Properties

Label 729.2.e.n.82.1
Level $729$
Weight $2$
Character 729.82
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
Inner twists $12$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 82.1
Root \(0.984808 + 0.173648i\) of defining polynomial
Character \(\chi\) \(=\) 729.82
Dual form 729.2.e.n.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.300767 - 1.70574i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-2.65366 - 2.22668i) q^{5} +(0.939693 + 0.342020i) q^{7} +(-0.866025 - 1.50000i) q^{8} +(-3.00000 + 5.19615i) q^{10} +(2.65366 - 2.22668i) q^{11} +(0.868241 - 4.92404i) q^{13} +(0.300767 - 1.70574i) q^{14} +(-3.83022 + 3.21394i) q^{16} +(0.500000 + 0.866025i) q^{19} +(3.25519 + 1.18479i) q^{20} +(-4.59627 - 3.85673i) q^{22} +(-6.51038 + 2.36959i) q^{23} +(1.21554 + 6.89365i) q^{25} -8.66025 q^{26} -1.00000 q^{28} +(0.601535 + 3.41147i) q^{29} +(-4.69846 + 1.71010i) q^{31} +(3.98048 + 3.34002i) q^{32} +(-1.73205 - 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{37} +(1.32683 - 1.11334i) q^{38} +(-1.04189 + 5.90885i) q^{40} +(-0.601535 + 3.41147i) q^{41} +(-0.766044 + 0.642788i) q^{43} +(-1.73205 + 3.00000i) q^{44} +(6.00000 + 10.3923i) q^{46} +(-3.25519 - 1.18479i) q^{47} +(-4.59627 - 3.85673i) q^{49} +(11.3932 - 4.14677i) q^{50} +(0.868241 + 4.92404i) q^{52} +10.3923 q^{53} -12.0000 q^{55} +(-0.300767 - 1.70574i) q^{56} +(5.63816 - 2.05212i) q^{58} +(-2.65366 - 2.22668i) q^{59} +(-1.87939 - 0.684040i) q^{61} +(4.33013 + 7.50000i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-13.2683 + 11.1334i) q^{65} +(1.38919 - 7.87846i) q^{67} +(-4.59627 + 3.85673i) q^{70} +(5.19615 - 9.00000i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(-1.62760 - 0.592396i) q^{74} +(-0.766044 - 0.642788i) q^{76} +(3.25519 - 1.18479i) q^{77} +(-0.173648 - 0.984808i) q^{79} +17.3205 q^{80} +6.00000 q^{82} +(-1.20307 - 6.82295i) q^{83} +(1.32683 + 1.11334i) q^{86} +(-5.63816 - 2.05212i) q^{88} +(5.19615 + 9.00000i) q^{89} +(2.50000 - 4.33013i) q^{91} +(5.30731 - 4.45336i) q^{92} +(-1.04189 + 5.90885i) q^{94} +(0.601535 - 3.41147i) q^{95} +(13.0228 - 10.9274i) q^{97} +(-5.19615 + 9.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 36 q^{10} + 6 q^{19} - 12 q^{28} + 6 q^{37} + 72 q^{46} - 144 q^{55} - 6 q^{64} - 12 q^{73} + 72 q^{82} + 30 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.300767 1.70574i −0.212675 1.20614i −0.884896 0.465788i \(-0.845771\pi\)
0.672222 0.740350i \(-0.265340\pi\)
\(3\) 0 0
\(4\) −0.939693 + 0.342020i −0.469846 + 0.171010i
\(5\) −2.65366 2.22668i −1.18675 0.995802i −0.999910 0.0134121i \(-0.995731\pi\)
−0.186841 0.982390i \(-0.559825\pi\)
\(6\) 0 0
\(7\) 0.939693 + 0.342020i 0.355170 + 0.129271i 0.513442 0.858124i \(-0.328370\pi\)
−0.158272 + 0.987396i \(0.550592\pi\)
\(8\) −0.866025 1.50000i −0.306186 0.530330i
\(9\) 0 0
\(10\) −3.00000 + 5.19615i −0.948683 + 1.64317i
\(11\) 2.65366 2.22668i 0.800107 0.671370i −0.148117 0.988970i \(-0.547321\pi\)
0.948225 + 0.317600i \(0.102877\pi\)
\(12\) 0 0
\(13\) 0.868241 4.92404i 0.240807 1.36568i −0.589226 0.807968i \(-0.700567\pi\)
0.830033 0.557714i \(-0.188322\pi\)
\(14\) 0.300767 1.70574i 0.0803835 0.455877i
\(15\) 0 0
\(16\) −3.83022 + 3.21394i −0.957556 + 0.803485i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 3.25519 + 1.18479i 0.727883 + 0.264928i
\(21\) 0 0
\(22\) −4.59627 3.85673i −0.979927 0.822257i
\(23\) −6.51038 + 2.36959i −1.35751 + 0.494093i −0.915283 0.402811i \(-0.868033\pi\)
−0.442225 + 0.896904i \(0.645811\pi\)
\(24\) 0 0
\(25\) 1.21554 + 6.89365i 0.243107 + 1.37873i
\(26\) −8.66025 −1.69842
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 0.601535 + 3.41147i 0.111702 + 0.633495i 0.988330 + 0.152326i \(0.0486764\pi\)
−0.876628 + 0.481169i \(0.840212\pi\)
\(30\) 0 0
\(31\) −4.69846 + 1.71010i −0.843869 + 0.307143i −0.727538 0.686067i \(-0.759336\pi\)
−0.116331 + 0.993211i \(0.537113\pi\)
\(32\) 3.98048 + 3.34002i 0.703657 + 0.590438i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.73205 3.00000i −0.292770 0.507093i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 1.32683 1.11334i 0.215240 0.180608i
\(39\) 0 0
\(40\) −1.04189 + 5.90885i −0.164737 + 0.934271i
\(41\) −0.601535 + 3.41147i −0.0939440 + 0.532783i 0.901122 + 0.433566i \(0.142745\pi\)
−0.995066 + 0.0992168i \(0.968366\pi\)
\(42\) 0 0
\(43\) −0.766044 + 0.642788i −0.116821 + 0.0980242i −0.699327 0.714802i \(-0.746517\pi\)
0.582506 + 0.812826i \(0.302072\pi\)
\(44\) −1.73205 + 3.00000i −0.261116 + 0.452267i
\(45\) 0 0
\(46\) 6.00000 + 10.3923i 0.884652 + 1.53226i
\(47\) −3.25519 1.18479i −0.474818 0.172820i 0.0935154 0.995618i \(-0.470190\pi\)
−0.568334 + 0.822798i \(0.692412\pi\)
