Properties

Label 729.2.e.j.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 \(-3.10658i\) of defining polynomial
Character \(\chi\) \(=\) 729.649
Dual form 729.2.e.j.82.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.369007 + 2.09274i) q^{2} +(-2.36403 - 0.860436i) q^{4} +(-1.58643 + 1.33117i) q^{5} +(-4.55626 + 1.65834i) q^{7} +(0.547989 - 0.949144i) q^{8} +O(q^{10})\) \(q+(-0.369007 + 2.09274i) q^{2} +(-2.36403 - 0.860436i) q^{4} +(-1.58643 + 1.33117i) q^{5} +(-4.55626 + 1.65834i) q^{7} +(0.547989 - 0.949144i) q^{8} +(-2.20040 - 3.81121i) q^{10} +(3.17869 + 2.66724i) q^{11} +(-0.211159 - 1.19754i) q^{13} +(-1.78920 - 10.1470i) q^{14} +(-2.07024 - 1.73714i) q^{16} +(-1.18182 - 2.04697i) q^{17} +(0.919003 - 1.59176i) q^{19} +(4.89576 - 1.78191i) q^{20} +(-6.75481 + 5.66796i) q^{22} +(4.04403 + 1.47191i) q^{23} +(-0.123500 + 0.700401i) q^{25} +2.58407 q^{26} +12.1980 q^{28} +(0.517788 - 2.93652i) q^{29} +(-1.38472 - 0.503996i) q^{31} +(6.07846 - 5.10043i) q^{32} +(4.71989 - 1.71790i) q^{34} +(5.02066 - 8.69603i) q^{35} +(-4.48554 - 7.76918i) q^{37} +(2.99203 + 2.51061i) q^{38} +(0.394130 + 2.23522i) q^{40} +(0.392536 + 2.22618i) q^{41} +(-4.20164 - 3.52560i) q^{43} +(-5.21953 - 9.04050i) q^{44} +(-4.57260 + 7.91998i) q^{46} +(-6.74994 + 2.45678i) q^{47} +(12.6471 - 10.6122i) q^{49} +(-1.42019 - 0.516906i) q^{50} +(-0.531222 + 3.01271i) q^{52} -6.32803 q^{53} -8.59334 q^{55} +(-0.922773 + 5.23330i) q^{56} +(5.95432 + 2.16719i) q^{58} +(0.200900 - 0.168575i) q^{59} +(4.18690 - 1.52391i) q^{61} +(1.56571 - 2.71188i) q^{62} +(5.72840 + 9.92188i) q^{64} +(1.92913 + 1.61873i) q^{65} +(0.717359 + 4.06834i) q^{67} +(1.03257 + 5.85598i) q^{68} +(16.3459 + 13.7159i) q^{70} +(-1.54276 - 2.67213i) q^{71} +(-6.38003 + 11.0505i) q^{73} +(17.9141 - 6.52021i) q^{74} +(-3.54216 + 2.97222i) q^{76} +(-18.9062 - 6.88128i) q^{77} +(0.790517 - 4.48325i) q^{79} +5.59674 q^{80} -4.80368 q^{82} +(-1.46786 + 8.32464i) q^{83} +(4.59975 + 1.67417i) q^{85} +(8.92862 - 7.49200i) q^{86} +(4.27348 - 1.55542i) q^{88} +(-8.48158 + 14.6905i) q^{89} +(2.94803 + 5.10614i) q^{91} +(-8.29373 - 6.95926i) q^{92} +(-2.65063 - 15.0325i) q^{94} +(0.660975 + 3.74857i) q^{95} +(-3.91431 - 3.28450i) q^{97} +(17.5417 + 30.3831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 12 q^{11} - 3 q^{13} + 15 q^{14} - 36 q^{16} - 9 q^{17} - 12 q^{19} + 42 q^{20} + 6 q^{22} + 6 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} + 12 q^{29} + 6 q^{31} + 54 q^{32} - 9 q^{34} + 30 q^{35} - 3 q^{37} + 42 q^{38} - 57 q^{40} + 24 q^{41} + 6 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} + 33 q^{49} + 21 q^{50} + 45 q^{52} + 18 q^{53} + 30 q^{55} + 3 q^{56} + 33 q^{58} + 15 q^{59} + 33 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} + 42 q^{67} - 18 q^{68} + 24 q^{70} - 12 q^{73} - 3 q^{74} - 87 q^{76} - 57 q^{77} - 48 q^{79} + 42 q^{80} - 42 q^{82} + 12 q^{83} - 36 q^{85} - 30 q^{86} + 30 q^{88} - 9 q^{89} - 18 q^{91} - 48 q^{92} + 33 q^{94} + 30 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.369007 + 2.09274i −0.260928 + 1.47979i 0.519458 + 0.854496i \(0.326134\pi\)
−0.780386 + 0.625298i \(0.784977\pi\)
\(3\) 0 0
\(4\) −2.36403 0.860436i −1.18201 0.430218i
\(5\) −1.58643 + 1.33117i −0.709474 + 0.595319i −0.924452 0.381300i \(-0.875477\pi\)
0.214977 + 0.976619i \(0.431032\pi\)
\(6\) 0 0
\(7\) −4.55626 + 1.65834i −1.72211 + 0.626795i −0.998019 0.0629144i \(-0.979960\pi\)
−0.724086 + 0.689709i \(0.757738\pi\)
\(8\) 0.547989 0.949144i 0.193743 0.335573i
\(9\) 0 0
\(10\) −2.20040 3.81121i −0.695829 1.20521i
\(11\) 3.17869 + 2.66724i 0.958412 + 0.804203i 0.980694 0.195549i \(-0.0626487\pi\)
−0.0222820 + 0.999752i \(0.507093\pi\)
\(12\) 0 0
\(13\) −0.211159 1.19754i −0.0585649 0.332138i 0.941422 0.337230i \(-0.109490\pi\)
−0.999987 + 0.00509231i \(0.998379\pi\)
\(14\) −1.78920 10.1470i −0.478183 2.71191i
\(15\) 0 0
\(16\) −2.07024 1.73714i −0.517561 0.434285i
\(17\) −1.18182 2.04697i −0.286633 0.496463i 0.686371 0.727252i \(-0.259203\pi\)
−0.973004 + 0.230789i \(0.925869\pi\)
\(18\) 0 0
\(19\) 0.919003 1.59176i 0.210834 0.365175i −0.741142 0.671348i \(-0.765715\pi\)
0.951976 + 0.306174i \(0.0990488\pi\)
\(20\) 4.89576 1.78191i 1.09473 0.398448i
\(21\) 0 0
\(22\) −6.75481 + 5.66796i −1.44013 + 1.20841i
\(23\) 4.04403 + 1.47191i 0.843239 + 0.306914i 0.727281 0.686340i \(-0.240784\pi\)
0.115958 + 0.993254i \(0.463006\pi\)
\(24\) 0 0
\(25\) −0.123500 + 0.700401i −0.0246999 + 0.140080i
\(26\) 2.58407 0.506777
\(27\) 0 0
\(28\) 12.1980 2.30521
\(29\) 0.517788 2.93652i 0.0961507 0.545298i −0.898238 0.439510i \(-0.855152\pi\)
0.994389 0.105788i \(-0.0337366\pi\)
\(30\) 0 0
\(31\) −1.38472 0.503996i −0.248703 0.0905204i 0.214661 0.976689i \(-0.431135\pi\)
−0.463364 + 0.886168i \(0.653358\pi\)
\(32\) 6.07846 5.10043i 1.07453 0.901638i
\(33\) 0 0
\(34\) 4.71989 1.71790i 0.809454 0.294617i
\(35\) 5.02066 8.69603i 0.848646 1.46990i
\(36\) 0 0
