Properties

Label 729.2.e.c.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.c.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.152704 - 0.866025i) q^{2} +(1.15270 - 0.419550i) q^{4} +(2.97178 + 2.49362i) q^{5} +(2.05303 + 0.747243i) q^{7} +(-1.41875 - 2.45734i) q^{8} +O(q^{10})\) \(q+(-0.152704 - 0.866025i) q^{2} +(1.15270 - 0.419550i) q^{4} +(2.97178 + 2.49362i) q^{5} +(2.05303 + 0.747243i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(1.70574 - 2.95442i) q^{10} +(0.124485 - 0.104455i) q^{11} +(0.418748 - 2.37484i) q^{13} +(0.333626 - 1.89209i) q^{14} +(-0.0320889 + 0.0269258i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.79813 - 3.11446i) q^{19} +(4.47178 + 1.62760i) q^{20} +(-0.109470 - 0.0918566i) q^{22} +(-2.66637 + 0.970481i) q^{23} +(1.74510 + 9.89695i) q^{25} -2.12061 q^{26} +2.68004 q^{28} +(1.16637 + 6.61484i) q^{29} +(4.87211 - 1.77330i) q^{31} +(-4.31908 - 3.62414i) q^{32} +(2.47906 + 0.902302i) q^{34} +(4.23783 + 7.34013i) q^{35} +(3.31908 - 5.74881i) q^{37} +(-2.42262 + 2.03282i) q^{38} +(1.91147 - 10.8405i) q^{40} +(-1.00727 + 5.71253i) q^{41} +(-4.76991 + 4.00243i) q^{43} +(0.0996702 - 0.172634i) q^{44} +(1.24763 + 2.16095i) q^{46} +(-6.95084 - 2.52990i) q^{47} +(-1.70574 - 1.43128i) q^{49} +(8.30453 - 3.02260i) q^{50} +(-0.513671 - 2.91317i) q^{52} +1.40373 q^{53} +0.630415 q^{55} +(-1.07650 - 6.10516i) q^{56} +(5.55051 - 2.02022i) q^{58} +(-3.92262 - 3.29147i) q^{59} +(3.55303 + 1.29320i) q^{61} +(-2.27972 - 3.94858i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(7.16637 - 6.01330i) q^{65} +(-1.01842 + 5.77574i) q^{67} +(-0.639033 + 3.62414i) q^{68} +(5.70961 - 4.79093i) q^{70} +(7.65910 - 13.2660i) q^{71} +(-4.34002 - 7.51714i) q^{73} +(-5.48545 - 1.99654i) q^{74} +(-3.37939 - 2.83564i) q^{76} +(0.333626 - 0.121430i) q^{77} +(-0.220285 - 1.24930i) q^{79} -0.162504 q^{80} +5.10101 q^{82} +(-1.47178 - 8.34689i) q^{83} +(-10.9363 + 3.98048i) q^{85} +(4.19459 + 3.51968i) q^{86} +(-0.433296 - 0.157707i) q^{88} +(-3.86097 - 6.68739i) q^{89} +(2.63429 - 4.56272i) q^{91} +(-2.66637 + 2.23735i) q^{92} +(-1.12954 + 6.40593i) q^{94} +(2.42262 - 13.7394i) q^{95} +(-2.99273 + 2.51120i) q^{97} +(-0.979055 + 1.69577i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} - 6 q^{8} - 12 q^{11} + 21 q^{14} + 9 q^{16} - 9 q^{17} + 3 q^{19} + 12 q^{20} - 18 q^{22} + 3 q^{23} + 9 q^{25} - 24 q^{26} - 24 q^{28} - 12 q^{29} - 9 q^{32} + 18 q^{34} + 6 q^{35} + 3 q^{37} + 12 q^{38} - 9 q^{40} - 24 q^{41} + 15 q^{44} - 9 q^{46} - 30 q^{47} - 3 q^{50} + 18 q^{52} + 36 q^{53} + 18 q^{55} + 24 q^{56} + 36 q^{58} + 3 q^{59} + 9 q^{61} + 12 q^{62} - 12 q^{64} + 24 q^{65} - 18 q^{67} - 27 q^{68} + 9 q^{71} - 6 q^{73} + 3 q^{74} - 9 q^{76} + 21 q^{77} - 27 q^{79} - 6 q^{80} + 36 q^{82} + 6 q^{83} - 18 q^{85} + 21 q^{86} - 36 q^{88} + 6 q^{91} + 3 q^{92} + 36 q^{94} - 12 q^{95} - 9 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.152704 0.866025i −0.107978 0.612372i −0.989989 0.141144i \(-0.954922\pi\)
0.882011 0.471228i \(-0.156189\pi\)
\(3\) 0 0
\(4\) 1.15270 0.419550i 0.576352 0.209775i
\(5\) 2.97178 + 2.49362i 1.32902 + 1.11518i 0.984305 + 0.176474i \(0.0564692\pi\)
0.344716 + 0.938707i \(0.387975\pi\)
\(6\) 0 0
\(7\) 2.05303 + 0.747243i 0.775974 + 0.282431i 0.699493 0.714640i \(-0.253409\pi\)
0.0764810 + 0.997071i \(0.475632\pi\)
\(8\) −1.41875 2.45734i −0.501603 0.868802i
\(9\) 0 0
\(10\) 1.70574 2.95442i 0.539401 0.934271i
\(11\) 0.124485 0.104455i 0.0375337 0.0314945i −0.623828 0.781562i \(-0.714423\pi\)
0.661362 + 0.750067i \(0.269979\pi\)
\(12\) 0 0
\(13\) 0.418748 2.37484i 0.116140 0.658662i −0.870040 0.492982i \(-0.835907\pi\)
0.986180 0.165680i \(-0.0529819\pi\)
\(14\) 0.333626 1.89209i 0.0891652 0.505681i
\(15\) 0 0
\(16\) −0.0320889 + 0.0269258i −0.00802222 + 0.00673144i
\(17\) −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
\(19\) −1.79813 3.11446i −0.412520 0.714506i 0.582645 0.812727i \(-0.302018\pi\)
−0.995165 + 0.0982214i \(0.968685\pi\)
\(20\) 4.47178 + 1.62760i 0.999921 + 0.363941i
\(21\) 0 0
\(22\) −0.109470 0.0918566i −0.0233392 0.0195839i
\(23\) −2.66637 + 0.970481i −0.555977 + 0.202359i −0.604700 0.796453i \(-0.706707\pi\)
0.0487229 + 0.998812i \(0.484485\pi\)
\(24\) 0 0
\(25\) 1.74510 + 9.89695i 0.349020 + 1.97939i
\(26\) −2.12061 −0.415887
\(27\) 0 0
\(28\) 2.68004 0.506481
\(29\) 1.16637 + 6.61484i 0.216590 + 1.22834i 0.878126 + 0.478430i \(0.158794\pi\)
−0.661535 + 0.749914i \(0.730095\pi\)
\(30\) 0 0
\(31\) 4.87211 1.77330i 0.875057 0.318495i 0.134844 0.990867i \(-0.456947\pi\)
0.740213 + 0.672372i \(0.234725\pi\)
\(32\) −4.31908 3.62414i −0.763512 0.640663i
\(33\) 0 0
\(34\) 2.47906 + 0.902302i 0.425155 + 0.154744i
\(35\) 4.23783 + 7.34013i 0.716323 + 1.24071i
\(36\) 0 0
\(37\) 3.31908 5.74881i 0.545653 0.945099i −0.452912 0.891555i \(-0.649615\pi\)
0.998566 0.0535438i \(-0.0170517\pi\)
\(38\) −2.42262 + 2.03282i −0.393001 + 0.329767i
