Properties

Label 729.2.e.l.325.2
Level $729$
Weight $2$
Character 729.325
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 325.2
Root \(-1.22778i\) of defining polynomial
Character \(\chi\) \(=\) 729.325
Dual form 729.2.e.l.406.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.20913 - 1.01458i) q^{2} +(0.0853237 - 0.483895i) q^{4} +(1.57728 - 0.574083i) q^{5} +(0.482617 + 2.73706i) q^{7} +(1.19062 + 2.06222i) q^{8} +O(q^{10})\) \(q+(1.20913 - 1.01458i) q^{2} +(0.0853237 - 0.483895i) q^{4} +(1.57728 - 0.574083i) q^{5} +(0.482617 + 2.73706i) q^{7} +(1.19062 + 2.06222i) q^{8} +(1.32468 - 2.29442i) q^{10} +(-3.90087 - 1.41980i) q^{11} +(5.26736 + 4.41984i) q^{13} +(3.36051 + 2.81980i) q^{14} +(4.45535 + 1.62162i) q^{16} +(0.488276 - 0.845718i) q^{17} +(-1.34264 - 2.32553i) q^{19} +(-0.143217 - 0.812221i) q^{20} +(-6.15715 + 2.24102i) q^{22} +(-0.280124 + 1.58866i) q^{23} +(-1.67198 + 1.40296i) q^{25} +10.8532 q^{26} +1.36563 q^{28} +(6.30292 - 5.28878i) q^{29} +(0.181301 - 1.02821i) q^{31} +(2.55707 - 0.930697i) q^{32} +(-0.267660 - 1.51798i) q^{34} +(2.33252 + 4.04005i) q^{35} +(0.654172 - 1.13306i) q^{37} +(-3.98286 - 1.44964i) q^{38} +(3.06183 + 2.56918i) q^{40} +(3.71391 + 3.11634i) q^{41} +(-9.24679 - 3.36556i) q^{43} +(-1.01987 + 1.76647i) q^{44} +(1.27312 + 2.20510i) q^{46} +(-2.17020 - 12.3078i) q^{47} +(-0.680721 + 0.247762i) q^{49} +(-0.598226 + 3.39271i) q^{50} +(2.58817 - 2.17173i) q^{52} -7.34280 q^{53} -6.96786 q^{55} +(-5.06980 + 4.25406i) q^{56} +(2.25515 - 12.7896i) q^{58} +(8.50598 - 3.09592i) q^{59} +(-0.223267 - 1.26621i) q^{61} +(-0.823982 - 1.42718i) q^{62} +(-2.59373 + 4.49247i) q^{64} +(10.8455 + 3.94742i) q^{65} +(-3.55927 - 2.98658i) q^{67} +(-0.367577 - 0.308434i) q^{68} +(6.91926 + 2.51841i) q^{70} +(2.81187 - 4.87030i) q^{71} +(2.28072 + 3.95033i) q^{73} +(-0.358600 - 2.03372i) q^{74} +(-1.23987 + 0.451276i) q^{76} +(2.00345 - 11.3621i) q^{77} +(3.56732 - 2.99333i) q^{79} +7.95828 q^{80} +7.65237 q^{82} +(-4.41578 + 3.70528i) q^{83} +(0.284635 - 1.61425i) q^{85} +(-14.5952 + 5.31221i) q^{86} +(-1.71652 - 9.73490i) q^{88} +(2.27221 + 3.93558i) q^{89} +(-9.55523 + 16.5502i) q^{91} +(0.744844 + 0.271101i) q^{92} +(-15.1113 - 12.6799i) q^{94} +(-3.45278 - 2.89722i) q^{95} +(-8.05828 - 2.93297i) q^{97} +(-0.571704 + 0.990221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} + 27 q^{16} + 9 q^{17} - 12 q^{19} + 39 q^{20} - 39 q^{22} + 21 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} + 6 q^{31} + 27 q^{32} - 18 q^{34} - 30 q^{35} - 3 q^{37} + 3 q^{38} + 33 q^{40} - 15 q^{41} - 30 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} - 3 q^{49} + 6 q^{50} - 18 q^{53} + 30 q^{55} + 15 q^{56} - 3 q^{58} + 30 q^{59} - 30 q^{61} + 30 q^{62} - 6 q^{64} - 12 q^{65} - 39 q^{67} + 18 q^{68} + 51 q^{70} - 12 q^{73} + 57 q^{74} + 57 q^{76} - 24 q^{77} + 15 q^{79} - 42 q^{80} - 42 q^{82} - 21 q^{83} + 54 q^{85} - 60 q^{86} + 12 q^{88} + 9 q^{89} - 18 q^{91} - 15 q^{92} + 33 q^{94} + 42 q^{95} - 12 q^{97} - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20913 1.01458i 0.854982 0.717415i −0.105899 0.994377i \(-0.533772\pi\)
0.960881 + 0.276961i \(0.0893274\pi\)
\(3\) 0 0
\(4\) 0.0853237 0.483895i 0.0426619 0.241948i
\(5\) 1.57728 0.574083i 0.705382 0.256738i 0.0356747 0.999363i \(-0.488642\pi\)
0.669707 + 0.742626i \(0.266420\pi\)
\(6\) 0 0
\(7\) 0.482617 + 2.73706i 0.182412 + 1.03451i 0.929235 + 0.369488i \(0.120467\pi\)
−0.746823 + 0.665023i \(0.768422\pi\)
\(8\) 1.19062 + 2.06222i 0.420948 + 0.729104i
\(9\) 0 0
\(10\) 1.32468 2.29442i 0.418901 0.725558i
\(11\) −3.90087 1.41980i −1.17616 0.428086i −0.321314 0.946973i \(-0.604125\pi\)
−0.854843 + 0.518886i \(0.826347\pi\)
\(12\) 0 0
\(13\) 5.26736 + 4.41984i 1.46090 + 1.22584i 0.924110 + 0.382128i \(0.124809\pi\)
0.536792 + 0.843715i \(0.319636\pi\)
\(14\) 3.36051 + 2.81980i 0.898133 + 0.753623i
\(15\) 0 0
\(16\) 4.45535 + 1.62162i 1.11384 + 0.405404i
\(17\) 0.488276 0.845718i 0.118424 0.205117i −0.800719 0.599040i \(-0.795549\pi\)
0.919143 + 0.393923i \(0.128882\pi\)
\(18\) 0 0
\(19\) −1.34264 2.32553i −0.308024 0.533513i 0.669906 0.742446i \(-0.266334\pi\)
−0.977930 + 0.208933i \(0.933001\pi\)
\(20\) −0.143217 0.812221i −0.0320242 0.181618i
\(21\) 0 0
\(22\) −6.15715 + 2.24102i −1.31271 + 0.477787i
\(23\) −0.280124 + 1.58866i −0.0584099 + 0.331259i −0.999985 0.00554518i \(-0.998235\pi\)
0.941575 + 0.336804i \(0.109346\pi\)
\(24\) 0 0
\(25\) −1.67198 + 1.40296i −0.334396 + 0.280591i
\(26\) 10.8532 2.12848
\(27\) 0 0
\(28\) 1.36563 0.258079
\(29\) 6.30292 5.28878i 1.17042 0.982101i 0.170428 0.985370i \(-0.445485\pi\)
0.999995 + 0.00326885i \(0.00104051\pi\)
\(30\) 0 0
\(31\) 0.181301 1.02821i 0.0325626 0.184672i −0.964188 0.265219i \(-0.914556\pi\)
0.996751 + 0.0805475i \(0.0256669\pi\)
\(32\) 2.55707 0.930697i 0.452030 0.164526i
\(33\) 0 0
\(34\) −0.267660 1.51798i −0.0459033 0.260331i