\(37\) −4.48554 7.76918i −0.737418 1.27725i −0.953654 0.300905i \(-0.902711\pi\)
0.216236 0.976341i \(-0.430622\pi\)
\(38\) 2.99203 + 2.51061i 0.485371 + 0.407275i
\(39\) 0 0
\(40\) 0.394130 + 2.23522i 0.0623174 + 0.353420i
\(41\) 0.392536 + 2.22618i 0.0613038 + 0.347671i 0.999996 + 0.00291413i \(0.000927599\pi\)
−0.938692 + 0.344757i \(0.887961\pi\)
\(42\) 0 0
\(43\) −4.20164 3.52560i −0.640745 0.537649i 0.263502 0.964659i \(-0.415122\pi\)
−0.904247 + 0.427010i \(0.859567\pi\)
\(44\) −5.21953 9.04050i −0.786874 1.36291i
\(45\) 0 0
\(46\) −4.57260 + 7.91998i −0.674194 + 1.16774i
\(47\) −6.74994 + 2.45678i −0.984579 + 0.358358i −0.783619 0.621242i \(-0.786628\pi\)
−0.200960 + 0.979599i \(0.564406\pi\)
\(48\) 0 0
\(49\) 12.6471 10.6122i 1.80673 1.51603i
\(50\) −1.42019 0.516906i −0.200845 0.0731016i
\(51\) 0 0
\(52\) −0.531222 + 3.01271i −0.0736673 + 0.417788i
\(53\) −6.32803 −0.869222 −0.434611 0.900618i \(-0.643114\pi\)
−0.434611 + 0.900618i \(0.643114\pi\)
\(54\) 0 0
\(55\) −8.59334 −1.15873
\(56\) −0.922773 + 5.23330i −0.123311 + 0.699330i
\(57\) 0 0
\(58\) 5.95432 + 2.16719i 0.781840 + 0.284567i
\(59\) 0.200900 0.168575i 0.0261550 0.0219466i −0.629616 0.776906i \(-0.716788\pi\)
0.655771 + 0.754959i \(0.272343\pi\)
\(60\) 0 0
\(61\) 4.18690 1.52391i 0.536078 0.195116i −0.0597724 0.998212i \(-0.519037\pi\)
0.595850 + 0.803096i \(0.296815\pi\)
\(62\) 1.56571 2.71188i 0.198845 0.344410i
\(63\) 0 0
\(64\) 5.72840 + 9.92188i 0.716050 + 1.24024i
\(65\) 1.92913 + 1.61873i 0.239279 + 0.200779i
\(66\) 0 0
\(67\) 0.717359 + 4.06834i 0.0876393 + 0.497027i 0.996756 + 0.0804853i \(0.0256470\pi\)
−0.909116 + 0.416542i \(0.863242\pi\)
\(68\) 1.03257 + 5.85598i 0.125217 + 0.710142i
\(69\) 0 0
\(70\) 16.3459 + 13.7159i 1.95371 + 1.63936i
\(71\) −1.54276 2.67213i −0.183091 0.317124i 0.759840 0.650110i \(-0.225277\pi\)
−0.942932 + 0.332986i \(0.891944\pi\)
\(72\) 0 0
\(73\) −6.38003 + 11.0505i −0.746726 + 1.29337i 0.202658 + 0.979250i \(0.435042\pi\)
−0.949384 + 0.314118i \(0.898291\pi\)
\(74\) 17.9141 6.52021i 2.08247 0.757958i
\(75\) 0 0
\(76\) −3.54216 + 2.97222i −0.406313 + 0.340937i
\(77\) −18.9062 6.88128i −2.15456 0.784195i
\(78\) 0 0
\(79\) 0.790517 4.48325i 0.0889401 0.504404i −0.907497 0.420060i \(-0.862009\pi\)
0.996437 0.0843449i \(-0.0268797\pi\)
\(80\) 5.59674 0.625734
\(81\) 0 0
\(82\) −4.80368 −0.530478
\(83\) −1.46786 + 8.32464i −0.161118 + 0.913748i 0.791859 + 0.610705i \(0.209114\pi\)
−0.952977 + 0.303043i \(0.901997\pi\)
\(84\) 0 0
\(85\) 4.59975 + 1.67417i 0.498913 + 0.181590i
\(86\) 8.92862 7.49200i 0.962797 0.807883i
\(87\) 0 0
\(88\) 4.27348 1.55542i 0.455555 0.165808i
\(89\) −8.48158 + 14.6905i −0.899046 + 1.55719i −0.0703304 + 0.997524i \(0.522405\pi\)
−0.828716 + 0.559670i \(0.810928\pi\)
\(90\) 0 0
\(91\) 2.94803 + 5.10614i 0.309038 + 0.535269i
\(92\) −8.29373 6.95926i −0.864681 0.725553i
\(93\) 0 0
\(94\) −2.65063 15.0325i −0.273391 1.55048i
\(95\) 0.660975 + 3.74857i 0.0678146 + 0.384596i
\(96\) 0 0
\(97\) −3.91431 3.28450i −0.397438 0.333490i 0.422064 0.906566i \(-0.361306\pi\)
−0.819502 + 0.573076i \(0.805750\pi\)
\(98\) 17.5417 + 30.3831i 1.77198 + 3.06916i
\(99\) 0 0
\(100\) 0.894607 1.54951i 0.0894607 0.154951i
\(101\) −17.4594 + 6.35469i −1.73727 + 0.632316i −0.999105 0.0423013i \(-0.986531\pi\)
−0.738168 + 0.674617i \(0.764309\pi\)
\(102\) 0 0
\(103\) 6.89882 5.78880i 0.679761 0.570387i −0.236176 0.971710i \(-0.575894\pi\)
0.915936 + 0.401323i \(0.131450\pi\)
\(104\) −1.25235 0.455819i −0.122803 0.0446967i
\(105\) 0 0
\(106\) 2.33509 13.2429i 0.226804 1.28627i
\(107\) 7.42680 0.717976 0.358988 0.933342i \(-0.383122\pi\)
0.358988 + 0.933342i \(0.383122\pi\)
\(108\) 0 0
\(109\) −5.62396 −0.538678 −0.269339 0.963045i \(-0.586805\pi\)
−0.269339 + 0.963045i \(0.586805\pi\)
\(110\) 3.17101 17.9837i 0.302344 1.71468i
\(111\) 0 0
\(112\) 12.3133 + 4.48169i 1.16350 + 0.423480i
\(113\) −1.84055 + 1.54441i −0.173144 + 0.145285i −0.725242 0.688494i \(-0.758272\pi\)
0.552097 + 0.833780i \(0.313828\pi\)
\(114\) 0 0
\(115\) −8.37495 + 3.04823i −0.780968 + 0.284249i
\(116\) −3.75075 + 6.49649i −0.348249 + 0.603184i
\(117\) 0 0
\(118\) 0.278652 + 0.482639i 0.0256520 + 0.0444305i
\(119\) 8.77926 + 7.36667i 0.804793 + 0.675302i
\(120\) 0 0
\(121\) 1.07979 + 6.12379i 0.0981626 + 0.556708i
\(122\) 1.64415 + 9.32445i 0.148854 + 0.844196i
\(123\) 0 0
\(124\) 2.83986 + 2.38292i 0.255027 + 0.213993i
\(125\) −5.91378 10.2430i −0.528945 0.916159i
\(126\) 0 0
\(127\) 4.61735 7.99748i 0.409723 0.709662i −0.585135 0.810936i \(-0.698959\pi\)
0.994859 + 0.101274i \(0.0322919\pi\)
\(128\) −7.96511 + 2.89906i −0.704023 + 0.256243i
\(129\) 0 0
\(130\) −4.09945 + 3.43985i −0.359545 + 0.301694i
\(131\) 14.4140 + 5.24625i 1.25935 + 0.458367i 0.883552 0.468334i \(-0.155145\pi\)
0.375801 + 0.926700i \(0.377368\pi\)
\(132\) 0 0
\(133\) −1.54753 + 8.77650i −0.134188 + 0.761019i
\(134\) −8.77871 −0.758365
\(135\) 0 0
\(136\) −2.59049 −0.222133
