Properties

Label 729.2.e.g.82.1
Level $729$
Weight $2$
Character 729.82
Analytic conductor $5.821$
Analytic rank $0$
Dimension $6$
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: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 82.1
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 729.82
Dual form 729.2.e.g.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.439693 - 2.49362i) q^{2} +(-4.14543 + 1.50881i) q^{4} +(-0.358441 - 0.300767i) q^{5} +(3.03209 + 1.10359i) q^{7} +(3.05303 + 5.28801i) q^{8} +O(q^{10})\) \(q+(-0.439693 - 2.49362i) q^{2} +(-4.14543 + 1.50881i) q^{4} +(-0.358441 - 0.300767i) q^{5} +(3.03209 + 1.10359i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-0.592396 + 1.02606i) q^{10} +(2.37939 - 1.99654i) q^{11} +(-0.379385 + 2.15160i) q^{13} +(1.41875 - 8.04612i) q^{14} +(5.08512 - 4.26692i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.0209445 - 0.0362770i) q^{19} +(1.93969 + 0.705990i) q^{20} +(-6.02481 - 5.05542i) q^{22} +(5.73783 - 2.08840i) q^{23} +(-0.830222 - 4.70842i) q^{25} +5.53209 q^{26} -14.2344 q^{28} +(-1.14156 - 6.47410i) q^{29} +(5.85117 - 2.12965i) q^{31} +(-3.52094 - 2.95442i) q^{32} +(-7.13816 - 2.59808i) q^{34} +(-0.754900 - 1.30753i) q^{35} +(-1.79813 + 3.11446i) q^{37} +(-0.0812519 + 0.0681784i) q^{38} +(0.496130 - 2.81369i) q^{40} +(-1.33750 + 7.58532i) q^{41} +(-0.450837 + 0.378297i) q^{43} +(-6.85117 + 11.8666i) q^{44} +(-7.73055 - 13.3897i) q^{46} +(-9.07785 - 3.30407i) q^{47} +(2.61334 + 2.19285i) q^{49} +(-11.3760 + 4.14052i) q^{50} +(-1.67365 - 9.49173i) q^{52} -4.95811 q^{53} -1.45336 q^{55} +(3.42127 + 19.4030i) q^{56} +(-15.6420 + 5.69323i) q^{58} +(6.53596 + 5.48432i) q^{59} +(1.19207 + 0.433877i) q^{61} +(-7.88326 - 13.6542i) q^{62} +(0.819078 - 1.41868i) q^{64} +(0.783119 - 0.657115i) q^{65} +(1.73783 - 9.85570i) q^{67} +(-2.29813 + 13.0334i) q^{68} +(-2.92855 + 2.45734i) q^{70} +(5.91534 - 10.2457i) q^{71} +(4.11721 + 7.13122i) q^{73} +(8.55690 + 3.11446i) q^{74} +(0.141559 + 0.118782i) q^{76} +(9.41787 - 3.42782i) q^{77} +(1.91875 + 10.8818i) q^{79} -3.10607 q^{80} +19.5030 q^{82} +(0.262174 + 1.48686i) q^{83} +(-1.31908 + 0.480105i) q^{85} +(1.14156 + 0.957882i) q^{86} +(17.8221 + 6.48670i) q^{88} +(-7.93629 - 13.7461i) q^{89} +(-3.52481 + 6.10516i) q^{91} +(-20.6348 + 17.3146i) q^{92} +(-4.24763 + 24.0895i) q^{94} +(-0.00340357 + 0.0193026i) q^{95} +(14.2836 - 11.9854i) q^{97} +(4.31908 - 7.48086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8} + 3 q^{11} + 9 q^{13} + 6 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 15 q^{23} + 18 q^{25} + 24 q^{26} - 24 q^{28} - 15 q^{29} + 9 q^{31} - 18 q^{32} - 9 q^{34} - 6 q^{35} + 3 q^{37} - 3 q^{38} + 27 q^{40} - 3 q^{41} + 9 q^{43} - 15 q^{44} - 9 q^{46} - 15 q^{47} + 9 q^{49} - 15 q^{50} - 9 q^{52} - 36 q^{53} + 18 q^{55} + 3 q^{56} - 36 q^{58} + 6 q^{59} + 18 q^{61} - 12 q^{62} - 12 q^{64} + 21 q^{65} - 9 q^{67} - 18 q^{70} - 9 q^{71} - 6 q^{73} + 15 q^{74} + 9 q^{76} - 3 q^{77} + 9 q^{79} + 6 q^{80} + 36 q^{82} + 21 q^{83} + 9 q^{85} + 15 q^{86} + 9 q^{88} + 6 q^{91} - 48 q^{92} - 9 q^{94} - 42 q^{95} + 36 q^{97} + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.439693 2.49362i −0.310910 1.76326i −0.594292 0.804249i \(-0.702568\pi\)
0.283383 0.959007i \(-0.408543\pi\)
\(3\) 0 0
\(4\) −4.14543 + 1.50881i −2.07271 + 0.754407i
\(5\) −0.358441 0.300767i −0.160300 0.134507i 0.559110 0.829094i \(-0.311143\pi\)
−0.719409 + 0.694586i \(0.755587\pi\)
\(6\) 0 0
\(7\) 3.03209 + 1.10359i 1.14602 + 0.417118i 0.844085 0.536210i \(-0.180144\pi\)
0.301937 + 0.953328i \(0.402367\pi\)
\(8\) 3.05303 + 5.28801i 1.07941 + 1.86959i
\(9\) 0 0
\(10\) −0.592396 + 1.02606i −0.187332 + 0.324469i
\(11\) 2.37939 1.99654i 0.717412 0.601980i −0.209256 0.977861i \(-0.567104\pi\)
0.926668 + 0.375881i \(0.122660\pi\)
\(12\) 0 0
\(13\) −0.379385 + 2.15160i −0.105223 + 0.596747i 0.885909 + 0.463860i \(0.153536\pi\)
−0.991131 + 0.132887i \(0.957575\pi\)
\(14\) 1.41875 8.04612i 0.379176 2.15042i
\(15\) 0 0
\(16\) 5.08512 4.26692i 1.27128 1.06673i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) −0.0209445 0.0362770i −0.00480501 0.00832251i 0.863613 0.504155i \(-0.168196\pi\)
−0.868418 + 0.495833i \(0.834863\pi\)
\(20\) 1.93969 + 0.705990i 0.433728 + 0.157864i
\(21\) 0 0
\(22\) −6.02481 5.05542i −1.28449 1.07782i
\(23\) 5.73783 2.08840i 1.19642 0.435461i 0.334446 0.942415i \(-0.391451\pi\)
0.861973 + 0.506954i \(0.169229\pi\)
\(24\) 0 0
\(25\) −0.830222 4.70842i −0.166044 0.941685i
\(26\) 5.53209 1.08493
\(27\) 0 0
\(28\) −14.2344 −2.69005
\(29\) −1.14156 6.47410i −0.211982 1.20221i −0.886067 0.463557i \(-0.846573\pi\)
0.674085 0.738654i \(-0.264538\pi\)
\(30\) 0 0
\(31\) 5.85117 2.12965i 1.05090 0.382497i 0.241898 0.970302i \(-0.422230\pi\)
0.809003 + 0.587805i \(0.200008\pi\)
\(32\) −3.52094 2.95442i −0.622421 0.522273i
\(33\) 0 0
\(34\) −7.13816 2.59808i −1.22418 0.445566i
\(35\) −0.754900 1.30753i −0.127601 0.221012i
\(36\) 0 0
\(37\) −1.79813 + 3.11446i −0.295611 + 0.512014i −0.975127 0.221647i \(-0.928857\pi\)
0.679516 + 0.733661i \(0.262190\pi\)
\(38\) −0.0812519 + 0.0681784i −0.0131808 + 0.0110600i
\(39\) 0 0
\(40\) 0.496130 2.81369i 0.0784450 0.444884i
\(41\) −1.33750 + 7.58532i −0.208882 + 1.18463i 0.682331 + 0.731043i \(0.260966\pi\)
−0.891213 + 0.453585i \(0.850145\pi\)
\(42\) 0 0
\(43\) −0.450837 + 0.378297i −0.0687520 + 0.0576898i −0.676516 0.736428i \(-0.736511\pi\)
0.607764 + 0.794118i \(0.292067\pi\)
\(44\) −6.85117 + 11.8666i −1.03285 + 1.78895i
\(45\) 0 0
\(46\) −7.73055 13.3897i −1.13981 1.97420i
\(47\) −9.07785 3.30407i −1.32414 0.481948i −0.419358 0.907821i \(-0.637745\pi\)
−0.904783 + 0.425874i \(0.859967\pi\)
\(48\) 0 0
\(49\) 2.61334 + 2.19285i 0.373334 + 0.313265i
\(50\) −11.3760 + 4.14052i −1.60881 + 0.585558i
\(51\) 0 0
\(52\) −1.67365 9.49173i −0.232093 1.31627i
\(53\) −4.95811 −0.681049 −0.340524 0.940236i \(-0.610605\pi\)
−0.340524 + 0.940236i \(0.610605\pi\)
\(54\) 0 0
\(55\) −1.45336 −0.195971
\(56\) 3.42127 + 19.4030i 0.457187 + 2.59284i
\(57\) 0 0
\(58\) −15.6420 + 5.69323i −2.05390 + 0.747558i
\(59\) 6.53596 + 5.48432i 0.850909 + 0.713998i 0.959990 0.280035i \(-0.0903461\pi\)
−0.109080 + 0.994033i \(0.534791\pi\)
\(60\) 0 0
\(61\) 1.19207 + 0.433877i 0.152628 + 0.0555522i 0.417205 0.908813i \(-0.363010\pi\)
−0.264576 + 0.964365i \(0.585232\pi\)
\(62\) −7.88326 13.6542i −1.00117 1.73409i
