Properties

Label 666.2.bs.b.557.5
Level $666$
Weight $2$
Character 666.557
Analytic conductor $5.318$
Analytic rank $0$
Dimension $96$
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] = [666,2,Mod(17,666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(666, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("666.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.bs (of order \(36\), degree \(12\), 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: \(5.31803677462\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(8\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 557.5
Character \(\chi\) \(=\) 666.557
Dual form 666.2.bs.b.611.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-3.03635 - 1.41587i) q^{5} +(-1.63046 + 0.593439i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\) \(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-3.03635 - 1.41587i) q^{5} +(-1.63046 + 0.593439i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.67512 + 2.90139i) q^{10} +(0.408947 + 0.708318i) q^{11} +(3.82328 + 5.46021i) q^{13} +(0.449077 + 1.67598i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-0.771448 + 1.10174i) q^{17} +(-1.63867 + 0.143365i) q^{19} +(2.74436 + 1.92162i) q^{20} +(0.741264 - 0.345657i) q^{22} +(4.85685 - 1.30139i) q^{23} +(4.00077 + 4.76794i) q^{25} +(5.77265 - 3.33284i) q^{26} +(1.70874 - 0.301297i) q^{28} +(-3.12298 - 0.836800i) q^{29} +(5.52010 + 5.52010i) q^{31} +(0.422618 - 0.906308i) q^{32} +(1.03031 + 0.864536i) q^{34} +(5.79088 + 0.506636i) q^{35} +(4.15058 - 4.44665i) q^{37} +1.64493i q^{38} +(2.15349 - 2.56643i) q^{40} +(-0.631977 + 3.58412i) q^{41} +(-7.38109 + 7.38109i) q^{43} +(-0.279736 - 0.768570i) q^{44} +(-0.873134 - 4.95179i) q^{46} +(-2.69999 - 1.55884i) q^{47} +(-3.05608 + 2.56435i) q^{49} +(5.09848 - 3.57000i) q^{50} +(-2.81704 - 6.04116i) q^{52} +(-1.64843 + 4.52901i) q^{53} +(-0.238819 - 2.72972i) q^{55} +(-0.151224 - 1.72850i) q^{56} +(-1.10580 + 3.03817i) q^{58} +(3.21090 + 6.88580i) q^{59} +(-9.61763 + 6.73434i) q^{61} +(5.98021 - 5.01799i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.87785 - 21.9924i) q^{65} +(1.99855 + 5.49098i) q^{67} +(0.951044 - 0.951044i) q^{68} +(1.00942 - 5.72469i) q^{70} +(-7.41721 + 8.83948i) q^{71} +6.79194i q^{73} +(-4.06798 - 4.52233i) q^{74} +(1.63867 + 0.143365i) q^{76} +(-1.08712 - 0.912199i) q^{77} +(3.68293 - 7.89808i) q^{79} +(-2.36898 - 2.36898i) q^{80} +(3.51540 + 0.941948i) q^{82} +(8.80119 - 1.55189i) q^{83} +(3.90231 - 2.25300i) q^{85} +(6.70970 + 7.99631i) q^{86} +(-0.790026 + 0.211687i) q^{88} +(-4.08541 + 1.90506i) q^{89} +(-9.47401 - 6.63377i) q^{91} +(-5.00904 + 0.438235i) q^{92} +(-1.78823 + 2.55386i) q^{94} +(5.17856 + 1.88484i) q^{95} +(-2.31502 - 8.63977i) q^{97} +(2.28824 + 3.26795i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{36}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0871557 0.996195i 0.0616284 0.704416i
\(3\) 0 0
\(4\) −0.984808 0.173648i −0.492404 0.0868241i
\(5\) −3.03635 1.41587i −1.35790 0.633197i −0.398999 0.916951i \(-0.630642\pi\)
−0.958897 + 0.283754i \(0.908420\pi\)
\(6\) 0 0
\(7\) −1.63046 + 0.593439i −0.616256 + 0.224299i −0.631238 0.775589i \(-0.717453\pi\)
0.0149822 + 0.999888i \(0.495231\pi\)
\(8\) −0.258819 + 0.965926i −0.0915064 + 0.341506i
\(9\) 0 0
\(10\) −1.67512 + 2.90139i −0.529719 + 0.917501i
\(11\) 0.408947 + 0.708318i 0.123302 + 0.213566i 0.921068 0.389402i \(-0.127318\pi\)
−0.797766 + 0.602967i \(0.793985\pi\)
\(12\) 0 0
\(13\) 3.82328 + 5.46021i 1.06039 + 1.51439i 0.842710 + 0.538368i \(0.180959\pi\)
0.217677 + 0.976021i \(0.430152\pi\)
\(14\) 0.449077 + 1.67598i 0.120021 + 0.447924i
\(15\) 0 0
\(16\) 0.939693 + 0.342020i 0.234923 + 0.0855050i
\(17\) −0.771448 + 1.10174i −0.187104 + 0.267212i −0.901735 0.432290i \(-0.857706\pi\)
0.714631 + 0.699502i \(0.246595\pi\)
\(18\) 0 0
\(19\) −1.63867 + 0.143365i −0.375937 + 0.0328902i −0.273559 0.961855i \(-0.588201\pi\)
−0.102378 + 0.994746i \(0.532645\pi\)
\(20\) 2.74436 + 1.92162i 0.613656 + 0.429687i
\(21\) 0 0
\(22\) 0.741264 0.345657i 0.158038 0.0736944i
\(23\) 4.85685 1.30139i 1.01272 0.271358i 0.285956 0.958243i \(-0.407689\pi\)
0.726766 + 0.686885i \(0.241022\pi\)
\(24\) 0 0
\(25\) 4.00077 + 4.76794i 0.800155 + 0.953588i
\(26\) 5.77265 3.33284i 1.13211 0.653624i
\(27\) 0 0
\(28\) 1.70874 0.301297i 0.322922 0.0569398i
\(29\) −3.12298 0.836800i −0.579923 0.155390i −0.0430794 0.999072i \(-0.513717\pi\)
−0.536844 + 0.843682i \(0.680384\pi\)
\(30\) 0 0
\(31\) 5.52010 + 5.52010i 0.991440 + 0.991440i 0.999964 0.00852369i \(-0.00271321\pi\)
−0.00852369 + 0.999964i \(0.502713\pi\)
\(32\) 0.422618 0.906308i 0.0747091 0.160214i
\(33\) 0 0
\(34\) 1.03031 + 0.864536i 0.176697 + 0.148267i
\(35\) 5.79088 + 0.506636i 0.978837 + 0.0856372i
\(36\) 0 0
\(37\) 4.15058 4.44665i 0.682351 0.731025i
\(38\) 1.64493i 0.266843i
\(39\) 0 0
\(40\) 2.15349 2.56643i 0.340497 0.405789i
\(41\) −0.631977 + 3.58412i −0.0986982 + 0.559745i 0.894853 + 0.446361i \(0.147280\pi\)
−0.993551 + 0.113384i \(0.963831\pi\)
\(42\) 0 0
