Properties

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

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 163.2
Root \(-0.0878222i\) of defining polynomial
Character \(\chi\) \(=\) 729.163
Dual form 729.2.e.k.568.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.162544 - 0.0591613i) q^{2} +(-1.50917 + 1.26634i) q^{4} +(0.648847 + 3.67980i) q^{5} +(2.32226 + 1.94861i) q^{7} +(-0.343364 + 0.594724i) q^{8} +O(q^{10})\) \(q+(0.162544 - 0.0591613i) q^{2} +(-1.50917 + 1.26634i) q^{4} +(0.648847 + 3.67980i) q^{5} +(2.32226 + 1.94861i) q^{7} +(-0.343364 + 0.594724i) q^{8} +(0.323168 + 0.559743i) q^{10} +(0.432678 - 2.45384i) q^{11} +(0.718995 + 0.261693i) q^{13} +(0.492752 + 0.179347i) q^{14} +(0.663574 - 3.76332i) q^{16} +(2.31139 + 4.00345i) q^{17} +(0.305922 - 0.529872i) q^{19} +(-5.63910 - 4.73177i) q^{20} +(-0.0748430 - 0.424456i) q^{22} +(-4.99796 + 4.19379i) q^{23} +(-8.42143 + 3.06515i) q^{25} +0.132351 q^{26} -5.97229 q^{28} +(-6.15583 + 2.24054i) q^{29} +(5.01792 - 4.21053i) q^{31} +(-0.353281 - 2.00355i) q^{32} +(0.612552 + 0.513992i) q^{34} +(-5.66369 + 9.80980i) q^{35} +(-2.47984 - 4.29522i) q^{37} +(0.0183779 - 0.104226i) q^{38} +(-2.41125 - 0.877625i) q^{40} +(4.94301 + 1.79911i) q^{41} +(0.967320 - 5.48594i) q^{43} +(2.45442 + 4.25118i) q^{44} +(-0.564280 + 0.977362i) q^{46} +(-0.848483 - 0.711962i) q^{47} +(0.380286 + 2.15671i) q^{49} +(-1.18752 + 0.996445i) q^{50} +(-1.41648 + 0.515556i) q^{52} -8.84310 q^{53} +9.31038 q^{55} +(-1.95627 + 0.712023i) q^{56} +(-0.868041 + 0.728373i) q^{58} +(2.05804 + 11.6717i) q^{59} +(6.27161 + 5.26250i) q^{61} +(0.566533 - 0.981264i) q^{62} +(3.64541 + 6.31404i) q^{64} +(-0.496458 + 2.81555i) q^{65} +(1.13923 + 0.414644i) q^{67} +(-8.55801 - 3.11486i) q^{68} +(-0.340240 + 1.92960i) q^{70} +(-2.45973 - 4.26038i) q^{71} +(-2.14972 + 3.72343i) q^{73} +(-0.657195 - 0.551452i) q^{74} +(0.209312 + 1.18707i) q^{76} +(5.78637 - 4.85534i) q^{77} +(11.0833 - 4.03399i) q^{79} +14.2788 q^{80} +0.909895 q^{82} +(8.47234 - 3.08368i) q^{83} +(-13.2321 + 11.1031i) q^{85} +(-0.167323 - 0.948936i) q^{86} +(1.31079 + 1.09989i) q^{88} +(3.76943 - 6.52884i) q^{89} +(1.15976 + 2.00876i) q^{91} +(2.23199 - 12.6583i) q^{92} +(-0.180037 - 0.0655279i) q^{94} +(2.14832 + 0.781924i) q^{95} +(-0.164680 + 0.933947i) q^{97} +(0.189407 + 0.328062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 6 q^{10} + 15 q^{11} - 3 q^{13} + 21 q^{14} + 9 q^{16} + 9 q^{17} - 12 q^{19} + 3 q^{20} + 33 q^{22} - 15 q^{23} - 12 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 27 q^{32} + 27 q^{34} - 30 q^{35} - 3 q^{37} + 39 q^{38} + 24 q^{40} + 39 q^{41} + 24 q^{43} + 33 q^{44} + 3 q^{46} + 42 q^{47} - 30 q^{49} + 15 q^{50} - 45 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} - 30 q^{58} - 15 q^{59} - 3 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} - 3 q^{67} - 36 q^{68} - 75 q^{70} - 12 q^{73} - 60 q^{74} + 30 q^{76} - 33 q^{77} + 33 q^{79} - 42 q^{80} - 42 q^{82} + 33 q^{83} - 18 q^{85} + 30 q^{86} - 42 q^{88} + 9 q^{89} - 18 q^{91} - 33 q^{92} - 66 q^{94} - 12 q^{95} + 15 q^{97} - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.162544 0.0591613i 0.114936 0.0418333i −0.283912 0.958850i \(-0.591632\pi\)
0.398848 + 0.917017i \(0.369410\pi\)
\(3\) 0 0
\(4\) −1.50917 + 1.26634i −0.754584 + 0.633171i
\(5\) 0.648847 + 3.67980i 0.290173 + 1.64565i 0.686198 + 0.727415i \(0.259278\pi\)
−0.396025 + 0.918240i \(0.629611\pi\)
\(6\) 0 0
\(7\) 2.32226 + 1.94861i 0.877733 + 0.736505i 0.965712 0.259617i \(-0.0835964\pi\)
−0.0879791 + 0.996122i \(0.528041\pi\)
\(8\) −0.343364 + 0.594724i −0.121398 + 0.210267i
\(9\) 0 0
\(10\) 0.323168 + 0.559743i 0.102195 + 0.177006i
\(11\) 0.432678 2.45384i 0.130457 0.739861i −0.847458 0.530862i \(-0.821868\pi\)
0.977916 0.208999i \(-0.0670206\pi\)
\(12\) 0 0
\(13\) 0.718995 + 0.261693i 0.199413 + 0.0725805i 0.439796 0.898098i \(-0.355051\pi\)
−0.240383 + 0.970678i \(0.577273\pi\)
\(14\) 0.492752 + 0.179347i 0.131694 + 0.0479326i
\(15\) 0 0
\(16\) 0.663574 3.76332i 0.165894 0.940829i
\(17\) 2.31139 + 4.00345i 0.560595 + 0.970979i 0.997445 + 0.0714442i \(0.0227608\pi\)
−0.436850 + 0.899534i \(0.643906\pi\)
\(18\) 0 0
\(19\) 0.305922 0.529872i 0.0701833 0.121561i −0.828798 0.559548i \(-0.810975\pi\)
0.898982 + 0.437987i \(0.144308\pi\)
\(20\) −5.63910 4.73177i −1.26094 1.05806i
\(21\) 0 0
\(22\) −0.0748430 0.424456i −0.0159566 0.0904942i
\(23\) −4.99796 + 4.19379i −1.04215 + 0.874465i −0.992246 0.124289i \(-0.960335\pi\)
−0.0499011 + 0.998754i \(0.515891\pi\)
\(24\) 0 0
\(25\) −8.42143 + 3.06515i −1.68429 + 0.613030i
\(26\) 0.132351 0.0259561
\(27\) 0 0
\(28\) −5.97229 −1.12866
\(29\) −6.15583 + 2.24054i −1.14311 + 0.416057i −0.843035 0.537859i \(-0.819233\pi\)
−0.300073 + 0.953916i \(0.597011\pi\)
\(30\) 0 0
\(31\) 5.01792 4.21053i 0.901245 0.756234i −0.0691887 0.997604i \(-0.522041\pi\)
0.970433 + 0.241370i \(0.0775966\pi\)
\(32\) −0.353281 2.00355i −0.0624518 0.354182i
\(33\) 0 0
\(34\) 0.612552 + 0.513992i 0.105052 + 0.0881490i
\(35\) −5.66369 + 9.80980i −0.957338 + 1.65816i
\(36\) 0 0
\(37\) −2.47984 4.29522i −0.407684 0.706129i 0.586946 0.809626i \(-0.300330\pi\)
−0.994630 + 0.103497i \(0.966997\pi\)
\(38\) 0.0183779 0.104226i 0.00298129 0.0169078i
\(39\) 0 0
\(40\) −2.41125 0.877625i −0.381253 0.138765i
\(41\) 4.94301 + 1.79911i 0.771968 + 0.280973i 0.697819 0.716274i \(-0.254154\pi\)
0.0741488 + 0.997247i \(0.476376\pi\)
\(42\) 0 0
\(43\) 0.967320 5.48594i 0.147515 0.836599i −0.817798 0.575505i \(-0.804806\pi\)
0.965313 0.261094i \(-0.0840832\pi\)
\(44\) 2.45442 + 4.25118i 0.370018 + 0.640889i
\(45\) 0 0
\(46\) −0.564280 + 0.977362i −0.0831986 + 0.144104i
\(47\) −0.848483 0.711962i −0.123764 0.103850i 0.578805 0.815466i \(-0.303519\pi\)
−0.702569 + 0.711616i \(0.747964\pi\)
\(48\) 0 0
\(49\) 0.380286 + 2.15671i 0.0543265 + 0.308101i
\(50\) −1.18752 + 0.996445i −0.167940 + 0.140919i
\(51\) 0 0
\(52\) −1.41648 + 0.515556i −0.196430 + 0.0714947i
\(53\) −8.84310 −1.21469 −0.607346 0.794437i \(-0.707766\pi\)
−0.607346 + 0.794437i \(0.707766\pi\)
\(54\) 0 0
\(55\) 9.31038 1.25541
\(56\) −1.95627 + 0.712023i −0.261417 + 0.0951480i
\(57\) 0 0
\(58\) −0.868041 + 0.728373i −0.113979 + 0.0956400i
\(59\) 2.05804 + 11.6717i 0.267933 + 1.51953i 0.760550 + 0.649280i \(0.224929\pi\)
−0.492616 + 0.870247i \(0.663959\pi\)
\(60\) 0 0
\(61\) 6.27161 + 5.26250i 0.802997 + 0.673795i 0.948925 0.315500i \(-0.102172\pi\)