\(137\) −0.632769 + 3.58861i −0.0540611 + 0.306596i −0.999834 0.0182336i \(-0.994196\pi\)
0.945773 + 0.324829i \(0.105307\pi\)
\(138\) 0 0
\(139\) −12.4749 4.54050i −1.05811 0.385120i −0.246392 0.969170i \(-0.579245\pi\)
−0.811718 + 0.584050i \(0.801467\pi\)
\(140\) −19.3514 + 16.2377i −1.63549 + 1.37234i
\(141\) 0 0
\(142\) 6.16138 2.24256i 0.517051 0.188191i
\(143\) 2.52292 4.36983i 0.210977 0.365423i
\(144\) 0 0
\(145\) 3.08759 + 5.34786i 0.256410 + 0.444115i
\(146\) −20.7717 17.4295i −1.71908 1.44248i
\(147\) 0 0
\(148\) 3.91906 + 22.2261i 0.322145 + 1.82697i
\(149\) 1.54738 + 8.77561i 0.126766 + 0.718926i 0.980243 + 0.197796i \(0.0633782\pi\)
−0.853477 + 0.521130i \(0.825511\pi\)
\(150\) 0 0
\(151\) −0.545733 0.457924i −0.0444111 0.0372653i 0.620312 0.784355i \(-0.287006\pi\)
−0.664723 + 0.747090i \(0.731450\pi\)
\(152\) −1.00721 1.74453i −0.0816953 0.141500i
\(153\) 0 0
\(154\) 21.3773 37.0265i 1.72263 2.98368i
\(155\) 2.86767 1.04375i 0.230337 0.0838357i
\(156\) 0 0
\(157\) −10.5852 + 8.88207i −0.844794 + 0.708867i −0.958637 0.284632i \(-0.908129\pi\)
0.113842 + 0.993499i \(0.463684\pi\)
\(158\) 9.09058 + 3.30870i 0.723208 + 0.263226i
\(159\) 0 0
\(160\) −2.85350 + 16.1830i −0.225589 + 1.27938i
\(161\) −20.8666 −1.64452
\(162\) 0 0
\(163\) −1.19321 −0.0934597 −0.0467298 0.998908i \(-0.514880\pi\)
−0.0467298 + 0.998908i \(0.514880\pi\)
\(164\) 0.987521 5.60051i 0.0771124 0.437326i
\(165\) 0 0
\(166\) −16.8797 6.14370i −1.31012 0.476844i
\(167\) −18.3363 + 15.3860i −1.41890 + 1.19060i −0.466980 + 0.884268i \(0.654658\pi\)
−0.951924 + 0.306334i \(0.900897\pi\)
\(168\) 0 0
\(169\) 10.8265 3.94052i 0.832807 0.303117i
\(170\) −5.20096 + 9.00832i −0.398895 + 0.690907i
\(171\) 0 0
\(172\) 6.89926 + 11.9499i 0.526063 + 0.911169i
\(173\) −7.00165 5.87508i −0.532325 0.446674i 0.336578 0.941656i \(-0.390730\pi\)
−0.868904 + 0.494981i \(0.835175\pi\)
\(174\) 0 0
\(175\) −0.598809 3.39602i −0.0452657 0.256715i
\(176\) −1.94730 11.0437i −0.146783 0.832448i
\(177\) 0 0
\(178\) −27.6138 23.1707i −2.06974 1.73672i
\(179\) −5.30038 9.18052i −0.396169 0.686184i 0.597081 0.802181i \(-0.296327\pi\)
−0.993250 + 0.115997i \(0.962994\pi\)
\(180\) 0 0
\(181\) 0.731460 1.26693i 0.0543690 0.0941699i −0.837560 0.546345i \(-0.816019\pi\)
0.891929 + 0.452176i \(0.149352\pi\)
\(182\) −11.7737 + 4.28527i −0.872724 + 0.317645i
\(183\) 0 0
\(184\) 3.61314 3.03178i 0.266364 0.223506i
\(185\) 17.4581 + 6.35425i 1.28355 + 0.467174i
\(186\) 0 0
\(187\) 1.70312 9.65889i 0.124545 0.706328i
\(188\) 18.0709 1.31796
\(189\) 0 0
\(190\) −8.08871 −0.586817
\(191\) 2.15711 12.2336i 0.156083 0.885189i −0.801707 0.597718i \(-0.796074\pi\)
0.957789 0.287471i \(-0.0928145\pi\)
\(192\) 0 0
\(193\) −19.5205 7.10489i −1.40512 0.511421i −0.475425 0.879756i \(-0.657706\pi\)
−0.929693 + 0.368335i \(0.879928\pi\)
\(194\) 8.31803 6.97965i 0.597199 0.501110i
\(195\) 0 0
\(196\) −39.0292 + 14.2055i −2.78780 + 1.01468i
\(197\) 7.09433 12.2877i 0.505450 0.875465i −0.494530 0.869161i \(-0.664660\pi\)
0.999980 0.00630469i \(-0.00200686\pi\)
\(198\) 0 0
\(199\) −10.1643 17.6051i −0.720529 1.24799i −0.960788 0.277284i \(-0.910566\pi\)
0.240259 0.970709i \(-0.422768\pi\)
\(200\) 0.597105 + 0.501031i 0.0422217 + 0.0354282i
\(201\) 0 0
\(202\) −6.85611 38.8829i −0.482394 2.73579i
\(203\) 2.51058 + 14.2382i 0.176208 + 0.999327i
\(204\) 0 0
\(205\) −3.58617 3.00915i −0.250469 0.210168i
\(206\) 9.56876 + 16.5736i 0.666687 + 1.15474i
\(207\) 0 0
\(208\) −1.64315 + 2.84601i −0.113932 + 0.197336i
\(209\) 7.16684 2.60851i 0.495740 0.180435i
\(210\) 0 0
\(211\) −7.55574 + 6.34002i −0.520159 + 0.436465i −0.864687 0.502311i \(-0.832483\pi\)
0.344528 + 0.938776i \(0.388039\pi\)
\(212\) 14.9596 + 5.44487i 1.02743 + 0.373955i
\(213\) 0 0
\(214\) −2.74055 + 15.5424i −0.187340 + 1.06246i
\(215\) 11.3588 0.774665
\(216\) 0 0
\(217\) 7.14494 0.485030
\(218\) 2.07528 11.7695i 0.140556 0.797132i
\(219\) 0 0
\(220\) 20.3149 + 7.39402i 1.36963 + 0.498505i
\(221\) −2.20178 + 1.84751i −0.148108 + 0.124277i
\(222\) 0 0
\(223\) −14.1625 + 5.15472i −0.948389 + 0.345185i −0.769473 0.638679i \(-0.779481\pi\)
−0.178916 + 0.983864i \(0.557259\pi\)
\(224\) −19.2368 + 33.3191i −1.28531 + 2.22623i
\(225\) 0 0
\(226\) −2.55287 4.42170i −0.169814 0.294127i
\(227\) −17.3835 14.5865i −1.15378 0.968140i −0.153983 0.988074i \(-0.549210\pi\)
−0.999801 + 0.0199338i \(0.993654\pi\)
\(228\) 0 0
\(229\) 1.51364 + 8.58428i 0.100024 + 0.567265i 0.993092 + 0.117342i \(0.0374374\pi\)
−0.893067 + 0.449923i \(0.851451\pi\)
\(230\) −3.28875 18.6515i −0.216854 1.22984i
\(231\) 0 0
\(232\) −2.50344 2.10063i −0.164359 0.137913i
\(233\) 11.7945 + 20.4286i 0.772682 + 1.33832i 0.936088 + 0.351766i \(0.114419\pi\)
−0.163406 + 0.986559i \(0.552248\pi\)
\(234\) 0 0
\(235\) 7.43792 12.8829i 0.485196 0.840385i
\(236\) −0.619983 + 0.225655i −0.0403574 + 0.0146889i
\(237\) 0 0
\(238\) −18.6562 + 15.6544i −1.20930 + 1.01472i
\(239\) −9.35419 3.40465i −0.605072 0.220228i 0.0212736 0.999774i \(-0.493228\pi\)