\(35\) 2.33252 + 4.04005i 0.394268 + 0.682893i
\(36\) 0 0
\(37\) 0.654172 1.13306i 0.107545 0.186274i −0.807230 0.590237i \(-0.799034\pi\)
0.914775 + 0.403963i \(0.132368\pi\)
\(38\) −3.98286 1.44964i −0.646105 0.235163i
\(39\) 0 0
\(40\) 3.06183 + 2.56918i 0.484118 + 0.406223i
\(41\) 3.71391 + 3.11634i 0.580016 + 0.486691i 0.884952 0.465682i \(-0.154191\pi\)
−0.304936 + 0.952373i \(0.598635\pi\)
\(42\) 0 0
\(43\) −9.24679 3.36556i −1.41012 0.513243i −0.478957 0.877839i \(-0.658985\pi\)
−0.931166 + 0.364596i \(0.881207\pi\)
\(44\) −1.01987 + 1.76647i −0.153751 + 0.266305i
\(45\) 0 0
\(46\) 1.27312 + 2.20510i 0.187711 + 0.325125i
\(47\) −2.17020 12.3078i −0.316557 1.79528i −0.563355 0.826215i \(-0.690490\pi\)
0.246798 0.969067i \(-0.420621\pi\)
\(48\) 0 0
\(49\) −0.680721 + 0.247762i −0.0972458 + 0.0353946i
\(50\) −0.598226 + 3.39271i −0.0846019 + 0.479801i
\(51\) 0 0
\(52\) 2.58817 2.17173i 0.358914 0.301165i
\(53\) −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
\(56\) −5.06980 + 4.25406i −0.677480 + 0.568473i
\(57\) 0 0
\(58\) 2.25515 12.7896i 0.296116 1.67936i
\(59\) 8.50598 3.09592i 1.10738 0.403055i 0.277351 0.960769i \(-0.410544\pi\)
0.830033 + 0.557714i \(0.188321\pi\)
\(60\) 0 0
\(61\) −0.223267 1.26621i −0.0285864 0.162121i 0.967173 0.254120i \(-0.0817857\pi\)
−0.995759 + 0.0919982i \(0.970675\pi\)
\(62\) −0.823982 1.42718i −0.104646 0.181252i
\(63\) 0 0
\(64\) −2.59373 + 4.49247i −0.324216 + 0.561558i
\(65\) 10.8455 + 3.94742i 1.34521 + 0.489618i
\(66\) 0 0
\(67\) −3.55927 2.98658i −0.434834 0.364869i 0.398938 0.916978i \(-0.369379\pi\)
−0.833772 + 0.552109i \(0.813823\pi\)
\(68\) −0.367577 0.308434i −0.0445753 0.0374031i
\(69\) 0 0
\(70\) 6.91926 + 2.51841i 0.827010 + 0.301007i
\(71\) 2.81187 4.87030i 0.333707 0.577998i −0.649528 0.760337i \(-0.725034\pi\)
0.983236 + 0.182339i \(0.0583670\pi\)
\(72\) 0 0
\(73\) 2.28072 + 3.95033i 0.266938 + 0.462351i 0.968070 0.250681i \(-0.0806547\pi\)
−0.701131 + 0.713032i \(0.747321\pi\)
\(74\) −0.358600 2.03372i −0.0416864 0.236416i
\(75\) 0 0
\(76\) −1.23987 + 0.451276i −0.142223 + 0.0517649i
\(77\) 2.00345 11.3621i 0.228314 1.29484i
\(78\) 0 0
\(79\) 3.56732 2.99333i 0.401354 0.336776i −0.419662 0.907680i \(-0.637852\pi\)
0.821017 + 0.570904i \(0.193407\pi\)
\(80\) 7.95828 0.889763
\(81\) 0 0
\(82\) 7.65237 0.845063
\(83\) −4.41578 + 3.70528i −0.484695 + 0.406707i −0.852121 0.523346i \(-0.824684\pi\)
0.367426 + 0.930053i \(0.380239\pi\)
\(84\) 0 0
\(85\) 0.284635 1.61425i 0.0308730 0.175090i
\(86\) −14.5952 + 5.31221i −1.57384 + 0.572830i
\(87\) 0 0
\(88\) −1.71652 9.73490i −0.182982 1.03774i
\(89\) 2.27221 + 3.93558i 0.240854 + 0.417171i 0.960958 0.276695i \(-0.0892393\pi\)
−0.720104 + 0.693866i \(0.755906\pi\)
\(90\) 0 0
\(91\) −9.55523 + 16.5502i −1.00166 + 1.73493i
\(92\) 0.744844 + 0.271101i 0.0776554 + 0.0282643i
\(93\) 0 0
\(94\) −15.1113 12.6799i −1.55861 1.30783i
\(95\) −3.45278 2.89722i −0.354247 0.297249i
\(96\) 0 0
\(97\) −8.05828 2.93297i −0.818194 0.297798i −0.101190 0.994867i \(-0.532265\pi\)
−0.717004 + 0.697069i \(0.754487\pi\)
\(98\) −0.571704 + 0.990221i −0.0577508 + 0.100027i
\(99\) 0 0
\(100\) 0.536224 + 0.928767i 0.0536224 + 0.0928767i
\(101\) 1.35545 + 7.68712i 0.134872 + 0.764897i 0.974949 + 0.222429i \(0.0713987\pi\)
−0.840077 + 0.542467i \(0.817490\pi\)
\(102\) 0 0
\(103\) 2.03551 0.740866i 0.200565 0.0729997i −0.239784 0.970826i \(-0.577077\pi\)
0.440349 + 0.897826i \(0.354855\pi\)
\(104\) −2.84324 + 16.1248i −0.278802 + 1.58117i
\(105\) 0 0
\(106\) −8.87838 + 7.44984i −0.862344 + 0.723593i
\(107\) −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 \(0.698884\pi\)
\(110\) −8.42503 + 7.06944i −0.803295 + 0.674045i
\(111\) 0 0
\(112\) −2.28823 + 12.9772i −0.216217 + 1.22623i
\(113\) 0.423644 0.154194i 0.0398531 0.0145053i −0.322017 0.946734i \(-0.604361\pi\)
0.361870 + 0.932229i \(0.382138\pi\)
\(114\) 0 0
\(115\) 0.470190 + 2.66658i 0.0438455 + 0.248660i
\(116\) −2.02142 3.50121i −0.187685 0.325079i
\(117\) 0 0
\(118\) 7.14376 12.3734i 0.657636 1.13906i
\(119\) 2.55043 + 0.928281i 0.233798 + 0.0850954i
\(120\) 0 0
\(121\) 4.77448 + 4.00627i 0.434044 + 0.364206i
\(122\) −1.55463 1.30449i −0.140749 0.118103i
\(123\) 0 0
\(124\) −0.482075 0.175461i −0.0432916 0.0157569i
\(125\) −6.02803 + 10.4409i −0.539164 + 0.933859i
\(126\) 0 0
\(127\) 0.265534 + 0.459919i 0.0235624 + 0.0408112i 0.877566 0.479456i \(-0.159166\pi\)
−0.854004 + 0.520267i \(0.825833\pi\)
\(128\) 2.36687 + 13.4232i 0.209204 + 1.18645i
\(129\) 0 0
\(130\) 17.1185 6.23063i 1.50139 0.546462i
\(131\) 1.98237 11.2426i 0.173201 0.982271i −0.766999 0.641648i \(-0.778251\pi\)
0.940200 0.340623i \(-0.110638\pi\)
\(132\) 0 0
\(133\) 5.71712 4.79724i 0.495738 0.415973i
\(134\) −7.33374 −0.633539
\(135\) 0 0
\(136\) 2.32541 0.199402
\(137\) 3.23979 2.71850i 0.276794 0.232257i −0.493814 0.869568i \(-0.664397\pi\)
