Properties

Label 882.2.f.n.589.1
Level $882$
Weight $2$
Character 882.589
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(295,882)]
 
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([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.04280545828\)
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 589.1
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 882.589
Dual form 882.2.f.n.295.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.73025 + 0.0789082i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.296790 + 0.514055i) q^{5} +(-0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(2.98755 - 0.273062i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.73025 + 0.0789082i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.296790 + 0.514055i) q^{5} +(-0.933463 - 1.45899i) q^{6} -1.00000 q^{8} +(2.98755 - 0.273062i) q^{9} -0.593579 q^{10} +(0.296790 + 0.514055i) q^{11} +(0.796790 - 1.53790i) q^{12} +(-1.25729 + 2.17770i) q^{13} +(0.472958 - 0.912864i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.92101 q^{17} +(1.73025 + 2.45076i) q^{18} -5.38151 q^{19} +(-0.296790 - 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} +(-2.23025 + 3.86291i) q^{23} +(1.73025 - 0.0789082i) q^{24} +(2.32383 + 4.02499i) q^{25} -2.51459 q^{26} +(-5.14766 + 0.708209i) q^{27} +(-3.09718 - 5.36447i) q^{29} +(1.02704 - 0.0468383i) q^{30} +(3.93346 - 6.81296i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.554084 - 0.866025i) q^{33} +(-1.46050 - 2.52967i) q^{34} +(-1.25729 + 2.72382i) q^{36} -1.00000 q^{37} +(-2.69076 - 4.66053i) q^{38} +(2.00360 - 3.86718i) q^{39} +(0.296790 - 0.514055i) q^{40} +(-0.136673 + 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} -0.593579 q^{44} +(-0.746304 + 1.61680i) q^{45} -4.46050 q^{46} +(-6.08113 - 10.5328i) q^{47} +(0.933463 + 1.45899i) q^{48} +(-2.32383 + 4.02499i) q^{50} +(5.05408 - 0.230492i) q^{51} +(-1.25729 - 2.17770i) q^{52} -8.05408 q^{53} +(-3.18716 - 4.10390i) q^{54} -0.352336 q^{55} +(9.31138 - 0.424646i) q^{57} +(3.09718 - 5.36447i) q^{58} +(-4.32383 + 7.48910i) q^{59} +(0.554084 + 0.866025i) q^{60} +(3.32383 + 5.75705i) q^{61} +7.86693 q^{62} +1.00000 q^{64} +(-0.746304 - 1.29264i) q^{65} +(0.472958 - 0.912864i) q^{66} +(0.956906 - 1.65741i) q^{67} +(1.46050 - 2.52967i) q^{68} +(3.55408 - 6.85980i) q^{69} -14.4107 q^{71} +(-2.98755 + 0.273062i) q^{72} -7.91381 q^{73} +(-0.500000 - 0.866025i) q^{74} +(-4.33842 - 6.78089i) q^{75} +(2.69076 - 4.66053i) q^{76} +(4.35087 - 0.198422i) q^{78} +(4.62422 + 8.00938i) q^{79} +0.593579 q^{80} +(8.85087 - 1.63157i) q^{81} -0.273346 q^{82} +(3.85087 + 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(5.58113 - 9.66679i) q^{86} +(5.78220 + 9.03749i) q^{87} +(-0.296790 - 0.514055i) q^{88} +12.4356 q^{89} +(-1.77335 + 0.162084i) q^{90} +(-2.23025 - 3.86291i) q^{92} +(-6.26829 + 12.0985i) q^{93} +(6.08113 - 10.5328i) q^{94} +(1.59718 - 2.76639i) q^{95} +(-0.796790 + 1.53790i) q^{96} +(5.86693 + 10.1618i) q^{97} +(1.02704 + 1.45472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - 4 q^{9} + 2 q^{10} - q^{11} + 2 q^{12} + 8 q^{13} + 12 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + q^{20} + q^{22} - 7 q^{23} + 4 q^{24} + 2 q^{25} + 16 q^{26} - 7 q^{27} - 5 q^{29} - 3 q^{30} + 20 q^{31} + 3 q^{32} + 15 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} + 3 q^{38} + 4 q^{39} - q^{40} - 6 q^{43} + 2 q^{44} - 12 q^{45} - 14 q^{46} - 9 q^{47} + 2 q^{48} - 2 q^{50} + 12 q^{51} + 8 q^{52} - 30 q^{53} - 8 q^{54} - 26 q^{55} + 22 q^{57} + 5 q^{58} - 14 q^{59} - 15 q^{60} + 8 q^{61} + 40 q^{62} + 6 q^{64} - 12 q^{65} + 12 q^{66} + q^{67} - 4 q^{68} + 3 q^{69} + 14 q^{71} + 4 q^{72} - 38 q^{73} - 3 q^{74} + 17 q^{75} - 3 q^{76} + 5 q^{78} + 5 q^{79} - 2 q^{80} + 32 q^{81} + 2 q^{83} - 2 q^{85} + 6 q^{86} + 63 q^{87} + q^{88} + 18 q^{89} - 9 q^{90} - 7 q^{92} + q^{93} + 9 q^{94} - 4 q^{95} - 2 q^{96} + 28 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −1.73025 + 0.0789082i −0.998962 + 0.0455577i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.296790 + 0.514055i −0.132728 + 0.229892i −0.924727 0.380630i \(-0.875707\pi\)
0.791999 + 0.610522i \(0.209040\pi\)
\(6\) −0.933463 1.45899i −0.381085 0.595630i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 2.98755 0.273062i 0.995849 0.0910208i
\(10\) −0.593579 −0.187706
\(11\) 0.296790 + 0.514055i 0.0894855 + 0.154993i 0.907294 0.420497i \(-0.138144\pi\)
−0.817808 + 0.575491i \(0.804811\pi\)
\(12\) 0.796790 1.53790i 0.230013 0.443953i
\(13\) −1.25729 + 2.17770i −0.348711 + 0.603985i −0.986021 0.166623i \(-0.946714\pi\)
0.637310 + 0.770608i \(0.280047\pi\)
\(14\) 0 0
\(15\) 0.472958 0.912864i 0.122117 0.235700i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.92101 −0.708449 −0.354224 0.935160i \(-0.615255\pi\)
−0.354224 + 0.935160i \(0.615255\pi\)
\(18\) 1.73025 + 2.45076i 0.407824 + 0.577650i
\(19\) −5.38151 −1.23460 −0.617302 0.786726i \(-0.711774\pi\)
−0.617302 + 0.786726i \(0.711774\pi\)
\(20\) −0.296790 0.514055i −0.0663642 0.114946i
