Properties

Label 882.2.h.p.79.2
Level $882$
Weight $2$
Character 882.79
Analytic conductor $7.043$
Analytic rank $0$
Dimension $6$
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] = [882,2,Mod(67,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.h (of order \(3\), degree \(2\), not 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 882.79
Dual form 882.2.h.p.67.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.796790 - 1.53790i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.593579 q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(-1.73025 + 2.45076i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.796790 - 1.53790i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.593579 q^{5} +(0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(-1.73025 + 2.45076i) q^{9} +(-0.296790 - 0.514055i) q^{10} -0.593579 q^{11} +(1.73025 + 0.0789082i) q^{12} +(1.25729 + 2.17770i) q^{13} +(0.472958 + 0.912864i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.46050 - 2.52967i) q^{17} +(-2.98755 - 0.273062i) q^{18} +(-2.69076 + 4.66053i) q^{19} +(0.296790 - 0.514055i) q^{20} +(-0.296790 - 0.514055i) q^{22} +4.46050 q^{23} +(0.796790 + 1.53790i) q^{24} -4.64766 q^{25} +(-1.25729 + 2.17770i) q^{26} +(5.14766 + 0.708209i) q^{27} +(-3.09718 + 5.36447i) q^{29} +(-0.554084 + 0.866025i) q^{30} +(-3.93346 + 6.81296i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.472958 + 0.912864i) q^{33} +(1.46050 - 2.52967i) q^{34} +(-1.25729 - 2.72382i) q^{36} +(0.500000 - 0.866025i) q^{37} -5.38151 q^{38} +(2.34728 - 3.66876i) q^{39} +0.593579 q^{40} +(0.136673 + 0.236725i) q^{41} +(-5.58113 + 9.66679i) q^{43} +(0.296790 - 0.514055i) q^{44} +(1.02704 - 1.45472i) q^{45} +(2.23025 + 3.86291i) q^{46} +(6.08113 + 10.5328i) q^{47} +(-0.933463 + 1.45899i) q^{48} +(-2.32383 - 4.02499i) q^{50} +(-2.72665 + 4.26172i) q^{51} -2.51459 q^{52} +(4.02704 + 6.97504i) q^{53} +(1.96050 + 4.81211i) q^{54} +0.352336 q^{55} +(9.31138 + 0.424646i) q^{57} -6.19436 q^{58} +(4.32383 - 7.48910i) q^{59} +(-1.02704 - 0.0468383i) q^{60} +(-3.32383 - 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(-0.746304 - 1.29264i) q^{65} +(-0.554084 + 0.866025i) q^{66} +(0.956906 - 1.65741i) q^{67} +2.92101 q^{68} +(-3.55408 - 6.85980i) q^{69} -14.4107 q^{71} +(1.73025 - 2.45076i) q^{72} +(-3.95691 - 6.85356i) q^{73} +1.00000 q^{74} +(3.70321 + 7.14763i) q^{75} +(-2.69076 - 4.66053i) q^{76} +(4.35087 + 0.198422i) q^{78} +(4.62422 + 8.00938i) q^{79} +(0.296790 + 0.514055i) q^{80} +(-3.01245 - 8.48087i) q^{81} +(-0.136673 + 0.236725i) q^{82} +(-3.85087 + 6.66991i) q^{83} +(0.866926 + 1.50156i) q^{85} -11.1623 q^{86} +(10.7178 + 0.488786i) q^{87} +0.593579 q^{88} +(6.21780 - 10.7695i) q^{89} +(1.77335 + 0.162084i) q^{90} +(-2.23025 + 3.86291i) q^{92} +(13.6118 + 0.620765i) q^{93} +(-6.08113 + 10.5328i) q^{94} +(1.59718 - 2.76639i) q^{95} +(-1.73025 - 0.0789082i) q^{96} +(-5.86693 + 10.1618i) q^{97} +(1.02704 - 1.45472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23} + 2 q^{24} - 4 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} + 15 q^{30} - 20 q^{31} + 3 q^{32} + 12 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} + 6 q^{38} + q^{39} - 2 q^{40} - 6 q^{43} - q^{44} - 3 q^{45} + 7 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} - 18 q^{51} + 16 q^{52} + 15 q^{53} - q^{54} + 26 q^{55} + 22 q^{57} - 10 q^{58} + 14 q^{59} + 3 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} + 15 q^{66} + q^{67} - 8 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} - 19 q^{73} + 6 q^{74} + 25 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} - q^{80} - 40 q^{81} - 2 q^{83} - 2 q^{85} - 12 q^{86} + 36 q^{87} - 2 q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} + 37 q^{93} - 9 q^{94} - 4 q^{95} - 4 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.796790 1.53790i −0.460027 0.887905i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.593579 −0.265457 −0.132728 0.991152i \(-0.542374\pi\)
−0.132728 + 0.991152i \(0.542374\pi\)
\(6\) 0.933463 1.45899i 0.381085 0.595630i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −1.73025 + 2.45076i −0.576751 + 0.816920i
\(10\) −0.296790 0.514055i −0.0938531 0.162558i
\(11\) −0.593579 −0.178971 −0.0894855 0.995988i \(-0.528522\pi\)
−0.0894855 + 0.995988i \(0.528522\pi\)
\(12\) 1.73025 + 0.0789082i 0.499481 + 0.0227788i
\(13\) 1.25729 + 2.17770i 0.348711 + 0.603985i 0.986021 0.166623i \(-0.0532862\pi\)
−0.637310 + 0.770608i \(0.719953\pi\)
\(14\) 0 0
\(15\) 0.472958 + 0.912864i 0.122117 + 0.235700i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.46050 2.52967i −0.354224 0.613535i 0.632760 0.774348i \(-0.281922\pi\)
−0.986985 + 0.160813i \(0.948588\pi\)
\(18\) −2.98755 0.273062i −0.704172 0.0643614i
\(19\) −2.69076 + 4.66053i −0.617302 + 1.06920i 0.372674 + 0.927962i \(0.378441\pi\)
−0.989976 + 0.141236i \(0.954892\pi\)
\(20\) 0.296790 0.514055i 0.0663642 0.114946i
\(21\) 0 0
\(22\) −0.296790 0.514055i −0.0632758 0.109597i
\(23\) 4.46050 0.930080 0.465040 0.885290i \(-0.346040\pi\)
0.465040 + 0.885290i \(0.346040\pi\)
\(24\) 0.796790 + 1.53790i 0.162644 + 0.313922i
\(25\) −4.64766 −0.929533
\(26\) −1.25729 + 2.17770i −0.246576 + 0.427082i
\(27\) 5.14766 + 0.708209i 0.990668 + 0.136295i
\(28\) 0 0
\(29\) −3.09718 + 5.36447i −0.575132 + 0.996157i 0.420896 + 0.907109i \(0.361716\pi\)
−0.996027 + 0.0890480i \(0.971618\pi\)
\(30\) −0.554084 + 0.866025i −0.101161 + 0.158114i
