Properties

Label 81.2.g.a.58.5
Level $81$
Weight $2$
Character 81.58
Analytic conductor $0.647$
Analytic rank $0$
Dimension $144$
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] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.g (of order \(27\), degree \(18\), 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: \(0.646788256372\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 58.5
Character \(\chi\) \(=\) 81.58
Dual form 81.2.g.a.7.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.120683 + 0.162105i) q^{2} +(1.25647 - 1.19218i) q^{3} +(0.561893 + 1.87685i) q^{4} +(-0.761396 - 0.500778i) q^{5} +(0.0416250 + 0.347556i) q^{6} +(-0.112573 - 0.119321i) q^{7} +(-0.751874 - 0.273660i) q^{8} +(0.157410 - 2.99587i) q^{9} +O(q^{10})\) \(q+(-0.120683 + 0.162105i) q^{2} +(1.25647 - 1.19218i) q^{3} +(0.561893 + 1.87685i) q^{4} +(-0.761396 - 0.500778i) q^{5} +(0.0416250 + 0.347556i) q^{6} +(-0.112573 - 0.119321i) q^{7} +(-0.751874 - 0.273660i) q^{8} +(0.157410 - 2.99587i) q^{9} +(0.173067 - 0.0629911i) q^{10} +(-0.670227 - 0.336601i) q^{11} +(2.94355 + 1.68832i) q^{12} +(-1.39965 + 3.24476i) q^{13} +(0.0329282 - 0.00384876i) q^{14} +(-1.55369 + 0.278512i) q^{15} +(-3.13860 + 2.06429i) q^{16} +(-3.09332 - 2.59561i) q^{17} +(0.466650 + 0.387068i) q^{18} +(1.63194 - 1.36936i) q^{19} +(0.512064 - 1.71041i) q^{20} +(-0.283696 - 0.0157146i) q^{21} +(0.135450 - 0.0680255i) q^{22} +(-5.63041 + 5.96789i) q^{23} +(-1.27096 + 0.552526i) q^{24} +(-1.65145 - 3.82850i) q^{25} +(-0.357079 - 0.618479i) q^{26} +(-3.37383 - 3.95187i) q^{27} +(0.160693 - 0.278329i) q^{28} +(6.53664 + 0.764024i) q^{29} +(0.142355 - 0.285473i) q^{30} +(5.44474 + 1.29043i) q^{31} +(0.137190 - 2.35546i) q^{32} +(-1.24341 + 0.376105i) q^{33} +(0.794074 - 0.188199i) q^{34} +(0.0259597 + 0.147225i) q^{35} +(5.71125 - 1.38792i) q^{36} +(0.783915 - 4.44580i) q^{37} +(0.0250334 + 0.429806i) q^{38} +(2.10972 + 5.74556i) q^{39} +(0.435431 + 0.584886i) q^{40} +(6.53505 + 8.77810i) q^{41} +(0.0367848 - 0.0440923i) q^{42} +(0.201195 + 3.45438i) q^{43} +(0.255154 - 1.44705i) q^{44} +(-1.62012 + 2.20221i) q^{45} +(-0.287932 - 1.63294i) q^{46} +(8.68990 - 2.05954i) q^{47} +(-1.48254 + 6.33549i) q^{48} +(0.405449 - 6.96129i) q^{49} +(0.819923 + 0.194325i) q^{50} +(-6.98109 + 0.426511i) q^{51} +(-6.87639 - 0.803734i) q^{52} +(3.06986 - 5.31715i) q^{53} +(1.04778 - 0.0699940i) q^{54} +(0.341746 + 0.591922i) q^{55} +(0.0519877 + 0.120521i) q^{56} +(0.417952 - 3.66613i) q^{57} +(-0.912715 + 0.967421i) q^{58} +(-2.60584 + 1.30870i) q^{59} +(-1.39573 - 2.75955i) q^{60} +(2.02529 - 6.76493i) q^{61} +(-0.866274 + 0.726890i) q^{62} +(-0.375189 + 0.318472i) q^{63} +(-5.39019 - 4.52290i) q^{64} +(2.69059 - 1.76963i) q^{65} +(0.0890894 - 0.246952i) q^{66} +(-8.82173 + 1.03111i) q^{67} +(3.13345 - 7.26416i) q^{68} +(0.0403837 + 14.2109i) q^{69} +(-0.0269988 - 0.0135593i) q^{70} +(-8.94644 + 3.25624i) q^{71} +(-0.938201 + 2.20944i) q^{72} +(8.28233 + 3.01452i) q^{73} +(0.626083 + 0.663610i) q^{74} +(-6.63926 - 2.84155i) q^{75} +(3.48707 + 2.29348i) q^{76} +(0.0352862 + 0.117864i) q^{77} +(-1.18600 - 0.351395i) q^{78} +(-1.92557 + 2.58649i) q^{79} +3.42347 q^{80} +(-8.95044 - 0.943160i) q^{81} -2.21165 q^{82} +(-10.0492 + 13.4985i) q^{83} +(-0.129913 - 0.541286i) q^{84} +(1.05542 + 3.52535i) q^{85} +(-0.584255 - 0.384271i) q^{86} +(9.12392 - 6.83289i) q^{87} +(0.411812 + 0.436496i) q^{88} +(10.7409 + 3.90935i) q^{89} +(-0.161470 - 0.528400i) q^{90} +(0.544730 - 0.198266i) q^{91} +(-14.3645 - 7.21414i) q^{92} +(8.37955 - 4.86974i) q^{93} +(-0.714861 + 1.65723i) q^{94} +(-1.92830 + 0.225386i) q^{95} +(-2.63576 - 3.12311i) q^{96} +(3.78511 - 2.48950i) q^{97} +(1.07953 + 0.905836i) q^{98} +(-1.11391 + 1.95493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{19}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.120683 + 0.162105i −0.0853358 + 0.114626i −0.842741 0.538319i \(-0.819059\pi\)
0.757405 + 0.652945i \(0.226467\pi\)
\(3\) 1.25647 1.19218i 0.725421 0.688306i
\(4\) 0.561893 + 1.87685i 0.280946 + 0.938426i
\(5\) −0.761396 0.500778i −0.340507 0.223955i 0.367725 0.929934i \(-0.380137\pi\)
−0.708232 + 0.705980i \(0.750507\pi\)
\(6\) 0.0416250 + 0.347556i 0.0169933 + 0.141889i
\(7\) −0.112573 0.119321i −0.0425487 0.0450990i 0.705750 0.708461i \(-0.250610\pi\)
−0.748298 + 0.663362i \(0.769129\pi\)
\(8\) −0.751874 0.273660i −0.265828 0.0967534i
\(9\) 0.157410 2.99587i 0.0524701 0.998622i
\(10\) 0.173067 0.0629911i 0.0547284 0.0199195i
\(11\) −0.670227 0.336601i −0.202081 0.101489i 0.344881 0.938647i \(-0.387919\pi\)
−0.546962 + 0.837158i \(0.684216\pi\)
\(12\) 2.94355 + 1.68832i 0.849728 + 0.487377i
\(13\) −1.39965 + 3.24476i −0.388194 + 0.899934i 0.606310 + 0.795229i \(0.292649\pi\)
−0.994503 + 0.104705i \(0.966610\pi\)
\(14\) 0.0329282 0.00384876i 0.00880044 0.00102862i
\(15\) −1.55369 + 0.278512i −0.401160 + 0.0719114i
\(16\) −3.13860 + 2.06429i −0.784651 + 0.516073i
\(17\) −3.09332 2.59561i −0.750241 0.629527i 0.185326 0.982677i \(-0.440666\pi\)
−0.935567 + 0.353150i \(0.885110\pi\)
\(18\) 0.466650 + 0.387068i 0.109990 + 0.0912327i
\(19\) 1.63194 1.36936i 0.374394 0.314154i −0.436103 0.899897i \(-0.643642\pi\)
0.810497 + 0.585743i \(0.199197\pi\)
\(20\) 0.512064 1.71041i 0.114501 0.382460i
\(21\) −0.283696 0.0157146i −0.0619076 0.00342922i
\(22\) 0.135450 0.0680255i 0.0288780 0.0145031i
\(23\) −5.63041 + 5.96789i −1.17402 + 1.24439i −0.210255 + 0.977647i \(0.567429\pi\)
−0.963767 + 0.266744i \(0.914052\pi\)
\(24\) −1.27096 + 0.552526i −0.259433 + 0.112784i
\(25\) −1.65145 3.82850i −0.330291 0.765700i
\(26\) −0.357079 0.618479i −0.0700289 0.121294i
\(27\) −3.37383 3.95187i −0.649295 0.760537i
\(28\) 0.160693 0.278329i 0.0303682 0.0525992i
\(29\) 6.53664 + 0.764024i 1.21382 + 0.141876i 0.698811 0.715307i \(-0.253713\pi\)
0.515013 + 0.857182i \(0.327787\pi\)
\(30\) 0.142355 0.285473i 0.0259904 0.0521199i
\(31\) 5.44474 + 1.29043i 0.977905 + 0.231768i 0.688338 0.725390i \(-0.258341\pi\)
0.289567 + 0.957158i \(0.406489\pi\)
\(32\) 0.137190 2.35546i 0.0242520 0.416390i
\(33\) −1.24341 + 0.376105i −0.216449 + 0.0654714i
\(34\) 0.794074 0.188199i 0.136183 0.0322759i
\(35\) 0.0259597 + 0.147225i 0.00438799 + 0.0248855i
\(36\) 5.71125 1.38792i 0.951875 0.231320i
\(37\) 0.783915 4.44580i 0.128875 0.730885i −0.850056 0.526692i \(-0.823432\pi\)
0.978931 0.204193i \(-0.0654569\pi\)
\(38\) 0.0250334 + 0.429806i 0.00406095 + 0.0697237i
\(39\) 2.10972 + 5.74556i 0.337826 + 0.920027i
\(40\) 0.435431 + 0.584886i 0.0688478 + 0.0924786i
\(41\) 6.53505 + 8.77810i 1.02060 + 1.37091i 0.926900 + 0.375308i \(0.122463\pi\)
0.0937035 + 0.995600i \(0.470129\pi\)
\(42\) 0.0367848 0.0440923i 0.00567601 0.00680358i
\(43\) 0.201195 + 3.45438i 0.0306819 + 0.526788i 0.978275 + 0.207310i \(0.0664707\pi\)
−0.947593 + 0.319479i \(0.896492\pi\)
\(44\) 0.255154 1.44705i 0.0384659 0.218151i
\(45\) −1.62012 + 2.20221i −0.241513 + 0.328287i
\(46\) −0.287932 1.63294i −0.0424533 0.240764i
\(47\) 8.68990 2.05954i 1.26755 0.300416i 0.458787 0.888546i \(-0.348284\pi\)
0.808766 + 0.588131i \(0.200136\pi\)
\(48\) −1.48254 + 6.33549i −0.213986 + 0.914450i
\(49\) 0.405449 6.96129i 0.0579213 0.994470i
\(50\) 0.819923 + 0.194325i 0.115955 + 0.0274818i
\(51\) −6.98109 + 0.426511i −0.977547 + 0.0597235i
\(52\) −6.87639 0.803734i −0.953583 0.111458i
\(53\) 3.06986 5.31715i 0.421677 0.730366i −0.574426 0.818556i \(-0.694775\pi\)
0.996104 + 0.0881898i \(0.0281082\pi\)
\(54\) 1.04778 0.0699940i 0.142585 0.00952497i
\(55\) 0.341746 + 0.591922i 0.0460810 + 0.0798147i
\(56\) 0.0519877 + 0.120521i 0.00694715 + 0.0161053i
\(57\) 0.417952 3.66613i 0.0553591 0.485591i
\(58\) −0.912715 + 0.967421i −0.119845 + 0.127029i
\(59\) −2.60584 + 1.30870i −0.339251 + 0.170378i −0.610265 0.792197i \(-0.708937\pi\)
0.271014 + 0.962575i \(0.412641\pi\)
\(60\) −1.39573 2.75955i −0.180188 0.356256i
\(61\) 2.02529 6.76493i 0.259311 0.866160i −0.724853 0.688903i \(-0.758093\pi\)
0.984165 0.177257i \(-0.0567223\pi\)
\(62\) −0.866274 + 0.726890i −0.110017 + 0.0923151i
\(63\) −0.375189 + 0.318472i −0.0472694 + 0.0401238i
\(64\) −5.39019 4.52290i −0.673774 0.565363i
\(65\) 2.69059 1.76963i 0.333727 0.219496i
