Properties

Label 666.2.bs.a.557.3
Level $666$
Weight $2$
Character 666.557
Analytic conductor $5.318$
Analytic rank $0$
Dimension $72$
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: \(72\)
Relative dimension: \(6\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 557.3
Character \(\chi\) \(=\) 666.557
Dual form 666.2.bs.a.611.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0871557 + 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(2.82596 + 1.31777i) q^{5} +(1.97276 - 0.718026i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\) \(q+(-0.0871557 + 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(2.82596 + 1.31777i) q^{5} +(1.97276 - 0.718026i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-1.55905 + 2.70036i) q^{10} +(1.33922 + 2.31960i) q^{11} +(-0.527495 - 0.753341i) q^{13} +(0.543357 + 2.02783i) q^{14} +(0.939693 + 0.342020i) q^{16} +(2.87989 - 4.11292i) q^{17} +(-2.92670 + 0.256053i) q^{19} +(-2.55420 - 1.78847i) q^{20} +(-2.42750 + 1.13196i) q^{22} +(2.70753 - 0.725480i) q^{23} +(3.03561 + 3.61770i) q^{25} +(0.796448 - 0.459830i) q^{26} +(-2.06747 + 0.364552i) q^{28} +(4.95425 + 1.32749i) q^{29} +(-1.88370 - 1.88370i) q^{31} +(-0.422618 + 0.906308i) q^{32} +(3.84627 + 3.22740i) q^{34} +(6.52114 + 0.570526i) q^{35} +(-1.40496 + 5.91828i) q^{37} -2.93788i q^{38} +(2.00428 - 2.38861i) q^{40} +(0.366974 - 2.08121i) q^{41} +(-6.00144 + 6.00144i) q^{43} +(-0.916083 - 2.51692i) q^{44} +(0.486742 + 2.76045i) q^{46} +(-5.03071 - 2.90448i) q^{47} +(-1.98609 + 1.66652i) q^{49} +(-3.86850 + 2.70876i) q^{50} +(0.388665 + 0.833494i) q^{52} +(-2.29375 + 6.30203i) q^{53} +(0.727896 + 8.31989i) q^{55} +(-0.182972 - 2.09138i) q^{56} +(-1.75423 + 4.81970i) q^{58} +(5.91334 + 12.6812i) q^{59} +(5.22818 - 3.66081i) q^{61} +(2.04071 - 1.71236i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-0.497952 - 2.82403i) q^{65} +(-2.91868 - 8.01901i) q^{67} +(-3.55034 + 3.55034i) q^{68} +(-1.13671 + 6.44660i) q^{70} +(-3.95008 + 4.70753i) q^{71} -9.01662i q^{73} +(-5.77331 - 1.91543i) q^{74} +(2.92670 + 0.256053i) q^{76} +(4.30750 + 3.61442i) q^{77} +(0.222674 - 0.477526i) q^{79} +(2.20483 + 2.20483i) q^{80} +(2.04131 + 0.546967i) q^{82} +(3.14123 - 0.553883i) q^{83} +(13.5583 - 7.82791i) q^{85} +(-5.45554 - 6.50167i) q^{86} +(2.58718 - 0.693233i) q^{88} +(-2.30861 + 1.07652i) q^{89} +(-1.58154 - 1.10741i) q^{91} +(-2.79237 + 0.244301i) q^{92} +(3.33189 - 4.75842i) q^{94} +(-8.60817 - 3.13312i) q^{95} +(-3.13983 - 11.7180i) q^{97} +(-1.48708 - 2.12378i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 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
\(5\) 2.82596 + 1.31777i 1.26381 + 0.589324i 0.934857 0.355023i \(-0.115527\pi\)
0.328951 + 0.944347i \(0.393305\pi\)
\(6\) 0 0
\(7\) 1.97276 0.718026i 0.745634 0.271388i 0.0588664 0.998266i \(-0.481251\pi\)
0.686767 + 0.726877i \(0.259029\pi\)
\(8\) 0.258819 0.965926i 0.0915064 0.341506i
\(9\) 0 0
\(10\) −1.55905 + 2.70036i −0.493015 + 0.853928i
\(11\) 1.33922 + 2.31960i 0.403791 + 0.699387i 0.994180 0.107732i \(-0.0343590\pi\)
−0.590389 + 0.807119i \(0.701026\pi\)
\(12\) 0 0
\(13\) −0.527495 0.753341i −0.146301 0.208939i 0.739313 0.673362i \(-0.235151\pi\)
−0.885613 + 0.464423i \(0.846262\pi\)
\(14\) 0.543357 + 2.02783i 0.145218 + 0.541962i
\(15\) 0 0
\(16\) 0.939693 + 0.342020i 0.234923 + 0.0855050i
\(17\) 2.87989 4.11292i 0.698477 0.997528i −0.300565 0.953761i \(-0.597175\pi\)
0.999042 0.0437671i \(-0.0139359\pi\)
\(18\) 0 0
\(19\) −2.92670 + 0.256053i −0.671432 + 0.0587427i −0.417773 0.908551i \(-0.637189\pi\)
−0.253658 + 0.967294i \(0.581634\pi\)
\(20\) −2.55420 1.78847i −0.571137 0.399914i
\(21\) 0 0
\(22\) −2.42750 + 1.13196i −0.517544 + 0.241335i
\(23\) 2.70753 0.725480i 0.564558 0.151273i 0.0347586 0.999396i \(-0.488934\pi\)
0.529800 + 0.848123i \(0.322267\pi\)
\(24\) 0 0
\(25\) 3.03561 + 3.61770i 0.607122 + 0.723540i
\(26\) 0.796448 0.459830i 0.156196 0.0901800i
\(27\) 0 0
\(28\) −2.06747 + 0.364552i −0.390716 + 0.0688938i
\(29\) 4.95425 + 1.32749i 0.919981 + 0.246508i 0.687577 0.726111i \(-0.258674\pi\)
0.232404 + 0.972619i \(0.425341\pi\)
\(30\) 0 0
\(31\) −1.88370 1.88370i −0.338323 0.338323i 0.517413 0.855736i \(-0.326895\pi\)
−0.855736 + 0.517413i \(0.826895\pi\)
\(32\) −0.422618 + 0.906308i −0.0747091 + 0.160214i
\(33\) 0 0
\(34\) 3.84627 + 3.22740i 0.659629 + 0.553494i
\(35\) 6.52114 + 0.570526i 1.10227 + 0.0964365i
\(36\) 0 0
\(37\) −1.40496 + 5.91828i −0.230974 + 0.972960i
\(38\) 2.93788i 0.476587i
\(39\) 0 0
\(40\) 2.00428 2.38861i 0.316904 0.377672i
\(41\) 0.366974 2.08121i 0.0573117 0.325031i −0.942650 0.333783i \(-0.891675\pi\)
0.999962 + 0.00875197i \(0.00278587\pi\)
\(42\) 0 0
\(43\) −6.00144 + 6.00144i −0.915211 + 0.915211i −0.996676 0.0814648i \(-0.974040\pi\)
0.0814648 + 0.996676i \(0.474040\pi\)
\(44\) −0.916083 2.51692i −0.138105 0.379439i
\(45\) 0 0
\(46\) 0.486742 + 2.76045i 0.0717662 + 0.407007i
\(47\) −5.03071 2.90448i −0.733805 0.423662i 0.0860078 0.996294i \(-0.472589\pi\)
