Properties

Label 363.2.e.n.124.1
Level $363$
Weight $2$
Character 363.124
Analytic conductor $2.899$
Analytic rank $0$
Dimension $16$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,2,Mod(124,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.124");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.e (of order \(5\), degree \(4\), 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: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: 16.0.22502537891856000000000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 7x^{14} + 45x^{12} + 287x^{10} + 1829x^{8} + 1148x^{6} + 720x^{4} + 448x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 124.1
Root \(-2.04223 - 1.48377i\) of defining polynomial
Character \(\chi\) \(=\) 363.124
Dual form 363.2.e.n.202.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.04223 + 1.48377i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.35111 - 4.15829i) q^{4} +(1.91922 + 1.39439i) q^{5} +(-2.04223 - 1.48377i) q^{6} +(0.244830 - 0.753510i) q^{7} +(1.85053 + 5.69534i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-2.04223 + 1.48377i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.35111 - 4.15829i) q^{4} +(1.91922 + 1.39439i) q^{5} +(-2.04223 - 1.48377i) q^{6} +(0.244830 - 0.753510i) q^{7} +(1.85053 + 5.69534i) q^{8} +(-0.809017 + 0.587785i) q^{9} -5.98844 q^{10} +4.37228 q^{12} +(3.32418 - 2.41516i) q^{13} +(0.618034 + 1.90211i) q^{14} +(-0.733075 + 2.25617i) q^{15} +(-5.15528 - 3.74553i) q^{16} +(4.84475 + 3.51992i) q^{17} +(0.780063 - 2.40079i) q^{18} +(1.31530 + 4.04807i) q^{19} +(8.39135 - 6.09667i) q^{20} +0.792287 q^{21} +2.00000 q^{23} +(-4.84475 + 3.51992i) q^{24} +(0.193976 + 0.596996i) q^{25} +(-3.20521 + 9.86463i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.80252 - 2.03615i) q^{28} +(-0.780063 + 2.40079i) q^{29} +(-1.85053 - 5.69534i) q^{30} +(-5.96430 + 4.33332i) q^{31} +4.10891 q^{32} -15.1168 q^{34} +(1.52057 - 1.10476i) q^{35} +(1.35111 + 4.15829i) q^{36} +(1.54508 - 4.75528i) q^{37} +(-8.69253 - 6.31550i) q^{38} +(3.32418 + 2.41516i) q^{39} +(-4.38998 + 13.5110i) q^{40} +(-1.75938 - 5.41483i) q^{41} +(-1.61803 + 1.17557i) q^{42} -6.63325 q^{43} -2.37228 q^{45} +(-4.08446 + 2.96754i) q^{46} +(-0.387951 - 1.19399i) q^{47} +(1.96914 - 6.06040i) q^{48} +(5.15528 + 3.74553i) q^{49} +(-1.28195 - 0.931389i) q^{50} +(-1.85053 + 5.69534i) q^{51} +(-5.55159 - 17.0860i) q^{52} +(-10.6117 + 7.70989i) q^{53} +2.52434 q^{54} +4.74456 q^{56} +(-3.44349 + 2.50184i) q^{57} +(-1.96914 - 6.06040i) q^{58} +(-1.85410 + 5.70634i) q^{59} +(8.39135 + 6.09667i) q^{60} +(2.16154 + 1.57045i) q^{61} +(5.75085 - 17.6993i) q^{62} +(0.244830 + 0.753510i) q^{63} +(1.91922 - 1.39439i) q^{64} +9.74749 q^{65} +16.1168 q^{67} +(21.1826 - 15.3901i) q^{68} +(0.618034 + 1.90211i) q^{69} +(-1.46615 + 4.51235i) q^{70} +(-0.602364 - 0.437643i) q^{71} +(-4.84475 - 3.51992i) q^{72} +(2.29462 - 7.06210i) q^{73} +(3.90032 + 12.0039i) q^{74} +(-0.507835 + 0.368964i) q^{75} +18.6101 q^{76} -10.3723 q^{78} +(-4.72544 + 3.43323i) q^{79} +(-4.67136 - 14.3770i) q^{80} +(0.309017 - 0.951057i) q^{81} +(11.6274 + 8.44782i) q^{82} +(-6.88698 - 5.00368i) q^{83} +(1.07047 - 3.29456i) q^{84} +(4.38998 + 13.5110i) q^{85} +(13.5466 - 9.84221i) q^{86} -2.52434 q^{87} -6.37228 q^{89} +(4.84475 - 3.51992i) q^{90} +(-1.00599 - 3.09610i) q^{91} +(2.70222 - 8.31657i) q^{92} +(-5.96430 - 4.33332i) q^{93} +(2.56389 + 1.86278i) q^{94} +(-3.12025 + 9.60315i) q^{95} +(1.26972 + 3.90781i) q^{96} +(10.1039 - 7.34092i) q^{97} -16.0858 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9} + 24 q^{12} - 8 q^{14} - 2 q^{15} - 14 q^{16} + 30 q^{20} + 32 q^{23} - 14 q^{25} + 30 q^{26} - 4 q^{27} - 18 q^{31} - 104 q^{34} - 6 q^{36} - 20 q^{37} - 20 q^{38} - 8 q^{42} + 8 q^{45} + 28 q^{47} - 14 q^{48} + 14 q^{49} - 18 q^{53} - 16 q^{56} + 14 q^{58} + 24 q^{59} + 30 q^{60} - 2 q^{64} + 120 q^{67} - 8 q^{69} - 4 q^{70} + 20 q^{71} - 14 q^{75} - 120 q^{78} + 26 q^{80} - 4 q^{81} + 46 q^{82} + 44 q^{86} - 56 q^{89} + 36 q^{91} - 12 q^{92} - 18 q^{93} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.04223 + 1.48377i −1.44408 + 1.04918i −0.456905 + 0.889515i \(0.651042\pi\)
−0.987171 + 0.159667i \(0.948958\pi\)
\(3\) 0.309017 + 0.951057i 0.178411 + 0.549093i
\(4\) 1.35111 4.15829i 0.675555 2.07914i
\(5\) 1.91922 + 1.39439i 0.858299 + 0.623591i 0.927422 0.374017i \(-0.122020\pi\)
−0.0691223 + 0.997608i \(0.522020\pi\)
\(6\) −2.04223 1.48377i −0.833738 0.605746i
\(7\) 0.244830 0.753510i 0.0925371 0.284800i −0.894067 0.447933i \(-0.852160\pi\)
0.986604 + 0.163134i \(0.0521601\pi\)
\(8\) 1.85053 + 5.69534i 0.654261 + 2.01361i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) −5.98844 −1.89371
\(11\) 0 0
\(12\) 4.37228 1.26217
\(13\) 3.32418 2.41516i 0.921961 0.669844i −0.0220500 0.999757i \(-0.507019\pi\)
0.944011 + 0.329913i \(0.107019\pi\)
\(14\) 0.618034 + 1.90211i 0.165177 + 0.508361i
\(15\) −0.733075 + 2.25617i −0.189279 + 0.582542i
\(16\) −5.15528 3.74553i −1.28882 0.936383i
\(17\) 4.84475 + 3.51992i 1.17502 + 0.853705i 0.991602 0.129329i \(-0.0412823\pi\)
0.183423 + 0.983034i \(0.441282\pi\)
\(18\) 0.780063 2.40079i 0.183863 0.565871i
\(19\) 1.31530 + 4.04807i 0.301750 + 0.928690i 0.980870 + 0.194663i \(0.0623614\pi\)
−0.679120 + 0.734027i \(0.737639\pi\)
\(20\) 8.39135 6.09667i 1.87636 1.36326i
\(21\) 0.792287 0.172891
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) −4.84475 + 3.51992i −0.988930 + 0.718500i
\(25\) 0.193976 + 0.596996i 0.0387951 + 0.119399i
\(26\) −3.20521 + 9.86463i −0.628594 + 1.93461i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) −2.80252 2.03615i −0.529626 0.384796i