0.770607 + 0.637310i \(0.219953\pi\)
\(138\) 0 0
\(139\) −1.93714 + 10.9861i −0.164306 + 0.931825i 0.785471 + 0.618898i \(0.212421\pi\)
−0.949777 + 0.312927i \(0.898691\pi\)
\(140\) 2.15398 0.783984i 0.182044 0.0662588i
\(141\) 0 0
\(142\) −1.54139 8.74167i −0.129351 0.733585i
\(143\) −14.2720 24.7198i −1.19348 2.06718i
\(144\) 0 0
\(145\) 6.90528 11.9603i 0.573452 0.993248i
\(146\) 6.76560 + 2.46248i 0.559925 + 0.203796i
\(147\) 0 0
\(148\) −0.492465 0.413228i −0.0404804 0.0339671i
\(149\) −14.9208 12.5200i −1.22236 1.02568i −0.998698 0.0510127i \(-0.983755\pi\)
−0.223660 0.974667i \(-0.571800\pi\)
\(150\) 0 0
\(151\) 1.16791 + 0.425083i 0.0950429 + 0.0345928i 0.389104 0.921194i \(-0.372785\pi\)
−0.294061 + 0.955787i \(0.595007\pi\)
\(152\) 3.19716 5.53765i 0.259324 0.449163i
\(153\) 0 0
\(154\) −9.10535 15.7709i −0.733730 1.27086i
\(155\) −0.304315 1.72585i −0.0244431 0.138624i
\(156\) 0 0
\(157\) 3.32007 1.20840i 0.264970 0.0964412i −0.206119 0.978527i \(-0.566083\pi\)
0.471089 + 0.882086i \(0.343861\pi\)
\(158\) 1.27637 7.23865i 0.101542 0.575876i
\(159\) 0 0
\(160\) 3.49892 2.93594i 0.276614 0.232107i
\(161\) −4.48345 −0.353346
\(162\) 0 0
\(163\) 15.9509 1.24937 0.624685 0.780877i \(-0.285228\pi\)
0.624685 + 0.780877i \(0.285228\pi\)
\(164\) 1.82487 1.53125i 0.142498 0.119570i
\(165\) 0 0
\(166\) −1.57994 + 8.96031i −0.122628 + 0.695455i
\(167\) −13.6111 + 4.95404i −1.05326 + 0.383355i −0.809892 0.586579i \(-0.800474\pi\)
−0.243368 + 0.969934i \(0.578252\pi\)
\(168\) 0 0
\(169\) 5.95266 + 33.7592i 0.457897 + 2.59686i
\(170\) −1.29362 2.24061i −0.0992161 0.171847i
\(171\) 0 0
\(172\) −2.41755 + 4.18731i −0.184336 + 0.319280i
\(173\) −11.8565 4.31540i −0.901431 0.328094i −0.150605 0.988594i \(-0.548122\pi\)
−0.750826 + 0.660500i \(0.770344\pi\)
\(174\) 0 0
\(175\) −4.64690 3.89921i −0.351272 0.294753i
\(176\) −15.0774 12.6514i −1.13650 0.953637i
\(177\) 0 0
\(178\) 6.74035 + 2.45329i 0.505211 + 0.183882i
\(179\) −0.147949 + 0.256256i −0.0110582 + 0.0191534i −0.871502 0.490393i \(-0.836853\pi\)
0.860443 + 0.509546i \(0.170187\pi\)
\(180\) 0 0
\(181\) −0.710251 1.23019i −0.0527925 0.0914393i 0.838421 0.545022i \(-0.183479\pi\)
−0.891214 + 0.453583i \(0.850146\pi\)
\(182\) 5.23793 + 29.7058i 0.388261 + 2.20194i
\(183\) 0 0
\(184\) −3.60969 + 1.31382i −0.266110 + 0.0968560i
\(185\) 0.381343 2.16270i 0.0280369 0.159005i
\(186\) 0 0
\(187\) −3.10545 + 2.60578i −0.227093 + 0.190554i
\(188\) −6.14087 −0.447869
\(189\) 0 0
\(190\) −7.11431 −0.516126
\(191\) 15.7990 13.2569i 1.14317 0.959236i 0.143635 0.989631i \(-0.454121\pi\)
0.999538 + 0.0303946i \(0.00967639\pi\)
\(192\) 0 0
\(193\) −3.63896 + 20.6376i −0.261938 + 1.48552i 0.515676 + 0.856784i \(0.327541\pi\)
−0.777614 + 0.628741i \(0.783570\pi\)
\(194\) −12.7192 + 4.62942i −0.913187 + 0.332373i
\(195\) 0 0
\(196\) 0.0618092 + 0.350537i 0.00441494 + 0.0250384i
\(197\) 4.79810 + 8.31056i 0.341851 + 0.592103i 0.984776 0.173826i \(-0.0556129\pi\)
−0.642926 + 0.765929i \(0.722280\pi\)
\(198\) 0 0
\(199\) 5.34583 9.25925i 0.378956 0.656371i −0.611955 0.790893i \(-0.709616\pi\)
0.990911 + 0.134522i \(0.0429498\pi\)
\(200\) −4.88389 1.77759i −0.345344 0.125695i
\(201\) 0 0
\(202\) 9.43809 + 7.91950i 0.664062 + 0.557214i
\(203\) 17.5176 + 14.6990i 1.22949 + 1.03167i
\(204\) 0 0
\(205\) 7.64693 + 2.78325i 0.534085 + 0.194391i
\(206\) 1.70953 2.96099i 0.119108 0.206302i
\(207\) 0 0
\(208\) 16.3006 + 28.2335i 1.13025 + 1.95764i
\(209\) 1.93570 + 10.9779i 0.133895 + 0.759356i
\(210\) 0 0
\(211\) 14.1426 5.14749i 0.973617 0.354367i 0.194261 0.980950i \(-0.437769\pi\)
0.779355 + 0.626582i \(0.215547\pi\)
\(212\) −0.626515 + 3.55314i −0.0430292 + 0.244031i
\(213\) 0 0
\(214\) −15.2168 + 12.7684i −1.04020 + 0.872831i
\(215\) −16.5169 −1.12644
\(216\) 0 0
\(217\) 2.90176 0.196984
\(218\) −14.7683 + 12.3921i −1.00023 + 0.839296i
\(219\) 0 0
\(220\) −0.594524 + 3.37171i −0.0400828 + 0.227321i
\(221\) 6.30986 2.29660i 0.424447 0.154486i
\(222\) 0 0
\(223\) −2.13381 12.1014i −0.142890 0.810371i −0.969037 0.246916i \(-0.920583\pi\)
0.826147 0.563455i \(-0.190528\pi\)
\(224\) 3.78146 + 6.54968i 0.252659 + 0.437619i
\(225\) 0 0
\(226\) 0.355798 0.616261i 0.0236674 0.0409931i
\(227\) −3.52625 1.28345i −0.234046 0.0851856i 0.222335 0.974970i \(-0.428632\pi\)
−0.456380 + 0.889785i \(0.650854\pi\)
\(228\) 0 0
\(229\) −14.2503 11.9574i −0.941685 0.790168i 0.0361925 0.999345i \(-0.488477\pi\)
−0.977878 + 0.209177i \(0.932921\pi\)
\(230\) 3.27398 + 2.74719i 0.215880 + 0.181145i
\(231\) 0 0
\(232\) 18.4110 + 6.70106i 1.20874 + 0.439946i
\(233\) −0.272892 + 0.472663i −0.0178777 + 0.0309652i −0.874826 0.484438i \(-0.839024\pi\)
0.856948 + 0.515403i \(0.172358\pi\)
\(234\) 0 0
\(235\) −10.4887 18.1670i −0.684210 1.18509i
\(236\) −0.772340 4.38016i −0.0502750 0.285124i
\(237\) 0 0
\(238\) 4.02561 1.46520i 0.260942 0.0949750i
