Properties

Label 729.2.e.t.649.1
Level $729$
Weight $2$
Character 729.649
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 649.1
Root \(1.22778i\) of defining polynomial
Character \(\chi\) \(=\) 729.649
Dual form 729.2.e.t.82.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.274087 + 1.55442i) q^{2} +(-0.461727 - 0.168055i) q^{4} +(1.28581 - 1.07892i) q^{5} +(-2.61167 + 0.950570i) q^{7} +(-1.19062 + 2.06222i) q^{8} +O(q^{10})\) \(q+(-0.274087 + 1.55442i) q^{2} +(-0.461727 - 0.168055i) q^{4} +(1.28581 - 1.07892i) q^{5} +(-2.61167 + 0.950570i) q^{7} +(-1.19062 + 2.06222i) q^{8} +(1.32468 + 2.29442i) q^{10} +(-3.18002 - 2.66835i) q^{11} +(1.19401 + 6.77158i) q^{13} +(-0.761765 - 4.32018i) q^{14} +(-3.63204 - 3.04764i) q^{16} +(-0.488276 - 0.845718i) q^{17} +(-1.34264 + 2.32553i) q^{19} +(-0.775013 + 0.282082i) q^{20} +(5.01936 - 4.21174i) q^{22} +(-1.51588 - 0.551737i) q^{23} +(-0.379007 + 2.14945i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(-1.42876 + 8.10288i) q^{29} +(-0.981104 - 0.357093i) q^{31} +(2.08454 - 1.74914i) q^{32} +(1.44844 - 0.527187i) q^{34} +(-2.33252 + 4.04005i) q^{35} +(0.654172 + 1.13306i) q^{37} +(-3.24686 - 2.72444i) q^{38} +(0.694061 + 3.93621i) q^{40} +(-0.841876 - 4.77452i) q^{41} +(7.53805 + 6.32518i) q^{43} +(1.01987 + 1.76647i) q^{44} +(1.27312 - 2.20510i) q^{46} +(-11.7440 + 4.27447i) q^{47} +(0.554929 - 0.465640i) q^{49} +(-3.23728 - 1.17827i) q^{50} +(0.586690 - 3.32728i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(1.14923 - 6.51760i) q^{56} +(-12.2037 - 4.44179i) q^{58} +(6.93414 - 5.81843i) q^{59} +(1.20820 - 0.439750i) q^{61} +(0.823982 - 1.42718i) q^{62} +(-2.59373 - 4.49247i) q^{64} +(8.84130 + 7.41873i) q^{65} +(-0.806821 - 4.57571i) q^{67} +(0.0833230 + 0.472548i) q^{68} +(-5.64064 - 4.73306i) q^{70} +(-2.81187 - 4.87030i) q^{71} +(2.28072 - 3.95033i) q^{73} +(-1.94056 + 0.706305i) q^{74} +(1.01075 - 0.848122i) q^{76} +(10.8416 + 3.94603i) q^{77} +(0.808645 - 4.58605i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(1.00098 - 5.67682i) q^{83} +(-1.54030 - 0.560622i) q^{85} +(-11.8981 + 9.98369i) q^{86} +(9.28893 - 3.38089i) q^{88} +(-2.27221 + 3.93558i) q^{89} +(-9.55523 - 16.5502i) q^{91} +(0.607203 + 0.509504i) q^{92} +(-3.42546 - 19.4267i) q^{94} +(0.782681 + 4.43880i) q^{95} +(6.56917 + 5.51219i) q^{97} +(0.571704 + 0.990221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.274087 + 1.55442i −0.193809 + 1.09914i 0.720296 + 0.693667i \(0.244006\pi\)
−0.914105 + 0.405478i \(0.867105\pi\)
\(3\) 0 0
\(4\) −0.461727 0.168055i −0.230864 0.0840275i
\(5\) 1.28581 1.07892i 0.575032 0.482509i −0.308279 0.951296i \(-0.599753\pi\)
0.883311 + 0.468787i \(0.155309\pi\)
\(6\) 0 0
\(7\) −2.61167 + 0.950570i −0.987119 + 0.359282i −0.784604 0.619997i \(-0.787134\pi\)
−0.202515 + 0.979279i \(0.564911\pi\)
\(8\) −1.19062 + 2.06222i −0.420948 + 0.729104i
\(9\) 0 0
\(10\) 1.32468 + 2.29442i 0.418901 + 0.725558i
\(11\) −3.18002 2.66835i −0.958812 0.804539i 0.0219472 0.999759i \(-0.493013\pi\)
−0.980759 + 0.195220i \(0.937458\pi\)
\(12\) 0 0
\(13\) 1.19401 + 6.77158i 0.331160 + 1.87810i 0.462282 + 0.886733i \(0.347031\pi\)
−0.131123 + 0.991366i \(0.541858\pi\)
\(14\) −0.761765 4.32018i −0.203590 1.15462i
\(15\) 0 0
\(16\) −3.63204 3.04764i −0.908009 0.761910i
\(17\) −0.488276 0.845718i −0.118424 0.205117i 0.800719 0.599040i \(-0.204451\pi\)
−0.919143 + 0.393923i \(0.871118\pi\)
\(18\) 0 0
\(19\) −1.34264 + 2.32553i −0.308024 + 0.533513i −0.977930 0.208933i \(-0.933001\pi\)
0.669906 + 0.742446i \(0.266334\pi\)
\(20\) −0.775013 + 0.282082i −0.173298 + 0.0630754i
\(21\) 0 0
\(22\) 5.01936 4.21174i 1.07013 0.897946i
\(23\) −1.51588 0.551737i −0.316084 0.115045i 0.179106 0.983830i \(-0.442679\pi\)
−0.495190 + 0.868785i \(0.664902\pi\)
\(24\) 0 0
\(25\) −0.379007 + 2.14945i −0.0758013 + 0.429891i
\(26\) −10.8532 −2.12848
\(27\) 0 0
\(28\) 1.36563 0.258079
\(29\) −1.42876 + 8.10288i −0.265313 + 1.50467i 0.502828 + 0.864386i \(0.332293\pi\)
−0.768142 + 0.640280i \(0.778818\pi\)
\(30\) 0 0
\(31\) −0.981104 0.357093i −0.176212 0.0641357i 0.252408 0.967621i \(-0.418778\pi\)
−0.428619 + 0.903485i \(0.641000\pi\)
\(32\) 2.08454 1.74914i 0.368498 0.309207i
\(33\) 0 0
\(34\) 1.44844 0.527187i 0.248405 0.0904119i
\(35\) −2.33252 + 4.04005i −0.394268 + 0.682893i
\(36\) 0 0
\(37\) 0.654172 + 1.13306i 0.107545 + 0.186274i 0.914775 0.403963i \(-0.132368\pi\)
−0.807230 + 0.590237i \(0.799034\pi\)
\(38\) −3.24686 2.72444i −0.526710 0.441962i
\(39\) 0 0
\(40\) 0.694061 + 3.93621i 0.109741 + 0.622370i
\(41\) −0.841876 4.77452i −0.131479 0.745654i −0.977247 0.212104i \(-0.931969\pi\)
0.845768 0.533550i \(-0.179143\pi\)
\(42\) 0 0
\(43\) 7.53805 + 6.32518i 1.14954 + 0.964580i 0.999709 0.0241308i \(-0.00768182\pi\)
0.149833 + 0.988711i \(0.452126\pi\)
\(44\) 1.01987 + 1.76647i 0.153751 + 0.266305i
\(45\) 0 0
\(46\) 1.27312 2.20510i 0.187711 0.325125i