\(48\) 0 0
\(49\) −4.59627 3.85673i −0.656610 0.550961i
\(50\) 11.3932 4.14677i 1.61124 0.586442i
\(51\) 0 0
\(52\) 0.868241 + 4.92404i 0.120403 + 0.682841i
\(53\) 10.3923 1.42749 0.713746 0.700404i \(-0.246997\pi\)
0.713746 + 0.700404i \(0.246997\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) −0.300767 1.70574i −0.0401917 0.227939i
\(57\) 0 0
\(58\) 5.63816 2.05212i 0.740326 0.269457i
\(59\) −2.65366 2.22668i −0.345477 0.289889i 0.453494 0.891259i \(-0.350177\pi\)
−0.798971 + 0.601370i \(0.794622\pi\)
\(60\) 0 0
\(61\) −1.87939 0.684040i −0.240631 0.0875824i 0.218890 0.975750i \(-0.429756\pi\)
−0.459520 + 0.888167i \(0.651979\pi\)
\(62\) 4.33013 + 7.50000i 0.549927 + 0.952501i
\(63\) 0 0
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) −13.2683 + 11.1334i −1.64573 + 1.38093i
\(66\) 0 0
\(67\) 1.38919 7.87846i 0.169716 0.962507i −0.774352 0.632756i \(-0.781924\pi\)
0.944068 0.329752i \(-0.106965\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −4.59627 + 3.85673i −0.549359 + 0.460967i
\(71\) 5.19615 9.00000i 0.616670 1.06810i −0.373419 0.927663i \(-0.621815\pi\)
0.990089 0.140441i \(-0.0448520\pi\)
\(72\) 0 0
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) −1.62760 0.592396i −0.189204 0.0688647i
\(75\) 0 0
\(76\) −0.766044 0.642788i −0.0878713 0.0737328i
\(77\) 3.25519 1.18479i 0.370963 0.135020i
\(78\) 0 0
\(79\) −0.173648 0.984808i −0.0195369 0.110800i 0.973480 0.228773i \(-0.0734713\pi\)
−0.993017 + 0.117973i \(0.962360\pi\)
\(80\) 17.3205 1.93649
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) −1.20307 6.82295i −0.132054 0.748916i −0.976866 0.213852i \(-0.931399\pi\)
0.844812 0.535063i \(-0.179712\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.32683 + 1.11334i 0.143076 + 0.120055i
\(87\) 0 0
\(88\) −5.63816 2.05212i −0.601029 0.218757i
\(89\) 5.19615 + 9.00000i 0.550791 + 0.953998i 0.998218 + 0.0596775i \(0.0190072\pi\)
−0.447427 + 0.894321i \(0.647659\pi\)
\(90\) 0 0
\(91\) 2.50000 4.33013i 0.262071 0.453921i
\(92\) 5.30731 4.45336i 0.553325 0.464295i
\(93\) 0 0
\(94\) −1.04189 + 5.90885i −0.107463 + 0.609451i
\(95\) 0.601535 3.41147i 0.0617162 0.350010i
\(96\) 0 0
\(97\) 13.0228 10.9274i 1.32226 1.10951i 0.336440 0.941705i \(-0.390777\pi\)
0.985820 0.167803i \(-0.0536674\pi\)
\(98\) −5.19615 + 9.00000i −0.524891 + 0.909137i
\(99\) 0 0
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) −13.0208 4.73917i −1.29561 0.471565i −0.400048 0.916494i \(-0.631007\pi\)
−0.895566 + 0.444929i \(0.853229\pi\)
\(102\) 0 0
\(103\) 6.12836 + 5.14230i 0.603845 + 0.506686i 0.892679 0.450693i \(-0.148823\pi\)
−0.288834 + 0.957379i \(0.593268\pi\)
\(104\) −8.13798 + 2.96198i −0.797994 + 0.290446i
\(105\) 0 0
\(106\) −3.12567 17.7265i −0.303592 1.72175i
\(107\) −10.3923 −1.00466 −0.502331 0.864675i \(-0.667524\pi\)
−0.502331 + 0.864675i \(0.667524\pi\)
\(108\) 0 0
\(109\) 17.0000 1.62830 0.814152 0.580651i \(-0.197202\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) 3.60921 + 20.4688i 0.344125 + 1.95163i
\(111\) 0 0
\(112\) −4.69846 + 1.71010i −0.443963 + 0.161589i
\(113\) 13.2683 + 11.1334i 1.24817 + 1.04734i 0.996839 + 0.0794428i \(0.0253141\pi\)
0.251335 + 0.967900i \(0.419130\pi\)
\(114\) 0 0
\(115\) 22.5526 + 8.20848i 2.10304 + 0.765445i
\(116\) −1.73205 3.00000i −0.160817 0.278543i
\(117\) 0 0
\(118\) −3.00000 + 5.19615i −0.276172 + 0.478345i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.173648 0.984808i 0.0157862 0.0895280i
\(122\) −0.601535 + 3.41147i −0.0544604 + 0.308860i
\(123\) 0 0
\(124\) 3.83022 3.21394i 0.343964 0.288620i
\(125\) 3.46410 6.00000i 0.309839 0.536656i
\(126\) 0 0
\(127\) −8.50000 14.7224i −0.754253 1.30640i −0.945745 0.324910i \(-0.894666\pi\)
0.191492 0.981494i \(-0.438667\pi\)
\(128\) 11.3932 + 4.14677i 1.00702 + 0.366526i
\(129\) 0 0
\(130\) 22.9813 + 19.2836i 2.01560 + 1.69129i
\(131\) 3.25519 1.18479i 0.284407 0.103516i −0.195878 0.980628i \(-0.562756\pi\)
0.480285 + 0.877113i \(0.340533\pi\)
\(132\) 0 0
\(133\) 0.173648 + 0.984808i 0.0150572 + 0.0853937i
\(134\) −13.8564 −1.19701
\(135\) 0 0
\(136\) 0 0
\(137\) −1.20307 6.82295i −0.102785 0.582924i −0.992082 0.125593i \(-0.959917\pi\)
0.889297 0.457331i \(-0.151194\pi\)
\(138\) 0 0
\(139\) 12.2160 4.44626i 1.03615 0.377127i 0.232729 0.972542i \(-0.425234\pi\)
0.803419 + 0.595415i \(0.203012\pi\)
\(140\) 2.65366 + 2.22668i 0.224275 + 0.188189i
\(141\) 0 0
\(142\) −16.9145 6.15636i −1.41943 0.516630i
\(143\) −8.66025 15.0000i −0.724207 1.25436i
\(144\) 0 0
\(145\) 6.00000 10.3923i 0.498273 0.863034i
\(146\) −2.65366 + 2.22668i −0.219618 + 0.184281i
\(147\) 0 0
\(148\) −0.173648 + 0.984808i −0.0142738 + 0.0809507i
