Properties

Label 729.2.e.s.406.1
Level $729$
Weight $2$
Character 729.406
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 406.1
Root \(-1.22778i\) of defining polynomial
Character \(\chi\) \(=\) 729.406
Dual form 729.2.e.s.325.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20913 - 1.01458i) q^{2} +(0.0853237 + 0.483895i) q^{4} +(-1.57728 - 0.574083i) q^{5} +(0.482617 - 2.73706i) q^{7} +(-1.19062 + 2.06222i) q^{8} +O(q^{10})\) \(q+(-1.20913 - 1.01458i) q^{2} +(0.0853237 + 0.483895i) q^{4} +(-1.57728 - 0.574083i) q^{5} +(0.482617 - 2.73706i) q^{7} +(-1.19062 + 2.06222i) q^{8} +(1.32468 + 2.29442i) q^{10} +(3.90087 - 1.41980i) q^{11} +(5.26736 - 4.41984i) q^{13} +(-3.36051 + 2.81980i) q^{14} +(4.45535 - 1.62162i) q^{16} +(-0.488276 - 0.845718i) q^{17} +(-1.34264 + 2.32553i) q^{19} +(0.143217 - 0.812221i) q^{20} +(-6.15715 - 2.24102i) q^{22} +(0.280124 + 1.58866i) q^{23} +(-1.67198 - 1.40296i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(-6.30292 - 5.28878i) q^{29} +(0.181301 + 1.02821i) q^{31} +(-2.55707 - 0.930697i) q^{32} +(-0.267660 + 1.51798i) q^{34} +(-2.33252 + 4.04005i) q^{35} +(0.654172 + 1.13306i) q^{37} +(3.98286 - 1.44964i) q^{38} +(3.06183 - 2.56918i) q^{40} +(-3.71391 + 3.11634i) q^{41} +(-9.24679 + 3.36556i) q^{43} +(1.01987 + 1.76647i) q^{44} +(1.27312 - 2.20510i) q^{46} +(2.17020 - 12.3078i) q^{47} +(-0.680721 - 0.247762i) q^{49} +(0.598226 + 3.39271i) q^{50} +(2.58817 + 2.17173i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(5.06980 + 4.25406i) q^{56} +(2.25515 + 12.7896i) q^{58} +(-8.50598 - 3.09592i) q^{59} +(-0.223267 + 1.26621i) q^{61} +(0.823982 - 1.42718i) q^{62} +(-2.59373 - 4.49247i) q^{64} +(-10.8455 + 3.94742i) q^{65} +(-3.55927 + 2.98658i) q^{67} +(0.367577 - 0.308434i) q^{68} +(6.91926 - 2.51841i) q^{70} +(-2.81187 - 4.87030i) q^{71} +(2.28072 - 3.95033i) q^{73} +(0.358600 - 2.03372i) q^{74} +(-1.23987 - 0.451276i) q^{76} +(-2.00345 - 11.3621i) q^{77} +(3.56732 + 2.99333i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(4.41578 + 3.70528i) q^{83} +(0.284635 + 1.61425i) q^{85} +(14.5952 + 5.31221i) q^{86} +(-1.71652 + 9.73490i) q^{88} +(-2.27221 + 3.93558i) q^{89} +(-9.55523 - 16.5502i) q^{91} +(-0.744844 + 0.271101i) q^{92} +(-15.1113 + 12.6799i) q^{94} +(3.45278 - 2.89722i) q^{95} +(-8.05828 + 2.93297i) q^{97} +(0.571704 + 0.990221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

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

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 \(-0.466228\pi\)
−0.960881 + 0.276961i \(0.910673\pi\)
\(3\) 0 0
\(4\) 0.0853237 + 0.483895i 0.0426619 + 0.241948i
\(5\) −1.57728 0.574083i −0.705382 0.256738i −0.0356747 0.999363i \(-0.511358\pi\)
−0.669707 + 0.742626i \(0.733580\pi\)
\(6\) 0 0
\(7\) 0.482617 2.73706i 0.182412 1.03451i −0.746823 0.665023i \(-0.768422\pi\)
0.929235 0.369488i \(-0.120467\pi\)
\(8\) −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 \(-0.395875\pi\)
0.854843 + 0.518886i \(0.173653\pi\)
\(12\) 0 0
\(13\) 5.26736 4.41984i 1.46090 1.22584i 0.536792 0.843715i \(-0.319636\pi\)
0.924110 0.382128i \(-0.124809\pi\)
\(14\) −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 \(-0.204451\pi\)
−0.919143 + 0.393923i \(0.871118\pi\)
\(18\) 0 0
\(19\) −1.34264 + 2.32553i −0.308024 + 0.533513i −0.977930 0.208933i \(-0.933001\pi\)
0.669906 + 0.742446i \(0.266334\pi\)
\(20\) 0.143217 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 \(-0.00176509\pi\)
−0.941575 + 0.336804i \(0.890654\pi\)
\(24\) 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 \(-0.554515\pi\)
−0.999995 + 0.00326885i \(0.998959\pi\)
\(30\) 0 0
\(31\) 0.181301 + 1.02821i 0.0325626 + 0.184672i 0.996751 0.0805475i \(-0.0256669\pi\)
−0.964188 + 0.265219i \(0.914556\pi\)