\(43\) −7.38109 + 7.38109i −1.12561 + 1.12561i −0.134723 + 0.990883i \(0.543014\pi\)
−0.990883 + 0.134723i \(0.956986\pi\)
\(44\) −0.279736 0.768570i −0.0421719 0.115866i
\(45\) 0 0
\(46\) −0.873134 4.95179i −0.128737 0.730101i
\(47\) −2.69999 1.55884i −0.393834 0.227380i 0.289986 0.957031i \(-0.406349\pi\)
−0.683820 + 0.729651i \(0.739683\pi\)
\(48\) 0 0
\(49\) −3.05608 + 2.56435i −0.436583 + 0.366336i
\(50\) 5.09848 3.57000i 0.721035 0.504874i
\(51\) 0 0
\(52\) −2.81704 6.04116i −0.390653 0.837758i
\(53\) −1.64843 + 4.52901i −0.226429 + 0.622108i −0.999932 0.0116849i \(-0.996280\pi\)
0.773503 + 0.633793i \(0.218503\pi\)
\(54\) 0 0
\(55\) −0.238819 2.72972i −0.0322024 0.368075i
\(56\) −0.151224 1.72850i −0.0202081 0.230980i
\(57\) 0 0
\(58\) −1.10580 + 3.03817i −0.145199 + 0.398931i
\(59\) 3.21090 + 6.88580i 0.418024 + 0.896454i 0.996721 + 0.0809123i \(0.0257834\pi\)
−0.578698 + 0.815542i \(0.696439\pi\)
\(60\) 0 0
\(61\) −9.61763 + 6.73434i −1.23141 + 0.862243i −0.994023 0.109171i \(-0.965180\pi\)
−0.237388 + 0.971415i \(0.576291\pi\)
\(62\) 5.98021 5.01799i 0.759487 0.637285i
\(63\) 0 0
\(64\) −0.866025 0.500000i −0.108253 0.0625000i
\(65\) −3.87785 21.9924i −0.480988 2.72782i
\(66\) 0 0
\(67\) 1.99855 + 5.49098i 0.244162 + 0.670830i 0.999873 + 0.0159247i \(0.00506921\pi\)
−0.755711 + 0.654905i \(0.772709\pi\)
\(68\) 0.951044 0.951044i 0.115331 0.115331i
\(69\) 0 0
\(70\) 1.00942 5.72469i 0.120648 0.684231i
\(71\) −7.41721 + 8.83948i −0.880260 + 1.04905i 0.118167 + 0.992994i \(0.462298\pi\)
−0.998427 + 0.0560597i \(0.982146\pi\)
\(72\) 0 0
\(73\) 6.79194i 0.794936i 0.917616 + 0.397468i \(0.130111\pi\)
−0.917616 + 0.397468i \(0.869889\pi\)
\(74\) −4.06798 4.52233i −0.472894 0.525711i
\(75\) 0 0
\(76\) 1.63867 + 0.143365i 0.187968 + 0.0164451i
\(77\) −1.08712 0.912199i −0.123888 0.103955i
\(78\) 0 0
\(79\) 3.68293 7.89808i 0.414363 0.888603i −0.582749 0.812652i \(-0.698023\pi\)
0.997112 0.0759511i \(-0.0241993\pi\)
\(80\) −2.36898 2.36898i −0.264860 0.264860i
\(81\) 0 0
\(82\) 3.51540 + 0.941948i 0.388211 + 0.104021i
\(83\) 8.80119 1.55189i 0.966057 0.170342i 0.331702 0.943384i \(-0.392377\pi\)
0.634354 + 0.773042i \(0.281266\pi\)
\(84\) 0 0
\(85\) 3.90231 2.25300i 0.423265 0.244372i
\(86\) 6.70970 + 7.99631i 0.723526 + 0.862264i
\(87\) 0 0
\(88\) −0.790026 + 0.211687i −0.0842170 + 0.0225659i
\(89\) −4.08541 + 1.90506i −0.433052 + 0.201936i −0.626906 0.779095i \(-0.715679\pi\)
0.193854 + 0.981030i \(0.437901\pi\)
\(90\) 0 0
\(91\) −9.47401 6.63377i −0.993146 0.695408i
\(92\) −5.00904 + 0.438235i −0.522229 + 0.0456891i
\(93\) 0 0
\(94\) −1.78823 + 2.55386i −0.184442 + 0.263410i
\(95\) 5.17856 + 1.88484i 0.531309 + 0.193381i
\(96\) 0 0
\(97\) −2.31502 8.63977i −0.235055 0.877236i −0.978124 0.208022i \(-0.933298\pi\)
0.743070 0.669214i \(-0.233369\pi\)
\(98\) 2.28824 + 3.26795i 0.231147 + 0.330113i
\(99\) 0 0
\(100\) −3.11205 5.39023i −0.311205 0.539023i
\(101\) −0.210861 + 0.365223i −0.0209815 + 0.0363410i −0.876326 0.481719i \(-0.840012\pi\)
0.855344 + 0.518060i \(0.173346\pi\)
\(102\) 0 0
\(103\) 1.60026 5.97223i 0.157678 0.588462i −0.841183 0.540750i \(-0.818140\pi\)
0.998861 0.0477116i \(-0.0151929\pi\)
\(104\) −6.26369 + 2.27980i −0.614206 + 0.223553i
\(105\) 0 0
\(106\) 4.36811 + 2.03688i 0.424268 + 0.197839i
\(107\) −15.1622 2.67351i −1.46579 0.258458i −0.616903 0.787039i \(-0.711613\pi\)
−0.848882 + 0.528582i \(0.822724\pi\)
\(108\) 0 0
\(109\) 0.911651 10.4202i 0.0873204 0.998076i −0.818526 0.574470i \(-0.805208\pi\)
0.905846 0.423607i \(-0.139236\pi\)
\(110\) −2.74014 −0.261262
\(111\) 0 0
\(112\) −1.73510 −0.163952
\(113\) −0.178190 + 2.03672i −0.0167627 + 0.191599i 0.983196 + 0.182551i \(0.0584355\pi\)
−0.999959 + 0.00904765i \(0.997120\pi\)
\(114\) 0 0
\(115\) −16.5897 2.92521i −1.54699 0.272777i
\(116\) 2.93023 + 1.36639i 0.272065 + 0.126866i
\(117\) 0 0
\(118\) 7.13944 2.59854i 0.657239 0.239215i
\(119\) 0.603999 2.25416i 0.0553685 0.206638i
\(120\) 0 0
\(121\) 5.16552 8.94695i 0.469593 0.813359i
\(122\) 5.87048 + 10.1680i 0.531488 + 0.920564i
\(123\) 0 0
\(124\) −4.47769 6.39480i −0.402108 0.574270i
\(125\) −1.06142 3.96129i −0.0949367 0.354309i
\(126\) 0 0
\(127\) 14.0829 + 5.12576i 1.24966 + 0.454838i 0.880285 0.474445i \(-0.157351\pi\)
0.369371 + 0.929282i \(0.379573\pi\)
\(128\) −0.573576 + 0.819152i −0.0506975 + 0.0724035i
\(129\) 0 0
\(130\) −22.2466 + 1.94633i −1.95116 + 0.170704i
\(131\) 11.1992 + 7.84177i 0.978480 + 0.685139i 0.949279 0.314435i \(-0.101815\pi\)
0.0292006 + 0.999574i \(0.490704\pi\)
\(132\) 0 0
\(133\) 2.58671 1.20620i 0.224296 0.104591i
\(134\) 5.64427 1.51238i 0.487591 0.130650i
\(135\) 0 0
\(136\) −0.864536 1.03031i −0.0741333 0.0883487i
\(137\) −17.7917 + 10.2720i −1.52004 + 0.877598i −0.520324 + 0.853969i \(0.674189\pi\)
−0.999721 + 0.0236291i \(0.992478\pi\)
\(138\) 0 0
\(139\) 12.1974 2.15072i 1.03457 0.182422i 0.369519 0.929223i \(-0.379523\pi\)
0.665047 + 0.746801i \(0.268411\pi\)
\(140\) −5.61493 1.50452i −0.474548 0.127155i
\(141\) 0 0
\(142\) 8.15939 + 8.15939i 0.684721 + 0.684721i