\(149\) 1.20307 6.82295i 0.0985593 0.558958i −0.895039 0.445988i \(-0.852852\pi\)
0.993598 0.112970i \(-0.0360364\pi\)
\(150\) 0 0
\(151\) −12.2567 + 10.2846i −0.997437 + 0.836949i −0.986627 0.162993i \(-0.947885\pi\)
−0.0108097 + 0.999942i \(0.503441\pi\)
\(152\) 0.866025 1.50000i 0.0702439 0.121666i
\(153\) 0 0
\(154\) −3.00000 5.19615i −0.241747 0.418718i
\(155\) 16.2760 + 5.92396i 1.30732 + 0.475824i
\(156\) 0 0
\(157\) −9.95858 8.35624i −0.794781 0.666900i 0.152143 0.988359i \(-0.451383\pi\)
−0.946924 + 0.321458i \(0.895827\pi\)
\(158\) −1.62760 + 0.592396i −0.129485 + 0.0471285i
\(159\) 0 0
\(160\) −3.12567 17.7265i −0.247106 1.40141i
\(161\) −6.92820 −0.546019
\(162\) 0 0
\(163\) −1.00000 −0.0783260 −0.0391630 0.999233i \(-0.512469\pi\)
−0.0391630 + 0.999233i \(0.512469\pi\)
\(164\) −0.601535 3.41147i −0.0469720 0.266391i
\(165\) 0 0
\(166\) −11.2763 + 4.10424i −0.875212 + 0.318551i
\(167\) −18.5756 15.5868i −1.43742 1.20614i −0.941157 0.337970i \(-0.890260\pi\)
−0.496265 0.868171i \(-0.665296\pi\)
\(168\) 0 0
\(169\) −11.2763 4.10424i −0.867409 0.315711i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.500000 0.866025i 0.0381246 0.0660338i
\(173\) 10.6146 8.90673i 0.807015 0.677166i −0.142878 0.989740i \(-0.545636\pi\)
0.949893 + 0.312574i \(0.101191\pi\)
\(174\) 0 0
\(175\) −1.21554 + 6.89365i −0.0918860 + 0.521111i
\(176\) −3.00767 + 17.0574i −0.226712 + 1.28575i
\(177\) 0 0
\(178\) 13.7888 11.5702i 1.03351 0.867221i
\(179\) −10.3923 + 18.0000i −0.776757 + 1.34538i 0.157044 + 0.987592i \(0.449804\pi\)
−0.933801 + 0.357792i \(0.883530\pi\)
\(180\) 0 0
\(181\) −8.50000 14.7224i −0.631800 1.09431i −0.987184 0.159589i \(-0.948983\pi\)
0.355383 0.934721i \(-0.384350\pi\)
\(182\) −8.13798 2.96198i −0.603227 0.219557i
\(183\) 0 0
\(184\) 9.19253 + 7.71345i 0.677683 + 0.568643i
\(185\) −3.25519 + 1.18479i −0.239326 + 0.0871077i
\(186\) 0 0
\(187\) 0 0
\(188\) 3.46410 0.252646
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) −1.20307 6.82295i −0.0870511 0.493691i −0.996895 0.0787408i \(-0.974910\pi\)
0.909844 0.414950i \(-0.136201\pi\)
\(192\) 0 0
\(193\) 9.39693 3.42020i 0.676406 0.246191i 0.0191021 0.999818i \(-0.493919\pi\)
0.657303 + 0.753626i \(0.271697\pi\)
\(194\) −22.5561 18.9268i −1.61943 1.35886i
\(195\) 0 0
\(196\) 5.63816 + 2.05212i 0.402725 + 0.146580i
\(197\) −5.19615 9.00000i −0.370211 0.641223i 0.619387 0.785086i \(-0.287381\pi\)
−0.989598 + 0.143862i \(0.954048\pi\)
\(198\) 0 0
\(199\) 9.50000 16.4545i 0.673437 1.16643i −0.303486 0.952836i \(-0.598151\pi\)
0.976923 0.213591i \(-0.0685161\pi\)
\(200\) 9.28780 7.79339i 0.656746 0.551076i
\(201\) 0 0
\(202\) −4.16756 + 23.6354i −0.293228 + 1.66298i
\(203\) −0.601535 + 3.41147i −0.0422195 + 0.239439i
\(204\) 0 0
\(205\) 9.19253 7.71345i 0.642034 0.538731i
\(206\) 6.92820 12.0000i 0.482711 0.836080i
\(207\) 0 0
\(208\) 12.5000 + 21.6506i 0.866719 + 1.50120i
\(209\) 3.25519 + 1.18479i 0.225166 + 0.0819538i
\(210\) 0 0
\(211\) 3.83022 + 3.21394i 0.263683 + 0.221257i 0.765038 0.643985i \(-0.222720\pi\)
−0.501354 + 0.865242i \(0.667165\pi\)
\(212\) −9.76557 + 3.55438i −0.670702 + 0.244116i
\(213\) 0 0
\(214\) 3.12567 + 17.7265i 0.213666 + 1.21176i
\(215\) 3.46410 0.236250
\(216\) 0 0
\(217\) −5.00000 −0.339422
\(218\) −5.11305 28.9975i −0.346299 1.96396i
\(219\) 0 0
\(220\) 11.2763 4.10424i 0.760249 0.276708i
\(221\) 0 0
\(222\) 0 0
\(223\) 17.8542 + 6.49838i 1.19560 + 0.435164i 0.861688 0.507439i \(-0.169408\pi\)
0.333915 + 0.942603i \(0.391630\pi\)
\(224\) 2.59808 + 4.50000i 0.173591 + 0.300669i
\(225\) 0 0
\(226\) 15.0000 25.9808i 0.997785 1.72821i
\(227\) 10.6146 8.90673i 0.704517 0.591160i −0.218538 0.975829i \(-0.570129\pi\)
0.923055 + 0.384668i \(0.125684\pi\)
\(228\) 0 0
\(229\) 0.868241 4.92404i 0.0573750 0.325390i −0.942588 0.333957i \(-0.891616\pi\)
0.999963 + 0.00856731i \(0.00272709\pi\)
\(230\) 7.21842 40.9377i 0.475968 2.69935i
\(231\) 0 0
\(232\) 4.59627 3.85673i 0.301760 0.253206i
\(233\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(234\) 0 0
\(235\) 6.00000 + 10.3923i 0.391397 + 0.677919i
\(236\) 3.25519 + 1.18479i 0.211895 + 0.0771234i
\(237\) 0 0
\(238\) 0 0
\(239\) −6.51038 + 2.36959i −0.421122 + 0.153276i −0.543884 0.839160i \(-0.683047\pi\)
0.122763 + 0.992436i \(0.460825\pi\)
\(240\) 0 0
\(241\) −3.29932 18.7113i −0.212528 1.20530i −0.885146 0.465314i \(-0.845941\pi\)
0.672618 0.739990i \(-0.265170\pi\)
\(242\) −1.73205 −0.111340
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) 3.60921 + 20.4688i 0.230584 + 1.30771i
\(246\) 0 0
\(247\) 4.69846 1.71010i 0.298956 0.108811i
\(248\) 6.63414 + 5.56670i 0.421268 + 0.353486i
\(249\) 0 0
\(250\) −11.2763 4.10424i −0.713177 0.259575i