\(32\) −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 0.914775 0.403963i \(-0.132368\pi\)
−0.807230 + 0.590237i \(0.799034\pi\)
\(38\) 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 \(-0.845809\pi\)
0.304936 + 0.952373i \(0.401365\pi\)
\(42\) 0 0
\(43\) −9.24679 + 3.36556i −1.41012 + 0.513243i −0.931166 0.364596i \(-0.881207\pi\)
−0.478957 + 0.877839i \(0.658985\pi\)
\(44\) 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 −0.246798 0.969067i \(-0.579379\pi\)
0.563355 0.826215i \(-0.309510\pi\)
\(48\) 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 \(-0.331749\pi\)
0.504305 + 0.863525i \(0.331749\pi\)
\(54\) 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 \(-0.589456\pi\)
−0.830033 + 0.557714i \(0.811679\pi\)
\(60\) 0 0
\(61\) −0.223267 + 1.26621i −0.0285864 + 0.162121i −0.995759 0.0919982i \(-0.970675\pi\)
0.967173 + 0.254120i \(0.0817857\pi\)
\(62\) 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 −0.833772 0.552109i \(-0.813823\pi\)
0.398938 + 0.916978i \(0.369379\pi\)
\(68\) 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 \(-0.274966\pi\)
−0.983236 + 0.182339i \(0.941633\pi\)
\(72\) 0 0
\(73\) 2.28072 3.95033i 0.266938 0.462351i −0.701131 0.713032i \(-0.747321\pi\)
0.968070 + 0.250681i \(0.0806547\pi\)
\(74\) 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 0.821017 0.570904i \(-0.193407\pi\)
−0.419662 + 0.907680i \(0.637852\pi\)
\(80\) −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 \(-0.175316\pi\)
−0.367426 + 0.930053i \(0.619761\pi\)
\(84\) 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 \(-0.910761\pi\)
0.720104 + 0.693866i \(0.244094\pi\)
\(90\) 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 −0.717004 0.697069i \(-0.754487\pi\)
−0.101190 + 0.994867i \(0.532265\pi\)
\(98\) 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 0.840077 + 0.542467i \(0.182510\pi\)
−0.974949 + 0.222429i \(0.928601\pi\)
\(102\) 0 0
\(103\) 2.03551 + 0.740866i 0.200565 + 0.0729997i 0.440349 0.897826i \(-0.354855\pi\)
−0.239784 + 0.970826i \(0.577077\pi\)
\(104\) 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 \(-0.291845\pi\)
0.608317 + 0.793695i \(0.291845\pi\)
\(108\) 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 \(-0.395639\pi\)
−0.361870 + 0.932229i \(0.617862\pi\)
\(114\) 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 −0.854004 0.520267i \(-0.825833\pi\)
0.877566 + 0.479456i \(0.159166\pi\)
\(128\) −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 −0.940200 0.340623i \(-0.889362\pi\)
0.766999 0.641648i \(-0.221749\pi\)
\(132\) 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 \(-0.335603\pi\)
−0.770607 + 0.637310i \(0.780047\pi\)
\(138\) 0 0
\(139\) −1.93714 10.9861i −0.164306 0.931825i −0.949777 0.312927i \(-0.898691\pi\)
0.785471 0.618898i \(-0.212421\pi\)
\(140\) −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 0.223660 0.974667i \(-0.428200\pi\)
0.998698 0.0510127i \(-0.0162449\pi\)
\(150\) 0 0
\(151\) 1.16791 0.425083i 0.0950429 0.0345928i −0.294061 0.955787i \(-0.595007\pi\)
0.389104 + 0.921194i \(0.372785\pi\)
\(152\) −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 0.471089 0.882086i \(-0.343861\pi\)
−0.206119 + 0.978527i \(0.566083\pi\)
\(158\) −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 \(-0.199526\pi\)
0.243368 + 0.969934i \(0.421748\pi\)
\(168\) 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 \(-0.451878\pi\)
0.750826 + 0.660500i \(0.229656\pi\)
\(174\) 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 \(-0.163147\pi\)
−0.860443 + 0.509546i \(0.829813\pi\)
\(180\) 0 0
\(181\) −0.710251 + 1.23019i −0.0527925 + 0.0914393i −0.891214 0.453583i \(-0.850146\pi\)
0.838421 + 0.545022i \(0.183479\pi\)
\(182\) −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 \(-0.545879\pi\)