−0.145928 + 0.989295i \(0.546617\pi\)
\(62\) 0.566533 0.981264i 0.0719498 0.124621i
\(63\) 0 0
\(64\) 3.64541 + 6.31404i 0.455677 + 0.789255i
\(65\) −0.496458 + 2.81555i −0.0615781 + 0.349227i
\(66\) 0 0
\(67\) 1.13923 + 0.414644i 0.139179 + 0.0506568i 0.410670 0.911784i \(-0.365295\pi\)
−0.271492 + 0.962441i \(0.587517\pi\)
\(68\) −8.55801 3.11486i −1.03781 0.377733i
\(69\) 0 0
\(70\) −0.340240 + 1.92960i −0.0406665 + 0.230631i
\(71\) −2.45973 4.26038i −0.291916 0.505614i 0.682346 0.731029i \(-0.260960\pi\)
−0.974263 + 0.225415i \(0.927626\pi\)
\(72\) 0 0
\(73\) −2.14972 + 3.72343i −0.251606 + 0.435795i −0.963968 0.266017i \(-0.914292\pi\)
0.712362 + 0.701812i \(0.247625\pi\)
\(74\) −0.657195 0.551452i −0.0763973 0.0641050i
\(75\) 0 0
\(76\) 0.209312 + 1.18707i 0.0240098 + 0.136166i
\(77\) 5.78637 4.85534i 0.659418 0.553318i
\(78\) 0 0
\(79\) 11.0833 4.03399i 1.24697 0.453860i 0.367593 0.929987i \(-0.380182\pi\)
0.879376 + 0.476127i \(0.157960\pi\)
\(80\) 14.2788 1.59642
\(81\) 0 0
\(82\) 0.909895 0.100481
\(83\) 8.47234 3.08368i 0.929960 0.338478i 0.167766 0.985827i \(-0.446345\pi\)
0.762194 + 0.647349i \(0.224122\pi\)
\(84\) 0 0
\(85\) −13.2321 + 11.1031i −1.43523 + 1.20430i
\(86\) −0.167323 0.948936i −0.0180429 0.102326i
\(87\) 0 0
\(88\) 1.31079 + 1.09989i 0.139731 + 0.117248i
\(89\) 3.76943 6.52884i 0.399558 0.692055i −0.594113 0.804382i \(-0.702497\pi\)
0.993671 + 0.112326i \(0.0358302\pi\)
\(90\) 0 0
\(91\) 1.15976 + 2.00876i 0.121576 + 0.210575i
\(92\) 2.23199 12.6583i 0.232701 1.31972i
\(93\) 0 0
\(94\) −0.180037 0.0655279i −0.0185694 0.00675869i
\(95\) 2.14832 + 0.781924i 0.220413 + 0.0802237i
\(96\) 0 0
\(97\) −0.164680 + 0.933947i −0.0167207 + 0.0948279i −0.992026 0.126033i \(-0.959776\pi\)
0.975305 + 0.220861i \(0.0708866\pi\)
\(98\) 0.189407 + 0.328062i 0.0191330 + 0.0331393i
\(99\) 0 0
\(100\) 8.82783 15.2902i 0.882783 1.52902i
\(101\) 4.29610 + 3.60485i 0.427477 + 0.358696i 0.830999 0.556274i \(-0.187769\pi\)
−0.403521 + 0.914970i \(0.632214\pi\)
\(102\) 0 0
\(103\) −1.63664 9.28183i −0.161263 0.914566i −0.952835 0.303490i \(-0.901848\pi\)
0.791572 0.611076i \(-0.209263\pi\)
\(104\) −0.402512 + 0.337748i −0.0394696 + 0.0331189i
\(105\) 0 0
\(106\) −1.43739 + 0.523169i −0.139612 + 0.0508146i
\(107\) 1.27825 0.123573 0.0617864 0.998089i \(-0.480320\pi\)
0.0617864 + 0.998089i \(0.480320\pi\)
\(108\) 0 0
\(109\) −7.40689 −0.709451 −0.354726 0.934970i \(-0.615426\pi\)
−0.354726 + 0.934970i \(0.615426\pi\)
\(110\) 1.51335 0.550814i 0.144292 0.0525180i
\(111\) 0 0
\(112\) 8.87423 7.44636i 0.838535 0.703615i
\(113\) −1.62395 9.20989i −0.152768 0.866393i −0.960798 0.277251i \(-0.910577\pi\)
0.808029 0.589143i \(-0.200534\pi\)
\(114\) 0 0
\(115\) −18.6752 15.6704i −1.74147 1.46127i
\(116\) 6.45289 11.1767i 0.599136 1.03773i
\(117\) 0 0
\(118\) 1.02503 + 1.77541i 0.0943621 + 0.163440i
\(119\) −2.43350 + 13.8011i −0.223078 + 1.26514i
\(120\) 0 0
\(121\) 4.50249 + 1.63877i 0.409317 + 0.148979i
\(122\) 1.33075 + 0.484353i 0.120480 + 0.0438513i
\(123\) 0 0
\(124\) −2.24091 + 12.7088i −0.201239 + 1.14128i
\(125\) −7.40194 12.8205i −0.662050 1.14670i
\(126\) 0 0
\(127\) −10.3984 + 18.0106i −0.922710 + 1.59818i −0.127505 + 0.991838i \(0.540697\pi\)
−0.795204 + 0.606342i \(0.792636\pi\)
\(128\) 4.08306 + 3.42610i 0.360895 + 0.302827i
\(129\) 0 0
\(130\) 0.0858753 + 0.487023i 0.00753176 + 0.0427148i
\(131\) 0.502395 0.421559i 0.0438944 0.0368318i −0.620577 0.784146i \(-0.713101\pi\)
0.664471 + 0.747314i \(0.268657\pi\)
\(132\) 0 0
\(133\) 1.74295 0.634380i 0.151133 0.0550077i
\(134\) 0.209705 0.0181158
\(135\) 0 0
\(136\) −3.17460 −0.272219
\(137\) 8.06971 2.93713i 0.689442 0.250936i 0.0265455 0.999648i \(-0.491549\pi\)
0.662896 + 0.748711i \(0.269327\pi\)
\(138\) 0 0
\(139\) 10.3003 8.64301i 0.873664 0.733091i −0.0912026 0.995832i \(-0.529071\pi\)
0.964866 + 0.262742i \(0.0846267\pi\)
\(140\) −3.87510 21.9768i −0.327506 1.85738i
\(141\) 0 0
\(142\) −0.651865 0.546979i −0.0547033 0.0459015i
\(143\) 0.953247 1.65107i 0.0797145 0.138070i
\(144\) 0 0
\(145\) −12.2389 21.1984i −1.01639 1.76043i
\(146\) −0.129142 + 0.732403i −0.0106879 + 0.0606141i
\(147\) 0 0
\(148\) 9.18172 + 3.34187i 0.754732 + 0.274700i
\(149\) 9.04179 + 3.29094i 0.740732 + 0.269604i 0.684700 0.728825i \(-0.259933\pi\)
0.0560315 + 0.998429i \(0.482155\pi\)
\(150\) 0 0
\(151\) −1.23780 + 7.01991i −0.100731 + 0.571272i 0.892109 + 0.451820i \(0.149225\pi\)
−0.992840 + 0.119452i \(0.961886\pi\)
\(152\) 0.210085 + 0.363878i 0.0170402 + 0.0295144i
\(153\) 0 0
\(154\) 0.653293 1.13154i 0.0526439 0.0911818i
\(155\) 18.7498 + 15.7329i 1.50602 + 1.26370i
\(156\) 0 0
\(157\) 1.33462 + 7.56900i 0.106514 + 0.604072i 0.990605 + 0.136756i \(0.0436678\pi\)
−0.884090 + 0.467316i \(0.845221\pi\)
\(158\) 1.56287 1.31140i 0.124335 0.104330i
\(159\) 0 0
\(160\) 7.14344 2.60000i 0.564739 0.205548i
\(161\) −19.7786 −1.55877
\(162\) 0 0
\(163\) 1.04750 0.0820465 0.0410232 0.999158i \(-0.486938\pi\)
0.0410232 + 0.999158i \(0.486938\pi\)
\(164\) −9.73812 + 3.54439i −0.760419 + 0.276770i
\(165\) 0 0
\(166\) 1.19469 1.00247i 0.0927263 0.0778066i
\(167\) −1.45067 8.22716i −0.112256 0.636637i −0.988072 0.153991i \(-0.950787\pi\)
0.875816 0.482645i \(-0.160324\pi\)
\(168\) 0 0
\(169\) −9.51011 7.97993i −0.731547 0.613841i
\(170\) −1.49393 + 2.58757i −0.114580 + 0.198458i
\(171\) 0 0
\(172\) 5.48724 + 9.50417i 0.418398 + 0.724686i
\(173\) −3.79348 + 21.5139i −0.288413 + 1.63567i 0.404420 + 0.914573i \(0.367473\pi\)
−0.692833 + 0.721098i \(0.743638\pi\)
\(174\) 0 0
\(175\) −25.5295 9.29200i −1.92985 0.702409i
\(176\) −8.94747 3.25661i −0.674441 0.245476i
\(177\) 0 0
\(178\) 0.226444 1.28423i 0.0169727 0.0962570i
\(179\) −4.54433 7.87101i −0.339659 0.588307i 0.644709 0.764428i \(-0.276978\pi\)
−0.984369 + 0.176121i \(0.943645\pi\)
\(180\) 0 0
\(181\) 3.56539 6.17543i 0.265013 0.459016i −0.702554 0.711630i \(-0.747957\pi\)
0.967567 + 0.252614i \(0.0812904\pi\)
\(182\) 0.307353 + 0.257900i 0.0227825 + 0.0191168i
\(183\) 0 0
\(184\) −0.778026 4.41240i −0.0573568 0.325287i
\(185\) 14.1965 11.9123i 1.04375 0.875807i
\(186\) 0 0
\(187\) 10.8239 3.93958i 0.791523 0.288091i
\(188\) 2.18209 0.159145
\(189\) 0 0
\(190\) 0.395456 0.0286894
\(191\) 11.2346 4.08907i 0.812908 0.295874i 0.0980836 0.995178i \(-0.468729\pi\)
0.714825 + 0.699304i \(0.246507\pi\)
\(192\) 0 0
