(234\) 10.5000 2.59808i 0.686406 0.169842i
\(235\) 30.0000 1.95698
\(236\) −9.00000 5.19615i −0.585850 0.338241i
\(237\) −16.5000 9.52628i −1.07179 0.618798i
\(238\) −7.50000 2.59808i −0.486153 0.168408i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 3.00000 + 5.19615i 0.193649 + 0.335410i
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 2.00000 0.128565
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) −4.50000 2.59808i −0.288083 0.166325i
\(245\) 15.0000 19.0526i 0.958315 1.21722i
\(246\) −9.00000 −0.573819
\(247\) −17.5000 18.1865i −1.11350 1.15718i
\(248\) 4.00000 0.254000
\(249\) −12.0000 + 20.7846i −0.760469 + 1.31717i
\(250\) 6.00000 + 3.46410i 0.379473 + 0.219089i
\(251\) −15.0000 25.9808i −0.946792 1.63989i −0.752124 0.659022i \(-0.770970\pi\)
−0.194668 0.980869i \(-0.562363\pi\)
\(252\) 6.00000 5.19615i 0.377964 0.327327i
\(253\) −18.0000 + 10.3923i −1.13165 + 0.653359i
\(254\) −4.00000 6.92820i −0.250982 0.434714i
\(255\) −18.0000 −1.12720
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 13.5000 23.3827i 0.842107 1.45857i −0.0460033 0.998941i \(-0.514648\pi\)
0.888110 0.459631i \(-0.152018\pi\)
\(258\) 12.0000 + 6.92820i 0.747087 + 0.431331i
\(259\) −12.0000 13.8564i −0.745644 0.860995i
\(260\) −9.00000 + 8.66025i −0.558156 + 0.537086i
\(261\) 5.19615i 0.321634i
\(262\) 3.00000 5.19615i 0.185341 0.321019i
\(263\) 21.0000 + 12.1244i 1.29492 + 0.747620i 0.979521 0.201341i \(-0.0645299\pi\)
0.315394 + 0.948961i \(0.397863\pi\)
\(264\) 4.50000 2.59808i 0.276956 0.159901i
\(265\) 30.0000 1.84289
\(266\) −17.5000 6.06218i −1.07299 0.371696i
\(267\) −7.50000 12.9904i −0.458993 0.794998i
\(268\) 0 0
\(269\) −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i \(-0.905416\pi\)
0.224523 0.974469i \(-0.427917\pi\)
\(270\) 9.00000 15.5885i 0.547723 0.948683i
\(271\) 4.00000 6.92820i 0.242983 0.420858i −0.718580 0.695444i \(-0.755208\pi\)
0.961563 + 0.274586i \(0.0885408\pi\)
\(272\) 3.00000 0.181902
\(273\) 13.5000 + 9.52628i 0.817057 + 0.576557i
\(274\) 12.0000 0.724947
\(275\) 10.5000 18.1865i 0.633174 1.09669i
\(276\) 6.00000 10.3923i 0.361158 0.625543i
\(277\) 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i \(-0.00705893\pi\)
−0.519081 + 0.854725i \(0.673726\pi\)
\(278\) 5.19615i 0.311645i
\(279\) −6.00000 10.3923i −0.359211 0.622171i
\(280\) −3.00000 + 8.66025i −0.179284 + 0.517549i
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 7.50000 + 12.9904i 0.446619 + 0.773566i
\(283\) 3.00000 + 1.73205i 0.178331 + 0.102960i 0.586509 0.809943i \(-0.300502\pi\)
−0.408177 + 0.912903i \(0.633835\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) −42.0000 −2.48787
\(286\) 7.50000 + 7.79423i 0.443484 + 0.460882i
\(287\) −9.00000 10.3923i −0.531253 0.613438i
\(288\) −1.50000 + 2.59808i −0.0883883 + 0.153093i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 3.00000 + 5.19615i 0.176166 + 0.305129i
\(291\) 3.46410i 0.203069i
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) −6.00000 + 3.46410i −0.350524 + 0.202375i −0.664916 0.746918i \(-0.731533\pi\)
0.314392 + 0.949293i \(0.398199\pi\)
\(294\) 12.0000 + 1.73205i 0.699854 + 0.101015i
\(295\) −18.0000 31.1769i −1.04800 1.81519i
\(296\) 6.00000 + 3.46410i 0.348743 + 0.201347i
\(297\) −13.5000 7.79423i −0.783349 0.452267i
\(298\) −6.00000 −0.347571
\(299\) 24.0000 + 6.92820i 1.38796 + 0.400668i
\(300\) 12.1244i 0.700000i
\(301\) 4.00000 + 20.7846i 0.230556 + 1.19800i
\(302\) −7.50000 4.33013i −0.431577 0.249171i
\(303\) 0 0
\(304\) 7.00000 0.401478
\(305\) −9.00000 15.5885i −0.515339 0.892592i
\(306\) −4.50000 7.79423i −0.257248 0.445566i
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 7.50000 + 2.59808i 0.427352 + 0.148039i
\(309\) −3.00000 + 5.19615i −0.170664 + 0.295599i
\(310\) 12.0000 + 6.92820i 0.681554 + 0.393496i
\(311\) −3.00000 −0.170114 −0.0850572 0.996376i \(-0.527107\pi\)
−0.0850572 + 0.996376i \(0.527107\pi\)
\(312\) −6.00000 1.73205i −0.339683 0.0980581i
\(313\) 20.7846i 1.17482i −0.809291 0.587408i \(-0.800148\pi\)
0.809291 0.587408i \(-0.199852\pi\)
\(314\) 12.0000 + 6.92820i 0.677199 + 0.390981i
\(315\) 27.0000 5.19615i 1.52128 0.292770i
\(316\) 5.50000 + 9.52628i 0.309399 + 0.535895i
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 7.50000 + 12.9904i 0.420579 + 0.728464i
\(319\) 4.50000 2.59808i 0.251952 0.145464i
\(320\) 3.46410i 0.193649i
\(321\) −4.50000 7.79423i −0.251166 0.435031i
\(322\) 18.0000 3.46410i 1.00310 0.193047i
\(323\) −10.5000 + 18.1865i −0.584236 + 1.01193i
\(324\) 9.00000 0.500000
\(325\) −24.5000 + 6.06218i −1.35902 + 0.336269i
\(326\) 24.2487i 1.34301i
\(327\) −3.00000 + 5.19615i −0.165900 + 0.287348i
\(328\) 4.50000 + 2.59808i 0.248471 + 0.143455i
\(329\) −7.50000 + 21.6506i −0.413488 + 1.19364i
\(330\) 18.0000 0.990867
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 12.0000 6.92820i 0.658586 0.380235i