−0.999538 + 0.0303946i \(0.990324\pi\)
\(192\) 0 0
\(193\) −3.63896 20.6376i −0.261938 1.48552i −0.777614 0.628741i \(-0.783570\pi\)
0.515676 0.856784i \(-0.327541\pi\)
\(194\) 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 \(-0.944387\pi\)
0.642926 + 0.765929i \(0.277720\pi\)
\(198\) 0 0
\(199\) 5.34583 + 9.25925i 0.378956 + 0.656371i 0.990911 0.134522i \(-0.0429498\pi\)
−0.611955 + 0.790893i \(0.709616\pi\)
\(200\) 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 0.779355 0.626582i \(-0.215547\pi\)
0.194261 + 0.980950i \(0.437769\pi\)
\(212\) 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 0.826147 + 0.563455i \(0.190528\pi\)
−0.969037 + 0.246916i \(0.920583\pi\)
\(224\) −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 \(-0.571368\pi\)
0.456380 + 0.889785i \(0.349146\pi\)
\(228\) 0 0
\(229\) −14.2503 + 11.9574i −0.941685 + 0.790168i −0.977878 0.209177i \(-0.932921\pi\)
0.0361925 + 0.999345i \(0.488477\pi\)
\(230\) −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 \(-0.160976\pi\)
−0.856948 + 0.515403i \(0.827642\pi\)
\(234\) 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 0.861320 + 0.508062i \(0.169638\pi\)
−0.635609 + 0.772011i \(0.719251\pi\)
\(240\) 0 0
\(241\) 11.7138 + 9.82906i 0.754553 + 0.633145i 0.936703 0.350125i \(-0.113861\pi\)
−0.182150 + 0.983271i \(0.558305\pi\)
\(242\) −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 \(-0.701445\pi\)
0.994037 + 0.109042i \(0.0347782\pi\)
\(252\) 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 \(-0.588196\pi\)
0.899746 + 0.436413i \(0.143751\pi\)
\(258\) 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 −0.890549 0.454888i \(-0.849679\pi\)
0.992423 0.122869i \(-0.0392094\pi\)
\(264\) 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 \(-0.735845\pi\)
−0.674973 + 0.737842i \(0.735845\pi\)
\(270\) 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 0.712485 + 0.701687i \(0.247570\pi\)
−0.909508 + 0.415686i \(0.863542\pi\)
\(278\) −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 \(-0.814594\pi\)
−0.286139 + 0.958188i \(0.592372\pi\)
\(282\) 0 0
\(283\) 12.8274 10.7635i 0.762512 0.639824i −0.176267 0.984342i \(-0.556402\pi\)
0.938780 + 0.344519i \(0.111958\pi\)
\(284\) 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 −0.907271 0.420548i \(-0.861838\pi\)
0.708720 0.705490i \(-0.249273\pi\)
\(294\) 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 0.571258 0.820770i \(-0.306455\pi\)
−0.996437 + 0.0843392i \(0.973122\pi\)
\(308\) 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 \(-0.763786\pi\)
0.537573 + 0.843217i \(0.319341\pi\)
\(312\) 0 0
\(313\) −11.1529 + 4.05933i −0.630400 + 0.229447i −0.637405 0.770529i \(-0.719992\pi\)
0.00700533 + 0.999975i \(0.497770\pi\)
\(314\) −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 −0.828455 0.560056i \(-0.810780\pi\)
0.970043 0.242932i \(-0.0781092\pi\)
\(318\) 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 0.921379 + 0.388665i \(0.127064\pi\)
−0.998744 + 0.0500957i \(0.984047\pi\)
\(332\) −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 −0.944462 0.328620i \(-0.893417\pi\)
0.159623 + 0.987178i \(0.448972\pi\)
\(338\) −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 0.949855 + 0.312692i \(0.101231\pi\)
−0.785624 + 0.618704i \(0.787658\pi\)
\(348\) 0 0
\(349\) −13.0146 10.9205i −0.696653 0.584561i 0.224166 0.974551i \(-0.428034\pi\)
−0.920819 + 0.389990i \(0.872479\pi\)
\(350\) 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 \(-0.145632\pi\)
−0.279222 + 0.960227i \(0.590076\pi\)
\(354\) 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 \(-0.812731\pi\)
0.896551 + 0.442940i \(0.146065\pi\)
\(360\) 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 −0.309604 0.950866i \(-0.600196\pi\)
