Properties

Label 729.2.c.e.487.3
Level $729$
Weight $2$
Character 729.487
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
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(244,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.c (of order \(3\), degree \(2\), 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: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 487.3
Root \(0.500000 + 0.258654i\) of defining polynomial
Character \(\chi\) \(=\) 729.487
Dual form 729.2.c.e.244.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.207733 - 0.359804i) q^{2} +(0.913694 + 1.58256i) q^{4} +(-1.10759 - 1.91841i) q^{5} +(0.659815 - 1.14283i) q^{7} +1.59015 q^{8} +O(q^{10})\) \(q+(0.207733 - 0.359804i) q^{2} +(0.913694 + 1.58256i) q^{4} +(-1.10759 - 1.91841i) q^{5} +(0.659815 - 1.14283i) q^{7} +1.59015 q^{8} -0.920335 q^{10} +(2.60759 - 4.51648i) q^{11} +(0.00902926 + 0.0156391i) q^{13} +(-0.274131 - 0.474808i) q^{14} +(-1.49706 + 2.59299i) q^{16} -3.13280 q^{17} +0.417352 q^{19} +(2.02400 - 3.50568i) q^{20} +(-1.08337 - 1.87645i) q^{22} +(0.517193 + 0.895805i) q^{23} +(0.0464738 - 0.0804949i) q^{25} +0.00750270 q^{26} +2.41147 q^{28} +(3.90361 - 6.76125i) q^{29} +(-1.86483 - 3.22998i) q^{31} +(2.21213 + 3.83152i) q^{32} +(-0.650785 + 1.12719i) q^{34} -2.92322 q^{35} +4.42476 q^{37} +(0.0866979 - 0.150165i) q^{38} +(-1.76124 - 3.05056i) q^{40} +(1.83747 + 3.18259i) q^{41} +(4.15394 - 7.19483i) q^{43} +9.53017 q^{44} +0.429753 q^{46} +(3.54895 - 6.14697i) q^{47} +(2.62929 + 4.55406i) q^{49} +(-0.0193083 - 0.0334429i) q^{50} +(-0.0165000 + 0.0285788i) q^{52} -1.30057 q^{53} -11.5526 q^{55} +(1.04920 - 1.81728i) q^{56} +(-1.62182 - 2.80907i) q^{58} +(1.85091 + 3.20586i) q^{59} +(-3.45712 + 5.98791i) q^{61} -1.54955 q^{62} -4.15011 q^{64} +(0.0200015 - 0.0346436i) q^{65} +(5.51340 + 9.54949i) q^{67} +(-2.86242 - 4.95785i) q^{68} +(-0.607251 + 1.05179i) q^{70} -6.08428 q^{71} -0.546973 q^{73} +(0.919169 - 1.59205i) q^{74} +(0.381332 + 0.660487i) q^{76} +(-3.44106 - 5.96008i) q^{77} +(-0.244572 + 0.423611i) q^{79} +6.63254 q^{80} +1.52681 q^{82} +(-2.30684 + 3.99556i) q^{83} +(3.46986 + 6.00998i) q^{85} +(-1.72582 - 2.98921i) q^{86} +(4.14647 - 7.18189i) q^{88} -3.37307 q^{89} +0.0238305 q^{91} +(-0.945113 + 1.63698i) q^{92} +(-1.47447 - 2.55386i) q^{94} +(-0.462257 - 0.800652i) q^{95} +(-4.97068 + 8.60947i) q^{97} +2.18476 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.207733 0.359804i 0.146889 0.254420i −0.783187 0.621786i \(-0.786407\pi\)
0.930076 + 0.367366i \(0.119740\pi\)
\(3\) 0 0
\(4\) 0.913694 + 1.58256i 0.456847 + 0.791282i
\(5\) −1.10759 1.91841i −0.495331 0.857938i 0.504655 0.863321i \(-0.331620\pi\)
−0.999986 + 0.00538314i \(0.998286\pi\)
\(6\) 0 0
\(7\) 0.659815 1.14283i 0.249386 0.431950i −0.713969 0.700177i \(-0.753104\pi\)
0.963356 + 0.268227i \(0.0864377\pi\)
\(8\) 1.59015 0.562203
\(9\) 0 0
\(10\) −0.920335 −0.291036
\(11\) 2.60759 4.51648i 0.786219 1.36177i −0.142049 0.989860i \(-0.545369\pi\)
0.928268 0.371912i \(-0.121298\pi\)
\(12\) 0 0
\(13\) 0.00902926 + 0.0156391i 0.00250427 + 0.00433752i 0.867275 0.497830i \(-0.165870\pi\)
−0.864771 + 0.502167i \(0.832536\pi\)
\(14\) −0.274131 0.474808i −0.0732645 0.126898i
\(15\) 0 0
\(16\) −1.49706 + 2.59299i −0.374265 + 0.648246i
\(17\) −3.13280 −0.759814 −0.379907 0.925025i \(-0.624044\pi\)
−0.379907 + 0.925025i \(0.624044\pi\)
\(18\) 0 0
\(19\) 0.417352 0.0957472 0.0478736 0.998853i \(-0.484756\pi\)
0.0478736 + 0.998853i \(0.484756\pi\)
\(20\) 2.02400 3.50568i 0.452581 0.783893i
\(21\) 0 0
\(22\) −1.08337 1.87645i −0.230975 0.400060i
\(23\) 0.517193 + 0.895805i 0.107842 + 0.186788i 0.914896 0.403690i \(-0.132273\pi\)
−0.807054 + 0.590478i \(0.798939\pi\)
\(24\) 0 0
\(25\) 0.0464738 0.0804949i 0.00929475 0.0160990i
\(26\) 0.00750270 0.00147140
\(27\) 0 0
\(28\) 2.41147 0.455726
\(29\) 3.90361 6.76125i 0.724882 1.25553i −0.234140 0.972203i \(-0.575227\pi\)
0.959022 0.283330i \(-0.0914393\pi\)
\(30\) 0 0
\(31\) −1.86483 3.22998i −0.334934 0.580122i 0.648538 0.761182i \(-0.275381\pi\)
−0.983472 + 0.181060i \(0.942047\pi\)
\(32\) 2.21213 + 3.83152i 0.391053 + 0.677323i
\(33\) 0 0
\(34\) −0.650785 + 1.12719i −0.111609 + 0.193312i
\(35\) −2.92322 −0.494115
\(36\) 0 0
\(37\) 4.42476 0.727426 0.363713 0.931511i \(-0.381509\pi\)
0.363713 + 0.931511i \(0.381509\pi\)
\(38\) 0.0866979 0.150165i 0.0140643 0.0243600i
\(39\) 0 0
\(40\) −1.76124 3.05056i −0.278477 0.482335i
\(41\) 1.83747 + 3.18259i 0.286965 + 0.497037i 0.973084 0.230452i \(-0.0740205\pi\)
−0.686119 + 0.727489i \(0.740687\pi\)
\(42\) 0 0
\(43\) 4.15394 7.19483i 0.633469 1.09720i −0.353368 0.935484i \(-0.614964\pi\)