\(333\) 20.7846i 1.13899i
\(334\) −15.0000 + 8.66025i −0.820763 + 0.473868i
\(335\) 0 0
\(336\) −4.50000 + 0.866025i −0.245495 + 0.0472456i
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 0.500000 12.9904i 0.0271964 0.706584i
\(339\) −24.0000 −1.30350
\(340\) 9.00000 + 5.19615i 0.488094 + 0.281801i
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) −10.5000 18.1865i −0.567775 0.983415i
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −4.00000 6.92820i −0.215666 0.373544i
\(345\) 36.0000 20.7846i 1.93817 1.11901i
\(346\) 0 0
\(347\) 13.5000 7.79423i 0.724718 0.418416i −0.0917687 0.995780i \(-0.529252\pi\)
0.816487 + 0.577364i \(0.195919\pi\)
\(348\) −1.50000 + 2.59808i −0.0804084 + 0.139272i
\(349\) −1.00000 + 1.73205i −0.0535288 + 0.0927146i −0.891548 0.452926i \(-0.850380\pi\)
0.838019 + 0.545640i \(0.183714\pi\)
\(350\) −14.0000 + 12.1244i −0.748331 + 0.648074i
\(351\) 4.50000 + 18.1865i 0.240192 + 0.970725i
\(352\) −3.00000 −0.159901
\(353\) 18.0000 + 10.3923i 0.958043 + 0.553127i 0.895570 0.444920i \(-0.146768\pi\)
0.0624731 + 0.998047i \(0.480101\pi\)
\(354\) 9.00000 15.5885i 0.478345 0.828517i
\(355\) 18.0000 10.3923i 0.955341 0.551566i
\(356\) 8.66025i 0.458993i
\(357\) 4.50000 12.9904i 0.238165 0.687524i
\(358\) −21.0000 + 12.1244i −1.10988 + 0.640792i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) −9.00000 + 5.19615i −0.474342 + 0.273861i
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −1.50000 0.866025i −0.0788382 0.0455173i
\(363\) 3.46410i 0.181818i
\(364\) −4.00000 8.66025i −0.209657 0.453921i
\(365\) 13.8564i 0.725277i
\(366\) 4.50000 7.79423i 0.235219 0.407411i
\(367\) −18.0000 10.3923i −0.939592 0.542474i −0.0497598 0.998761i \(-0.515846\pi\)
−0.889833 + 0.456287i \(0.849179\pi\)
\(368\) −6.00000 + 3.46410i −0.312772 + 0.180579i
\(369\) 15.5885i 0.811503i
\(370\) 12.0000 + 20.7846i 0.623850 + 1.08054i
\(371\) −7.50000 + 21.6506i −0.389381 + 1.12404i
\(372\) 6.92820i 0.359211i
\(373\) 10.0000 + 17.3205i 0.517780 + 0.896822i 0.999787 + 0.0206542i \(0.00657489\pi\)
−0.482006 + 0.876168i \(0.660092\pi\)
\(374\) 4.50000 7.79423i 0.232689 0.403030i
\(375\) −6.00000 + 10.3923i −0.309839 + 0.536656i
\(376\) 8.66025i 0.446619i
\(377\) −6.00000 1.73205i −0.309016 0.0892052i
\(378\) 9.00000 + 10.3923i 0.462910 + 0.534522i
\(379\) −9.00000 5.19615i −0.462299 0.266908i 0.250711 0.968062i \(-0.419335\pi\)
−0.713010 + 0.701153i \(0.752669\pi\)
\(380\) 21.0000 + 12.1244i 1.07728 + 0.621966i
\(381\) 12.0000 6.92820i 0.614779 0.354943i
\(382\) 0 0
\(383\) −4.50000 + 2.59808i −0.229939 + 0.132755i −0.610544 0.791982i \(-0.709049\pi\)
0.380605 + 0.924738i \(0.375716\pi\)
\(384\) 1.50000 0.866025i 0.0765466 0.0441942i
\(385\) 18.0000 + 20.7846i 0.917365 + 1.05928i
\(386\) −10.5000 + 6.06218i −0.534436 + 0.308557i
\(387\) −12.0000 + 20.7846i −0.609994 + 1.05654i
\(388\) 1.00000 1.73205i 0.0507673 0.0879316i
\(389\) 20.7846i 1.05382i 0.849921 + 0.526911i \(0.176650\pi\)
−0.849921 + 0.526911i \(0.823350\pi\)
\(390\) −15.0000 15.5885i −0.759555 0.789352i
\(391\) 20.7846i 1.05112i
\(392\) −5.50000 4.33013i −0.277792 0.218704i
\(393\) 9.00000 + 5.19615i 0.453990 + 0.262111i
\(394\) −13.5000 23.3827i −0.680120 1.17800i
\(395\) 38.1051i 1.91728i
\(396\) 4.50000 + 7.79423i 0.226134 + 0.391675i
\(397\) −3.50000 6.06218i −0.175660 0.304252i 0.764730 0.644351i \(-0.222873\pi\)
−0.940389 + 0.340099i \(0.889539\pi\)
\(398\) 10.3923i 0.520919i
\(399\) 10.5000 30.3109i 0.525657 1.51744i
\(400\) 3.50000 6.06218i 0.175000 0.303109i
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 0 0
\(403\) −14.0000 + 3.46410i −0.697390 + 0.172559i
\(404\) 0 0
\(405\) 27.0000 + 15.5885i 1.34164 + 0.774597i
\(406\) −4.50000 + 0.866025i −0.223331 + 0.0429801i
\(407\) 18.0000 10.3923i 0.892227 0.515127i
\(408\) 5.19615i 0.257248i
\(409\) −2.00000 3.46410i −0.0988936 0.171289i 0.812333 0.583193i \(-0.198197\pi\)
−0.911227 + 0.411905i \(0.864864\pi\)
\(410\) 9.00000 + 15.5885i 0.444478 + 0.769859i
\(411\) 20.7846i 1.02523i
\(412\) 3.00000 1.73205i 0.147799 0.0853320i
\(413\) 27.0000 5.19615i 1.32858 0.255686i
\(414\) 18.0000 + 10.3923i 0.884652 + 0.510754i
\(415\) 48.0000 2.35623
\(416\) 2.50000 + 2.59808i 0.122573 + 0.127381i
\(417\) −9.00000 −0.440732
\(418\) 10.5000 18.1865i 0.513572 0.889532i
\(419\) −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i \(-0.928027\pi\)
0.681426 + 0.731887i \(0.261360\pi\)
\(420\) −15.0000 5.19615i −0.731925 0.253546i
\(421\) 24.2487i 1.18181i −0.806741 0.590905i \(-0.798771\pi\)
0.806741 0.590905i \(-0.201229\pi\)
\(422\) −11.0000 19.0526i −0.535472 0.927464i
\(423\) −22.5000 + 12.9904i −1.09399 + 0.631614i
\(424\) 8.66025i 0.420579i
\(425\) 10.5000 + 18.1865i 0.509325 + 0.882176i
\(426\) 9.00000 + 5.19615i 0.436051 + 0.251754i
\(427\) 13.5000 2.59808i 0.653311 0.125730i
\(428\) 5.19615i 0.251166i
\(429\) −13.5000 + 12.9904i −0.651786 + 0.627182i