\(193\) −6.79760 + 5.70386i −0.489302 + 0.410573i −0.853776 0.520640i \(-0.825693\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(194\) 0.0284857 + 0.161550i 0.00204515 + 0.0115986i
\(195\) 0 0
\(196\) −3.30505 2.77326i −0.236075 0.198090i
\(197\) 3.69895 6.40677i 0.263539 0.456464i −0.703641 0.710556i \(-0.748443\pi\)
0.967180 + 0.254093i \(0.0817768\pi\)
\(198\) 0 0
\(199\) 5.19187 + 8.99259i 0.368042 + 0.637468i 0.989259 0.146171i \(-0.0466948\pi\)
−0.621217 + 0.783638i \(0.713362\pi\)
\(200\) 1.06870 6.06089i 0.0755684 0.428570i
\(201\) 0 0
\(202\) 0.911573 + 0.331785i 0.0641381 + 0.0233443i
\(203\) −18.6614 6.79218i −1.30977 0.476718i
\(204\) 0 0
\(205\) −3.41309 + 19.3566i −0.238381 + 1.35192i
\(206\) −0.815151 1.41188i −0.0567942 0.0983705i
\(207\) 0 0
\(208\) 1.46194 2.53215i 0.101367 0.175573i
\(209\) −1.16786 0.979948i −0.0807824 0.0677845i
\(210\) 0 0
\(211\) 3.62250 + 20.5442i 0.249383 + 1.41432i 0.810089 + 0.586307i \(0.199419\pi\)
−0.560706 + 0.828015i \(0.689470\pi\)
\(212\) 13.3457 11.1984i 0.916588 0.769109i
\(213\) 0 0
\(214\) 0.207771 0.0756226i 0.0142030 0.00516946i
\(215\) 20.8148 1.41956
\(216\) 0 0
\(217\) 19.8576 1.34802
\(218\) −1.20395 + 0.438201i −0.0815416 + 0.0296787i
\(219\) 0 0
\(220\) −14.0509 + 11.7901i −0.947313 + 0.794890i
\(221\) 0.614206 + 3.48333i 0.0413160 + 0.234314i
\(222\) 0 0
\(223\) 18.0622 + 15.1560i 1.20953 + 1.01492i 0.999305 + 0.0372657i \(0.0118648\pi\)
0.210227 + 0.977653i \(0.432580\pi\)
\(224\) 3.08373 5.34118i 0.206041 0.356873i
\(225\) 0 0
\(226\) −0.808832 1.40094i −0.0538027 0.0931890i
\(227\) 1.82055 10.3249i 0.120834 0.685285i −0.862861 0.505441i \(-0.831330\pi\)
0.983695 0.179843i \(-0.0575591\pi\)
\(228\) 0 0
\(229\) 13.0452 + 4.74807i 0.862051 + 0.313761i 0.734944 0.678128i \(-0.237208\pi\)
0.127107 + 0.991889i \(0.459431\pi\)
\(230\) −3.96262 1.44228i −0.261288 0.0951009i
\(231\) 0 0
\(232\) 0.781188 4.43034i 0.0512875 0.290866i
\(233\) 3.79982 + 6.58149i 0.248935 + 0.431167i 0.963230 0.268676i \(-0.0865862\pi\)
−0.714296 + 0.699844i \(0.753253\pi\)
\(234\) 0 0
\(235\) 2.06934 3.58420i 0.134989 0.233807i
\(236\) −17.8863 15.0084i −1.16430 0.976963i
\(237\) 0 0
\(238\) 0.420937 + 2.38725i 0.0272853 + 0.154742i
\(239\) −12.6847 + 10.6437i −0.820504 + 0.688485i −0.953090 0.302687i \(-0.902116\pi\)
0.132586 + 0.991172i \(0.457672\pi\)
\(240\) 0 0
\(241\) 13.6429 4.96562i 0.878818 0.319863i 0.137085 0.990559i \(-0.456227\pi\)
0.741732 + 0.670696i \(0.234004\pi\)
\(242\) 0.828806 0.0532776
\(243\) 0 0
\(244\) −16.1290 −1.03256
\(245\) −7.68950 + 2.79875i −0.491264 + 0.178805i
\(246\) 0 0
\(247\) 0.358620 0.300918i 0.0228185 0.0191470i
\(248\) 0.781132 + 4.43002i 0.0496020 + 0.281307i
\(249\) 0 0
\(250\) −1.96162 1.64600i −0.124064 0.104102i
\(251\) 4.52591 7.83910i 0.285673 0.494800i −0.687099 0.726563i \(-0.741116\pi\)
0.972772 + 0.231764i \(0.0744497\pi\)
\(252\) 0 0
\(253\) 8.12838 + 14.0788i 0.511027 + 0.885125i
\(254\) −0.624673 + 3.54270i −0.0391955 + 0.222289i
\(255\) 0 0
\(256\) −12.8359 4.67189i −0.802244 0.291993i
\(257\) 9.11490 + 3.31755i 0.568572 + 0.206943i 0.610279 0.792187i \(-0.291057\pi\)
−0.0417069 + 0.999130i \(0.513280\pi\)
\(258\) 0 0
\(259\) 2.61085 14.8069i 0.162230 0.920054i
\(260\) −2.81622 4.87783i −0.174654 0.302510i
\(261\) 0 0
\(262\) 0.0567214 0.0982443i 0.00350426 0.00606955i
\(263\) 20.5723 + 17.2622i 1.26854 + 1.06443i 0.994717 + 0.102655i \(0.0327336\pi\)
0.273826 + 0.961779i \(0.411711\pi\)
\(264\) 0 0
\(265\) −5.73782 32.5408i −0.352471 1.99896i
\(266\) 0.245775 0.206230i 0.0150694 0.0126448i
\(267\) 0 0
\(268\) −2.24436 + 0.816882i −0.137096 + 0.0498990i
\(269\) −11.7388 −0.715729 −0.357865 0.933774i \(-0.616495\pi\)
−0.357865 + 0.933774i \(0.616495\pi\)
\(270\) 0 0
\(271\) 0.144576 0.00878238 0.00439119 0.999990i \(-0.498602\pi\)
0.00439119 + 0.999990i \(0.498602\pi\)
\(272\) 16.6000 6.04191i 1.00652 0.366345i
\(273\) 0 0
\(274\) 1.13792 0.954828i 0.0687443 0.0576833i
\(275\) 3.87762 + 21.9911i 0.233829 + 1.32611i
\(276\) 0 0
\(277\) −0.777094 0.652060i −0.0466911 0.0391785i 0.619144 0.785278i \(-0.287480\pi\)
−0.665835 + 0.746099i \(0.731924\pi\)
\(278\) 1.16293 2.01425i 0.0697479 0.120807i
\(279\) 0 0
\(280\) −3.88942 6.73667i −0.232437 0.402593i
\(281\) 4.78044 27.1112i 0.285177 1.61732i −0.419475 0.907767i \(-0.637786\pi\)
0.704652 0.709553i \(-0.251103\pi\)
\(282\) 0 0
\(283\) 25.1865 + 9.16713i 1.49718 + 0.544929i 0.955329 0.295545i \(-0.0955013\pi\)
0.541852 + 0.840474i \(0.317724\pi\)
\(284\) 9.10725 + 3.31477i 0.540416 + 0.196695i
\(285\) 0 0
\(286\) 0.0572653 0.324767i 0.00338617 0.0192039i
\(287\) 7.97320 + 13.8100i 0.470643 + 0.815178i
\(288\) 0 0
\(289\) −2.18506 + 3.78464i −0.128533 + 0.222626i
\(290\) −3.24349 2.72161i −0.190464 0.159818i
\(291\) 0 0
\(292\) −1.47084 8.34157i −0.0860747 0.488154i
\(293\) −14.2923 + 11.9927i −0.834964 + 0.700618i −0.956425 0.291978i \(-0.905687\pi\)
0.121461 + 0.992596i \(0.461242\pi\)
\(294\) 0 0
\(295\) −41.6141 + 15.1463i −2.42287 + 0.881852i
\(296\) 3.40596 0.197967
\(297\) 0 0
\(298\) 1.66439 0.0964153
\(299\) −4.69100 + 1.70738i −0.271287 + 0.0987405i
\(300\) 0 0
\(301\) 12.9363 10.8549i 0.745638 0.625664i
\(302\) 0.214110 + 1.21428i 0.0123206 + 0.0698737i
\(303\) 0 0
\(304\) −1.79108 1.50289i −0.102725 0.0861967i
\(305\) −15.2956 + 26.4928i −0.875825 + 1.51697i
\(306\) 0 0
\(307\) −16.8946 29.2624i −0.964227 1.67009i −0.711677 0.702507i \(-0.752064\pi\)
−0.252551 0.967584i \(-0.581269\pi\)
\(308\) −2.58408 + 14.6551i −0.147242 + 0.835049i
\(309\) 0 0
\(310\) 3.97844 + 1.44804i 0.225960 + 0.0822429i
\(311\) 32.5947 + 11.8635i 1.84828 + 0.672718i 0.986110 + 0.166093i \(0.0531152\pi\)
0.862167 + 0.506625i \(0.169107\pi\)
\(312\) 0 0
\(313\) 0.580051 3.28963i 0.0327864 0.185941i −0.964016 0.265843i \(-0.914350\pi\)
0.996803 + 0.0799021i \(0.0254608\pi\)
\(314\) 0.664726 + 1.15134i 0.0375127 + 0.0649739i
\(315\) 0 0
\(316\) −11.6182 + 20.1232i −0.653572 + 1.13202i
\(317\) −23.7725 19.9475i −1.33520 1.12036i −0.982832 0.184500i \(-0.940933\pi\)
−0.352364 0.935863i \(-0.614622\pi\)
\(318\) 0 0
\(319\) 2.83443 + 16.0749i 0.158698 + 0.900019i
\(320\) −20.8691 + 17.5112i −1.16662 + 0.978908i
\(321\) 0 0
\(322\) −3.21490 + 1.17013i −0.179159 + 0.0652087i
\(323\) 2.82842 0.157378
\(324\) 0 0
\(325\) −6.85710 −0.380363
\(326\) 0.170265 0.0619714i 0.00943011 0.00343228i
\(327\) 0 0
\(328\) −2.76722 + 2.32198i −0.152794 + 0.128210i