\(63\) 0 0
\(64\) 0.819078 1.41868i 0.102385 0.177336i
\(65\) 0.783119 0.657115i 0.0971339 0.0815050i
\(66\) 0 0
\(67\) 1.73783 9.85570i 0.212309 1.20407i −0.673206 0.739455i \(-0.735083\pi\)
0.885515 0.464610i \(-0.153806\pi\)
\(68\) −2.29813 + 13.0334i −0.278690 + 1.58053i
\(69\) 0 0
\(70\) −2.92855 + 2.45734i −0.350028 + 0.293709i
\(71\) 5.91534 10.2457i 0.702022 1.21594i −0.265733 0.964047i \(-0.585614\pi\)
0.967755 0.251892i \(-0.0810526\pi\)
\(72\) 0 0
\(73\) 4.11721 + 7.13122i 0.481883 + 0.834646i 0.999784 0.0207947i \(-0.00661964\pi\)
−0.517901 + 0.855441i \(0.673286\pi\)
\(74\) 8.55690 + 3.11446i 0.994720 + 0.362048i
\(75\) 0 0
\(76\) 0.141559 + 0.118782i 0.0162380 + 0.0136253i
\(77\) 9.41787 3.42782i 1.07327 0.390637i
\(78\) 0 0
\(79\) 1.91875 + 10.8818i 0.215876 + 1.22429i 0.879380 + 0.476121i \(0.157958\pi\)
−0.663504 + 0.748173i \(0.730931\pi\)
\(80\) −3.10607 −0.347269
\(81\) 0 0
\(82\) 19.5030 2.15375
\(83\) 0.262174 + 1.48686i 0.0287773 + 0.163204i 0.995810 0.0914488i \(-0.0291498\pi\)
−0.967032 + 0.254653i \(0.918039\pi\)
\(84\) 0 0
\(85\) −1.31908 + 0.480105i −0.143074 + 0.0520747i
\(86\) 1.14156 + 0.957882i 0.123098 + 0.103291i
\(87\) 0 0
\(88\) 17.8221 + 6.48670i 1.89984 + 0.691485i
\(89\) −7.93629 13.7461i −0.841245 1.45708i −0.888843 0.458212i \(-0.848490\pi\)
0.0475978 0.998867i \(-0.484843\pi\)
\(90\) 0 0
\(91\) −3.52481 + 6.10516i −0.369501 + 0.639995i
\(92\) −20.6348 + 17.3146i −2.15132 + 1.80517i
\(93\) 0 0
\(94\) −4.24763 + 24.0895i −0.438109 + 2.48464i
\(95\) −0.00340357 + 0.0193026i −0.000349199 + 0.00198040i
\(96\) 0 0
\(97\) 14.2836 11.9854i 1.45028 1.21693i 0.517902 0.855440i \(-0.326713\pi\)
0.932377 0.361488i \(-0.117731\pi\)
\(98\) 4.31908 7.48086i 0.436293 0.755681i
\(99\) 0 0
\(100\) 10.5458 + 18.2658i 1.05458 + 1.82658i
\(101\) 8.53849 + 3.10775i 0.849611 + 0.309233i 0.729882 0.683573i \(-0.239575\pi\)
0.119729 + 0.992807i \(0.461797\pi\)
\(102\) 0 0
\(103\) 0.199807 + 0.167658i 0.0196876 + 0.0165199i 0.652578 0.757721i \(-0.273687\pi\)
−0.632891 + 0.774241i \(0.718132\pi\)
\(104\) −12.5360 + 4.56272i −1.22925 + 0.447411i
\(105\) 0 0
\(106\) 2.18004 + 12.3636i 0.211745 + 1.20086i
\(107\) −4.04189 −0.390744 −0.195372 0.980729i \(-0.562591\pi\)
−0.195372 + 0.980729i \(0.562591\pi\)
\(108\) 0 0
\(109\) −5.40373 −0.517584 −0.258792 0.965933i \(-0.583324\pi\)
−0.258792 + 0.965933i \(0.583324\pi\)
\(110\) 0.639033 + 3.62414i 0.0609294 + 0.345548i
\(111\) 0 0
\(112\) 20.1275 7.32580i 1.90187 0.692223i
\(113\) −1.06031 0.889704i −0.0997453 0.0836963i 0.591551 0.806267i \(-0.298516\pi\)
−0.691297 + 0.722571i \(0.742960\pi\)
\(114\) 0 0
\(115\) −2.68479 0.977185i −0.250358 0.0911229i
\(116\) 14.5005 + 25.1155i 1.34633 + 2.33192i
\(117\) 0 0
\(118\) 10.8020 18.7096i 0.994405 1.72236i
\(119\) 7.41534 6.22221i 0.679764 0.570389i
\(120\) 0 0
\(121\) −0.234833 + 1.33180i −0.0213484 + 0.121073i
\(122\) 0.557781 3.16333i 0.0504991 0.286395i
\(123\) 0 0
\(124\) −21.0424 + 17.6566i −1.88966 + 1.58561i
\(125\) −2.28833 + 3.96351i −0.204675 + 0.354507i
\(126\) 0 0
\(127\) 3.31908 + 5.74881i 0.294521 + 0.510125i 0.974873 0.222760i \(-0.0715067\pi\)
−0.680353 + 0.732885i \(0.738173\pi\)
\(128\) −12.5360 4.56272i −1.10803 0.403291i
\(129\) 0 0
\(130\) −1.98293 1.66387i −0.173914 0.145931i
\(131\) −11.8785 + 4.32342i −1.03783 + 0.377739i −0.804057 0.594552i \(-0.797329\pi\)
−0.233773 + 0.972291i \(0.575107\pi\)
\(132\) 0 0
\(133\) −0.0234708 0.133109i −0.00203517 0.0115420i
\(134\) −25.3405 −2.18908
\(135\) 0 0
\(136\) 18.3182 1.57077
\(137\) −1.84343 10.4546i −0.157495 0.893196i −0.956470 0.291832i \(-0.905735\pi\)
0.798975 0.601364i \(-0.205376\pi\)
\(138\) 0 0
\(139\) 7.01114 2.55185i 0.594678 0.216445i −0.0271080 0.999633i \(-0.508630\pi\)
0.621785 + 0.783188i \(0.286408\pi\)
\(140\) 5.10220 + 4.28125i 0.431214 + 0.361832i
\(141\) 0 0
\(142\) −28.1498 10.2457i −2.36228 0.859798i
\(143\) 3.39306 + 5.87695i 0.283742 + 0.491455i
\(144\) 0 0
\(145\) −1.53802 + 2.66393i −0.127725 + 0.221227i
\(146\) 15.9722 13.4023i 1.32187 1.10918i
\(147\) 0 0
\(148\) 2.75490 15.6238i 0.226451 1.28427i
\(149\) 0.738703 4.18939i 0.0605169 0.343209i −0.939483 0.342596i \(-0.888694\pi\)
1.00000 0.000612725i \(-0.000195036\pi\)
\(150\) 0 0
\(151\) 0.103541 0.0868809i 0.00842602 0.00707027i −0.638565 0.769568i \(-0.720472\pi\)
0.646991 + 0.762498i \(0.276027\pi\)
\(152\) 0.127889 0.221510i 0.0103731 0.0179668i
\(153\) 0 0
\(154\) −12.6887 21.9774i −1.02248 1.77099i
\(155\) −2.73783 0.996487i −0.219907 0.0800398i
\(156\) 0 0
\(157\) 10.2083 + 8.56575i 0.814708 + 0.683621i 0.951727 0.306947i \(-0.0993075\pi\)
−0.137018 + 0.990568i \(0.543752\pi\)
\(158\) 26.2913 9.56926i 2.09163 0.761289i
\(159\) 0 0
\(160\) 0.373455 + 2.11797i 0.0295242 + 0.167440i
\(161\) 19.7023 1.55276
\(162\) 0 0
\(163\) −9.76382 −0.764762 −0.382381 0.924005i \(-0.624896\pi\)
−0.382381 + 0.924005i \(0.624896\pi\)
\(164\) −5.90033 33.4624i −0.460738 2.61298i
\(165\) 0 0
\(166\) 3.59240 1.30753i 0.278824 0.101484i
\(167\) 2.73783 + 2.29731i 0.211859 + 0.177771i 0.742542 0.669799i \(-0.233620\pi\)
−0.530683 + 0.847571i \(0.678064\pi\)
\(168\) 0 0
\(169\) 7.73055 + 2.81369i 0.594658 + 0.216438i
\(170\) 1.77719 + 3.07818i 0.136304 + 0.236086i
\(171\) 0 0
\(172\) 1.29813 2.24843i 0.0989817 0.171441i
\(173\) −14.3760 + 12.0629i −1.09299 + 0.917124i −0.996934 0.0782525i \(-0.975066\pi\)
−0.0960521 + 0.995376i \(0.530622\pi\)
\(174\) 0 0
\(175\) 2.67886 15.1926i 0.202503 1.14845i
\(176\) 3.58037 20.3053i 0.269881 1.53057i
\(177\) 0 0
\(178\) −30.7879 + 25.8341i −2.30765 + 1.93635i
\(179\) −2.54189 + 4.40268i −0.189990 + 0.329072i −0.945247 0.326357i \(-0.894179\pi\)
0.755257 + 0.655429i \(0.227512\pi\)
\(180\) 0 0
\(181\) −3.57532 6.19264i −0.265752 0.460295i 0.702009 0.712168i \(-0.252287\pi\)
−0.967760 + 0.251873i \(0.918953\pi\)
\(182\) 16.7738 + 6.10516i 1.24336 + 0.452544i
\(183\) 0 0
\(184\) 28.5612 + 23.9657i 2.10556 + 1.76678i
\(185\) 1.58125 0.575529i 0.116256 0.0423137i
\(186\) 0 0
\(187\) −1.61809 9.17664i −0.118326 0.671062i
\(188\) 42.6168 3.10815
\(189\) 0 0
\(190\) 0.0496299 0.00360053
\(191\) 1.82501 + 10.3501i 0.132053 + 0.748909i 0.976867 + 0.213849i \(0.0686000\pi\)
−0.844814 + 0.535060i \(0.820289\pi\)
\(192\) 0 0
\(193\) 9.53121 3.46908i 0.686072 0.249710i 0.0246193 0.999697i \(-0.492163\pi\)
0.661452 + 0.749987i \(0.269940\pi\)