\(430\) 27.7128i 1.33643i
\(431\) 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i \(-0.690607\pi\)
0.997173 + 0.0751385i \(0.0239399\pi\)
\(432\) −4.50000 2.59808i −0.216506 0.125000i
\(433\) −15.0000 + 8.66025i −0.720854 + 0.416185i −0.815067 0.579367i \(-0.803300\pi\)
0.0942129 + 0.995552i \(0.469967\pi\)
\(434\) −8.00000 + 6.92820i −0.384012 + 0.332564i
\(435\) −9.00000 + 5.19615i −0.431517 + 0.249136i
\(436\) 3.00000 1.73205i 0.143674 0.0829502i
\(437\) 48.4974i 2.31995i
\(438\) −6.00000 + 3.46410i −0.286691 + 0.165521i
\(439\) −3.00000 1.73205i −0.143182 0.0826663i 0.426698 0.904394i \(-0.359677\pi\)
−0.569880 + 0.821728i \(0.693010\pi\)
\(440\) −9.00000 5.19615i −0.429058 0.247717i
\(441\) −3.00000 + 20.7846i −0.142857 + 0.989743i
\(442\) −10.5000 + 2.59808i −0.499434 + 0.123578i
\(443\) 29.4449i 1.39897i −0.714648 0.699484i \(-0.753413\pi\)
0.714648 0.699484i \(-0.246587\pi\)
\(444\) −6.00000 + 10.3923i −0.284747 + 0.493197i
\(445\) −15.0000 + 25.9808i −0.711068 + 1.23161i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) 10.3923i 0.491539i
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) −18.0000 31.1769i −0.849473 1.47133i −0.881680 0.471848i \(-0.843587\pi\)
0.0322072 0.999481i \(-0.489746\pi\)
\(450\) −21.0000 −0.989949
\(451\) 13.5000 7.79423i 0.635690 0.367016i
\(452\) 12.0000 + 6.92820i 0.564433 + 0.325875i
\(453\) 7.50000 12.9904i 0.352381 0.610341i
\(454\) 10.3923i 0.487735i
\(455\) 3.00000 32.9090i 0.140642 1.54280i
\(456\) 12.1244i 0.567775i
\(457\) −6.00000 3.46410i −0.280668 0.162044i 0.353058 0.935602i \(-0.385142\pi\)
−0.633726 + 0.773558i \(0.718475\pi\)
\(458\) −6.50000 + 11.2583i −0.303725 + 0.526067i
\(459\) 13.5000 7.79423i 0.630126 0.363803i
\(460\) −24.0000 −1.11901
\(461\) −27.0000 + 15.5885i −1.25752 + 0.726027i −0.972591 0.232523i \(-0.925302\pi\)
−0.284925 + 0.958550i \(0.591969\pi\)
\(462\) −4.50000 + 12.9904i −0.209359 + 0.604367i
\(463\) 36.3731i 1.69040i −0.534450 0.845200i \(-0.679481\pi\)
0.534450 0.845200i \(-0.320519\pi\)
\(464\) 1.50000 0.866025i 0.0696358 0.0402042i
\(465\) −12.0000 + 20.7846i −0.556487 + 0.963863i
\(466\) 6.00000 + 3.46410i 0.277945 + 0.160471i
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 3.00000 10.3923i 0.138675 0.480384i
\(469\) 0 0
\(470\) 15.0000 25.9808i 0.691898 1.19840i
\(471\) −12.0000 + 20.7846i −0.552931 + 0.957704i
\(472\) −9.00000 + 5.19615i −0.414259 + 0.239172i
\(473\) −24.0000 −1.10352
\(474\) −16.5000 + 9.52628i −0.757870 + 0.437557i
\(475\) 24.5000 + 42.4352i 1.12414 + 1.94706i
\(476\) −6.00000 + 5.19615i −0.275010 + 0.238165i
\(477\) −22.5000 + 12.9904i −1.03020 + 0.594789i
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) 28.5000 + 16.4545i 1.30220 + 0.751825i 0.980781 0.195113i \(-0.0625074\pi\)
0.321417 + 0.946938i \(0.395841\pi\)
\(480\) 6.00000 0.273861
\(481\) −24.0000 6.92820i −1.09431 0.315899i
\(482\) 10.0000 0.455488
\(483\) 6.00000 + 31.1769i 0.273009 + 1.41860i
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 6.00000 3.46410i 0.272446 0.157297i
\(486\) 15.5885i 0.707107i
\(487\) 7.50000 4.33013i 0.339857 0.196217i −0.320352 0.947299i \(-0.603801\pi\)
0.660209 + 0.751082i \(0.270468\pi\)
\(488\) −4.50000 + 2.59808i −0.203705 + 0.117609i
\(489\) 42.0000 1.89931
\(490\) −9.00000 22.5167i −0.406579 1.01720i
\(491\) 9.00000 + 5.19615i 0.406164 + 0.234499i 0.689140 0.724628i \(-0.257988\pi\)
−0.282976 + 0.959127i \(0.591322\pi\)
\(492\) −4.50000 + 7.79423i −0.202876 + 0.351391i
\(493\) 5.19615i 0.234023i
\(494\) −24.5000 + 6.06218i −1.10231 + 0.272750i
\(495\) 31.1769i 1.40130i
\(496\) 2.00000 3.46410i 0.0898027 0.155543i
\(497\) 3.00000 + 15.5885i 0.134568 + 0.699238i
\(498\) 12.0000 + 20.7846i 0.537733 + 0.931381i
\(499\) 41.5692i 1.86089i 0.366427 + 0.930447i \(0.380581\pi\)
−0.366427 + 0.930447i \(0.619419\pi\)
\(500\) 6.00000 3.46410i 0.268328 0.154919i
\(501\) −15.0000 25.9808i −0.670151 1.16073i
\(502\) −30.0000 −1.33897
\(503\) 6.00000 + 10.3923i 0.267527 + 0.463370i 0.968223 0.250090i \(-0.0804603\pi\)
−0.700696 + 0.713460i \(0.747127\pi\)
\(504\) −1.50000 7.79423i −0.0668153 0.347183i
\(505\) 0 0
\(506\) 20.7846i 0.923989i
\(507\) 22.5000 + 0.866025i 0.999260 + 0.0384615i
\(508\) −8.00000 −0.354943
\(509\) 24.0000 + 13.8564i 1.06378 + 0.614174i 0.926476 0.376354i \(-0.122822\pi\)
0.137305 + 0.990529i \(0.456156\pi\)
\(510\) −9.00000 + 15.5885i −0.398527 + 0.690268i
\(511\) −10.0000 3.46410i −0.442374 0.153243i
\(512\) −1.00000 −0.0441942
\(513\) 31.5000 18.1865i 1.39076 0.802955i
\(514\) −13.5000 23.3827i −0.595459 1.03137i
\(515\) 12.0000 0.528783
\(516\) 12.0000 6.92820i 0.528271 0.304997i
\(517\) −22.5000 12.9904i −0.989549 0.571316i
\(518\) −18.0000 + 3.46410i −0.790875 + 0.152204i
\(519\) 0 0
\(520\) 3.00000 + 12.1244i 0.131559 + 0.531688i
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) −4.50000 2.59808i −0.196960 0.113715i