0.986837 0.161717i \(-0.0517031\pi\)
\(44\) 9.53017 1.43673
\(45\) 0 0
\(46\) 0.429753 0.0633636
\(47\) 3.54895 6.14697i 0.517668 0.896628i −0.482121 0.876105i \(-0.660133\pi\)
0.999789 0.0205231i \(-0.00653317\pi\)
\(48\) 0 0
\(49\) 2.62929 + 4.55406i 0.375613 + 0.650580i
\(50\) −0.0193083 0.0334429i −0.00273060 0.00472954i
\(51\) 0 0
\(52\) −0.0165000 + 0.0285788i −0.00228813 + 0.00396316i
\(53\) −1.30057 −0.178648 −0.0893238 0.996003i \(-0.528471\pi\)
−0.0893238 + 0.996003i \(0.528471\pi\)
\(54\) 0 0
\(55\) −11.5526 −1.55775
\(56\) 1.04920 1.81728i 0.140206 0.242844i
\(57\) 0 0
\(58\) −1.62182 2.80907i −0.212955 0.368849i
\(59\) 1.85091 + 3.20586i 0.240967 + 0.417368i 0.960990 0.276583i \(-0.0892020\pi\)
−0.720023 + 0.693950i \(0.755869\pi\)
\(60\) 0 0
\(61\) −3.45712 + 5.98791i −0.442639 + 0.766673i −0.997884 0.0650137i \(-0.979291\pi\)
0.555246 + 0.831686i \(0.312624\pi\)
\(62\) −1.54955 −0.196793
\(63\) 0 0
\(64\) −4.15011 −0.518764
\(65\) 0.0200015 0.0346436i 0.00248088 0.00429701i
\(66\) 0 0
\(67\) 5.51340 + 9.54949i 0.673569 + 1.16666i 0.976885 + 0.213765i \(0.0685728\pi\)
−0.303316 + 0.952890i \(0.598094\pi\)
\(68\) −2.86242 4.95785i −0.347119 0.601228i
\(69\) 0 0
\(70\) −0.607251 + 1.05179i −0.0725803 + 0.125713i
\(71\) −6.08428 −0.722071 −0.361035 0.932552i \(-0.617577\pi\)
−0.361035 + 0.932552i \(0.617577\pi\)
\(72\) 0 0
\(73\) −0.546973 −0.0640183 −0.0320092 0.999488i \(-0.510191\pi\)
−0.0320092 + 0.999488i \(0.510191\pi\)
\(74\) 0.919169 1.59205i 0.106851 0.185072i
\(75\) 0 0
\(76\) 0.381332 + 0.660487i 0.0437418 + 0.0757630i
\(77\) −3.44106 5.96008i −0.392145 0.679215i
\(78\) 0 0
\(79\) −0.244572 + 0.423611i −0.0275165 + 0.0476600i −0.879456 0.475981i \(-0.842093\pi\)
0.851939 + 0.523641i \(0.175427\pi\)
\(80\) 6.63254 0.741540
\(81\) 0 0
\(82\) 1.52681 0.168608
\(83\) −2.30684 + 3.99556i −0.253208 + 0.438569i −0.964407 0.264421i \(-0.914819\pi\)
0.711199 + 0.702991i \(0.248152\pi\)
\(84\) 0 0
\(85\) 3.46986 + 6.00998i 0.376360 + 0.651874i
\(86\) −1.72582 2.98921i −0.186100 0.322335i
\(87\) 0 0
\(88\) 4.14647 7.18189i 0.442015 0.765592i
\(89\) −3.37307 −0.357544 −0.178772 0.983891i \(-0.557212\pi\)
−0.178772 + 0.983891i \(0.557212\pi\)
\(90\) 0 0
\(91\) 0.0238305 0.00249812
\(92\) −0.945113 + 1.63698i −0.0985348 + 0.170667i
\(93\) 0 0
\(94\) −1.47447 2.55386i −0.152080 0.263410i
\(95\) −0.462257 0.800652i −0.0474265 0.0821452i
\(96\) 0 0
\(97\) −4.97068 + 8.60947i −0.504696 + 0.874159i 0.495289 + 0.868728i \(0.335062\pi\)
−0.999985 + 0.00543103i \(0.998271\pi\)
\(98\) 2.18476 0.220694
\(99\) 0 0
\(100\) 0.169851 0.0169851
\(101\) −6.89974 + 11.9507i −0.686550 + 1.18914i 0.286397 + 0.958111i \(0.407542\pi\)
−0.972947 + 0.231029i \(0.925791\pi\)
\(102\) 0 0
\(103\) −2.28256 3.95351i −0.224907 0.389551i 0.731384 0.681966i \(-0.238875\pi\)
−0.956292 + 0.292415i \(0.905541\pi\)
\(104\) 0.0143579 + 0.0248686i 0.00140791 + 0.00243856i
\(105\) 0 0
\(106\) −0.270172 + 0.467952i −0.0262415 + 0.0454515i
\(107\) −11.2965 −1.09207 −0.546035 0.837762i \(-0.683864\pi\)
−0.546035 + 0.837762i \(0.683864\pi\)
\(108\) 0 0
\(109\) 14.5032 1.38915 0.694577 0.719419i \(-0.255592\pi\)
0.694577 + 0.719419i \(0.255592\pi\)
\(110\) −2.39986 + 4.15668i −0.228818 + 0.396324i
\(111\) 0 0
\(112\) 1.97557 + 3.42178i 0.186673 + 0.323328i
\(113\) −6.27921 10.8759i −0.590699 1.02312i −0.994139 0.108114i \(-0.965519\pi\)
0.403440 0.915006i \(-0.367814\pi\)
\(114\) 0 0
\(115\) 1.14568 1.98438i 0.106835 0.185044i
\(116\) 14.2668 1.32464
\(117\) 0 0
\(118\) 1.53798 0.141582
\(119\) −2.06706 + 3.58026i −0.189487 + 0.328202i
\(120\) 0 0
\(121\) −8.09909 14.0280i −0.736281 1.27528i
\(122\) 1.43632 + 2.48777i 0.130038 + 0.225232i
\(123\) 0 0
\(124\) 3.40777 5.90243i 0.306027 0.530054i
\(125\) −11.2818 −1.00908
\(126\) 0 0
\(127\) −8.39499 −0.744935 −0.372467 0.928045i \(-0.621488\pi\)
−0.372467 + 0.928045i \(0.621488\pi\)
\(128\) −5.28637 + 9.15627i −0.467254 + 0.809307i
\(129\) 0 0
\(130\) −0.00830995 0.0143932i −0.000728831 0.00126237i
\(131\) 7.76745 + 13.4536i 0.678645 + 1.17545i 0.975389 + 0.220491i \(0.0707659\pi\)
−0.296744 + 0.954957i \(0.595901\pi\)
\(132\) 0 0
\(133\) 0.275375 0.476964i 0.0238781 0.0413580i
\(134\) 4.58126 0.395761
\(135\) 0 0
\(136\) −4.98162 −0.427170
\(137\) −6.00370 + 10.3987i −0.512930 + 0.888421i 0.486957 + 0.873426i \(0.338107\pi\)
−0.999888 + 0.0149956i \(0.995227\pi\)
\(138\) 0 0
\(139\) −3.07256 5.32183i −0.260611 0.451392i 0.705793 0.708418i \(-0.250591\pi\)
−0.966404 + 0.257026i \(0.917257\pi\)
\(140\) −2.67093 4.62619i −0.225735 0.390985i
\(141\) 0 0
\(142\) −1.26391 + 2.18915i −0.106065 + 0.183709i
\(143\) 0.0941785 0.00787561
