Properties

Label 729.2.e.k.649.2
Level $729$
Weight $2$
Character 729.649
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 649.2
Root \(-1.22778i\) of defining polynomial
Character \(\chi\) \(=\) 729.649
Dual form 729.2.e.k.82.2

$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

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

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 \(-0.755994\pi\)
0.914105 0.405478i \(-0.132895\pi\)
\(3\) 0 0
\(4\) −0.461727 0.168055i −0.230864 0.0840275i
\(5\) −1.28581 + 1.07892i −0.575032 + 0.482509i −0.883311 0.468787i \(-0.844691\pi\)
0.308279 + 0.951296i \(0.400247\pi\)
\(6\) 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 0.980759 0.195220i \(-0.0625421\pi\)
−0.0219472 + 0.999759i \(0.506987\pi\)
\(12\) 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 0.919143 0.393923i \(-0.128882\pi\)
−0.800719 + 0.599040i \(0.795549\pi\)
\(18\) 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 0.495190 0.868785i \(-0.335098\pi\)
−0.179106 + 0.983830i \(0.557321\pi\)
\(24\) 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 \(-0.667707\pi\)
0.768142 0.640280i \(-0.221182\pi\)
\(30\) 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 \(0.0680314\pi\)
−0.845768 + 0.533550i \(0.820857\pi\)
\(42\) 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 0.715837 0.698267i \(-0.246045\pi\)
0.997201 + 0.0747722i \(0.0238230\pi\)
\(48\) 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 −0.970726 0.240191i \(-0.922790\pi\)
0.0679775 + 0.997687i \(0.478345\pi\)
\(60\) 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 0.983236 0.182339i \(-0.0583670\pi\)
−0.649528 + 0.760337i \(0.725034\pi\)
\(72\) 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 \(0.158017\pi\)
−0.989162 + 0.146827i \(0.953094\pi\)
\(84\) 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 −0.720104 0.693866i \(-0.755906\pi\)
0.960958 + 0.276695i \(0.0892393\pi\)
\(90\) 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 −0.680104 0.733116i \(-0.738065\pi\)
−0.0497521 + 0.998762i \(0.515843\pi\)
\(102\) 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 \(-0.708155\pi\)
−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 −0.658887 0.752242i \(-0.728973\pi\)
0.626399 + 0.779503i \(0.284528\pi\)
\(114\) 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 −0.172184 0.985065i \(-0.555082\pi\)
−0.765088 + 0.643926i \(0.777305\pi\)
\(132\) 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 \(-0.886620\pi\)
0.999975 0.00712879i \(-0.00226918\pi\)
\(138\) 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 \(-0.761533\pi\)
0.455171 0.890404i \(-0.349578\pi\)
\(150\) 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 −0.103046 0.994677i \(-0.532859\pi\)
0.961671 + 0.274205i \(0.0884145\pi\)
\(168\) 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 0.931450 0.363869i \(-0.118545\pi\)
−0.196597 + 0.980484i \(0.562989\pi\)
\(174\) 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 0.860443 0.509546i \(-0.170187\pi\)
−0.871502 + 0.490393i \(0.836853\pi\)
\(180\) 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 \(-0.676343\pi\)
0.785228 0.619207i \(-0.212546\pi\)
\(192\) 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 −0.642926 0.765929i \(-0.722280\pi\)
0.984776 + 0.173826i \(0.0556129\pi\)
\(198\) 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 0.733182 0.680033i \(-0.238034\pi\)
−0.542386 + 0.840129i \(0.682479\pi\)
\(228\) 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 0.856948 0.515403i \(-0.172358\pi\)
−0.874826 + 0.484438i \(0.839024\pi\)
\(234\) 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 0.870655 0.491894i \(-0.163695\pi\)
0.350777 + 0.936459i \(0.385917\pi\)
\(240\) 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 −0.994037 0.109042i \(-0.965222\pi\)
0.591451 + 0.806341i \(0.298555\pi\)
\(252\) 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 \(-0.921529\pi\)
0.827818 0.560996i \(-0.189582\pi\)
\(258\) 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 −0.0513303 0.998682i \(-0.516346\pi\)
0.602619 + 0.798029i \(0.294124\pi\)
\(264\) 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 0.251436 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 0.0588373 0.998268i \(-0.481261\pi\)
−0.972885 + 0.231291i \(0.925705\pi\)
\(282\) 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 −0.256613 0.966514i \(-0.582606\pi\)
−0.817840 + 0.575446i \(0.804829\pi\)
\(294\) 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 0.999034 0.0439436i \(-0.0139922\pi\)
−0.953814 + 0.300396i \(0.902881\pi\)