\(523\) 28.5000 + 16.4545i 1.24622 + 0.719504i 0.970353 0.241692i \(-0.0777024\pi\)
0.275865 + 0.961196i \(0.411036\pi\)
\(524\) −3.00000 5.19615i −0.131056 0.226995i
\(525\) −21.0000 24.2487i −0.916515 1.05830i
\(526\) 21.0000 12.1244i 0.915644 0.528647i
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 5.19615i 0.226134i
\(529\) 12.5000 + 21.6506i 0.543478 + 0.941332i
\(530\) 15.0000 25.9808i 0.651558 1.12853i
\(531\) 27.0000 + 15.5885i 1.17170 + 0.676481i
\(532\) −14.0000 + 12.1244i −0.606977 + 0.525657i
\(533\) −18.0000 5.19615i −0.779667 0.225070i
\(534\) −15.0000 −0.649113
\(535\) −9.00000 + 15.5885i −0.389104 + 0.673948i
\(536\) 0 0
\(537\) −21.0000 36.3731i −0.906217 1.56961i
\(538\) −24.0000 −1.03471
\(539\) −19.5000 + 7.79423i −0.839924 + 0.335721i
\(540\) −9.00000 15.5885i −0.387298 0.670820i
\(541\) 31.1769i 1.34040i −0.742180 0.670200i \(-0.766208\pi\)
0.742180 0.670200i \(-0.233792\pi\)
\(542\) −4.00000 6.92820i −0.171815 0.297592i
\(543\) 1.50000 2.59808i 0.0643712 0.111494i
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) 12.0000 0.514024
\(546\) 15.0000 6.92820i 0.641941 0.296500i
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) 13.5000 + 7.79423i 0.576166 + 0.332650i
\(550\) −10.5000 18.1865i −0.447722 0.775476i
\(551\) 12.1244i 0.516515i
\(552\) −6.00000 10.3923i −0.255377 0.442326i
\(553\) −27.5000 9.52628i −1.16942 0.405099i
\(554\) 16.0000 0.679775
\(555\) −36.0000 + 20.7846i −1.52811 + 0.882258i
\(556\) 4.50000 + 2.59808i 0.190843 + 0.110183i
\(557\) −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i \(-0.853578\pi\)
0.832496 + 0.554031i \(0.186911\pi\)
\(558\) −12.0000 −0.508001
\(559\) 20.0000 + 20.7846i 0.845910 + 0.879095i
\(560\) 6.00000 + 6.92820i 0.253546 + 0.292770i
\(561\) 13.5000 + 7.79423i 0.569970 + 0.329073i
\(562\) 6.00000 10.3923i 0.253095 0.438373i
\(563\) −12.0000 20.7846i −0.505740 0.875967i −0.999978 0.00664037i \(-0.997886\pi\)
0.494238 0.869326i \(-0.335447\pi\)
\(564\) 15.0000 0.631614
\(565\) 24.0000 + 41.5692i 1.00969 + 1.74883i
\(566\) 3.00000 1.73205i 0.126099 0.0728035i
\(567\) −18.0000 + 15.5885i −0.755929 + 0.654654i
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) −15.0000 8.66025i −0.628833 0.363057i 0.151467 0.988462i \(-0.451600\pi\)
−0.780300 + 0.625406i \(0.784934\pi\)
\(570\) −21.0000 + 36.3731i −0.879593 + 1.52350i
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 10.5000 2.59808i 0.439027 0.108631i
\(573\) 0 0
\(574\) −13.5000 + 2.59808i −0.563479 + 0.108442i
\(575\) −42.0000 24.2487i −1.75152 1.01124i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) −10.5000 18.1865i −0.436365 0.755807i
\(580\) 6.00000 0.249136
\(581\) −12.0000 + 34.6410i −0.497844 + 1.43715i
\(582\) 3.00000 + 1.73205i 0.124354 + 0.0717958i
\(583\) −22.5000 12.9904i −0.931855 0.538007i
\(584\) 4.00000 0.165521
\(585\) 27.0000 25.9808i 1.11631 1.07417i
\(586\) 6.92820i 0.286201i
\(587\) −15.0000 8.66025i −0.619116 0.357447i 0.157409 0.987534i \(-0.449686\pi\)
−0.776525 + 0.630087i \(0.783019\pi\)
\(588\) 7.50000 9.52628i 0.309295 0.392857i
\(589\) 14.0000 + 24.2487i 0.576860 + 0.999151i
\(590\) −36.0000 −1.48210
\(591\) 40.5000 23.3827i 1.66595 0.961835i
\(592\) 6.00000 3.46410i 0.246598 0.142374i
\(593\) 8.66025i 0.355634i 0.984064 + 0.177817i \(0.0569035\pi\)
−0.984064 + 0.177817i \(0.943096\pi\)
\(594\) −13.5000 + 7.79423i −0.553912 + 0.319801i
\(595\) −27.0000 + 5.19615i −1.10689 + 0.213021i
\(596\) −3.00000 + 5.19615i −0.122885 + 0.212843i
\(597\) −18.0000 −0.736691
\(598\) 18.0000 17.3205i 0.736075 0.708288i
\(599\) 3.46410i 0.141539i −0.997493 0.0707697i \(-0.977454\pi\)
0.997493 0.0707697i \(-0.0225455\pi\)
\(600\) 10.5000 + 6.06218i 0.428661 + 0.247487i
\(601\) −27.0000 15.5885i −1.10135 0.635866i −0.164777 0.986331i \(-0.552690\pi\)
−0.936576 + 0.350464i \(0.886024\pi\)
\(602\) 20.0000 + 6.92820i 0.815139 + 0.282372i
\(603\) 0 0
\(604\) −7.50000 + 4.33013i −0.305171 + 0.176190i
\(605\) 6.00000 3.46410i 0.243935 0.140836i
\(606\) 0 0
\(607\) −6.00000 + 3.46410i −0.243532 + 0.140604i −0.616799 0.787121i \(-0.711571\pi\)
0.373267 + 0.927724i \(0.378238\pi\)
\(608\) 3.50000 6.06218i 0.141944 0.245854i
\(609\) −1.50000 7.79423i −0.0607831 0.315838i
\(610\) −18.0000 −0.728799
\(611\) 7.50000 + 30.3109i 0.303418 + 1.22625i
\(612\) −9.00000 −0.363803
\(613\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) −3.50000 + 6.06218i −0.141249 + 0.244650i
\(615\) −27.0000 + 15.5885i −1.08875 + 0.628587i
\(616\) 6.00000 5.19615i 0.241747 0.209359i
\(617\) 3.00000 + 5.19615i 0.120775 + 0.209189i 0.920074 0.391745i \(-0.128129\pi\)
−0.799298 + 0.600935i \(0.794795\pi\)
\(618\) 3.00000 + 5.19615i 0.120678 + 0.209020i
\(619\) 31.0000 1.24600 0.622998 0.782224i \(-0.285915\pi\)
0.622998 + 0.782224i \(0.285915\pi\)
\(620\) 12.0000 6.92820i 0.481932 0.278243i
