Properties

Label 729.2.e.n.649.1
Level $729$
Weight $2$
Character 729.649
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
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 649.1
Root \(0.984808 - 0.173648i\) of defining polynomial
Character \(\chi\) \(=\) 729.649
Dual form 729.2.e.n.82.1

$q$-expansion

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

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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 0.672222 + 0.740350i \(0.265340\pi\)
−0.884896 + 0.465788i \(0.845771\pi\)
\(3\) 0 0
\(4\) −0.939693 0.342020i −0.469846 0.171010i
\(5\) −2.65366 + 2.22668i −1.18675 + 0.995802i −0.186841 + 0.982390i \(0.559825\pi\)
−0.999910 + 0.0134121i \(0.995731\pi\)
\(6\) 0 0
\(7\) 0.939693 0.342020i 0.355170 0.129271i −0.158272 0.987396i \(-0.550592\pi\)
0.513442 + 0.858124i \(0.328370\pi\)
\(8\) −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 0.948225 0.317600i \(-0.102877\pi\)
−0.148117 + 0.988970i \(0.547321\pi\)
\(12\) 0 0
\(13\) 0.868241 + 4.92404i 0.240807 + 1.36568i 0.830033 + 0.557714i \(0.188322\pi\)
−0.589226 + 0.807968i \(0.700567\pi\)
\(14\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 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 −0.442225 0.896904i \(-0.645811\pi\)
−0.915283 + 0.402811i \(0.868033\pi\)
\(24\) 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 −0.876628 0.481169i \(-0.840212\pi\)
0.988330 0.152326i \(-0.0486764\pi\)
\(30\) 0 0
\(31\) −4.69846 1.71010i −0.843869 0.307143i −0.116331 0.993211i \(-0.537113\pi\)
−0.727538 + 0.686067i \(0.759336\pi\)
\(32\) 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 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 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 −0.995066 0.0992168i \(-0.968366\pi\)
0.901122 0.433566i \(-0.142745\pi\)
\(42\) 0 0
\(43\) −0.766044 0.642788i −0.116821 0.0980242i 0.582506 0.812826i \(-0.302072\pi\)
−0.699327 + 0.714802i \(0.746517\pi\)
\(44\) −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 −0.568334 0.822798i \(-0.692412\pi\)
0.0935154 + 0.995618i \(0.470190\pi\)
\(48\) 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 −0.798971 0.601370i \(-0.794622\pi\)
0.453494 + 0.891259i \(0.350177\pi\)
\(60\) 0 0
\(61\) −1.87939 + 0.684040i −0.240631 + 0.0875824i −0.459520 0.888167i \(-0.651979\pi\)
0.218890 + 0.975750i \(0.429756\pi\)
\(62\) 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 0.944068 + 0.329752i \(0.106965\pi\)
−0.774352 + 0.632756i \(0.781924\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −4.59627 3.85673i −0.549359 0.460967i
\(71\) 5.19615 + 9.00000i 0.616670 + 1.06810i 0.990089 + 0.140441i \(0.0448520\pi\)
−0.373419 + 0.927663i \(0.621815\pi\)
\(72\) 0 0
\(73\) −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) −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 −0.993017 0.117973i \(-0.962360\pi\)
0.973480 + 0.228773i \(0.0734713\pi\)
\(80\) 17.3205 1.93649
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) −1.20307 + 6.82295i −0.132054 + 0.748916i 0.844812 + 0.535063i \(0.179712\pi\)
−0.976866 + 0.213852i \(0.931399\pi\)
\(84\) 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 −0.447427 0.894321i \(-0.647659\pi\)
0.998218 0.0596775i \(-0.0190072\pi\)
\(90\) 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 0.985820 + 0.167803i \(0.0536674\pi\)
0.336440 + 0.941705i \(0.390777\pi\)
\(98\) −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 −0.895566 0.444929i \(-0.853229\pi\)