\(194\) −36.1673 30.3480i −2.59666 2.17886i
\(195\) 0 0
\(196\) −14.1420 5.14728i −1.01014 0.367663i
\(197\) 7.04189 + 12.1969i 0.501714 + 0.868994i 0.999998 + 0.00198008i \(0.000630281\pi\)
−0.498284 + 0.867014i \(0.666036\pi\)
\(198\) 0 0
\(199\) −5.13816 + 8.89955i −0.364234 + 0.630872i −0.988653 0.150218i \(-0.952003\pi\)
0.624419 + 0.781090i \(0.285336\pi\)
\(200\) 22.3635 18.7652i 1.58134 1.32690i
\(201\) 0 0
\(202\) 3.99525 22.6582i 0.281105 1.59423i
\(203\) 3.68345 20.8899i 0.258527 1.46618i
\(204\) 0 0
\(205\) 2.76083 2.31661i 0.192825 0.161799i
\(206\) 0.330222 0.571962i 0.0230077 0.0398505i
\(207\) 0 0
\(208\) 7.25150 + 12.5600i 0.502801 + 0.870877i
\(209\) −0.122264 0.0445003i −0.00845715 0.00307815i
\(210\) 0 0
\(211\) −5.47178 4.59137i −0.376693 0.316083i 0.434710 0.900571i \(-0.356851\pi\)
−0.811403 + 0.584488i \(0.801295\pi\)
\(212\) 20.5535 7.48086i 1.41162 0.513788i
\(213\) 0 0
\(214\) 1.77719 + 10.0789i 0.121486 + 0.688982i
\(215\) 0.275378 0.0187806
\(216\) 0 0
\(217\) 20.0915 1.36390
\(218\) 2.37598 + 13.4749i 0.160922 + 0.912633i
\(219\) 0 0
\(220\) 6.02481 2.19285i 0.406193 0.147842i
\(221\) 5.02094 + 4.21307i 0.337745 + 0.283402i
\(222\) 0 0
\(223\) 9.71213 + 3.53493i 0.650373 + 0.236716i 0.646074 0.763275i \(-0.276410\pi\)
0.00429825 + 0.999991i \(0.498632\pi\)
\(224\) −7.41534 12.8438i −0.495459 0.858159i
\(225\) 0 0
\(226\) −1.75237 + 3.03520i −0.116566 + 0.201899i
\(227\) 9.97565 8.37057i 0.662107 0.555574i −0.248610 0.968604i \(-0.579974\pi\)
0.910718 + 0.413030i \(0.135529\pi\)
\(228\) 0 0
\(229\) −4.87939 + 27.6724i −0.322439 + 1.82864i 0.204655 + 0.978834i \(0.434393\pi\)
−0.527093 + 0.849807i \(0.676718\pi\)
\(230\) −1.25624 + 7.12452i −0.0828343 + 0.469777i
\(231\) 0 0
\(232\) 30.7499 25.8022i 2.01883 1.69400i
\(233\) −6.95723 + 12.0503i −0.455784 + 0.789440i −0.998733 0.0503252i \(-0.983974\pi\)
0.542949 + 0.839765i \(0.317308\pi\)
\(234\) 0 0
\(235\) 2.26011 + 3.91463i 0.147434 + 0.255363i
\(236\) −35.3692 12.8733i −2.30234 0.837982i
\(237\) 0 0
\(238\) −18.7763 15.7552i −1.21709 1.02126i
\(239\) −14.1138 + 5.13701i −0.912946 + 0.332285i −0.755429 0.655231i \(-0.772571\pi\)
−0.157518 + 0.987516i \(0.550349\pi\)
\(240\) 0 0
\(241\) −2.25284 12.7765i −0.145118 0.823006i −0.967272 0.253741i \(-0.918339\pi\)
0.822154 0.569265i \(-0.192772\pi\)
\(242\) 3.42427 0.220120
\(243\) 0 0
\(244\) −5.59627 −0.358264
\(245\) −0.277189 1.57202i −0.0177089 0.100432i
\(246\) 0 0
\(247\) 0.0859997 0.0313013i 0.00547203 0.00199165i
\(248\) 29.1254 + 24.4391i 1.84947 + 1.55189i
\(249\) 0 0
\(250\) 10.8897 + 3.96351i 0.688722 + 0.250674i
\(251\) 0.436289 + 0.755675i 0.0275383 + 0.0476978i 0.879466 0.475961i \(-0.157900\pi\)
−0.851928 + 0.523659i \(0.824567\pi\)
\(252\) 0 0
\(253\) 9.48293 16.4249i 0.596186 1.03263i
\(254\) 12.8760 10.8042i 0.807911 0.677918i
\(255\) 0 0
\(256\) −5.29679 + 30.0396i −0.331049 + 1.87747i
\(257\) −0.794730 + 4.50714i −0.0495739 + 0.281147i −0.999510 0.0312963i \(-0.990036\pi\)
0.949936 + 0.312444i \(0.101148\pi\)
\(258\) 0 0
\(259\) −8.88919 + 7.45891i −0.552347 + 0.463474i
\(260\) −2.25490 + 3.90560i −0.139843 + 0.242215i
\(261\) 0 0
\(262\) 16.0039 + 27.7195i 0.988722 + 1.71252i
\(263\) 4.03849 + 1.46989i 0.249024 + 0.0906372i 0.463516 0.886088i \(-0.346588\pi\)
−0.214493 + 0.976726i \(0.568810\pi\)
\(264\) 0 0
\(265\) 1.77719 + 1.49124i 0.109172 + 0.0916061i
\(266\) −0.321604 + 0.117054i −0.0197188 + 0.00717706i
\(267\) 0 0
\(268\) 7.66637 + 43.4782i 0.468298 + 2.65585i
\(269\) −12.1257 −0.739315 −0.369657 0.929168i \(-0.620525\pi\)
−0.369657 + 0.929168i \(0.620525\pi\)
\(270\) 0 0
\(271\) −0.319955 −0.0194359 −0.00971795 0.999953i \(-0.503093\pi\)
−0.00971795 + 0.999953i \(0.503093\pi\)
\(272\) −3.45811 19.6119i −0.209679 1.18915i
\(273\) 0 0
\(274\) −25.2592 + 9.19361i −1.52597 + 0.555406i
\(275\) −11.3760 9.54558i −0.685998 0.575620i
\(276\) 0 0
\(277\) 25.2037 + 9.17339i 1.51434 + 0.551175i 0.959728 0.280932i \(-0.0906435\pi\)
0.554615 + 0.832107i \(0.312866\pi\)
\(278\) −9.44609 16.3611i −0.566539 0.981274i
\(279\) 0 0
\(280\) 4.60947 7.98384i 0.275469 0.477126i
\(281\) −20.4388 + 17.1502i −1.21928 + 1.02310i −0.220415 + 0.975406i \(0.570741\pi\)
−0.998862 + 0.0476892i \(0.984814\pi\)
\(282\) 0 0
\(283\) −1.61381 + 9.15236i −0.0959309 + 0.544051i 0.898527 + 0.438918i \(0.144638\pi\)
−0.994458 + 0.105133i \(0.966473\pi\)
\(284\) −9.06283 + 51.3979i −0.537780 + 3.04990i
\(285\) 0 0
\(286\) 13.1630 11.0450i 0.778343 0.653107i
\(287\) −12.4265 + 21.5233i −0.733512 + 1.27048i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 7.31908 + 2.66393i 0.429791 + 0.156431i
\(291\) 0 0
\(292\) −27.8273 23.3499i −1.62847 1.36645i
\(293\) −18.4547 + 6.71696i −1.07814 + 0.392409i −0.819213 0.573489i \(-0.805590\pi\)
−0.258922 + 0.965898i \(0.583367\pi\)
\(294\) 0 0
\(295\) −0.693249 3.93161i −0.0403625 0.228907i
\(296\) −21.9590 −1.27634
\(297\) 0 0
\(298\) −10.7716 −0.623980
\(299\) 2.31655 + 13.1378i 0.133970 + 0.759780i
\(300\) 0 0
\(301\) −1.78446 + 0.649491i −0.102855 + 0.0374361i
\(302\) −0.262174 0.219990i −0.0150864 0.0126590i
\(303\) 0 0
\(304\) −0.261297 0.0951042i −0.0149864 0.00545460i
\(305\) −0.296789 0.514054i −0.0169941 0.0294346i
\(306\) 0 0
\(307\) −14.1716 + 24.5459i −0.808815 + 1.40091i 0.104870 + 0.994486i \(0.466557\pi\)
−0.913685 + 0.406423i \(0.866776\pi\)
\(308\) −33.8692 + 28.4196i −1.92988 + 1.61936i
\(309\) 0 0
\(310\) −1.28106 + 7.26525i −0.0727593 + 0.412638i
\(311\) 0.355037 2.01352i 0.0201323 0.114176i −0.973086 0.230444i \(-0.925982\pi\)
0.993218 + 0.116268i \(0.0370932\pi\)
\(312\) 0 0
\(313\) 6.44356 5.40679i 0.364212 0.305610i −0.442255 0.896889i \(-0.645821\pi\)
0.806467 + 0.591279i \(0.201377\pi\)
\(314\) 16.8712 29.2218i 0.952099 1.64908i
\(315\) 0 0
\(316\) −24.3726 42.2145i −1.37106 2.37475i
\(317\) 29.2511 + 10.6465i 1.64290 + 0.597968i 0.987543 0.157347i \(-0.0502942\pi\)
0.655361 + 0.755316i \(0.272516\pi\)
\(318\) 0 0
\(319\) −15.6420 13.1252i −0.875785 0.734871i
\(320\) −0.720285 + 0.262162i −0.0402652 + 0.0146553i
\(321\) 0 0
\(322\) −8.66297 49.1301i −0.482768 2.73792i
\(323\) −0.125667 −0.00699231
\(324\) 0 0
\(325\) 10.4456 0.579419
\(326\) 4.29308 + 24.3473i 0.237772 + 1.34847i
\(327\) 0 0
\(328\) −44.1946 + 16.0855i −2.44024 + 0.888175i
\(329\) −23.8785 20.0364i −1.31646 1.10465i
\(330\) 0 0
\(331\) −29.1596 10.6132i −1.60275 0.583355i −0.622766 0.782408i \(-0.713991\pi\)