\(144\) 0 0
\(145\) −17.2945 −1.43623
\(146\) −0.113624 + 0.196803i −0.00940362 + 0.0162876i
\(147\) 0 0
\(148\) 4.04287 + 7.00246i 0.332322 + 0.575599i
\(149\) −0.441410 0.764545i −0.0361617 0.0626340i 0.847378 0.530990i \(-0.178180\pi\)
−0.883540 + 0.468356i \(0.844846\pi\)
\(150\) 0 0
\(151\) −4.11274 + 7.12347i −0.334690 + 0.579700i −0.983425 0.181314i \(-0.941965\pi\)
0.648735 + 0.761014i \(0.275298\pi\)
\(152\) 0.663653 0.0538294
\(153\) 0 0
\(154\) −2.85929 −0.230408
\(155\) −4.13095 + 7.15502i −0.331806 + 0.574705i
\(156\) 0 0
\(157\) −6.27991 10.8771i −0.501192 0.868089i −0.999999 0.00137640i \(-0.999562\pi\)
0.498808 0.866713i \(-0.333771\pi\)
\(158\) 0.101611 + 0.175996i 0.00808377 + 0.0140015i
\(159\) 0 0
\(160\) 4.90028 8.48753i 0.387401 0.670998i
\(161\) 1.36501 0.107578
\(162\) 0 0
\(163\) 3.31466 0.259624 0.129812 0.991539i \(-0.458563\pi\)
0.129812 + 0.991539i \(0.458563\pi\)
\(164\) −3.35777 + 5.81583i −0.262198 + 0.454140i
\(165\) 0 0
\(166\) 0.958412 + 1.66002i 0.0743872 + 0.128842i
\(167\) 10.2815 + 17.8081i 0.795606 + 1.37803i 0.922454 + 0.386107i \(0.126180\pi\)
−0.126848 + 0.991922i \(0.540486\pi\)
\(168\) 0 0
\(169\) 6.49984 11.2580i 0.499987 0.866004i
\(170\) 2.88322 0.221133
\(171\) 0 0
\(172\) 15.1817 1.15759
\(173\) −7.01663 + 12.1532i −0.533465 + 0.923988i 0.465771 + 0.884905i \(0.345777\pi\)
−0.999236 + 0.0390830i \(0.987556\pi\)
\(174\) 0 0
\(175\) −0.0613281 0.106223i −0.00463597 0.00802974i
\(176\) 7.80745 + 13.5229i 0.588509 + 1.01933i
\(177\) 0 0
\(178\) −0.700697 + 1.21364i −0.0525195 + 0.0909664i
\(179\) 10.1900 0.761636 0.380818 0.924650i \(-0.375642\pi\)
0.380818 + 0.924650i \(0.375642\pi\)
\(180\) 0 0
\(181\) 24.0547 1.78797 0.893987 0.448093i \(-0.147897\pi\)
0.893987 + 0.448093i \(0.147897\pi\)
\(182\) 0.00495039 0.00857433i 0.000366948 0.000635572i
\(183\) 0 0
\(184\) 0.822415 + 1.42446i 0.0606292 + 0.105013i
\(185\) −4.90083 8.48849i −0.360316 0.624086i
\(186\) 0 0
\(187\) −8.16906 + 14.1492i −0.597381 + 1.03469i
\(188\) 12.9706 0.945981
\(189\) 0 0
\(190\) −0.384104 −0.0278658
\(191\) −5.47318 + 9.47983i −0.396026 + 0.685937i −0.993232 0.116151i \(-0.962944\pi\)
0.597206 + 0.802088i \(0.296278\pi\)
\(192\) 0 0
\(193\) 5.40298 + 9.35824i 0.388915 + 0.673621i 0.992304 0.123826i \(-0.0395166\pi\)
−0.603389 + 0.797447i \(0.706183\pi\)
\(194\) 2.06515 + 3.57694i 0.148269 + 0.256810i
\(195\) 0 0
\(196\) −4.80473 + 8.32204i −0.343195 + 0.594431i
\(197\) −22.0734 −1.57266 −0.786331 0.617806i \(-0.788022\pi\)
−0.786331 + 0.617806i \(0.788022\pi\)
\(198\) 0 0
\(199\) 12.8868 0.913518 0.456759 0.889590i \(-0.349010\pi\)
0.456759 + 0.889590i \(0.349010\pi\)
\(200\) 0.0739003 0.127999i 0.00522554 0.00905090i
\(201\) 0 0
\(202\) 2.86661 + 4.96512i 0.201694 + 0.349344i
\(203\) −5.15132 8.92235i −0.361552 0.626226i
\(204\) 0 0
\(205\) 4.07034 7.05003i 0.284285 0.492396i
\(206\) −1.89665 −0.132146
\(207\) 0 0
\(208\) −0.0540694 −0.00374904
\(209\) 1.08829 1.88497i 0.0752783 0.130386i
\(210\) 0 0
\(211\) 11.9978 + 20.7808i 0.825964 + 1.43061i 0.901181 + 0.433444i \(0.142702\pi\)
−0.0752168 + 0.997167i \(0.523965\pi\)
\(212\) −1.18833 2.05824i −0.0816146 0.141361i
\(213\) 0 0
\(214\) −2.34665 + 4.06452i −0.160414 + 0.277845i
\(215\) −18.4035 −1.25511
\(216\) 0 0
\(217\) −4.92177 −0.334112
\(218\) 3.01279 5.21831i 0.204052 0.353428i
\(219\) 0 0
\(220\) −10.5556 18.2828i −0.711655 1.23262i
\(221\) −0.0282868 0.0489942i −0.00190278 0.00329571i
\(222\) 0 0
\(223\) −10.8311 + 18.7600i −0.725303 + 1.25626i 0.233546 + 0.972346i \(0.424967\pi\)
−0.958849 + 0.283916i \(0.908366\pi\)
\(224\) 5.83838 0.390093
\(225\) 0 0
\(226\) −5.21760 −0.347070
\(227\) −10.8209 + 18.7424i −0.718211 + 1.24398i 0.243497 + 0.969902i \(0.421705\pi\)
−0.961708 + 0.274076i \(0.911628\pi\)
\(228\) 0 0
\(229\) 5.40268 + 9.35772i 0.357019 + 0.618375i 0.987461 0.157861i \(-0.0504598\pi\)
−0.630442 + 0.776236i \(0.717126\pi\)
\(230\) −0.475991 0.824441i −0.0313859 0.0543620i
\(231\) 0 0
\(232\) 6.20733 10.7514i 0.407531 0.705865i
\(233\) 7.63900 0.500447 0.250224 0.968188i \(-0.419496\pi\)
0.250224 + 0.968188i \(0.419496\pi\)
\(234\) 0 0
\(235\) −15.7232 −1.02567
\(236\) −3.38232 + 5.85835i −0.220170 + 0.381346i
\(237\) 0 0
\(238\) 0.858795 + 1.48748i 0.0556674 + 0.0964188i
\(239\) 1.61575 + 2.79855i 0.104514 + 0.181023i 0.913540 0.406750i \(-0.133338\pi\)
−0.809026 + 0.587773i \(0.800005\pi\)
\(240\) 0 0
\(241\) 13.2725 22.9886i 0.854955 1.48083i −0.0217316 0.999764i \(-0.506918\pi\)
0.876687 0.481062i \(-0.159749\pi\)
\(242\) −6.72979 −0.432608
\(243\) 0 0
\(244\) −12.6350 −0.808873
\(245\) 5.82437 10.0881i 0.372105 0.644505i
\(246\) 0 0
