Properties

Label 729.2.e.i.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.i.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.233956 + 1.32683i) q^{2} +(0.173648 - 0.0632028i) q^{4} +(1.26604 + 1.06234i) q^{5} +(-2.26604 - 0.824773i) q^{7} +(1.47178 + 2.54920i) q^{8} +O(q^{10})\) \(q+(0.233956 + 1.32683i) q^{2} +(0.173648 - 0.0632028i) q^{4} +(1.26604 + 1.06234i) q^{5} +(-2.26604 - 0.824773i) q^{7} +(1.47178 + 2.54920i) q^{8} +(-1.11334 + 1.92836i) q^{10} +(4.55303 - 3.82045i) q^{11} +(-0.560307 + 3.17766i) q^{13} +(0.564178 - 3.19961i) q^{14} +(-2.75490 + 2.31164i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(3.31908 + 5.74881i) q^{19} +(0.286989 + 0.104455i) q^{20} +(6.13429 + 5.14728i) q^{22} +(2.76604 - 1.00676i) q^{23} +(-0.393933 - 2.23411i) q^{25} -4.34730 q^{26} -0.445622 q^{28} +(-0.224155 - 1.27125i) q^{29} +(0.553033 - 0.201288i) q^{31} +(0.798133 + 0.669713i) q^{32} +(-3.79813 - 1.38241i) q^{34} +(-1.99273 - 3.45150i) q^{35} +(-0.0209445 + 0.0362770i) q^{37} +(-6.85117 + 5.74881i) q^{38} +(-0.844770 + 4.79093i) q^{40} +(-0.851167 + 4.82721i) q^{41} +(-3.97178 + 3.33272i) q^{43} +(0.549163 - 0.951178i) q^{44} +(1.98293 + 3.43453i) q^{46} +(3.51114 + 1.27795i) q^{47} +(-0.907604 - 0.761570i) q^{49} +(2.87211 - 1.04536i) q^{50} +(0.103541 + 0.587208i) q^{52} +11.6382 q^{53} +9.82295 q^{55} +(-1.23261 - 6.99049i) q^{56} +(1.63429 - 0.594831i) q^{58} +(-5.62836 - 4.72275i) q^{59} +(-10.3833 - 3.77920i) q^{61} +(0.396459 + 0.686688i) q^{62} +(-4.29813 + 7.44459i) q^{64} +(-4.08512 + 3.42782i) q^{65} +(0.322481 - 1.82888i) q^{67} +(-0.0962667 + 0.545955i) q^{68} +(4.11334 - 3.45150i) q^{70} +(2.75624 - 4.77396i) q^{71} +(-2.77719 - 4.81023i) q^{73} +(-0.0530334 - 0.0193026i) q^{74} +(0.939693 + 0.788496i) q^{76} +(-13.4684 + 4.90209i) q^{77} +(-0.656574 - 3.72362i) q^{79} -5.94356 q^{80} -6.60401 q^{82} +(0.692066 + 3.92490i) q^{83} +(-4.65910 + 1.69577i) q^{85} +(-5.35117 - 4.49016i) q^{86} +(16.4402 + 5.98373i) q^{88} +(-4.07532 - 7.05866i) q^{89} +(3.89053 - 6.73859i) q^{91} +(0.416689 - 0.349643i) q^{92} +(-0.874171 + 4.95767i) q^{94} +(-1.90508 + 10.8042i) q^{95} +(0.199807 - 0.167658i) q^{97} +(0.798133 - 1.38241i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8} + 15 q^{11} - 9 q^{13} - 15 q^{14} - 18 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} + 27 q^{22} + 12 q^{23} - 27 q^{25} - 24 q^{26} - 24 q^{28} - 3 q^{29} - 9 q^{31} - 9 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} - 15 q^{38} - 18 q^{40} + 21 q^{41} - 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} - 9 q^{49} - 12 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 21 q^{56} + 3 q^{59} - 27 q^{61} + 12 q^{62} - 12 q^{64} - 3 q^{65} + 27 q^{67} + 27 q^{68} + 18 q^{70} + 9 q^{71} - 6 q^{73} + 12 q^{74} - 24 q^{77} + 18 q^{79} - 6 q^{80} + 36 q^{82} + 15 q^{83} + 9 q^{85} - 6 q^{86} + 27 q^{88} + 6 q^{91} - 51 q^{92} - 27 q^{94} - 30 q^{95} - 36 q^{97} - 9 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.233956 + 1.32683i 0.165432 + 0.938209i 0.948618 + 0.316423i \(0.102482\pi\)
−0.783187 + 0.621786i \(0.786407\pi\)
\(3\) 0 0
\(4\) 0.173648 0.0632028i 0.0868241 0.0316014i
\(5\) 1.26604 + 1.06234i 0.566192 + 0.475092i 0.880380 0.474269i \(-0.157288\pi\)
−0.314188 + 0.949361i \(0.601732\pi\)
\(6\) 0 0
\(7\) −2.26604 0.824773i −0.856484 0.311735i −0.123803 0.992307i \(-0.539509\pi\)
−0.732681 + 0.680572i \(0.761731\pi\)
\(8\) 1.47178 + 2.54920i 0.520353 + 0.901278i
\(9\) 0 0
\(10\) −1.11334 + 1.92836i −0.352069 + 0.609802i
\(11\) 4.55303 3.82045i 1.37279 1.15191i 0.400997 0.916080i \(-0.368664\pi\)
0.971795 0.235829i \(-0.0757806\pi\)
\(12\) 0 0
\(13\) −0.560307 + 3.17766i −0.155401 + 0.881325i 0.803017 + 0.595957i \(0.203227\pi\)
−0.958418 + 0.285368i \(0.907884\pi\)
\(14\) 0.564178 3.19961i 0.150783 0.855132i
\(15\) 0 0
\(16\) −2.75490 + 2.31164i −0.688725 + 0.577909i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) 3.31908 + 5.74881i 0.761449 + 1.31887i 0.942104 + 0.335321i \(0.108845\pi\)
−0.180655 + 0.983547i \(0.557822\pi\)
\(20\) 0.286989 + 0.104455i 0.0641727 + 0.0233569i
\(21\) 0 0
\(22\) 6.13429 + 5.14728i 1.30783 + 1.09740i
\(23\) 2.76604 1.00676i 0.576760 0.209924i −0.0371361 0.999310i \(-0.511824\pi\)
0.613896 + 0.789387i \(0.289601\pi\)
\(24\) 0 0
\(25\) −0.393933 2.23411i −0.0787866 0.446821i
\(26\) −4.34730 −0.852575
\(27\) 0 0
\(28\) −0.445622 −0.0842147
\(29\) −0.224155 1.27125i −0.0416246 0.236065i 0.956897 0.290429i \(-0.0937980\pi\)
−0.998521 + 0.0543640i \(0.982687\pi\)
\(30\) 0 0
\(31\) 0.553033 0.201288i 0.0993277 0.0361523i −0.291878 0.956455i \(-0.594280\pi\)
0.391206 + 0.920303i \(0.372058\pi\)
\(32\) 0.798133 + 0.669713i 0.141091 + 0.118390i
\(33\) 0 0
\(34\) −3.79813 1.38241i −0.651374 0.237081i
\(35\) −1.99273 3.45150i −0.336832 0.583410i
\(36\) 0 0
\(37\) −0.0209445 + 0.0362770i −0.00344326 + 0.00596390i −0.867742 0.497015i \(-0.834429\pi\)
0.864299 + 0.502979i \(0.167763\pi\)
\(38\) −6.85117 + 5.74881i −1.11141 + 0.932580i
\(39\) 0 0
\(40\) −0.844770 + 4.79093i −0.133570 + 0.757512i
\(41\) −0.851167 + 4.82721i −0.132930 + 0.753883i 0.843349 + 0.537366i \(0.180581\pi\)
−0.976279 + 0.216517i \(0.930530\pi\)
\(42\) 0 0
\(43\) −3.97178 + 3.33272i −0.605691 + 0.508235i −0.893269 0.449522i \(-0.851594\pi\)
0.287578 + 0.957757i \(0.407150\pi\)
\(44\) 0.549163 0.951178i 0.0827894 0.143396i
\(45\) 0 0
\(46\) 1.98293 + 3.43453i 0.292366 + 0.506394i
\(47\) 3.51114 + 1.27795i 0.512153 + 0.186408i 0.585152 0.810924i \(-0.301035\pi\)
−0.0729991 + 0.997332i \(0.523257\pi\)
\(48\) 0 0
\(49\) −0.907604 0.761570i −0.129658 0.108796i
\(50\) 2.87211 1.04536i 0.406178 0.147837i
\(51\) 0 0
\(52\) 0.103541 + 0.587208i 0.0143585 + 0.0814311i
\(53\) 11.6382 1.59862 0.799312 0.600916i \(-0.205198\pi\)
0.799312 + 0.600916i \(0.205198\pi\)
\(54\) 0 0
\(55\) 9.82295 1.32453
\(56\) −1.23261 6.99049i −0.164715 0.934143i
\(57\) 0 0
\(58\) 1.63429 0.594831i 0.214592 0.0781052i
\(59\) −5.62836 4.72275i −0.732749 0.614850i 0.198130 0.980176i \(-0.436513\pi\)
−0.930880 + 0.365326i \(0.880958\pi\)
\(60\) 0 0
\(61\) −10.3833 3.77920i −1.32944 0.483876i −0.422969 0.906144i \(-0.639012\pi\)
−0.906471 + 0.422268i \(0.861234\pi\)
\(62\) 0.396459 + 0.686688i 0.0503504 + 0.0872094i
\(63\) 0 0
\(64\) −4.29813 + 7.44459i −0.537267 + 0.930573i
\(65\) −4.08512 + 3.42782i −0.506697 + 0.425169i
\(66\) 0 0