−0.819812 + 0.572632i \(0.805922\pi\)
\(48\) 0 0
\(49\) −1.98609 + 1.66652i −0.283727 + 0.238075i
\(50\) −3.86850 + 2.70876i −0.547089 + 0.383076i
\(51\) 0 0
\(52\) 0.388665 + 0.833494i 0.0538981 + 0.115585i
\(53\) −2.29375 + 6.30203i −0.315071 + 0.865650i 0.676542 + 0.736404i \(0.263478\pi\)
−0.991613 + 0.129246i \(0.958744\pi\)
\(54\) 0 0
\(55\) 0.727896 + 8.31989i 0.0981495 + 1.12185i
\(56\) −0.182972 2.09138i −0.0244507 0.279472i
\(57\) 0 0
\(58\) −1.75423 + 4.81970i −0.230341 + 0.632857i
\(59\) 5.91334 + 12.6812i 0.769851 + 1.65095i 0.759071 + 0.651008i \(0.225654\pi\)
0.0107801 + 0.999942i \(0.496569\pi\)
\(60\) 0 0
\(61\) 5.22818 3.66081i 0.669400 0.468719i −0.188813 0.982013i \(-0.560464\pi\)
0.858213 + 0.513294i \(0.171575\pi\)
\(62\) 2.04071 1.71236i 0.259170 0.217470i
\(63\) 0 0
\(64\) −0.866025 0.500000i −0.108253 0.0625000i
\(65\) −0.497952 2.82403i −0.0617634 0.350278i
\(66\) 0 0
\(67\) −2.91868 8.01901i −0.356574 0.979678i −0.980209 0.197963i \(-0.936567\pi\)
0.623636 0.781715i \(-0.285655\pi\)
\(68\) −3.55034 + 3.55034i −0.430542 + 0.430542i
\(69\) 0 0
\(70\) −1.13671 + 6.44660i −0.135863 + 0.770516i
\(71\) −3.95008 + 4.70753i −0.468789 + 0.558681i −0.947692 0.319187i \(-0.896590\pi\)
0.478903 + 0.877868i \(0.341035\pi\)
\(72\) 0 0
\(73\) 9.01662i 1.05532i −0.849457 0.527658i \(-0.823070\pi\)
0.849457 0.527658i \(-0.176930\pi\)
\(74\) −5.77331 1.91543i −0.671134 0.222664i
\(75\) 0 0
\(76\) 2.92670 + 0.256053i 0.335716 + 0.0293713i
\(77\) 4.30750 + 3.61442i 0.490886 + 0.411902i
\(78\) 0 0
\(79\) 0.222674 0.477526i 0.0250528 0.0537259i −0.893383 0.449296i \(-0.851675\pi\)
0.918436 + 0.395570i \(0.129453\pi\)
\(80\) 2.20483 + 2.20483i 0.246508 + 0.246508i
\(81\) 0 0
\(82\) 2.04131 + 0.546967i 0.225425 + 0.0604024i
\(83\) 3.14123 0.553883i 0.344795 0.0607966i 0.00143059 0.999999i \(-0.499545\pi\)
0.343364 + 0.939202i \(0.388434\pi\)
\(84\) 0 0
\(85\) 13.5583 7.82791i 1.47061 0.849056i
\(86\) −5.45554 6.50167i −0.588287 0.701093i
\(87\) 0 0
\(88\) 2.58718 0.693233i 0.275794 0.0738989i
\(89\) −2.30861 + 1.07652i −0.244712 + 0.114111i −0.541105 0.840955i \(-0.681994\pi\)
0.296393 + 0.955066i \(0.404216\pi\)
\(90\) 0 0
\(91\) −1.58154 1.10741i −0.165790 0.116088i
\(92\) −2.79237 + 0.244301i −0.291125 + 0.0254701i
\(93\) 0 0
\(94\) 3.33189 4.75842i 0.343658 0.490794i
\(95\) −8.60817 3.13312i −0.883179 0.321451i
\(96\) 0 0
\(97\) −3.13983 11.7180i −0.318801 1.18978i −0.920398 0.390982i \(-0.872135\pi\)
0.601597 0.798800i \(-0.294531\pi\)
\(98\) −1.48708 2.12378i −0.150218 0.214534i
\(99\) 0 0
\(100\) −2.36129 4.08987i −0.236129 0.408987i
\(101\) 8.25498 14.2980i 0.821401 1.42271i −0.0832381 0.996530i \(-0.526526\pi\)
0.904639 0.426179i \(-0.140140\pi\)
\(102\) 0 0
\(103\) −1.49274 + 5.57097i −0.147084 + 0.548924i 0.852570 + 0.522613i \(0.175043\pi\)
−0.999654 + 0.0263109i \(0.991624\pi\)
\(104\) −0.864197 + 0.314542i −0.0847415 + 0.0308434i
\(105\) 0 0
\(106\) −6.07813 2.83428i −0.590360 0.275290i
\(107\) −19.4213 3.42449i −1.87752 0.331058i −0.886285 0.463141i \(-0.846722\pi\)
−0.991239 + 0.132083i \(0.957833\pi\)
\(108\) 0 0
\(109\) 0.366026 4.18369i 0.0350589 0.400725i −0.958308 0.285737i \(-0.907762\pi\)
0.993367 0.114988i \(-0.0366829\pi\)
\(110\) −8.35167 −0.796301
\(111\) 0 0
\(112\) 2.09937 0.198372
\(113\) −0.703066 + 8.03608i −0.0661389 + 0.755971i 0.888630 + 0.458624i \(0.151657\pi\)
−0.954769 + 0.297347i \(0.903898\pi\)
\(114\) 0 0
\(115\) 8.60738 + 1.51771i 0.802642 + 0.141527i
\(116\) −4.64847 2.16762i −0.431599 0.201258i
\(117\) 0 0
\(118\) −13.1483 + 4.78560i −1.21040 + 0.440550i
\(119\) 2.72816 10.1816i 0.250090 0.933349i
\(120\) 0 0
\(121\) 1.91296 3.31335i 0.173906 0.301213i
\(122\) 3.19121 + 5.52735i 0.288919 + 0.500422i
\(123\) 0 0
\(124\) 1.52798 + 2.18219i 0.137217 + 0.195966i
\(125\) −0.223892 0.835578i −0.0200256 0.0747364i
\(126\) 0 0
\(127\) 2.16274 + 0.787173i 0.191912 + 0.0698503i 0.436188 0.899855i \(-0.356328\pi\)
−0.244276 + 0.969706i \(0.578550\pi\)
\(128\) 0.573576 0.819152i 0.0506975 0.0724035i
\(129\) 0 0
\(130\) 2.85668 0.249927i 0.250547 0.0219201i
\(131\) −5.84384 4.09190i −0.510578 0.357511i 0.289721 0.957111i \(-0.406437\pi\)
−0.800300 + 0.599600i \(0.795326\pi\)
\(132\) 0 0
\(133\) −5.58983 + 2.60658i −0.484700 + 0.226019i
\(134\) 8.24288 2.20867i 0.712076 0.190800i
\(135\) 0 0
\(136\) −3.22740 3.84627i −0.276747 0.329815i
\(137\) 9.65245 5.57285i 0.824665 0.476120i −0.0273576 0.999626i \(-0.508709\pi\)
0.852022 + 0.523505i \(0.175376\pi\)
\(138\) 0 0
\(139\) −19.7613 + 3.48445i −1.67613 + 0.295547i −0.929261 0.369423i \(-0.879555\pi\)
−0.746870 + 0.664970i \(0.768444\pi\)
\(140\) −6.32300 1.69424i −0.534391 0.143190i
\(141\) 0 0
\(142\) −4.34534 4.34534i −0.364653 0.364653i
\(143\) 1.04102 2.23247i 0.0870543 0.186689i
\(144\) 0 0
\(145\) 12.2512 + 10.2800i 1.01741 + 0.853705i
\(146\) 8.98231 + 0.785850i 0.743381 + 0.0650374i
\(147\) 0 0
\(148\) 2.41132 5.58440i 0.198209 0.459035i