\(29\) −0.780063 + 2.40079i −0.144854 + 0.445815i −0.996992 0.0775019i \(-0.975306\pi\)
0.852138 + 0.523317i \(0.175306\pi\)
\(30\) −1.85053 5.69534i −0.337859 1.03982i
\(31\) −5.96430 + 4.33332i −1.07122 + 0.778287i −0.976131 0.217182i \(-0.930314\pi\)
−0.0950889 + 0.995469i \(0.530314\pi\)
\(32\) 4.10891 0.726360
\(33\) 0 0
\(34\) −15.1168 −2.59252
\(35\) 1.52057 1.10476i 0.257023 0.186738i
\(36\) 1.35111 + 4.15829i 0.225185 + 0.693048i
\(37\) 1.54508 4.75528i 0.254010 0.781764i −0.740013 0.672593i \(-0.765181\pi\)
0.994023 0.109171i \(-0.0348195\pi\)
\(38\) −8.69253 6.31550i −1.41012 1.02451i
\(39\) 3.32418 + 2.41516i 0.532295 + 0.386735i
\(40\) −4.38998 + 13.5110i −0.694116 + 2.13627i
\(41\) −1.75938 5.41483i −0.274770 0.845654i −0.989280 0.146029i \(-0.953351\pi\)
0.714511 0.699625i \(-0.246649\pi\)
\(42\) −1.61803 + 1.17557i −0.249668 + 0.181394i
\(43\) −6.63325 −1.01156 −0.505781 0.862662i \(-0.668795\pi\)
−0.505781 + 0.862662i \(0.668795\pi\)
\(44\) 0 0
\(45\) −2.37228 −0.353639
\(46\) −4.08446 + 2.96754i −0.602221 + 0.437539i
\(47\) −0.387951 1.19399i −0.0565885 0.174162i 0.918767 0.394800i \(-0.129186\pi\)
−0.975356 + 0.220638i \(0.929186\pi\)
\(48\) 1.96914 6.06040i 0.284221 0.874743i
\(49\) 5.15528 + 3.74553i 0.736469 + 0.535076i
\(50\) −1.28195 0.931389i −0.181295 0.131718i
\(51\) −1.85053 + 5.69534i −0.259126 + 0.797508i
\(52\) −5.55159 17.0860i −0.769867 2.36941i
\(53\) −10.6117 + 7.70989i −1.45764 + 1.05903i −0.473665 + 0.880705i \(0.657069\pi\)
−0.983971 + 0.178329i \(0.942931\pi\)
\(54\) 2.52434 0.343519
\(55\) 0 0
\(56\) 4.74456 0.634019
\(57\) −3.44349 + 2.50184i −0.456101 + 0.331377i
\(58\) −1.96914 6.06040i −0.258561 0.795769i
\(59\) −1.85410 + 5.70634i −0.241384 + 0.742902i 0.754827 + 0.655924i \(0.227721\pi\)
−0.996210 + 0.0869778i \(0.972279\pi\)
\(60\) 8.39135 + 6.09667i 1.08332 + 0.787077i
\(61\) 2.16154 + 1.57045i 0.276757 + 0.201076i 0.717502 0.696557i \(-0.245286\pi\)
−0.440745 + 0.897633i \(0.645286\pi\)
\(62\) 5.75085 17.6993i 0.730358 2.24781i
\(63\) 0.244830 + 0.753510i 0.0308457 + 0.0949333i
\(64\) 1.91922 1.39439i 0.239902 0.174299i
\(65\) 9.74749 1.20903
\(66\) 0 0
\(67\) 16.1168 1.96899 0.984493 0.175424i \(-0.0561297\pi\)
0.984493 + 0.175424i \(0.0561297\pi\)
\(68\) 21.1826 15.3901i 2.56877 1.86632i
\(69\) 0.618034 + 1.90211i 0.0744025 + 0.228988i
\(70\) −1.46615 + 4.51235i −0.175239 + 0.539329i
\(71\) −0.602364 0.437643i −0.0714874 0.0519387i 0.551468 0.834196i \(-0.314068\pi\)
−0.622955 + 0.782258i \(0.714068\pi\)
\(72\) −4.84475 3.51992i −0.570959 0.414826i
\(73\) 2.29462 7.06210i 0.268565 0.826557i −0.722286 0.691594i \(-0.756909\pi\)
0.990851 0.134962i \(-0.0430914\pi\)
\(74\) 3.90032 + 12.0039i 0.453403 + 1.39543i
\(75\) −0.507835 + 0.368964i −0.0586397 + 0.0426043i
\(76\) 18.6101 2.13473
\(77\) 0 0
\(78\) −10.3723 −1.17443
\(79\) −4.72544 + 3.43323i −0.531653 + 0.386269i −0.820976 0.570963i \(-0.806570\pi\)
0.289323 + 0.957232i \(0.406570\pi\)
\(80\) −4.67136 14.3770i −0.522274 1.60739i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 11.6274 + 8.44782i 1.28403 + 0.932905i
\(83\) −6.88698 5.00368i −0.755944 0.549226i 0.141719 0.989907i \(-0.454737\pi\)
−0.897664 + 0.440681i \(0.854737\pi\)
\(84\) 1.07047 3.29456i 0.116797 0.359466i
\(85\) 4.38998 + 13.5110i 0.476160 + 1.46547i
\(86\) 13.5466 9.84221i 1.46077 1.06131i
\(87\) −2.52434 −0.270637
\(88\) 0 0
\(89\) −6.37228 −0.675460 −0.337730 0.941243i \(-0.609659\pi\)
−0.337730 + 0.941243i \(0.609659\pi\)
\(90\) 4.84475 3.51992i 0.510681 0.371032i
\(91\) −1.00599 3.09610i −0.105456 0.324560i
\(92\) 2.70222 8.31657i 0.281726 0.867063i
\(93\) −5.96430 4.33332i −0.618469 0.449344i
\(94\) 2.56389 + 1.86278i 0.264446 + 0.192131i
\(95\) −3.12025 + 9.60315i −0.320131 + 0.985263i
\(96\) 1.26972 + 3.90781i 0.129591 + 0.398839i
\(97\) 10.1039 7.34092i 1.02590 0.745358i 0.0584137 0.998292i \(-0.481396\pi\)
0.967483 + 0.252935i \(0.0813957\pi\)
\(98\) −16.0858 −1.62491
\(99\) 0 0
\(100\) 2.74456 0.274456
\(101\) 4.32309 3.14091i 0.430163 0.312532i −0.351551 0.936169i \(-0.614346\pi\)
0.781714 + 0.623637i \(0.214346\pi\)
\(102\) −4.67136 14.3770i −0.462534 1.42353i
\(103\) 2.50824 7.71958i 0.247144 0.760633i −0.748132 0.663550i \(-0.769049\pi\)
0.995276 0.0970824i \(-0.0309511\pi\)
\(104\) 19.9066 + 14.4630i 1.95201 + 1.41822i
\(105\) 1.52057 + 1.10476i 0.148392 + 0.107813i
\(106\) 10.2320 31.4908i 0.993817 3.05865i
\(107\) −0.0911457 0.280518i −0.00881139 0.0271187i 0.946554 0.322545i \(-0.104538\pi\)
−0.955366 + 0.295426i \(0.904538\pi\)
\(108\) −3.53725 + 2.56996i −0.340372 + 0.247295i
\(109\) 9.94987 0.953025 0.476513 0.879168i \(-0.341901\pi\)
0.476513 + 0.879168i \(0.341901\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) −4.08446 + 2.96754i −0.385946 + 0.280406i
\(113\) −1.35111 4.15829i −0.127102 0.391179i 0.867176 0.498001i \(-0.165932\pi\)
−0.994278 + 0.106822i \(0.965932\pi\)
\(114\) 3.32025 10.2187i 0.310970 0.957068i
\(115\) 3.83843 + 2.78878i 0.357936 + 0.260055i
\(116\) 8.92921 + 6.48745i 0.829057 + 0.602345i
\(117\) −1.26972 + 3.90781i −0.117386 + 0.361277i
\(118\) −4.68038 14.4047i −0.430864 1.32606i
\(119\) 3.83843 2.78878i 0.351868 0.255647i
\(120\) −14.2063 −1.29685
\(121\) 0 0
\(122\) −6.74456 −0.610624
\(123\) 4.60613 3.34655i 0.415320 0.301748i
\(124\) 9.96076 + 30.6561i 0.894502 + 2.75300i
\(125\) 3.20521 9.86463i 0.286683 0.882319i
\(126\) −1.61803 1.17557i −0.144146 0.104728i
\(127\) −15.9355 11.5778i −1.41405 1.02737i −0.992718 0.120458i \(-0.961564\pi\)
−0.421329 0.906908i \(-0.638436\pi\)
\(128\) −4.38998 + 13.5110i −0.388023 + 1.19421i