\(39\) 0 0
\(40\) 1.91147 10.8405i 0.302231 1.71403i
\(41\) −1.00727 + 5.71253i −0.157310 + 0.892148i 0.799334 + 0.600887i \(0.205186\pi\)
−0.956644 + 0.291261i \(0.905925\pi\)
\(42\) 0 0
\(43\) −4.76991 + 4.00243i −0.727405 + 0.610365i −0.929423 0.369016i \(-0.879695\pi\)
0.202018 + 0.979382i \(0.435250\pi\)
\(44\) 0.0996702 0.172634i 0.0150259 0.0260255i
\(45\) 0 0
\(46\) 1.24763 + 2.16095i 0.183952 + 0.318615i
\(47\) −6.95084 2.52990i −1.01388 0.369024i −0.218961 0.975734i \(-0.570267\pi\)
−0.794923 + 0.606710i \(0.792489\pi\)
\(48\) 0 0
\(49\) −1.70574 1.43128i −0.243677 0.204469i
\(50\) 8.30453 3.02260i 1.17444 0.427460i
\(51\) 0 0
\(52\) −0.513671 2.91317i −0.0712333 0.403984i
\(53\) 1.40373 0.192818 0.0964088 0.995342i \(-0.469264\pi\)
0.0964088 + 0.995342i \(0.469264\pi\)
\(54\) 0 0
\(55\) 0.630415 0.0850051
\(56\) −1.07650 6.10516i −0.143854 0.815836i
\(57\) 0 0
\(58\) 5.55051 2.02022i 0.728817 0.265268i
\(59\) −3.92262 3.29147i −0.510681 0.428513i 0.350687 0.936493i \(-0.385948\pi\)
−0.861369 + 0.507980i \(0.830392\pi\)
\(60\) 0 0
\(61\) 3.55303 + 1.29320i 0.454919 + 0.165577i 0.559309 0.828959i \(-0.311067\pi\)
−0.104389 + 0.994536i \(0.533289\pi\)
\(62\) −2.27972 3.94858i −0.289524 0.501470i
\(63\) 0 0
\(64\) −2.52094 + 4.36640i −0.315118 + 0.545801i
\(65\) 7.16637 6.01330i 0.888879 0.745858i
\(66\) 0 0
\(67\) −1.01842 + 5.77574i −0.124420 + 0.705619i 0.857231 + 0.514932i \(0.172183\pi\)
−0.981651 + 0.190687i \(0.938928\pi\)
\(68\) −0.639033 + 3.62414i −0.0774941 + 0.439491i
\(69\) 0 0
\(70\) 5.70961 4.79093i 0.682429 0.572626i
\(71\) 7.65910 13.2660i 0.908968 1.57438i 0.0934675 0.995622i \(-0.470205\pi\)
0.815500 0.578756i \(-0.196462\pi\)
\(72\) 0 0
\(73\) −4.34002 7.51714i −0.507961 0.879815i −0.999958 0.00921733i \(-0.997066\pi\)
0.491996 0.870597i \(-0.336267\pi\)
\(74\) −5.48545 1.99654i −0.637671 0.232093i
\(75\) 0 0
\(76\) −3.37939 2.83564i −0.387642 0.325270i
\(77\) 0.333626 0.121430i 0.0380202 0.0138382i
\(78\) 0 0
\(79\) −0.220285 1.24930i −0.0247840 0.140557i 0.969905 0.243484i \(-0.0782903\pi\)
−0.994689 + 0.102927i \(0.967179\pi\)
\(80\) −0.162504 −0.0181685
\(81\) 0 0
\(82\) 5.10101 0.563313
\(83\) −1.47178 8.34689i −0.161549 0.916190i −0.952552 0.304377i \(-0.901552\pi\)
0.791003 0.611813i \(-0.209559\pi\)
\(84\) 0 0
\(85\) −10.9363 + 3.98048i −1.18621 + 0.431744i
\(86\) 4.19459 + 3.51968i 0.452315 + 0.379537i
\(87\) 0 0
\(88\) −0.433296 0.157707i −0.0461895 0.0168116i
\(89\) −3.86097 6.68739i −0.409262 0.708862i 0.585546 0.810640i \(-0.300880\pi\)
−0.994807 + 0.101778i \(0.967547\pi\)
\(90\) 0 0
\(91\) 2.63429 4.56272i 0.276148 0.478303i
\(92\) −2.66637 + 2.23735i −0.277989 + 0.233260i
\(93\) 0 0
\(94\) −1.12954 + 6.40593i −0.116503 + 0.660721i
\(95\) 2.42262 13.7394i 0.248555 1.40963i
\(96\) 0 0
\(97\) −2.99273 + 2.51120i −0.303865 + 0.254973i −0.781951 0.623340i \(-0.785775\pi\)
0.478086 + 0.878313i \(0.341331\pi\)
\(98\) −0.979055 + 1.69577i −0.0988995 + 0.171299i
\(99\) 0 0
\(100\) 6.16385 + 10.6761i 0.616385 + 1.06761i
\(101\) 7.62449 + 2.77509i 0.758665 + 0.276131i 0.692247 0.721661i \(-0.256621\pi\)
0.0664176 + 0.997792i \(0.478843\pi\)
\(102\) 0 0
\(103\) 14.2836 + 11.9854i 1.40740 + 1.18095i 0.957698 + 0.287775i \(0.0929155\pi\)
0.449705 + 0.893177i \(0.351529\pi\)
\(104\) −6.42989 + 2.34029i −0.630503 + 0.229484i
\(105\) 0 0
\(106\) −0.214355 1.21567i −0.0208200 0.118076i
\(107\) 7.59627 0.734359 0.367179 0.930150i \(-0.380324\pi\)
0.367179 + 0.930150i \(0.380324\pi\)
\(108\) 0 0
\(109\) −15.6382 −1.49786 −0.748932 0.662647i \(-0.769433\pi\)
−0.748932 + 0.662647i \(0.769433\pi\)
\(110\) −0.0962667 0.545955i −0.00917867 0.0520548i
\(111\) 0 0
\(112\) −0.0859997 + 0.0313013i −0.00812620 + 0.00295770i
\(113\) −1.77197 1.48686i −0.166693 0.139872i 0.555625 0.831433i \(-0.312479\pi\)
−0.722318 + 0.691561i \(0.756923\pi\)
\(114\) 0 0
\(115\) −10.3439 3.76487i −0.964573 0.351076i
\(116\) 4.11974 + 7.13559i 0.382508 + 0.662523i
\(117\) 0 0
\(118\) −2.25150 + 3.89971i −0.207267 + 0.358997i
\(119\) −5.02094 + 4.21307i −0.460269 + 0.386212i
\(120\) 0 0
\(121\) −1.90554 + 10.8069i −0.173231 + 0.982444i
\(122\) 0.577382 3.27449i 0.0522737 0.296459i
\(123\) 0 0
\(124\) 4.87211 4.08819i 0.437529 0.367130i
\(125\) −9.79473 + 16.9650i −0.876067 + 1.51739i
\(126\) 0 0
\(127\) −0.0209445 0.0362770i −0.00185853 0.00321906i 0.865095 0.501609i \(-0.167258\pi\)
−0.866953 + 0.498390i \(0.833925\pi\)
\(128\) −6.42989 2.34029i −0.568328 0.206854i
\(129\) 0 0
\(130\) −6.30200 5.28801i −0.552722 0.463789i
\(131\) −17.2417 + 6.27546i −1.50641 + 0.548290i −0.957712 0.287728i \(-0.907100\pi\)
−0.548702 + 0.836018i \(0.684878\pi\)
\(132\) 0 0
\(133\) −1.36437 7.73773i −0.118306 0.670946i
\(134\) 5.15745 0.445536
\(135\) 0 0
\(136\) 8.51249 0.729940
\(137\) 2.48545 + 14.0957i 0.212347 + 1.20428i 0.885452 + 0.464731i \(0.153849\pi\)