\(47\) −11.7440 + 4.27447i −1.71304 + 0.623495i −0.997201 0.0747722i \(-0.976177\pi\)
−0.715837 + 0.698267i \(0.753955\pi\)
\(48\) 0 0
\(49\) 0.554929 0.465640i 0.0792755 0.0665201i
\(50\) −3.23728 1.17827i −0.457821 0.166633i
\(51\) 0 0
\(52\) 0.586690 3.32728i 0.0813593 0.461411i
\(53\) 7.34280 1.00861 0.504305 0.863525i \(-0.331749\pi\)
0.504305 + 0.863525i \(0.331749\pi\)
\(54\) 0 0
\(55\) −6.96786 −0.939546
\(56\) 1.14923 6.51760i 0.153572 0.870951i
\(57\) 0 0
\(58\) −12.2037 4.44179i −1.60243 0.583235i
\(59\) 6.93414 5.81843i 0.902748 0.757496i −0.0679775 0.997687i \(-0.521655\pi\)
0.970726 + 0.240191i \(0.0772102\pi\)
\(60\) 0 0
\(61\) 1.20820 0.439750i 0.154694 0.0563042i −0.263512 0.964656i \(-0.584881\pi\)
0.418207 + 0.908352i \(0.362659\pi\)
\(62\) 0.823982 1.42718i 0.104646 0.181252i
\(63\) 0 0
\(64\) −2.59373 4.49247i −0.324216 0.561558i
\(65\) 8.84130 + 7.41873i 1.09663 + 0.920180i
\(66\) 0 0
\(67\) −0.806821 4.57571i −0.0985689 0.559012i −0.993595 0.112999i \(-0.963954\pi\)
0.895026 0.446014i \(-0.147157\pi\)
\(68\) 0.0833230 + 0.472548i 0.0101044 + 0.0573049i
\(69\) 0 0
\(70\) −5.64064 4.73306i −0.674185 0.565708i
\(71\) −2.81187 4.87030i −0.333707 0.577998i 0.649528 0.760337i \(-0.274966\pi\)
−0.983236 + 0.182339i \(0.941633\pi\)
\(72\) 0 0
\(73\) 2.28072 3.95033i 0.266938 0.462351i −0.701131 0.713032i \(-0.747321\pi\)
0.968070 + 0.250681i \(0.0806547\pi\)
\(74\) −1.94056 + 0.706305i −0.225585 + 0.0821062i
\(75\) 0 0
\(76\) 1.01075 0.848122i 0.115941 0.0972862i
\(77\) 10.8416 + 3.94603i 1.23552 + 0.449692i
\(78\) 0 0
\(79\) 0.808645 4.58605i 0.0909797 0.515971i −0.904926 0.425570i \(-0.860074\pi\)
0.995905 0.0904018i \(-0.0288151\pi\)
\(80\) −7.95828 −0.889763
\(81\) 0 0
\(82\) 7.65237 0.845063
\(83\) 1.00098 5.67682i 0.109871 0.623112i −0.879291 0.476285i \(-0.841983\pi\)
0.989162 0.146827i \(-0.0469059\pi\)
\(84\) 0 0
\(85\) −1.54030 0.560622i −0.167069 0.0608080i
\(86\) −11.8981 + 9.98369i −1.28300 + 1.07657i
\(87\) 0 0
\(88\) 9.28893 3.38089i 0.990203 0.360405i
\(89\) −2.27221 + 3.93558i −0.240854 + 0.417171i −0.960958 0.276695i \(-0.910761\pi\)
0.720104 + 0.693866i \(0.244094\pi\)
\(90\) 0 0
\(91\) −9.55523 16.5502i −1.00166 1.73493i
\(92\) 0.607203 + 0.509504i 0.0633053 + 0.0531194i
\(93\) 0 0
\(94\) −3.42546 19.4267i −0.353309 2.00371i
\(95\) 0.782681 + 4.43880i 0.0803013 + 0.455411i
\(96\) 0 0
\(97\) 6.56917 + 5.51219i 0.666998 + 0.559678i 0.912175 0.409800i \(-0.134402\pi\)
−0.245177 + 0.969478i \(0.578846\pi\)
\(98\) 0.571704 + 0.990221i 0.0577508 + 0.100027i
\(99\) 0 0
\(100\) 0.536224 0.928767i 0.0536224 0.0928767i
\(101\) 7.33496 2.66971i 0.729856 0.265646i 0.0497521 0.998762i \(-0.484157\pi\)
0.680104 + 0.733116i \(0.261935\pi\)
\(102\) 0 0
\(103\) −1.65937 + 1.39237i −0.163502 + 0.137195i −0.720868 0.693073i \(-0.756257\pi\)
0.557366 + 0.830267i \(0.311812\pi\)
\(104\) −15.3861 5.60008i −1.50873 0.549133i
\(105\) 0 0
\(106\) −2.01257 + 11.4138i −0.195478 + 1.10861i
\(107\) 12.5849 1.21663 0.608317 0.793695i \(-0.291845\pi\)
0.608317 + 0.793695i \(0.291845\pi\)
\(108\) 0 0
\(109\) −12.2140 −1.16989 −0.584945 0.811073i \(-0.698884\pi\)
−0.584945 + 0.811073i \(0.698884\pi\)
\(110\) 1.90980 10.8310i 0.182092 1.03270i
\(111\) 0 0
\(112\) 12.3827 + 4.50693i 1.17005 + 0.425864i
\(113\) 0.345358 0.289790i 0.0324886 0.0272611i −0.626399 0.779503i \(-0.715472\pi\)
0.658887 + 0.752242i \(0.271027\pi\)
\(114\) 0 0
\(115\) −2.54442 + 0.926094i −0.237269 + 0.0863587i
\(116\) 2.02142 3.50121i 0.187685 0.325079i
\(117\) 0 0
\(118\) 7.14376 + 12.3734i 0.657636 + 1.13906i
\(119\) 2.07913 + 1.74460i 0.190594 + 0.159927i
\(120\) 0 0
\(121\) 1.08229 + 6.13796i 0.0983898 + 0.557996i
\(122\) 0.352405 + 1.99859i 0.0319053 + 0.180944i
\(123\) 0 0
\(124\) 0.392991 + 0.329759i 0.0352917 + 0.0296132i
\(125\) 6.02803 + 10.4409i 0.539164 + 0.933859i
\(126\) 0 0
\(127\) 0.265534 0.459919i 0.0235624 0.0408112i −0.854004 0.520267i \(-0.825833\pi\)
0.877566 + 0.479456i \(0.159166\pi\)
\(128\) 12.8082 4.66182i 1.13210 0.412051i
\(129\) 0 0
\(130\) −13.9551 + 11.7098i −1.22395 + 1.02701i
\(131\) 10.7276 + 3.90451i 0.937272 + 0.341139i 0.765088 0.643926i \(-0.222695\pi\)
0.172184 + 0.985065i \(0.444918\pi\)
\(132\) 0 0
\(133\) 1.29597 7.34979i 0.112375 0.637308i
\(134\) 7.33374 0.633539
\(135\) 0 0
\(136\) 2.32541 0.199402
\(137\) −0.734400 + 4.16499i −0.0627440 + 0.355839i 0.937231 + 0.348710i \(0.113380\pi\)
−0.999975 + 0.00712879i \(0.997731\pi\)
\(138\) 0 0
\(139\) 10.4828 + 3.81542i 0.889137 + 0.323619i 0.745891 0.666068i \(-0.232024\pi\)
0.143246 + 0.989687i \(0.454246\pi\)
\(140\) 1.75594 1.47341i 0.148404 0.124526i
\(141\) 0 0
\(142\) 8.34121 3.03595i 0.699978 0.254771i
\(143\) 14.2720 24.7198i 1.19348 2.06718i
\(144\) 0 0
\(145\) 6.90528 + 11.9603i 0.573452 + 0.993248i
\(146\) 5.51537 + 4.62794i 0.456455 + 0.383011i
\(147\) 0 0
\(148\) −0.111633 0.633101i −0.00917616 0.0520406i