\(31\) −3.93346 + 6.81296i −0.706471 + 1.22364i 0.259687 + 0.965693i \(0.416380\pi\)
−0.966158 + 0.257951i \(0.916953\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0.472958 + 0.912864i 0.0823314 + 0.158909i
\(34\) 1.46050 2.52967i 0.250475 0.433835i
\(35\) 0 0
\(36\) −1.25729 2.72382i −0.209549 0.453970i
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −5.38151 −0.872997
\(39\) 2.34728 3.66876i 0.375865 0.587471i
\(40\) 0.593579 0.0938531
\(41\) 0.136673 + 0.236725i 0.0213448 + 0.0369702i 0.876500 0.481401i \(-0.159872\pi\)
−0.855156 + 0.518371i \(0.826539\pi\)
\(42\) 0 0
\(43\) −5.58113 + 9.66679i −0.851114 + 1.47417i 0.0290902 + 0.999577i \(0.490739\pi\)
−0.880204 + 0.474596i \(0.842594\pi\)
\(44\) 0.296790 0.514055i 0.0447427 0.0774967i
\(45\) 1.02704 1.45472i 0.153102 0.216857i
\(46\) 2.23025 + 3.86291i 0.328833 + 0.569555i
\(47\) 6.08113 + 10.5328i 0.887023 + 1.53637i 0.843377 + 0.537323i \(0.180564\pi\)
0.0436467 + 0.999047i \(0.486102\pi\)
\(48\) −0.933463 + 1.45899i −0.134734 + 0.210587i
\(49\) 0 0
\(50\) −2.32383 4.02499i −0.328639 0.569220i
\(51\) −2.72665 + 4.26172i −0.381808 + 0.596760i
\(52\) −2.51459 −0.348711
\(53\) 4.02704 + 6.97504i 0.553157 + 0.958096i 0.998044 + 0.0625092i \(0.0199103\pi\)
−0.444888 + 0.895586i \(0.646756\pi\)
\(54\) 1.96050 + 4.81211i 0.266791 + 0.654845i
\(55\) 0.352336 0.0475090
\(56\) 0 0
\(57\) 9.31138 + 0.424646i 1.23332 + 0.0562457i
\(58\) −6.19436 −0.813359
\(59\) 4.32383 7.48910i 0.562915 0.974997i −0.434325 0.900756i \(-0.643013\pi\)
0.997240 0.0742412i \(-0.0236535\pi\)
\(60\) −1.02704 0.0468383i −0.132591 0.00604680i
\(61\) −3.32383 5.75705i −0.425573 0.737114i 0.570901 0.821019i \(-0.306594\pi\)
−0.996474 + 0.0839050i \(0.973261\pi\)
\(62\) −7.86693 −0.999101
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.746304 1.29264i −0.0925676 0.160332i
\(66\) −0.554084 + 0.866025i −0.0682031 + 0.106600i
\(67\) 0.956906 1.65741i 0.116905 0.202485i −0.801635 0.597814i \(-0.796036\pi\)
0.918540 + 0.395329i \(0.129369\pi\)
\(68\) 2.92101 0.354224
\(69\) −3.55408 6.85980i −0.427861 0.825822i
\(70\) 0 0
\(71\) −14.4107 −1.71023 −0.855117 0.518435i \(-0.826515\pi\)
−0.855117 + 0.518435i \(0.826515\pi\)
\(72\) 1.73025 2.45076i 0.203912 0.288825i
\(73\) −3.95691 6.85356i −0.463121 0.802149i 0.535994 0.844222i \(-0.319937\pi\)
−0.999115 + 0.0420732i \(0.986604\pi\)
\(74\) 1.00000 0.116248
\(75\) 3.70321 + 7.14763i 0.427610 + 0.825337i
\(76\) −2.69076 4.66053i −0.308651 0.534599i
\(77\) 0 0
\(78\) 4.35087 + 0.198422i 0.492639 + 0.0224668i
\(79\) 4.62422 + 8.00938i 0.520265 + 0.901126i 0.999722 + 0.0235607i \(0.00750031\pi\)
−0.479457 + 0.877565i \(0.659166\pi\)
\(80\) 0.296790 + 0.514055i 0.0331821 + 0.0574731i
\(81\) −3.01245 8.48087i −0.334717 0.942319i
\(82\) −0.136673 + 0.236725i −0.0150930 + 0.0261419i
\(83\) −3.85087 + 6.66991i −0.422688 + 0.732118i −0.996201 0.0870787i \(-0.972247\pi\)
0.573513 + 0.819196i \(0.305580\pi\)
\(84\) 0 0
\(85\) 0.866926 + 1.50156i 0.0940313 + 0.162867i
\(86\) −11.1623 −1.20366
\(87\) 10.7178 + 0.488786i 1.14907 + 0.0524033i
\(88\) 0.593579 0.0632758
\(89\) 6.21780 10.7695i 0.659085 1.14157i −0.321767 0.946819i \(-0.604277\pi\)
0.980853 0.194751i \(-0.0623898\pi\)
\(90\) 1.77335 + 0.162084i 0.186927 + 0.0170852i
\(91\) 0 0
\(92\) −2.23025 + 3.86291i −0.232520 + 0.402736i
\(93\) 13.6118 + 0.620765i 1.41147 + 0.0643704i
\(94\) −6.08113 + 10.5328i −0.627220 + 1.08638i
\(95\) 1.59718 2.76639i 0.163867 0.283826i
\(96\) −1.73025 0.0789082i −0.176593 0.00805354i
\(97\) −5.86693 + 10.1618i −0.595696 + 1.03178i 0.397752 + 0.917493i \(0.369790\pi\)
−0.993448 + 0.114283i \(0.963543\pi\)
\(98\) 0 0
\(99\) 1.02704 1.45472i 0.103222 0.146205i
\(100\) 2.32383 4.02499i 0.232383 0.402499i
\(101\) 1.62276 0.161470 0.0807352 0.996736i \(-0.474273\pi\)
0.0807352 + 0.996736i \(0.474273\pi\)
\(102\) −5.05408 0.230492i −0.500429 0.0228221i
\(103\) −6.38151 −0.628789 −0.314395 0.949292i \(-0.601802\pi\)
−0.314395 + 0.949292i \(0.601802\pi\)
\(104\) −1.25729 2.17770i −0.123288 0.213541i
\(105\) 0 0
\(106\) −4.02704 + 6.97504i −0.391141 + 0.677476i
\(107\) 9.35447 16.2024i 0.904331 1.56635i 0.0825182 0.996590i \(-0.473704\pi\)
0.821813 0.569758i \(-0.192963\pi\)
\(108\) −3.18716 + 4.10390i −0.306684 + 0.394898i
\(109\) −1.43346 2.48283i −0.137301 0.237812i 0.789173 0.614171i \(-0.210509\pi\)
−0.926474 + 0.376359i \(0.877176\pi\)
\(110\) 0.176168 + 0.305132i 0.0167970 + 0.0290932i
\(111\) −1.73025 0.0789082i −0.164228 0.00748964i
\(112\) 0 0
\(113\) −6.16012 10.6696i −0.579495 1.00371i −0.995537 0.0943695i \(-0.969916\pi\)
0.416042 0.909345i \(-0.363417\pi\)
\(114\) 4.28794 + 8.27621i 0.401602 + 0.775138i
\(115\) −2.64766 −0.246896
\(116\) −3.09718 5.36447i −0.287566 0.498078i
\(117\) −7.51245 0.686640i −0.694527 0.0634799i
\(118\) 8.64766 0.796082
\(119\) 0 0
\(120\) −0.472958 0.912864i −0.0431750 0.0833327i
\(121\) −10.6477 −0.967969
\(122\) 3.32383 5.75705i 0.300926 0.521218i
\(123\) 0.255158 0.398809i 0.0230069 0.0359594i
\(124\) −3.93346 6.81296i −0.353235 0.611822i
\(125\) 5.72665 0.512207
\(126\) 0 0
\(127\) 12.3346 1.09452 0.547261 0.836962i \(-0.315671\pi\)
0.547261 + 0.836962i \(0.315671\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 19.3135 + 0.880794i 1.70046 + 0.0775496i
\(130\) 0.746304 1.29264i 0.0654552 0.113372i
\(131\) 1.18716 0.103723 0.0518613 0.998654i \(-0.483485\pi\)
0.0518613 + 0.998654i \(0.483485\pi\)
\(132\) −1.02704 0.0468383i −0.0893925 0.00407675i