−0.626346 + 0.779545i \(0.715450\pi\)
\(240\) 0 0
\(241\) 0.992130 5.62665i 0.0639087 0.362444i −0.936036 0.351905i \(-0.885534\pi\)
0.999944 0.0105394i \(-0.00335485\pi\)
\(242\) −13.2140 −0.849427
\(243\) 0 0
\(244\) −11.2092 −0.717594
\(245\) −5.93711 + 33.6710i −0.379308 + 2.15116i
\(246\) 0 0
\(247\) −2.10025 0.764430i −0.133636 0.0486395i
\(248\) −1.23718 + 1.03811i −0.0785607 + 0.0659203i
\(249\) 0 0
\(250\) 23.6182 8.59631i 1.49374 0.543678i
\(251\) 3.64483 6.31303i 0.230060 0.398475i −0.727766 0.685826i \(-0.759441\pi\)
0.957825 + 0.287351i \(0.0927745\pi\)
\(252\) 0 0
\(253\) 8.92881 + 15.4651i 0.561349 + 0.972285i
\(254\) 15.0328 + 12.6141i 0.943245 + 0.791476i
\(255\) 0 0
\(256\) 0.851090 + 4.82677i 0.0531931 + 0.301673i
\(257\) −4.03612 22.8900i −0.251766 1.42784i −0.804239 0.594306i \(-0.797427\pi\)
0.552473 0.833531i \(-0.313684\pi\)
\(258\) 0 0
\(259\) 33.3213 + 27.9599i 2.07048 + 1.73734i
\(260\) −3.16770 5.48661i −0.196452 0.340265i
\(261\) 0 0
\(262\) −16.2979 + 28.2288i −1.00689 + 1.74398i
\(263\) 25.7472 9.37122i 1.58764 0.577854i 0.610793 0.791790i \(-0.290851\pi\)
0.976848 + 0.213936i \(0.0686284\pi\)
\(264\) 0 0
\(265\) 10.0390 8.42371i 0.616690 0.517465i
\(266\) −17.7959 6.47719i −1.09114 0.397142i
\(267\) 0 0
\(268\) 1.80469 10.2349i 0.110239 0.625197i
\(269\) 9.41973 0.574331 0.287166 0.957881i \(-0.407287\pi\)
0.287166 + 0.957881i \(0.407287\pi\)
\(270\) 0 0
\(271\) 26.2797 1.59638 0.798189 0.602408i \(-0.205792\pi\)
0.798189 + 0.602408i \(0.205792\pi\)
\(272\) −1.10922 + 6.29071i −0.0672565 + 0.381430i
\(273\) 0 0
\(274\) −7.27655 2.64845i −0.439592 0.159999i
\(275\) −2.26071 + 1.89696i −0.136326 + 0.114391i
\(276\) 0 0
\(277\) −0.352208 + 0.128193i −0.0211621 + 0.00770238i −0.352580 0.935782i \(-0.614695\pi\)
0.331417 + 0.943484i \(0.392473\pi\)
\(278\) 14.1054 24.4314i 0.845989 1.46530i
\(279\) 0 0
\(280\) −5.50253 9.53065i −0.328839 0.569566i
\(281\) 10.7105 + 8.98719i 0.638936 + 0.536131i 0.903691 0.428185i \(-0.140847\pi\)
−0.264755 + 0.964316i \(0.585291\pi\)
\(282\) 0 0
\(283\) 2.70229 + 15.3255i 0.160635 + 0.911005i 0.953452 + 0.301545i \(0.0975024\pi\)
−0.792817 + 0.609459i \(0.791387\pi\)
\(284\) 1.34792 + 7.64444i 0.0799844 + 0.453614i
\(285\) 0 0
\(286\) 8.21396 + 6.89233i 0.485701 + 0.407552i
\(287\) −5.48027 9.49211i −0.323490 0.560301i
\(288\) 0 0
\(289\) 5.70661 9.88413i 0.335683 0.581420i
\(290\) −12.3310 + 4.48813i −0.724103 + 0.263552i
\(291\) 0 0
\(292\) 24.5909 20.6342i 1.43907 1.20752i
\(293\) −23.1392 8.42198i −1.35181 0.492017i −0.438295 0.898831i \(-0.644418\pi\)
−0.913511 + 0.406814i \(0.866640\pi\)
\(294\) 0 0
\(295\) −0.0943115 + 0.534867i −0.00549103 + 0.0311412i
\(296\) −9.83210 −0.571479
\(297\) 0 0
\(298\) −18.9361 −1.09694
\(299\) 0.908737 5.15370i 0.0525536 0.298046i
\(300\) 0 0
\(301\) 24.9904 + 9.09578i 1.44043 + 0.524272i
\(302\) 1.15970 0.973102i 0.0667331 0.0559957i
\(303\) 0 0
\(304\) −4.66767 + 1.69889i −0.267709 + 0.0974382i
\(305\) −4.61365 + 7.99107i −0.264177 + 0.457567i
\(306\) 0 0
\(307\) 10.1956 + 17.6593i 0.581893 + 1.00787i 0.995255 + 0.0973012i \(0.0310210\pi\)
−0.413362 + 0.910567i \(0.635646\pi\)
\(308\) 38.7738 + 32.5351i 2.20934 + 1.85386i
\(309\) 0 0
\(310\) 1.12610 + 6.38645i 0.0639584 + 0.362726i
\(311\) 3.85135 + 21.8421i 0.218390 + 1.23855i 0.874926 + 0.484256i \(0.160910\pi\)
−0.656536 + 0.754294i \(0.727979\pi\)
\(312\) 0 0
\(313\) −8.55828 7.18125i −0.483742 0.405908i 0.368035 0.929812i \(-0.380031\pi\)
−0.851777 + 0.523904i \(0.824475\pi\)
\(314\) −14.6819 25.4298i −0.828547 1.43508i
\(315\) 0 0
\(316\) −5.72635 + 9.91833i −0.322132 + 0.557950i
\(317\) −23.6959 + 8.62461i −1.33089 + 0.484406i −0.906933 0.421274i \(-0.861583\pi\)
−0.423962 + 0.905680i \(0.639361\pi\)
\(318\) 0 0
\(319\) 9.47829 7.95323i 0.530682 0.445295i
\(320\) −22.2955 8.11489i −1.24636 0.453636i
\(321\) 0 0
\(322\) 7.69993 43.6685i 0.429100 2.43355i
\(323\) −4.34438 −0.241728
\(324\) 0 0
\(325\) 0.864837 0.0479725
\(326\) 0.440305 2.49709i 0.0243862 0.138301i
\(327\) 0 0
\(328\) 2.32807 + 0.847349i 0.128546 + 0.0467870i
\(329\) 26.6803 22.3874i 1.47093 1.23426i
\(330\) 0 0
\(331\) 24.5877 8.94919i 1.35146 0.491892i 0.438059 0.898946i \(-0.355666\pi\)
0.913404 + 0.407054i \(0.133444\pi\)
\(332\) 10.6329 18.4167i 0.583555 1.01075i
\(333\) 0 0
\(334\) −25.4327 44.0507i −1.39161 2.41035i
\(335\) −6.55372 5.49922i −0.358068 0.300455i
\(336\) 0 0
\(337\) 1.90076 + 10.7798i 0.103541 + 0.587211i 0.991793 + 0.127854i \(0.0408089\pi\)
−0.888252 + 0.459357i \(0.848080\pi\)
\(338\) 4.25145 + 24.1112i 0.231248 + 1.31147i
\(339\) 0 0
\(340\) −9.43343 7.91559i −0.511599 0.429283i
\(341\) −3.05732 5.29543i −0.165563 0.286763i
\(342\) 0 0
\(343\) −23.0545 + 39.9316i −1.24483 + 2.15611i
\(344\) −5.64876 + 2.05598i −0.304560 + 0.110851i
\(345\) 0 0
\(346\) 14.8787 12.4847i 0.799884 0.671182i
\(347\) −3.30150 1.20165i −0.177234 0.0645078i 0.251879 0.967759i \(-0.418951\pi\)
