Properties

Label 729.2.e.k.82.2
Level $729$
Weight $2$
Character 729.82
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 82.2
Root \(1.22778i\) of defining polynomial
Character \(\chi\) \(=\) 729.82
Dual form 729.2.e.k.649.2

$q$-expansion

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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 0.914105 + 0.405478i \(0.132895\pi\)
−0.720296 + 0.693667i \(0.755994\pi\)
\(3\) 0 0
\(4\) −0.461727 + 0.168055i −0.230864 + 0.0840275i
\(5\) −1.28581 1.07892i −0.575032 0.482509i 0.308279 0.951296i \(-0.400247\pi\)
−0.883311 + 0.468787i \(0.844691\pi\)
\(6\) 0 0
\(7\) −2.61167 0.950570i −0.987119 0.359282i −0.202515 0.979279i \(-0.564911\pi\)
−0.784604 + 0.619997i \(0.787134\pi\)
\(8\) 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 \(-0.506987\pi\)
0.980759 + 0.195220i \(0.0625421\pi\)
\(12\) 0 0
\(13\) 1.19401 6.77158i 0.331160 1.87810i −0.131123 0.991366i \(-0.541858\pi\)
0.462282 0.886733i \(-0.347031\pi\)
\(14\) 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 \(-0.795549\pi\)
0.919143 + 0.393923i \(0.128882\pi\)
\(18\) 0 0
\(19\) −1.34264 2.32553i −0.308024 0.533513i 0.669906 0.742446i \(-0.266334\pi\)
−0.977930 + 0.208933i \(0.933001\pi\)
\(20\) 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 \(-0.557321\pi\)
0.495190 + 0.868785i \(0.335098\pi\)
\(24\) 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 0.768142 + 0.640280i \(0.221182\pi\)
−0.502828 + 0.864386i \(0.667707\pi\)
\(30\) 0 0
\(31\) −0.981104 + 0.357093i −0.176212 + 0.0641357i −0.428619 0.903485i \(-0.641000\pi\)
0.252408 + 0.967621i \(0.418778\pi\)
\(32\) −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 −0.807230 0.590237i \(-0.799034\pi\)
0.914775 + 0.403963i \(0.132368\pi\)
\(38\) 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 −0.845768 0.533550i \(-0.820857\pi\)
0.977247 0.212104i \(-0.0680314\pi\)
\(42\) 0 0
\(43\) 7.53805 6.32518i 1.14954 0.964580i 0.149833 0.988711i \(-0.452126\pi\)
0.999709 + 0.0241308i \(0.00768182\pi\)
\(44\) −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 \(-0.0238230\pi\)
0.715837 + 0.698267i \(0.246045\pi\)
\(48\) 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 \(-0.668251\pi\)
−0.504305 + 0.863525i \(0.668251\pi\)
\(54\) 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 \(-0.478345\pi\)
−0.970726 + 0.240191i \(0.922790\pi\)
\(60\) 0 0
\(61\) 1.20820 + 0.439750i 0.154694 + 0.0563042i 0.418207 0.908352i \(-0.362659\pi\)
−0.263512 + 0.964656i \(0.584881\pi\)
\(62\) −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 0.895026 + 0.446014i \(0.147157\pi\)
−0.993595 + 0.112999i \(0.963954\pi\)
\(68\) −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 \(-0.725034\pi\)
0.983236 + 0.182339i \(0.0583670\pi\)
\(72\) 0 0
\(73\) 2.28072 + 3.95033i 0.266938 + 0.462351i 0.968070 0.250681i \(-0.0806547\pi\)
−0.701131 + 0.713032i \(0.747321\pi\)
\(74\) 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 0.995905 + 0.0904018i \(0.0288151\pi\)
−0.904926 + 0.425570i \(0.860074\pi\)
\(80\) 7.95828 0.889763
\(81\) 0 0
\(82\) 7.65237 0.845063
\(83\) −1.00098 5.67682i −0.109871 0.623112i −0.989162 0.146827i \(-0.953094\pi\)
0.879291 0.476285i \(-0.158017\pi\)
\(84\) 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 \(-0.0892393\pi\)
−0.720104 + 0.693866i \(0.755906\pi\)
\(90\) 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 −0.245177 0.969478i \(-0.578846\pi\)