\(251\) 10.3923 + 18.0000i 0.655956 + 1.13615i 0.981653 + 0.190676i \(0.0610679\pi\)
−0.325697 + 0.945474i \(0.605599\pi\)
\(252\) 0 0
\(253\) −12.0000 + 20.7846i −0.754434 + 1.30672i
\(254\) −22.5561 + 18.9268i −1.41529 + 1.18757i
\(255\) 0 0
\(256\) 3.29932 18.7113i 0.206207 1.16946i
\(257\) −0.601535 + 3.41147i −0.0375227 + 0.212802i −0.997804 0.0662307i \(-0.978903\pi\)
0.960282 + 0.279033i \(0.0900138\pi\)
\(258\) 0 0
\(259\) 0.766044 0.642788i 0.0475997 0.0399409i
\(260\) 8.66025 15.0000i 0.537086 0.930261i
\(261\) 0 0
\(262\) −3.00000 5.19615i −0.185341 0.321019i
\(263\) −13.0208 4.73917i −0.802895 0.292230i −0.0922092 0.995740i \(-0.529393\pi\)
−0.710685 + 0.703510i \(0.751615\pi\)
\(264\) 0 0
\(265\) −27.5776 23.1404i −1.69408 1.42150i
\(266\) 1.62760 0.592396i 0.0997943 0.0363221i
\(267\) 0 0
\(268\) 1.38919 + 7.87846i 0.0848580 + 0.481254i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −11.2763 + 4.10424i −0.681227 + 0.247946i
\(275\) 18.5756 + 15.5868i 1.12015 + 0.939918i
\(276\) 0 0
\(277\) −15.9748 5.81434i −0.959831 0.349350i −0.185864 0.982576i \(-0.559508\pi\)
−0.773967 + 0.633226i \(0.781731\pi\)
\(278\) −11.2583 19.5000i −0.675230 1.16953i
\(279\) 0 0
\(280\) −3.00000 + 5.19615i −0.179284 + 0.310530i
\(281\) 10.6146 8.90673i 0.633215 0.531331i −0.268711 0.963221i \(-0.586598\pi\)
0.901926 + 0.431890i \(0.142153\pi\)
\(282\) 0 0
\(283\) −2.25743 + 12.8025i −0.134190 + 0.761030i 0.841230 + 0.540677i \(0.181832\pi\)
−0.975420 + 0.220353i \(0.929279\pi\)
\(284\) −1.80460 + 10.2344i −0.107084 + 0.607301i
\(285\) 0 0
\(286\) −22.9813 + 19.2836i −1.35891 + 1.14026i
\(287\) −1.73205 + 3.00000i −0.102240 + 0.177084i
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −19.5311 7.10876i −1.14691 0.417440i
\(291\) 0 0
\(292\) 1.53209 + 1.28558i 0.0896587 + 0.0752326i
\(293\) 13.0208 4.73917i 0.760681 0.276865i 0.0675880 0.997713i \(-0.478470\pi\)
0.693093 + 0.720848i \(0.256247\pi\)
\(294\) 0 0
\(295\) 2.08378 + 11.8177i 0.121322 + 0.688053i
\(296\) −1.73205 −0.100673
\(297\) 0 0
\(298\) −12.0000 −0.695141
\(299\) 6.01535 + 34.1147i 0.347877 + 1.97291i
\(300\) 0 0
\(301\) −0.939693 + 0.342020i −0.0541630 + 0.0197137i
\(302\) 21.2292 + 17.8135i 1.22161 + 1.02505i
\(303\) 0 0
\(304\) −4.69846 1.71010i −0.269475 0.0980810i
\(305\) 3.46410 + 6.00000i 0.198354 + 0.343559i
\(306\) 0 0
\(307\) −10.0000 + 17.3205i −0.570730 + 0.988534i 0.425761 + 0.904836i \(0.360006\pi\)
−0.996491 + 0.0836980i \(0.973327\pi\)
\(308\) −2.65366 + 2.22668i −0.151206 + 0.126877i
\(309\) 0 0
\(310\) 5.20945 29.5442i 0.295877 1.67800i
\(311\) −2.40614 + 13.6459i −0.136440 + 0.773788i 0.837407 + 0.546580i \(0.184071\pi\)
−0.973846 + 0.227208i \(0.927040\pi\)
\(312\) 0 0
\(313\) −0.766044 + 0.642788i −0.0432994 + 0.0363325i −0.664181 0.747572i \(-0.731219\pi\)
0.620881 + 0.783905i \(0.286775\pi\)
\(314\) −11.2583 + 19.5000i −0.635344 + 1.10045i
\(315\) 0 0
\(316\) 0.500000 + 0.866025i 0.0281272 + 0.0487177i
\(317\) 26.0415 + 9.47834i 1.46264 + 0.532357i 0.946091 0.323902i \(-0.104995\pi\)
0.516547 + 0.856259i \(0.327217\pi\)
\(318\) 0 0
\(319\) 9.19253 + 7.71345i 0.514683 + 0.431870i
\(320\) 3.25519 1.18479i 0.181971 0.0662319i
\(321\) 0 0
\(322\) 2.08378 + 11.8177i 0.116124 + 0.658574i
\(323\) 0 0
\(324\) 0 0
\(325\) 35.0000 1.94145
\(326\) 0.300767 + 1.70574i 0.0166580 + 0.0944720i
\(327\) 0 0
\(328\) 5.63816 2.05212i 0.311315 0.113309i
\(329\) −2.65366 2.22668i −0.146301 0.122761i
\(330\) 0 0
\(331\) 17.8542 + 6.49838i 0.981353 + 0.357183i 0.782366 0.622819i \(-0.214013\pi\)
0.198987 + 0.980002i \(0.436235\pi\)
\(332\) 3.46410 + 6.00000i 0.190117 + 0.329293i
\(333\) 0 0
\(334\) −21.0000 + 36.3731i −1.14907 + 1.99025i
\(335\) −21.2292 + 17.8135i −1.15988 + 0.973253i
\(336\) 0 0
\(337\) 0.868241 4.92404i 0.0472961 0.268229i −0.951985 0.306145i \(-0.900961\pi\)
0.999281 + 0.0379157i \(0.0120718\pi\)
\(338\) −3.60921 + 20.4688i −0.196315 + 1.11336i
\(339\) 0 0
\(340\) 0 0
\(341\) −8.66025 + 15.0000i −0.468979 + 0.812296i
\(342\) 0 0
\(343\) −6.50000 11.2583i −0.350967 0.607893i
\(344\) 1.62760 + 0.592396i 0.0877541 + 0.0319399i
\(345\) 0 0
\(346\) −18.3851 15.4269i −0.988387 0.829355i
\(347\) 22.7863 8.29355i 1.22323 0.445221i 0.351959 0.936015i \(-0.385516\pi\)
0.871275 + 0.490794i \(0.163293\pi\)
\(348\) 0 0
\(349\) −0.173648 0.984808i −0.00929517 0.0527156i 0.979807 0.199944i \(-0.0640759\pi\)
−0.989103 + 0.147228i \(0.952965\pi\)
\(350\) 12.1244 0.648074
\(351\) 0 0
\(352\) 18.0000 0.959403
\(353\) −3.00767 17.0574i −0.160082 0.907872i −0.953991 0.299835i \(-0.903068\pi\)
0.793909 0.608037i \(-0.208043\pi\)
\(354\) 0 0
\(355\) −33.8289 + 12.3127i −1.79545 + 0.653492i
\(356\) −7.96097 6.68004i −0.421930 0.354042i