\(149\) 21.9435i 1.79768i 0.438274 + 0.898841i \(0.355590\pi\)
−0.438274 + 0.898841i \(0.644410\pi\)
\(150\) 0 0
\(151\) 7.27082 8.66503i 0.591691 0.705150i −0.384239 0.923234i \(-0.625536\pi\)
0.975930 + 0.218084i \(0.0699806\pi\)
\(152\) −0.510158 + 2.89325i −0.0413793 + 0.234674i
\(153\) 0 0
\(154\) −3.97609 + 3.97609i −0.320403 + 0.320403i
\(155\) −2.84099 7.80555i −0.228194 0.626957i
\(156\) 0 0
\(157\) −3.86195 21.9022i −0.308217 1.74799i −0.607960 0.793968i \(-0.708012\pi\)
0.299742 0.954020i \(-0.403099\pi\)
\(158\) 0.456302 + 0.263446i 0.0363014 + 0.0209586i
\(159\) 0 0
\(160\) −2.38861 + 2.00428i −0.188836 + 0.158452i
\(161\) 4.82039 3.37527i 0.379900 0.266009i
\(162\) 0 0
\(163\) −7.50039 16.0846i −0.587476 1.25985i −0.945344 0.326074i \(-0.894274\pi\)
0.357868 0.933772i \(-0.383504\pi\)
\(164\) −0.722798 + 1.98587i −0.0564410 + 0.155070i
\(165\) 0 0
\(166\) 0.278000 + 3.17755i 0.0215770 + 0.246626i
\(167\) −1.26304 14.4366i −0.0977370 1.11714i −0.873734 0.486403i \(-0.838309\pi\)
0.775997 0.630736i \(-0.217247\pi\)
\(168\) 0 0
\(169\) 4.15699 11.4212i 0.319768 0.878557i
\(170\) 6.61643 + 14.1890i 0.507457 + 1.08825i
\(171\) 0 0
\(172\) 6.95241 4.86813i 0.530116 0.371191i
\(173\) 5.96864 5.00828i 0.453787 0.380773i −0.387052 0.922058i \(-0.626507\pi\)
0.840839 + 0.541285i \(0.182062\pi\)
\(174\) 0 0
\(175\) 8.58614 + 4.95721i 0.649051 + 0.374730i
\(176\) 0.465107 + 2.63775i 0.0350588 + 0.198828i
\(177\) 0 0
\(178\) −0.871218 2.39365i −0.0653005 0.179412i
\(179\) −8.58212 + 8.58212i −0.641458 + 0.641458i −0.950914 0.309456i \(-0.899853\pi\)
0.309456 + 0.950914i \(0.399853\pi\)
\(180\) 0 0
\(181\) −0.181925 + 1.03175i −0.0135224 + 0.0766892i −0.990822 0.135172i \(-0.956841\pi\)
0.977300 + 0.211861i \(0.0679524\pi\)
\(182\) 1.24103 1.47900i 0.0919914 0.109631i
\(183\) 0 0
\(184\) 2.80304i 0.206643i
\(185\) −11.7693 + 14.8734i −0.865296 + 1.09352i
\(186\) 0 0
\(187\) 13.3972 + 1.17210i 0.979697 + 0.0857124i
\(188\) 4.44992 + 3.73393i 0.324544 + 0.272325i
\(189\) 0 0
\(190\) 3.87145 8.30234i 0.280864 0.602315i
\(191\) −16.2499 16.2499i −1.17580 1.17580i −0.980803 0.194999i \(-0.937530\pi\)
−0.194999 0.980803i \(-0.562470\pi\)
\(192\) 0 0
\(193\) 10.1485 + 2.71928i 0.730505 + 0.195738i 0.604854 0.796336i \(-0.293231\pi\)
0.125651 + 0.992075i \(0.459898\pi\)
\(194\) 11.9471 2.10659i 0.857749 0.151244i
\(195\) 0 0
\(196\) 2.24530 1.29633i 0.160379 0.0925947i
\(197\) 16.0720 + 19.1539i 1.14508 + 1.36466i 0.920755 + 0.390142i \(0.127574\pi\)
0.224328 + 0.974514i \(0.427981\pi\)
\(198\) 0 0
\(199\) −0.892139 + 0.239048i −0.0632421 + 0.0169457i −0.290301 0.956935i \(-0.593756\pi\)
0.227059 + 0.973881i \(0.427089\pi\)
\(200\) 4.28010 1.99584i 0.302649 0.141128i
\(201\) 0 0
\(202\) 13.5242 + 9.46972i 0.951557 + 0.666287i
\(203\) 10.7267 0.938466i 0.752868 0.0658674i
\(204\) 0 0
\(205\) 3.77961 5.39784i 0.263979 0.377002i
\(206\) −5.41967 1.97260i −0.377606 0.137437i
\(207\) 0 0
\(208\) −0.238025 0.888323i −0.0165041 0.0615941i
\(209\) −4.51345 6.44588i −0.312202 0.445871i
\(210\) 0 0
\(211\) 8.85635 + 15.3396i 0.609696 + 1.05602i 0.991290 + 0.131695i \(0.0420419\pi\)
−0.381594 + 0.924330i \(0.624625\pi\)
\(212\) 3.35324 5.80798i 0.230301 0.398894i
\(213\) 0 0
\(214\) 5.10413 19.0489i 0.348911 1.30215i
\(215\) −24.8684 + 9.05134i −1.69601 + 0.617296i
\(216\) 0 0
\(217\) −5.06864 2.36355i −0.344082 0.160448i
\(218\) 4.13587 + 0.729266i 0.280117 + 0.0493921i
\(219\) 0 0
\(220\) 0.727896 8.31989i 0.0490748 0.560927i
\(221\) −4.61756 −0.310610
\(222\) 0 0
\(223\) 8.46993 0.567188 0.283594 0.958944i \(-0.408473\pi\)
0.283594 + 0.958944i \(0.408473\pi\)
\(224\) −0.182972 + 2.09138i −0.0122253 + 0.139736i
\(225\) 0 0
\(226\) −7.94423 1.40078i −0.528442 0.0931786i
\(227\) 7.92901 + 3.69736i 0.526267 + 0.245402i 0.667547 0.744567i \(-0.267344\pi\)
−0.141281 + 0.989970i \(0.545122\pi\)
\(228\) 0 0
\(229\) −20.8633 + 7.59364i −1.37869 + 0.501802i −0.921780 0.387712i \(-0.873265\pi\)
−0.456908 + 0.889514i \(0.651043\pi\)
\(230\) −2.26212 + 8.44235i −0.149160 + 0.556672i
\(231\) 0 0
\(232\) 2.56451 4.44186i 0.168368 0.291622i
\(233\) 3.82433 + 6.62394i 0.250540 + 0.433949i 0.963675 0.267079i \(-0.0860583\pi\)
−0.713134 + 0.701027i \(0.752725\pi\)
\(234\) 0 0
\(235\) −10.3892 14.8373i −0.677714 0.967876i
\(236\) −3.62143 13.5154i −0.235735 0.879776i
\(237\) 0 0
\(238\) 9.90512 + 3.60517i 0.642054 + 0.233688i
\(239\) 8.37474 11.9604i 0.541717 0.773652i −0.451205 0.892420i \(-0.649006\pi\)
0.992922 + 0.118768i \(0.0378946\pi\)
\(240\) 0 0
\(241\) −26.4890 + 2.31749i −1.70631 + 0.149283i −0.898152 0.439684i \(-0.855090\pi\)
−0.808157 + 0.588967i \(0.799535\pi\)
\(242\) 3.13401 + 2.19446i 0.201462 + 0.141065i
\(243\) 0 0
\(244\) −5.78445 + 2.69733i −0.370311 + 0.172679i
\(245\) −7.80869 + 2.09233i −0.498879 + 0.133674i
\(246\) 0 0
\(247\) 1.73672 + 2.06974i 0.110505 + 0.131694i
\(248\) −2.30706 + 1.33198i −0.146498 + 0.0845808i
\(249\) 0 0
\(250\) 0.851912 0.150215i 0.0538796 0.00950044i