\(66\) 0.0890894 0.246952i 0.0109661 0.0303977i
\(67\) −8.82173 + 1.03111i −1.07775 + 0.125970i −0.636394 0.771364i \(-0.719575\pi\)
−0.441351 + 0.897334i \(0.645501\pi\)
\(68\) 3.13345 7.26416i 0.379987 0.880909i
\(69\) 0.0403837 + 14.2109i 0.00486162 + 1.71079i
\(70\) −0.0269988 0.0135593i −0.00322698 0.00162065i
\(71\) −8.94644 + 3.25624i −1.06175 + 0.386444i −0.813084 0.582146i \(-0.802213\pi\)
−0.248663 + 0.968590i \(0.579991\pi\)
\(72\) −0.938201 + 2.20944i −0.110568 + 0.260385i
\(73\) 8.28233 + 3.01452i 0.969373 + 0.352823i 0.777700 0.628636i \(-0.216386\pi\)
0.191673 + 0.981459i \(0.438609\pi\)
\(74\) 0.626083 + 0.663610i 0.0727807 + 0.0771431i
\(75\) −6.63926 2.84155i −0.766635 0.328113i
\(76\) 3.48707 + 2.29348i 0.399994 + 0.263080i
\(77\) 0.0352862 + 0.117864i 0.00402124 + 0.0134319i
\(78\) −1.18600 0.351395i −0.134288 0.0397876i
\(79\) −1.92557 + 2.58649i −0.216644 + 0.291003i −0.897138 0.441750i \(-0.854358\pi\)
0.680494 + 0.732754i \(0.261765\pi\)
\(80\) 3.42347 0.382756
\(81\) −8.95044 0.943160i −0.994494 0.104796i
\(82\) −2.21165 −0.244236
\(83\) −10.0492 + 13.4985i −1.10305 + 1.48165i −0.243987 + 0.969778i \(0.578456\pi\)
−0.859061 + 0.511873i \(0.828952\pi\)
\(84\) −0.129913 0.541286i −0.0141747 0.0590592i
\(85\) 1.05542 + 3.52535i 0.114477 + 0.382378i
\(86\) −0.584255 0.384271i −0.0630018 0.0414370i
\(87\) 9.12392 6.83289i 0.978187 0.732563i
\(88\) 0.411812 + 0.436496i 0.0438993 + 0.0465306i
\(89\) 10.7409 + 3.90935i 1.13853 + 0.414390i 0.841382 0.540442i \(-0.181743\pi\)
0.297146 + 0.954832i \(0.403965\pi\)
\(90\) −0.161470 0.528400i −0.0170205 0.0556982i
\(91\) 0.544730 0.198266i 0.0571033 0.0207839i
\(92\) −14.3645 7.21414i −1.49761 0.752126i
\(93\) 8.37955 4.86974i 0.868919 0.504969i
\(94\) −0.714861 + 1.65723i −0.0737322 + 0.170931i
\(95\) −1.92830 + 0.225386i −0.197840 + 0.0231241i
\(96\) −2.63576 3.12311i −0.269011 0.318751i
\(97\) 3.78511 2.48950i 0.384319 0.252771i −0.342618 0.939475i \(-0.611314\pi\)
0.726937 + 0.686704i \(0.240943\pi\)
\(98\) 1.07953 + 0.905836i 0.109049 + 0.0915032i
\(99\) −1.11391 + 1.95493i −0.111952 + 0.196478i
\(100\) 6.25759 5.25074i 0.625759 0.525074i
\(101\) −0.660124 + 2.20497i −0.0656848 + 0.219402i −0.984530 0.175215i \(-0.943938\pi\)
0.918845 + 0.394618i \(0.129123\pi\)
\(102\) 0.773359 1.18314i 0.0765740 0.117149i
\(103\) 2.32565 1.16798i 0.229153 0.115085i −0.330519 0.943799i \(-0.607224\pi\)
0.559671 + 0.828715i \(0.310927\pi\)
\(104\) 1.94032 2.05662i 0.190264 0.201668i
\(105\) 0.208136 + 0.154034i 0.0203120 + 0.0150322i
\(106\) 0.491459 + 1.13933i 0.0477347 + 0.110662i
\(107\) −5.97720 10.3528i −0.577837 1.00084i −0.995727 0.0923460i \(-0.970563\pi\)
0.417890 0.908498i \(-0.362770\pi\)
\(108\) 5.52133 8.55271i 0.531291 0.822985i
\(109\) −9.06553 + 15.7020i −0.868320 + 1.50397i −0.00460743 + 0.999989i \(0.501467\pi\)
−0.863712 + 0.503985i \(0.831867\pi\)
\(110\) −0.137197 0.0160360i −0.0130812 0.00152897i
\(111\) −4.31524 6.52056i −0.409584 0.618904i
\(112\) 0.599636 + 0.142116i 0.0566603 + 0.0134287i
\(113\) 0.691929 11.8800i 0.0650912 1.11757i −0.794725 0.606969i \(-0.792385\pi\)
0.859817 0.510603i \(-0.170578\pi\)
\(114\) 0.543860 + 0.510192i 0.0509372 + 0.0477839i
\(115\) 7.27556 1.72434i 0.678450 0.160796i
\(116\) 2.23893 + 12.6976i 0.207880 + 1.17894i
\(117\) 9.50055 + 4.70393i 0.878326 + 0.434879i
\(118\) 0.102333 0.580358i 0.00942050 0.0534263i
\(119\) 0.0385160 + 0.661294i 0.00353075 + 0.0606207i
\(120\) 1.24439 + 0.215776i 0.113597 + 0.0196976i
\(121\) −6.23284 8.37216i −0.566622 0.761105i
\(122\) 0.852214 + 1.14472i 0.0771558 + 0.103638i
\(123\) 18.6761 + 3.23841i 1.68397 + 0.291998i
\(124\) 0.637419 + 10.9441i 0.0572419 + 0.982806i
\(125\) −1.45106 + 8.22939i −0.129787 + 0.736059i
\(126\) −0.00634713 0.0992545i −0.000565447 0.00884229i
\(127\) 2.53378 + 14.3698i 0.224837 + 1.27511i 0.862997 + 0.505209i \(0.168585\pi\)
−0.638160 + 0.769903i \(0.720304\pi\)
\(128\) 5.97539 1.41619i 0.528155 0.125175i
\(129\) 4.37104 + 4.10045i 0.384849 + 0.361025i
\(130\) −0.0378422 + 0.649725i −0.00331898 + 0.0569846i
\(131\) −6.48742 1.53755i −0.566808 0.134336i −0.0627866 0.998027i \(-0.519999\pi\)
−0.504022 + 0.863691i \(0.668147\pi\)
\(132\) −1.40455 2.12236i −0.122251 0.184728i
\(133\) −0.347107 0.0405710i −0.0300980 0.00351795i
\(134\) 0.897484 1.55449i 0.0775308 0.134287i
\(135\) 0.589817 + 4.69848i 0.0507634 + 0.404381i
\(136\) 1.61548 + 2.79809i 0.138526 + 0.239934i
\(137\) −5.79364 13.4312i −0.494984 1.14750i −0.964381 0.264516i \(-0.914788\pi\)
0.469397 0.882987i \(-0.344471\pi\)
\(138\) −2.30854 1.70847i −0.196516 0.145435i
\(139\) 2.27516 2.41153i 0.192976 0.204543i −0.623660 0.781696i \(-0.714355\pi\)
0.816636 + 0.577153i \(0.195836\pi\)
\(140\) −0.261732 + 0.131447i −0.0221204 + 0.0111093i
\(141\) 8.46321 12.9477i 0.712731 1.09039i
\(142\) 0.551830 1.84324i 0.0463085 0.154681i
\(143\) 2.03027 1.70360i 0.169780 0.142462i
\(144\) 5.69030 + 9.72778i 0.474191 + 0.810649i
\(145\) −4.59437 3.85513i −0.381542 0.320151i
\(146\) −1.48821 + 0.978809i −0.123165 + 0.0810068i
\(147\) −7.78969 9.22999i −0.642482 0.761277i
\(148\) 8.78459 1.02677i 0.722089 0.0844000i
\(149\) 1.94162 4.50117i 0.159063 0.368750i −0.819983 0.572388i \(-0.806017\pi\)
0.979046 + 0.203638i \(0.0652764\pi\)
\(150\) 1.26188 0.733334i 0.103032 0.0598764i
\(151\) 14.4384 + 7.25124i 1.17498 + 0.590098i 0.925672 0.378326i \(-0.123500\pi\)
0.249309 + 0.968424i \(0.419797\pi\)
\(152\) −1.60176 + 0.582992i −0.129920 + 0.0472869i
\(153\) −8.26301 + 8.85861i −0.668025 + 0.716176i
\(154\) −0.0233649 0.00850413i −0.00188280 0.000685282i
\(155\) −3.49939 3.70914i −0.281078 0.297925i
\(156\) −9.59814 + 7.18803i −0.768466 + 0.575503i
\(157\) −10.3296 6.79388i −0.824391 0.542211i 0.0657814 0.997834i \(-0.479046\pi\)
−0.890173 + 0.455623i \(0.849416\pi\)
\(158\) −0.186901 0.624292i −0.0148690 0.0496660i
\(159\) −2.48183 10.3406i −0.196822 0.820066i
\(160\) −1.28402 + 1.72474i −0.101511 + 0.136352i
\(161\) 1.34593 0.106074
\(162\) 1.23306 1.33709i 0.0968782 0.105052i
\(163\) −12.1435 −0.951151 −0.475576 0.879675i \(-0.657760\pi\)
−0.475576 + 0.879675i \(0.657760\pi\)
\(164\) −12.8032 + 17.1977i −0.999762 + 1.34291i
\(165\) 1.13507 + 0.336306i 0.0883650 + 0.0261814i
\(166\) −0.975404 3.25808i −0.0757061 0.252876i
\(167\) −2.12309 1.39638i −0.164289 0.108055i 0.464702 0.885467i \(-0.346162\pi\)
−0.628991 + 0.777412i \(0.716532\pi\)
\(168\) 0.209004 + 0.0894517i 0.0161250 + 0.00690135i
\(169\) 0.351711 + 0.372792i 0.0270547 + 0.0286763i
\(170\) −0.698851 0.254361i −0.0535994 0.0195086i
\(171\) −3.84555 5.10464i −0.294076 0.390362i
\(172\) −6.37031 + 2.31860i −0.485732 + 0.176792i
\(173\) −8.70104 4.36982i −0.661528 0.332232i 0.0861609 0.996281i \(-0.472540\pi\)
−0.747689 + 0.664050i \(0.768836\pi\)
\(174\) 0.00654637 + 2.30365i 0.000496279 + 0.174639i
\(175\) −0.270910 + 0.628040i −0.0204789 + 0.0474753i
\(176\) 2.79842 0.327088i 0.210939 0.0246552i
\(177\) −1.71394 + 4.75096i −0.128827 + 0.357104i
\(178\) −1.92997 + 1.26936i −0.144657 + 0.0951425i
\(179\) −2.85196 2.39308i −0.213165 0.178867i 0.529953 0.848027i \(-0.322210\pi\)
−0.743118 + 0.669160i \(0.766654\pi\)
\(180\) −5.04356 1.80331i −0.375925 0.134411i
\(181\) −5.59668 + 4.69618i −0.415998 + 0.349064i −0.826638 0.562734i \(-0.809750\pi\)
0.410640 + 0.911798i \(0.365305\pi\)
\(182\) −0.0335998 + 0.112231i −0.00249058 + 0.00831912i
\(183\) −5.52031 10.9144i −0.408073 0.806816i
\(184\) 5.86654 2.94628i 0.432487 0.217203i
\(185\) −2.82323 + 2.99245i −0.207568 + 0.220009i
\(186\) −0.221859 + 1.94607i −0.0162675 + 0.142693i
\(187\) 1.19955 + 2.78086i 0.0877195 + 0.203357i
\(188\) 8.74825 + 15.1524i 0.638032 + 1.10510i
\(189\) −0.0917357 + 0.847443i −0.00667279 + 0.0616424i
\(190\) 0.196177 0.339789i 0.0142322 0.0246509i
\(191\) 20.6359 + 2.41199i 1.49316 + 0.174525i 0.823149 0.567825i \(-0.192215\pi\)
0.670012 + 0.742351i \(0.266289\pi\)
\(192\) −12.1647 + 0.743205i −0.877912 + 0.0536362i
\(193\) −3.39877 0.805522i −0.244649 0.0579828i 0.106462 0.994317i \(-0.466048\pi\)
−0.351111 + 0.936334i \(0.614196\pi\)
\(194\) −0.0532360 + 0.914028i −0.00382213 + 0.0656234i
\(195\) 1.27092 5.43116i 0.0910123 0.388933i