\(21\) 0 0
\(22\) −0.296790 + 0.514055i −0.0632758 + 0.109597i
\(23\) −2.23025 + 3.86291i −0.465040 + 0.805473i −0.999203 0.0399086i \(-0.987293\pi\)
0.534164 + 0.845381i \(0.320627\pi\)
\(24\) 1.73025 0.0789082i 0.353186 0.0161071i
\(25\) 2.32383 + 4.02499i 0.464766 + 0.804999i
\(26\) −2.51459 −0.493151
\(27\) −5.14766 + 0.708209i −0.990668 + 0.136295i
\(28\) 0 0
\(29\) −3.09718 5.36447i −0.575132 0.996157i −0.996027 0.0890480i \(-0.971618\pi\)
0.420896 0.907109i \(-0.361716\pi\)
\(30\) 1.02704 0.0468383i 0.187511 0.00855147i
\(31\) 3.93346 6.81296i 0.706471 1.22364i −0.259687 0.965693i \(-0.583620\pi\)
0.966158 0.257951i \(-0.0830472\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −0.554084 0.866025i −0.0964537 0.150756i
\(34\) −1.46050 2.52967i −0.250475 0.433835i
\(35\) 0 0
\(36\) −1.25729 + 2.72382i −0.209549 + 0.453970i
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) −2.69076 4.66053i −0.436498 0.756038i
\(39\) 2.00360 3.86718i 0.320833 0.619244i
\(40\) 0.296790 0.514055i 0.0469266 0.0812792i
\(41\) −0.136673 + 0.236725i −0.0213448 + 0.0369702i −0.876500 0.481401i \(-0.840128\pi\)
0.855156 + 0.518371i \(0.173461\pi\)
\(42\) 0 0
\(43\) −5.58113 9.66679i −0.851114 1.47417i −0.880204 0.474596i \(-0.842594\pi\)
0.0290902 0.999577i \(-0.490739\pi\)
\(44\) −0.593579 −0.0894855
\(45\) −0.746304 + 1.61680i −0.111252 + 0.241019i
\(46\) −4.46050 −0.657666
\(47\) −6.08113 10.5328i −0.887023 1.53637i −0.843377 0.537323i \(-0.819436\pi\)
−0.0436467 0.999047i \(-0.513898\pi\)
\(48\) 0.933463 + 1.45899i 0.134734 + 0.210587i
\(49\) 0 0
\(50\) −2.32383 + 4.02499i −0.328639 + 0.569220i
\(51\) 5.05408 0.230492i 0.707713 0.0322753i
\(52\) −1.25729 2.17770i −0.174355 0.301992i
\(53\) −8.05408 −1.10631 −0.553157 0.833077i \(-0.686577\pi\)
−0.553157 + 0.833077i \(0.686577\pi\)
\(54\) −3.18716 4.10390i −0.433717 0.558470i
\(55\) −0.352336 −0.0475090
\(56\) 0 0
\(57\) 9.31138 0.424646i 1.23332 0.0562457i
\(58\) 3.09718 5.36447i 0.406679 0.704389i
\(59\) −4.32383 + 7.48910i −0.562915 + 0.974997i 0.434325 + 0.900756i \(0.356987\pi\)
−0.997240 + 0.0742412i \(0.976347\pi\)
\(60\) 0.554084 + 0.866025i 0.0715320 + 0.111803i
\(61\) 3.32383 + 5.75705i 0.425573 + 0.737114i 0.996474 0.0839050i \(-0.0267392\pi\)
−0.570901 + 0.821019i \(0.693406\pi\)
\(62\) 7.86693 0.999101
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.746304 1.29264i −0.0925676 0.160332i
\(66\) 0.472958 0.912864i 0.0582171 0.112366i
\(67\) 0.956906 1.65741i 0.116905 0.202485i −0.801635 0.597814i \(-0.796036\pi\)
0.918540 + 0.395329i \(0.129369\pi\)
\(68\) 1.46050 2.52967i 0.177112 0.306767i
\(69\) 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 \(0.826515\pi\)
\(72\) −2.98755 + 0.273062i −0.352086 + 0.0321807i
\(73\) −7.91381 −0.926242 −0.463121 0.886295i \(-0.653270\pi\)
−0.463121 + 0.886295i \(0.653270\pi\)
\(74\) −0.500000 0.866025i −0.0581238 0.100673i
\(75\) −4.33842 6.78089i −0.500958 0.782989i
\(76\) 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 \(0.659166\pi\)
\(80\) 0.593579 0.0663642
\(81\) 8.85087 1.63157i 0.983430 0.181286i
\(82\) −0.273346 −0.0301860
\(83\) 3.85087 + 6.66991i 0.422688 + 0.732118i 0.996201 0.0870787i \(-0.0277532\pi\)
−0.573513 + 0.819196i \(0.694420\pi\)
\(84\) 0 0
\(85\) 0.866926 1.50156i 0.0940313 0.162867i
\(86\) 5.58113 9.66679i 0.601828 1.04240i
\(87\) 5.78220 + 9.03749i 0.619917 + 0.968921i
\(88\) −0.296790 0.514055i −0.0316379 0.0547984i
\(89\) 12.4356 1.31817 0.659085 0.752068i \(-0.270944\pi\)
0.659085 + 0.752068i \(0.270944\pi\)
\(90\) −1.77335 + 0.162084i −0.186927 + 0.0170852i
\(91\) 0 0
\(92\) −2.23025 3.86291i −0.232520 0.402736i
\(93\) −6.26829 + 12.0985i −0.649991 + 1.25456i
\(94\) 6.08113 10.5328i 0.627220 1.08638i
\(95\) 1.59718 2.76639i 0.163867 0.283826i
\(96\) −0.796790 + 1.53790i −0.0813220 + 0.156961i
\(97\) 5.86693 + 10.1618i 0.595696 + 1.03178i 0.993448 + 0.114283i \(0.0364570\pi\)
−0.397752 + 0.917493i \(0.630210\pi\)
\(98\) 0 0
\(99\) 1.02704 + 1.45472i 0.103222 + 0.146205i
\(100\) −4.64766 −0.464766
\(101\) 0.811379 + 1.40535i 0.0807352 + 0.139837i 0.903566 0.428449i \(-0.140940\pi\)
−0.822831 + 0.568287i \(0.807607\pi\)
\(102\) 2.72665 + 4.26172i 0.269979 + 0.421973i
\(103\) −3.19076 + 5.52655i −0.314395 + 0.544548i −0.979309 0.202372i \(-0.935135\pi\)
0.664914 + 0.746920i \(0.268468\pi\)
\(104\) 1.25729 2.17770i 0.123288 0.213541i
\(105\) 0 0
\(106\) −4.02704 6.97504i −0.391141 0.677476i
\(107\) −18.7089 −1.80866 −0.904331 0.426832i \(-0.859630\pi\)
−0.904331 + 0.426832i \(0.859630\pi\)
\(108\) 1.96050 4.81211i 0.188650 0.463046i
\(109\) 2.86693 0.274602 0.137301 0.990529i \(-0.456157\pi\)
0.137301 + 0.990529i \(0.456157\pi\)
\(110\) −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 0.416042 + 0.909345i \(0.363417\pi\)
−0.995537 + 0.0943695i \(0.969916\pi\)
\(114\) 5.02344 + 7.85157i 0.470489 + 0.735367i
\(115\) −1.32383 2.29294i −0.123448 0.213818i
\(116\) 6.19436 0.575132
\(117\) −3.16158 + 6.84929i −0.292288 + 0.633218i