\(67\) 0.322481 1.82888i 0.0393974 0.223434i −0.958752 0.284244i \(-0.908257\pi\)
0.998149 + 0.0608104i \(0.0193685\pi\)
\(68\) −0.0962667 + 0.545955i −0.0116740 + 0.0662068i
\(69\) 0 0
\(70\) 4.11334 3.45150i 0.491638 0.412533i
\(71\) 2.75624 4.77396i 0.327106 0.566564i −0.654830 0.755776i \(-0.727260\pi\)
0.981936 + 0.189212i \(0.0605932\pi\)
\(72\) 0 0
\(73\) −2.77719 4.81023i −0.325045 0.562995i 0.656476 0.754347i \(-0.272046\pi\)
−0.981522 + 0.191352i \(0.938713\pi\)
\(74\) −0.0530334 0.0193026i −0.00616501 0.00224388i
\(75\) 0 0
\(76\) 0.939693 + 0.788496i 0.107790 + 0.0904467i
\(77\) −13.4684 + 4.90209i −1.53486 + 0.558645i
\(78\) 0 0
\(79\) −0.656574 3.72362i −0.0738704 0.418940i −0.999208 0.0397952i \(-0.987329\pi\)
0.925338 0.379144i \(-0.123782\pi\)
\(80\) −5.94356 −0.664511
\(81\) 0 0
\(82\) −6.60401 −0.729291
\(83\) 0.692066 + 3.92490i 0.0759642 + 0.430814i 0.998943 + 0.0459637i \(0.0146359\pi\)
−0.922979 + 0.384850i \(0.874253\pi\)
\(84\) 0 0
\(85\) −4.65910 + 1.69577i −0.505350 + 0.183932i
\(86\) −5.35117 4.49016i −0.577031 0.484187i
\(87\) 0 0
\(88\) 16.4402 + 5.98373i 1.75253 + 0.637868i
\(89\) −4.07532 7.05866i −0.431983 0.748217i 0.565061 0.825049i \(-0.308853\pi\)
−0.997044 + 0.0768323i \(0.975519\pi\)
\(90\) 0 0
\(91\) 3.89053 6.73859i 0.407838 0.706397i
\(92\) 0.416689 0.349643i 0.0434428 0.0364528i
\(93\) 0 0
\(94\) −0.874171 + 4.95767i −0.0901638 + 0.511344i
\(95\) −1.90508 + 10.8042i −0.195457 + 1.10849i
\(96\) 0 0
\(97\) 0.199807 0.167658i 0.0202874 0.0170231i −0.632588 0.774489i \(-0.718007\pi\)
0.652875 + 0.757466i \(0.273563\pi\)
\(98\) 0.798133 1.38241i 0.0806236 0.139644i
\(99\) 0 0
\(100\) −0.209607 0.363051i −0.0209607 0.0363051i
\(101\) −10.3623 3.77157i −1.03109 0.375286i −0.229593 0.973287i \(-0.573740\pi\)
−0.801495 + 0.598001i \(0.795962\pi\)
\(102\) 0 0
\(103\) −2.99273 2.51120i −0.294882 0.247435i 0.483328 0.875439i \(-0.339428\pi\)
−0.778210 + 0.628004i \(0.783872\pi\)
\(104\) −8.92514 + 3.24849i −0.875182 + 0.318540i
\(105\) 0 0
\(106\) 2.72281 + 15.4418i 0.264463 + 1.49984i
\(107\) −2.63816 −0.255040 −0.127520 0.991836i \(-0.540702\pi\)
−0.127520 + 0.991836i \(0.540702\pi\)
\(108\) 0 0
\(109\) −8.95811 −0.858031 −0.429016 0.903297i \(-0.641140\pi\)
−0.429016 + 0.903297i \(0.641140\pi\)
\(110\) 2.29813 + 13.0334i 0.219118 + 1.24268i
\(111\) 0 0
\(112\) 8.14930 2.96610i 0.770036 0.280270i
\(113\) 12.2023 + 10.2390i 1.14790 + 0.963202i 0.999668 0.0257512i \(-0.00819777\pi\)
0.148231 + 0.988953i \(0.452642\pi\)
\(114\) 0 0
\(115\) 4.57145 + 1.66387i 0.426290 + 0.155157i
\(116\) −0.119271 0.206583i −0.0110740 0.0191807i
\(117\) 0 0
\(118\) 4.94949 8.57277i 0.455638 0.789188i
\(119\) 5.54189 4.65020i 0.508024 0.426283i
\(120\) 0 0
\(121\) 4.22416 23.9564i 0.384014 2.17785i
\(122\) 2.58512 14.6610i 0.234046 1.32734i
\(123\) 0 0
\(124\) 0.0833113 0.0699065i 0.00748158 0.00627779i
\(125\) 6.00640 10.4034i 0.537228 0.930507i
\(126\) 0 0
\(127\) −1.79813 3.11446i −0.159559 0.276363i 0.775151 0.631776i \(-0.217674\pi\)
−0.934710 + 0.355412i \(0.884340\pi\)
\(128\) −8.92514 3.24849i −0.788879 0.287128i
\(129\) 0 0
\(130\) −5.50387 4.61830i −0.482721 0.405051i
\(131\) 16.6395 6.05628i 1.45380 0.529140i 0.510150 0.860085i \(-0.329590\pi\)
0.943650 + 0.330946i \(0.107368\pi\)
\(132\) 0 0
\(133\) −2.77972 15.7645i −0.241032 1.36696i
\(134\) 2.50206 0.216145
\(135\) 0 0
\(136\) −8.83069 −0.757225
\(137\) −0.682266 3.86932i −0.0582899 0.330579i 0.941693 0.336474i \(-0.109234\pi\)
−0.999983 + 0.00589552i \(0.998123\pi\)
\(138\) 0 0
\(139\) −11.2442 + 4.09256i −0.953723 + 0.347127i −0.771571 0.636144i \(-0.780529\pi\)
−0.182152 + 0.983270i \(0.558306\pi\)
\(140\) −0.564178 0.473401i −0.0476817 0.0400097i
\(141\) 0 0
\(142\) 6.97906 + 2.54017i 0.585669 + 0.213166i
\(143\) 9.58899 + 16.6086i 0.801872 + 1.38888i
\(144\) 0 0
\(145\) 1.06670 1.84759i 0.0885849 0.153434i
\(146\) 5.73261 4.81023i 0.474434 0.398098i
\(147\) 0 0
\(148\) −0.00134417 + 0.00762319i −0.000110490 + 0.000626622i
\(149\) 3.56418 20.2135i 0.291989 1.65595i −0.387206 0.921993i \(-0.626560\pi\)
0.679195 0.733958i \(-0.262329\pi\)
\(150\) 0 0
\(151\) 12.2626 10.2896i 0.997920 0.837354i 0.0112247 0.999937i \(-0.496427\pi\)
0.986695 + 0.162583i \(0.0519825\pi\)
\(152\) −9.76991 + 16.9220i −0.792445 + 1.37255i
\(153\) 0 0
\(154\) −9.65523 16.7233i −0.778041 1.34761i
\(155\) 0.914000 + 0.332669i 0.0734143 + 0.0267206i
\(156\) 0 0
\(157\) −16.8327 14.1244i −1.34340 1.12725i −0.980739 0.195325i \(-0.937424\pi\)
−0.362661 0.931921i \(-0.618132\pi\)
\(158\) 4.78699 1.74232i 0.380832 0.138612i
\(159\) 0 0
\(160\) 0.299011 + 1.69577i 0.0236389 + 0.134063i
\(161\) −7.09833 −0.559426
\(162\) 0 0
\(163\) 20.5107 1.60652 0.803262 0.595625i \(-0.203096\pi\)
0.803262 + 0.595625i \(0.203096\pi\)
\(164\) 0.157289 + 0.892032i 0.0122822 + 0.0696560i
\(165\) 0 0
\(166\) −5.04576 + 1.83651i −0.391627 + 0.142541i
\(167\) 3.28699 + 2.75811i 0.254355 + 0.213429i 0.761045 0.648699i \(-0.224687\pi\)
−0.506690 + 0.862128i \(0.669131\pi\)
\(168\) 0 0
\(169\) 2.43242 + 0.885328i 0.187109 + 0.0681022i
\(170\) −3.34002 5.78509i −0.256168 0.443696i
\(171\) 0 0
\(172\) −0.479055 + 0.829748i −0.0365276 + 0.0632677i
\(173\) 2.90554 2.43804i 0.220904 0.185361i −0.525619 0.850720i \(-0.676166\pi\)
0.746523 + 0.665359i \(0.231722\pi\)
\(174\) 0 0
\(175\) −0.949960 + 5.38749i −0.0718102 + 0.407256i
\(176\) −3.71167 + 21.0499i −0.279777 + 1.58670i
\(177\) 0 0
\(178\) 8.41219 7.05866i 0.630520 0.529069i
\(179\) −4.13816 + 7.16750i −0.309300 + 0.535724i −0.978209 0.207620i \(-0.933428\pi\)
0.668909 + 0.743344i \(0.266761\pi\)
\(180\) 0 0
\(181\) −3.36097 5.82137i −0.249819 0.432699i 0.713657 0.700496i \(-0.247038\pi\)
−0.963475 + 0.267797i \(0.913704\pi\)
\(182\) 9.85117 + 3.58553i 0.730217 + 0.265777i
\(183\) 0 0
\(184\) 6.63744 + 5.56947i 0.489319 + 0.410587i
\(185\) −0.0650551 + 0.0236781i −0.00478295 + 0.00174085i
\(186\) 0 0
\(187\) 3.09627 + 17.5598i 0.226421 + 1.28410i
\(188\) 0.690474 0.0503580
\(189\) 0 0
\(190\) −14.7811 −1.07233
\(191\) −0.870767 4.93837i −0.0630065 0.357328i −0.999969 0.00789719i \(-0.997486\pi\)
0.936962 0.349430i \(-0.113625\pi\)
\(192\) 0 0
\(193\) 16.7875 6.11013i 1.20839 0.439817i 0.342243 0.939611i \(-0.388813\pi\)
0.866144 + 0.499794i \(0.166591\pi\)
\(194\) 0.269200 + 0.225885i 0.0193274 + 0.0162176i
\(195\) 0 0
\(196\) −0.205737 0.0748822i −0.0146955 0.00534873i
