Properties

Label 729.2.e.m.649.2
Level $729$
Weight $2$
Character 729.649
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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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: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 649.2
Root \(0.642788 + 0.766044i\) of defining polynomial
Character \(\chi\) \(=\) 729.649
Dual form 729.2.e.m.82.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.342020 - 1.93969i) q^{2} +(-1.76604 - 0.642788i) q^{4} +(-2.83564 + 2.37939i) q^{5} +(2.20574 - 0.802823i) q^{7} +(0.118782 - 0.205737i) q^{8} +O(q^{10})\) \(q+(0.342020 - 1.93969i) q^{2} +(-1.76604 - 0.642788i) q^{4} +(-2.83564 + 2.37939i) q^{5} +(2.20574 - 0.802823i) q^{7} +(0.118782 - 0.205737i) q^{8} +(3.64543 + 6.31407i) q^{10} +(1.66885 + 1.40033i) q^{11} +(-0.819078 - 4.64522i) q^{13} +(-0.802823 - 4.55303i) q^{14} +(-3.23783 - 2.71686i) q^{16} +(-1.46756 - 2.54189i) q^{17} +(3.11334 - 5.39246i) q^{19} +(6.53731 - 2.37939i) q^{20} +(3.28699 - 2.75811i) q^{22} +(0.487728 + 0.177519i) q^{23} +(1.51114 - 8.57013i) q^{25} -9.29044 q^{26} -4.41147 q^{28} +(0.606511 - 3.43969i) q^{29} +(4.04576 + 1.47254i) q^{31} +(-6.01330 + 5.04576i) q^{32} +(-5.43242 + 1.97724i) q^{34} +(-4.34445 + 7.52481i) q^{35} +(-1.20574 - 2.08840i) q^{37} +(-9.39490 - 7.88326i) q^{38} +(0.152704 + 0.866025i) q^{40} +(-0.433877 - 2.46064i) q^{41} +(0.815207 + 0.684040i) q^{43} +(-2.04715 - 3.54576i) q^{44} +(0.511144 - 0.885328i) q^{46} +(-0.223238 + 0.0812519i) q^{47} +(-1.14156 + 0.957882i) q^{49} +(-16.1066 - 5.86231i) q^{50} +(-1.53936 + 8.73016i) q^{52} -4.66717 q^{53} -8.06418 q^{55} +(0.0968323 - 0.549163i) q^{56} +(-6.46451 - 2.35289i) q^{58} +(10.1977 - 8.55690i) q^{59} +(3.45336 - 1.25692i) q^{61} +(4.24000 - 7.34389i) q^{62} +(3.50387 + 6.06888i) q^{64} +(13.3754 + 11.2233i) q^{65} +(2.48293 + 14.0814i) q^{67} +(0.957882 + 5.43242i) q^{68} +(13.1099 + 11.0005i) q^{70} +(0.601535 + 1.04189i) q^{71} +(2.34002 - 4.05304i) q^{73} +(-4.46324 + 1.62449i) q^{74} +(-8.96451 + 7.52211i) q^{76} +(4.80526 + 1.74897i) q^{77} +(-2.22281 + 12.6062i) q^{79} +15.6458 q^{80} -4.92127 q^{82} +(1.96291 - 11.1322i) q^{83} +(10.2096 + 3.71599i) q^{85} +(1.60565 - 1.34730i) q^{86} +(0.486329 - 0.177009i) q^{88} +(0.349643 - 0.605600i) q^{89} +(-5.53596 - 9.58856i) q^{91} +(-0.747243 - 0.627011i) q^{92} +(0.0812519 + 0.460802i) q^{94} +(4.00243 + 22.6989i) q^{95} +(-5.42855 - 4.55509i) q^{97} +(1.46756 + 2.54189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 12 q^{4} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 12 q^{4} + 6 q^{7} + 12 q^{10} + 24 q^{13} + 24 q^{19} + 24 q^{22} + 6 q^{25} - 12 q^{28} - 12 q^{31} - 18 q^{34} + 6 q^{37} + 6 q^{40} + 24 q^{43} - 6 q^{46} - 30 q^{49} - 36 q^{52} - 60 q^{55} - 12 q^{58} - 12 q^{61} - 6 q^{64} - 12 q^{67} + 60 q^{70} - 12 q^{73} - 42 q^{76} - 48 q^{79} - 24 q^{82} + 54 q^{85} + 48 q^{88} + 6 q^{94} - 66 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.342020 1.93969i 0.241845 1.37157i −0.585863 0.810410i \(-0.699244\pi\)
0.827708 0.561160i \(-0.189645\pi\)
\(3\) 0 0
\(4\) −1.76604 0.642788i −0.883022 0.321394i
\(5\) −2.83564 + 2.37939i −1.26814 + 1.06409i −0.273372 + 0.961908i \(0.588139\pi\)
−0.994765 + 0.102185i \(0.967417\pi\)
\(6\) 0 0
\(7\) 2.20574 0.802823i 0.833690 0.303438i 0.110318 0.993896i \(-0.464813\pi\)
0.723373 + 0.690458i \(0.242591\pi\)
\(8\) 0.118782 0.205737i 0.0419959 0.0727390i
\(9\) 0 0
\(10\) 3.64543 + 6.31407i 1.15279 + 1.99668i
\(11\) 1.66885 + 1.40033i 0.503177 + 0.422215i 0.858720 0.512444i \(-0.171260\pi\)
−0.355544 + 0.934660i \(0.615704\pi\)
\(12\) 0 0
\(13\) −0.819078 4.64522i −0.227171 1.28835i −0.858490 0.512829i \(-0.828597\pi\)
0.631319 0.775523i \(-0.282514\pi\)
\(14\) −0.802823 4.55303i −0.214563 1.21685i
\(15\) 0 0
\(16\) −3.23783 2.71686i −0.809456 0.679215i
\(17\) −1.46756 2.54189i −0.355936 0.616499i 0.631342 0.775505i \(-0.282504\pi\)
−0.987278 + 0.159006i \(0.949171\pi\)
\(18\) 0 0
\(19\) 3.11334 5.39246i 0.714249 1.23712i −0.248999 0.968504i \(-0.580102\pi\)
0.963248 0.268612i \(-0.0865651\pi\)
\(20\) 6.53731 2.37939i 1.46179 0.532047i
\(21\) 0 0
\(22\) 3.28699 2.75811i 0.700788 0.588031i
\(23\) 0.487728 + 0.177519i 0.101698 + 0.0370152i 0.392368 0.919808i \(-0.371656\pi\)
−0.290670 + 0.956823i \(0.593878\pi\)
\(24\) 0 0
\(25\) 1.51114 8.57013i 0.302229 1.71403i
\(26\) −9.29044 −1.82201
\(27\) 0 0
\(28\) −4.41147 −0.833690
\(29\) 0.606511 3.43969i 0.112626 0.638735i −0.875272 0.483631i \(-0.839318\pi\)
0.987898 0.155104i \(-0.0495712\pi\)
\(30\) 0 0
\(31\) 4.04576 + 1.47254i 0.726640 + 0.264475i 0.678742 0.734377i \(-0.262526\pi\)
0.0478980 + 0.998852i \(0.484748\pi\)
\(32\) −6.01330 + 5.04576i −1.06301 + 0.891973i
\(33\) 0 0
\(34\) −5.43242 + 1.97724i −0.931652 + 0.339094i
\(35\) −4.34445 + 7.52481i −0.734347 + 1.27193i
\(36\) 0 0
\(37\) −1.20574 2.08840i −0.198222 0.343330i 0.749730 0.661744i \(-0.230183\pi\)