\(129\) −2.04979 6.30860i −0.180474 0.555441i
\(130\) −19.9066 + 14.4630i −1.74593 + 1.26849i
\(131\) 6.63325 0.579550 0.289775 0.957095i \(-0.406420\pi\)
0.289775 + 0.957095i \(0.406420\pi\)
\(132\) 0 0
\(133\) 3.37228 0.292414
\(134\) −32.9143 + 23.9137i −2.84337 + 2.06583i
\(135\) −0.733075 2.25617i −0.0630931 0.194181i
\(136\) −11.0818 + 34.1062i −0.950255 + 2.92458i
\(137\) −0.602364 0.437643i −0.0514634 0.0373904i 0.561756 0.827303i \(-0.310126\pi\)
−0.613220 + 0.789912i \(0.710126\pi\)
\(138\) −4.08446 2.96754i −0.347693 0.252614i
\(139\) −3.21140 + 9.88367i −0.272387 + 0.838322i 0.717512 + 0.696547i \(0.245281\pi\)
−0.989899 + 0.141775i \(0.954719\pi\)
\(140\) −2.53945 7.81561i −0.214622 0.660540i
\(141\) 1.01567 0.737928i 0.0855349 0.0621447i
\(142\) 1.87953 0.157726
\(143\) 0 0
\(144\) 6.37228 0.531023
\(145\) −4.84475 + 3.51992i −0.402335 + 0.292313i
\(146\) 5.79239 + 17.8271i 0.479381 + 1.47538i
\(147\) −1.96914 + 6.06040i −0.162412 + 0.499853i
\(148\) −17.6862 12.8498i −1.45380 1.05625i
\(149\) 4.84475 + 3.51992i 0.396897 + 0.288363i 0.768276 0.640119i \(-0.221115\pi\)
−0.371379 + 0.928481i \(0.621115\pi\)
\(150\) 0.489660 1.50702i 0.0399806 0.123048i
\(151\) 0.671952 + 2.06805i 0.0546827 + 0.168296i 0.974668 0.223657i \(-0.0717996\pi\)
−0.919985 + 0.391953i \(0.871800\pi\)
\(152\) −20.6211 + 14.9821i −1.67259 + 1.21521i
\(153\) −5.98844 −0.484137
\(154\) 0 0
\(155\) −17.4891 −1.40476
\(156\) 14.5342 10.5597i 1.16367 0.845457i
\(157\) 2.04808 + 6.30334i 0.163454 + 0.503061i 0.998919 0.0464833i \(-0.0148014\pi\)
−0.835465 + 0.549544i \(0.814801\pi\)
\(158\) 4.55632 14.0229i 0.362481 1.11560i
\(159\) −10.6117 7.70989i −0.841566 0.611434i
\(160\) 7.88589 + 5.72943i 0.623434 + 0.452951i
\(161\) 0.489660 1.50702i 0.0385906 0.118770i
\(162\) 0.780063 + 2.40079i 0.0612876 + 0.188624i
\(163\) 7.58233 5.50889i 0.593894 0.431489i −0.249812 0.968294i \(-0.580369\pi\)
0.843706 + 0.536805i \(0.180369\pi\)
\(164\) −24.8935 −1.94386
\(165\) 0 0
\(166\) 21.4891 1.66788
\(167\) 2.32527 1.68941i 0.179935 0.130730i −0.494172 0.869364i \(-0.664529\pi\)
0.674107 + 0.738634i \(0.264529\pi\)
\(168\) 1.46615 + 4.51235i 0.113116 + 0.348135i
\(169\) 1.19996 3.69310i 0.0923047 0.284085i
\(170\) −29.0125 21.0788i −2.22516 1.61667i
\(171\) −3.44349 2.50184i −0.263330 0.191321i
\(172\) −8.96224 + 27.5830i −0.683365 + 2.10318i
\(173\) −2.14093 6.58911i −0.162772 0.500961i 0.836093 0.548588i \(-0.184834\pi\)
−0.998865 + 0.0476266i \(0.984834\pi\)
\(174\) 5.15528 3.74553i 0.390821 0.283948i
\(175\) 0.497333 0.0375949
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) 13.0137 9.45499i 0.975416 0.708681i
\(179\) −7.48862 23.0476i −0.559726 1.72266i −0.683125 0.730302i \(-0.739379\pi\)
0.123399 0.992357i \(-0.460621\pi\)
\(180\) −3.20521 + 9.86463i −0.238902 + 0.735266i
\(181\) −13.7533 9.99235i −1.02227 0.742725i −0.0555261 0.998457i \(-0.517684\pi\)
−0.966748 + 0.255732i \(0.917684\pi\)
\(182\) 6.64836 + 4.83032i 0.492809 + 0.358047i
\(183\) −0.825636 + 2.54105i −0.0610328 + 0.187840i
\(184\) 3.70106 + 11.3907i 0.272846 + 0.839733i
\(185\) 9.59608 6.97196i 0.705518 0.512589i
\(186\) 18.6101 1.36456
\(187\) 0 0
\(188\) −5.48913 −0.400336
\(189\) −0.640974 + 0.465695i −0.0466240 + 0.0338743i
\(190\) −7.87657 24.2416i −0.571427 1.75867i
\(191\) −5.40444 + 16.6331i −0.391051 + 1.20353i 0.540943 + 0.841059i \(0.318067\pi\)
−0.931994 + 0.362473i \(0.881933\pi\)
\(192\) 1.91922 + 1.39439i 0.138507 + 0.100632i
\(193\) 13.8933 + 10.0941i 1.00006 + 0.726586i 0.962101 0.272693i \(-0.0879144\pi\)
0.0379588 + 0.999279i \(0.487914\pi\)
\(194\) −9.74231 + 29.9837i −0.699457 + 2.15271i
\(195\) 3.01214 + 9.27042i 0.215704 + 0.663868i
\(196\) 22.5404 16.3765i 1.61003 1.16975i
\(197\) 21.1345 1.50577 0.752884 0.658153i \(-0.228662\pi\)
0.752884 + 0.658153i \(0.228662\pi\)
\(198\) 0 0
\(199\) −6.86141 −0.486392 −0.243196 0.969977i \(-0.578196\pi\)
−0.243196 + 0.969977i \(0.578196\pi\)
\(200\) −3.04114 + 2.20952i −0.215041 + 0.156236i
\(201\) 4.98038 + 15.3280i 0.351289 + 1.08116i
\(202\) −4.16837 + 12.8289i −0.293285 + 0.902640i
\(203\) 1.61803 + 1.17557i 0.113564 + 0.0825089i
\(204\) 21.1826 + 15.3901i 1.48308 + 1.07752i
\(205\) 4.17375 12.8455i 0.291508 0.897168i
\(206\) 6.33165 + 19.4868i 0.441147 + 1.35771i
\(207\) −1.61803 + 1.17557i −0.112461 + 0.0817078i
\(208\) −26.1831 −1.81547
\(209\) 0 0
\(210\) −4.74456 −0.327406
\(211\) −10.0918 + 7.33216i −0.694752 + 0.504767i −0.878219 0.478259i \(-0.841268\pi\)
0.183467 + 0.983026i \(0.441268\pi\)
\(212\) 17.7223 + 54.5436i 1.21717 + 3.74607i
\(213\) 0.230083 0.708121i 0.0157650 0.0485197i
\(214\) 0.602364 + 0.437643i 0.0411767 + 0.0299167i
\(215\) −12.7306 9.24935i −0.868222 0.630800i
\(216\) 1.85053 5.69534i 0.125913 0.387519i
\(217\) 1.80496 + 5.55509i 0.122528 + 0.377104i
\(218\) −20.3200 + 14.7633i −1.37624 + 0.999898i
\(219\) 7.42554 0.501771
\(220\) 0 0
\(221\) 24.6060 1.65518
\(222\) −10.2112 + 7.41884i −0.685328 + 0.497920i
\(223\) −1.50226 4.62347i −0.100599 0.309611i 0.888074 0.459701i \(-0.152043\pi\)
−0.988672 + 0.150091i \(0.952043\pi\)
\(224\) 1.00599 3.09610i 0.0672152 0.206867i
\(225\) −0.507835 0.368964i −0.0338557 0.0245976i
\(226\) 8.92921 + 6.48745i 0.593962 + 0.431539i
\(227\) 7.80063 24.0079i 0.517746 1.59346i −0.260483 0.965478i \(-0.583882\pi\)
0.778229 0.627980i \(-0.216118\pi\)
\(228\) 5.75085 + 17.6993i 0.380859 + 1.17216i
\(229\) 2.93489 2.13232i 0.193943 0.140908i −0.486576 0.873638i \(-0.661754\pi\)
0.680519 + 0.732730i \(0.261754\pi\)
\(230\) −11.9769 −0.789732
\(231\) 0 0
\(232\) −15.1168 −0.992469
\(233\) −2.04223 + 1.48377i −0.133791 + 0.0972049i −0.652668 0.757644i \(-0.726350\pi\)