\(196\) 13.2931 3.15053i 0.949510 0.225038i
\(197\) −0.205736 1.16678i −0.0146580 0.0831299i 0.976601 0.215058i \(-0.0689942\pi\)
−0.991259 + 0.131928i \(0.957883\pi\)
\(198\) −0.182474 0.416498i −0.0129679 0.0295992i
\(199\) −0.191285 + 1.08483i −0.0135599 + 0.0769018i −0.990837 0.135065i \(-0.956876\pi\)
0.977277 + 0.211967i \(0.0679868\pi\)
\(200\) 0.193979 + 3.33049i 0.0137164 + 0.235501i
\(201\) −9.85492 + 11.8127i −0.695113 + 0.833200i
\(202\) −0.277771 0.373112i −0.0195439 0.0262521i
\(203\) −0.644688 0.865966i −0.0452482 0.0607789i
\(204\) −4.72312 12.8628i −0.330684 0.900577i
\(205\) −0.579884 9.95622i −0.0405008 0.695373i
\(206\) −0.0913296 + 0.517956i −0.00636324 + 0.0360877i
\(207\) 16.9927 + 17.8074i 1.18108 + 1.23770i
\(208\) −2.30518 13.0733i −0.159835 0.906470i
\(209\) −1.55470 + 0.368471i −0.107541 + 0.0254877i
\(210\) −0.0500882 + 0.0151507i −0.00345642 + 0.00104549i
\(211\) 0.871220 14.9583i 0.0599773 1.02977i −0.825297 0.564700i \(-0.808992\pi\)
0.885274 0.465070i \(-0.153971\pi\)
\(212\) 11.7044 + 2.77400i 0.803864 + 0.190519i
\(213\) −7.35887 + 14.7571i −0.504221 + 1.01114i
\(214\) 2.39959 + 0.280472i 0.164033 + 0.0191727i
\(215\) 1.57669 2.73091i 0.107529 0.186246i
\(216\) 1.45523 + 3.89459i 0.0990161 + 0.264993i
\(217\) −0.458958 0.794939i −0.0311561 0.0539640i
\(218\) −1.45132 3.36453i −0.0982956 0.227875i
\(219\) 14.0003 6.08639i 0.946053 0.411280i
\(220\) −0.918925 + 0.974003i −0.0619539 + 0.0656673i
\(221\) 12.7517 6.40414i 0.857772 0.430789i
\(222\) 1.57779 + 0.0873979i 0.105895 + 0.00586577i
\(223\) −1.46299 + 4.88672i −0.0979689 + 0.327239i −0.992898 0.118970i \(-0.962041\pi\)
0.894929 + 0.446209i \(0.147226\pi\)
\(224\) −0.296499 + 0.248792i −0.0198107 + 0.0166231i
\(225\) −11.7296 + 4.34489i −0.781975 + 0.289659i
\(226\) 1.84230 + 1.54588i 0.122548 + 0.102830i
\(227\) 14.0054 9.21152i 0.929573 0.611390i 0.00815667 0.999967i \(-0.497404\pi\)
0.921416 + 0.388577i \(0.127033\pi\)
\(228\) 7.11563 1.27554i 0.471244 0.0844745i
\(229\) −16.0140 + 1.87177i −1.05824 + 0.123690i −0.627366 0.778724i \(-0.715867\pi\)
−0.430870 + 0.902414i \(0.641793\pi\)
\(230\) −0.598512 + 1.38751i −0.0394647 + 0.0914896i
\(231\) 0.184851 + 0.106025i 0.0121623 + 0.00697592i
\(232\) −4.70565 2.36327i −0.308941 0.155156i
\(233\) 9.85526 3.58702i 0.645639 0.234993i 0.00161517 0.999999i \(-0.499486\pi\)
0.644024 + 0.765005i \(0.277264\pi\)
\(234\) −1.90909 + 0.972406i −0.124801 + 0.0635682i
\(235\) −7.64784 2.78358i −0.498890 0.181581i
\(236\) −3.92044 4.15542i −0.255199 0.270495i
\(237\) 0.664152 + 5.54547i 0.0431413 + 0.360217i
\(238\) −0.111848 0.0735633i −0.00725000 0.00476840i
\(239\) −0.0155911 0.0520778i −0.00100850 0.00336863i 0.957484 0.288487i \(-0.0931522\pi\)
−0.958492 + 0.285118i \(0.907967\pi\)
\(240\) 4.30148 4.08140i 0.277659 0.263453i
\(241\) 7.10393 9.54223i 0.457604 0.614669i −0.512108 0.858921i \(-0.671135\pi\)
0.969712 + 0.244252i \(0.0785425\pi\)
\(242\) 2.10937 0.135596
\(243\) −12.3703 + 9.48550i −0.793558 + 0.608495i
\(244\) 13.8348 0.885680
\(245\) −3.79477 + 5.09726i −0.242439 + 0.325652i
\(246\) −2.77886 + 2.63668i −0.177174 + 0.168109i
\(247\) 2.15910 + 7.21190i 0.137380 + 0.458882i
\(248\) −3.74062 2.46025i −0.237530 0.156226i
\(249\) 3.46610 + 28.9409i 0.219655 + 1.83406i
\(250\) −1.15891 1.22837i −0.0732959 0.0776891i
\(251\) 4.18194 + 1.52210i 0.263961 + 0.0960741i 0.470611 0.882341i \(-0.344034\pi\)
−0.206649 + 0.978415i \(0.566256\pi\)
\(252\) −0.808542 0.525228i −0.0509334 0.0330862i
\(253\) 5.78245 2.10464i 0.363540 0.132318i
\(254\) −2.63521 1.32345i −0.165348 0.0830407i
\(255\) 5.52896 + 3.17123i 0.346237 + 0.198590i
\(256\) 5.08239 11.7823i 0.317649 0.736394i
\(257\) 15.3697 1.79646i 0.958735 0.112060i 0.377691 0.925932i \(-0.376718\pi\)
0.581045 + 0.813872i \(0.302644\pi\)
\(258\) −1.19222 + 0.213715i −0.0742241 + 0.0133053i
\(259\) −0.618724 + 0.406941i −0.0384456 + 0.0252861i
\(260\) 4.83316 + 4.05550i 0.299740 + 0.251512i
\(261\) 3.31785 19.4626i 0.205370 1.20471i
\(262\) 1.03217 0.866090i 0.0637674 0.0535072i
\(263\) −4.11141 + 13.7331i −0.253520 + 0.846817i 0.732582 + 0.680679i \(0.238315\pi\)
−0.986102 + 0.166138i \(0.946870\pi\)
\(264\) 1.03781 + 0.0574868i 0.0638728 + 0.00353807i
\(265\) −5.00009 + 2.51114i −0.307153 + 0.154258i
\(266\) 0.0484667 0.0513717i 0.00297168 0.00314980i
\(267\) 18.1562 7.89307i 1.11114 0.483048i
\(268\) −6.89211 15.9777i −0.421003 0.975994i
\(269\) −0.910225 1.57656i −0.0554974 0.0961243i 0.836942 0.547292i \(-0.184341\pi\)
−0.892439 + 0.451167i \(0.851008\pi\)
\(270\) −0.832830 0.471414i −0.0506844 0.0286894i
\(271\) 6.79318 11.7661i 0.412656 0.714742i −0.582523 0.812814i \(-0.697934\pi\)
0.995179 + 0.0980726i \(0.0312677\pi\)
\(272\) 15.0668 + 1.76106i 0.913559 + 0.106780i
\(273\) 0.448066 0.898531i 0.0271182 0.0543816i
\(274\) 2.87646 + 0.681734i 0.173773 + 0.0411851i
\(275\) −0.181827 + 3.12184i −0.0109646 + 0.188254i
\(276\) −26.6491 + 8.06080i −1.60409 + 0.485203i
\(277\) −21.2963 + 5.04731i −1.27957 + 0.303263i −0.813541 0.581507i \(-0.802463\pi\)
−0.466027 + 0.884770i \(0.654315\pi\)
\(278\) 0.116349 + 0.659846i 0.00697813 + 0.0395749i
\(279\) 4.72301 16.1086i 0.282759 0.964397i
\(280\) 0.0207711 0.117799i 0.00124131 0.00703981i
\(281\) 1.46889 + 25.2199i 0.0876268 + 1.50449i 0.700124 + 0.714021i \(0.253128\pi\)
−0.612497 + 0.790473i \(0.709835\pi\)
\(282\) 1.07752 + 2.93450i 0.0641656 + 0.174747i
\(283\) 13.3658 + 17.9534i 0.794516 + 1.06722i 0.996142 + 0.0877573i \(0.0279700\pi\)
−0.201626 + 0.979463i \(0.564623\pi\)
\(284\) −11.1384 14.9615i −0.660943 0.887801i
\(285\) −2.15415 + 2.58208i −0.127601 + 0.152949i
\(286\) 0.0311435 + 0.534714i 0.00184156 + 0.0316183i
\(287\) 0.311737 1.76795i 0.0184012 0.104359i
\(288\) −7.03505 0.781776i −0.414544 0.0460666i
\(289\) −0.120543 0.683633i −0.00709076 0.0402137i
\(290\) 1.17940 0.279523i 0.0692568 0.0164142i
\(291\) 1.78792 7.64051i 0.104810 0.447894i
\(292\) −1.00403 + 17.2385i −0.0587564 + 1.00881i
\(293\) −12.7408 3.01963i −0.744326 0.176408i −0.159081 0.987265i \(-0.550853\pi\)
−0.585244 + 0.810857i \(0.699001\pi\)
\(294\) 2.43632 0.148847i 0.142089 0.00868095i
\(295\) 2.63944 + 0.308506i 0.153674 + 0.0179619i
\(296\) −1.80604 + 3.12816i −0.104974 + 0.181820i
\(297\) 0.931035 + 3.78428i 0.0540241 + 0.219586i
\(298\) 0.495345 + 0.857962i 0.0286945 + 0.0497004i
\(299\) −11.4837 26.6223i −0.664122 1.53961i
\(300\) 1.60261 14.0575i 0.0925268 0.811613i
\(301\) 0.389530 0.412878i 0.0224522 0.0237979i
\(302\) −2.91794 + 1.46544i −0.167908 + 0.0843268i
\(303\) 1.79930 + 3.55745i 0.103367 + 0.204370i
\(304\) −2.29526 + 7.66670i −0.131642 + 0.439715i
\(305\) −4.92977 + 4.13657i −0.282278 + 0.236859i
\(306\) −0.438824 2.40856i −0.0250859 0.137688i
\(307\) 11.2563 + 9.44513i 0.642429 + 0.539062i 0.904763 0.425915i \(-0.140048\pi\)
−0.262334 + 0.964977i \(0.584492\pi\)
\(308\) −0.201387 + 0.132454i −0.0114751 + 0.00754727i
\(309\) 1.52965 4.24012i 0.0870186 0.241212i
\(310\) 1.02359 0.119640i 0.0581359 0.00679511i
\(311\) −13.2219 + 30.6518i −0.749745 + 1.73810i −0.0784433 + 0.996919i \(0.524995\pi\)
−0.671301 + 0.741185i \(0.734264\pi\)
\(312\) −0.0139168 4.89729i −0.000787883 0.277254i
\(313\) −20.4283 10.2595i −1.15467 0.579899i −0.234773 0.972050i \(-0.575435\pi\)
−0.919901 + 0.392152i \(0.871731\pi\)
\(314\) 2.34793 0.854577i 0.132501 0.0482266i
\(315\) 0.445152 0.0545971i 0.0250815 0.00307620i
\(316\) −5.93643 2.16069i −0.333950 0.121548i
\(317\) −12.8911 13.6638i −0.724039 0.767437i 0.255907 0.966702i \(-0.417626\pi\)
−0.979946 + 0.199265i \(0.936145\pi\)
\(318\) 1.97579 + 0.845621i 0.110797 + 0.0474201i
\(319\) −4.12386 2.71231i −0.230892 0.151860i
\(320\) 1.83910 + 6.14301i 0.102809 + 0.343405i
\(321\) −19.8526 5.88205i −1.10806 0.328304i
\(322\) −0.162431 + 0.218182i −0.00905191 + 0.0121588i
\(323\) −8.60246 −0.478654
\(324\) −3.25902 17.3286i −0.181056 0.962701i
\(325\) 14.7340 0.817296
\(326\) 1.46551 1.96853i 0.0811673 0.109027i
\(327\) 7.32905 + 30.5367i 0.405297 + 1.68868i
\(328\) −2.51132 8.38841i −0.138665 0.463172i
\(329\) −1.22400 0.805036i −0.0674812 0.0443831i
\(330\) −0.191501 + 0.143415i −0.0105418 + 0.00789471i