\(118\) −8.64766 −0.796082
\(119\) 0 0
\(120\) −0.472958 + 0.912864i −0.0431750 + 0.0833327i
\(121\) 5.32383 9.22115i 0.483985 0.838286i
\(122\) −3.32383 + 5.75705i −0.300926 + 0.521218i
\(123\) 0.217799 0.420378i 0.0196383 0.0379042i
\(124\) 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
\(129\) 10.4195 + 16.2856i 0.917390 + 1.43387i
\(130\) 0.746304 1.29264i 0.0654552 0.113372i
\(131\) 0.593579 1.02811i 0.0518613 0.0898264i −0.838929 0.544240i \(-0.816818\pi\)
0.890791 + 0.454414i \(0.150151\pi\)
\(132\) 1.02704 0.0468383i 0.0893925 0.00407675i
\(133\) 0 0
\(134\) 1.91381 0.165328
\(135\) 1.16372 2.85637i 0.100157 0.245837i
\(136\) 2.92101 0.250475
\(137\) −1.26089 2.18393i −0.107725 0.186586i 0.807123 0.590383i \(-0.201023\pi\)
−0.914848 + 0.403797i \(0.867690\pi\)
\(138\) 7.71780 0.351971i 0.656983 0.0299617i
\(139\) 2.45691 4.25549i 0.208392 0.360946i −0.742816 0.669496i \(-0.766510\pi\)
0.951208 + 0.308550i \(0.0998437\pi\)
\(140\) 0 0
\(141\) 11.3530 + 17.7446i 0.956096 + 1.49436i
\(142\) −7.20535 12.4800i −0.604659 1.04730i
\(143\) −1.49261 −0.124818
\(144\) −1.73025 2.45076i −0.144188 0.204230i
\(145\) 3.67684 0.305345
\(146\) −3.95691 6.85356i −0.327476 0.567205i
\(147\) 0 0
\(148\) 0.500000 0.866025i 0.0410997 0.0711868i
\(149\) −9.02558 + 15.6328i −0.739404 + 1.28069i 0.213360 + 0.976974i \(0.431559\pi\)
−0.952764 + 0.303712i \(0.901774\pi\)
\(150\) 3.70321 7.14763i 0.302366 0.583601i
\(151\) −0.823832 1.42692i −0.0670425 0.116121i 0.830556 0.556936i \(-0.188023\pi\)
−0.897598 + 0.440815i \(0.854690\pi\)
\(152\) 5.38151 0.436498
\(153\) −8.72665 + 0.797618i −0.705508 + 0.0644836i
\(154\) 0 0
\(155\) 2.33482 + 4.04403i 0.187537 + 0.324824i
\(156\) 2.34728 + 3.66876i 0.187932 + 0.293736i
\(157\) 3.30039 5.71644i 0.263400 0.456222i −0.703743 0.710454i \(-0.748490\pi\)
0.967143 + 0.254233i \(0.0818229\pi\)
\(158\) −4.62422 + 8.00938i −0.367883 + 0.637192i
\(159\) 13.9356 0.635534i 1.10516 0.0504011i
\(160\) 0.296790 + 0.514055i 0.0234633 + 0.0406396i
\(161\) 0 0
\(162\) 5.83842 + 6.84929i 0.458710 + 0.538131i
\(163\) 5.98229 0.468569 0.234285 0.972168i \(-0.424725\pi\)
0.234285 + 0.972168i \(0.424725\pi\)
\(164\) −0.136673 0.236725i −0.0106724 0.0184851i
\(165\) 0.609631 0.0278023i 0.0474597 0.00216440i
\(166\) −3.85087 + 6.66991i −0.298886 + 0.517685i
\(167\) 3.73025 6.46099i 0.288656 0.499966i −0.684833 0.728700i \(-0.740125\pi\)
0.973489 + 0.228733i \(0.0734584\pi\)
\(168\) 0 0
\(169\) 3.33842 + 5.78231i 0.256802 + 0.444793i
\(170\) 1.73385 0.132980
\(171\) −16.0775 + 1.46949i −1.22948 + 0.112375i
\(172\) 11.1623 0.851114
\(173\) 12.8296 + 22.2215i 0.975414 + 1.68947i 0.678562 + 0.734543i \(0.262603\pi\)
0.296851 + 0.954924i \(0.404063\pi\)
\(174\) −4.93560 + 9.52628i −0.374167 + 0.722185i
\(175\) 0 0
\(176\) 0.296790 0.514055i 0.0223714 0.0387483i
\(177\) 6.89037 13.2992i 0.517912 0.999630i
\(178\) 6.21780 + 10.7695i 0.466044 + 0.807211i
\(179\) −15.0364 −1.12387 −0.561936 0.827181i \(-0.689943\pi\)
−0.561936 + 0.827181i \(0.689943\pi\)
\(180\) −1.02704 1.45472i −0.0765512 0.108428i
\(181\) −0.0861875 −0.00640627 −0.00320313 0.999995i \(-0.501020\pi\)
−0.00320313 + 0.999995i \(0.501020\pi\)
\(182\) 0 0
\(183\) −6.20535 9.69886i −0.458712 0.716961i
\(184\) 2.23025 3.86291i 0.164416 0.284778i
\(185\) 0.296790 0.514055i 0.0218204 0.0377941i
\(186\) −13.6118 + 0.620765i −0.998063 + 0.0455167i
\(187\) −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 \(0.879354\pi\)
\(192\) −1.73025 + 0.0789082i −0.124870 + 0.00569471i
\(193\) −3.39037 + 5.87229i −0.244044 + 0.422697i −0.961862 0.273534i \(-0.911808\pi\)
0.717818 + 0.696230i \(0.245141\pi\)
\(194\) −5.86693 + 10.1618i −0.421221 + 0.729576i
\(195\) 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 \(0.371113\pi\)
\(198\) −0.746304 + 1.61680i −0.0530375 + 0.114901i
\(199\) −5.61849 −0.398284 −0.199142 0.979971i \(-0.563815\pi\)
−0.199142 + 0.979971i \(0.563815\pi\)
\(200\) −2.32383 4.02499i −0.164320 0.284610i
\(201\) −1.52491 + 2.94325i −0.107559 + 0.207601i
\(202\) −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
\(206\) −6.38151 −0.444621
\(207\) −5.60817 + 12.1496i −0.389795 + 0.844457i
\(208\) 2.51459 0.174355
\(209\) −1.59718 2.76639i −0.110479 0.191355i
\(210\) 0 0
\(211\) 9.66225 16.7355i 0.665177 1.15212i −0.314060 0.949403i \(-0.601689\pi\)
0.979237 0.202717i \(-0.0649772\pi\)
\(212\) 4.02704 6.97504i 0.276578 0.479048i
\(213\) 24.9341 1.13712i 1.70846 0.0779143i
\(214\) −9.35447 16.2024i −0.639459 1.10757i
\(215\) 6.62568 0.451868
\(216\) 5.14766 0.708209i 0.350254 0.0481875i
\(217\) 0 0
\(218\) 1.43346 + 2.48283i 0.0970863 + 0.168158i
\(219\) 13.6929 0.624465i 0.925280 0.0421974i
\(220\) 0.176168 0.305132i 0.0118773 0.0205720i
\(221\) 3.67257 6.36108i 0.247044 0.427892i
\(222\) 0.933463 + 1.45899i 0.0626499 + 0.0979209i
\(223\) 12.6623 + 21.9317i 0.847927 + 1.46865i 0.883055 + 0.469270i \(0.155483\pi\)
−0.0351275 + 0.999383i \(0.511184\pi\)
\(224\) 0 0
\(225\) 8.04163 + 11.3903i 0.536109 + 0.759354i