\(149\) 3.38227 + 19.1818i 0.277086 + 1.57143i 0.732257 + 0.681029i \(0.238467\pi\)
−0.455171 + 0.890404i \(0.650422\pi\)
\(150\) 0 0
\(151\) −0.952086 0.798895i −0.0774797 0.0650131i 0.603225 0.797571i \(-0.293882\pi\)
−0.680705 + 0.732558i \(0.738326\pi\)
\(152\) −3.19716 5.53765i −0.259324 0.449163i
\(153\) 0 0
\(154\) −9.10535 + 15.7709i −0.733730 + 1.27086i
\(155\) −1.64679 + 0.599383i −0.132273 + 0.0481436i
\(156\) 0 0
\(157\) −2.70654 + 2.27106i −0.216006 + 0.181250i −0.744370 0.667768i \(-0.767250\pi\)
0.528364 + 0.849018i \(0.322806\pi\)
\(158\) 6.90704 + 2.51396i 0.549494 + 0.200000i
\(159\) 0 0
\(160\) 0.793141 4.49812i 0.0627033 0.355608i
\(161\) 4.48345 0.353346
\(162\) 0 0
\(163\) 15.9509 1.24937 0.624685 0.780877i \(-0.285228\pi\)
0.624685 + 0.780877i \(0.285228\pi\)
\(164\) −0.413664 + 2.34601i −0.0323017 + 0.183192i
\(165\) 0 0
\(166\) 8.54983 + 3.11188i 0.663596 + 0.241529i
\(167\) −11.0959 + 9.31055i −0.858625 + 0.720472i −0.961671 0.274205i \(-0.911585\pi\)
0.103046 + 0.994677i \(0.467141\pi\)
\(168\) 0 0
\(169\) −32.2127 + 11.7244i −2.47790 + 0.901881i
\(170\) 1.29362 2.24061i 0.0992161 0.171847i
\(171\) 0 0
\(172\) −2.41755 4.18731i −0.184336 0.319280i
\(173\) −9.66549 8.11031i −0.734853 0.616615i 0.196597 0.980484i \(-0.437011\pi\)
−0.931450 + 0.363869i \(0.881455\pi\)
\(174\) 0 0
\(175\) −1.05337 5.97394i −0.0796270 0.451587i
\(176\) 3.41777 + 19.3831i 0.257624 + 1.46106i
\(177\) 0 0
\(178\) −5.49478 4.61067i −0.411851 0.345584i
\(179\) 0.147949 + 0.256256i 0.0110582 + 0.0191534i 0.871502 0.490393i \(-0.163147\pi\)
−0.860443 + 0.509546i \(0.829813\pi\)
\(180\) 0 0
\(181\) −0.710251 + 1.23019i −0.0527925 + 0.0914393i −0.891214 0.453583i \(-0.850146\pi\)
0.838421 + 0.545022i \(0.183479\pi\)
\(182\) 28.3449 10.3167i 2.10107 0.764725i
\(183\) 0 0
\(184\) 2.94265 2.46917i 0.216935 0.182030i
\(185\) 2.06363 + 0.751099i 0.151721 + 0.0552219i
\(186\) 0 0
\(187\) −0.703949 + 3.99229i −0.0514779 + 0.291945i
\(188\) 6.14087 0.447869
\(189\) 0 0
\(190\) −7.11431 −0.516126
\(191\) −3.58133 + 20.3108i −0.259136 + 1.46963i 0.526091 + 0.850428i \(0.323657\pi\)
−0.785228 + 0.619207i \(0.787454\pi\)
\(192\) 0 0
\(193\) 19.6921 + 7.16735i 1.41747 + 0.515917i 0.933313 0.359063i \(-0.116904\pi\)
0.484158 + 0.874981i \(0.339126\pi\)
\(194\) −10.3688 + 8.70046i −0.744437 + 0.624657i
\(195\) 0 0
\(196\) −0.334479 + 0.121740i −0.0238913 + 0.00869574i
\(197\) −4.79810 + 8.31056i −0.341851 + 0.592103i −0.984776 0.173826i \(-0.944387\pi\)
0.642926 + 0.765929i \(0.277720\pi\)
\(198\) 0 0
\(199\) 5.34583 + 9.25925i 0.378956 + 0.656371i 0.990911 0.134522i \(-0.0429498\pi\)
−0.611955 + 0.790893i \(0.709616\pi\)
\(200\) −3.98139 3.34078i −0.281527 0.236229i
\(201\) 0 0
\(202\) 2.13944 + 12.1334i 0.150531 + 0.853701i
\(203\) −3.97092 22.5202i −0.278704 1.58061i
\(204\) 0 0
\(205\) −6.23383 5.23081i −0.435390 0.365335i
\(206\) −1.70953 2.96099i −0.119108 0.206302i
\(207\) 0 0
\(208\) 16.3006 28.2335i 1.13025 1.95764i
\(209\) 10.4750 3.81258i 0.724569 0.263722i
\(210\) 0 0
\(211\) −11.5292 + 9.67411i −0.793700 + 0.665993i −0.946658 0.322240i \(-0.895564\pi\)
0.152959 + 0.988233i \(0.451120\pi\)
\(212\) −3.39037 1.23399i −0.232851 0.0847510i
\(213\) 0 0
\(214\) −3.44937 + 19.5624i −0.235794 + 1.33726i
\(215\) 16.5169 1.12644
\(216\) 0 0
\(217\) 2.90176 0.196984
\(218\) 3.34770 18.9857i 0.226735 1.28588i
\(219\) 0 0
\(220\) 3.21725 + 1.17098i 0.216907 + 0.0789477i
\(221\) 5.14384 4.31620i 0.346012 0.290339i
\(222\) 0 0
\(223\) 11.5470 4.20278i 0.773247 0.281439i 0.0748934 0.997192i \(-0.476138\pi\)
0.698354 + 0.715753i \(0.253916\pi\)
\(224\) −3.78146 + 6.54968i −0.252659 + 0.437619i
\(225\) 0 0
\(226\) 0.355798 + 0.616261i 0.0236674 + 0.0409931i
\(227\) −2.87463 2.41210i −0.190796 0.160097i 0.542386 0.840129i \(-0.317521\pi\)
−0.733182 + 0.680033i \(0.761966\pi\)
\(228\) 0 0
\(229\) −3.23028 18.3198i −0.213463 1.21061i −0.883554 0.468329i \(-0.844856\pi\)
0.670092 0.742278i \(-0.266255\pi\)
\(230\) −0.742150 4.20894i −0.0489359 0.277529i
\(231\) 0 0
\(232\) −15.0088 12.5939i −0.985375 0.826828i
\(233\) 0.272892 + 0.472663i 0.0178777 + 0.0309652i 0.874826 0.484438i \(-0.160976\pi\)
−0.856948 + 0.515403i \(0.827642\pi\)
\(234\) 0 0
\(235\) −10.4887 + 18.1670i −0.684210 + 1.18509i
\(236\) −4.17950 + 1.52121i −0.272062 + 0.0990225i
\(237\) 0 0
\(238\) −3.28171 + 2.75368i −0.212721 + 0.178495i
\(239\) −18.8829 6.87281i −1.22143 0.444565i −0.350777 0.936459i \(-0.614083\pi\)
−0.870655 + 0.491894i \(0.836305\pi\)
\(240\) 0 0
\(241\) 2.65531 15.0590i 0.171043 0.970035i −0.771569 0.636146i \(-0.780528\pi\)
0.942612 0.333889i \(-0.108361\pi\)
\(242\) −9.83763 −0.632387
\(243\) 0 0
\(244\) −0.631762 −0.0404444
\(245\) 0.211143 1.19745i 0.0134894 0.0765024i
\(246\) 0 0
\(247\) −17.3506 6.31512i −1.10399 0.401821i
\(248\) 1.90453 1.59809i 0.120938 0.101479i
\(249\) 0 0
