Properties

Label 729.2.e.u.163.2
Level $729$
Weight $2$
Character 729.163
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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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: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) 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 163.2
Root \(-1.91182i\) of defining polynomial
Character \(\chi\) \(=\) 729.163
Dual form 729.2.e.u.568.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.30957 - 0.840614i) q^{2} +(3.09538 - 2.59733i) q^{4} +(-0.534882 - 3.03347i) q^{5} +(-2.03666 - 1.70896i) q^{7} +(2.50784 - 4.34371i) q^{8} +O(q^{10})\) \(q+(2.30957 - 0.840614i) q^{2} +(3.09538 - 2.59733i) q^{4} +(-0.534882 - 3.03347i) q^{5} +(-2.03666 - 1.70896i) q^{7} +(2.50784 - 4.34371i) q^{8} +(-3.78532 - 6.55636i) q^{10} +(-0.596367 + 3.38217i) q^{11} +(3.14229 + 1.14370i) q^{13} +(-6.14037 - 2.23491i) q^{14} +(0.737316 - 4.18153i) q^{16} +(-1.28641 - 2.22813i) q^{17} +(1.04838 - 1.81585i) q^{19} +(-9.53458 - 8.00046i) q^{20} +(1.46574 + 8.31265i) q^{22} +(0.409408 - 0.343534i) q^{23} +(-4.21736 + 1.53499i) q^{25} +8.21874 q^{26} -10.7430 q^{28} +(-2.37826 + 0.865617i) q^{29} +(5.90980 - 4.95891i) q^{31} +(-0.0702390 - 0.398345i) q^{32} +(-4.84404 - 4.06463i) q^{34} +(-4.09470 + 7.09222i) q^{35} +(5.14783 + 8.91631i) q^{37} +(0.894879 - 5.07511i) q^{38} +(-14.5179 - 5.28408i) q^{40} +(4.59040 + 1.67077i) q^{41} +(0.476055 - 2.69984i) q^{43} +(6.93862 + 12.0180i) q^{44} +(0.656775 - 1.13757i) q^{46} +(-4.33428 - 3.63689i) q^{47} +(0.0118968 + 0.0674701i) q^{49} +(-8.44994 + 7.09034i) q^{50} +(12.6971 - 4.62138i) q^{52} +6.42657 q^{53} +10.5787 q^{55} +(-12.5308 + 4.56085i) q^{56} +(-4.76511 + 3.99840i) q^{58} +(0.287379 + 1.62981i) q^{59} +(11.0098 + 9.23828i) q^{61} +(9.48056 - 16.4208i) q^{62} +(3.74896 + 6.49338i) q^{64} +(1.78862 - 10.1438i) q^{65} +(5.52444 + 2.01073i) q^{67} +(-9.76910 - 3.55566i) q^{68} +(-3.49516 + 19.8220i) q^{70} +(-7.40813 - 12.8313i) q^{71} +(-0.940699 + 1.62934i) q^{73} +(19.3844 + 16.2655i) q^{74} +(-1.47123 - 8.34374i) q^{76} +(6.99457 - 5.86915i) q^{77} +(-16.1566 + 5.88052i) q^{79} -13.0789 q^{80} +12.0063 q^{82} +(-3.72944 + 1.35740i) q^{83} +(-6.07087 + 5.09406i) q^{85} +(-1.17004 - 6.63564i) q^{86} +(13.1955 + 11.0724i) q^{88} +(-2.54940 + 4.41569i) q^{89} +(-4.44523 - 7.69937i) q^{91} +(0.375001 - 2.12674i) q^{92} +(-13.0675 - 4.75619i) q^{94} +(-6.06908 - 2.20897i) q^{95} +(-1.84621 + 10.4704i) q^{97} +(0.0841927 + 0.145826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30957 0.840614i 1.63311 0.594404i 0.647295 0.762239i \(-0.275900\pi\)
0.985815 + 0.167836i \(0.0536779\pi\)
\(3\) 0 0
\(4\) 3.09538 2.59733i 1.54769 1.29867i
\(5\) −0.534882 3.03347i −0.239207 1.35661i −0.833571 0.552412i \(-0.813708\pi\)
0.594365 0.804196i \(-0.297404\pi\)
\(6\) 0 0
\(7\) −2.03666 1.70896i −0.769784 0.645926i 0.170870 0.985294i \(-0.445342\pi\)
−0.940654 + 0.339368i \(0.889787\pi\)
\(8\) 2.50784 4.34371i 0.886656 1.53573i
\(9\) 0 0
\(10\) −3.78532 6.55636i −1.19702 2.07330i
\(11\) −0.596367 + 3.38217i −0.179811 + 1.01976i 0.752631 + 0.658443i \(0.228784\pi\)
−0.932442 + 0.361319i \(0.882327\pi\)
\(12\) 0 0
\(13\) 3.14229 + 1.14370i 0.871515 + 0.317205i 0.738780 0.673946i \(-0.235402\pi\)
0.132734 + 0.991152i \(0.457624\pi\)
\(14\) −6.14037 2.23491i −1.64108 0.597305i
\(15\) 0 0
\(16\) 0.737316 4.18153i 0.184329 1.04538i
\(17\) −1.28641 2.22813i −0.312000 0.540400i 0.666795 0.745241i \(-0.267666\pi\)
−0.978795 + 0.204841i \(0.934332\pi\)
\(18\) 0 0
\(19\) 1.04838 1.81585i 0.240515 0.416585i −0.720346 0.693615i \(-0.756017\pi\)
0.960861 + 0.277030i \(0.0893503\pi\)
\(20\) −9.53458 8.00046i −2.13200 1.78896i
\(21\) 0 0
\(22\) 1.46574 + 8.31265i 0.312498 + 1.77226i
\(23\) 0.409408 0.343534i 0.0853674 0.0716318i −0.599105 0.800670i \(-0.704477\pi\)
0.684473 + 0.729038i \(0.260032\pi\)
\(24\) 0 0
\(25\) −4.21736 + 1.53499i −0.843472 + 0.306999i
\(26\) 8.21874 1.61183
\(27\) 0 0
\(28\) −10.7430 −2.03023
\(29\) −2.37826 + 0.865617i −0.441632 + 0.160741i −0.553259 0.833009i \(-0.686616\pi\)
0.111627 + 0.993750i \(0.464394\pi\)
\(30\) 0 0
\(31\) 5.90980 4.95891i 1.06143 0.890647i 0.0671832 0.997741i \(-0.478599\pi\)
0.994249 + 0.107093i \(0.0341544\pi\)
\(32\) −0.0702390 0.398345i −0.0124166 0.0704182i
\(33\) 0 0
\(34\) −4.84404 4.06463i −0.830746 0.697079i
\(35\) −4.09470 + 7.09222i −0.692130 + 1.19880i
\(36\) 0 0
\(37\) 5.14783 + 8.91631i 0.846298 + 1.46583i 0.884489 + 0.466561i \(0.154507\pi\)
−0.0381907 + 0.999270i \(0.512159\pi\)
\(38\) 0.894879 5.07511i 0.145169 0.823292i
\(39\) 0 0
\(40\) −14.5179 5.28408i −2.29548 0.835487i
\(41\) 4.59040 + 1.67077i 0.716901 + 0.260931i 0.674610 0.738175i \(-0.264312\pi\)
0.0422913 + 0.999105i \(0.486534\pi\)
\(42\) 0 0
\(43\) 0.476055 2.69984i 0.0725977 0.411722i −0.926752 0.375673i \(-0.877412\pi\)