\(226\) −12.3202 −0.819530
\(227\) −2.40856 4.17174i −0.159862 0.276888i 0.774957 0.632014i \(-0.217771\pi\)
−0.934819 + 0.355126i \(0.884438\pi\)
\(228\) −4.28794 + 8.27621i −0.283975 + 0.548106i
\(229\) 4.64766 8.04999i 0.307126 0.531958i −0.670606 0.741814i \(-0.733966\pi\)
0.977732 + 0.209855i \(0.0672993\pi\)
\(230\) 1.32383 2.29294i 0.0872909 0.151192i
\(231\) 0 0
\(232\) 3.09718 + 5.36447i 0.203340 + 0.352195i
\(233\) −0.194356 −0.0127327 −0.00636634 0.999980i \(-0.502026\pi\)
−0.00636634 + 0.999980i \(0.502026\pi\)
\(234\) −7.51245 + 0.686640i −0.491104 + 0.0448870i
\(235\) 7.21926 0.470933
\(236\) −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 −0.997811 0.0661361i \(-0.978933\pi\)
0.556181 + 0.831061i \(0.312266\pi\)
\(240\) −1.02704 + 0.0468383i −0.0662953 + 0.00302340i
\(241\) 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i \(-0.0291519\pi\)
−0.577107 + 0.816668i \(0.695819\pi\)
\(242\) 10.6477 0.684458
\(243\) −15.1855 + 3.52144i −0.974150 + 0.225901i
\(244\) −6.64766 −0.425573
\(245\) 0 0
\(246\) 0.472958 0.0215693i 0.0301547 0.00137521i
\(247\) 6.76615 11.7193i 0.430520 0.745682i
\(248\) −3.93346 + 6.81296i −0.249775 + 0.432623i
\(249\) −7.18929 11.2368i −0.455603 0.712101i
\(250\) −2.86333 4.95943i −0.181093 0.313662i
\(251\) −19.5438 −1.23359 −0.616796 0.787123i \(-0.711570\pi\)
−0.616796 + 0.787123i \(0.711570\pi\)
\(252\) 0 0
\(253\) −2.64766 −0.166457
\(254\) 6.16731 + 10.6821i 0.386972 + 0.670255i
\(255\) −1.38151 + 2.66648i −0.0865138 + 0.166982i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −4.16372 + 7.21177i −0.259725 + 0.449858i −0.966168 0.257912i \(-0.916965\pi\)
0.706443 + 0.707770i \(0.250299\pi\)
\(258\) −8.89397 + 17.1664i −0.553714 + 1.06873i
\(259\) 0 0
\(260\) 1.49261 0.0925676
\(261\) −10.7178 15.1809i −0.663415 0.939673i
\(262\) 1.18716 0.0733429
\(263\) 8.54523 + 14.8008i 0.526921 + 0.912655i 0.999508 + 0.0313704i \(0.00998713\pi\)
−0.472586 + 0.881284i \(0.656680\pi\)
\(264\) 0.554084 + 0.866025i 0.0341015 + 0.0533002i
\(265\) 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
\(269\) 10.0144 0.610588 0.305294 0.952258i \(-0.401245\pi\)
0.305294 + 0.952258i \(0.401245\pi\)
\(270\) 3.05555 0.420378i 0.185955 0.0255834i
\(271\) −10.2091 −0.620161 −0.310081 0.950710i \(-0.600356\pi\)
−0.310081 + 0.950710i \(0.600356\pi\)
\(272\) 1.46050 + 2.52967i 0.0885561 + 0.153384i
\(273\) 0 0
\(274\) 1.26089 2.18393i 0.0761733 0.131936i
\(275\) −1.37938 + 2.38915i −0.0831797 + 0.144071i
\(276\) 4.16372 + 6.50783i 0.250626 + 0.391725i
\(277\) −9.67111 16.7508i −0.581081 1.00646i −0.995352 0.0963074i \(-0.969297\pi\)
0.414271 0.910154i \(-0.364037\pi\)
\(278\) 4.91381 0.294711
\(279\) 9.89104 21.4281i 0.592161 1.28287i
\(280\) 0 0
\(281\) −6.40136 11.0875i −0.381873 0.661424i 0.609457 0.792819i \(-0.291388\pi\)
−0.991330 + 0.131396i \(0.958054\pi\)
\(282\) −9.69076 + 18.7043i −0.577076 + 1.11382i
\(283\) 8.17617 14.1615i 0.486023 0.841816i −0.513848 0.857881i \(-0.671781\pi\)
0.999871 + 0.0160650i \(0.00511388\pi\)
\(284\) 7.20535 12.4800i 0.427559 0.740553i
\(285\) −2.54523 + 4.91259i −0.150766 + 0.290997i
\(286\) −0.746304 1.29264i −0.0441299 0.0764352i
\(287\) 0 0
\(288\) 1.25729 2.72382i 0.0740868 0.160503i
\(289\) −8.46770 −0.498100
\(290\) 1.83842 + 3.18424i 0.107956 + 0.186985i
\(291\) −10.9531 17.1196i −0.642083 1.00357i
\(292\) 3.95691 6.85356i 0.231560 0.401074i
\(293\) −10.3889 + 17.9941i −0.606926 + 1.05123i 0.384817 + 0.922993i \(0.374264\pi\)
−0.991744 + 0.128235i \(0.959069\pi\)
\(294\) 0 0
\(295\) −2.56654 4.44537i −0.149430 0.258820i
\(296\) 1.00000 0.0581238
\(297\) −1.89183 2.43599i −0.109775 0.141351i
\(298\) −18.0512 −1.04568
\(299\) −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
\(303\) −1.51478 2.36758i −0.0870221 0.136014i
\(304\) 2.69076 + 4.66053i 0.154326 + 0.267300i
\(305\) −3.94592 −0.225942
\(306\) −5.05408 7.15869i −0.288923 0.409235i
\(307\) −22.6768 −1.29424 −0.647118 0.762390i \(-0.724026\pi\)
−0.647118 + 0.762390i \(0.724026\pi\)
\(308\) 0 0
\(309\) 5.08472 9.81411i 0.289260 0.558305i
\(310\) −2.33482 + 4.04403i −0.132609 + 0.229686i
\(311\) 3.25729 5.64180i 0.184704 0.319917i −0.758773 0.651356i \(-0.774201\pi\)
0.943477 + 0.331439i \(0.107534\pi\)
\(312\) −2.00360 + 3.86718i −0.113431 + 0.218936i
\(313\) −0.133074 0.230492i −0.00752181 0.0130282i 0.862240 0.506500i \(-0.169061\pi\)
−0.869762 + 0.493472i \(0.835728\pi\)
\(314\) 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 \(0.978910\pi\)
\(318\) 7.51819 + 11.7508i 0.421599 + 0.658953i
\(319\) 1.83842 3.18424i 0.102932 0.178283i
\(320\) −0.296790 + 0.514055i −0.0165910 + 0.0287365i
\(321\) 32.3712 1.47629i 1.80678 0.0823985i
\(322\) 0 0
\(323\) 15.7195 0.874654
\(324\) −3.01245 + 8.48087i −0.167359 + 0.471159i
\(325\) −11.6870 −0.648276
\(326\) 2.99115 + 5.18082i 0.165664 + 0.286939i
\(327\) −4.96050 + 0.226224i −0.274317 + 0.0125102i
\(328\) 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 \(0.590274\pi\)
\(332\) −7.70175 −0.422688