−0.947952 + 0.318413i \(0.896850\pi\)
\(38\) −9.39490 7.88326i −1.52405 1.27883i
\(39\) 0 0
\(40\) 0.152704 + 0.866025i 0.0241446 + 0.136931i
\(41\) −0.433877 2.46064i −0.0677602 0.384287i −0.999762 0.0218325i \(-0.993050\pi\)
0.932001 0.362454i \(-0.118061\pi\)
\(42\) 0 0
\(43\) 0.815207 + 0.684040i 0.124318 + 0.104315i 0.702827 0.711361i \(-0.251921\pi\)
−0.578509 + 0.815676i \(0.696365\pi\)
\(44\) −2.04715 3.54576i −0.308619 0.534543i
\(45\) 0 0
\(46\) 0.511144 0.885328i 0.0753641 0.130534i
\(47\) −0.223238 + 0.0812519i −0.0325626 + 0.0118518i −0.358250 0.933626i \(-0.616626\pi\)
0.325688 + 0.945477i \(0.394404\pi\)
\(48\) 0 0
\(49\) −1.14156 + 0.957882i −0.163080 + 0.136840i
\(50\) −16.1066 5.86231i −2.27781 0.829056i
\(51\) 0 0
\(52\) −1.53936 + 8.73016i −0.213471 + 1.21066i
\(53\) −4.66717 −0.641085 −0.320543 0.947234i \(-0.603865\pi\)
−0.320543 + 0.947234i \(0.603865\pi\)
\(54\) 0 0
\(55\) −8.06418 −1.08737
\(56\) 0.0968323 0.549163i 0.0129398 0.0733850i
\(57\) 0 0
\(58\) −6.46451 2.35289i −0.848831 0.308949i
\(59\) 10.1977 8.55690i 1.32763 1.11401i 0.343005 0.939334i \(-0.388555\pi\)
0.984625 0.174680i \(-0.0558892\pi\)
\(60\) 0 0
\(61\) 3.45336 1.25692i 0.442158 0.160932i −0.111341 0.993782i \(-0.535515\pi\)
0.553499 + 0.832850i \(0.313292\pi\)
\(62\) 4.24000 7.34389i 0.538480 0.932675i
\(63\) 0 0
\(64\) 3.50387 + 6.06888i 0.437984 + 0.758610i
\(65\) 13.3754 + 11.2233i 1.65901 + 1.39208i
\(66\) 0 0
\(67\) 2.48293 + 14.0814i 0.303338 + 1.72031i 0.631228 + 0.775598i \(0.282551\pi\)
−0.327890 + 0.944716i \(0.606338\pi\)
\(68\) 0.957882 + 5.43242i 0.116160 + 0.658778i
\(69\) 0 0
\(70\) 13.1099 + 11.0005i 1.56694 + 1.31482i
\(71\) 0.601535 + 1.04189i 0.0713891 + 0.123649i 0.899510 0.436900i \(-0.143923\pi\)
−0.828121 + 0.560549i \(0.810590\pi\)
\(72\) 0 0
\(73\) 2.34002 4.05304i 0.273879 0.474372i −0.695973 0.718068i \(-0.745027\pi\)
0.969852 + 0.243696i \(0.0783599\pi\)
\(74\) −4.46324 + 1.62449i −0.518841 + 0.188843i
\(75\) 0 0
\(76\) −8.96451 + 7.52211i −1.02830 + 0.862846i
\(77\) 4.80526 + 1.74897i 0.547610 + 0.199314i
\(78\) 0 0
\(79\) −2.22281 + 12.6062i −0.250086 + 1.41831i 0.558293 + 0.829644i \(0.311457\pi\)
−0.808379 + 0.588663i \(0.799655\pi\)
\(80\) 15.6458 1.74925
\(81\) 0 0
\(82\) −4.92127 −0.543464
\(83\) 1.96291 11.1322i 0.215458 1.22192i −0.664653 0.747152i \(-0.731421\pi\)
0.880111 0.474768i \(-0.157468\pi\)
\(84\) 0 0
\(85\) 10.2096 + 3.71599i 1.10739 + 0.403056i
\(86\) 1.60565 1.34730i 0.173141 0.145283i
\(87\) 0 0
\(88\) 0.486329 0.177009i 0.0518429 0.0188693i
\(89\) 0.349643 0.605600i 0.0370621 0.0641935i −0.846899 0.531753i \(-0.821533\pi\)
0.883961 + 0.467560i \(0.154867\pi\)
\(90\) 0 0
\(91\) −5.53596 9.58856i −0.580326 1.00515i
\(92\) −0.747243 0.627011i −0.0779055 0.0653705i
\(93\) 0 0
\(94\) 0.0812519 + 0.460802i 0.00838049 + 0.0475281i
\(95\) 4.00243 + 22.6989i 0.410641 + 2.32886i
\(96\) 0 0
\(97\) −5.42855 4.55509i −0.551186 0.462500i 0.324157 0.946003i \(-0.394919\pi\)
−0.875342 + 0.483504i \(0.839364\pi\)
\(98\) 1.46756 + 2.54189i 0.148246 + 0.256770i
\(99\) 0 0
\(100\) −8.17752 + 14.1639i −0.817752 + 1.41639i
\(101\) 4.39506 1.59967i 0.437325 0.159173i −0.113969 0.993484i \(-0.536357\pi\)
0.551294 + 0.834311i \(0.314134\pi\)
\(102\) 0 0
\(103\) −10.4363 + 8.75709i −1.02832 + 0.862861i −0.990650 0.136429i \(-0.956437\pi\)
−0.0376683 + 0.999290i \(0.511993\pi\)
\(104\) −1.05299 0.383256i −0.103254 0.0375813i
\(105\) 0 0
\(106\) −1.59627 + 9.05288i −0.155043 + 0.879293i
\(107\) −11.6340 −1.12470 −0.562350 0.826900i \(-0.690102\pi\)
−0.562350 + 0.826900i \(0.690102\pi\)
\(108\) 0 0
\(109\) 14.6040 1.39881 0.699405 0.714725i \(-0.253448\pi\)
0.699405 + 0.714725i \(0.253448\pi\)
\(110\) −2.75811 + 15.6420i −0.262976 + 1.49141i
\(111\) 0 0
\(112\) −9.32295 3.39328i −0.880936 0.320634i
\(113\) −3.59721 + 3.01842i −0.338397 + 0.283949i −0.796111 0.605151i \(-0.793113\pi\)
0.457714 + 0.889100i \(0.348668\pi\)
\(114\) 0 0
\(115\) −1.80541 + 0.657115i −0.168355 + 0.0612762i
\(116\) −3.28212 + 5.68479i −0.304737 + 0.527820i
\(117\) 0 0
\(118\) −13.1099 22.7071i −1.20687 2.09036i
\(119\) −5.27774 4.42855i −0.483809 0.405964i
\(120\) 0 0
\(121\) −1.08600 6.15901i −0.0987272 0.559910i
\(122\) −1.25692 7.12836i −0.113796 0.645371i
\(123\) 0 0
\(124\) −6.19846 5.20113i −0.556638 0.467075i
\(125\) 6.85240 + 11.8687i 0.612897 + 1.06157i
\(126\) 0 0
\(127\) −3.04576 + 5.27541i −0.270267 + 0.468117i −0.968930 0.247334i \(-0.920445\pi\)
0.698663 + 0.715451i \(0.253779\pi\)
\(128\) −1.78265 + 0.648833i −0.157566 + 0.0573493i
\(129\) 0 0
\(130\) 26.3444 22.1055i 2.31055 1.93878i
\(131\) 9.72432 + 3.53936i 0.849618 + 0.309236i 0.729884 0.683571i \(-0.239574\pi\)
0.119733 + 0.992806i \(0.461796\pi\)
\(132\) 0 0
\(133\) 2.53802 14.3938i 0.220074 1.24810i
\(134\) 28.1627 2.43289
\(135\) 0 0
\(136\) −0.697281 −0.0597914
\(137\) −3.31402 + 18.7947i −0.283136 + 1.60574i 0.428734 + 0.903431i \(0.358960\pi\)