\(197\) −0.361844 0.626733i −0.0257803 0.0446529i 0.852847 0.522160i \(-0.174874\pi\)
−0.878628 + 0.477507i \(0.841540\pi\)
\(198\) 0 0
\(199\) 5.09627 8.82699i 0.361265 0.625729i −0.626905 0.779096i \(-0.715678\pi\)
0.988169 + 0.153367i \(0.0490117\pi\)
\(200\) 5.11540 4.29233i 0.361713 0.303514i
\(201\) 0 0
\(202\) 2.57991 14.6314i 0.181522 1.02946i
\(203\) −0.540545 + 3.06558i −0.0379388 + 0.215162i
\(204\) 0 0
\(205\) −6.20574 + 5.20723i −0.433427 + 0.363689i
\(206\) 2.63176 4.55834i 0.183363 0.317595i
\(207\) 0 0
\(208\) −5.80200 10.0494i −0.402297 0.696798i
\(209\) 37.0749 + 13.4942i 2.56453 + 0.933411i
\(210\) 0 0
\(211\) −11.3871 9.55493i −0.783922 0.657789i 0.160311 0.987067i \(-0.448750\pi\)
−0.944233 + 0.329278i \(0.893195\pi\)
\(212\) 2.02094 0.735564i 0.138799 0.0505187i
\(213\) 0 0
\(214\) −0.617211 3.50038i −0.0421917 0.239281i
\(215\) −8.56893 −0.584396
\(216\) 0 0
\(217\) −1.41921 −0.0963426
\(218\) −2.09580 11.8859i −0.141945 0.805013i
\(219\) 0 0
\(220\) 1.70574 0.620838i 0.115001 0.0418569i
\(221\) −7.41534 6.22221i −0.498810 0.418551i
\(222\) 0 0
\(223\) 10.2883 + 3.74465i 0.688958 + 0.250760i 0.662689 0.748895i \(-0.269415\pi\)
0.0262688 + 0.999655i \(0.491637\pi\)
\(224\) −1.25624 2.17588i −0.0839364 0.145382i
\(225\) 0 0
\(226\) −10.7306 + 18.5859i −0.713786 + 1.23631i
\(227\) −13.2777 + 11.1413i −0.881269 + 0.739472i −0.966440 0.256894i \(-0.917301\pi\)
0.0851707 + 0.996366i \(0.472856\pi\)
\(228\) 0 0
\(229\) 0.271259 1.53839i 0.0179253 0.101659i −0.974532 0.224246i \(-0.928008\pi\)
0.992458 + 0.122587i \(0.0391191\pi\)
\(230\) −1.13816 + 6.45480i −0.0750478 + 0.425617i
\(231\) 0 0
\(232\) 2.91076 2.44242i 0.191101 0.160353i
\(233\) −8.39440 + 14.5395i −0.549935 + 0.952516i 0.448343 + 0.893862i \(0.352014\pi\)
−0.998278 + 0.0586545i \(0.981319\pi\)
\(234\) 0 0
\(235\) 3.08765 + 5.34796i 0.201416 + 0.348863i
\(236\) −1.27584 0.464369i −0.0830504 0.0302279i
\(237\) 0 0
\(238\) 7.46657 + 6.26519i 0.483986 + 0.406112i
\(239\) 3.78611 1.37803i 0.244903 0.0891375i −0.216652 0.976249i \(-0.569514\pi\)
0.461555 + 0.887111i \(0.347292\pi\)
\(240\) 0 0
\(241\) −0.582129 3.30142i −0.0374982 0.212663i 0.960301 0.278965i \(-0.0899912\pi\)
−0.997800 + 0.0663015i \(0.978880\pi\)
\(242\) 32.7743 2.10681
\(243\) 0 0
\(244\) −2.04189 −0.130719
\(245\) −0.340022 1.92836i −0.0217232 0.123199i
\(246\) 0 0
\(247\) −20.1275 + 7.32580i −1.28068 + 0.466130i
\(248\) 1.32707 + 1.11354i 0.0842688 + 0.0707100i
\(249\) 0 0
\(250\) 15.2087 + 5.53553i 0.961885 + 0.350097i
\(251\) 11.5753 + 20.0490i 0.730628 + 1.26548i 0.956615 + 0.291354i \(0.0941059\pi\)
−0.225987 + 0.974130i \(0.572561\pi\)
\(252\) 0 0
\(253\) 8.74763 15.1513i 0.549959 0.952556i
\(254\) 3.71167 3.11446i 0.232891 0.195418i
\(255\) 0 0
\(256\) −0.763356 + 4.32921i −0.0477098 + 0.270575i
\(257\) 2.08600 11.8303i 0.130121 0.737953i −0.848013 0.529976i \(-0.822201\pi\)
0.978134 0.207977i \(-0.0666880\pi\)
\(258\) 0 0
\(259\) 0.0773815 0.0649308i 0.00480825 0.00403460i
\(260\) −0.492726 + 0.853427i −0.0305576 + 0.0529273i
\(261\) 0 0
\(262\) 11.9285 + 20.6609i 0.736948 + 1.27643i
\(263\) −15.8824 5.78071i −0.979349 0.356454i −0.197762 0.980250i \(-0.563367\pi\)
−0.781587 + 0.623796i \(0.785590\pi\)
\(264\) 0 0
\(265\) 14.7344 + 12.3636i 0.905128 + 0.759493i
\(266\) 20.2665 7.37641i 1.24262 0.452277i
\(267\) 0 0
\(268\) −0.0595922 0.337964i −0.00364017 0.0206444i
\(269\) −7.91447 −0.482554 −0.241277 0.970456i \(-0.577566\pi\)
−0.241277 + 0.970456i \(0.577566\pi\)
\(270\) 0 0
\(271\) −17.2344 −1.04692 −0.523458 0.852051i \(-0.675358\pi\)
−0.523458 + 0.852051i \(0.675358\pi\)
\(272\) −1.87346 10.6249i −0.113595 0.644229i
\(273\) 0 0
\(274\) 4.97431 1.81050i 0.300509 0.109376i
\(275\) −10.3289 8.66696i −0.622855 0.522637i
\(276\) 0 0
\(277\) −24.8405 9.04120i −1.49252 0.543233i −0.538409 0.842684i \(-0.680974\pi\)
−0.954112 + 0.299451i \(0.903197\pi\)
\(278\) −8.06077 13.9617i −0.483453 0.837365i
\(279\) 0 0
\(280\) 5.86571 10.1597i 0.350543 0.607159i
\(281\) −14.5517 + 12.2103i −0.868081 + 0.728406i −0.963693 0.267012i \(-0.913964\pi\)
0.0956121 + 0.995419i \(0.469519\pi\)
\(282\) 0 0
\(283\) −2.88026 + 16.3348i −0.171214 + 0.971002i 0.771210 + 0.636581i \(0.219652\pi\)
−0.942424 + 0.334421i \(0.891459\pi\)
\(284\) 0.176890 1.00319i 0.0104965 0.0595284i
\(285\) 0 0
\(286\) −19.7934 + 16.6086i −1.17041 + 0.982088i
\(287\) 5.91013 10.2366i 0.348864 0.604250i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 2.70099 + 0.983080i 0.158608 + 0.0577284i
\(291\) 0 0
\(292\) −0.786274 0.659762i −0.0460132 0.0386097i
\(293\) −18.1903 + 6.62073i −1.06269 + 0.386787i −0.813438 0.581652i \(-0.802407\pi\)
−0.249251 + 0.968439i \(0.580185\pi\)
\(294\) 0 0
\(295\) −2.10859 11.9584i −0.122767 0.696246i
\(296\) −0.123303 −0.00716685
\(297\) 0 0
\(298\) 27.6536 1.60193
\(299\) 1.64930 + 9.35365i 0.0953815 + 0.540935i
\(300\) 0 0
\(301\) 11.7490 4.27628i 0.677199 0.246480i
\(302\) 16.5214 + 13.8631i 0.950700 + 0.797732i
\(303\) 0 0
\(304\) −22.4329 8.16490i −1.28661 0.468289i
\(305\) −9.13088 15.8152i −0.522833 0.905573i
\(306\) 0 0
\(307\) −10.4029 + 18.0183i −0.593722 + 1.02836i 0.400003 + 0.916514i \(0.369009\pi\)
−0.993726 + 0.111844i \(0.964324\pi\)
\(308\) −2.02893 + 1.70248i −0.115609 + 0.0970077i
\(309\) 0 0
\(310\) −0.227559 + 1.29055i −0.0129245 + 0.0732984i
\(311\) −1.85204 + 10.5035i −0.105020 + 0.595597i 0.886193 + 0.463317i \(0.153341\pi\)
−0.991212 + 0.132280i \(0.957770\pi\)
\(312\) 0 0
\(313\) 2.92262 2.45237i 0.165196 0.138616i −0.556442 0.830886i \(-0.687834\pi\)
0.721638 + 0.692270i \(0.243389\pi\)
\(314\) 14.8025 25.6386i 0.835352 1.44687i
\(315\) 0 0
\(316\) −0.349356 0.605102i −0.0196528 0.0340396i
\(317\) −24.7977 9.02563i −1.39278 0.506930i −0.466752 0.884388i \(-0.654576\pi\)
−0.926027 + 0.377458i \(0.876798\pi\)
\(318\) 0 0
\(319\) −5.87733 4.93166i −0.329067 0.276120i
\(320\) −13.3503 + 4.85911i −0.746304 + 0.271632i
\(321\) 0 0
\(322\) −1.66069 9.41826i −0.0925468 0.524859i
\(323\) −19.9145 −1.10807
\(324\) 0 0
\(325\) 7.31996 0.406038
\(326\) 4.79860 + 27.2142i 0.265770 + 1.50726i
\(327\) 0 0
\(328\) −13.5582 + 4.93480i −0.748629 + 0.272479i
\(329\) −6.90239 5.79179i −0.380541 0.319312i
\(330\) 0 0
\(331\) 1.47683 + 0.537524i 0.0811741 + 0.0295450i 0.382288 0.924043i \(-0.375136\pi\)
−0.301114 + 0.953588i \(0.597358\pi\)
\(332\) 0.368241 + 0.637812i 0.0202098 + 0.0350045i