\(251\) −20.4793 5.48741i −1.29264 0.346363i −0.453979 0.891012i \(-0.649996\pi\)
−0.838664 + 0.544650i \(0.816663\pi\)
\(252\) 0 0
\(253\) 5.30881 + 5.30881i 0.333762 + 0.333762i
\(254\) −0.972672 + 2.08590i −0.0610309 + 0.130881i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) 9.77498 + 0.855200i 0.609747 + 0.0533459i 0.387847 0.921724i \(-0.373219\pi\)
0.221899 + 0.975070i \(0.428774\pi\)
\(258\) 0 0
\(259\) 1.47783 + 12.6842i 0.0918278 + 0.788155i
\(260\) 2.86759i 0.177841i
\(261\) 0 0
\(262\) 4.58565 5.46497i 0.283303 0.337627i
\(263\) 2.26517 12.8464i 0.139676 0.792142i −0.831813 0.555057i \(-0.812697\pi\)
0.971489 0.237086i \(-0.0761923\pi\)
\(264\) 0 0
\(265\) −14.7867 + 14.7867i −0.908337 + 0.908337i
\(266\) −2.10948 5.79574i −0.129340 0.355360i
\(267\) 0 0
\(268\) 1.48185 + 8.40401i 0.0905186 + 0.513357i
\(269\) 9.84514 + 5.68409i 0.600269 + 0.346565i 0.769147 0.639072i \(-0.220681\pi\)
−0.168879 + 0.985637i \(0.554015\pi\)
\(270\) 0 0
\(271\) −18.5306 + 15.5490i −1.12566 + 0.944537i −0.998876 0.0473935i \(-0.984909\pi\)
−0.126780 + 0.991931i \(0.540464\pi\)
\(272\) 4.11292 2.87989i 0.249382 0.174619i
\(273\) 0 0
\(274\) 4.71037 + 10.1014i 0.284564 + 0.610250i
\(275\) −4.32626 + 11.8863i −0.260884 + 0.716772i
\(276\) 0 0
\(277\) −0.0302720 0.346010i −0.00181887 0.0207898i 0.995231 0.0975459i \(-0.0310993\pi\)
−0.997050 + 0.0767561i \(0.975544\pi\)
\(278\) −1.74888 19.9898i −0.104891 1.19891i
\(279\) 0 0
\(280\) 2.23888 6.15127i 0.133799 0.367609i
\(281\) −0.395455 0.848057i −0.0235909 0.0505908i 0.894159 0.447749i \(-0.147774\pi\)
−0.917750 + 0.397158i \(0.869996\pi\)
\(282\) 0 0
\(283\) −8.50619 + 5.95610i −0.505641 + 0.354053i −0.798395 0.602134i \(-0.794317\pi\)
0.292754 + 0.956188i \(0.405428\pi\)
\(284\) 4.70753 3.95008i 0.279340 0.234394i
\(285\) 0 0
\(286\) 2.13324 + 1.23163i 0.126141 + 0.0728278i
\(287\) −0.770414 4.36923i −0.0454761 0.257908i
\(288\) 0 0
\(289\) −2.80794 7.71475i −0.165173 0.453809i
\(290\) −11.3086 + 11.3086i −0.664065 + 0.664065i
\(291\) 0 0
\(292\) −1.56572 + 8.87964i −0.0916268 + 0.519641i
\(293\) −10.9767 + 13.0815i −0.641266 + 0.764231i −0.984570 0.174993i \(-0.944010\pi\)
0.343303 + 0.939225i \(0.388454\pi\)
\(294\) 0 0
\(295\) 43.6290i 2.54018i
\(296\) 5.35299 + 2.88885i 0.311136 + 0.167911i
\(297\) 0 0
\(298\) −21.8600 1.91250i −1.26632 0.110788i
\(299\) −1.97474 1.65700i −0.114202 0.0958270i
\(300\) 0 0
\(301\) −7.53022 + 16.1486i −0.434035 + 0.930790i
\(302\) 7.99836 + 7.99836i 0.460254 + 0.460254i
\(303\) 0 0
\(304\) −2.83778 0.760380i −0.162758 0.0436108i
\(305\) 19.5987 3.45579i 1.12222 0.197878i
\(306\) 0 0
\(307\) 15.4922 8.94445i 0.884189 0.510487i 0.0121515 0.999926i \(-0.496132\pi\)
0.872037 + 0.489440i \(0.162799\pi\)
\(308\) −3.61442 4.30750i −0.205951 0.245443i
\(309\) 0 0
\(310\) 8.02346 2.14988i 0.455702 0.122105i
\(311\) 8.92073 4.15980i 0.505848 0.235881i −0.152904 0.988241i \(-0.548862\pi\)
0.658752 + 0.752360i \(0.271085\pi\)
\(312\) 0 0
\(313\) −4.60506 3.22450i −0.260293 0.182259i 0.436144 0.899877i \(-0.356344\pi\)
−0.696437 + 0.717618i \(0.745233\pi\)
\(314\) 22.1555 1.93835i 1.25031 0.109388i
\(315\) 0 0
\(316\) −0.302213 + 0.431605i −0.0170008 + 0.0242797i
\(317\) −30.0782 10.9476i −1.68936 0.614878i −0.694817 0.719186i \(-0.744515\pi\)
−0.994545 + 0.104309i \(0.966737\pi\)
\(318\) 0 0
\(319\) 3.55560 + 13.2697i 0.199076 + 0.742960i
\(320\) −1.78847 2.55420i −0.0999786 0.142784i
\(321\) 0 0
\(322\) 2.94230 + 5.09622i 0.163968 + 0.284001i
\(323\) −7.37547 + 12.7747i −0.410382 + 0.710803i
\(324\) 0 0
\(325\) 1.12409 4.19517i 0.0623534 0.232706i
\(326\) 16.6771 6.06998i 0.923661 0.336185i
\(327\) 0 0
\(328\) −1.91532 0.893127i −0.105756 0.0493147i
\(329\) −12.0099 2.11767i −0.662126 0.116751i
\(330\) 0 0
\(331\) 0.753073 8.60767i 0.0413926 0.473120i −0.947004 0.321223i \(-0.895906\pi\)
0.988396 0.151897i \(-0.0485383\pi\)
\(332\) −3.18969 −0.175057
\(333\) 0 0
\(334\) 14.4918 0.792954
\(335\) 2.31911 26.5076i 0.126707 1.44826i
\(336\) 0 0
\(337\) 33.5843 + 5.92181i 1.82945 + 0.322582i 0.979060 0.203570i \(-0.0652544\pi\)
0.850391 + 0.526151i \(0.176366\pi\)
\(338\) 11.0155 + 5.13660i 0.599163 + 0.279394i
\(339\) 0 0
\(340\) −14.7117 + 5.35461i −0.797852 + 0.290394i
\(341\) 1.84674 6.89214i 0.100007 0.373230i
\(342\) 0 0
\(343\) −10.0693 + 17.4405i −0.543689 + 0.941696i
\(344\) 4.24366 + 7.35024i 0.228803 + 0.396298i
\(345\) 0 0
\(346\) 4.46902 + 6.38243i 0.240256 + 0.343121i
\(347\) 0.541394 + 2.02051i 0.0290635 + 0.108467i 0.978934 0.204177i \(-0.0654520\pi\)
−0.949870 + 0.312644i \(0.898785\pi\)
\(348\) 0 0
\(349\) 2.20609 + 0.802950i 0.118089 + 0.0429809i 0.400389 0.916345i \(-0.368875\pi\)
−0.282300 + 0.959326i \(0.591097\pi\)
\(350\) −5.68668 + 8.12141i −0.303966 + 0.434108i
\(351\) 0 0
\(352\) −2.66825 + 0.233442i −0.142218 + 0.0124425i
\(353\) 19.6609 + 13.7667i 1.04645 + 0.732729i 0.964547 0.263912i \(-0.0850128\pi\)
0.0818985 + 0.996641i \(0.473902\pi\)
\(354\) 0 0
\(355\) −17.3662 + 8.09800i −0.921703 + 0.429797i