0.374035 + 0.927415i \(0.377974\pi\)
\(368\) 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 0.565412 0.824809i \(-0.308717\pi\)
−0.0970463 + 0.995280i \(0.530939\pi\)
\(374\) 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 \(-0.0597732\pi\)
0.632581 + 0.774494i \(0.281995\pi\)
\(384\) 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 \(-0.734877\pi\)
−0.0397455 + 0.999210i \(0.512655\pi\)
\(390\) 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 −0.574991 0.818159i \(-0.694995\pi\)
0.996043 + 0.0888774i \(0.0283279\pi\)
\(398\) 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 −0.987325 0.158712i \(-0.949266\pi\)
0.873499 0.486825i \(-0.161845\pi\)
\(402\) 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 0.874680 + 0.484700i \(0.161071\pi\)
−0.656153 + 0.754628i \(0.727818\pi\)
\(410\) −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 \(-0.622065\pi\)
0.848309 + 0.529501i \(0.177621\pi\)
\(420\) 0 0
\(421\) 16.6112 6.04597i 0.809579 0.294663i 0.0961292 0.995369i \(-0.469354\pi\)
0.713450 + 0.700706i \(0.247132\pi\)
\(422\) −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 \(-0.623408\pi\)
−0.378059 + 0.925782i \(0.623408\pi\)
\(432\) 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 −0.642761 0.766067i \(-0.722211\pi\)
0.866008 0.500030i \(-0.166678\pi\)
\(440\) 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 \(-0.302294\pi\)
0.968527 + 0.248908i \(0.0800718\pi\)
\(444\) 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 \(-0.329500\pi\)
−0.999927 + 0.0120419i \(0.996167\pi\)
\(450\) 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 0.504447 0.863443i \(-0.331697\pi\)
−0.762729 + 0.646718i \(0.776141\pi\)
\(458\) 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 \(-0.458810\pi\)
−0.954166 + 0.299277i \(0.903254\pi\)
\(462\) 0 0
\(463\) 0.864046 + 4.90025i 0.0401556 + 0.227734i 0.998281 0.0586166i \(-0.0186690\pi\)
−0.958125 + 0.286350i \(0.907558\pi\)
\(464\) −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 \(-0.926584\pi\)
0.684735 + 0.728792i \(0.259918\pi\)
\(468\) 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 0.635068 + 0.772456i \(0.280972\pi\)
−0.860964 + 0.508666i \(0.830139\pi\)
\(480\) 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 \(-0.298583\pi\)
−0.0653150 + 0.997865i \(0.520805\pi\)
\(492\) 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 −0.681041 0.732245i \(-0.738472\pi\)
0.602859 + 0.797847i \(0.294028\pi\)
\(500\) −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 0.798920 + 0.601437i \(0.205405\pi\)
0.121399 + 0.992604i \(0.461262\pi\)
\(504\) 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 −0.980458 0.196728i \(-0.936968\pi\)
0.854044 0.520200i \(-0.174143\pi\)
\(510\) 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 \(-0.898613\pi\)
0.746053 + 0.665887i \(0.231947\pi\)
\(522\) 0 0
\(523\) 11.3736 + 19.6996i 0.497331 + 0.861402i 0.999995 0.00307938i \(-0.000980199\pi\)
−0.502664 + 0.864482i \(0.667647\pi\)
\(524\) 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 −0.651266 0.758850i \(-0.725762\pi\)
0.871531 0.490340i \(-0.163127\pi\)
\(548\) 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 \(-0.109620\pi\)
−0.763025 + 0.646369i \(0.776287\pi\)
\(558\) 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 0.906228 + 0.422788i \(0.138949\pi\)
−0.706974 + 0.707240i \(0.749940\pi\)
\(564\) 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 \(-0.125598\pi\)
−0.218273 + 0.975888i \(0.570042\pi\)
\(570\) 0 0
\(571\) −7.78872 44.1720i −0.325948 1.84854i −0.502929 0.864328i \(-0.667744\pi\)
0.176981 0.984214i \(-0.443367\pi\)
\(572\) 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 0.713395 0.700762i \(-0.247157\pi\)