\(133\) 0 0
\(134\) 1.91381 0.165328
\(135\) −3.05555 0.420378i −0.262980 0.0361804i
\(136\) 1.46050 + 2.52967i 0.125237 + 0.216917i
\(137\) 2.52179 0.215451 0.107725 0.994181i \(-0.465643\pi\)
0.107725 + 0.994181i \(0.465643\pi\)
\(138\) 4.16372 6.50783i 0.354439 0.553983i
\(139\) −2.45691 4.25549i −0.208392 0.360946i 0.742816 0.669496i \(-0.233490\pi\)
−0.951208 + 0.308550i \(0.900156\pi\)
\(140\) 0 0
\(141\) 11.3530 17.7446i 0.956096 1.49436i
\(142\) −7.20535 12.4800i −0.604659 1.04730i
\(143\) −0.746304 1.29264i −0.0624091 0.108096i
\(144\) 2.98755 + 0.273062i 0.248962 + 0.0227552i
\(145\) 1.83842 3.18424i 0.152673 0.264437i
\(146\) 3.95691 6.85356i 0.327476 0.567205i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 18.0512 1.47881 0.739404 0.673262i \(-0.235107\pi\)
0.739404 + 0.673262i \(0.235107\pi\)
\(150\) −4.33842 + 6.78089i −0.354231 + 0.553657i
\(151\) 1.64766 0.134085 0.0670425 0.997750i \(-0.478644\pi\)
0.0670425 + 0.997750i \(0.478644\pi\)
\(152\) 2.69076 4.66053i 0.218249 0.378019i
\(153\) 8.72665 + 0.797618i 0.705508 + 0.0644836i
\(154\) 0 0
\(155\) 2.33482 4.04403i 0.187537 0.324824i
\(156\) 2.00360 + 3.86718i 0.160416 + 0.309622i
\(157\) −3.30039 + 5.71644i −0.263400 + 0.456222i −0.967143 0.254233i \(-0.918177\pi\)
0.703743 + 0.710454i \(0.251510\pi\)
\(158\) −4.62422 + 8.00938i −0.367883 + 0.637192i
\(159\) 7.51819 11.7508i 0.596231 0.931900i
\(160\) −0.296790 + 0.514055i −0.0234633 + 0.0406396i
\(161\) 0 0
\(162\) 5.83842 6.84929i 0.458710 0.538131i
\(163\) −2.99115 + 5.18082i −0.234285 + 0.405793i −0.959065 0.283188i \(-0.908608\pi\)
0.724780 + 0.688980i \(0.241941\pi\)
\(164\) −0.273346 −0.0213448
\(165\) −0.280738 0.541857i −0.0218554 0.0421835i
\(166\) −7.70175 −0.597772
\(167\) −3.73025 6.46099i −0.288656 0.499966i 0.684833 0.728700i \(-0.259875\pi\)
−0.973489 + 0.228733i \(0.926542\pi\)
\(168\) 0 0
\(169\) 3.33842 5.78231i 0.256802 0.444793i
\(170\) −0.866926 + 1.50156i −0.0664902 + 0.115164i
\(171\) −6.76615 14.6583i −0.517420 1.12095i
\(172\) −5.58113 9.66679i −0.425557 0.737086i
\(173\) −12.8296 22.2215i −0.975414 1.68947i −0.678562 0.734543i \(-0.737397\pi\)
−0.296851 0.954924i \(-0.595937\pi\)
\(174\) 4.93560 + 9.52628i 0.374167 + 0.722185i
\(175\) 0 0
\(176\) 0.296790 + 0.514055i 0.0223714 + 0.0387483i
\(177\) −14.9626 0.682372i −1.12466 0.0512902i
\(178\) 12.4356 0.932088
\(179\) 7.51819 + 13.0219i 0.561936 + 0.973301i 0.997328 + 0.0730602i \(0.0232765\pi\)
−0.435392 + 0.900241i \(0.643390\pi\)
\(180\) 0.746304 + 1.61680i 0.0556262 + 0.120510i
\(181\) 0.0861875 0.00640627 0.00320313 0.999995i \(-0.498980\pi\)
0.00320313 + 0.999995i \(0.498980\pi\)
\(182\) 0 0
\(183\) −6.20535 + 9.69886i −0.458712 + 0.716961i
\(184\) −4.46050 −0.328833
\(185\) −0.296790 + 0.514055i −0.0218204 + 0.0377941i
\(186\) 6.26829 + 12.0985i 0.459613 + 0.887106i
\(187\) 0.866926 + 1.50156i 0.0633959 + 0.109805i
\(188\) −12.1623 −0.887023
\(189\) 0 0
\(190\) 3.19436 0.231743
\(191\) −1.99115 3.44877i −0.144074 0.249544i 0.784953 0.619555i \(-0.212687\pi\)
−0.929027 + 0.370011i \(0.879354\pi\)
\(192\) −0.796790 1.53790i −0.0575033 0.110988i
\(193\) −3.39037 + 5.87229i −0.244044 + 0.422697i −0.961862 0.273534i \(-0.911808\pi\)
0.717818 + 0.696230i \(0.245141\pi\)
\(194\) −11.7339 −0.842441
\(195\) −1.39329 + 2.17770i −0.0997759 + 0.155948i
\(196\) 0 0
\(197\) 11.0584 0.787875 0.393938 0.919137i \(-0.371113\pi\)
0.393938 + 0.919137i \(0.371113\pi\)
\(198\) 1.77335 + 0.162084i 0.126026 + 0.0115188i
\(199\) −2.80924 4.86575i −0.199142 0.344924i 0.749109 0.662447i \(-0.230482\pi\)
−0.948250 + 0.317523i \(0.897149\pi\)
\(200\) 4.64766 0.328639
\(201\) −3.31138 0.151016i −0.233567 0.0106518i
\(202\) 0.811379 + 1.40535i 0.0570884 + 0.0988800i
\(203\) 0 0
\(204\) −2.32743 4.49221i −0.162953 0.314518i
\(205\) −0.0811263 0.140515i −0.00566611 0.00981399i
\(206\) −3.19076 5.52655i −0.222311 0.385053i
\(207\) −7.71780 + 10.9316i −0.536424 + 0.759801i
\(208\) 1.25729 2.17770i 0.0871777 0.150996i
\(209\) 1.59718 2.76639i 0.110479 0.191355i
\(210\) 0 0
\(211\) 9.66225 + 16.7355i 0.665177 + 1.15212i 0.979237 + 0.202717i \(0.0649772\pi\)
−0.314060 + 0.949403i \(0.601689\pi\)
\(212\) −8.05408 −0.553157
\(213\) 11.4823 + 22.1622i 0.786754 + 1.51853i
\(214\) 18.7089 1.27892
\(215\) 3.31284 5.73801i 0.225934 0.391329i
\(216\) −5.14766 0.708209i −0.350254 0.0481875i
\(217\) 0 0
\(218\) 1.43346 2.48283i 0.0970863 0.168158i
\(219\) −7.38725 + 11.5462i −0.499184 + 0.780217i
\(220\) −0.176168 + 0.305132i −0.0118773 + 0.0205720i
\(221\) 3.67257 6.36108i 0.247044 0.427892i
\(222\) −0.796790 1.53790i −0.0534770 0.103217i
\(223\) −12.6623 + 21.9317i −0.847927 + 1.46865i 0.0351275 + 0.999383i \(0.488816\pi\)
−0.883055 + 0.469270i \(0.844517\pi\)
\(224\) 0 0
\(225\) 8.04163 11.3903i 0.536109 0.759354i
\(226\) 6.16012 10.6696i 0.409765 0.709734i
\(227\) −4.81711 −0.319723 −0.159862 0.987139i \(-0.551105\pi\)
−0.159862 + 0.987139i \(0.551105\pi\)
\(228\) −5.02344 + 7.85157i −0.332686 + 0.519983i
\(229\) 9.29533 0.614253 0.307126 0.951669i \(-0.400633\pi\)
0.307126 + 0.951669i \(0.400633\pi\)
\(230\) −1.32383 2.29294i −0.0872909 0.151192i
\(231\) 0 0
\(232\) 3.09718 5.36447i 0.203340 0.352195i
\(233\) 0.0971780 0.168317i 0.00636634 0.0110268i −0.862825 0.505503i \(-0.831307\pi\)
0.869191 + 0.494476i \(0.164640\pi\)
\(234\) −3.16158 6.84929i −0.206679 0.447752i
\(235\) −3.60963 6.25206i −0.235466 0.407840i
\(236\) 4.32383 + 7.48910i 0.281457 + 0.487499i