\(333\) −2.98755 + 0.273062i −0.163717 + 0.0149637i
\(334\) 7.46050 0.408221
\(335\) 0.568000 + 0.983804i 0.0310331 + 0.0537510i
\(336\) 0 0
\(337\) −9.36693 + 16.2240i −0.510249 + 0.883777i 0.489681 + 0.871902i \(0.337113\pi\)
−0.999929 + 0.0118752i \(0.996220\pi\)
\(338\) −3.33842 + 5.78231i −0.181586 + 0.314516i
\(339\) 9.81663 18.9472i 0.533166 1.02907i
\(340\) 0.866926 + 1.50156i 0.0470156 + 0.0814335i
\(341\) 4.66964 0.252875
\(342\) −9.31138 13.1888i −0.503502 0.713169i
\(343\) 0 0
\(344\) 5.58113 + 9.66679i 0.300914 + 0.521199i
\(345\) 2.47150 + 3.86291i 0.133061 + 0.207972i
\(346\) −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 \(0.959797\pi\)
\(348\) −10.7178 + 0.488786i −0.574534 + 0.0262017i
\(349\) 1.89543 + 3.28298i 0.101460 + 0.175734i 0.912286 0.409553i \(-0.134315\pi\)
−0.810826 + 0.585287i \(0.800982\pi\)
\(350\) 0 0
\(351\) 4.92986 12.1005i 0.263137 0.645876i
\(352\) 0.593579 0.0316379
\(353\) −3.41741 5.91913i −0.181890 0.315043i 0.760634 0.649181i \(-0.224888\pi\)
−0.942524 + 0.334138i \(0.891555\pi\)
\(354\) 14.9626 0.682372i 0.795255 0.0362677i
\(355\) 4.27694 7.40789i 0.226997 0.393170i
\(356\) −6.21780 + 10.7695i −0.329543 + 0.570785i
\(357\) 0 0
\(358\) −7.51819 13.0219i −0.397349 0.688228i
\(359\) 12.6447 0.667364 0.333682 0.942686i \(-0.391709\pi\)
0.333682 + 0.942686i \(0.391709\pi\)
\(360\) 0.746304 1.61680i 0.0393337 0.0852131i
\(361\) 9.96070 0.524247
\(362\) −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
\(366\) 5.29679 10.2234i 0.276868 0.534387i
\(367\) −3.27188 5.66707i −0.170791 0.295819i 0.767906 0.640563i \(-0.221299\pi\)
−0.938697 + 0.344744i \(0.887966\pi\)
\(368\) 4.46050 0.232520
\(369\) −0.343677 + 0.744547i −0.0178911 + 0.0387595i
\(370\) 0.593579 0.0308587
\(371\) 0 0
\(372\) −7.34348 11.4778i −0.380742 0.595094i
\(373\) −4.71420 + 8.16524i −0.244092 + 0.422780i −0.961876 0.273486i \(-0.911823\pi\)
0.717784 + 0.696266i \(0.245157\pi\)
\(374\) 0.866926 1.50156i 0.0448277 0.0776438i
\(375\) 9.90856 0.451880i 0.511676 0.0233350i
\(376\) 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
\(381\) −21.3420 + 0.973304i −1.09338 + 0.0498639i
\(382\) 1.99115 3.44877i 0.101876 0.176454i
\(383\) 12.0416 20.8567i 0.615299 1.06573i −0.375033 0.927011i \(-0.622369\pi\)
0.990332 0.138717i \(-0.0442979\pi\)
\(384\) −0.933463 1.45899i −0.0476356 0.0744537i
\(385\) 0 0
\(386\) −6.78074 −0.345130
\(387\) −19.3135 27.3560i −0.981761 1.39058i
\(388\) −11.7339 −0.595696
\(389\) 8.14913 + 14.1147i 0.413177 + 0.715644i 0.995235 0.0975035i \(-0.0310857\pi\)
−0.582058 + 0.813147i \(0.697752\pi\)
\(390\) −1.18929 + 2.29548i −0.0602223 + 0.116236i
\(391\) 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
\(395\) −5.48968 −0.276216
\(396\) −1.77335 + 0.162084i −0.0891140 + 0.00814504i
\(397\) 12.1724 0.610914 0.305457 0.952206i \(-0.401191\pi\)
0.305457 + 0.952206i \(0.401191\pi\)
\(398\) −2.80924 4.86575i −0.140815 0.243898i
\(399\) 0 0
\(400\) 2.32383 4.02499i 0.116192 0.201250i
\(401\) 16.6804 28.8914i 0.832981 1.44277i −0.0626819 0.998034i \(-0.519965\pi\)
0.895663 0.444733i \(-0.146701\pi\)
\(402\) −3.31138 + 0.151016i −0.165157 + 0.00753197i
\(403\) 9.89104 + 17.1318i 0.492708 + 0.853395i
\(404\) −1.62276 −0.0807352
\(405\) −1.78813 + 5.03407i −0.0888529 + 0.250145i
\(406\) 0 0
\(407\) −0.296790 0.514055i −0.0147113 0.0254808i
\(408\) −5.05408 + 0.230492i −0.250214 + 0.0114110i
\(409\) 2.89037 5.00627i 0.142920 0.247544i −0.785675 0.618639i \(-0.787684\pi\)
0.928595 + 0.371095i \(0.121018\pi\)
\(410\) 0.0811263 0.140515i 0.00400654 0.00693954i
\(411\) 2.35399 + 3.67926i 0.116114 + 0.181484i
\(412\) −3.19076 5.52655i −0.157197 0.272274i
\(413\) 0 0
\(414\) −13.3260 + 1.21800i −0.654936 + 0.0598612i
\(415\) −4.57160 −0.224411
\(416\) 1.25729 + 2.17770i 0.0616439 + 0.106770i
\(417\) −3.91528 + 7.55694i −0.191732 + 0.370065i
\(418\) 1.59718 2.76639i 0.0781205 0.135309i
\(419\) 15.4356 26.7352i 0.754078 1.30610i −0.191753 0.981443i \(-0.561417\pi\)
0.945831 0.324659i \(-0.105249\pi\)
\(420\) 0 0
\(421\) −1.86693 3.23361i −0.0909884 0.157597i 0.816939 0.576724i \(-0.195669\pi\)
−0.907927 + 0.419128i \(0.862336\pi\)
\(422\) 19.3245 0.940702
\(423\) −21.0438 29.8068i −1.02318 1.44925i
\(424\) 8.05408 0.391141
\(425\) −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
\(429\) 2.58259 0.117779i 0.124689 0.00568643i
\(430\) 3.31284 + 5.73801i 0.159759 + 0.276711i
\(431\) 28.1957 1.35814 0.679070 0.734074i \(-0.262383\pi\)
0.679070 + 0.734074i \(0.262383\pi\)
\(432\) 3.18716 + 4.10390i 0.153342 + 0.197449i
\(433\) 12.5438 0.602815 0.301407 0.953495i \(-0.402544\pi\)
0.301407 + 0.953495i \(0.402544\pi\)
\(434\) 0 0
\(435\) −6.36186 + 0.290133i −0.305028 + 0.0139108i
\(436\) −1.43346 + 2.48283i −0.0686504 + 0.118906i
\(437\) 12.0021 20.7883i 0.574140 0.994440i
\(438\) 7.38725 + 11.5462i 0.352976 + 0.551697i
\(439\) −13.0203 22.5519i −0.621426 1.07634i −0.989220 0.146434i \(-0.953220\pi\)
0.367794 0.929907i \(-0.380113\pi\)