−0.979989 + 0.199053i \(0.936213\pi\)
\(332\) −3.33022 5.76811i −0.182770 0.316566i
\(333\) 0 0
\(334\) 4.52481 7.83721i 0.247587 0.428833i
\(335\) −3.58718 + 3.01000i −0.195989 + 0.164454i
\(336\) 0 0
\(337\) 4.12061 23.3692i 0.224464 1.27300i −0.639243 0.769005i \(-0.720752\pi\)
0.863707 0.503995i \(-0.168137\pi\)
\(338\) 3.61721 20.5142i 0.196750 1.11583i
\(339\) 0 0
\(340\) 4.74376 3.98048i 0.257266 0.215872i
\(341\) 9.67024 16.7494i 0.523673 0.907028i
\(342\) 0 0
\(343\) −5.78952 10.0277i −0.312604 0.541447i
\(344\) −3.37686 1.22908i −0.182068 0.0662673i
\(345\) 0 0
\(346\) 36.4013 + 30.5443i 1.95694 + 1.64207i
\(347\) −1.69934 + 0.618509i −0.0912254 + 0.0332033i −0.387230 0.921983i \(-0.626568\pi\)
0.296004 + 0.955187i \(0.404346\pi\)
\(348\) 0 0
\(349\) 2.65002 + 15.0290i 0.141852 + 0.804483i 0.969841 + 0.243739i \(0.0783739\pi\)
−0.827989 + 0.560744i \(0.810515\pi\)
\(350\) −39.0624 −2.08797
\(351\) 0 0
\(352\) −14.2763 −0.760930
\(353\) 5.62314 + 31.8904i 0.299290 + 1.69736i 0.649237 + 0.760586i \(0.275088\pi\)
−0.349947 + 0.936769i \(0.613801\pi\)
\(354\) 0 0
\(355\) −5.20187 + 1.89332i −0.276086 + 0.100487i
\(356\) 53.6396 + 45.0089i 2.84289 + 2.38547i
\(357\) 0 0
\(358\) 12.0963 + 4.40268i 0.639308 + 0.232689i
\(359\) −0.957234 1.65798i −0.0505209 0.0875047i 0.839659 0.543114i \(-0.182755\pi\)
−0.890180 + 0.455609i \(0.849421\pi\)
\(360\) 0 0
\(361\) 9.49912 16.4530i 0.499954 0.865945i
\(362\) −13.8701 + 11.6384i −0.728994 + 0.611698i
\(363\) 0 0
\(364\) 5.40033 30.6268i 0.283054 1.60528i
\(365\) 0.669063 3.79444i 0.0350203 0.198610i
\(366\) 0 0
\(367\) −20.5797 + 17.2684i −1.07425 + 0.901402i −0.995431 0.0954866i \(-0.969559\pi\)
−0.0788188 + 0.996889i \(0.525115\pi\)
\(368\) 20.2665 35.1026i 1.05646 1.82985i
\(369\) 0 0
\(370\) −2.13041 3.68999i −0.110755 0.191833i
\(371\) −15.0334 5.47172i −0.780497 0.284078i
\(372\) 0 0
\(373\) 11.3682 + 9.53909i 0.588625 + 0.493915i 0.887767 0.460294i \(-0.152256\pi\)
−0.299142 + 0.954209i \(0.596700\pi\)
\(374\) −22.1716 + 8.06980i −1.14647 + 0.417279i
\(375\) 0 0
\(376\) −10.2430 58.0912i −0.528244 2.99582i
\(377\) 14.3628 0.739721
\(378\) 0 0
\(379\) −33.7870 −1.73552 −0.867762 0.496980i \(-0.834442\pi\)
−0.867762 + 0.496980i \(0.834442\pi\)
\(380\) −0.0150147 0.0851529i −0.000770240 0.00436825i
\(381\) 0 0
\(382\) 25.0069 9.10175i 1.27946 0.465686i
\(383\) 7.10813 + 5.96443i 0.363208 + 0.304768i 0.806068 0.591823i \(-0.201592\pi\)
−0.442860 + 0.896591i \(0.646036\pi\)
\(384\) 0 0
\(385\) −4.40673 1.60392i −0.224588 0.0817432i
\(386\) −12.8414 22.2419i −0.653608 1.13208i
\(387\) 0 0
\(388\) −41.1279 + 71.2357i −2.08796 + 3.61644i
\(389\) 12.2404 10.2709i 0.620610 0.520754i −0.277385 0.960759i \(-0.589468\pi\)
0.897995 + 0.440005i \(0.145023\pi\)
\(390\) 0 0
\(391\) 3.18092 18.0399i 0.160866 0.912317i
\(392\) −3.61721 + 20.5142i −0.182697 + 1.03612i
\(393\) 0 0
\(394\) 27.3182 22.9227i 1.37627 1.15483i
\(395\) 2.58512 4.47756i 0.130072 0.225291i
\(396\) 0 0
\(397\) −9.85251 17.0650i −0.494483 0.856470i 0.505496 0.862829i \(-0.331309\pi\)
−0.999980 + 0.00635841i \(0.997976\pi\)
\(398\) 24.4513 + 8.89955i 1.22563 + 0.446094i
\(399\) 0 0
\(400\) −24.3123 20.4004i −1.21561 1.02002i
\(401\) 1.07873 0.392624i 0.0538690 0.0196067i −0.314945 0.949110i \(-0.601986\pi\)
0.368814 + 0.929503i \(0.379764\pi\)
\(402\) 0 0
\(403\) 2.36231 + 13.3973i 0.117675 + 0.667369i
\(404\) −40.0847 −1.99429
\(405\) 0 0
\(406\) −53.7110 −2.66563
\(407\) 1.93969 + 11.0005i 0.0961470 + 0.545277i
\(408\) 0 0
\(409\) 2.91400 1.06061i 0.144088 0.0524438i −0.268969 0.963149i \(-0.586683\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(410\) −6.99067 5.86587i −0.345244 0.289694i
\(411\) 0 0
\(412\) −1.08125 0.393544i −0.0532695 0.0193885i
\(413\) 13.7652 + 23.8420i 0.677340 + 1.17319i
\(414\) 0 0
\(415\) 0.353226 0.611806i 0.0173392 0.0300324i
\(416\) 7.69253 6.45480i 0.377157 0.316473i
\(417\) 0 0
\(418\) −0.0572085 + 0.324446i −0.00279816 + 0.0158692i
\(419\) −6.15570 + 34.9107i −0.300725 + 1.70550i 0.342247 + 0.939610i \(0.388812\pi\)
−0.642973 + 0.765889i \(0.722299\pi\)
\(420\) 0 0
\(421\) 7.06077 5.92469i 0.344121 0.288752i −0.454303 0.890847i \(-0.650112\pi\)
0.798424 + 0.602095i \(0.205667\pi\)
\(422\) −9.04323 + 15.6633i −0.440218 + 0.762479i
\(423\) 0 0
\(424\) −15.1373 26.2185i −0.735131 1.27328i
\(425\) −13.4782 4.90566i −0.653788 0.237959i
\(426\) 0 0
\(427\) 3.13563 + 2.63111i 0.151744 + 0.127328i
\(428\) 16.7554 6.09845i 0.809901 0.294780i
\(429\) 0 0
\(430\) −0.121082 0.686688i −0.00583907 0.0331150i
\(431\) −11.5794 −0.557758 −0.278879 0.960326i \(-0.589963\pi\)
−0.278879 + 0.960326i \(0.589963\pi\)
\(432\) 0 0
\(433\) 6.06511 0.291471 0.145735 0.989324i \(-0.453445\pi\)
0.145735 + 0.989324i \(0.453445\pi\)
\(434\) −8.83409 50.1006i −0.424050 2.40491i
\(435\) 0 0
\(436\) 22.4008 8.15322i 1.07280 0.390469i
\(437\) −0.195937 0.164411i −0.00937293 0.00786482i
\(438\) 0 0
\(439\) −27.2567 9.92063i −1.30089 0.473486i −0.403605 0.914933i \(-0.632243\pi\)
−0.897287 + 0.441448i \(0.854465\pi\)
\(440\) −4.43717 7.68540i −0.211534 0.366387i
\(441\) 0 0
\(442\) 8.29813 14.3728i 0.394702 0.683644i
\(443\) −23.6648 + 19.8571i −1.12435 + 0.943440i −0.998816 0.0486498i \(-0.984508\pi\)
−0.125532 + 0.992090i \(0.540064\pi\)
\(444\) 0 0
\(445\) −1.28968 + 7.31412i −0.0611366 + 0.346723i
\(446\) 4.54442 25.7727i 0.215184 1.22037i
\(447\) 0 0
\(448\) 4.04916 3.39765i 0.191305 0.160524i
\(449\) −19.5410 + 33.8460i −0.922197 + 1.59729i −0.126190 + 0.992006i \(0.540275\pi\)
−0.796008 + 0.605287i \(0.793059\pi\)
\(450\) 0 0
\(451\) 11.9620 + 20.7188i 0.563268 + 0.975608i
\(452\) 5.73783 + 2.08840i 0.269885 + 0.0982300i
\(453\) 0 0
\(454\) −25.2592 21.1950i −1.18547 0.994731i
\(455\) 3.09967 1.12819i 0.145315 0.0528903i
\(456\) 0 0
\(457\) −0.261297 1.48189i −0.0122229 0.0693198i 0.978086 0.208200i \(-0.0667606\pi\)
−0.990309 + 0.138881i \(0.955650\pi\)
\(458\) 71.1498 3.32461
\(459\) 0 0
\(460\) 12.6040 0.587665
\(461\) −4.55603 25.8385i −0.212195 1.20342i −0.885708 0.464243i \(-0.846326\pi\)
0.673512 0.739176i \(-0.264785\pi\)
\(462\) 0 0
\(463\) −6.34895 + 2.31083i −0.295061 + 0.107393i −0.485309 0.874343i \(-0.661293\pi\)
0.190248 + 0.981736i \(0.439071\pi\)
\(464\) −33.4295 28.0507i −1.55192 1.30222i
\(465\) 0 0
\(466\) 33.1079 + 12.0503i 1.53369 + 0.558219i