−0.963575 + 0.267437i \(0.913823\pi\)
\(578\) −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 −0.860956 0.508680i \(-0.830134\pi\)
0.983012 0.183539i \(-0.0587554\pi\)
\(588\) 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 \(-0.400836\pi\)
0.306519 + 0.951865i \(0.400836\pi\)
\(594\) 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 \(-0.299712\pi\)
−0.0688523 + 0.997627i \(0.521934\pi\)
\(600\) 0 0
\(601\) −7.86926 + 44.6288i −0.320994 + 1.82045i 0.215456 + 0.976514i \(0.430876\pi\)
−0.536449 + 0.843933i \(0.680235\pi\)
\(602\) 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 −0.178269 0.983982i \(-0.557050\pi\)
0.938077 + 0.346427i \(0.112605\pi\)
\(608\) 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 −0.491046 0.871134i \(-0.663385\pi\)
0.999947 0.0103088i \(-0.00328145\pi\)
\(614\) −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 \(-0.0814817\pi\)
−0.995671 + 0.0929492i \(0.970371\pi\)
\(618\) 0 0
\(619\) −34.2958 28.7776i −1.37846 1.15667i −0.969776 0.243995i \(-0.921542\pi\)
−0.408688 0.912674i \(-0.634014\pi\)
\(620\) 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 −0.988495 0.151255i \(-0.951668\pi\)
0.363256 0.931689i \(-0.381665\pi\)
\(632\) −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 0.106926 + 0.994267i \(0.465899\pi\)
−0.440537 + 0.897734i \(0.645212\pi\)
\(642\) 0 0
\(643\) 26.3418 + 9.58763i 1.03882 + 0.378099i 0.804432 0.594044i \(-0.202470\pi\)
0.234387 + 0.972143i \(0.424692\pi\)
\(644\) 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 \(-0.235696\pi\)
0.738159 + 0.674627i \(0.235696\pi\)
\(648\) 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 \(-0.420782\pi\)
−0.434301 + 0.900768i \(0.643004\pi\)
\(654\) 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 \(-0.372301\pi\)
0.890895 + 0.454210i \(0.150078\pi\)
\(660\) 0 0
\(661\) 1.02149 0.857133i 0.0397314 0.0333386i −0.622706 0.782456i \(-0.713967\pi\)
0.662437 + 0.749118i \(0.269522\pi\)
\(662\) 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 0.588406 0.808565i \(-0.299756\pi\)
−0.694106 + 0.719873i \(0.744200\pi\)
\(674\) 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 \(-0.0265457\pi\)
0.0910111 + 0.995850i \(0.470990\pi\)
\(678\) 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 −0.230675 0.973031i \(-0.574093\pi\)
0.958007 0.286745i \(-0.0925733\pi\)
\(684\) 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 −0.351840 0.936060i \(-0.614444\pi\)
0.332163 + 0.943222i \(0.392222\pi\)
\(692\) 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 \(-0.616973\pi\)
−0.359267 + 0.933235i \(0.616973\pi\)
\(702\) 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 −0.919165 0.393874i \(-0.871135\pi\)
0.998445 0.0557476i \(-0.0177542\pi\)
\(710\) 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 \(-0.108311\pi\)
−0.760361 + 0.649501i \(0.774978\pi\)
\(720\) 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 0.702287 0.711894i \(-0.252162\pi\)
−0.579128 + 0.815237i \(0.696607\pi\)
\(728\) 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 0.923039 + 0.384707i \(0.125697\pi\)
−0.735795 + 0.677204i \(0.763191\pi\)
\(734\) −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 −0.940606 0.339501i \(-0.889742\pi\)
0.176287 0.984339i \(-0.443591\pi\)
\(740\) 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 \(-0.850484\pi\)
0.290918 + 0.956748i \(0.406039\pi\)
\(744\) 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 0.919280 0.393605i \(-0.128772\pi\)
0.451205 + 0.892420i \(0.350994\pi\)
\(752\) −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 \(-0.113253\pi\)
0.494163 + 0.869369i \(0.335475\pi\)
\(762\) 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 −0.608847 0.793288i \(-0.708368\pi\)