\(440\) 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 \(0.644137\pi\)
\(444\) −0.796790 + 1.53790i −0.0378140 + 0.0729853i
\(445\) −3.69076 + 6.39258i −0.174959 + 0.303037i
\(446\) −12.6623 + 21.9317i −0.599575 + 1.03849i
\(447\) 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 \(0.395321\pi\)
\(450\) −5.84348 + 12.6594i −0.275464 + 0.596770i
\(451\) −0.162253 −0.00764018
\(452\) −6.16012 10.6696i −0.289748 0.501857i
\(453\) 1.53803 + 2.40392i 0.0722631 + 0.112946i
\(454\) 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 \(0.658221\pi\)
\(458\) 9.29533 0.434342
\(459\) 15.0364 2.06869i 0.701838 0.0965580i
\(460\) 2.64766 0.123448
\(461\) −3.98755 6.90663i −0.185719 0.321674i 0.758100 0.652138i \(-0.226128\pi\)
−0.943818 + 0.330464i \(0.892795\pi\)
\(462\) 0 0
\(463\) −14.3676 + 24.8854i −0.667719 + 1.15652i 0.310821 + 0.950468i \(0.399396\pi\)
−0.978540 + 0.206055i \(0.933937\pi\)
\(464\) −3.09718 + 5.36447i −0.143783 + 0.249039i
\(465\) −4.35894 6.81296i −0.202141 0.315943i
\(466\) −0.0971780 0.168317i −0.00450168 0.00779714i
\(467\) −33.5657 −1.55324 −0.776619 0.629971i \(-0.783067\pi\)
−0.776619 + 0.629971i \(0.783067\pi\)
\(468\) −4.35087 6.16266i −0.201119 0.284869i
\(469\) 0 0
\(470\) 3.60963 + 6.25206i 0.166500 + 0.288386i
\(471\) −5.25943 + 10.1513i −0.242342 + 0.467748i
\(472\) 4.32383 7.48910i 0.199020 0.344714i
\(473\) 3.31284 5.73801i 0.152325 0.263834i
\(474\) 7.36906 14.2231i 0.338472 0.653291i
\(475\) −12.5057 21.6606i −0.573802 0.993855i
\(476\) 0 0
\(477\) −24.0620 + 2.19927i −1.10172 + 0.100698i
\(478\) −13.6549 −0.624559
\(479\) −0.183560 0.317935i −0.00838707 0.0145268i 0.861801 0.507246i \(-0.169336\pi\)
−0.870188 + 0.492719i \(0.836003\pi\)
\(480\) −0.554084 0.866025i −0.0252904 0.0395285i
\(481\) 1.25729 2.17770i 0.0573277 0.0992945i
\(482\) −6.50000 + 11.2583i −0.296067 + 0.512803i
\(483\) 0 0
\(484\) 5.32383 + 9.22115i 0.241992 + 0.419143i
\(485\) −6.96497 −0.316263
\(486\) −10.6424 11.3903i −0.482749 0.516675i
\(487\) 29.9076 1.35524 0.677621 0.735412i \(-0.263011\pi\)
0.677621 + 0.735412i \(0.263011\pi\)
\(488\) −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 −0.871726 0.489994i \(-0.836999\pi\)
0.860210 + 0.509939i \(0.170332\pi\)
\(492\) 0.255158 + 0.398809i 0.0115034 + 0.0179797i
\(493\) 9.04689 + 15.6697i 0.407451 + 0.705726i
\(494\) 13.5323 0.608847
\(495\) −1.05262 + 0.0962098i −0.0473118 + 0.00432431i
\(496\) −7.86693 −0.353235
\(497\) 0 0
\(498\) 6.13667 11.8445i 0.274991 0.530764i
\(499\) 9.50953 16.4710i 0.425705 0.737343i −0.570781 0.821102i \(-0.693359\pi\)
0.996486 + 0.0837597i \(0.0266928\pi\)
\(500\) 2.86333 4.95943i 0.128052 0.221792i
\(501\) −5.94445 + 11.4735i −0.265579 + 0.512598i
\(502\) −9.77188 16.9254i −0.436141 0.755418i
\(503\) −37.7807 −1.68456 −0.842280 0.539040i \(-0.818787\pi\)
−0.842280 + 0.539040i \(0.818787\pi\)
\(504\) 0 0
\(505\) −0.963235 −0.0428634
\(506\) −1.32383 2.29294i −0.0588515 0.101934i
\(507\) −6.23258 9.74143i −0.276799 0.432632i
\(508\) −6.16731 + 10.6821i −0.273630 + 0.473942i
\(509\) 5.60817 9.71363i 0.248578 0.430549i −0.714554 0.699581i \(-0.753370\pi\)
0.963131 + 0.269031i \(0.0867035\pi\)
\(510\) −3.00000 + 0.136815i −0.132842 + 0.00605828i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 27.7022 3.81124i 1.22308 0.168270i
\(514\) −8.32743 −0.367307
\(515\) −1.89397 3.28045i −0.0834582 0.144554i
\(516\) −19.3135 + 0.880794i −0.850230 + 0.0387748i
\(517\) 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
\(521\) 27.4720 1.20357 0.601785 0.798658i \(-0.294457\pi\)
0.601785 + 0.798658i \(0.294457\pi\)
\(522\) 7.78813 16.8723i 0.340877 0.738482i
\(523\) −22.1838 −0.970032 −0.485016 0.874505i \(-0.661186\pi\)
−0.485016 + 0.874505i \(0.661186\pi\)
\(524\) 0.593579 + 1.02811i 0.0259306 + 0.0449132i
\(525\) 0 0
\(526\) −8.54523 + 14.8008i −0.372590 + 0.645344i
\(527\) −11.4897 + 19.9007i −0.500498 + 0.866889i
\(528\) −0.472958 + 0.912864i −0.0205829 + 0.0397273i
\(529\) 1.55195 + 2.68805i 0.0674760 + 0.116872i
\(530\) 4.78074 0.207662
\(531\) −10.8727 + 23.5547i −0.471833 + 1.02219i
\(532\) 0 0
\(533\) −0.343677 0.595265i −0.0148863 0.0257838i
\(534\) −11.6082 18.1434i −0.502335 0.785141i
\(535\) 5.55262 9.61742i 0.240061 0.415797i
\(536\) −0.956906 + 1.65741i −0.0413321 + 0.0715892i
\(537\) 26.0167 1.18649i 1.12270 0.0512010i
\(538\) 5.00720 + 8.67272i 0.215876 + 0.373908i
\(539\) 0 0
\(540\) 1.89183 + 2.43599i 0.0814115 + 0.104828i
\(541\) −29.8492 −1.28332 −0.641659 0.766990i \(-0.721754\pi\)
−0.641659 + 0.766990i \(0.721754\pi\)
\(542\) −5.10457 8.84137i −0.219260 0.379770i
\(543\) 0.149126 0.00680090i 0.00639961 0.000291855i
\(544\) −1.46050 + 2.52967i −0.0626186 + 0.108459i
\(545\) −0.850874 + 1.47376i −0.0364474 + 0.0631288i
\(546\) 0 0
\(547\) 8.84348 + 15.3174i 0.378120 + 0.654923i 0.990789 0.135417i \(-0.0432373\pi\)
−0.612669 + 0.790340i \(0.709904\pi\)
\(548\) 2.52179 0.107725
\(549\) 11.5021 + 16.2918i 0.490899 + 0.695318i
\(550\) −2.75876 −0.117634
\(551\) 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