0.912175 + 0.409800i \(0.134402\pi\)
\(98\) −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 \(-0.515843\pi\)
−0.680104 + 0.733116i \(0.738065\pi\)
\(102\) 0 0
\(103\) −1.65937 1.39237i −0.163502 0.137195i 0.557366 0.830267i \(-0.311812\pi\)
−0.720868 + 0.693073i \(0.756257\pi\)
\(104\) 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 \(-0.708155\pi\)
−0.608317 + 0.793695i \(0.708155\pi\)
\(108\) 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 \(-0.284528\pi\)
−0.658887 + 0.752242i \(0.728973\pi\)
\(114\) 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 0.877566 0.479456i \(-0.159166\pi\)
−0.854004 + 0.520267i \(0.825833\pi\)
\(128\) −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 \(-0.777305\pi\)
−0.172184 + 0.985065i \(0.555082\pi\)
\(132\) 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 0.999975 + 0.00712879i \(0.00226918\pi\)
−0.937231 + 0.348710i \(0.886620\pi\)
\(138\) 0 0
\(139\) 10.4828 3.81542i 0.889137 0.323619i 0.143246 0.989687i \(-0.454246\pi\)
0.745891 + 0.666068i \(0.232024\pi\)
\(140\) −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 0.455171 + 0.890404i \(0.349578\pi\)
−0.732257 + 0.681029i \(0.761533\pi\)
\(150\) 0 0
\(151\) −0.952086 + 0.798895i −0.0774797 + 0.0650131i −0.680705 0.732558i \(-0.738326\pi\)
0.603225 + 0.797571i \(0.293882\pi\)
\(152\) 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 0.528364 0.849018i \(-0.322806\pi\)
−0.744370 + 0.667768i \(0.767250\pi\)
\(158\) −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 \(-0.0884145\pi\)
−0.103046 + 0.994677i \(0.532859\pi\)
\(168\) 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 \(-0.562989\pi\)
0.931450 + 0.363869i \(0.118545\pi\)
\(174\) 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 \(-0.836853\pi\)
0.860443 + 0.509546i \(0.170187\pi\)
\(180\) 0 0
\(181\) −0.710251 1.23019i −0.0527925 0.0914393i 0.838421 0.545022i \(-0.183479\pi\)
−0.891214 + 0.453583i \(0.850146\pi\)
\(182\) −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 0.785228 + 0.619207i \(0.212546\pi\)
−0.526091 + 0.850428i \(0.676343\pi\)
\(192\) 0 0
\(193\) 19.6921 7.16735i 1.41747 0.515917i 0.484158 0.874981i \(-0.339126\pi\)
0.933313 + 0.359063i \(0.116904\pi\)
\(194\) 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 \(-0.0556129\pi\)
−0.642926 + 0.765929i \(0.722280\pi\)
\(198\) 0 0
\(199\) 5.34583 9.25925i 0.378956 0.656371i −0.611955 0.790893i \(-0.709616\pi\)
0.990911 + 0.134522i \(0.0429498\pi\)
\(200\) 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 0.152959 0.988233i \(-0.451120\pi\)
−0.946658 + 0.322240i \(0.895564\pi\)
\(212\) 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 0.698354 0.715753i \(-0.253916\pi\)
0.0748934 + 0.997192i \(0.476138\pi\)
\(224\) 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 \(-0.682479\pi\)
0.733182 + 0.680033i \(0.238034\pi\)
\(228\) 0 0
\(229\) −3.23028 + 18.3198i −0.213463 + 1.21061i 0.670092 + 0.742278i \(0.266255\pi\)
−0.883554 + 0.468329i \(0.844856\pi\)
\(230\) 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 \(-0.839024\pi\)
0.856948 + 0.515403i \(0.172358\pi\)
\(234\) 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 \(-0.385917\pi\)
0.870655 + 0.491894i \(0.163695\pi\)
\(240\) 0 0
\(241\) 2.65531 + 15.0590i 0.171043 + 0.970035i 0.942612 + 0.333889i \(0.108361\pi\)
−0.771569 + 0.636146i \(0.780528\pi\)