\(331\) 4.06203 + 4.30550i 0.223270 + 0.236652i 0.829320 0.558775i \(-0.188728\pi\)
−0.606050 + 0.795427i \(0.707247\pi\)
\(332\) −30.9813 11.2763i −1.70032 0.618865i
\(333\) −13.1956 3.04832i −0.723116 0.167047i
\(334\) 0.482581 0.175645i 0.0264056 0.00961087i
\(335\) 7.23319 + 3.63264i 0.395191 + 0.198473i
\(336\) 0.922850 0.536310i 0.0503456 0.0292581i
\(337\) −4.80653 + 11.1428i −0.261828 + 0.606986i −0.997524 0.0703261i \(-0.977596\pi\)
0.735696 + 0.677312i \(0.236855\pi\)
\(338\) −0.102877 + 0.0120246i −0.00559579 + 0.000654054i
\(339\) −13.2937 15.7517i −0.722013 0.855513i
\(340\) −6.02353 + 3.96174i −0.326672 + 0.214856i
\(341\) −3.21485 2.69758i −0.174094 0.146082i
\(342\) 1.29158 0.00734073i 0.0698408 0.000396941i
\(343\) −1.75592 + 1.47339i −0.0948108 + 0.0795557i
\(344\) 0.794052 2.65232i 0.0428124 0.143004i
\(345\) 7.08577 10.8404i 0.381485 0.583625i
\(346\) 1.75844 0.883122i 0.0945343 0.0474769i
\(347\) 1.67386 1.77419i 0.0898577 0.0952436i −0.680884 0.732391i \(-0.738404\pi\)
0.770742 + 0.637148i \(0.219886\pi\)
\(348\) 17.9510 + 13.2849i 0.962274 + 0.712145i
\(349\) 9.10243 + 21.1018i 0.487242 + 1.12955i 0.967602 + 0.252482i \(0.0812468\pi\)
−0.480360 + 0.877071i \(0.659494\pi\)
\(350\) −0.0691144 0.119710i −0.00369432 0.00639875i
\(351\) 17.5450 5.41604i 0.936485 0.289087i
\(352\) −0.884797 + 1.53251i −0.0471598 + 0.0816833i
\(353\) 22.9990 + 2.68819i 1.22411 + 0.143078i 0.703488 0.710708i \(-0.251625\pi\)
0.520625 + 0.853786i \(0.325699\pi\)
\(354\) −0.563314 0.851199i −0.0299398 0.0452407i
\(355\) 8.44244 + 2.00089i 0.448078 + 0.106196i
\(356\) −1.30207 + 22.3556i −0.0690094 + 1.18485i
\(357\) 0.836776 + 0.784975i 0.0442869 + 0.0415453i
\(358\) 0.732114 0.173514i 0.0386934 0.00917051i
\(359\) −5.43706 30.8351i −0.286957 1.62741i −0.698211 0.715892i \(-0.746020\pi\)
0.411254 0.911521i \(-0.365091\pi\)
\(360\) 1.82078 1.21243i 0.0959636 0.0639006i
\(361\) −2.51123 + 14.2419i −0.132170 + 0.749574i
\(362\) −0.0858508 1.47400i −0.00451222 0.0774718i
\(363\) −17.8125 3.08865i −0.934912 0.162112i
\(364\) 0.678195 + 0.910975i 0.0355471 + 0.0477480i
\(365\) −4.79653 6.44285i −0.251062 0.337234i
\(366\) 2.43549 + 0.422310i 0.127305 + 0.0220745i
\(367\) −0.446242 7.66168i −0.0232937 0.399937i −0.989722 0.143002i \(-0.954324\pi\)
0.966429 0.256935i \(-0.0827125\pi\)
\(368\) 5.35217 30.3537i 0.279001 1.58229i
\(369\) 27.3267 18.1964i 1.42257 0.947266i
\(370\) −0.144376 0.818799i −0.00750577 0.0425673i
\(371\) −0.980030 + 0.232271i −0.0508806 + 0.0120589i
\(372\) 13.8482 + 12.9909i 0.717995 + 0.673548i
\(373\) −1.50909 + 25.9100i −0.0781376 + 1.34157i 0.700300 + 0.713849i \(0.253050\pi\)
−0.778438 + 0.627722i \(0.783988\pi\)
\(374\) −0.595558 0.141150i −0.0307955 0.00729868i
\(375\) 7.98771 + 12.0699i 0.412483 + 0.623286i
\(376\) −7.09733 0.829559i −0.366017 0.0427812i
\(377\) −11.6281 + 20.1405i −0.598878 + 1.03729i
\(378\) −0.126304 0.117143i −0.00649639 0.00602518i
\(379\) −13.2851 23.0104i −0.682408 1.18197i −0.974244 0.225497i \(-0.927599\pi\)
0.291835 0.956469i \(-0.405734\pi\)
\(380\) −1.50652 3.49250i −0.0772827 0.179161i
\(381\) 20.3150 + 15.0344i 1.04077 + 0.770236i
\(382\) −2.88140 + 3.05411i −0.147425 + 0.156262i
\(383\) −2.40889 + 1.20979i −0.123089 + 0.0618175i −0.509278 0.860602i \(-0.670087\pi\)
0.386189 + 0.922420i \(0.373791\pi\)
\(384\) 5.81952 8.90315i 0.296976 0.454337i
\(385\) 0.0321570 0.107412i 0.00163887 0.00547422i
\(386\) 0.540753 0.453746i 0.0275236 0.0230951i
\(387\) 10.3805 0.0589980i 0.527673 0.00299904i
\(388\) 6.79926 + 5.70525i 0.345180 + 0.289640i
\(389\) 19.7963 13.0202i 1.00371 0.660152i 0.0625269 0.998043i \(-0.480084\pi\)
0.941185 + 0.337892i \(0.109714\pi\)
\(390\) 0.727042 + 0.861471i 0.0368152 + 0.0436223i
\(391\) 32.9070 3.84627i 1.66418 0.194514i
\(392\) −2.20987 + 5.12306i −0.111615 + 0.258754i
\(393\) −9.98425 + 5.80230i −0.503639 + 0.292687i
\(394\) 0.213971 + 0.107460i 0.0107797 + 0.00541377i
\(395\) 2.76138 1.00506i 0.138940 0.0505702i
\(396\) −4.29501 0.992188i −0.215832 0.0498593i
\(397\) −0.102939 0.0374669i −0.00516638 0.00188041i 0.339436 0.940629i \(-0.389764\pi\)
−0.344602 + 0.938749i \(0.611986\pi\)
\(398\) −0.152773 0.161929i −0.00765780 0.00811679i
\(399\) −0.484496 + 0.362838i −0.0242551 + 0.0181646i
\(400\) 13.0864 + 8.60706i 0.654320 + 0.430353i
\(401\) 2.42258 + 8.09197i 0.120978 + 0.404094i 0.996929 0.0783050i \(-0.0249508\pi\)
−0.875952 + 0.482399i \(0.839766\pi\)
\(402\) −0.725573 3.02312i −0.0361883 0.150780i
\(403\) −11.8079 + 15.8607i −0.588192 + 0.790079i
\(404\) −4.50932 −0.224347
\(405\) 6.34252 + 5.20031i 0.315162 + 0.258405i
\(406\) 0.218181 0.0108281
\(407\) −2.02186 + 2.71583i −0.100220 + 0.134619i
\(408\) 5.36562 + 1.58976i 0.265638 + 0.0787049i
\(409\) 1.44994 + 4.84314i 0.0716949 + 0.239478i 0.986324 0.164815i \(-0.0527028\pi\)
−0.914630 + 0.404293i \(0.867518\pi\)
\(410\) 1.68394 + 1.10755i 0.0831639 + 0.0546978i
\(411\) −23.2919 9.96874i −1.14890 0.491722i
\(412\) 3.49890 + 3.70861i 0.172378 + 0.182710i
\(413\) 0.449503 + 0.163606i 0.0221186 + 0.00805050i
\(414\) −4.93741 + 0.605564i −0.242660 + 0.0297619i
\(415\) 14.4112 5.24525i 0.707418 0.257479i
\(416\) 7.45088 + 3.74197i 0.365309 + 0.183465i
\(417\) −0.0163184 5.74240i −0.000799114 0.281206i
\(418\) 0.127895 0.296494i 0.00625555 0.0145020i
\(419\) −12.6886 + 1.48309i −0.619879 + 0.0724534i −0.420235 0.907415i \(-0.638052\pi\)
−0.199644 + 0.979869i \(0.563978\pi\)
\(420\) −0.172149 + 0.477191i −0.00840002 + 0.0232845i
\(421\) 15.2120 10.0051i 0.741388 0.487618i −0.121767 0.992559i \(-0.538856\pi\)
0.863154 + 0.504940i \(0.168486\pi\)
\(422\) 2.31968 + 1.94644i 0.112920 + 0.0947512i
\(423\) −4.80224 26.3580i −0.233493 1.28157i
\(424\) −3.76324 + 3.15773i −0.182759 + 0.153353i
\(425\) −4.82880 + 16.1293i −0.234231 + 0.782386i
\(426\) −1.50412 2.97385i −0.0728749 0.144083i
\(427\) −1.03519 + 0.519892i −0.0500963 + 0.0251593i
\(428\) 16.0721 17.0355i 0.776877 0.823441i
\(429\) 0.519967 4.56097i 0.0251042 0.220206i
\(430\) 0.252415 + 0.585164i 0.0121725 + 0.0282191i
\(431\) −11.5675 20.0355i −0.557188 0.965077i −0.997730 0.0673455i \(-0.978547\pi\)
0.440542 0.897732i \(-0.354786\pi\)
\(432\) 18.7469 + 5.43876i 0.901962 + 0.261672i
\(433\) 16.7531 29.0173i 0.805104 1.39448i −0.111116 0.993807i \(-0.535443\pi\)
0.916221 0.400674i \(-0.131224\pi\)
\(434\) 0.184252 + 0.0215360i 0.00884440 + 0.00103376i
\(435\) −10.3687 + 0.633477i −0.497140 + 0.0303729i
\(436\) −34.5641 8.19184i −1.65532 0.392318i
\(437\) −1.01631 + 17.4493i −0.0486166 + 0.834715i
\(438\) −0.702963 + 3.00405i −0.0335889 + 0.143539i
\(439\) −30.8003 + 7.29981i −1.47002 + 0.348401i −0.886132 0.463433i \(-0.846617\pi\)
−0.583888 + 0.811834i \(0.698469\pi\)
\(440\) −0.0949649 0.538573i −0.00452727 0.0256755i
\(441\) −20.7913 2.31045i −0.990061 0.110021i
\(442\) −0.500767 + 2.83999i −0.0238191 + 0.135085i
\(443\) 1.31468 + 22.5722i 0.0624623 + 1.07244i 0.873306 + 0.487173i \(0.161972\pi\)
−0.810843 + 0.585263i \(0.800991\pi\)
\(444\) 9.81343 11.7629i 0.465725 0.558243i
\(445\) −6.22033 8.35535i −0.294872 0.396082i
\(446\) −0.615606 0.826902i −0.0291498 0.0391550i
\(447\) −2.92664 7.97032i −0.138425 0.376983i
\(448\) 0.0671150 + 1.15232i 0.00317088 + 0.0544420i
\(449\) −3.12921 + 17.7466i −0.147677 + 0.837515i 0.817503 + 0.575925i \(0.195358\pi\)
−0.965179 + 0.261590i \(0.915753\pi\)
\(450\) 0.711237 2.42579i 0.0335281 0.114353i
\(451\) −1.42525 8.08302i −0.0671126 0.380615i
\(452\) 22.6857 5.37661i 1.06705 0.252895i
\(453\) 26.7862 8.10226i 1.25852 0.380677i
\(454\) −0.196981 + 3.38203i −0.00924477 + 0.158727i
\(455\) −0.514043 0.121830i −0.0240987 0.00571150i
\(456\) −1.31752 + 2.64209i −0.0616985 + 0.123727i
\(457\) 23.4000 + 2.73507i 1.09461 + 0.127941i 0.644181 0.764873i \(-0.277198\pi\)
0.450426 + 0.892814i \(0.351272\pi\)
\(458\) 1.62920 2.82185i 0.0761274 0.131856i
\(459\) 0.178876 + 20.9815i 0.00834921 + 0.979335i
\(460\) 7.32442 + 12.6863i 0.341503 + 0.591500i
\(461\) −15.9112 36.8862i −0.741056 1.71796i −0.694985 0.719024i \(-0.744589\pi\)
−0.0460709 0.998938i \(-0.514670\pi\)
\(462\) −0.0394956 + 0.0171700i −0.00183750 + 0.000798822i
\(463\) 7.53656 7.98829i 0.350254 0.371247i −0.528163 0.849143i \(-0.677119\pi\)