−0.673106 + 0.739546i \(0.735040\pi\)
\(138\) 0 0
\(139\) −9.86231 + 3.58959i −0.836510 + 0.304465i −0.724528 0.689245i \(-0.757942\pi\)
−0.111982 + 0.993710i \(0.535720\pi\)
\(140\) 7.96451 + 6.68302i 0.673124 + 0.564818i
\(141\) 0 0
\(142\) −12.6582 4.60722i −1.06225 0.386629i
\(143\) −0.195937 0.339373i −0.0163851 0.0283798i
\(144\) 0 0
\(145\) −13.0287 + 22.5663i −1.08197 + 1.87403i
\(146\) −5.84730 + 4.90646i −0.483926 + 0.406062i
\(147\) 0 0
\(148\) 1.41400 8.01919i 0.116230 0.659174i
\(149\) −0.220752 + 1.25195i −0.0180847 + 0.102563i −0.992514 0.122131i \(-0.961027\pi\)
0.974429 + 0.224694i \(0.0721383\pi\)
\(150\) 0 0
\(151\) 6.01889 5.05044i 0.489810 0.410999i −0.364148 0.931341i \(-0.618640\pi\)
0.853958 + 0.520342i \(0.174195\pi\)
\(152\) −5.10220 + 8.83726i −0.413843 + 0.716797i
\(153\) 0 0
\(154\) −0.156107 0.270386i −0.0125795 0.0217883i
\(155\) 18.9008 + 6.87933i 1.51815 + 0.552561i
\(156\) 0 0
\(157\) −9.46245 7.93994i −0.755186 0.633676i 0.181683 0.983357i \(-0.441845\pi\)
−0.936869 + 0.349681i \(0.886290\pi\)
\(158\) −1.04829 + 0.381545i −0.0833971 + 0.0303541i
\(159\) 0 0
\(160\) −3.79813 21.5403i −0.300269 1.70291i
\(161\) −6.19934 −0.488576
\(162\) 0 0
\(163\) −13.7469 −1.07674 −0.538371 0.842708i \(-0.680960\pi\)
−0.538371 + 0.842708i \(0.680960\pi\)
\(164\) 1.23560 + 7.00746i 0.0964845 + 0.547191i
\(165\) 0 0
\(166\) −7.00387 + 2.54920i −0.543606 + 0.197856i
\(167\) −2.84730 2.38917i −0.220330 0.184879i 0.525941 0.850521i \(-0.323713\pi\)
−0.746271 + 0.665642i \(0.768158\pi\)
\(168\) 0 0
\(169\) 6.75150 + 2.45734i 0.519346 + 0.189026i
\(170\) 5.11721 + 8.86327i 0.392472 + 0.679782i
\(171\) 0 0
\(172\) −3.81908 + 6.61484i −0.291202 + 0.504377i
\(173\) −1.19459 + 1.00238i −0.0908232 + 0.0762097i −0.687069 0.726592i \(-0.741103\pi\)
0.596246 + 0.802802i \(0.296658\pi\)
\(174\) 0 0
\(175\) −3.81268 + 21.6228i −0.288212 + 1.63453i
\(176\) −0.00118205 + 0.00670372i −8.91001e−5 + 0.000505312i
\(177\) 0 0
\(178\) −5.20187 + 4.36488i −0.389896 + 0.327162i
\(179\) 6.09627 10.5590i 0.455656 0.789220i −0.543069 0.839688i \(-0.682738\pi\)
0.998726 + 0.0504679i \(0.0160713\pi\)
\(180\) 0 0
\(181\) 8.43629 + 14.6121i 0.627064 + 1.08611i 0.988138 + 0.153570i \(0.0490771\pi\)
−0.361073 + 0.932537i \(0.617590\pi\)
\(182\) −4.35369 1.58461i −0.322717 0.117459i
\(183\) 0 0
\(184\) 6.16772 + 5.17533i 0.454690 + 0.381530i
\(185\) 24.1989 8.80769i 1.77914 0.647554i
\(186\) 0 0
\(187\) 0.0846555 + 0.480105i 0.00619062 + 0.0351088i
\(188\) −9.07367 −0.661766
\(189\) 0 0
\(190\) −12.2686 −0.890056
\(191\) −3.03462 17.2102i −0.219577 1.24528i −0.872785 0.488105i \(-0.837688\pi\)
0.653208 0.757179i \(-0.273423\pi\)
\(192\) 0 0
\(193\) 1.87211 0.681393i 0.134758 0.0490477i −0.273761 0.961798i \(-0.588268\pi\)
0.408519 + 0.912750i \(0.366046\pi\)
\(194\) 2.63176 + 2.20831i 0.188949 + 0.158547i
\(195\) 0 0
\(196\) −2.56670 0.934204i −0.183336 0.0667288i
\(197\) −10.5963 18.3533i −0.754953 1.30762i −0.945398 0.325919i \(-0.894326\pi\)
0.190445 0.981698i \(-0.439007\pi\)
\(198\) 0 0
\(199\) 1.54189 2.67063i 0.109302 0.189316i −0.806186 0.591662i \(-0.798472\pi\)
0.915488 + 0.402346i \(0.131805\pi\)
\(200\) 21.8444 18.3296i 1.54463 1.29610i
\(201\) 0 0
\(202\) 1.23901 7.02676i 0.0871763 0.494401i
\(203\) −2.54829 + 14.4520i −0.178855 + 1.01433i
\(204\) 0 0
\(205\) −17.2383 + 14.4646i −1.20397 + 1.01025i
\(206\) 8.19846 14.2002i 0.571214 0.989372i
\(207\) 0 0
\(208\) 0.0505072 + 0.0874810i 0.00350204 + 0.00606572i
\(209\) −0.549163 0.199879i −0.0379864 0.0138259i
\(210\) 0 0
\(211\) 0.771974 + 0.647763i 0.0531449 + 0.0445939i 0.668973 0.743287i \(-0.266734\pi\)
−0.615828 + 0.787880i \(0.711179\pi\)
\(212\) 1.61809 0.588936i 0.111131 0.0404483i
\(213\) 0 0
\(214\) −1.15998 6.57856i −0.0792944 0.449701i
\(215\) −24.1557 −1.64740
\(216\) 0 0
\(217\) 11.3277 0.768974
\(218\) 2.38800 + 13.5430i 0.161736 + 0.917250i
\(219\) 0 0
\(220\) 0.726682 0.264490i 0.0489929 0.0178319i
\(221\) 5.54189 + 4.65020i 0.372788 + 0.312806i
\(222\) 0 0
\(223\) −17.1814 6.25351i −1.15055 0.418766i −0.304838 0.952404i \(-0.598602\pi\)
−0.845713 + 0.533638i \(0.820825\pi\)
\(224\) −6.15910 10.6679i −0.411522 0.712777i
\(225\) 0 0
\(226\) −1.01707 + 1.76162i −0.0676548 + 0.117181i
\(227\) −2.02616 + 1.70015i −0.134481 + 0.112843i −0.707547 0.706666i \(-0.750198\pi\)
0.573066 + 0.819509i \(0.305754\pi\)
\(228\) 0 0
\(229\) −0.601319 + 3.41025i −0.0397363 + 0.225356i −0.998209 0.0598300i \(-0.980944\pi\)
0.958472 + 0.285186i \(0.0920553\pi\)
\(230\) −1.68092 + 9.53298i −0.110837 + 0.628586i
\(231\) 0 0
\(232\) 14.6001 12.2510i 0.958546 0.804316i
\(233\) −3.06283 + 5.30498i −0.200653 + 0.347541i −0.948739 0.316061i \(-0.897640\pi\)
0.748086 + 0.663602i \(0.230973\pi\)
\(234\) 0 0
\(235\) −14.3478 24.8511i −0.935945 1.62110i
\(236\) −5.90255 2.14835i −0.384223 0.139846i
\(237\) 0 0
\(238\) 4.41534 + 3.70491i 0.286204 + 0.240154i