0.999350 0.0360490i \(-0.0114772\pi\)
\(44\) 6.93862 + 12.0180i 1.04604 + 1.81179i
\(45\) 0 0
\(46\) 0.656775 1.13757i 0.0968363 0.167725i
\(47\) −4.33428 3.63689i −0.632219 0.530495i 0.269398 0.963029i \(-0.413175\pi\)
−0.901618 + 0.432534i \(0.857620\pi\)
\(48\) 0 0
\(49\) 0.0118968 + 0.0674701i 0.00169954 + 0.00963858i
\(50\) −8.44994 + 7.09034i −1.19500 + 1.00273i
\(51\) 0 0
\(52\) 12.6971 4.62138i 1.76078 0.640871i
\(53\) 6.42657 0.882758 0.441379 0.897321i \(-0.354489\pi\)
0.441379 + 0.897321i \(0.354489\pi\)
\(54\) 0 0
\(55\) 10.5787 1.42643
\(56\) −12.5308 + 4.56085i −1.67450 + 0.609469i
\(57\) 0 0
\(58\) −4.76511 + 3.99840i −0.625689 + 0.525015i
\(59\) 0.287379 + 1.62981i 0.0374136 + 0.212183i 0.997783 0.0665462i \(-0.0211980\pi\)
−0.960370 + 0.278729i \(0.910087\pi\)
\(60\) 0 0
\(61\) 11.0098 + 9.23828i 1.40965 + 1.18284i 0.956617 + 0.291349i \(0.0941039\pi\)
0.453037 + 0.891492i \(0.350341\pi\)
\(62\) 9.48056 16.4208i 1.20403 2.08544i
\(63\) 0 0
\(64\) 3.74896 + 6.49338i 0.468620 + 0.811673i
\(65\) 1.78862 10.1438i 0.221851 1.25818i
\(66\) 0 0
\(67\) 5.52444 + 2.01073i 0.674917 + 0.245650i 0.656664 0.754184i \(-0.271967\pi\)
0.0182537 + 0.999833i \(0.494189\pi\)
\(68\) −9.76910 3.55566i −1.18468 0.431187i
\(69\) 0 0
\(70\) −3.49516 + 19.8220i −0.417751 + 2.36918i
\(71\) −7.40813 12.8313i −0.879184 1.52279i −0.852238 0.523154i \(-0.824755\pi\)
−0.0269456 0.999637i \(-0.508578\pi\)
\(72\) 0 0
\(73\) −0.940699 + 1.62934i −0.110101 + 0.190700i −0.915811 0.401610i \(-0.868451\pi\)
0.805710 + 0.592310i \(0.201784\pi\)
\(74\) 19.3844 + 16.2655i 2.25339 + 1.89082i
\(75\) 0 0
\(76\) −1.47123 8.34374i −0.168761 0.957092i
\(77\) 6.99457 5.86915i 0.797106 0.668851i
\(78\) 0 0
\(79\) −16.1566 + 5.88052i −1.81776 + 0.661610i −0.822013 + 0.569469i \(0.807149\pi\)
−0.995746 + 0.0921413i \(0.970629\pi\)
\(80\) −13.0789 −1.46227
\(81\) 0 0
\(82\) 12.0063 1.32588
\(83\) −3.72944 + 1.35740i −0.409359 + 0.148994i −0.538488 0.842633i \(-0.681004\pi\)
0.129129 + 0.991628i \(0.458782\pi\)
\(84\) 0 0
\(85\) −6.07087 + 5.09406i −0.658478 + 0.552529i
\(86\) −1.17004 6.63564i −0.126169 0.715539i
\(87\) 0 0
\(88\) 13.1955 + 11.0724i 1.40665 + 1.18032i
\(89\) −2.54940 + 4.41569i −0.270236 + 0.468062i −0.968922 0.247366i \(-0.920435\pi\)
0.698686 + 0.715428i \(0.253768\pi\)
\(90\) 0 0
\(91\) −4.44523 7.69937i −0.465987 0.807113i
\(92\) 0.375001 2.12674i 0.0390965 0.221727i
\(93\) 0 0
\(94\) −13.0675 4.75619i −1.34781 0.490563i
\(95\) −6.06908 2.20897i −0.622675 0.226635i
\(96\) 0 0
\(97\) −1.84621 + 10.4704i −0.187454 + 1.06310i 0.735308 + 0.677733i \(0.237037\pi\)
−0.922762 + 0.385371i \(0.874074\pi\)
\(98\) 0.0841927 + 0.145826i 0.00850475 + 0.0147307i
\(99\) 0 0
\(100\) −9.06744 + 15.7053i −0.906744 + 1.57053i
\(101\) 4.33435 + 3.63695i 0.431284 + 0.361890i 0.832436 0.554121i \(-0.186946\pi\)
−0.401152 + 0.916011i \(0.631390\pi\)
\(102\) 0 0
\(103\) 1.80083 + 10.2130i 0.177441 + 1.00632i 0.935289 + 0.353885i \(0.115140\pi\)
−0.757848 + 0.652431i \(0.773749\pi\)
\(104\) 12.8483 10.7810i 1.25988 1.05716i
\(105\) 0 0
\(106\) 14.8426 5.40227i 1.44164 0.524714i
\(107\) −14.2457 −1.37719 −0.688594 0.725147i \(-0.741772\pi\)
−0.688594 + 0.725147i \(0.741772\pi\)
\(108\) 0 0
\(109\) 5.76064 0.551769 0.275884 0.961191i \(-0.411029\pi\)
0.275884 + 0.961191i \(0.411029\pi\)
\(110\) 24.4321 8.89257i 2.32951 0.847874i
\(111\) 0 0
\(112\) −8.64771 + 7.25629i −0.817132 + 0.685655i
\(113\) −1.98249 11.2432i −0.186497 1.05768i −0.924017 0.382351i \(-0.875115\pi\)
0.737520 0.675325i \(-0.235997\pi\)
\(114\) 0 0
\(115\) −1.26108 1.05818i −0.117597 0.0986753i
\(116\) −5.11333 + 8.85654i −0.474761 + 0.822309i
\(117\) 0 0
\(118\) 2.03376 + 3.52257i 0.187223 + 0.324279i
\(119\) −1.18780 + 6.73635i −0.108885 + 0.617520i
\(120\) 0 0
\(121\) −0.746770 0.271802i −0.0678882 0.0247093i
\(122\) 33.1936 + 12.0815i 3.00520 + 1.09381i
\(123\) 0 0
\(124\) 5.41314 30.6994i 0.486114 2.75689i
\(125\) −0.788517 1.36575i −0.0705271 0.122157i
\(126\) 0 0
\(127\) −1.29510 + 2.24317i −0.114921 + 0.199049i −0.917748 0.397163i \(-0.869995\pi\)
0.802827 + 0.596212i \(0.203328\pi\)
\(128\) 14.7366 + 12.3655i 1.30254 + 1.09296i
\(129\) 0 0
\(130\) −4.39606 24.9313i −0.385560 2.18662i
\(131\) −3.37901 + 2.83533i −0.295226 + 0.247724i −0.778354 0.627826i \(-0.783945\pi\)
0.483128 + 0.875550i \(0.339501\pi\)
\(132\) 0 0
\(133\) −5.23841 + 1.90662i −0.454227 + 0.165325i
\(134\) 14.4493 1.24823
\(135\) 0 0
\(136\) −12.9044 −1.10655
\(137\) −17.0720 + 6.21371i −1.45856 + 0.530873i −0.944969 0.327160i \(-0.893908\pi\)
−0.513594 + 0.858033i \(0.671686\pi\)
\(138\) 0 0
\(139\) 1.49987 1.25854i 0.127217 0.106748i −0.576959 0.816773i \(-0.695761\pi\)
0.704177 + 0.710025i \(0.251316\pi\)
\(140\) 5.74621 + 32.5884i 0.485644 + 2.75422i
\(141\) 0 0
\(142\) −27.8957 23.4073i −2.34096 1.96430i
\(143\) −5.74214 + 9.94568i −0.480182 + 0.831700i
\(144\) 0 0