0.878416 + 0.477896i \(0.158600\pi\)
\(464\) −22.0931 + 11.0956i −1.02565 + 0.515099i
\(465\) −8.81882 0.488496i −0.408963 0.0226535i
\(466\) −0.607887 + 2.03048i −0.0281598 + 0.0940603i
\(467\) −1.29116 + 1.08341i −0.0597479 + 0.0501344i −0.672173 0.740395i \(-0.734639\pi\)
0.612425 + 0.790529i \(0.290194\pi\)
\(468\) −3.49029 + 20.4742i −0.161339 + 0.946421i
\(469\) 1.11612 + 0.936540i 0.0515378 + 0.0432454i
\(470\) 1.37420 0.903825i 0.0633871 0.0416903i
\(471\) −21.0783 + 3.77847i −0.971237 + 0.174103i
\(472\) 2.31740 0.270865i 0.106667 0.0124676i
\(473\) 1.02790 2.38294i 0.0472629 0.109568i
\(474\) −0.979104 0.561582i −0.0449717 0.0257943i
\(475\) −7.93769 3.98646i −0.364206 0.182911i
\(476\) −1.21951 + 0.443865i −0.0558961 + 0.0203445i
\(477\) −15.4462 10.0339i −0.707235 0.459419i
\(478\) 0.0103237 + 0.00375751i 0.000472194 + 0.000171864i
\(479\) 13.6490 + 14.4671i 0.623640 + 0.661020i 0.959767 0.280797i \(-0.0905987\pi\)
−0.336127 + 0.941817i \(0.609117\pi\)
\(480\) 0.442872 + 3.69785i 0.0202143 + 0.168783i
\(481\) 13.3283 + 8.76619i 0.607720 + 0.399704i
\(482\) 0.689524 + 2.30317i 0.0314070 + 0.104907i
\(483\) 1.69111 1.60459i 0.0769482 0.0730113i
\(484\) 12.2111 16.4024i 0.555051 0.745562i
\(485\) −4.12866 −0.187473
\(486\) −0.0447608 3.15004i −0.00203039 0.142889i
\(487\) −16.9386 −0.767563 −0.383782 0.923424i \(-0.625378\pi\)
−0.383782 + 0.923424i \(0.625378\pi\)
\(488\) −3.37405 + 4.53213i −0.152736 + 0.205160i
\(489\) −15.2579 + 14.4772i −0.689985 + 0.654683i
\(490\) −0.368330 1.23031i −0.0166394 0.0555796i
\(491\) 28.7372 + 18.9008i 1.29689 + 0.852980i 0.994953 0.100346i \(-0.0319951\pi\)
0.301941 + 0.953327i \(0.402365\pi\)
\(492\) 4.41597 + 36.8720i 0.199087 + 1.66232i
\(493\) −18.2368 19.3299i −0.821346 0.870576i
\(494\) −1.42965 0.520352i −0.0643232 0.0234117i
\(495\) 1.82711 0.930651i 0.0821226 0.0418297i
\(496\) −19.7527 + 7.18940i −0.886923 + 0.322814i
\(497\) 1.39567 + 0.700930i 0.0626042 + 0.0314410i
\(498\) −5.10978 2.93080i −0.228975 0.131332i
\(499\) 6.96828 16.1543i 0.311943 0.723165i −0.688054 0.725660i \(-0.741535\pi\)
0.999997 + 0.00249447i \(0.000794016\pi\)
\(500\) −16.2607 + 1.90060i −0.727200 + 0.0849975i
\(501\) −4.33232 + 0.776605i −0.193554 + 0.0346961i
\(502\) −0.751430 + 0.494223i −0.0335379 + 0.0220583i
\(503\) 17.6438 + 14.8049i 0.786697 + 0.660117i 0.944925 0.327286i \(-0.106134\pi\)
−0.158229 + 0.987402i \(0.550578\pi\)
\(504\) 0.369248 0.136777i 0.0164476 0.00609253i
\(505\) 1.60682 1.34828i 0.0715023 0.0599976i
\(506\) −0.356670 + 1.19136i −0.0158559 + 0.0529625i
\(507\) 0.886349 + 0.0490971i 0.0393641 + 0.00218048i
\(508\) −25.5463 + 12.8298i −1.13343 + 0.569231i
\(509\) 21.9775 23.2948i 0.974134 1.03252i −0.0253261 0.999679i \(-0.508062\pi\)
0.999461 0.0328429i \(-0.0104561\pi\)
\(510\) −1.18133 + 0.513561i −0.0523100 + 0.0227409i
\(511\) −0.572674 1.32761i −0.0253336 0.0587299i
\(512\) 7.43754 + 12.8822i 0.328696 + 0.569318i
\(513\) −10.9174 1.82922i −0.482017 0.0807618i
\(514\) −1.56365 + 2.70831i −0.0689695 + 0.119459i
\(515\) −2.35564 0.275335i −0.103802 0.0121327i
\(516\) −5.23988 + 10.5078i −0.230673 + 0.462581i
\(517\) −6.51745 1.54466i −0.286637 0.0679343i
\(518\) 0.00870211 0.149409i 0.000382349 0.00656468i
\(519\) −16.1422 + 4.88267i −0.708563 + 0.214326i
\(520\) −2.50727 + 0.594233i −0.109951 + 0.0260588i
\(521\) 0.436835 + 2.47742i 0.0191381 + 0.108538i 0.992880 0.119116i \(-0.0380059\pi\)
−0.973742 + 0.227653i \(0.926895\pi\)
\(522\) 2.75459 + 2.88665i 0.120565 + 0.126345i
\(523\) 4.83329 27.4110i 0.211345 1.19860i −0.675792 0.737092i \(-0.736198\pi\)
0.887137 0.461506i \(-0.152691\pi\)
\(524\) −0.759485 13.0399i −0.0331783 0.569649i
\(525\) 0.408348 + 1.11208i 0.0178218 + 0.0485353i
\(526\) −1.73003 2.32383i −0.0754328 0.101324i
\(527\) −13.4929 18.1241i −0.587760 0.789499i
\(528\) 3.12617 3.74720i 0.136049 0.163076i
\(529\) −2.57682 44.2423i −0.112036 1.92358i
\(530\) 0.196357 1.11359i 0.00852919 0.0483714i
\(531\) 3.51051 + 8.01274i 0.152343 + 0.347723i
\(532\) −0.118891 0.674265i −0.00515458 0.0292331i
\(533\) −37.6296 + 8.91838i −1.62992 + 0.386298i
\(534\) −0.911631 + 3.89577i −0.0394501 + 0.168587i
\(535\) −0.633446 + 10.8758i −0.0273862 + 0.470204i
\(536\) 6.91500 + 1.63889i 0.298683 + 0.0707891i
\(537\) −6.43637 + 0.393231i −0.277750 + 0.0169692i
\(538\) 0.365417 + 0.0427112i 0.0157543 + 0.00184141i
\(539\) −2.61492 + 4.52917i −0.112633 + 0.195085i
\(540\) −8.48694 + 3.74704i −0.365220 + 0.161247i
\(541\) 3.23851 + 5.60926i 0.139234 + 0.241161i 0.927207 0.374549i \(-0.122203\pi\)
−0.787973 + 0.615710i \(0.788869\pi\)
\(542\) 1.08753 + 2.52118i 0.0467135 + 0.108294i
\(543\) −1.43335 + 12.5728i −0.0615109 + 0.539552i
\(544\) −6.53822 + 6.93010i −0.280324 + 0.297126i
\(545\) 14.7657 7.41559i 0.632491 0.317649i
\(546\) 0.0915828 + 0.181072i 0.00391938 + 0.00774915i
\(547\) −4.41664 + 14.7526i −0.188842 + 0.630776i 0.810164 + 0.586203i \(0.199378\pi\)
−0.999006 + 0.0445731i \(0.985807\pi\)
\(548\) 21.9529 18.4207i 0.937783 0.786893i
\(549\) −19.9480 7.13236i −0.851361 0.304402i
\(550\) −0.484125 0.406229i −0.0206431 0.0173217i
\(551\) 11.7137 7.70419i 0.499019 0.328210i
\(552\) 3.85859 10.6959i 0.164233 0.455247i
\(553\) 0.525391 0.0614094i 0.0223419 0.00261139i
\(554\) 1.75190 4.06137i 0.0744312 0.172551i
\(555\) 0.0202494 + 7.12571i 0.000859538 + 0.302469i
\(556\) 5.80447 + 2.91512i 0.246165 + 0.123628i
\(557\) 21.2492 7.73409i 0.900359 0.327704i 0.149963 0.988692i \(-0.452085\pi\)
0.750397 + 0.660988i \(0.229862\pi\)
\(558\) 2.04131 + 2.70966i 0.0864154 + 0.114709i
\(559\) −11.4902 4.18210i −0.485985 0.176884i
\(560\) −0.385392 0.408491i −0.0162858 0.0172619i
\(561\) 4.82248 + 2.06398i 0.203605 + 0.0871412i
\(562\) −4.26556 2.80550i −0.179932 0.118343i
\(563\) −6.80463 22.7291i −0.286781 0.957916i −0.973055 0.230573i \(-0.925940\pi\)
0.686274 0.727343i \(-0.259245\pi\)
\(564\) 29.0563 + 8.60899i 1.22349 + 0.362504i
\(565\) −6.47606 + 8.69885i −0.272450 + 0.365963i
\(566\) −4.52338 −0.190132
\(567\) 0.895043 + 1.17415i 0.0375883 + 0.0493096i
\(568\) 7.61770 0.319632
\(569\) −0.377798 + 0.507471i −0.0158381 + 0.0212743i −0.809972 0.586469i \(-0.800518\pi\)
0.794134 + 0.607743i \(0.207925\pi\)
\(570\) −0.158600 0.660812i −0.00664302 0.0276784i
\(571\) −11.4987 38.4084i −0.481207 1.60734i −0.762002 0.647575i \(-0.775783\pi\)
0.280795 0.959768i \(-0.409402\pi\)
\(572\) 4.33820 + 2.85328i 0.181389 + 0.119302i
\(573\) 28.8038 21.5711i 1.20330 0.901147i
\(574\) 0.248973 + 0.263895i 0.0103919 + 0.0110148i
\(575\) 32.1464 + 11.7003i 1.34060 + 0.487938i
\(576\) −14.3985 + 15.4363i −0.599937 + 0.643181i
\(577\) 15.7332 5.72640i 0.654980 0.238393i 0.00691246 0.999976i \(-0.497800\pi\)
0.648068 + 0.761583i \(0.275577\pi\)
\(578\) 0.125368 + 0.0629622i 0.00521463 + 0.00261888i
\(579\) −5.23076 + 3.03983i −0.217383 + 0.126331i
\(580\) 4.65397 10.7891i 0.193246 0.447994i
\(581\) 2.74193 0.320485i 0.113754 0.0132960i
\(582\) 1.02280 + 1.21191i 0.0423963 + 0.0502353i
\(583\) −3.84726 + 2.53038i −0.159337 + 0.104798i
\(584\) −5.40231 4.53308i −0.223549 0.187580i
\(585\) −4.87805 8.33922i −0.201683 0.344784i
\(586\) 2.02710 1.70094i 0.0837386 0.0702650i
\(587\) −4.72396 + 15.7791i −0.194979 + 0.651274i 0.803457 + 0.595363i \(0.202992\pi\)
−0.998436 + 0.0559115i \(0.982194\pi\)
\(588\) 12.9464 19.8064i 0.533899 0.816800i
\(589\) 10.6526 5.34993i 0.438932 0.220440i
\(590\) −0.368547 + 0.390636i −0.0151728 + 0.0160823i
\(591\) −1.64952 1.22075i −0.0678521 0.0502149i
\(592\) 6.71703 + 15.5718i 0.276068 + 0.639998i
\(593\) 20.1750 + 34.9441i 0.828487 + 1.43498i 0.899225 + 0.437487i \(0.144131\pi\)
−0.0707373 + 0.997495i \(0.522535\pi\)
\(594\) −0.725813 0.305773i −0.0297805 0.0125460i
\(595\) 0.301836 0.522795i 0.0123741 0.0214325i
\(596\) 9.53902 + 1.11495i 0.390733 + 0.0456702i
\(597\) 1.05297 + 1.59110i 0.0430954 + 0.0651195i
\(598\) 5.70151 + 1.35128i 0.233152 + 0.0552581i
\(599\) −0.327503 + 5.62300i −0.0133814 + 0.229750i 0.984986 + 0.172633i \(0.0552276\pi\)
−0.998368 + 0.0571162i \(0.981809\pi\)
\(600\) 4.21427 + 3.95338i 0.172047 + 0.161396i
\(601\) 16.6314 3.94172i 0.678410 0.160786i 0.123056 0.992400i \(-0.460731\pi\)