−0.400048 + 0.916494i \(0.631007\pi\)
\(102\) 0 0
\(103\) 6.12836 5.14230i 0.603845 0.506686i −0.288834 0.957379i \(-0.593268\pi\)
0.892679 + 0.450693i \(0.148823\pi\)
\(104\) −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 0.251335 0.967900i \(-0.419130\pi\)
0.996839 0.0794428i \(-0.0253141\pi\)
\(114\) 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 0.191492 + 0.981494i \(0.438667\pi\)
−0.945745 + 0.324910i \(0.894666\pi\)
\(128\) 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 0.480285 0.877113i \(-0.340533\pi\)
−0.195878 + 0.980628i \(0.562756\pi\)
\(132\) 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 0.889297 + 0.457331i \(0.151194\pi\)
−0.992082 + 0.125593i \(0.959917\pi\)
\(138\) 0 0
\(139\) 12.2160 + 4.44626i 1.03615 + 0.377127i 0.803419 0.595415i \(-0.203012\pi\)
0.232729 + 0.972542i \(0.425234\pi\)
\(140\) 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 0.993598 + 0.112970i \(0.0360364\pi\)
−0.895039 + 0.445988i \(0.852852\pi\)
\(150\) 0 0
\(151\) −12.2567 10.2846i −0.997437 0.836949i −0.0108097 0.999942i \(-0.503441\pi\)
−0.986627 + 0.162993i \(0.947885\pi\)
\(152\) 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 −0.946924 0.321458i \(-0.895827\pi\)
0.152143 + 0.988359i \(0.451383\pi\)
\(158\) −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 −0.496265 + 0.868171i \(0.665296\pi\)
−0.941157 + 0.337970i \(0.890260\pi\)
\(168\) 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 0.949893 0.312574i \(-0.101191\pi\)
−0.142878 + 0.989740i \(0.545636\pi\)
\(174\) 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 −0.933801 0.357792i \(-0.883530\pi\)
0.157044 0.987592i \(-0.449804\pi\)
\(180\) 0 0
\(181\) −8.50000 + 14.7224i −0.631800 + 1.09431i 0.355383 + 0.934721i \(0.384350\pi\)
−0.987184 + 0.159589i \(0.948983\pi\)
\(182\) −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 0.909844 + 0.414950i \(0.136201\pi\)
−0.996895 + 0.0787408i \(0.974910\pi\)
\(192\) 0 0
\(193\) 9.39693 + 3.42020i 0.676406 + 0.246191i 0.657303 0.753626i \(-0.271697\pi\)
0.0191021 + 0.999818i \(0.493919\pi\)
\(194\) −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 −0.989598 0.143862i \(-0.954048\pi\)
0.619387 + 0.785086i \(0.287381\pi\)
\(198\) 0 0
\(199\) 9.50000 + 16.4545i 0.673437 + 1.16643i 0.976923 + 0.213591i \(0.0685161\pi\)
−0.303486 + 0.952836i \(0.598151\pi\)
\(200\) 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 −0.501354 0.865242i \(-0.667165\pi\)
0.765038 + 0.643985i \(0.222720\pi\)
\(212\) −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 0.333915 0.942603i \(-0.391630\pi\)
0.861688 + 0.507439i \(0.169408\pi\)
\(224\) 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 0.923055 0.384668i \(-0.125684\pi\)
−0.218538 + 0.975829i \(0.570129\pi\)
\(228\) 0 0
\(229\) 0.868241 + 4.92404i 0.0573750 + 0.325390i 0.999963 0.00856731i \(-0.00272709\pi\)
−0.942588 + 0.333957i \(0.891616\pi\)
\(230\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 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 0.122763 0.992436i \(-0.460825\pi\)
−0.543884 + 0.839160i \(0.683047\pi\)
\(240\) 0 0
\(241\) −3.29932 + 18.7113i −0.212528 + 1.20530i 0.672618 + 0.739990i \(0.265170\pi\)
−0.885146 + 0.465314i \(0.845941\pi\)
\(242\) −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 −0.325697 0.945474i \(-0.605599\pi\)
0.981653 0.190676i \(-0.0610679\pi\)
\(252\) 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 0.960282 0.279033i \(-0.0900138\pi\)