\(239\) 27.2053 9.90193i 1.75977 0.640503i 0.759813 0.650142i \(-0.225291\pi\)
0.999954 + 0.00963943i \(0.00306837\pi\)
\(240\) 0 0
\(241\) 3.87686 + 21.9868i 0.249730 + 1.41629i 0.809245 + 0.587471i \(0.199876\pi\)
−0.559515 + 0.828820i \(0.689012\pi\)
\(242\) 9.65002 0.620326
\(243\) 0 0
\(244\) 4.63816 0.296927
\(245\) −1.50000 8.50692i −0.0958315 0.543487i
\(246\) 0 0
\(247\) −8.14930 + 2.96610i −0.518528 + 0.188729i
\(248\) −11.2699 9.45658i −0.715640 0.600494i
\(249\) 0 0
\(250\) 16.1878 + 5.89187i 1.02381 + 0.372635i
\(251\) 11.3610 + 19.6778i 0.717098 + 1.24205i 0.962145 + 0.272539i \(0.0878633\pi\)
−0.245047 + 0.969511i \(0.578803\pi\)
\(252\) 0 0
\(253\) −0.230552 + 0.399328i −0.0144947 + 0.0251055i
\(254\) −0.0282185 + 0.0236781i −0.00177059 + 0.00148570i
\(255\) 0 0
\(256\) −2.79591 + 15.8564i −0.174744 + 0.991025i
\(257\) −3.40167 + 19.2919i −0.212191 + 1.20339i 0.673525 + 0.739164i \(0.264779\pi\)
−0.885716 + 0.464228i \(0.846332\pi\)
\(258\) 0 0
\(259\) 11.1099 9.32234i 0.690338 0.579262i
\(260\) 5.73783 9.93821i 0.355845 0.616341i
\(261\) 0 0
\(262\) 8.06758 + 13.9735i 0.498417 + 0.863283i
\(263\) −16.7271 6.08818i −1.03144 0.375414i −0.229811 0.973235i \(-0.573811\pi\)
−0.801629 + 0.597822i \(0.796033\pi\)
\(264\) 0 0
\(265\) 4.17159 + 3.50038i 0.256259 + 0.215027i
\(266\) −6.49273 + 2.36316i −0.398095 + 0.144895i
\(267\) 0 0
\(268\) 1.24928 + 7.08499i 0.0763116 + 0.432785i
\(269\) 22.7888 1.38946 0.694729 0.719272i \(-0.255524\pi\)
0.694729 + 0.719272i \(0.255524\pi\)
\(270\) 0 0
\(271\) −3.44562 −0.209307 −0.104653 0.994509i \(-0.533373\pi\)
−0.104653 + 0.994509i \(0.533373\pi\)
\(272\) −0.0218219 0.123758i −0.00132315 0.00750393i
\(273\) 0 0
\(274\) 11.8277 4.30493i 0.714537 0.260070i
\(275\) 1.25103 + 1.04974i 0.0754399 + 0.0633016i
\(276\) 0 0
\(277\) 2.45589 + 0.893871i 0.147560 + 0.0537075i 0.414744 0.909938i \(-0.363871\pi\)
−0.267184 + 0.963645i \(0.586093\pi\)
\(278\) 4.61468 + 7.99287i 0.276770 + 0.479380i
\(279\) 0 0
\(280\) 12.0248 20.8276i 0.718620 1.24469i
\(281\) −10.4834 + 8.79661i −0.625387 + 0.524762i −0.899492 0.436938i \(-0.856063\pi\)
0.274105 + 0.961700i \(0.411618\pi\)
\(282\) 0 0
\(283\) 3.97313 22.5327i 0.236178 1.33943i −0.603941 0.797029i \(-0.706404\pi\)
0.840119 0.542402i \(-0.182485\pi\)
\(284\) 3.26295 18.5051i 0.193620 1.09807i
\(285\) 0 0
\(286\) −0.263985 + 0.221510i −0.0156098 + 0.0130981i
\(287\) −6.33662 + 10.9753i −0.374039 + 0.647854i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 21.5326 + 7.83721i 1.26444 + 0.460217i
\(291\) 0 0
\(292\) −8.15657 6.84418i −0.477327 0.400525i
\(293\) −22.8170 + 8.30472i −1.33298 + 0.485167i −0.907596 0.419844i \(-0.862085\pi\)
−0.425388 + 0.905011i \(0.639862\pi\)
\(294\) 0 0
\(295\) −3.44949 19.5630i −0.200837 1.13900i
\(296\) −18.8357 −1.09481
\(297\) 0 0
\(298\) 1.11793 0.0647597
\(299\) 1.18820 + 6.73859i 0.0687152 + 0.389703i
\(300\) 0 0
\(301\) −12.7836 + 4.65284i −0.736834 + 0.268186i
\(302\) −5.29292 4.44129i −0.304573 0.255567i
\(303\) 0 0
\(304\) 0.141559 + 0.0515234i 0.00811898 + 0.00295507i
\(305\) 7.33409 + 12.7030i 0.419949 + 0.727373i
\(306\) 0 0
\(307\) 8.07444 13.9853i 0.460833 0.798186i −0.538170 0.842836i \(-0.680884\pi\)
0.999003 + 0.0446505i \(0.0142174\pi\)
\(308\) 0.333626 0.279945i 0.0190101 0.0159514i
\(309\) 0 0
\(310\) 3.07145 17.4191i 0.174447 0.989337i
\(311\) 3.24897 18.4258i 0.184232 1.04483i −0.742706 0.669618i \(-0.766458\pi\)
0.926938 0.375215i \(-0.122431\pi\)
\(312\) 0 0
\(313\) 2.12449 1.78265i 0.120083 0.100762i −0.580769 0.814069i \(-0.697248\pi\)
0.700852 + 0.713307i \(0.252803\pi\)
\(314\) −5.43124 + 9.40718i −0.306502 + 0.530878i
\(315\) 0 0
\(316\) −0.778066 1.34765i −0.0437696 0.0758112i
\(317\) −16.4281 5.97935i −0.922696 0.335834i −0.163386 0.986562i \(-0.552241\pi\)
−0.759311 + 0.650728i \(0.774464\pi\)
\(318\) 0 0
\(319\) 0.836152 + 0.701615i 0.0468155 + 0.0392829i
\(320\) −18.3799 + 6.68972i −1.02746 + 0.373967i
\(321\) 0 0
\(322\) 0.946662 + 5.36879i 0.0527554 + 0.299191i
\(323\) 10.7888 0.600305
\(324\) 0 0
\(325\) 24.2344 1.34428
\(326\) 2.09920 + 11.9052i 0.116264 + 0.659367i
\(327\) 0 0
\(328\) 15.4667 5.62943i 0.854007 0.310833i
\(329\) −12.3799 10.3879i −0.682523 0.572705i
\(330\) 0 0
\(331\) 30.5018 + 11.1018i 1.67653 + 0.610207i 0.992828 0.119553i \(-0.0381460\pi\)
0.683703 + 0.729760i \(0.260368\pi\)
\(332\) −5.19846 9.00400i −0.285303 0.494159i
\(333\) 0 0
\(334\) −1.63429 + 2.83067i −0.0894241 + 0.154887i
\(335\) −17.4290 + 14.6247i −0.952249 + 0.799032i
\(336\) 0 0
\(337\) 1.43882 8.15993i 0.0783773 0.444500i −0.920213 0.391418i \(-0.871985\pi\)
0.998590 0.0530814i \(-0.0169043\pi\)
\(338\) 1.09714 6.22221i 0.0596768 0.338444i
\(339\) 0 0
\(340\) −10.9363 + 9.17664i −0.593104 + 0.497673i
\(341\) 0.421274 0.729669i 0.0228133 0.0395138i
\(342\) 0 0
\(343\) −10.0792 17.4577i −0.544225 0.942626i
\(344\) 16.6027 + 6.04288i 0.895156 + 0.325810i