\(467\) 16.8735 + 29.2257i 0.780810 + 1.35240i 0.931470 + 0.363818i \(0.118527\pi\)
−0.150660 + 0.988586i \(0.548140\pi\)
\(468\) 0 0
\(469\) 16.1459 27.9655i 0.745548 1.29133i
\(470\) 8.76786 7.35710i 0.404431 0.339358i
\(471\) 0 0
\(472\) −9.04664 + 51.3060i −0.416405 + 2.36155i
\(473\) −0.317429 + 1.80023i −0.0145954 + 0.0827746i
\(474\) 0 0
\(475\) −0.153419 + 0.128734i −0.00703934 + 0.00590671i
\(476\) −21.3516 + 36.9821i −0.978651 + 1.69507i
\(477\) 0 0
\(478\) 19.0155 + 32.9358i 0.869748 + 1.50645i
\(479\) 10.4556 + 3.80552i 0.477728 + 0.173879i 0.569650 0.821887i \(-0.307079\pi\)
−0.0919220 + 0.995766i \(0.529301\pi\)
\(480\) 0 0
\(481\) −6.01889 5.05044i −0.274438 0.230280i
\(482\) −30.8692 + 11.2355i −1.40605 + 0.511761i
\(483\) 0 0
\(484\) −1.03596 5.87522i −0.0470891 0.267055i
\(485\) −8.72462 −0.396165
\(486\) 0 0
\(487\) −4.74691 −0.215103 −0.107552 0.994200i \(-0.534301\pi\)
−0.107552 + 0.994200i \(0.534301\pi\)
\(488\) 1.34507 + 7.62830i 0.0608887 + 0.345317i
\(489\) 0 0
\(490\) −3.79813 + 1.38241i −0.171582 + 0.0624508i
\(491\) −17.1138 14.3602i −0.772335 0.648066i 0.168971 0.985621i \(-0.445956\pi\)
−0.941306 + 0.337555i \(0.890400\pi\)
\(492\) 0 0
\(493\) −18.5326 6.74530i −0.834664 0.303793i
\(494\) −0.115867 0.200688i −0.00521310 0.00902936i
\(495\) 0 0
\(496\) 20.6668 35.7960i 0.927969 1.60729i
\(497\) 29.2429 24.5377i 1.31172 1.10067i
\(498\) 0 0
\(499\) −1.81655 + 10.3022i −0.0813200 + 0.461189i 0.916770 + 0.399415i \(0.130787\pi\)
−0.998090 + 0.0617736i \(0.980324\pi\)
\(500\) 3.50593 19.8831i 0.156790 0.889200i
\(501\) 0 0
\(502\) 1.69253 1.42020i 0.0755415 0.0633868i
\(503\) 12.5209 21.6869i 0.558281 0.966972i −0.439359 0.898312i \(-0.644794\pi\)
0.997640 0.0686600i \(-0.0218723\pi\)
\(504\) 0 0
\(505\) −2.12583 3.68204i −0.0945982 0.163849i
\(506\) −45.1271 16.4249i −2.00614 0.730176i
\(507\) 0 0
\(508\) −22.4329 18.8234i −0.995298 0.835154i
\(509\) 16.9731 6.17771i 0.752321 0.273822i 0.0627387 0.998030i \(-0.480017\pi\)
0.689582 + 0.724208i \(0.257794\pi\)
\(510\) 0 0
\(511\) 4.61381 + 26.1662i 0.204103 + 1.15752i
\(512\) 50.5553 2.23425
\(513\) 0 0
\(514\) 11.5885 0.511148
\(515\) −0.0211929 0.120191i −0.000933872 0.00529625i
\(516\) 0 0
\(517\) −28.1964 + 10.2627i −1.24008 + 0.451351i
\(518\) 22.5082 + 18.8866i 0.988954 + 0.829831i
\(519\) 0 0
\(520\) 5.86571 + 2.13495i 0.257229 + 0.0936236i
\(521\) −12.9791 22.4804i −0.568623 0.984883i −0.996703 0.0811425i \(-0.974143\pi\)
0.428080 0.903741i \(-0.359190\pi\)
\(522\) 0 0
\(523\) −12.7973 + 22.1655i −0.559585 + 0.969230i 0.437946 + 0.899001i \(0.355706\pi\)
−0.997531 + 0.0702283i \(0.977627\pi\)
\(524\) 42.7183 35.8449i 1.86616 1.56589i
\(525\) 0 0
\(526\) 1.88965 10.7168i 0.0823928 0.467273i
\(527\) 3.24376 18.3963i 0.141300 0.801353i
\(528\) 0 0
\(529\) 10.9422 9.18161i 0.475749 0.399201i
\(530\) 2.93717 5.08732i 0.127582 0.220979i
\(531\) 0 0
\(532\) 0.298133 + 0.516382i 0.0129257 + 0.0223880i
\(533\) −15.8131 5.75552i −0.684943 0.249299i
\(534\) 0 0
\(535\) 1.44878 + 1.21567i 0.0626361 + 0.0525579i
\(536\) 57.4227 20.9001i 2.48028 0.902749i
\(537\) 0 0
\(538\) 5.33157 + 30.2368i 0.229860 + 1.30360i
\(539\) 10.5963 0.456414
\(540\) 0 0
\(541\) 27.8476 1.19726 0.598631 0.801025i \(-0.295712\pi\)
0.598631 + 0.801025i \(0.295712\pi\)
\(542\) 0.140682 + 0.797847i 0.00604281 + 0.0342705i
\(543\) 0 0
\(544\) −12.9572 + 4.71605i −0.555537 + 0.202199i
\(545\) 1.93692 + 1.62527i 0.0829685 + 0.0696188i
\(546\) 0 0
\(547\) 5.55216 + 2.02082i 0.237393 + 0.0864040i 0.457977 0.888964i \(-0.348574\pi\)
−0.220584 + 0.975368i \(0.570796\pi\)
\(548\) 23.4158 + 40.5574i 1.00027 + 1.73253i
\(549\) 0 0
\(550\) −18.8011 + 32.5645i −0.801683 + 1.38856i
\(551\) −0.210952 + 0.177009i −0.00898684 + 0.00754086i
\(552\) 0 0
\(553\) −6.19119 + 35.1120i −0.263276 + 1.49311i
\(554\) 11.7931 66.8819i 0.501040 2.84154i
\(555\) 0 0
\(556\) −25.2139 + 21.1570i −1.06931 + 0.897257i
\(557\) 13.3525 23.1272i 0.565764 0.979932i −0.431214 0.902250i \(-0.641915\pi\)
0.996978 0.0776824i \(-0.0247520\pi\)
\(558\) 0 0
\(559\) −0.642903 1.11354i −0.0271919 0.0470978i
\(560\) −9.41787 3.42782i −0.397978 0.144852i
\(561\) 0 0
\(562\) 51.7529 + 43.4258i 2.18306 + 1.83181i
\(563\) 33.8876 12.3341i 1.42819 0.519819i 0.491779 0.870720i \(-0.336347\pi\)
0.936413 + 0.350901i \(0.114125\pi\)
\(564\) 0 0
\(565\) 0.112463 + 0.637812i 0.00473137 + 0.0268329i
\(566\) 23.5321 0.989127
\(567\) 0 0
\(568\) 72.2390 3.03108
\(569\) 1.57104 + 8.90982i 0.0658615 + 0.373519i 0.999868 + 0.0162624i \(0.00517671\pi\)
−0.934006 + 0.357257i \(0.883712\pi\)
\(570\) 0 0
\(571\) −28.7349 + 10.4586i −1.20252 + 0.437681i −0.864102 0.503316i \(-0.832113\pi\)
−0.338415 + 0.940997i \(0.609891\pi\)
\(572\) −22.9329 19.2430i −0.958872 0.804589i
\(573\) 0 0
\(574\) 59.1348 + 21.5233i 2.46824 + 0.898366i
\(575\) −14.5967 25.2823i −0.608726 1.05434i
\(576\) 0 0
\(577\) 12.5744 21.7796i 0.523481 0.906696i −0.476146 0.879367i \(-0.657966\pi\)
0.999626 0.0273292i \(-0.00870022\pi\)
\(578\) 15.5175 13.0208i 0.645445 0.541592i
\(579\) 0 0
\(580\) 2.35638 13.3637i 0.0978434 0.554898i
\(581\) −0.845952 + 4.79763i −0.0350960 + 0.199039i
\(582\) 0 0
\(583\) −11.7973 + 9.89907i −0.488592 + 0.409978i
\(584\) −25.1400 + 43.5437i −1.04030 + 1.80185i
\(585\) 0 0
\(586\) 24.8640 + 43.0656i 1.02712 + 1.77903i
\(587\) 19.6147 + 7.13916i 0.809585 + 0.294665i 0.713452 0.700704i \(-0.247131\pi\)
0.0961324 + 0.995369i \(0.469353\pi\)
\(588\) 0 0
\(589\) −0.199807 0.167658i −0.00823292 0.00690824i
\(590\) −9.49912 + 3.45740i −0.391073 + 0.142339i
\(591\) 0 0
\(592\) 4.14543 + 23.5099i 0.170376 + 0.966251i
\(593\) −15.6212 −0.641488 −0.320744 0.947166i \(-0.603933\pi\)
−0.320744 + 0.947166i \(0.603933\pi\)
\(594\) 0 0
\(595\) −4.52940 −0.185687
\(596\) 3.25877 + 18.4814i 0.133484 + 0.757028i
\(597\) 0 0
\(598\) 31.7422 11.5532i 1.29803 0.472446i
\(599\) 0.343426 + 0.288169i 0.0140320 + 0.0117742i 0.649777 0.760125i \(-0.274862\pi\)
−0.635745 + 0.771899i \(0.719307\pi\)
\(600\) 0 0
\(601\) 16.6065 + 6.04428i 0.677395 + 0.246551i 0.657728 0.753255i \(-0.271517\pi\)
0.0196662 + 0.999807i \(0.493740\pi\)
\(602\) 2.40420 + 4.16420i 0.0979879 + 0.169720i
\(603\) 0 0
\(604\) −0.298133 + 0.516382i −0.0121309 + 0.0210113i
\(605\) 0.484737 0.406743i 0.0197074 0.0165364i
\(606\) 0 0
\(607\) 4.54933 25.8005i 0.184651 1.04721i −0.741751 0.670675i \(-0.766004\pi\)