−0.997804 + 0.0662307i \(0.978903\pi\)
\(258\) 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 −0.710685 0.703510i \(-0.751615\pi\)
−0.0922092 + 0.995740i \(0.529393\pi\)
\(264\) 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 −0.773967 0.633226i \(-0.781731\pi\)
−0.185864 + 0.982576i \(0.559508\pi\)
\(278\) −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 0.901926 0.431890i \(-0.142153\pi\)
−0.268711 + 0.963221i \(0.586598\pi\)
\(282\) 0 0
\(283\) −2.25743 12.8025i −0.134190 0.761030i −0.975420 0.220353i \(-0.929279\pi\)
0.841230 0.540677i \(-0.181832\pi\)
\(284\) −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 0.693093 0.720848i \(-0.256247\pi\)
0.0675880 + 0.997713i \(0.478470\pi\)
\(294\) 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 −0.996491 0.0836980i \(-0.973327\pi\)
0.425761 0.904836i \(-0.360006\pi\)
\(308\) −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 −0.973846 0.227208i \(-0.927040\pi\)
0.837407 0.546580i \(-0.184071\pi\)
\(312\) 0 0
\(313\) −0.766044 0.642788i −0.0432994 0.0363325i 0.620881 0.783905i \(-0.286775\pi\)
−0.664181 + 0.747572i \(0.731219\pi\)
\(314\) −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 0.516547 0.856259i \(-0.327217\pi\)
0.946091 + 0.323902i \(0.104995\pi\)
\(318\) 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 0.198987 0.980002i \(-0.436235\pi\)
0.782366 + 0.622819i \(0.214013\pi\)
\(332\) 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 0.999281 0.0379157i \(-0.0120718\pi\)
−0.951985 + 0.306145i \(0.900961\pi\)
\(338\) −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 0.871275 0.490794i \(-0.163293\pi\)
0.351959 + 0.936015i \(0.385516\pi\)
\(348\) 0 0
\(349\) −0.173648 + 0.984808i −0.00929517 + 0.0527156i −0.989103 0.147228i \(-0.952965\pi\)
0.979807 + 0.199944i \(0.0640759\pi\)
\(350\) 12.1244 0.648074
\(351\) 0 0
\(352\) 18.0000 0.959403
\(353\) −3.00767 + 17.0574i −0.160082 + 0.907872i 0.793909 + 0.608037i \(0.208043\pi\)
−0.953991 + 0.299835i \(0.903068\pi\)
\(354\) 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 −0.0809166 0.996721i \(-0.525785\pi\)
0.903644 0.428285i \(-0.140882\pi\)
\(360\) 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 0.264160 0.964479i \(-0.414905\pi\)
−0.903955 + 0.427627i \(0.859350\pi\)
\(368\) 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 −0.0602727 0.998182i \(-0.519197\pi\)
0.972551 + 0.232689i \(0.0747526\pi\)
\(374\) 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 −0.237437 0.971403i \(-0.576307\pi\)
0.915415 + 0.402512i \(0.131863\pi\)
\(384\) 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 0.498250 0.867034i \(-0.333976\pi\)
−0.767341 + 0.641239i \(0.778421\pi\)
\(390\) 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 −0.853206 0.521575i \(-0.825345\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(398\) −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 0.422017 0.906588i \(-0.361322\pi\)
−0.259460 + 0.965754i \(0.583545\pi\)
\(402\) 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 0.223235 0.974765i \(-0.428338\pi\)
−0.455559 + 0.890206i \(0.650561\pi\)
\(410\) −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 0.521658 + 0.853155i \(0.325314\pi\)
−0.198402 + 0.980121i \(0.563575\pi\)
\(420\) 0 0
\(421\) −14.5548 12.2130i −0.709360 0.595223i 0.215060 0.976601i \(-0.431005\pi\)
−0.924419 + 0.381377i \(0.875450\pi\)