0.518877 + 0.854849i \(0.326350\pi\)
\(234\) −3.20521 9.86463i −0.209531 0.644871i
\(235\) 0.920330 2.83248i 0.0600357 0.184771i
\(236\) 21.2235 + 15.4198i 1.38153 + 1.00374i
\(237\) −4.72544 3.43323i −0.306950 0.223012i
\(238\) −3.70106 + 11.3907i −0.239904 + 0.738349i
\(239\) −9.05339 27.8635i −0.585615 1.80234i −0.596786 0.802400i \(-0.703556\pi\)
0.0111708 0.999938i \(-0.496444\pi\)
\(240\) 12.2298 8.88546i 0.789429 0.573554i
\(241\) −13.2665 −0.854570 −0.427285 0.904117i \(-0.640530\pi\)
−0.427285 + 0.904117i \(0.640530\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 9.45088 6.86646i 0.605030 0.439580i
\(245\) 4.67136 + 14.3770i 0.298442 + 0.918511i
\(246\) −4.44128 + 13.6689i −0.283166 + 0.871494i
\(247\) 14.1490 + 10.2798i 0.900279 + 0.654091i
\(248\) −35.7169 25.9498i −2.26802 1.64781i
\(249\) 2.63059 8.09613i 0.166707 0.513072i
\(250\) 8.09104 + 24.9016i 0.511722 + 1.57492i
\(251\) 0.413306 0.300285i 0.0260877 0.0189538i −0.574665 0.818389i \(-0.694868\pi\)
0.600753 + 0.799435i \(0.294868\pi\)
\(252\) 3.46410 0.218218
\(253\) 0 0
\(254\) 49.7228 3.11989
\(255\) −11.4931 + 8.35023i −0.719726 + 0.522912i
\(256\) −9.61563 29.5939i −0.600977 1.84962i
\(257\) 7.53145 23.1794i 0.469799 1.44589i −0.383047 0.923729i \(-0.625125\pi\)
0.852846 0.522163i \(-0.174875\pi\)
\(258\) 13.5466 + 9.84221i 0.843377 + 0.612749i
\(259\) −3.20487 2.32847i −0.199141 0.144684i
\(260\) 13.1699 40.5329i 0.816764 2.51374i
\(261\) −0.780063 2.40079i −0.0482847 0.148605i
\(262\) −13.5466 + 9.84221i −0.836914 + 0.608054i
\(263\) −22.3692 −1.37934 −0.689671 0.724122i \(-0.742245\pi\)
−0.689671 + 0.724122i \(0.742245\pi\)
\(264\) 0 0
\(265\) −31.1168 −1.91149
\(266\) −6.88698 + 5.00368i −0.422268 + 0.306796i
\(267\) −1.96914 6.06040i −0.120510 0.370890i
\(268\) 21.7756 67.0185i 1.33016 4.09380i
\(269\) −7.37568 5.35875i −0.449703 0.326729i 0.339775 0.940507i \(-0.389649\pi\)
−0.789479 + 0.613778i \(0.789649\pi\)
\(270\) 4.84475 + 3.51992i 0.294842 + 0.214215i
\(271\) −3.21140 + 9.88367i −0.195079 + 0.600390i 0.804897 + 0.593414i \(0.202220\pi\)
−0.999976 + 0.00697572i \(0.997780\pi\)
\(272\) −11.7921 36.2923i −0.715001 2.20055i
\(273\) 2.63370 1.91350i 0.159399 0.115810i
\(274\) 1.87953 0.113546
\(275\) 0 0
\(276\) 8.74456 0.526361
\(277\) 7.00629 5.09037i 0.420967 0.305851i −0.357060 0.934082i \(-0.616221\pi\)
0.778027 + 0.628231i \(0.216221\pi\)
\(278\) −8.10666 24.9497i −0.486205 1.49638i
\(279\) 2.27816 7.01146i 0.136390 0.419765i
\(280\) 9.10584 + 6.61578i 0.544178 + 0.395368i
\(281\) 0.477245 + 0.346739i 0.0284701 + 0.0206847i 0.601929 0.798549i \(-0.294399\pi\)
−0.573459 + 0.819234i \(0.694399\pi\)
\(282\) −0.979321 + 3.01404i −0.0583177 + 0.179483i
\(283\) −0.734490 2.26053i −0.0436609 0.134375i 0.926850 0.375432i \(-0.122506\pi\)
−0.970511 + 0.241058i \(0.922506\pi\)
\(284\) −2.63370 + 1.91350i −0.156282 + 0.113545i
\(285\) −10.0974 −0.598115
\(286\) 0 0
\(287\) −4.51087 −0.266269
\(288\) −3.32418 + 2.41516i −0.195879 + 0.142315i
\(289\) 5.82850 + 17.9383i 0.342853 + 1.05519i
\(290\) 4.67136 14.3770i 0.274312 0.844245i
\(291\) 10.1039 + 7.34092i 0.592302 + 0.430333i
\(292\) −26.2660 19.0834i −1.53710 1.11677i
\(293\) 2.03282 6.25638i 0.118759 0.365502i −0.873954 0.486009i \(-0.838452\pi\)
0.992712 + 0.120508i \(0.0384522\pi\)
\(294\) −4.97078 15.2985i −0.289902 0.892226i
\(295\) −11.5153 + 8.36635i −0.670446 + 0.487108i
\(296\) 29.9422 1.74035
\(297\) 0 0
\(298\) −15.1168 −0.875695
\(299\) 6.64836 4.83032i 0.384485 0.279344i
\(300\) 0.848116 + 2.61023i 0.0489660 + 0.150702i
\(301\) −1.62402 + 4.99822i −0.0936069 + 0.288092i
\(302\) −4.44080 3.22643i −0.255539 0.185660i
\(303\) 4.32309 + 3.14091i 0.248355 + 0.180440i
\(304\) 8.38144 25.7954i 0.480708 1.47947i
\(305\) 1.95864 + 6.02808i 0.112151 + 0.345167i
\(306\) 12.2298 8.88546i 0.699130 0.507948i
\(307\) −17.8178 −1.01692 −0.508459 0.861086i \(-0.669785\pi\)
−0.508459 + 0.861086i \(0.669785\pi\)
\(308\) 0 0
\(309\) 8.11684 0.461751
\(310\) 35.7169 25.9498i 2.02858 1.47385i
\(311\) −2.01197 6.19221i −0.114088 0.351128i 0.877667 0.479270i \(-0.159099\pi\)
−0.991756 + 0.128142i \(0.959099\pi\)
\(312\) −7.60366 + 23.4017i −0.430473 + 1.32486i
\(313\) −7.37568 5.35875i −0.416898 0.302894i 0.359490 0.933149i \(-0.382951\pi\)
−0.776389 + 0.630255i \(0.782951\pi\)
\(314\) −13.5353 9.83400i −0.763843 0.554965i
\(315\) −0.580806 + 1.78754i −0.0327247 + 0.100716i
\(316\) 7.89178 + 24.2884i 0.443947 + 1.36633i
\(317\) −12.3419 + 8.96692i −0.693191 + 0.503632i −0.877707 0.479197i \(-0.840928\pi\)
0.184517 + 0.982829i \(0.440928\pi\)
\(318\) 33.1113 1.85679
\(319\) 0 0
\(320\) 5.62772 0.314599
\(321\) 0.238623 0.173369i 0.0133186 0.00967654i
\(322\) 1.23607 + 3.80423i 0.0688834 + 0.212001i
\(323\) −7.87657 + 24.2416i −0.438264 + 1.34884i
\(324\) −3.53725 2.56996i −0.196514 0.142776i
\(325\) 2.08665 + 1.51604i 0.115746 + 0.0840947i
\(326\) −7.31097 + 22.5009i −0.404917 + 1.24621i
\(327\) 3.07468 + 9.46289i 0.170030 + 0.523299i
\(328\) 27.5835 20.0406i 1.52304 1.10656i
\(329\) −0.994667 −0.0548377
\(330\) 0 0
\(331\) −0.627719 −0.0345025 −0.0172513 0.999851i \(-0.505492\pi\)
−0.0172513 + 0.999851i \(0.505492\pi\)
\(332\) −30.1118 + 21.8775i −1.65260 + 1.20068i
\(333\) 1.54508 + 4.75528i 0.0846701 + 0.260588i
\(334\) −2.24205 + 6.90033i −0.122680 + 0.377569i
\(335\) 30.9317 + 22.4732i 1.68998 + 1.22784i
\(336\) −4.08446 2.96754i −0.222826 0.161892i
\(337\) 4.72595 14.5450i 0.257439 0.792316i −0.735900 0.677090i \(-0.763241\pi\)
0.993339 0.115226i \(-0.0367592\pi\)
\(338\) 3.02911 + 9.32263i 0.164762 + 0.507084i