\(145\) 3.89791 + 6.75138i 0.323704 + 0.560671i
\(146\) −0.802963 + 4.55383i −0.0664537 + 0.376878i
\(147\) 0 0
\(148\) 39.0931 + 14.2287i 3.21343 + 1.16959i
\(149\) −6.87403 2.50194i −0.563142 0.204967i 0.0447337 0.998999i \(-0.485756\pi\)
−0.607876 + 0.794032i \(0.707978\pi\)
\(150\) 0 0
\(151\) 0.842365 4.77729i 0.0685507 0.388770i −0.931158 0.364617i \(-0.881200\pi\)
0.999708 0.0241532i \(-0.00768897\pi\)
\(152\) −5.25835 9.10773i −0.426508 0.738734i
\(153\) 0 0
\(154\) 11.2208 19.4349i 0.904194 1.56611i
\(155\) −18.2038 15.2748i −1.46216 1.22690i
\(156\) 0 0
\(157\) 0.256427 + 1.45427i 0.0204651 + 0.116063i 0.993329 0.115315i \(-0.0367877\pi\)
−0.972864 + 0.231378i \(0.925677\pi\)
\(158\) −32.3715 + 27.1629i −2.57534 + 2.16096i
\(159\) 0 0
\(160\) −1.17080 + 0.426136i −0.0925597 + 0.0336890i
\(161\) −1.42091 −0.111983
\(162\) 0 0
\(163\) −17.2536 −1.35141 −0.675703 0.737174i \(-0.736160\pi\)
−0.675703 + 0.737174i \(0.736160\pi\)
\(164\) 18.5486 6.75113i 1.44840 0.527175i
\(165\) 0 0
\(166\) −7.47233 + 6.27003i −0.579965 + 0.486649i
\(167\) 1.18782 + 6.73644i 0.0919160 + 0.521282i 0.995649 + 0.0931847i \(0.0297047\pi\)
−0.903733 + 0.428097i \(0.859184\pi\)
\(168\) 0 0
\(169\) −1.39264 1.16856i −0.107126 0.0898893i
\(170\) −9.73894 + 16.8683i −0.746942 + 1.29374i
\(171\) 0 0
\(172\) −5.53881 9.59350i −0.422330 0.731497i
\(173\) −4.16189 + 23.6033i −0.316423 + 1.79452i 0.247705 + 0.968835i \(0.420324\pi\)
−0.564128 + 0.825687i \(0.690788\pi\)
\(174\) 0 0
\(175\) 11.2126 + 4.08104i 0.847589 + 0.308497i
\(176\) 13.7029 + 4.98745i 1.03290 + 0.375943i
\(177\) 0 0
\(178\) −2.17612 + 12.3414i −0.163107 + 0.925026i
\(179\) 10.2861 + 17.8161i 0.768820 + 1.33163i 0.938203 + 0.346084i \(0.112489\pi\)
−0.169384 + 0.985550i \(0.554178\pi\)
\(180\) 0 0
\(181\) 7.73507 13.3975i 0.574943 0.995830i −0.421105 0.907012i \(-0.638358\pi\)
0.996048 0.0888184i \(-0.0283091\pi\)
\(182\) −16.7388 14.0455i −1.24076 1.04112i
\(183\) 0 0
\(184\) −0.465482 2.63988i −0.0343158 0.194614i
\(185\) 24.2938 20.3849i 1.78612 1.49873i
\(186\) 0 0
\(187\) 8.30306 3.02207i 0.607180 0.220995i
\(188\) −22.8624 −1.66741
\(189\) 0 0
\(190\) −15.8738 −1.15161
\(191\) 10.2904 3.74541i 0.744589 0.271008i 0.0582623 0.998301i \(-0.481444\pi\)
0.686327 + 0.727293i \(0.259222\pi\)
\(192\) 0 0
\(193\) 0.877007 0.735896i 0.0631284 0.0529710i −0.610678 0.791879i \(-0.709103\pi\)
0.673806 + 0.738908i \(0.264658\pi\)
\(194\) 4.53759 + 25.7339i 0.325780 + 1.84759i
\(195\) 0 0
\(196\) 0.212067 + 0.177946i 0.0151477 + 0.0127104i
\(197\) 2.52097 4.36645i 0.179612 0.311097i −0.762136 0.647417i \(-0.775849\pi\)
0.941748 + 0.336320i \(0.109182\pi\)
\(198\) 0 0
\(199\) −6.86291 11.8869i −0.486499 0.842640i 0.513381 0.858161i \(-0.328393\pi\)
−0.999880 + 0.0155206i \(0.995059\pi\)
\(200\) −3.90890 + 22.1685i −0.276401 + 1.56755i
\(201\) 0 0
\(202\) 13.0677 + 4.75627i 0.919443 + 0.334650i
\(203\) 6.32301 + 2.30139i 0.443788 + 0.161526i
\(204\) 0 0
\(205\) 2.61290 14.8185i 0.182493 1.03497i
\(206\) 12.7443 + 22.0738i 0.887938 + 1.53795i
\(207\) 0 0
\(208\) 7.09927 12.2963i 0.492246 0.852595i
\(209\) 5.51629 + 4.62871i 0.381569 + 0.320175i
\(210\) 0 0
\(211\) −1.01326 5.74648i −0.0697557 0.395604i −0.999616 0.0276926i \(-0.991184\pi\)
0.929861 0.367912i \(-0.119927\pi\)
\(212\) 19.8927 16.6919i 1.36623 1.14641i
\(213\) 0 0
\(214\) −32.9015 + 11.9752i −2.24910 + 0.818605i
\(215\) −8.44451 −0.575911
\(216\) 0 0
\(217\) −20.5108 −1.39237
\(218\) 13.3046 4.84247i 0.901099 0.327973i
\(219\) 0 0
\(220\) 32.7450 27.4763i 2.20767 1.85245i
\(221\) −1.49396 8.47269i −0.100495 0.569934i
\(222\) 0 0
\(223\) 6.68656 + 5.61069i 0.447765 + 0.375719i 0.838606 0.544739i \(-0.183371\pi\)
−0.390841 + 0.920458i \(0.627816\pi\)
\(224\) −0.537703 + 0.931329i −0.0359268 + 0.0622270i
\(225\) 0 0
\(226\) −14.0299 24.3005i −0.933256 1.61645i
\(227\) 4.21662 23.9136i 0.279867 1.58720i −0.443199 0.896423i \(-0.646157\pi\)
0.723066 0.690779i \(-0.242732\pi\)
\(228\) 0 0
\(229\) −17.0568 6.20815i −1.12714 0.410246i −0.289888 0.957060i \(-0.593618\pi\)
−0.837254 + 0.546814i \(0.815840\pi\)
\(230\) −3.80207 1.38384i −0.250701 0.0912478i
\(231\) 0 0
\(232\) −2.20432 + 12.5013i −0.144721 + 0.820751i
\(233\) −5.26900 9.12617i −0.345183 0.597875i 0.640204 0.768205i \(-0.278850\pi\)
−0.985387 + 0.170330i \(0.945517\pi\)
\(234\) 0 0
\(235\) −8.71406 + 15.0932i −0.568442 + 0.984571i
\(236\) 5.12270 + 4.29845i 0.333459 + 0.279805i
\(237\) 0 0
\(238\) 2.91936 + 16.5565i 0.189234 + 1.07320i
\(239\) −7.30546 + 6.13001i −0.472551 + 0.396517i −0.847724 0.530437i \(-0.822028\pi\)
0.375173 + 0.926955i \(0.377583\pi\)
\(240\) 0 0
\(241\) 6.61288 2.40689i 0.425973 0.155042i −0.120133 0.992758i \(-0.538332\pi\)
0.546106 + 0.837716i \(0.316110\pi\)
\(242\) −1.95320 −0.125556
\(243\) 0 0
\(244\) 58.0742 3.71782
\(245\) 0.198305 0.0721771i 0.0126692 0.00461122i
\(246\) 0 0