\(356\) 2.46047 0.659282i 0.130405 0.0349419i
\(357\) 0 0
\(358\) −7.80148 9.29744i −0.412321 0.491385i
\(359\) 4.26996 2.46526i 0.225360 0.130111i −0.383070 0.923719i \(-0.625133\pi\)
0.608430 + 0.793608i \(0.291800\pi\)
\(360\) 0 0
\(361\) −10.2113 + 1.80053i −0.537438 + 0.0947648i
\(362\) −1.01197 0.271156i −0.0531878 0.0142516i
\(363\) 0 0
\(364\) 1.36521 + 1.36521i 0.0715566 + 0.0715566i
\(365\) 11.8818 25.4806i 0.621922 1.33372i
\(366\) 0 0
\(367\) 12.7810 + 10.7245i 0.667164 + 0.559817i 0.912224 0.409691i \(-0.134363\pi\)
−0.245061 + 0.969508i \(0.578808\pi\)
\(368\) 2.79237 + 0.244301i 0.145562 + 0.0127351i
\(369\) 0 0
\(370\) −13.7911 13.0208i −0.716964 0.676920i
\(371\) 14.0794i 0.730964i
\(372\) 0 0
\(373\) 4.09324 4.87814i 0.211940 0.252580i −0.649593 0.760283i \(-0.725061\pi\)
0.861533 + 0.507702i \(0.169505\pi\)
\(374\) −2.33528 + 13.2440i −0.120754 + 0.684832i
\(375\) 0 0
\(376\) −4.10756 + 4.10756i −0.211831 + 0.211831i
\(377\) −1.61329 4.43248i −0.0830887 0.228284i
\(378\) 0 0
\(379\) 1.18223 + 6.70474i 0.0607269 + 0.344400i 0.999999 + 0.00122683i \(0.000390514\pi\)
−0.939272 + 0.343173i \(0.888498\pi\)
\(380\) 7.93333 + 4.58031i 0.406971 + 0.234965i
\(381\) 0 0
\(382\) 17.6044 14.7718i 0.900717 0.755791i
\(383\) −15.6041 + 10.9261i −0.797335 + 0.558300i −0.899731 0.436444i \(-0.856238\pi\)
0.102397 + 0.994744i \(0.467349\pi\)
\(384\) 0 0
\(385\) 7.40987 + 15.8905i 0.377642 + 0.809856i
\(386\) −3.59343 + 9.87288i −0.182901 + 0.502516i
\(387\) 0 0
\(388\) 1.05732 + 12.0852i 0.0536772 + 0.613533i
\(389\) −0.304271 3.47784i −0.0154272 0.176333i −0.999999 0.00135294i \(-0.999569\pi\)
0.984572 0.174980i \(-0.0559862\pi\)
\(390\) 0 0
\(391\) 4.81355 13.2251i 0.243432 0.668824i
\(392\) 1.09570 + 2.34974i 0.0553413 + 0.118680i
\(393\) 0 0
\(394\) −20.4817 + 14.3415i −1.03186 + 0.722513i
\(395\) 1.25854 1.05604i 0.0633239 0.0531351i
\(396\) 0 0
\(397\) 27.3753 + 15.8051i 1.37393 + 0.793237i 0.991420 0.130716i \(-0.0417275\pi\)
0.382507 + 0.923953i \(0.375061\pi\)
\(398\) −0.160383 0.909579i −0.00803929 0.0455931i
\(399\) 0 0
\(400\) 1.61521 + 4.43776i 0.0807607 + 0.221888i
\(401\) −9.88686 + 9.88686i −0.493726 + 0.493726i −0.909478 0.415752i \(-0.863518\pi\)
0.415752 + 0.909478i \(0.363518\pi\)
\(402\) 0 0
\(403\) −0.425427 + 2.41271i −0.0211920 + 0.120186i
\(404\) −10.6124 + 12.6474i −0.527986 + 0.629230i
\(405\) 0 0
\(406\) 10.7677i 0.534392i
\(407\) −15.6096 + 4.66695i −0.773740 + 0.231332i
\(408\) 0 0
\(409\) −35.6100 3.11547i −1.76080 0.154050i −0.839618 0.543177i \(-0.817221\pi\)
−0.921184 + 0.389127i \(0.872777\pi\)
\(410\) 5.04789 + 4.23568i 0.249297 + 0.209185i
\(411\) 0 0
\(412\) 2.43745 5.22712i 0.120084 0.257522i
\(413\) 20.7710 + 20.7710i 1.02208 + 1.02208i
\(414\) 0 0
\(415\) 9.60688 + 2.57416i 0.471583 + 0.126360i
\(416\) 0.905688 0.159697i 0.0444050 0.00782980i
\(417\) 0 0
\(418\) 6.81472 3.93448i 0.333319 0.192442i
\(419\) 3.78686 + 4.51301i 0.185000 + 0.220475i 0.850571 0.525860i \(-0.176256\pi\)
−0.665571 + 0.746335i \(0.731812\pi\)
\(420\) 0 0
\(421\) 10.7741 2.88690i 0.525096 0.140699i 0.0134732 0.999909i \(-0.495711\pi\)
0.511623 + 0.859210i \(0.329045\pi\)
\(422\) −16.0532 + 7.48571i −0.781455 + 0.364399i
\(423\) 0 0
\(424\) 5.49363 + 3.84668i 0.266794 + 0.186811i
\(425\) 23.6215 2.06662i 1.14581 0.100246i
\(426\) 0 0
\(427\) 7.68539 10.9759i 0.371922 0.531160i
\(428\) 18.5315 + 6.74493i 0.895756 + 0.326028i
\(429\) 0 0
\(430\) −6.84948 25.5626i −0.330311 1.23274i
\(431\) −2.44990 3.49882i −0.118007 0.168532i 0.755803 0.654800i \(-0.227247\pi\)
−0.873810 + 0.486267i \(0.838358\pi\)
\(432\) 0 0
\(433\) 10.9074 + 18.8921i 0.524174 + 0.907896i 0.999604 + 0.0281424i \(0.00895918\pi\)
−0.475430 + 0.879754i \(0.657707\pi\)
\(434\) 2.79632 4.84336i 0.134227 0.232489i
\(435\) 0 0
\(436\) −1.08696 + 4.05657i −0.0520557 + 0.194275i
\(437\) −7.73836 + 2.81653i −0.370176 + 0.134733i
\(438\) 0 0
\(439\) 7.84924 + 3.66016i 0.374624 + 0.174690i 0.600806 0.799395i \(-0.294847\pi\)
−0.226182 + 0.974085i \(0.572624\pi\)
\(440\) 8.22479 + 1.45025i 0.392102 + 0.0691381i
\(441\) 0 0
\(442\) 0.402447 4.59998i 0.0191424 0.218799i
\(443\) 13.2524 0.629642 0.314821 0.949151i \(-0.398056\pi\)
0.314821 + 0.949151i \(0.398056\pi\)
\(444\) 0 0
\(445\) −7.94265 −0.376518
\(446\) −0.738203 + 8.43770i −0.0349549 + 0.399536i
\(447\) 0 0
\(448\) −2.06747 0.364552i −0.0976790 0.0172234i
\(449\) 8.00777 + 3.73409i 0.377910 + 0.176222i 0.602286 0.798280i \(-0.294257\pi\)
−0.224376 + 0.974503i \(0.572034\pi\)
\(450\) 0 0
\(451\) 5.31905 1.93598i 0.250464 0.0911615i
\(452\) 2.08784 7.79191i 0.0982036 0.366501i
\(453\) 0 0
\(454\) −4.37435 + 7.57659i −0.205298 + 0.355587i
\(455\) −3.01007 5.21359i −0.141114 0.244417i
\(456\) 0 0
\(457\) −8.62766 12.3216i −0.403585 0.576379i 0.564991 0.825097i \(-0.308880\pi\)
−0.968576 + 0.248718i \(0.919991\pi\)
\(458\) −5.74638 21.4458i −0.268511 1.00210i
\(459\) 0 0
\(460\) −8.21307 2.98931i −0.382936 0.139377i