\(422\) 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 −0.749043 0.662522i \(-0.769486\pi\)
−0.147939 + 0.988996i \(0.547264\pi\)
\(440\) 10.3923 18.0000i 0.495434 0.858116i
\(441\) 0 0
\(442\) 0 0
\(443\) 10.6146 + 8.90673i 0.504316 + 0.423171i 0.859124 0.511768i \(-0.171009\pi\)
−0.354808 + 0.934939i \(0.615454\pi\)
\(444\) 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 0.716972 0.697102i \(-0.245527\pi\)
−0.962194 + 0.272365i \(0.912194\pi\)
\(450\) 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 −0.834569 0.550904i \(-0.814283\pi\)
0.972658 0.232241i \(-0.0746059\pi\)
\(458\) −8.66025 −0.404667
\(459\) 0 0
\(460\) −24.0000 −1.11901
\(461\) −4.81228 + 27.2918i −0.224130 + 1.27111i 0.640211 + 0.768199i \(0.278847\pi\)
−0.864341 + 0.502906i \(0.832264\pi\)
\(462\) 0 0
\(463\) 29.1305 + 10.6026i 1.35381 + 0.492746i 0.914134 0.405412i \(-0.132872\pi\)
0.439674 + 0.898158i \(0.355094\pi\)
\(464\) −13.2683 + 11.1334i −0.615964 + 0.516855i
\(465\) 0 0
\(466\) 0 0
\(467\) −5.19615 + 9.00000i −0.240449 + 0.416470i −0.960842 0.277096i \(-0.910628\pi\)
0.720393 + 0.693566i \(0.243961\pi\)
\(468\) 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 −0.621898 0.783098i \(-0.713638\pi\)
0.0269642 + 0.999636i \(0.491416\pi\)
\(480\) 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 0.330473 0.943815i \(-0.392792\pi\)
0.986863 0.161561i \(-0.0516527\pi\)
\(492\) 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 −0.876231 0.481891i \(-0.839950\pi\)
0.658571 0.752518i \(-0.271161\pi\)
\(500\) −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 0.788739 + 0.614729i \(0.210734\pi\)
0.138001 + 0.990432i \(0.455932\pi\)
\(504\) 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 −0.307223 0.951638i \(-0.599400\pi\)
−0.847047 + 0.531517i \(0.821622\pi\)
\(510\) 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 −0.998705 0.0508731i \(-0.983800\pi\)
0.543410 + 0.839467i \(0.317133\pi\)
\(522\) 0 0
\(523\) −10.0000 17.3205i −0.437269 0.757373i 0.560208 0.828352i \(-0.310721\pi\)
−0.997478 + 0.0709788i \(0.977388\pi\)
\(524\) −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 −0.710964 0.703229i \(-0.751741\pi\)
−0.0926033 + 0.995703i \(0.529519\pi\)
\(548\) 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 0.954859 0.297060i \(-0.0960061\pi\)
−0.734691 + 0.678402i \(0.762673\pi\)
\(558\) 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 0.919712 0.392593i \(-0.128422\pi\)
0.452187 + 0.891923i \(0.350644\pi\)
\(564\) 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 −0.759847 0.650102i \(-0.774726\pi\)
0.936371 0.351013i \(-0.114163\pi\)
\(570\) 0 0
\(571\) −38.5274 14.0228i −1.61232 0.586837i −0.630424 0.776251i \(-0.717119\pi\)
−0.981897 + 0.189414i \(0.939341\pi\)
\(572\) 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 0.965701 + 0.259656i \(0.0836092\pi\)
−0.257982 + 0.966150i \(0.583058\pi\)
\(578\) 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 −0.204150 0.978940i \(-0.565443\pi\)
0.472862 + 0.881136i \(0.343221\pi\)
\(588\) 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 −0.937861 0.347012i \(-0.887196\pi\)
0.178883 + 0.983870i \(0.442752\pi\)
\(600\) 0 0
\(601\) −32.8892 + 11.9707i −1.34158 + 0.488295i −0.910310 0.413928i \(-0.864157\pi\)
−0.431270 + 0.902223i \(0.641934\pi\)
\(602\) 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 −0.995729 0.0923229i \(-0.970571\pi\)
0.904103 0.427315i \(-0.140540\pi\)