0.675511 + 0.737350i \(0.263923\pi\)
\(770\) 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 \(-0.158664\pi\)
−0.853183 + 0.521612i \(0.825331\pi\)
\(774\) 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 0
\(781\) −17.8836 15.0061i −0.639925 0.536961i
\(782\) −2.48653 −0.0889181
\(783\) 0 0
\(784\) −3.43462 −0.122665
\(785\) −4.54295 3.81199i −0.162145 0.136056i
\(786\) 0 0
\(787\) −6.88542 39.0491i −0.245439 1.39195i −0.819472 0.573119i \(-0.805733\pi\)
0.574033 0.818832i \(-0.305378\pi\)
\(788\) −4.43083 1.61269i −0.157842 0.0574497i
\(789\) 0 0
\(790\) −2.14239 + 12.1501i −0.0762230 + 0.432282i
\(791\) −0.626496 + 1.08512i −0.0222756 + 0.0385825i
\(792\) 0 0
\(793\) 4.42041 + 7.65637i 0.156973 + 0.271886i
\(794\) −24.8865 + 9.05795i −0.883190 + 0.321455i
\(795\) 0 0
\(796\) −4.02438 + 3.37686i −0.142640 + 0.119689i
\(797\) 2.52325 2.11726i 0.0893781 0.0749971i −0.597004 0.802238i \(-0.703642\pi\)
0.686382 + 0.727241i \(0.259198\pi\)
\(798\) 0 0
\(799\) −11.4686 + 4.17423i −0.405730 + 0.147674i
\(800\) 2.96964 + 5.14356i 0.104993 + 0.181852i
\(801\) 0 0
\(802\) −10.3593 + 17.9428i −0.365800 + 0.633583i
\(803\) 3.28813 18.6479i 0.116035 0.658070i
\(804\) 0 0
\(805\) −7.07167 2.57388i −0.249244 0.0907172i
\(806\) −1.96769 11.1593i −0.0693089 0.393070i
\(807\) 0 0
\(808\) −14.2387 11.9477i −0.500915 0.420318i
\(809\) 6.54436 0.230087 0.115044 0.993360i \(-0.463299\pi\)
0.115044 + 0.993360i \(0.463299\pi\)
\(810\) 0 0
\(811\) −44.7516 −1.57144 −0.785721 0.618581i \(-0.787708\pi\)
−0.785721 + 0.618581i \(0.787708\pi\)
\(812\) −8.60744 7.22250i −0.302062 0.253460i
\(813\) 0 0
\(814\) −1.48863 8.44244i −0.0521764 0.295907i
\(815\) −25.1590 9.15714i −0.881282 0.320760i
\(816\) 0 0
\(817\) 4.58845 26.0224i 0.160530 0.910409i
\(818\) 20.0856 34.7893i 0.702276 1.21638i
\(819\) 0 0
\(820\) 1.99927 + 3.46283i 0.0698174 + 0.120927i
\(821\) −46.6876 + 16.9929i −1.62941 + 0.593057i −0.985142 0.171743i \(-0.945060\pi\)
−0.644268 + 0.764800i \(0.722838\pi\)
\(822\) 0 0
\(823\) 8.13586 6.82680i 0.283598 0.237967i −0.489880 0.871790i \(-0.662959\pi\)
0.773479 + 0.633822i \(0.218515\pi\)
\(824\) −3.95135 + 3.31558i −0.137652 + 0.115504i
\(825\) 0 0
\(826\) 37.3143 13.5813i 1.29833 0.472554i
\(827\) −8.20039 14.2035i −0.285156 0.493904i 0.687491 0.726193i \(-0.258712\pi\)
−0.972647 + 0.232289i \(0.925379\pi\)
\(828\) 0 0
\(829\) 1.47823 2.56036i 0.0513409 0.0889251i −0.839213 0.543803i \(-0.816984\pi\)
0.890554 + 0.454878i \(0.150317\pi\)
\(830\) −2.65195 + 15.0400i −0.0920505 + 0.522044i
\(831\) 0 0
\(832\) −33.5181 12.1996i −1.16203 0.422944i
\(833\) 0.122842 + 0.696674i 0.00425624 + 0.0241383i
\(834\) 0 0
\(835\) −18.6245 15.6278i −0.644528 0.540823i
\(836\) −5.47730 −0.189436
\(837\) 0 0
\(838\) −19.9985 −0.690835
\(839\) 24.8554 + 20.8562i 0.858104 + 0.720035i 0.961559 0.274599i \(-0.0885452\pi\)
−0.103455 + 0.994634i \(0.532990\pi\)
\(840\) 0 0
\(841\) 6.71983 + 38.1100i 0.231718 + 1.31414i
\(842\) −26.2191 9.54299i −0.903572 0.328873i
\(843\) 0 0
\(844\) −1.28414 + 7.28274i −0.0442020 + 0.250682i
\(845\) −28.7696 + 49.8304i −0.989705 + 1.71422i
\(846\) 0 0
\(847\) −8.66114 15.0015i −0.297600 0.515459i
\(848\) 32.7147 11.9072i 1.12343 0.408895i
\(849\) 0 0
\(850\) 2.57717 2.16251i 0.0883964 0.0741734i
\(851\) −1.61680 + 1.35666i −0.0554232 + 0.0465056i
\(852\) 0 0
\(853\) −26.6244 + 9.69049i −0.911602 + 0.331796i −0.754892 0.655849i \(-0.772311\pi\)
−0.156710 + 0.987645i \(0.550089\pi\)
\(854\) −2.82017 4.88467i −0.0965041 0.167150i
\(855\) 0 0
\(856\) −14.9839 + 25.9529i −0.512140 + 0.887052i
\(857\) −2.43168 + 13.7907i −0.0830644 + 0.471082i 0.914693 + 0.404149i \(0.132432\pi\)
−0.997757 + 0.0669326i \(0.978679\pi\)
\(858\) 0 0