−0.711870 + 0.702311i \(0.752151\pi\)
\(138\) 0 0
\(139\) 21.8983 + 7.97032i 1.85739 + 0.676034i 0.980870 + 0.194662i \(0.0623610\pi\)
0.876517 + 0.481371i \(0.159861\pi\)
\(140\) 12.5094 10.4966i 1.05723 0.887124i
\(141\) 0 0
\(142\) 2.22668 0.810446i 0.186859 0.0680111i
\(143\) 5.13793 8.89915i 0.429655 0.744184i
\(144\) 0 0
\(145\) 6.46451 + 11.1969i 0.536848 + 0.929848i
\(146\) −7.06131 5.92514i −0.584398 0.490368i
\(147\) 0 0
\(148\) 0.786989 + 4.46324i 0.0646901 + 0.366876i
\(149\) −2.69258 15.2704i −0.220585 1.25100i −0.870948 0.491375i \(-0.836494\pi\)
0.650363 0.759623i \(-0.274617\pi\)
\(150\) 0 0
\(151\) −4.52094 3.79352i −0.367909 0.308713i 0.440025 0.897986i \(-0.354970\pi\)
−0.807934 + 0.589273i \(0.799414\pi\)
\(152\) −0.739620 1.28106i −0.0599911 0.103908i
\(153\) 0 0
\(154\) 5.03596 8.72254i 0.405809 0.702882i
\(155\) −14.9761 + 5.45084i −1.20291 + 0.437822i
\(156\) 0 0
\(157\) −0.928548 + 0.779145i −0.0741062 + 0.0621825i −0.679088 0.734057i \(-0.737625\pi\)
0.604982 + 0.796239i \(0.293180\pi\)
\(158\) 23.6919 + 8.62314i 1.88483 + 0.686020i
\(159\) 0 0
\(160\) 5.04576 28.6159i 0.398902 2.26229i
\(161\) 1.21832 0.0960168
\(162\) 0 0
\(163\) 2.77332 0.217223 0.108612 0.994084i \(-0.465360\pi\)
0.108612 + 0.994084i \(0.465360\pi\)
\(164\) −0.815422 + 4.62449i −0.0636737 + 0.361112i
\(165\) 0 0
\(166\) −20.9217 7.61489i −1.62384 0.591030i
\(167\) 2.93247 2.46064i 0.226922 0.190410i −0.522237 0.852800i \(-0.674902\pi\)
0.749159 + 0.662390i \(0.230458\pi\)
\(168\) 0 0
\(169\) −8.69119 + 3.16333i −0.668553 + 0.243333i
\(170\) 10.6998 18.5326i 0.820635 1.42138i
\(171\) 0 0
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 5.38484 + 4.51842i 0.409402 + 0.343529i 0.824114 0.566424i \(-0.191673\pi\)
−0.414712 + 0.909953i \(0.636118\pi\)
\(174\) 0 0
\(175\) −3.54710 20.1166i −0.268136 1.52067i
\(176\) −1.59894 9.06805i −0.120525 0.683530i
\(177\) 0 0
\(178\) −1.05509 0.885328i −0.0790825 0.0663581i
\(179\) −7.19269 12.4581i −0.537607 0.931163i −0.999032 0.0439838i \(-0.985995\pi\)
0.461425 0.887179i \(-0.347338\pi\)
\(180\) 0 0
\(181\) −6.60014 + 11.4318i −0.490584 + 0.849717i −0.999941 0.0108384i \(-0.996550\pi\)
0.509357 + 0.860555i \(0.329883\pi\)
\(182\) −20.4923 + 7.45858i −1.51899 + 0.552867i
\(183\) 0 0
\(184\) 0.0944557 0.0792577i 0.00696336 0.00584296i
\(185\) 8.38814 + 3.05303i 0.616708 + 0.224463i
\(186\) 0 0
\(187\) 1.11035 6.29710i 0.0811967 0.460489i
\(188\) 0.446476 0.0325626
\(189\) 0 0
\(190\) 45.3979 3.29351
\(191\) −2.33094 + 13.2194i −0.168661 + 0.956523i 0.776548 + 0.630058i \(0.216969\pi\)
−0.945209 + 0.326465i \(0.894142\pi\)
\(192\) 0 0
\(193\) −14.1001 5.13203i −1.01495 0.369412i −0.219618 0.975586i \(-0.570481\pi\)
−0.795332 + 0.606174i \(0.792703\pi\)
\(194\) −10.6922 + 8.97178i −0.767652 + 0.644136i
\(195\) 0 0
\(196\) 2.63176 0.957882i 0.187983 0.0684201i
\(197\) −11.1606 + 19.3307i −0.795158 + 1.37725i 0.127580 + 0.991828i \(0.459279\pi\)
−0.922739 + 0.385426i \(0.874054\pi\)
\(198\) 0 0
\(199\) 4.55051 + 7.88171i 0.322577 + 0.558720i 0.981019 0.193912i \(-0.0621176\pi\)
−0.658442 + 0.752631i \(0.728784\pi\)
\(200\) −1.58370 1.32888i −0.111984 0.0939659i
\(201\) 0 0
\(202\) −1.59967 9.07218i −0.112552 0.638316i
\(203\) −1.42366 8.07398i −0.0999214 0.566682i
\(204\) 0 0
\(205\) 7.08512 + 5.94512i 0.494846 + 0.415225i
\(206\) 13.4166 + 23.2383i 0.934781 + 1.61909i
\(207\) 0 0
\(208\) −9.96838 + 17.2657i −0.691183 + 1.19716i
\(209\) 12.7469 4.63950i 0.881723 0.320921i
\(210\) 0 0
\(211\) −4.57919 + 3.84240i −0.315245 + 0.264522i −0.786656 0.617392i \(-0.788189\pi\)
0.471411 + 0.881914i \(0.343745\pi\)
\(212\) 8.24243 + 3.00000i 0.566093 + 0.206041i
\(213\) 0 0
\(214\) −3.97906 + 22.5663i −0.272003 + 1.54260i
\(215\) −3.93923 −0.268653
\(216\) 0 0
\(217\) 10.1061 0.686045
\(218\) 4.99486 28.3273i 0.338295 1.91857i
\(219\) 0 0
\(220\) 14.2417 + 5.18355i 0.960175 + 0.349475i
\(221\) −10.6056 + 8.89915i −0.713409 + 0.598621i
\(222\) 0 0
\(223\) 8.36484 3.04455i 0.560151 0.203878i −0.0463999 0.998923i \(-0.514775\pi\)
0.606551 + 0.795045i \(0.292553\pi\)
\(224\) −9.21291 + 15.9572i −0.615564 + 1.06619i
\(225\) 0 0
\(226\) 4.62449 + 8.00984i 0.307616 + 0.532807i
\(227\) 8.17253 + 6.85756i 0.542430 + 0.455152i 0.872368 0.488850i \(-0.162583\pi\)
−0.329938 + 0.944003i \(0.607028\pi\)
\(228\) 0 0
\(229\) −1.43629 8.14560i −0.0949127 0.538276i −0.994774 0.102101i \(-0.967444\pi\)
0.899861 0.436176i \(-0.143667\pi\)
\(230\) 0.657115 + 3.72668i 0.0433288 + 0.245730i
\(231\) 0 0
\(232\) −0.635630 0.533356i −0.0417311 0.0350166i
\(233\) 6.36965 + 11.0326i 0.417290 + 0.722767i 0.995666 0.0930034i \(-0.0296467\pi\)
−0.578376 + 0.815770i \(0.696313\pi\)
\(234\) 0 0
\(235\) 0.439693 0.761570i 0.0286824 0.0496793i
\(236\) −23.5099 + 8.55690i −1.53036 + 0.557007i
\(237\) 0 0
\(238\) −10.3951 + 8.72254i −0.673815 + 0.565398i
\(239\) 14.1100 + 5.13563i 0.912702 + 0.332196i 0.755331 0.655343i \(-0.227476\pi\)