\(357\) 0 0
\(358\) 33.8289 + 12.3127i 1.78791 + 0.650748i
\(359\) 15.5885 + 27.0000i 0.822727 + 1.42501i 0.903644 + 0.428285i \(0.140882\pi\)
−0.0809166 + 0.996721i \(0.525785\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) −22.5561 + 18.9268i −1.18552 + 0.994770i
\(363\) 0 0
\(364\) −0.868241 + 4.92404i −0.0455082 + 0.258090i
\(365\) −1.20307 + 6.82295i −0.0629716 + 0.357129i
\(366\) 0 0
\(367\) −12.2567 + 10.2846i −0.639795 + 0.536852i −0.903955 0.427627i \(-0.859350\pi\)
0.264160 + 0.964479i \(0.414905\pi\)
\(368\) 17.3205 30.0000i 0.902894 1.56386i
\(369\) 0 0
\(370\) 3.00000 + 5.19615i 0.155963 + 0.270135i
\(371\) 9.76557 + 3.55438i 0.507003 + 0.184534i
\(372\) 0 0
\(373\) 17.6190 + 14.7841i 0.912278 + 0.765492i 0.972551 0.232689i \(-0.0747526\pi\)
−0.0602727 + 0.998182i \(0.519197\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.04189 + 5.90885i 0.0537313 + 0.304725i
\(377\) 17.3205 0.892052
\(378\) 0 0
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) 0.601535 + 3.41147i 0.0308581 + 0.175005i
\(381\) 0 0
\(382\) −11.2763 + 4.10424i −0.576946 + 0.209991i
\(383\) 13.2683 + 11.1334i 0.677977 + 0.568891i 0.915415 0.402512i \(-0.131863\pi\)
−0.237437 + 0.971403i \(0.576307\pi\)
\(384\) 0 0
\(385\) −11.2763 4.10424i −0.574694 0.209172i
\(386\) −8.66025 15.0000i −0.440795 0.763480i
\(387\) 0 0
\(388\) −8.50000 + 14.7224i −0.431522 + 0.747418i
\(389\) −5.30731 + 4.45336i −0.269091 + 0.225794i −0.767341 0.641239i \(-0.778421\pi\)
0.498250 + 0.867034i \(0.333976\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.80460 + 10.2344i −0.0911463 + 0.516916i
\(393\) 0 0
\(394\) −13.7888 + 11.5702i −0.694670 + 0.582897i
\(395\) −1.73205 + 3.00000i −0.0871489 + 0.150946i
\(396\) 0 0
\(397\) 0.500000 + 0.866025i 0.0250943 + 0.0434646i 0.878300 0.478110i \(-0.158678\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −30.9243 11.2555i −1.55010 0.564189i
\(399\) 0 0
\(400\) −26.8116 22.4976i −1.34058 1.12488i
\(401\) 3.25519 1.18479i 0.162556 0.0591657i −0.259460 0.965754i \(-0.583545\pi\)
0.422017 + 0.906588i \(0.361322\pi\)
\(402\) 0 0
\(403\) 4.34120 + 24.6202i 0.216251 + 1.22642i
\(404\) 13.8564 0.689382
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) −0.601535 3.41147i −0.0298170 0.169100i
\(408\) 0 0
\(409\) −4.69846 + 1.71010i −0.232324 + 0.0845590i −0.455559 0.890206i \(-0.650561\pi\)
0.223235 + 0.974765i \(0.428338\pi\)
\(410\) −15.9219 13.3601i −0.786328 0.659808i
\(411\) 0 0
\(412\) −7.51754 2.73616i −0.370363 0.134801i
\(413\) −1.73205 3.00000i −0.0852286 0.147620i
\(414\) 0 0
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) 19.9024 16.7001i 0.975796 0.818790i
\(417\) 0 0
\(418\) 1.04189 5.90885i 0.0509605 0.289011i
\(419\) 6.61688 37.5262i 0.323256 1.83328i −0.198402 0.980121i \(-0.563575\pi\)
0.521658 0.853155i \(-0.325314\pi\)
\(420\) 0 0
\(421\) −14.5548 + 12.2130i −0.709360 + 0.595223i −0.924419 0.381377i \(-0.875450\pi\)
0.215060 + 0.976601i \(0.431005\pi\)
\(422\) 4.33013 7.50000i 0.210787 0.365094i
\(423\) 0 0
\(424\) −9.00000 15.5885i −0.437079 0.757042i
\(425\) 0 0
\(426\) 0 0
\(427\) −1.53209 1.28558i −0.0741430 0.0622133i
\(428\) 9.76557 3.55438i 0.472037 0.171807i
\(429\) 0 0
\(430\) −1.04189 5.90885i −0.0502444 0.284950i
\(431\) 20.7846 1.00116 0.500580 0.865690i \(-0.333120\pi\)
0.500580 + 0.865690i \(0.333120\pi\)
\(432\) 0 0
\(433\) −1.00000 −0.0480569 −0.0240285 0.999711i \(-0.507649\pi\)
−0.0240285 + 0.999711i \(0.507649\pi\)
\(434\) 1.50384 + 8.52869i 0.0721865 + 0.409390i
\(435\) 0 0
\(436\) −15.9748 + 5.81434i −0.765053 + 0.278457i
\(437\) −5.30731 4.45336i −0.253883 0.213033i
\(438\) 0 0
\(439\) −18.7939 6.84040i −0.896982 0.326475i −0.147939 0.988996i \(-0.547264\pi\)
−0.749043 + 0.662522i \(0.769486\pi\)
\(440\) 10.3923 + 18.0000i 0.495434 + 0.858116i
\(441\) 0 0
\(442\) 0 0
\(443\) 10.6146 8.90673i 0.504316 0.423171i −0.354808 0.934939i \(-0.615454\pi\)
0.859124 + 0.511768i \(0.171009\pi\)
\(444\) 0 0
\(445\) 6.25133 35.4531i 0.296342 1.68064i
\(446\) 5.71458 32.4090i 0.270593 1.53461i
\(447\) 0 0
\(448\) −0.766044 + 0.642788i −0.0361922 + 0.0303689i
\(449\) −5.19615 + 9.00000i −0.245222 + 0.424736i −0.962194 0.272365i \(-0.912194\pi\)
0.716972 + 0.697102i \(0.245527\pi\)
\(450\) 0 0
\(451\) 6.00000 + 10.3923i 0.282529 + 0.489355i
\(452\) −16.2760 5.92396i −0.765556 0.278640i
\(453\) 0 0
\(454\) −18.3851 15.4269i −0.862854 0.724020i
\(455\) −16.2760 + 5.92396i −0.763028 + 0.277720i
\(456\) 0 0
\(457\) 2.95202 + 16.7417i 0.138090 + 0.783145i 0.972658 + 0.232241i \(0.0746059\pi\)
−0.834569 + 0.550904i \(0.814283\pi\)
\(458\) −8.66025 −0.404667
\(459\) 0 0
\(460\) −24.0000 −1.11901