0.926402 0.376535i \(-0.122884\pi\)
\(608\) −0.0334331 + 0.189608i −0.00135589 + 0.00768963i
\(609\) 0 0
\(610\) −1.15136 + 0.966105i −0.0466172 + 0.0391165i
\(611\) 10.5530 18.2784i 0.426930 0.739465i
\(612\) 0 0
\(613\) −7.27719 12.6045i −0.293923 0.509089i 0.680811 0.732459i \(-0.261628\pi\)
−0.974734 + 0.223370i \(0.928294\pi\)
\(614\) 67.4393 + 24.5459i 2.72163 + 0.990592i
\(615\) 0 0
\(616\) 46.8794 + 39.3365i 1.88883 + 1.58491i
\(617\) 13.1750 4.79531i 0.530405 0.193052i −0.0629140 0.998019i \(-0.520039\pi\)
0.593319 + 0.804967i \(0.297817\pi\)
\(618\) 0 0
\(619\) −5.50681 31.2307i −0.221337 1.25527i −0.869565 0.493819i \(-0.835600\pi\)
0.648227 0.761447i \(-0.275511\pi\)
\(620\) 12.8530 0.516188
\(621\) 0 0
\(622\) −5.17705 −0.207581
\(623\) −8.89352 50.4377i −0.356311 2.02074i
\(624\) 0 0
\(625\) −20.4513 + 7.44367i −0.818052 + 0.297747i
\(626\) −16.3157 13.6905i −0.652105 0.547181i
\(627\) 0 0
\(628\) −55.2418 20.1064i −2.20439 0.802331i
\(629\) 5.39440 + 9.34337i 0.215089 + 0.372545i
\(630\) 0 0
\(631\) 19.2879 33.4077i 0.767840 1.32994i −0.170892 0.985290i \(-0.554665\pi\)
0.938732 0.344648i \(-0.112002\pi\)
\(632\) −51.6848 + 43.3687i −2.05591 + 1.72512i
\(633\) 0 0
\(634\) 13.6869 77.6223i 0.543577 3.08278i
\(635\) 0.539363 3.05888i 0.0214040 0.121388i
\(636\) 0 0
\(637\) −5.70961 + 4.79093i −0.226223 + 0.189824i
\(638\) −25.8516 + 44.7763i −1.02348 + 1.77271i
\(639\) 0 0
\(640\) 3.12108 + 5.40587i 0.123372 + 0.213686i
\(641\) −28.7704 10.4716i −1.13636 0.413602i −0.295764 0.955261i \(-0.595574\pi\)
−0.840598 + 0.541659i \(0.817796\pi\)
\(642\) 0 0
\(643\) −26.2178 21.9994i −1.03393 0.867570i −0.0426164 0.999092i \(-0.513569\pi\)
−0.991313 + 0.131521i \(0.958014\pi\)
\(644\) −81.6746 + 29.7271i −3.21843 + 1.17141i
\(645\) 0 0
\(646\) 0.0552549 + 0.313366i 0.00217398 + 0.0123292i
\(647\) 12.8726 0.506073 0.253037 0.967457i \(-0.418571\pi\)
0.253037 + 0.967457i \(0.418571\pi\)
\(648\) 0 0
\(649\) 26.5012 1.04026
\(650\) −4.59286 26.0474i −0.180147 1.02166i
\(651\) 0 0
\(652\) 40.4752 14.7318i 1.58513 0.576941i
\(653\) 8.67096 + 7.27580i 0.339321 + 0.284724i 0.796485 0.604658i \(-0.206690\pi\)
−0.457164 + 0.889382i \(0.651135\pi\)
\(654\) 0 0
\(655\) 5.55809 + 2.02298i 0.217172 + 0.0790443i
\(656\) 25.5646 + 44.2793i 0.998132 + 1.72881i
\(657\) 0 0
\(658\) −39.4641 + 68.3538i −1.53847 + 2.66471i
\(659\) 10.5478 8.85067i 0.410885 0.344773i −0.413798 0.910369i \(-0.635798\pi\)
0.824683 + 0.565595i \(0.191354\pi\)
\(660\) 0 0
\(661\) −3.51930 + 19.9589i −0.136885 + 0.776312i 0.836644 + 0.547747i \(0.184514\pi\)
−0.973529 + 0.228565i \(0.926597\pi\)
\(662\) −13.6441 + 77.3795i −0.530292 + 3.00744i
\(663\) 0 0
\(664\) −7.06212 + 5.92582i −0.274063 + 0.229966i
\(665\) −0.0316221 + 0.0547710i −0.00122625 + 0.00212393i
\(666\) 0 0
\(667\) −20.0706 34.7633i −0.777136 1.34604i
\(668\) −14.8157 5.39246i −0.573236 0.208641i
\(669\) 0 0
\(670\) 9.08306 + 7.62159i 0.350909 + 0.294448i
\(671\) 3.70264 1.34765i 0.142939 0.0520255i
\(672\) 0 0
\(673\) −5.30406 30.0808i −0.204457 1.15953i −0.898293 0.439398i \(-0.855192\pi\)
0.693836 0.720133i \(-0.255919\pi\)
\(674\) −60.0856 −2.31441
\(675\) 0 0
\(676\) −36.2918 −1.39584
\(677\) 0.645840 + 3.66274i 0.0248217 + 0.140771i 0.994700 0.102819i \(-0.0327862\pi\)
−0.969878 + 0.243589i \(0.921675\pi\)
\(678\) 0 0
\(679\) 56.5360 20.5774i 2.16965 0.789689i
\(680\) −6.56599 5.50952i −0.251794 0.211280i
\(681\) 0 0
\(682\) −46.0185 16.7494i −1.76214 0.641366i
\(683\) −10.8735 18.8334i −0.416061 0.720639i 0.579478 0.814988i \(-0.303256\pi\)
−0.995539 + 0.0943487i \(0.969923\pi\)
\(684\) 0 0
\(685\) −2.48364 + 4.30179i −0.0948950 + 0.164363i
\(686\) −22.4598 + 18.8460i −0.857518 + 0.719543i
\(687\) 0 0
\(688\) −0.678396 + 3.84737i −0.0258636 + 0.146680i
\(689\) 1.88103 10.6679i 0.0716617 0.406414i
\(690\) 0 0
\(691\) −28.7993 + 24.1655i −1.09558 + 0.919299i −0.997120 0.0758425i \(-0.975835\pi\)
−0.0984578 + 0.995141i \(0.531391\pi\)
\(692\) 41.3940 71.6965i 1.57356 2.72549i
\(693\) 0 0
\(694\) 2.28952 + 3.96556i 0.0869088 + 0.150530i
\(695\) −3.28059 1.19404i −0.124440 0.0452924i
\(696\) 0 0
\(697\) 17.7010 + 14.8529i 0.670473 + 0.562593i
\(698\) 36.3114 13.2163i 1.37441 0.500243i
\(699\) 0 0
\(700\) 11.8177 + 67.0217i 0.446668 + 2.53318i
\(701\) −23.3351 −0.881355 −0.440678 0.897665i \(-0.645262\pi\)
−0.440678 + 0.897665i \(0.645262\pi\)
\(702\) 0 0
\(703\) 0.150644 0.00568166
\(704\) −0.883560 5.01092i −0.0333004 0.188856i
\(705\) 0 0
\(706\) 77.0502 28.0440i 2.89982 1.05545i
\(707\) 22.4598 + 18.8460i 0.844686 + 0.708776i
\(708\) 0 0
\(709\) −6.18227 2.25016i −0.232180 0.0845066i 0.223310 0.974747i \(-0.428314\pi\)
−0.455490 + 0.890241i \(0.650536\pi\)
\(710\) 7.00846 + 12.1390i 0.263023 + 0.455569i
\(711\) 0 0
\(712\) 48.4595 83.9343i 1.81610 3.14557i
\(713\) 29.1254 24.4391i 1.09076 0.915253i
\(714\) 0 0
\(715\) 0.551385 3.12706i 0.0206206 0.116945i
\(716\) 3.89440 22.0862i 0.145541 0.825402i
\(717\) 0 0
\(718\) −3.71348 + 3.11598i −0.138586 + 0.116287i
\(719\) −8.41622 + 14.5773i −0.313872 + 0.543642i −0.979197 0.202911i \(-0.934960\pi\)
0.665325 + 0.746554i \(0.268293\pi\)
\(720\) 0 0
\(721\) 0.420807 + 0.728860i 0.0156717 + 0.0271442i
\(722\) −45.2041 16.4530i −1.68232 0.612316i
\(723\) 0 0
\(724\) 24.1648 + 20.2767i 0.898077 + 0.753576i
\(725\) −29.5351 + 10.7499i −1.09691 + 0.399241i
\(726\) 0 0
\(727\) 4.43882 + 25.1738i 0.164627 + 0.933644i 0.949449 + 0.313922i \(0.101643\pi\)
−0.784822 + 0.619721i \(0.787246\pi\)
\(728\) −43.0455 −1.59537
\(729\) 0 0
\(730\) −9.75608 −0.361089
\(731\) 0.306589 + 1.73875i 0.0113396 + 0.0643102i
\(732\) 0 0
\(733\) 13.9055 5.06120i 0.513613 0.186940i −0.0721937 0.997391i \(-0.523000\pi\)
0.585807 + 0.810451i \(0.300778\pi\)
\(734\) 52.1095 + 43.7251i 1.92340 + 1.61392i
\(735\) 0 0
\(736\) −26.3726 9.59883i −0.972106 0.353818i
\(737\) −15.5424 26.9202i −0.572510 0.991616i
\(738\) 0 0
\(739\) −4.59539 + 7.95945i −0.169044 + 0.292793i −0.938084 0.346408i \(-0.887401\pi\)
0.769040 + 0.639201i \(0.220735\pi\)
\(740\) −5.68660 + 4.77163i −0.209044 + 0.175408i
\(741\) 0 0
\(742\) −7.03431 + 39.8936i −0.258238 + 1.46454i
\(743\) −7.71853 + 43.7740i −0.283165 + 1.60591i 0.428600 + 0.903494i \(0.359007\pi\)
−0.711766 + 0.702417i \(0.752104\pi\)
\(744\) 0 0
\(745\) −1.52481 + 1.27947i −0.0558649 + 0.0468762i
\(746\) 18.7883 32.5423i 0.687890 1.19146i