\(608\) −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 −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 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 0.207629 0.978208i \(-0.433425\pi\)
−0.469727 + 0.882812i \(0.655648\pi\)
\(618\) 0 0
\(619\) 3.47296 19.6962i 0.139590 0.791655i −0.831963 0.554832i \(-0.812783\pi\)
0.971553 0.236823i \(-0.0761063\pi\)
\(620\) −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 0.645748 0.763550i \(-0.276545\pi\)
−0.984128 + 0.177459i \(0.943212\pi\)
\(632\) −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 −0.992098 0.125467i \(-0.959957\pi\)
−0.679342 + 0.733822i \(0.737735\pi\)
\(642\) 0 0
\(643\) 33.7060 28.2827i 1.32923 1.11536i 0.344977 0.938611i \(-0.387887\pi\)
0.984256 0.176748i \(-0.0565577\pi\)
\(644\) 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 −0.345135 0.938553i \(-0.612167\pi\)
0.864362 + 0.502869i \(0.167722\pi\)
\(654\) 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 0.127620 0.991823i \(-0.459266\pi\)
−0.954594 + 0.297910i \(0.903711\pi\)
\(660\) 0 0
\(661\) −1.73648 9.84808i −0.0675413 0.383046i −0.999775 0.0211902i \(-0.993254\pi\)
0.932234 0.361856i \(-0.117857\pi\)
\(662\) 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 0.566557 + 0.824023i \(0.308275\pi\)
−0.814221 + 0.580554i \(0.802836\pi\)
\(674\) −8.66025 −0.333581
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) −3.00767 + 17.0574i −0.115594 + 0.655568i 0.870860 + 0.491531i \(0.163563\pi\)
−0.986454 + 0.164037i \(0.947548\pi\)
\(678\) 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 −0.127347 0.991858i \(-0.540646\pi\)
0.922648 0.385643i \(-0.126021\pi\)
\(684\) 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 0.855960 0.517042i \(-0.172967\pi\)
−0.360551 + 0.932739i \(0.617411\pi\)
\(692\) −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 0.0157523 0.999876i \(-0.494986\pi\)
0.654775 + 0.755824i \(0.272763\pi\)
\(710\) 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 0.946501 0.322700i \(-0.104591\pi\)
−0.752717 + 0.658344i \(0.771257\pi\)
\(720\) 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 0.888939 + 0.458025i \(0.151443\pi\)
−0.991984 + 0.126367i \(0.959668\pi\)
\(728\) −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 −0.488113 0.872780i \(-0.662315\pi\)
−0.934929 + 0.354835i \(0.884537\pi\)
\(734\) 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 0.986154 0.165831i \(-0.0530307\pi\)
−0.636691 + 0.771119i \(0.719697\pi\)
\(740\) 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 0.998891 0.0470853i \(-0.0149933\pi\)
−0.954755 + 0.297395i \(0.903882\pi\)
\(744\) 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 −0.570224 0.821489i \(-0.693144\pi\)
0.709991 + 0.704211i \(0.248699\pi\)
\(752\) 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 −0.171037 0.985265i \(-0.554712\pi\)
0.940596 + 0.339528i \(0.110267\pi\)
\(762\) 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 −0.998075 0.0620244i \(-0.980244\pi\)
0.916670 0.399646i \(-0.130867\pi\)
\(770\) −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 0.990144 0.140050i \(-0.0447264\pi\)
−0.616359 + 0.787465i \(0.711393\pi\)
\(774\) 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
\(784\) 30.0000 1.07143
\(785\) 7.81995 44.3492i 0.279106 1.58289i
\(786\) 0 0
\(787\) 26.3114 + 9.57656i 0.937900 + 0.341368i 0.765336 0.643631i \(-0.222573\pi\)
0.172564 + 0.984998i \(0.444795\pi\)
\(788\) 7.96097 6.68004i 0.283598 0.237967i
\(789\) 0 0
\(790\) 5.63816 2.05212i 0.200597 0.0730112i