\(859\) 2.02952 + 0.738685i 0.0692464 + 0.0252036i 0.376411 0.926453i \(-0.377158\pi\)
−0.307165 + 0.951656i \(0.599380\pi\)
\(860\) 1.40928 + 7.99244i 0.0480562 + 0.272540i
\(861\) 0 0
\(862\) 18.9802 + 15.9262i 0.646467 + 0.542450i
\(863\) 14.9487 0.508859 0.254430 0.967091i \(-0.418112\pi\)
0.254430 + 0.967091i \(0.418112\pi\)
\(864\) 0 0
\(865\) −21.1784 −0.720087
\(866\) 15.2663 + 12.8099i 0.518769 + 0.435299i
\(867\) 0 0
\(868\) 0.247589 + 1.40415i 0.00840373 + 0.0476599i
\(869\) 18.1656 + 6.61173i 0.616225 + 0.224288i
\(870\) 0 0
\(871\) −5.54774 + 31.4628i −0.187978 + 1.06608i
\(872\) 14.5423 25.1879i 0.492463 0.852971i
\(873\) 0 0
\(874\) 3.41869 + 5.92134i 0.115639 + 0.200292i
\(875\) 31.4865 11.4601i 1.06444 0.387424i
\(876\) 0 0
\(877\) −1.44559 + 1.21299i −0.0488140 + 0.0409598i −0.666868 0.745176i \(-0.732366\pi\)
0.618054 + 0.786135i \(0.287921\pi\)
\(878\) −32.5702 + 27.3296i −1.09919 + 0.922330i
\(879\) 0 0
\(880\) −31.0443 + 11.2992i −1.04650 + 0.380895i
\(881\) 23.4129 + 40.5523i 0.788800 + 1.36624i 0.926702 + 0.375796i \(0.122631\pi\)
−0.137902 + 0.990446i \(0.544036\pi\)
\(882\) 0 0
\(883\) 15.0317 26.0357i 0.505858 0.876172i −0.494119 0.869394i \(-0.664509\pi\)
0.999977 0.00677750i \(-0.00215736\pi\)
\(884\) 0.572933 3.24926i 0.0192698 0.109285i
\(885\) 0 0
\(886\) −51.5089 18.7477i −1.73048 0.629842i
\(887\) 5.19449 + 29.4594i 0.174414 + 0.989150i 0.938818 + 0.344413i \(0.111922\pi\)
−0.764404 + 0.644737i \(0.776967\pi\)
\(888\) 0 0
\(889\) −1.13067 0.948748i −0.0379216 0.0318200i
\(890\) −12.0398 −0.403576
\(891\) 0 0
\(892\) −6.03788 −0.202163
\(893\) 25.7084 + 21.5719i 0.860299 + 0.721877i
\(894\) 0 0
\(895\) −0.0862455 0.489122i −0.00288287 0.0163496i
\(896\) 35.5977 + 12.9565i 1.18924 + 0.432847i
\(897\) 0 0
\(898\) −5.68624 + 32.2483i −0.189752 + 1.07614i
\(899\) 4.29524 7.43957i 0.143254 0.248123i
\(900\) 0 0
\(901\) −3.58531 6.20994i −0.119444 0.206883i
\(902\) 29.8509 10.8648i 0.993927 0.361760i
\(903\) 0 0
\(904\) 0.822382 0.690060i 0.0273520 0.0229511i
\(905\) 1.82650 1.53261i 0.0607148 0.0509458i
\(906\) 0 0
\(907\) −25.1511 + 9.15425i −0.835129 + 0.303962i −0.723962 0.689840i \(-0.757681\pi\)
−0.111167 + 0.993802i \(0.535459\pi\)
\(908\) 0.921928 + 1.59683i 0.0305953 + 0.0529926i
\(909\) 0 0
\(910\) 25.3153 43.8474i 0.839194 1.45353i
\(911\) −0.0766027 + 0.434435i −0.00253796 + 0.0143935i −0.986050 0.166447i \(-0.946771\pi\)
0.983512 + 0.180840i \(0.0578817\pi\)
\(912\) 0 0
\(913\) 22.4862 + 8.18429i 0.744183 + 0.270861i
\(914\) 1.97555 + 11.2039i 0.0653453 + 0.370591i
\(915\) 0 0
\(916\) −7.00202 5.87539i −0.231353 0.194128i
\(917\) −31.7284 −1.04776
\(918\) 0 0
\(919\) 49.0749 1.61883 0.809416 0.587236i \(-0.199784\pi\)
0.809416 + 0.587236i \(0.199784\pi\)
\(920\) 4.93925 + 4.14452i 0.162842 + 0.136641i
\(921\) 0 0
\(922\) 6.33877 + 35.9489i 0.208756 + 1.18391i
\(923\) −36.3370 13.2256i −1.19605 0.435326i
\(924\) 0 0
\(925\) 0.495871 2.81223i 0.0163041 0.0924654i
\(926\) 3.92694 6.80167i 0.129047 0.223517i
\(927\) 0 0
\(928\) 11.1948 + 19.3899i 0.367486 + 0.636504i
\(929\) 30.4754 11.0921i 0.999865 0.363921i 0.210333 0.977630i \(-0.432545\pi\)
0.789533 + 0.613709i \(0.210323\pi\)
\(930\) 0 0
\(931\) 1.49014 1.25038i 0.0488375 0.0409795i
\(932\) −0.205435 + 0.172380i −0.00672924 + 0.00564651i
\(933\) 0 0
\(934\) 18.5125 6.73802i 0.605749 0.220475i
\(935\) 3.40224 + 5.89284i 0.111265 + 0.192717i
\(936\) 0 0
\(937\) −24.3079 + 42.1025i −0.794103 + 1.37543i 0.129303 + 0.991605i \(0.458726\pi\)
−0.923407 + 0.383822i \(0.874607\pi\)
\(938\) 3.53939 20.0729i 0.115565 0.655402i
\(939\) 0 0
\(940\) −9.68588 3.52537i −0.315918 0.114985i
\(941\) 0.123366 + 0.699641i 0.00402160 + 0.0228076i 0.986753 0.162233i \(-0.0518695\pi\)
−0.982731 + 0.185040i \(0.940758\pi\)