\(239\) −3.48942 + 19.7895i −0.225712 + 1.28007i 0.635609 + 0.772011i \(0.280749\pi\)
−0.861320 + 0.508062i \(0.830362\pi\)
\(240\) 0 0
\(241\) 11.7138 9.82906i 0.754553 0.633145i −0.182150 0.983271i \(-0.558305\pi\)
0.936703 + 0.350125i \(0.113861\pi\)
\(242\) 9.83763 0.632387
\(243\) 0 0
\(244\) −0.631762 −0.0404444
\(245\) −0.931452 + 0.781581i −0.0595083 + 0.0499334i
\(246\) 0 0
\(247\) 3.20627 18.1837i 0.204010 1.15700i
\(248\) 2.33625 0.850325i 0.148352 0.0539957i
\(249\) 0 0
\(250\) 3.30441 + 18.7403i 0.208989 + 1.18524i
\(251\) −6.37816 11.0473i −0.402586 0.697299i 0.591451 0.806341i \(-0.298555\pi\)
−0.994037 + 0.109042i \(0.965222\pi\)
\(252\) 0 0
\(253\) 3.34831 5.79945i 0.210507 0.364608i
\(254\) 0.787689 + 0.286695i 0.0494240 + 0.0179889i
\(255\) 0 0
\(256\) 8.53308 + 7.16010i 0.533317 + 0.447506i
\(257\) −10.0388 8.42354i −0.626202 0.525446i 0.273544 0.961860i \(-0.411804\pi\)
−0.899746 + 0.436413i \(0.856249\pi\)
\(258\) 0 0
\(259\) 3.41697 + 1.24367i 0.212320 + 0.0772781i
\(260\) 2.83551 4.91125i 0.175851 0.304583i
\(261\) 0 0
\(262\) −9.00956 15.6050i −0.556613 0.964081i
\(263\) −1.65212 9.36963i −0.101874 0.577756i −0.992423 0.122869i \(-0.960791\pi\)
0.890549 0.454888i \(-0.150321\pi\)
\(264\) 0 0
\(265\) −11.5817 + 4.21538i −0.711455 + 0.258949i
\(266\) 2.04556 11.6009i 0.125421 0.711299i
\(267\) 0 0
\(268\) −1.74888 + 1.46749i −0.106830 + 0.0896411i
\(269\) 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 \(0.177020\pi\)
\(272\) 3.54687 2.97618i 0.215060 0.180457i
\(273\) 0 0
\(274\) 1.15918 6.57404i 0.0700286 0.397152i
\(275\) 8.51409 3.09888i 0.513419 0.186869i
\(276\) 0 0
\(277\) −3.27912 18.5968i −0.197023 1.11737i −0.909508 0.415686i \(-0.863542\pi\)
0.712485 0.701687i \(-0.247570\pi\)
\(278\) 8.80397 + 15.2489i 0.528027 + 0.914569i
\(279\) 0 0
\(280\) −5.55431 + 9.62034i −0.331933 + 0.574925i
\(281\) 18.7955 + 6.84100i 1.12125 + 0.408100i 0.835106 0.550088i \(-0.185406\pi\)
0.286139 + 0.958188i \(0.407628\pi\)
\(282\) 0 0
\(283\) 12.8274 + 10.7635i 0.762512 + 0.639824i 0.938780 0.344519i \(-0.111958\pi\)
−0.176267 + 0.984342i \(0.556402\pi\)
\(284\) −2.11679 1.77620i −0.125609 0.105398i
\(285\) 0 0
\(286\) −42.3369 15.4094i −2.50343 0.911175i
\(287\) −6.73722 + 11.6692i −0.397685 + 0.688811i
\(288\) 0 0
\(289\) 8.02317 + 13.8965i 0.471951 + 0.817444i
\(290\) −3.78529 21.4675i −0.222280 1.26061i
\(291\) 0 0
\(292\) 2.10614 0.766573i 0.123253 0.0448603i
\(293\) 3.39864 19.2747i 0.198551 1.12604i −0.708720 0.705490i \(-0.750727\pi\)
0.907271 0.420548i \(-0.138162\pi\)
\(294\) 0 0
\(295\) 11.6390 9.76628i 0.677649 0.568615i
\(296\) 3.11549 0.181084
\(297\) 0 0
\(298\) −30.7437 −1.78093
\(299\) −8.49714 + 7.12995i −0.491402 + 0.412335i
\(300\) 0 0
\(301\) 4.74906 26.9333i 0.273731 1.55241i
\(302\) 1.84343 0.670953i 0.106077 0.0386090i
\(303\) 0 0
\(304\) −2.21084 12.5383i −0.126800 0.719121i
\(305\) −1.07906 1.86899i −0.0617870 0.107018i
\(306\) 0 0
\(307\) −7.44973 + 12.9033i −0.425179 + 0.736431i −0.996437 0.0843392i \(-0.973122\pi\)
0.571258 + 0.820770i \(0.306455\pi\)
\(308\) −5.32714 1.93892i −0.303542 0.110480i
\(309\) 0 0
\(310\) −2.11897 1.77803i −0.120349 0.100985i
\(311\) 3.51795 + 2.95191i 0.199485 + 0.167388i 0.737058 0.675829i \(-0.236214\pi\)
−0.537573 + 0.843217i \(0.680659\pi\)
\(312\) 0 0
\(313\) −11.1529 4.05933i −0.630400 0.229447i 0.00700533 0.999975i \(-0.497770\pi\)
−0.637405 + 0.770529i \(0.719992\pi\)
\(314\) 2.78836 4.82958i 0.157356 0.272549i
\(315\) 0 0
\(316\) −1.14408 1.98161i −0.0643597 0.111474i
\(317\) −2.52091 14.2968i −0.141588 0.802988i −0.970043 0.242932i \(-0.921891\pi\)
0.828455 0.560056i \(-0.189220\pi\)
\(318\) 0 0
\(319\) −32.0959 + 11.6820i −1.79703 + 0.654064i
\(320\) −1.51199 + 8.57490i −0.0845226 + 0.479351i
\(321\) 0 0
\(322\) −5.42107 + 4.54882i −0.302104 + 0.253496i
\(323\) −2.62232 −0.145910
\(324\) 0 0
\(325\) −15.0077 −0.832480
\(326\) 19.2867 16.1834i 1.06819 0.896317i
\(327\) 0 0
\(328\) −2.00471 + 11.3693i −0.110692 + 0.627764i
\(329\) 32.6399 11.8799i 1.79949 0.654963i
\(330\) 0 0
\(331\) −1.40754 7.98256i −0.0773654 0.438761i −0.998744 0.0500957i \(-0.984047\pi\)
0.921379 0.388665i \(-0.127064\pi\)
\(332\) 1.41620 + 2.45292i 0.0777238 + 0.134622i
\(333\) 0 0
\(334\) −11.4313 + 19.7996i −0.625494 + 1.08339i
\(335\) −7.32852 2.66736i −0.400400 0.145734i
\(336\) 0 0
\(337\) −14.4077 12.0895i −0.784839 0.658558i 0.159623 0.987178i \(-0.448972\pi\)
−0.944462 + 0.328620i \(0.893417\pi\)
\(338\) 41.4489 + 34.7798i 2.25452 + 1.89177i
\(339\) 0 0
\(340\) −0.756840 0.275467i −0.0410454 0.0149393i
\(341\) −2.16708 + 3.75350i −0.117354 + 0.203263i
\(342\) 0 0
\(343\) 8.72082 + 15.1049i 0.470880 + 0.815588i
\(344\) −4.06892 23.0760i −0.219382 1.24417i
\(345\) 0 0
\(346\) −18.7143 + 6.81145i −1.00609 + 0.366186i
\(347\) −3.05927 + 17.3500i −0.164230 + 0.931396i 0.785624 + 0.618704i \(0.212342\pi\)
−0.949855 + 0.312692i \(0.898769\pi\)