\(461\) −4.81228 27.2918i −0.224130 1.27111i −0.864341 0.502906i \(-0.832264\pi\)
0.640211 0.768199i \(-0.278847\pi\)
\(462\) 0 0
\(463\) 29.1305 10.6026i 1.35381 0.492746i 0.439674 0.898158i \(-0.355094\pi\)
0.914134 + 0.405412i \(0.132872\pi\)
\(464\) −13.2683 11.1334i −0.615964 0.516855i
\(465\) 0 0
\(466\) 0 0
\(467\) −5.19615 9.00000i −0.240449 0.416470i 0.720393 0.693566i \(-0.243961\pi\)
−0.960842 + 0.277096i \(0.910628\pi\)
\(468\) 0 0
\(469\) 4.00000 6.92820i 0.184703 0.319915i
\(470\) 15.9219 13.3601i 0.734424 0.616255i
\(471\) 0 0
\(472\) −1.04189 + 5.90885i −0.0479568 + 0.271977i
\(473\) −0.601535 + 3.41147i −0.0276586 + 0.156860i
\(474\) 0 0
\(475\) −5.36231 + 4.49951i −0.246040 + 0.206452i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.00000 + 10.3923i 0.274434 + 0.475333i
\(479\) −13.0208 4.73917i −0.594934 0.216538i 0.0269642 0.999636i \(-0.491416\pi\)
−0.621898 + 0.783098i \(0.713638\pi\)
\(480\) 0 0
\(481\) −3.83022 3.21394i −0.174643 0.146543i
\(482\) −30.9243 + 11.2555i −1.40856 + 0.512675i
\(483\) 0 0
\(484\) 0.173648 + 0.984808i 0.00789310 + 0.0447640i
\(485\) −58.8897 −2.67404
\(486\) 0 0
\(487\) −19.0000 −0.860972 −0.430486 0.902597i \(-0.641658\pi\)
−0.430486 + 0.902597i \(0.641658\pi\)
\(488\) 0.601535 + 3.41147i 0.0272302 + 0.154430i
\(489\) 0 0
\(490\) 33.8289 12.3127i 1.52824 0.556232i
\(491\) 29.1902 + 24.4935i 1.31734 + 1.10538i 0.986863 + 0.161561i \(0.0516527\pi\)
0.330473 + 0.943815i \(0.392792\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −4.33013 7.50000i −0.194822 0.337441i
\(495\) 0 0
\(496\) 12.5000 21.6506i 0.561267 0.972142i
\(497\) 7.96097 6.68004i 0.357098 0.299641i
\(498\) 0 0
\(499\) −4.86215 + 27.5746i −0.217660 + 1.23441i 0.658571 + 0.752518i \(0.271161\pi\)
−0.876231 + 0.481891i \(0.839950\pi\)
\(500\) −1.20307 + 6.82295i −0.0538029 + 0.305132i
\(501\) 0 0
\(502\) 27.5776 23.1404i 1.23085 1.03280i
\(503\) 20.7846 36.0000i 0.926740 1.60516i 0.138001 0.990432i \(-0.455932\pi\)
0.788739 0.614729i \(-0.210734\pi\)
\(504\) 0 0
\(505\) 24.0000 + 41.5692i 1.06799 + 1.84981i
\(506\) 39.0623 + 14.2175i 1.73653 + 0.632045i
\(507\) 0 0
\(508\) 13.0228 + 10.9274i 0.577791 + 0.484825i
\(509\) −26.0415 + 9.47834i −1.15427 + 0.420120i −0.847047 0.531517i \(-0.821622\pi\)
−0.307223 + 0.951638i \(0.599400\pi\)
\(510\) 0 0
\(511\) −0.347296 1.96962i −0.0153635 0.0871307i
\(512\) −8.66025 −0.382733
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) −4.81228 27.2918i −0.212054 1.20262i
\(516\) 0 0
\(517\) −11.2763 + 4.10424i −0.495932 + 0.180504i
\(518\) −1.32683 1.11334i −0.0582975 0.0489174i
\(519\) 0 0
\(520\) 28.1908 + 10.2606i 1.23625 + 0.449957i
\(521\) −10.3923 18.0000i −0.455295 0.788594i 0.543410 0.839467i \(-0.317133\pi\)
−0.998705 + 0.0508731i \(0.983800\pi\)
\(522\) 0 0
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) −2.65366 + 2.22668i −0.115925 + 0.0972730i
\(525\) 0 0
\(526\) −4.16756 + 23.6354i −0.181714 + 1.03055i
\(527\) 0 0
\(528\) 0 0
\(529\) 19.1511 16.0697i 0.832657 0.698682i
\(530\) −31.1769 + 54.0000i −1.35424 + 2.34561i
\(531\) 0 0
\(532\) −0.500000 0.866025i −0.0216777 0.0375470i
\(533\) 16.2760 + 5.92396i 0.704990 + 0.256595i
\(534\) 0 0
\(535\) 27.5776 + 23.1404i 1.19228 + 1.00044i
\(536\) −13.0208 + 4.73917i −0.562411 + 0.204701i
\(537\) 0 0
\(538\) 0 0
\(539\) −20.7846 −0.895257
\(540\) 0 0
\(541\) 17.0000 0.730887 0.365444 0.930834i \(-0.380917\pi\)
0.365444 + 0.930834i \(0.380917\pi\)
\(542\) 4.81228 + 27.2918i 0.206705 + 1.17228i
\(543\) 0 0
\(544\) 0 0
\(545\) −45.1121 37.8536i −1.93239 1.62147i
\(546\) 0 0
\(547\) −18.7939 6.84040i −0.803567 0.292475i −0.0926033 0.995703i \(-0.529519\pi\)
−0.710964 + 0.703229i \(0.751741\pi\)
\(548\) 3.46410 + 6.00000i 0.147979 + 0.256307i
\(549\) 0 0
\(550\) 21.0000 36.3731i 0.895443 1.55095i
\(551\) −2.65366 + 2.22668i −0.113050 + 0.0948598i
\(552\) 0 0
\(553\) 0.173648 0.984808i 0.00738427 0.0418783i
\(554\) −5.11305 + 28.9975i −0.217233 + 1.23199i
\(555\) 0 0
\(556\) −9.95858 + 8.35624i −0.422338 + 0.354383i
\(557\) 5.19615 9.00000i 0.220168 0.381342i −0.734691 0.678402i \(-0.762673\pi\)
0.954859 + 0.297060i \(0.0960061\pi\)
\(558\) 0 0
\(559\) 2.50000 + 4.33013i 0.105739 + 0.183145i
\(560\) 16.2760 + 5.92396i 0.687785 + 0.250333i
\(561\) 0 0
\(562\) −18.3851 15.4269i −0.775527 0.650745i
\(563\) 32.5519 11.8479i 1.37190 0.499331i 0.452187 0.891923i \(-0.350644\pi\)
0.919712 + 0.392593i \(0.128422\pi\)
\(564\) 0 0
\(565\) −10.4189 59.0885i −0.438326 2.48587i
\(566\) 22.5167 0.946446
\(567\) 0 0
\(568\) −18.0000 −0.755263
\(569\) 4.21074 + 23.8803i 0.176524 + 1.00112i 0.936371 + 0.351013i \(0.114163\pi\)
−0.759847 + 0.650102i \(0.774726\pi\)
\(570\) 0 0
