Properties

Label 567.2.u.a.100.10
Level $567$
Weight $2$
Character 567.100
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(100,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.u (of order \(9\), degree \(6\), 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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 100.10
Character \(\chi\) \(=\) 567.100
Dual form 567.2.u.a.550.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0570934 + 0.323793i) q^{2} +(1.77780 + 0.647067i) q^{4} +(-1.85642 - 0.675680i) q^{5} +(-2.33644 + 1.24140i) q^{7} +(-0.639805 + 1.10817i) q^{8} +O(q^{10})\) \(q+(-0.0570934 + 0.323793i) q^{2} +(1.77780 + 0.647067i) q^{4} +(-1.85642 - 0.675680i) q^{5} +(-2.33644 + 1.24140i) q^{7} +(-0.639805 + 1.10817i) q^{8} +(0.324770 - 0.562517i) q^{10} +(3.32802 - 1.21130i) q^{11} +(3.07096 + 1.11774i) q^{13} +(-0.268561 - 0.827397i) q^{14} +(2.57627 + 2.16174i) q^{16} +(-3.33900 + 5.78332i) q^{17} +(3.31187 + 5.73632i) q^{19} +(-2.86313 - 2.40245i) q^{20} +(0.202202 + 1.14675i) q^{22} +(1.04852 + 5.94644i) q^{23} +(-0.840487 - 0.705253i) q^{25} +(-0.537247 + 0.930538i) q^{26} +(-4.95699 + 0.695130i) q^{28} +(4.03401 - 1.46826i) q^{29} +(-3.97516 - 1.44684i) q^{31} +(-2.80752 + 2.35579i) q^{32} +(-1.68196 - 1.41134i) q^{34} +(5.17618 - 0.725868i) q^{35} +2.07250 q^{37} +(-2.04647 + 0.744853i) q^{38} +(1.93651 - 1.62493i) q^{40} +(0.663863 + 0.241626i) q^{41} +(1.66178 - 9.42445i) q^{43} +6.70035 q^{44} -1.98528 q^{46} +(-7.26473 + 2.64414i) q^{47} +(3.91786 - 5.80089i) q^{49} +(0.276342 - 0.231879i) q^{50} +(4.73630 + 3.97423i) q^{52} +(-0.108967 - 0.188737i) q^{53} -6.99663 q^{55} +(0.119177 - 3.38343i) q^{56} +(0.245097 + 1.39001i) q^{58} +(3.08240 - 2.58644i) q^{59} +(-5.32489 + 1.93810i) q^{61} +(0.695433 - 1.20453i) q^{62} +(2.76058 + 4.78146i) q^{64} +(-4.94574 - 4.14997i) q^{65} +(0.695751 + 3.94580i) q^{67} +(-9.67829 + 8.12105i) q^{68} +(-0.0604953 + 1.71745i) q^{70} +(4.16488 + 7.21379i) q^{71} -5.42623 q^{73} +(-0.118326 + 0.671061i) q^{74} +(2.17606 + 12.3411i) q^{76} +(-6.27199 + 6.96152i) q^{77} +(2.08876 - 11.8459i) q^{79} +(-3.32197 - 5.75383i) q^{80} +(-0.116139 + 0.201159i) q^{82} +(9.05188 - 3.29461i) q^{83} +(10.1063 - 8.48015i) q^{85} +(2.95669 + 1.07615i) q^{86} +(-0.786951 + 4.46302i) q^{88} +(-1.14565 - 1.98432i) q^{89} +(-8.56264 + 1.20076i) q^{91} +(-1.98369 + 11.2501i) q^{92} +(-0.441387 - 2.50323i) q^{94} +(-2.27228 - 12.8868i) q^{95} +(0.870524 - 4.93699i) q^{97} +(1.65460 + 1.59977i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0570934 + 0.323793i −0.0403712 + 0.228956i −0.998317 0.0579928i \(-0.981530\pi\)
0.957946 + 0.286949i \(0.0926411\pi\)
\(3\) 0 0
\(4\) 1.77780 + 0.647067i 0.888901 + 0.323534i
\(5\) −1.85642 0.675680i −0.830214 0.302173i −0.108267 0.994122i \(-0.534530\pi\)
−0.721947 + 0.691949i \(0.756752\pi\)
\(6\) 0 0
\(7\) −2.33644 + 1.24140i −0.883090 + 0.469204i
\(8\) −0.639805 + 1.10817i −0.226205 + 0.391799i
\(9\) 0 0
\(10\) 0.324770 0.562517i 0.102701 0.177884i
\(11\) 3.32802 1.21130i 1.00344 0.365221i 0.212527 0.977155i \(-0.431831\pi\)
0.790908 + 0.611935i \(0.209608\pi\)
\(12\) 0 0
\(13\) 3.07096 + 1.11774i 0.851730 + 0.310004i 0.730745 0.682650i \(-0.239173\pi\)
0.120984 + 0.992654i \(0.461395\pi\)
\(14\) −0.268561 0.827397i −0.0717759 0.221131i
\(15\) 0 0
\(16\) 2.57627 + 2.16174i 0.644067 + 0.540436i
\(17\) −3.33900 + 5.78332i −0.809827 + 1.40266i 0.103156 + 0.994665i \(0.467106\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(18\) 0 0
\(19\) 3.31187 + 5.73632i 0.759795 + 1.31600i 0.942955 + 0.332920i \(0.108034\pi\)
−0.183161 + 0.983083i \(0.558633\pi\)
\(20\) −2.86313 2.40245i −0.640215 0.537205i
\(21\) 0 0
\(22\) 0.202202 + 1.14675i 0.0431097 + 0.244487i
\(23\) 1.04852 + 5.94644i 0.218631 + 1.23992i 0.874493 + 0.485037i \(0.161194\pi\)
−0.655863 + 0.754880i \(0.727695\pi\)
\(24\) 0 0
\(25\) −0.840487 0.705253i −0.168097 0.141051i
\(26\) −0.537247 + 0.930538i −0.105363 + 0.182494i
\(27\) 0 0
\(28\) −4.95699 + 0.695130i −0.936783 + 0.131367i
\(29\) 4.03401 1.46826i 0.749098 0.272649i 0.0608717 0.998146i \(-0.480612\pi\)
0.688226 + 0.725496i \(0.258390\pi\)
\(30\) 0 0
\(31\) −3.97516 1.44684i −0.713961 0.259860i −0.0406009 0.999175i \(-0.512927\pi\)
−0.673360 + 0.739315i \(0.735149\pi\)
\(32\) −2.80752 + 2.35579i −0.496304 + 0.416449i
\(33\) 0 0
\(34\) −1.68196 1.41134i −0.288454 0.242042i
\(35\) 5.17618 0.725868i 0.874935 0.122694i
\(36\) 0 0
\(37\) 2.07250 0.340717 0.170358 0.985382i \(-0.445507\pi\)
0.170358 + 0.985382i \(0.445507\pi\)
\(38\) −2.04647 + 0.744853i −0.331981 + 0.120831i
\(39\) 0 0
\(40\) 1.93651 1.62493i 0.306190 0.256924i
\(41\) 0.663863 + 0.241626i 0.103678 + 0.0377357i 0.393338 0.919394i \(-0.371320\pi\)
−0.289660 + 0.957130i \(0.593542\pi\)
\(42\) 0 0
\(43\) 1.66178 9.42445i 0.253420 1.43722i −0.546677 0.837344i \(-0.684107\pi\)
0.800096 0.599871i \(-0.204782\pi\)
\(44\) 6.70035 1.01012
\(45\) 0 0
\(46\) −1.98528 −0.292713