\(247\) 5.37111 4.50689i 0.341755 0.286767i
\(248\) −6.71923 38.1066i −0.426671 2.41977i
\(249\) 0 0
\(250\) −2.96920 2.49146i −0.187789 0.157574i
\(251\) 7.79350 13.4987i 0.491921 0.852033i −0.508035 0.861336i \(-0.669628\pi\)
0.999957 + 0.00930331i \(0.00296138\pi\)
\(252\) 0 0
\(253\) 0.917731 + 1.58956i 0.0576973 + 0.0999346i
\(254\) −1.10547 + 6.26944i −0.0693634 + 0.393379i
\(255\) 0 0
\(256\) 30.3383 + 11.0422i 1.89614 + 0.690140i
\(257\) 11.4546 + 4.16915i 0.714521 + 0.260064i 0.673598 0.739098i \(-0.264748\pi\)
0.0409230 + 0.999162i \(0.486970\pi\)
\(258\) 0 0
\(259\) 4.75323 26.9569i 0.295351 1.67502i
\(260\) −20.8103 36.0445i −1.29060 2.23538i
\(261\) 0 0
\(262\) −5.42064 + 9.38882i −0.334888 + 0.580043i
\(263\) 5.27777 + 4.42857i 0.325441 + 0.273077i 0.790839 0.612024i \(-0.209644\pi\)
−0.465398 + 0.885101i \(0.654089\pi\)
\(264\) 0 0
\(265\) −3.43746 19.4948i −0.211161 1.19756i
\(266\) −10.4957 + 8.80695i −0.643534 + 0.539989i
\(267\) 0 0
\(268\) 22.3228 8.12482i 1.36358 0.496302i
\(269\) −7.05875 −0.430380 −0.215190 0.976572i \(-0.569037\pi\)
−0.215190 + 0.976572i \(0.569037\pi\)
\(270\) 0 0
\(271\) 23.7575 1.44316 0.721581 0.692330i \(-0.243416\pi\)
0.721581 + 0.692330i \(0.243416\pi\)
\(272\) −10.2655 + 3.73632i −0.622435 + 0.226548i
\(273\) 0 0
\(274\) −34.2057 + 28.7020i −2.06644 + 1.73395i
\(275\) −2.67651 15.1792i −0.161399 0.915342i
\(276\) 0 0
\(277\) −0.0800238 0.0671480i −0.00480817 0.00403453i 0.640380 0.768058i \(-0.278777\pi\)
−0.645189 + 0.764023i \(0.723221\pi\)
\(278\) 2.40611 4.16750i 0.144309 0.249950i
\(279\) 0 0
\(280\) 20.5377 + 35.5723i 1.22736 + 2.12585i
\(281\) −1.41561 + 8.02835i −0.0844485 + 0.478931i 0.913026 + 0.407902i \(0.133739\pi\)
−0.997474 + 0.0710292i \(0.977372\pi\)
\(282\) 0 0
\(283\) −22.1918 8.07714i −1.31916 0.480136i −0.415973 0.909377i \(-0.636559\pi\)
−0.903190 + 0.429240i \(0.858781\pi\)
\(284\) −56.2580 20.4762i −3.33830 1.21504i
\(285\) 0 0
\(286\) −4.90139 + 27.7971i −0.289825 + 1.64368i
\(287\) −6.49380 11.2476i −0.383317 0.663925i
\(288\) 0 0
\(289\) 5.19030 8.98987i 0.305312 0.528816i
\(290\) 14.6778 + 12.3161i 0.861909 + 0.723227i
\(291\) 0 0
\(292\) 1.32011 + 7.48673i 0.0772537 + 0.438127i
\(293\) −16.5663 + 13.9008i −0.967813 + 0.812091i −0.982206 0.187805i \(-0.939863\pi\)
0.0143935 + 0.999896i \(0.495418\pi\)
\(294\) 0 0
\(295\) 4.79025 1.74351i 0.278899 0.101511i
\(296\) 51.6398 3.00150
\(297\) 0 0
\(298\) −17.9792 −1.04151
\(299\) 1.67938 0.611244i 0.0971210 0.0353491i
\(300\) 0 0
\(301\) −5.58348 + 4.68509i −0.321826 + 0.270044i
\(302\) −2.07036 11.7416i −0.119136 0.675651i
\(303\) 0 0
\(304\) −6.82004 5.72269i −0.391156 0.328219i
\(305\) 22.1351 38.3391i 1.26745 2.19529i
\(306\) 0 0
\(307\) −8.17997 14.1681i −0.466855 0.808617i 0.532428 0.846475i \(-0.321280\pi\)
−0.999283 + 0.0378581i \(0.987946\pi\)
\(308\) 6.40674 36.3344i 0.365058 2.07035i
\(309\) 0 0
\(310\) −54.8829 19.9758i −3.11714 1.13455i
\(311\) 7.28719 + 2.65232i 0.413218 + 0.150399i 0.540260 0.841498i \(-0.318326\pi\)
−0.127041 + 0.991897i \(0.540548\pi\)
\(312\) 0 0
\(313\) 2.67732 15.1838i 0.151331 0.858240i −0.810733 0.585416i \(-0.800931\pi\)
0.962064 0.272824i \(-0.0879577\pi\)
\(314\) 1.81471 + 3.14317i 0.102410 + 0.177380i
\(315\) 0 0
\(316\) −34.7371 + 60.1664i −1.95412 + 3.38463i
\(317\) 6.61572 + 5.55125i 0.371576 + 0.311789i 0.809385 0.587279i \(-0.199801\pi\)
−0.437809 + 0.899068i \(0.644245\pi\)
\(318\) 0 0
\(319\) −1.50934 8.55990i −0.0845069 0.479262i
\(320\) 17.6922 14.8455i 0.989025 0.829890i
\(321\) 0 0
\(322\) −3.28168 + 1.19444i −0.182881 + 0.0665633i
\(323\) −5.39459 −0.300163
\(324\) 0 0
\(325\) −15.0077 −0.832480
\(326\) −39.8483 + 14.5036i −2.20700 + 0.803281i
\(327\) 0 0
\(328\) 18.7693 15.7494i 1.03636 0.869612i
\(329\) 2.61214 + 14.8142i 0.144012 + 0.816733i
\(330\) 0 0
\(331\) 15.7380 + 13.2058i 0.865039 + 0.725854i 0.963048 0.269331i \(-0.0868027\pi\)
−0.0980081 + 0.995186i \(0.531247\pi\)
\(332\) −8.01839 + 13.8883i −0.440066 + 0.762217i
\(333\) 0 0
\(334\) 8.40609 + 14.5598i 0.459961 + 0.796675i
\(335\) 3.14456 17.8337i 0.171806 0.974359i
\(336\) 0 0
\(337\) −15.0146 5.46487i −0.817897 0.297690i −0.101015 0.994885i \(-0.532209\pi\)
−0.716882 + 0.697195i \(0.754431\pi\)
\(338\) −4.19869 1.52820i −0.228379 0.0831231i
\(339\) 0 0
\(340\) −5.56067 + 31.5361i −0.301569 + 1.71029i
\(341\) 13.2475 + 22.9453i 0.717390 + 1.24256i
\(342\) 0 0
\(343\) −9.21426 + 15.9596i −0.497523 + 0.861736i
\(344\) −10.5335 8.83861i −0.567926 0.476546i
\(345\) 0 0
\(346\) 10.2291 + 58.0118i 0.549917 + 3.11874i
\(347\) −7.51051 + 6.30207i −0.403185 + 0.338313i −0.821723 0.569887i \(-0.806987\pi\)
0.418538 + 0.908199i \(0.362543\pi\)
\(348\) 0 0
\(349\) 8.86598 3.22695i 0.474585 0.172735i −0.0936433 0.995606i \(-0.529851\pi\)
0.568228 + 0.822871i \(0.307629\pi\)
\(350\) 29.3267 1.56758
\(351\) 0 0
\(352\) 1.38916 0.0740424