\(143\) −2.30404 + 4.94103i −0.192674 + 0.413190i
\(144\) 0 0
\(145\) 8.29765 + 6.96256i 0.689083 + 0.578209i
\(146\) 6.76609 + 0.591956i 0.559966 + 0.0489906i
\(147\) 0 0
\(148\) −4.85967 + 3.65836i −0.399463 + 0.300715i
\(149\) 19.4180i 1.59078i 0.606095 + 0.795392i \(0.292735\pi\)
−0.606095 + 0.795392i \(0.707265\pi\)
\(150\) 0 0
\(151\) 12.6426 15.0668i 1.02884 1.22612i 0.0550915 0.998481i \(-0.482455\pi\)
0.973746 0.227639i \(-0.0731006\pi\)
\(152\) 0.285639 1.61994i 0.0231684 0.131395i
\(153\) 0 0
\(154\) −1.00348 + 1.00348i −0.0808624 + 0.0808624i
\(155\) −8.94519 24.5767i −0.718495 1.97405i
\(156\) 0 0
\(157\) −0.731079 4.14615i −0.0583465 0.330899i 0.941637 0.336630i \(-0.109287\pi\)
−0.999984 + 0.00573047i \(0.998176\pi\)
\(158\) −7.54704 4.35728i −0.600410 0.346647i
\(159\) 0 0
\(160\) −2.56643 + 2.15349i −0.202894 + 0.170248i
\(161\) −7.14660 + 5.00411i −0.563231 + 0.394379i
\(162\) 0 0
\(163\) −8.79852 18.8685i −0.689153 1.47789i −0.869316 0.494257i \(-0.835440\pi\)
0.180163 0.983637i \(-0.442337\pi\)
\(164\) 1.24475 3.41993i 0.0971987 0.267051i
\(165\) 0 0
\(166\) −0.778908 8.90296i −0.0604550 0.691004i
\(167\) −0.789044 9.01881i −0.0610581 0.697897i −0.963609 0.267314i \(-0.913864\pi\)
0.902551 0.430582i \(-0.141692\pi\)
\(168\) 0 0
\(169\) −10.7501 + 29.5358i −0.826934 + 2.27198i
\(170\) −1.90432 4.08382i −0.146055 0.313215i
\(171\) 0 0
\(172\) 8.55067 5.98724i 0.651983 0.456523i
\(173\) 8.81124 7.39351i 0.669906 0.562118i −0.243131 0.969993i \(-0.578175\pi\)
0.913038 + 0.407875i \(0.133730\pi\)
\(174\) 0 0
\(175\) −9.35259 5.39972i −0.706989 0.408180i
\(176\) 0.142026 + 0.805469i 0.0107056 + 0.0607145i
\(177\) 0 0
\(178\) 1.54174 + 4.23590i 0.115558 + 0.317494i
\(179\) −12.1575 + 12.1575i −0.908692 + 0.908692i −0.996167 0.0874747i \(-0.972120\pi\)
0.0874747 + 0.996167i \(0.472120\pi\)
\(180\) 0 0
\(181\) −3.32936 + 18.8817i −0.247469 + 1.40347i 0.567219 + 0.823567i \(0.308019\pi\)
−0.814688 + 0.579900i \(0.803092\pi\)
\(182\) −7.43424 + 8.85978i −0.551063 + 0.656731i
\(183\) 0 0
\(184\) 5.02818i 0.370682i
\(185\) −18.8985 + 7.62489i −1.38944 + 0.560593i
\(186\) 0 0
\(187\) −1.09587 0.0958758i −0.0801376 0.00701113i
\(188\) 2.38828 + 2.00401i 0.174184 + 0.146157i
\(189\) 0 0
\(190\) 2.32901 4.99458i 0.168964 0.362345i
\(191\) −0.602298 0.602298i −0.0435807 0.0435807i 0.684981 0.728561i \(-0.259811\pi\)
−0.728561 + 0.684981i \(0.759811\pi\)
\(192\) 0 0
\(193\) −11.7976 3.16116i −0.849211 0.227545i −0.192134 0.981369i \(-0.561541\pi\)
−0.657077 + 0.753823i \(0.728207\pi\)
\(194\) −8.80866 + 1.55320i −0.632425 + 0.111514i
\(195\) 0 0
\(196\) 3.45495 1.99471i 0.246782 0.142480i
\(197\) −10.3433 12.3266i −0.736927 0.878236i 0.259230 0.965816i \(-0.416531\pi\)
−0.996158 + 0.0875797i \(0.972087\pi\)
\(198\) 0 0
\(199\) 1.01938 0.273141i 0.0722617 0.0193625i −0.222507 0.974931i \(-0.571424\pi\)
0.294769 + 0.955569i \(0.404757\pi\)
\(200\) −5.64095 + 2.63042i −0.398875 + 0.185999i
\(201\) 0 0
\(202\) 0.345455 + 0.241890i 0.0243061 + 0.0170193i
\(203\) 5.58849 0.488929i 0.392235 0.0343161i
\(204\) 0 0
\(205\) 6.99355 9.98783i 0.488451 0.697580i
\(206\) −5.81004 2.11468i −0.404804 0.147337i
\(207\) 0 0
\(208\) 1.72521 + 6.43855i 0.119621 + 0.446433i
\(209\) −0.771678 1.10207i −0.0533781 0.0762318i
\(210\) 0 0
\(211\) −2.02817 3.51289i −0.139625 0.241838i 0.787730 0.616021i \(-0.211256\pi\)
−0.927355 + 0.374183i \(0.877923\pi\)
\(212\) 2.40984 4.17396i 0.165508 0.286669i
\(213\) 0 0
\(214\) −3.98480 + 14.8715i −0.272396 + 1.01659i
\(215\) 32.8622 11.9609i 2.24119 0.815725i
\(216\) 0 0
\(217\) −12.2762 5.72447i −0.833360 0.388602i
\(218\) −10.3011 1.81636i −0.697680 0.123020i
\(219\) 0 0
\(220\) −0.238819 + 2.72972i −0.0161012 + 0.184037i
\(221\) −8.96520 −0.603065
\(222\) 0 0
\(223\) 10.8070 0.723688 0.361844 0.932239i \(-0.382147\pi\)
0.361844 + 0.932239i \(0.382147\pi\)
\(224\) −0.151224 + 1.72850i −0.0101041 + 0.115490i
\(225\) 0 0
\(226\) 2.01344 + 0.355024i 0.133932 + 0.0236159i
\(227\) −13.6816 6.37985i −0.908082 0.423446i −0.0882819 0.996096i \(-0.528138\pi\)
−0.819800 + 0.572650i \(0.805915\pi\)
\(228\) 0 0
\(229\) −14.2293 + 5.17903i −0.940296 + 0.342240i −0.766283 0.642504i \(-0.777896\pi\)
−0.174013 + 0.984743i \(0.555674\pi\)
\(230\) −4.35996 + 16.2716i −0.287487 + 1.07292i
\(231\) 0 0
\(232\) 1.61657 2.79999i 0.106133 0.183828i
\(233\) 10.1069 + 17.5057i 0.662128 + 1.14684i 0.980056 + 0.198724i \(0.0636797\pi\)
−0.317928 + 0.948115i \(0.602987\pi\)
\(234\) 0 0
\(235\) 5.99100 + 8.55603i 0.390810 + 0.558134i
\(236\) −1.96641 7.33875i −0.128003 0.477712i
\(237\) 0 0
\(238\) −2.19294 0.798163i −0.142147 0.0517372i
\(239\) 13.6639 19.5141i 0.883846 1.26226i −0.0802681 0.996773i \(-0.525578\pi\)
0.964114 0.265489i \(-0.0855335\pi\)
\(240\) 0 0
\(241\) −8.22920 + 0.719962i −0.530090 + 0.0463768i −0.349059 0.937101i \(-0.613499\pi\)
−0.181030 + 0.983477i \(0.557943\pi\)
\(242\) −8.46270 5.92565i −0.544003 0.380915i
\(243\) 0 0
\(244\) 10.6409 4.96194i 0.681215 0.317656i