0.157371 + 0.987540i \(0.449698\pi\)
\(240\) 0 0
\(241\) 0.138156 0.783520i 0.00889939 0.0504710i −0.980035 0.198827i \(-0.936287\pi\)
0.988934 + 0.148356i \(0.0473980\pi\)
\(242\) −12.3180 −0.791832
\(243\) 0 0
\(244\) −6.90673 −0.442158
\(245\) 0.957882 5.43242i 0.0611968 0.347064i
\(246\) 0 0
\(247\) −27.5993 10.0453i −1.75610 0.639168i
\(248\) 0.783520 0.657451i 0.0497536 0.0417482i
\(249\) 0 0
\(250\) 25.3653 9.23222i 1.60424 0.583897i
\(251\) 4.15749 7.20099i 0.262419 0.454522i −0.704465 0.709738i \(-0.748813\pi\)
0.966884 + 0.255216i \(0.0821465\pi\)
\(252\) 0 0
\(253\) 0.565360 + 0.979232i 0.0355439 + 0.0615638i
\(254\) 9.19096 + 7.71213i 0.576692 + 0.483902i
\(255\) 0 0
\(256\) 3.08260 + 17.4823i 0.192662 + 1.09264i
\(257\) 4.44891 + 25.2310i 0.277515 + 1.57387i 0.730857 + 0.682531i \(0.239121\pi\)
−0.453341 + 0.891337i \(0.649768\pi\)
\(258\) 0 0
\(259\) −4.33615 3.63846i −0.269435 0.226083i
\(260\) −16.4073 28.4183i −1.01754 1.76243i
\(261\) 0 0
\(262\) 10.1912 17.6517i 0.629614 1.09052i
\(263\) 26.3725 9.59879i 1.62620 0.591887i 0.641648 0.767000i \(-0.278251\pi\)
0.984548 + 0.175113i \(0.0560290\pi\)
\(264\) 0 0
\(265\) 13.2344 11.1050i 0.812984 0.682175i
\(266\) −27.0515 9.84595i −1.65864 0.603694i
\(267\) 0 0
\(268\) 4.66637 26.4643i 0.285044 1.61657i
\(269\) 30.1710 1.83956 0.919778 0.392439i \(-0.128369\pi\)
0.919778 + 0.392439i \(0.128369\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) −2.15425 + 12.2173i −0.130620 + 0.740786i
\(273\) 0 0
\(274\) 35.3225 + 12.8564i 2.13391 + 0.776681i
\(275\) 14.5229 12.1861i 0.875762 0.734852i
\(276\) 0 0
\(277\) −19.8478 + 7.22400i −1.19254 + 0.434048i −0.860613 0.509259i \(-0.829920\pi\)
−0.331923 + 0.943306i \(0.607697\pi\)
\(278\) 22.9496 39.7499i 1.37643 2.38404i
\(279\) 0 0
\(280\) 1.03209 + 1.78763i 0.0616791 + 0.106831i
\(281\) 1.33851 + 1.12314i 0.0798487 + 0.0670010i 0.681838 0.731503i \(-0.261181\pi\)
−0.601990 + 0.798504i \(0.705625\pi\)
\(282\) 0 0
\(283\) −1.26558 7.17745i −0.0752308 0.426655i −0.999040 0.0438023i \(-0.986053\pi\)
0.923809 0.382853i \(-0.125058\pi\)
\(284\) −0.392624 2.22668i −0.0232980 0.132129i
\(285\) 0 0
\(286\) −15.5043 13.0097i −0.916791 0.769279i
\(287\) −2.93247 5.07919i −0.173098 0.299815i
\(288\) 0 0
\(289\) 4.19253 7.26168i 0.246620 0.427158i
\(290\) 23.9294 8.70961i 1.40519 0.511446i
\(291\) 0 0
\(292\) −6.73783 + 5.65371i −0.394301 + 0.330858i
\(293\) −14.4251 5.25031i −0.842725 0.306727i −0.115654 0.993290i \(-0.536896\pi\)
−0.727070 + 0.686563i \(0.759119\pi\)
\(294\) 0 0
\(295\) −8.55690 + 48.5286i −0.498202 + 2.82545i
\(296\) −0.572881 −0.0332980
\(297\) 0 0
\(298\) −30.5408 −1.76918
\(299\) 0.425126 2.41101i 0.0245857 0.139432i
\(300\) 0 0
\(301\) 2.34730 + 0.854346i 0.135296 + 0.0492437i
\(302\) −8.90452 + 7.47178i −0.512398 + 0.429953i
\(303\) 0 0
\(304\) −24.7310 + 9.00135i −1.41842 + 0.516263i
\(305\) −6.80180 + 11.7811i −0.389470 + 0.674581i
\(306\) 0 0
\(307\) −8.38191 14.5179i −0.478381 0.828580i 0.521312 0.853366i \(-0.325443\pi\)
−0.999693 + 0.0247861i \(0.992110\pi\)
\(308\) −7.36208 6.17752i −0.419493 0.351997i
\(309\) 0 0
\(310\) 5.45084 + 30.9132i 0.309587 + 1.75575i
\(311\) −2.78239 15.7797i −0.157775 0.894786i −0.956205 0.292698i \(-0.905447\pi\)
0.798430 0.602088i \(-0.205664\pi\)
\(312\) 0 0
\(313\) 26.3562 + 22.1155i 1.48974 + 1.25004i 0.894954 + 0.446159i \(0.147208\pi\)
0.594788 + 0.803883i \(0.297236\pi\)
\(314\) 1.19372 + 2.06758i 0.0673654 + 0.116680i
\(315\) 0 0
\(316\) 12.0287 20.8343i 0.676666 1.17202i
\(317\) 15.3274 5.57873i 0.860874 0.313332i 0.126408 0.991978i \(-0.459655\pi\)
0.734466 + 0.678646i \(0.237433\pi\)
\(318\) 0 0
\(319\) 5.82888 4.89101i 0.326355 0.273844i
\(320\) −24.3759 8.87211i −1.36266 0.495966i
\(321\) 0 0
\(322\) 0.416689 2.36316i 0.0232212 0.131694i
\(323\) −18.2761 −1.01691
\(324\) 0 0
\(325\) −41.0479 −2.27693
\(326\) 0.948531 5.37939i 0.0525343 0.297937i
\(327\) 0 0
\(328\) −0.557781 0.203016i −0.0307983 0.0112097i
\(329\) −0.427173 + 0.358441i −0.0235508 + 0.0197615i
\(330\) 0 0
\(331\) 29.6755 10.8010i 1.63111 0.593676i 0.645658 0.763627i \(-0.276583\pi\)
0.985453 + 0.169951i \(0.0543609\pi\)
\(332\) −10.6222 + 18.3983i −0.582972 + 1.00974i
\(333\) 0 0
\(334\) −3.76991 6.52968i −0.206281 0.357288i
\(335\) −40.5457 34.0219i −2.21525 1.85881i
\(336\) 0 0
\(337\) 1.04277 + 5.91382i 0.0568031 + 0.322146i 0.999948 0.0102366i \(-0.00325846\pi\)
−0.943144 + 0.332383i \(0.892147\pi\)
\(338\) 3.16333 + 17.9402i 0.172063 + 0.975816i
\(339\) 0 0
\(340\) −15.6420 13.1252i −0.848308 0.711815i
\(341\) 4.68972 + 8.12284i 0.253963 + 0.439876i
\(342\) 0 0
\(343\) −9.96451 + 17.2590i −0.538033 + 0.931900i
\(344\) 0.237565 0.0864665i 0.0128086 0.00466196i
\(345\) 0 0
\(346\) 10.6061 8.89955i 0.570186 0.478443i
\(347\) −21.6415 7.87686i −1.16178 0.422852i −0.312045 0.950067i \(-0.601014\pi\)
−0.849732 + 0.527216i \(0.823236\pi\)
\(348\) 0 0