\(353\) 3.18101 1.15779i 0.169308 0.0616232i −0.255975 0.966683i \(-0.582397\pi\)
0.425284 + 0.905060i \(0.360174\pi\)
\(354\) 0 0
\(355\) −34.9607 + 29.3355i −1.85552 + 1.55697i
\(356\) 3.57765 + 20.2899i 0.189615 + 1.07536i
\(357\) 0 0
\(358\) 38.7329 + 32.5007i 2.04710 + 1.71772i
\(359\) −17.6137 + 30.5078i −0.929614 + 1.61014i −0.145646 + 0.989337i \(0.546526\pi\)
−0.783968 + 0.620801i \(0.786807\pi\)
\(360\) 0 0
\(361\) 7.30179 + 12.6471i 0.384305 + 0.665636i
\(362\) 6.60251 37.4447i 0.347020 1.96805i
\(363\) 0 0
\(364\) −33.7575 12.2867i −1.76937 0.643999i
\(365\) 5.44571 + 1.98208i 0.285041 + 0.103747i
\(366\) 0 0
\(367\) −5.47781 + 31.0662i −0.285939 + 1.62164i 0.415972 + 0.909377i \(0.363441\pi\)
−0.701911 + 0.712264i \(0.747670\pi\)
\(368\) −1.13463 1.96524i −0.0591469 0.102445i
\(369\) 0 0
\(370\) 38.9724 67.5021i 2.02608 3.50927i
\(371\) −13.0887 10.9827i −0.679533 0.570196i
\(372\) 0 0
\(373\) 2.50788 + 14.2229i 0.129853 + 0.736434i 0.978306 + 0.207163i \(0.0664232\pi\)
−0.848453 + 0.529270i \(0.822466\pi\)
\(374\) 16.6361 13.9593i 0.860231 0.721820i
\(375\) 0 0
\(376\) −26.6673 + 9.70609i −1.37526 + 0.500553i
\(377\) −8.46320 −0.435877
\(378\) 0 0
\(379\) 1.00099 0.0514176 0.0257088 0.999669i \(-0.491816\pi\)
0.0257088 + 0.999669i \(0.491816\pi\)
\(380\) −24.5235 + 8.92583i −1.25803 + 0.457885i
\(381\) 0 0
\(382\) 20.6180 17.3006i 1.05491 0.885173i
\(383\) 0.714969 + 4.05479i 0.0365332 + 0.207190i 0.997610 0.0690897i \(-0.0220095\pi\)
−0.961077 + 0.276280i \(0.910898\pi\)
\(384\) 0 0
\(385\) −21.5451 18.0785i −1.09804 0.921366i
\(386\) 1.40690 2.43683i 0.0716094 0.124031i
\(387\) 0 0
\(388\) 21.4803 + 37.2049i 1.09050 + 1.88879i
\(389\) −2.69501 + 15.2841i −0.136642 + 0.774936i 0.837060 + 0.547111i \(0.184273\pi\)
−0.973702 + 0.227825i \(0.926839\pi\)
\(390\) 0 0
\(391\) −1.29210 0.470287i −0.0653445 0.0237834i
\(392\) 0.322906 + 0.117528i 0.0163092 + 0.00593606i
\(393\) 0 0
\(394\) 2.15186 12.2038i 0.108409 0.614818i
\(395\) 26.4802 + 45.8651i 1.33237 + 2.30772i
\(396\) 0 0
\(397\) 0.774463 1.34141i 0.0388692 0.0673234i −0.845936 0.533284i \(-0.820958\pi\)
0.884806 + 0.465960i \(0.154291\pi\)
\(398\) −25.8426 21.6845i −1.29537 1.08695i
\(399\) 0 0
\(400\) 3.30909 + 18.7668i 0.165454 + 0.938339i
\(401\) 6.08805 5.10848i 0.304022 0.255105i −0.477994 0.878363i \(-0.658636\pi\)
0.782016 + 0.623258i \(0.214191\pi\)
\(402\) 0 0
\(403\) 24.2418 8.82331i 1.20757 0.439520i
\(404\) 22.8628 1.13747
\(405\) 0 0
\(406\) 16.5380 0.820766
\(407\) −33.2264 + 12.0934i −1.64697 + 0.599449i
\(408\) 0 0
\(409\) 20.2660 17.0052i 1.00209 0.840853i 0.0148172 0.999890i \(-0.495283\pi\)
0.987273 + 0.159037i \(0.0508389\pi\)
\(410\) −6.42196 36.4208i −0.317158 1.79869i
\(411\) 0 0
\(412\) 32.1007 + 26.9357i 1.58149 + 1.32703i
\(413\) 2.19998 3.81048i 0.108254 0.187501i
\(414\) 0 0
\(415\) 6.11245 + 10.5871i 0.300048 + 0.519699i
\(416\) 0.234876 1.33205i 0.0115158 0.0653091i
\(417\) 0 0
\(418\) 16.6312 + 6.05326i 0.813458 + 0.296074i
\(419\) −36.0278 13.1130i −1.76007 0.640614i −0.760116 0.649788i \(-0.774858\pi\)
−0.999958 + 0.00917341i \(0.997080\pi\)
\(420\) 0 0
\(421\) 1.27536 7.23292i 0.0621572 0.352511i −0.937828 0.347100i \(-0.887167\pi\)
0.999985 0.00541096i \(-0.00172237\pi\)
\(422\) −7.17076 12.4201i −0.349067 0.604602i
\(423\) 0 0
\(424\) 16.1168 27.9152i 0.782702 1.35568i
\(425\) 8.84541 + 7.42218i 0.429065 + 0.360028i
\(426\) 0 0
\(427\) −6.63526 37.6304i −0.321103 1.82106i
\(428\) −44.0959 + 37.0009i −2.13146 + 1.78851i
\(429\) 0 0
\(430\) −19.5032 + 7.09857i −0.940526 + 0.342323i
\(431\) −15.8463 −0.763289 −0.381644 0.924309i \(-0.624642\pi\)
−0.381644 + 0.924309i \(0.624642\pi\)
\(432\) 0 0
\(433\) −23.8507 −1.14619 −0.573097 0.819488i \(-0.694258\pi\)
−0.573097 + 0.819488i \(0.694258\pi\)
\(434\) −47.3711 + 17.2417i −2.27389 + 0.827627i
\(435\) 0 0
\(436\) 17.8313 14.9623i 0.853967 0.716563i
\(437\) −0.194591 1.10358i −0.00930853 0.0527913i
\(438\) 0 0
\(439\) −16.4469 13.8006i −0.784969 0.658667i 0.159526 0.987194i \(-0.449003\pi\)
−0.944495 + 0.328527i \(0.893448\pi\)
\(440\) 26.5296 45.9507i 1.26475 2.19061i
\(441\) 0 0
\(442\) −10.5727 18.3124i −0.502890 0.871031i
\(443\) 5.47824 31.0686i 0.260279 1.47612i −0.521871 0.853025i \(-0.674766\pi\)
0.782150 0.623091i \(-0.214123\pi\)
\(444\) 0 0
\(445\) 14.7585 + 5.37164i 0.699618 + 0.254640i
\(446\) 20.1595 + 7.33745i 0.954578 + 0.347438i
\(447\) 0 0
\(448\) 3.46158 19.6316i 0.163544 0.927506i
\(449\) −10.3949 18.0045i −0.490565 0.849684i 0.509376 0.860544i \(-0.329876\pi\)
−0.999941 + 0.0108605i \(0.996543\pi\)
\(450\) 0 0
\(451\) −8.38839 + 14.5291i −0.394994 + 0.684149i
\(452\) −35.3390 29.6529i −1.66221 1.39476i
\(453\) 0 0
\(454\) −10.3636 58.7746i −0.486386 2.75843i
\(455\) −20.9781 + 17.6027i −0.983469 + 0.825228i
\(456\) 0 0
\(457\) 16.3767 5.96064i 0.766070 0.278827i 0.0707185 0.997496i \(-0.477471\pi\)
0.695352 + 0.718670i \(0.255249\pi\)