\(237\) 8.63307 13.4934i 0.560778 0.876488i
\(238\) 0 0
\(239\) −6.82743 11.8255i −0.441630 0.764925i 0.556181 0.831061i \(-0.312266\pi\)
−0.997811 + 0.0661361i \(0.978933\pi\)
\(240\) 0.554084 0.866025i 0.0357660 0.0559017i
\(241\) 13.0000 0.837404 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(242\) −5.32383 9.22115i −0.342229 0.592758i
\(243\) −10.6424 + 11.3903i −0.682711 + 0.730689i
\(244\) 6.64766 0.425573
\(245\) 0 0
\(246\) 0.472958 + 0.0215693i 0.0301547 + 0.00137521i
\(247\) −13.5323 −0.861039
\(248\) 3.93346 6.81296i 0.249775 0.432623i
\(249\) 13.3260 + 0.607731i 0.844499 + 0.0385134i
\(250\) 2.86333 + 4.95943i 0.181093 + 0.313662i
\(251\) 19.5438 1.23359 0.616796 0.787123i \(-0.288430\pi\)
0.616796 + 0.787123i \(0.288430\pi\)
\(252\) 0 0
\(253\) −2.64766 −0.166457
\(254\) 6.16731 + 10.6821i 0.386972 + 0.670255i
\(255\) 1.61849 2.52967i 0.101353 0.158414i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.32743 −0.519451 −0.259725 0.965683i \(-0.583632\pi\)
−0.259725 + 0.965683i \(0.583632\pi\)
\(258\) 8.89397 + 17.1664i 0.553714 + 1.06873i
\(259\) 0 0
\(260\) 1.49261 0.0925676
\(261\) −7.78813 16.8723i −0.482073 1.04437i
\(262\) 0.593579 + 1.02811i 0.0366715 + 0.0635168i
\(263\) −17.0905 −1.05384 −0.526921 0.849914i \(-0.676654\pi\)
−0.526921 + 0.849914i \(0.676654\pi\)
\(264\) −0.472958 0.912864i −0.0291085 0.0561829i
\(265\) −2.39037 4.14024i −0.146839 0.254333i
\(266\) 0 0
\(267\) −21.5167 0.981271i −1.31680 0.0600528i
\(268\) 0.956906 + 1.65741i 0.0584524 + 0.101242i
\(269\) 5.00720 + 8.67272i 0.305294 + 0.528785i 0.977327 0.211737i \(-0.0679119\pi\)
−0.672033 + 0.740522i \(0.734579\pi\)
\(270\) −1.16372 2.85637i −0.0708215 0.173833i
\(271\) −5.10457 + 8.84137i −0.310081 + 0.537075i −0.978380 0.206818i \(-0.933689\pi\)
0.668299 + 0.743893i \(0.267023\pi\)
\(272\) −1.46050 + 2.52967i −0.0885561 + 0.153384i
\(273\) 0 0
\(274\) 1.26089 + 2.18393i 0.0761733 + 0.131936i
\(275\) 2.75876 0.166359
\(276\) 7.71780 + 0.351971i 0.464557 + 0.0211861i
\(277\) 19.3422 1.16216 0.581081 0.813846i \(-0.302630\pi\)
0.581081 + 0.813846i \(0.302630\pi\)
\(278\) 2.45691 4.25549i 0.147355 0.255227i
\(279\) −9.89104 21.4281i −0.592161 1.28287i
\(280\) 0 0
\(281\) −6.40136 + 11.0875i −0.381873 + 0.661424i −0.991330 0.131396i \(-0.958054\pi\)
0.609457 + 0.792819i \(0.291388\pi\)
\(282\) 21.0438 + 0.959702i 1.25314 + 0.0571494i
\(283\) −8.17617 + 14.1615i −0.486023 + 0.841816i −0.999871 0.0160650i \(-0.994886\pi\)
0.513848 + 0.857881i \(0.328219\pi\)
\(284\) 7.20535 12.4800i 0.427559 0.740553i
\(285\) −5.52704 0.252061i −0.327394 0.0149308i
\(286\) 0.746304 1.29264i 0.0441299 0.0764352i
\(287\) 0 0
\(288\) 1.25729 + 2.72382i 0.0740868 + 0.160503i
\(289\) 4.23385 7.33325i 0.249050 0.431367i
\(290\) 3.67684 0.215912
\(291\) 20.3025 + 0.925898i 1.19016 + 0.0542771i
\(292\) 7.91381 0.463121
\(293\) 10.3889 + 17.9941i 0.606926 + 1.05123i 0.991744 + 0.128235i \(0.0409311\pi\)
−0.384817 + 0.922993i \(0.625736\pi\)
\(294\) 0 0
\(295\) −2.56654 + 4.44537i −0.149430 + 0.258820i
\(296\) −0.500000 + 0.866025i −0.0290619 + 0.0503367i
\(297\) −3.05555 0.420378i −0.177301 0.0243928i
\(298\) 9.02558 + 15.6328i 0.522838 + 0.905582i
\(299\) 5.60817 + 9.71363i 0.324329 + 0.561754i
\(300\) −8.04163 0.366739i −0.464284 0.0211737i
\(301\) 0 0
\(302\) 0.823832 + 1.42692i 0.0474062 + 0.0821099i
\(303\) −1.29300 2.49563i −0.0742807 0.143370i
\(304\) 5.38151 0.308651
\(305\) 1.97296 + 3.41726i 0.112971 + 0.195672i
\(306\) 3.67257 + 7.95631i 0.209947 + 0.454832i
\(307\) 22.6768 1.29424 0.647118 0.762390i \(-0.275974\pi\)
0.647118 + 0.762390i \(0.275974\pi\)
\(308\) 0 0
\(309\) 5.08472 + 9.81411i 0.289260 + 0.558305i
\(310\) 4.66964 0.265218
\(311\) −3.25729 + 5.64180i −0.184704 + 0.319917i −0.943477 0.331439i \(-0.892466\pi\)
0.758773 + 0.651356i \(0.225799\pi\)
\(312\) −2.34728 + 3.66876i −0.132888 + 0.207702i
\(313\) 0.133074 + 0.230492i 0.00752181 + 0.0130282i 0.869762 0.493472i \(-0.164272\pi\)
−0.862240 + 0.506500i \(0.830939\pi\)
\(314\) −6.60078 −0.372503
\(315\) 0 0
\(316\) −9.24844 −0.520265
\(317\) −7.86186 13.6171i −0.441566 0.764815i 0.556240 0.831022i \(-0.312244\pi\)
−0.997806 + 0.0662067i \(0.978910\pi\)
\(318\) 13.9356 + 0.635534i 0.781470 + 0.0356390i
\(319\) 1.83842 3.18424i 0.102932 0.178283i
\(320\) −0.593579 −0.0331821
\(321\) −32.3712 1.47629i −1.80678 0.0823985i
\(322\) 0 0
\(323\) 15.7195 0.874654
\(324\) 8.85087 + 1.63157i 0.491715 + 0.0906430i
\(325\) −5.84348 10.1212i −0.324138 0.561424i
\(326\) −5.98229 −0.331328
\(327\) −2.67617 + 4.18281i −0.147992 + 0.231310i
\(328\) −0.136673 0.236725i −0.00754651 0.0130709i
\(329\) 0 0
\(330\) 0.328893 0.514055i 0.0181050 0.0282978i
\(331\) 12.5811 + 21.7912i 0.691521 + 1.19775i 0.971339 + 0.237697i \(0.0763925\pi\)
−0.279818 + 0.960053i \(0.590274\pi\)
\(332\) −3.85087 6.66991i −0.211344 0.366059i
\(333\) 1.25729 + 2.72382i 0.0688993 + 0.149265i
\(334\) 3.73025 6.46099i 0.204110 0.353529i
\(335\) −0.568000 + 0.983804i −0.0310331 + 0.0537510i
\(336\) 0 0
\(337\) −9.36693 16.2240i −0.510249 0.883777i −0.999929 0.0118752i \(-0.996220\pi\)
0.489681 0.871902i \(-0.337113\pi\)
\(338\) 6.67684 0.363172
\(339\) −11.5005 + 17.9751i −0.624620 + 0.976272i
\(340\) −1.73385 −0.0940313
\(341\) 2.33482 4.04403i 0.126438 0.218997i
\(342\) 9.31138 13.1888i 0.503502 0.713169i
\(343\) 0 0
\(344\) 5.58113 9.66679i 0.300914 0.521199i
\(345\) 2.10963 + 4.07183i 0.113579 + 0.219220i