\(250\) −17.8817 + 6.50842i −1.13094 + 0.411629i
\(251\) 6.37816 11.0473i 0.402586 0.697299i −0.591451 0.806341i \(-0.701445\pi\)
0.994037 + 0.109042i \(0.0347782\pi\)
\(252\) 0 0
\(253\) 3.34831 + 5.79945i 0.210507 + 0.364608i
\(254\) 0.642130 + 0.538811i 0.0402908 + 0.0338080i
\(255\) 0 0
\(256\) 1.93429 + 10.9699i 0.120893 + 0.685619i
\(257\) 2.27561 + 12.9056i 0.141949 + 0.805030i 0.969767 + 0.244034i \(0.0784708\pi\)
−0.827818 + 0.560996i \(0.810418\pi\)
\(258\) 0 0
\(259\) −2.78554 2.33734i −0.173085 0.145235i
\(260\) −2.83551 4.91125i −0.175851 0.304583i
\(261\) 0 0
\(262\) −9.00956 + 15.6050i −0.556613 + 0.964081i
\(263\) −8.94040 + 3.25404i −0.551289 + 0.200653i −0.602619 0.798029i \(-0.705876\pi\)
0.0513303 + 0.998682i \(0.483654\pi\)
\(264\) 0 0
\(265\) 9.44145 7.92232i 0.579984 0.486664i
\(266\) 11.0695 + 4.02897i 0.678714 + 0.247032i
\(267\) 0 0
\(268\) −0.396440 + 2.24832i −0.0242164 + 0.137338i
\(269\) −22.1408 −1.34995 −0.674973 0.737842i \(-0.735845\pi\)
−0.674973 + 0.737842i \(0.735845\pi\)
\(270\) 0 0
\(271\) 27.9627 1.69861 0.849307 0.527899i \(-0.177020\pi\)
0.849307 + 0.527899i \(0.177020\pi\)
\(272\) −0.804010 + 4.55977i −0.0487503 + 0.276476i
\(273\) 0 0
\(274\) −6.27287 2.28314i −0.378958 0.137929i
\(275\) 6.94075 5.82398i 0.418543 0.351199i
\(276\) 0 0
\(277\) 17.7449 6.45860i 1.06618 0.388060i 0.251436 0.967874i \(-0.419097\pi\)
0.814749 + 0.579814i \(0.196875\pi\)
\(278\) −8.80397 + 15.2489i −0.528027 + 0.914569i
\(279\) 0 0
\(280\) −5.55431 9.62034i −0.331933 0.574925i
\(281\) 15.3222 + 12.8569i 0.914047 + 0.766977i 0.972885 0.231291i \(-0.0742949\pi\)
−0.0588373 + 0.998268i \(0.518739\pi\)
\(282\) 0 0
\(283\) 2.90775 + 16.4906i 0.172848 + 0.980267i 0.940599 + 0.339519i \(0.110264\pi\)
−0.767752 + 0.640748i \(0.778624\pi\)
\(284\) 0.479838 + 2.72130i 0.0284732 + 0.161479i
\(285\) 0 0
\(286\) 34.5133 + 28.9601i 2.04082 + 1.71245i
\(287\) 6.73722 + 11.6692i 0.397685 + 0.688811i
\(288\) 0 0
\(289\) 8.02317 13.8965i 0.471951 0.817444i
\(290\) −20.4840 + 7.45557i −1.20286 + 0.437806i
\(291\) 0 0
\(292\) −1.71694 + 1.44069i −0.100476 + 0.0843098i
\(293\) 18.3917 + 6.69402i 1.07445 + 0.391069i 0.817840 0.575446i \(-0.195171\pi\)
0.256613 + 0.966514i \(0.417394\pi\)
\(294\) 0 0
\(295\) 2.63835 14.9628i 0.153611 0.871169i
\(296\) −3.11549 −0.181084
\(297\) 0 0
\(298\) −30.7437 −1.78093
\(299\) 1.92615 10.9237i 0.111392 0.631735i
\(300\) 0 0
\(301\) −25.6994 9.35383i −1.48129 0.539146i
\(302\) 1.50278 1.26098i 0.0864751 0.0725612i
\(303\) 0 0
\(304\) 11.9639 4.35451i 0.686177 0.249748i
\(305\) 1.07906 1.86899i 0.0617870 0.107018i
\(306\) 0 0
\(307\) −7.44973 12.9033i −0.425179 0.736431i 0.571258 0.820770i \(-0.306455\pi\)
−0.996437 + 0.0843392i \(0.973122\pi\)
\(308\) −4.34272 3.64398i −0.247450 0.207635i
\(309\) 0 0
\(310\) −0.480331 2.72410i −0.0272810 0.154718i
\(311\) −0.797455 4.52259i −0.0452195 0.256453i 0.953814 0.300396i \(-0.0971189\pi\)
−0.999034 + 0.0439436i \(0.986008\pi\)
\(312\) 0 0
\(313\) 9.09194 + 7.62904i 0.513907 + 0.431219i 0.862501 0.506055i \(-0.168897\pi\)
−0.348595 + 0.937274i \(0.613341\pi\)
\(314\) −2.78836 4.82958i −0.157356 0.272549i
\(315\) 0 0
\(316\) −1.14408 + 1.98161i −0.0643597 + 0.111474i
\(317\) −13.6418 + 4.96522i −0.766202 + 0.278875i −0.695407 0.718616i \(-0.744776\pi\)
−0.0707952 + 0.997491i \(0.522554\pi\)
\(318\) 0 0
\(319\) 26.1648 21.9549i 1.46495 1.22924i
\(320\) −8.18207 2.97803i −0.457392 0.166477i
\(321\) 0 0
\(322\) −1.22886 + 6.96919i −0.0684815 + 0.388378i
\(323\) 2.62232 0.145910
\(324\) 0 0
\(325\) −15.0077 −0.832480
\(326\) −4.37193 + 24.7944i −0.242139 + 1.37324i
\(327\) 0 0
\(328\) 10.8484 + 3.94851i 0.599005 + 0.218020i
\(329\) 26.6083 22.3270i 1.46696 1.23093i
\(330\) 0 0
\(331\) 7.61687 2.77231i 0.418661 0.152380i −0.124095 0.992270i \(-0.539603\pi\)
0.542756 + 0.839890i \(0.317381\pi\)
\(332\) −1.41620 + 2.45292i −0.0777238 + 0.134622i
\(333\) 0 0
\(334\) −11.4313 19.7996i −0.625494 1.08339i
\(335\) −5.97426 5.01300i −0.326409 0.273890i
\(336\) 0 0
\(337\) −3.26597 18.5222i −0.177909 1.00897i −0.934733 0.355351i \(-0.884361\pi\)
0.756824 0.653618i \(-0.226750\pi\)
\(338\) −9.39570 53.2857i −0.511059 2.89836i
\(339\) 0 0
\(340\) 0.616981 + 0.517709i 0.0334605 + 0.0280767i
\(341\) 2.16708 + 3.75350i 0.117354 + 0.203263i
\(342\) 0 0
\(343\) 8.72082 15.1049i 0.470880 0.815588i
\(344\) −22.0189 + 8.01421i −1.18718 + 0.432097i
\(345\) 0 0
\(346\) 15.2560 12.8013i 0.820170 0.688204i
\(347\) −16.5552 6.02558i −0.888727 0.323470i −0.143001 0.989723i \(-0.545675\pi\)
−0.745726 + 0.666252i \(0.767897\pi\)
\(348\) 0 0
\(349\) −2.95016 + 16.7312i −0.157918 + 0.895600i 0.798151 + 0.602458i \(0.205812\pi\)
−0.956069 + 0.293142i \(0.905299\pi\)
\(350\) 9.57475 0.511792
\(351\) 0 0
\(352\) −11.2962 −0.602090
\(353\) 2.63174 14.9254i 0.140074 0.794396i −0.831118 0.556096i \(-0.812299\pi\)