\(333\) 0 0
\(334\) −2.89053 + 5.00654i −0.158163 + 0.273946i
\(335\) 2.35117 1.97286i 0.128458 0.107789i
\(336\) 0 0
\(337\) −1.39187 + 7.89371i −0.0758202 + 0.429998i 0.923142 + 0.384458i \(0.125612\pi\)
−0.998963 + 0.0455394i \(0.985499\pi\)
\(338\) −0.605600 + 3.43453i −0.0329403 + 0.186814i
\(339\) 0 0
\(340\) −0.701867 + 0.588936i −0.0380641 + 0.0319395i
\(341\) 1.74897 3.02931i 0.0947121 0.164046i
\(342\) 0 0
\(343\) 9.86871 + 17.0931i 0.532860 + 0.922941i
\(344\) −14.3414 5.21983i −0.773235 0.281434i
\(345\) 0 0
\(346\) 3.91463 + 3.28476i 0.210452 + 0.176590i
\(347\) −18.6484 + 6.78747i −1.00110 + 0.364371i −0.790009 0.613096i \(-0.789924\pi\)
−0.211091 + 0.977466i \(0.567702\pi\)
\(348\) 0 0
\(349\) 1.92633 + 10.9247i 0.103114 + 0.584788i 0.991957 + 0.126576i \(0.0403988\pi\)
−0.888843 + 0.458212i \(0.848490\pi\)
\(350\) −7.37052 −0.393971
\(351\) 0 0
\(352\) 6.19253 0.330063
\(353\) −0.497312 2.82039i −0.0264692 0.150114i 0.968709 0.248200i \(-0.0798391\pi\)
−0.995178 + 0.0980859i \(0.968728\pi\)
\(354\) 0 0
\(355\) 8.56108 3.11598i 0.454375 0.165379i
\(356\) −1.15380 0.968153i −0.0611512 0.0513120i
\(357\) 0 0
\(358\) −10.4782 3.81374i −0.553789 0.201563i
\(359\) −14.3944 24.9318i −0.759707 1.31585i −0.943000 0.332793i \(-0.892009\pi\)
0.183292 0.983058i \(-0.441324\pi\)
\(360\) 0 0
\(361\) −12.5326 + 21.7070i −0.659608 + 1.14247i
\(362\) 6.93763 5.82137i 0.364634 0.305964i
\(363\) 0 0
\(364\) 0.249686 1.41604i 0.0130871 0.0742205i
\(365\) 1.59405 9.04028i 0.0834361 0.473190i
\(366\) 0 0
\(367\) −8.42056 + 7.06569i −0.439550 + 0.368826i −0.835541 0.549428i \(-0.814846\pi\)
0.395991 + 0.918254i \(0.370401\pi\)
\(368\) −5.29292 + 9.16760i −0.275912 + 0.477894i
\(369\) 0 0
\(370\) −0.0466368 0.0807773i −0.00242453 0.00419941i
\(371\) −26.3726 9.59883i −1.36920 0.498347i
\(372\) 0 0
\(373\) 25.5933 + 21.4754i 1.32517 + 1.11195i 0.985180 + 0.171523i \(0.0548689\pi\)
0.339992 + 0.940428i \(0.389576\pi\)
\(374\) −22.5744 + 8.21643i −1.16730 + 0.424861i
\(375\) 0 0
\(376\) 1.90988 + 10.8315i 0.0984946 + 0.558591i
\(377\) 4.16519 0.214518
\(378\) 0 0
\(379\) 20.9394 1.07559 0.537794 0.843077i \(-0.319258\pi\)
0.537794 + 0.843077i \(0.319258\pi\)
\(380\) 0.352044 + 1.99654i 0.0180595 + 0.102420i
\(381\) 0 0
\(382\) 6.34864 2.31072i 0.324825 0.118227i
\(383\) −3.14930 2.64258i −0.160922 0.135029i 0.558771 0.829322i \(-0.311273\pi\)
−0.719693 + 0.694292i \(0.755717\pi\)
\(384\) 0 0
\(385\) −22.2592 8.10170i −1.13444 0.412901i
\(386\) 12.0346 + 20.8446i 0.612546 + 1.06096i
\(387\) 0 0
\(388\) 0.0240997 0.0417419i 0.00122348 0.00211912i
\(389\) 13.0949 10.9879i 0.663939 0.557111i −0.247326 0.968932i \(-0.579552\pi\)
0.911265 + 0.411822i \(0.135107\pi\)
\(390\) 0 0
\(391\) −1.53343 + 8.69653i −0.0775490 + 0.439802i
\(392\) 0.605600 3.43453i 0.0305874 0.173470i
\(393\) 0 0
\(394\) 0.746911 0.626733i 0.0376288 0.0315743i
\(395\) 3.12449 5.41177i 0.157210 0.272296i
\(396\) 0 0
\(397\) −11.2010 19.4007i −0.562162 0.973692i −0.997308 0.0733324i \(-0.976637\pi\)
0.435146 0.900360i \(-0.356697\pi\)
\(398\) 12.9042 + 4.69674i 0.646829 + 0.235427i
\(399\) 0 0
\(400\) 6.24969 + 5.24411i 0.312484 + 0.262205i
\(401\) 13.7023 4.98724i 0.684262 0.249051i 0.0235855 0.999722i \(-0.492492\pi\)
0.660676 + 0.750671i \(0.270270\pi\)
\(402\) 0 0
\(403\) 0.329755 + 1.87014i 0.0164263 + 0.0931581i
\(404\) −2.03777 −0.101383
\(405\) 0 0
\(406\) −4.19396 −0.208143
\(407\) 0.0432332 + 0.245188i 0.00214299 + 0.0121535i
\(408\) 0 0
\(409\) 16.4474 5.98638i 0.813273 0.296007i 0.0982980 0.995157i \(-0.468660\pi\)
0.714975 + 0.699150i \(0.246438\pi\)
\(410\) −8.36097 7.01568i −0.412919 0.346480i
\(411\) 0 0
\(412\) −0.678396 0.246916i −0.0334222 0.0121647i
\(413\) 8.85891 + 15.3441i 0.435918 + 0.755033i
\(414\) 0 0
\(415\) −3.29339 + 5.70431i −0.161666 + 0.280014i
\(416\) −2.57532 + 2.16095i −0.126266 + 0.105949i
\(417\) 0 0
\(418\) −9.23055 + 52.3491i −0.451481 + 2.56048i
\(419\) 3.27538 18.5756i 0.160013 0.907477i −0.794046 0.607858i \(-0.792029\pi\)
0.954059 0.299619i \(-0.0968597\pi\)
\(420\) 0 0
\(421\) −24.7690 + 20.7837i −1.20717 + 1.01294i −0.207773 + 0.978177i \(0.566622\pi\)
−0.999396 + 0.0347581i \(0.988934\pi\)
\(422\) 10.0137 17.3442i 0.487458 0.844302i
\(423\) 0 0
\(424\) 17.1288 + 29.6680i 0.831849 + 1.44080i
\(425\) 6.39528 + 2.32769i 0.310217 + 0.112910i
\(426\) 0 0
\(427\) 20.4119 + 17.1277i 0.987803 + 0.828865i
\(428\) −0.458111 + 0.166739i −0.0221436 + 0.00805962i
\(429\) 0 0
\(430\) −2.00475 11.3695i −0.0966775 0.548285i
\(431\) 34.3164 1.65297 0.826483 0.562962i \(-0.190338\pi\)
0.826483 + 0.562962i \(0.190338\pi\)
\(432\) 0 0
\(433\) −25.0669 −1.20464 −0.602318 0.798256i \(-0.705756\pi\)
−0.602318 + 0.798256i \(0.705756\pi\)
\(434\) −0.332033 1.88305i −0.0159381 0.0903895i
\(435\) 0 0
\(436\) −1.55556 + 0.566177i −0.0744978 + 0.0271150i
\(437\) 14.9684 + 12.5600i 0.716035 + 0.600824i
\(438\) 0 0
\(439\) 21.8084 + 7.93761i 1.04086 + 0.378841i 0.805205 0.592996i \(-0.202055\pi\)
0.235653 + 0.971837i \(0.424277\pi\)
\(440\) 14.4572 + 25.0407i 0.689222 + 1.19377i
\(441\) 0 0
\(442\) 6.52094 11.2946i 0.310170 0.537230i
\(443\) −3.15729 + 2.64928i −0.150007 + 0.125871i −0.714703 0.699428i \(-0.753438\pi\)
0.564695 + 0.825299i \(0.308994\pi\)
\(444\) 0 0
\(445\) 2.33915 13.2660i 0.110886 0.628866i
\(446\) −2.56149 + 14.5269i −0.121290 + 0.687870i
\(447\) 0 0
\(448\) 15.8799 13.3248i 0.750252 0.629537i
\(449\) −9.17071 + 15.8841i −0.432793 + 0.749619i −0.997113 0.0759373i \(-0.975805\pi\)
0.564320 + 0.825556i \(0.309138\pi\)
\(450\) 0 0
\(451\) 14.5667 + 25.2303i 0.685919 + 1.18805i
\(452\) 2.76604 + 1.00676i 0.130104 + 0.0473539i
\(453\) 0 0
\(454\) −17.8889 15.0106i −0.839569 0.704482i
\(455\) 12.0842 4.39831i 0.566518 0.206196i
\(456\) 0 0
\(457\) −3.37939 19.1654i −0.158081 0.896522i −0.955915 0.293644i \(-0.905132\pi\)
0.797834 0.602877i \(-0.205979\pi\)
\(458\) 2.10464 0.0983432
\(459\) 0 0
\(460\) 0.898986 0.0419154
\(461\) 4.81861 + 27.3277i 0.224425 + 1.27278i 0.863781 + 0.503867i \(0.168090\pi\)
−0.639356 + 0.768911i \(0.720799\pi\)
\(462\) 0 0
\(463\) −36.3530 + 13.2314i −1.68947 + 0.614915i −0.994558 0.104183i \(-0.966777\pi\)
−0.694908 + 0.719099i \(0.744555\pi\)
\(464\) 3.55619 + 2.98400i 0.165092 + 0.138529i
\(465\) 0 0
\(466\) −21.2554 7.73632i −0.984636 0.358378i
\(467\) −14.8819 25.7762i −0.688653 1.19278i −0.972274 0.233845i \(-0.924869\pi\)