\(245\) 12.9101 3.45925i 0.824797 0.221004i
\(246\) 0 0
\(247\) −7.04790 8.39936i −0.448447 0.534438i
\(248\) −6.76072 + 3.90330i −0.429306 + 0.247860i
\(249\) 0 0
\(250\) −4.03873 + 0.712136i −0.255431 + 0.0450395i
\(251\) 26.3270 + 7.05430i 1.66175 + 0.445264i 0.962867 0.269976i \(-0.0870158\pi\)
0.698879 + 0.715240i \(0.253683\pi\)
\(252\) 0 0
\(253\) 2.90799 + 2.90799i 0.182824 + 0.182824i
\(254\) 6.33366 13.5826i 0.397409 0.852247i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) 11.1131 + 0.972272i 0.693217 + 0.0606486i 0.428319 0.903628i \(-0.359106\pi\)
0.264898 + 0.964276i \(0.414662\pi\)
\(258\) 0 0
\(259\) −4.12854 + 9.71321i −0.256535 + 0.603549i
\(260\) 22.3316i 1.38495i
\(261\) 0 0
\(262\) 8.78801 10.4731i 0.542925 0.647033i
\(263\) −1.86233 + 10.5618i −0.114836 + 0.651269i 0.871995 + 0.489515i \(0.162826\pi\)
−0.986831 + 0.161754i \(0.948285\pi\)
\(264\) 0 0
\(265\) 11.4177 11.4177i 0.701383 0.701383i
\(266\) −0.976166 2.68199i −0.0598526 0.164444i
\(267\) 0 0
\(268\) −1.01469 5.75460i −0.0619822 0.351518i
\(269\) 12.7358 + 7.35301i 0.776515 + 0.448321i 0.835194 0.549956i \(-0.185355\pi\)
−0.0586788 + 0.998277i \(0.518689\pi\)
\(270\) 0 0
\(271\) 15.0829 12.6560i 0.916218 0.768798i −0.0570735 0.998370i \(-0.518177\pi\)
0.973292 + 0.229572i \(0.0737325\pi\)
\(272\) −1.10174 + 0.771448i −0.0668029 + 0.0467759i
\(273\) 0 0
\(274\) 8.68229 + 18.6192i 0.524516 + 1.12483i
\(275\) −1.74111 + 4.78365i −0.104993 + 0.288465i
\(276\) 0 0
\(277\) −0.361843 4.13588i −0.0217410 0.248501i −0.999286 0.0377754i \(-0.987973\pi\)
0.977545 0.210726i \(-0.0675827\pi\)
\(278\) −1.07947 12.3384i −0.0647422 0.740007i
\(279\) 0 0
\(280\) −1.98816 + 5.46243i −0.118815 + 0.326443i
\(281\) −3.39778 7.28656i −0.202695 0.434680i 0.778515 0.627626i \(-0.215973\pi\)
−0.981209 + 0.192946i \(0.938196\pi\)
\(282\) 0 0
\(283\) −17.3177 + 12.1260i −1.02943 + 0.720817i −0.960918 0.276833i \(-0.910715\pi\)
−0.0685151 + 0.997650i \(0.521826\pi\)
\(284\) 8.83948 7.41721i 0.524527 0.440130i
\(285\) 0 0
\(286\) 4.72142 + 2.72591i 0.279183 + 0.161187i
\(287\) −1.09654 6.21880i −0.0647269 0.367084i
\(288\) 0 0
\(289\) 5.19564 + 14.2749i 0.305626 + 0.839700i
\(290\) 7.65925 7.65925i 0.449767 0.449767i
\(291\) 0 0
\(292\) 1.17941 6.68875i 0.0690196 0.391430i
\(293\) −19.0596 + 22.7143i −1.11347 + 1.32698i −0.173848 + 0.984773i \(0.555620\pi\)
−0.939623 + 0.342210i \(0.888824\pi\)
\(294\) 0 0
\(295\) 25.4539i 1.48198i
\(296\) 3.22089 + 5.16003i 0.187210 + 0.299921i
\(297\) 0 0
\(298\) 19.3441 + 1.69239i 1.12057 + 0.0980375i
\(299\) 25.6749 + 21.5438i 1.48482 + 1.24591i
\(300\) 0 0
\(301\) 7.65435 16.4148i 0.441190 0.946134i
\(302\) −13.9076 13.9076i −0.800293 0.800293i
\(303\) 0 0
\(304\) −1.58888 0.425739i −0.0911286 0.0244178i
\(305\) 38.7374 6.83045i 2.21810 0.391111i
\(306\) 0 0
\(307\) −0.876906 + 0.506282i −0.0500476 + 0.0288950i −0.524815 0.851216i \(-0.675866\pi\)
0.474767 + 0.880111i \(0.342532\pi\)
\(308\) 0.912199 + 1.08712i 0.0519773 + 0.0619442i
\(309\) 0 0
\(310\) −25.2628 + 6.76915i −1.43483 + 0.384462i
\(311\) 20.1595 9.40054i 1.14314 0.533056i 0.243594 0.969877i \(-0.421674\pi\)
0.899548 + 0.436822i \(0.143896\pi\)
\(312\) 0 0
\(313\) 0.248543 + 0.174032i 0.0140485 + 0.00983686i 0.580580 0.814203i \(-0.302826\pi\)
−0.566531 + 0.824040i \(0.691715\pi\)
\(314\) −4.19410 + 0.366936i −0.236686 + 0.0207074i
\(315\) 0 0
\(316\) −4.99847 + 7.13855i −0.281186 + 0.401575i
\(317\) 4.54976 + 1.65598i 0.255540 + 0.0930088i 0.466614 0.884461i \(-0.345474\pi\)
−0.211074 + 0.977470i \(0.567696\pi\)
\(318\) 0 0
\(319\) −0.684415 2.55427i −0.0383199 0.143012i
\(320\) 1.92162 + 2.74436i 0.107422 + 0.153414i
\(321\) 0 0
\(322\) 4.36220 + 7.55554i 0.243096 + 0.421054i
\(323\) 1.10620 1.91599i 0.0615505 0.106609i
\(324\) 0 0
\(325\) −10.7379 + 40.0742i −0.595629 + 2.22292i
\(326\) −19.5635 + 7.12054i −1.08352 + 0.394370i
\(327\) 0 0
\(328\) −3.29842 1.53808i −0.182125 0.0849263i
\(329\) 5.32731 + 0.939349i 0.293704 + 0.0517880i
\(330\) 0 0
\(331\) −0.0646081 + 0.738474i −0.00355118 + 0.0405902i −0.997764 0.0668426i \(-0.978707\pi\)
0.994212 + 0.107433i \(0.0342630\pi\)
\(332\) −8.93697 −0.490480
\(333\) 0 0
\(334\) −9.05326 −0.495373
\(335\) 1.70622 19.5022i 0.0932209 1.06552i
\(336\) 0 0
\(337\) 8.58179 + 1.51320i 0.467480 + 0.0824294i 0.402426 0.915452i \(-0.368167\pi\)
0.0650538 + 0.997882i \(0.479278\pi\)
\(338\) 28.4864 + 13.2834i 1.54946 + 0.722524i
\(339\) 0 0
\(340\) −4.23426 + 1.54114i −0.229635 + 0.0835802i
\(341\) −1.65255 + 6.16742i −0.0894909 + 0.333984i
\(342\) 0 0
\(343\) 9.53388 16.5132i 0.514781 0.891627i
\(344\) −5.21922 9.03996i −0.281402 0.487402i
\(345\) 0 0
\(346\) −6.59742 9.42210i −0.354680 0.506535i
\(347\) 1.84100 + 6.87072i 0.0988302 + 0.368840i 0.997572 0.0696382i \(-0.0221845\pi\)
−0.898742 + 0.438478i \(0.855518\pi\)
\(348\) 0 0
\(349\) 19.7211 + 7.17791i 1.05565 + 0.384225i 0.810792 0.585335i \(-0.199037\pi\)
0.244857 + 0.969559i \(0.421259\pi\)
\(350\) −6.19430 + 8.84638i −0.331099 + 0.472859i
\(351\) 0 0
\(352\) 0.814782 0.0712842i 0.0434280 0.00379946i