\(329\) −0.583065 3.30672i −0.0321454 0.182306i
\(330\) 0 0
\(331\) 2.50625 + 2.10299i 0.137756 + 0.115591i 0.709062 0.705146i \(-0.249119\pi\)
−0.571306 + 0.820737i \(0.693563\pi\)
\(332\) −8.88119 + 15.3827i −0.487419 + 0.844234i
\(333\) 0 0
\(334\) −0.722527 1.25145i −0.0395349 0.0684765i
\(335\) −0.786622 + 4.46116i −0.0429778 + 0.243739i
\(336\) 0 0
\(337\) −5.98190 2.17723i −0.325855 0.118602i 0.173912 0.984761i \(-0.444359\pi\)
−0.499768 + 0.866160i \(0.666581\pi\)
\(338\) −2.01792 0.734461i −0.109760 0.0399494i
\(339\) 0 0
\(340\) 5.90921 33.5128i 0.320472 1.81749i
\(341\) −8.16083 14.1350i −0.441934 0.765452i
\(342\) 0 0
\(343\) 7.29078 12.6280i 0.393665 0.681848i
\(344\) 2.93048 + 2.45896i 0.158001 + 0.132578i
\(345\) 0 0
\(346\) 0.656181 + 3.72139i 0.0352765 + 0.200063i
\(347\) −6.73538 + 5.65165i −0.361574 + 0.303397i −0.805418 0.592708i \(-0.798059\pi\)
0.443844 + 0.896104i \(0.353615\pi\)
\(348\) 0 0
\(349\) −13.5318 + 4.92517i −0.724340 + 0.263638i −0.677767 0.735277i \(-0.737052\pi\)
−0.0465728 + 0.998915i \(0.514830\pi\)
\(350\) −4.69941 −0.251194
\(351\) 0 0
\(352\) −5.06926 −0.270192
\(353\) −31.1982 + 11.3552i −1.66051 + 0.604378i −0.990444 0.137919i \(-0.955959\pi\)
−0.670071 + 0.742297i \(0.733737\pi\)
\(354\) 0 0
\(355\) 14.0813 11.8156i 0.747360 0.627109i
\(356\) 2.57905 + 14.6265i 0.136689 + 0.775203i
\(357\) 0 0
\(358\) −1.20431 1.01054i −0.0636500 0.0534087i
\(359\) −2.47257 + 4.28262i −0.130497 + 0.226028i −0.923868 0.382710i \(-0.874991\pi\)
0.793371 + 0.608738i \(0.208324\pi\)
\(360\) 0 0
\(361\) 9.31282 + 16.1303i 0.490149 + 0.848962i
\(362\) 0.214187 1.21471i 0.0112574 0.0638439i
\(363\) 0 0
\(364\) −4.29405 1.56291i −0.225069 0.0819185i
\(365\) −15.0963 5.49461i −0.790177 0.287601i
\(366\) 0 0
\(367\) −0.432810 + 2.45459i −0.0225925 + 0.128128i −0.994018 0.109216i \(-0.965166\pi\)
0.971426 + 0.237345i \(0.0762770\pi\)
\(368\) 12.4660 + 21.5918i 0.649837 + 1.12555i
\(369\) 0 0
\(370\) 1.60281 2.77615i 0.0833262 0.144325i
\(371\) −20.5360 17.2317i −1.06618 0.894627i
\(372\) 0 0
\(373\) −4.87041 27.6215i −0.252180 1.43019i −0.803208 0.595699i \(-0.796875\pi\)
0.551028 0.834487i \(-0.314236\pi\)
\(374\) 1.52629 1.28071i 0.0789228 0.0662241i
\(375\) 0 0
\(376\) 0.714759 0.260151i 0.0368609 0.0134163i
\(377\) −5.01234 −0.258149
\(378\) 0 0
\(379\) 5.13991 0.264019 0.132010 0.991248i \(-0.457857\pi\)
0.132010 + 0.991248i \(0.457857\pi\)
\(380\) −4.23236 + 1.54045i −0.217115 + 0.0790235i
\(381\) 0 0
\(382\) 1.58421 1.32931i 0.0810551 0.0680133i
\(383\) −0.00775737 0.0439942i −0.000396383 0.00224800i 0.984609 0.174772i \(-0.0559189\pi\)
−0.985005 + 0.172524i \(0.944808\pi\)
\(384\) 0 0
\(385\) 21.6211 + 18.1423i 1.10192 + 0.924617i
\(386\) −0.767463 + 1.32928i −0.0390628 + 0.0676588i
\(387\) 0 0
\(388\) −0.934167 1.61802i −0.0474251 0.0821427i
\(389\) 3.64353 20.6635i 0.184734 1.04768i −0.741562 0.670885i \(-0.765915\pi\)
0.926296 0.376796i \(-0.122974\pi\)
\(390\) 0 0
\(391\) −28.3419 10.3156i −1.43331 0.521682i
\(392\) −1.41322 0.514371i −0.0713785 0.0259797i
\(393\) 0 0
\(394\) 0.222210 1.26022i 0.0111948 0.0634889i
\(395\) 22.0356 + 38.1668i 1.10873 + 1.92038i
\(396\) 0 0
\(397\) 0.00122821 0.00212731i 6.16419e−5 0.000106767i −0.865995 0.500053i \(-0.833314\pi\)
0.866056 + 0.499947i \(0.166647\pi\)
\(398\) 1.37592 + 1.15454i 0.0689687 + 0.0578716i
\(399\) 0 0
\(400\) 5.94688 + 33.7265i 0.297344 + 1.68632i
\(401\) 19.3475 16.2345i 0.966166 0.810710i −0.0157788 0.999876i \(-0.505023\pi\)
0.981945 + 0.189166i \(0.0605783\pi\)
\(402\) 0 0
\(403\) 4.70972 1.71420i 0.234608 0.0853904i
\(404\) −11.0485 −0.549684
\(405\) 0 0
\(406\) −3.43513 −0.170483
\(407\) −11.6128 + 4.22670i −0.575623 + 0.209510i
\(408\) 0 0
\(409\) −17.8401 + 14.9696i −0.882134 + 0.740198i −0.966617 0.256227i \(-0.917521\pi\)
0.0844827 + 0.996425i \(0.473076\pi\)
\(410\) 0.590383 + 3.34823i 0.0291569 + 0.165357i
\(411\) 0 0
\(412\) 14.2239 + 11.9353i 0.700763 + 0.588010i
\(413\) −17.9643 + 31.1151i −0.883965 + 1.53107i
\(414\) 0 0
\(415\) 16.8446 + 29.1756i 0.826867 + 1.43218i
\(416\) 0.270309 1.53300i 0.0132530 0.0751613i
\(417\) 0 0
\(418\) −0.247803 0.0901931i −0.0121205 0.00441149i
\(419\) −29.4014 10.7013i −1.43635 0.522790i −0.497609 0.867401i \(-0.665789\pi\)
−0.938746 + 0.344611i \(0.888011\pi\)
\(420\) 0 0
\(421\) 5.30141 30.0658i 0.258375 1.46532i −0.528885 0.848694i \(-0.677390\pi\)
0.787259 0.616622i \(-0.211499\pi\)
\(422\) 1.80424 + 3.12503i 0.0878289 + 0.152124i
\(423\) 0 0
\(424\) 3.03640 5.25920i 0.147461 0.255409i
\(425\) −31.7364 26.6300i −1.53944 1.29174i
\(426\) 0 0
\(427\) 4.30975 + 24.4418i 0.208564 + 1.18282i
\(428\) −1.92909 + 1.61870i −0.0932460 + 0.0782427i
\(429\) 0 0
\(430\) 3.38332 1.23143i 0.163158 0.0593848i
\(431\) 12.4246 0.598474 0.299237 0.954179i \(-0.403268\pi\)
0.299237 + 0.954179i \(0.403268\pi\)
\(432\) 0 0
\(433\) −0.760649 −0.0365545 −0.0182772 0.999833i \(-0.505818\pi\)
−0.0182772 + 0.999833i \(0.505818\pi\)
\(434\) 3.22774 1.17480i 0.154936 0.0563922i
\(435\) 0 0
\(436\) 11.1782 9.37966i 0.535341 0.449204i
\(437\) 0.693186 + 3.93125i 0.0331596 + 0.188057i
\(438\) 0 0
\(439\) 23.0651 + 19.3539i 1.10084 + 0.923712i 0.997481 0.0709321i \(-0.0225974\pi\)
0.103356 + 0.994644i \(0.467042\pi\)
\(440\) −3.19685 + 5.53711i −0.152404 + 0.263971i
\(441\) 0 0
\(442\) 0.305914 + 0.529859i 0.0145508 + 0.0252028i
\(443\) −2.37231 + 13.4540i −0.112712 + 0.639220i 0.875146 + 0.483859i \(0.160765\pi\)
−0.987858 + 0.155361i \(0.950346\pi\)
\(444\) 0 0
\(445\) 26.4706 + 9.63450i 1.25483 + 0.456719i
\(446\) 3.83255 + 1.39493i 0.181476 + 0.0660520i
\(447\) 0 0
\(448\) −3.83800 + 21.7664i −0.181328 + 1.02836i
\(449\) −10.9995 19.0516i −0.519097 0.899102i −0.999754 0.0221934i \(-0.992935\pi\)
0.480657 0.876909i \(-0.340398\pi\)
\(450\) 0 0
\(451\) 6.55346 11.3509i 0.308590 0.534494i
\(452\) 14.1137 + 11.8428i 0.663852 + 0.557038i
\(453\) 0 0
\(454\) −0.314911 1.78595i −0.0147795 0.0838188i
\(455\) −6.63932 + 5.57105i −0.311256 + 0.261175i
\(456\) 0 0
\(457\) 1.39904 0.509209i 0.0654443 0.0238198i −0.309091 0.951033i \(-0.600025\pi\)
0.374535 + 0.927213i \(0.377802\pi\)
\(458\) 2.40132 0.112206
\(459\) 0 0
\(460\) 48.0281 2.23932
\(461\) −6.68435 + 2.43290i −0.311321 + 0.113312i −0.492956 0.870054i \(-0.664083\pi\)
0.181634 + 0.983366i \(0.441861\pi\)
\(462\) 0 0
\(463\) −20.3314 + 17.0601i −0.944879 + 0.792848i −0.978428 0.206589i \(-0.933764\pi\)