\(47\) −7.26473 + 2.64414i −1.05967 + 0.385688i −0.812304 0.583234i \(-0.801787\pi\)
−0.247365 + 0.968922i \(0.579565\pi\)
\(48\) 0 0
\(49\) 3.91786 5.80089i 0.559695 0.828699i
\(50\) 0.276342 0.231879i 0.0390807 0.0327926i
\(51\) 0 0
\(52\) 4.73630 + 3.97423i 0.656807 + 0.551126i
\(53\) −0.108967 0.188737i −0.0149678 0.0259250i 0.858444 0.512906i \(-0.171431\pi\)
−0.873412 + 0.486981i \(0.838098\pi\)
\(54\) 0 0
\(55\) −6.99663 −0.943426
\(56\) 0.119177 3.38343i 0.0159257 0.452130i
\(57\) 0 0
\(58\) 0.245097 + 1.39001i 0.0321828 + 0.182518i
\(59\) 3.08240 2.58644i 0.401294 0.336726i −0.419700 0.907663i \(-0.637865\pi\)
0.820994 + 0.570937i \(0.193420\pi\)
\(60\) 0 0
\(61\) −5.32489 + 1.93810i −0.681782 + 0.248148i −0.659613 0.751606i \(-0.729280\pi\)
−0.0221696 + 0.999754i \(0.507057\pi\)
\(62\) 0.695433 1.20453i 0.0883201 0.152975i
\(63\) 0 0
\(64\) 2.76058 + 4.78146i 0.345072 + 0.597683i
\(65\) −4.94574 4.14997i −0.613443 0.514740i
\(66\) 0 0
\(67\) 0.695751 + 3.94580i 0.0849995 + 0.482056i 0.997357 + 0.0726609i \(0.0231491\pi\)
−0.912357 + 0.409395i \(0.865740\pi\)
\(68\) −9.67829 + 8.12105i −1.17366 + 0.984822i
\(69\) 0 0
\(70\) −0.0604953 + 1.71745i −0.00723057 + 0.205275i
\(71\) 4.16488 + 7.21379i 0.494281 + 0.856119i 0.999978 0.00659150i \(-0.00209816\pi\)
−0.505698 + 0.862711i \(0.668765\pi\)
\(72\) 0 0
\(73\) −5.42623 −0.635092 −0.317546 0.948243i \(-0.602859\pi\)
−0.317546 + 0.948243i \(0.602859\pi\)
\(74\) −0.118326 + 0.671061i −0.0137551 + 0.0780093i
\(75\) 0 0
\(76\) 2.17606 + 12.3411i 0.249611 + 1.41562i
\(77\) −6.27199 + 6.96152i −0.714760 + 0.793339i
\(78\) 0 0
\(79\) 2.08876 11.8459i 0.235004 1.33277i −0.607603 0.794241i \(-0.707869\pi\)
0.842606 0.538530i \(-0.181020\pi\)
\(80\) −3.32197 5.75383i −0.371408 0.643297i
\(81\) 0 0
\(82\) −0.116139 + 0.201159i −0.0128254 + 0.0222143i
\(83\) 9.05188 3.29461i 0.993573 0.361631i 0.206470 0.978453i \(-0.433802\pi\)
0.787103 + 0.616822i \(0.211580\pi\)
\(84\) 0 0
\(85\) 10.1063 8.48015i 1.09618 0.919802i
\(86\) 2.95669 + 1.07615i 0.318829 + 0.116044i
\(87\) 0 0
\(88\) −0.786951 + 4.46302i −0.0838892 + 0.475759i
\(89\) −1.14565 1.98432i −0.121438 0.210337i 0.798897 0.601468i \(-0.205417\pi\)
−0.920335 + 0.391131i \(0.872084\pi\)
\(90\) 0 0
\(91\) −8.56264 + 1.20076i −0.897609 + 0.125874i
\(92\) −1.98369 + 11.2501i −0.206814 + 1.17290i
\(93\) 0 0
\(94\) −0.441387 2.50323i −0.0455256 0.258189i
\(95\) −2.27228 12.8868i −0.233131 1.32215i
\(96\) 0 0
\(97\) 0.870524 4.93699i 0.0883883 0.501275i −0.908186 0.418568i \(-0.862532\pi\)
0.996574 0.0827074i \(-0.0263567\pi\)
\(98\) 1.65460 + 1.59977i 0.167140 + 0.161601i
\(99\) 0 0
\(100\) −1.03787 1.79765i −0.103787 0.179765i
\(101\) 2.56747 14.5609i 0.255473 1.44886i −0.539382 0.842061i \(-0.681342\pi\)
0.794855 0.606800i \(-0.207547\pi\)
\(102\) 0 0
\(103\) 4.98262 + 1.81352i 0.490952 + 0.178692i 0.575620 0.817717i \(-0.304761\pi\)
−0.0846681 + 0.996409i \(0.526983\pi\)
\(104\) −3.20346 + 2.68802i −0.314125 + 0.263582i
\(105\) 0 0
\(106\) 0.0673330 0.0245072i 0.00653996 0.00238035i
\(107\) 10.3111 17.8593i 0.996811 1.72653i 0.429297 0.903163i \(-0.358761\pi\)
0.567514 0.823364i \(-0.307905\pi\)
\(108\) 0 0
\(109\) 6.05840 + 10.4935i 0.580290 + 1.00509i 0.995445 + 0.0953403i \(0.0303939\pi\)
−0.415155 + 0.909751i \(0.636273\pi\)
\(110\) 0.399462 2.26546i 0.0380872 0.216003i
\(111\) 0 0
\(112\) −8.70286 1.85260i −0.822343 0.175055i
\(113\) 0.221866 + 1.25826i 0.0208714 + 0.118367i 0.993463 0.114151i \(-0.0364146\pi\)
−0.972592 + 0.232518i \(0.925304\pi\)
\(114\) 0 0
\(115\) 2.07140 11.7475i 0.193159 1.09546i
\(116\) 8.12175 0.754085
\(117\) 0 0
\(118\) 0.661486 + 1.14573i 0.0608947 + 0.105473i
\(119\) 0.621960 17.6574i 0.0570150 1.61865i
\(120\) 0 0
\(121\) 1.18197 0.991788i 0.107452 0.0901626i
\(122\) −0.323527 1.83481i −0.0292908 0.166116i
\(123\) 0 0
\(124\) −6.13085 5.14440i −0.550567 0.461981i
\(125\) 6.02266 + 10.4316i 0.538683 + 0.933026i
\(126\) 0 0
\(127\) −5.71616 + 9.90068i −0.507227 + 0.878543i 0.492738 + 0.870178i \(0.335996\pi\)
−0.999965 + 0.00836519i \(0.997337\pi\)
\(128\) −8.59368 + 3.12785i −0.759582 + 0.276465i
\(129\) 0 0
\(130\) 1.62610 1.36446i 0.142618 0.119671i
\(131\) −2.35278 13.3433i −0.205563 1.16581i −0.896551 0.442940i \(-0.853936\pi\)
0.690988 0.722866i \(-0.257176\pi\)
\(132\) 0 0
\(133\) −14.8590 9.29120i −1.28844 0.805650i
\(134\) −1.31734 −0.113801
\(135\) 0 0
\(136\) −4.27262 7.40040i −0.366374 0.634579i
\(137\) −4.08938 3.43140i −0.349379 0.293164i 0.451161 0.892442i \(-0.351010\pi\)
−0.800541 + 0.599278i \(0.795454\pi\)
\(138\) 0 0
\(139\) 8.02455 6.73339i 0.680633 0.571119i −0.235558 0.971860i \(-0.575692\pi\)
0.916191 + 0.400741i \(0.131247\pi\)
\(140\) 9.67192 + 2.05889i 0.817426 + 0.174008i
\(141\) 0 0
\(142\) −2.57356 + 0.936700i −0.215969 + 0.0786061i
\(143\) 11.5741 0.967875
\(144\) 0 0
\(145\) −8.48088 −0.704299
\(146\) 0.309802 1.75697i 0.0256394 0.145408i
\(147\) 0 0