\(345\) 0 0
\(346\) 1.05051 + 0.881480i 0.0564756 + 0.0473887i
\(347\) −14.0608 + 5.11770i −0.754822 + 0.274733i −0.690633 0.723205i \(-0.742668\pi\)
−0.0641886 + 0.997938i \(0.520446\pi\)
\(348\) 0 0
\(349\) 5.84255 + 33.1347i 0.312744 + 1.77366i 0.584598 + 0.811323i \(0.301252\pi\)
−0.271853 + 0.962339i \(0.587637\pi\)
\(350\) 19.3081 1.03206
\(351\) 0 0
\(352\) −0.916222 −0.0488348
\(353\) −2.73560 15.5144i −0.145602 0.825747i −0.966882 0.255223i \(-0.917851\pi\)
0.821281 0.570524i \(-0.193260\pi\)
\(354\) 0 0
\(355\) 55.8414 20.3246i 2.96375 1.07872i
\(356\) −7.25624 6.08871i −0.384580 0.322701i
\(357\) 0 0
\(358\) −10.0753 3.66712i −0.532497 0.193813i
\(359\) −9.06283 15.6973i −0.478318 0.828471i 0.521373 0.853329i \(-0.325420\pi\)
−0.999691 + 0.0248577i \(0.992087\pi\)
\(360\) 0 0
\(361\) 3.03343 5.25406i 0.159654 0.276529i
\(362\) 11.3662 9.53736i 0.597393 0.501272i
\(363\) 0 0
\(364\) 1.12226 6.36467i 0.0588226 0.333600i
\(365\) 5.84730 33.1617i 0.306061 1.73576i
\(366\) 0 0
\(367\) −14.6643 + 12.3048i −0.765471 + 0.642306i −0.939545 0.342426i \(-0.888751\pi\)
0.174074 + 0.984733i \(0.444307\pi\)
\(368\) 0.0594300 0.102936i 0.00309800 0.00536590i
\(369\) 0 0
\(370\) −11.3229 19.6119i −0.588652 1.01958i
\(371\) 2.88191 + 1.04893i 0.149621 + 0.0544577i
\(372\) 0 0
\(373\) −11.6821 9.80245i −0.604876 0.507552i 0.288132 0.957591i \(-0.406966\pi\)
−0.893009 + 0.450039i \(0.851410\pi\)
\(374\) 0.402856 0.146628i 0.0208312 0.00758193i
\(375\) 0 0
\(376\) 3.64466 + 20.6699i 0.187959 + 1.06597i
\(377\) 16.1976 0.834218
\(378\) 0 0
\(379\) 9.84760 0.505837 0.252919 0.967488i \(-0.418610\pi\)
0.252919 + 0.967488i \(0.418610\pi\)
\(380\) −2.97178 16.8538i −0.152449 0.864582i
\(381\) 0 0
\(382\) −14.4410 + 5.25611i −0.738868 + 0.268926i
\(383\) 21.7481 + 18.2488i 1.11128 + 0.932471i 0.998131 0.0611076i \(-0.0194633\pi\)
0.113144 + 0.993579i \(0.463908\pi\)
\(384\) 0 0
\(385\) 1.29426 + 0.471073i 0.0659617 + 0.0240081i
\(386\) −0.875982 1.51724i −0.0445863 0.0772257i
\(387\) 0 0
\(388\) −2.39615 + 4.15026i −0.121646 + 0.210698i
\(389\) 8.33796 6.99638i 0.422752 0.354731i −0.406457 0.913670i \(-0.633236\pi\)
0.829209 + 0.558939i \(0.188791\pi\)
\(390\) 0 0
\(391\) 1.47818 8.38316i 0.0747547 0.423955i
\(392\) −1.09714 + 6.22221i −0.0554141 + 0.314269i
\(393\) 0 0
\(394\) −14.2763 + 11.9792i −0.719230 + 0.603506i
\(395\) 2.46064 4.26195i 0.123808 0.214442i
\(396\) 0 0
\(397\) 9.05350 + 15.6811i 0.454382 + 0.787013i 0.998652 0.0518969i \(-0.0165267\pi\)
−0.544270 + 0.838910i \(0.683193\pi\)
\(398\) −2.54829 0.927500i −0.127734 0.0464914i
\(399\) 0 0
\(400\) −0.322481 0.270594i −0.0161241 0.0135297i
\(401\) −1.34730 + 0.490376i −0.0672808 + 0.0244882i −0.375441 0.926846i \(-0.622509\pi\)
0.308161 + 0.951334i \(0.400287\pi\)
\(402\) 0 0
\(403\) −2.17112 12.3130i −0.108151 0.613356i
\(404\) 9.95306 0.495183
\(405\) 0 0
\(406\) 12.9050 0.640463
\(407\) −0.187319 1.06234i −0.00928505 0.0526581i
\(408\) 0 0
\(409\) −8.08512 + 2.94274i −0.399784 + 0.145509i −0.534084 0.845431i \(-0.679343\pi\)
0.134301 + 0.990941i \(0.457121\pi\)
\(410\) 15.1591 + 12.7200i 0.748655 + 0.628196i
\(411\) 0 0
\(412\) 21.4932 + 7.82288i 1.05889 + 0.385406i
\(413\) −5.59374 9.68864i −0.275250 0.476747i
\(414\) 0 0
\(415\) 16.4402 28.4752i 0.807016 1.39779i
\(416\) −10.4153 + 8.73951i −0.510654 + 0.428490i
\(417\) 0 0
\(418\) −0.0892411 + 0.506111i −0.00436492 + 0.0247547i
\(419\) −2.13785 + 12.1244i −0.104441 + 0.592314i 0.887001 + 0.461767i \(0.152784\pi\)
−0.991442 + 0.130547i \(0.958327\pi\)
\(420\) 0 0
\(421\) 8.51573 7.14555i 0.415031 0.348253i −0.411238 0.911528i \(-0.634903\pi\)
0.826269 + 0.563275i \(0.190459\pi\)
\(422\) 0.443096 0.767465i 0.0215696 0.0373596i
\(423\) 0 0
\(424\) −1.99154 3.44946i −0.0967179 0.167520i
\(425\) −28.3307 10.3115i −1.37424 0.500183i
\(426\) 0 0
\(427\) 6.32816 + 5.30996i 0.306241 + 0.256967i
\(428\) 8.75624 3.18701i 0.423249 0.154050i
\(429\) 0 0
\(430\) 3.68866 + 20.9194i 0.177883 + 1.00883i
\(431\) −36.8958 −1.77721 −0.888604 0.458675i \(-0.848324\pi\)
−0.888604 + 0.458675i \(0.848324\pi\)
\(432\) 0 0
\(433\) −37.9982 −1.82608 −0.913040 0.407871i \(-0.866271\pi\)
−0.913040 + 0.407871i \(0.866271\pi\)
\(434\) −1.72978 9.81007i −0.0830321 0.470899i
\(435\) 0 0
\(436\) −18.0262 + 6.56099i −0.863296 + 0.314214i
\(437\) 7.81702 + 6.55926i 0.373939 + 0.313772i
\(438\) 0 0
\(439\) −0.189845 0.0690979i −0.00906081 0.00329786i 0.337486 0.941331i \(-0.390424\pi\)
−0.346547 + 0.938033i \(0.612646\pi\)
\(440\) −0.894400 1.54915i −0.0426388 0.0738526i
\(441\) 0 0
\(442\) 3.18092 5.50952i 0.151301 0.262061i
\(443\) 16.2626 13.6460i 0.772661 0.648340i −0.168728 0.985663i \(-0.553966\pi\)
0.941389 + 0.337323i \(0.109521\pi\)
\(444\) 0 0
\(445\) 5.20187 29.5013i 0.246592 1.39849i
\(446\) −2.79204 + 15.8345i −0.132207 + 0.749783i
\(447\) 0 0
\(448\) −8.43835 + 7.08062i −0.398674 + 0.334528i