\(747\) 0 0
\(748\) 20.5535 + 35.5997i 0.751510 + 1.30165i
\(749\) −12.2554 4.46059i −0.447801 0.162986i
\(750\) 0 0
\(751\) −27.4290 23.0157i −1.00090 0.839854i −0.0137902 0.999905i \(-0.504390\pi\)
−0.987109 + 0.160051i \(0.948834\pi\)
\(752\) −60.2602 + 21.9329i −2.19746 + 0.799811i
\(753\) 0 0
\(754\) −6.31521 35.8153i −0.229986 1.30432i
\(755\) −0.0632441 −0.00230169
\(756\) 0 0
\(757\) −45.8976 −1.66818 −0.834088 0.551632i \(-0.814005\pi\)
−0.834088 + 0.551632i \(0.814005\pi\)
\(758\) 14.8559 + 84.2521i 0.539591 + 3.06017i
\(759\) 0 0
\(760\) −0.112463 + 0.0409333i −0.00407948 + 0.00148481i
\(761\) 28.4932 + 23.9086i 1.03288 + 0.866687i 0.991191 0.132444i \(-0.0422824\pi\)
0.0416869 + 0.999131i \(0.486727\pi\)
\(762\) 0 0
\(763\) −16.3846 5.96351i −0.593162 0.215893i
\(764\) −23.1819 40.1522i −0.838690 1.45265i
\(765\) 0 0
\(766\) 11.7476 20.3475i 0.424459 0.735185i
\(767\) −14.2797 + 11.9821i −0.515611 + 0.432649i
\(768\) 0 0
\(769\) −6.65657 + 37.7513i −0.240042 + 1.36135i 0.591688 + 0.806167i \(0.298462\pi\)
−0.831730 + 0.555180i \(0.812649\pi\)
\(770\) −2.06196 + 11.6939i −0.0743077 + 0.421420i
\(771\) 0 0
\(772\) −34.2768 + 28.7616i −1.23365 + 1.03515i
\(773\) 26.4136 45.7497i 0.950031 1.64550i 0.204680 0.978829i \(-0.434385\pi\)
0.745351 0.666673i \(-0.232282\pi\)
\(774\) 0 0
\(775\) −14.8851 25.7817i −0.534687 0.926106i
\(776\) 106.987 + 38.9401i 3.84061 + 1.39787i
\(777\) 0 0
\(778\) −30.9937 26.0068i −1.11118 0.932388i
\(779\) 0.303186 0.110351i 0.0108628 0.00395372i
\(780\) 0 0
\(781\) −6.38103 36.1886i −0.228331 1.29493i
\(782\) −46.3833 −1.65866
\(783\) 0 0
\(784\) 22.6459 0.808782
\(785\) −1.08276 6.14063i −0.0386453 0.219168i
\(786\) 0 0
\(787\) −42.5121 + 15.4731i −1.51539 + 0.551558i −0.959992 0.280026i \(-0.909657\pi\)
−0.555400 + 0.831584i \(0.687435\pi\)
\(788\) −47.5945 39.9365i −1.69548 1.42268i
\(789\) 0 0
\(790\) −12.3020 4.47756i −0.437686 0.159305i
\(791\) −2.23308 3.86780i −0.0793991 0.137523i
\(792\) 0 0
\(793\) −1.38578 + 2.40024i −0.0492106 + 0.0852352i
\(794\) −38.2217 + 32.0718i −1.35644 + 1.13819i
\(795\) 0 0
\(796\) 7.87211 44.6450i 0.279020 1.58240i
\(797\) 2.93794 16.6619i 0.104067 0.590194i −0.887522 0.460766i \(-0.847575\pi\)
0.991589 0.129428i \(-0.0413141\pi\)
\(798\) 0 0
\(799\) −22.2010 + 18.6288i −0.785415 + 0.659041i
\(800\) −10.9875 + 19.0309i −0.388467 + 0.672845i
\(801\) 0 0
\(802\) −1.45336 2.51730i −0.0513200 0.0888889i
\(803\) 24.0342 + 8.74774i 0.848149 + 0.308701i
\(804\) 0 0
\(805\) −7.06212 5.92582i −0.248907 0.208858i
\(806\) 32.3692 11.7814i 1.14016 0.414983i
\(807\) 0 0
\(808\) 9.63445 + 54.6397i 0.338939 + 1.92222i
\(809\) 34.9145 1.22753 0.613764 0.789490i \(-0.289655\pi\)
0.613764 + 0.789490i \(0.289655\pi\)
\(810\) 0 0
\(811\) 18.0419 0.633536 0.316768 0.948503i \(-0.397402\pi\)
0.316768 + 0.948503i \(0.397402\pi\)
\(812\) 16.2494 + 92.1551i 0.570243 + 3.23401i
\(813\) 0 0
\(814\) 26.5783 9.67372i 0.931569 0.339064i
\(815\) 3.49975 + 2.93664i 0.122591 + 0.102866i
\(816\) 0 0
\(817\) 0.0231661 + 0.00843175i 0.000810478 + 0.000294990i
\(818\) −3.92602 6.80007i −0.137270 0.237759i
\(819\) 0 0
\(820\) −7.94949 + 13.7689i −0.277608 + 0.480832i
\(821\) −31.1313 + 26.1223i −1.08649 + 0.911675i −0.996444 0.0842628i \(-0.973146\pi\)
−0.0900480 + 0.995937i \(0.528702\pi\)
\(822\) 0 0
\(823\) 4.52347 25.6539i 0.157678 0.894238i −0.798618 0.601838i \(-0.794435\pi\)
0.956296 0.292400i \(-0.0944537\pi\)
\(824\) −0.276560 + 1.56845i −0.00963442 + 0.0546395i
\(825\) 0 0
\(826\) 53.4004 44.8082i 1.85804 1.55908i
\(827\) −18.8097 + 32.5794i −0.654079 + 1.13290i 0.328045 + 0.944662i \(0.393610\pi\)
−0.982124 + 0.188236i \(0.939723\pi\)
\(828\) 0 0
\(829\) 17.5107 + 30.3295i 0.608173 + 1.05339i 0.991541 + 0.129791i \(0.0414306\pi\)
−0.383368 + 0.923595i \(0.625236\pi\)
\(830\) −1.68092 0.611806i −0.0583457 0.0212361i
\(831\) 0 0
\(832\) 2.74170 + 2.30056i 0.0950512 + 0.0797574i
\(833\) 9.61721 3.50038i 0.333217 0.121281i
\(834\) 0 0
\(835\) −0.290393 1.64690i −0.0100494 0.0569933i
\(836\) 0.573978 0.0198514
\(837\) 0 0
\(838\) 89.7606 3.10073
\(839\) −4.62149 26.2098i −0.159552 0.904862i −0.954506 0.298193i \(-0.903616\pi\)
0.794954 0.606670i \(-0.207495\pi\)
\(840\) 0 0
\(841\) −13.3598 + 4.86256i −0.460682 + 0.167675i
\(842\) −17.8785 15.0018i −0.616134 0.516998i
\(843\) 0 0
\(844\) 29.6104 + 10.7773i 1.01923 + 0.370970i
\(845\) −1.92468 3.33364i −0.0662109 0.114681i
\(846\) 0 0
\(847\) −2.18180 + 3.77899i −0.0749675 + 0.129848i
\(848\) −25.2126 + 21.1559i −0.865804 + 0.726496i
\(849\) 0 0
\(850\) −6.30659 + 35.7664i −0.216314 + 1.22678i
\(851\) −3.81315 + 21.6254i −0.130713 + 0.741310i
\(852\) 0 0
\(853\) 1.88073 1.57812i 0.0643949 0.0540338i −0.610022 0.792384i \(-0.708839\pi\)
0.674417 + 0.738351i \(0.264395\pi\)
\(854\) 5.18227 8.97595i 0.177334 0.307151i
\(855\) 0 0
\(856\) −12.3400 21.3735i −0.421773 0.730533i
\(857\) −9.23695 3.36197i −0.315528 0.114843i 0.179401 0.983776i \(-0.442584\pi\)
−0.494930 + 0.868933i \(0.664806\pi\)
\(858\) 0 0
\(859\) 6.75418 + 5.66743i 0.230450 + 0.193370i 0.750699 0.660644i \(-0.229717\pi\)
−0.520250 + 0.854014i \(0.674161\pi\)
\(860\) −1.14156 + 0.415494i −0.0389268 + 0.0141682i
\(861\) 0 0
\(862\) 5.09136 + 28.8745i 0.173412 + 0.983470i
\(863\) 6.62124 0.225390 0.112695 0.993630i \(-0.464052\pi\)
0.112695 + 0.993630i \(0.464052\pi\)
\(864\) 0 0
\(865\) 8.78106 0.298565
\(866\) −2.66678 15.1241i −0.0906210 0.513937i
\(867\) 0 0
\(868\) −83.2880 + 30.3143i −2.82698 + 1.02894i
\(869\) 26.2913 + 22.0610i 0.891872 + 0.748370i
\(870\) 0 0
\(871\) 20.5462 + 7.47821i 0.696182 + 0.253390i
\(872\) −16.4978 28.5750i −0.558685 0.967671i
\(873\) 0 0
\(874\) −0.323826 + 0.560882i −0.0109536 + 0.0189721i
\(875\) −11.3125 + 9.49233i −0.382433 + 0.320899i
\(876\) 0 0
\(877\) −0.707796 + 4.01411i −0.0239006 + 0.135547i −0.994423 0.105463i \(-0.966368\pi\)
0.970523 + 0.241010i \(0.0774787\pi\)
\(878\) −12.7537 + 72.3299i −0.430417 + 2.44102i
\(879\) 0 0
\(880\) −7.39053 + 6.20139i −0.249135 + 0.209049i
\(881\) 4.62567 8.01189i 0.155843 0.269927i −0.777523 0.628855i \(-0.783524\pi\)
0.933366 + 0.358927i \(0.116857\pi\)
\(882\) 0 0
\(883\) 18.8851 + 32.7099i 0.635533 + 1.10078i 0.986402 + 0.164351i \(0.0525530\pi\)
−0.350869 + 0.936425i \(0.614114\pi\)
\(884\) −27.1707 9.88933i −0.913850 0.332614i
\(885\) 0 0
\(886\) 59.9213 + 50.2800i 2.01310 + 1.68919i