\(148\) 3.68450 + 1.34105i 0.302864 + 0.110233i
\(149\) −1.60443 + 1.34627i −0.131440 + 0.110291i −0.706138 0.708075i \(-0.749564\pi\)
0.574698 + 0.818366i \(0.305120\pi\)
\(150\) 0 0
\(151\) −9.45486 + 3.44129i −0.769426 + 0.280048i −0.696756 0.717308i \(-0.745374\pi\)
−0.0726694 + 0.997356i \(0.523152\pi\)
\(152\) −8.47580 −0.687478
\(153\) 0 0
\(154\) −1.89600 2.42828i −0.152784 0.195677i
\(155\) 6.40195 + 5.37188i 0.514217 + 0.431480i
\(156\) 0 0
\(157\) −7.43472 + 6.23847i −0.593355 + 0.497884i −0.889302 0.457320i \(-0.848809\pi\)
0.295947 + 0.955204i \(0.404365\pi\)
\(158\) 3.71638 + 1.35265i 0.295659 + 0.107611i
\(159\) 0 0
\(160\) 6.80369 2.47634i 0.537879 0.195772i
\(161\) −9.83169 12.5918i −0.774845 0.992376i
\(162\) 0 0
\(163\) 3.25591 5.63940i 0.255023 0.441712i −0.709879 0.704324i \(-0.751250\pi\)
0.964902 + 0.262611i \(0.0845837\pi\)
\(164\) 1.02387 + 0.859128i 0.0799508 + 0.0670867i
\(165\) 0 0
\(166\) 0.549970 + 3.11904i 0.0426860 + 0.242084i
\(167\) −1.07006 6.06859i −0.0828035 0.469602i −0.997809 0.0661605i \(-0.978925\pi\)
0.915006 0.403441i \(-0.132186\pi\)
\(168\) 0 0
\(169\) −1.77715 1.49120i −0.136704 0.114708i
\(170\) 2.16881 + 3.75649i 0.166340 + 0.288110i
\(171\) 0 0
\(172\) 9.05258 15.6795i 0.690253 1.19555i
\(173\) 3.54075 + 2.97104i 0.269198 + 0.225884i 0.767387 0.641185i \(-0.221557\pi\)
−0.498188 + 0.867069i \(0.666001\pi\)
\(174\) 0 0
\(175\) 2.83924 + 0.604398i 0.214627 + 0.0456882i
\(176\) 11.1924 + 4.07369i 0.843657 + 0.307066i
\(177\) 0 0
\(178\) 0.707917 0.257661i 0.0530606 0.0193125i
\(179\) −11.2466 + 19.4797i −0.840609 + 1.45598i 0.0487707 + 0.998810i \(0.484470\pi\)
−0.889380 + 0.457168i \(0.848864\pi\)
\(180\) 0 0
\(181\) 3.82076 6.61776i 0.283995 0.491894i −0.688370 0.725360i \(-0.741673\pi\)
0.972365 + 0.233466i \(0.0750067\pi\)
\(182\) 0.100074 2.84108i 0.00741795 0.210595i
\(183\) 0 0
\(184\) −7.26053 2.64262i −0.535254 0.194816i
\(185\) −3.84742 1.40035i −0.282868 0.102956i
\(186\) 0 0
\(187\) −4.10693 + 23.2915i −0.300328 + 1.70325i
\(188\) −14.6262 −1.06672
\(189\) 0 0
\(190\) 4.30238 0.312127
\(191\) −0.451657 + 2.56147i −0.0326807 + 0.185342i −0.996778 0.0802068i \(-0.974442\pi\)
0.964098 + 0.265548i \(0.0855530\pi\)
\(192\) 0 0
\(193\) −10.8716 3.95695i −0.782557 0.284827i −0.0803184 0.996769i \(-0.525594\pi\)
−0.702238 + 0.711942i \(0.747816\pi\)
\(194\) 1.54886 + 0.563739i 0.111202 + 0.0404741i
\(195\) 0 0
\(196\) 10.7188 7.77772i 0.765625 0.555552i
\(197\) 3.06268 5.30472i 0.218207 0.377946i −0.736053 0.676924i \(-0.763312\pi\)
0.954260 + 0.298978i \(0.0966458\pi\)
\(198\) 0 0
\(199\) 5.74234 9.94603i 0.407064 0.705055i −0.587495 0.809227i \(-0.699886\pi\)
0.994559 + 0.104172i \(0.0332193\pi\)
\(200\) 1.31929 0.480183i 0.0932879 0.0339540i
\(201\) 0 0
\(202\) 4.56812 + 1.66266i 0.321412 + 0.116984i
\(203\) −7.60252 + 8.43831i −0.533592 + 0.592254i
\(204\) 0 0
\(205\) −1.06914 0.897118i −0.0746722 0.0626574i
\(206\) −0.871681 + 1.50980i −0.0607329 + 0.105192i
\(207\) 0 0
\(208\) 5.49534 + 9.51820i 0.381033 + 0.659969i
\(209\) 17.9704 + 15.0789i 1.24304 + 1.04303i
\(210\) 0 0
\(211\) −2.17536 12.3371i −0.149758 0.849320i −0.963423 0.267986i \(-0.913642\pi\)
0.813665 0.581334i \(-0.197469\pi\)
\(212\) −0.0715969 0.406046i −0.00491730 0.0278874i
\(213\) 0 0
\(214\) 5.19403 + 4.35831i 0.355057 + 0.297928i
\(215\) −9.45288 + 16.3729i −0.644681 + 1.11662i
\(216\) 0 0
\(217\) 11.0838 1.55431i 0.752419 0.105513i
\(218\) −3.74360 + 1.36256i −0.253549 + 0.0922842i
\(219\) 0 0
\(220\) −12.4386 4.52729i −0.838613 0.305230i
\(221\) −16.7182 + 14.0282i −1.12458 + 0.943639i
\(222\) 0 0
\(223\) 6.81490 + 5.71838i 0.456360 + 0.382931i 0.841790 0.539806i \(-0.181502\pi\)
−0.385430 + 0.922737i \(0.625947\pi\)
\(224\) 3.63512 8.98940i 0.242882 0.600630i
\(225\) 0 0
\(226\) −0.420084 −0.0279436
\(227\) 13.5318 4.92518i 0.898138 0.326895i 0.148632 0.988893i \(-0.452513\pi\)
0.749506 + 0.661997i \(0.230291\pi\)
\(228\) 0 0
\(229\) −13.6724 + 11.4725i −0.903499 + 0.758125i −0.970871 0.239603i \(-0.922983\pi\)
0.0673725 + 0.997728i \(0.478538\pi\)
\(230\) 3.68550 + 1.34141i 0.243015 + 0.0884501i
\(231\) 0 0
\(232\) −0.953892 + 5.40979i −0.0626261 + 0.355170i
\(233\) 5.15441 0.337677 0.168838 0.985644i \(-0.445998\pi\)
0.168838 + 0.985644i \(0.445998\pi\)
\(234\) 0 0
\(235\) 15.2729 0.996297
\(236\) 7.15350 2.60366i 0.465653 0.169484i
\(237\) 0 0
\(238\) 5.68183 + 1.20951i 0.368298 + 0.0784007i
\(239\) 11.4287 9.58981i 0.739260 0.620313i −0.193379 0.981124i \(-0.561945\pi\)
0.932639 + 0.360811i \(0.117500\pi\)
\(240\) 0 0
\(241\) 10.4840 + 8.79711i 0.675333 + 0.566672i 0.914639 0.404273i \(-0.132475\pi\)
−0.239306 + 0.970944i \(0.576920\pi\)
\(242\) 0.253652 + 0.439337i 0.0163053 + 0.0282417i
\(243\) 0 0
\(244\) −10.7207 −0.686321
\(245\) −11.1927 + 8.12165i −0.715077 + 0.518873i
\(246\) 0 0
\(247\) 3.75890 + 21.3178i 0.239173 + 1.35642i
\(248\) 4.14668 3.47948i 0.263315 0.220947i
\(249\) 0 0