\(555\) −0.472958 + 0.912864i −0.0200759 + 0.0387489i
\(556\) 2.45691 + 4.25549i 0.104196 + 0.180473i
\(557\) −30.1301 −1.27666 −0.638328 0.769765i \(-0.720374\pi\)
−0.638328 + 0.769765i \(0.720374\pi\)
\(558\) 23.5028 2.14816i 0.994953 0.0909389i
\(559\) 28.0685 1.18717
\(560\) 0 0
\(561\) 1.61849 + 2.52967i 0.0683325 + 0.106803i
\(562\) 6.40136 11.0875i 0.270025 0.467697i
\(563\) −2.04883 + 3.54867i −0.0863478 + 0.149559i −0.905965 0.423353i \(-0.860853\pi\)
0.819617 + 0.572912i \(0.194186\pi\)
\(564\) −21.0438 + 0.959702i −0.886102 + 0.0404107i
\(565\) −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 \(0.875067\pi\)
\(570\) −5.52704 + 0.252061i −0.231502 + 0.0105577i
\(571\) −17.8011 + 30.8323i −0.744951 + 1.29029i 0.205266 + 0.978706i \(0.434194\pi\)
−0.950218 + 0.311587i \(0.899139\pi\)
\(572\) 0.746304 1.29264i 0.0312045 0.0540479i
\(573\) 3.71732 + 5.81012i 0.155293 + 0.242721i
\(574\) 0 0
\(575\) −20.7309 −0.864539
\(576\) 2.98755 0.273062i 0.124481 0.0113776i
\(577\) −46.2776 −1.92656 −0.963281 0.268494i \(-0.913474\pi\)
−0.963281 + 0.268494i \(0.913474\pi\)
\(578\) −4.23385 7.33325i −0.176105 0.305023i
\(579\) 5.40282 10.4281i 0.224534 0.433376i
\(580\) −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
\(584\) 7.91381 0.327476
\(585\) −2.58259 3.65802i −0.106777 0.151241i
\(586\) −20.7778 −0.858324
\(587\) 1.13161 + 1.96001i 0.0467066 + 0.0808982i 0.888434 0.459005i \(-0.151794\pi\)
−0.841727 + 0.539903i \(0.818461\pi\)
\(588\) 0 0
\(589\) −21.1680 + 36.6640i −0.872212 + 1.51072i
\(590\) 2.56654 4.44537i 0.105663 0.183013i
\(591\) −19.1337 + 0.872595i −0.787057 + 0.0358938i
\(592\) 0.500000 + 0.866025i 0.0205499 + 0.0355934i
\(593\) −46.1957 −1.89703 −0.948515 0.316732i \(-0.897414\pi\)
−0.948515 + 0.316732i \(0.897414\pi\)
\(594\) 1.16372 2.85637i 0.0477478 0.117198i
\(595\) 0 0
\(596\) −9.02558 15.6328i −0.369702 0.640343i
\(597\) 9.72140 0.443345i 0.397870 0.0181449i
\(598\) 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 \(0.0552842\pi\)
\(600\) 4.33842 + 6.78089i 0.177115 + 0.276829i
\(601\) −5.69961 9.87202i −0.232492 0.402688i 0.726049 0.687643i \(-0.241355\pi\)
−0.958541 + 0.284955i \(0.908021\pi\)
\(602\) 0 0
\(603\) 2.40623 5.21289i 0.0979891 0.212285i
\(604\) 1.64766 0.0670425
\(605\) 3.16012 + 5.47348i 0.128477 + 0.222529i
\(606\) 1.29300 2.49563i 0.0525244 0.101378i
\(607\) 7.21420 12.4954i 0.292815 0.507171i −0.681659 0.731670i \(-0.738741\pi\)
0.974474 + 0.224499i \(0.0720745\pi\)
\(608\) −2.69076 + 4.66053i −0.109125 + 0.189009i
\(609\) 0 0
\(610\) −1.97296 3.41726i −0.0798827 0.138361i
\(611\) 30.5831 1.23726
\(612\) 3.67257 7.95631i 0.148455 0.321615i
\(613\) −24.4107 −0.985939 −0.492969 0.870047i \(-0.664089\pi\)
−0.492969 + 0.870047i \(0.664089\pi\)
\(614\) −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 0.343710 0.939076i \(-0.388316\pi\)
0.641408 0.767200i \(-0.278350\pi\)
\(618\) 11.0416 0.503554i 0.444160 0.0202559i
\(619\) 22.3296 + 38.6759i 0.897501 + 1.55452i 0.830678 + 0.556753i \(0.187953\pi\)
0.0668227 + 0.997765i \(0.478714\pi\)
\(620\) −4.66964 −0.187537
\(621\) 8.74484 21.4644i 0.350918 0.861339i
\(622\) 6.51459 0.261211
\(623\) 0 0
\(624\) −4.35087 + 0.198422i −0.174174 + 0.00794323i
\(625\) −9.91955 + 17.1812i −0.396782 + 0.687246i
\(626\) 0.133074 0.230492i 0.00531873 0.00921230i
\(627\) 2.98181 + 4.66053i 0.119082 + 0.186124i
\(628\) 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
\(633\) −15.3976 + 29.7191i −0.611998 + 1.18123i
\(634\) 7.86186 13.6171i 0.312235 0.540806i
\(635\) −3.66079 + 6.34067i −0.145274 + 0.251622i
\(636\) −6.41741 + 12.3863i −0.254467 + 0.491151i
\(637\) 0 0
\(638\) 3.67684 0.145568
\(639\) −43.0526 + 3.93502i −1.70314 + 0.155667i
\(640\) −0.593579 −0.0234633
\(641\) −15.3940 26.6631i −0.608025 1.05313i −0.991566 0.129606i \(-0.958629\pi\)
0.383540 0.923524i \(-0.374705\pi\)
\(642\) 17.4641 + 27.2961i 0.689253 + 1.07729i
\(643\) −13.7345 + 23.7889i −0.541637 + 0.938142i 0.457174 + 0.889378i \(0.348862\pi\)
−0.998810 + 0.0487649i \(0.984471\pi\)
\(644\) 0 0
\(645\) −11.4641 + 0.522821i −0.451399 + 0.0205861i
\(646\) 7.85973 + 13.6134i 0.309237 + 0.535614i
\(647\) 13.2704 0.521714 0.260857 0.965377i \(-0.415995\pi\)
0.260857 + 0.965377i \(0.415995\pi\)
\(648\) −8.85087 + 1.63157i −0.347695 + 0.0640943i
\(649\) −5.13307 −0.201491
\(650\) −5.84348 10.1212i −0.229200 0.396986i
\(651\) 0 0
\(652\) −2.99115 + 5.18082i −0.117142 + 0.202896i
\(653\) 8.57081 14.8451i 0.335402 0.580933i −0.648160 0.761504i \(-0.724461\pi\)
0.983562 + 0.180571i \(0.0577946\pi\)
\(654\) −2.67617 4.18281i −0.104646 0.163561i
\(655\) 0.352336 + 0.610265i 0.0137669 + 0.0238450i
\(656\) 0.273346 0.0106724
\(657\) −23.6429 + 2.16096i −0.922397 + 0.0843072i
\(658\) 0 0
\(659\) 4.26089 + 7.38008i 0.165981 + 0.287487i 0.937003 0.349321i \(-0.113588\pi\)
−0.771022 + 0.636808i \(0.780254\pi\)
\(660\) −0.280738 + 0.541857i −0.0109277 + 0.0210918i
\(661\) −17.1680 + 29.7358i −0.667757 + 1.15659i 0.310773 + 0.950484i \(0.399412\pi\)