\(349\) −2.00846 + 11.3905i −0.107510 + 0.609721i 0.882678 + 0.469979i \(0.155738\pi\)
−0.990188 + 0.139742i \(0.955373\pi\)
\(350\) −40.2332 −2.15056
\(351\) 0 0
\(352\) −17.1010 −0.911487
\(353\) −0.370674 + 2.10220i −0.0197290 + 0.111889i −0.993082 0.117423i \(-0.962537\pi\)
0.973353 + 0.229312i \(0.0736476\pi\)
\(354\) 0 0
\(355\) −4.18479 1.52314i −0.222106 0.0808399i
\(356\) −1.00676 + 0.844770i −0.0533581 + 0.0447727i
\(357\) 0 0
\(358\) −26.6250 + 9.69069i −1.40717 + 0.512169i
\(359\) −12.1118 + 20.9782i −0.639234 + 1.10719i 0.346367 + 0.938099i \(0.387415\pi\)
−0.985601 + 0.169087i \(0.945918\pi\)
\(360\) 0 0
\(361\) −9.88578 17.1227i −0.520304 0.901193i
\(362\) 19.9167 + 16.7121i 1.04680 + 0.878370i
\(363\) 0 0
\(364\) 3.61334 + 20.4923i 0.189391 + 1.07409i
\(365\) 3.00827 + 17.0608i 0.157460 + 0.893002i
\(366\) 0 0
\(367\) −2.17159 1.82218i −0.113356 0.0951170i 0.584348 0.811503i \(-0.301350\pi\)
−0.697704 + 0.716386i \(0.745795\pi\)
\(368\) −1.09689 1.89986i −0.0571792 0.0990372i
\(369\) 0 0
\(370\) 8.79086 15.2262i 0.457015 0.791573i
\(371\) −10.2946 + 3.74691i −0.534467 + 0.194530i
\(372\) 0 0
\(373\) −22.0876 + 18.5337i −1.14366 + 0.959641i −0.999552 0.0299222i \(-0.990474\pi\)
−0.144103 + 0.989563i \(0.546030\pi\)
\(374\) −11.8347 4.30747i −0.611956 0.222734i
\(375\) 0 0
\(376\) −0.00980018 + 0.0555796i −0.000505406 + 0.00286630i
\(377\) −16.4749 −0.848501
\(378\) 0 0
\(379\) 32.1985 1.65393 0.826963 0.562256i \(-0.190066\pi\)
0.826963 + 0.562256i \(0.190066\pi\)
\(380\) 7.52211 42.6600i 0.385876 2.18841i
\(381\) 0 0
\(382\) 24.8444 + 9.04261i 1.27115 + 0.462660i
\(383\) 0.514973 0.432114i 0.0263139 0.0220800i −0.629536 0.776971i \(-0.716755\pi\)
0.655850 + 0.754891i \(0.272310\pi\)
\(384\) 0 0
\(385\) −17.7875 + 6.47410i −0.906533 + 0.329951i
\(386\) −14.7771 + 25.5947i −0.752134 + 1.30273i
\(387\) 0 0
\(388\) 6.65910 + 11.5339i 0.338065 + 0.585545i
\(389\) −3.26281 2.73783i −0.165431 0.138813i 0.556314 0.830972i \(-0.312215\pi\)
−0.721745 + 0.692159i \(0.756660\pi\)
\(390\) 0 0
\(391\) −0.264538 1.50027i −0.0133783 0.0758719i
\(392\) 0.0614747 + 0.348641i 0.00310494 + 0.0176090i
\(393\) 0 0
\(394\) 33.6785 + 28.2596i 1.69670 + 1.42370i
\(395\) −23.6919 41.0355i −1.19207 2.06472i
\(396\) 0 0
\(397\) 4.43242 7.67717i 0.222457 0.385306i −0.733097 0.680124i \(-0.761926\pi\)
0.955553 + 0.294818i \(0.0952591\pi\)
\(398\) 16.8445 6.13088i 0.844336 0.307313i
\(399\) 0 0
\(400\) −28.1766 + 23.6430i −1.40883 + 1.18215i
\(401\) −34.8475 12.6834i −1.74020 0.633381i −0.740930 0.671582i \(-0.765615\pi\)
−0.999270 + 0.0382006i \(0.987837\pi\)
\(402\) 0 0
\(403\) 3.52646 19.9996i 0.175666 0.996250i
\(404\) −8.79012 −0.437325
\(405\) 0 0
\(406\) −16.1480 −0.801410
\(407\) 0.912254 5.17365i 0.0452187 0.256448i
\(408\) 0 0
\(409\) 3.18479 + 1.15917i 0.157478 + 0.0573173i 0.419556 0.907729i \(-0.362186\pi\)
−0.262078 + 0.965047i \(0.584408\pi\)
\(410\) 13.9550 11.7096i 0.689187 0.578296i
\(411\) 0 0
\(412\) 24.0599 8.75709i 1.18535 0.431431i
\(413\) 15.6238 27.0612i 0.768798 1.33160i
\(414\) 0 0
\(415\) 20.9217 + 36.2375i 1.02701 + 1.77883i
\(416\) 28.3640 + 23.8002i 1.39066 + 1.16690i
\(417\) 0 0
\(418\) −4.63950 26.3119i −0.226925 1.28696i
\(419\) −3.58694 20.3425i −0.175233 0.993799i −0.937874 0.346976i \(-0.887209\pi\)
0.762641 0.646823i \(-0.223903\pi\)
\(420\) 0 0
\(421\) 21.0915 + 17.6979i 1.02794 + 0.862542i 0.990604 0.136761i \(-0.0436691\pi\)
0.0373336 + 0.999303i \(0.488114\pi\)
\(422\) 5.88690 + 10.1964i 0.286570 + 0.496353i
\(423\) 0 0
\(424\) −0.554378 + 0.960210i −0.0269230 + 0.0466319i
\(425\) −24.0020 + 8.73601i −1.16427 + 0.423759i
\(426\) 0 0
\(427\) 6.60813 5.54488i 0.319790 0.268335i
\(428\) 20.5461 + 7.47818i 0.993134 + 0.361471i
\(429\) 0 0
\(430\) −1.34730 + 7.64090i −0.0649724 + 0.368477i
\(431\) −2.58110 −0.124327 −0.0621636 0.998066i \(-0.519800\pi\)
−0.0621636 + 0.998066i \(0.519800\pi\)
\(432\) 0 0
\(433\) −27.0137 −1.29820 −0.649098 0.760704i \(-0.724854\pi\)
−0.649098 + 0.760704i \(0.724854\pi\)
\(434\) 3.45648 19.6027i 0.165916 0.940958i
\(435\) 0 0
\(436\) −25.7913 9.38728i −1.23518 0.449569i
\(437\) 2.47573 2.07738i 0.118430 0.0993746i
\(438\) 0 0
\(439\) −11.0039 + 4.00508i −0.525186 + 0.191152i −0.590988 0.806681i \(-0.701262\pi\)
0.0658015 + 0.997833i \(0.479040\pi\)
\(440\) −0.957882 + 1.65910i −0.0456652 + 0.0790945i
\(441\) 0 0
\(442\) 13.6343 + 23.6153i 0.648517 + 1.12326i
\(443\) 1.59397 + 1.33750i 0.0757316 + 0.0635464i 0.679868 0.733335i \(-0.262037\pi\)
−0.604136 + 0.796881i \(0.706482\pi\)
\(444\) 0 0
\(445\) 0.449493 + 2.54920i 0.0213080 + 0.120844i
\(446\) −3.04455 17.2665i −0.144164 0.817593i
\(447\) 0 0
\(448\) 12.6009 + 10.5734i 0.595334 + 0.499545i
\(449\) −5.27541 9.13728i −0.248962 0.431215i 0.714276 0.699864i \(-0.246756\pi\)
−0.963238 + 0.268649i \(0.913423\pi\)
\(450\) 0 0
\(451\) 2.72163 4.71400i 0.128157 0.221974i
\(452\) 8.29304 3.01842i 0.390072 0.141974i
\(453\) 0 0
\(454\) 16.0967 13.5068i 0.755457 0.633904i