\(458\) −44.6124 −2.08460
\(459\) 0 0
\(460\) −6.65196 −0.310149
\(461\) 29.1347 10.6042i 1.35694 0.493885i 0.441831 0.897098i \(-0.354329\pi\)
0.915106 + 0.403214i \(0.132107\pi\)
\(462\) 0 0
\(463\) 4.97006 4.17037i 0.230978 0.193814i −0.519952 0.854196i \(-0.674050\pi\)
0.750930 + 0.660382i \(0.229606\pi\)
\(464\) 1.86607 + 10.5830i 0.0866300 + 0.491303i
\(465\) 0 0
\(466\) −19.8407 16.6483i −0.919102 0.771218i
\(467\) −0.971950 + 1.68347i −0.0449765 + 0.0779016i −0.887637 0.460543i \(-0.847655\pi\)
0.842661 + 0.538445i \(0.180988\pi\)
\(468\) 0 0
\(469\) −7.81513 13.5362i −0.360869 0.625044i
\(470\) −7.43816 + 42.1839i −0.343097 + 1.94580i
\(471\) 0 0
\(472\) 7.80011 + 2.83901i 0.359029 + 0.130676i
\(473\) 8.84740 + 3.22019i 0.406804 + 0.148065i
\(474\) 0 0
\(475\) −1.63408 + 9.26735i −0.0749769 + 0.425215i
\(476\) 13.8198 + 23.9367i 0.633431 + 1.09713i
\(477\) 0 0
\(478\) −11.7195 + 20.2987i −0.536036 + 0.928442i
\(479\) 1.01837 + 0.854516i 0.0465306 + 0.0390438i 0.665756 0.746169i \(-0.268109\pi\)
−0.619226 + 0.785213i \(0.712553\pi\)
\(480\) 0 0
\(481\) 5.97840 + 33.9052i 0.272592 + 1.54594i
\(482\) 13.2496 11.1178i 0.603504 0.506400i
\(483\) 0 0
\(484\) −3.01750 + 1.09828i −0.137159 + 0.0499217i
\(485\) 32.7490 1.48705
\(486\) 0 0
\(487\) 21.2040 0.960844 0.480422 0.877037i \(-0.340484\pi\)
0.480422 + 0.877037i \(0.340484\pi\)
\(488\) 67.7391 24.6550i 3.06640 1.11608i
\(489\) 0 0
\(490\) 0.397325 0.333396i 0.0179493 0.0150613i
\(491\) 4.69026 + 26.5998i 0.211669 + 1.20043i 0.886595 + 0.462547i \(0.153064\pi\)
−0.674926 + 0.737885i \(0.735825\pi\)
\(492\) 0 0
\(493\) 4.98812 + 4.18553i 0.224654 + 0.188507i
\(494\) 8.61638 14.9240i 0.387669 0.671463i
\(495\) 0 0
\(496\) −16.3784 28.3683i −0.735414 1.27377i
\(497\) −6.84027 + 38.7931i −0.306828 + 1.74011i
\(498\) 0 0
\(499\) −14.1320 5.14361i −0.632633 0.230260i 0.00574369 0.999984i \(-0.498172\pi\)
−0.638377 + 0.769724i \(0.720394\pi\)
\(500\) −5.98807 2.17948i −0.267794 0.0974692i
\(501\) 0 0
\(502\) 6.65239 37.7276i 0.296911 1.68386i
\(503\) −2.30325 3.98934i −0.102697 0.177876i 0.810098 0.586294i \(-0.199414\pi\)
−0.912795 + 0.408418i \(0.866080\pi\)
\(504\) 0 0
\(505\) 8.71420 15.0934i 0.387777 0.671649i
\(506\) 3.45577 + 2.89973i 0.153628 + 0.128909i
\(507\) 0 0
\(508\) 1.81745 + 10.3073i 0.0806363 + 0.457311i
\(509\) 22.8256 19.1529i 1.01173 0.848938i 0.0231600 0.999732i \(-0.492627\pi\)
0.988565 + 0.150793i \(0.0481828\pi\)
\(510\) 0 0
\(511\) 4.70035 1.71079i 0.207931 0.0756808i
\(512\) 40.8760 1.80648
\(513\) 0 0
\(514\) 29.9599 1.32147
\(515\) 30.0175 10.9255i 1.32273 0.481435i
\(516\) 0 0
\(517\) 14.8854 12.4903i 0.654658 0.549324i
\(518\) −11.6824 66.2544i −0.513297 2.91105i
\(519\) 0 0
\(520\) −39.5760 33.2082i −1.73552 1.45628i
\(521\) 5.88104 10.1863i 0.257653 0.446268i −0.707960 0.706253i \(-0.750384\pi\)
0.965613 + 0.259985i \(0.0837175\pi\)
\(522\) 0 0
\(523\) −14.6926 25.4484i −0.642464 1.11278i −0.984881 0.173232i \(-0.944579\pi\)
0.342417 0.939548i \(-0.388754\pi\)
\(524\) −3.09503 + 17.5528i −0.135207 + 0.766798i
\(525\) 0 0
\(526\) 15.9121 + 5.79152i 0.693799 + 0.252522i
\(527\) −18.6515 6.78859i −0.812473 0.295716i
\(528\) 0 0
\(529\) −3.94431 + 22.3693i −0.171492 + 0.972578i
\(530\) −24.3266 42.1350i −1.05668 1.83023i
\(531\) 0 0
\(532\) −11.2627 + 19.5076i −0.488301 + 0.845761i
\(533\) 12.5135 + 10.5001i 0.542021 + 0.454810i
\(534\) 0 0
\(535\) 7.61979 + 43.2140i 0.329432 + 1.86830i
\(536\) 22.5884 18.9539i 0.975672 0.818686i
\(537\) 0 0
\(538\) −16.3027 + 5.93368i −0.702858 + 0.255819i
\(539\) −0.235290 −0.0101347
\(540\) 0 0
\(541\) −22.9116 −0.985046 −0.492523 0.870300i \(-0.663925\pi\)
−0.492523 + 0.870300i \(0.663925\pi\)
\(542\) 54.8694 19.9708i 2.35684 0.857821i
\(543\) 0 0
\(544\) −0.797207 + 0.668936i −0.0341800 + 0.0286804i
\(545\) −3.08126 17.4747i −0.131987 0.748534i
\(546\) 0 0
\(547\) −10.5390 8.84328i −0.450615 0.378111i 0.389049 0.921217i \(-0.372804\pi\)
−0.839664 + 0.543106i \(0.817248\pi\)
\(548\) −36.7053 + 63.5755i −1.56797 + 2.71581i
\(549\) 0 0
\(550\) −18.9414 32.8075i −0.807665 1.39892i
\(551\) −0.921496 + 5.22606i −0.0392571 + 0.222638i
\(552\) 0 0
\(553\) 42.9550 + 15.6343i 1.82663 + 0.664840i
\(554\) −0.241266 0.0878136i −0.0102504 0.00373084i
\(555\) 0 0
\(556\) 1.37382 7.79133i 0.0582630 0.330426i
\(557\) −10.9520 18.9695i −0.464053 0.803763i 0.535106 0.844785i \(-0.320272\pi\)
−0.999158 + 0.0410224i \(0.986938\pi\)
\(558\) 0 0
\(559\) 4.58371 7.93922i 0.193870 0.335793i
\(560\) 26.6372 + 22.3513i 1.12563 + 0.944514i
\(561\) 0 0
\(562\) 3.47928 + 19.7320i 0.146765 + 0.832344i
\(563\) 11.1601 9.36440i 0.470341 0.394663i −0.376578 0.926385i \(-0.622899\pi\)
0.846919 + 0.531722i \(0.178455\pi\)
\(564\) 0 0
\(565\) −33.0456 + 12.0276i −1.39024 + 0.506006i
\(566\) −58.0431 −2.43973
\(567\) 0 0
\(568\) −74.3137 −3.11813