\(571\) −38.5274 + 14.0228i −1.61232 + 0.586837i −0.981897 0.189414i \(-0.939341\pi\)
−0.630424 + 0.776251i \(0.717119\pi\)
\(572\) 13.2683 + 11.1334i 0.554775 + 0.465511i
\(573\) 0 0
\(574\) 5.63816 + 2.05212i 0.235332 + 0.0856539i
\(575\) −24.2487 42.0000i −1.01124 1.75152i
\(576\) 0 0
\(577\) 17.0000 29.4449i 0.707719 1.22581i −0.257982 0.966150i \(-0.583058\pi\)
0.965701 0.259656i \(-0.0836092\pi\)
\(578\) 22.5561 18.9268i 0.938209 0.787251i
\(579\) 0 0
\(580\) −2.08378 + 11.8177i −0.0865242 + 0.490703i
\(581\) 1.20307 6.82295i 0.0499117 0.283064i
\(582\) 0 0
\(583\) 27.5776 23.1404i 1.14215 0.958376i
\(584\) −1.73205 + 3.00000i −0.0716728 + 0.124141i
\(585\) 0 0
\(586\) −12.0000 20.7846i −0.495715 0.858604i
\(587\) 6.51038 + 2.36959i 0.268712 + 0.0978032i 0.472862 0.881136i \(-0.343221\pi\)
−0.204150 + 0.978940i \(0.565443\pi\)
\(588\) 0 0
\(589\) −3.83022 3.21394i −0.157822 0.132428i
\(590\) 19.5311 7.10876i 0.804084 0.292663i
\(591\) 0 0
\(592\) 0.868241 + 4.92404i 0.0356845 + 0.202377i
\(593\) −20.7846 −0.853522 −0.426761 0.904365i \(-0.640345\pi\)
−0.426761 + 0.904365i \(0.640345\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.20307 + 6.82295i 0.0492797 + 0.279479i
\(597\) 0 0
\(598\) 56.3816 20.5212i 2.30561 0.839175i
\(599\) −18.5756 15.5868i −0.758978 0.636858i 0.178883 0.983870i \(-0.442752\pi\)
−0.937861 + 0.347012i \(0.887196\pi\)
\(600\) 0 0
\(601\) −32.8892 11.9707i −1.34158 0.488295i −0.431270 0.902223i \(-0.641934\pi\)
−0.910310 + 0.413928i \(0.864157\pi\)
\(602\) 0.866025 + 1.50000i 0.0352966 + 0.0611354i
\(603\) 0 0
\(604\) 8.00000 13.8564i 0.325515 0.563809i
\(605\) −2.65366 + 2.22668i −0.107886 + 0.0905275i
\(606\) 0 0
\(607\) −2.25743 + 12.8025i −0.0916261 + 0.519637i 0.904103 + 0.427315i \(0.140540\pi\)
−0.995729 + 0.0923229i \(0.970571\pi\)
\(608\) −0.902302 + 5.11721i −0.0365932 + 0.207530i
\(609\) 0 0
\(610\) 9.19253 7.71345i 0.372195 0.312309i
\(611\) −8.66025 + 15.0000i −0.350356 + 0.606835i
\(612\) 0 0
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 32.5519 + 11.8479i 1.31369 + 0.478143i
\(615\) 0 0
\(616\) −4.59627 3.85673i −0.185189 0.155392i
\(617\) −6.51038 + 2.36959i −0.262098 + 0.0953959i −0.469727 0.882812i \(-0.655648\pi\)
0.207629 + 0.978208i \(0.433425\pi\)
\(618\) 0 0
\(619\) 3.47296 + 19.6962i 0.139590 + 0.791655i 0.971553 + 0.236823i \(0.0761063\pi\)
−0.831963 + 0.554832i \(0.812783\pi\)
\(620\) −17.3205 −0.695608
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 1.80460 + 10.2344i 0.0723000 + 0.410033i
\(624\) 0 0
\(625\) 10.3366 3.76222i 0.413465 0.150489i
\(626\) 1.32683 + 1.11334i 0.0530307 + 0.0444980i
\(627\) 0 0
\(628\) 12.2160 + 4.44626i 0.487472 + 0.177425i
\(629\) 0 0
\(630\) 0 0
\(631\) −8.50000 + 14.7224i −0.338380 + 0.586091i −0.984128 0.177459i \(-0.943212\pi\)
0.645748 + 0.763550i \(0.276545\pi\)
\(632\) −1.32683 + 1.11334i −0.0527784 + 0.0442863i
\(633\) 0 0
\(634\) 8.33511 47.2708i 0.331030 1.87736i
\(635\) −10.2261 + 57.9951i −0.405810 + 2.30146i
\(636\) 0 0
\(637\) −22.9813 + 19.2836i −0.910554 + 0.764045i
\(638\) 10.3923 18.0000i 0.411435 0.712627i
\(639\) 0 0
\(640\) −21.0000 36.3731i −0.830098 1.43777i
\(641\) −42.3175 15.4023i −1.67144 0.608354i −0.679342 0.733822i \(-0.737735\pi\)
−0.992098 + 0.125467i \(0.959957\pi\)
\(642\) 0 0
\(643\) 33.7060 + 28.2827i 1.32923 + 1.11536i 0.984256 + 0.176748i \(0.0565577\pi\)
0.344977 + 0.938611i \(0.387887\pi\)
\(644\) 6.51038 2.36959i 0.256545 0.0933747i
\(645\) 0 0
\(646\) 0 0
\(647\) 20.7846 0.817127 0.408564 0.912730i \(-0.366030\pi\)
0.408564 + 0.912730i \(0.366030\pi\)
\(648\) 0 0
\(649\) −12.0000 −0.471041
\(650\) −10.5269 59.7008i −0.412897 2.34166i
\(651\) 0 0
\(652\) 0.939693 0.342020i 0.0368012 0.0133945i
\(653\) 13.2683 + 11.1334i 0.519228 + 0.435684i 0.864362 0.502869i \(-0.167722\pi\)
−0.345135 + 0.938553i \(0.612167\pi\)
\(654\) 0 0
\(655\) −11.2763 4.10424i −0.440602 0.160366i
\(656\) −8.66025 15.0000i −0.338126 0.585652i
\(657\) 0 0
\(658\) −3.00000 + 5.19615i −0.116952 + 0.202567i
\(659\) −21.2292 + 17.8135i −0.826974 + 0.693914i −0.954594 0.297910i \(-0.903711\pi\)
0.127620 + 0.991823i \(0.459266\pi\)
\(660\) 0 0
\(661\) −1.73648 + 9.84808i −0.0675413 + 0.383046i 0.932234 + 0.361856i \(0.117857\pi\)
−0.999775 + 0.0211902i \(0.993254\pi\)
\(662\) 5.71458 32.4090i 0.222104 1.25961i
\(663\) 0 0
\(664\) −9.19253 + 7.71345i −0.356739 + 0.299340i
\(665\) 1.73205 3.00000i 0.0671660 0.116335i
\(666\) 0 0
\(667\) −12.0000 20.7846i −0.464642 0.804783i
\(668\) 22.7863 + 8.29355i 0.881630 + 0.320887i
\(669\) 0 0
\(670\) 36.7701 + 30.8538i 1.42055 + 1.19199i
\(671\) −6.51038 + 2.36959i −0.251330 + 0.0914768i
\(672\) 0 0