\(242\) 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 \(-0.298555\pi\)
−0.994037 + 0.109042i \(0.965222\pi\)
\(252\) 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 0.827818 + 0.560996i \(0.189582\pi\)
−0.969767 + 0.244034i \(0.921529\pi\)
\(258\) 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 \(-0.294124\pi\)
−0.0513303 + 0.998682i \(0.516346\pi\)
\(264\) 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 \(-0.264155\pi\)
0.674973 + 0.737842i \(0.264155\pi\)
\(270\) 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 0.814749 0.579814i \(-0.196875\pi\)
0.251436 + 0.967874i \(0.419097\pi\)
\(278\) 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 \(-0.925705\pi\)
0.0588373 + 0.998268i \(0.481261\pi\)
\(282\) 0 0
\(283\) 2.90775 16.4906i 0.172848 0.980267i −0.767752 0.640748i \(-0.778624\pi\)
0.940599 0.339519i \(-0.110264\pi\)
\(284\) −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 \(-0.804829\pi\)
−0.256613 + 0.966514i \(0.582606\pi\)
\(294\) 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 −0.996437 0.0843392i \(-0.973122\pi\)
0.571258 + 0.820770i \(0.306455\pi\)
\(308\) 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 \(-0.902881\pi\)
0.999034 + 0.0439436i \(0.0139922\pi\)
\(312\) 0 0
\(313\) 9.09194 7.62904i 0.513907 0.431219i −0.348595 0.937274i \(-0.613341\pi\)
0.862501 + 0.506055i \(0.168897\pi\)
\(314\) 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 \(-0.255224\pi\)
0.0707952 + 0.997491i \(0.477446\pi\)
\(318\) 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 0.542756 0.839890i \(-0.317381\pi\)
−0.124095 + 0.992270i \(0.539603\pi\)
\(332\) 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 0.756824 + 0.653618i \(0.226750\pi\)
−0.934733 + 0.355351i \(0.884361\pi\)
\(338\) 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 \(-0.454325\pi\)
0.745726 + 0.666252i \(0.232103\pi\)
\(348\) 0 0
\(349\) −2.95016 16.7312i −0.157918 0.895600i −0.956069 0.293142i \(-0.905299\pi\)
0.798151 0.602458i \(-0.205812\pi\)
\(350\) −9.57475 −0.511792
\(351\) 0 0
\(352\) −11.2962 −0.602090
\(353\) −2.63174 14.9254i −0.140074 0.794396i −0.971192 0.238300i \(-0.923410\pi\)
0.831118 0.556096i \(-0.187701\pi\)
\(354\) 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 \(-0.187269\pi\)
−0.896551 + 0.442940i \(0.853935\pi\)
\(360\) 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 −0.668672 0.743557i \(-0.733137\pi\)
0.616148 + 0.787631i \(0.288693\pi\)
\(368\) −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 0.431599 0.902065i \(-0.357949\pi\)
−0.813415 + 0.581684i \(0.802394\pi\)
\(374\) 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 0.987022 + 0.160584i \(0.0513379\pi\)
0.329539 + 0.944142i \(0.393107\pi\)
\(384\) 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 \(-0.845988\pi\)
0.304401 + 0.952544i \(0.401544\pi\)
\(390\) 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 0.996043 0.0888774i \(-0.0283279\pi\)
−0.574991 + 0.818159i \(0.694995\pi\)
\(398\) 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 \(-0.717401\pi\)
0.0151464 + 0.999885i \(0.495179\pi\)
\(402\) 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 −0.857103 0.515145i \(-0.827738\pi\)
−0.325450 + 0.945559i \(0.605516\pi\)
\(410\) −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 0.882716 + 0.469907i \(0.155713\pi\)
−0.990199 + 0.139662i \(0.955398\pi\)
\(420\) 0 0
\(421\) −13.5416 + 11.3627i −0.659975 + 0.553785i −0.910079 0.414434i \(-0.863980\pi\)