\(461\) 1.62400 2.31931i 0.0756372 0.108021i −0.779551 0.626339i \(-0.784553\pi\)
0.855188 + 0.518318i \(0.173442\pi\)
\(462\) 0 0
\(463\) −36.1930 + 3.16648i −1.68203 + 0.147159i −0.887729 0.460366i \(-0.847718\pi\)
−0.794301 + 0.607524i \(0.792163\pi\)
\(464\) 4.20144 + 2.94188i 0.195047 + 0.136573i
\(465\) 0 0
\(466\) −6.93205 + 3.23247i −0.321121 + 0.149741i
\(467\) 34.6623 9.28773i 1.60398 0.429785i 0.657738 0.753247i \(-0.271513\pi\)
0.946241 + 0.323462i \(0.104847\pi\)
\(468\) 0 0
\(469\) −11.5157 13.7239i −0.531747 0.633711i
\(470\) 15.6863 9.05648i 0.723554 0.417744i
\(471\) 0 0
\(472\) 13.7796 2.42971i 0.634256 0.111836i
\(473\) −21.9582 5.88369i −1.00964 0.270532i
\(474\) 0 0
\(475\) −9.81065 9.81065i −0.450144 0.450144i
\(476\) −4.45474 + 9.55322i −0.204183 + 0.437871i
\(477\) 0 0
\(478\) 11.1849 + 9.38529i 0.511588 + 0.429273i
\(479\) −26.0672 2.28058i −1.19104 0.104203i −0.525652 0.850700i \(-0.676179\pi\)
−0.665388 + 0.746497i \(0.731734\pi\)
\(480\) 0 0
\(481\) 5.19959 2.06345i 0.237081 0.0940852i
\(482\) 26.5902i 1.21115i
\(483\) 0 0
\(484\) −2.45926 + 2.93083i −0.111784 + 0.133219i
\(485\) 6.56856 37.2522i 0.298263 1.69153i
\(486\) 0 0
\(487\) 0.689631 0.689631i 0.0312502 0.0312502i −0.691309 0.722559i \(-0.742966\pi\)
0.722559 + 0.691309i \(0.242966\pi\)
\(488\) −2.18292 5.99752i −0.0988161 0.271495i
\(489\) 0 0
\(490\) −1.40380 7.96134i −0.0634172 0.359657i
\(491\) 37.2091 + 21.4827i 1.67922 + 0.969501i 0.962157 + 0.272497i \(0.0878496\pi\)
0.717068 + 0.697003i \(0.245484\pi\)
\(492\) 0 0
\(493\) 19.7276 16.5534i 0.888484 0.745527i
\(494\) −2.21323 + 1.54972i −0.0995778 + 0.0697251i
\(495\) 0 0
\(496\) −1.12584 2.41437i −0.0505516 0.108408i
\(497\) −4.41245 + 12.1231i −0.197925 + 0.543795i
\(498\) 0 0
\(499\) −1.11174 12.7072i −0.0497682 0.568854i −0.979612 0.200899i \(-0.935614\pi\)
0.929844 0.367955i \(-0.119942\pi\)
\(500\) 0.0753944 + 0.861762i 0.00337174 + 0.0385392i
\(501\) 0 0
\(502\) 7.25142 19.9231i 0.323647 0.889212i
\(503\) 4.67196 + 10.0191i 0.208313 + 0.446728i 0.982508 0.186219i \(-0.0596232\pi\)
−0.774196 + 0.632946i \(0.781845\pi\)
\(504\) 0 0
\(505\) 42.1697 29.5276i 1.87653 1.31396i
\(506\) −5.75130 + 4.82591i −0.255676 + 0.214538i
\(507\) 0 0
\(508\) −1.99319 1.15077i −0.0884336 0.0510571i
\(509\) −3.73654 21.1910i −0.165619 0.939273i −0.948424 0.317005i \(-0.897323\pi\)
0.782805 0.622268i \(-0.213788\pi\)
\(510\) 0 0
\(511\) −6.47417 17.7876i −0.286400 0.786879i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) −1.70389 + 9.66325i −0.0751554 + 0.426228i
\(515\) −11.5597 + 13.7763i −0.509379 + 0.607054i
\(516\) 0 0
\(517\) 15.5590i 0.684284i
\(518\) −12.7647 + 0.366707i −0.560848 + 0.0161122i
\(519\) 0 0
\(520\) −2.85668 0.249927i −0.125274 0.0109600i
\(521\) −0.350028 0.293708i −0.0153350 0.0128676i 0.635088 0.772440i \(-0.280964\pi\)
−0.650423 + 0.759572i \(0.725408\pi\)
\(522\) 0 0
\(523\) −7.60898 + 16.3175i −0.332717 + 0.713515i −0.999496 0.0317411i \(-0.989895\pi\)
0.666779 + 0.745256i \(0.267673\pi\)
\(524\) 5.04451 + 5.04451i 0.220370 + 0.220370i
\(525\) 0 0
\(526\) 12.6001 + 3.37618i 0.549390 + 0.147209i
\(527\) −13.1724 + 2.32265i −0.573798 + 0.101176i
\(528\) 0 0
\(529\) −13.1142 + 7.57149i −0.570183 + 0.329195i
\(530\) −13.4416 16.0191i −0.583868 0.695827i
\(531\) 0 0
\(532\) 5.95754 1.59632i 0.258292 0.0692092i
\(533\) −1.76144 + 0.821373i −0.0762964 + 0.0355776i
\(534\) 0 0
\(535\) −50.3710 35.2702i −2.17773 1.52486i
\(536\) −8.50118 + 0.743757i −0.367195 + 0.0321254i
\(537\) 0 0
\(538\) −6.52052 + 9.31227i −0.281120 + 0.401481i
\(539\) −6.52549 2.37508i −0.281073 0.102302i
\(540\) 0 0
\(541\) 8.95812 + 33.4321i 0.385139 + 1.43736i 0.837947 + 0.545752i \(0.183756\pi\)
−0.452807 + 0.891608i \(0.649577\pi\)
\(542\) −13.8748 19.8153i −0.595975 0.851140i
\(543\) 0 0
\(544\) 2.51047 + 4.34826i 0.107636 + 0.186430i
\(545\) 6.54751 11.3406i 0.280465 0.485779i
\(546\) 0 0
\(547\) 7.37760 27.5336i 0.315444 1.17725i −0.608132 0.793836i \(-0.708081\pi\)
0.923576 0.383416i \(-0.125252\pi\)
\(548\) −10.4735 + 3.81205i −0.447407 + 0.162843i
\(549\) 0 0
\(550\) −11.4640 5.34576i −0.488828 0.227944i
\(551\) −14.8395 2.61661i −0.632185 0.111471i
\(552\) 0 0
\(553\) 0.0964065 1.10193i 0.00409962 0.0468589i
\(554\) 0.347332 0.0147567
\(555\) 0 0
\(556\) 20.0662 0.850994
\(557\) 1.56837 17.9266i 0.0664540 0.759573i −0.887732 0.460360i \(-0.847720\pi\)
0.954186 0.299213i \(-0.0967241\pi\)
\(558\) 0 0
\(559\) 7.68686 + 1.35540i 0.325120 + 0.0573274i
\(560\) 5.93274 + 2.76648i 0.250704 + 0.116905i
\(561\) 0 0
\(562\) 0.879296 0.320037i 0.0370908 0.0135000i
\(563\) −4.39452 + 16.4006i −0.185207 + 0.691201i 0.809379 + 0.587286i \(0.199804\pi\)
−0.994586 + 0.103915i \(0.966863\pi\)
\(564\) 0 0
\(565\) −12.5765 + 21.7832i −0.529099 + 0.916426i
\(566\) −5.19207 8.99293i −0.218239 0.378001i
\(567\) 0 0
\(568\) 3.52477 + 5.03389i 0.147896 + 0.211217i
\(569\) 0.0672038 + 0.250808i 0.00281733 + 0.0105144i 0.967320 0.253558i \(-0.0816009\pi\)