\(346\) 12.8296 22.2215i 0.689722 1.19463i
\(347\) −11.2719 + 19.5235i −0.605106 + 1.04808i 0.386928 + 0.922110i \(0.373536\pi\)
−0.992035 + 0.125965i \(0.959797\pi\)
\(348\) −5.78220 + 9.03749i −0.309958 + 0.484461i
\(349\) −1.89543 + 3.28298i −0.101460 + 0.175734i −0.912286 0.409553i \(-0.865685\pi\)
0.810826 + 0.585287i \(0.199018\pi\)
\(350\) 0 0
\(351\) 4.92986 + 12.1005i 0.263137 + 0.645876i
\(352\) −0.296790 + 0.514055i −0.0158189 + 0.0273992i
\(353\) −6.83482 −0.363781 −0.181890 0.983319i \(-0.558222\pi\)
−0.181890 + 0.983319i \(0.558222\pi\)
\(354\) −6.89037 13.2992i −0.366219 0.706845i
\(355\) 8.55389 0.453993
\(356\) 6.21780 + 10.7695i 0.329543 + 0.570785i
\(357\) 0 0
\(358\) −7.51819 + 13.0219i −0.397349 + 0.688228i
\(359\) −6.32237 + 10.9507i −0.333682 + 0.577954i −0.983231 0.182366i \(-0.941624\pi\)
0.649549 + 0.760320i \(0.274958\pi\)
\(360\) −1.02704 + 1.45472i −0.0541299 + 0.0766705i
\(361\) −4.98035 8.62622i −0.262124 0.454012i
\(362\) 0.0430937 + 0.0746406i 0.00226496 + 0.00392302i
\(363\) 8.48395 + 16.3750i 0.445292 + 0.859465i
\(364\) 0 0
\(365\) 2.34874 + 4.06813i 0.122939 + 0.212936i
\(366\) −11.5021 0.524555i −0.601226 0.0274190i
\(367\) −6.54377 −0.341582 −0.170791 0.985307i \(-0.554632\pi\)
−0.170791 + 0.985307i \(0.554632\pi\)
\(368\) −2.23025 3.86291i −0.116260 0.201368i
\(369\) −0.816635 0.0746406i −0.0425123 0.00388563i
\(370\) −0.593579 −0.0308587
\(371\) 0 0
\(372\) −7.34348 + 11.4778i −0.380742 + 0.595094i
\(373\) 9.42840 0.488184 0.244092 0.969752i \(-0.421510\pi\)
0.244092 + 0.969752i \(0.421510\pi\)
\(374\) −0.866926 + 1.50156i −0.0448277 + 0.0776438i
\(375\) −4.56294 8.80700i −0.235629 0.454792i
\(376\) −6.08113 10.5328i −0.313610 0.543189i
\(377\) −15.5763 −0.802218
\(378\) 0 0
\(379\) −7.27762 −0.373826 −0.186913 0.982376i \(-0.559848\pi\)
−0.186913 + 0.982376i \(0.559848\pi\)
\(380\) 1.59718 + 2.76639i 0.0819335 + 0.141913i
\(381\) −9.82810 18.9694i −0.503509 0.971831i
\(382\) 1.99115 3.44877i 0.101876 0.176454i
\(383\) 24.0833 1.23060 0.615299 0.788294i \(-0.289035\pi\)
0.615299 + 0.788294i \(0.289035\pi\)
\(384\) 0.933463 1.45899i 0.0476356 0.0744537i
\(385\) 0 0
\(386\) −6.78074 −0.345130
\(387\) −14.0342 30.4040i −0.713400 1.54552i
\(388\) −5.86693 10.1618i −0.297848 0.515888i
\(389\) −16.2983 −0.826354 −0.413177 0.910651i \(-0.635581\pi\)
−0.413177 + 0.910651i \(0.635581\pi\)
\(390\) −2.58259 0.117779i −0.130774 0.00596398i
\(391\) −6.51459 11.2836i −0.329457 0.570636i
\(392\) 0 0
\(393\) −0.945916 1.82573i −0.0477151 0.0920958i
\(394\) 5.52918 + 9.57682i 0.278556 + 0.482473i
\(395\) −2.74484 4.75420i −0.138108 0.239210i
\(396\) 0.746304 + 1.61680i 0.0375032 + 0.0812475i
\(397\) 6.08619 10.5416i 0.305457 0.529067i −0.671906 0.740636i \(-0.734524\pi\)
0.977363 + 0.211569i \(0.0678574\pi\)
\(398\) 2.80924 4.86575i 0.140815 0.243898i
\(399\) 0 0
\(400\) 2.32383 + 4.02499i 0.116192 + 0.201250i
\(401\) −33.3609 −1.66596 −0.832981 0.553301i \(-0.813368\pi\)
−0.832981 + 0.553301i \(0.813368\pi\)
\(402\) −1.52491 2.94325i −0.0760554 0.146796i
\(403\) −19.7821 −0.985416
\(404\) −0.811379 + 1.40535i −0.0403676 + 0.0699187i
\(405\) 1.78813 + 5.03407i 0.0888529 + 0.250145i
\(406\) 0 0
\(407\) −0.296790 + 0.514055i −0.0147113 + 0.0254808i
\(408\) 2.72665 4.26172i 0.134989 0.210987i
\(409\) −2.89037 + 5.00627i −0.142920 + 0.247544i −0.928595 0.371095i \(-0.878982\pi\)
0.785675 + 0.618639i \(0.212316\pi\)
\(410\) 0.0811263 0.140515i 0.00400654 0.00693954i
\(411\) −2.00933 3.87825i −0.0991131 0.191300i
\(412\) 3.19076 5.52655i 0.157197 0.272274i
\(413\) 0 0
\(414\) −13.3260 1.21800i −0.654936 0.0598612i
\(415\) 2.28580 3.95912i 0.112205 0.194346i
\(416\) 2.51459 0.123288
\(417\) −4.58686 + 7.16920i −0.224620 + 0.351077i
\(418\) 3.19436 0.156241
\(419\) −15.4356 26.7352i −0.754078 1.30610i −0.945831 0.324659i \(-0.894751\pi\)
0.191753 0.981443i \(-0.438583\pi\)
\(420\) 0 0
\(421\) −1.86693 + 3.23361i −0.0909884 + 0.157597i −0.907927 0.419128i \(-0.862336\pi\)
0.816939 + 0.576724i \(0.195669\pi\)
\(422\) −9.66225 + 16.7355i −0.470351 + 0.814672i
\(423\) −36.3353 3.32105i −1.76668 0.161475i
\(424\) −4.02704 6.97504i −0.195570 0.338738i
\(425\) 6.78794 + 11.7570i 0.329263 + 0.570301i
\(426\) −13.4518 + 21.0250i −0.651744 + 1.01867i
\(427\) 0 0
\(428\) 9.35447 + 16.2024i 0.452165 + 0.783174i
\(429\) −1.39329 + 2.17770i −0.0672689 + 0.105140i
\(430\) 6.62568 0.319519
\(431\) −14.0979 24.4182i −0.679070 1.17618i −0.975261 0.221055i \(-0.929050\pi\)
0.296192 0.955128i \(-0.404283\pi\)
\(432\) −1.96050 4.81211i −0.0943248 0.231523i
\(433\) −12.5438 −0.602815 −0.301407 0.953495i \(-0.597456\pi\)
−0.301407 + 0.953495i \(0.597456\pi\)
\(434\) 0 0
\(435\) −6.36186 0.290133i −0.305028 0.0139108i
\(436\) 2.86693 0.137301
\(437\) −12.0021 + 20.7883i −0.574140 + 0.994440i
\(438\) −13.6929 0.624465i −0.654272 0.0298381i
\(439\) 13.0203 + 22.5519i 0.621426 + 1.07634i 0.989220 + 0.146434i \(0.0467797\pi\)
−0.367794 + 0.929907i \(0.619887\pi\)
\(440\) −0.352336 −0.0167970
\(441\) 0 0
\(442\) 7.34514 0.349373
\(443\) 11.7865 + 20.4148i 0.559992 + 0.969935i 0.997496 + 0.0707186i \(0.0225292\pi\)
−0.437504 + 0.899216i \(0.644137\pi\)
\(444\) 0.933463 1.45899i 0.0443002 0.0692405i
\(445\) −3.69076 + 6.39258i −0.174959 + 0.303037i
\(446\) −25.3245 −1.19915
\(447\) −14.3830 27.7608i −0.680291 1.31304i
\(448\) 0 0
\(449\) 13.6870 0.645928 0.322964 0.946411i \(-0.395321\pi\)
0.322964 + 0.946411i \(0.395321\pi\)