\(621\) −18.0000 + 31.1769i −0.722315 + 1.25109i
\(622\) −1.50000 + 2.59808i −0.0601445 + 0.104173i
\(623\) −15.0000 17.3205i −0.600962 0.693932i
\(624\) −4.50000 + 4.33013i −0.180144 + 0.173344i
\(625\) −11.0000 −0.440000
\(626\) −18.0000 10.3923i −0.719425 0.415360i
\(627\) 31.5000 + 18.1865i 1.25799 + 0.726300i
\(628\) 12.0000 6.92820i 0.478852 0.276465i
\(629\) 20.7846i 0.828737i
\(630\) 9.00000 25.9808i 0.358569 1.03510i
\(631\) −40.5000 + 23.3827i −1.61228 + 0.930850i −0.623439 + 0.781872i \(0.714265\pi\)
−0.988841 + 0.148978i \(0.952402\pi\)
\(632\) 11.0000 0.437557
\(633\) 33.0000 19.0526i 1.31163 0.757271i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) −24.0000 13.8564i −0.952411 0.549875i
\(636\) 15.0000 0.594789
\(637\) 23.0000 + 10.3923i 0.911293 + 0.411758i
\(638\) 5.19615i 0.205718i
\(639\) −9.00000 + 15.5885i −0.356034 + 0.616670i
\(640\) −3.00000 1.73205i −0.118585 0.0684653i
\(641\) 3.00000 1.73205i 0.118493 0.0684119i −0.439582 0.898202i \(-0.644873\pi\)
0.558075 + 0.829790i \(0.311540\pi\)
\(642\) −9.00000 −0.355202
\(643\) −23.5000 40.7032i −0.926750 1.60518i −0.788723 0.614749i \(-0.789257\pi\)
−0.138027 0.990429i \(-0.544076\pi\)
\(644\) 6.00000 17.3205i 0.236433 0.682524i
\(645\) 48.0000 1.89000
\(646\) 10.5000 + 18.1865i 0.413117 + 0.715540i
\(647\) 10.5000 18.1865i 0.412798 0.714986i −0.582397 0.812905i \(-0.697885\pi\)
0.995194 + 0.0979182i \(0.0312184\pi\)
\(648\) 4.50000 7.79423i 0.176777 0.306186i
\(649\) 31.1769i 1.22380i
\(650\) −7.00000 + 24.2487i −0.274563 + 0.951113i
\(651\) −12.0000 13.8564i −0.470317 0.543075i
\(652\) −21.0000 12.1244i −0.822423 0.474826i
\(653\) −4.50000 2.59808i −0.176099 0.101671i 0.409360 0.912373i \(-0.365752\pi\)
−0.585458 + 0.810702i \(0.699085\pi\)
\(654\) 3.00000 + 5.19615i 0.117309 + 0.203186i
\(655\) 20.7846i 0.812122i
\(656\) 4.50000 2.59808i 0.175695 0.101438i
\(657\) −6.00000 10.3923i −0.234082 0.405442i
\(658\) 15.0000 + 17.3205i 0.584761 + 0.675224i
\(659\) −1.50000 + 0.866025i −0.0584317 + 0.0337356i −0.528931 0.848665i \(-0.677407\pi\)
0.470500 + 0.882400i \(0.344074\pi\)
\(660\) 9.00000 15.5885i 0.350325 0.606780i
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) 0 0
\(663\) −4.50000 18.1865i −0.174766 0.706306i
\(664\) 13.8564i 0.537733i
\(665\) −63.0000 + 12.1244i −2.44304 + 0.470162i
\(666\) −18.0000 10.3923i −0.697486 0.402694i
\(667\) −6.00000 10.3923i −0.232321 0.402392i
\(668\) 17.3205i 0.670151i
\(669\) −24.0000 + 13.8564i −0.927894 + 0.535720i
\(670\) 0 0
\(671\) 15.5885i 0.601786i
\(672\) −1.50000 + 4.33013i −0.0578638 + 0.167038i
\(673\) 14.5000 25.1147i 0.558934 0.968102i −0.438652 0.898657i \(-0.644544\pi\)
0.997586 0.0694449i \(-0.0221228\pi\)
\(674\) −9.50000 + 16.4545i −0.365926 + 0.633803i
\(675\) 36.3731i 1.40000i
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) −12.0000 + 20.7846i −0.460857 + 0.798228i
\(679\) 1.00000 + 5.19615i 0.0383765 + 0.199410i
\(680\) 9.00000 5.19615i 0.345134 0.199263i
\(681\) 18.0000 0.689761
\(682\) −6.00000 10.3923i −0.229752 0.397942i
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) −21.0000 −0.802955
\(685\) 36.0000 20.7846i 1.37549 0.794139i
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) −19.5000 11.2583i −0.743971 0.429532i
\(688\) −8.00000 −0.304997
\(689\) 7.50000 + 30.3109i 0.285727 + 1.15475i
\(690\) 41.5692i 1.58251i
\(691\) 4.00000 6.92820i 0.152167 0.263561i −0.779857 0.625958i \(-0.784708\pi\)
0.932024 + 0.362397i \(0.118041\pi\)
\(692\) 0 0
\(693\) −22.5000 7.79423i −0.854704 0.296078i
\(694\) 15.5885i 0.591730i
\(695\) 9.00000 + 15.5885i 0.341389 + 0.591304i
\(696\) 1.50000 + 2.59808i 0.0568574 + 0.0984798i
\(697\) 15.5885i 0.590455i
\(698\) 1.00000 + 1.73205i 0.0378506 + 0.0655591i
\(699\) −6.00000 + 10.3923i −0.226941 + 0.393073i
\(700\) 3.50000 + 18.1865i 0.132288 + 0.687386i
\(701\) 12.1244i 0.457931i 0.973435 + 0.228965i \(0.0735342\pi\)
−0.973435 + 0.228965i \(0.926466\pi\)
\(702\) 18.0000 + 5.19615i 0.679366 + 0.196116i
\(703\) 48.4974i 1.82911i
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 45.0000 + 25.9808i 1.69480 + 0.978492i
\(706\) 18.0000 10.3923i 0.677439 0.391120i
\(707\) 0 0
\(708\) −9.00000 15.5885i −0.338241 0.585850i
\(709\) 21.0000 12.1244i 0.788672 0.455340i −0.0508231 0.998708i \(-0.516184\pi\)
0.839495 + 0.543368i \(0.182851\pi\)
\(710\) 20.7846i 0.780033i
\(711\) −16.5000 28.5788i −0.618798 1.07179i
\(712\) 7.50000 + 4.33013i 0.281074 + 0.162278i
\(713\) −24.0000 13.8564i −0.898807 0.518927i
\(714\) −9.00000 10.3923i −0.336817 0.388922i
\(715\) 36.0000 + 10.3923i 1.34632 + 0.388650i
\(716\) 24.2487i 0.906217i
\(717\) 18.0000 + 10.3923i 0.672222 + 0.388108i
\(718\) −12.0000 + 20.7846i −0.447836 + 0.775675i
\(719\) 10.5000 + 18.1865i 0.391584 + 0.678243i 0.992659 0.120950i \(-0.0385939\pi\)
−0.601075 + 0.799193i \(0.705261\pi\)
\(720\) 10.3923i 0.387298i