0.283621 0.958936i \(-0.408464\pi\)
\(468\) 0 0
\(469\) −2.23917 + 3.87836i −0.103395 + 0.179086i
\(470\) −6.37346 + 5.34796i −0.293986 + 0.246683i
\(471\) 0 0
\(472\) 3.75553 21.2987i 0.172862 0.980350i
\(473\) −5.35117 + 30.3480i −0.246047 + 1.39540i
\(474\) 0 0
\(475\) 11.5360 9.67982i 0.529306 0.444141i
\(476\) 0.668434 1.15776i 0.0306376 0.0530659i
\(477\) 0 0
\(478\) 2.71419 + 4.70112i 0.124144 + 0.215024i
\(479\) 35.4038 + 12.8859i 1.61764 + 0.588773i 0.982930 0.183977i \(-0.0588973\pi\)
0.634710 + 0.772750i \(0.281120\pi\)
\(480\) 0 0
\(481\) −0.103541 0.0868809i −0.00472105 0.00396143i
\(482\) 4.24422 1.54477i 0.193319 0.0703624i
\(483\) 0 0
\(484\) −0.780592 4.42696i −0.0354815 0.201225i
\(485\) 0.431074 0.0195741
\(486\) 0 0
\(487\) −0.763823 −0.0346121 −0.0173061 0.999850i \(-0.505509\pi\)
−0.0173061 + 0.999850i \(0.505509\pi\)
\(488\) −5.64796 32.0311i −0.255671 1.44998i
\(489\) 0 0
\(490\) 2.47906 0.902302i 0.111992 0.0407619i
\(491\) −0.381445 0.320070i −0.0172144 0.0144446i 0.634140 0.773218i \(-0.281354\pi\)
−0.651354 + 0.758774i \(0.725799\pi\)
\(492\) 0 0
\(493\) 3.63903 + 1.32450i 0.163894 + 0.0596525i
\(494\) −14.4290 24.9918i −0.649192 1.12443i
\(495\) 0 0
\(496\) −1.05825 + 1.83294i −0.0475167 + 0.0823014i
\(497\) −10.1832 + 8.54472i −0.456779 + 0.383283i
\(498\) 0 0
\(499\) 1.55690 8.82964i 0.0696966 0.395269i −0.929925 0.367750i \(-0.880128\pi\)
0.999621 0.0275190i \(-0.00876067\pi\)
\(500\) 0.385477 2.18615i 0.0172391 0.0977676i
\(501\) 0 0
\(502\) −23.8935 + 20.0490i −1.06642 + 0.894833i
\(503\) −9.18092 + 15.9018i −0.409357 + 0.709027i −0.994818 0.101673i \(-0.967580\pi\)
0.585461 + 0.810701i \(0.300914\pi\)
\(504\) 0 0
\(505\) −9.11246 15.7832i −0.405499 0.702345i
\(506\) 22.1498 + 8.06186i 0.984677 + 0.358393i
\(507\) 0 0
\(508\) −0.509085 0.427173i −0.0225870 0.0189527i
\(509\) 26.6596 9.70329i 1.18166 0.430091i 0.324875 0.945757i \(-0.394678\pi\)
0.856790 + 0.515666i \(0.172456\pi\)
\(510\) 0 0
\(511\) 2.32588 + 13.1907i 0.102891 + 0.583524i
\(512\) −24.9186 −1.10126
\(513\) 0 0
\(514\) 16.1848 0.713881
\(515\) −1.12119 6.35857i −0.0494054 0.280192i
\(516\) 0 0
\(517\) 20.8687 7.59559i 0.917805 0.334054i
\(518\) 0.104256 + 0.0874810i 0.00458074 + 0.00384370i
\(519\) 0 0
\(520\) −14.7506 5.36879i −0.646857 0.235437i
\(521\) 16.3191 + 28.2655i 0.714952 + 1.23833i 0.962978 + 0.269580i \(0.0868847\pi\)
−0.248026 + 0.968753i \(0.579782\pi\)
\(522\) 0 0
\(523\) 11.0116 19.0727i 0.481504 0.833990i −0.518271 0.855217i \(-0.673424\pi\)
0.999775 + 0.0212271i \(0.00675730\pi\)
\(524\) 2.50665 2.10332i 0.109503 0.0918842i
\(525\) 0 0
\(526\) 3.95424 22.4256i 0.172413 0.977803i
\(527\) −0.306589 + 1.73875i −0.0133552 + 0.0757413i
\(528\) 0 0
\(529\) −10.9816 + 9.21464i −0.477460 + 0.400637i
\(530\) −12.9572 + 22.4426i −0.562826 + 0.974844i
\(531\) 0 0
\(532\) −1.47906 2.56180i −0.0641252 0.111068i
\(533\) −14.8623 5.40944i −0.643758 0.234309i
\(534\) 0 0
\(535\) −3.34002 2.80261i −0.144402 0.121167i
\(536\) 5.13681 1.86965i 0.221876 0.0807564i
\(537\) 0 0
\(538\) −1.85163 10.5011i −0.0798296 0.452736i
\(539\) −7.04189 −0.303316
\(540\) 0 0
\(541\) −15.7870 −0.678738 −0.339369 0.940653i \(-0.610214\pi\)
−0.339369 + 0.940653i \(0.610214\pi\)
\(542\) −4.03209 22.8671i −0.173193 0.982227i
\(543\) 0 0
\(544\) −2.93717 + 1.06904i −0.125930 + 0.0458348i
\(545\) −11.3414 9.51654i −0.485811 0.407644i
\(546\) 0 0
\(547\) 25.7656 + 9.37792i 1.10166 + 0.400971i 0.827928 0.560835i \(-0.189520\pi\)
0.273731 + 0.961806i \(0.411742\pi\)
\(548\) −0.363026 0.628780i −0.0155077 0.0268602i
\(549\) 0 0
\(550\) 9.08306 15.7323i 0.387303 0.670829i
\(551\) 6.56418 5.50800i 0.279643 0.234649i
\(552\) 0 0
\(553\) −1.58331 + 8.97940i −0.0673292 + 0.381843i
\(554\) 6.18454 35.0743i 0.262756 1.49016i
\(555\) 0 0
\(556\) −1.69388 + 1.42133i −0.0718364 + 0.0602779i
\(557\) −14.7010 + 25.4629i −0.622901 + 1.07890i 0.366042 + 0.930598i \(0.380713\pi\)
−0.988943 + 0.148298i \(0.952621\pi\)
\(558\) 0 0
\(559\) −8.36484 14.4883i −0.353795 0.612791i
\(560\) 13.4684 + 4.90209i 0.569143 + 0.207151i
\(561\) 0 0
\(562\) −19.6054 16.4509i −0.827005 0.693940i
\(563\) 9.74510 3.54693i 0.410707 0.149485i −0.128400 0.991722i \(-0.540984\pi\)
0.539107 + 0.842237i \(0.318762\pi\)
\(564\) 0 0
\(565\) 4.57145 + 25.9260i 0.192322 + 1.09071i
\(566\) −22.3473 −0.939327
\(567\) 0 0
\(568\) 16.2264 0.680843
\(569\) −5.72503 32.4683i −0.240006 1.36114i −0.831811 0.555060i \(-0.812695\pi\)
0.591805 0.806081i \(-0.298416\pi\)
\(570\) 0 0
\(571\) 0.692944 0.252211i 0.0289988 0.0105547i −0.327480 0.944858i \(-0.606199\pi\)
0.356479 + 0.934303i \(0.383977\pi\)
\(572\) 2.71482 + 2.27801i 0.113512 + 0.0952482i
\(573\) 0 0
\(574\) 14.9650 + 5.44681i 0.624626 + 0.227345i
\(575\) −3.33884 5.78304i −0.139239 0.241169i
\(576\) 0 0
\(577\) −9.67159 + 16.7517i −0.402634 + 0.697382i −0.994043 0.108990i \(-0.965238\pi\)
0.591409 + 0.806371i \(0.298572\pi\)
\(578\) −8.25671 + 6.92820i −0.343434 + 0.288175i
\(579\) 0 0
\(580\) 0.0684587 0.388249i 0.00284259 0.0161211i
\(581\) 1.66890 9.46480i 0.0692377 0.392666i
\(582\) 0 0
\(583\) 52.9889 44.4630i 2.19458 1.84147i
\(584\) 8.17483 14.1592i 0.338277 0.585913i
\(585\) 0 0
\(586\) −13.0403 22.5865i −0.538690 0.933038i
\(587\) 29.9876 + 10.9146i 1.23772 + 0.450493i 0.876234 0.481885i \(-0.160048\pi\)
0.361485 + 0.932378i \(0.382270\pi\)
\(588\) 0 0
\(589\) 2.99273 + 2.51120i 0.123313 + 0.103472i
\(590\) 15.3735 5.59548i 0.632915 0.230362i
\(591\) 0 0
\(592\) −0.0261591 0.148356i −0.00107513 0.00609738i
\(593\) 31.6783 1.30087 0.650436 0.759561i \(-0.274586\pi\)
0.650436 + 0.759561i \(0.274586\pi\)
\(594\) 0 0
\(595\) 11.9564 0.490163
\(596\) −0.658633 3.73530i −0.0269787 0.153004i
\(597\) 0 0
\(598\) −12.0248 + 4.37667i −0.491731 + 0.178976i
\(599\) −9.67024 8.11430i −0.395115 0.331541i 0.423487 0.905902i \(-0.360806\pi\)
−0.818602 + 0.574361i \(0.805251\pi\)
\(600\) 0 0
\(601\) 8.37123 + 3.04688i 0.341470 + 0.124285i 0.507062 0.861909i \(-0.330731\pi\)
−0.165592 + 0.986194i \(0.552954\pi\)
\(602\) 8.42262 + 14.5884i 0.343280 + 0.594579i
\(603\) 0 0
\(604\) 1.47906 2.56180i 0.0601819 0.104238i
\(605\) 30.7977 25.8424i 1.25211 1.05064i
\(606\) 0 0
\(607\) −5.75196 + 32.6210i −0.233465 + 1.32405i 0.612357 + 0.790581i \(0.290221\pi\)
−0.845822 + 0.533465i \(0.820890\pi\)
\(608\) −1.20099 + 6.81115i −0.0487065 + 0.276229i