\(247\) 0.00376838 + 0.00652703i 0.000239776 + 0.000415305i
\(248\) −2.96536 5.13616i −0.188301 0.326147i
\(249\) 0 0
\(250\) −2.34361 + 4.05925i −0.148223 + 0.256730i
\(251\) −4.49930 −0.283993 −0.141997 0.989867i \(-0.545352\pi\)
−0.141997 + 0.989867i \(0.545352\pi\)
\(252\) 0 0
\(253\) 5.39452 0.339150
\(254\) −1.74392 + 3.02055i −0.109423 + 0.189526i
\(255\) 0 0
\(256\) −1.95380 3.38409i −0.122113 0.211506i
\(257\) −6.86771 11.8952i −0.428396 0.742003i 0.568335 0.822797i \(-0.307588\pi\)
−0.996731 + 0.0807940i \(0.974254\pi\)
\(258\) 0 0
\(259\) 2.91952 5.05676i 0.181410 0.314211i
\(260\) 0.0731010 0.00453353
\(261\) 0 0
\(262\) 6.45423 0.398743
\(263\) 12.1013 20.9600i 0.746197 1.29245i −0.203437 0.979088i \(-0.565211\pi\)
0.949634 0.313363i \(-0.101456\pi\)
\(264\) 0 0
\(265\) 1.44051 + 2.49503i 0.0884897 + 0.153269i
\(266\) −0.114409 0.198162i −0.00701487 0.0121501i
\(267\) 0 0
\(268\) −10.0751 + 17.4506i −0.615436 + 1.06597i
\(269\) 12.0062 0.732032 0.366016 0.930609i \(-0.380722\pi\)
0.366016 + 0.930609i \(0.380722\pi\)
\(270\) 0 0
\(271\) 3.71777 0.225839 0.112919 0.993604i \(-0.463980\pi\)
0.112919 + 0.993604i \(0.463980\pi\)
\(272\) 4.68999 8.12329i 0.284372 0.492547i
\(273\) 0 0
\(274\) 2.49433 + 4.32031i 0.150688 + 0.261000i
\(275\) −0.242369 0.419796i −0.0146154 0.0253146i
\(276\) 0 0
\(277\) 11.7416 20.3370i 0.705482 1.22193i −0.261035 0.965329i \(-0.584064\pi\)
0.966517 0.256601i \(-0.0826027\pi\)
\(278\) −2.55309 −0.153124
\(279\) 0 0
\(280\) −4.64837 −0.277793
\(281\) 10.1859 17.6424i 0.607638 1.05246i −0.383991 0.923337i \(-0.625451\pi\)
0.991629 0.129123i \(-0.0412162\pi\)
\(282\) 0 0
\(283\) −5.79997 10.0458i −0.344772 0.597163i 0.640540 0.767925i \(-0.278711\pi\)
−0.985312 + 0.170761i \(0.945377\pi\)
\(284\) −5.55917 9.62876i −0.329876 0.571362i
\(285\) 0 0
\(286\) 0.0195640 0.0338858i 0.00115684 0.00200371i
\(287\) 4.84956 0.286260
\(288\) 0 0
\(289\) −7.18559 −0.422682
\(290\) −3.59263 + 6.22262i −0.210967 + 0.365405i
\(291\) 0 0
\(292\) −0.499766 0.865620i −0.0292466 0.0506566i
\(293\) −15.7871 27.3440i −0.922291 1.59745i −0.795861 0.605479i \(-0.792981\pi\)
−0.126430 0.991976i \(-0.540352\pi\)
\(294\) 0 0
\(295\) 4.10010 7.10158i 0.238717 0.413470i
\(296\) 7.03603 0.408961
\(297\) 0 0
\(298\) −0.366782 −0.0212471
\(299\) −0.00933974 + 0.0161769i −0.000540131 + 0.000935535i
\(300\) 0 0
\(301\) −5.48166 9.49451i −0.315957 0.547254i
\(302\) 1.70870 + 2.95956i 0.0983248 + 0.170304i
\(303\) 0 0
\(304\) −0.624802 + 1.08219i −0.0358348 + 0.0620678i
\(305\) 15.3163 0.877010
\(306\) 0 0
\(307\) −8.12054 −0.463464 −0.231732 0.972780i \(-0.574439\pi\)
−0.231732 + 0.972780i \(0.574439\pi\)
\(308\) 6.28814 10.8914i 0.358300 0.620594i
\(309\) 0 0
\(310\) 1.71627 + 2.97267i 0.0974776 + 0.168836i
\(311\) 11.9243 + 20.6535i 0.676164 + 1.17115i 0.976127 + 0.217199i \(0.0696922\pi\)
−0.299963 + 0.953951i \(0.596974\pi\)
\(312\) 0 0
\(313\) −13.4552 + 23.3051i −0.760535 + 1.31728i 0.182040 + 0.983291i \(0.441730\pi\)
−0.942575 + 0.333994i \(0.891604\pi\)
\(314\) −5.21818 −0.294479
\(315\) 0 0
\(316\) −0.893856 −0.0502833
\(317\) 4.16617 7.21601i 0.233995 0.405292i −0.724985 0.688765i \(-0.758153\pi\)
0.958980 + 0.283473i \(0.0914867\pi\)
\(318\) 0 0
\(319\) −20.3581 35.2612i −1.13983 1.97425i
\(320\) 4.59664 + 7.96161i 0.256960 + 0.445068i
\(321\) 0 0
\(322\) 0.283557 0.491135i 0.0158020 0.0273699i
\(323\) −1.30748 −0.0727501
\(324\) 0 0
\(325\) 0.00167849 9.31061e−5
\(326\) 0.688565 1.19263i 0.0381361 0.0660536i
\(327\) 0 0
\(328\) 2.92185 + 5.06080i 0.161332 + 0.279436i
\(329\) −4.68330 8.11172i −0.258199 0.447214i
\(330\) 0 0
\(331\) 3.21013 5.56011i 0.176445 0.305611i −0.764216 0.644961i \(-0.776874\pi\)
0.940660 + 0.339350i \(0.110207\pi\)
\(332\) −8.43096 −0.462709
\(333\) 0 0
\(334\) 8.54322 0.467464
\(335\) 12.2132 21.1539i 0.667279 1.15576i
\(336\) 0 0
\(337\) −3.73745 6.47345i −0.203592 0.352631i 0.746091 0.665844i \(-0.231928\pi\)
−0.949683 + 0.313212i \(0.898595\pi\)
\(338\) −2.70046 4.67734i −0.146886 0.254414i
\(339\) 0 0
\(340\) −6.34079 + 10.9826i −0.343877 + 0.595613i
\(341\) −19.4509 −1.05333
\(342\) 0 0
\(343\) 16.1768 0.873464
\(344\) 6.60538 11.4409i 0.356138 0.616850i
\(345\) 0 0
\(346\) 2.91517 + 5.04923i 0.156721 + 0.271448i
\(347\) 15.7272 + 27.2404i 0.844283 + 1.46234i 0.886243 + 0.463222i \(0.153307\pi\)
−0.0419596 + 0.999119i \(0.513360\pi\)
\(348\) 0 0
\(349\) −5.92647 + 10.2650i −0.317237 + 0.549470i −0.979910 0.199438i \(-0.936088\pi\)
0.662674 + 0.748908i \(0.269422\pi\)
\(350\) −0.0509595 −0.00272390
\(351\) 0 0
\(352\) 23.0733 1.22981
\(353\) 4.10354 7.10754i 0.218409 0.378296i −0.735912 0.677077i \(-0.763246\pi\)