\(250\) −3.72152 + 1.35452i −0.235369 + 0.0856675i
\(251\) 4.85765 8.41369i 0.306612 0.531067i −0.671007 0.741451i \(-0.734138\pi\)
0.977619 + 0.210384i \(0.0674713\pi\)
\(252\) 0 0
\(253\) 10.6924 + 18.5198i 0.672225 + 1.16433i
\(254\) −2.87941 2.41612i −0.180671 0.151601i
\(255\) 0 0
\(256\) 1.39535 + 7.91340i 0.0872092 + 0.494588i
\(257\) 2.80389 2.35274i 0.174902 0.146760i −0.551135 0.834416i \(-0.685805\pi\)
0.726036 + 0.687657i \(0.241360\pi\)
\(258\) 0 0
\(259\) −4.84226 + 2.57280i −0.300884 + 0.159866i
\(260\) −6.10724 10.5780i −0.378755 0.656023i
\(261\) 0 0
\(262\) 4.45478 0.275217
\(263\) −0.613089 + 3.47700i −0.0378047 + 0.214401i −0.997858 0.0654158i \(-0.979163\pi\)
0.960053 + 0.279817i \(0.0902737\pi\)
\(264\) 0 0
\(265\) 0.0747629 + 0.424001i 0.00459265 + 0.0260462i
\(266\) 3.85678 4.28078i 0.236474 0.262472i
\(267\) 0 0
\(268\) −1.31629 + 7.46505i −0.0804052 + 0.456000i
\(269\) 0.434332 + 0.752285i 0.0264817 + 0.0458676i 0.878963 0.476891i \(-0.158236\pi\)
−0.852481 + 0.522758i \(0.824903\pi\)
\(270\) 0 0
\(271\) −3.54947 + 6.14785i −0.215615 + 0.373456i −0.953463 0.301511i \(-0.902509\pi\)
0.737848 + 0.674967i \(0.235842\pi\)
\(272\) −21.1042 + 7.68131i −1.27963 + 0.465748i
\(273\) 0 0
\(274\) 1.34454 1.12820i 0.0812266 0.0681572i
\(275\) −3.65143 1.32901i −0.220189 0.0801424i
\(276\) 0 0
\(277\) 0.668043 3.78866i 0.0401388 0.227639i −0.958139 0.286304i \(-0.907573\pi\)
0.998278 + 0.0586652i \(0.0186844\pi\)
\(278\) 1.72208 + 2.98272i 0.103283 + 0.178892i
\(279\) 0 0
\(280\) −2.50736 + 6.20053i −0.149843 + 0.370552i
\(281\) −2.68129 + 15.2064i −0.159952 + 0.907136i 0.794165 + 0.607702i \(0.207909\pi\)
−0.954117 + 0.299433i \(0.903202\pi\)
\(282\) 0 0
\(283\) −4.03012 22.8560i −0.239566 1.35865i −0.832781 0.553602i \(-0.813253\pi\)
0.593215 0.805044i \(-0.297858\pi\)
\(284\) 2.73653 + 15.5197i 0.162383 + 0.920922i
\(285\) 0 0
\(286\) −0.660806 + 3.74761i −0.0390743 + 0.221601i
\(287\) −1.85103 + 0.259574i −0.109263 + 0.0153222i
\(288\) 0 0
\(289\) −13.7979 23.8986i −0.811640 1.40580i
\(290\) 0.484203 2.74605i 0.0284334 0.161254i
\(291\) 0 0
\(292\) −9.64677 3.51114i −0.564534 0.205474i
\(293\) −11.6223 + 9.75229i −0.678983 + 0.569735i −0.915709 0.401842i \(-0.868370\pi\)
0.236726 + 0.971577i \(0.423926\pi\)
\(294\) 0 0
\(295\) −7.46982 + 2.71879i −0.434910 + 0.158294i
\(296\) −1.32600 + 2.29669i −0.0770719 + 0.133492i
\(297\) 0 0
\(298\) −0.344312 0.596366i −0.0199455 0.0345466i
\(299\) −3.42660 + 19.4332i −0.198165 + 1.12385i
\(300\) 0 0
\(301\) 7.81684 + 24.0826i 0.450555 + 1.38810i
\(302\) −0.574454 3.25789i −0.0330561 0.187471i
\(303\) 0 0
\(304\) −3.86821 + 21.9377i −0.221857 + 1.25821i
\(305\) 11.1947 0.641009
\(306\) 0 0
\(307\) −2.22517 3.85410i −0.126997 0.219965i 0.795515 0.605934i \(-0.207201\pi\)
−0.922512 + 0.385969i \(0.873867\pi\)
\(308\) −15.6549 + 8.31780i −0.892023 + 0.473951i
\(309\) 0 0
\(310\) −2.10489 + 1.76621i −0.119549 + 0.100314i
\(311\) −5.55693 31.5149i −0.315105 1.78705i −0.571631 0.820511i \(-0.693689\pi\)
0.256526 0.966537i \(-0.417422\pi\)
\(312\) 0 0
\(313\) 18.9280 + 15.8825i 1.06987 + 0.897732i 0.995041 0.0994643i \(-0.0317129\pi\)
0.0748338 + 0.997196i \(0.476157\pi\)
\(314\) −1.59550 2.76348i −0.0900392 0.155952i
\(315\) 0 0
\(316\) 11.3785 19.7082i 0.640091 1.10867i
\(317\) −12.6372 + 4.59956i −0.709775 + 0.258337i −0.671578 0.740933i \(-0.734383\pi\)
−0.0381961 + 0.999270i \(0.512161\pi\)
\(318\) 0 0
\(319\) 11.6468 9.77280i 0.652094 0.547172i
\(320\) −1.89404 10.7417i −0.105880 0.600477i
\(321\) 0 0
\(322\) 4.63847 2.46452i 0.258492 0.137342i
\(323\) −44.2333 −2.46121
\(324\) 0 0
\(325\) −1.79281 3.10524i −0.0994473 0.172248i
\(326\) 1.64011 + 1.37621i 0.0908372 + 0.0762215i
\(327\) 0 0
\(328\) −0.692507 + 0.581082i −0.0382373 + 0.0320849i
\(329\) 13.6911 15.1963i 0.754816 0.837799i
\(330\) 0 0
\(331\) 21.6307 7.87292i 1.18893 0.432735i 0.329582 0.944127i \(-0.393092\pi\)
0.859348 + 0.511392i \(0.170870\pi\)
\(332\) 18.2243 1.00019
\(333\) 0 0
\(334\) 2.02606 0.110861
\(335\) 1.37449 7.79514i 0.0750966 0.425894i
\(336\) 0 0
\(337\) 6.68806 + 2.43426i 0.364322 + 0.132602i 0.517693 0.855566i \(-0.326791\pi\)
−0.153371 + 0.988169i \(0.549013\pi\)
\(338\) 0.584305 0.490290i 0.0317820 0.0266682i
\(339\) 0 0
\(340\) 23.4542 8.53661i 1.27198 0.462963i
\(341\) −14.9820 −0.811319
\(342\) 0 0
\(343\) −1.95262 + 18.4170i −0.105431 + 0.994427i
\(344\) 9.38072 + 7.87136i 0.505774 + 0.424395i
\(345\) 0 0
\(346\) −1.16416 + 0.976842i −0.0625854 + 0.0525154i
\(347\) 13.2935 + 4.83843i 0.713631 + 0.259740i 0.673219 0.739443i \(-0.264911\pi\)
0.0404113 + 0.999183i \(0.487133\pi\)
\(348\) 0 0
\(349\) −6.25442 + 2.27642i −0.334792 + 0.121854i −0.503945 0.863735i \(-0.668119\pi\)
0.169154 + 0.985590i \(0.445897\pi\)
\(350\) −0.357802 + 0.884820i −0.0191253 + 0.0472956i
\(351\) 0 0
\(352\) −6.48991 + 11.2409i −0.345914 + 0.599140i
\(353\) 18.6678 + 15.6642i 0.993589 + 0.833720i 0.986083 0.166252i \(-0.0531664\pi\)