−0.964503 + 0.264072i \(0.914934\pi\)
\(570\) 0 0
\(571\) −43.2375 15.7372i −1.80943 0.658579i −0.997161 0.0752988i \(-0.976009\pi\)
−0.812271 0.583280i \(-0.801769\pi\)
\(572\) −1.41287 + 2.01778i −0.0590749 + 0.0843677i
\(573\) 0 0
\(574\) 4.41975 0.386678i 0.184477 0.0161396i
\(575\) 10.8436 + 7.59274i 0.452208 + 0.316639i
\(576\) 0 0
\(577\) 37.8768 17.6623i 1.57683 0.735289i 0.579985 0.814627i \(-0.303058\pi\)
0.996848 + 0.0793374i \(0.0252804\pi\)
\(578\) 7.93012 2.12487i 0.329849 0.0883829i
\(579\) 0 0
\(580\) −10.2800 12.2512i −0.426853 0.508703i
\(581\) 5.79919 3.34817i 0.240591 0.138905i
\(582\) 0 0
\(583\) −17.6900 + 3.11923i −0.732647 + 0.129185i
\(584\) −8.70939 2.33367i −0.360397 0.0965681i
\(585\) 0 0
\(586\) −12.0751 12.0751i −0.498817 0.498817i
\(587\) 11.5283 24.7225i 0.475823 1.02041i −0.511146 0.859494i \(-0.670779\pi\)
0.986969 0.160912i \(-0.0514435\pi\)
\(588\) 0 0
\(589\) 5.99537 + 5.03071i 0.247035 + 0.207287i
\(590\) −43.4629 3.80251i −1.78934 0.156547i
\(591\) 0 0
\(592\) −3.34441 + 5.08084i −0.137454 + 0.208821i
\(593\) 8.69991i 0.357263i 0.983916 + 0.178631i \(0.0571669\pi\)
−0.983916 + 0.178631i \(0.942833\pi\)
\(594\) 0 0
\(595\) 21.1267 25.1778i 0.866111 1.03219i
\(596\) 3.81045 21.6101i 0.156082 0.885186i
\(597\) 0 0
\(598\) 1.82281 1.82281i 0.0745402 0.0745402i
\(599\) 11.1752 + 30.7035i 0.456605 + 1.25451i 0.927997 + 0.372589i \(0.121530\pi\)
−0.471391 + 0.881924i \(0.656248\pi\)
\(600\) 0 0
\(601\) −5.74854 32.6016i −0.234488 1.32985i −0.843690 0.536831i \(-0.819621\pi\)
0.609202 0.793015i \(-0.291490\pi\)
\(602\) −15.4309 8.90901i −0.628915 0.363104i
\(603\) 0 0
\(604\) −8.66503 + 7.27082i −0.352575 + 0.295845i
\(605\) 9.77218 6.84255i 0.397296 0.278189i
\(606\) 0 0
\(607\) 12.8041 + 27.4585i 0.519703 + 1.11451i 0.974598 + 0.223962i \(0.0718990\pi\)
−0.454895 + 0.890545i \(0.650323\pi\)
\(608\) 1.00481 2.76071i 0.0407506 0.111961i
\(609\) 0 0
\(610\) 1.73449 + 19.8253i 0.0702276 + 0.802705i
\(611\) 0.465609 + 5.32194i 0.0188365 + 0.215303i
\(612\) 0 0
\(613\) 15.1841 41.7181i 0.613282 1.68498i −0.109574 0.993979i \(-0.534949\pi\)
0.722856 0.690999i \(-0.242829\pi\)
\(614\) 7.56017 + 16.2128i 0.305104 + 0.654297i
\(615\) 0 0
\(616\) 4.60613 3.22525i 0.185586 0.129949i
\(617\) −27.7168 + 23.2571i −1.11583 + 0.936296i −0.998387 0.0567827i \(-0.981916\pi\)
−0.117448 + 0.993079i \(0.537471\pi\)
\(618\) 0 0
\(619\) 26.5570 + 15.3327i 1.06742 + 0.616274i 0.927475 0.373886i \(-0.121975\pi\)
0.139943 + 0.990160i \(0.455308\pi\)
\(620\) 1.44241 + 8.18030i 0.0579285 + 0.328529i
\(621\) 0 0
\(622\) 3.36648 + 9.24933i 0.134984 + 0.370864i
\(623\) −3.78137 + 3.78137i −0.151497 + 0.151497i
\(624\) 0 0
\(625\) 4.56871 25.9105i 0.182749 1.03642i
\(626\) 3.61358 4.30650i 0.144428 0.172122i
\(627\) 0 0
\(628\) 22.2401i 0.887477i
\(629\) 20.2953 + 22.8225i 0.809225 + 0.909994i
\(630\) 0 0
\(631\) 1.73147 + 0.151484i 0.0689289 + 0.00603049i 0.121568 0.992583i \(-0.461208\pi\)
−0.0526391 + 0.998614i \(0.516763\pi\)
\(632\) −0.403623 0.338680i −0.0160553 0.0134720i
\(633\) 0 0
\(634\) 13.5274 29.0096i 0.537242 1.15212i
\(635\) 5.07451 + 5.07451i 0.201376 + 0.201376i
\(636\) 0 0
\(637\) 2.30311 + 0.617117i 0.0912526 + 0.0244511i
\(638\) −13.5291 + 2.38554i −0.535622 + 0.0944445i
\(639\) 0 0
\(640\) 2.70036 1.55905i 0.106741 0.0616269i
\(641\) 6.24611 + 7.44382i 0.246706 + 0.294013i 0.875160 0.483834i \(-0.160756\pi\)
−0.628453 + 0.777847i \(0.716312\pi\)
\(642\) 0 0
\(643\) 32.9105 8.81835i 1.29786 0.347762i 0.457222 0.889352i \(-0.348844\pi\)
0.840642 + 0.541591i \(0.182178\pi\)
\(644\) −5.33327 + 2.48694i −0.210160 + 0.0979993i
\(645\) 0 0
\(646\) −12.0833 8.46079i −0.475410 0.332885i
\(647\) −31.7137 + 2.77459i −1.24679 + 0.109080i −0.691378 0.722493i \(-0.742996\pi\)
−0.555415 + 0.831573i \(0.687441\pi\)
\(648\) 0 0
\(649\) −21.4960 + 30.6995i −0.843794 + 1.20506i
\(650\) 4.08123 + 1.48545i 0.160079 + 0.0582640i
\(651\) 0 0
\(652\) 4.59337 + 17.1427i 0.179890 + 0.671360i
\(653\) −2.69304 3.84606i −0.105387 0.150508i 0.762995 0.646405i \(-0.223728\pi\)
−0.868381 + 0.495897i \(0.834839\pi\)
\(654\) 0 0
\(655\) −11.1223 19.2644i −0.434584 0.752721i
\(656\) 1.05666 1.83019i 0.0412556 0.0714568i
\(657\) 0 0
\(658\) 3.15634 11.7796i 0.123047 0.459217i
\(659\) 27.0882 9.85932i 1.05521 0.384064i 0.244582 0.969629i \(-0.421349\pi\)
0.810626 + 0.585564i \(0.199127\pi\)
\(660\) 0 0
\(661\) −27.7552 12.9425i −1.07955 0.503403i −0.200288 0.979737i \(-0.564188\pi\)
−0.879265 + 0.476334i \(0.841965\pi\)
\(662\) 8.50928 + 1.50041i 0.330722 + 0.0583153i
\(663\) 0 0
\(664\) 0.278000 3.17755i 0.0107885 0.123313i
\(665\) −19.2315 −0.745766
\(666\) 0 0
\(667\) 14.3768 0.556673
\(668\) −1.26304 + 14.4366i −0.0488685 + 0.558570i
\(669\) 0 0
\(670\) 26.2046 + 4.62057i 1.01237 + 0.178508i
\(671\) 15.4933 + 7.22466i 0.598113 + 0.278905i
\(672\) 0 0
\(673\) 13.9137 5.06416i 0.536332 0.195209i −0.0596314 0.998220i \(-0.518993\pi\)
0.595963 + 0.803012i \(0.296770\pi\)
\(674\) −8.82634 + 32.9403i −0.339978 + 1.26881i