\(449\) 16.6297 28.8035i 0.784804 1.35932i −0.144312 0.989532i \(-0.546097\pi\)
0.929116 0.369788i \(-0.120570\pi\)
\(450\) 0 0
\(451\) 0.471315 + 0.816341i 0.0221933 + 0.0384400i
\(452\) −2.66637 0.970481i −0.125416 0.0456476i
\(453\) 0 0
\(454\) 1.78177 + 1.49509i 0.0836228 + 0.0701679i
\(455\) 19.2062 6.99049i 0.900401 0.327719i
\(456\) 0 0
\(457\) −0.00592979 0.0336295i −0.000277384 0.00157312i 0.984669 0.174435i \(-0.0558098\pi\)
−0.984946 + 0.172862i \(0.944699\pi\)
\(458\) 3.04519 0.142292
\(459\) 0 0
\(460\) −13.5030 −0.629580
\(461\) −2.60236 14.7587i −0.121204 0.687382i −0.983490 0.180961i \(-0.942079\pi\)
0.862286 0.506421i \(-0.169032\pi\)
\(462\) 0 0
\(463\) 28.6065 10.4119i 1.32946 0.483883i 0.422981 0.906138i \(-0.360984\pi\)
0.906477 + 0.422255i \(0.138761\pi\)
\(464\) −0.215537 0.180857i −0.0100061 0.00839609i
\(465\) 0 0
\(466\) 5.06196 + 1.84240i 0.234491 + 0.0853476i
\(467\) 0.255367 + 0.442308i 0.0118170 + 0.0204676i 0.871873 0.489731i \(-0.162905\pi\)
−0.860056 + 0.510199i \(0.829572\pi\)
\(468\) 0 0
\(469\) −6.40673 + 11.0968i −0.295835 + 0.512401i
\(470\) −19.3307 + 16.2204i −0.891658 + 0.748190i
\(471\) 0 0
\(472\) −2.52306 + 14.3090i −0.116133 + 0.658624i
\(473\) −0.175708 + 0.996487i −0.00807904 + 0.0458185i
\(474\) 0 0
\(475\) 27.6857 23.2311i 1.27031 1.06592i
\(476\) −4.02007 + 6.96296i −0.184259 + 0.319147i
\(477\) 0 0
\(478\) −12.7297 22.0484i −0.582242 1.00847i
\(479\) 14.5189 + 5.28444i 0.663385 + 0.241452i 0.651697 0.758479i \(-0.274057\pi\)
0.0116878 + 0.999932i \(0.496280\pi\)
\(480\) 0 0
\(481\) −12.2626 10.2896i −0.559128 0.469164i
\(482\) 18.4491 6.71492i 0.840333 0.305856i
\(483\) 0 0
\(484\) 2.33750 + 13.2566i 0.106250 + 0.602573i
\(485\) −15.1557 −0.688185
\(486\) 0 0
\(487\) 29.5107 1.33726 0.668629 0.743596i \(-0.266881\pi\)
0.668629 + 0.743596i \(0.266881\pi\)
\(488\) −1.86303 10.5657i −0.0843352 0.478289i
\(489\) 0 0
\(490\) −7.13816 + 2.59808i −0.322469 + 0.117369i
\(491\) 1.65270 + 1.38678i 0.0745855 + 0.0625846i 0.679318 0.733844i \(-0.262276\pi\)
−0.604733 + 0.796428i \(0.706720\pi\)
\(492\) 0 0
\(493\) −18.9354 6.89193i −0.852808 0.310397i
\(494\) 3.81315 + 6.60457i 0.171562 + 0.297153i
\(495\) 0 0
\(496\) −0.108593 + 0.188089i −0.00487597 + 0.00844543i
\(497\) 25.6373 21.5122i 1.14999 0.964955i
\(498\) 0 0
\(499\) 1.30154 7.38138i 0.0582648 0.330436i −0.941717 0.336405i \(-0.890789\pi\)
0.999982 + 0.00596898i \(0.00190000\pi\)
\(500\) −4.17277 + 23.6650i −0.186612 + 1.05833i
\(501\) 0 0
\(502\) 15.3066 12.8438i 0.683167 0.573245i
\(503\) −14.2981 + 24.7651i −0.637522 + 1.10422i 0.348453 + 0.937326i \(0.386707\pi\)
−0.985975 + 0.166894i \(0.946626\pi\)
\(504\) 0 0
\(505\) 15.7383 + 27.2595i 0.700345 + 1.21303i
\(506\) 0.381034 + 0.138685i 0.0169390 + 0.00616530i
\(507\) 0 0
\(508\) −0.0393628 0.0330293i −0.00174644 0.00146544i
\(509\) 1.58987 0.578665i 0.0704698 0.0256489i −0.306545 0.951856i \(-0.599173\pi\)
0.377015 + 0.926207i \(0.376951\pi\)
\(510\) 0 0
\(511\) −3.29308 18.6760i −0.145677 0.826177i
\(512\) 0.473897 0.0209435
\(513\) 0 0
\(514\) 17.2267 0.759836
\(515\) 12.5608 + 71.2357i 0.553494 + 3.13902i
\(516\) 0 0
\(517\) −1.12954 + 0.411118i −0.0496770 + 0.0180810i
\(518\) −9.76991 8.19793i −0.429265 0.360196i
\(519\) 0 0
\(520\) −24.9440 9.07888i −1.09387 0.398135i
\(521\) 11.2019 + 19.4022i 0.490763 + 0.850026i 0.999943 0.0106337i \(-0.00338487\pi\)
−0.509181 + 0.860660i \(0.670052\pi\)
\(522\) 0 0
\(523\) −1.21436 + 2.10332i −0.0531000 + 0.0919720i −0.891354 0.453309i \(-0.850244\pi\)
0.838254 + 0.545281i \(0.183577\pi\)
\(524\) −17.2417 + 14.4675i −0.753207 + 0.632016i
\(525\) 0 0
\(526\) −2.71823 + 15.4158i −0.118520 + 0.672162i
\(527\) −2.70099 + 15.3181i −0.117657 + 0.667266i
\(528\) 0 0
\(529\) −11.4513 + 9.60878i −0.497883 + 0.417773i
\(530\) 2.39440 4.14722i 0.104006 0.180144i
\(531\) 0 0
\(532\) −4.81908 8.34689i −0.208934 0.361883i
\(533\) 13.1446 + 4.78423i 0.569354 + 0.207228i
\(534\) 0 0
\(535\) 22.5744 + 18.9422i 0.975978 + 0.818943i
\(536\) 15.6379 5.69171i 0.675452 0.245845i
\(537\) 0 0
\(538\) −3.47993 19.7357i −0.150031 0.850866i
\(539\) −0.361844 −0.0155857
\(540\) 0 0
\(541\) 38.9394 1.67414 0.837069 0.547098i \(-0.184267\pi\)
0.837069 + 0.547098i \(0.184267\pi\)
\(542\) 0.526159 + 2.98400i 0.0226005 + 0.128174i
\(543\) 0 0
\(544\) 15.8944 5.78509i 0.681467 0.248034i
\(545\) −46.4732 38.9956i −1.99069 1.67039i
\(546\) 0 0
\(547\) 13.7875 + 5.01822i 0.589509 + 0.214564i 0.619513 0.784986i \(-0.287330\pi\)
−0.0300044 + 0.999550i \(0.509552\pi\)
\(548\) 8.77884 + 15.2054i 0.375013 + 0.649542i
\(549\) 0 0
\(550\) 0.718063 1.24372i 0.0306183 0.0530325i
\(551\) 18.5043 15.5270i 0.788311 0.661472i
\(552\) 0 0
\(553\) 0.481277 2.72946i 0.0204660 0.116068i
\(554\) 0.399091 2.26336i 0.0169558 0.0961609i
\(555\) 0 0
\(556\) −9.86231 + 8.27546i −0.418255 + 0.350958i