\(312\) 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 0.0707952 0.997491i \(-0.477446\pi\)
0.695407 + 0.718616i \(0.255224\pi\)
\(318\) 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 0.745726 0.666252i \(-0.232103\pi\)
0.143001 + 0.989723i \(0.454325\pi\)
\(348\) 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 \(0.187701\pi\)
−0.971192 + 0.238300i \(0.923410\pi\)
\(354\) 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 −0.896551 0.442940i \(-0.853935\pi\)
0.831873 + 0.554966i \(0.187269\pi\)
\(360\) 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 \(-0.393107\pi\)
0.987022 0.160584i \(-0.0513379\pi\)
\(384\) 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 0.304401 0.952544i \(-0.401544\pi\)
−0.885214 + 0.465184i \(0.845988\pi\)
\(390\) 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 0.0151464 0.999885i \(-0.495179\pi\)
−0.631111 + 0.775693i \(0.717401\pi\)
\(402\) 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 \(-0.955398\pi\)
0.882716 0.469907i \(-0.155713\pi\)
\(420\) 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 \(-0.376592\pi\)
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 −0.866043 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 \(0.0310394\pi\)
0.268703 + 0.963223i \(0.413405\pi\)
\(444\) 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 0.999927 0.0120419i \(-0.00383314\pi\)
−0.510392 + 0.859942i \(0.670500\pi\)
\(450\) 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 \(-0.763412\pi\)
0.923305 0.384067i \(-0.125477\pi\)
\(462\) 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 −0.684735 0.728792i \(-0.740082\pi\)
0.973520 + 0.228602i \(0.0734156\pi\)
\(468\) 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 −0.870999 0.491284i \(-0.836528\pi\)
−0.351433 + 0.936213i \(0.614306\pi\)
\(480\) 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 −0.402666 0.915347i \(-0.631916\pi\)
0.831519 + 0.555497i \(0.187472\pi\)
\(492\) 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 \(-0.794595\pi\)
−0.121399 0.992604i \(-0.538738\pi\)
\(504\) 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 −0.0234843 0.999724i \(-0.507476\pi\)
−0.660600 + 0.750738i \(0.729698\pi\)
\(510\) 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 −0.746053 0.665887i \(-0.768053\pi\)
0.949701 + 0.313157i \(0.101387\pi\)
\(522\) 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 0.763025 0.646369i \(-0.223713\pi\)
−0.941284 + 0.337615i \(0.890380\pi\)
\(558\) 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 0.819260 0.573423i \(-0.194385\pi\)
0.259000 + 0.965877i \(0.416607\pi\)
\(564\) 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 \(0.207735\pi\)
−0.954280 + 0.298914i \(0.903376\pi\)
\(570\) 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 0.0100523 0.999949i \(-0.496800\pi\)
0.650456 + 0.759544i \(0.274578\pi\)
\(588\) 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 −0.405909 0.913914i \(-0.633045\pi\)
0.829544 + 0.558441i \(0.188600\pi\)
\(600\) 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 0.264433 0.964404i \(-0.414815\pi\)
−0.417339 + 0.908751i \(0.637037\pi\)
\(618\) 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 \(0.799232\pi\)
−0.997729 + 0.0673508i \(0.978545\pi\)
\(642\) 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 \(-0.764304\pi\)
−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 −0.716190 0.697905i \(-0.754116\pi\)
0.562938 + 0.826499i \(0.309671\pi\)
\(654\) 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 0.992516 0.122114i \(-0.0389672\pi\)
0.0520901 + 0.998642i \(0.483412\pi\)
\(660\) 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 \(0.306788\pi\)
−0.816926 + 0.576743i \(0.804323\pi\)
\(678\) 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 \(0.425907\pi\)
−0.958007 + 0.286745i \(0.907427\pi\)
\(684\) 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 \(-0.383027\pi\)
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 −0.547501 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 0.760361 0.649501i \(-0.225022\pi\)
−0.942665 + 0.333741i \(0.891689\pi\)
\(720\) 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 \(0.0727060\pi\)
−0.837842 + 0.545913i \(0.816183\pi\)
\(744\) 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 0.167019 0.985954i \(-0.446586\pi\)
0.999977 + 0.00672735i \(0.00214140\pi\)
\(762\) 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 0.853183 0.521612i \(-0.174669\pi\)
−0.878321 + 0.478072i \(0.841336\pi\)
\(774\) 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 4.45267i −0.438315 0.159533i
\(780\)