−0.429113 + 0.903251i \(0.641174\pi\)
\(348\) 0 0
\(349\) −5.06998 + 28.7533i −0.271390 + 1.53913i 0.478811 + 0.877918i \(0.341068\pi\)
−0.750201 + 0.661210i \(0.770043\pi\)
\(350\) 7.32796 0.391696
\(351\) 0 0
\(352\) 32.9256 1.75494
\(353\) −4.35454 + 24.6958i −0.231769 + 1.31443i 0.617544 + 0.786537i \(0.288128\pi\)
−0.849313 + 0.527890i \(0.822983\pi\)
\(354\) 0 0
\(355\) 6.00455 + 2.18548i 0.318688 + 0.115993i
\(356\) 32.6910 27.4310i 1.73262 1.45384i
\(357\) 0 0
\(358\) 21.1684 7.70466i 1.11878 0.407204i
\(359\) −2.10362 + 3.64358i −0.111025 + 0.192301i −0.916184 0.400758i \(-0.868747\pi\)
0.805159 + 0.593059i \(0.202080\pi\)
\(360\) 0 0
\(361\) 7.81087 + 13.5288i 0.411098 + 0.712043i
\(362\) 2.38144 + 1.99826i 0.125166 + 0.105026i
\(363\) 0 0
\(364\) −2.57572 14.6076i −0.135005 0.765649i
\(365\) −4.58871 26.0239i −0.240184 1.36215i
\(366\) 0 0
\(367\) 13.4032 + 11.2466i 0.699641 + 0.587069i 0.921672 0.387971i \(-0.126824\pi\)
−0.222030 + 0.975040i \(0.571268\pi\)
\(368\) −5.81522 10.0723i −0.303139 0.525053i
\(369\) 0 0
\(370\) −19.7400 + 34.1907i −1.02623 + 1.77749i
\(371\) 28.8322 10.4940i 1.49689 0.544824i
\(372\) 0 0
\(373\) −22.7167 + 19.0616i −1.17623 + 0.986972i −0.176230 + 0.984349i \(0.556390\pi\)
−0.999997 + 0.00262266i \(0.999165\pi\)
\(374\) 19.5851 + 7.12840i 1.01272 + 0.368601i
\(375\) 0 0
\(376\) −1.36705 + 7.75295i −0.0705004 + 0.399828i
\(377\) −3.62594 −0.186745
\(378\) 0 0
\(379\) 20.9523 1.07625 0.538124 0.842865i \(-0.319133\pi\)
0.538124 + 0.842865i \(0.319133\pi\)
\(380\) 1.66285 9.43046i 0.0853022 0.483773i
\(381\) 0 0
\(382\) 24.8057 + 9.02854i 1.26917 + 0.461940i
\(383\) 7.58137 6.36152i 0.387390 0.325059i −0.428205 0.903681i \(-0.640854\pi\)
0.815595 + 0.578623i \(0.196410\pi\)
\(384\) 0 0
\(385\) 39.1535 14.2507i 1.99545 0.726284i
\(386\) 22.0719 38.2297i 1.12343 1.94584i
\(387\) 0 0
\(388\) 6.42745 + 11.1327i 0.326304 + 0.565175i
\(389\) −16.1748 13.5723i −0.820097 0.688143i 0.132898 0.991130i \(-0.457572\pi\)
−0.952995 + 0.302986i \(0.902016\pi\)
\(390\) 0 0
\(391\) −1.76636 10.0175i −0.0893288 0.506609i
\(392\) −3.14202 17.8193i −0.158696 0.900010i
\(393\) 0 0
\(394\) 23.0972 + 19.3809i 1.16362 + 0.976395i
\(395\) 4.71388 + 8.16468i 0.237181 + 0.410810i
\(396\) 0 0
\(397\) 4.88955 8.46894i 0.245399 0.425044i −0.716845 0.697233i \(-0.754414\pi\)
0.962244 + 0.272189i \(0.0877476\pi\)
\(398\) 40.5937 14.7749i 2.03478 0.740599i
\(399\) 0 0
\(400\) 1.47237 1.23546i 0.0736185 0.0617732i
\(401\) 17.9851 + 6.54604i 0.898133 + 0.326894i 0.749504 0.662000i \(-0.230292\pi\)
0.148628 + 0.988893i \(0.452514\pi\)
\(402\) 0 0
\(403\) −0.311161 + 1.76468i −0.0155000 + 0.0879050i
\(404\) 46.7423 2.32552
\(405\) 0 0
\(406\) −30.7234 −1.52478
\(407\) 6.46412 36.6599i 0.320415 1.81716i
\(408\) 0 0
\(409\) −14.0912 5.12878i −0.696766 0.253602i −0.0307364 0.999528i \(-0.509785\pi\)
−0.666029 + 0.745926i \(0.732007\pi\)
\(410\) 7.62071 6.39454i 0.376360 0.315804i
\(411\) 0 0
\(412\) −21.2899 + 7.74889i −1.04888 + 0.381760i
\(413\) −0.635799 + 1.10124i −0.0312856 + 0.0541883i
\(414\) 0 0
\(415\) −8.75289 15.1604i −0.429662 0.744197i
\(416\) −7.39150 6.20221i −0.362398 0.304088i
\(417\) 0 0
\(418\) 2.81434 + 15.9609i 0.137654 + 0.780674i
\(419\) 1.00921 + 5.72351i 0.0493031 + 0.279612i 0.999485 0.0320837i \(-0.0102143\pi\)
−0.950182 + 0.311695i \(0.899103\pi\)
\(420\) 0 0
\(421\) −10.1987 8.55776i −0.497056 0.417080i 0.359491 0.933149i \(-0.382950\pi\)
−0.856547 + 0.516069i \(0.827395\pi\)
\(422\) −10.4799 18.1518i −0.510154 0.883613i
\(423\) 0 0
\(424\) −3.46769 + 6.00621i −0.168406 + 0.291687i
\(425\) 1.57965 0.574947i 0.0766245 0.0278890i
\(426\) 0 0
\(427\) −16.5495 + 13.8866i −0.800884 + 0.672022i
\(428\) −17.5572 6.39029i −0.848658 0.308886i
\(429\) 0 0
\(430\) −4.19149 + 23.7711i −0.202131 + 1.14634i
\(431\) −36.4166 −1.75413 −0.877064 0.480374i \(-0.840501\pi\)
−0.877064 + 0.480374i \(0.840501\pi\)
\(432\) 0 0
\(433\) −10.8761 −0.522674 −0.261337 0.965248i \(-0.584163\pi\)
−0.261337 + 0.965248i \(0.584163\pi\)
\(434\) −2.63654 + 14.9525i −0.126558 + 0.717745i
\(435\) 0 0
\(436\) 13.2952 + 4.83906i 0.636725 + 0.231749i
\(437\) 6.05940 5.08444i 0.289860 0.243222i
\(438\) 0 0
\(439\) −8.88316 + 3.23321i −0.423970 + 0.154313i −0.545189 0.838313i \(-0.683542\pi\)
0.121219 + 0.992626i \(0.461320\pi\)
\(440\) −4.70906 + 8.15632i −0.224495 + 0.388837i
\(441\) 0 0
\(442\) −3.05390 5.28951i −0.145259 0.251596i
\(443\) 12.6581 + 10.6214i 0.601402 + 0.504636i 0.891896 0.452241i \(-0.149375\pi\)
−0.290494 + 0.956877i \(0.593820\pi\)
\(444\) 0 0
\(445\) −6.10021 34.5960i −0.289178 1.64001i
\(446\) −5.56145 31.5406i −0.263342 1.49349i
\(447\) 0 0
\(448\) −42.5540 35.7070i −2.01049 1.68700i
\(449\) 2.37181 + 4.10809i 0.111933 + 0.193873i 0.916549 0.399921i \(-0.130963\pi\)
−0.804617 + 0.593794i \(0.797629\pi\)
\(450\) 0 0
\(451\) −4.69001 + 8.12334i −0.220844 + 0.382513i
\(452\) 5.67998 2.06734i 0.267164 0.0972396i