\(455\) 38.5129 + 14.0175i 1.80551 + 0.657152i
\(456\) 0 0
\(457\) −1.37346 + 7.78925i −0.0642475 + 0.364366i 0.935686 + 0.352834i \(0.114782\pi\)
−0.999934 + 0.0115320i \(0.996329\pi\)
\(458\) −16.2912 −0.761238
\(459\) 0 0
\(460\) 3.61081 0.168355
\(461\) −6.78839 + 38.4989i −0.316167 + 1.79307i 0.249434 + 0.968392i \(0.419756\pi\)
−0.565600 + 0.824679i \(0.691356\pi\)
\(462\) 0 0
\(463\) −22.2640 8.10343i −1.03470 0.376598i −0.231828 0.972757i \(-0.574471\pi\)
−0.802867 + 0.596158i \(0.796693\pi\)
\(464\) −11.3089 + 9.48932i −0.525004 + 0.440531i
\(465\) 0 0
\(466\) 23.5783 8.58180i 1.09224 0.397544i
\(467\) 17.3576 30.0642i 0.803214 1.39121i −0.114277 0.993449i \(-0.536455\pi\)
0.917490 0.397758i \(-0.130212\pi\)
\(468\) 0 0
\(469\) 16.7815 + 29.0665i 0.774899 + 1.34216i
\(470\) −1.32683 1.11334i −0.0612020 0.0513546i
\(471\) 0 0
\(472\) −0.549163 3.11446i −0.0252773 0.143355i
\(473\) 0.402575 + 2.28312i 0.0185104 + 0.104978i
\(474\) 0 0
\(475\) −41.5094 34.8305i −1.90458 1.59813i
\(476\) 6.47410 + 11.2135i 0.296740 + 0.513969i
\(477\) 0 0
\(478\) 14.7875 25.6126i 0.676362 1.17149i
\(479\) 6.09083 2.21688i 0.278297 0.101292i −0.199101 0.979979i \(-0.563802\pi\)
0.477398 + 0.878687i \(0.341580\pi\)
\(480\) 0 0
\(481\) −8.71348 + 7.31148i −0.397300 + 0.333375i
\(482\) −1.47254 0.535959i −0.0670722 0.0244123i
\(483\) 0 0
\(484\) −2.04101 + 11.5752i −0.0927733 + 0.526143i
\(485\) 26.2317 1.19112
\(486\) 0 0
\(487\) 19.9828 0.905505 0.452753 0.891636i \(-0.350442\pi\)
0.452753 + 0.891636i \(0.350442\pi\)
\(488\) 0.151603 0.859785i 0.00686276 0.0389206i
\(489\) 0 0
\(490\) −10.2096 3.71599i −0.461223 0.167871i
\(491\) −20.0911 + 16.8584i −0.906699 + 0.760811i −0.971488 0.237088i \(-0.923807\pi\)
0.0647892 + 0.997899i \(0.479363\pi\)
\(492\) 0 0
\(493\) −9.63341 + 3.50627i −0.433867 + 0.157915i
\(494\) −28.9243 + 50.0984i −1.30137 + 2.25403i
\(495\) 0 0
\(496\) −9.09879 15.7596i −0.408548 0.707626i
\(497\) 2.16328 + 1.81521i 0.0970364 + 0.0814232i
\(498\) 0 0
\(499\) 1.09698 + 6.22129i 0.0491077 + 0.278503i 0.999467 0.0326518i \(-0.0103952\pi\)
−0.950359 + 0.311155i \(0.899284\pi\)
\(500\) −4.47259 25.3653i −0.200020 1.13437i
\(501\) 0 0
\(502\) −12.5458 10.5271i −0.559945 0.469849i
\(503\) 10.9131 + 18.9020i 0.486589 + 0.842798i 0.999881 0.0154166i \(-0.00490745\pi\)
−0.513292 + 0.858214i \(0.671574\pi\)
\(504\) 0 0
\(505\) −8.65657 + 14.9936i −0.385212 + 0.667208i
\(506\) 2.09277 0.761707i 0.0930351 0.0338620i
\(507\) 0 0
\(508\) 8.76991 7.35883i 0.389102 0.326495i
\(509\) −27.3386 9.95043i −1.21176 0.441045i −0.344447 0.938806i \(-0.611933\pi\)
−0.867314 + 0.497761i \(0.834156\pi\)
\(510\) 0 0
\(511\) 1.90760 10.8186i 0.0843874 0.478585i
\(512\) 31.1704 1.37755
\(513\) 0 0
\(514\) 50.4620 2.22579
\(515\) 8.75709 49.6639i 0.385883 2.18845i
\(516\) 0 0
\(517\) −0.486329 0.177009i −0.0213887 0.00778487i
\(518\) −8.54055 + 7.16637i −0.375250 + 0.314872i
\(519\) 0 0
\(520\) 3.89780 1.41868i 0.170930 0.0622134i
\(521\) 6.84743 11.8601i 0.299991 0.519600i −0.676142 0.736771i \(-0.736350\pi\)
0.976134 + 0.217171i \(0.0696829\pi\)
\(522\) 0 0
\(523\) −6.57532 11.3888i −0.287519 0.497997i 0.685698 0.727886i \(-0.259497\pi\)
−0.973217 + 0.229889i \(0.926164\pi\)
\(524\) −14.8985 12.5013i −0.650845 0.546124i
\(525\) 0 0
\(526\) −9.59879 54.4375i −0.418527 2.37359i
\(527\) −2.19437 12.4449i −0.0955884 0.542109i
\(528\) 0 0
\(529\) −17.4127 14.6110i −0.757072 0.635259i
\(530\) −17.0138 29.4688i −0.739034 1.28004i
\(531\) 0 0
\(532\) −13.7344 + 23.7887i −0.595463 + 1.03137i
\(533\) −11.0748 + 4.03091i −0.479704 + 0.174598i
\(534\) 0 0
\(535\) 32.9898 27.6817i 1.42627 1.19679i
\(536\) 3.19199 + 1.16179i 0.137873 + 0.0501816i
\(537\) 0 0
\(538\) 10.3191 58.5224i 0.444887 2.52308i
\(539\) −3.24644 −0.139834
\(540\) 0 0
\(541\) 6.26083 0.269174 0.134587 0.990902i \(-0.457029\pi\)
0.134587 + 0.990902i \(0.457029\pi\)
\(542\) −6.49838 + 36.8542i −0.279129 + 1.58302i
\(543\) 0 0
\(544\) 21.6506 + 7.88019i 0.928264 + 0.337860i
\(545\) −41.4117 + 34.7486i −1.77388 + 1.48846i
\(546\) 0 0
\(547\) 29.4859 10.7320i 1.26073 0.458867i 0.376714 0.926330i \(-0.377054\pi\)
0.884013 + 0.467463i \(0.154832\pi\)
\(548\) 17.9337 31.0621i 0.766091 1.32691i
\(549\) 0 0
\(550\) −18.6702 32.3378i −0.796102 1.37889i
\(551\) −16.6601 13.9795i −0.709746 0.595548i
\(552\) 0 0
\(553\) 5.21760 + 29.5905i 0.221875 + 1.25831i
\(554\) 7.22400 + 40.9693i 0.306918 + 1.74062i
\(555\) 0 0
\(556\) −33.5501 28.1519i −1.42284 1.19391i
\(557\) 21.7196 + 37.6195i 0.920290 + 1.59399i 0.798966 + 0.601376i \(0.205381\pi\)
0.121324 + 0.992613i \(0.461286\pi\)
\(558\) 0 0
\(559\) 2.50980 4.34710i 0.106153 0.183863i
\(560\) 34.5104 12.5608i 1.45833 0.530790i
\(561\) 0 0
\(562\) 2.63634 2.21216i 0.111207 0.0933142i
\(563\) 30.0867 + 10.9507i 1.26800 + 0.461516i 0.886447 0.462829i \(-0.153166\pi\)
0.381557 + 0.924345i \(0.375388\pi\)
\(564\) 0 0
\(565\) 3.01842 17.1183i 0.126986 0.720172i