0.0335484 + 0.999437i \(0.489319\pi\)
\(464\) 4.34700 + 24.6531i 0.201805 + 1.14449i
\(465\) 0 0
\(466\) 1.00701 + 0.844980i 0.0466487 + 0.0391429i
\(467\) 13.0760 22.6482i 0.605084 1.04804i −0.386955 0.922099i \(-0.626473\pi\)
0.992038 0.125937i \(-0.0401937\pi\)
\(468\) 0 0
\(469\) 1.83760 + 3.18282i 0.0848525 + 0.146969i
\(470\) 0.124313 0.705015i 0.00573414 0.0325199i
\(471\) 0 0
\(472\) −7.64810 2.78368i −0.352032 0.128129i
\(473\) −13.0431 4.74730i −0.599722 0.218281i
\(474\) 0 0
\(475\) −0.952162 + 5.39998i −0.0436882 + 0.247768i
\(476\) −13.8043 23.9098i −0.632719 1.09590i
\(477\) 0 0
\(478\) −1.43213 + 2.48052i −0.0655040 + 0.113456i
\(479\) 7.97188 + 6.68920i 0.364244 + 0.305637i 0.806480 0.591262i \(-0.201370\pi\)
−0.442235 + 0.896899i \(0.645814\pi\)
\(480\) 0 0
\(481\) −0.658969 3.73720i −0.0300464 0.170402i
\(482\) 1.92381 1.61426i 0.0876269 0.0735277i
\(483\) 0 0
\(484\) −8.87026 + 3.22851i −0.403194 + 0.146751i
\(485\) −3.54358 −0.160906
\(486\) 0 0
\(487\) −18.4664 −0.836791 −0.418396 0.908265i \(-0.637407\pi\)
−0.418396 + 0.908265i \(0.637407\pi\)
\(488\) −5.28318 + 1.92292i −0.239158 + 0.0870466i
\(489\) 0 0
\(490\) −1.08431 + 0.909841i −0.0489839 + 0.0411024i
\(491\) 2.94749 + 16.7160i 0.133018 + 0.754383i 0.976219 + 0.216785i \(0.0695572\pi\)
−0.843201 + 0.537598i \(0.819332\pi\)
\(492\) 0 0
\(493\) −23.1984 19.4658i −1.04480 0.876694i
\(494\) 0.0404890 0.0701289i 0.00182168 0.00315525i
\(495\) 0 0
\(496\) −12.5158 21.6780i −0.561976 0.973371i
\(497\) 2.58967 14.6868i 0.116163 0.658792i
\(498\) 0 0
\(499\) −23.1598 8.42949i −1.03678 0.377356i −0.233119 0.972448i \(-0.574893\pi\)
−0.803657 + 0.595093i \(0.797115\pi\)
\(500\) 27.4060 + 9.97496i 1.22563 + 0.446094i
\(501\) 0 0
\(502\) 0.271889 1.54196i 0.0121350 0.0688210i
\(503\) 20.0569 + 34.7395i 0.894291 + 1.54896i 0.834679 + 0.550736i \(0.185653\pi\)
0.0596120 + 0.998222i \(0.481014\pi\)
\(504\) 0 0
\(505\) −10.4776 + 18.1478i −0.466248 + 0.807564i
\(506\) 2.15414 + 1.80754i 0.0957632 + 0.0803548i
\(507\) 0 0
\(508\) −7.11461 40.3489i −0.315660 1.79019i
\(509\) −3.79079 + 3.18085i −0.168024 + 0.140989i −0.722922 0.690929i \(-0.757202\pi\)
0.554899 + 0.831918i \(0.312757\pi\)
\(510\) 0 0
\(511\) −12.2477 + 4.45781i −0.541808 + 0.197202i
\(512\) −13.0229 −0.575537
\(513\) 0 0
\(514\) 1.67785 0.0740066
\(515\) 33.0933 12.0450i 1.45827 0.530765i
\(516\) 0 0
\(517\) −2.11416 + 1.77399i −0.0929807 + 0.0780201i
\(518\) −0.451614 2.56123i −0.0198428 0.112534i
\(519\) 0 0
\(520\) −1.50401 1.26202i −0.0659553 0.0553431i
\(521\) 3.86979 6.70267i 0.169539 0.293649i −0.768719 0.639586i \(-0.779106\pi\)
0.938258 + 0.345937i \(0.112439\pi\)
\(522\) 0 0
\(523\) −18.0070 31.1891i −0.787391 1.36380i −0.927560 0.373674i \(-0.878098\pi\)
0.140169 0.990128i \(-0.455236\pi\)
\(524\) −0.224360 + 1.27241i −0.00980120 + 0.0555854i
\(525\) 0 0
\(526\) 4.36516 + 1.58879i 0.190330 + 0.0692745i
\(527\) 28.4550 + 10.3568i 1.23952 + 0.451148i
\(528\) 0 0
\(529\) 3.39786 19.2702i 0.147733 0.837835i
\(530\) −2.85780 4.94986i −0.124135 0.215008i
\(531\) 0 0
\(532\) −1.82705 + 3.16455i −0.0792129 + 0.137201i
\(533\) 3.08319 + 2.58710i 0.133548 + 0.112060i
\(534\) 0 0
\(535\) 0.829386 + 4.70368i 0.0358575 + 0.203358i
\(536\) −0.637768 + 0.535151i −0.0275474 + 0.0231150i
\(537\) 0 0
\(538\) −1.90808 + 0.694484i −0.0822631 + 0.0299413i
\(539\) 5.45676 0.235039
\(540\) 0 0
\(541\) −24.4147 −1.04967 −0.524834 0.851204i \(-0.675873\pi\)
−0.524834 + 0.851204i \(0.675873\pi\)
\(542\) 0.0235000 0.00855331i 0.00100941 0.000367396i
\(543\) 0 0
\(544\) 7.20455 6.04534i 0.308893 0.259192i
\(545\) −4.80594 27.2558i −0.205864 1.16751i
\(546\) 0 0
\(547\) −21.7264 18.2306i −0.928953 0.779484i 0.0466761 0.998910i \(-0.485137\pi\)
−0.975629 + 0.219426i \(0.929582\pi\)
\(548\) −8.45913 + 14.6516i −0.361356 + 0.625887i
\(549\) 0 0
\(550\) 1.93130 + 3.34512i 0.0823511 + 0.142636i
\(551\) −0.696003 + 3.94723i −0.0296507 + 0.168158i
\(552\) 0 0
\(553\) 33.5990 + 12.2290i 1.42878 + 0.520032i
\(554\) −0.164889 0.0600146i −0.00700546 0.00254978i
\(555\) 0 0
\(556\) −4.59993 + 26.0875i −0.195081 + 1.10636i
\(557\) −18.4687 31.9887i −0.782542 1.35540i −0.930456 0.366403i \(-0.880589\pi\)
0.147914 0.989000i \(-0.452744\pi\)
\(558\) 0 0
\(559\) 2.13113 3.69123i 0.0901372 0.156122i
\(560\) 33.1591 + 27.8238i 1.40123 + 1.17577i
\(561\) 0 0
\(562\) −0.826901 4.68959i −0.0348807 0.197818i
\(563\) −17.4470 + 14.6398i −0.735303 + 0.616992i −0.931572 0.363558i \(-0.881562\pi\)
0.196269 + 0.980550i \(0.437117\pi\)
\(564\) 0 0
\(565\) 32.8368 11.9516i 1.38145 0.502808i
\(566\) 4.63625 0.194876
\(567\) 0 0
\(568\) 3.37833 0.141752
\(569\) 29.0071 10.5577i 1.21604 0.442603i 0.347247 0.937774i \(-0.387117\pi\)
0.868796 + 0.495170i \(0.164894\pi\)
\(570\) 0 0
\(571\) 9.82107 8.24085i 0.410999 0.344869i −0.413728 0.910401i \(-0.635773\pi\)
0.824727 + 0.565532i \(0.191329\pi\)
\(572\) 0.652213 + 3.69888i 0.0272704 + 0.154658i
\(573\) 0 0
\(574\) 2.11301 + 1.77303i 0.0881955 + 0.0740048i
\(575\) 29.2354 50.6372i 1.21920 2.11172i
\(576\) 0 0
\(577\) 11.7632 + 20.3745i 0.489708 + 0.848200i 0.999930 0.0118433i \(-0.00376992\pi\)
−0.510222 + 0.860043i \(0.670437\pi\)
\(578\) −0.131265 + 0.744442i −0.00545991 + 0.0309647i
\(579\) 0 0
\(580\) 45.3150 + 16.4933i 1.88160 + 0.684848i
\(581\) 25.6839 + 9.34816i 1.06555 + 0.387827i
\(582\) 0 0
\(583\) −3.82622 + 21.6996i −0.158466 + 0.898704i
\(584\) −1.47628 2.55699i −0.0610888 0.105809i
\(585\) 0 0
\(586\) −1.61363 + 2.79489i −0.0666584 + 0.115456i
\(587\) −8.72329 7.31971i −0.360049 0.302117i 0.444762 0.895649i \(-0.353288\pi\)
−0.804810 + 0.593532i \(0.797733\pi\)
\(588\) 0 0
\(589\) −0.695954 3.94695i −0.0286763 0.162631i
\(590\) −5.86806 + 4.92389i −0.241584 + 0.202713i
\(591\) 0 0
\(592\) −17.8098 + 6.48224i −0.731979 + 0.266419i
\(593\) 37.7324 1.54948 0.774742 0.632277i \(-0.217880\pi\)
0.774742 + 0.632277i \(0.217880\pi\)
\(594\) 0 0
\(595\) −52.3640 −2.14672
\(596\) −17.8130 + 6.48341i −0.729650 + 0.265571i
\(597\) 0 0
\(598\) −0.661483 + 0.555050i −0.0270501 + 0.0226977i
\(599\) −8.22366 46.6387i −0.336010 1.90561i −0.417028 0.908894i \(-0.636928\pi\)
0.0810181 0.996713i \(-0.474183\pi\)
\(600\) 0 0
\(601\) −23.8297 19.9955i −0.972033 0.815632i 0.0108354 0.999941i \(-0.496551\pi\)
−0.982868 + 0.184309i \(0.940995\pi\)
\(602\) 1.46054 2.52973i 0.0595271 0.103104i
\(603\) 0 0
\(604\) −7.02156 12.1617i −0.285703 0.494853i