\(348\) 0 0
\(349\) −13.0146 + 10.9205i −0.696653 + 0.584561i −0.920819 0.389990i \(-0.872479\pi\)
0.224166 + 0.974551i \(0.428034\pi\)
\(350\) −9.57475 −0.511792
\(351\) 0 0
\(352\) −11.2962 −0.602090
\(353\) −11.6099 + 9.74183i −0.617931 + 0.518505i −0.897152 0.441721i \(-0.854368\pi\)
0.279222 + 0.960227i \(0.409924\pi\)
\(354\) 0 0
\(355\) 1.63915 9.29607i 0.0869970 0.493384i
\(356\) 2.09828 0.763712i 0.111209 0.0404767i
\(357\) 0 0
\(358\) 0.0811020 + 0.459952i 0.00428637 + 0.0243092i
\(359\) −1.22548 2.12259i −0.0646783 0.112026i 0.831873 0.554966i \(-0.187269\pi\)
−0.896551 + 0.442940i \(0.853935\pi\)
\(360\) 0 0
\(361\) 5.89461 10.2098i 0.310243 0.537356i
\(362\) −2.10691 0.766852i −0.110737 0.0403049i
\(363\) 0 0
\(364\) 7.19325 + 6.03585i 0.377029 + 0.316365i
\(365\) 5.86516 + 4.92145i 0.306996 + 0.257600i
\(366\) 0 0
\(367\) 1.23432 + 0.449255i 0.0644309 + 0.0234509i 0.374035 0.927415i \(-0.377974\pi\)
−0.309604 + 0.950866i \(0.600196\pi\)
\(368\) −3.82425 + 6.62379i −0.199353 + 0.345289i
\(369\) 0 0
\(370\) −1.73314 3.00189i −0.0901017 0.156061i
\(371\) −3.54376 20.0977i −0.183983 1.04342i
\(372\) 0 0
\(373\) 9.04564 3.29234i 0.468366 0.170471i −0.0970463 0.995280i \(-0.530939\pi\)
0.565412 + 0.824809i \(0.308717\pi\)
\(374\) −1.11112 + 6.30145i −0.0574544 + 0.325840i
\(375\) 0 0
\(376\) 22.7975 19.1294i 1.17569 0.986524i
\(377\) 56.5753 2.91377
\(378\) 0 0
\(379\) −8.56311 −0.439857 −0.219929 0.975516i \(-0.570582\pi\)
−0.219929 + 0.975516i \(0.570582\pi\)
\(380\) −1.69656 + 1.42358i −0.0870314 + 0.0730281i
\(381\) 0 0
\(382\) 5.65279 32.0586i 0.289222 1.64026i
\(383\) −31.6062 + 11.5037i −1.61500 + 0.587813i −0.982420 0.186681i \(-0.940227\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(384\) 0 0
\(385\) −3.36281 19.0714i −0.171385 0.971970i
\(386\) 16.5385 + 28.6455i 0.841786 + 1.45802i
\(387\) 0 0
\(388\) −2.10681 + 3.64911i −0.106957 + 0.185255i
\(389\) 14.0521 + 5.11456i 0.712472 + 0.259319i 0.672727 0.739891i \(-0.265123\pi\)
0.0397455 + 0.999210i \(0.487345\pi\)
\(390\) 0 0
\(391\) 1.20678 + 1.01261i 0.0610296 + 0.0512099i
\(392\) −1.32142 1.10880i −0.0667418 0.0560030i
\(393\) 0 0
\(394\) 14.2332 + 5.18048i 0.717060 + 0.260989i
\(395\) 3.90824 6.76927i 0.196645 0.340599i
\(396\) 0 0
\(397\) 8.38938 + 14.5308i 0.421051 + 0.729282i 0.996043 0.0888774i \(-0.0283279\pi\)
−0.574991 + 0.818159i \(0.694995\pi\)
\(398\) −2.93045 16.6194i −0.146890 0.833055i
\(399\) 0 0
\(400\) −9.72430 + 3.53936i −0.486215 + 0.176968i
\(401\) 2.27936 12.9269i 0.113826 0.645537i −0.873499 0.486825i \(-0.838155\pi\)
0.987325 0.158712i \(-0.0507341\pi\)
\(402\) 0 0
\(403\) 5.49948 4.61462i 0.273949 0.229870i
\(404\) 3.83541 0.190819
\(405\) 0 0
\(406\) 36.0943 1.79133
\(407\) −4.16056 + 3.49113i −0.206231 + 0.173049i
\(408\) 0 0
\(409\) 4.41943 25.0639i 0.218527 1.23933i −0.656153 0.754628i \(-0.727818\pi\)
0.874680 0.484700i \(-0.161071\pi\)
\(410\) 12.0699 4.39310i 0.596092 0.216960i
\(411\) 0 0
\(412\) −0.184824 1.04819i −0.00910561 0.0516405i
\(413\) 12.5789 + 21.7872i 0.618965 + 1.07208i
\(414\) 0 0
\(415\) −4.83779 + 8.37929i −0.237478 + 0.411323i
\(416\) 17.5825 + 6.39952i 0.862054 + 0.313762i
\(417\) 0 0
\(418\) 13.4784 + 11.3097i 0.659251 + 0.553178i
\(419\) −9.70582 8.14415i −0.474160 0.397868i 0.374149 0.927369i \(-0.377935\pi\)
−0.848309 + 0.529501i \(0.822379\pi\)
\(420\) 0 0
\(421\) 16.6112 + 6.04597i 0.809579 + 0.294663i 0.713450 0.700706i \(-0.247132\pi\)
0.0961292 + 0.995369i \(0.469354\pi\)
\(422\) 11.8777 20.5727i 0.578196 1.00147i
\(423\) 0 0
\(424\) −8.74249 15.1424i −0.424573 0.735382i
\(425\) 0.370119 + 2.09905i 0.0179534 + 0.101819i
\(426\) 0 0
\(427\) 3.35793 1.22219i 0.162502 0.0591458i
\(428\) −1.07380 + 6.08979i −0.0519038 + 0.294361i
\(429\) 0 0
\(430\) −19.9710 + 16.7577i −0.963089 + 0.808128i
\(431\) 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 \(0.598115\pi\)
\(434\) 3.50860 2.94407i 0.168418 0.141320i
\(435\) 0 0
\(436\) −1.04214 + 5.91029i −0.0499097 + 0.283052i
\(437\) 4.07059 1.48157i 0.194723 0.0708732i
\(438\) 0 0
\(439\) 4.67755 + 26.5277i 0.223247 + 1.26610i 0.866008 + 0.500030i \(0.166678\pi\)
−0.642761 + 0.766067i \(0.722211\pi\)
\(440\) −8.29608 14.3692i −0.395500 0.685027i
\(441\) 0 0
\(442\) 5.29934 9.17873i 0.252064 0.436588i
\(443\) −32.6335 11.8776i −1.55047 0.564324i −0.581940 0.813232i \(-0.697706\pi\)
−0.968527 + 0.248908i \(0.919928\pi\)
\(444\) 0 0
\(445\) 5.84327 + 4.90308i 0.276997 + 0.232428i
\(446\) −14.8579 12.4673i −0.703542 0.590342i
\(447\) 0 0
\(448\) −13.5479 4.93104i −0.640079 0.232970i
\(449\) 10.3731 17.9667i 0.489535 0.847900i −0.510392 0.859942i \(-0.670500\pi\)
0.999927 + 0.0120419i \(0.00383314\pi\)
\(450\) 0 0
\(451\) −10.0629 17.4295i −0.473844 0.820722i
\(452\) −0.0384668 0.218156i −0.00180932 0.0102612i
\(453\) 0 0
\(454\) −5.56585 + 2.02580i −0.261218 + 0.0950757i