\(353\) −19.5114 13.6621i −1.03849 0.727158i −0.0756226 0.997137i \(-0.524094\pi\)
−0.962866 + 0.269979i \(0.912983\pi\)
\(354\) 0 0
\(355\) 35.0368 16.3379i 1.85956 0.867127i
\(356\) 4.35415 1.16669i 0.230769 0.0618345i
\(357\) 0 0
\(358\) 11.0516 + 13.1708i 0.584096 + 0.696099i
\(359\) 21.6682 12.5101i 1.14360 0.660259i 0.196281 0.980548i \(-0.437113\pi\)
0.947320 + 0.320289i \(0.103780\pi\)
\(360\) 0 0
\(361\) −16.0467 + 2.82946i −0.844561 + 0.148919i
\(362\) 18.5197 + 4.96234i 0.973374 + 0.260815i
\(363\) 0 0
\(364\) 8.17813 + 8.17813i 0.428651 + 0.428651i
\(365\) 9.61651 20.6227i 0.503351 1.07944i
\(366\) 0 0
\(367\) 4.09410 + 3.43536i 0.213710 + 0.179324i 0.743359 0.668893i \(-0.233232\pi\)
−0.529648 + 0.848217i \(0.677676\pi\)
\(368\) 5.00904 + 0.438235i 0.261114 + 0.0228446i
\(369\) 0 0
\(370\) 5.94877 + 19.4911i 0.309262 + 1.01330i
\(371\) 8.36262i 0.434165i
\(372\) 0 0
\(373\) −18.0104 + 21.4640i −0.932544 + 1.11136i 0.0610250 + 0.998136i \(0.480563\pi\)
−0.993569 + 0.113227i \(0.963881\pi\)
\(374\) −0.191022 + 1.08334i −0.00987751 + 0.0560181i
\(375\) 0 0
\(376\) 2.20453 2.20453i 0.113690 0.113690i
\(377\) −7.37092 20.2514i −0.379622 1.04300i
\(378\) 0 0
\(379\) 3.89565 + 22.0933i 0.200106 + 1.13486i 0.904957 + 0.425503i \(0.139903\pi\)
−0.704851 + 0.709355i \(0.748986\pi\)
\(380\) −4.77259 2.75545i −0.244829 0.141352i
\(381\) 0 0
\(382\) −0.652499 + 0.547512i −0.0333848 + 0.0280131i
\(383\) 25.7936 18.0609i 1.31799 0.922869i 0.318309 0.947987i \(-0.396885\pi\)
0.999684 + 0.0251179i \(0.00799611\pi\)
\(384\) 0 0
\(385\) 2.00931 + 4.30897i 0.102404 + 0.219605i
\(386\) −4.17736 + 11.4772i −0.212622 + 0.584174i
\(387\) 0 0
\(388\) 0.779569 + 8.91051i 0.0395766 + 0.452363i
\(389\) −2.18251 24.9462i −0.110658 1.26482i −0.825043 0.565070i \(-0.808849\pi\)
0.714385 0.699752i \(-0.246706\pi\)
\(390\) 0 0
\(391\) −2.31301 + 6.35495i −0.116974 + 0.321383i
\(392\) −1.68600 3.61565i −0.0851561 0.182618i
\(393\) 0 0
\(394\) −13.1812 + 9.22957i −0.664059 + 0.464979i
\(395\) −22.3653 + 18.7667i −1.12532 + 0.944258i
\(396\) 0 0
\(397\) −3.61960 2.08978i −0.181662 0.104883i 0.406411 0.913690i \(-0.366780\pi\)
−0.588074 + 0.808807i \(0.700113\pi\)
\(398\) −0.183257 1.03930i −0.00918586 0.0520956i
\(399\) 0 0
\(400\) 2.12877 + 5.84874i 0.106438 + 0.292437i
\(401\) 2.65103 2.65103i 0.132386 0.132386i −0.637809 0.770195i \(-0.720159\pi\)
0.770195 + 0.637809i \(0.220159\pi\)
\(402\) 0 0
\(403\) −9.03602 + 51.2458i −0.450116 + 2.55274i
\(404\) 0.271078 0.323058i 0.0134866 0.0160728i
\(405\) 0 0
\(406\) 5.60984i 0.278411i
\(407\) 4.84701 + 1.12148i 0.240257 + 0.0555897i
\(408\) 0 0
\(409\) 0.413946 + 0.0362156i 0.0204683 + 0.00179075i 0.0973853 0.995247i \(-0.468952\pi\)
−0.0769170 + 0.997038i \(0.524508\pi\)
\(410\) −9.34029 7.83744i −0.461284 0.387063i
\(411\) 0 0
\(412\) −2.61301 + 5.60362i −0.128734 + 0.276071i
\(413\) −9.32155 9.32155i −0.458683 0.458683i
\(414\) 0 0
\(415\) −28.9208 7.74929i −1.41966 0.380398i
\(416\) 6.56442 1.15748i 0.321847 0.0567503i
\(417\) 0 0
\(418\) −1.16513 + 0.672690i −0.0569885 + 0.0329023i
\(419\) 9.74603 + 11.6149i 0.476124 + 0.567423i 0.949632 0.313367i \(-0.101457\pi\)
−0.473508 + 0.880790i \(0.657012\pi\)
\(420\) 0 0
\(421\) 6.39946 1.71473i 0.311891 0.0835708i −0.0994784 0.995040i \(-0.531717\pi\)
0.411369 + 0.911469i \(0.365051\pi\)
\(422\) −3.67629 + 1.71428i −0.178959 + 0.0834500i
\(423\) 0 0
\(424\) −3.94805 2.76445i −0.191734 0.134254i
\(425\) −8.33943 + 0.729605i −0.404522 + 0.0353911i
\(426\) 0 0
\(427\) 11.6847 16.6875i 0.565465 0.807567i
\(428\) 14.4676 + 5.26578i 0.699318 + 0.254531i
\(429\) 0 0
\(430\) −9.05123 33.7797i −0.436489 1.62900i
\(431\) 10.7562 + 15.3614i 0.518108 + 0.739935i 0.989899 0.141776i \(-0.0452812\pi\)
−0.471791 + 0.881710i \(0.656392\pi\)
\(432\) 0 0
\(433\) −8.51178 14.7428i −0.409050 0.708495i 0.585734 0.810504i \(-0.300806\pi\)
−0.994784 + 0.102008i \(0.967473\pi\)
\(434\) −6.77262 + 11.7305i −0.325096 + 0.563083i
\(435\) 0 0
\(436\) −2.70725 + 10.1036i −0.129654 + 0.483875i
\(437\) −7.77220 + 2.82885i −0.371795 + 0.135322i
\(438\) 0 0
\(439\) −5.76976 2.69048i −0.275375 0.128410i 0.280025 0.959993i \(-0.409657\pi\)
−0.555400 + 0.831583i \(0.687435\pi\)
\(440\) 2.69851 + 0.475821i 0.128647 + 0.0226839i
\(441\) 0 0
\(442\) −0.781369 + 8.93109i −0.0371659 + 0.424808i
\(443\) −37.3415 −1.77415 −0.887075 0.461626i \(-0.847266\pi\)
−0.887075 + 0.461626i \(0.847266\pi\)
\(444\) 0 0
\(445\) 15.1020 0.715905
\(446\) 0.941890 10.7658i 0.0445998 0.509778i
\(447\) 0 0
\(448\) 1.70874 + 0.301297i 0.0807304 + 0.0142349i
\(449\) −19.1943 8.95045i −0.905835 0.422398i −0.0868558 0.996221i \(-0.527682\pi\)
−0.818979 + 0.573823i \(0.805460\pi\)
\(450\) 0 0
\(451\) −2.79714 + 1.01808i −0.131712 + 0.0479393i
\(452\) 0.529157 1.97484i 0.0248894 0.0928886i
\(453\) 0 0
\(454\) −7.54801 + 13.0735i −0.354245 + 0.613571i
\(455\) 19.3738 + 33.5564i 0.908258 + 1.57315i
\(456\) 0 0
\(457\) −2.18859 3.12562i −0.102378 0.146211i 0.764695 0.644393i \(-0.222890\pi\)