\(605\) −3.10892 + 17.6316i −0.126396 + 0.716825i
\(606\) 0 0
\(607\) −27.7082 10.0850i −1.12464 0.409336i −0.288297 0.957541i \(-0.593089\pi\)
−0.836344 + 0.548205i \(0.815311\pi\)
\(608\) −1.16970 0.425737i −0.0474378 0.0172659i
\(609\) 0 0
\(610\) −0.918868 + 5.21116i −0.0372039 + 0.210994i
\(611\) −0.423740 0.733939i −0.0171427 0.0296920i
\(612\) 0 0
\(613\) 3.05214 5.28646i 0.123275 0.213518i −0.797782 0.602945i \(-0.793994\pi\)
0.921057 + 0.389427i \(0.127327\pi\)
\(614\) −4.47732 3.75692i −0.180690 0.151617i
\(615\) 0 0
\(616\) 0.900757 + 5.10844i 0.0362925 + 0.205825i
\(617\) 14.6469 12.2902i 0.589660 0.494784i −0.298443 0.954427i \(-0.596467\pi\)
0.888103 + 0.459644i \(0.152023\pi\)
\(618\) 0 0
\(619\) 6.34655 2.30995i 0.255089 0.0928449i −0.211310 0.977419i \(-0.567773\pi\)
0.466400 + 0.884574i \(0.345551\pi\)
\(620\) −48.2198 −1.93655
\(621\) 0 0
\(622\) 5.99994 0.240576
\(623\) 21.4757 7.81653i 0.860408 0.313163i
\(624\) 0 0
\(625\) 8.04818 6.75322i 0.321927 0.270129i
\(626\) −0.100335 0.569027i −0.00401019 0.0227429i
\(627\) 0 0
\(628\) −11.5991 9.73282i −0.462855 0.388382i
\(629\) 11.4638 19.8559i 0.457091 0.791705i
\(630\) 0 0
\(631\) 0.228453 + 0.395693i 0.00909458 + 0.0157523i 0.870537 0.492103i \(-0.163772\pi\)
−0.861442 + 0.507855i \(0.830438\pi\)
\(632\) −1.40650 + 7.97663i −0.0559474 + 0.317294i
\(633\) 0 0
\(634\) −5.04420 1.83594i −0.200331 0.0729145i
\(635\) −73.0222 26.5779i −2.89780 1.05471i
\(636\) 0 0
\(637\) −0.290971 + 1.65018i −0.0115287 + 0.0653825i
\(638\) 1.41173 + 2.44519i 0.0558909 + 0.0968058i
\(639\) 0 0
\(640\) −9.95805 + 17.2479i −0.393627 + 0.681781i
\(641\) −2.19934 1.84546i −0.0868686 0.0728914i 0.598319 0.801258i \(-0.295835\pi\)
−0.685188 + 0.728366i \(0.740280\pi\)
\(642\) 0 0
\(643\) −0.295696 1.67697i −0.0116611 0.0661334i 0.978422 0.206617i \(-0.0662454\pi\)
−0.990083 + 0.140484i \(0.955134\pi\)
\(644\) 29.8493 25.0465i 1.17623 0.986971i
\(645\) 0 0
\(646\) 0.459744 0.167333i 0.0180884 0.00658363i
\(647\) 36.1004 1.41925 0.709626 0.704579i \(-0.248864\pi\)
0.709626 + 0.704579i \(0.248864\pi\)
\(648\) 0 0
\(649\) 29.5310 1.15919
\(650\) −1.11458 + 0.405674i −0.0437175 + 0.0159119i
\(651\) 0 0
\(652\) −1.58085 + 1.32649i −0.0619110 + 0.0519495i
\(653\) −7.56550 42.9061i −0.296061 1.67904i −0.662859 0.748744i \(-0.730657\pi\)
0.366798 0.930301i \(-0.380454\pi\)
\(654\) 0 0
\(655\) 1.87723 + 1.57518i 0.0733494 + 0.0615475i
\(656\) 10.0507 17.4083i 0.392412 0.679678i
\(657\) 0 0
\(658\) −0.290404 0.502994i −0.0113211 0.0196087i
\(659\) 4.42473 25.0939i 0.172363 0.977518i −0.768781 0.639512i \(-0.779136\pi\)
0.941144 0.338006i \(-0.109752\pi\)
\(660\) 0 0
\(661\) −32.1067 11.6859i −1.24880 0.454528i −0.368807 0.929506i \(-0.620234\pi\)
−0.879998 + 0.474978i \(0.842456\pi\)
\(662\) 0.531792 + 0.193557i 0.0206687 + 0.00752279i
\(663\) 0 0
\(664\) −1.07516 + 6.09753i −0.0417242 + 0.236630i
\(665\) 3.46529 + 6.00207i 0.134378 + 0.232750i
\(666\) 0 0
\(667\) 21.3702 37.0143i 0.827459 1.43320i
\(668\) 12.6077 + 10.5791i 0.487807 + 0.409319i
\(669\) 0 0
\(670\) 0.136067 + 0.771673i 0.00525672 + 0.0298123i
\(671\) 15.6269 13.1126i 0.603271 0.506205i
\(672\) 0 0
\(673\) 27.7620 10.1045i 1.07015 0.389502i 0.253916 0.967226i \(-0.418281\pi\)
0.816232 + 0.577725i \(0.196059\pi\)
\(674\) −1.10113 −0.0424140
\(675\) 0 0
\(676\) 24.4577 0.940680
\(677\) −38.3209 + 13.9477i −1.47279 + 0.536052i −0.948857 0.315706i \(-0.897759\pi\)
−0.523935 + 0.851759i \(0.675536\pi\)
\(678\) 0 0
\(679\) −2.20233 + 1.84797i −0.0845176 + 0.0709186i
\(680\) −2.05983 11.6819i −0.0789908 0.447979i
\(681\) 0 0
\(682\) −2.16274 1.81475i −0.0828156 0.0694905i
\(683\) −15.8213 + 27.4033i −0.605384 + 1.04856i 0.386606 + 0.922245i \(0.373647\pi\)
−0.991991 + 0.126312i \(0.959686\pi\)
\(684\) 0 0
\(685\) 16.0441 + 27.7891i 0.613012 + 1.06177i
\(686\) 0.437986 2.48394i 0.0167224 0.0948373i
\(687\) 0 0
\(688\) −20.0035 7.28066i −0.762624 0.277573i
\(689\) −6.35814 2.31418i −0.242226 0.0881631i
\(690\) 0 0
\(691\) −4.96369 + 28.1505i −0.188828 + 1.07090i 0.732110 + 0.681186i \(0.238536\pi\)
−0.920938 + 0.389709i \(0.872576\pi\)
\(692\) −21.5190 37.2719i −0.818028 1.41687i
\(693\) 0 0
\(694\) −0.760438 + 1.31712i −0.0288658 + 0.0499971i
\(695\) 38.4879 + 32.2952i 1.45993 + 1.22503i
\(696\) 0 0
\(697\) 4.22259 + 23.9475i 0.159942 + 0.907077i
\(698\) −1.90813 + 1.60111i −0.0722239 + 0.0606031i
\(699\) 0 0
\(700\) 50.2952 18.3060i 1.90098 0.691901i
\(701\) −7.52982 −0.284397 −0.142199 0.989838i \(-0.545417\pi\)
−0.142199 + 0.989838i \(0.545417\pi\)
\(702\) 0 0
\(703\) −3.03455 −0.114450
\(704\) 17.0710 6.21332i 0.643386 0.234173i
\(705\) 0 0
\(706\) −4.39930 + 3.69145i −0.165570 + 0.138930i
\(707\) 2.95221 + 16.7428i 0.111029 + 0.629679i
\(708\) 0 0
\(709\) 6.13907 + 5.15129i 0.230558 + 0.193461i 0.750746 0.660590i \(-0.229694\pi\)
−0.520189 + 0.854051i \(0.674138\pi\)
\(710\) 1.58981 2.75363i 0.0596646 0.103342i
\(711\) 0 0
\(712\) 2.58857 + 4.48354i 0.0970108 + 0.168028i
\(713\) −7.42128 + 42.0882i −0.277929 + 1.57621i
\(714\) 0 0
\(715\) 6.69412 + 2.43646i 0.250346 + 0.0911184i
\(716\) 16.8256 + 6.12400i 0.628801 + 0.228865i
\(717\) 0 0
\(718\) −0.148537 + 0.842396i −0.00554335 + 0.0314379i
\(719\) −13.4913 23.3676i −0.503140 0.871464i −0.999993 0.00362928i \(-0.998845\pi\)
0.496854 0.867834i \(-0.334489\pi\)
\(720\) 0 0
\(721\) 14.2860 24.7440i 0.532037 0.921515i
\(722\) 2.46803 + 2.07093i 0.0918507 + 0.0770719i
\(723\) 0 0
\(724\) 2.43944 + 13.8348i 0.0906611 + 0.514165i
\(725\) 44.9733 37.7371i 1.67027 1.40152i
\(726\) 0 0
\(727\) 13.8082 5.02576i 0.512116 0.186395i −0.0730194 0.997331i \(-0.523263\pi\)
0.585136 + 0.810935i \(0.301041\pi\)
\(728\) −1.59288 −0.0590360
\(729\) 0 0
\(730\) −2.77889 −0.102851
\(731\) 24.1985 8.80755i 0.895015 0.325759i
\(732\) 0 0
\(733\) −24.0107 + 20.1474i −0.886856 + 0.744161i −0.967577 0.252576i \(-0.918722\pi\)
0.0807207 + 0.996737i \(0.474278\pi\)
\(734\) 0.0748657 + 0.424584i 0.00276334 + 0.0156717i
\(735\) 0 0
\(736\) 10.1682 + 8.53210i 0.374803 + 0.314497i
\(737\) 1.51039 2.61607i 0.0556359 0.0963642i
\(738\) 0 0
\(739\) −0.241454 0.418211i −0.00888205 0.0153842i 0.861550 0.507672i \(-0.169494\pi\)
−0.870432 + 0.492288i \(0.836161\pi\)
\(740\) −6.33987 + 35.9552i −0.233058 + 1.32174i
\(741\) 0 0
\(742\) −4.35746 1.58598i −0.159967 0.0582233i
\(743\) −40.4545 14.7242i −1.48413 0.540179i −0.532233 0.846598i \(-0.678647\pi\)