\(673\) −6.42498 36.4379i −0.247665 1.40458i −0.814221 0.580554i \(-0.802836\pi\)
0.566557 0.824023i \(-0.308275\pi\)
\(674\) −8.66025 −0.333581
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) −3.00767 17.0574i −0.115594 0.655568i −0.986454 0.164037i \(-0.947548\pi\)
0.870860 0.491531i \(-0.163563\pi\)
\(678\) 0 0
\(679\) 15.9748 5.81434i 0.613056 0.223134i
\(680\) 0 0
\(681\) 0 0
\(682\) 28.1908 + 10.2606i 1.07948 + 0.392899i
\(683\) 20.7846 + 36.0000i 0.795301 + 1.37750i 0.922648 + 0.385643i \(0.126021\pi\)
−0.127347 + 0.991858i \(0.540646\pi\)
\(684\) 0 0
\(685\) −12.0000 + 20.7846i −0.458496 + 0.794139i
\(686\) −17.2488 + 14.4734i −0.658561 + 0.552598i
\(687\) 0 0
\(688\) 0.868241 4.92404i 0.0331014 0.187727i
\(689\) 9.02302 51.1721i 0.343750 1.94950i
\(690\) 0 0
\(691\) 13.0228 10.9274i 0.495409 0.415697i −0.360551 0.932739i \(-0.617411\pi\)
0.855960 + 0.517042i \(0.172967\pi\)
\(692\) −6.92820 + 12.0000i −0.263371 + 0.456172i
\(693\) 0 0
\(694\) −21.0000 36.3731i −0.797149 1.38070i
\(695\) −42.3175 15.4023i −1.60519 0.584243i
\(696\) 0 0
\(697\) 0 0
\(698\) −1.62760 + 0.592396i −0.0616054 + 0.0224225i
\(699\) 0 0
\(700\) −1.21554 6.89365i −0.0459430 0.260556i
\(701\) 41.5692 1.57005 0.785024 0.619466i \(-0.212651\pi\)
0.785024 + 0.619466i \(0.212651\pi\)
\(702\) 0 0
\(703\) 1.00000 0.0377157
\(704\) 0.601535 + 3.41147i 0.0226712 + 0.128575i
\(705\) 0 0
\(706\) −28.1908 + 10.2606i −1.06097 + 0.386163i
\(707\) −10.6146 8.90673i −0.399204 0.334972i
\(708\) 0 0
\(709\) 17.8542 + 6.49838i 0.670527 + 0.244052i 0.654775 0.755824i \(-0.272763\pi\)
0.0157523 + 0.999876i \(0.494986\pi\)
\(710\) 31.1769 + 54.0000i 1.17005 + 2.02658i
\(711\) 0 0
\(712\) 9.00000 15.5885i 0.337289 0.584202i
\(713\) 26.5366 22.2668i 0.993802 0.833899i
\(714\) 0 0
\(715\) −10.4189 + 59.0885i −0.389644 + 2.20978i
\(716\) 3.60921 20.4688i 0.134882 0.764957i
\(717\) 0 0
\(718\) 41.3664 34.7105i 1.54378 1.29539i
\(719\) 5.19615 9.00000i 0.193784 0.335643i −0.752717 0.658344i \(-0.771257\pi\)
0.946501 + 0.322700i \(0.104591\pi\)
\(720\) 0 0
\(721\) 4.00000 + 6.92820i 0.148968 + 0.258020i
\(722\) −29.2967 10.6631i −1.09031 0.396841i
\(723\) 0 0
\(724\) 13.0228 + 10.9274i 0.483987 + 0.406113i
\(725\) −22.7863 + 8.29355i −0.846263 + 0.308015i
\(726\) 0 0
\(727\) −2.77837 15.7569i −0.103044 0.584392i −0.991984 0.126367i \(-0.959668\pi\)
0.888939 0.458025i \(-0.151443\pi\)
\(728\) −8.66025 −0.320970
\(729\) 0 0
\(730\) 12.0000 0.444140
\(731\) 0 0
\(732\) 0 0
\(733\) −38.5274 + 14.0228i −1.42304 + 0.517945i −0.934929 0.354835i \(-0.884537\pi\)
−0.488113 + 0.872780i \(0.662315\pi\)
\(734\) 21.2292 + 17.8135i 0.783586 + 0.657507i
\(735\) 0 0
\(736\) −33.8289 12.3127i −1.24695 0.453853i
\(737\) −13.8564 24.0000i −0.510407 0.884051i
\(738\) 0 0
\(739\) 9.50000 16.4545i 0.349463 0.605288i −0.636691 0.771119i \(-0.719697\pi\)
0.986154 + 0.165831i \(0.0530307\pi\)
\(740\) 2.65366 2.22668i 0.0975503 0.0818544i
\(741\) 0 0
\(742\) 3.12567 17.7265i 0.114747 0.650762i
\(743\) 1.20307 6.82295i 0.0441364 0.250310i −0.954755 0.297395i \(-0.903882\pi\)
0.998891 + 0.0470853i \(0.0149933\pi\)
\(744\) 0 0
\(745\) −18.3851 + 15.4269i −0.673577 + 0.565198i
\(746\) 19.9186 34.5000i 0.729271 1.26313i
\(747\) 0 0
\(748\) 0 0
\(749\) −9.76557 3.55438i −0.356826 0.129874i
\(750\) 0 0
\(751\) 3.83022 + 3.21394i 0.139767 + 0.117278i 0.709991 0.704211i \(-0.248699\pi\)
−0.570224 + 0.821489i \(0.693144\pi\)
\(752\) 16.2760 5.92396i 0.593523 0.216025i
\(753\) 0 0
\(754\) −5.20945 29.5442i −0.189717 1.07594i
\(755\) 55.4256 2.01715
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 5.71458 + 32.4090i 0.207563 + 1.17715i
\(759\) 0 0
\(760\) −5.63816 + 2.05212i −0.204517 + 0.0744382i
\(761\) 21.2292 + 17.8135i 0.769560 + 0.645737i 0.940596 0.339528i \(-0.110267\pi\)
−0.171037 + 0.985265i \(0.554712\pi\)
\(762\) 0 0
\(763\) 15.9748 + 5.81434i 0.578326 + 0.210493i
\(764\) 3.46410 + 6.00000i 0.125327 + 0.217072i
\(765\) 0 0
\(766\) 15.0000 25.9808i 0.541972 0.938723i
\(767\) −13.2683 + 11.1334i −0.479090 + 0.402004i
\(768\) 0 0
\(769\) −2.25743 + 12.8025i −0.0814049 + 0.461670i 0.916670 + 0.399646i \(0.130867\pi\)
−0.998075 + 0.0620244i \(0.980244\pi\)
\(770\) −3.60921 + 20.4688i −0.130067 + 0.737646i
\(771\) 0 0
\(772\) −7.66044 + 6.42788i −0.275705 + 0.231344i
\(773\) 10.3923 18.0000i 0.373785 0.647415i −0.616359 0.787465i \(-0.711393\pi\)
0.990144 + 0.140050i \(0.0447264\pi\)
\(774\) 0 0
\(775\) −17.5000 30.3109i −0.628619 1.08880i
\(776\) −27.6691 10.0707i −0.993264 0.361518i
\(777\) 0 0
\(778\) 9.19253 + 7.71345i 0.329568 + 0.276541i
\(779\) −3.25519 + 1.18479i −0.116629 + 0.0424496i
\(780\) 0 0
\(781\) −6.25133 35.4531i −0.223690 1.26861i
\(782\) 0 0
\(783\) 0 0