0.00750578 + 0.999972i \(0.497611\pi\)
\(354\) 0 0
\(355\) −2.85754 16.2059i −0.151663 0.860121i
\(356\) −0.752746 4.26904i −0.0398955 0.226258i
\(357\) 0 0
\(358\) −5.66527 4.75373i −0.299419 0.251242i
\(359\) −2.69724 4.67175i −0.142355 0.246566i 0.786028 0.618191i \(-0.212134\pi\)
−0.928383 + 0.371625i \(0.878801\pi\)
\(360\) 0 0
\(361\) −12.4369 + 21.5414i −0.654576 + 1.13376i
\(362\) 1.92464 + 1.61497i 0.101157 + 0.0848808i
\(363\) 0 0
\(364\) −15.9997 3.40590i −0.838610 0.178517i
\(365\) 10.0733 + 3.66639i 0.527262 + 0.191908i
\(366\) 0 0
\(367\) −11.7511 + 4.27703i −0.613400 + 0.223259i −0.629990 0.776603i \(-0.716941\pi\)
0.0165902 + 0.999862i \(0.494719\pi\)
\(368\) −10.1534 + 17.5862i −0.529283 + 0.916745i
\(369\) 0 0
\(370\) 0.673085 1.16582i 0.0349920 0.0606080i
\(371\) 0.488893 + 0.305700i 0.0253821 + 0.0158712i
\(372\) 0 0
\(373\) 1.07733 + 0.392117i 0.0557822 + 0.0203030i 0.369761 0.929127i \(-0.379440\pi\)
−0.313978 + 0.949430i \(0.601662\pi\)
\(374\) −7.30716 2.65959i −0.377844 0.137524i
\(375\) 0 0
\(376\) 1.71783 9.74232i 0.0885905 0.502422i
\(377\) 14.0294 0.722551
\(378\) 0 0
\(379\) 28.2287 1.45001 0.725006 0.688742i \(-0.241837\pi\)
0.725006 + 0.688742i \(0.241837\pi\)
\(380\) 4.29893 24.3804i 0.220530 1.25069i
\(381\) 0 0
\(382\) −0.803600 0.292487i −0.0411158 0.0149649i
\(383\) −11.9552 4.35134i −0.610883 0.222343i 0.0180067 0.999838i \(-0.494268\pi\)
−0.628889 + 0.777495i \(0.716490\pi\)
\(384\) 0 0
\(385\) 16.3472 8.68561i 0.833130 0.442660i
\(386\) 1.90193 3.29424i 0.0968057 0.167672i
\(387\) 0 0
\(388\) 4.74218 8.21370i 0.240748 0.416988i
\(389\) −7.37415 + 2.68397i −0.373884 + 0.136083i −0.522126 0.852868i \(-0.674861\pi\)
0.148242 + 0.988951i \(0.452639\pi\)
\(390\) 0 0
\(391\) −37.8912 13.7913i −1.91624 0.697454i
\(392\) 3.92173 + 8.05311i 0.198077 + 0.406744i
\(393\) 0 0
\(394\) 1.54277 + 1.29454i 0.0777238 + 0.0652180i
\(395\) −11.8817 + 20.5796i −0.597831 + 1.03547i
\(396\) 0 0
\(397\) −6.77414 11.7332i −0.339985 0.588871i 0.644445 0.764651i \(-0.277089\pi\)
−0.984429 + 0.175780i \(0.943755\pi\)
\(398\) 2.89260 + 2.42718i 0.144993 + 0.121664i
\(399\) 0 0
\(400\) −0.640743 3.63384i −0.0320372 0.181692i
\(401\) 5.39809 + 30.6141i 0.269568 + 1.52880i 0.755704 + 0.654913i \(0.227295\pi\)
−0.486136 + 0.873883i \(0.661594\pi\)
\(402\) 0 0
\(403\) −10.5904 8.88637i −0.527544 0.442662i
\(404\) 13.9863 24.2250i 0.695846 1.20524i
\(405\) 0 0
\(406\) −2.29821 2.94341i −0.114058 0.146079i
\(407\) 6.89732 2.51042i 0.341887 0.124437i
\(408\) 0 0
\(409\) 8.59389 + 3.12792i 0.424941 + 0.154666i 0.545633 0.838024i \(-0.316289\pi\)
−0.120692 + 0.992690i \(0.538511\pi\)
\(410\) 0.351522 0.294962i 0.0173604 0.0145671i
\(411\) 0 0
\(412\) 7.68464 + 6.44818i 0.378595 + 0.317679i
\(413\) −3.99102 + 9.86953i −0.196385 + 0.485648i
\(414\) 0 0
\(415\) −19.0302 −0.934153
\(416\) −11.2549 + 4.09646i −0.551818 + 0.200845i
\(417\) 0 0
\(418\) −5.90844 + 4.95777i −0.288991 + 0.242492i
\(419\) 31.3856 + 11.4234i 1.53329 + 0.558070i 0.964423 0.264362i \(-0.0851614\pi\)
0.568862 + 0.822433i \(0.307384\pi\)
\(420\) 0 0
\(421\) −5.85790 + 33.2218i −0.285497 + 1.61913i 0.418009 + 0.908443i \(0.362728\pi\)
−0.703506 + 0.710690i \(0.748383\pi\)
\(422\) 4.11886 0.200503
\(423\) 0 0
\(424\) 0.278871 0.0135432
\(425\) 6.88509 2.50597i 0.333976 0.121557i
\(426\) 0 0
\(427\) 10.0353 11.1386i 0.485642 0.539032i
\(428\) 29.8873 25.0784i 1.44466 1.21221i
\(429\) 0 0
\(430\) −4.76172 3.99556i −0.229631 0.192683i
\(431\) −5.98641 10.3688i −0.288355 0.499446i 0.685062 0.728485i \(-0.259775\pi\)
−0.973417 + 0.229039i \(0.926442\pi\)
\(432\) 0 0
\(433\) 25.0145 1.20212 0.601060 0.799204i \(-0.294745\pi\)
0.601060 + 0.799204i \(0.294745\pi\)
\(434\) −0.129539 + 3.67760i −0.00621808 + 0.176531i
\(435\) 0 0
\(436\) 3.98067 + 22.5755i 0.190639 + 1.08117i
\(437\) −30.6381 + 25.7084i −1.46562 + 1.22980i
\(438\) 0 0
\(439\) −11.0829 + 4.03383i −0.528956 + 0.192524i −0.592672 0.805444i \(-0.701927\pi\)
0.0637163 + 0.997968i \(0.479705\pi\)
\(440\) 4.47648 7.75349i 0.213408 0.369633i
\(441\) 0 0
\(442\) −3.58774 6.21414i −0.170651 0.295577i
\(443\) 28.1368 + 23.6096i 1.33682 + 1.12173i 0.982431 + 0.186629i \(0.0597561\pi\)
0.354391 + 0.935097i \(0.384688\pi\)
\(444\) 0 0
\(445\) 0.786032 + 4.45781i 0.0372615 + 0.211320i
\(446\) −2.24066 + 1.88014i −0.106098 + 0.0890270i
\(447\) 0 0
\(448\) −12.3856 7.74460i −0.585165 0.365898i
\(449\) −6.54227 11.3315i −0.308749 0.534769i 0.669340 0.742956i \(-0.266577\pi\)
−0.978089 + 0.208188i \(0.933244\pi\)
\(450\) 0 0
\(451\) 2.50203 0.117816
\(452\) −0.419747 + 2.38051i −0.0197433 + 0.111970i
\(453\) 0 0
\(454\) 0.822160 + 4.66270i 0.0385859 + 0.218831i
\(455\) 16.7072 + 3.55650i 0.783243 + 0.166731i
\(456\) 0 0
\(457\) 2.25853 12.8088i 0.105650 0.599168i −0.885309 0.465003i \(-0.846053\pi\)
0.990959 0.134166i \(-0.0428355\pi\)
\(458\) −2.93412 5.08204i −0.137102 0.237468i
\(459\) 0 0
\(460\) 11.2840 19.5444i 0.526118 0.911264i