\(721\) −3.00000 + 8.66025i −0.111726 + 0.322525i
\(722\) 15.0000 + 25.9808i 0.558242 + 0.966904i
\(723\) 17.3205i 0.644157i
\(724\) −1.50000 + 0.866025i −0.0557471 + 0.0321856i
\(725\) 10.5000 + 6.06218i 0.389960 + 0.225144i
\(726\) 3.00000 + 1.73205i 0.111340 + 0.0642824i
\(727\) 34.6410i 1.28476i 0.766385 + 0.642382i \(0.222054\pi\)
−0.766385 + 0.642382i \(0.777946\pi\)
\(728\) −9.50000 0.866025i −0.352093 0.0320970i
\(729\) −27.0000 −1.00000
\(730\) 12.0000 + 6.92820i 0.444140 + 0.256424i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) −4.50000 7.79423i −0.166325 0.288083i
\(733\) −13.0000 −0.480166 −0.240083 0.970752i \(-0.577175\pi\)
−0.240083 + 0.970752i \(0.577175\pi\)
\(734\) −18.0000 + 10.3923i −0.664392 + 0.383587i
\(735\) 39.0000 15.5885i 1.43854 0.574989i
\(736\) 6.92820i 0.255377i
\(737\) 0 0
\(738\) −13.5000 7.79423i −0.496942 0.286910i
\(739\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 24.0000 0.882258
\(741\) −10.5000 42.4352i −0.385727 1.55890i
\(742\) 15.0000 + 17.3205i 0.550667 + 0.635856i
\(743\) 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i \(-0.798229\pi\)
0.915794 + 0.401648i \(0.131563\pi\)
\(744\) 6.00000 + 3.46410i 0.219971 + 0.127000i
\(745\) −18.0000 + 10.3923i −0.659469 + 0.380745i
\(746\) 20.0000 0.732252
\(747\) −36.0000 + 20.7846i −1.31717 + 0.760469i
\(748\) −4.50000 7.79423i −0.164536 0.284985i
\(749\) −9.00000 10.3923i −0.328853 0.379727i
\(750\) 6.00000 + 10.3923i 0.219089 + 0.379473i
\(751\) −15.5000 + 26.8468i −0.565603 + 0.979653i 0.431390 + 0.902165i \(0.358023\pi\)
−0.996993 + 0.0774878i \(0.975310\pi\)
\(752\) −7.50000 4.33013i −0.273497 0.157903i
\(753\) 51.9615i 1.89358i
\(754\) −4.50000 + 4.33013i −0.163880 + 0.157694i
\(755\) −30.0000 −1.09181
\(756\) 13.5000 2.59808i 0.490990 0.0944911i
\(757\) −10.0000 + 17.3205i −0.363456 + 0.629525i −0.988527 0.151043i \(-0.951737\pi\)
0.625071 + 0.780568i \(0.285070\pi\)
\(758\) −9.00000 + 5.19615i −0.326895 + 0.188733i
\(759\) −36.0000 −1.30672
\(760\) 21.0000 12.1244i 0.761750 0.439797i
\(761\) 6.00000 3.46410i 0.217500 0.125574i −0.387292 0.921957i \(-0.626590\pi\)
0.604792 + 0.796383i \(0.293256\pi\)
\(762\) 13.8564i 0.501965i
\(763\) −3.00000 + 8.66025i −0.108607 + 0.313522i
\(764\) 0 0
\(765\) −27.0000 15.5885i −0.976187 0.563602i
\(766\) 5.19615i 0.187745i
\(767\) 27.0000 25.9808i 0.974913 0.938111i
\(768\) 1.73205i 0.0625000i
\(769\) 20.0000 34.6410i 0.721218 1.24919i −0.239293 0.970947i \(-0.576916\pi\)
0.960512 0.278240i \(-0.0897509\pi\)
\(770\) 27.0000 5.19615i 0.973012 0.187256i
\(771\) 40.5000 23.3827i 1.45857 0.842107i
\(772\) 12.1244i 0.436365i
\(773\) 9.00000 5.19615i 0.323708 0.186893i −0.329336 0.944213i \(-0.606825\pi\)
0.653044 + 0.757320i \(0.273492\pi\)
\(774\) 12.0000 + 20.7846i 0.431331 + 0.747087i
\(775\) 28.0000 1.00579
\(776\) −1.00000 1.73205i −0.0358979 0.0621770i
\(777\) −6.00000 31.1769i −0.215249 1.11847i
\(778\) 18.0000 + 10.3923i 0.645331 + 0.372582i
\(779\) 36.3731i 1.30320i
\(780\) −21.0000 + 5.19615i −0.751921 + 0.186052i
\(781\) −18.0000 −0.644091
\(782\) −18.0000 10.3923i −0.643679 0.371628i
\(783\) 4.50000 7.79423i 0.160817 0.278543i
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) 48.0000 1.71319
\(786\) 9.00000 5.19615i 0.321019 0.185341i
\(787\) 8.50000 + 14.7224i 0.302992 + 0.524798i 0.976812 0.214097i \(-0.0686810\pi\)
−0.673820 + 0.738896i \(0.735348\pi\)
\(788\) −27.0000 −0.961835
\(789\) 21.0000 + 36.3731i 0.747620 + 1.29492i
\(790\) 33.0000 + 19.0526i 1.17409 + 0.677860i
\(791\) −36.0000 + 6.92820i −1.28001 + 0.246339i
\(792\) 9.00000 0.319801
\(793\) 13.5000 12.9904i 0.479399 0.461302i
\(794\) −7.00000 −0.248421
\(795\) 45.0000 + 25.9808i 1.59599 + 0.921443i
\(796\) 9.00000 + 5.19615i 0.318997 + 0.184173i
\(797\) 6.00000 + 10.3923i 0.212531 + 0.368114i 0.952506 0.304520i \(-0.0984960\pi\)
−0.739975 + 0.672634i \(0.765163\pi\)
\(798\) −21.0000 24.2487i −0.743392 0.858395i
\(799\) 22.5000 12.9904i 0.795993 0.459567i
\(800\) −3.50000 6.06218i −0.123744 0.214330i
\(801\) 25.9808i 0.917985i
\(802\) 9.00000 + 15.5885i 0.317801 + 0.550448i
\(803\) 6.00000 10.3923i 0.211735 0.366736i
\(804\) 0 0
\(805\) 48.0000 41.5692i 1.69178 1.46512i
\(806\) −4.00000 + 13.8564i −0.140894 + 0.488071i
\(807\) 41.5692i 1.46331i
\(808\) 0 0
\(809\) 42.0000 + 24.2487i 1.47664 + 0.852539i 0.999652 0.0263699i \(-0.00839478\pi\)
0.476989 + 0.878909i \(0.341728\pi\)
\(810\) 27.0000 15.5885i 0.948683 0.547723i
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) −1.50000 + 4.33013i −0.0526397 + 0.151958i
\(813\) 12.0000 6.92820i 0.420858 0.242983i
\(814\) 20.7846i 0.728500i
\(815\) −42.0000 72.7461i −1.47120 2.54819i
\(816\) 4.50000 + 2.59808i 0.157532 + 0.0909509i
\(817\) 28.0000 48.4974i 0.979596 1.69671i
\(818\) −4.00000 −0.139857
\(819\) 12.0000 + 25.9808i 0.419314 + 0.907841i
\(820\) 18.0000 0.628587