0.971192 0.238300i \(-0.0765902\pi\)
\(354\) 0 0
\(355\) −8.87021 3.22849i −0.470782 0.171351i
\(356\) 1.71054 1.43531i 0.0906582 0.0760712i
\(357\) 0 0
\(358\) −0.438881 + 0.159740i −0.0231956 + 0.00844250i
\(359\) 1.22548 2.12259i 0.0646783 0.112026i −0.831873 0.554966i \(-0.812731\pi\)
0.896551 + 0.442940i \(0.146065\pi\)
\(360\) 0 0
\(361\) 5.89461 + 10.2098i 0.310243 + 0.537356i
\(362\) −1.71757 1.44121i −0.0902734 0.0757484i
\(363\) 0 0
\(364\) 1.63058 + 9.24746i 0.0854654 + 0.484699i
\(365\) −1.32952 7.54010i −0.0695904 0.394667i
\(366\) 0 0
\(367\) −1.00622 0.844323i −0.0525245 0.0440733i 0.616148 0.787631i \(-0.288693\pi\)
−0.668672 + 0.743557i \(0.733137\pi\)
\(368\) 3.82425 + 6.62379i 0.199353 + 0.345289i
\(369\) 0 0
\(370\) −1.73314 + 3.00189i −0.0901017 + 0.156061i
\(371\) −19.1770 + 6.97984i −0.995618 + 0.362375i
\(372\) 0 0
\(373\) −7.37407 + 6.18758i −0.381815 + 0.320381i −0.813415 0.581684i \(-0.802394\pi\)
0.431599 + 0.902065i \(0.357949\pi\)
\(374\) −6.01278 2.18847i −0.310913 0.113163i
\(375\) 0 0
\(376\) 5.16778 29.3080i 0.266508 1.51144i
\(377\) −56.5753 −2.91377
\(378\) 0 0
\(379\) −8.56311 −0.439857 −0.219929 0.975516i \(-0.570582\pi\)
−0.219929 + 0.975516i \(0.570582\pi\)
\(380\) 0.384578 2.18105i 0.0197284 0.111885i
\(381\) 0 0
\(382\) −30.5899 11.1338i −1.56512 0.569656i
\(383\) −25.7656 + 21.6199i −1.31656 + 1.10473i −0.329539 + 0.944142i \(0.606893\pi\)
−0.987022 + 0.160584i \(0.948662\pi\)
\(384\) 0 0
\(385\) 18.1977 6.62344i 0.927443 0.337562i
\(386\) −16.5385 + 28.6455i −0.841786 + 1.45802i
\(387\) 0 0
\(388\) −2.10681 3.64911i −0.106957 0.185255i
\(389\) 11.4554 + 9.61223i 0.580813 + 0.487360i 0.885214 0.465184i \(-0.154012\pi\)
−0.304401 + 0.952544i \(0.598456\pi\)
\(390\) 0 0
\(391\) 0.273555 + 1.55141i 0.0138343 + 0.0784582i
\(392\) 0.299542 + 1.69879i 0.0151291 + 0.0858016i
\(393\) 0 0
\(394\) −11.6030 9.73611i −0.584553 0.490498i
\(395\) −3.90824 6.76927i −0.196645 0.340599i
\(396\) 0 0
\(397\) 8.38938 14.5308i 0.421051 0.729282i −0.574991 0.818159i \(-0.694995\pi\)
0.996043 + 0.0888774i \(0.0283279\pi\)
\(398\) −15.8580 + 5.77185i −0.794891 + 0.289317i
\(399\) 0 0
\(400\) 7.92732 6.65182i 0.396366 0.332591i
\(401\) 12.3347 + 4.48946i 0.615965 + 0.224193i 0.631111 0.775693i \(-0.282599\pi\)
−0.0151464 + 0.999885i \(0.504821\pi\)
\(402\) 0 0
\(403\) 1.24663 7.07000i 0.0620992 0.352182i
\(404\) −3.83541 −0.190819
\(405\) 0 0
\(406\) 36.0943 1.79133
\(407\) 0.943123 5.34872i 0.0467489 0.265126i
\(408\) 0 0
\(409\) −23.9157 8.70459i −1.18255 0.430414i −0.325450 0.945559i \(-0.605516\pi\)
−0.857103 + 0.515145i \(0.827738\pi\)
\(410\) 9.83951 8.25633i 0.485939 0.407751i
\(411\) 0 0
\(412\) 1.00017 0.364032i 0.0492748 0.0179346i
\(413\) −12.5789 + 21.7872i −0.618965 + 1.07208i
\(414\) 0 0
\(415\) −4.83779 8.37929i −0.237478 0.411323i
\(416\) 14.3334 + 12.0272i 0.702753 + 0.589680i
\(417\) 0 0
\(418\) 3.05531 + 17.3275i 0.149440 + 0.847517i
\(419\) 2.20013 + 12.4776i 0.107483 + 0.609569i 0.990199 + 0.139662i \(0.0446015\pi\)
−0.882716 + 0.469907i \(0.844287\pi\)
\(420\) 0 0
\(421\) −13.5416 11.3627i −0.659975 0.553785i 0.250104 0.968219i \(-0.419535\pi\)
−0.910079 + 0.414434i \(0.863980\pi\)
\(422\) −11.8777 20.5727i −0.578196 1.00147i
\(423\) 0 0
\(424\) −8.74249 + 15.1424i −0.424573 + 0.735382i
\(425\) 2.00289 0.728993i 0.0971545 0.0353614i
\(426\) 0 0
\(427\) −2.73741 + 2.29696i −0.132473 + 0.111158i
\(428\) −5.81081 2.11496i −0.280876 0.102231i
\(429\) 0 0
\(430\) −4.52707 + 25.6743i −0.218315 + 1.23812i
\(431\) −15.6974 −0.756117 −0.378059 0.925782i \(-0.623408\pi\)
−0.378059 + 0.925782i \(0.623408\pi\)
\(432\) 0 0
\(433\) −12.6258 −0.606759 −0.303380 0.952870i \(-0.598115\pi\)
−0.303380 + 0.952870i \(0.598115\pi\)
\(434\) −0.795335 + 4.51057i −0.0381773 + 0.216514i
\(435\) 0 0
\(436\) 5.63954 + 2.05262i 0.270085 + 0.0983028i
\(437\) 3.31837 2.78444i 0.158739 0.133198i
\(438\) 0 0
\(439\) −25.3124 + 9.21297i −1.20810 + 0.439711i −0.866043 0.499970i \(-0.833344\pi\)
−0.342053 + 0.939681i \(0.611122\pi\)
\(440\) 8.29608 14.3692i 0.395500 0.685027i
\(441\) 0 0
\(442\) 5.29934 + 9.17873i 0.252064 + 0.436588i
\(443\) −26.6031 22.3227i −1.26395 1.06058i −0.995249 0.0973585i \(-0.968961\pi\)
−0.268703 0.963223i \(-0.586595\pi\)
\(444\) 0 0
\(445\) 1.32456 + 7.51196i 0.0627902 + 0.356101i
\(446\) 3.36801 + 19.1009i 0.159480 + 0.904456i
\(447\) 0 0
\(448\) 11.0444 + 9.26732i 0.521797 + 0.437840i
\(449\) −10.3731 17.9667i −0.489535 0.847900i 0.510392 0.859942i \(-0.329500\pi\)
−0.999927 + 0.0120419i \(0.996167\pi\)
\(450\) 0 0
\(451\) −10.0629 + 17.4295i −0.473844 + 0.820722i
\(452\) −0.208162 + 0.0757647i −0.00979111 + 0.00356367i
\(453\) 0 0
\(454\) 4.53732 3.80727i 0.212947 0.178684i
\(455\) −30.1426 10.9710i −1.41311 0.514329i
\(456\) 0 0
\(457\) −1.25161 + 7.09823i −0.0585478 + 0.332041i −0.999987 0.00514224i \(-0.998363\pi\)
0.941439 + 0.337183i \(0.109474\pi\)