\(461\) −26.8426 + 9.76990i −1.25018 + 0.455030i −0.880464 0.474113i \(-0.842769\pi\)
−0.369720 + 0.929143i \(0.620546\pi\)
\(462\) 0 0
\(463\) 18.1417 15.2227i 0.843115 0.707458i −0.115147 0.993348i \(-0.536734\pi\)
0.958262 + 0.285891i \(0.0922895\pi\)
\(464\) 13.5667 + 4.93787i 0.629818 + 0.229235i
\(465\) 0 0
\(466\) −0.294283 + 1.66896i −0.0136324 + 0.0773132i
\(467\) 2.86818 + 4.96783i 0.132723 + 0.229884i 0.924725 0.380635i \(-0.124294\pi\)
−0.792002 + 0.610518i \(0.790961\pi\)
\(468\) 0 0
\(469\) −6.52388 8.35540i −0.301245 0.385816i
\(470\) −0.871985 + 4.94527i −0.0402217 + 0.228108i
\(471\) 0 0
\(472\) 0.894093 + 5.07065i 0.0411539 + 0.233396i
\(473\) −5.88538 33.3777i −0.270610 1.53471i
\(474\) 0 0
\(475\) 1.26197 7.15701i 0.0579033 0.328386i
\(476\) 12.5312 30.9889i 0.574369 1.42037i
\(477\) 0 0
\(478\) 2.45261 + 4.24804i 0.112180 + 0.194301i
\(479\) 4.90286 27.8055i 0.224018 1.27047i −0.640537 0.767928i \(-0.721288\pi\)
0.864554 0.502539i \(-0.167601\pi\)
\(480\) 0 0
\(481\) 6.36455 + 2.31651i 0.290199 + 0.105624i
\(482\) −3.44701 + 2.89238i −0.157007 + 0.131745i
\(483\) 0 0
\(484\) 2.74306 0.998392i 0.124684 0.0453814i
\(485\) −4.95188 + 8.57691i −0.224853 + 0.389457i
\(486\) 0 0
\(487\) −15.9865 27.6895i −0.724420 1.25473i −0.959212 0.282686i \(-0.908774\pi\)
0.234793 0.972045i \(-0.424559\pi\)
\(488\) 1.25914 7.14091i 0.0569984 0.323254i
\(489\) 0 0
\(490\) −1.99070 4.08782i −0.0899307 0.184669i
\(491\) 0.954103 + 5.41099i 0.0430581 + 0.244194i 0.998739 0.0502112i \(-0.0159894\pi\)
−0.955681 + 0.294406i \(0.904878\pi\)
\(492\) 0 0
\(493\) −4.97816 + 28.2325i −0.224205 + 1.27153i
\(494\) −7.11716 −0.320216
\(495\) 0 0
\(496\) −7.11338 12.3207i −0.319400 0.553217i
\(497\) −18.6862 11.6843i −0.838189 0.524111i
\(498\) 0 0
\(499\) 19.8712 16.6740i 0.889559 0.746429i −0.0785626 0.996909i \(-0.525033\pi\)
0.968122 + 0.250480i \(0.0805886\pi\)
\(500\) 3.95718 + 22.4423i 0.176971 + 1.00365i
\(501\) 0 0
\(502\) 2.44695 + 2.05324i 0.109213 + 0.0916405i
\(503\) 8.11379 + 14.0535i 0.361776 + 0.626614i 0.988253 0.152826i \(-0.0488372\pi\)
−0.626477 + 0.779440i \(0.715504\pi\)
\(504\) 0 0
\(505\) −14.6048 + 25.2962i −0.649905 + 1.12567i
\(506\) −6.60704 + 2.40477i −0.293719 + 0.106905i
\(507\) 0 0
\(508\) −16.5686 + 13.9027i −0.735113 + 0.616833i
\(509\) −2.15414 12.2167i −0.0954805 0.541497i −0.994599 0.103792i \(-0.966902\pi\)
0.899119 0.437705i \(-0.144209\pi\)
\(510\) 0 0
\(511\) 12.6780 6.73611i 0.560843 0.297988i
\(512\) −20.9324 −0.925090
\(513\) 0 0
\(514\) 0.601717 + 1.04220i 0.0265406 + 0.0459697i
\(515\) −8.02444 6.73331i −0.353599 0.296705i
\(516\) 0 0
\(517\) −20.9743 + 17.5995i −0.922448 + 0.774026i
\(518\) −0.556592 1.71478i −0.0244553 0.0753431i
\(519\) 0 0
\(520\) 7.76319 2.82557i 0.340438 0.123909i
\(521\) −24.6079 −1.07809 −0.539047 0.842276i \(-0.681215\pi\)
−0.539047 + 0.842276i \(0.681215\pi\)
\(522\) 0 0
\(523\) 24.0758 1.05276 0.526380 0.850250i \(-0.323549\pi\)
0.526380 + 0.850250i \(0.323549\pi\)
\(524\) 4.45121 25.2441i 0.194452 1.10279i
\(525\) 0 0
\(526\) −1.09082 0.397028i −0.0475622 0.0173112i
\(527\) 21.6406 18.1586i 0.942681 0.791003i
\(528\) 0 0
\(529\) −12.6478 + 4.60342i −0.549903 + 0.200148i
\(530\) −0.141557 −0.00614885
\(531\) 0 0
\(532\) −20.4044 26.1327i −0.884642 1.13300i
\(533\) 1.76862 + 1.48405i 0.0766074 + 0.0642812i
\(534\) 0 0
\(535\) −31.2089 + 26.1873i −1.34928 + 1.13218i
\(536\) −4.81778 1.75353i −0.208096 0.0757408i
\(537\) 0 0
\(538\) −0.268382 + 0.0976831i −0.0115708 + 0.00421142i
\(539\) 6.01210 24.0512i 0.258959 1.03596i
\(540\) 0 0
\(541\) −6.25983 + 10.8424i −0.269131 + 0.466149i −0.968638 0.248477i \(-0.920070\pi\)
0.699506 + 0.714626i \(0.253403\pi\)
\(542\) −1.78798 1.50029i −0.0768004 0.0644432i
\(543\) 0 0
\(544\) −4.24997 24.1028i −0.182216 1.03340i
\(545\) −4.15669 23.5738i −0.178053 1.00979i
\(546\) 0 0
\(547\) −20.6948 17.3650i −0.884845 0.742473i 0.0823242 0.996606i \(-0.473766\pi\)
−0.967169 + 0.254132i \(0.918210\pi\)
\(548\) −5.04977 8.74645i −0.215715 0.373630i
\(549\) 0 0
\(550\) 0.638797 1.10643i 0.0272384 0.0471783i
\(551\) 21.7825 + 18.2777i 0.927968 + 0.778657i
\(552\) 0 0
\(553\) 9.82527 + 30.2702i 0.417813 + 1.28722i
\(554\) 1.18860 + 0.432616i 0.0504988 + 0.0183801i
\(555\) 0 0
\(556\) 18.6230 6.77823i 0.789792 0.287461i
\(557\) 17.3337 30.0228i 0.734451 1.27211i −0.220512 0.975384i \(-0.570773\pi\)
0.954964 0.296723i \(-0.0958938\pi\)
\(558\) 0 0
\(559\) 15.6373 27.0846i 0.661388 1.14556i
\(560\) 14.9044 + 9.31955i 0.629824 + 0.393823i
\(561\) 0 0
\(562\) −4.77063 1.73637i −0.201237 0.0732442i
\(563\) −21.8184 7.94126i −0.919537 0.334684i −0.161483 0.986876i \(-0.551628\pi\)
−0.758054 + 0.652191i \(0.773850\pi\)
\(564\) 0 0
\(565\) 0.438308 2.48577i 0.0184398 0.104577i
\(566\) 7.63069 0.320742
\(567\) 0 0
\(568\) −10.6589 −0.447235
\(569\) 6.67248 37.8415i 0.279725 1.58640i −0.443816 0.896118i \(-0.646376\pi\)
0.723541 0.690281i \(-0.242513\pi\)