\(821\) 1.50000 2.59808i 0.0523504 0.0906735i −0.838663 0.544651i \(-0.816662\pi\)
0.891013 + 0.453978i \(0.149995\pi\)
\(822\) 18.0000 + 10.3923i 0.627822 + 0.362473i
\(823\) 8.00000 + 13.8564i 0.278862 + 0.483004i 0.971102 0.238664i \(-0.0767093\pi\)
−0.692240 + 0.721668i \(0.743376\pi\)
\(824\) 3.46410i 0.120678i
\(825\) 31.5000 18.1865i 1.09669 0.633174i
\(826\) 9.00000 25.9808i 0.313150 0.903986i
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 18.0000 10.3923i 0.625543 0.361158i
\(829\) 13.5000 + 7.79423i 0.468874 + 0.270705i 0.715768 0.698338i \(-0.246077\pi\)
−0.246894 + 0.969042i \(0.579410\pi\)
\(830\) 24.0000 41.5692i 0.833052 1.44289i
\(831\) 27.7128i 0.961347i
\(832\) 3.50000 0.866025i 0.121341 0.0300240i
\(833\) 3.00000 20.7846i 0.103944 0.720144i
\(834\) −4.50000 + 7.79423i −0.155822 + 0.269892i
\(835\) −30.0000 + 51.9615i −1.03819 + 1.79820i
\(836\) −10.5000 18.1865i −0.363150 0.628994i
\(837\) 20.7846i 0.718421i
\(838\) 6.00000 + 10.3923i 0.207267 + 0.358996i
\(839\) −27.0000 + 15.5885i −0.932144 + 0.538173i −0.887489 0.460829i \(-0.847552\pi\)
−0.0446547 + 0.999002i \(0.514219\pi\)
\(840\) −12.0000 + 10.3923i −0.414039 + 0.358569i
\(841\) −13.0000 22.5167i −0.448276 0.776437i
\(842\) −21.0000 12.1244i −0.723708 0.417833i
\(843\) 18.0000 + 10.3923i 0.619953 + 0.357930i
\(844\) −22.0000 −0.757271
\(845\) −21.0000 39.8372i −0.722422 1.37044i
\(846\) 25.9808i 0.893237i
\(847\) 1.00000 + 5.19615i 0.0343604 + 0.178542i
\(848\) −7.50000 4.33013i −0.257551 0.148697i
\(849\) 3.00000 + 5.19615i 0.102960 + 0.178331i
\(850\) 21.0000 0.720294
\(851\) −24.0000 41.5692i −0.822709 1.42497i
\(852\) 9.00000 5.19615i 0.308335 0.178017i
\(853\) −35.0000 −1.19838 −0.599189 0.800608i \(-0.704510\pi\)
−0.599189 + 0.800608i \(0.704510\pi\)
\(854\) 4.50000 12.9904i 0.153987 0.444522i
\(855\) −63.0000 36.3731i −2.15455 1.24393i
\(856\) 4.50000 + 2.59808i 0.153807 + 0.0888004i
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 4.50000 + 18.1865i 0.153627 + 0.620878i
\(859\) 39.8372i 1.35923i 0.733571 + 0.679613i \(0.237852\pi\)
−0.733571 + 0.679613i \(0.762148\pi\)
\(860\) −24.0000 13.8564i −0.818393 0.472500i
\(861\) −4.50000 23.3827i −0.153360 0.796880i
\(862\) −9.00000 15.5885i −0.306541 0.530945i
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) −4.50000 + 2.59808i −0.153093 + 0.0883883i
\(865\) 0 0
\(866\) 17.3205i 0.588575i
\(867\) 12.0000 6.92820i 0.407541 0.235294i
\(868\) 2.00000 + 10.3923i 0.0678844 + 0.352738i
\(869\) 16.5000 28.5788i 0.559724 0.969471i
\(870\) 10.3923i 0.352332i
\(871\) 0 0
\(872\) 3.46410i 0.117309i
\(873\) −3.00000 + 5.19615i −0.101535 + 0.175863i
\(874\) −42.0000 24.2487i −1.42067 0.820225i
\(875\) −6.00000 + 17.3205i −0.202837 + 0.585540i
\(876\) 6.92820i 0.234082i
\(877\) 21.0000 12.1244i 0.709120 0.409410i −0.101615 0.994824i \(-0.532401\pi\)
0.810735 + 0.585413i \(0.199068\pi\)
\(878\) −3.00000 + 1.73205i −0.101245 + 0.0584539i
\(879\) −12.0000 −0.404750
\(880\) −9.00000 + 5.19615i −0.303390 + 0.175162i
\(881\) 15.0000 25.9808i 0.505363 0.875314i −0.494618 0.869111i \(-0.664692\pi\)
0.999981 0.00620358i \(-0.00197467\pi\)
\(882\) 16.5000 + 12.9904i 0.555584 + 0.437409i
\(883\) 2.00000 0.0673054 0.0336527 0.999434i \(-0.489286\pi\)
0.0336527 + 0.999434i \(0.489286\pi\)
\(884\) −3.00000 + 10.3923i −0.100901 + 0.349531i
\(885\) 62.3538i 2.09600i
\(886\) −25.5000 14.7224i −0.856689 0.494610i
\(887\) 13.5000 23.3827i 0.453286 0.785114i −0.545302 0.838240i \(-0.683585\pi\)
0.998588 + 0.0531258i \(0.0169184\pi\)
\(888\) 6.00000 + 10.3923i 0.201347 + 0.348743i
\(889\) 16.0000 13.8564i 0.536623 0.464729i
\(890\) 15.0000 + 25.9808i 0.502801 + 0.870877i
\(891\) −13.5000 23.3827i −0.452267 0.783349i
\(892\) 16.0000 0.535720
\(893\) 52.5000 30.3109i 1.75685 1.01432i
\(894\) −9.00000 5.19615i −0.301005 0.173785i
\(895\) −42.0000 + 72.7461i −1.40391 + 2.43164i
\(896\) 2.00000 1.73205i 0.0668153 0.0578638i
\(897\) 30.0000 + 31.1769i 1.00167 + 1.04097i
\(898\) −36.0000 −1.20134
\(899\) 6.00000 + 3.46410i 0.200111 + 0.115534i
\(900\) −10.5000 + 18.1865i −0.350000 + 0.606218i
\(901\) 22.5000 12.9904i 0.749584 0.432772i
\(902\) 15.5885i 0.519039i
\(903\) −12.0000 + 34.6410i −0.399335 + 1.15278i
\(904\) 12.0000 6.92820i 0.399114 0.230429i
\(905\) −6.00000 −0.199447
\(906\) −7.50000 12.9904i −0.249171 0.431577i
\(907\) 5.00000 8.66025i 0.166022 0.287559i −0.770996 0.636841i \(-0.780241\pi\)
0.937018 + 0.349281i \(0.113574\pi\)
\(908\) −9.00000 5.19615i −0.298675 0.172440i
\(909\) 0 0
\(910\) −27.0000 19.0526i −0.895041 0.631586i
\(911\) 48.4974i 1.60679i 0.595446 + 0.803396i \(0.296976\pi\)
−0.595446 + 0.803396i \(0.703024\pi\)
\(912\) 10.5000 + 6.06218i 0.347690 + 0.200739i
\(913\) −36.0000 20.7846i −1.19143 0.687870i
\(914\) −6.00000 + 3.46410i −0.198462 + 0.114582i
\(915\) 31.1769i 1.03068i
\(916\) 6.50000 + 11.2583i 0.214766 + 0.371986i