\(458\) 29.3621 1.37200
\(459\) 0 0
\(460\) 1.33046 0.0620332
\(461\) −4.01593 + 22.7755i −0.187041 + 1.06076i 0.736265 + 0.676694i \(0.236588\pi\)
−0.923305 + 0.384067i \(0.874523\pi\)
\(462\) 0 0
\(463\) −4.67576 1.70184i −0.217301 0.0790911i 0.231076 0.972936i \(-0.425775\pi\)
−0.448377 + 0.893845i \(0.647998\pi\)
\(464\) 29.8839 25.0756i 1.38733 1.16411i
\(465\) 0 0
\(466\) −0.809515 + 0.294639i −0.0375000 + 0.0136489i
\(467\) −6.24068 + 10.8092i −0.288784 + 0.500189i −0.973520 0.228602i \(-0.926584\pi\)
0.684735 + 0.728792i \(0.259918\pi\)
\(468\) 0 0
\(469\) 6.45669 + 11.1833i 0.298142 + 0.516397i
\(470\) −25.3645 21.2833i −1.16998 0.981726i
\(471\) 0 0
\(472\) 3.74294 + 21.2273i 0.172283 + 0.977064i
\(473\) −7.09335 40.2284i −0.326153 1.84970i
\(474\) 0 0
\(475\) −4.48974 3.76734i −0.206004 0.172858i
\(476\) −0.666803 1.15494i −0.0305628 0.0529364i
\(477\) 0 0
\(478\) 15.8588 27.4683i 0.725365 1.25637i
\(479\) 26.7542 9.73775i 1.22243 0.444929i 0.351433 0.936213i \(-0.385694\pi\)
0.870999 + 0.491284i \(0.163472\pi\)
\(480\) 0 0
\(481\) −6.89152 + 5.78267i −0.314226 + 0.263667i
\(482\) 22.6803 + 8.25495i 1.03306 + 0.376003i
\(483\) 0 0
\(484\) 0.531793 3.01595i 0.0241724 0.137088i
\(485\) 14.3939 0.653595
\(486\) 0 0
\(487\) 29.6841 1.34511 0.672557 0.740045i \(-0.265196\pi\)
0.672557 + 0.740045i \(0.265196\pi\)
\(488\) −0.531653 + 3.01515i −0.0240668 + 0.136489i
\(489\) 0 0
\(490\) 1.80348 + 0.656412i 0.0814728 + 0.0296537i
\(491\) −9.50275 + 7.97375i −0.428853 + 0.359850i −0.831519 0.555497i \(-0.812528\pi\)
0.402666 + 0.915347i \(0.368084\pi\)
\(492\) 0 0
\(493\) 7.55038 2.74811i 0.340052 0.123769i
\(494\) 14.5720 25.2394i 0.655623 1.13557i
\(495\) 0 0
\(496\) 2.47512 + 4.28702i 0.111136 + 0.192493i
\(497\) 11.9732 + 10.0467i 0.537073 + 0.450658i
\(498\) 0 0
\(499\) −0.395887 2.24519i −0.0177223 0.100508i 0.974664 0.223676i \(-0.0718058\pi\)
−0.992386 + 0.123168i \(0.960695\pi\)
\(500\) −1.02867 5.83387i −0.0460035 0.260899i
\(501\) 0 0
\(502\) 15.4240 + 12.9423i 0.688407 + 0.577642i
\(503\) 20.6406 + 35.7506i 0.920320 + 1.59404i 0.798920 + 0.601437i \(0.205405\pi\)
0.121399 + 0.992604i \(0.461262\pi\)
\(504\) 0 0
\(505\) 6.55097 11.3466i 0.291514 0.504917i
\(506\) −9.93253 + 3.61515i −0.441555 + 0.160713i
\(507\) 0 0
\(508\) −0.199896 + 0.167733i −0.00886896 + 0.00744194i
\(509\) 15.4337 + 5.61739i 0.684085 + 0.248986i 0.660600 0.750738i \(-0.270302\pi\)
0.0234843 + 0.999724i \(0.492524\pi\)
\(510\) 0 0
\(511\) −2.20143 + 12.4849i −0.0973856 + 0.552301i
\(512\) 9.67844 0.427731
\(513\) 0 0
\(514\) −20.6845 −0.912355
\(515\) −0.631366 + 3.58066i −0.0278213 + 0.157783i
\(516\) 0 0
\(517\) 48.7519 + 17.7443i 2.14411 + 0.780391i
\(518\) 4.39670 3.68927i 0.193180 0.162097i
\(519\) 0 0
\(520\) −25.8257 + 9.39978i −1.13253 + 0.412208i
\(521\) −4.64836 + 8.05119i −0.203648 + 0.352729i −0.949701 0.313157i \(-0.898613\pi\)
0.746053 + 0.665887i \(0.231947\pi\)
\(522\) 0 0
\(523\) 11.3736 + 19.6996i 0.497331 + 0.861402i 0.999995 0.00307938i \(-0.000980199\pi\)
−0.502664 + 0.864482i \(0.667647\pi\)
\(524\) −4.29704 3.60564i −0.187717 0.157513i
\(525\) 0 0
\(526\) −2.60771 14.7891i −0.113702 0.644834i
\(527\) 0.177049 + 1.00410i 0.00771239 + 0.0437392i
\(528\) 0 0
\(529\) −15.6255 13.1114i −0.679371 0.570060i
\(530\) 9.72687 + 16.8474i 0.422508 + 0.731806i
\(531\) 0 0
\(532\) −1.83355 + 3.17581i −0.0794946 + 0.137689i
\(533\) 31.3258 11.4017i 1.35687 0.493861i
\(534\) 0 0
\(535\) 16.1819 13.5782i 0.699603 0.587037i
\(536\) 10.3967 + 3.78410i 0.449070 + 0.163448i
\(537\) 0 0
\(538\) 6.06850 34.4162i 0.261632 1.48379i
\(539\) −3.00718 −0.129528
\(540\) 0 0
\(541\) 2.38959 0.102737 0.0513683 0.998680i \(-0.483642\pi\)
0.0513683 + 0.998680i \(0.483642\pi\)
\(542\) −7.66422 + 43.4659i −0.329206 + 1.86702i
\(543\) 0 0
\(544\) −2.49711 0.908874i −0.107063 0.0389676i
\(545\) −15.7049 + 13.1780i −0.672724 + 0.564482i
\(546\) 0 0
\(547\) −27.8777 + 10.1466i −1.19196 + 0.433839i −0.860412 0.509599i \(-0.829794\pi\)
−0.331550 + 0.943438i \(0.607572\pi\)
\(548\) 1.03904 1.79967i 0.0443856 0.0768781i
\(549\) 0 0
\(550\) 7.15057 + 12.3852i 0.304901 + 0.528105i
\(551\) −16.9252 14.2019i −0.721036 0.605021i
\(552\) 0 0
\(553\) 2.24745 + 12.7459i 0.0955714 + 0.542012i
\(554\) 5.17577 + 29.3533i 0.219897 + 1.24710i
\(555\) 0 0
\(556\) −4.19898 3.52336i −0.178076 0.149424i
\(557\) 4.20706 + 7.28685i 0.178259 + 0.308754i 0.941284 0.337615i \(-0.109620\pi\)
−0.763025 + 0.646369i \(0.776287\pi\)
\(558\) 0 0
\(559\) −33.8309 + 58.5969i −1.43090 + 2.47838i
\(560\) 20.7844 7.56491i 0.878302 0.319676i
\(561\) 0 0
\(562\) −24.1847 + 20.2933i −1.02017 + 0.856023i
\(563\) −25.5845 9.31201i −1.07826 0.392455i −0.259000 0.965877i \(-0.583393\pi\)
−0.819260 + 0.573423i \(0.805615\pi\)
\(564\) 0 0
\(565\) 0.131404 0.745230i 0.00552822 0.0313521i
\(566\) −26.4304 −1.11095
\(567\) 0 0