\(609\) 0 0
\(610\) 18.8478 15.8152i 0.763124 0.640337i
\(611\) −6.02822 + 10.4412i −0.243876 + 0.422405i
\(612\) 0 0
\(613\) −8.84002 15.3114i −0.357045 0.618420i 0.630421 0.776254i \(-0.282882\pi\)
−0.987466 + 0.157833i \(0.949549\pi\)
\(614\) −26.3410 9.58732i −1.06303 0.386913i
\(615\) 0 0
\(616\) −32.3189 27.1188i −1.30217 1.09265i
\(617\) 24.1805 8.80099i 0.973471 0.354314i 0.194172 0.980967i \(-0.437798\pi\)
0.779298 + 0.626653i \(0.215576\pi\)
\(618\) 0 0
\(619\) 4.82651 + 27.3725i 0.193994 + 1.10019i 0.913844 + 0.406065i \(0.133099\pi\)
−0.719850 + 0.694129i \(0.755790\pi\)
\(620\) 0.179740 0.00721854
\(621\) 0 0
\(622\) −14.3696 −0.576168
\(623\) 3.41307 + 19.3565i 0.136742 + 0.775500i
\(624\) 0 0
\(625\) 7.99747 2.91084i 0.319899 0.116434i
\(626\) 3.93763 + 3.30407i 0.157379 + 0.132057i
\(627\) 0 0
\(628\) −3.81567 1.38879i −0.152262 0.0554188i
\(629\) −0.0628336 0.108831i −0.00250534 0.00433938i
\(630\) 0 0
\(631\) −13.4069 + 23.2214i −0.533720 + 0.924430i 0.465504 + 0.885046i \(0.345873\pi\)
−0.999224 + 0.0393842i \(0.987460\pi\)
\(632\) 8.52591 7.15409i 0.339143 0.284574i
\(633\) 0 0
\(634\) 6.17390 35.0139i 0.245197 1.39058i
\(635\) 1.03209 5.85327i 0.0409572 0.232280i
\(636\) 0 0
\(637\) 2.92855 2.45734i 0.116033 0.0973635i
\(638\) 5.16843 8.95199i 0.204620 0.354413i
\(639\) 0 0
\(640\) −7.84864 13.5942i −0.310245 0.537360i
\(641\) −11.9251 4.34040i −0.471015 0.171435i 0.0955971 0.995420i \(-0.469524\pi\)
−0.566612 + 0.823985i \(0.691746\pi\)
\(642\) 0 0
\(643\) 11.8558 + 9.94816i 0.467545 + 0.392317i 0.845898 0.533344i \(-0.179065\pi\)
−0.378353 + 0.925661i \(0.623509\pi\)
\(644\) −1.23261 + 0.448634i −0.0485717 + 0.0176787i
\(645\) 0 0
\(646\) −4.65910 26.4231i −0.183310 1.03960i
\(647\) 11.1506 0.438377 0.219189 0.975683i \(-0.429659\pi\)
0.219189 + 0.975683i \(0.429659\pi\)
\(648\) 0 0
\(649\) −43.6691 −1.71416
\(650\) 1.71254 + 9.71232i 0.0671715 + 0.380949i
\(651\) 0 0
\(652\) 3.56165 1.29634i 0.139485 0.0507684i
\(653\) 34.1596 + 28.6633i 1.33677 + 1.12168i 0.982444 + 0.186558i \(0.0597332\pi\)
0.354323 + 0.935123i \(0.384711\pi\)
\(654\) 0 0
\(655\) 27.5002 + 10.0092i 1.07452 + 0.391093i
\(656\) −8.81386 15.2661i −0.344124 0.596039i
\(657\) 0 0
\(658\) 6.06986 10.5133i 0.236628 0.409851i
\(659\) −10.7986 + 9.06110i −0.420654 + 0.352970i −0.828412 0.560120i \(-0.810755\pi\)
0.407758 + 0.913090i \(0.366311\pi\)
\(660\) 0 0
\(661\) 6.27126 35.5661i 0.243924 1.38336i −0.579055 0.815288i \(-0.696578\pi\)
0.822979 0.568072i \(-0.192310\pi\)
\(662\) −0.367688 + 2.08526i −0.0142906 + 0.0810460i
\(663\) 0 0
\(664\) −8.98680 + 7.54082i −0.348755 + 0.292640i
\(665\) 13.2280 22.9116i 0.512961 0.888474i
\(666\) 0 0
\(667\) −1.89986 3.29066i −0.0735630 0.127415i
\(668\) 0.745100 + 0.271194i 0.0288288 + 0.0104928i
\(669\) 0 0
\(670\) 3.16772 + 2.65803i 0.122380 + 0.102689i
\(671\) −61.7135 + 22.4619i −2.38242 + 0.867132i
\(672\) 0 0
\(673\) 0.389348 + 2.20810i 0.0150082 + 0.0851160i 0.991392 0.130928i \(-0.0417957\pi\)
−0.976384 + 0.216044i \(0.930685\pi\)
\(674\) −10.7992 −0.415971
\(675\) 0 0
\(676\) 0.478340 0.0183977
\(677\) 6.10829 + 34.6418i 0.234761 + 1.33139i 0.843117 + 0.537730i \(0.180718\pi\)
−0.608357 + 0.793664i \(0.708171\pi\)
\(678\) 0 0
\(679\) −0.591052 + 0.215125i −0.0226825 + 0.00825575i
\(680\) −11.1800 9.38117i −0.428735 0.359752i
\(681\) 0 0
\(682\) 4.42855 + 1.61186i 0.169578 + 0.0617213i
\(683\) 8.88191 + 15.3839i 0.339857 + 0.588649i 0.984406 0.175914i \(-0.0562880\pi\)
−0.644549 + 0.764563i \(0.722955\pi\)
\(684\) 0 0
\(685\) 3.24675 5.62353i 0.124052 0.214864i
\(686\) −20.3708 + 17.0931i −0.777760 + 0.652618i
\(687\) 0 0
\(688\) 3.23783 18.3626i 0.123441 0.700068i
\(689\) −6.52094 + 36.9821i −0.248428 + 1.40891i
\(690\) 0 0
\(691\) −33.7294 + 28.3023i −1.28313 + 1.07667i −0.290323 + 0.956929i \(0.593763\pi\)
−0.992805 + 0.119743i \(0.961793\pi\)
\(692\) 0.350452 0.607000i 0.0133222 0.0230747i
\(693\) 0 0
\(694\) −13.3687 23.1553i −0.507469 0.878962i
\(695\) −18.5834 6.76379i −0.704907 0.256565i
\(696\) 0 0
\(697\) −11.2647 9.45221i −0.426681 0.358028i
\(698\) −14.0446 + 5.11181i −0.531595 + 0.193485i
\(699\) 0 0
\(700\) 0.175545 + 0.995568i 0.00663499 + 0.0376289i
\(701\) −30.1052 −1.13706 −0.568530 0.822663i \(-0.692488\pi\)
−0.568530 + 0.822663i \(0.692488\pi\)
\(702\) 0 0
\(703\) −0.278066 −0.0104875
\(704\) 8.87211 + 50.3162i 0.334380 + 1.89636i
\(705\) 0 0
\(706\) 3.62583 1.31969i 0.136460 0.0496673i
\(707\) 20.3708 + 17.0931i 0.766122 + 0.642852i
\(708\) 0 0
\(709\) 23.2456 + 8.46069i 0.873006 + 0.317748i 0.739384 0.673284i \(-0.235117\pi\)
0.133622 + 0.991032i \(0.457339\pi\)
\(710\) 6.13728 + 10.6301i 0.230328 + 0.398940i
\(711\) 0 0
\(712\) 11.9960 20.7776i 0.449568 0.778674i
\(713\) 1.32707 1.11354i 0.0496991 0.0417025i
\(714\) 0 0
\(715\) −5.50387 + 31.2140i −0.205833 + 1.16734i
\(716\) −0.265578 + 1.50617i −0.00992510 + 0.0562880i
\(717\) 0 0
\(718\) 29.7126 24.9318i 1.10886 0.930448i
\(719\) 21.7763 37.7177i 0.812119 1.40663i −0.0992586 0.995062i \(-0.531647\pi\)
0.911378 0.411570i \(-0.135020\pi\)
\(720\) 0 0
\(721\) 4.71048 + 8.15880i 0.175428 + 0.303850i
\(722\) −31.7335 11.5501i −1.18100 0.429849i
\(723\) 0 0
\(724\) −0.951552 0.798447i −0.0353642 0.0296741i
\(725\) −2.75180 + 1.00157i −0.102199 + 0.0371975i
\(726\) 0 0
\(727\) 3.56624 + 20.2251i 0.132264 + 0.750109i 0.976726 + 0.214492i \(0.0688096\pi\)
−0.844461 + 0.535617i \(0.820079\pi\)
\(728\) 22.9040 0.848880
\(729\) 0 0
\(730\) 12.3678 0.457754
\(731\) −2.70099 15.3181i −0.0998997 0.566559i
\(732\) 0 0
\(733\) −13.1613 + 4.79033i −0.486125 + 0.176935i −0.573443 0.819246i \(-0.694393\pi\)
0.0873183 + 0.996180i \(0.472170\pi\)
\(734\) −11.3450 9.51958i −0.418751 0.351374i
\(735\) 0 0
\(736\) 2.88191 + 1.04893i 0.106229 + 0.0386641i
\(737\) −5.51889 9.55899i −0.203291 0.352110i
\(738\) 0 0
\(739\) 20.9907 36.3569i 0.772154 1.33741i −0.164226 0.986423i \(-0.552513\pi\)
0.936380 0.350987i \(-0.114154\pi\)
\(740\) −0.00980018 + 0.00822333i −0.000360262 + 0.000302296i
\(741\) 0 0
\(742\) 6.56599 37.2376i 0.241045 1.36703i
\(743\) 4.83821 27.4389i 0.177497 1.00663i −0.757726 0.652573i \(-0.773689\pi\)
0.935222 0.354061i \(-0.115199\pi\)
\(744\) 0 0
\(745\) 25.9859 21.8048i 0.952050 0.798865i
\(746\) −22.5064 + 38.9822i −0.824018 + 1.42724i
\(747\) 0 0
\(748\) 1.64749 + 2.85353i 0.0602382 + 0.104336i