\(791\) 8.66025 15.0000i 0.307923 0.533339i
\(792\) 0 0
\(793\) −5.00000 8.66025i −0.177555 0.307535i
\(794\) 1.32683 + 1.11334i 0.0470874 + 0.0395110i
\(795\) 0 0
\(796\) −3.29932 18.7113i −0.116941 0.663206i
\(797\) −2.40614 13.6459i −0.0852298 0.483362i −0.997307 0.0733433i \(-0.976633\pi\)
0.912077 0.410019i \(-0.134478\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −18.1865 31.5000i −0.642991 1.11369i
\(801\) 0 0
\(802\) −3.00000 + 5.19615i −0.105934 + 0.183483i
\(803\) −6.51038 + 2.36959i −0.229746 + 0.0836208i
\(804\) 0 0
\(805\) 18.3851 15.4269i 0.647988 0.543727i
\(806\) 40.6899 + 14.8099i 1.43324 + 0.521657i
\(807\) 0 0
\(808\) 4.16756 23.6354i 0.146614 0.831490i
\(809\) 31.1769 1.09612 0.548061 0.836438i \(-0.315366\pi\)
0.548061 + 0.836438i \(0.315366\pi\)
\(810\) 0 0
\(811\) 35.0000 1.22902 0.614508 0.788911i \(-0.289355\pi\)
0.614508 + 0.788911i \(0.289355\pi\)
\(812\) −0.601535 + 3.41147i −0.0211097 + 0.119719i
\(813\) 0 0
\(814\) −5.63816 2.05212i −0.197617 0.0719268i
\(815\) 2.65366 2.22668i 0.0929535 0.0779973i
\(816\) 0 0
\(817\) −0.939693 + 0.342020i −0.0328757 + 0.0119658i
\(818\) 4.33013 7.50000i 0.151399 0.262231i
\(819\) 0 0
\(820\) −6.00000 10.3923i −0.209529 0.362915i
\(821\) −29.1902 24.4935i −1.01875 0.854829i −0.0292761 0.999571i \(-0.509320\pi\)
−0.989469 + 0.144742i \(0.953765\pi\)
\(822\) 0 0
\(823\) 3.99391 + 22.6506i 0.139219 + 0.789550i 0.971828 + 0.235689i \(0.0757347\pi\)
−0.832610 + 0.553860i \(0.813154\pi\)
\(824\) 2.40614 + 13.6459i 0.0838218 + 0.475377i
\(825\) 0 0
\(826\) −4.59627 3.85673i −0.159925 0.134193i
\(827\) −5.19615 9.00000i −0.180688 0.312961i 0.761427 0.648251i \(-0.224499\pi\)
−0.942115 + 0.335290i \(0.891166\pi\)
\(828\) 0 0
\(829\) 9.50000 16.4545i 0.329949 0.571488i −0.652553 0.757743i \(-0.726302\pi\)
0.982501 + 0.186256i \(0.0596352\pi\)
\(830\) 39.0623 14.2175i 1.35587 0.493497i
\(831\) 0 0
\(832\) 3.83022 3.21394i 0.132789 0.111423i
\(833\) 0 0
\(834\) 0 0
\(835\) 14.5864 82.7239i 0.504785 2.86278i
\(836\) −3.46410 −0.119808
\(837\) 0 0
\(838\) −66.0000 −2.27993
\(839\) 0.601535 3.41147i 0.0207673 0.117777i −0.972662 0.232226i \(-0.925399\pi\)
0.993429 + 0.114449i \(0.0365102\pi\)
\(840\) 0 0
\(841\) 15.9748 + 5.81434i 0.550854 + 0.200495i
\(842\) 25.2097 21.1535i 0.868785 0.728997i
\(843\) 0 0
\(844\) −4.69846 + 1.71010i −0.161728 + 0.0588641i
\(845\) 20.7846 36.0000i 0.715012 1.23844i
\(846\) 0 0
\(847\) 0.500000 + 0.866025i 0.0171802 + 0.0297570i
\(848\) −39.8048 33.4002i −1.36690 1.14697i
\(849\) 0 0
\(850\) 0 0
\(851\) −1.20307 6.82295i −0.0412407 0.233888i
\(852\) 0 0
\(853\) 1.53209 + 1.28558i 0.0524577 + 0.0440173i 0.668640 0.743587i \(-0.266877\pi\)
−0.616182 + 0.787604i \(0.711321\pi\)
\(854\) −1.73205 3.00000i −0.0592696 0.102658i
\(855\) 0 0
\(856\) 9.00000 15.5885i 0.307614 0.532803i
\(857\) 35.8071 13.0327i 1.22315 0.445189i 0.351902 0.936037i \(-0.385535\pi\)
0.871245 + 0.490848i \(0.163313\pi\)
\(858\) 0 0
\(859\) −37.5362 + 31.4966i −1.28072 + 1.07465i −0.287573 + 0.957759i \(0.592848\pi\)
−0.993145 + 0.116891i \(0.962707\pi\)
\(860\) −3.25519 1.18479i −0.111001 0.0404011i
\(861\) 0 0
\(862\) −6.25133 + 35.4531i −0.212921 + 1.20754i
\(863\) −10.3923 −0.353758 −0.176879 0.984233i \(-0.556600\pi\)
−0.176879 + 0.984233i \(0.556600\pi\)
\(864\) 0 0
\(865\) −48.0000 −1.63205
\(866\) 0.300767 1.70574i 0.0102205 0.0579633i
\(867\) 0 0
\(868\) 4.69846 + 1.71010i 0.159476 + 0.0580446i