−0.867072 + 0.498182i \(0.834001\pi\)
\(458\) 3.91916 + 14.6265i 0.183130 + 0.683451i
\(459\) 0 0
\(460\) 15.8297 + 5.76153i 0.738063 + 0.268633i
\(461\) 3.94703 5.63695i 0.183832 0.262539i −0.716650 0.697433i \(-0.754325\pi\)
0.900481 + 0.434894i \(0.143214\pi\)
\(462\) 0 0
\(463\) −3.21677 + 0.281431i −0.149496 + 0.0130792i −0.161658 0.986847i \(-0.551684\pi\)
0.0121620 + 0.999926i \(0.496129\pi\)
\(464\) −2.64844 1.85446i −0.122951 0.0860910i
\(465\) 0 0
\(466\) 18.3200 8.54275i 0.848657 0.395735i
\(467\) −31.6040 + 8.46826i −1.46246 + 0.391864i −0.900338 0.435191i \(-0.856681\pi\)
−0.562120 + 0.827056i \(0.690014\pi\)
\(468\) 0 0
\(469\) −6.51712 7.76681i −0.300933 0.358638i
\(470\) 9.04562 5.22249i 0.417243 0.240896i
\(471\) 0 0
\(472\) −7.48221 + 1.31932i −0.344397 + 0.0607264i
\(473\) −8.24664 2.20968i −0.379181 0.101601i
\(474\) 0 0
\(475\) −7.23951 7.23951i −0.332171 0.332171i
\(476\) −0.986253 + 2.11503i −0.0452048 + 0.0969421i
\(477\) 0 0
\(478\) −18.2490 15.3127i −0.834688 0.700386i
\(479\) 12.4516 + 1.08937i 0.568928 + 0.0497748i 0.367991 0.929829i \(-0.380046\pi\)
0.200937 + 0.979604i \(0.435601\pi\)
\(480\) 0 0
\(481\) 40.1484 + 5.66222i 1.83061 + 0.258175i
\(482\) 8.26064i 0.376262i
\(483\) 0 0
\(484\) −6.64067 + 7.91404i −0.301849 + 0.359729i
\(485\) −5.20361 + 29.5111i −0.236284 + 1.34003i
\(486\) 0 0
\(487\) 19.6770 19.6770i 0.891648 0.891648i −0.103030 0.994678i \(-0.532854\pi\)
0.994678 + 0.103030i \(0.0328538\pi\)
\(488\) −4.01564 11.0329i −0.181780 0.499435i
\(489\) 0 0
\(490\) −2.32090 13.1625i −0.104848 0.594620i
\(491\) −29.7687 17.1870i −1.34344 0.775638i −0.356134 0.934435i \(-0.615905\pi\)
−0.987311 + 0.158797i \(0.949239\pi\)
\(492\) 0 0
\(493\) 3.33116 2.79517i 0.150028 0.125888i
\(494\) −8.98166 + 6.28903i −0.404104 + 0.282957i
\(495\) 0 0
\(496\) 3.29921 + 7.07519i 0.148139 + 0.317685i
\(497\) 6.84777 18.8141i 0.307164 0.843927i
\(498\) 0 0
\(499\) −1.75238 20.0298i −0.0784475 0.896659i −0.928833 0.370499i \(-0.879187\pi\)
0.850386 0.526160i \(-0.176369\pi\)
\(500\) 0.357428 + 4.08542i 0.0159847 + 0.182706i
\(501\) 0 0
\(502\) 9.32201 25.6120i 0.416062 1.14312i
\(503\) 1.35987 + 2.91624i 0.0606334 + 0.130029i 0.934290 0.356515i \(-0.116035\pi\)
−0.873656 + 0.486544i \(0.838257\pi\)
\(504\) 0 0
\(505\) 1.15736 0.810390i 0.0515017 0.0360619i
\(506\) 3.15037 2.64348i 0.140051 0.117517i
\(507\) 0 0
\(508\) −12.9789 7.49336i −0.575845 0.332464i
\(509\) 2.19317 + 12.4381i 0.0972105 + 0.551308i 0.994048 + 0.108947i \(0.0347479\pi\)
−0.896837 + 0.442361i \(0.854141\pi\)
\(510\) 0 0
\(511\) −4.03060 11.0740i −0.178303 0.489884i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 1.93714 10.9861i 0.0854438 0.484576i
\(515\) −13.3149 + 15.8680i −0.586722 + 0.699229i
\(516\) 0 0
\(517\) 2.54994i 0.112146i
\(518\) 9.31642 + 4.95939i 0.409340 + 0.217903i
\(519\) 0 0
\(520\) 22.2466 + 1.94633i 0.975580 + 0.0853522i
\(521\) 24.5741 + 20.6201i 1.07661 + 0.903384i 0.995635 0.0933320i \(-0.0297518\pi\)
0.0809762 + 0.996716i \(0.474196\pi\)
\(522\) 0 0
\(523\) −6.24419 + 13.3907i −0.273039 + 0.585535i −0.994238 0.107193i \(-0.965814\pi\)
0.721199 + 0.692728i \(0.243591\pi\)
\(524\) −9.66736 9.66736i −0.422321 0.422321i
\(525\) 0 0
\(526\) 10.3593 + 2.77577i 0.451687 + 0.121029i
\(527\) −10.3402 + 1.82326i −0.450426 + 0.0794223i
\(528\) 0 0
\(529\) 1.97676 1.14128i 0.0859461 0.0496210i
\(530\) −10.3791 12.3694i −0.450841 0.537291i
\(531\) 0 0
\(532\) −2.75687 + 0.738700i −0.119525 + 0.0320267i
\(533\) −21.9862 + 10.2524i −0.952330 + 0.444079i
\(534\) 0 0
\(535\) 42.2524 + 29.5854i 1.82673 + 1.27909i
\(536\) −5.82114 + 0.509284i −0.251435 + 0.0219977i
\(537\) 0 0
\(538\) 8.43503 12.0465i 0.363660 0.519360i
\(539\) −3.06615 1.11599i −0.132069 0.0480690i
\(540\) 0 0
\(541\) −7.38298 27.5537i −0.317419 1.18462i −0.921716 0.387865i \(-0.873213\pi\)
0.604297 0.796759i \(-0.293454\pi\)
\(542\) −11.2933 16.1285i −0.485089 0.692779i
\(543\) 0 0
\(544\) 0.672489 + 1.16479i 0.0288327 + 0.0499398i
\(545\) −17.5218 + 30.3486i −0.750551 + 1.29999i
\(546\) 0 0
\(547\) −8.29393 + 30.9534i −0.354623 + 1.32347i 0.526335 + 0.850277i \(0.323566\pi\)
−0.880958 + 0.473194i \(0.843101\pi\)
\(548\) 19.3051 7.02648i 0.824673 0.300156i
\(549\) 0 0
\(550\) 4.61370 + 2.15141i 0.196729 + 0.0917362i
\(551\) 5.23751 + 0.923514i 0.223125 + 0.0393430i
\(552\) 0 0
\(553\) −1.31785 + 15.0631i −0.0560407 + 0.640548i
\(554\) −4.15168 −0.176388
\(555\) 0 0
\(556\) −12.3855 −0.525263
\(557\) 2.44565 27.9540i 0.103626 1.18445i −0.749233 0.662306i \(-0.769578\pi\)
0.852859 0.522141i \(-0.174867\pi\)
\(558\) 0 0
\(559\) −68.5223 12.0823i −2.89818 0.511028i
\(560\) 5.26837 + 2.45668i 0.222629 + 0.103814i
\(561\) 0 0
\(562\) −7.55497 + 2.74978i −0.318687 + 0.115993i
\(563\) 1.80695 6.74362i 0.0761538 0.284210i −0.917339 0.398108i \(-0.869667\pi\)
0.993492 + 0.113898i \(0.0363337\pi\)
\(564\) 0 0
\(565\) 3.42479 5.93191i 0.144082 0.249557i
\(566\) 10.5705 + 18.3087i 0.444313 + 0.769572i
\(567\) 0 0
\(568\) −6.61857 9.45230i −0.277709 0.396610i