\(566\) −14.3549 −0.603381
\(567\) 0 0
\(568\) 0.285807 0.0119922
\(569\) −1.17594 + 6.66906i −0.0492978 + 0.279582i −0.999485 0.0320990i \(-0.989781\pi\)
0.950187 + 0.311681i \(0.100892\pi\)
\(570\) 0 0
\(571\) 19.8773 + 7.23475i 0.831840 + 0.302765i 0.722614 0.691252i \(-0.242940\pi\)
0.109226 + 0.994017i \(0.465163\pi\)
\(572\) −14.7941 + 12.4137i −0.618571 + 0.519043i
\(573\) 0 0
\(574\) −10.8550 + 3.95091i −0.453080 + 0.164908i
\(575\) 2.25838 3.91164i 0.0941811 0.163127i
\(576\) 0 0
\(577\) −5.95811 10.3198i −0.248039 0.429617i 0.714942 0.699183i \(-0.246453\pi\)
−0.962982 + 0.269567i \(0.913120\pi\)
\(578\) −12.6515 10.6159i −0.526233 0.441562i
\(579\) 0 0
\(580\) −4.21941 23.9294i −0.175201 0.993616i
\(581\) −4.60754 26.1306i −0.191153 1.08408i
\(582\) 0 0
\(583\) −7.78880 6.53558i −0.322579 0.270676i
\(584\) −0.555907 0.962859i −0.0230036 0.0398434i
\(585\) 0 0
\(586\) −15.1177 + 26.1846i −0.624506 + 1.08168i
\(587\) 0.122030 0.0444153i 0.00503672 0.00183322i −0.339501 0.940606i \(-0.610258\pi\)
0.344537 + 0.938773i \(0.388036\pi\)
\(588\) 0 0
\(589\) 20.5364 17.2321i 0.846189 0.710037i
\(590\) 91.2040 + 33.1955i 3.75481 + 1.36664i
\(591\) 0 0
\(592\) −1.76991 + 10.0377i −0.0727431 + 0.412546i
\(593\) 26.2622 1.07846 0.539230 0.842158i \(-0.318715\pi\)
0.539230 + 0.842158i \(0.318715\pi\)
\(594\) 0 0
\(595\) 25.5030 1.04552
\(596\) −5.06040 + 28.6989i −0.207282 + 1.17555i
\(597\) 0 0
\(598\) −4.53121 1.64923i −0.185295 0.0674419i
\(599\) 21.1391 17.7378i 0.863721 0.724748i −0.0990454 0.995083i \(-0.531579\pi\)
0.962766 + 0.270335i \(0.0871345\pi\)
\(600\) 0 0
\(601\) −1.25237 + 0.455827i −0.0510854 + 0.0185936i −0.367436 0.930049i \(-0.619764\pi\)
0.316351 + 0.948642i \(0.397542\pi\)
\(602\) 2.45999 4.26083i 0.100262 0.173658i
\(603\) 0 0
\(604\) 5.54576 + 9.60554i 0.225654 + 0.390844i
\(605\) 17.7342 + 14.8807i 0.720996 + 0.604988i
\(606\) 0 0
\(607\) −2.18180 12.3736i −0.0885565 0.502229i −0.996532 0.0832064i \(-0.973484\pi\)
0.907976 0.419023i \(-0.137627\pi\)
\(608\) 8.48762 + 48.1357i 0.344218 + 1.95216i
\(609\) 0 0
\(610\) 20.5253 + 17.2228i 0.831044 + 0.697329i
\(611\) 0.560282 + 0.970437i 0.0226666 + 0.0392597i
\(612\) 0 0
\(613\) 6.99912 12.1228i 0.282692 0.489637i −0.689355 0.724424i \(-0.742106\pi\)
0.972047 + 0.234787i \(0.0754393\pi\)
\(614\) −31.0270 + 11.2929i −1.25215 + 0.455745i
\(615\) 0 0
\(616\) 0.930608 0.780873i 0.0374953 0.0314623i
\(617\) −22.5965 8.22446i −0.909702 0.331104i −0.155568 0.987825i \(-0.549721\pi\)
−0.754134 + 0.656721i \(0.771943\pi\)
\(618\) 0 0
\(619\) 1.19325 6.76725i 0.0479607 0.271999i −0.951392 0.307984i \(-0.900346\pi\)
0.999352 + 0.0359850i \(0.0114569\pi\)
\(620\) 29.9521 1.20291
\(621\) 0 0
\(622\) −31.5594 −1.26542
\(623\) 0.285032 1.61650i 0.0114196 0.0647635i
\(624\) 0 0
\(625\) −6.78359 2.46902i −0.271343 0.0987609i
\(626\) 51.9116 43.5590i 2.07481 1.74097i
\(627\) 0 0
\(628\) 2.14068 0.779145i 0.0854225 0.0310913i
\(629\) −3.53898 + 6.12970i −0.141109 + 0.244407i
\(630\) 0 0
\(631\) 17.6887 + 30.6377i 0.704175 + 1.21967i 0.966989 + 0.254820i \(0.0820161\pi\)
−0.262814 + 0.964847i \(0.584651\pi\)
\(632\) 2.32953 + 1.95471i 0.0926637 + 0.0777541i
\(633\) 0 0
\(634\) −5.57873 31.6385i −0.221560 1.25653i
\(635\) −3.91555 22.2062i −0.155384 0.881226i
\(636\) 0 0
\(637\) 5.38460 + 4.51822i 0.213346 + 0.179018i
\(638\) −7.49346 12.9791i −0.296669 0.513846i
\(639\) 0 0
\(640\) 3.51114 6.08148i 0.138790 0.240392i
\(641\) 18.0174 6.55778i 0.711643 0.259017i 0.0392691 0.999229i \(-0.487497\pi\)
0.672374 + 0.740212i \(0.265275\pi\)
\(642\) 0 0
\(643\) 14.8432 12.4549i 0.585358 0.491173i −0.301344 0.953516i \(-0.597435\pi\)
0.886702 + 0.462342i \(0.152991\pi\)
\(644\) −2.15160 0.783119i −0.0847849 0.0308592i
\(645\) 0 0
\(646\) −6.25078 + 35.4499i −0.245934 + 1.39476i
\(647\) 8.77141 0.344840 0.172420 0.985024i \(-0.444841\pi\)
0.172420 + 0.985024i \(0.444841\pi\)
\(648\) 0 0
\(649\) 29.0009 1.13839
\(650\) −14.0392 + 79.6203i −0.550663 + 3.12296i
\(651\) 0 0
\(652\) −4.89780 1.78265i −0.191813 0.0698141i
\(653\) 25.1334 21.0895i 0.983547 0.825294i −0.00107333 0.999999i \(-0.500342\pi\)
0.984621 + 0.174705i \(0.0558972\pi\)
\(654\) 0 0
\(655\) −35.9962 + 13.1015i −1.40649 + 0.511920i
\(656\) −5.28039 + 9.14590i −0.206164 + 0.357087i
\(657\) 0 0
\(658\) 0.549163 + 0.951178i 0.0214086 + 0.0370808i
\(659\) 14.2880 + 11.9890i 0.556580 + 0.467026i 0.877162 0.480195i \(-0.159434\pi\)
−0.320582 + 0.947221i \(0.603879\pi\)
\(660\) 0 0
\(661\) 6.32207 + 35.8542i 0.245900 + 1.39457i 0.818393 + 0.574659i \(0.194865\pi\)
−0.572493 + 0.819910i \(0.694024\pi\)
\(662\) −10.8010 61.2554i −0.419792 2.38076i
\(663\) 0 0
\(664\) −2.05715 1.72616i −0.0798330 0.0669878i
\(665\) 27.0515 + 46.8546i 1.04901 + 1.81694i
\(666\) 0 0
\(667\) 0.906422 1.56997i 0.0350968 0.0607894i
\(668\) −6.76055 + 2.46064i −0.261573 + 0.0952049i
\(669\) 0 0
\(670\) −79.8594 + 67.0100i −3.08524 + 2.58882i