\(557\) 5.55350 9.61894i 0.235309 0.407568i −0.724053 0.689744i \(-0.757723\pi\)
0.959363 + 0.282176i \(0.0910563\pi\)
\(558\) 0 0
\(559\) 7.50774 + 13.0038i 0.317544 + 0.550002i
\(560\) −0.333626 0.121430i −0.0140983 0.00513135i
\(561\) 0 0
\(562\) 9.21894 + 7.73561i 0.388878 + 0.326307i
\(563\) −15.3246 + 5.57770i −0.645855 + 0.235072i −0.644117 0.764927i \(-0.722775\pi\)
−0.00173729 + 0.999998i \(0.500553\pi\)
\(564\) 0 0
\(565\) −1.55825 8.83726i −0.0655560 0.371786i
\(566\) −20.1206 −0.845733
\(567\) 0 0
\(568\) −43.4653 −1.82376
\(569\) 6.25418 + 35.4692i 0.262189 + 1.48695i 0.776922 + 0.629597i \(0.216780\pi\)
−0.514733 + 0.857351i \(0.672109\pi\)
\(570\) 0 0
\(571\) −36.7968 + 13.3930i −1.53990 + 0.560478i −0.966021 0.258462i \(-0.916784\pi\)
−0.573879 + 0.818940i \(0.694562\pi\)
\(572\) −0.368241 0.308991i −0.0153969 0.0129196i
\(573\) 0 0
\(574\) 10.4726 + 3.81170i 0.437116 + 0.159097i
\(575\) −14.2579 24.6954i −0.594595 1.02987i
\(576\) 0 0
\(577\) −5.90286 + 10.2240i −0.245739 + 0.425633i −0.962339 0.271852i \(-0.912364\pi\)
0.716600 + 0.697484i \(0.245697\pi\)
\(578\) 5.38919 4.52206i 0.224161 0.188093i
\(579\) 0 0
\(580\) −5.55051 + 31.4785i −0.230472 + 1.30707i
\(581\) 3.21554 18.2362i 0.133403 0.756566i
\(582\) 0 0
\(583\) 0.174744 0.146628i 0.00723716 0.00607269i
\(584\) −12.3148 + 21.3299i −0.509590 + 0.882636i
\(585\) 0 0
\(586\) 10.6763 + 18.4920i 0.441035 + 0.763896i
\(587\) 37.5514 + 13.6676i 1.54991 + 0.564123i 0.968397 0.249412i \(-0.0802374\pi\)
0.581516 + 0.813535i \(0.302460\pi\)
\(588\) 0 0
\(589\) −14.2836 11.9854i −0.588545 0.493848i
\(590\) −16.4153 + 5.97470i −0.675809 + 0.245974i
\(591\) 0 0
\(592\) 0.0482857 + 0.273842i 0.00198453 + 0.0112548i
\(593\) −29.2995 −1.20319 −0.601594 0.798802i \(-0.705467\pi\)
−0.601594 + 0.798802i \(0.705467\pi\)
\(594\) 0 0
\(595\) −25.4270 −1.04240
\(596\) 0.270792 + 1.53574i 0.0110921 + 0.0629063i
\(597\) 0 0
\(598\) 5.65435 2.05802i 0.231224 0.0841585i
\(599\) 7.71554 + 6.47410i 0.315248 + 0.264525i 0.786657 0.617390i \(-0.211810\pi\)
−0.471409 + 0.881915i \(0.656254\pi\)
\(600\) 0 0
\(601\) 28.5847 + 10.4040i 1.16599 + 0.424387i 0.851235 0.524784i \(-0.175854\pi\)
0.314759 + 0.949172i \(0.398076\pi\)
\(602\) 5.98158 + 10.3604i 0.243791 + 0.422259i
\(603\) 0 0
\(604\) 4.81908 8.34689i 0.196085 0.339630i
\(605\) −32.6111 + 27.3640i −1.32583 + 1.11250i
\(606\) 0 0
\(607\) −4.00681 + 22.7237i −0.162631 + 0.922328i 0.788842 + 0.614596i \(0.210681\pi\)
−0.951473 + 0.307732i \(0.900430\pi\)
\(608\) −3.52094 + 19.9683i −0.142793 + 0.809820i
\(609\) 0 0
\(610\) 9.88120 8.29131i 0.400078 0.335705i
\(611\) −8.91875 + 15.4477i −0.360814 + 0.624948i
\(612\) 0 0
\(613\) −0.382789 0.663010i −0.0154607 0.0267787i 0.858192 0.513330i \(-0.171588\pi\)
−0.873652 + 0.486551i \(0.838255\pi\)
\(614\) −13.3447 4.85706i −0.538547 0.196015i
\(615\) 0 0
\(616\) −0.771726 0.647555i −0.0310937 0.0260907i
\(617\) 8.72803 3.17674i 0.351377 0.127891i −0.160301 0.987068i \(-0.551246\pi\)
0.511678 + 0.859177i \(0.329024\pi\)
\(618\) 0 0
\(619\) −6.09199 34.5494i −0.244858 1.38866i −0.820823 0.571182i \(-0.806485\pi\)
0.575966 0.817474i \(-0.304626\pi\)
\(620\) 24.6732 0.990901
\(621\) 0 0
\(622\) −16.4534 −0.659720
\(623\) −2.92959 16.6145i −0.117371 0.665647i
\(624\) 0 0
\(625\) −24.1942 + 8.80596i −0.967767 + 0.352238i
\(626\) −1.86824 1.56764i −0.0746699 0.0626555i
\(627\) 0 0
\(628\) −14.2386 5.18243i −0.568182 0.206801i
\(629\) 9.95723 + 17.2464i 0.397021 + 0.687660i
\(630\) 0 0
\(631\) −17.8810 + 30.9709i −0.711833 + 1.23293i 0.252336 + 0.967640i \(0.418801\pi\)
−0.964168 + 0.265291i \(0.914532\pi\)
\(632\) −2.75743 + 2.31376i −0.109685 + 0.0920362i
\(633\) 0 0
\(634\) −2.66964 + 15.1403i −0.106025 + 0.601296i
\(635\) 0.0282185 0.160035i 0.00111982 0.00635080i
\(636\) 0 0
\(637\) −4.11334 + 3.45150i −0.162976 + 0.136754i
\(638\) 0.479933 0.831268i 0.0190007 0.0329102i
\(639\) 0 0
\(640\) −13.2724 22.9885i −0.524639 0.908702i
\(641\) −2.74985 1.00086i −0.108612 0.0395317i 0.287142 0.957888i \(-0.407295\pi\)
−0.395755 + 0.918356i \(0.629517\pi\)
\(642\) 0 0
\(643\) −15.5137 13.0175i −0.611799 0.513361i 0.283414 0.958998i \(-0.408533\pi\)
−0.895214 + 0.445637i \(0.852977\pi\)
\(644\) −7.14600 + 2.60093i −0.281592 + 0.102491i
\(645\) 0 0
\(646\) −1.64749 9.34337i −0.0648196 0.367610i
\(647\) 10.7219 0.421523 0.210761 0.977538i \(-0.432406\pi\)
0.210761 + 0.977538i \(0.432406\pi\)
\(648\) 0 0
\(649\) −0.832119 −0.0326635
\(650\) −3.70068 20.9876i −0.145153 0.823202i
\(651\) 0 0
\(652\) −15.8461 + 5.76751i −0.620582 + 0.225873i
\(653\) 27.3685 + 22.9649i 1.07101 + 0.898685i 0.995144 0.0984334i \(-0.0313831\pi\)
0.0758669 + 0.997118i \(0.475828\pi\)
\(654\) 0 0
\(655\) −66.8872 24.3449i −2.61350 0.951236i
\(656\) −0.121492 0.210430i −0.00474347 0.00821593i
\(657\) 0 0
\(658\) −7.10576 + 12.3075i −0.277011 + 0.479798i