\(339\) 3.53725 2.56996i 0.192117 0.139581i
\(340\) 62.1138 3.36859
\(341\) 0 0
\(342\) 10.7446 0.580999
\(343\) 8.57128 6.22740i 0.462806 0.336248i
\(344\) −12.2750 37.7786i −0.661825 2.03689i
\(345\) −1.46615 + 4.51235i −0.0789349 + 0.242937i
\(346\) 14.1490 + 10.2798i 0.760655 + 0.552648i
\(347\) 14.5787 + 10.5920i 0.782624 + 0.568609i 0.905765 0.423780i \(-0.139297\pi\)
−0.123142 + 0.992389i \(0.539297\pi\)
\(348\) −3.41066 + 10.4969i −0.182830 + 0.562694i
\(349\) −8.02850 24.7092i −0.429756 1.32265i −0.898366 0.439247i \(-0.855245\pi\)
0.468611 0.883405i \(-0.344755\pi\)
\(350\) −1.01567 + 0.737928i −0.0542899 + 0.0394439i
\(351\) −4.10891 −0.219317
\(352\) 0 0
\(353\) −29.3505 −1.56217 −0.781086 0.624424i \(-0.785334\pi\)
−0.781086 + 0.624424i \(0.785334\pi\)
\(354\) 12.2534 8.90261i 0.651260 0.473168i
\(355\) −0.545820 1.67986i −0.0289691 0.0891578i
\(356\) −8.60965 + 26.4978i −0.456310 + 1.40438i
\(357\) 3.83843 + 2.78878i 0.203151 + 0.147598i
\(358\) 49.4908 + 35.9572i 2.61567 + 1.90040i
\(359\) −0.398515 + 1.22650i −0.0210328 + 0.0647323i −0.961022 0.276472i \(-0.910835\pi\)
0.939989 + 0.341204i \(0.110835\pi\)
\(360\) −4.38998 13.5110i −0.231372 0.712090i
\(361\) 0.714488 0.519106i 0.0376046 0.0273214i
\(362\) 42.9137 2.25550
\(363\) 0 0
\(364\) −14.2337 −0.746048
\(365\) 14.2512 10.3541i 0.745942 0.541959i
\(366\) −2.08418 6.41446i −0.108942 0.335289i
\(367\) −7.33075 + 22.5617i −0.382662 + 1.17771i 0.555500 + 0.831517i \(0.312527\pi\)
−0.938162 + 0.346196i \(0.887473\pi\)
\(368\) −10.3106 7.49107i −0.537475 0.390499i
\(369\) 4.60613 + 3.34655i 0.239785 + 0.174214i
\(370\) −9.25265 + 28.4767i −0.481022 + 1.48043i
\(371\) 3.21140 + 9.88367i 0.166728 + 0.513135i
\(372\) −26.0776 + 18.9465i −1.35206 + 0.982330i
\(373\) −24.4511 −1.26603 −0.633015 0.774140i \(-0.718183\pi\)
−0.633015 + 0.774140i \(0.718183\pi\)
\(374\) 0 0
\(375\) 10.3723 0.535622
\(376\) 6.08228 4.41903i 0.313670 0.227894i
\(377\) 3.20521 + 9.86463i 0.165077 + 0.508054i
\(378\) 0.618034 1.90211i 0.0317882 0.0978341i
\(379\) −19.1922 13.9439i −0.985835 0.716251i −0.0268299 0.999640i \(-0.508541\pi\)
−0.959005 + 0.283389i \(0.908541\pi\)
\(380\) 35.7169 + 25.9498i 1.83224 + 1.33120i
\(381\) 6.08682 18.7333i 0.311837 0.959737i
\(382\) −13.6426 41.9877i −0.698017 2.14828i
\(383\) 19.0031 13.8066i 0.971013 0.705482i 0.0153309 0.999882i \(-0.495120\pi\)
0.955682 + 0.294400i \(0.0951198\pi\)
\(384\) −14.2063 −0.724960
\(385\) 0 0
\(386\) −43.3505 −2.20648
\(387\) 5.36641 3.89893i 0.272790 0.198194i
\(388\) −16.8742 51.9334i −0.856656 2.63652i
\(389\) −2.81726 + 8.67063i −0.142841 + 0.439619i −0.996727 0.0808411i \(-0.974239\pi\)
0.853886 + 0.520460i \(0.174239\pi\)
\(390\) −19.9066 14.4630i −1.00801 0.732364i
\(391\) 9.68950 + 7.03983i 0.490019 + 0.356020i
\(392\) −11.7921 + 36.2923i −0.595591 + 1.83304i
\(393\) 2.04979 + 6.30860i 0.103398 + 0.318227i
\(394\) −43.1615 + 31.3587i −2.17444 + 1.57983i
\(395\) −13.8564 −0.697191
\(396\) 0 0
\(397\) 24.4891 1.22907 0.614537 0.788888i \(-0.289343\pi\)
0.614537 + 0.788888i \(0.289343\pi\)
\(398\) 14.0126 10.1807i 0.702387 0.510314i
\(399\) 1.04209 + 3.20723i 0.0521699 + 0.160562i
\(400\) 1.23607 3.80423i 0.0618034 0.190211i
\(401\) 15.4659 + 11.2366i 0.772328 + 0.561129i 0.902667 0.430341i \(-0.141607\pi\)
−0.130339 + 0.991470i \(0.541607\pi\)
\(402\) −32.9143 23.9137i −1.64162 1.19271i
\(403\) −9.36076 + 28.8095i −0.466293 + 1.43510i
\(404\) −7.21983 22.2203i −0.359200 1.10550i
\(405\) 1.91922 1.39439i 0.0953666 0.0692879i
\(406\) −5.04868 −0.250562
\(407\) 0 0
\(408\) −35.8614 −1.77540
\(409\) −0.357934 + 0.260054i −0.0176987 + 0.0128588i −0.596599 0.802539i \(-0.703482\pi\)
0.578901 + 0.815398i \(0.303482\pi\)
\(410\) 10.5360 + 32.4264i 0.520334 + 1.60142i
\(411\) 0.230083 0.708121i 0.0113491 0.0349290i
\(412\) −28.7113 20.8600i −1.41450 1.02770i
\(413\) 3.84584 + 2.79417i 0.189242 + 0.137492i
\(414\) 1.56013 4.80158i 0.0766760 0.235985i
\(415\) −6.24051 19.2063i −0.306334 0.942800i
\(416\) 13.6588 9.92367i 0.669676 0.486548i
\(417\) −10.3923 −0.508913
\(418\) 0 0
\(419\) −8.51087 −0.415783 −0.207892 0.978152i \(-0.566660\pi\)
−0.207892 + 0.978152i \(0.566660\pi\)
\(420\) 6.64836 4.83032i 0.324407 0.235695i
\(421\) 1.89693 + 5.83815i 0.0924507 + 0.284534i 0.986581 0.163273i \(-0.0522052\pi\)
−0.894130 + 0.447807i \(0.852205\pi\)
\(422\) 9.73067 29.9479i 0.473682 1.45784i
\(423\) 1.01567 + 0.737928i 0.0493836 + 0.0358793i
\(424\) −63.5478 46.1702i −3.08615 2.24222i
\(425\) −1.16161 + 3.57507i −0.0563465 + 0.173417i
\(426\) 0.580806 + 1.78754i 0.0281401 + 0.0866065i
\(427\) 1.71256 1.24425i 0.0828767 0.0602135i
\(428\) −1.28962 −0.0623362
\(429\) 0 0
\(430\) 39.7228 1.91560
\(431\) −19.1404 + 13.9063i −0.921959 + 0.669843i −0.944011 0.329914i \(-0.892980\pi\)
0.0220516 + 0.999757i \(0.492980\pi\)
\(432\) 1.96914 + 6.06040i 0.0947404 + 0.291581i
\(433\) −7.17960 + 22.0966i −0.345030 + 1.06189i 0.616538 + 0.787325i \(0.288535\pi\)
−0.961568 + 0.274567i \(0.911465\pi\)
\(434\) −11.9286 8.66664i −0.572591 0.416012i
\(435\) −4.84475 3.51992i −0.232288 0.168767i
\(436\) 13.4434 41.3744i 0.643821 1.98148i
\(437\) 2.63059 + 8.09613i 0.125838 + 0.387291i
\(438\) −15.1647 + 11.0178i −0.724596 + 0.526450i
\(439\) 24.4511 1.16699 0.583493 0.812118i \(-0.301685\pi\)
0.583493 + 0.812118i \(0.301685\pi\)
\(440\) 0 0
\(441\) −6.37228 −0.303442
\(442\) −50.2511 + 36.5096i −2.39020 + 1.73658i
\(443\) 6.41042 + 19.7293i 0.304568 + 0.937365i 0.979838 + 0.199794i \(0.0640273\pi\)
−0.675270 + 0.737571i \(0.735973\pi\)
\(444\) 6.75555 20.7914i 0.320604 0.986718i
\(445\) −12.2298 8.88546i −0.579747 0.421211i