0.250104 + 0.968219i \(0.419535\pi\)
\(422\) 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 \(-0.376592\pi\)
0.378059 + 0.925782i \(0.376592\pi\)
\(432\) 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 −0.342053 0.939681i \(-0.611122\pi\)
−0.866043 + 0.499970i \(0.833344\pi\)
\(440\) −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 0.268703 0.963223i \(-0.413405\pi\)
0.995249 0.0973585i \(-0.0310394\pi\)
\(444\) 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 \(-0.670500\pi\)
0.999927 + 0.0120419i \(0.00383314\pi\)
\(450\) 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 0.941439 0.337183i \(-0.109474\pi\)
−0.999987 + 0.00514224i \(0.998363\pi\)
\(458\) −29.3621 −1.37200
\(459\) 0 0
\(460\) 1.33046 0.0620332
\(461\) 4.01593 + 22.7755i 0.187041 + 1.06076i 0.923305 + 0.384067i \(0.125477\pi\)
−0.736265 + 0.676694i \(0.763412\pi\)
\(462\) 0 0
\(463\) −4.67576 + 1.70184i −0.217301 + 0.0790911i −0.448377 0.893845i \(-0.647998\pi\)
0.231076 + 0.972936i \(0.425775\pi\)
\(464\) −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 \(-0.0734156\pi\)
−0.684735 + 0.728792i \(0.740082\pi\)
\(468\) 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 \(-0.614306\pi\)
−0.870999 + 0.491284i \(0.836528\pi\)
\(480\) 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 \(-0.187472\pi\)
−0.402666 + 0.915347i \(0.631916\pi\)
\(492\) 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 −0.992386 0.123168i \(-0.960695\pi\)
0.974664 + 0.223676i \(0.0718058\pi\)
\(500\) 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 −0.121399 + 0.992604i \(0.538738\pi\)
−0.798920 + 0.601437i \(0.794595\pi\)
\(504\) 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 \(-0.729698\pi\)
−0.0234843 + 0.999724i \(0.507476\pi\)
\(510\) 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 \(-0.101387\pi\)
−0.746053 + 0.665887i \(0.768053\pi\)
\(522\) 0 0
\(523\) 11.3736 19.6996i 0.497331 0.861402i −0.502664 0.864482i \(-0.667647\pi\)
0.999995 + 0.00307938i \(0.000980199\pi\)
\(524\) 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 −0.331550 0.943438i \(-0.607572\pi\)
−0.860412 + 0.509599i \(0.829794\pi\)
\(548\) −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 \(-0.890380\pi\)
0.763025 + 0.646369i \(0.223713\pi\)
\(558\) 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 \(-0.416607\pi\)
0.819260 + 0.573423i \(0.194385\pi\)
\(564\) 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 −0.954280 0.298914i \(-0.903376\pi\)
0.794495 0.607270i \(-0.207735\pi\)
\(570\) 0 0
\(571\) 42.1485 15.3408i 1.76386 0.641992i 0.763864 0.645377i \(-0.223300\pi\)
0.999994 + 0.00338488i \(0.00107744\pi\)
\(572\) 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 −0.963575 0.267437i \(-0.913823\pi\)
0.713395 + 0.700762i \(0.247157\pi\)
\(578\) −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 \(-0.274578\pi\)
0.0100523 + 0.999949i \(0.496800\pi\)
\(588\) 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 \(-0.599164\pi\)
−0.306519 + 0.951865i \(0.599164\pi\)
\(594\) 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 \(-0.188600\pi\)
−0.405909 + 0.913914i \(0.633045\pi\)
\(600\) 0 0
\(601\) 42.5843 + 15.4994i 1.73705 + 0.632234i 0.999092 0.0426125i \(-0.0135681\pi\)
0.737958 + 0.674847i \(0.235790\pi\)
\(602\) −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 −0.769053 0.639185i \(-0.779272\pi\)