\(570\) 0 0
\(571\) −12.9888 4.72755i −0.543566 0.197842i 0.0556194 0.998452i \(-0.482287\pi\)
−0.599186 + 0.800610i \(0.704509\pi\)
\(572\) 20.5765 + 7.48923i 0.860346 + 0.313140i
\(573\) 0 0
\(574\) 0.0216334 0.614170i 0.000902960 0.0256350i
\(575\) 3.31247 5.73737i 0.138140 0.239265i
\(576\) 0 0
\(577\) 13.3633 23.1460i 0.556323 0.963580i −0.441476 0.897273i \(-0.645545\pi\)
0.997799 0.0663071i \(-0.0211217\pi\)
\(578\) 8.52598 3.10320i 0.354634 0.129076i
\(579\) 0 0
\(580\) −15.0773 5.48770i −0.626052 0.227864i
\(581\) −17.0592 + 18.9346i −0.707735 + 0.785541i
\(582\) 0 0
\(583\) −0.591262 0.496128i −0.0244876 0.0205475i
\(584\) 3.47173 6.01321i 0.143661 0.248828i
\(585\) 0 0
\(586\) −2.49416 4.32002i −0.103033 0.178458i
\(587\) −29.4089 24.6770i −1.21384 1.01853i −0.999124 0.0418527i \(-0.986674\pi\)
−0.214713 0.976677i \(-0.568882\pi\)
\(588\) 0 0
\(589\) −4.86567 27.5946i −0.200486 1.13701i
\(590\) −0.453848 2.57390i −0.0186846 0.105966i
\(591\) 0 0
\(592\) 5.33931 + 4.48021i 0.219444 + 0.184136i
\(593\) −12.5149 + 21.6764i −0.513925 + 0.890143i 0.485945 + 0.873989i \(0.338476\pi\)
−0.999870 + 0.0161540i \(0.994858\pi\)
\(594\) 0 0
\(595\) −13.0854 + 32.3592i −0.536448 + 1.32660i
\(596\) −3.72349 + 1.35524i −0.152520 + 0.0555127i
\(597\) 0 0
\(598\) −6.09670 2.21902i −0.249313 0.0907424i
\(599\) 30.1410 25.2913i 1.23153 1.03337i 0.233389 0.972383i \(-0.425018\pi\)
0.998138 0.0609908i \(-0.0194260\pi\)
\(600\) 0 0
\(601\) 2.59982 + 2.18151i 0.106049 + 0.0889856i 0.694270 0.719714i \(-0.255727\pi\)
−0.588221 + 0.808700i \(0.700172\pi\)
\(602\) −8.24405 + 1.15608i −0.336003 + 0.0471184i
\(603\) 0 0
\(604\) −19.0356 −0.774548
\(605\) −2.86435 + 1.04254i −0.116453 + 0.0423853i
\(606\) 0 0
\(607\) 27.5928 23.1531i 1.11996 0.939757i 0.121356 0.992609i \(-0.461276\pi\)
0.998602 + 0.0528524i \(0.0168313\pi\)
\(608\) −22.8117 8.30278i −0.925137 0.336722i
\(609\) 0 0
\(610\) −0.639146 + 3.62478i −0.0258783 + 0.146763i
\(611\) −25.2651 −1.02212
\(612\) 0 0
\(613\) −5.12560 −0.207021 −0.103511 0.994628i \(-0.533008\pi\)
−0.103511 + 0.994628i \(0.533008\pi\)
\(614\) 1.37497 0.500450i 0.0554894 0.0201965i
\(615\) 0 0
\(616\) −3.70172 11.4045i −0.149147 0.459499i
\(617\) −1.10793 + 0.929660i −0.0446034 + 0.0374267i −0.664817 0.747006i \(-0.731490\pi\)
0.620213 + 0.784433i \(0.287046\pi\)
\(618\) 0 0
\(619\) −8.23815 6.91263i −0.331119 0.277842i 0.462037 0.886861i \(-0.347119\pi\)
−0.793156 + 0.609019i \(0.791563\pi\)
\(620\) 7.90545 + 13.6926i 0.317490 + 0.549909i
\(621\) 0 0
\(622\) 10.5216 0.421877
\(623\) 5.14006 + 3.21403i 0.205932 + 0.128767i
\(624\) 0 0
\(625\) −3.17955 18.0321i −0.127182 0.721285i
\(626\) −6.22331 + 5.22197i −0.248733 + 0.208712i
\(627\) 0 0
\(628\) −17.2542 + 6.28000i −0.688516 + 0.250599i
\(629\) −6.92008 + 11.9859i −0.275922 + 0.477911i
\(630\) 0 0
\(631\) 20.5448 + 35.5847i 0.817877 + 1.41660i 0.907244 + 0.420605i \(0.138182\pi\)
−0.0893674 + 0.995999i \(0.528485\pi\)
\(632\) 11.7910 + 9.89379i 0.469019 + 0.393554i
\(633\) 0 0
\(634\) −0.767804 4.35443i −0.0304934 0.172937i
\(635\) 17.3013 14.5175i 0.686579 0.576108i
\(636\) 0 0
\(637\) 18.5154 13.4351i 0.733609 0.532320i
\(638\) 2.49941 + 4.32910i 0.0989526 + 0.171391i
\(639\) 0 0
\(640\) 18.0669 0.714156
\(641\) 0.139391 0.790524i 0.00550560 0.0312238i −0.981931 0.189238i \(-0.939398\pi\)
0.987437 + 0.158014i \(0.0505093\pi\)
\(642\) 0 0
\(643\) −1.59030 9.01902i −0.0627152 0.355675i −0.999975 0.00704426i \(-0.997758\pi\)
0.937260 0.348631i \(-0.113353\pi\)
\(644\) −9.33103 28.7476i −0.367694 1.13281i
\(645\) 0 0
\(646\) 2.52543 14.3224i 0.0993619 0.563509i
\(647\) 21.1182 + 36.5778i 0.830242 + 1.43802i 0.897846 + 0.440309i \(0.145131\pi\)
−0.0676045 + 0.997712i \(0.521536\pi\)
\(648\) 0 0
\(649\) 7.12532 12.3414i 0.279693 0.484443i
\(650\) 1.10781 0.403211i 0.0434520 0.0158152i
\(651\) 0 0
\(652\) 9.43744 7.91895i 0.369599 0.310130i
\(653\) −20.8576 7.59154i −0.816221 0.297080i −0.100030 0.994984i \(-0.531894\pi\)
−0.716191 + 0.697904i \(0.754116\pi\)
\(654\) 0 0
\(655\) −4.64804 + 26.3603i −0.181614 + 1.02998i
\(656\) 1.18795 + 2.05760i 0.0463818 + 0.0803356i
\(657\) 0 0
\(658\) 4.13878 + 5.30070i 0.161346 + 0.206643i
\(659\) −8.10575 + 45.9700i −0.315755 + 1.79074i 0.252198 + 0.967676i \(0.418846\pi\)
−0.567954 + 0.823061i \(0.692265\pi\)
\(660\) 0 0
\(661\) 3.94116 + 22.3514i 0.153293 + 0.869369i 0.960330 + 0.278868i \(0.0899590\pi\)
−0.807036 + 0.590502i \(0.798930\pi\)
\(662\) 1.31423 + 7.45335i 0.0510789 + 0.289683i
\(663\) 0 0
\(664\) −2.14043 + 12.1390i −0.0830647 + 0.471083i
\(665\) 21.3066 + 27.2883i 0.826236 + 1.05819i
\(666\) 0 0
\(667\) 12.9607 + 22.4485i 0.501839 + 0.869210i
\(668\) 2.02444 11.4812i 0.0783279 0.444220i
\(669\) 0 0
\(670\) 2.44554 + 0.890103i 0.0944794 + 0.0343877i
\(671\) −15.3737 + 12.9001i −0.593495 + 0.498002i
\(672\) 0 0
\(673\) −44.9112 + 16.3463i −1.73120 + 0.630105i −0.998715 0.0506794i \(-0.983861\pi\)