\(569\) 9.55065 + 35.6435i 0.400384 + 1.49425i 0.812413 + 0.583083i \(0.198154\pi\)
−0.412028 + 0.911171i \(0.635180\pi\)
\(570\) 0 0
\(571\) 14.9607 + 5.44523i 0.626084 + 0.227876i 0.635526 0.772079i \(-0.280783\pi\)
−0.00944192 + 0.999955i \(0.503006\pi\)
\(572\) 3.12704 4.46587i 0.130748 0.186728i
\(573\) 0 0
\(574\) −6.29071 + 0.550366i −0.262569 + 0.0229718i
\(575\) 25.6361 + 17.9506i 1.06910 + 0.748591i
\(576\) 0 0
\(577\) 23.2050 10.8207i 0.966035 0.450470i 0.125421 0.992104i \(-0.459972\pi\)
0.840614 + 0.541634i \(0.182194\pi\)
\(578\) 14.6734 3.93173i 0.610333 0.163538i
\(579\) 0 0
\(580\) −6.96256 8.29765i −0.289105 0.344541i
\(581\) −13.4291 + 7.75327i −0.557131 + 0.321660i
\(582\) 0 0
\(583\) −3.88210 + 0.684519i −0.160780 + 0.0283499i
\(584\) −6.56051 1.75788i −0.271476 0.0727417i
\(585\) 0 0
\(586\) 20.9667 + 20.9667i 0.866127 + 0.866127i
\(587\) 1.66266 3.56560i 0.0686255 0.147168i −0.869003 0.494807i \(-0.835239\pi\)
0.937628 + 0.347639i \(0.113017\pi\)
\(588\) 0 0
\(589\) −9.83702 8.25424i −0.405328 0.340110i
\(590\) −25.3570 2.21845i −1.04393 0.0913323i
\(591\) 0 0
\(592\) 5.42111 2.75890i 0.222806 0.113390i
\(593\) 48.1508i 1.97732i −0.150186 0.988658i \(-0.547987\pi\)
0.150186 0.988658i \(-0.452013\pi\)
\(594\) 0 0
\(595\) −5.02555 + 5.98921i −0.206027 + 0.245534i
\(596\) 3.37190 19.1230i 0.138118 0.783308i
\(597\) 0 0
\(598\) 23.6996 23.6996i 0.969147 0.969147i
\(599\) 12.6466 + 34.7463i 0.516726 + 1.41969i 0.874106 + 0.485734i \(0.161448\pi\)
−0.357380 + 0.933959i \(0.616330\pi\)
\(600\) 0 0
\(601\) 1.37685 + 7.80848i 0.0561627 + 0.318514i 0.999927 0.0121053i \(-0.00385335\pi\)
−0.943764 + 0.330620i \(0.892742\pi\)
\(602\) −15.6852 9.05587i −0.639282 0.369090i
\(603\) 0 0
\(604\) −15.0668 + 12.6426i −0.613060 + 0.514419i
\(605\) −28.3521 + 19.8523i −1.15268 + 0.807112i
\(606\) 0 0
\(607\) 7.35163 + 15.7656i 0.298394 + 0.639907i 0.997149 0.0754532i \(-0.0240404\pi\)
−0.698756 + 0.715360i \(0.746263\pi\)
\(608\) −0.562599 + 1.54573i −0.0228164 + 0.0626876i
\(609\) 0 0
\(610\) −3.42827 39.1853i −0.138807 1.58657i
\(611\) −1.81123 20.7024i −0.0732744 0.837530i
\(612\) 0 0
\(613\) −11.8053 + 32.4349i −0.476812 + 1.31003i 0.435372 + 0.900251i \(0.356617\pi\)
−0.912184 + 0.409781i \(0.865605\pi\)
\(614\) 0.427928 + 0.917694i 0.0172698 + 0.0370351i
\(615\) 0 0
\(616\) 1.16248 0.813979i 0.0468378 0.0327962i
\(617\) −5.88742 + 4.94013i −0.237018 + 0.198882i −0.753558 0.657381i \(-0.771664\pi\)
0.516540 + 0.856263i \(0.327220\pi\)
\(618\) 0 0
\(619\) −28.1737 16.2661i −1.13240 0.653790i −0.187860 0.982196i \(-0.560155\pi\)
−0.944537 + 0.328406i \(0.893489\pi\)
\(620\) 4.54159 + 25.7567i 0.182395 + 1.03441i
\(621\) 0 0
\(622\) −7.60775 20.9021i −0.305043 0.838099i
\(623\) 5.53056 5.53056i 0.221577 0.221577i
\(624\) 0 0
\(625\) 3.01819 17.1170i 0.120728 0.684681i
\(626\) 0.195032 0.232430i 0.00779503 0.00928975i
\(627\) 0 0
\(628\) 4.21012i 0.168002i
\(629\) 1.69711 + 8.00323i 0.0676681 + 0.319110i
\(630\) 0 0
\(631\) −45.5685 3.98673i −1.81405 0.158709i −0.870986 0.491308i \(-0.836519\pi\)
−0.943068 + 0.332599i \(0.892074\pi\)
\(632\) 6.67574 + 5.60161i 0.265547 + 0.222820i
\(633\) 0 0
\(634\) 2.04621 4.38811i 0.0812654 0.174274i
\(635\) −35.5032 35.5032i −1.40890 1.40890i
\(636\) 0 0
\(637\) −25.6861 6.88258i −1.01772 0.272698i
\(638\) −2.60420 + 0.459191i −0.103101 + 0.0181795i
\(639\) 0 0
\(640\) 2.90139 1.67512i 0.114688 0.0662149i
\(641\) −11.9478 14.2389i −0.471912 0.562402i 0.476610 0.879115i \(-0.341865\pi\)
−0.948522 + 0.316712i \(0.897421\pi\)
\(642\) 0 0
\(643\) −3.08212 + 0.825851i −0.121547 + 0.0325684i −0.319080 0.947728i \(-0.603374\pi\)
0.197533 + 0.980296i \(0.436707\pi\)
\(644\) 7.90698 3.68709i 0.311579 0.145292i
\(645\) 0 0
\(646\) −1.81229 1.26898i −0.0713036 0.0499273i
\(647\) −26.5704 + 2.32461i −1.04459 + 0.0913897i −0.596511 0.802605i \(-0.703447\pi\)
−0.448078 + 0.893994i \(0.647891\pi\)
\(648\) 0 0
\(649\) −3.56424 + 5.09027i −0.139909 + 0.199810i
\(650\) 38.9859 + 14.1897i 1.52915 + 0.556565i
\(651\) 0 0
\(652\) 5.38837 + 20.1097i 0.211025 + 0.787556i
\(653\) 4.16408 + 5.94692i 0.162953 + 0.232721i 0.892322 0.451400i \(-0.149075\pi\)
−0.729369 + 0.684121i \(0.760186\pi\)
\(654\) 0 0
\(655\) −22.9018 39.6670i −0.894846 1.54992i
\(656\) −1.81970 + 3.15182i −0.0710475 + 0.123058i
\(657\) 0 0
\(658\) 1.40008 5.22517i 0.0545808 0.203698i
\(659\) 32.3747 11.7834i 1.26114 0.459018i 0.376989 0.926218i \(-0.376960\pi\)
0.884151 + 0.467200i \(0.154737\pi\)
\(660\) 0 0
\(661\) −33.1559 15.4608i −1.28961 0.601357i −0.347825 0.937560i \(-0.613080\pi\)
−0.941790 + 0.336203i \(0.890857\pi\)
\(662\) 0.730033 + 0.128724i 0.0283735 + 0.00500302i
\(663\) 0 0
\(664\) −0.778908 + 8.90296i −0.0302275 + 0.345502i
\(665\) −9.56198 −0.370798
\(666\) 0 0
\(667\) −16.2568 −0.629467
\(668\) −0.789044 + 9.01881i −0.0305290 + 0.348948i
\(669\) 0 0
\(670\) −19.2793 3.39946i −0.744824 0.131333i
\(671\) −8.70315 4.05835i −0.335981 0.156671i
\(672\) 0 0
\(673\) 37.0570 13.4876i 1.42844 0.519910i 0.491957 0.870619i \(-0.336282\pi\)