\(450\) 13.8851 + 1.26910i 0.654551 + 0.0598260i
\(451\) −0.0811263 0.140515i −0.00382009 0.00661659i
\(452\) 12.3202 0.579495
\(453\) −1.31284 2.53394i −0.0616827 0.119055i
\(454\) −2.40856 4.17174i −0.113039 0.195790i
\(455\) 0 0
\(456\) −9.31138 0.424646i −0.436045 0.0198859i
\(457\) 11.1762 + 19.3577i 0.522799 + 0.905515i 0.999648 + 0.0265293i \(0.00844554\pi\)
−0.476849 + 0.878985i \(0.658221\pi\)
\(458\) 4.64766 + 8.04999i 0.217171 + 0.376151i
\(459\) −5.72665 14.0562i −0.267297 0.656088i
\(460\) 1.32383 2.29294i 0.0617240 0.106909i
\(461\) 3.98755 6.90663i 0.185719 0.321674i −0.758100 0.652138i \(-0.773872\pi\)
0.943818 + 0.330464i \(0.107205\pi\)
\(462\) 0 0
\(463\) −14.3676 24.8854i −0.667719 1.15652i −0.978540 0.206055i \(-0.933937\pi\)
0.310821 0.950468i \(-0.399396\pi\)
\(464\) 6.19436 0.287566
\(465\) −8.07966 0.368473i −0.374685 0.0170875i
\(466\) 0.194356 0.00900336
\(467\) −16.7829 + 29.0688i −0.776619 + 1.34514i 0.157261 + 0.987557i \(0.449733\pi\)
−0.933880 + 0.357586i \(0.883600\pi\)
\(468\) 4.35087 6.16266i 0.201119 0.284869i
\(469\) 0 0
\(470\) 3.60963 6.25206i 0.166500 0.288386i
\(471\) 11.4210 + 0.520856i 0.526252 + 0.0239998i
\(472\) −4.32383 + 7.48910i −0.199020 + 0.344714i
\(473\) 3.31284 5.73801i 0.152325 0.263834i
\(474\) 16.0021 + 0.729778i 0.735002 + 0.0335198i
\(475\) 12.5057 21.6606i 0.573802 0.993855i
\(476\) 0 0
\(477\) −24.0620 2.19927i −1.10172 0.100698i
\(478\) 6.82743 11.8255i 0.312279 0.540884i
\(479\) −0.367120 −0.0167741 −0.00838707 0.999965i \(-0.502670\pi\)
−0.00838707 + 0.999965i \(0.502670\pi\)
\(480\) 1.02704 + 0.0468383i 0.0468778 + 0.00213787i
\(481\) 2.51459 0.114655
\(482\) 6.50000 + 11.2583i 0.296067 + 0.512803i
\(483\) 0 0
\(484\) 5.32383 9.22115i 0.241992 0.419143i
\(485\) 3.48249 6.03184i 0.158132 0.273892i
\(486\) −15.1855 3.52144i −0.688828 0.159736i
\(487\) −14.9538 25.9007i −0.677621 1.17367i −0.975695 0.219131i \(-0.929678\pi\)
0.298075 0.954543i \(-0.403656\pi\)
\(488\) 3.32383 + 5.75705i 0.150463 + 0.260609i
\(489\) 10.3509 + 0.472052i 0.468083 + 0.0213469i
\(490\) 0 0
\(491\) −0.255158 0.441947i −0.0115151 0.0199448i 0.860210 0.509939i \(-0.170332\pi\)
−0.871726 + 0.489994i \(0.836999\pi\)
\(492\) 0.217799 + 0.420378i 0.00981916 + 0.0189521i
\(493\) 18.0938 0.814903
\(494\) −6.76615 11.7193i −0.304423 0.527277i
\(495\) −0.609631 + 0.863492i −0.0274009 + 0.0388111i
\(496\) 7.86693 0.353235
\(497\) 0 0
\(498\) 6.13667 + 11.8445i 0.274991 + 0.530764i
\(499\) −19.0191 −0.851410 −0.425705 0.904862i \(-0.639974\pi\)
−0.425705 + 0.904862i \(0.639974\pi\)
\(500\) −2.86333 + 4.95943i −0.128052 + 0.221792i
\(501\) −6.96410 + 10.8848i −0.311133 + 0.486297i
\(502\) 9.77188 + 16.9254i 0.436141 + 0.755418i
\(503\) 37.7807 1.68456 0.842280 0.539040i \(-0.181213\pi\)
0.842280 + 0.539040i \(0.181213\pi\)
\(504\) 0 0
\(505\) −0.963235 −0.0428634
\(506\) −1.32383 2.29294i −0.0588515 0.101934i
\(507\) −11.5526 0.526858i −0.513070 0.0233986i
\(508\) −6.16731 + 10.6821i −0.273630 + 0.473942i
\(509\) 11.2163 0.497155 0.248578 0.968612i \(-0.420037\pi\)
0.248578 + 0.968612i \(0.420037\pi\)
\(510\) 3.00000 + 0.136815i 0.132842 + 0.00605828i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −17.1517 + 22.0852i −0.757268 + 0.975086i
\(514\) −4.16372 7.21177i −0.183654 0.318097i
\(515\) 3.78794 0.166916
\(516\) −10.4195 + 16.2856i −0.458695 + 0.716933i
\(517\) −3.60963 6.25206i −0.158751 0.274965i
\(518\) 0 0
\(519\) −23.9518 + 37.4364i −1.05137 + 1.64327i
\(520\) 0.746304 + 1.29264i 0.0327276 + 0.0566859i
\(521\) 13.7360 + 23.7914i 0.601785 + 1.04232i 0.992551 + 0.121831i \(0.0388767\pi\)
−0.390766 + 0.920490i \(0.627790\pi\)
\(522\) 10.7178 15.1809i 0.469105 0.664449i
\(523\) −11.0919 + 19.2118i −0.485016 + 0.840072i −0.999852 0.0172166i \(-0.994520\pi\)
0.514836 + 0.857289i \(0.327853\pi\)
\(524\) −0.593579 + 1.02811i −0.0259306 + 0.0449132i
\(525\) 0 0
\(526\) −8.54523 14.8008i −0.372590 0.645344i
\(527\) 22.9794 1.00100
\(528\) 0.554084 0.866025i 0.0241134 0.0376889i
\(529\) −3.10390 −0.134952
\(530\) 2.39037 4.14024i 0.103831 0.179841i
\(531\) 10.8727 + 23.5547i 0.471833 + 1.02219i
\(532\) 0 0
\(533\) −0.343677 + 0.595265i −0.0148863 + 0.0257838i
\(534\) −9.90856 19.1247i −0.428785 0.827605i
\(535\) −5.55262 + 9.61742i −0.240061 + 0.415797i
\(536\) −0.956906 + 1.65741i −0.0413321 + 0.0715892i
\(537\) 14.0359 21.9379i 0.605694 0.946690i
\(538\) −5.00720 + 8.67272i −0.215876 + 0.373908i
\(539\) 0 0
\(540\) 1.89183 2.43599i 0.0814115 0.104828i
\(541\) 14.9246 25.8502i 0.641659 1.11139i −0.343403 0.939188i \(-0.611580\pi\)
0.985062 0.172198i \(-0.0550869\pi\)
\(542\) −10.2091 −0.438520
\(543\) −0.0686733 0.132547i −0.00294705 0.00568816i
\(544\) −2.92101 −0.125237
\(545\) 0.850874 + 1.47376i 0.0364474 + 0.0631288i
\(546\) 0 0
\(547\) 8.84348 15.3174i 0.378120 0.654923i −0.612669 0.790340i \(-0.709904\pi\)
0.990789 + 0.135417i \(0.0432373\pi\)
\(548\) −1.26089 + 2.18393i −0.0538627 + 0.0932929i
\(549\) 19.8602 + 1.81523i 0.847613 + 0.0774720i
\(550\) 1.37938 + 2.38915i 0.0588169 + 0.101874i
\(551\) −16.6675 28.8690i −0.710060 1.22986i
\(552\) 3.55408 + 6.85980i 0.151272 + 0.291972i
\(553\) 0 0
\(554\) 9.67111 + 16.7508i 0.410886 + 0.711675i
\(555\) 1.02704 + 0.0468383i 0.0435955 + 0.00198818i
\(556\) 4.91381 0.208392
\(557\) 15.0651 + 26.0935i 0.638328 + 1.10562i 0.985800 + 0.167926i \(0.0537069\pi\)
−0.347472 + 0.937690i \(0.612960\pi\)
\(558\) 13.6118 19.2799i 0.576232 0.816185i
\(559\) −28.0685 −1.18717