\(446\) 9.92812 + 7.21320i 0.470110 + 0.341555i
\(447\) −1.85053 + 5.69534i −0.0875270 + 0.269381i
\(448\) −0.580806 1.78754i −0.0274405 0.0844532i
\(449\) −19.9066 + 14.4630i −0.939453 + 0.682552i −0.948289 0.317409i \(-0.897187\pi\)
0.00883611 + 0.999961i \(0.497187\pi\)
\(450\) 1.58457 0.0746975
\(451\) 0 0
\(452\) −19.1168 −0.899181
\(453\) −1.75919 + 1.27813i −0.0826541 + 0.0600517i
\(454\) 19.6914 + 60.6040i 0.924165 + 2.84429i
\(455\) 2.38648 7.34483i 0.111880 0.344331i
\(456\) −20.6211 14.9821i −0.965673 0.701603i
\(457\) 6.84256 + 4.97141i 0.320082 + 0.232553i 0.736210 0.676753i \(-0.236613\pi\)
−0.416129 + 0.909306i \(0.636613\pi\)
\(458\) −2.82985 + 8.70938i −0.132230 + 0.406963i
\(459\) −1.85053 5.69534i −0.0863753 0.265836i
\(460\) 16.7827 12.1933i 0.782498 0.568518i
\(461\) 14.5012 0.675389 0.337694 0.941256i \(-0.390353\pi\)
0.337694 + 0.941256i \(0.390353\pi\)
\(462\) 0 0
\(463\) −3.25544 −0.151293 −0.0756465 0.997135i \(-0.524102\pi\)
−0.0756465 + 0.997135i \(0.524102\pi\)
\(464\) 13.0137 9.45499i 0.604145 0.438937i
\(465\) −5.40444 16.6331i −0.250625 0.771344i
\(466\) 1.96914 6.06040i 0.0912188 0.280743i
\(467\) 17.9874 + 13.0686i 0.832359 + 0.604744i 0.920226 0.391388i \(-0.128005\pi\)
−0.0878667 + 0.996132i \(0.528005\pi\)
\(468\) 14.5342 + 10.5597i 0.671846 + 0.488125i
\(469\) 3.94589 12.1442i 0.182204 0.560767i
\(470\) 2.32322 + 7.15015i 0.107162 + 0.329812i
\(471\) −5.36194 + 3.89568i −0.247065 + 0.179503i
\(472\) −35.9306 −1.65384
\(473\) 0 0
\(474\) 14.7446 0.677240
\(475\) −2.16154 + 1.57045i −0.0991784 + 0.0720573i
\(476\) −6.41042 19.7293i −0.293821 0.904289i
\(477\) 4.05333 12.4749i 0.185589 0.571185i
\(478\) 59.8321 + 43.4705i 2.73666 + 1.98830i
\(479\) −30.3504 22.0509i −1.38675 1.00753i −0.996213 0.0869422i \(-0.972290\pi\)
−0.390534 0.920589i \(-0.627710\pi\)
\(480\) −3.01214 + 9.27042i −0.137485 + 0.423135i
\(481\) −6.34862 19.5390i −0.289472 0.890903i
\(482\) 27.0933 19.6844i 1.23406 0.896600i
\(483\) 1.58457 0.0721006
\(484\) 0 0
\(485\) 29.6277 1.34533
\(486\) −2.04223 + 1.48377i −0.0926375 + 0.0673051i
\(487\) −3.93829 12.1208i −0.178461 0.549246i 0.821314 0.570477i \(-0.193242\pi\)
−0.999775 + 0.0212308i \(0.993242\pi\)
\(488\) −4.94427 + 15.2169i −0.223817 + 0.688837i
\(489\) 7.58233 + 5.50889i 0.342885 + 0.249121i
\(490\) −30.8721 22.4299i −1.39466 1.01328i
\(491\) 5.75085 17.6993i 0.259532 0.798758i −0.733371 0.679829i \(-0.762054\pi\)
0.992903 0.118929i \(-0.0379460\pi\)
\(492\) −7.69252 23.6751i −0.346806 1.06736i
\(493\) −12.2298 + 8.88546i −0.550802 + 0.400181i
\(494\) −44.1485 −1.98633
\(495\) 0 0
\(496\) 46.9783 2.10939
\(497\) −0.477245 + 0.346739i −0.0214074 + 0.0155534i
\(498\) 6.64050 + 20.4374i 0.297568 + 0.915821i
\(499\) −11.6931 + 35.9877i −0.523455 + 1.61103i 0.243896 + 0.969801i \(0.421574\pi\)
−0.767351 + 0.641227i \(0.778426\pi\)
\(500\) −36.6894 26.6564i −1.64080 1.19211i
\(501\) 2.32527 + 1.68941i 0.103885 + 0.0754772i
\(502\) −0.398515 + 1.22650i −0.0177866 + 0.0547415i
\(503\) 6.82131 + 20.9938i 0.304147 + 0.936069i 0.979994 + 0.199027i \(0.0637781\pi\)
−0.675847 + 0.737042i \(0.736222\pi\)
\(504\) −3.83843 + 2.78878i −0.170977 + 0.124222i
\(505\) 12.6766 0.564101
\(506\) 0 0
\(507\) 3.88316 0.172457
\(508\) −69.6745 + 50.6215i −3.09131 + 2.24597i
\(509\) −12.6630 38.9726i −0.561277 1.72743i −0.678763 0.734357i \(-0.737484\pi\)
0.117487 0.993074i \(-0.462516\pi\)
\(510\) 11.0818 34.1062i 0.490710 1.51025i
\(511\) −4.75957 3.45803i −0.210551 0.152974i
\(512\) 40.5616 + 29.4697i 1.79259 + 1.30239i
\(513\) 1.31530 4.04807i 0.0580718 0.178726i
\(514\) 19.0119 + 58.5127i 0.838580 + 2.58088i
\(515\) 15.5780 11.3181i 0.686448 0.498733i
\(516\) −29.0024 −1.27676
\(517\) 0 0
\(518\) 10.0000 0.439375
\(519\) 5.60503 4.07230i 0.246034 0.178754i
\(520\) 18.0380 + 55.5153i 0.791020 + 2.43451i
\(521\) 5.24657 16.1473i 0.229856 0.707425i −0.767906 0.640563i \(-0.778701\pi\)
0.997762 0.0668623i \(-0.0212988\pi\)
\(522\) 5.15528 + 3.74553i 0.225641 + 0.163938i
\(523\) 5.53014 + 4.01788i 0.241816 + 0.175690i 0.702092 0.712086i \(-0.252250\pi\)
−0.460276 + 0.887776i \(0.652250\pi\)
\(524\) 8.96224 27.5830i 0.391517 1.20497i
\(525\) 0.153684 + 0.472992i 0.00670734 + 0.0206431i
\(526\) 45.6831 33.1907i 1.99188 1.44718i
\(527\) −44.1485 −1.92314
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 63.5478 46.1702i 2.76034 2.00551i
\(531\) −1.85410 5.70634i −0.0804612 0.247634i
\(532\) 4.55632 14.0229i 0.197542 0.607970i
\(533\) −18.9262 13.7507i −0.819783 0.595607i
\(534\) 13.0137 + 9.45499i 0.563157 + 0.409157i
\(535\) 0.216223 0.665467i 0.00934814 0.0287706i
\(536\) 29.8247 + 91.7910i 1.28823 + 3.96477i
\(537\) 19.6055 14.2442i 0.846038 0.614683i
\(538\) 23.0140 0.992204
\(539\) 0 0
\(540\) −10.3723 −0.446352
\(541\) 22.4201 16.2892i 0.963917 0.700327i 0.00985982 0.999951i \(-0.496861\pi\)
0.954057 + 0.299625i \(0.0968615\pi\)
\(542\) −8.10666 24.9497i −0.348211 1.07168i
\(543\) 5.25329 16.1680i 0.225440 0.693834i
\(544\) 19.9066 + 14.4630i 0.853490 + 0.620097i
\(545\) 19.0960 + 13.8740i 0.817981 + 0.594298i
\(546\) −2.53945 + 7.81561i −0.108678 + 0.334477i
\(547\) 12.9707 + 39.9196i 0.554586 + 1.70684i 0.697034 + 0.717038i \(0.254502\pi\)
−0.142448 + 0.989802i \(0.545498\pi\)
\(548\) −2.63370 + 1.91350i −0.112506 + 0.0817406i
\(549\) −2.67181 −0.114030
\(550\) 0 0
\(551\) −10.7446 −0.457734
\(552\) −9.68950 + 7.03983i −0.412412 + 0.299635i
\(553\) 1.43004 + 4.40122i 0.0608116 + 0.187159i
\(554\) −6.75555 + 20.7914i −0.287016 + 0.883343i
\(555\) 9.59608 + 6.97196i 0.407331 + 0.295943i
\(556\) 36.7602 + 26.7078i 1.55898 + 1.13266i