\(455\) −5.57012 + 31.5897i −0.261131 + 1.48095i
\(456\) 0 0
\(457\) −5.52144 + 4.63304i −0.258282 + 0.216725i −0.762729 0.646718i \(-0.776141\pi\)
0.504447 + 0.863443i \(0.331697\pi\)
\(458\) −29.3621 −1.37200
\(459\) 0 0
\(460\) 1.33046 0.0620332
\(461\) 17.7162 14.8656i 0.825125 0.692362i −0.129041 0.991639i \(-0.541190\pi\)
0.954166 + 0.299277i \(0.0967455\pi\)
\(462\) 0 0
\(463\) 0.864046 4.90025i 0.0401556 0.227734i −0.958125 0.286350i \(-0.907558\pi\)
0.998281 + 0.0586166i \(0.0186690\pi\)
\(464\) 36.6581 13.3424i 1.70181 0.619408i
\(465\) 0 0
\(466\) 0.149592 + 0.848380i 0.00692973 + 0.0393004i
\(467\) 6.24068 + 10.8092i 0.288784 + 0.500189i 0.973520 0.228602i \(-0.0734156\pi\)
−0.684735 + 0.728792i \(0.740082\pi\)
\(468\) 0 0
\(469\) 6.45669 11.1833i 0.298142 0.516397i
\(470\) −31.1141 11.3246i −1.43519 0.522365i
\(471\) 0 0
\(472\) 16.5119 + 13.8551i 0.760021 + 0.637733i
\(473\) 31.2921 + 26.2572i 1.43881 + 1.20731i
\(474\) 0 0
\(475\) 5.50749 + 2.00456i 0.252701 + 0.0919756i
\(476\) 0.666803 1.15494i 0.0305628 0.0529364i
\(477\) 0 0
\(478\) 15.8588 + 27.4683i 0.725365 + 1.25637i
\(479\) 4.94398 + 28.0387i 0.225896 + 1.28112i 0.860964 + 0.508666i \(0.169861\pi\)
−0.635068 + 0.772456i \(0.719028\pi\)
\(480\) 0 0
\(481\) 8.45370 3.07689i 0.385455 0.140294i
\(482\) 4.19115 23.7692i 0.190902 1.08266i
\(483\) 0 0
\(484\) 2.34599 1.96852i 0.106636 0.0894781i
\(485\) −14.3939 −0.653595
\(486\) 0 0
\(487\) 29.6841 1.34511 0.672557 0.740045i \(-0.265196\pi\)
0.672557 + 0.740045i \(0.265196\pi\)
\(488\) 2.34537 1.96800i 0.106170 0.0890872i
\(489\) 0 0
\(490\) −0.333269 + 1.89006i −0.0150556 + 0.0853843i
\(491\) −11.6568 + 4.24274i −0.526066 + 0.191472i −0.591381 0.806392i \(-0.701417\pi\)
0.0653150 + 0.997865i \(0.479195\pi\)
\(492\) 0 0
\(493\) −1.39525 7.91287i −0.0628390 0.356378i
\(494\) −14.5720 25.2394i −0.655623 1.13557i
\(495\) 0 0
\(496\) 2.47512 4.28702i 0.111136 0.192493i
\(497\) 14.6873 + 5.34576i 0.658817 + 0.239790i
\(498\) 0 0
\(499\) −1.74645 1.46544i −0.0781816 0.0656022i 0.602859 0.797847i \(-0.294028\pi\)
−0.681041 + 0.732245i \(0.738472\pi\)
\(500\) 4.53795 + 3.80779i 0.202943 + 0.170290i
\(501\) 0 0
\(502\) −18.9204 6.88645i −0.844457 0.307357i
\(503\) −20.6406 + 35.7506i −0.920320 + 1.59404i −0.121399 + 0.992604i \(0.538738\pi\)
−0.798920 + 0.601437i \(0.794595\pi\)
\(504\) 0 0
\(505\) 6.55097 + 11.3466i 0.291514 + 0.504917i
\(506\) −1.83546 10.4094i −0.0815961 0.462754i
\(507\) 0 0
\(508\) 0.245209 0.0892487i 0.0108794 0.00395977i
\(509\) 2.85202 16.1746i 0.126414 0.716928i −0.854044 0.520200i \(-0.825857\pi\)
0.980458 0.196728i \(-0.0630315\pi\)
\(510\) 0 0
\(511\) −9.71156 + 8.14896i −0.429614 + 0.360489i
\(512\) −9.67844 −0.427731
\(513\) 0 0
\(514\) −20.6845 −0.912355
\(515\) 2.78526 2.33711i 0.122733 0.102985i
\(516\) 0 0
\(517\) −9.00899 + 51.0925i −0.396215 + 2.24705i
\(518\) 5.39335 1.96302i 0.236970 0.0862501i
\(519\) 0 0
\(520\) 4.77239 + 27.0656i 0.209283 + 1.18690i
\(521\) 4.64836 + 8.05119i 0.203648 + 0.352729i 0.949701 0.313157i \(-0.101387\pi\)
−0.746053 + 0.665887i \(0.768053\pi\)
\(522\) 0 0
\(523\) 11.3736 19.6996i 0.497331 0.861402i −0.502664 0.864482i \(-0.667647\pi\)
0.999995 + 0.00307938i \(0.000980199\pi\)
\(524\) −5.27110 1.91852i −0.230269 0.0838110i
\(525\) 0 0
\(526\) −11.5039 9.65288i −0.501592 0.420886i
\(527\) −0.781049 0.655378i −0.0340230 0.0285487i
\(528\) 0 0
\(529\) 19.1676 + 6.97642i 0.833372 + 0.303323i
\(530\) −9.72687 + 16.8474i −0.422508 + 0.731806i
\(531\) 0 0
\(532\) −1.83355 3.17581i −0.0794946 0.137689i
\(533\) 5.78878 + 32.8298i 0.250740 + 1.42202i
\(534\) 0 0
\(535\) −19.8500 + 7.22481i −0.858191 + 0.312356i
\(536\) 1.92124 10.8959i 0.0829849 0.470631i
\(537\) 0 0
\(538\) 26.7710 22.4636i 1.15418 0.968473i
\(539\) 3.00718 0.129528
\(540\) 0 0
\(541\) 2.38959 0.102737 0.0513683 0.998680i \(-0.483642\pi\)
0.0513683 + 0.998680i \(0.483642\pi\)
\(542\) 33.8105 28.3704i 1.45229 1.21861i
\(543\) 0 0
\(544\) 0.461447 2.61700i 0.0197844 0.112203i
\(545\) −19.2649 + 7.01185i −0.825218 + 0.300355i
\(546\) 0 0
\(547\) 5.15158 + 29.2161i 0.220266 + 1.24919i 0.871531 + 0.490340i \(0.163127\pi\)
−0.651266 + 0.758850i \(0.725762\pi\)
\(548\) −1.03904 1.79967i −0.0443856 0.0768781i
\(549\) 0 0
\(550\) 7.15057 12.3852i 0.304901 0.528105i
\(551\) −20.7618 7.55667i −0.884482 0.321925i
\(552\) 0 0
\(553\) 9.91458 + 8.31932i 0.421611 + 0.353773i
\(554\) −22.8328 19.1590i −0.970072 0.813987i
\(555\) 0 0
\(556\) 5.15081 + 1.87474i 0.218443 + 0.0795068i
\(557\) −4.20706 + 7.28685i −0.178259 + 0.308754i −0.941284 0.337615i \(-0.890380\pi\)
0.763025 + 0.646369i \(0.223713\pi\)
\(558\) 0 0
\(559\) −33.8309 58.5969i −1.43090 2.47838i
\(560\) 3.84080 + 21.7823i 0.162304 + 0.920470i
\(561\) 0 0
\(562\) 29.6669 10.7979i 1.25142 0.455480i
\(563\) −4.72783 + 26.8129i −0.199254 + 1.13003i 0.706974 + 0.707240i \(0.250060\pi\)