\(569\) 21.0087 7.64655i 0.880732 0.320560i 0.138227 0.990401i \(-0.455860\pi\)
0.742505 + 0.669840i \(0.233637\pi\)
\(570\) 0 0
\(571\) −11.8171 + 9.91573i −0.494531 + 0.414961i −0.855647 0.517560i \(-0.826840\pi\)
0.361116 + 0.932521i \(0.382396\pi\)
\(572\) 8.05812 + 45.6999i 0.336927 + 1.91081i
\(573\) 0 0
\(574\) −24.4528 20.5183i −1.02064 0.856417i
\(575\) −1.19930 + 2.07724i −0.0500142 + 0.0866271i
\(576\) 0 0
\(577\) −16.4040 28.4126i −0.682909 1.18283i −0.974089 0.226165i \(-0.927381\pi\)
0.291180 0.956668i \(-0.405952\pi\)
\(578\) 4.43035 25.1257i 0.184278 1.04509i
\(579\) 0 0
\(580\) 29.6011 + 10.7739i 1.22912 + 0.447362i
\(581\) 9.91533 + 3.60889i 0.411357 + 0.149722i
\(582\) 0 0
\(583\) −3.83260 + 21.7357i −0.158730 + 0.900202i
\(584\) 4.71825 + 8.17225i 0.195242 + 0.338170i
\(585\) 0 0
\(586\) −26.5758 + 46.0306i −1.09784 + 1.90151i
\(587\) 23.1608 + 19.4342i 0.955948 + 0.802136i 0.980289 0.197568i \(-0.0633044\pi\)
−0.0243412 + 0.999704i \(0.507749\pi\)
\(588\) 0 0
\(589\) −2.80892 15.9302i −0.115739 0.656391i
\(590\) 9.59779 8.05350i 0.395135 0.331557i
\(591\) 0 0
\(592\) 41.0793 14.9517i 1.68835 0.614509i
\(593\) 41.1023 1.68787 0.843935 0.536446i \(-0.180234\pi\)
0.843935 + 0.536446i \(0.180234\pi\)
\(594\) 0 0
\(595\) 21.0698 0.863778
\(596\) −27.7761 + 10.1097i −1.13775 + 0.414108i
\(597\) 0 0
\(598\) 3.36482 2.82342i 0.137598 0.115458i
\(599\) 6.34693 + 35.9952i 0.259329 + 1.47073i 0.784712 + 0.619860i \(0.212811\pi\)
−0.525384 + 0.850865i \(0.676078\pi\)
\(600\) 0 0
\(601\) 3.02266 + 2.53631i 0.123297 + 0.103458i 0.702351 0.711831i \(-0.252134\pi\)
−0.579054 + 0.815289i \(0.696578\pi\)
\(602\) −8.95706 + 15.5141i −0.365062 + 0.632307i
\(603\) 0 0
\(604\) −9.80076 16.9754i −0.398787 0.690720i
\(605\) −0.425069 + 2.41068i −0.0172815 + 0.0980082i
\(606\) 0 0
\(607\) −9.40775 3.42414i −0.381849 0.138982i 0.143962 0.989583i \(-0.454016\pi\)
−0.525811 + 0.850602i \(0.676238\pi\)
\(608\) −0.796973 0.290074i −0.0323215 0.0117641i
\(609\) 0 0
\(610\) 18.8941 107.154i 0.765000 4.33853i
\(611\) −9.46005 16.3853i −0.382712 0.662877i
\(612\) 0 0
\(613\) 9.37838 16.2438i 0.378789 0.656082i −0.612097 0.790783i \(-0.709674\pi\)
0.990886 + 0.134700i \(0.0430072\pi\)
\(614\) −30.8021 25.8460i −1.24307 1.04306i
\(615\) 0 0
\(616\) −7.95257 45.1013i −0.320418 1.81718i
\(617\) −17.6267 + 14.7906i −0.709626 + 0.595447i −0.924494 0.381196i \(-0.875512\pi\)
0.214869 + 0.976643i \(0.431068\pi\)
\(618\) 0 0
\(619\) −6.96690 + 2.53574i −0.280023 + 0.101920i −0.478214 0.878243i \(-0.658716\pi\)
0.198191 + 0.980163i \(0.436493\pi\)
\(620\) −96.0211 −3.85630
\(621\) 0 0
\(622\) 19.0598 0.764229
\(623\) 12.7385 4.63643i 0.510356 0.185754i
\(624\) 0 0
\(625\) −20.9113 + 17.5467i −0.836452 + 0.701867i
\(626\) −6.58028 37.3186i −0.263001 1.49155i
\(627\) 0 0
\(628\) 4.57095 + 3.83549i 0.182401 + 0.153053i
\(629\) 13.2444 22.9400i 0.528090 0.914679i
\(630\) 0 0
\(631\) 15.4962 + 26.8402i 0.616894 + 1.06849i 0.990049 + 0.140723i \(0.0449426\pi\)
−0.373155 + 0.927769i \(0.621724\pi\)
\(632\) −14.9749 + 84.9269i −0.595670 + 3.37821i
\(633\) 0 0
\(634\) 19.9459 + 7.25971i 0.792153 + 0.288320i
\(635\) 7.49732 + 2.72880i 0.297522 + 0.108289i
\(636\) 0 0
\(637\) −0.0397824 + 0.225617i −0.00157623 + 0.00893927i
\(638\) −10.6815 18.5009i −0.422884 0.732457i
\(639\) 0 0
\(640\) 29.6279 51.3171i 1.17115 2.02849i
\(641\) −27.0767 22.7201i −1.06947 0.897388i −0.0744616 0.997224i \(-0.523724\pi\)
−0.995004 + 0.0998358i \(0.968168\pi\)
\(642\) 0 0
\(643\) −3.42103 19.4016i −0.134912 0.765126i −0.974921 0.222552i \(-0.928561\pi\)
0.840008 0.542573i \(-0.182550\pi\)
\(644\) −4.39825 + 3.69057i −0.173315 + 0.145429i
\(645\) 0 0
\(646\) −12.4592 + 4.53476i −0.490199 + 0.178418i
\(647\) 46.8317 1.84114 0.920572 0.390572i \(-0.127723\pi\)
0.920572 + 0.390572i \(0.127723\pi\)
\(648\) 0 0
\(649\) −5.68366 −0.223103
\(650\) −34.6614 + 12.6157i −1.35953 + 0.494829i
\(651\) 0 0
\(652\) −53.4064 + 44.8133i −2.09156 + 1.75502i
\(653\) 3.00875 + 17.0635i 0.117742 + 0.667746i 0.985356 + 0.170509i \(0.0545410\pi\)
−0.867615 + 0.497237i \(0.834348\pi\)
\(654\) 0 0
\(655\) 10.4082 + 8.73355i 0.406684 + 0.341248i
\(656\) 10.3709 17.9630i 0.404918 0.701338i
\(657\) 0 0
\(658\) 18.4859 + 32.0186i 0.720657 + 1.24821i
\(659\) 7.59436 43.0698i 0.295834 1.67776i −0.367957 0.929843i \(-0.619943\pi\)
0.663792 0.747917i \(-0.268946\pi\)
\(660\) 0 0
\(661\) 8.53885 + 3.10789i 0.332123 + 0.120883i 0.502699 0.864462i \(-0.332341\pi\)
−0.170576 + 0.985345i \(0.554563\pi\)
\(662\) 47.4489 + 17.2700i 1.84416 + 0.671218i
\(663\) 0 0
\(664\) −3.45667 + 19.6037i −0.134145 + 0.760773i
\(665\) 8.58561 + 14.8707i 0.332936 + 0.576661i
\(666\) 0 0
\(667\) −0.676311 + 1.17140i −0.0261868 + 0.0453570i
\(668\) 21.1735 + 17.7667i 0.819228 + 0.687414i
\(669\) 0 0
\(670\) −7.72867 43.8315i −0.298585 1.69336i
\(671\) −37.8112 + 31.7274i −1.45969 + 1.22482i
\(672\) 0 0