\(749\) 5.97818 + 2.17588i 0.218438 + 0.0795049i
\(750\) 0 0
\(751\) −40.5276 34.0067i −1.47887 1.24092i −0.907379 0.420314i \(-0.861920\pi\)
−0.571493 0.820607i \(-0.693635\pi\)
\(752\) −12.6270 + 4.59586i −0.460460 + 0.167594i
\(753\) 0 0
\(754\) 0.974470 + 5.52649i 0.0354881 + 0.201263i
\(755\) 26.4561 0.962834
\(756\) 0 0
\(757\) −41.4858 −1.50783 −0.753913 0.656975i \(-0.771836\pi\)
−0.753913 + 0.656975i \(0.771836\pi\)
\(758\) 4.89890 + 27.7830i 0.177936 + 1.00913i
\(759\) 0 0
\(760\) −30.3460 + 11.0450i −1.10077 + 0.400646i
\(761\) −34.7688 29.1745i −1.26037 1.05757i −0.995643 0.0932500i \(-0.970274\pi\)
−0.264725 0.964324i \(-0.585281\pi\)
\(762\) 0 0
\(763\) 20.2995 + 7.38841i 0.734890 + 0.267478i
\(764\) −0.463326 0.802503i −0.0167625 0.0290336i
\(765\) 0 0
\(766\) 2.76945 4.79682i 0.100064 0.173316i
\(767\) 18.1609 15.2388i 0.655752 0.550242i
\(768\) 0 0
\(769\) 0.888470 5.03876i 0.0320391 0.181703i −0.964589 0.263759i \(-0.915038\pi\)
0.996628 + 0.0820564i \(0.0261488\pi\)
\(770\) 5.54189 31.4296i 0.199716 1.13264i
\(771\) 0 0
\(772\) 2.52893 2.12203i 0.0910183 0.0763734i
\(773\) 26.3214 45.5899i 0.946713 1.63976i 0.194430 0.980916i \(-0.437714\pi\)
0.752284 0.658839i \(-0.228952\pi\)
\(774\) 0 0
\(775\) −0.667556 1.15624i −0.0239793 0.0415334i
\(776\) 0.721467 + 0.262593i 0.0258992 + 0.00942652i
\(777\) 0 0
\(778\) 17.6427 + 14.8040i 0.632523 + 0.530750i
\(779\) −30.5758 + 11.1287i −1.09549 + 0.398726i
\(780\) 0 0
\(781\) −5.68938 32.2661i −0.203582 1.15457i
\(782\) −11.8976 −0.425456
\(783\) 0 0
\(784\) 4.26083 0.152172
\(785\) −6.30618 35.7641i −0.225077 1.27648i
\(786\) 0 0
\(787\) 19.5103 7.10116i 0.695466 0.253129i 0.0299921 0.999550i \(-0.490452\pi\)
0.665474 + 0.746421i \(0.268230\pi\)
\(788\) −0.102445 0.0859614i −0.00364945 0.00306225i
\(789\) 0 0
\(790\) 7.91147 + 2.87954i 0.281478 + 0.102449i
\(791\) −19.2062 33.2661i −0.682894 1.18281i
\(792\) 0 0
\(793\) 17.8268 30.8770i 0.633049 1.09647i
\(794\) 23.1208 19.4007i 0.820528 0.688504i
\(795\) 0 0
\(796\) 0.327067 1.85489i 0.0115926 0.0657448i
\(797\) −7.91488 + 44.8875i −0.280359 + 1.59000i 0.441046 + 0.897484i \(0.354607\pi\)
−0.721406 + 0.692513i \(0.756504\pi\)
\(798\) 0 0
\(799\) −8.58693 + 7.20529i −0.303784 + 0.254905i
\(800\) 1.18180 2.04694i 0.0417829 0.0723701i
\(801\) 0 0
\(802\) 9.82295 + 17.0138i 0.346860 + 0.600780i
\(803\) −31.0219 11.2910i −1.09474 0.398452i
\(804\) 0 0
\(805\) −8.98680 7.54082i −0.316743 0.265779i
\(806\) −2.40420 + 0.875057i −0.0846843 + 0.0308226i
\(807\) 0 0
\(808\) −5.63656 31.9665i −0.198294 1.12458i
\(809\) −4.21120 −0.148058 −0.0740290 0.997256i \(-0.523586\pi\)
−0.0740290 + 0.997256i \(0.523586\pi\)
\(810\) 0 0
\(811\) 11.3618 0.398968 0.199484 0.979901i \(-0.436073\pi\)
0.199484 + 0.979901i \(0.436073\pi\)
\(812\) 0.0998887 + 0.566497i 0.00350540 + 0.0198801i
\(813\) 0 0
\(814\) −0.315207 + 0.114726i −0.0110480 + 0.00402115i
\(815\) 25.9675 + 21.7893i 0.909602 + 0.763247i
\(816\) 0 0
\(817\) −32.3418 11.7715i −1.13150 0.411831i
\(818\) 11.7909 + 20.4224i 0.412258 + 0.714051i
\(819\) 0 0
\(820\) −0.748503 + 1.29645i −0.0261389 + 0.0452739i
\(821\) 1.25806 1.05563i 0.0439064 0.0368419i −0.620570 0.784151i \(-0.713099\pi\)
0.664477 + 0.747309i \(0.268654\pi\)
\(822\) 0 0
\(823\) 1.94815 11.0485i 0.0679082 0.385126i −0.931844 0.362859i \(-0.881800\pi\)
0.999752 0.0222670i \(-0.00708839\pi\)
\(824\) 1.99690 11.3250i 0.0695653 0.394525i
\(825\) 0 0
\(826\) −18.2864 + 15.3441i −0.636264 + 0.533889i
\(827\) 4.80659 8.32526i 0.167141 0.289498i −0.770272 0.637715i \(-0.779880\pi\)
0.937414 + 0.348218i \(0.113213\pi\)
\(828\) 0 0
\(829\) −16.7469 29.0065i −0.581644 1.00744i −0.995285 0.0969971i \(-0.969076\pi\)
0.413640 0.910440i \(-0.364257\pi\)
\(830\) −8.33915 3.03520i −0.289456 0.105353i
\(831\) 0 0
\(832\) −21.2481 17.8293i −0.736645 0.618119i
\(833\) 3.34002 1.21567i 0.115725 0.0421204i
\(834\) 0 0
\(835\) 1.23143 + 6.98378i 0.0426154 + 0.241684i
\(836\) 7.29086 0.252160
\(837\) 0 0
\(838\) 25.4129 0.877874
\(839\) −5.55572 31.5081i −0.191805 1.08778i −0.916896 0.399126i \(-0.869314\pi\)
0.725091 0.688653i \(-0.241798\pi\)
\(840\) 0 0
\(841\) 25.6853 9.34867i 0.885699 0.322368i
\(842\) −33.3712 28.0018i −1.15005 0.965005i
\(843\) 0 0
\(844\) −2.58125 0.939499i −0.0888504 0.0323389i
\(845\) 2.13903 + 3.70491i 0.0735850 + 0.127453i
\(846\) 0 0
\(847\) −29.3307 + 50.8022i −1.00781 + 1.74559i
\(848\) −32.0620 + 26.9032i −1.10101 + 0.923859i
\(849\) 0 0
\(850\) −1.59223 + 9.03001i −0.0546132 + 0.309727i
\(851\) −0.0214114 + 0.121430i −0.000733972 + 0.00416256i
\(852\) 0 0
\(853\) 26.9971 22.6532i 0.924362 0.775632i −0.0504347 0.998727i \(-0.516061\pi\)
0.974797 + 0.223096i \(0.0716162\pi\)
\(854\) −17.9500 + 31.0902i −0.614235 + 1.06389i
\(855\) 0 0
\(856\) −3.88279 6.72519i −0.132711 0.229862i
\(857\) 19.9675 + 7.26758i 0.682077 + 0.248256i 0.659739 0.751495i \(-0.270667\pi\)
0.0223378 + 0.999750i \(0.492889\pi\)
\(858\) 0 0
\(859\) 39.7105 + 33.3211i 1.35491 + 1.13690i 0.977519 + 0.210846i \(0.0676217\pi\)
0.377387 + 0.926056i \(0.376823\pi\)
\(860\) −1.48798 + 0.541580i −0.0507396 + 0.0184677i
\(861\) 0 0
\(862\) 8.02852 + 45.5320i 0.273453 + 1.55083i
\(863\) −22.6783 −0.771978 −0.385989 0.922503i \(-0.626140\pi\)
−0.385989 + 0.922503i \(0.626140\pi\)
\(864\) 0 0
\(865\) 6.26857 0.213138
\(866\) −5.86453 33.2594i −0.199285 1.13020i
\(867\) 0 0
\(868\) −0.246444 + 0.0896983i −0.00836486 + 0.00304456i
\(869\) −17.2153 14.4453i −0.583989 0.490025i
\(870\) 0 0
\(871\) 5.63088 + 2.04947i 0.190795 + 0.0694438i
\(872\) −13.1844 22.8360i −0.446480 0.773325i
\(873\) 0 0
\(874\) −13.1630 + 22.7989i −0.445244 + 0.771185i
\(875\) −22.1912 + 18.6206i −0.750199 + 0.629492i
\(876\) 0 0
\(877\) 0.196814 1.11619i 0.00664594 0.0376910i −0.981304 0.192462i \(-0.938353\pi\)
0.987950 + 0.154771i \(0.0494639\pi\)
\(878\) −5.42964 + 30.7930i −0.183242 + 1.03921i
\(879\) 0 0
\(880\) −27.0612 + 22.7071i −0.912234 + 0.765455i
\(881\) 15.4145 26.6986i 0.519327 0.899500i −0.480421 0.877038i \(-0.659516\pi\)
0.999748 0.0224621i \(-0.00715051\pi\)
\(882\) 0 0
\(883\) 4.66756 + 8.08444i 0.157076 + 0.272063i 0.933813 0.357762i \(-0.116460\pi\)
−0.776737 + 0.629825i \(0.783127\pi\)
\(884\) −1.68092 0.611806i −0.0565355 0.0205772i
\(885\) 0 0
\(886\) −4.25380 3.56937i −0.142909 0.119915i
\(887\) 13.2442 4.82050i 0.444697 0.161857i −0.109959 0.993936i \(-0.535072\pi\)