0.555355 + 0.831614i \(0.312582\pi\)
\(602\) 0.0199201 + 0.112972i 0.000811882 + 0.00460441i
\(603\) 1.70044 + 26.5910i 0.0692475 + 1.08287i
\(604\) −5.49667 + 31.1732i −0.223656 + 1.26842i
\(605\) 0.553067 + 9.49580i 0.0224854 + 0.386059i
\(606\) −0.793827 0.137648i −0.0322470 0.00559158i
\(607\) 10.8231 + 14.5380i 0.439297 + 0.590079i 0.965540 0.260256i \(-0.0838069\pi\)
−0.526242 + 0.850335i \(0.676400\pi\)
\(608\) −3.00159 4.03184i −0.121731 0.163513i
\(609\) −1.84242 0.319472i −0.0746584 0.0129457i
\(610\) −0.0756207 1.29836i −0.00306179 0.0525689i
\(611\) −5.48012 + 31.0793i −0.221702 + 1.25733i
\(612\) −21.2692 10.5309i −0.859758 0.425685i
\(613\) 3.85172 + 21.8442i 0.155570 + 0.882279i 0.958263 + 0.285887i \(0.0922883\pi\)
−0.802694 + 0.596392i \(0.796601\pi\)
\(614\) −2.88955 + 0.684836i −0.116613 + 0.0276377i
\(615\) −12.5982 11.8183i −0.508009 0.476561i
\(616\) 0.00572390 0.0982755i 0.000230622 0.00395963i
\(617\) 9.76840 + 2.31515i 0.393261 + 0.0932046i 0.422489 0.906368i \(-0.361157\pi\)
−0.0292277 + 0.999573i \(0.509305\pi\)
\(618\) 0.502745 + 0.759675i 0.0202234 + 0.0305586i
\(619\) 19.8020 + 2.31452i 0.795910 + 0.0930285i 0.504322 0.863516i \(-0.331742\pi\)
0.291588 + 0.956544i \(0.405817\pi\)
\(620\) 4.99522 8.65197i 0.200613 0.347472i
\(621\) 42.5804 + 2.11596i 1.70869 + 0.0849105i
\(622\) −3.37316 5.84249i −0.135252 0.234263i
\(623\) −0.742667 1.72169i −0.0297543 0.0689783i
\(624\) −18.4821 13.6780i −0.739877 0.547557i
\(625\) −9.08048 + 9.62475i −0.363219 + 0.384990i
\(626\) 4.12846 2.07339i 0.165006 0.0828693i
\(627\) −1.51414 + 2.31646i −0.0604691 + 0.0925103i
\(628\) 6.94699 23.2046i 0.277215 0.925962i
\(629\) −13.9644 + 11.7176i −0.556799 + 0.467210i
\(630\) −0.0448718 + 0.0787505i −0.00178774 + 0.00313750i
\(631\) 1.55588 + 1.30554i 0.0619385 + 0.0519726i 0.673231 0.739432i \(-0.264906\pi\)
−0.611293 + 0.791404i \(0.709350\pi\)
\(632\) 2.15561 1.41777i 0.0857455 0.0563957i
\(633\) −16.7383 19.8332i −0.665288 0.788299i
\(634\) 3.77072 0.440734i 0.149755 0.0175038i
\(635\) 5.26686 12.2100i 0.209009 0.484538i
\(636\) 18.0133 10.4684i 0.714275 0.415098i
\(637\) 22.0202 + 11.0590i 0.872473 + 0.438172i
\(638\) 0.937360 0.341171i 0.0371105 0.0135071i
\(639\) 8.34700 + 27.3149i 0.330202 + 1.08056i
\(640\) −5.25884 1.91406i −0.207874 0.0756599i
\(641\) −18.3587 19.4590i −0.725123 0.768586i 0.255007 0.966939i \(-0.417922\pi\)
−0.980131 + 0.198354i \(0.936441\pi\)
\(642\) 3.34938 2.50835i 0.132189 0.0989965i
\(643\) 7.31393 + 4.81045i 0.288433 + 0.189706i 0.685477 0.728094i \(-0.259594\pi\)
−0.397044 + 0.917800i \(0.629964\pi\)
\(644\) 0.756267 + 2.52611i 0.0298011 + 0.0995426i
\(645\) −1.27468 5.31099i −0.0501904 0.209120i
\(646\) 1.03817 1.39451i 0.0408463 0.0548661i
\(647\) 1.73387 0.0681653 0.0340827 0.999419i \(-0.489149\pi\)
0.0340827 + 0.999419i \(0.489149\pi\)
\(648\) 6.47150 + 3.15852i 0.254225 + 0.124078i
\(649\) 2.18701 0.0858477
\(650\) −1.77815 + 2.38846i −0.0697446 + 0.0936833i
\(651\) −1.52438 0.451652i −0.0597450 0.0177016i
\(652\) −6.82333 22.7915i −0.267222 0.892585i
\(653\) −21.6103 14.2133i −0.845678 0.556211i 0.0510991 0.998694i \(-0.483728\pi\)
−0.896777 + 0.442482i \(0.854098\pi\)
\(654\) −5.83466 2.49718i −0.228153 0.0976476i
\(655\) 4.16953 + 4.41944i 0.162917 + 0.172682i
\(656\) −38.6315 14.0607i −1.50831 0.548979i
\(657\) 10.3348 24.3382i 0.403200 0.949525i
\(658\) 0.278217 0.101263i 0.0108460 0.00394763i
\(659\) −6.95554 3.49320i −0.270949 0.136076i 0.308137 0.951342i \(-0.400294\pi\)
−0.579087 + 0.815266i \(0.696591\pi\)
\(660\) 0.00659091 + 2.31933i 0.000256551 + 0.0902796i
\(661\) 3.09964 7.18577i 0.120562 0.279494i −0.847239 0.531213i \(-0.821737\pi\)
0.967800 + 0.251719i \(0.0809958\pi\)
\(662\) −1.18816 + 0.138877i −0.0461793 + 0.00539759i
\(663\) 8.38717 23.2489i 0.325731 0.902912i
\(664\) 11.2498 7.39909i 0.436576 0.287140i
\(665\) 0.243969 + 0.204714i 0.00946070 + 0.00793847i
\(666\) 2.08664 1.77120i 0.0808556 0.0686328i
\(667\) −41.3636 + 34.7082i −1.60161 + 1.34391i
\(668\) 1.42784 4.76933i 0.0552450 0.184531i
\(669\) 3.98766 + 7.88414i 0.154172 + 0.304818i
\(670\) −1.46180 + 0.734141i −0.0564741 + 0.0283623i
\(671\) −3.63448 + 3.85232i −0.140308 + 0.148717i
\(672\) −0.0759354 + 0.666079i −0.00292927 + 0.0256946i
\(673\) 2.50537 + 5.80809i 0.0965748 + 0.223886i 0.959654 0.281183i \(-0.0907266\pi\)
−0.863079 + 0.505068i \(0.831467\pi\)
\(674\) −1.22624 2.12391i −0.0472330 0.0818099i
\(675\) −9.55798 + 19.4430i −0.367887 + 0.748363i
\(676\) −0.502052 + 0.869580i −0.0193097 + 0.0334454i
\(677\) −24.4993 2.86355i −0.941583 0.110055i −0.368569 0.929600i \(-0.620152\pi\)
−0.573015 + 0.819545i \(0.694226\pi\)
\(678\) 4.15775 0.254019i 0.159677 0.00975553i
\(679\) −0.723152 0.171390i −0.0277520 0.00657735i
\(680\) 0.171203 2.93945i 0.00656535 0.112723i
\(681\) 6.61554 28.2710i 0.253508 1.08335i
\(682\) 0.825272 0.195593i 0.0316013 0.00748964i
\(683\) −3.77494 21.4087i −0.144444 0.819183i −0.967812 0.251675i \(-0.919019\pi\)
0.823368 0.567508i \(-0.192092\pi\)
\(684\) 7.41987 10.0858i 0.283706 0.385640i
\(685\) −2.31478 + 13.1278i −0.0884433 + 0.501587i
\(686\) −0.0269351 0.462458i −0.00102839 0.0176567i
\(687\) −17.8896 + 21.4434i −0.682530 + 0.818117i
\(688\) −7.76232 10.4266i −0.295936 0.397511i
\(689\) 12.9561 + 17.4031i 0.493589 + 0.663005i
\(690\) 0.902150 + 2.45689i 0.0343443 + 0.0935322i
\(691\) 2.82508 + 48.5047i 0.107471 + 1.84520i 0.435080 + 0.900392i \(0.356720\pi\)
−0.327609 + 0.944813i \(0.606243\pi\)
\(692\) 3.31247 18.7859i 0.125921 0.714134i
\(693\) 0.358660 0.0871598i 0.0136244 0.00331093i
\(694\) 0.0855992 + 0.485457i 0.00324930 + 0.0184277i
\(695\) −2.93994 + 0.696778i −0.111518 + 0.0264303i
\(696\) −8.72993 + 2.64062i −0.330907 + 0.100093i
\(697\) 2.56946 44.1159i 0.0973252 1.67101i
\(698\) −4.51923 1.07108i −0.171055 0.0405408i
\(699\) 8.10641 16.2562i 0.306613 0.614866i
\(700\) −1.33096 0.155567i −0.0503055 0.00587988i
\(701\) −12.9938 + 22.5060i −0.490770 + 0.850039i −0.999944 0.0106253i \(-0.996618\pi\)
0.509174 + 0.860664i \(0.329951\pi\)
\(702\) −1.23942 + 3.49777i −0.0467789 + 0.132015i
\(703\) −4.80861 8.32876i −0.181360 0.314125i
\(704\) 2.09024 + 4.84571i 0.0787788 + 0.182630i
\(705\) −12.9278 + 5.62012i −0.486888 + 0.211666i
\(706\) −3.21136 + 3.40384i −0.120861 + 0.128105i
\(707\) 0.337411 0.169454i 0.0126896 0.00637297i
\(708\) −9.87990 0.547272i −0.371309 0.0205677i
\(709\) −10.4008 + 34.7411i −0.390610 + 1.30473i 0.506239 + 0.862393i \(0.331035\pi\)
−0.896849 + 0.442336i \(0.854150\pi\)
\(710\) −1.34322 + 1.12709i −0.0504100 + 0.0422990i
\(711\) 7.44569 + 6.17590i 0.279235 + 0.231615i
\(712\) −7.00594 5.87868i −0.262559 0.220313i
\(713\) −38.3573 + 25.2280i −1.43649 + 0.944795i
\(714\) −0.228233 + 0.0409128i −0.00854142 + 0.00153112i
\(715\) −2.39897 + 0.280399i −0.0897163 + 0.0104863i
\(716\) 2.88896 6.69736i 0.107965 0.250292i
\(717\) −0.0816757 0.0468465i −0.00305024 0.00174952i
\(718\) 5.65470 + 2.83990i 0.211031 + 0.105984i
\(719\) 0.547249 0.199183i 0.0204090 0.00742825i −0.331795 0.943351i \(-0.607654\pi\)
0.352204 + 0.935923i \(0.385432\pi\)
\(720\) 0.538890 10.2563i 0.0200832 0.382229i
\(721\) −0.401170 0.146014i −0.0149404 0.00543785i
\(722\) −2.00563 2.12584i −0.0746417 0.0791156i
\(723\) −2.45022 20.4586i −0.0911248 0.760865i
\(724\) −11.9588 7.86540i −0.444444 0.292315i
\(725\) −7.86990 26.2873i −0.292281 0.976285i
\(726\) 2.65035 2.51475i 0.0983638 0.0933312i
\(727\) 11.9433 16.0426i 0.442951 0.594986i −0.523440 0.852062i \(-0.675352\pi\)
0.966391 + 0.257076i \(0.0827591\pi\)
\(728\) −0.463826 −0.0171905
\(729\) −4.23448 + 26.6659i −0.156832 + 0.987625i
\(730\) 1.62328 0.0600803
\(731\) 8.34385 11.2077i 0.308609 0.414533i
\(732\) 17.3829 16.4935i 0.642490 0.609618i
\(733\) 12.2974 + 41.0761i 0.454214 + 1.51718i 0.812158 + 0.583438i \(0.198293\pi\)
−0.357944 + 0.933743i \(0.616522\pi\)
\(734\) 1.29585 + 0.852297i 0.0478309 + 0.0314589i
\(735\) 1.30886 + 10.9286i 0.0482780 + 0.403107i
\(736\) 13.2847 + 14.0809i 0.489680 + 0.519030i
\(737\) 6.25963 + 2.27832i 0.230577 + 0.0839230i
\(738\) −0.348136 + 6.62580i −0.0128151 + 0.243899i
\(739\) −30.4321 + 11.0764i −1.11946 + 0.407452i −0.834457 0.551074i \(-0.814218\pi\)