0.954322 + 0.298780i \(0.0965798\pi\)
\(354\) 0 0
\(355\) 6.73891 + 11.6721i 0.357664 + 0.619492i
\(356\) −3.08195 5.33809i −0.163343 0.282918i
\(357\) 0 0
\(358\) 2.11680 3.66640i 0.111876 0.193775i
\(359\) 17.7273 0.935611 0.467806 0.883831i \(-0.345045\pi\)
0.467806 + 0.883831i \(0.345045\pi\)
\(360\) 0 0
\(361\) −18.8258 −0.990832
\(362\) 4.99696 8.65499i 0.262635 0.454896i
\(363\) 0 0
\(364\) 0.0217738 + 0.0377134i 0.00114126 + 0.00197672i
\(365\) 0.605824 + 1.04932i 0.0317103 + 0.0549238i
\(366\) 0 0
\(367\) 10.1598 17.5972i 0.530335 0.918568i −0.469038 0.883178i \(-0.655399\pi\)
0.999374 0.0353899i \(-0.0112673\pi\)
\(368\) −3.09708 −0.161446
\(369\) 0 0
\(370\) −4.07226 −0.211707
\(371\) −0.858138 + 1.48634i −0.0445523 + 0.0771668i
\(372\) 0 0
\(373\) 4.84072 + 8.38437i 0.250643 + 0.434126i 0.963703 0.266977i \(-0.0860247\pi\)
−0.713060 + 0.701103i \(0.752691\pi\)
\(374\) 3.39397 + 5.87852i 0.175498 + 0.303971i
\(375\) 0 0
\(376\) 5.64337 9.77461i 0.291035 0.504087i
\(377\) 0.140987 0.00726119
\(378\) 0 0
\(379\) −4.12905 −0.212095 −0.106048 0.994361i \(-0.533820\pi\)
−0.106048 + 0.994361i \(0.533820\pi\)
\(380\) 0.844722 1.46310i 0.0433333 0.0750555i
\(381\) 0 0
\(382\) 2.27392 + 3.93855i 0.116344 + 0.201514i
\(383\) −2.37509 4.11378i −0.121362 0.210204i 0.798943 0.601406i \(-0.205393\pi\)
−0.920305 + 0.391202i \(0.872059\pi\)
\(384\) 0 0
\(385\) −7.62258 + 13.2027i −0.388483 + 0.672872i
\(386\) 4.48951 0.228510
\(387\) 0 0
\(388\) −18.1667 −0.922275
\(389\) 10.9067 18.8909i 0.552990 0.957806i −0.445067 0.895497i \(-0.646820\pi\)
0.998057 0.0623089i \(-0.0198464\pi\)
\(390\) 0 0
\(391\) −1.62026 2.80637i −0.0819401 0.141924i
\(392\) 4.18097 + 7.24165i 0.211171 + 0.365758i
\(393\) 0 0
\(394\) −4.58537 + 7.94209i −0.231007 + 0.400117i
\(395\) 1.08355 0.0545191
\(396\) 0 0
\(397\) −34.8490 −1.74902 −0.874512 0.485005i \(-0.838818\pi\)
−0.874512 + 0.485005i \(0.838818\pi\)
\(398\) 2.67701 4.63671i 0.134186 0.232417i
\(399\) 0 0
\(400\) 0.139148 + 0.241012i 0.00695740 + 0.0120506i
\(401\) 9.41304 + 16.3039i 0.470065 + 0.814176i 0.999414 0.0342279i \(-0.0108972\pi\)
−0.529349 + 0.848404i \(0.677564\pi\)
\(402\) 0 0
\(403\) 0.0336761 0.0583287i 0.00167753 0.00290556i
\(404\) −25.2170 −1.25459
\(405\) 0 0
\(406\) −4.28040 −0.212433
\(407\) 11.5380 19.9843i 0.571916 0.990587i
\(408\) 0 0
\(409\) 3.17998 + 5.50788i 0.157240 + 0.272347i 0.933872 0.357607i \(-0.116407\pi\)
−0.776633 + 0.629954i \(0.783074\pi\)
\(410\) −1.69109 2.92905i −0.0835169 0.144656i
\(411\) 0 0
\(412\) 4.17112 7.22459i 0.205496 0.355930i
\(413\) 4.88502 0.240376
\(414\) 0 0
\(415\) 10.2201 0.501687
\(416\) −0.0399478 + 0.0691916i −0.00195860 + 0.00339240i
\(417\) 0 0
\(418\) −0.452146 0.783139i −0.0221152 0.0383046i
\(419\) 12.1590 + 21.0600i 0.594005 + 1.02885i 0.993686 + 0.112193i \(0.0357875\pi\)
−0.399681 + 0.916654i \(0.630879\pi\)
\(420\) 0 0
\(421\) 3.99502 6.91957i 0.194705 0.337239i −0.752099 0.659051i \(-0.770958\pi\)
0.946804 + 0.321811i \(0.104292\pi\)
\(422\) 9.96937 0.485302
\(423\) 0 0
\(424\) −2.06811 −0.100436
\(425\) −0.145593 + 0.252174i −0.00706229 + 0.0122322i
\(426\) 0 0
\(427\) 4.56211 + 7.90181i 0.220776 + 0.382396i
\(428\) −10.3215 17.8774i −0.498909 0.864136i
\(429\) 0 0
\(430\) −3.82301 + 6.62166i −0.184362 + 0.319325i
\(431\) 9.87124 0.475481 0.237740 0.971329i \(-0.423593\pi\)
0.237740 + 0.971329i \(0.423593\pi\)
\(432\) 0 0
\(433\) −6.10369 −0.293325 −0.146662 0.989187i \(-0.546853\pi\)
−0.146662 + 0.989187i \(0.546853\pi\)
\(434\) −1.02242 + 1.77088i −0.0490775 + 0.0850047i
\(435\) 0 0
\(436\) 13.2515 + 22.9522i 0.634630 + 1.09921i
\(437\) 0.215852 + 0.373866i 0.0103256 + 0.0178844i
\(438\) 0 0
\(439\) 7.56701 13.1064i 0.361154 0.625537i −0.626997 0.779021i \(-0.715716\pi\)
0.988151 + 0.153485i \(0.0490496\pi\)
\(440\) −18.3704 −0.875774
\(441\) 0 0
\(442\) −0.0235044 −0.00111799
\(443\) 0.361397 0.625957i 0.0171705 0.0297401i −0.857312 0.514796i \(-0.827868\pi\)
0.874483 + 0.485056i \(0.161201\pi\)
\(444\) 0 0
\(445\) 3.73598 + 6.47092i 0.177103 + 0.306751i
\(446\) 4.49995 + 7.79414i 0.213079 + 0.369063i
\(447\) 0 0
\(448\) −2.73831 + 4.74288i −0.129373 + 0.224080i
\(449\) 1.66845 0.0787389 0.0393695 0.999225i \(-0.487465\pi\)
0.0393695 + 0.999225i \(0.487465\pi\)
\(450\) 0 0
\(451\) 19.1655 0.902468
\(452\) 11.4746 19.8745i 0.539718 0.934819i
\(453\) 0 0
\(454\) 4.49573 + 7.78684i 0.210995 + 0.365455i
\(455\) −0.0263946 0.0457167i −0.00123740 0.00214323i
\(456\) 0 0
\(457\) −5.54172 + 9.59855i −0.259231 + 0.449001i −0.966036 0.258407i \(-0.916802\pi\)
0.706805 + 0.707408i \(0.250136\pi\)
\(458\) 4.48926 0.209769
\(459\) 0 0