\(568\) 13.3915 0.561894
\(569\) 3.81146 21.6159i 0.159785 0.906184i −0.794495 0.607270i \(-0.792265\pi\)
0.954280 0.298914i \(-0.0966243\pi\)
\(570\) 0 0
\(571\) 42.1485 + 15.3408i 1.76386 + 0.641992i 0.999994 0.00338488i \(-0.00107744\pi\)
0.763864 + 0.645377i \(0.223300\pi\)
\(572\) −10.7441 + 9.01533i −0.449232 + 0.376950i
\(573\) 0 0
\(574\) −19.9855 + 7.27412i −0.834178 + 0.303616i
\(575\) 1.76046 3.04921i 0.0734163 0.127161i
\(576\) 0 0
\(577\) −6.00955 10.4088i −0.250181 0.433326i 0.713395 0.700762i \(-0.247157\pi\)
−0.963575 + 0.267437i \(0.913823\pi\)
\(578\) 19.4021 + 16.2803i 0.807020 + 0.677170i
\(579\) 0 0
\(580\) −1.17837 6.68286i −0.0489291 0.277491i
\(581\) 2.78199 + 15.7775i 0.115417 + 0.654560i
\(582\) 0 0
\(583\) −23.3502 19.5932i −0.967068 0.811467i
\(584\) 5.43095 + 9.40669i 0.224734 + 0.389252i
\(585\) 0 0
\(586\) −15.4463 + 26.7537i −0.638079 + 1.10519i
\(587\) −16.0028 + 5.82456i −0.660508 + 0.240405i −0.650456 0.759544i \(-0.725422\pi\)
−0.0100523 + 0.999949i \(0.503200\pi\)
\(588\) 0 0
\(589\) 2.14770 1.80214i 0.0884946 0.0742558i
\(590\) 22.5354 + 8.20223i 0.927769 + 0.337680i
\(591\) 0 0
\(592\) 1.07718 6.10899i 0.0442718 0.251078i
\(593\) 14.9284 0.613037 0.306519 0.951865i \(-0.400836\pi\)
0.306519 + 0.951865i \(0.400836\pi\)
\(594\) 0 0
\(595\) 4.55566 0.186764
\(596\) 1.66191 9.42516i 0.0680745 0.386070i
\(597\) 0 0
\(598\) 16.4522 + 5.98810i 0.672779 + 0.244871i
\(599\) −10.3683 + 8.70000i −0.423636 + 0.355472i −0.829544 0.558441i \(-0.811400\pi\)
0.405909 + 0.913914i \(0.366955\pi\)
\(600\) 0 0
\(601\) 42.5843 15.4994i 1.73705 0.632234i 0.737958 0.674847i \(-0.235790\pi\)
0.999092 + 0.0426125i \(0.0135681\pi\)
\(602\) 21.5837 37.3841i 0.879686 1.52366i
\(603\) 0 0
\(604\) 0.305346 + 0.528874i 0.0124243 + 0.0215196i
\(605\) 8.01401 + 6.72455i 0.325816 + 0.273392i
\(606\) 0 0
\(607\) 4.24340 + 24.0655i 0.172234 + 0.976790i 0.941288 + 0.337605i \(0.109617\pi\)
−0.769053 + 0.639185i \(0.779272\pi\)
\(608\) 1.26887 + 7.19613i 0.0514596 + 0.291842i
\(609\) 0 0
\(610\) 2.60945 + 2.18959i 0.105654 + 0.0886539i
\(611\) −42.9674 74.4217i −1.73827 3.01078i
\(612\) 0 0
\(613\) 12.5998 21.8235i 0.508901 0.881443i −0.491046 0.871134i \(-0.663385\pi\)
0.999947 0.0103088i \(-0.00328145\pi\)
\(614\) 22.0991 8.04342i 0.891847 0.324606i
\(615\) 0 0
\(616\) −21.0458 + 17.6596i −0.847961 + 0.711524i
\(617\) 3.79810 + 1.38239i 0.152906 + 0.0556531i 0.417339 0.908751i \(-0.362963\pi\)
−0.264433 + 0.964404i \(0.585185\pi\)
\(618\) 0 0
\(619\) −7.77423 + 44.0898i −0.312473 + 1.77212i 0.273582 + 0.961849i \(0.411791\pi\)
−0.586055 + 0.810271i \(0.699320\pi\)
\(620\) 0.861097 0.0345825
\(621\) 0 0
\(622\) 7.24860 0.290642
\(623\) 2.19321 12.4383i 0.0878693 0.498332i
\(624\) 0 0
\(625\) 8.76089 + 3.18870i 0.350435 + 0.127548i
\(626\) −14.3508 + 12.0417i −0.573572 + 0.481284i
\(627\) 0 0
\(628\) 1.63135 0.593762i 0.0650978 0.0236937i
\(629\) 0.638833 1.10649i 0.0254719 0.0441187i
\(630\) 0 0
\(631\) −15.7058 27.2033i −0.625238 1.08294i −0.988495 0.151255i \(-0.951668\pi\)
0.363256 0.931689i \(-0.381665\pi\)
\(632\) 8.49465 + 7.12786i 0.337899 + 0.283531i
\(633\) 0 0
\(634\) −3.97902 22.5661i −0.158027 0.896215i
\(635\) −0.154790 0.877861i −0.00614267 0.0348368i
\(636\) 0 0
\(637\) 3.81571 + 3.20176i 0.151184 + 0.126859i
\(638\) 26.9558 + 46.6888i 1.06719 + 1.84843i
\(639\) 0 0
\(640\) 11.4392 19.8133i 0.452176 0.783191i
\(641\) 45.7072 16.6361i 1.80533 0.657085i 0.807597 0.589734i \(-0.200768\pi\)
0.997729 0.0673508i \(-0.0214547\pi\)
\(642\) 0 0
\(643\) −21.4740 + 18.0189i −0.846853 + 0.710594i −0.959094 0.283087i \(-0.908642\pi\)
0.112241 + 0.993681i \(0.464197\pi\)
\(644\) −2.07013 0.753467i −0.0815747 0.0296907i
\(645\) 0 0
\(646\) −0.718744 + 4.07620i −0.0282786 + 0.160376i
\(647\) 37.5519 1.47632 0.738159 0.674627i \(-0.235696\pi\)
0.738159 + 0.674627i \(0.235696\pi\)
\(648\) 0 0
\(649\) −37.5763 −1.47500
\(650\) 4.11343 23.3284i 0.161342 0.915015i
\(651\) 0 0
\(652\) −7.36496 2.68062i −0.288434 0.104981i
\(653\) 3.91619 3.28607i 0.153252 0.128594i −0.562938 0.826499i \(-0.690329\pi\)
0.716190 + 0.697905i \(0.245884\pi\)
\(654\) 0 0
\(655\) 18.0063 6.55376i 0.703564 0.256076i
\(656\) −11.4933 + 19.9069i −0.448737 + 0.777236i
\(657\) 0 0
\(658\) 27.4126 + 47.4801i 1.06866 + 1.85097i
\(659\) −26.8161 22.5014i −1.04461 0.876529i −0.0520901 0.998642i \(-0.516588\pi\)
−0.992516 + 0.122114i \(0.961033\pi\)
\(660\) 0 0
\(661\) 0.231553 + 1.31320i 0.00900637 + 0.0510777i 0.988980 0.148051i \(-0.0473000\pi\)
−0.979973 + 0.199129i \(0.936189\pi\)
\(662\) 2.22167 + 12.5997i 0.0863476 + 0.489701i
\(663\) 0 0
\(664\) 10.5151 + 8.82317i 0.408063 + 0.342406i
\(665\) −6.26350 10.8487i −0.242888 0.420694i
\(666\) 0 0
\(667\) 6.63648 11.4947i 0.256966 0.445077i
\(668\) 6.68795 2.43422i 0.258765 0.0941827i
\(669\) 0 0
\(670\) 9.42980 7.91255i 0.364305 0.305688i