−0.285008 + 0.958525i \(0.591996\pi\)
\(740\) −7.20274 3.61735i −0.264778 0.132976i
\(741\) 11.3107 + 6.48746i 0.415510 + 0.238323i
\(742\) 0.0806206 0.186899i 0.00295967 0.00686130i
\(743\) −12.4511 + 1.45532i −0.456786 + 0.0533906i −0.341375 0.939927i \(-0.610893\pi\)
−0.115411 + 0.993318i \(0.536818\pi\)
\(744\) −7.63302 + 1.36828i −0.279840 + 0.0501638i
\(745\) −3.73243 + 2.45486i −0.136746 + 0.0899390i
\(746\) −4.01804 3.37153i −0.147111 0.123441i
\(747\) 38.8578 + 32.2310i 1.42173 + 1.17927i
\(748\) −4.54525 + 3.81392i −0.166191 + 0.139451i
\(749\) −0.562432 + 1.87865i −0.0205508 + 0.0686445i
\(750\) −2.92057 0.161778i −0.106644 0.00590729i
\(751\) −21.8955 + 10.9963i −0.798977 + 0.401261i −0.800946 0.598737i \(-0.795670\pi\)
0.00196900 + 0.999998i \(0.499373\pi\)
\(752\) −23.0227 + 24.4026i −0.839550 + 0.889871i
\(753\) 7.06908 3.07316i 0.257611 0.111992i
\(754\) −1.86156 4.31559i −0.0677942 0.157165i
\(755\) −7.36209 12.7515i −0.267934 0.464075i
\(756\) −1.64207 + 0.303998i −0.0597215 + 0.0110563i
\(757\) −10.7313 + 18.5872i −0.390037 + 0.675564i −0.992454 0.122617i \(-0.960871\pi\)
0.602417 + 0.798182i \(0.294205\pi\)
\(758\) 5.33340 + 0.623385i 0.193718 + 0.0226424i
\(759\) 4.75634 9.53813i 0.172644 0.346212i
\(760\) 1.51152 + 0.358237i 0.0548286 + 0.0129946i
\(761\) 2.07041 35.5475i 0.0750522 1.28860i −0.725035 0.688712i \(-0.758176\pi\)
0.800087 0.599884i \(-0.204787\pi\)
\(762\) −4.88884 + 1.47877i −0.177104 + 0.0535703i
\(763\) 2.89411 0.685916i 0.104774 0.0248318i
\(764\) 7.06821 + 40.0858i 0.255719 + 1.45025i
\(765\) 10.7276 2.60698i 0.387858 0.0942554i
\(766\) 0.0945988 0.536496i 0.00341799 0.0193844i
\(767\) −0.599151 10.2870i −0.0216341 0.371443i
\(768\) −7.66079 20.8632i −0.276435 0.752835i
\(769\) −9.90767 13.3083i −0.357280 0.479910i 0.586751 0.809767i \(-0.300407\pi\)
−0.944031 + 0.329857i \(0.892999\pi\)
\(770\) 0.0135313 + 0.0181756i 0.000487633 + 0.000655005i
\(771\) 17.1698 20.5806i 0.618355 0.741194i
\(772\) −0.397895 6.83160i −0.0143206 0.245875i
\(773\) 1.97712 11.2128i 0.0711121 0.403297i −0.928386 0.371617i \(-0.878803\pi\)
0.999498 0.0316795i \(-0.0100856\pi\)
\(774\) −1.24319 + 1.68986i −0.0446856 + 0.0607409i
\(775\) −4.05134 22.9763i −0.145528 0.825332i
\(776\) −3.52720 + 0.835962i −0.126619 + 0.0300093i
\(777\) −0.292258 + 1.24894i −0.0104847 + 0.0448054i
\(778\) −0.278427 + 4.78041i −0.00998210 + 0.171386i
\(779\) 22.6852 + 5.37650i 0.812783 + 0.192633i
\(780\) 10.9076 0.666402i 0.390555 0.0238610i
\(781\) 7.09220 + 0.828959i 0.253779 + 0.0296625i
\(782\) −3.34781 + 5.79858i −0.119718 + 0.207357i
\(783\) −19.0342 28.4096i −0.680228 1.01528i
\(784\) 13.0976 + 22.6857i 0.467771 + 0.810204i
\(785\) 4.46269 + 10.3457i 0.159280 + 0.369253i
\(786\) 0.264345 2.31874i 0.00942887 0.0827068i
\(787\) 29.5496 31.3207i 1.05333 1.11646i 0.0603481 0.998177i \(-0.480779\pi\)
0.992980 0.118285i \(-0.0377396\pi\)
\(788\) 2.07428 1.04174i 0.0738932 0.0371105i
\(789\) 11.2064 + 22.1567i 0.398960 + 0.788798i
\(790\) −0.170326 + 0.568930i −0.00605994 + 0.0202416i
\(791\) −1.49542 + 1.25480i −0.0531709 + 0.0446157i
\(792\) 1.37251 1.16503i 0.0487699 0.0413974i
\(793\) 19.1159 + 16.0401i 0.678824 + 0.569601i
\(794\) 0.0184966 0.0121654i 0.000656421 0.000431735i
\(795\) −3.28871 + 9.11617i −0.116638 + 0.323317i
\(796\) −2.14355 + 0.250546i −0.0759763 + 0.00888035i
\(797\) 12.9510 30.0238i 0.458748 1.06350i −0.519201 0.854652i \(-0.673770\pi\)
0.977949 0.208845i \(-0.0669704\pi\)
\(798\) −0.000347623 0.122328i −1.23057e−5 0.00433036i
\(799\) −32.2264 16.1847i −1.14009 0.572575i
\(800\) −9.24443 + 3.36470i −0.326840 + 0.118960i
\(801\) 13.4026 31.5628i 0.473558 1.11522i
\(802\) −1.60412 0.583851i −0.0566433 0.0206165i
\(803\) −4.53635 4.80825i −0.160084 0.169679i
\(804\) −27.7080 11.8588i −0.977186 0.418227i
\(805\) −1.02478 0.674011i −0.0361189 0.0237558i
\(806\) −1.14610 3.82824i −0.0403697 0.134844i
\(807\) −3.02321 0.895736i −0.106422 0.0315314i
\(808\) 1.09974 1.47721i 0.0386888 0.0519680i
\(809\) 25.5159 0.897092 0.448546 0.893760i \(-0.351942\pi\)
0.448546 + 0.893760i \(0.351942\pi\)
\(810\) −1.60843 + 0.400569i −0.0565146 + 0.0140745i
\(811\) −8.80464 −0.309173 −0.154586 0.987979i \(-0.549404\pi\)
−0.154586 + 0.987979i \(0.549404\pi\)
\(812\) 1.26304 1.69656i 0.0443242 0.0595377i
\(813\) −5.49196 22.8824i −0.192611 0.802522i
\(814\) −0.196247 0.655509i −0.00687844 0.0229756i
\(815\) 9.24600 + 6.08119i 0.323873 + 0.213015i
\(816\) 21.0304 15.7496i 0.736212 0.551348i
\(817\) 5.05864 + 5.36185i 0.176980 + 0.187587i
\(818\) −0.960082 0.349441i −0.0335685 0.0122179i
\(819\) −0.508232 1.66315i −0.0177590 0.0581151i
\(820\) 18.3605 6.68268i 0.641177 0.233369i
\(821\) 5.26569 + 2.64453i 0.183774 + 0.0922947i 0.538307 0.842749i \(-0.319064\pi\)
−0.354533 + 0.935043i \(0.615360\pi\)
\(822\) 4.42693 2.57269i 0.154407 0.0897328i
\(823\) −17.9055 + 41.5096i −0.624146 + 1.44693i 0.253363 + 0.967371i \(0.418463\pi\)
−0.877509 + 0.479561i \(0.840796\pi\)
\(824\) −2.06822 + 0.241741i −0.0720500 + 0.00842144i
\(825\) 3.49334 + 4.13926i 0.121623 + 0.144110i
\(826\) −0.0807687 + 0.0531224i −0.00281030 + 0.00184837i
\(827\) −3.29612 2.76578i −0.114617 0.0961755i 0.583678 0.811986i \(-0.301613\pi\)
−0.698295 + 0.715810i \(0.746058\pi\)
\(828\) −23.8737 + 41.8987i −0.829670 + 1.45608i
\(829\) 39.1908 32.8850i 1.36115 1.14214i 0.385529 0.922696i \(-0.374019\pi\)
0.975624 0.219448i \(-0.0704255\pi\)
\(830\) −0.888905 + 2.96915i −0.0308543 + 0.103061i
\(831\) −20.7407 + 31.7308i −0.719487 + 1.10073i
\(832\) 22.2201 11.1594i 0.770344 0.386881i
\(833\) −19.3230 + 20.4811i −0.669501 + 0.709629i
\(834\) 0.932844 + 0.690365i 0.0323017 + 0.0239054i
\(835\) 0.917236 + 2.12639i 0.0317422 + 0.0735868i
\(836\) −1.56514 2.71090i −0.0541315 0.0937586i
\(837\) −13.2701 25.8706i −0.458681 0.894218i
\(838\) 1.29088 2.23588i 0.0445928 0.0772370i
\(839\) −22.1161 2.58500i −0.763532 0.0892441i −0.274591 0.961561i \(-0.588542\pi\)
−0.488941 + 0.872317i \(0.662617\pi\)
\(840\) −0.114339 0.172773i −0.00394507 0.00596122i
\(841\) 13.9257 + 3.30044i 0.480195 + 0.113808i
\(842\) −0.213951 + 3.67339i −0.00737323 + 0.126594i
\(843\) 31.9123 + 29.9368i 1.09912 + 1.03108i
\(844\) 28.5640 6.76979i 0.983213 0.233026i
\(845\) −0.0811055 0.459972i −0.00279011 0.0158235i
\(846\) 4.85232 + 2.40249i 0.166826 + 0.0825994i
\(847\) −0.297321 + 1.68619i −0.0102161 + 0.0579381i
\(848\) 1.34108 + 23.0255i 0.0460530 + 0.790699i
\(849\) 38.1974 + 6.62337i 1.31093 + 0.227313i
\(850\) −2.03190 2.72931i −0.0696934 0.0936145i
\(851\) 22.1183 + 29.7100i 0.758205 + 1.01845i
\(852\) −31.8318 5.51959i −1.09054 0.189098i
\(853\) 0.388118 + 6.66373i 0.0132889 + 0.228162i 0.998413 + 0.0563169i \(0.0179357\pi\)
−0.985124 + 0.171845i \(0.945027\pi\)
\(854\) 0.0406525 0.230552i 0.00139110 0.00788933i
\(855\) 0.371693 + 5.81242i 0.0127116 + 0.198781i
\(856\) 1.66095 + 9.41973i 0.0567702 + 0.321960i
\(857\) −3.14898 + 0.746322i −0.107567 + 0.0254939i −0.284047 0.958810i \(-0.591677\pi\)
0.176480 + 0.984304i \(0.443529\pi\)
\(858\) 0.676607 + 0.634721i 0.0230990 + 0.0216690i
\(859\) 0.520474 8.93620i 0.0177584 0.304899i −0.977720 0.209912i \(-0.932682\pi\)
0.995479 0.0949867i \(-0.0302809\pi\)
\(860\) 6.01144 + 1.42474i 0.204988 + 0.0485831i
\(861\) −1.71603 2.59301i −0.0584820 0.0883696i
\(862\) 4.64387 + 0.542791i 0.158171 + 0.0184875i
\(863\) 8.30305 14.3813i 0.282639 0.489546i −0.689395 0.724386i \(-0.742123\pi\)
0.972034 + 0.234840i \(0.0754567\pi\)
\(864\) −9.77131 + 7.40477i −0.332427 + 0.251915i
\(865\) 4.43662 + 7.68446i 0.150850 + 0.261279i
\(866\) 2.68204 + 6.21767i 0.0911395 + 0.211285i
\(867\) −0.966472 0.715252i −0.0328231 0.0242912i
\(868\) 1.23410 1.30807i 0.0418880 0.0443987i
\(869\) 2.16119 1.08539i 0.0733133 0.0368193i
\(870\) 1.14863 1.75727i 0.0389423 0.0595770i
\(871\) 9.00164 30.0676i 0.305009 1.01880i
\(872\) 11.1131 9.32502i 0.376338 0.315785i
\(873\) −6.86241 11.7316i −0.232257 0.397053i
\(874\) −2.70598 2.27059i −0.0915312 0.0768038i
\(875\) 1.14529 0.753268i 0.0387178 0.0254651i
\(876\) 19.2899 + 22.8566i 0.651746 + 0.772253i
\(877\) −5.55689 + 0.649507i −0.187643 + 0.0219323i −0.209395 0.977831i \(-0.567150\pi\)