\(460\) 4.18720 0.195229
\(461\) 10.9422 18.9524i 0.509629 0.882703i −0.490309 0.871549i \(-0.663116\pi\)
0.999938 0.0111543i \(-0.00355060\pi\)
\(462\) 0 0
\(463\) −12.4259 21.5222i −0.577479 1.00022i −0.995767 0.0919086i \(-0.970703\pi\)
0.418289 0.908314i \(-0.362630\pi\)
\(464\) 11.6879 + 20.2440i 0.542597 + 0.939805i
\(465\) 0 0
\(466\) 1.58687 2.74854i 0.0735105 0.127324i
\(467\) −11.8355 −0.547683 −0.273842 0.961775i \(-0.588294\pi\)
−0.273842 + 0.961775i \(0.588294\pi\)
\(468\) 0 0
\(469\) 14.5513 0.671916
\(470\) −3.26623 + 5.65727i −0.150660 + 0.260951i
\(471\) 0 0
\(472\) 2.94322 + 5.09780i 0.135473 + 0.234645i
\(473\) −21.6636 37.5224i −0.996091 1.72528i
\(474\) 0 0
\(475\) 0.0193959 0.0335947i 0.000889946 0.00154143i
\(476\) −7.55465 −0.346267
\(477\) 0 0
\(478\) 1.34258 0.0614080
\(479\) −1.44368 + 2.50052i −0.0659632 + 0.114252i −0.897121 0.441785i \(-0.854345\pi\)
0.831158 + 0.556037i \(0.187679\pi\)
\(480\) 0 0
\(481\) 0.0399523 + 0.0691994i 0.00182167 + 0.00315522i
\(482\) −5.51426 9.55099i −0.251168 0.435035i
\(483\) 0 0
\(484\) 14.8002 25.6347i 0.672735 1.16521i
\(485\) 22.0220 0.999966
\(486\) 0 0
\(487\) 8.75903 0.396910 0.198455 0.980110i \(-0.436408\pi\)
0.198455 + 0.980110i \(0.436408\pi\)
\(488\) −5.49734 + 9.52167i −0.248853 + 0.431026i
\(489\) 0 0
\(490\) −2.41983 4.19127i −0.109317 0.189342i
\(491\) 11.2865 + 19.5488i 0.509354 + 0.882226i 0.999941 + 0.0108346i \(0.00344882\pi\)
−0.490588 + 0.871392i \(0.663218\pi\)
\(492\) 0 0
\(493\) −12.2292 + 21.1816i −0.550776 + 0.953972i
\(494\) 0.00313127 0.000140883
\(495\) 0 0
\(496\) 11.1671 0.501416
\(497\) −4.01449 + 6.95331i −0.180075 + 0.311899i
\(498\) 0 0
\(499\) 12.6664 + 21.9389i 0.567026 + 0.982118i 0.996858 + 0.0792092i \(0.0252395\pi\)
−0.429832 + 0.902909i \(0.641427\pi\)
\(500\) −10.3081 17.8542i −0.460994 0.798465i
\(501\) 0 0
\(502\) −0.934653 + 1.61887i −0.0417156 + 0.0722536i
\(503\) 3.74414 0.166943 0.0834714 0.996510i \(-0.473399\pi\)
0.0834714 + 0.996510i \(0.473399\pi\)
\(504\) 0 0
\(505\) 30.5684 1.36028
\(506\) 1.12062 1.94097i 0.0498176 0.0862867i
\(507\) 0 0
\(508\) −7.67045 13.2856i −0.340321 0.589454i
\(509\) −12.1749 21.0876i −0.539645 0.934692i −0.998923 0.0463997i \(-0.985225\pi\)
0.459278 0.888292i \(-0.348108\pi\)
\(510\) 0 0
\(511\) −0.360901 + 0.625098i −0.0159653 + 0.0276527i
\(512\) −22.7690 −1.00626
\(513\) 0 0
\(514\) −5.70660 −0.251707
\(515\) −5.05630 + 8.75776i −0.222807 + 0.385913i
\(516\) 0 0
\(517\) −18.5085 32.0576i −0.814001 1.40989i
\(518\) −1.21296 2.10091i −0.0532945 0.0923087i
\(519\) 0 0
\(520\) 0.0318054 0.0550885i 0.00139476 0.00241579i
\(521\) 19.6209 0.859608 0.429804 0.902922i \(-0.358583\pi\)
0.429804 + 0.902922i \(0.358583\pi\)
\(522\) 0 0
\(523\) 20.8154 0.910194 0.455097 0.890442i \(-0.349605\pi\)
0.455097 + 0.890442i \(0.349605\pi\)
\(524\) −14.1941 + 24.5850i −0.620074 + 1.07400i
\(525\) 0 0
\(526\) −5.02767 8.70819i −0.219217 0.379695i
\(527\) 5.84214 + 10.1189i 0.254488 + 0.440785i
\(528\) 0 0
\(529\) 10.9650 18.9920i 0.476740 0.825738i
\(530\) 1.19696 0.0519928
\(531\) 0 0
\(532\) 1.00643 0.0436345
\(533\) −0.0331820 + 0.0574729i −0.00143727 + 0.00248943i
\(534\) 0 0
\(535\) 12.5119 + 21.6712i 0.540936 + 0.936929i
\(536\) 8.76713 + 15.1851i 0.378682 + 0.655897i
\(537\) 0 0
\(538\) 2.49409 4.31989i 0.107528 0.186244i
\(539\) 27.4245 1.18126
\(540\) 0 0
\(541\) −30.6272 −1.31676 −0.658382 0.752684i \(-0.728759\pi\)
−0.658382 + 0.752684i \(0.728759\pi\)
\(542\) 0.772305 1.33767i 0.0331733 0.0574579i
\(543\) 0 0
\(544\) −6.93015 12.0034i −0.297128 0.514640i
\(545\) −16.0636 27.8230i −0.688090 1.19181i
\(546\) 0 0
\(547\) −11.3238 + 19.6135i −0.484172 + 0.838611i −0.999835 0.0181808i \(-0.994213\pi\)
0.515662 + 0.856792i \(0.327546\pi\)
\(548\) −21.9422 −0.937323
\(549\) 0 0
\(550\) −0.201393 −0.00858741
\(551\) 1.62918 2.82182i 0.0694055 0.120214i
\(552\) 0 0
\(553\) 0.322744 + 0.559010i 0.0137245 + 0.0237715i
\(554\) −4.87822 8.44933i −0.207256 0.358978i
\(555\) 0 0
\(556\) 5.61476 9.72504i 0.238119 0.412434i
\(557\) 36.4518 1.54451 0.772256 0.635311i \(-0.219128\pi\)
0.772256 + 0.635311i \(0.219128\pi\)
\(558\) 0 0
\(559\) 0.150028 0.00634550
\(560\) 4.37625 7.57988i 0.184930 0.320308i
\(561\) 0 0
\(562\) −4.23188 7.32984i −0.178511 0.309191i
\(563\) −13.2581 22.9637i −0.558763 0.967806i −0.997600 0.0692393i \(-0.977943\pi\)
0.438837 0.898567i \(-0.355391\pi\)
\(564\) 0 0
\(565\) −13.9096 + 24.0922i −0.585183 + 1.01357i
\(566\) −4.81938 −0.202574
\(567\) 0 0
\(568\) −9.67492 −0.405950
\(569\) −11.4837 + 19.8904i −0.481422 + 0.833847i −0.999773 0.0213210i \(-0.993213\pi\)
0.518351 + 0.855168i \(0.326546\pi\)