\(942\) 0 0
\(943\) −5.99117 5.02719i −0.195099 0.163708i
\(944\) −42.9175 −1.39685
\(945\) 0 0
\(946\) 64.4762 2.09630
\(947\) −19.9997 16.7817i −0.649902 0.545333i 0.257139 0.966374i \(-0.417220\pi\)
−0.907041 + 0.421042i \(0.861665\pi\)
\(948\) 0 0
\(949\) −5.44642 30.8882i −0.176798 1.00267i
\(950\) −8.69304 3.16401i −0.282039 0.102654i
\(951\) 0 0
\(952\) 1.12228 6.36477i 0.0363733 0.206284i
\(953\) −25.5027 + 44.1720i −0.826114 + 1.43087i 0.0749515 + 0.997187i \(0.476120\pi\)
−0.901065 + 0.433684i \(0.857214\pi\)
\(954\) 0 0
\(955\) 17.3088 + 29.9798i 0.560101 + 0.970123i
\(956\) −9.27829 + 3.37702i −0.300081 + 0.109221i
\(957\) 0 0
\(958\) 34.4254 28.8863i 1.11223 0.933275i
\(959\) −9.00428 + 7.55549i −0.290763 + 0.243979i
\(960\) 0 0
\(961\) 28.1061 10.2298i 0.906649 0.329993i
\(962\) −7.09985 12.2973i −0.228908 0.396481i
\(963\) 0 0
\(964\) −3.75677 + 6.50691i −0.120997 + 0.209573i
\(965\) −6.10802 + 34.6403i −0.196624 + 1.11511i
\(966\) 0 0
\(967\) −9.40146 3.42185i −0.302330 0.110039i 0.186401 0.982474i \(-0.440318\pi\)
−0.488731 + 0.872435i \(0.662540\pi\)
\(968\) 2.57719 + 14.6160i 0.0828340 + 0.469775i
\(969\) 0 0
\(970\) −17.4041 14.6038i −0.558812 0.468899i
\(971\) −44.6269 −1.43215 −0.716073 0.698025i \(-0.754062\pi\)
−0.716073 + 0.698025i \(0.754062\pi\)
\(972\) 0 0
\(973\) −31.0044 −0.993954
\(974\) −35.8918 30.1168i −1.15005 0.965006i
\(975\) 0 0
\(976\) 1.05857 + 6.00346i 0.0338840 + 0.192166i
\(977\) −36.7285 13.3681i −1.17505 0.427683i −0.320598 0.947215i \(-0.603884\pi\)
−0.854451 + 0.519533i \(0.826106\pi\)
\(978\) 0 0
\(979\) −3.27585 + 18.5783i −0.104697 + 0.593765i
\(980\) −0.298728 + 0.517412i −0.00954252 + 0.0165281i
\(981\) 0 0
\(982\) −9.79001 16.9568i −0.312412 0.541113i
\(983\) 6.38482 2.32389i 0.203644 0.0741204i −0.238184 0.971220i \(-0.576552\pi\)
0.441828 + 0.897100i \(0.354330\pi\)
\(984\) 0 0
\(985\) 12.3389 10.3536i 0.393151 0.329892i
\(986\) 9.71527 8.15208i 0.309397 0.259615i
\(987\) 0 0
\(988\) −8.52541 + 3.10300i −0.271229 + 0.0987194i
\(989\) −7.93698 13.7473i −0.252381 0.437137i
\(990\) 0 0
\(991\) −8.60230 + 14.8996i −0.273261 + 0.473302i −0.969695 0.244319i \(-0.921436\pi\)
0.696434 + 0.717621i \(0.254769\pi\)
\(992\) 0.493351 2.79793i 0.0156639 0.0888345i
\(993\) 0 0
\(994\) 23.1826 + 8.43776i 0.735306 + 0.267630i
\(995\) −3.11630 17.6734i −0.0987933 0.560284i
\(996\) 0 0
\(997\) 5.61793 + 4.71400i 0.177922 + 0.149294i 0.727399 0.686214i \(-0.240729\pi\)
−0.549478 + 0.835508i \(0.685173\pi\)
\(998\) 3.59848 0.113908
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 729.2.e.s.406.1 12
3.2 odd 2 729.2.e.l.406.2 12
9.2 odd 6 729.2.e.k.649.2 12
9.4 even 3 729.2.e.j.163.2 12
9.5 odd 6 729.2.e.u.163.1 12
9.7 even 3 729.2.e.t.649.1 12
27.2 odd 18 729.2.c.a.244.3 12
27.4 even 9 729.2.e.t.82.1 12
27.5 odd 18 729.2.e.l.325.2 12
27.7 even 9 729.2.a.b.1.3 6
27.11 odd 18 729.2.c.a.487.3 12
27.13 even 9 729.2.e.j.568.2 12
27.14 odd 18 729.2.e.u.568.1 12
27.16 even 9 729.2.c.d.487.4 12
27.20 odd 18 729.2.a.e.1.4 yes 6
27.22 even 9 inner 729.2.e.s.325.1 12
27.23 odd 18 729.2.e.k.82.2 12
27.25 even 9 729.2.c.d.244.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.3 6 27.7 even 9
729.2.a.e.1.4 yes 6 27.20 odd 18
729.2.c.a.244.3 12 27.2 odd 18
729.2.c.a.487.3 12 27.11 odd 18
729.2.c.d.244.4 12 27.25 even 9
729.2.c.d.487.4 12 27.16 even 9
729.2.e.j.163.2 12 9.4 even 3
729.2.e.j.568.2 12 27.13 even 9
729.2.e.k.82.2 12 27.23 odd 18
729.2.e.k.649.2 12 9.2 odd 6
729.2.e.l.325.2 12 27.5 odd 18
729.2.e.l.406.2 12 3.2 odd 2
729.2.e.s.325.1 12 27.22 even 9 inner
729.2.e.s.406.1 12 1.1 even 1 trivial
729.2.e.t.82.1 12 27.4 even 9
729.2.e.t.649.1 12 9.7 even 3
729.2.e.u.163.1 12 9.5 odd 6
729.2.e.u.568.1 12 27.14 odd 18