0.941288 0.337605i \(-0.109617\pi\)
\(608\) −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 0.999947 + 0.0103088i \(0.00328145\pi\)
−0.491046 + 0.871134i \(0.663385\pi\)
\(614\) −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 \(-0.637037\pi\)
0.264433 + 0.964404i \(0.414815\pi\)
\(618\) 0 0
\(619\) −7.77423 44.0898i −0.312473 1.77212i −0.586055 0.810271i \(-0.699320\pi\)
0.273582 0.961849i \(-0.411791\pi\)
\(620\) −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 0.363256 + 0.931689i \(0.381665\pi\)
−0.988495 + 0.151255i \(0.951668\pi\)
\(632\) −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 −0.997729 0.0673508i \(-0.978545\pi\)
−0.807597 0.589734i \(-0.799232\pi\)
\(642\) 0 0
\(643\) −21.4740 18.0189i −0.846853 0.710594i 0.112241 0.993681i \(-0.464197\pi\)
−0.959094 + 0.283087i \(0.908642\pi\)
\(644\) 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 \(-0.764304\pi\)
−0.738159 + 0.674627i \(0.764304\pi\)
\(648\) 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 \(-0.309671\pi\)
−0.716190 + 0.697905i \(0.754116\pi\)
\(654\) 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 \(-0.483412\pi\)
0.992516 + 0.122114i \(0.0389672\pi\)
\(660\) 0 0
\(661\) 0.231553 1.31320i 0.00900637 0.0510777i −0.979973 0.199129i \(-0.936189\pi\)
0.988980 + 0.148051i \(0.0473000\pi\)
\(662\) −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 0.970481 0.241177i \(-0.0775333\pi\)
−0.994441 + 0.105292i \(0.966422\pi\)
\(674\) −29.6866 −1.14348
\(675\) 0 0
\(676\) 16.8438 0.647839
\(677\) −6.41437 36.3777i −0.246524 1.39811i −0.816926 0.576743i \(-0.804323\pi\)
0.570401 0.821366i \(-0.306788\pi\)
\(678\) 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 −0.958007 0.286745i \(-0.907427\pi\)
0.230675 0.973031i \(-0.425907\pi\)
\(684\) 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 −0.634732 0.772733i \(-0.718889\pi\)
0.650773 + 0.759272i \(0.274445\pi\)
\(692\) −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 \(-0.383027\pi\)
0.359267 + 0.933235i \(0.383027\pi\)
\(702\) 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 0.118478 0.992957i \(-0.462199\pi\)
−0.547501 + 0.836805i \(0.684421\pi\)
\(710\) −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 \(-0.891689\pi\)
0.760361 + 0.649501i \(0.225022\pi\)
\(720\) 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 0.995580 0.0939207i \(-0.0299400\pi\)
−0.967662 + 0.252252i \(0.918829\pi\)
\(728\) −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 −0.794685 0.607022i \(-0.792364\pi\)
−0.218578 + 0.975819i \(0.570142\pi\)
\(734\) −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 0.176287 + 0.984339i \(0.443591\pi\)
−0.940606 + 0.339501i \(0.889742\pi\)
\(740\) 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 −0.837842 0.545913i \(-0.816183\pi\)
0.974027 0.226432i \(-0.0727060\pi\)
\(744\) 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 −0.118768 0.992922i \(-0.537894\pi\)
−0.998461 + 0.0554555i \(0.982339\pi\)
\(752\) −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 \(-0.00214140\pi\)
0.167019 + 0.985954i \(0.446586\pi\)
\(762\) 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 −0.976319 0.216334i \(-0.930590\pi\)
0.991431 + 0.130633i \(0.0417010\pi\)
\(770\) −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 \(-0.841336\pi\)
0.853183 + 0.521612i \(0.174669\pi\)
\(774\) 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