\(560\) 0 0
\(561\) 1.61849 2.52967i 0.0683325 0.106803i
\(562\) −12.8027 −0.540050
\(563\) 2.04883 3.54867i 0.0863478 0.149559i −0.819617 0.572912i \(-0.805814\pi\)
0.905965 + 0.423353i \(0.139147\pi\)
\(564\) 9.69076 + 18.7043i 0.408054 + 0.787593i
\(565\) 3.65652 + 6.33327i 0.153831 + 0.266443i
\(566\) −16.3523 −0.687340
\(567\) 0 0
\(568\) 14.4107 0.604659
\(569\) −3.11849 5.40138i −0.130734 0.226437i 0.793226 0.608927i \(-0.208400\pi\)
−0.923960 + 0.382490i \(0.875067\pi\)
\(570\) −2.54523 4.91259i −0.106608 0.205766i
\(571\) −17.8011 + 30.8323i −0.744951 + 1.29029i 0.205266 + 0.978706i \(0.434194\pi\)
−0.950218 + 0.311587i \(0.899139\pi\)
\(572\) 1.49261 0.0624091
\(573\) −3.71732 + 5.81012i −0.155293 + 0.242721i
\(574\) 0 0
\(575\) −20.7309 −0.864539
\(576\) −1.73025 + 2.45076i −0.0720939 + 0.102115i
\(577\) −23.1388 40.0776i −0.963281 1.66845i −0.714164 0.699979i \(-0.753193\pi\)
−0.249118 0.968473i \(-0.580141\pi\)
\(578\) 8.46770 0.352210
\(579\) 11.7324 + 0.535056i 0.487581 + 0.0222362i
\(580\) 1.83842 + 3.18424i 0.0763363 + 0.132218i
\(581\) 0 0
\(582\) 9.34941 + 18.0455i 0.387546 + 0.748008i
\(583\) −2.39037 4.14024i −0.0989990 0.171471i
\(584\) 3.95691 + 6.85356i 0.163738 + 0.283602i
\(585\) 4.45924 + 0.407575i 0.184367 + 0.0168512i
\(586\) −10.3889 + 17.9941i −0.429162 + 0.743330i
\(587\) −1.13161 + 1.96001i −0.0467066 + 0.0808982i −0.888434 0.459005i \(-0.848206\pi\)
0.841727 + 0.539903i \(0.181539\pi\)
\(588\) 0 0
\(589\) −21.1680 36.6640i −0.872212 1.51072i
\(590\) −5.13307 −0.211325
\(591\) −8.81118 17.0066i −0.362444 0.699558i
\(592\) −1.00000 −0.0410997
\(593\) −23.0979 + 40.0067i −0.948515 + 1.64288i −0.199960 + 0.979804i \(0.564081\pi\)
−0.748555 + 0.663072i \(0.769252\pi\)
\(594\) −1.16372 2.85637i −0.0477478 0.117198i
\(595\) 0 0
\(596\) −9.02558 + 15.6328i −0.369702 + 0.640343i
\(597\) −5.24465 + 8.19731i −0.214649 + 0.335493i
\(598\) −5.60817 + 9.71363i −0.229335 + 0.397220i
\(599\) 8.39037 14.5325i 0.342821 0.593784i −0.642134 0.766592i \(-0.721951\pi\)
0.984955 + 0.172808i \(0.0552842\pi\)
\(600\) −3.70321 7.14763i −0.151183 0.291801i
\(601\) 5.69961 9.87202i 0.232492 0.402688i −0.726049 0.687643i \(-0.758645\pi\)
0.958541 + 0.284955i \(0.0919787\pi\)
\(602\) 0 0
\(603\) 2.40623 + 5.21289i 0.0979891 + 0.212285i
\(604\) −0.823832 + 1.42692i −0.0335212 + 0.0580605i
\(605\) 6.32023 0.256954
\(606\) 1.51478 2.36758i 0.0615339 0.0961765i
\(607\) 14.4284 0.585631 0.292815 0.956169i \(-0.405408\pi\)
0.292815 + 0.956169i \(0.405408\pi\)
\(608\) 2.69076 + 4.66053i 0.109125 + 0.189009i
\(609\) 0 0
\(610\) −1.97296 + 3.41726i −0.0798827 + 0.138361i
\(611\) −15.2915 + 26.4857i −0.618629 + 1.07150i
\(612\) −5.05408 + 7.15869i −0.204299 + 0.289373i
\(613\) 12.2053 + 21.1403i 0.492969 + 0.853848i 0.999967 0.00809942i \(-0.00257815\pi\)
−0.506998 + 0.861947i \(0.669245\pi\)
\(614\) 11.3384 + 19.6387i 0.457581 + 0.792554i
\(615\) −0.151457 + 0.236725i −0.00610733 + 0.00954566i
\(616\) 0 0
\(617\) 24.4698 + 42.3830i 0.985119 + 1.70628i 0.641408 + 0.767200i \(0.278350\pi\)
0.343710 + 0.939076i \(0.388316\pi\)
\(618\) −5.95691 + 9.31056i −0.239622 + 0.374525i
\(619\) 44.6591 1.79500 0.897501 0.441012i \(-0.145380\pi\)
0.897501 + 0.441012i \(0.145380\pi\)
\(620\) 2.33482 + 4.04403i 0.0937687 + 0.162412i
\(621\) 22.9612 + 3.15897i 0.921400 + 0.126765i
\(622\) −6.51459 −0.261211
\(623\) 0 0
\(624\) −4.35087 0.198422i −0.174174 0.00794323i
\(625\) 19.8391 0.793564
\(626\) −0.133074 + 0.230492i −0.00531873 + 0.00921230i
\(627\) −5.52704 0.252061i −0.220729 0.0100663i
\(628\) −3.30039 5.71644i −0.131700 0.228111i
\(629\) −2.92101 −0.116468
\(630\) 0 0
\(631\) 33.2852 1.32506 0.662532 0.749034i \(-0.269482\pi\)
0.662532 + 0.749034i \(0.269482\pi\)
\(632\) −4.62422 8.00938i −0.183942 0.318596i
\(633\) 18.0387 28.1942i 0.716974 1.12062i
\(634\) 7.86186 13.6171i 0.312235 0.540806i
\(635\) −7.32158 −0.290548
\(636\) 6.41741 + 12.3863i 0.254467 + 0.491151i
\(637\) 0 0
\(638\) 3.67684 0.145568
\(639\) 24.9341 35.3172i 0.986379 1.39713i
\(640\) −0.296790 0.514055i −0.0117316 0.0203198i
\(641\) 30.7879 1.21605 0.608025 0.793918i \(-0.291962\pi\)
0.608025 + 0.793918i \(0.291962\pi\)
\(642\) −14.9071 28.7724i −0.588336 1.13556i
\(643\) 13.7345 + 23.7889i 0.541637 + 0.938142i 0.998810 + 0.0487649i \(0.0155285\pi\)
−0.457174 + 0.889378i \(0.651138\pi\)
\(644\) 0 0
\(645\) −11.4641 0.522821i −0.451399 0.0205861i
\(646\) 7.85973 + 13.6134i 0.309237 + 0.535614i
\(647\) 6.63521 + 11.4925i 0.260857 + 0.451818i 0.966470 0.256780i \(-0.0826615\pi\)
−0.705613 + 0.708598i \(0.749328\pi\)
\(648\) 3.01245 + 8.48087i 0.118340 + 0.333160i
\(649\) −2.56654 + 4.44537i −0.100745 + 0.174496i
\(650\) 5.84348 10.1212i 0.229200 0.396986i
\(651\) 0 0
\(652\) −2.99115 5.18082i −0.117142 0.202896i
\(653\) −17.1416 −0.670803 −0.335402 0.942075i \(-0.608872\pi\)
−0.335402 + 0.942075i \(0.608872\pi\)
\(654\) −4.96050 0.226224i −0.193971 0.00884606i
\(655\) −0.704673 −0.0275338
\(656\) 0.136673 0.236725i 0.00533619 0.00924255i
\(657\) 23.6429 + 2.16096i 0.922397 + 0.0843072i
\(658\) 0 0
\(659\) 4.26089 7.38008i 0.165981 0.287487i −0.771022 0.636808i \(-0.780254\pi\)
0.937003 + 0.349321i \(0.113588\pi\)
\(660\) 0.609631 + 0.0278023i 0.0237299 + 0.00108220i
\(661\) 17.1680 29.7358i 0.667757 1.15659i −0.310773 0.950484i \(-0.600588\pi\)
0.978530 0.206105i \(-0.0660789\pi\)
\(662\) −12.5811 + 21.7912i −0.488979 + 0.846937i
\(663\) −12.7089 0.579592i −0.493575 0.0225095i