0.936485 + 0.350709i \(0.114059\pi\)
\(674\) 2.25540 8.41725i 0.0868746 0.324220i
\(675\) 0 0
\(676\) 15.7157 27.2203i 0.604448 1.04694i
\(677\) −21.1366 36.6096i −0.812344 1.40702i −0.911220 0.411921i \(-0.864858\pi\)
0.0988759 0.995100i \(-0.468475\pi\)
\(678\) 0 0
\(679\) 8.90173 + 12.7130i 0.341617 + 0.487880i
\(680\) 1.16624 + 4.35246i 0.0447232 + 0.166909i
\(681\) 0 0
\(682\) 5.99992 + 2.18379i 0.229749 + 0.0836217i
\(683\) 5.32225 7.60097i 0.203650 0.290843i −0.704315 0.709887i \(-0.748746\pi\)
0.907966 + 0.419044i \(0.137635\pi\)
\(684\) 0 0
\(685\) 68.5656 5.99871i 2.61976 0.229199i
\(686\) −15.6194 10.9368i −0.596351 0.417570i
\(687\) 0 0
\(688\) −9.46044 + 4.41148i −0.360676 + 0.168186i
\(689\) −31.0317 + 8.31493i −1.18221 + 0.316773i
\(690\) 0 0
\(691\) 8.66544 + 10.3271i 0.329649 + 0.392860i 0.905256 0.424866i \(-0.139679\pi\)
−0.575608 + 0.817726i \(0.695234\pi\)
\(692\) −9.96125 + 5.75113i −0.378670 + 0.218625i
\(693\) 0 0
\(694\) 7.00503 1.23518i 0.265907 0.0468866i
\(695\) −40.0806 10.7396i −1.52034 0.407374i
\(696\) 0 0
\(697\) −3.46124 3.46124i −0.131104 0.131104i
\(698\) 8.86941 19.0205i 0.335712 0.719937i
\(699\) 0 0
\(700\) 8.27285 + 6.94174i 0.312684 + 0.262373i
\(701\) 17.4580 + 1.52738i 0.659381 + 0.0576884i 0.411935 0.911213i \(-0.364853\pi\)
0.247446 + 0.968902i \(0.420409\pi\)
\(702\) 0 0
\(703\) −6.16394 + 7.88165i −0.232477 + 0.297262i
\(704\) 0.817895i 0.0308256i
\(705\) 0 0
\(706\) −15.3106 + 18.2465i −0.576222 + 0.686715i
\(707\) 0.127064 0.720615i 0.00477873 0.0271015i
\(708\) 0 0
\(709\) 11.5743 11.5743i 0.434682 0.434682i −0.455536 0.890217i \(-0.650552\pi\)
0.890217 + 0.455536i \(0.150552\pi\)
\(710\) −13.2221 36.3274i −0.496216 1.36334i
\(711\) 0 0
\(712\) −0.782762 4.43926i −0.0293352 0.166368i
\(713\) 33.9941 + 19.6265i 1.27309 + 0.735018i
\(714\) 0 0
\(715\) 13.9917 11.7405i 0.523261 0.439068i
\(716\) 14.0839 9.86165i 0.526340 0.368547i
\(717\) 0 0
\(718\) −10.5740 22.6760i −0.394618 0.846262i
\(719\) 0.0849192 0.233314i 0.00316695 0.00870113i −0.938099 0.346367i \(-0.887415\pi\)
0.941266 + 0.337666i \(0.109637\pi\)
\(720\) 0 0
\(721\) 0.935004 + 10.6871i 0.0348214 + 0.398010i
\(722\) 1.42013 + 16.2322i 0.0528519 + 0.604100i
\(723\) 0 0
\(724\) 6.55755 18.0167i 0.243710 0.669586i
\(725\) −8.50453 18.2380i −0.315850 0.677343i
\(726\) 0 0
\(727\) 22.6187 15.8378i 0.838882 0.587392i −0.0732381 0.997314i \(-0.523333\pi\)
0.912120 + 0.409923i \(0.134444\pi\)
\(728\) 8.85978 7.43424i 0.328365 0.275531i
\(729\) 0 0
\(730\) −19.7061 11.3773i −0.729354 0.421093i
\(731\) −2.43793 13.8262i −0.0901701 0.511380i
\(732\) 0 0
\(733\) 17.1150 + 47.0230i 0.632156 + 1.73683i 0.675069 + 0.737754i \(0.264114\pi\)
−0.0429139 + 0.999079i \(0.513664\pi\)
\(734\) 3.77911 3.77911i 0.139489 0.139489i
\(735\) 0 0
\(736\) 0.873134 4.95179i 0.0321841 0.182525i
\(737\) −3.07205 + 3.66113i −0.113161 + 0.134860i
\(738\) 0 0
\(739\) 9.81171i 0.360930i 0.983581 + 0.180465i \(0.0577602\pi\)
−0.983581 + 0.180465i \(0.942240\pi\)
\(740\) 19.9354 4.22737i 0.732841 0.155401i
\(741\) 0 0
\(742\) −8.33079 0.728850i −0.305833 0.0267569i
\(743\) −8.68448 7.28714i −0.318603 0.267339i 0.469434 0.882967i \(-0.344458\pi\)
−0.788037 + 0.615628i \(0.788902\pi\)
\(744\) 0 0
\(745\) 27.4934 58.9598i 1.00728 2.16012i
\(746\) 19.8126 + 19.8126i 0.725391 + 0.725391i
\(747\) 0 0
\(748\) 1.06257 + 0.284714i 0.0388513 + 0.0104102i
\(749\) 26.3079 4.63880i 0.961271 0.169498i
\(750\) 0 0
\(751\) 9.74676 5.62729i 0.355664 0.205343i −0.311513 0.950242i \(-0.600836\pi\)
0.667177 + 0.744899i \(0.267502\pi\)
\(752\) −2.00401 2.38828i −0.0730787 0.0870918i
\(753\) 0 0
\(754\) −20.8168 + 5.57784i −0.758103 + 0.203133i
\(755\) −59.7199 + 27.8478i −2.17343 + 1.01349i
\(756\) 0 0
\(757\) −36.7598 25.7395i −1.33606 0.935519i −0.336079 0.941834i \(-0.609101\pi\)
−0.999980 + 0.00631526i \(0.997990\pi\)
\(758\) 22.3488 1.95527i 0.811744 0.0710184i
\(759\) 0 0
\(760\) −3.16093 + 4.51427i −0.114659 + 0.163750i
\(761\) 43.7804 + 15.9348i 1.58704 + 0.577635i 0.976719 0.214521i \(-0.0688190\pi\)
0.610319 + 0.792156i \(0.291041\pi\)
\(762\) 0 0
\(763\) 4.69736 + 17.5308i 0.170056 + 0.634657i
\(764\) 0.488559 + 0.697735i 0.0176755 + 0.0252432i
\(765\) 0 0
\(766\) −15.7441 27.2696i −0.568858 0.985291i
\(767\) −25.3217 + 43.8585i −0.914314 + 1.58364i
\(768\) 0 0
\(769\) −6.23702 + 23.2769i −0.224913 + 0.839385i 0.757527 + 0.652804i \(0.226407\pi\)
−0.982439 + 0.186581i \(0.940259\pi\)
\(770\) 4.46770 1.62611i 0.161005 0.0586009i
\(771\) 0 0
\(772\) 11.0695 + 5.16177i 0.398398 + 0.185776i
\(773\) −19.9357 3.51520i −0.717036 0.126433i −0.196786 0.980447i \(-0.563050\pi\)
−0.520250 + 0.854014i \(0.674161\pi\)
\(774\) 0 0
\(775\) −4.23482 + 48.4042i −0.152119 + 1.73873i
\(776\) 8.94455 0.321091
\(777\) 0 0
\(778\) −25.0415 −0.897781
\(779\) 0.521764 5.96379i 0.0186941 0.213675i
\(780\) 0 0
\(781\) −9.29441 1.63885i −0.332580 0.0586428i
\(782\) 6.12917 + 2.85808i 0.219179 + 0.102205i
\(783\) 0 0
\(784\) −3.74884 + 1.36446i −0.133887 + 0.0487309i