\(570\) 0 0
\(571\) 2.39900 + 4.15519i 0.100395 + 0.173889i 0.911848 0.410529i \(-0.134656\pi\)
−0.811452 + 0.584419i \(0.801323\pi\)
\(572\) 0.0860504 + 0.149044i 0.00359795 + 0.00623183i
\(573\) 0 0
\(574\) 1.00741 1.74489i 0.0420486 0.0728304i
\(575\) 0.0961436 0.00400947
\(576\) 0 0
\(577\) −4.31333 −0.179566 −0.0897831 0.995961i \(-0.528617\pi\)
−0.0897831 + 0.995961i \(0.528617\pi\)
\(578\) −1.49269 + 2.58541i −0.0620876 + 0.107539i
\(579\) 0 0
\(580\) −15.8018 27.3696i −0.656136 1.13646i
\(581\) 3.04417 + 5.27265i 0.126293 + 0.218746i
\(582\) 0 0
\(583\) −3.39137 + 5.87402i −0.140456 + 0.243277i
\(584\) −0.869769 −0.0359913
\(585\) 0 0
\(586\) −13.1180 −0.541899
\(587\) −20.9111 + 36.2191i −0.863094 + 1.49492i 0.00583407 + 0.999983i \(0.498143\pi\)
−0.868928 + 0.494939i \(0.835190\pi\)
\(588\) 0 0
\(589\) −0.778292 1.34804i −0.0320690 0.0555451i
\(590\) −1.70345 2.95047i −0.0701301 0.121469i
\(591\) 0 0
\(592\) −6.62413 + 11.4733i −0.272250 + 0.471551i
\(593\) −31.5370 −1.29507 −0.647536 0.762035i \(-0.724200\pi\)
−0.647536 + 0.762035i \(0.724200\pi\)
\(594\) 0 0
\(595\) 9.15786 0.375436
\(596\) 0.806628 1.39712i 0.0330408 0.0572283i
\(597\) 0 0
\(598\) 0.00388035 + 0.00672096i 0.000158679 + 0.000274840i
\(599\) 6.31515 + 10.9382i 0.258030 + 0.446921i 0.965714 0.259608i \(-0.0835933\pi\)
−0.707684 + 0.706529i \(0.750260\pi\)
\(600\) 0 0
\(601\) −10.2715 + 17.7907i −0.418983 + 0.725699i −0.995837 0.0911474i \(-0.970947\pi\)
0.576855 + 0.816847i \(0.304280\pi\)
\(602\) −4.55489 −0.185643
\(603\) 0 0
\(604\) −15.0311 −0.611608
\(605\) −17.9410 + 31.0747i −0.729405 + 1.26337i
\(606\) 0 0
\(607\) −6.45628 11.1826i −0.262052 0.453888i 0.704735 0.709471i \(-0.251066\pi\)
−0.966787 + 0.255583i \(0.917733\pi\)
\(608\) 0.923237 + 1.59909i 0.0374422 + 0.0648518i
\(609\) 0 0
\(610\) 3.18171 5.51088i 0.128824 0.223129i
\(611\) 0.128178 0.00518552
\(612\) 0 0
\(613\) −31.1598 −1.25853 −0.629265 0.777191i \(-0.716644\pi\)
−0.629265 + 0.777191i \(0.716644\pi\)
\(614\) −1.68690 + 2.92180i −0.0680779 + 0.117914i
\(615\) 0 0
\(616\) −5.47180 9.47743i −0.220465 0.381857i
\(617\) 3.57039 + 6.18410i 0.143739 + 0.248962i 0.928902 0.370327i \(-0.120754\pi\)
−0.785163 + 0.619289i \(0.787421\pi\)
\(618\) 0 0
\(619\) 5.01545 8.68702i 0.201588 0.349161i −0.747452 0.664316i \(-0.768723\pi\)
0.949040 + 0.315155i \(0.102056\pi\)
\(620\) −15.0977 −0.606338
\(621\) 0 0
\(622\) 9.90827 0.397285
\(623\) −2.22560 + 3.85485i −0.0891667 + 0.154441i
\(624\) 0 0
\(625\) 12.2633 + 21.2407i 0.490532 + 0.849627i
\(626\) 5.59020 + 9.68250i 0.223429 + 0.386991i
\(627\) 0 0
\(628\) 11.4758 19.8767i 0.457936 0.793168i
\(629\) −13.8619 −0.552708
\(630\) 0 0
\(631\) −7.07560 −0.281675 −0.140838 0.990033i \(-0.544980\pi\)
−0.140838 + 0.990033i \(0.544980\pi\)
\(632\) −0.388906 + 0.673606i −0.0154699 + 0.0267946i
\(633\) 0 0
\(634\) −1.73090 2.99801i −0.0687429 0.119066i
\(635\) 9.29823 + 16.1050i 0.368989 + 0.639108i
\(636\) 0 0
\(637\) −0.0474811 + 0.0822396i −0.00188127 + 0.00325845i
\(638\) −16.9162 −0.669718
\(639\) 0 0
\(640\) 23.4206 0.925781
\(641\) 2.50561 4.33984i 0.0989655 0.171413i −0.812291 0.583252i \(-0.801780\pi\)
0.911257 + 0.411839i \(0.135113\pi\)
\(642\) 0 0
\(643\) −0.819202 1.41890i −0.0323062 0.0559559i 0.849420 0.527717i \(-0.176952\pi\)
−0.881726 + 0.471761i \(0.843618\pi\)
\(644\) 1.24720 + 2.16021i 0.0491465 + 0.0851242i
\(645\) 0 0
\(646\) −0.271607 + 0.470437i −0.0106862 + 0.0185091i
\(647\) 34.4927 1.35605 0.678024 0.735040i \(-0.262836\pi\)
0.678024 + 0.735040i \(0.262836\pi\)
\(648\) 0 0
\(649\) 19.3056 0.757813
\(650\) 0.000348679 0 0.000603929i 1.36763e−5 0 2.36881e-5i
\(651\) 0 0
\(652\) 3.02858 + 5.24566i 0.118609 + 0.205436i
\(653\) −19.3803 33.5677i −0.758410 1.31360i −0.943661 0.330913i \(-0.892643\pi\)
0.185252 0.982691i \(-0.440690\pi\)
\(654\) 0 0
\(655\) 17.2064 29.8023i 0.672308 1.16447i
\(656\) −11.0032 −0.429604
\(657\) 0 0
\(658\) −3.89151 −0.151707
\(659\) −4.69596 + 8.13364i −0.182929 + 0.316842i −0.942877 0.333142i \(-0.891891\pi\)
0.759948 + 0.649984i \(0.225224\pi\)
\(660\) 0 0
\(661\) 12.0737 + 20.9123i 0.469613 + 0.813394i 0.999396 0.0347394i \(-0.0110601\pi\)
−0.529783 + 0.848133i \(0.677727\pi\)
\(662\) −1.33370 2.31004i −0.0518357 0.0897821i
\(663\) 0 0
\(664\) −3.66821 + 6.35353i −0.142354 + 0.246565i
\(665\) −1.22001 −0.0473101
\(666\) 0 0
\(667\) 8.07569 0.312692
\(668\) −18.7883 + 32.5422i −0.726940 + 1.25910i
\(669\) 0 0
\(670\) −5.07417 8.78873i −0.196032 0.339538i
\(671\) 18.0295 + 31.2280i 0.696022 + 1.20555i
\(672\) 0 0
\(673\) 13.2331 22.9203i 0.510097 0.883514i −0.489834 0.871816i \(-0.662943\pi\)
0.999932 0.0116988i \(-0.00372393\pi\)