\(453\) 0 0
\(454\) 36.9405 30.9967i 1.73370 1.45475i
\(455\) −11.4740 4.17620i −0.537910 0.195783i
\(456\) 0 0
\(457\) −3.89120 + 22.0681i −0.182023 + 1.03230i 0.747698 + 0.664039i \(0.231159\pi\)
−0.929721 + 0.368264i \(0.879952\pi\)
\(458\) −18.5232 −0.865534
\(459\) 0 0
\(460\) 22.4214 1.04540
\(461\) −2.59122 + 14.6956i −0.120685 + 0.684440i 0.863092 + 0.505047i \(0.168525\pi\)
−0.983777 + 0.179394i \(0.942586\pi\)
\(462\) 0 0
\(463\) 13.9518 + 5.07803i 0.648394 + 0.235996i 0.645218 0.763999i \(-0.276767\pi\)
0.00317653 + 0.999995i \(0.498989\pi\)
\(464\) −6.17309 + 5.17984i −0.286579 + 0.240468i
\(465\) 0 0
\(466\) −47.1042 + 17.1445i −2.18206 + 0.794204i
\(467\) 7.67571 13.2947i 0.355190 0.615206i −0.631961 0.775000i \(-0.717750\pi\)
0.987150 + 0.159794i \(0.0510830\pi\)
\(468\) 0 0
\(469\) −10.0152 17.3468i −0.462458 0.801001i
\(470\) 24.2159 + 20.3195i 1.11700 + 0.937270i
\(471\) 0 0
\(472\) −0.0499113 0.283061i −0.00229735 0.0130289i
\(473\) −3.95212 22.4136i −0.181719 1.03058i
\(474\) 0 0
\(475\) 1.00137 + 0.840253i 0.0459462 + 0.0385534i
\(476\) −14.4159 24.9690i −0.660750 1.14445i
\(477\) 0 0
\(478\) 10.5768 18.3196i 0.483772 0.837918i
\(479\) −9.81848 + 3.57363i −0.448618 + 0.163284i −0.556442 0.830886i \(-0.687834\pi\)
0.107824 + 0.994170i \(0.465612\pi\)
\(480\) 0 0
\(481\) −8.35676 + 7.01215i −0.381035 + 0.319727i
\(482\) 11.4090 + 4.15255i 0.519667 + 0.189143i
\(483\) 0 0
\(484\) 2.71648 15.4059i 0.123476 0.700268i
\(485\) 10.5820 0.480505
\(486\) 0 0
\(487\) −16.1649 −0.732500 −0.366250 0.930516i \(-0.619359\pi\)
−0.366250 + 0.930516i \(0.619359\pi\)
\(488\) 0.847966 4.80906i 0.0383856 0.217696i
\(489\) 0 0
\(490\) −68.2740 24.8497i −3.08431 1.12260i
\(491\) −8.25592 + 6.92754i −0.372585 + 0.312636i −0.809783 0.586730i \(-0.800415\pi\)
0.437198 + 0.899365i \(0.355971\pi\)
\(492\) 0 0
\(493\) −6.62290 + 2.41054i −0.298280 + 0.108565i
\(494\) 2.37477 4.11322i 0.106846 0.185062i
\(495\) 0 0
\(496\) 1.99119 + 3.44885i 0.0894071 + 0.154858i
\(497\) 11.4605 + 9.61651i 0.514074 + 0.431359i
\(498\) 0 0
\(499\) −3.33182 18.8957i −0.149153 0.845887i −0.963938 0.266125i \(-0.914257\pi\)
0.814786 0.579762i \(-0.196855\pi\)
\(500\) 5.16693 + 29.3031i 0.231072 + 1.31048i
\(501\) 0 0
\(502\) 11.8666 + 9.95726i 0.529632 + 0.444414i
\(503\) 6.01253 + 10.4140i 0.268086 + 0.464338i 0.968367 0.249529i \(-0.0802757\pi\)
−0.700282 + 0.713866i \(0.746942\pi\)
\(504\) 0 0
\(505\) 19.2389 33.3228i 0.856120 1.48284i
\(506\) −35.6594 + 12.9790i −1.58525 + 0.576985i
\(507\) 0 0
\(508\) −17.7969 + 14.9333i −0.789608 + 0.662560i
\(509\) 14.0512 + 5.11423i 0.622810 + 0.226684i 0.634099 0.773252i \(-0.281371\pi\)
−0.0112886 + 0.999936i \(0.503593\pi\)
\(510\) 0 0
\(511\) 10.7435 60.9294i 0.475265 2.69536i
\(512\) −27.3678 −1.20950
\(513\) 0 0
\(514\) 49.3922 2.17860
\(515\) −3.23861 + 18.3671i −0.142710 + 0.809350i
\(516\) 0 0
\(517\) −28.0088 10.1944i −1.23182 0.448348i
\(518\) −70.8087 + 59.4155i −3.11115 + 2.61057i
\(519\) 0 0
\(520\) 2.59355 0.943974i 0.113735 0.0413960i
\(521\) −18.7094 + 32.4056i −0.819673 + 1.41972i 0.0862502 + 0.996274i \(0.472512\pi\)
−0.905923 + 0.423442i \(0.860822\pi\)
\(522\) 0 0
\(523\) 4.22489 + 7.31773i 0.184742 + 0.319982i 0.943489 0.331403i \(-0.107522\pi\)
−0.758748 + 0.651385i \(0.774188\pi\)
\(524\) −29.5609 24.8046i −1.29138 1.08359i
\(525\) 0 0
\(526\) 10.1107 + 57.3404i 0.440846 + 2.50016i
\(527\) 0.604821 + 3.43011i 0.0263464 + 0.149418i
\(528\) 0 0
\(529\) −3.43134 2.87924i −0.149189 0.125184i
\(530\) 13.9242 + 24.1175i 0.604829 + 1.04760i
\(531\) 0 0
\(532\) 11.2100 19.4163i 0.486017 0.841805i
\(533\) 2.58306 0.940156i 0.111885 0.0407227i
\(534\) 0 0
\(535\) −11.7821 + 9.88637i −0.509386 + 0.427425i
\(536\) 4.25455 + 1.54853i 0.183769 + 0.0668863i
\(537\) 0 0
\(538\) −3.47595 + 19.7131i −0.149859 + 0.849892i
\(539\) 68.5065 2.95078
\(540\) 0 0
\(541\) 12.6259 0.542828 0.271414 0.962463i \(-0.412509\pi\)
0.271414 + 0.962463i \(0.412509\pi\)
\(542\) −9.69740 + 54.9967i −0.416539 + 2.36231i
\(543\) 0 0
\(544\) −17.6241 6.41464i −0.755626 0.275025i
\(545\) 8.92204 7.48648i 0.382178 0.320685i
\(546\) 0 0
\(547\) −29.5017 + 10.7377i −1.26140 + 0.459113i −0.884239 0.467034i \(-0.845322\pi\)
−0.377162 + 0.926147i \(0.623100\pi\)
\(548\) 4.58365 7.93912i 0.195804 0.339142i
\(549\) 0 0
\(550\) −3.13563 5.43107i −0.133704 0.231582i
\(551\) −4.19839 3.52286i −0.178857 0.150079i
\(552\) 0 0
\(553\) 3.83296 + 21.7378i 0.162994 + 0.924385i
\(554\) −0.138308 0.784385i −0.00587616 0.0333253i
\(555\) 0 0
\(556\) 25.5843 + 21.4678i 1.08501 + 0.910436i
\(557\) 7.96515 + 13.7960i 0.337494 + 0.584557i 0.983961 0.178385i \(-0.0570874\pi\)
−0.646467 + 0.762942i \(0.723754\pi\)
\(558\) 0 0
\(559\) −3.33484 + 5.77610i −0.141048 + 0.244303i
\(560\) −25.5002 + 9.28132i −1.07758 + 0.392207i
\(561\) 0 0
\(562\) −22.7602 + 19.0980i −0.960079 + 0.805602i
\(563\) 23.3616 + 8.50291i 0.984572 + 0.358355i 0.783616 0.621245i \(-0.213373\pi\)