\(664\) 3.85087 6.66991i 0.149443 0.258843i
\(665\) 0 0
\(666\) −1.73025 + 2.45076i −0.0670459 + 0.0949650i
\(667\) −13.8150 + 23.9282i −0.534918 + 0.926505i
\(668\) 7.46050 0.288656
\(669\) 43.8178 + 1.99831i 1.69409 + 0.0772592i
\(670\) −1.13600 −0.0438875
\(671\) 1.97296 + 3.41726i 0.0761652 + 0.131922i
\(672\) 0 0
\(673\) −7.70155 + 13.3395i −0.296873 + 0.514199i −0.975419 0.220359i \(-0.929277\pi\)
0.678546 + 0.734558i \(0.262610\pi\)
\(674\) 9.36693 16.2240i 0.360800 0.624925i
\(675\) −23.9246 3.29152i −0.920859 0.126691i
\(676\) 3.33842 + 5.78231i 0.128401 + 0.222397i
\(677\) −3.69076 6.39258i −0.141847 0.245687i 0.786345 0.617788i \(-0.211971\pi\)
−0.928192 + 0.372101i \(0.878638\pi\)
\(678\) −21.3171 0.972168i −0.818679 0.0373359i
\(679\) 0 0
\(680\) −0.866926 1.50156i −0.0332451 0.0575822i
\(681\) 3.83823 + 7.40822i 0.147081 + 0.283884i
\(682\) 4.66964 0.178810
\(683\) 4.79893 + 8.31198i 0.183626 + 0.318049i 0.943113 0.332474i \(-0.107883\pi\)
−0.759487 + 0.650523i \(0.774550\pi\)
\(684\) 16.0775 + 1.46949i 0.614740 + 0.0561873i
\(685\) −1.49688 −0.0571929
\(686\) 0 0
\(687\) −7.40642 14.2953i −0.282573 0.545398i
\(688\) 11.1623 0.425557
\(689\) −10.1264 + 17.5394i −0.385783 + 0.668197i
\(690\) −2.47150 + 3.86291i −0.0940882 + 0.147058i
\(691\) −7.07227 12.2495i −0.269042 0.465994i 0.699573 0.714561i \(-0.253374\pi\)
−0.968615 + 0.248567i \(0.920040\pi\)
\(692\) 25.6591 0.975414
\(693\) 0 0
\(694\) −22.5438 −0.855750
\(695\) 1.45837 + 2.52597i 0.0553191 + 0.0958155i
\(696\) −10.7178 0.488786i −0.406257 0.0185274i
\(697\) 0.399223 0.691475i 0.0151217 0.0261915i
\(698\) −3.79086 −0.143486
\(699\) −0.336285 0.0153363i −0.0127195 0.000580072i
\(700\) 0 0
\(701\) 37.3753 1.41164 0.705822 0.708389i \(-0.250578\pi\)
0.705822 + 0.708389i \(0.250578\pi\)
\(702\) −8.01439 + 10.3196i −0.302484 + 0.389489i
\(703\) 2.69076 + 4.66053i 0.101484 + 0.175775i
\(704\) −0.593579 −0.0223714
\(705\) −6.73891 + 10.5328i −0.253802 + 0.396689i
\(706\) −3.41741 5.91913i −0.128616 0.222769i
\(707\) 0 0
\(708\) 8.07227 12.6168i 0.303375 0.474170i
\(709\) 5.24338 + 9.08180i 0.196919 + 0.341074i 0.947528 0.319673i \(-0.103573\pi\)
−0.750609 + 0.660747i \(0.770240\pi\)
\(710\) 4.27694 + 7.40789i 0.160511 + 0.278013i
\(711\) −27.6301 2.52540i −1.03621 0.0947099i
\(712\) −6.21780 + 10.7695i −0.233022 + 0.403606i
\(713\) −17.5452 + 30.3892i −0.657074 + 1.13809i
\(714\) 0 0
\(715\) 0.442991 + 0.767282i 0.0165669 + 0.0286947i
\(716\) −15.0364 −0.561936
\(717\) −12.7463 + 19.9223i −0.476019 + 0.744011i
\(718\) −12.6447 −0.471897
\(719\) −1.11995 + 1.93981i −0.0417670 + 0.0723426i −0.886153 0.463392i \(-0.846632\pi\)
0.844386 + 0.535735i \(0.179965\pi\)
\(720\) −1.77335 0.162084i −0.0660887 0.00604052i
\(721\) 0 0
\(722\) 4.98035 8.62622i 0.185349 0.321035i
\(723\) −10.3583 19.9927i −0.385228 0.743535i
\(724\) −0.0430937 + 0.0746406i −0.00160157 + 0.00277399i
\(725\) 14.3946 24.9322i 0.534604 0.925961i
\(726\) −9.93920 + 15.5348i −0.368878 + 0.576551i
\(727\) −0.185023 + 0.320469i −0.00686211 + 0.0118855i −0.869436 0.494045i \(-0.835518\pi\)
0.862574 + 0.505931i \(0.168851\pi\)
\(728\) 0 0
\(729\) 25.9969 + 7.29124i 0.962847 + 0.270046i
\(730\) −2.34874 + 4.06813i −0.0869307 + 0.150568i
\(731\) 32.6050 1.20594
\(732\) −5.29679 10.2234i −0.195775 0.377868i
\(733\) −14.0191 −0.517806 −0.258903 0.965903i \(-0.583361\pi\)
−0.258903 + 0.965903i \(0.583361\pi\)
\(734\) −3.27188 5.66707i −0.120767 0.209175i
\(735\) 0 0
\(736\) 2.23025 3.86291i 0.0822082 0.142389i
\(737\) −0.568000 + 0.983804i −0.0209225 + 0.0362389i
\(738\) −0.343677 0.744547i −0.0126509 0.0274071i
\(739\) 13.3872 + 23.1874i 0.492458 + 0.852962i 0.999962 0.00868705i \(-0.00276521\pi\)
−0.507504 + 0.861649i \(0.669432\pi\)
\(740\) −0.296790 0.514055i −0.0109102 0.0188970i
\(741\) 10.7824 + 20.8113i 0.396101 + 0.764521i
\(742\) 0 0
\(743\) −5.04669 8.74113i −0.185145 0.320681i 0.758480 0.651696i \(-0.225942\pi\)
−0.943625 + 0.331015i \(0.892609\pi\)
\(744\) −13.6118 0.620765i −0.499032 0.0227584i
\(745\) −10.7148 −0.392560
\(746\) 4.71420 + 8.16524i 0.172599 + 0.298951i
\(747\) −9.68337 20.9782i −0.354296 0.767552i
\(748\) −1.73385 −0.0633959
\(749\) 0 0
\(750\) 5.34562 8.35512i 0.195194 0.305086i
\(751\) 11.5146 0.420173 0.210087 0.977683i \(-0.432625\pi\)
0.210087 + 0.977683i \(0.432625\pi\)
\(752\) 6.08113 10.5328i 0.221756 0.384092i
\(753\) −15.5723 30.0563i −0.567485 1.09531i
\(754\) −7.78813 13.4894i −0.283627 0.491256i
\(755\) −0.978019 −0.0355938
\(756\) 0 0
\(757\) −15.2484 −0.554214 −0.277107 0.960839i \(-0.589376\pi\)
−0.277107 + 0.960839i \(0.589376\pi\)
\(758\) −3.63881 6.30260i −0.132168 0.228921i
\(759\) 2.10963 + 4.07183i 0.0765748 + 0.147798i
\(760\) −1.59718 + 2.76639i −0.0579357 + 0.100348i
\(761\) 1.70175 0.0616883 0.0308442 0.999524i \(-0.490180\pi\)
0.0308442 + 0.999524i \(0.490180\pi\)
\(762\) 11.5139 17.9961i 0.417105 0.651929i
\(763\) 0 0
\(764\) 3.98229 0.144074
\(765\) −5.17996 0.473449i −0.187282 0.0171176i
\(766\) 12.0416 + 20.8567i 0.435082 + 0.753584i
\(767\) 21.7453 0.785178
\(768\) 1.73025 + 0.0789082i 0.0624351 + 0.00284736i
\(769\) −24.1211 41.7790i −0.869829 1.50659i −0.862171 0.506618i \(-0.830896\pi\)
−0.00765823 0.999971i \(-0.502438\pi\)
\(770\) 0 0
\(771\) 6.63521 + 12.8067i 0.238961 + 0.461223i
\(772\) −3.39037 5.87229i −0.122022 0.211348i
\(773\) −3.10243 5.37357i −0.111587 0.193274i 0.804823 0.593514i \(-0.202260\pi\)
−0.916410 +