−0.951897 + 0.306418i \(0.900869\pi\)
\(744\) 0 0
\(745\) −6.24325 + 35.4072i −0.228735 + 1.29722i
\(746\) −2.42578 4.20157i −0.0888140 0.153830i
\(747\) 0 0
\(748\) −11.3462 + 19.6523i −0.414860 + 0.718558i
\(749\) 2.96842 + 2.49080i 0.108464 + 0.0910119i
\(750\) 0 0
\(751\) 7.62691 + 43.2543i 0.278310 + 1.57837i 0.728248 + 0.685314i \(0.240335\pi\)
−0.449938 + 0.893060i \(0.648554\pi\)
\(752\) −3.24237 + 2.72067i −0.118237 + 0.0992126i
\(753\) 0 0
\(754\) −0.814727 + 0.296536i −0.0296706 + 0.0107992i
\(755\) −26.6350 −0.969346
\(756\) 0 0
\(757\) 22.4143 0.814661 0.407331 0.913281i \(-0.366460\pi\)
0.407331 + 0.913281i \(0.366460\pi\)
\(758\) 0.835463 0.304084i 0.0303454 0.0110448i
\(759\) 0 0
\(760\) −1.20268 + 1.00917i −0.0436260 + 0.0366065i
\(761\) −1.73592 9.84487i −0.0629269 0.356876i −0.999971 0.00766415i \(-0.997560\pi\)
0.937044 0.349212i \(-0.113551\pi\)
\(762\) 0 0
\(763\) −17.2007 14.4331i −0.622708 0.522514i
\(764\) −11.7768 + 20.3980i −0.426069 + 0.737972i
\(765\) 0 0
\(766\) −0.00386367 0.00669207i −0.000139600 0.000241794i
\(767\) −1.57468 + 8.93047i −0.0568585 + 0.322461i
\(768\) 0 0
\(769\) 7.04412 + 2.56385i 0.254017 + 0.0924547i 0.465890 0.884842i \(-0.345734\pi\)
−0.211873 + 0.977297i \(0.567956\pi\)
\(770\) 4.58771 + 1.66979i 0.165330 + 0.0601751i
\(771\) 0 0
\(772\) 3.03568 17.2162i 0.109256 0.619624i
\(773\) 9.91954 + 17.1812i 0.356781 + 0.617963i 0.987421 0.158112i \(-0.0505408\pi\)
−0.630640 + 0.776076i \(0.717207\pi\)
\(774\) 0 0
\(775\) −29.3521 + 50.8394i −1.05436 + 1.82620i
\(776\) −0.498895 0.418623i −0.0179093 0.0150277i
\(777\) 0 0
\(778\) −0.630243 3.57429i −0.0225953 0.128144i
\(779\) 2.46547 2.06878i 0.0883347 0.0741216i
\(780\) 0 0
\(781\) −11.5186 + 4.19242i −0.412167 + 0.150016i
\(782\) −5.21709 −0.186563
\(783\) 0 0
\(784\) 8.36872 0.298883
\(785\) −26.9864 + 9.82226i −0.963187 + 0.350571i
\(786\) 0 0
\(787\) 30.4336 25.5368i 1.08484 0.910290i 0.0885273 0.996074i \(-0.471784\pi\)
0.996314 + 0.0857841i \(0.0273395\pi\)
\(788\) 2.53083 + 14.3530i 0.0901570 + 0.511306i
\(789\) 0 0
\(790\) 5.83976 + 4.90014i 0.207769 + 0.174339i
\(791\) 14.1752 24.5522i 0.504013 0.872976i
\(792\) 0 0
\(793\) 3.13210 + 5.42495i 0.111224 + 0.192646i
\(794\) 7.37831e−5 0 0.000418445i 2.61846e−6 0 1.48500e-5i
\(795\) 0 0
\(796\) −19.2231 6.99664i −0.681345 0.247989i
\(797\) 8.55680 + 3.11442i 0.303097 + 0.110318i 0.489092 0.872232i \(-0.337328\pi\)
−0.185994 + 0.982551i \(0.559551\pi\)
\(798\) 0 0
\(799\) 0.889125 5.04248i 0.0314550 0.178390i
\(800\) 9.11632 + 15.7899i 0.322311 + 0.558258i
\(801\) 0 0
\(802\) 2.18437 3.78344i 0.0771327 0.133598i
\(803\) 8.20657 + 6.88613i 0.289604 + 0.243006i
\(804\) 0 0
\(805\) −12.8333 72.7813i −0.452315 2.56520i
\(806\) 0.664124 0.557266i 0.0233928 0.0196289i
\(807\) 0 0
\(808\) −3.61902 + 1.31721i −0.127317 + 0.0463394i
\(809\) 3.01910 0.106146 0.0530730 0.998591i \(-0.483098\pi\)
0.0530730 + 0.998591i \(0.483098\pi\)
\(810\) 0 0
\(811\) 33.1722 1.16483 0.582416 0.812891i \(-0.302107\pi\)
0.582416 + 0.812891i \(0.302107\pi\)
\(812\) 36.7644 13.3811i 1.29018 0.469586i
\(813\) 0 0
\(814\) −1.63753 + 1.37405i −0.0573954 + 0.0481604i
\(815\) 0.679667 + 3.85458i 0.0238077 + 0.135020i
\(816\) 0 0
\(817\) −2.61093 2.19083i −0.0913447 0.0766473i
\(818\) −2.01418 + 3.48866i −0.0704241 + 0.121978i
\(819\) 0 0
\(820\) −19.3612 33.5345i −0.676121 1.17108i
\(821\) 7.42554 42.1123i 0.259153 1.46973i −0.526030 0.850466i \(-0.676320\pi\)
0.785183 0.619264i \(-0.212569\pi\)
\(822\) 0 0
\(823\) 33.1043 + 12.0490i 1.15394 + 0.420001i 0.846930 0.531704i \(-0.178448\pi\)
0.307013 + 0.951705i \(0.400670\pi\)
\(824\) 6.08209 + 2.21370i 0.211880 + 0.0771179i
\(825\) 0 0
\(826\) −1.07918 + 6.12036i −0.0375496 + 0.212955i
\(827\) −13.0190 22.5495i −0.452714 0.784125i 0.545839 0.837890i \(-0.316211\pi\)
−0.998554 + 0.0537655i \(0.982878\pi\)
\(828\) 0 0
\(829\) 3.95134 6.84392i 0.137236 0.237699i −0.789214 0.614119i \(-0.789512\pi\)
0.926449 + 0.376420i \(0.122845\pi\)
\(830\) 4.46405 + 3.74578i 0.154950 + 0.130018i
\(831\) 0 0
\(832\) 0.968696 + 5.49375i 0.0335835 + 0.190461i
\(833\) −7.75528 + 6.50745i −0.268704 + 0.225470i
\(834\) 0 0
\(835\) 29.3330 10.6763i 1.01511 0.369470i
\(836\) 3.00344 0.103876
\(837\) 0 0
\(838\) −5.41213 −0.186959
\(839\) −4.83791 + 1.76085i −0.167023 + 0.0607914i −0.424178 0.905579i \(-0.639437\pi\)
0.257155 + 0.966370i \(0.417215\pi\)
\(840\) 0 0
\(841\) 10.6589 8.94387i 0.367548 0.308409i
\(842\) −0.917016 5.20065i −0.0316024 0.179226i
\(843\) 0 0
\(844\) −31.4830 26.4174i −1.08369 0.909323i
\(845\) 23.1939 40.1730i 0.797894 1.38199i
\(846\) 0 0
\(847\) 7.26264 + 12.5793i 0.249547 + 0.432228i
\(848\) −5.86805 + 33.2794i −0.201510 + 1.14282i
\(849\) 0 0
\(850\) −6.73403 2.45099i −0.230975 0.0840681i
\(851\) 30.4074 + 11.0674i 1.04235 + 0.379385i
\(852\) 0 0
\(853\) 4.51320 25.5956i 0.154529 0.876377i −0.804686 0.593700i \(-0.797667\pi\)
0.959215 0.282677i \(-0.0912223\pi\)
\(854\) 2.14653 + 3.71791i 0.0734529 + 0.127224i
\(855\) 0 0
\(856\) −0.438904 + 0.760204i −0.0150014 + 0.0259832i
\(857\) −3.15544 2.64773i −0.107788 0.0904447i 0.587301 0.809369i \(-0.300190\pi\)
−0.695089 + 0.718924i \(0.744635\pi\)
\(858\) 0 0
\(859\) −1.11646 6.33175i −0.0380931 0.216036i 0.959819 0.280619i \(-0.0905396\pi\)
−0.997912 + 0.0645822i \(0.979429\pi\)
\(860\) −31.4130 + 26.3587i −1.07118 + 0.898823i
\(861\) 0 0
\(862\) 2.01955 0.735058i 0.0687863 0.0250362i
\(863\) 29.6195 1.00826 0.504129 0.863628i \(-0.331813\pi\)
0.504129 + 0.863628i \(0.331813\pi\)
\(864\) 0 0
\(865\) −81.6282 −2.77544
\(866\) −0.123639 + 0.0450010i −0.00420143 + 0.00152920i
\(867\) 0 0
\(868\) −29.9685 + 25.1465i −1.01720 + 0.853529i
\(869\) −5.10327 28.9421i −0.173117 0.981793i
\(870\) 0 0
\(871\) 0.710588 + 0.596254i 0.0240774 + 0.0202033i
\(872\) 2.54326 4.40505i 0.0861256 0.149174i
\(873\) 0 0
\(874\) 0.345251 + 0.597993i 0.0116783 + 0.0202274i
\(875\) 7.79297 44.1961i 0.263451 1.49410i
\(876\) 0 0
\(877\) 29.9458 + 10.8994i 1.01120 + 0.368046i 0.793893 0.608057i \(-0.208051\pi\)
0.217306 + 0.976104i \(0.430273\pi\)
\(878\) 4.89410 + 1.78131i 0.165168 + 0.0601162i
\(879\) 0 0
\(880\) 6.17813 35.0379i 0.208265 1.18113i
\(881\) −17.3932 30.1259i −0.585991 1.01497i −0.994751 0.102325i \(-0.967372\pi\)
0.408760 0.912642i \(-0.365961\pi\)
\(882\) 0 0
\(883\) 15.1882 26.3067i 0.511124 0.885292i −0.488793 0.872400i \(-0.662563\pi\)