\(673\) −7.04458 + 2.56402i −0.271549 + 0.0988356i −0.474205 0.880414i \(-0.657265\pi\)
0.202657 + 0.979250i \(0.435042\pi\)
\(674\) −39.2711 −1.51266
\(675\) 0 0
\(676\) −7.34587 −0.282534
\(677\) −14.4361 + 5.25430i −0.554823 + 0.201939i −0.604188 0.796842i \(-0.706503\pi\)
0.0493648 + 0.998781i \(0.484280\pi\)
\(678\) 0 0
\(679\) 21.6535 18.1694i 0.830985 0.697279i
\(680\) 6.90235 + 39.1452i 0.264693 + 1.50115i
\(681\) 0 0
\(682\) 49.8840 + 41.8576i 1.91016 + 1.60281i
\(683\) −3.31079 + 5.73445i −0.126684 + 0.219423i −0.922390 0.386260i \(-0.873767\pi\)
0.795706 + 0.605683i \(0.207100\pi\)
\(684\) 0 0
\(685\) 27.9806 + 48.4639i 1.06908 + 1.85171i
\(686\) −7.86512 + 44.6053i −0.300292 + 1.70304i
\(687\) 0 0
\(688\) −10.9385 3.98127i −0.417025 0.151785i
\(689\) 20.1942 + 7.35008i 0.769336 + 0.280016i
\(690\) 0 0
\(691\) −3.23973 + 18.3734i −0.123245 + 0.698958i 0.859090 + 0.511825i \(0.171030\pi\)
−0.982335 + 0.187132i \(0.940081\pi\)
\(692\) 48.4228 + 83.8708i 1.84076 + 3.18829i
\(693\) 0 0
\(694\) −12.0484 + 20.8685i −0.457352 + 0.792157i
\(695\) −4.62000 3.87664i −0.175247 0.147049i
\(696\) 0 0
\(697\) −2.18245 12.3773i −0.0826662 0.468823i
\(698\) 17.7639 14.9057i 0.672375 0.564190i
\(699\) 0 0
\(700\) 45.3069 16.4904i 1.71244 0.623277i
\(701\) 24.8903 0.940092 0.470046 0.882642i \(-0.344237\pi\)
0.470046 + 0.882642i \(0.344237\pi\)
\(702\) 0 0
\(703\) 21.5876 0.814190
\(704\) −24.1975 + 8.80715i −0.911976 + 0.331932i
\(705\) 0 0
\(706\) 6.37350 5.34801i 0.239870 0.201275i
\(707\) −2.61219 14.8144i −0.0982413 0.557154i
\(708\) 0 0
\(709\) −20.0541 16.8274i −0.753147 0.631965i 0.183186 0.983078i \(-0.441359\pi\)
−0.936333 + 0.351113i \(0.885803\pi\)
\(710\) −56.0843 + 97.1409i −2.10481 + 3.64563i
\(711\) 0 0
\(712\) 12.7870 + 22.1477i 0.479212 + 0.830020i
\(713\) 0.715965 4.06044i 0.0268131 0.152065i
\(714\) 0 0
\(715\) 33.2413 + 12.0988i 1.24315 + 0.452471i
\(716\) 78.1136 + 28.4310i 2.91924 + 1.06252i
\(717\) 0 0
\(718\) −15.0347 + 85.2660i −0.561090 + 3.18210i
\(719\) −10.5145 18.2117i −0.392125 0.679181i 0.600604 0.799546i \(-0.294927\pi\)
−0.992730 + 0.120365i \(0.961593\pi\)
\(720\) 0 0
\(721\) 13.7859 23.8779i 0.513414 0.889259i
\(722\) 27.4953 + 23.0713i 1.02327 + 0.858624i
\(723\) 0 0
\(724\) −10.8549 61.5609i −0.403417 2.28789i
\(725\) 8.70127 7.30123i 0.323157 0.271161i
\(726\) 0 0
\(727\) −38.8992 + 14.1582i −1.44269 + 0.525097i −0.940540 0.339683i \(-0.889680\pi\)
−0.502152 + 0.864779i \(0.667458\pi\)
\(728\) −44.5918 −1.65268
\(729\) 0 0
\(730\) 14.2434 0.527171
\(731\) −6.62799 + 2.41239i −0.245145 + 0.0892254i
\(732\) 0 0
\(733\) 25.7596 21.6148i 0.951451 0.798362i −0.0280903 0.999605i \(-0.508943\pi\)
0.979541 + 0.201243i \(0.0644982\pi\)
\(734\) 13.4633 + 76.3541i 0.496939 + 2.81828i
\(735\) 0 0
\(736\) −0.165602 0.138956i −0.00610416 0.00512200i
\(737\) −10.0952 + 17.4854i −0.371862 + 0.644084i
\(738\) 0 0
\(739\) 6.47268 + 11.2110i 0.238101 + 0.412403i 0.960169 0.279418i \(-0.0901417\pi\)
−0.722068 + 0.691822i \(0.756808\pi\)
\(740\) 22.2522 126.198i 0.818005 4.63914i
\(741\) 0 0
\(742\) −39.4615 14.3628i −1.44868 0.527276i
\(743\) 0.0826264 + 0.0300735i 0.00303127 + 0.00110329i 0.343535 0.939140i \(-0.388375\pi\)
−0.340504 + 0.940243i \(0.610598\pi\)
\(744\) 0 0
\(745\) −3.91276 + 22.1904i −0.143353 + 0.812993i
\(746\) 17.7481 + 30.7406i 0.649803 + 1.12549i
\(747\) 0 0
\(748\) 17.8518 30.9202i 0.652727 1.13056i
\(749\) 29.0137 + 24.3454i 1.06014 + 0.889561i
\(750\) 0 0
\(751\) 8.66435 + 49.1380i 0.316167 + 1.79307i 0.565601 + 0.824679i \(0.308644\pi\)
−0.249434 + 0.968392i \(0.580245\pi\)
\(752\) −18.4035 + 15.4424i −0.671106 + 0.563125i
\(753\) 0 0
\(754\) −19.5463 + 7.11428i −0.711835 + 0.259087i
\(755\) −14.9423 −0.543806
\(756\) 0 0
\(757\) −11.8679 −0.431348 −0.215674 0.976465i \(-0.569195\pi\)
−0.215674 + 0.976465i \(0.569195\pi\)
\(758\) 2.31186 0.841448i 0.0839705 0.0305628i
\(759\) 0 0
\(760\) −24.8154 + 20.8226i −0.900149 + 0.755315i
\(761\) 0.658179 + 3.73272i 0.0238590 + 0.135311i 0.994411 0.105582i \(-0.0336707\pi\)
−0.970552 + 0.240893i \(0.922560\pi\)
\(762\) 0 0
\(763\) −11.7324 9.84469i −0.424743 0.356402i
\(764\) 22.1247 38.3211i 0.800444 1.38641i
\(765\) 0 0
\(766\) 5.05978 + 8.76379i 0.182817 + 0.316649i
\(767\) −0.960983 + 5.45000i −0.0346991 + 0.196788i
\(768\) 0 0
\(769\) −5.89140 2.14430i −0.212449 0.0773253i 0.233603 0.972332i \(-0.424948\pi\)
−0.446053 + 0.895007i \(0.647171\pi\)
\(770\) −64.9570 23.6424i −2.34089 0.852013i
\(771\) 0 0
\(772\) 0.803302 4.55575i 0.0289115 0.163965i
\(773\) 0.647678 + 1.12181i 0.0232954 + 0.0403487i 0.877438 0.479690i \(-0.159251\pi\)
−0.854143 + 0.520039i \(0.825918\pi\)
\(774\) 0 0
\(775\) −17.3119 + 29.9850i −0.621861 + 1.07709i
\(776\) 40.8502 + 34.2774i 1.46644 + 1.23049i
\(777\) 0 0
\(778\) 6.62376 + 37.5652i 0.237473 + 1.34678i
\(779\) 7.84636 6.58388i 0.281125 0.235892i
\(780\)