\(671\) 7.52324 + 2.73824i 0.290432 + 0.105708i
\(672\) 0 0
\(673\) 6.84002 38.7917i 0.263663 1.49531i −0.509151 0.860677i \(-0.670040\pi\)
0.772814 0.634632i \(-0.218849\pi\)
\(674\) 11.8276 0.455584
\(675\) 0 0
\(676\) 17.3824 0.668553
\(677\) 5.50038 31.1942i 0.211397 1.19889i −0.675654 0.737218i \(-0.736139\pi\)
0.887051 0.461671i \(-0.152750\pi\)
\(678\) 0 0
\(679\) −15.6309 5.68918i −0.599858 0.218331i
\(680\) 1.97724 1.65910i 0.0758236 0.0636236i
\(681\) 0 0
\(682\) 17.3598 6.31844i 0.664741 0.241946i
\(683\) 14.5328 25.1716i 0.556083 0.963164i −0.441735 0.897145i \(-0.645637\pi\)
0.997818 0.0660187i \(-0.0210297\pi\)
\(684\) 0 0
\(685\) −35.3225 61.1804i −1.34960 2.33758i
\(686\) 30.0692 + 25.2310i 1.14805 + 0.963325i
\(687\) 0 0
\(688\) −0.781059 4.42961i −0.0297776 0.168877i
\(689\) 3.82278 + 21.6800i 0.145636 + 0.825944i
\(690\) 0 0
\(691\) 4.10401 + 3.44367i 0.156124 + 0.131003i 0.717503 0.696555i \(-0.245285\pi\)
−0.561380 + 0.827558i \(0.689729\pi\)
\(692\) −6.60549 11.4410i −0.251103 0.434923i
\(693\) 0 0
\(694\) −22.6805 + 39.2838i −0.860940 + 1.49119i
\(695\) −81.0601 + 29.5035i −3.07478 + 1.11913i
\(696\) 0 0
\(697\) −5.61793 + 4.71400i −0.212794 + 0.178555i
\(698\) 21.4072 + 7.79157i 0.810274 + 0.294915i
\(699\) 0 0
\(700\) −6.66637 + 37.8069i −0.251965 + 1.42897i
\(701\) −25.6536 −0.968922 −0.484461 0.874813i \(-0.660984\pi\)
−0.484461 + 0.874813i \(0.660984\pi\)
\(702\) 0 0
\(703\) −15.0155 −0.566320
\(704\) −2.65101 + 15.0346i −0.0999136 + 0.566638i
\(705\) 0 0
\(706\) 3.95084 + 1.43799i 0.148692 + 0.0541194i
\(707\) 8.41009 7.05690i 0.316294 0.265402i
\(708\) 0 0
\(709\) 4.40760 1.60424i 0.165531 0.0602484i −0.257925 0.966165i \(-0.583039\pi\)
0.423456 + 0.905916i \(0.360817\pi\)
\(710\) −4.38571 + 7.59627i −0.164593 + 0.285083i
\(711\) 0 0
\(712\) −0.0830629 0.143869i −0.00311291 0.00539173i
\(713\) 1.71183 + 1.43639i 0.0641085 + 0.0537934i
\(714\) 0 0
\(715\) 6.60519 + 37.4599i 0.247020 + 1.40092i
\(716\) 4.69470 + 26.6250i 0.175449 + 0.995021i
\(717\) 0 0
\(718\) 36.5488 + 30.6680i 1.36399 + 1.14452i
\(719\) −19.5335 33.8330i −0.728476 1.26176i −0.957527 0.288343i \(-0.906896\pi\)
0.229052 0.973414i \(-0.426438\pi\)
\(720\) 0 0
\(721\) −15.9893 + 27.6943i −0.595473 + 1.03139i
\(722\) −36.5939 + 13.3191i −1.36188 + 0.495685i
\(723\) 0 0
\(724\) 19.0043 15.9465i 0.706291 0.592648i
\(725\) −28.5621 10.3957i −1.06077 0.386088i
\(726\) 0 0
\(727\) −1.87980 + 10.6609i −0.0697178 + 0.395389i 0.929902 + 0.367808i \(0.119892\pi\)
−0.999620 + 0.0275812i \(0.991220\pi\)
\(728\) −2.63030 −0.0974853
\(729\) 0 0
\(730\) 34.1215 1.26290
\(731\) 0.542388 3.07604i 0.0200610 0.113771i
\(732\) 0 0
\(733\) 3.20661 + 1.16711i 0.118439 + 0.0431083i 0.400560 0.916271i \(-0.368816\pi\)
−0.282121 + 0.959379i \(0.591038\pi\)
\(734\) −4.27719 + 3.58899i −0.157874 + 0.132472i
\(735\) 0 0
\(736\) −3.82857 + 1.39349i −0.141123 + 0.0513646i
\(737\) −15.5749 + 26.9766i −0.573710 + 0.993695i
\(738\) 0 0
\(739\) −13.1505 22.7773i −0.483748 0.837877i 0.516077 0.856542i \(-0.327392\pi\)
−0.999826 + 0.0186653i \(0.994058\pi\)
\(740\) −12.8514 10.7836i −0.472426 0.396412i
\(741\) 0 0
\(742\) 3.74691 + 21.2498i 0.137553 + 0.780104i
\(743\) 5.02606 + 28.5042i 0.184388 + 1.04572i 0.926739 + 0.375706i \(0.122600\pi\)
−0.742351 + 0.670011i \(0.766289\pi\)
\(744\) 0 0
\(745\) 43.9693 + 36.8946i 1.61091 + 1.35171i
\(746\) 28.3953 + 49.1822i 1.03963 + 1.80069i
\(747\) 0 0
\(748\) −6.00862 + 10.4072i −0.219697 + 0.380526i
\(749\) −25.6615 + 9.34002i −0.937651 + 0.341277i
\(750\) 0 0
\(751\) −14.8983 + 12.5011i −0.543646 + 0.456173i −0.872782 0.488109i \(-0.837687\pi\)
0.329137 + 0.944282i \(0.393242\pi\)
\(752\) 0.943555 + 0.343426i 0.0344079 + 0.0125235i
\(753\) 0 0
\(754\) −5.63475 + 31.9563i −0.205206 + 1.16378i
\(755\) 21.8460 0.795058
\(756\) 0 0
\(757\) 6.59627 0.239745 0.119873 0.992789i \(-0.461751\pi\)
0.119873 + 0.992789i \(0.461751\pi\)
\(758\) 11.0125 62.4552i 0.399994 2.26848i
\(759\) 0 0
\(760\) 5.14543 + 1.87278i 0.186644 + 0.0679330i
\(761\) 7.91301 6.63980i 0.286846 0.240693i −0.487998 0.872845i \(-0.662273\pi\)
0.774844 + 0.632152i \(0.217828\pi\)
\(762\) 0 0
\(763\) 32.2126 11.7244i 1.16617 0.424453i
\(764\) 12.6138 21.8478i 0.456352 0.790424i
\(765\) 0 0
\(766\) −0.662037 1.14668i −0.0239204 0.0414313i
\(767\) −48.1014 40.3619i −1.73684 1.45738i
\(768\) 0 0
\(769\) 7.78968 + 44.1775i 0.280903 + 1.59308i 0.719563 + 0.694427i \(0.244342\pi\)
−0.438660 + 0.898653i \(0.644547\pi\)
\(770\) 6.47410 + 36.7165i 0.233311 + 1.32317i
\(771\) 0 0
\(772\) 21.6027 + 18.1268i 0.777497 + 0.652397i
\(773\) −21.4677 37.1832i −0.772141 1.33739i −0.936388 0.350968i \(-0.885853\pi\)
0.164247 0.986419i \(-0.447481\pi\)
\(774\) 0 0
\(775\) 18.7335 32.4475i 0.672929 1.16555i
\(776\) −1.58197 + 0.575789i −0.0567893 + 0.0206696i
\(777\) 0 0
\(778\) −6.42649 + 5.39246i −0.230401 + 0.193329i
\(779\) −14.6197 5.32114i −0.523805 0.190650i
\(780\) 0 0