0.200956 + 0.979600i \(0.435595\pi\)
\(564\) 0 0
\(565\) 0.864036 4.90019i 0.0363503 0.206153i
\(566\) −33.0695 −1.39001
\(567\) 0 0
\(568\) −3.38165 −0.141891
\(569\) 3.33231 18.8985i 0.139698 0.792265i −0.831775 0.555113i \(-0.812675\pi\)
0.971473 0.237152i \(-0.0762139\pi\)
\(570\) 0 0
\(571\) 19.1502 + 6.97011i 0.801412 + 0.291690i 0.710071 0.704130i \(-0.248663\pi\)
0.0913403 + 0.995820i \(0.470885\pi\)
\(572\) −9.72422 + 8.15959i −0.406590 + 0.341169i
\(573\) 0 0
\(574\) 21.8868 7.96615i 0.913538 0.332501i
\(575\) −1.53036 + 2.65066i −0.0638205 + 0.110540i
\(576\) 0 0
\(577\) −11.6495 20.1776i −0.484976 0.840004i 0.514875 0.857265i \(-0.327838\pi\)
−0.999851 + 0.0172619i \(0.994505\pi\)
\(578\) 18.5792 + 15.5898i 0.772792 + 0.648450i
\(579\) 0 0
\(580\) −2.69765 15.2992i −0.112014 0.635263i
\(581\) −7.11716 40.3634i −0.295270 1.67456i
\(582\) 0 0
\(583\) −20.1149 16.8784i −0.833072 0.699031i
\(584\) 6.99237 + 12.1111i 0.289346 + 0.501163i
\(585\) 0 0
\(586\) 26.1636 45.3167i 1.08081 1.87201i
\(587\) 34.6834 12.6237i 1.43154 0.521036i 0.494165 0.869368i \(-0.335474\pi\)
0.937371 + 0.348332i \(0.113252\pi\)
\(588\) 0 0
\(589\) −2.07480 + 1.74097i −0.0854907 + 0.0717352i
\(590\) −1.08454 0.394740i −0.0446497 0.0162512i
\(591\) 0 0
\(592\) −4.21000 + 23.8761i −0.173030 + 0.981302i
\(593\) 4.36830 0.179385 0.0896923 0.995970i \(-0.471412\pi\)
0.0896923 + 0.995970i \(0.471412\pi\)
\(594\) 0 0
\(595\) −23.7340 −0.973000
\(596\) 3.89281 22.0772i 0.159456 0.904318i
\(597\) 0 0
\(598\) 10.4501 + 3.80351i 0.427334 + 0.155537i
\(599\) −23.9049 + 20.0586i −0.976727 + 0.819571i −0.983592 0.180405i \(-0.942259\pi\)
0.00686530 + 0.999976i \(0.497815\pi\)
\(600\) 0 0
\(601\) −41.2874 + 15.0274i −1.68415 + 0.612979i −0.993869 0.110565i \(-0.964734\pi\)
−0.690278 + 0.723544i \(0.742512\pi\)
\(602\) −28.2568 + 48.9422i −1.15166 + 1.99474i
\(603\) 0 0
\(604\) 0.896114 + 1.55211i 0.0364623 + 0.0631546i
\(605\) −9.86485 8.27759i −0.401063 0.336532i
\(606\) 0 0
\(607\) 3.01430 + 17.0949i 0.122347 + 0.693862i 0.982849 + 0.184415i \(0.0590390\pi\)
−0.860502 + 0.509447i \(0.829850\pi\)
\(608\) −2.53254 14.3628i −0.102708 0.582487i
\(609\) 0 0
\(610\) −15.0208 12.6039i −0.608174 0.510319i
\(611\) 4.36740 + 7.56456i 0.176686 + 0.306029i
\(612\) 0 0
\(613\) 0.599024 1.03754i 0.0241944 0.0419059i −0.853675 0.520807i \(-0.825631\pi\)
0.877869 + 0.478901i \(0.158965\pi\)
\(614\) −40.7186 + 14.8204i −1.64327 + 0.598101i
\(615\) 0 0
\(616\) −16.8917 + 14.1738i −0.680586 + 0.571079i
\(617\) −24.4449 8.89721i −0.984114 0.358188i −0.200676 0.979658i \(-0.564314\pi\)
−0.783439 + 0.621469i \(0.786536\pi\)
\(618\) 0 0
\(619\) 1.67247 9.48503i 0.0672221 0.381235i −0.932573 0.360982i \(-0.882442\pi\)
0.999795 0.0202534i \(-0.00644731\pi\)
\(620\) −7.67733 −0.308329
\(621\) 0 0
\(622\) −47.1311 −1.88978
\(623\) 14.2824 80.9993i 0.572211 3.24517i
\(624\) 0 0
\(625\) 19.6754 + 7.16127i 0.787017 + 0.286451i
\(626\) 18.1866 15.2604i 0.726882 0.609927i
\(627\) 0 0
\(628\) 32.6663 11.8896i 1.30353 0.474445i
\(629\) −10.6022 + 18.3635i −0.422737 + 0.732202i
\(630\) 0 0
\(631\) 7.08366 + 12.2693i 0.281996 + 0.488431i 0.971876 0.235492i \(-0.0756702\pi\)
−0.689880 + 0.723924i \(0.742337\pi\)
\(632\) −3.82205 3.20708i −0.152033 0.127571i
\(633\) 0 0
\(634\) −9.30513 52.7720i −0.369554 2.09585i
\(635\) 3.32093 + 18.8340i 0.131787 + 0.747403i
\(636\) 0 0
\(637\) −15.3791 12.9046i −0.609341 0.511298i
\(638\) 13.1465 + 22.7704i 0.520476 + 0.901490i
\(639\) 0 0
\(640\) 8.77695 15.2021i 0.346939 0.600917i
\(641\) −20.8620 + 7.59316i −0.824001 + 0.299912i −0.719394 0.694602i \(-0.755581\pi\)
−0.104606 + 0.994514i \(0.533358\pi\)
\(642\) 0 0
\(643\) 16.4981 13.8436i 0.650623 0.545938i −0.256637 0.966508i \(-0.582614\pi\)
0.907260 + 0.420570i \(0.138170\pi\)
\(644\) 49.3292 + 17.9544i 1.94384 + 0.707502i
\(645\) 0 0
\(646\) 1.60311 9.09168i 0.0630735 0.357707i
\(647\) 13.4037 0.526952 0.263476 0.964666i \(-0.415131\pi\)
0.263476 + 0.964666i \(0.415131\pi\)
\(648\) 0 0
\(649\) 1.08823 0.0427168
\(650\) −0.319131 + 1.80988i −0.0125174 + 0.0709895i
\(651\) 0 0
\(652\) 2.82079 + 1.02668i 0.110471 + 0.0402080i
\(653\) −14.4866 + 12.1557i −0.566903 + 0.475688i −0.880617 0.473830i \(-0.842871\pi\)
0.313714 + 0.949518i \(0.398427\pi\)
\(654\) 0 0
\(655\) −29.8504 + 10.8647i −1.16635 + 0.424518i
\(656\) 3.05455 5.29063i 0.119260 0.206564i
\(657\) 0 0
\(658\) 37.0059 + 64.0962i 1.44264 + 2.49873i
\(659\) −0.0215882 0.0181147i −0.000840958 0.000705648i 0.642367 0.766397i \(-0.277952\pi\)
−0.643208 + 0.765692i \(0.722397\pi\)
\(660\) 0 0
\(661\) −7.82141 44.3574i −0.304218 1.72530i −0.627164 0.778887i \(-0.715784\pi\)
0.322946 0.946417i \(-0.395327\pi\)
\(662\) 9.65533 + 54.7581i 0.375265 + 2.12823i
\(663\) 0 0
\(664\) 7.09691 + 5.95502i 0.275414 + 0.231099i
\(665\) −9.22800 15.9834i −0.357846 0.619808i
\(666\) 0 0
\(667\) 6.41623 11.1132i 0.248438 0.430306i
\(668\) 56.5862 20.5957i 2.18938 0.796871i