0.0217525 + 0.999763i \(0.493075\pi\)
\(878\) 2.53374 5.87387i 0.0855096 0.198233i
\(879\) −19.6083 + 11.3953i −0.661372 + 0.384353i
\(880\) −2.29450 1.15234i −0.0773477 0.0388455i
\(881\) −8.40136 + 3.05784i −0.283049 + 0.103021i −0.479643 0.877464i \(-0.659234\pi\)
0.196595 + 0.980485i \(0.437012\pi\)
\(882\) 2.88369 3.09155i 0.0970990 0.104098i
\(883\) 13.8259 + 5.03222i 0.465279 + 0.169348i 0.564013 0.825766i \(-0.309257\pi\)
−0.0987335 + 0.995114i \(0.531479\pi\)
\(884\) 19.1847 + 20.3346i 0.645252 + 0.683927i
\(885\) 3.68416 2.75906i 0.123842 0.0927449i
\(886\) −3.81773 2.51096i −0.128259 0.0843574i
\(887\) −1.26449 4.22369i −0.0424574 0.141818i 0.934133 0.356925i \(-0.116175\pi\)
−0.976590 + 0.215108i \(0.930990\pi\)
\(888\) 1.46010 + 6.08355i 0.0489977 + 0.204151i
\(889\) 1.42938 1.91999i 0.0479398 0.0643943i
\(890\) 2.10514 0.0705643
\(891\) 5.68136 + 3.64486i 0.190333 + 0.122107i
\(892\) −9.99369 −0.334614
\(893\) 11.3612 15.2607i 0.380187 0.510680i
\(894\) 1.64523 + 0.487459i 0.0550247 + 0.0163031i
\(895\) 0.973070 + 3.25028i 0.0325261 + 0.108645i
\(896\) −0.841651 0.553563i −0.0281176 0.0184932i
\(897\) −46.1675 19.7593i −1.54149 0.659744i
\(898\) −2.49918 2.64898i −0.0833988 0.0883976i
\(899\) 34.6044 + 12.5950i 1.15412 + 0.420066i
\(900\) −14.7455 19.5734i −0.491517 0.652447i
\(901\) −23.2973 + 8.47952i −0.776145 + 0.282494i
\(902\) 1.48231 + 0.744442i 0.0493554 + 0.0247872i
\(903\) −0.00279387 0.983157i −9.29743e−5 0.0327174i
\(904\) −3.77131 + 8.74288i −0.125432 + 0.290784i
\(905\) 6.61304 0.772953i 0.219825 0.0256938i
\(906\) −1.91921 + 5.31999i −0.0637616 + 0.176745i
\(907\) −2.73796 + 1.80079i −0.0909126 + 0.0597941i −0.594151 0.804353i \(-0.702512\pi\)
0.503239 + 0.864147i \(0.332142\pi\)
\(908\) 25.1582 + 21.1102i 0.834904 + 0.700568i
\(909\) 6.50188 + 2.32473i 0.215654 + 0.0771064i
\(910\) 0.0817857 0.0686263i 0.00271117 0.00227494i
\(911\) 12.0728 40.3259i 0.399989 1.33606i −0.486651 0.873596i \(-0.661782\pi\)
0.886640 0.462460i \(-0.153033\pi\)
\(912\) 6.25618 + 12.3693i 0.207163 + 0.409589i
\(913\) 11.2789 5.66446i 0.373276 0.187466i
\(914\) −3.26736 + 3.46320i −0.108075 + 0.114552i
\(915\) −1.26255 + 11.0746i −0.0417386 + 0.366116i
\(916\) −12.5112 29.0042i −0.413382 0.958326i
\(917\) 0.546849 + 0.947170i 0.0180585 + 0.0312783i
\(918\) −3.42281 2.50312i −0.112970 0.0826153i
\(919\) 15.0654 26.0940i 0.496962 0.860763i −0.503032 0.864268i \(-0.667782\pi\)
0.999994 + 0.00350463i \(0.00111556\pi\)
\(920\) −5.94219 0.694543i −0.195908 0.0228984i
\(921\) 25.4034 1.55203i 0.837071 0.0511410i
\(922\) 7.89966 + 1.87225i 0.260162 + 0.0616594i
\(923\) 1.95620 33.5866i 0.0643891 1.10552i
\(924\) −0.0951262 + 0.406513i −0.00312942 + 0.0133733i
\(925\) −18.3153 + 4.34082i −0.602205 + 0.142725i
\(926\) 0.385410 + 2.18577i 0.0126654 + 0.0718288i
\(927\) −3.13304 7.15118i −0.102903 0.234876i
\(928\) 2.69639 15.2920i 0.0885133 0.501984i
\(929\) −2.07372 35.6043i −0.0680364 1.16814i −0.843636 0.536915i \(-0.819589\pi\)
0.775600 0.631225i \(-0.217448\pi\)
\(930\) 1.14347 1.37063i 0.0374959 0.0449446i
\(931\) −8.87087 11.9156i −0.290731 0.390519i
\(932\) 12.2699 + 16.4813i 0.401914 + 0.539864i
\(933\) 19.9296 + 54.2758i 0.652466 + 1.77691i
\(934\) −0.0198059 0.340054i −0.000648069 0.0111269i
\(935\) 0.479264 2.71804i 0.0156736 0.0888895i
\(936\) −5.85594 6.13668i −0.191407 0.200584i
\(937\) −2.81383 15.9580i −0.0919239 0.521326i −0.995647 0.0932080i \(-0.970288\pi\)
0.903723 0.428118i \(-0.140823\pi\)
\(938\) −0.286516 + 0.0679054i −0.00935506 + 0.00221719i
\(939\) −37.8985 + 11.4635i −1.23677 + 0.374098i
\(940\) 0.927114 15.9179i 0.0302391 0.519186i
\(941\) −15.2035 3.60329i −0.495619 0.117464i −0.0247977 0.999692i \(-0.507894\pi\)
−0.470821 + 0.882229i \(0.656042\pi\)
\(942\) 1.93128 3.87291i 0.0629247 0.126186i
\(943\) −89.1818 10.4239i −2.90416 0.339447i
\(944\) 5.47715 9.48670i 0.178266 0.308766i
\(945\) 0.494228 0.599301i 0.0160772 0.0194953i
\(946\) 0.262238 + 0.454209i 0.00852609 + 0.0147676i
\(947\) 20.1940 + 46.8149i 0.656216 + 1.52128i 0.842450 + 0.538774i \(0.181113\pi\)
−0.186234 + 0.982505i \(0.559628\pi\)
\(948\) −10.0349 + 4.36248i −0.325917 + 0.141687i
\(949\) −21.3738 + 22.6549i −0.693822 + 0.735408i
\(950\) 1.60417 0.805645i 0.0520462 0.0261386i
\(951\) −32.4870 1.79954i −1.05346 0.0583540i
\(952\) 0.152010 0.507750i 0.00492668 0.0164563i
\(953\) −30.4826 + 25.5779i −0.987428 + 0.828550i −0.985193 0.171447i \(-0.945156\pi\)
−0.00223469 + 0.999998i \(0.500711\pi\)
\(954\) 3.49064 1.29300i 0.113014 0.0418626i
\(955\) −14.5042 12.1705i −0.469346 0.393828i
\(956\) 0.0889818 0.0585242i 0.00287788 0.00189281i
\(957\) −8.41505 + 1.50847i −0.272020 + 0.0487619i
\(958\) −3.99241 + 0.466645i −0.128989 + 0.0150766i
\(959\) −0.950408 + 2.20329i −0.0306903 + 0.0711481i
\(960\) 9.63434 + 5.52595i 0.310947 + 0.178349i
\(961\) 0.277414 + 0.139323i 0.00894885 + 0.00449428i
\(962\) −3.02955 + 1.10267i −0.0976767 + 0.0355514i
\(963\) −31.9565 + 16.2773i −1.02978 + 0.524527i
\(964\) 21.9010 + 7.97131i 0.705384 + 0.256739i
\(965\) 2.18442 + 2.31535i 0.0703190 + 0.0745338i
\(966\) 0.0560242 + 0.467785i 0.00180255 + 0.0150507i
\(967\) −18.8634 12.4066i −0.606605 0.398970i 0.208719 0.977976i \(-0.433071\pi\)
−0.815324 + 0.579006i \(0.803441\pi\)
\(968\) 2.39519 + 8.00049i 0.0769843 + 0.257145i
\(969\) −10.8087 + 10.2557i −0.347225 + 0.329460i
\(970\) 0.498259 0.669278i 0.0159981 0.0214892i
\(971\) 7.94868 0.255085 0.127543 0.991833i \(-0.459291\pi\)
0.127543 + 0.991833i \(0.459291\pi\)
\(972\) −24.7537 17.8875i −0.793975 0.573741i
\(973\) −0.543867 −0.0174356
\(974\) 2.04421 2.74585i 0.0655007 0.0879826i
\(975\) 18.5128 17.5656i 0.592883 0.562550i
\(976\) 7.60821 + 25.4132i 0.243533 + 0.813457i
\(977\) −32.3908 21.3038i −1.03628 0.681569i −0.0870620 0.996203i \(-0.527748\pi\)
−0.949213 + 0.314634i \(0.898118\pi\)
\(978\) −0.505472 4.22054i −0.0161632 0.134958i
\(979\) −5.88292 6.23553i −0.188019 0.199288i
\(980\) −11.6991 4.25811i −0.373713 0.136020i
\(981\) 45.6140 + 29.6308i 1.45634 + 0.946037i
\(982\) −6.53202 + 2.37746i −0.208445 + 0.0758678i
\(983\) 15.0544 + 7.56062i 0.480162 + 0.241146i 0.672380 0.740206i \(-0.265272\pi\)
−0.192219 + 0.981352i \(0.561568\pi\)
\(984\) −13.1559 7.54579i −0.419394 0.240551i
\(985\) −0.427654 + 0.991413i −0.0136262 + 0.0315890i
\(986\) 5.33437 0.623498i 0.169881 0.0198562i
\(987\) −2.49766 + 0.447727i −0.0795014 + 0.0142513i
\(988\) −12.3225 + 8.10462i −0.392030 + 0.257842i
\(989\) −21.7482 18.2489i −0.691552 0.580281i
\(990\) −0.0696379 + 0.408499i −0.00221324 + 0.0129829i
\(991\) −5.22377 + 4.38327i −0.165939 + 0.139239i −0.721976 0.691919i \(-0.756766\pi\)
0.556037 + 0.831158i \(0.312321\pi\)
\(992\) 3.78651 12.6478i 0.120222 0.401569i
\(993\) 10.2367 + 0.567039i 0.324853 + 0.0179944i
\(994\) −0.282058 + 0.141655i −0.00894634 + 0.00449302i
\(995\) 0.688905 0.730197i 0.0218398 0.0231488i
\(996\) −52.3702 + 22.7670i −1.65941 + 0.721401i
\(997\) −4.68352 10.8576i −0.148329 0.343864i 0.827811 0.561007i \(-0.189586\pi\)
−0.976140 + 0.217142i \(0.930326\pi\)
\(998\) 1.77775 + 3.07914i 0.0562735 + 0.0974686i
\(999\) −20.2140 + 11.9015i −0.639543 + 0.376546i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 81.2.g.a.58.5 yes 144
3.2 odd 2 243.2.g.a.226.4 144
9.2 odd 6 729.2.g.a.433.5 144
9.4 even 3 729.2.g.c.676.5 144
9.5 odd 6 729.2.g.b.676.4 144
9.7 even 3 729.2.g.d.433.4 144
81.7 even 27 inner 81.2.g.a.7.5 144
81.13 even 27 6561.2.a.c.1.36 72
81.20 odd 54 729.2.g.b.55.4 144
81.34 even 27 729.2.g.d.298.4 144
81.47 odd 54 729.2.g.a.298.5 144
81.61 even 27 729.2.g.c.55.5 144
81.68 odd 54 6561.2.a.d.1.37 72
81.74 odd 54 243.2.g.a.100.4 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.7.5 144 81.7 even 27 inner
81.2.g.a.58.5 yes 144 1.1 even 1 trivial
243.2.g.a.100.4 144 81.74 odd 54
243.2.g.a.226.4 144 3.2 odd 2
729.2.g.a.298.5 144 81.47 odd 54
729.2.g.a.433.5 144 9.2 odd 6
729.2.g.b.55.4 144 81.20 odd 54
729.2.g.b.676.4 144 9.5 odd 6
729.2.g.c.55.5 144 81.61 even 27
729.2.g.c.676.5 144 9.4 even 3
729.2.g.d.298.4 144 81.34 even 27
729.2.g.d.433.4 144 9.7 even 3
6561.2.a.c.1.36 72 81.13 even 27
6561.2.a.d.1.37 72 81.68 odd 54