\(557\) 2.93796 9.04212i 0.124485 0.383127i −0.869322 0.494247i \(-0.835444\pi\)
0.993807 + 0.111120i \(0.0354439\pi\)
\(558\) 5.75085 + 17.6993i 0.243453 + 0.749270i
\(559\) −22.0501 + 16.0203i −0.932620 + 0.677588i
\(560\) −11.9769 −0.506116
\(561\) 0 0
\(562\) −1.48913 −0.0628150
\(563\) −11.7761 + 8.55587i −0.496305 + 0.360587i −0.807604 0.589725i \(-0.799236\pi\)
0.311299 + 0.950312i \(0.399236\pi\)
\(564\) −1.69623 5.22047i −0.0714243 0.219821i
\(565\) 3.20521 9.86463i 0.134844 0.415008i
\(566\) 4.85410 + 3.52671i 0.204033 + 0.148239i
\(567\) −0.640974 0.465695i −0.0269184 0.0195573i
\(568\) 1.37784 4.24054i 0.0578127 0.177929i
\(569\) 7.58441 + 23.3424i 0.317955 + 0.978565i 0.974521 + 0.224296i \(0.0720083\pi\)
−0.656566 + 0.754269i \(0.727992\pi\)
\(570\) 20.6211 14.9821i 0.863724 0.627532i
\(571\) 4.55134 0.190468 0.0952339 0.995455i \(-0.469640\pi\)
0.0952339 + 0.995455i \(0.469640\pi\)
\(572\) 0 0
\(573\) −17.4891 −0.730619
\(574\) 9.21225 6.69309i 0.384512 0.279364i
\(575\) 0.387951 + 1.19399i 0.0161787 + 0.0497929i
\(576\) −0.733075 + 2.25617i −0.0305448 + 0.0940072i
\(577\) 13.3400 + 9.69206i 0.555351 + 0.403486i 0.829754 0.558129i \(-0.188480\pi\)
−0.274404 + 0.961615i \(0.588480\pi\)
\(578\) −38.5194 27.9860i −1.60219 1.16406i
\(579\) −5.30676 + 16.3325i −0.220541 + 0.678757i
\(580\) 8.09104 + 24.9016i 0.335962 + 1.03398i
\(581\) −5.45647 + 3.96435i −0.226372 + 0.164469i
\(582\) −31.5268 −1.30683
\(583\) 0 0
\(584\) 44.4674 1.84007
\(585\) −7.88589 + 5.72943i −0.326041 + 0.236883i
\(586\) 5.13153 + 15.7932i 0.211981 + 0.652412i
\(587\) 12.0449 37.0705i 0.497148 1.53006i −0.316434 0.948614i \(-0.602486\pi\)
0.813582 0.581450i \(-0.197514\pi\)
\(588\) 22.5404 + 16.3765i 0.929548 + 0.675356i
\(589\) −25.3864 18.4443i −1.04603 0.759984i
\(590\) 11.1032 34.1721i 0.457111 1.40684i
\(591\) 6.53091 + 20.1001i 0.268646 + 0.826806i
\(592\) −25.7764 + 18.7277i −1.05940 + 0.769702i
\(593\) 27.7677 1.14028 0.570142 0.821546i \(-0.306888\pi\)
0.570142 + 0.821546i \(0.306888\pi\)
\(594\) 0 0
\(595\) 11.2554 0.461428
\(596\) 21.1826 15.3901i 0.867673 0.630402i
\(597\) −2.12029 6.52559i −0.0867777 0.267074i
\(598\) −6.41042 + 19.7293i −0.262142 + 0.806789i
\(599\) −32.7388 23.7861i −1.33767 0.971875i −0.999526 0.0307807i \(-0.990201\pi\)
−0.338145 0.941094i \(-0.609799\pi\)
\(600\) −3.04114 2.20952i −0.124154 0.0902032i
\(601\) −12.4354 + 38.2723i −0.507252 + 1.56116i 0.289699 + 0.957118i \(0.406445\pi\)
−0.796951 + 0.604044i \(0.793555\pi\)
\(602\) −4.09957 12.6172i −0.167086 0.514238i
\(603\) −13.0388 + 9.47324i −0.530981 + 0.385780i
\(604\) 9.50744 0.386852
\(605\) 0 0
\(606\) −13.4891 −0.547958
\(607\) −21.1382 + 15.3578i −0.857973 + 0.623354i −0.927333 0.374238i \(-0.877904\pi\)
0.0693600 + 0.997592i \(0.477904\pi\)
\(608\) 5.40444 + 16.6331i 0.219179 + 0.674563i
\(609\) −0.618034 + 1.90211i −0.0250440 + 0.0770775i
\(610\) −12.9443 9.40456i −0.524098 0.380780i
\(611\) −4.17330 3.03208i −0.168834 0.122665i
\(612\) −8.09104 + 24.9016i −0.327061 + 1.00659i
\(613\) −13.4148 41.2864i −0.541817 1.66754i −0.728440 0.685110i \(-0.759754\pi\)
0.186623 0.982432i \(-0.440246\pi\)
\(614\) 36.3882 26.4376i 1.46851 1.06693i
\(615\) 13.5065 0.544637
\(616\) 0 0
\(617\) 43.8614 1.76579 0.882897 0.469567i \(-0.155590\pi\)
0.882897 + 0.469567i \(0.155590\pi\)
\(618\) −16.5765 + 12.0435i −0.666804 + 0.484461i
\(619\) 3.16238 + 9.73282i 0.127107 + 0.391195i 0.994279 0.106814i \(-0.0340648\pi\)
−0.867172 + 0.498009i \(0.834065\pi\)
\(620\) −23.6297 + 72.7248i −0.948992 + 2.92070i
\(621\) −1.61803 1.17557i −0.0649295 0.0471740i
\(622\) 13.2967 + 9.66063i 0.533150 + 0.387356i
\(623\) −1.56013 + 4.80158i −0.0625052 + 0.192371i
\(624\) −8.09104 24.9016i −0.323901 0.996864i
\(625\) 22.4458 16.3078i 0.897833 0.652314i
\(626\) 23.0140 0.919824
\(627\) 0 0
\(628\) 28.9783 1.15636
\(629\) 24.2237 17.5996i 0.965864 0.701741i
\(630\) −1.46615 4.51235i −0.0584128 0.179776i
\(631\) 6.87059 21.1455i 0.273514 0.841789i −0.716095 0.698003i \(-0.754072\pi\)
0.989609 0.143786i \(-0.0459277\pi\)
\(632\) −28.2980 20.5597i −1.12563 0.817821i
\(633\) −10.0918 7.33216i −0.401115 0.291427i
\(634\) 11.9002 36.6251i 0.472618 1.45457i
\(635\) −14.4397 44.4407i −0.573020 1.76357i
\(636\) −46.3976 + 33.7098i −1.83978 + 1.33668i
\(637\) 26.1831 1.03741
\(638\) 0 0
\(639\) 0.744563 0.0294544
\(640\) −27.2649 + 19.8091i −1.07774 + 0.783023i
\(641\) 2.19923 + 6.76852i 0.0868642 + 0.267340i 0.985048 0.172279i \(-0.0551132\pi\)
−0.898184 + 0.439620i \(0.855113\pi\)
\(642\) −0.230083 + 0.708121i −0.00908063 + 0.0279473i
\(643\) −17.0663 12.3994i −0.673029 0.488984i 0.198009 0.980200i \(-0.436553\pi\)
−0.871038 + 0.491216i \(0.836553\pi\)
\(644\) −5.60503 4.07230i −0.220869 0.160471i
\(645\) 4.86267 14.9658i 0.191467 0.589276i
\(646\) −19.8831 61.1940i −0.782291 2.40765i
\(647\) 9.70820 7.05342i 0.381669 0.277299i −0.380364 0.924837i \(-0.624201\pi\)
0.762033 + 0.647538i \(0.224201\pi\)
\(648\) 5.98844 0.235248
\(649\) 0 0
\(650\) −6.51087 −0.255378
\(651\) −4.72544 + 3.43323i −0.185205 + 0.134559i
\(652\) −12.6630 38.9726i −0.495920 1.52629i
\(653\) 1.39394 4.29010i 0.0545490 0.167884i −0.920070 0.391753i \(-0.871869\pi\)
0.974619 + 0.223869i \(0.0718687\pi\)
\(654\) −20.3200 14.7633i −0.794573 0.577291i
\(655\) 12.7306 + 9.24935i 0.497427 + 0.361402i
\(656\) −11.2113 + 34.5048i −0.437727 + 1.34719i
\(657\) 2.29462 + 7.06210i 0.0895215 + 0.275519i
\(658\) 2.03134 1.47586i 0.0791899 0.0575348i
\(659\) 22.3692 0.871380 0.435690 0.900097i \(-0.356504\pi\)
0.435690 + 0.900097i \(0.356504\pi\)
\(660\) 0 0
\(661\) −26.7228 −1.03940 −0.519698 0.854350i \(-0.673956\pi\)