\(917\) 15.0000 + 5.19615i 0.495344 + 0.171592i
\(918\) 15.5885i 0.514496i
\(919\) −14.5000 25.1147i −0.478311 0.828459i 0.521380 0.853325i \(-0.325417\pi\)
−0.999691 + 0.0248659i \(0.992084\pi\)
\(920\) −12.0000 + 20.7846i −0.395628 + 0.685248i
\(921\) −10.5000 6.06218i −0.345987 0.199756i
\(922\) 31.1769i 1.02676i
\(923\) 15.0000 + 15.5885i 0.493731 + 0.513100i
\(924\) 9.00000 + 10.3923i 0.296078 + 0.341882i
\(925\) 42.0000 + 24.2487i 1.38095 + 0.797293i
\(926\) −31.5000 18.1865i −1.03515 0.597647i
\(927\) −9.00000 + 5.19615i −0.295599 + 0.170664i
\(928\) 1.73205i 0.0568574i
\(929\) −25.5000 + 14.7224i −0.836628 + 0.483027i −0.856117 0.516783i \(-0.827129\pi\)
0.0194887 + 0.999810i \(0.493796\pi\)
\(930\) 12.0000 + 20.7846i 0.393496 + 0.681554i
\(931\) 7.00000 48.4974i 0.229416 1.58944i
\(932\) 6.00000 3.46410i 0.196537 0.113470i
\(933\) −4.50000 2.59808i −0.147323 0.0850572i
\(934\) 3.00000 5.19615i 0.0981630 0.170023i
\(935\) 31.1769i 1.01959i
\(936\) −7.50000 7.79423i −0.245145 0.254762i
\(937\) 38.1051i 1.24484i −0.782683 0.622420i \(-0.786150\pi\)
0.782683 0.622420i \(-0.213850\pi\)
\(938\) 0 0
\(939\) 18.0000 31.1769i 0.587408 1.01742i
\(940\) −15.0000 25.9808i −0.489246 0.847399i
\(941\) 38.1051i 1.24219i −0.783735 0.621096i \(-0.786688\pi\)
0.783735 0.621096i \(-0.213312\pi\)
\(942\) 12.0000 + 20.7846i 0.390981 + 0.677199i
\(943\) −18.0000 31.1769i −0.586161 1.01526i
\(944\) 10.3923i 0.338241i
\(945\) 45.0000 + 15.5885i 1.46385 + 0.507093i
\(946\) −12.0000 + 20.7846i −0.390154 + 0.675766i
\(947\) 1.50000 2.59808i 0.0487435 0.0844261i −0.840624 0.541619i \(-0.817812\pi\)
0.889368 + 0.457193i \(0.151145\pi\)
\(948\) 19.0526i 0.618798i
\(949\) −14.0000 + 3.46410i −0.454459 + 0.112449i
\(950\) 49.0000 1.58977
\(951\) 27.0000 + 15.5885i 0.875535 + 0.505490i
\(952\) 1.50000 + 7.79423i 0.0486153 + 0.252612i
\(953\) −33.0000 + 19.0526i −1.06897 + 0.617173i −0.927901 0.372826i \(-0.878389\pi\)
−0.141074 + 0.989999i \(0.545055\pi\)
\(954\) 25.9808i 0.841158i
\(955\) 0 0
\(956\) −6.00000 10.3923i −0.194054 0.336111i
\(957\) 9.00000 0.290929
\(958\) 28.5000 16.4545i 0.920793 0.531620i
\(959\) 6.00000 + 31.1769i 0.193750 + 1.00676i
\(960\) 3.00000 5.19615i 0.0968246 0.167705i
\(961\) −15.0000 −0.483871
\(962\) −18.0000 + 17.3205i −0.580343 + 0.558436i
\(963\) 15.5885i 0.502331i
\(964\) 5.00000 8.66025i 0.161039 0.278928i
\(965\) −21.0000 + 36.3731i −0.676014 + 1.17089i
\(966\) 30.0000 + 10.3923i 0.965234 + 0.334367i
\(967\) 24.2487i 0.779786i 0.920860 + 0.389893i \(0.127488\pi\)
−0.920860 + 0.389893i \(0.872512\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) −31.5000 + 18.1865i −1.01193 + 0.584236i
\(970\) 6.92820i 0.222451i
\(971\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(972\) 13.5000 + 7.79423i 0.433013 + 0.250000i
\(973\) −13.5000 + 2.59808i −0.432790 + 0.0832905i
\(974\) 8.66025i 0.277492i
\(975\) −42.0000 12.1244i −1.34508 0.388290i
\(976\) 5.19615i 0.166325i
\(977\) 9.00000 15.5885i 0.287936 0.498719i −0.685381 0.728184i \(-0.740364\pi\)
0.973317 + 0.229465i \(0.0736978\pi\)
\(978\) 21.0000 36.3731i 0.671506 1.16308i
\(979\) 22.5000 12.9904i 0.719103 0.415174i
\(980\) −24.0000 3.46410i −0.766652 0.110657i
\(981\) −9.00000 + 5.19615i −0.287348 + 0.165900i
\(982\) 9.00000 5.19615i 0.287202 0.165816i
\(983\) 58.8897i 1.87829i 0.343520 + 0.939145i \(0.388381\pi\)
−0.343520 + 0.939145i \(0.611619\pi\)
\(984\) 4.50000 + 7.79423i 0.143455 + 0.248471i
\(985\) −81.0000 46.7654i −2.58087 1.49007i
\(986\) 4.50000 + 2.59808i 0.143309 + 0.0827396i
\(987\) −30.0000 + 25.9808i −0.954911 + 0.826977i
\(988\) −7.00000 + 24.2487i −0.222700 + 0.771454i
\(989\) 55.4256i 1.76243i
\(990\) 27.0000 + 15.5885i 0.858116 + 0.495434i
\(991\) 8.50000 14.7224i 0.270011 0.467673i −0.698853 0.715265i \(-0.746306\pi\)
0.968864 + 0.247592i \(0.0796392\pi\)
\(992\) −2.00000 3.46410i −0.0635001 0.109985i
\(993\) 0 0
\(994\) 15.0000 + 5.19615i 0.475771 + 0.164812i
\(995\) 18.0000 + 31.1769i 0.570638 + 0.988375i
\(996\) 24.0000 0.760469
\(997\) −19.5000 + 11.2583i −0.617571 + 0.356555i −0.775923 0.630828i \(-0.782715\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) 36.0000 + 20.7846i 1.13956 + 0.657925i
\(999\) 18.0000 31.1769i 0.569495 0.986394i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 546.2.q.d.251.1 yes 2
3.2 odd 2 546.2.q.b.251.1 yes 2
7.6 odd 2 546.2.q.c.251.1 yes 2
13.10 even 6 546.2.q.a.335.1 yes 2
21.20 even 2 546.2.q.a.251.1 2
39.23 odd 6 546.2.q.c.335.1 yes 2
91.62 odd 6 546.2.q.b.335.1 yes 2
273.62 even 6 inner 546.2.q.d.335.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.q.a.251.1 2 21.20 even 2
546.2.q.a.335.1 yes 2 13.10 even 6
546.2.q.b.251.1 yes 2 3.2 odd 2
546.2.q.b.335.1 yes 2 91.62 odd 6
546.2.q.c.251.1 yes 2 7.6 odd 2
546.2.q.c.335.1 yes 2 39.23 odd 6
546.2.q.d.251.1 yes 2 1.1 even 1 trivial
546.2.q.d.335.1 yes 2 273.62 even 6 inner