\(674\) −3.10557 −0.119622
\(675\) 0 0
\(676\) 23.7554 0.913671
\(677\) −15.5334 + 26.9047i −0.596998 + 1.03403i 0.396264 + 0.918137i \(0.370307\pi\)
−0.993262 + 0.115894i \(0.963027\pi\)
\(678\) 0 0
\(679\) 6.55945 + 11.3613i 0.251729 + 0.436007i
\(680\) 5.51760 + 9.55677i 0.211590 + 0.366485i
\(681\) 0 0
\(682\) −4.04060 + 6.99852i −0.154722 + 0.267987i
\(683\) 38.1361 1.45924 0.729619 0.683854i \(-0.239697\pi\)
0.729619 + 0.683854i \(0.239697\pi\)
\(684\) 0 0
\(685\) 26.5986 1.01628
\(686\) 3.36045 5.82047i 0.128303 0.222227i
\(687\) 0 0
\(688\) 12.4374 + 21.5422i 0.474171 + 0.821288i
\(689\) −0.0117432 0.0203399i −0.000447381 0.000774887i
\(690\) 0 0
\(691\) −16.4648 + 28.5178i −0.626349 + 1.08487i 0.361929 + 0.932206i \(0.382118\pi\)
−0.988278 + 0.152663i \(0.951215\pi\)
\(692\) −25.6442 −0.974847
\(693\) 0 0
\(694\) 13.0683 0.496065
\(695\) −6.80629 + 11.7888i −0.258177 + 0.447176i
\(696\) 0 0
\(697\) −5.75642 9.97041i −0.218040 0.377656i
\(698\) 2.46225 + 4.26474i 0.0931975 + 0.161423i
\(699\) 0 0
\(700\) 0.112070 0.194111i 0.00423586 0.00733672i
\(701\) −2.30710 −0.0871381 −0.0435690 0.999050i \(-0.513873\pi\)
−0.0435690 + 0.999050i \(0.513873\pi\)
\(702\) 0 0
\(703\) 1.84668 0.0696490
\(704\) −10.8218 + 18.7439i −0.407862 + 0.706438i
\(705\) 0 0
\(706\) −1.70488 2.95294i −0.0641641 0.111136i
\(707\) 9.10510 + 15.7705i 0.342433 + 0.593111i
\(708\) 0 0
\(709\) 5.57603 9.65797i 0.209412 0.362713i −0.742117 0.670270i \(-0.766178\pi\)
0.951530 + 0.307557i \(0.0995116\pi\)
\(710\) 5.59958 0.210148
\(711\) 0 0
\(712\) −5.36368 −0.201012
\(713\) 1.92896 3.34105i 0.0722400 0.125123i
\(714\) 0 0
\(715\) −0.104312 0.180673i −0.00390103 0.00675678i
\(716\) 9.31053 + 16.1263i 0.347951 + 0.602669i
\(717\) 0 0
\(718\) 3.68255 6.37836i 0.137431 0.238038i
\(719\) −32.1700 −1.19974 −0.599869 0.800098i \(-0.704781\pi\)
−0.599869 + 0.800098i \(0.704781\pi\)
\(720\) 0 0
\(721\) −6.02426 −0.224355
\(722\) −3.91075 + 6.77361i −0.145543 + 0.252088i
\(723\) 0 0
\(724\) 21.9787 + 38.0681i 0.816830 + 1.41479i
\(725\) −0.362831 0.628442i −0.0134752 0.0233397i
\(726\) 0 0
\(727\) 2.68275 4.64667i 0.0994979 0.172335i −0.811979 0.583687i \(-0.801610\pi\)
0.911477 + 0.411351i \(0.134943\pi\)
\(728\) 0.0378942 0.00140445
\(729\) 0 0
\(730\) 0.503399 0.0186316
\(731\) −13.0134 + 22.5399i −0.481319 + 0.833669i
\(732\) 0 0
\(733\) 7.29818 + 12.6408i 0.269564 + 0.466899i 0.968749 0.248042i \(-0.0797870\pi\)
−0.699185 + 0.714941i \(0.746454\pi\)
\(734\) −4.22104 7.31105i −0.155801 0.269856i
\(735\) 0 0
\(736\) −2.28820 + 3.96327i −0.0843440 + 0.146088i
\(737\) 57.5068 2.11829
\(738\) 0 0
\(739\) −43.2165 −1.58975 −0.794873 0.606776i \(-0.792463\pi\)
−0.794873 + 0.606776i \(0.792463\pi\)
\(740\) 8.95572 15.5118i 0.329219 0.570224i
\(741\) 0 0
\(742\) 0.356527 + 0.617523i 0.0130885 + 0.0226700i
\(743\) −4.05610 7.02538i −0.148804 0.257736i 0.781982 0.623301i \(-0.214209\pi\)
−0.930786 + 0.365565i \(0.880876\pi\)
\(744\) 0 0
\(745\) −0.977806 + 1.69361i −0.0358240 + 0.0620491i
\(746\) 4.02231 0.147267
\(747\) 0 0
\(748\) −29.8561 −1.09165
\(749\) −7.45357 + 12.9100i −0.272348 + 0.471720i
\(750\) 0 0
\(751\) −4.37773 7.58245i −0.159746 0.276687i 0.775031 0.631923i \(-0.217734\pi\)
−0.934777 + 0.355235i \(0.884401\pi\)
\(752\) 10.6260 + 18.4048i 0.387490 + 0.671153i
\(753\) 0 0
\(754\) 0.0292876 0.0507277i 0.00106659 0.00184739i
\(755\) 18.2210 0.663129
\(756\) 0 0
\(757\) −32.1511 −1.16855 −0.584276 0.811555i \(-0.698622\pi\)
−0.584276 + 0.811555i \(0.698622\pi\)
\(758\) −0.857741 + 1.48565i −0.0311546 + 0.0539613i
\(759\) 0 0
\(760\) −0.735058 1.27316i −0.0266633 0.0461823i
\(761\) 12.2730 + 21.2574i 0.444894 + 0.770580i 0.998045 0.0625018i \(-0.0199079\pi\)
−0.553151 + 0.833081i \(0.686575\pi\)
\(762\) 0 0
\(763\) 9.56941 16.5747i 0.346436 0.600045i
\(764\) −20.0033 −0.723693
\(765\) 0 0
\(766\) −1.97354 −0.0713069
\(767\) −0.0334246 + 0.0578931i −0.00120689 + 0.00209040i
\(768\) 0 0
\(769\) −15.7072 27.2057i −0.566416 0.981061i −0.996916 0.0784710i \(-0.974996\pi\)
0.430500 0.902590i \(-0.358337\pi\)
\(770\) 3.16693 + 5.48528i 0.114128 + 0.197676i
\(771\) 0 0
\(772\) −9.87335 + 17.1011i −0.355349 + 0.615483i
\(773\) 28.7145 1.03279 0.516395 0.856351i \(-0.327274\pi\)
0.516395 + 0.856351i \(0.327274\pi\)
\(774\) 0 0
\(775\) −0.346663 −0.0124525
\(776\) −7.90413 + 13.6904i −0.283742 + 0.491455i
\(777\) 0 0
\(778\) −4.53135 7.84853i −0.162457 0.281383i
\(779\) 0.766872 + 1.32826i 0.0274761 + 0.0475899i
\(780\) 0 0
\(781\) −15.8653 + 27.4795i −0.567706 + 0.983295i
\(782\) −1.34633 −0.0481446
\(783\) 0 0
\(784\) −15.7448 −0.562315
\(785\) −13.9112 + 24.0949i