\(671\) −5.01552 1.82550i −0.193622 0.0704726i
\(672\) 0 0
\(673\) −0.621579 + 3.52515i −0.0239601 + 0.135884i −0.994441 0.105292i \(-0.966422\pi\)
0.970481 + 0.241177i \(0.0775333\pi\)
\(674\) 29.6866 1.14348
\(675\) 0 0
\(676\) 16.8438 0.647839
\(677\) 6.41437 36.3777i 0.246524 1.39811i −0.570401 0.821366i \(-0.693212\pi\)
0.816926 0.576743i \(-0.195677\pi\)
\(678\) 0 0
\(679\) −22.3962 8.15156i −0.859488 0.312828i
\(680\) 2.99003 2.50894i 0.114663 0.0962133i
\(681\) 0 0
\(682\) −6.42850 + 2.33978i −0.246160 + 0.0895948i
\(683\) 19.0083 32.9233i 0.727332 1.25978i −0.230675 0.973031i \(-0.574093\pi\)
0.958007 0.286745i \(-0.0925733\pi\)
\(684\) 0 0
\(685\) 3.54941 + 6.14775i 0.135616 + 0.234894i
\(686\) 21.0892 + 17.6959i 0.805188 + 0.675633i
\(687\) 0 0
\(688\) −8.10161 45.9465i −0.308871 1.75170i
\(689\) 8.76739 + 49.7223i 0.334011 + 1.89427i
\(690\) 0 0
\(691\) 0.421680 + 0.353832i 0.0160415 + 0.0134604i 0.650773 0.759272i \(-0.274445\pi\)
−0.634732 + 0.772733i \(0.718889\pi\)
\(692\) 3.09984 + 5.36908i 0.117838 + 0.204102i
\(693\) 0 0
\(694\) 13.9039 24.0822i 0.527784 0.914148i
\(695\) 17.5954 6.40420i 0.667432 0.242925i
\(696\) 0 0
\(697\) −3.62683 + 3.04327i −0.137376 + 0.115272i
\(698\) −25.1988 9.17160i −0.953788 0.347150i
\(699\) 0 0
\(700\) −0.517582 + 2.93535i −0.0195628 + 0.110946i
\(701\) −19.0242 −0.718534 −0.359267 0.933235i \(-0.616973\pi\)
−0.359267 + 0.933235i \(0.616973\pi\)
\(702\) 0 0
\(703\) −3.51328 −0.132506
\(704\) −3.73939 + 21.2071i −0.140933 + 0.799273i
\(705\) 0 0
\(706\) 22.4790 + 8.18169i 0.846009 + 0.307922i
\(707\) −16.6188 + 13.9448i −0.625013 + 0.524448i
\(708\) 0 0
\(709\) −11.4236 + 4.15786i −0.429024 + 0.156152i −0.547501 0.836805i \(-0.684421\pi\)
0.118478 + 0.992957i \(0.462199\pi\)
\(710\) 7.44966 12.9032i 0.279581 0.484248i
\(711\) 0 0
\(712\) −5.41068 9.37158i −0.202774 0.351215i
\(713\) 1.29022 + 1.08262i 0.0483191 + 0.0405445i
\(714\) 0 0
\(715\) −8.31971 47.1834i −0.311140 1.76456i
\(716\) −0.0252472 0.143184i −0.000943531 0.00535103i
\(717\) 0 0
\(718\) 2.96352 + 2.48669i 0.110598 + 0.0928024i
\(719\) 4.88834 + 8.46685i 0.182304 + 0.315760i 0.942665 0.333741i \(-0.108311\pi\)
−0.760361 + 0.649501i \(0.774978\pi\)
\(720\) 0 0
\(721\) 3.01017 5.21376i 0.112104 0.194171i
\(722\) −17.4859 + 6.36437i −0.650760 + 0.236857i
\(723\) 0 0
\(724\) 0.534682 0.448651i 0.0198713 0.0166740i
\(725\) −16.8752 6.14209i −0.626731 0.228111i
\(726\) 0 0
\(727\) 0.752752 4.26907i 0.0279180 0.158331i −0.967662 0.252252i \(-0.918829\pi\)
0.995580 + 0.0939207i \(0.0299400\pi\)
\(728\) 45.5067 1.68659
\(729\) 0 0
\(730\) 12.0849 0.447283
\(731\) 1.66867 9.46350i 0.0617180 0.350020i
\(732\) 0 0
\(733\) −27.4331 9.98482i −1.01326 0.368798i −0.218578 0.975819i \(-0.570142\pi\)
−0.794685 + 0.607022i \(0.792364\pi\)
\(734\) 1.58823 1.33268i 0.0586226 0.0491902i
\(735\) 0 0
\(736\) −4.12499 + 1.50137i −0.152049 + 0.0553413i
\(737\) −9.64391 + 16.7037i −0.355238 + 0.615290i
\(738\) 0 0
\(739\) −20.7777 35.9880i −0.764319 1.32384i −0.940606 0.339501i \(-0.889742\pi\)
0.176287 0.984339i \(-0.443591\pi\)
\(740\) −0.826607 0.693606i −0.0303867 0.0254975i
\(741\) 0 0
\(742\) −5.59349 31.7222i −0.205343 1.16456i
\(743\) −3.71214 21.0526i −0.136185 0.772345i −0.974027 0.226432i \(-0.927294\pi\)
0.837842 0.545913i \(-0.183817\pi\)
\(744\) 0 0
\(745\) 25.0446 + 21.0149i 0.917565 + 0.769928i
\(746\) −7.59699 13.1584i −0.278146 0.481763i
\(747\) 0 0
\(748\) 0.995957 1.72505i 0.0364158 0.0630740i
\(749\) −32.8677 + 11.9629i −1.20096 + 0.437114i
\(750\) 0 0
\(751\) −30.6170 + 25.6907i −1.11723 + 0.937467i −0.998461 0.0554555i \(-0.982339\pi\)
−0.118768 + 0.992922i \(0.537894\pi\)
\(752\) 55.6816 + 20.2665i 2.03050 + 0.739042i
\(753\) 0 0
\(754\) 15.5065 87.9420i 0.564715 3.20266i
\(755\) −2.08615 −0.0759228
\(756\) 0 0
\(757\) 6.68348 0.242915 0.121458 0.992597i \(-0.461243\pi\)
0.121458 + 0.992597i \(0.461243\pi\)
\(758\) 2.34704 13.3107i 0.0852482 0.483467i
\(759\) 0 0
\(760\) −10.0857 3.67088i −0.365845 0.133157i
\(761\) −32.1930 + 27.0132i −1.16700 + 0.979226i −0.999977 0.00672735i \(-0.997859\pi\)
−0.167019 + 0.985954i \(0.553414\pi\)
\(762\) 0 0
\(763\) 31.8989 11.6103i 1.15482 0.420320i
\(764\) 5.06692 8.77617i 0.183315 0.317511i
\(765\) 0 0
\(766\) −26.5445 45.9764i −0.959092 1.66120i
\(767\) 47.6795 + 40.0078i 1.72161 + 1.44460i
\(768\) 0 0
\(769\) 0.419053 + 2.37657i 0.0151114 + 0.0857013i 0.991431 0.130633i \(-0.0417010\pi\)
−0.976319 + 0.216334i \(0.930590\pi\)
\(770\) 5.30787 + 30.1024i 0.191282 + 1.08482i
\(771\) 0 0
\(772\) −7.88789 6.61872i −0.283891 0.238213i
\(773\) 0.698900 + 1.21053i 0.0251377 + 0.0435398i 0.878321 0.478072i \(-0.158664\pi\)
−0.853183 + 0.521612i \(0.825331\pi\)
\(774\) 0 0
\(775\) 1.13940 1.97350i 0.0409284 0.0708901i
\(776\) −19.1887 + 6.98413i −0.688835 + 0.250715i
\(777\) 0 0
\(778\) −18.0813 + 15.1720i −0.648245 + 0.543942i
\(779\) 12.2336