−0.906228 + 0.422788i \(0.861051\pi\)
\(564\) 0 0
\(565\) 0.579686 0.486415i 0.0243876 0.0204636i
\(566\) 26.4304 1.11095
\(567\) 0 0
\(568\) 13.3915 0.561894
\(569\) −16.8141 + 14.1087i −0.704886 + 0.591469i −0.923159 0.384418i \(-0.874402\pi\)
0.218273 + 0.975888i \(0.429958\pi\)
\(570\) 0 0
\(571\) −7.78872 + 44.1720i −0.325948 + 1.84854i 0.176981 + 0.984214i \(0.443367\pi\)
−0.502929 + 0.864328i \(0.667744\pi\)
\(572\) −13.1795 + 4.79696i −0.551064 + 0.200571i
\(573\) 0 0
\(574\) 3.69317 + 20.9450i 0.154150 + 0.874227i
\(575\) −1.76046 3.04921i −0.0734163 0.127161i
\(576\) 0 0
\(577\) −6.00955 + 10.4088i −0.250181 + 0.433326i −0.963575 0.267437i \(-0.913823\pi\)
0.713395 + 0.700762i \(0.247157\pi\)
\(578\) 23.8002 + 8.66256i 0.989957 + 0.360315i
\(579\) 0 0
\(580\) −5.19834 4.36193i −0.215849 0.181119i
\(581\) −12.2727 10.2980i −0.509157 0.427234i
\(582\) 0 0
\(583\) 28.6433 + 10.4253i 1.18628 + 0.431772i
\(584\) −5.43095 + 9.40669i −0.224734 + 0.389252i
\(585\) 0 0
\(586\) −15.4463 26.7537i −0.638079 1.10519i
\(587\) −2.95721 16.7711i −0.122057 0.692219i −0.983012 0.183539i \(-0.941245\pi\)
0.860956 0.508680i \(-0.169866\pi\)
\(588\) 0 0
\(589\) −2.63455 + 0.958897i −0.108555 + 0.0395107i
\(590\) 4.16438 23.6174i 0.171445 0.972312i
\(591\) 0 0
\(592\) 4.75195 3.98736i 0.195304 0.163880i
\(593\) −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
\(596\) −7.33147 + 6.15184i −0.300309 + 0.251989i
\(597\) 0 0
\(598\) −3.04024 + 17.2420i −0.124324 + 0.705079i
\(599\) −12.7186 + 4.62917i −0.519666 + 0.189143i −0.588518 0.808484i \(-0.700288\pi\)
0.0688523 + 0.997627i \(0.478066\pi\)
\(600\) 0 0
\(601\) −7.86926 44.6288i −0.320994 1.82045i −0.536449 0.843933i \(-0.680235\pi\)
0.215456 0.976514i \(-0.430876\pi\)
\(602\) −21.5837 37.3841i −0.879686 1.52366i
\(603\) 0 0
\(604\) 0.305346 0.528874i 0.0124243 0.0215196i
\(605\) 9.83063 + 3.57806i 0.399672 + 0.145469i
\(606\) 0 0
\(607\) 18.7197 + 15.7077i 0.759808 + 0.637554i 0.938077 0.346427i \(-0.112605\pi\)
−0.178269 + 0.983982i \(0.557050\pi\)
\(608\) −5.59760 4.69694i −0.227013 0.190486i
\(609\) 0 0
\(610\) −3.20097 1.16506i −0.129603 0.0471718i
\(611\) 42.9674 74.4217i 1.73827 3.01078i
\(612\) 0 0
\(613\) 12.5998 + 21.8235i 0.508901 + 0.881443i 0.999947 + 0.0103088i \(0.00328145\pi\)
−0.491046 + 0.871134i \(0.663385\pi\)
\(614\) 4.08375 + 23.1601i 0.164807 + 0.934665i
\(615\) 0 0
\(616\) 25.8166 9.39646i 1.04018 0.378594i
\(617\) 0.701860 3.98045i 0.0282558 0.160247i −0.967415 0.253196i \(-0.918518\pi\)
0.995671 + 0.0929492i \(0.0296294\pi\)
\(618\) 0 0
\(619\) −34.2958 + 28.7776i −1.37846 + 1.15667i −0.408688 + 0.912674i \(0.634014\pi\)
−0.969776 + 0.243995i \(0.921542\pi\)
\(620\) −0.861097 −0.0345825
\(621\) 0 0
\(622\) 7.24860 0.290642
\(623\) −9.67531 + 8.11855i −0.387633 + 0.325263i
\(624\) 0 0
\(625\) −1.61895 + 9.18150i −0.0647579 + 0.367260i
\(626\) −17.6038 + 6.40726i −0.703590 + 0.256086i
\(627\) 0 0
\(628\) −0.301461 1.70967i −0.0120296 0.0682232i
\(629\) −0.638833 1.10649i −0.0254719 0.0441187i
\(630\) 0 0
\(631\) −15.7058 + 27.2033i −0.625238 + 1.08294i 0.363256 + 0.931689i \(0.381665\pi\)
−0.988495 + 0.151255i \(0.951668\pi\)
\(632\) 10.4202 + 3.79265i 0.414495 + 0.150864i
\(633\) 0 0
\(634\) −17.5533 14.7290i −0.697132 0.584963i
\(635\) 0.682854 + 0.572983i 0.0270982 + 0.0227381i
\(636\) 0 0
\(637\) −4.68067 1.70362i −0.185455 0.0675000i
\(638\) −26.9558 + 46.6888i −1.06719 + 1.84843i
\(639\) 0 0
\(640\) 11.4392 + 19.8133i 0.452176 + 0.783191i
\(641\) 8.44635 + 47.9016i 0.333611 + 1.89200i 0.440537 + 0.897734i \(0.354788\pi\)
−0.106926 + 0.994267i \(0.534101\pi\)
\(642\) 0 0
\(643\) 26.3418 9.58763i 1.03882 0.378099i 0.234387 0.972143i \(-0.424692\pi\)
0.804432 + 0.594044i \(0.202470\pi\)
\(644\) −0.382545 + 2.16952i −0.0150744 + 0.0854911i
\(645\) 0 0
\(646\) −3.17072 + 2.66055i −0.124750 + 0.104678i
\(647\) −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
\(650\) −18.1463 + 15.2265i −0.711756 + 0.597234i
\(651\) 0 0
\(652\) 1.36099 7.71855i 0.0533004 0.302282i
\(653\) 4.80391 1.74848i 0.187992 0.0684234i −0.246309 0.969191i \(-0.579218\pi\)
0.434301 + 0.900768i \(0.356996\pi\)
\(654\) 0 0
\(655\) −3.32743 18.8708i −0.130013 0.737343i
\(656\) 11.4933 + 19.9069i 0.448737 + 0.777236i
\(657\) 0 0
\(658\) 27.4126 47.4801i 1.06866 1.85097i
\(659\) −32.8948 11.9727i −1.28140 0.466391i −0.390505 0.920601i \(-0.627699\pi\)
−0.890895 + 0.454210i \(0.849922\pi\)
\(660\) 0 0
\(661\) 1.02149 + 0.857133i 0.0397314 + 0.0333386i 0.662437 0.749118i \(-0.269522\pi\)
−0.622706 + 0.782456i \(0.713967\pi\)
\(662\) −9.80083 8.22387i −0.380920 0.319630i
\(663\) 0 0
\(664\) −12.8986 4.69471i −0.500563 0.182190i
\(665\) 6.26350 10.8487i 0.242888 0.420694i
\(666\) 0 0
\(667\) 6.63648 + 11.4947i 0.256966 + 0.445077i
\(668\) 1.23588 + 7.00905i 0.0478178 + 0.271188i
\(669\) 0 0
\(670\) −11.5674 + 4.21018i −0.446886 + 0.162653i