−0.978530 + 0.206105i \(0.933921\pi\)
\(662\) −12.5811 + 21.7912i −0.488979 + 0.846937i
\(663\) −5.85253 + 11.2961i −0.227293 + 0.438703i
\(664\) −3.85087 6.66991i −0.149443 0.258843i
\(665\) 0 0
\(666\) −1.73025 2.45076i −0.0670459 0.0949650i
\(667\) 27.6300 1.06984
\(668\) 3.73025 + 6.46099i 0.144328 + 0.249983i
\(669\) −23.6395 36.9482i −0.913955 1.42850i
\(670\) −0.568000 + 0.983804i −0.0219437 + 0.0380077i
\(671\) −1.97296 + 3.41726i −0.0761652 + 0.131922i
\(672\) 0 0
\(673\) −7.70155 13.3395i −0.296873 0.514199i 0.678546 0.734558i \(-0.262610\pi\)
−0.975419 + 0.220359i \(0.929277\pi\)
\(674\) −18.7339 −0.721601
\(675\) −14.8128 19.0736i −0.570147 0.734142i
\(676\) −6.67684 −0.256802
\(677\) 3.69076 + 6.39258i 0.141847 + 0.245687i 0.928192 0.372101i \(-0.121362\pi\)
−0.786345 + 0.617788i \(0.788029\pi\)
\(678\) 21.3171 0.972168i 0.818679 0.0373359i
\(679\) 0 0
\(680\) −0.866926 + 1.50156i −0.0332451 + 0.0575822i
\(681\) 4.49660 + 7.02811i 0.172310 + 0.269318i
\(682\) 2.33482 + 4.04403i 0.0894050 + 0.154854i
\(683\) −9.59785 −0.367252 −0.183626 0.982996i \(-0.558783\pi\)
−0.183626 + 0.982996i \(0.558783\pi\)
\(684\) 6.76615 14.6583i 0.258710 0.560474i
\(685\) 1.49688 0.0571929
\(686\) 0 0
\(687\) −7.40642 + 14.2953i −0.282573 + 0.545398i
\(688\) −5.58113 + 9.66679i −0.212778 + 0.368543i
\(689\) 10.1264 17.5394i 0.385783 0.668197i
\(690\) −2.10963 + 4.07183i −0.0803123 + 0.155012i
\(691\) 7.07227 + 12.2495i 0.269042 + 0.465994i 0.968615 0.248567i \(-0.0799597\pi\)
−0.699573 + 0.714561i \(0.746626\pi\)
\(692\) −25.6591 −0.975414
\(693\) 0 0
\(694\) −22.5438 −0.855750
\(695\) 1.45837 + 2.52597i 0.0553191 + 0.0958155i
\(696\) −5.78220 9.03749i −0.219174 0.342565i
\(697\) 0.399223 0.691475i 0.0151217 0.0261915i
\(698\) −1.89543 + 3.28298i −0.0717431 + 0.124263i
\(699\) 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 \(0.250578\pi\)
\(702\) 12.9443 1.78085i 0.488550 0.0672140i
\(703\) 5.38151 0.202968
\(704\) 0.296790 + 0.514055i 0.0111857 + 0.0193742i
\(705\) −12.4911 + 0.569659i −0.470444 + 0.0214546i
\(706\) 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 \(0.770240\pi\)
\(710\) 8.55389 0.321022
\(711\) 16.0021 + 22.6657i 0.600127 + 0.850031i
\(712\) −12.4356 −0.466044
\(713\) 17.5452 + 30.3892i 0.657074 + 1.13809i
\(714\) 0 0
\(715\) 0.442991 0.767282i 0.0165669 0.0286947i
\(716\) 7.51819 13.0219i 0.280968 0.486651i
\(717\) 10.8801 20.9998i 0.406323 0.784251i
\(718\) 6.32237 + 10.9507i 0.235949 + 0.408675i
\(719\) −2.23990 −0.0835340 −0.0417670 0.999127i \(-0.513299\pi\)
−0.0417670 + 0.999127i \(0.513299\pi\)
\(720\) 1.77335 0.162084i 0.0660887 0.00604052i
\(721\) 0 0
\(722\) 4.98035 + 8.62622i 0.185349 + 0.321035i
\(723\) −12.1350 18.9668i −0.451306 0.705385i
\(724\) 0.0430937 0.0746406i 0.00160157 0.00277399i
\(725\) 14.3946 24.9322i 0.534604 0.925961i
\(726\) −18.4231 + 0.840188i −0.683747 + 0.0311823i
\(727\) 0.185023 + 0.320469i 0.00686211 + 0.0118855i 0.869436 0.494045i \(-0.164482\pi\)
−0.862574 + 0.505931i \(0.831149\pi\)
\(728\) 0 0
\(729\) 25.9969 7.29124i 0.962847 0.270046i
\(730\) 4.69748 0.173861
\(731\) 16.3025 + 28.2368i 0.602971 + 1.04438i
\(732\) 11.5021 0.524555i 0.425131 0.0193881i
\(733\) −7.00953 + 12.1409i −0.258903 + 0.448433i −0.965948 0.258735i \(-0.916694\pi\)
0.707045 + 0.707168i \(0.250028\pi\)
\(734\) 3.27188 5.66707i 0.120767 0.209175i
\(735\) 0 0
\(736\) 2.23025 + 3.86291i 0.0822082 + 0.142389i
\(737\) 1.13600 0.0418451
\(738\) −0.816635 + 0.0746406i −0.0300607 + 0.00274756i
\(739\) −26.7745 −0.984916 −0.492458 0.870336i \(-0.663901\pi\)
−0.492458 + 0.870336i \(0.663901\pi\)
\(740\) 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 −0.943625 0.331015i \(-0.892609\pi\)
0.758480 + 0.651696i \(0.225942\pi\)
\(744\) 6.26829 12.0985i 0.229806 0.443553i
\(745\) −5.35740 9.27928i −0.196280 0.339967i
\(746\) −9.42840 −0.345198
\(747\) 13.3260 + 18.8751i 0.487572 + 0.690605i
\(748\) 1.73385 0.0633959
\(749\) 0 0
\(750\) 5.34562 + 8.35512i 0.195194 + 0.305086i
\(751\) −5.75729 + 9.97193i −0.210087 + 0.363881i −0.951741 0.306901i \(-0.900708\pi\)
0.741655 + 0.670782i \(0.234041\pi\)
\(752\) −6.08113 + 10.5328i −0.221756 + 0.384092i
\(753\) 33.8157 1.54216i 1.23231 0.0561996i
\(754\) 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
\(759\) 4.58113 0.208922i 0.166284 0.00758341i
\(760\) −1.59718 + 2.76639i −0.0579357 + 0.100348i
\(761\) 0.850874 1.47376i 0.0308442 0.0534236i −0.850191 0.526474i \(-0.823514\pi\)
0.881035 + 0.473050i \(0.156847\pi\)
\(762\) −11.5139 17.9961i −0.417105 0.651929i
\(763\) 0 0
\(764\) 3.98229 0.144074
\(765\) 2.17996 4.72270i 0.0788167 0.170750i
\(766\) 24.0833 0.870164
\(767\) −10.8727 18.8320i −0.392589 0.679984i
\(768\) 0.796790 1.53790i 0.0287517 0.0554941i
\(769\) 24.1211 41.7790i 0.869829 1.50659i 0.00765823 0.999971i \(-0.497562\pi\)
0.862171 0.506618i \(-0.169104\pi\)
\(770\) 0 0
\(771\) 6.63521 12.8067i 0.238961 0.461223i
\(772\) −3.39037 5.87229i −0.122022 0.211348i
\(773\) −6.20487 −0.223174 &minus