\(869\) −2.65366 + 2.22668i −0.0900191 + 0.0755350i
\(870\) 0 0
\(871\) −37.5877 + 13.6808i −1.27361 + 0.463556i
\(872\) −14.7224 + 25.5000i −0.498564 + 0.863539i
\(873\) 0 0
\(874\) −6.00000 10.3923i −0.202953 0.351525i
\(875\) 5.30731 + 4.45336i 0.179420 + 0.150551i
\(876\) 0 0
\(877\) 3.99391 + 22.6506i 0.134865 + 0.764856i 0.974954 + 0.222407i \(0.0713915\pi\)
−0.840089 + 0.542448i \(0.817497\pi\)
\(878\) −6.01535 34.1147i −0.203008 1.15132i
\(879\) 0 0
\(880\) 45.9627 + 38.5673i 1.54940 + 1.30010i
\(881\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(882\) 0 0
\(883\) 9.50000 16.4545i 0.319700 0.553737i −0.660725 0.750628i \(-0.729751\pi\)
0.980425 + 0.196891i \(0.0630844\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −18.3851 + 15.4269i −0.617658 + 0.518277i
\(887\) 13.0208 + 4.73917i 0.437194 + 0.159126i 0.551234 0.834350i \(-0.314157\pi\)
−0.114040 + 0.993476i \(0.536379\pi\)
\(888\) 0 0
\(889\) −2.95202 + 16.7417i −0.0990075 + 0.561500i
\(890\) −62.3538 −2.09011
\(891\) 0 0
\(892\) −19.0000 −0.636167
\(893\) −0.601535 + 3.41147i −0.0201296 + 0.114161i
\(894\) 0 0
\(895\) 67.6579 + 24.6255i 2.26155 + 0.823138i
\(896\) 9.28780 7.79339i 0.310283 0.260359i
\(897\) 0 0
\(898\) 16.9145 6.15636i 0.564443 0.205440i
\(899\) −8.66025 + 15.0000i −0.288836 + 0.500278i
\(900\) 0 0
\(901\) 0 0
\(902\) 15.9219 + 13.3601i 0.530142 + 0.444842i
\(903\) 0 0
\(904\) 5.20945 + 29.5442i 0.173264 + 0.982627i
\(905\) −10.2261 57.9951i −0.339927 1.92782i
\(906\) 0 0
\(907\) −28.3436 23.7831i −0.941135 0.789706i 0.0366472 0.999328i \(-0.488332\pi\)
−0.977782 + 0.209622i \(0.932777\pi\)
\(908\) −6.92820 12.0000i −0.229920 0.398234i
\(909\) 0 0
\(910\) 15.0000 25.9808i 0.497245 0.861254i
\(911\) 26.0415 9.47834i 0.862794 0.314031i 0.127549 0.991832i \(-0.459289\pi\)
0.735246 + 0.677801i \(0.237067\pi\)
\(912\) 0 0
\(913\) −18.3851 + 15.4269i −0.608457 + 0.510556i
\(914\) 27.6691 + 10.0707i 0.915213 + 0.333110i
\(915\) 0 0
\(916\) 0.868241 4.92404i 0.0286875 0.162695i
\(917\) 3.46410 0.114395
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) −7.21842 + 40.9377i −0.237984 + 1.34968i
\(921\) 0 0
\(922\) −45.1052 16.4170i −1.48546 0.540664i
\(923\) −39.8048 + 33.4002i −1.31019 + 1.09938i
\(924\) 0 0
\(925\) 6.57785 2.39414i 0.216278 0.0787189i
\(926\) −26.8468 + 46.5000i −0.882240 + 1.52808i
\(927\) 0 0
\(928\) −9.00000 15.5885i −0.295439 0.511716i
\(929\) −5.30731 4.45336i −0.174127 0.146110i 0.551559 0.834136i \(-0.314033\pi\)
−0.725686 + 0.688026i \(0.758478\pi\)
\(930\) 0 0
\(931\) 1.04189 + 5.90885i 0.0341465 + 0.193655i
\(932\) 0 0
\(933\) 0 0
\(934\) −13.7888 11.5702i −0.451183 0.378588i
\(935\) 0 0
\(936\) 0 0
\(937\) 18.5000 32.0429i 0.604369 1.04680i −0.387782 0.921751i \(-0.626759\pi\)
0.992151 0.125046i \(-0.0399079\pi\)
\(938\) −13.0208 + 4.73917i −0.425143 + 0.154739i
\(939\) 0 0
\(940\) −9.19253 + 7.71345i −0.299827 + 0.251585i
\(941\) 3.25519 + 1.18479i 0.106116 + 0.0386231i 0.394533 0.918882i \(-0.370907\pi\)
−0.288416 + 0.957505i \(0.593129\pi\)
\(942\) 0 0
\(943\) −4.16756 + 23.6354i −0.135714 + 0.769674i
\(944\) 17.3205 0.563735
\(945\) 0 0
\(946\) 6.00000 0.195077
\(947\) 2.40614 13.6459i 0.0781890 0.443432i −0.920431 0.390906i \(-0.872162\pi\)
0.998620 0.0525259i \(-0.0167272\pi\)
\(948\) 0 0
\(949\) −9.39693 3.42020i −0.305037 0.111024i
\(950\) 9.28780 7.79339i 0.301336 0.252851i
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(954\) 0 0
\(955\) −12.0000 20.7846i −0.388311 0.672574i