0.999917 0.0128924i \(-0.00410388\pi\)
\(884\) −5.33803 4.47914i −0.179538 0.150650i
\(885\) 0 0
\(886\) 0.410352 + 2.32722i 0.0137861 + 0.0781846i
\(887\) −38.3234 + 32.1571i −1.28677 + 1.07973i −0.294502 + 0.955651i \(0.595154\pi\)
−0.992272 + 0.124080i \(0.960402\pi\)
\(888\) 0 0
\(889\) −59.2434 + 21.5628i −1.98696 + 0.723194i
\(890\) 4.87263 0.163331
\(891\) 0 0
\(892\) −46.4515 −1.55531
\(893\) −0.636818 + 0.231783i −0.0213103 + 0.00775632i
\(894\) 0 0
\(895\) 26.0151 21.8293i 0.869590 0.729673i
\(896\) 2.80582 + 15.9126i 0.0937358 + 0.531602i
\(897\) 0 0
\(898\) −2.91502 2.44599i −0.0972754 0.0816238i
\(899\) −21.4556 + 37.1621i −0.715583 + 1.23943i
\(900\) 0 0
\(901\) −20.4399 35.4029i −0.680950 1.17944i
\(902\) 0.393692 2.23274i 0.0131085 0.0743420i
\(903\) 0 0
\(904\) 6.03495 + 2.19654i 0.200719 + 0.0730559i
\(905\) 25.0377 + 9.11298i 0.832282 + 0.302926i
\(906\) 0 0
\(907\) −7.65169 + 43.3949i −0.254070 + 1.44090i 0.544378 + 0.838840i \(0.316766\pi\)
−0.798448 + 0.602063i \(0.794345\pi\)
\(908\) 10.3273 + 17.8874i 0.342723 + 0.593614i
\(909\) 0 0
\(910\) −0.749593 + 1.29833i −0.0248488 + 0.0430393i
\(911\) −28.4802 23.8977i −0.943591 0.791767i 0.0346154 0.999401i \(-0.488979\pi\)
−0.978207 + 0.207634i \(0.933424\pi\)
\(912\) 0 0
\(913\) −3.90106 22.1240i −0.129106 0.732198i
\(914\) 0.197280 0.165538i 0.00652546 0.00547551i
\(915\) 0 0
\(916\) −25.7001 + 9.35407i −0.849155 + 0.309067i
\(917\) 1.98815 0.0656544
\(918\) 0 0
\(919\) 12.3976 0.408958 0.204479 0.978871i \(-0.434450\pi\)
0.204479 + 0.978871i \(0.434450\pi\)
\(920\) 15.7319 5.72595i 0.518666 0.188779i
\(921\) 0 0
\(922\) −0.942569 + 0.790909i −0.0310418 + 0.0260472i
\(923\) −0.653624 3.70689i −0.0215143 0.122014i
\(924\) 0 0
\(925\) 34.0493 + 28.5708i 1.11953 + 0.939401i
\(926\) −2.29545 + 3.97584i −0.0754333 + 0.130654i
\(927\) 0 0
\(928\) 6.66377 + 11.5420i 0.218749 + 0.378884i
\(929\) 5.79780 32.8810i 0.190220 1.07879i −0.728844 0.684680i \(-0.759942\pi\)
0.919064 0.394109i \(-0.128947\pi\)
\(930\) 0 0
\(931\) 1.25912 + 0.458281i 0.0412659 + 0.0150196i
\(932\) −14.0690 5.12069i −0.460845 0.167734i
\(933\) 0 0
\(934\) 0.785525 4.45493i 0.0257031 0.145770i
\(935\) 21.5199 + 37.2736i 0.703777 + 1.21898i
\(936\) 0 0
\(937\) 12.4220 21.5156i 0.405810 0.702884i −0.588605 0.808421i \(-0.700323\pi\)
0.994415 + 0.105537i \(0.0336561\pi\)
\(938\) 0.486991 + 0.408634i 0.0159008 + 0.0133424i
\(939\) 0 0
\(940\) 1.41584 + 8.02965i 0.0461797 + 0.261898i
\(941\) 19.4804 16.3460i 0.635044 0.532865i −0.267448 0.963572i \(-0.586180\pi\)
0.902492 + 0.430707i \(0.141736\pi\)
\(942\) 0 0
\(943\) −32.2500 + 11.7381i −1.05021 + 0.382244i
\(944\) 45.2900 1.47406
\(945\) 0 0
\(946\) −2.40094 −0.0780612
\(947\) −15.6272 + 5.68785i −0.507817 + 0.184830i −0.583206 0.812324i \(-0.698202\pi\)
0.0753897 + 0.997154i \(0.475980\pi\)
\(948\) 0 0
\(949\) −2.52004 + 2.11456i −0.0818039 + 0.0686416i
\(950\) 0.164701 + 0.934067i 0.00534361 + 0.0303051i
\(951\) 0 0
\(952\) −7.37224 6.18605i −0.238936 0.200491i
\(953\) −7.13357 + 12.3557i −0.231079 + 0.400240i −0.958126 0.286347i \(-0.907559\pi\)
0.727047 + 0.686588i \(0.240892\pi\)
\(954\) 0 0
\(955\) 22.3365 + 38.6879i 0.722791 + 1.25191i
\(956\) 5.66474 32.1263i 0.183211 1.03904i
\(957\) 0 0
\(958\) 1.69152 + 0.615664i 0.0546507 + 0.0198912i
\(959\) 24.4633 + 8.90391i 0.789961 + 0.287522i
\(960\) 0 0
\(961\) 2.06782 11.7272i 0.0667037 0.378296i
\(962\) −0.328209 0.568474i −0.0105819 0.0183283i
\(963\) 0 0
\(964\) −14.3013 + 24.7706i −0.460613 + 0.797806i
\(965\) −25.3997 21.3128i −0.817644 0.686085i
\(966\) 0 0
\(967\) −6.78700 38.4910i −0.218255 1.23779i −0.875168 0.483819i \(-0.839249\pi\)
0.656913 0.753967i \(-0.271862\pi\)
\(968\) −2.52061 + 2.11504i −0.0810155 + 0.0679801i
\(969\) 0 0
\(970\) −0.575989 + 0.209643i −0.0184939 + 0.00673123i
\(971\) −4.40370 −0.141321 −0.0706607 0.997500i \(-0.522511\pi\)
−0.0706607 + 0.997500i \(0.522511\pi\)
\(972\) 0 0
\(973\) 40.7619 1.30677
\(974\) −3.00160 + 1.09249i −0.0961775 + 0.0350058i
\(975\) 0 0
\(976\) 23.9661 20.1100i 0.767138 0.643705i
\(977\) 7.31520 + 41.4866i 0.234034 + 1.32727i 0.844639 + 0.535337i \(0.179815\pi\)
−0.610605 + 0.791936i \(0.709074\pi\)
\(978\) 0 0
\(979\) −14.3898 12.0745i −0.459899 0.385901i
\(980\) 8.06057 13.9613i 0.257486 0.445978i
\(981\) 0 0
\(982\) 1.46804 + 2.54272i 0.0468470 + 0.0811413i
\(983\) −3.54696 + 20.1158i −0.113131 + 0.641595i 0.874528 + 0.484974i \(0.161171\pi\)
−0.987659 + 0.156621i \(0.949940\pi\)
\(984\) 0 0
\(985\) 25.9757 + 9.45437i 0.827654 + 0.301241i
\(986\) −4.92238 1.79160i −0.156761 0.0570562i
\(987\) 0 0
\(988\) −0.160153 + 0.908272i −0.00509514 + 0.0288960i
\(989\) 18.1723 + 31.4753i 0.577844 + 1.00086i
\(990\) 0 0
\(991\) −0.0340356 + 0.0589514i −0.00108118 + 0.00187265i −0.866565 0.499063i \(-0.833677\pi\)
0.865484 + 0.500936i \(0.167011\pi\)
\(992\) −10.2088 8.56617i −0.324128 0.271976i
\(993\) 0 0
\(994\) −0.447951 2.54046i −0.0142082 0.0805784i
\(995\) −29.7222 + 24.9399i −0.942256 + 0.790647i
\(996\) 0 0
\(997\) −10.0041 + 3.64118i −0.316832 + 0.115317i −0.495541 0.868585i \(-0.665030\pi\)
0.178709 + 0.983902i \(0.442808\pi\)
\(998\) −4.26319 −0.134949
\(999\) 0 0
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 729.2.e.k.163.2 12
3.2 odd 2 729.2.e.t.163.1 12
9.2 odd 6 729.2.e.j.406.2 12
9.4 even 3 729.2.e.l.649.1 12
9.5 odd 6 729.2.e.s.649.2 12
9.7 even 3 729.2.e.u.406.1 12
27.2 odd 18 729.2.a.b.1.4 6
27.4 even 9 inner 729.2.e.k.568.2 12
27.5 odd 18 729.2.e.s.82.2 12
27.7 even 9 729.2.c.a.487.4 12
27.11 odd 18 729.2.c.d.244.3 12
27.13 even 9 729.2.e.u.325.1 12
27.14 odd 18 729.2.e.j.325.2 12
27.16 even 9 729.2.c.a.244.4 12
27.20 odd 18 729.2.c.d.487.3 12
27.22 even 9 729.2.e.l.82.1 12
27.23 odd 18 729.2.e.t.568.1 12
27.25 even 9 729.2.a.e.1.3 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.4 6 27.2 odd 18
729.2.a.e.1.3 yes 6 27.25 even 9
729.2.c.a.244.4 12 27.16 even 9
729.2.c.a.487.4 12 27.7 even 9
729.2.c.d.244.3 12 27.11 odd 18
729.2.c.d.487.3 12 27.20 odd 18
729.2.e.j.325.2 12 27.14 odd 18
729.2.e.j.406.2 12 9.2 odd 6
729.2.e.k.163.2 12 1.1 even 1 trivial
729.2.e.k.568.2 12 27.4 even 9 inner
729.2.e.l.82.1 12 27.22 even 9
729.2.e.l.649.1 12 9.4 even 3
729.2.e.s.82.2 12 27.5 odd 18
729.2.e.s.649.2 12 9.5 odd 6
729.2.e.t.163.1 12 3.2 odd 2
729.2.e.t.568.1 12 27.23 odd 18
729.2.e.u.325.1 12 27.13 even 9
729.2.e.u.406.1 12 9.7 even 3