−0.519698 + 0.854350i \(0.673956\pi\)
\(662\) 1.28195 0.931389i 0.0498243 0.0361995i
\(663\) 7.60366 + 23.4017i 0.295302 + 0.908845i
\(664\) 15.7531 48.4832i 0.611341 1.88151i
\(665\) 6.47214 + 4.70228i 0.250979 + 0.182347i
\(666\) −10.2112 7.41884i −0.395674 0.287474i
\(667\) −1.56013 + 4.80158i −0.0604083 + 0.185918i
\(668\) −3.88335 11.9517i −0.150251 0.462426i
\(669\) 3.93296 2.85746i 0.152057 0.110476i
\(670\) −96.5147 −3.72869
\(671\) 0 0
\(672\) 3.25544 0.125581
\(673\) −33.5553 + 24.3794i −1.29346 + 0.939755i −0.999869 0.0161752i \(-0.994851\pi\)
−0.293593 + 0.955931i \(0.594851\pi\)
\(674\) 11.9299 + 36.7165i 0.459523 + 1.41427i
\(675\) 0.193976 0.596996i 0.00746613 0.0229784i
\(676\) −13.7357 9.97957i −0.528296 0.383829i
\(677\) −29.3515 21.3251i −1.12807 0.819592i −0.142658 0.989772i \(-0.545565\pi\)
−0.985413 + 0.170180i \(0.945565\pi\)
\(678\) −3.41066 + 10.4969i −0.130985 + 0.403132i
\(679\) −3.05771 9.41068i −0.117344 0.361149i
\(680\) −68.8258 + 50.0049i −2.63935 + 1.91760i
\(681\) 25.2434 0.967328
\(682\) 0 0
\(683\) 2.00000 0.0765279 0.0382639 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) −15.0559 + 10.9388i −0.575677 + 0.418254i
\(685\) −0.545820 1.67986i −0.0208547 0.0641843i
\(686\) −8.26452 + 25.4356i −0.315541 + 0.971135i
\(687\) 2.93489 + 2.13232i 0.111973 + 0.0813531i
\(688\) 34.1963 + 24.8451i 1.30372 + 0.947209i
\(689\) −16.6548 + 51.2581i −0.634496 + 1.95278i
\(690\) −3.70106 11.3907i −0.140897 0.433636i
\(691\) 3.33060 2.41982i 0.126702 0.0920543i −0.522629 0.852560i \(-0.675049\pi\)
0.649331 + 0.760506i \(0.275049\pi\)
\(692\) −30.2921 −1.15153
\(693\) 0 0
\(694\) −45.4891 −1.72674
\(695\) −19.9451 + 14.4909i −0.756560 + 0.549673i
\(696\) −4.67136 14.3770i −0.177068 0.544958i
\(697\) 10.5360 32.4264i 0.399078 1.22824i
\(698\) 53.0587 + 38.5494i 2.00830 + 1.45912i
\(699\) −2.04223 1.48377i −0.0772443 0.0561213i
\(700\) 0.671952 2.06805i 0.0253974 0.0781651i
\(701\) 3.10329 + 9.55094i 0.117210 + 0.360734i 0.992401 0.123042i \(-0.0392650\pi\)
−0.875192 + 0.483776i \(0.839265\pi\)
\(702\) 8.39135 6.09667i 0.316711 0.230104i
\(703\) 21.2819 0.802664
\(704\) 0 0
\(705\) 2.97825 0.112167
\(706\) 59.9406 43.5494i 2.25589 1.63900i
\(707\) −1.30828 4.02648i −0.0492030 0.151431i
\(708\) −8.10666 + 24.9497i −0.304667 + 0.937668i
\(709\) −4.85410 3.52671i −0.182300 0.132448i 0.492893 0.870090i \(-0.335939\pi\)
−0.675192 + 0.737642i \(0.735939\pi\)
\(710\) 3.60722 + 2.62080i 0.135377 + 0.0983568i
\(711\) 1.80496 5.55509i 0.0676912 0.208332i
\(712\) −11.7921 36.2923i −0.441927 1.36011i
\(713\) −11.9286 + 8.66664i −0.446730 + 0.324568i
\(714\) −11.9769 −0.448223
\(715\) 0 0
\(716\) −105.957 −3.95978
\(717\) 23.7021 17.2206i 0.885171 0.643114i
\(718\) −1.00599 3.09610i −0.0375430 0.115546i
\(719\) −1.85410 + 5.70634i −0.0691463 + 0.212811i −0.979659 0.200672i \(-0.935688\pi\)
0.910512 + 0.413482i \(0.135688\pi\)
\(720\) 12.2298 + 8.88546i 0.455777 + 0.331141i
\(721\) −5.20268 3.77997i −0.193758 0.140773i
\(722\) −0.688918 + 2.12027i −0.0256389 + 0.0789083i
\(723\) −4.09957 12.6172i −0.152465 0.469238i
\(724\) −60.1332 + 43.6894i −2.23483 + 1.62370i
\(725\) −1.58457 −0.0588496
\(726\) 0 0
\(727\) 7.25544 0.269089 0.134545 0.990908i \(-0.457043\pi\)
0.134545 + 0.990908i \(0.457043\pi\)
\(728\) 15.7718 11.4589i 0.584541 0.424694i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −13.7412 + 42.2910i −0.508584 + 1.56526i
\(731\) −32.1364 23.3485i −1.18861 0.863575i
\(732\) 9.45088 + 6.86646i 0.349314 + 0.253792i
\(733\) −2.82985 + 8.70938i −0.104523 + 0.321688i −0.989618 0.143721i \(-0.954093\pi\)
0.885095 + 0.465410i \(0.154093\pi\)
\(734\) −18.5053 56.9534i −0.683043 2.10219i
\(735\) −12.2298 + 8.88546i −0.451102 + 0.327745i
\(736\) 8.21782 0.302913
\(737\) 0 0
\(738\) −14.3723 −0.529051
\(739\) 31.4687 22.8633i 1.15759 0.841041i 0.168122 0.985766i \(-0.446230\pi\)
0.989472 + 0.144725i \(0.0462299\pi\)
\(740\) −16.0261 49.3231i −0.589130 1.81315i
\(741\) −5.40444 + 16.6331i −0.198537 + 0.611034i
\(742\) −21.2235 15.4198i −0.779139 0.566078i
\(743\) 19.9451 + 14.4909i 0.731714 + 0.531621i 0.890105 0.455755i \(-0.150631\pi\)
−0.158391 + 0.987376i \(0.550631\pi\)
\(744\) 13.6426 41.9877i 0.500163 1.53934i
\(745\) 4.38998 + 13.5110i 0.160836 + 0.495003i
\(746\) 49.9348 36.2798i 1.82824 1.32830i
\(747\) 8.51278 0.311466
\(748\) 0 0
\(749\) −0.233688 −0.00853877
\(750\) −21.1826 + 15.3901i −0.773479 + 0.561966i
\(751\) −5.05259 15.5503i −0.184372 0.567438i 0.815565 0.578665i \(-0.196426\pi\)
−0.999937 + 0.0112273i \(0.996426\pi\)
\(752\) −2.47214 + 7.60845i −0.0901495 + 0.277452i
\(753\) 0.413306 + 0.300285i 0.0150617 + 0.0109430i
\(754\) −21.1826 15.3901i −0.771425 0.560473i
\(755\) −1.59406 + 4.90601i −0.0580137 + 0.178548i
\(756\) 1.07047 + 3.29456i 0.0389325 + 0.119822i
\(757\) −7.69446 + 5.59035i −0.279660 + 0.203185i −0.718769 0.695249i \(-0.755294\pi\)
0.439109 + 0.898434i \(0.355294\pi\)
\(758\) 59.8844 2.17510
\(759\) 0 0
\(760\) −60.4674 −2.19338
\(761\) −32.8699 + 23.8814i −1.19153 + 0.865700i −0.993426 0.114480i \(-0.963480\pi\)
−0.198108 + 0.980180i \(0.563480\pi\)
\(762\) 15.3652 + 47.2892i 0.556622 + 1.71311i
\(763\) 2.43603 7.49733i 0.0881902 0.271421i
\(764\) 61.8634 + 44.9464i 2.23814 + 1.62610i
\(765\) −11.4931 8.35023i −0.415534 0.301903i
\(766\) −18.3230 + 56.3924i −0.662037 + 2.03754i
\(767\) 7.61834 + 23.4468i 0.275082 + 0.846616i
\(768\) 25.1741 18.2900i 0.908390 0.659984i
\(769\) 34.7885 1.25451 0.627253 0.778816i \(-0.284179\pi\)
0.627253 + 0.778816i \(0.284179\pi\)
\(770\) 0 0
\(771\) 24.3723 0.877746
\(772\) 60.7453 44.1340i 2.18627 1.58842i
\(773\)