\(956\) 5.30731 + 4.45336i 0.171651 + 0.144032i
\(957\) 0 0
\(958\) −4.16756 23.6354i −0.134648 0.763625i
\(959\) 1.20307 + 6.82295i 0.0388492 + 0.220324i
\(960\) 0 0
\(961\) −4.59627 3.85673i −0.148267 0.124411i
\(962\) −4.33013 7.50000i −0.139609 0.241810i
\(963\) 0 0
\(964\) 9.50000 16.4545i 0.305974 0.529963i
\(965\) −32.5519 + 11.8479i −1.04788 + 0.381398i
\(966\) 0 0
\(967\) 6.12836 5.14230i 0.197075 0.165365i −0.538910 0.842363i \(-0.681164\pi\)
0.735985 + 0.676998i \(0.236719\pi\)
\(968\) −1.62760 0.592396i −0.0523129 0.0190403i
\(969\) 0 0
\(970\) 17.7121 100.450i 0.568702 3.22527i
\(971\) −51.9615 −1.66752 −0.833762 0.552124i \(-0.813818\pi\)
−0.833762 + 0.552124i \(0.813818\pi\)
\(972\) 0 0
\(973\) 13.0000 0.416761
\(974\) 5.71458 32.4090i 0.183107 1.03845i
\(975\) 0 0
\(976\) 9.39693 + 3.42020i 0.300788 + 0.109478i
\(977\) −2.65366 + 2.22668i −0.0848980 + 0.0712379i −0.684249 0.729248i \(-0.739870\pi\)
0.599351 + 0.800486i \(0.295425\pi\)
\(978\) 0 0
\(979\) 33.8289 12.3127i 1.08118 0.393516i
\(980\) −10.3923 + 18.0000i −0.331970 + 0.574989i
\(981\) 0 0
\(982\) 33.0000 + 57.1577i 1.05307 + 1.82397i
\(983\) −5.30731 4.45336i −0.169277 0.142040i 0.554214 0.832374i \(-0.313019\pi\)
−0.723491 + 0.690334i \(0.757463\pi\)
\(984\) 0 0
\(985\) −6.25133 35.4531i −0.199184 1.12963i
\(986\) 0 0
\(987\) 0 0
\(988\) −3.83022 3.21394i −0.121856 0.102249i
\(989\) 3.46410 + 6.00000i 0.110152 + 0.190789i
\(990\) 0 0
\(991\) −10.0000 + 17.3205i −0.317660 + 0.550204i −0.979999 0.199000i \(-0.936231\pi\)
0.662339 + 0.749204i \(0.269564\pi\)
\(992\) −24.4139 + 8.88594i −0.775143 + 0.282129i
\(993\) 0 0
\(994\) −13.7888 + 11.5702i −0.437354 + 0.366984i
\(995\) −61.8486 22.5111i −1.96073 0.713649i
\(996\) 0 0
\(997\) 0.347296 1.96962i 0.0109990 0.0623783i −0.978814 0.204750i \(-0.934362\pi\)
0.989813 + 0.142372i \(0.0454729\pi\)
\(998\) 48.4974 1.53516
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 729.2.e.n.649.1 12
3.2 odd 2 inner 729.2.e.n.649.2 12
9.2 odd 6 inner 729.2.e.n.163.1 12
9.4 even 3 inner 729.2.e.n.406.1 12
9.5 odd 6 inner 729.2.e.n.406.2 12
9.7 even 3 inner 729.2.e.n.163.2 12
27.2 odd 18 243.2.c.d.163.1 4
27.4 even 9 inner 729.2.e.n.325.1 12
27.5 odd 18 inner 729.2.e.n.568.1 12
27.7 even 9 243.2.c.d.82.2 4
27.11 odd 18 243.2.a.c.1.2 yes 2
27.13 even 9 inner 729.2.e.n.82.1 12
27.14 odd 18 inner 729.2.e.n.82.2 12
27.16 even 9 243.2.a.c.1.1 2
27.20 odd 18 243.2.c.d.82.1 4
27.22 even 9 inner 729.2.e.n.568.2 12
27.23 odd 18 inner 729.2.e.n.325.2 12
27.25 even 9 243.2.c.d.163.2 4
108.11 even 18 3888.2.a.ba.1.2 2
108.43 odd 18 3888.2.a.ba.1.1 2
135.119 odd 18 6075.2.a.bm.1.1 2
135.124 even 18 6075.2.a.bm.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.c.1.1 2 27.16 even 9
243.2.a.c.1.2 yes 2 27.11 odd 18
243.2.c.d.82.1 4 27.20 odd 18
243.2.c.d.82.2 4 27.7 even 9
243.2.c.d.163.1 4 27.2 odd 18
243.2.c.d.163.2 4 27.25 even 9
729.2.e.n.82.1 12 27.13 even 9 inner
729.2.e.n.82.2 12 27.14 odd 18 inner
729.2.e.n.163.1 12 9.2 odd 6 inner
729.2.e.n.163.2 12 9.7 even 3 inner
729.2.e.n.325.1 12 27.4 even 9 inner
729.2.e.n.325.2 12 27.23 odd 18 inner
729.2.e.n.406.1 12 9.4 even 3 inner
729.2.e.n.406.2 12 9.5 odd 6 inner
729.2.e.n.568.1 12 27.5 odd 18 inner
729.2.e.n.568.2 12 27.22 even 9 inner
729.2.e.n.649.1 12 1.1 even 1 trivial
729.2.e.n.649.2 12 3.2 odd 2 inner
3888.2.a.ba.1.1 2 108.43 odd 18
3888.2.a.ba.1.2 2 108.11 even 18
6075.2.a.bm.1.1 2 135.119 odd 18
6075.2.a.bm.1.2 2 135.124 even 18