0.554656 + 0.832079i \(0.312850\pi\)
\(888\) 0 0
\(889\) 1.50593 + 8.54055i 0.0505073 + 0.286441i
\(890\) 18.1489 0.608352
\(891\) 0 0
\(892\) 2.02322 0.0677425
\(893\) 4.30706 + 24.4265i 0.144130 + 0.817403i
\(894\) 0 0
\(895\) −12.8534 + 4.67825i −0.429641 + 0.156377i
\(896\) 17.5455 + 14.7224i 0.586154 + 0.491842i
\(897\) 0 0
\(898\) −23.2211 8.45177i −0.774897 0.282039i
\(899\) −0.379852 0.657923i −0.0126688 0.0219430i
\(900\) 0 0
\(901\) −17.4572 + 30.2368i −0.581585 + 1.00733i
\(902\) −30.0683 + 25.2303i −1.00116 + 0.840076i
\(903\) 0 0
\(904\) −8.14203 + 46.1757i −0.270800 + 1.53578i
\(905\) 1.92912 10.9406i 0.0641261 0.363677i
\(906\) 0 0
\(907\) −6.69459 + 5.61743i −0.222290 + 0.186524i −0.747131 0.664677i \(-0.768569\pi\)
0.524841 + 0.851200i \(0.324125\pi\)
\(908\) −1.60148 + 2.77385i −0.0531470 + 0.0920533i
\(909\) 0 0
\(910\) 8.66297 + 15.0047i 0.287175 + 0.497401i
\(911\) 19.4055 + 7.06304i 0.642934 + 0.234009i 0.642851 0.765991i \(-0.277751\pi\)
8.31009e−5 1.00000i \(0.499974\pi\)
\(912\) 0 0
\(913\) 18.1459 + 15.2262i 0.600542 + 0.503914i
\(914\) 24.6386 8.96773i 0.814973 0.296626i
\(915\) 0 0
\(916\) −0.0501266 0.284282i −0.00165623 0.00939295i
\(917\) −42.7009 −1.41011
\(918\) 0 0
\(919\) −2.36009 −0.0778522 −0.0389261 0.999242i \(-0.512394\pi\)
−0.0389261 + 0.999242i \(0.512394\pi\)
\(920\) 2.48663 + 14.1024i 0.0819819 + 0.464942i
\(921\) 0 0
\(922\) −35.1318 + 12.7869i −1.15700 + 0.421115i
\(923\) 13.6257 + 11.4333i 0.448494 + 0.376331i
\(924\) 0 0
\(925\) 0.0892974 + 0.0325016i 0.00293608 + 0.00106865i
\(926\) −26.0608 45.1386i −0.856410 1.48335i
\(927\) 0 0
\(928\) 0.672466 1.16475i 0.0220748 0.0382346i
\(929\) −20.5455 + 17.2397i −0.674076 + 0.565617i −0.914269 0.405108i \(-0.867234\pi\)
0.240192 + 0.970725i \(0.422789\pi\)
\(930\) 0 0
\(931\) 1.36571 7.74535i 0.0447595 0.253844i
\(932\) −0.538734 + 3.05531i −0.0176468 + 0.100080i
\(933\) 0 0
\(934\) 30.7189 25.7762i 1.00515 0.843424i
\(935\) −14.7344 + 25.5208i −0.481867 + 0.834618i
\(936\) 0 0
\(937\) −0.966567 1.67414i −0.0315764 0.0546919i 0.849805 0.527097i \(-0.176719\pi\)
−0.881382 + 0.472405i \(0.843386\pi\)
\(938\) −5.66978 2.06363i −0.185125 0.0673799i
\(939\) 0 0
\(940\) 0.874171 + 0.733516i 0.0285123 + 0.0239247i
\(941\) −11.1921 + 4.07358i −0.364851 + 0.132795i −0.517939 0.855418i \(-0.673300\pi\)
0.153088 + 0.988213i \(0.451078\pi\)
\(942\) 0 0
\(943\) 2.50546 + 14.2092i 0.0815891 + 0.462715i
\(944\) 26.4228 0.859990
\(945\) 0 0
\(946\) −41.5185 −1.34988
\(947\) −0.0548444 0.311038i −0.00178220 0.0101074i 0.983904 0.178700i \(-0.0571890\pi\)
−0.985686 + 0.168592i \(0.946078\pi\)
\(948\) 0 0
\(949\) 16.8414 6.12976i 0.546694 0.198980i
\(950\) 15.5424 + 13.0416i 0.504261 + 0.423125i
\(951\) 0 0
\(952\) 20.0107 + 7.28331i 0.648552 + 0.236053i
\(953\) −1.62567 2.81574i −0.0526605 0.0912107i 0.838494 0.544912i \(-0.183437\pi\)
−0.891154 + 0.453701i \(0.850103\pi\)
\(954\) 0 0
\(955\) 4.14378 7.17724i 0.134090 0.232250i
\(956\) 0.570356 0.478585i 0.0184466 0.0154786i
\(957\) 0 0
\(958\) −8.81449 + 49.9895i −0.284783 + 1.61509i
\(959\) −1.64527 + 9.33078i −0.0531285 + 0.301306i
\(960\) 0 0
\(961\) −23.4820 + 19.7038i −0.757485 + 0.635606i
\(962\) 0.0910521 0.157707i 0.00293564 0.00508467i
\(963\) 0 0
\(964\) −0.309745 0.536493i −0.00997620 0.0172793i
\(965\) 27.7447 + 10.0982i 0.893133 + 0.325074i
\(966\) 0 0
\(967\) 8.40167 + 7.04984i 0.270180 + 0.226708i 0.767804 0.640685i \(-0.221350\pi\)
−0.497624 + 0.867393i \(0.665794\pi\)
\(968\) 67.2866 24.4903i 2.16267 0.787149i
\(969\) 0 0
\(970\) 0.100852 + 0.571962i 0.00323817 + 0.0183646i
\(971\) 23.3868 0.750519 0.375259 0.926920i \(-0.377554\pi\)
0.375259 + 0.926920i \(0.377554\pi\)
\(972\) 0 0
\(973\) 28.8553 0.925060
\(974\) −0.178701 1.01346i −0.00572594 0.0324734i
\(975\) 0 0
\(976\) 37.3410 13.5910i 1.19525 0.435037i
\(977\) −38.4372 32.2527i −1.22972 1.03185i −0.998257 0.0590092i \(-0.981206\pi\)
−0.231458 0.972845i \(-0.574350\pi\)
\(978\) 0 0
\(979\) −45.5223 16.5688i −1.45490 0.529540i
\(980\) −0.180922 0.313366i −0.00577935 0.0100101i
\(981\) 0 0
\(982\) 0.335437 0.580994i 0.0107042 0.0185402i
\(983\) −11.2567 + 9.44550i −0.359033 + 0.301265i −0.804405 0.594081i \(-0.797516\pi\)
0.445372 + 0.895346i \(0.353071\pi\)
\(984\) 0 0
\(985\) 0.207691 1.17787i 0.00661757 0.0375301i
\(986\) −0.906011 + 5.13824i −0.0288533 + 0.163635i
\(987\) 0 0
\(988\) −3.03209 + 2.54422i −0.0964636 + 0.0809426i
\(989\) −7.63088 + 13.2171i −0.242648 + 0.420279i
\(990\) 0 0
\(991\) −1.00000 1.73205i −0.0317660 0.0550204i 0.849705 0.527258i \(-0.176780\pi\)
−0.881471 + 0.472237i \(0.843446\pi\)
\(992\) 0.576199 + 0.209719i 0.0182944 + 0.00665860i
\(993\) 0 0
\(994\) −13.7198 11.5123i −0.435165 0.365147i
\(995\) 15.8293 5.76141i 0.501824 0.182649i
\(996\) 0 0
\(997\) −7.96807 45.1892i −0.252351 1.43116i −0.802781 0.596274i \(-0.796647\pi\)
0.550429 0.834882i \(-0.314464\pi\)
\(998\) 12.0797 0.382375
\(999\) 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.i.82.1 6
3.2 odd 2 729.2.e.a.82.1 6
9.2 odd 6 729.2.e.h.325.1 6
9.4 even 3 729.2.e.b.568.1 6
9.5 odd 6 729.2.e.g.568.1 6
9.7 even 3 729.2.e.c.325.1 6
27.2 odd 18 729.2.e.a.649.1 6
27.4 even 9 243.2.c.e.163.2 6
27.5 odd 18 243.2.a.e.1.2 3
27.7 even 9 729.2.e.c.406.1 6
27.11 odd 18 729.2.e.g.163.1 6
27.13 even 9 243.2.c.e.82.2 6
27.14 odd 18 243.2.c.f.82.2 6
27.16 even 9 729.2.e.b.163.1 6
27.20 odd 18 729.2.e.h.406.1 6
27.22 even 9 243.2.a.f.1.2 yes 3
27.23 odd 18 243.2.c.f.163.2 6
27.25 even 9 inner 729.2.e.i.649.1 6
108.59 even 18 3888.2.a.bd.1.2 3
108.103 odd 18 3888.2.a.bk.1.2 3
135.49 even 18 6075.2.a.bq.1.2 3
135.59 odd 18 6075.2.a.bv.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.e.1.2 3 27.5 odd 18
243.2.a.f.1.2 yes 3 27.22 even 9
243.2.c.e.82.2 6 27.13 even 9
243.2.c.e.163.2 6 27.4 even 9
243.2.c.f.82.2 6 27.14 odd 18
243.2.c.f.163.2 6 27.23 odd 18
729.2.e.a.82.1 6 3.2 odd 2
729.2.e.a.649.1 6 27.2 odd 18
729.2.e.b.163.1 6 27.16 even 9
729.2.e.b.568.1 6 9.4 even 3
729.2.e.c.325.1 6 9.7 even 3
729.2.e.c.406.1 6 27.7 even 9
729.2.e.g.163.1 6 27.11 odd 18
729.2.e.g.568.1 6 9.5 odd 6
729.2.e.h.325.1 6 9.2 odd 6
729.2.e.h.406.1 6 27.20 odd 18
729.2.e.i.82.1 6 1.1 even 1 trivial
729.2.e.i.649.1 6 27.25 even 9 inner
3888.2.a.bd.1.2 3 108.59 even 18
3888.2.a.bk.1.2 3 108.103 odd 18
6075.2.a.bq.1.2 3 135.49 even 18
6075.2.a.bv.1.2 3 135.59 odd 18