\(669\) 0 0
\(670\) 13.9268 11.6860i 0.538041 0.451470i
\(671\) 17.3735 + 6.32343i 0.670696 + 0.244113i
\(672\) 0 0
\(673\) −1.69475 + 9.61142i −0.0653279 + 0.370493i 0.934564 + 0.355795i \(0.115790\pi\)
−0.999892 + 0.0146980i \(0.995321\pi\)
\(674\) −23.2607 −0.895968
\(675\) 0 0
\(676\) −28.9847 −1.11480
\(677\) 7.09887 40.2597i 0.272832 1.54731i −0.472934 0.881098i \(-0.656805\pi\)
0.745766 0.666208i \(-0.232084\pi\)
\(678\) 0 0
\(679\) 23.2815 + 8.47376i 0.893460 + 0.325193i
\(680\) 4.10964 3.44840i 0.157598 0.132240i
\(681\) 0 0
\(682\) 12.2101 4.44413i 0.467551 0.170175i
\(683\) 22.0126 38.1269i 0.842287 1.45888i −0.0456696 0.998957i \(-0.514542\pi\)
0.887957 0.459927i \(-0.152125\pi\)
\(684\) 0 0
\(685\) −3.77322 6.53541i −0.144167 0.249705i
\(686\) −75.0594 62.9823i −2.86578 2.40468i
\(687\) 0 0
\(688\) 2.57397 + 14.5977i 0.0981316 + 0.556532i
\(689\) 1.33622 + 7.57808i 0.0509059 + 0.288702i
\(690\) 0 0
\(691\) 16.5095 + 13.8531i 0.628051 + 0.526997i 0.900323 0.435223i \(-0.143331\pi\)
−0.272272 + 0.962220i \(0.587775\pi\)
\(692\) 11.4970 + 19.9133i 0.437049 + 0.756991i
\(693\) 0 0
\(694\) 3.73302 6.46577i 0.141703 0.245437i
\(695\) 25.8348 9.40311i 0.979971 0.356680i
\(696\) 0 0
\(697\) 4.09302 3.43445i 0.155034 0.130089i
\(698\) −58.3024 21.2203i −2.20678 0.803202i
\(699\) 0 0
\(700\) −1.50645 + 8.54352i −0.0569386 + 0.322915i
\(701\) −12.8521 −0.485419 −0.242709 0.970099i \(-0.578036\pi\)
−0.242709 + 0.970099i \(0.578036\pi\)
\(702\) 0 0
\(703\) −16.4889 −0.621891
\(704\) −8.25521 + 46.8176i −0.311130 + 1.76451i
\(705\) 0 0
\(706\) −50.0752 18.2259i −1.88461 0.685940i
\(707\) 69.0112 57.9073i 2.59543 2.17783i
\(708\) 0 0
\(709\) 46.7137 17.0024i 1.75437 0.638539i 0.754528 0.656268i \(-0.227866\pi\)
0.999843 + 0.0177295i \(0.00564379\pi\)
\(710\) −6.78937 + 11.7595i −0.254800 + 0.441327i
\(711\) 0 0
\(712\) 9.29562 + 16.1005i 0.348368 + 0.603392i
\(713\) −4.85801 4.07635i −0.181934 0.152661i
\(714\) 0 0
\(715\) 1.81456 + 10.2909i 0.0678607 + 0.384857i
\(716\) 4.63099 + 26.2637i 0.173068 + 0.981519i
\(717\) 0 0
\(718\) −6.84883 5.74685i −0.255596 0.214471i
\(719\) 2.81873 + 4.88218i 0.105121 + 0.182075i 0.913788 0.406192i \(-0.133144\pi\)
−0.808667 + 0.588267i \(0.799810\pi\)
\(720\) 0 0
\(721\) −21.8330 + 37.8159i −0.813104 + 1.40834i
\(722\) −31.1946 + 11.3539i −1.16094 + 0.422549i
\(723\) 0 0
\(724\) −2.81930 + 2.36568i −0.104779 + 0.0879196i
\(725\) 1.99279 + 0.725318i 0.0740105 + 0.0269376i
\(726\) 0 0
\(727\) −7.88611 + 44.7243i −0.292480 + 1.65873i 0.384794 + 0.923002i \(0.374272\pi\)
−0.677273 + 0.735731i \(0.736839\pi\)
\(728\) 6.46195 0.239496
\(729\) 0 0
\(730\) 56.1546 2.07837
\(731\) −2.25121 + 12.7673i −0.0832641 + 0.472214i
\(732\) 0 0
\(733\) 24.1190 + 8.77858i 0.890854 + 0.324244i 0.746582 0.665294i \(-0.231694\pi\)
0.144272 + 0.989538i \(0.453916\pi\)
\(734\) −28.4822 + 23.8994i −1.05130 + 0.882143i
\(735\) 0 0
\(736\) 32.0889 11.6794i 1.18281 0.430508i
\(737\) −8.57098 + 14.8454i −0.315716 + 0.546837i
\(738\) 0 0
\(739\) 7.22763 + 12.5186i 0.265873 + 0.460505i 0.967792 0.251752i \(-0.0810066\pi\)
−0.701919 + 0.712256i \(0.747673\pi\)
\(740\) −35.8041 30.0432i −1.31619 1.10441i
\(741\) 0 0
\(742\) 11.3221 + 64.2107i 0.415647 + 2.35725i
\(743\) 6.04187 + 34.2651i 0.221655 + 1.25707i 0.868978 + 0.494851i \(0.164777\pi\)
−0.647323 + 0.762215i \(0.724112\pi\)
\(744\) 0 0
\(745\) −14.1367 11.8621i −0.517928 0.434593i
\(746\) −31.5084 54.5742i −1.15360 1.99810i
\(747\) 0 0
\(748\) −12.3371 + 21.3685i −0.451089 + 0.781308i
\(749\) −33.8385 + 12.3162i −1.23643 + 0.450024i
\(750\) 0 0
\(751\) 13.8795 11.6463i 0.506471 0.424980i −0.353414 0.935467i \(-0.614979\pi\)
0.859885 + 0.510487i \(0.170535\pi\)
\(752\) 18.2418 + 6.63946i 0.665209 + 0.242116i
\(753\) 0 0
\(754\) 1.33800 7.58816i 0.0487270 0.276345i
\(755\) 1.47535 0.0536933
\(756\) 0 0
\(757\) −37.0045 −1.34495 −0.672475 0.740120i \(-0.734769\pi\)
−0.672475 + 0.740120i \(0.734769\pi\)
\(758\) −7.73156 + 43.8479i −0.280823 + 1.59263i
\(759\) 0 0
\(760\) 3.92014 + 1.42682i 0.142199 + 0.0517560i
\(761\) −9.53298 + 7.99912i −0.345570 + 0.289968i −0.799008 0.601320i \(-0.794642\pi\)
0.453438 + 0.891288i \(0.350197\pi\)
\(762\) 0 0
\(763\) 25.6242 9.32646i 0.927660 0.337641i
\(764\) −15.6257 + 27.0644i −0.565316 + 0.979156i
\(765\) 0 0
\(766\) 10.5155 + 18.2133i 0.379939 + 0.658074i
\(767\) −0.244298 0.204990i −0.00882108 0.00740177i
\(768\) 0 0
\(769\) −7.09970 40.2644i −0.256022 1.45197i −0.793436 0.608654i \(-0.791710\pi\)
0.537414 0.843318i \(-0.319401\pi\)
\(770\) 15.3752 + 87.1970i 0.554083 + 3.14236i
\(771\) 0 0
\(772\) 40.0338 + 33.5923i 1.44085 + 1.20901i
\(773\) 18.2081 + 31.5374i 0.654900 + 1.13432i 0.981919 + 0.189302i \(0.0606226\pi\)
−0.327019 + 0.945018i \(0.606044\pi\)
\(774\) 0 0
\(775\) 0.524012 0.907615i 0.0188231 0.0326025i
\(776\) −5.26246 + 1.91538i −0.188911 + 0.0687581i
\(777\) 0 0
\(778\) 34.3720 28.8415i 1.23230 1.03402i
\(779\)