\(887\) 17.8341 6.49108i 0.598810 0.217949i −0.0247898 0.999693i \(-0.507892\pi\)
0.623600 + 0.781744i \(0.285669\pi\)
\(888\) 0 0
\(889\) 3.71941 + 21.0938i 0.124745 + 0.707464i
\(890\) 18.8057 0.630369
\(891\) 0 0
\(892\) −45.5945 −1.52662
\(893\) 0.0702697 + 0.398519i 0.00235149 + 0.0133359i
\(894\) 0 0
\(895\) 2.23530 0.813583i 0.0747178 0.0271951i
\(896\) −32.9748 27.6691i −1.10161 0.924360i
\(897\) 0 0
\(898\) 92.9912 + 33.8460i 3.10316 + 1.12946i
\(899\) −20.4670 35.4499i −0.682614 1.18232i
\(900\) 0 0
\(901\) −7.43717 + 12.8816i −0.247768 + 0.429147i
\(902\) 46.4051 38.9385i 1.54512 1.29651i
\(903\) 0 0
\(904\) 1.46761 8.32321i 0.0488119 0.276826i
\(905\) −0.581004 + 3.29503i −0.0193132 + 0.109531i
\(906\) 0 0
\(907\) 7.38919 6.20026i 0.245354 0.205876i −0.511815 0.859096i \(-0.671027\pi\)
0.757169 + 0.653220i \(0.226582\pi\)
\(908\) −28.7237 + 49.7510i −0.953231 + 1.65104i
\(909\) 0 0
\(910\) −4.17617 7.23335i −0.138439 0.239783i
\(911\) −6.14068 2.23503i −0.203450 0.0740497i 0.238285 0.971195i \(-0.423415\pi\)
−0.441735 + 0.897146i \(0.645637\pi\)
\(912\) 0 0
\(913\) 3.59240 + 3.01438i 0.118891 + 0.0997614i
\(914\) −3.58037 + 1.30315i −0.118428 + 0.0431044i
\(915\) 0 0
\(916\) −21.5253 122.076i −0.711215 4.03350i
\(917\) −40.7880 −1.34694
\(918\) 0 0
\(919\) 3.89124 0.128360 0.0641802 0.997938i \(-0.479557\pi\)
0.0641802 + 0.997938i \(0.479557\pi\)
\(920\) −3.02940 17.1806i −0.0998764 0.566427i
\(921\) 0 0
\(922\) −62.4282 + 22.7220i −2.05596 + 0.748309i
\(923\) 19.8004 + 16.6145i 0.651738 + 0.546874i
\(924\) 0 0
\(925\) 16.1570 + 5.88068i 0.531240 + 0.193356i
\(926\) 8.55391 + 14.8158i 0.281099 + 0.486878i
\(927\) 0 0
\(928\) −15.1079 + 26.1676i −0.495940 + 0.858994i
\(929\) 30.5292 25.6170i 1.00163 0.840467i 0.0144197 0.999896i \(-0.495410\pi\)
0.987209 + 0.159430i \(0.0509655\pi\)
\(930\) 0 0
\(931\) 0.0248149 0.140732i 0.000813276 0.00461232i
\(932\) 10.6591 60.4508i 0.349150 1.98013i
\(933\) 0 0
\(934\) 65.4586 54.9263i 2.14187 1.79724i
\(935\) −2.18004 + 3.77595i −0.0712951 + 0.123487i
\(936\) 0 0
\(937\) −16.5326 28.6352i −0.540095 0.935472i −0.998898 0.0469340i \(-0.985055\pi\)
0.458803 0.888538i \(-0.348278\pi\)
\(938\) −76.8346 27.9655i −2.50874 0.913106i
\(939\) 0 0
\(940\) −15.2756 12.8177i −0.498235 0.418069i
\(941\) −50.5617 + 18.4030i −1.64826 + 0.599919i −0.988455 0.151514i \(-0.951585\pi\)
−0.659809 + 0.751433i \(0.729363\pi\)
\(942\) 0 0
\(943\) 8.16684 + 46.3165i 0.265949 + 1.50827i
\(944\) 56.6373 1.84339
\(945\) 0 0
\(946\) 4.62866 0.150491
\(947\) −7.33409 41.5937i −0.238326 1.35161i −0.835495 0.549498i \(-0.814819\pi\)
0.597169 0.802116i \(-0.296292\pi\)
\(948\) 0 0
\(949\) −16.9055 + 6.15311i −0.548777 + 0.199739i
\(950\) 0.388470 + 0.325965i 0.0126036 + 0.0105757i
\(951\) 0 0
\(952\) 55.5424 + 20.2158i 1.80014 + 0.655197i
\(953\) 12.2888 + 21.2848i 0.398073 + 0.689483i 0.993488 0.113935i \(-0.0363456\pi\)
−0.595415 + 0.803418i \(0.703012\pi\)
\(954\) 0 0
\(955\) 2.45883 4.25881i 0.0795657 0.137812i
\(956\) 50.7570 42.5902i 1.64160 1.37747i
\(957\) 0 0
\(958\) 4.89228 27.7455i 0.158063 0.896417i
\(959\) 5.94815 33.7336i 0.192076 1.08932i
\(960\) 0 0
\(961\) 5.95336 4.99546i 0.192044 0.161144i
\(962\) −9.94743 + 17.2295i −0.320718 + 0.555500i
\(963\) 0 0
\(964\) 28.6163 + 49.5649i 0.921670 + 1.59638i
\(965\) −4.45976 1.62322i −0.143565 0.0522533i
\(966\) 0 0
\(967\) 3.42577 + 2.87457i 0.110165 + 0.0924398i 0.696206 0.717842i \(-0.254870\pi\)
−0.586041 + 0.810281i \(0.699314\pi\)
\(968\) −7.75954 + 2.82424i −0.249401 + 0.0907746i
\(969\) 0 0
\(970\) 3.83615 + 21.7559i 0.123171 + 0.698540i
\(971\) 4.61949 0.148246 0.0741232 0.997249i \(-0.476384\pi\)
0.0741232 + 0.997249i \(0.476384\pi\)
\(972\) 0 0
\(973\) 24.0746 0.771796
\(974\) 2.08718 + 11.8370i 0.0668776 + 0.379282i
\(975\) 0 0
\(976\) 7.91312 2.88014i 0.253293 0.0921911i
\(977\) 8.64156 + 7.25113i 0.276468 + 0.231984i 0.770470 0.637477i \(-0.220022\pi\)
−0.494002 + 0.869461i \(0.664466\pi\)
\(978\) 0 0
\(979\) −46.3281 16.8620i −1.48065 0.538913i
\(980\) 3.52094 + 6.09845i 0.112472 + 0.194808i
\(981\) 0 0
\(982\) −28.2841 + 48.9894i −0.902580 + 1.56332i
\(983\) 13.0719 10.9686i 0.416929 0.349845i −0.410064 0.912057i \(-0.634494\pi\)
0.826994 + 0.562211i \(0.190049\pi\)
\(984\) 0 0
\(985\) 1.14433 6.48984i 0.0364615 0.206783i
\(986\) −8.67159 + 49.1790i −0.276160 + 1.56618i
\(987\) 0 0
\(988\) −0.309278 + 0.259515i −0.00983943 + 0.00825627i
\(989\) −1.79679 + 3.11213i −0.0571346 + 0.0989600i
\(990\) 0 0
\(991\) −1.00000 1.73205i −0.0317660 0.0550204i 0.849705 0.527258i \(-0.176780\pi\)
−0.881471 + 0.472237i \(0.843446\pi\)
\(992\) −26.8935 9.78844i −0.853870 0.310783i
\(993\) 0 0
\(994\) −74.0456 62.1316i −2.34858 1.97069i
\(995\) 4.51842 1.64457i 0.143243 0.0521364i
\(996\) 0 0
\(997\) 3.88707 + 22.0447i 0.123105 + 0.698162i 0.982415 + 0.186708i \(0.0597818\pi\)
−0.859311 + 0.511454i \(0.829107\pi\)
\(998\) 26.4884 0.838477
\(999\) 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.g.82.1 6
3.2 odd 2 729.2.e.b.82.1 6
9.2 odd 6 729.2.e.i.325.1 6
9.4 even 3 729.2.e.h.568.1 6
9.5 odd 6 729.2.e.c.568.1 6
9.7 even 3 729.2.e.a.325.1 6
27.2 odd 18 729.2.e.b.649.1 6
27.4 even 9 243.2.c.f.163.3 6
27.5 odd 18 243.2.a.f.1.3 yes 3
27.7 even 9 729.2.e.a.406.1 6
27.11 odd 18 729.2.e.c.163.1 6
27.13 even 9 243.2.c.f.82.3 6
27.14 odd 18 243.2.c.e.82.1 6
27.16 even 9 729.2.e.h.163.1 6
27.20 odd 18 729.2.e.i.406.1 6
27.22 even 9 243.2.a.e.1.1 3
27.23 odd 18 243.2.c.e.163.1 6
27.25 even 9 inner 729.2.e.g.649.1 6
108.59 even 18 3888.2.a.bk.1.1 3
108.103 odd 18 3888.2.a.bd.1.3 3
135.49 even 18 6075.2.a.bv.1.3 3
135.59 odd 18 6075.2.a.bq.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.e.1.1 3 27.22 even 9
243.2.a.f.1.3 yes 3 27.5 odd 18
243.2.c.e.82.1 6 27.14 odd 18
243.2.c.e.163.1 6 27.23 odd 18
243.2.c.f.82.3 6 27.13 even 9
243.2.c.f.163.3 6 27.4 even 9
729.2.e.a.325.1 6 9.7 even 3
729.2.e.a.406.1 6 27.7 even 9
729.2.e.b.82.1 6 3.2 odd 2
729.2.e.b.649.1 6 27.2 odd 18
729.2.e.c.163.1 6 27.11 odd 18
729.2.e.c.568.1 6 9.5 odd 6
729.2.e.g.82.1 6 1.1 even 1 trivial
729.2.e.g.649.1 6 27.25 even 9 inner
729.2.e.h.163.1 6 27.16 even 9
729.2.e.h.568.1 6 9.4 even 3
729.2.e.i.325.1 6 9.2 odd 6
729.2.e.i.406.1 6 27.20 odd 18
3888.2.a.bd.1.3 3 108.103 odd 18
3888.2.a.bk.1.1 3 108.59 even 18
6075.2.a.bq.1.1 3 135.59 odd 18
6075.2.a.bv.1.3 3 135.49 even 18