\(675\) 0 0
\(676\) −6.07711 + 10.5259i −0.233735 + 0.404841i
\(677\) 16.1053 + 27.8952i 0.618977 + 1.07210i 0.989673 + 0.143345i \(0.0457860\pi\)
−0.370696 + 0.928754i \(0.620881\pi\)
\(678\) 0 0
\(679\) −14.6080 20.8623i −0.560602 0.800622i
\(680\) −4.05202 15.1224i −0.155388 0.579916i
\(681\) 0 0
\(682\) 6.70496 + 2.44041i 0.256746 + 0.0934480i
\(683\) 5.46876 7.81020i 0.209256 0.298849i −0.700780 0.713377i \(-0.747165\pi\)
0.910036 + 0.414528i \(0.136053\pi\)
\(684\) 0 0
\(685\) 34.6212 3.02896i 1.32281 0.115731i
\(686\) −16.4965 11.5510i −0.629839 0.441018i
\(687\) 0 0
\(688\) −7.69213 + 3.58690i −0.293260 + 0.136749i
\(689\) 5.95752 1.59631i 0.226963 0.0608146i
\(690\) 0 0
\(691\) 22.0361 + 26.2616i 0.838292 + 0.999037i 0.999926 + 0.0121863i \(0.00387911\pi\)
−0.161634 + 0.986851i \(0.551676\pi\)
\(692\) −6.74764 + 3.89575i −0.256507 + 0.148094i
\(693\) 0 0
\(694\) −2.06001 + 0.363234i −0.0781967 + 0.0137882i
\(695\) −60.4364 16.1939i −2.29248 0.614269i
\(696\) 0 0
\(697\) −7.50301 7.50301i −0.284197 0.284197i
\(698\) −0.992168 + 2.12771i −0.0375541 + 0.0805350i
\(699\) 0 0
\(700\) −7.59488 6.37286i −0.287060 0.240872i
\(701\) −46.0964 4.03291i −1.74104 0.152321i −0.828143 0.560517i \(-0.810603\pi\)
−0.912894 + 0.408196i \(0.866158\pi\)
\(702\) 0 0
\(703\) 2.59651 17.6808i 0.0979293 0.666844i
\(704\) 2.67845i 0.100948i
\(705\) 0 0
\(706\) −15.4279 + 18.3863i −0.580637 + 0.691976i
\(707\) 6.01873 34.1339i 0.226358 1.28374i
\(708\) 0 0
\(709\) −11.3364 + 11.3364i −0.425749 + 0.425749i −0.887177 0.461428i \(-0.847337\pi\)
0.461428 + 0.887177i \(0.347337\pi\)
\(710\) −6.55362 18.0059i −0.245953 0.675750i
\(711\) 0 0
\(712\) 0.442329 + 2.50857i 0.0165770 + 0.0940127i
\(713\) −6.46676 3.73359i −0.242182 0.139824i
\(714\) 0 0
\(715\) 5.88375 4.93705i 0.220040 0.184635i
\(716\) 9.94200 6.96147i 0.371550 0.260162i
\(717\) 0 0
\(718\) 2.08373 + 4.46857i 0.0777641 + 0.166766i
\(719\) 5.95733 16.3676i 0.222171 0.610409i −0.777662 0.628682i \(-0.783595\pi\)
0.999833 + 0.0182729i \(0.00581678\pi\)
\(720\) 0 0
\(721\) 1.05529 + 12.0620i 0.0393010 + 0.449213i
\(722\) −0.903705 10.3294i −0.0336324 0.384420i
\(723\) 0 0
\(724\) 0.358322 0.984483i 0.0133169 0.0365880i
\(725\) 10.2367 + 21.9527i 0.380182 + 0.815303i
\(726\) 0 0
\(727\) 0.525227 0.367768i 0.0194796 0.0136398i −0.563796 0.825914i \(-0.690660\pi\)
0.583276 + 0.812274i \(0.301771\pi\)
\(728\) −1.47900 + 1.24103i −0.0548156 + 0.0459957i
\(729\) 0 0
\(730\) 24.3481 + 14.0574i 0.901163 + 0.520287i
\(731\) 7.39990 + 41.9669i 0.273695 + 1.55220i
\(732\) 0 0
\(733\) −5.99689 16.4763i −0.221500 0.608567i 0.778313 0.627876i \(-0.216076\pi\)
−0.999814 + 0.0193090i \(0.993853\pi\)
\(734\) −11.7977 + 11.7977i −0.435460 + 0.435460i
\(735\) 0 0
\(736\) −0.486742 + 2.76045i −0.0179416 + 0.101752i
\(737\) 14.6922 17.5094i 0.541193 0.644968i
\(738\) 0 0
\(739\) 40.3640i 1.48482i 0.669949 + 0.742408i \(0.266316\pi\)
−0.669949 + 0.742408i \(0.733684\pi\)
\(740\) 14.1732 12.6038i 0.521018 0.463323i
\(741\) 0 0
\(742\) −14.0258 1.22710i −0.514903 0.0450482i
\(743\) 5.88578 + 4.93876i 0.215928 + 0.181185i 0.744336 0.667805i \(-0.232766\pi\)
−0.528407 + 0.848991i \(0.677211\pi\)
\(744\) 0 0
\(745\) −28.9165 + 62.0115i −1.05942 + 2.27193i
\(746\) 4.50283 + 4.50283i 0.164860 + 0.164860i
\(747\) 0 0
\(748\) −12.9901 3.48068i −0.474965 0.127266i
\(749\) −40.7724 + 7.18927i −1.48979 + 0.262690i
\(750\) 0 0
\(751\) 2.63599 1.52189i 0.0961885 0.0555345i −0.451134 0.892456i \(-0.648980\pi\)
0.547323 + 0.836922i \(0.315647\pi\)
\(752\) −3.73393 4.44992i −0.136162 0.162272i
\(753\) 0 0
\(754\) 4.55622 1.22084i 0.165928 0.0444602i
\(755\) 31.9656 14.9058i 1.16335 0.542477i
\(756\) 0 0
\(757\) −21.5392 15.0819i −0.782857 0.548162i 0.112426 0.993660i \(-0.464138\pi\)
−0.895283 + 0.445498i \(0.853027\pi\)
\(758\) −6.78227 + 0.593372i −0.246343 + 0.0215522i
\(759\) 0 0
\(760\) −5.25432 + 7.50394i −0.190594 + 0.272197i
\(761\) −3.54295 1.28953i −0.128432 0.0467453i 0.277005 0.960869i \(-0.410658\pi\)
−0.405436 + 0.914123i \(0.632880\pi\)
\(762\) 0 0
\(763\) −2.28192 8.51624i −0.0826111 0.308309i
\(764\) 13.1813 + 18.8248i 0.476882 + 0.681058i
\(765\) 0 0
\(766\) −9.52457 16.4970i −0.344137 0.596062i
\(767\) 6.43400 11.1440i 0.232318 0.402387i
\(768\) 0 0
\(769\) 4.44019 16.5710i 0.160117 0.597566i −0.838495 0.544909i \(-0.816564\pi\)
0.998613 0.0526572i \(-0.0167691\pi\)
\(770\) −16.4759 + 5.99672i −0.593749 + 0.216107i
\(771\) 0 0
\(772\) −9.52212 4.44024i −0.342709 0.159808i
\(773\) −29.9348 5.27830i −1.07668 0.189847i −0.392932 0.919567i \(-0.628539\pi\)
−0.683746 + 0.729720i \(0.739650\pi\)
\(774\) 0 0
\(775\) 1.09648 12.5329i 0.0393868 0.450193i
\(776\) −12.1314 −0.435490
\(777\) 0 0
\(778\) 3.49112 0.125163
\(779\) −0.541122 + 6.18506i −0.0193877 + 0.221603i
\(780\) 0 0
\(781\) −16.2096 2.85820i −0.580027 0.102274i
\(782\) 12.7553 + 5.94788i 0.456128 + 0.212696i
\(783\) 0 0
\(784\) −2.43630 + 0.886739i −0.0870105 + 0.0316692i