−0.732484 + 0.680784i \(0.761639\pi\)
\(674\) −1.17004 + 2.02657i −0.0450682 + 0.0780605i
\(675\) 0 0
\(676\) −2.19451 3.80100i −0.0844042 0.146192i
\(677\) 6.32092 35.8477i 0.242933 1.37774i −0.582312 0.812965i \(-0.697852\pi\)
0.825245 0.564775i \(-0.191037\pi\)
\(678\) 0 0
\(679\) 4.09484 + 12.6156i 0.157146 + 0.484143i
\(680\) 2.93146 + 16.6251i 0.112416 + 0.637545i
\(681\) 0 0
\(682\) 0.855373 4.85106i 0.0327539 0.185757i
\(683\) 0.934222 0.0357470 0.0178735 0.999840i \(-0.494310\pi\)
0.0178735 + 0.999840i \(0.494310\pi\)
\(684\) 0 0
\(685\) 5.27306 + 9.13321i 0.201473 + 0.348962i
\(686\) −5.85183 1.68374i −0.223424 0.0642853i
\(687\) 0 0
\(688\) 24.6544 20.6875i 0.939942 0.788705i
\(689\) −0.123676 0.701400i −0.00471167 0.0267212i
\(690\) 0 0
\(691\) −1.66900 1.40046i −0.0634918 0.0532760i 0.610489 0.792024i \(-0.290973\pi\)
−0.673981 + 0.738748i \(0.735417\pi\)
\(692\) 4.37229 + 7.57303i 0.166209 + 0.287883i
\(693\) 0 0
\(694\) −2.32562 + 4.02809i −0.0882793 + 0.152904i
\(695\) −19.4465 + 7.07795i −0.737648 + 0.268482i
\(696\) 0 0
\(697\) −3.61404 + 3.03254i −0.136892 + 0.114866i
\(698\) −0.380004 2.15511i −0.0143834 0.0815720i
\(699\) 0 0
\(700\) 4.65653 + 2.91168i 0.176000 + 0.110051i
\(701\) 28.5717 1.07914 0.539569 0.841942i \(-0.318587\pi\)
0.539569 + 0.841942i \(0.318587\pi\)
\(702\) 0 0
\(703\) 6.86385 + 11.8885i 0.258875 + 0.448384i
\(704\) 14.9790 + 12.5689i 0.564544 + 0.473709i
\(705\) 0 0
\(706\) −6.13776 + 5.15020i −0.230998 + 0.193830i
\(707\) 12.0771 + 37.2078i 0.454206 + 1.39934i
\(708\) 0 0
\(709\) −6.12624 + 2.22977i −0.230076 + 0.0837407i −0.454485 0.890754i \(-0.650177\pi\)
0.224410 + 0.974495i \(0.427955\pi\)
\(710\) 5.41051 0.203053
\(711\) 0 0
\(712\) 2.93196 0.109880
\(713\) 4.43552 25.1551i 0.166112 0.942066i
\(714\) 0 0
\(715\) −21.4864 7.82039i −0.803544 0.292466i
\(716\) −32.5989 + 27.3537i −1.21828 + 1.02226i
\(717\) 0 0
\(718\) 1.66667 0.606620i 0.0621997 0.0226389i
\(719\) 1.83299 0.0683589 0.0341795 0.999416i \(-0.489118\pi\)
0.0341795 + 0.999416i \(0.489118\pi\)
\(720\) 0 0
\(721\) −13.8929 + 1.94823i −0.517397 + 0.0725558i
\(722\) −6.26489 5.25687i −0.233155 0.195640i
\(723\) 0 0
\(724\) 11.0747 9.29278i 0.411588 0.345363i
\(725\) −4.42603 1.61094i −0.164379 0.0598290i
\(726\) 0 0
\(727\) 24.1007 8.77195i 0.893846 0.325334i 0.146062 0.989275i \(-0.453340\pi\)
0.747784 + 0.663942i \(0.231118\pi\)
\(728\) 4.14777 10.2572i 0.153727 0.380155i
\(729\) 0 0
\(730\) −1.76227 + 3.05235i −0.0652247 + 0.112972i
\(731\) 48.9559 + 41.0789i 1.81070 + 1.51936i
\(732\) 0 0
\(733\) 5.51821 + 31.2953i 0.203820 + 1.15592i 0.899286 + 0.437360i \(0.144087\pi\)
−0.695467 + 0.718558i \(0.744802\pi\)
\(734\) −0.713966 4.04910i −0.0263530 0.149455i
\(735\) 0 0
\(736\) −16.9523 14.2247i −0.624870 0.524328i
\(737\) 7.09501 + 12.2889i 0.261348 + 0.452668i
\(738\) 0 0
\(739\) 4.02667 6.97440i 0.148123 0.256557i −0.782410 0.622763i \(-0.786010\pi\)
0.930534 + 0.366206i \(0.119343\pi\)
\(740\) −5.93384 4.97908i −0.218132 0.183035i
\(741\) 0 0
\(742\) −0.126896 + 0.140847i −0.00465850 + 0.00517064i
\(743\) −44.5501 16.2149i −1.63438 0.594867i −0.648340 0.761351i \(-0.724536\pi\)
−0.986044 + 0.166484i \(0.946759\pi\)
\(744\) 0 0
\(745\) 3.88814 1.41517i 0.142450 0.0518477i
\(746\) −0.188473 + 0.326445i −0.00690050 + 0.0119520i
\(747\) 0 0
\(748\) −22.3725 + 38.7503i −0.818019 + 1.41685i
\(749\) −1.92066 + 54.5274i −0.0701794 + 1.99239i
\(750\) 0 0
\(751\) 30.5572 + 11.1219i 1.11505 + 0.405845i 0.832843 0.553509i \(-0.186711\pi\)
0.282206 + 0.959354i \(0.408934\pi\)
\(752\) −24.4318 8.89246i −0.890937 0.324275i
\(753\) 0 0
\(754\) −0.800987 + 4.54262i −0.0291702 + 0.165433i
\(755\) 19.8774 0.723411
\(756\) 0 0
\(757\) −49.9205 −1.81439 −0.907195 0.420710i \(-0.861781\pi\)
−0.907195 + 0.420710i \(0.861781\pi\)
\(758\) −1.61168 + 9.14026i −0.0585387 + 0.331989i
\(759\) 0 0
\(760\) 15.7346 + 5.72693i 0.570754 + 0.207737i
\(761\) 11.2752 + 4.10382i 0.408724 + 0.148763i 0.538196 0.842820i \(-0.319106\pi\)
−0.129472 + 0.991583i \(0.541328\pi\)
\(762\) 0 0
\(763\) −27.1816 16.9964i −0.984041 0.615311i
\(764\) −2.46040 + 4.26154i −0.0890142 + 0.154177i
\(765\) 0 0
\(766\) 2.09150 3.62258i 0.0755689 0.130889i
\(767\) 12.3569 4.49753i 0.446180 0.162396i
\(768\) 0 0
\(769\) 40.0547 + 14.5787i 1.44441 + 0.525722i 0.941024 0.338341i \(-0.109866\pi\)
0.503385 + 0.864062i \(0.332088\pi\)
\(770\) 1.87902 + 5.78900i 0.0677152 + 0.208621i
\(771\) 0 0
\(772\) −16.7672 14.0693i −0.603465 0.506367i
\(773\) −0.285981 + 0.495334i −0.0102860 + 0.0178159i −0.871123 0.491066i \(-0.836608\pi\)
0.860837 + 0.508882i \(0.169941\pi\)
\(774\) 0 0
\(775\) 2.32069 + 4.01955i 0.0833615 + 0.144386i
\(776\) 4.91408 + 4.12340i 0.176405 + 0.148021i
\(777\) 0 0
\(778\) −0.448035 2.54093i −0.0160628 0.0910969i
\(779\) 0.812580 + 4.60837i 0.0291137 + 0.165112i
\(780\) 0 0
\(781\) 22.5989 + 18.9627i 0.808651 + 0.678539i
\(782\) 6.62885 11.4815i 0.237047 0.410578i
\(783\) 0