\(671\) −0.926830 + 5.25631i −0.0357799 + 0.202918i
\(672\) 0 0
\(673\) −2.74208 + 2.30088i −0.105699 + 0.0886923i −0.694106 0.719873i \(-0.744200\pi\)
0.588406 + 0.808565i \(0.299756\pi\)
\(674\) −29.6866 −1.14348
\(675\) 0 0
\(676\) 16.8438 0.647839
\(677\) −28.2968 + 23.7439i −1.08754 + 0.912551i −0.996525 0.0832991i \(-0.973454\pi\)
−0.0910111 + 0.995850i \(0.529010\pi\)
\(678\) 0 0
\(679\) 4.13866 23.4715i 0.158827 0.900753i
\(680\) 3.66782 1.33498i 0.140654 0.0511940i
\(681\) 0 0
\(682\) 1.18794 + 6.73713i 0.0454885 + 0.257978i
\(683\) −19.0083 32.9233i −0.727332 1.25978i −0.958007 0.286745i \(-0.907427\pi\)
0.230675 0.973031i \(-0.425907\pi\)
\(684\) 0 0
\(685\) 3.54941 6.14775i 0.135616 0.234894i
\(686\) 25.8697 + 9.41580i 0.987710 + 0.359497i
\(687\) 0 0
\(688\) −35.7401 29.9895i −1.36258 1.14334i
\(689\) −38.6771 32.4540i −1.47348 1.23640i
\(690\) 0 0
\(691\) −0.517267 0.188270i −0.0196778 0.00716212i 0.332163 0.943222i \(-0.392222\pi\)
−0.351840 + 0.936060i \(0.614444\pi\)
\(692\) −3.09984 + 5.36908i −0.117838 + 0.204102i
\(693\) 0 0
\(694\) 13.9039 + 24.0822i 0.527784 + 0.914148i
\(695\) 3.25150 + 18.4402i 0.123336 + 0.699476i
\(696\) 0 0
\(697\) 4.44896 1.61929i 0.168516 0.0613350i
\(698\) −4.65654 + 26.4086i −0.176253 + 0.999579i
\(699\) 0 0
\(700\) −2.28330 + 1.91592i −0.0863006 + 0.0724148i
\(701\) 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
\(704\) 16.4962 13.8420i 0.621724 0.521689i
\(705\) 0 0
\(706\) −4.15395 + 23.5582i −0.156336 + 0.886626i
\(707\) −20.3859 + 7.41987i −0.766692 + 0.279053i
\(708\) 0 0
\(709\) 2.11100 + 11.9721i 0.0792804 + 0.449621i 0.998445 + 0.0557476i \(0.0177542\pi\)
−0.919165 + 0.393874i \(0.871135\pi\)
\(710\) −7.44966 12.9032i −0.279581 0.484248i
\(711\) 0 0
\(712\) −5.41068 + 9.37158i −0.202774 + 0.351215i
\(713\) 1.58269 + 0.576051i 0.0592721 + 0.0215733i
\(714\) 0 0
\(715\) −36.7022 30.7968i −1.37258 1.15173i
\(716\) 0.111377 + 0.0934566i 0.00416236 + 0.00349264i
\(717\) 0 0
\(718\) −3.63530 1.32314i −0.135668 0.0493791i
\(719\) −4.88834 + 8.46685i −0.182304 + 0.315760i −0.942665 0.333741i \(-0.891689\pi\)
0.760361 + 0.649501i \(0.225022\pi\)
\(720\) 0 0
\(721\) 3.01017 + 5.21376i 0.112104 + 0.194171i
\(722\) −3.23127 18.3255i −0.120256 0.682003i
\(723\) 0 0
\(724\) −0.655884 + 0.238722i −0.0243757 + 0.00887205i
\(725\) −3.11842 + 17.6854i −0.115815 + 0.656821i
\(726\) 0 0
\(727\) 3.32075 2.78644i 0.123160 0.103343i −0.579128 0.815237i \(-0.696607\pi\)
0.702287 + 0.711894i \(0.252162\pi\)
\(728\) −45.5067 −1.68659
\(729\) 0 0
\(730\) 12.0849 0.447283
\(731\) −7.36129 + 6.17686i −0.272267 + 0.228459i
\(732\) 0 0
\(733\) 5.06943 28.7501i 0.187244 1.06191i −0.735795 0.677204i \(-0.763191\pi\)
0.923039 0.384707i \(-0.125697\pi\)
\(734\) 1.94825 0.709106i 0.0719113 0.0261736i
\(735\) 0 0
\(736\) 0.762267 + 4.32303i 0.0280975 + 0.159349i
\(737\) 9.64391 + 16.7037i 0.355238 + 0.615290i
\(738\) 0 0
\(739\) −20.7777 + 35.9880i −0.764319 + 1.32384i 0.176287 + 0.984339i \(0.443591\pi\)
−0.940606 + 0.339501i \(0.889742\pi\)
\(740\) −1.01398 0.369060i −0.0372748 0.0135669i
\(741\) 0 0
\(742\) −24.6755 20.7052i −0.905867 0.760112i
\(743\) 16.3760 + 13.7411i 0.600777 + 0.504112i 0.891695 0.452636i \(-0.149516\pi\)
−0.290918 + 0.956748i \(0.593961\pi\)
\(744\) 0 0
\(745\) −30.7218 11.1818i −1.12556 0.409670i
\(746\) 7.59699 13.1584i 0.278146 0.481763i
\(747\) 0 0
\(748\) 0.995957 + 1.72505i 0.0364158 + 0.0630740i
\(749\) −6.07371 34.4457i −0.221929 1.25862i
\(750\) 0 0
\(751\) 37.5573 13.6697i 1.37048 0.498816i 0.451205 0.892420i \(-0.350994\pi\)
0.919280 + 0.393605i \(0.128772\pi\)
\(752\) 10.2896 58.3549i 0.375221 2.12799i
\(753\) 0 0
\(754\) 68.4067 57.4000i 2.49123 2.09039i
\(755\) 2.08615 0.0759228
\(756\) 0 0
\(757\) 6.68348 0.242915 0.121458 0.992597i \(-0.461243\pi\)
0.121458 + 0.992597i \(0.461243\pi\)
\(758\) −10.3539 + 8.68795i −0.376070 + 0.315561i
\(759\) 0 0
\(760\) 1.86375 10.5699i 0.0676054 0.383410i
\(761\) −39.4906 + 14.3734i −1.43153 + 0.521035i −0.937370 0.348334i \(-0.886747\pi\)
−0.494163 + 0.869369i \(0.664525\pi\)
\(762\) 0 0
\(763\) −5.89469 33.4304i −0.213402 1.21026i
\(764\) −5.06692 8.77617i −0.183315 0.317511i
\(765\) 0 0
\(766\) −26.5445 + 45.9764i −0.959092 + 1.66120i
\(767\) 58.4875 + 21.2877i 2.11186 + 0.768655i
\(768\) 0 0
\(769\) 1.84864 + 1.55120i 0.0666638 + 0.0559375i 0.675511 0.737350i \(-0.263923\pi\)
−0.608847 + 0.793288i \(0.708368\pi\)
\(770\) −23.4155 19.6480i −0.843837 0.708064i
\(771\) 0 0
\(772\) 9.67593 + 3.52175i 0.348244 + 0.126751i
\(773\) −0.698900 + 1.21053i −0.0251377 + 0.0435398i −0.878321 0.478072i \(-0.841336\pi\)
0.853183 + 0.521612i \(0.174669\pi\)
\(774\) 0 0
\(775\) 1.13940 + 1.97350i 0.0409284 + 0.0708901i
\(776\) −3.54593 20.1100i −0.127292 0.721907i
\(777\) 0 0
\(778\) 22.1800 8.07285i 0.795190 0.289426i
\(779\) 2.26068 12.8210i 0.0809973 0.459358i
\(780\) 0