\(659\) 23.6446 19.8401i 0.921061 0.772862i −0.0531299 0.998588i \(-0.516920\pi\)
0.974191 + 0.225726i \(0.0724753\pi\)
\(660\) 0 0
\(661\) −1.71007 + 9.69831i −0.0665142 + 0.377221i 0.933321 + 0.359044i \(0.116897\pi\)
−0.999835 + 0.0181766i \(0.994214\pi\)
\(662\) 4.95666 28.1106i 0.192646 1.09255i
\(663\) 0 0
\(664\) −18.4231 + 15.4588i −0.714954 + 0.599918i
\(665\) 15.2404 26.3971i 0.590996 1.02363i
\(666\) 0 0
\(667\) −9.52956 16.5057i −0.368986 0.639103i
\(668\) −4.28446 1.55942i −0.165771 0.0603357i
\(669\) 0 0
\(670\) 15.3268 + 12.8607i 0.592127 + 0.496853i
\(671\) 0.577382 0.210150i 0.0222896 0.00811274i
\(672\) 0 0
\(673\) −3.42040 19.3980i −0.131847 0.747739i −0.977004 0.213222i \(-0.931604\pi\)
0.845157 0.534518i \(-0.179507\pi\)
\(674\) −7.28642 −0.280662
\(675\) 0 0
\(676\) 8.81345 0.338979
\(677\) −4.94150 28.0247i −0.189917 1.07708i −0.919473 0.393153i \(-0.871384\pi\)
0.729555 0.683922i \(-0.239727\pi\)
\(678\) 0 0
\(679\) −8.02064 + 2.91927i −0.307804 + 0.112031i
\(680\) 25.2973 + 21.2269i 0.970105 + 0.814015i
\(681\) 0 0
\(682\) −0.696242 0.253411i −0.0266605 0.00970362i
\(683\) −6.25537 10.8346i −0.239355 0.414575i 0.721174 0.692754i \(-0.243603\pi\)
−0.960529 + 0.278179i \(0.910269\pi\)
\(684\) 0 0
\(685\) −27.7631 + 48.0871i −1.06077 + 1.83731i
\(686\) −13.5797 + 11.3947i −0.518474 + 0.435051i
\(687\) 0 0
\(688\) 0.0452926 0.256867i 0.00172677 0.00979297i
\(689\) 0.587811 3.33364i 0.0223938 0.127002i
\(690\) 0 0
\(691\) 32.6530 27.3991i 1.24218 1.04231i 0.244828 0.969566i \(-0.421268\pi\)
0.997351 0.0727455i \(-0.0231761\pi\)
\(692\) −0.956462 + 1.65664i −0.0363592 + 0.0629760i
\(693\) 0 0
\(694\) 6.57919 + 11.3955i 0.249743 + 0.432567i
\(695\) −38.2597 13.9254i −1.45127 0.528220i
\(696\) 0 0
\(697\) −13.3307 11.1858i −0.504936 0.423691i
\(698\) 27.8033 10.1196i 1.05237 0.383032i
\(699\) 0 0
\(700\) 4.67695 + 26.5243i 0.176772 + 1.00252i
\(701\) 51.7701 1.95533 0.977665 0.210167i \(-0.0674008\pi\)
0.977665 + 0.210167i \(0.0674008\pi\)
\(702\) 0 0
\(703\) −23.8726 −0.900371
\(704\) 0.142275 + 0.806879i 0.00536217 + 0.0304104i
\(705\) 0 0
\(706\) −13.0181 + 4.73821i −0.489943 + 0.178325i
\(707\) 13.5797 + 11.3947i 0.510716 + 0.428541i
\(708\) 0 0
\(709\) −14.2442 5.18447i −0.534953 0.194707i 0.0603955 0.998175i \(-0.480764\pi\)
−0.595349 + 0.803468i \(0.702986\pi\)
\(710\) −26.1288 45.2564i −0.980597 1.69844i
\(711\) 0 0
\(712\) −10.9555 + 18.9754i −0.410574 + 0.711135i
\(713\) −11.2699 + 9.45658i −0.422062 + 0.354152i
\(714\) 0 0
\(715\) 0.263985 1.49713i 0.00987248 0.0559896i
\(716\) 2.59714 14.7291i 0.0970598 0.550454i
\(717\) 0 0
\(718\) −12.2103 + 10.2457i −0.455685 + 0.382365i
\(719\) 1.30747 2.26460i 0.0487603 0.0844553i −0.840615 0.541633i \(-0.817806\pi\)
0.889375 + 0.457178i \(0.151140\pi\)
\(720\) 0 0
\(721\) 20.3687 + 35.2796i 0.758570 + 1.31388i
\(722\) −5.01337 1.82472i −0.186578 0.0679089i
\(723\) 0 0
\(724\) 15.8550 + 13.3040i 0.589248 + 0.494438i
\(725\) −63.4313 + 23.0871i −2.35578 + 0.857433i
\(726\) 0 0
\(727\) −0.711829 4.03698i −0.0264003 0.149723i 0.968758 0.248007i \(-0.0797757\pi\)
−0.995158 + 0.0982840i \(0.968665\pi\)
\(728\) −14.9495 −0.554067
\(729\) 0 0
\(730\) −29.6117 −1.09598
\(731\) −3.24376 18.3963i −0.119975 0.680410i
\(732\) 0 0
\(733\) 35.9038 13.0679i 1.32614 0.482674i 0.420717 0.907192i \(-0.361779\pi\)
0.905420 + 0.424518i \(0.139556\pi\)
\(734\) 12.8956 + 10.8207i 0.475985 + 0.399399i
\(735\) 0 0
\(736\) 15.0334 + 5.47172i 0.554140 + 0.201690i
\(737\) 0.476529 + 0.825373i 0.0175532 + 0.0304030i
\(738\) 0 0
\(739\) 12.1047 20.9660i 0.445279 0.771247i −0.552792 0.833319i \(-0.686438\pi\)
0.998072 + 0.0620725i \(0.0197710\pi\)
\(740\) 24.1989 20.3053i 0.889570 0.746438i
\(741\) 0 0
\(742\) 0.468322 2.65598i 0.0171926 0.0975042i
\(743\) −0.575017 + 3.26109i −0.0210953 + 0.119638i −0.993537 0.113509i \(-0.963791\pi\)
0.972442 + 0.233146i \(0.0749021\pi\)
\(744\) 0 0
\(745\) −3.77790 + 3.17004i −0.138412 + 0.116141i
\(746\) −6.70527 + 11.6139i −0.245497 + 0.425214i
\(747\) 0 0
\(748\) 0.299011 + 0.517902i 0.0109329 + 0.0189364i
\(749\) 15.5954 + 5.67626i 0.569843 + 0.207406i
\(750\) 0 0
\(751\) 10.5032 + 8.81327i 0.383269 + 0.321601i 0.813984 0.580887i \(-0.197294\pi\)
−0.430715 + 0.902488i \(0.641739\pi\)
\(752\) 0.291164 0.105975i 0.0106177 0.00386451i
\(753\) 0 0
\(754\) −2.47343 14.0275i −0.0900770 0.510852i
\(755\) 30.4807 1.10931
\(756\) 0 0
\(757\) 12.3833 0.450079 0.225040 0.974350i \(-0.427749\pi\)
0.225040 + 0.974350i \(0.427749\pi\)
\(758\) −1.50376 8.52827i −0.0546192 0.309761i
\(759\) 0 0
\(760\) −37.1994 + 13.5395i −1.34936 + 0.491128i
\(761\) 5.80865 + 4.87404i 0.210563 + 0.176684i 0.741970 0.670433i \(-0.233892\pi\)
−0.531406 + 0.847117i \(0.678336\pi\)
\(762\) 0 0
\(763\) −32.1057 11.6855i −1.16230 0.423044i
\(764\) −10.7185 18.5650i −0.387783 0.671660i
\(765\) 0 0
\(766\) 12.4829 21.6211i 0.451026 0.781201i
\(767\) −9.45929 + 7.93729i −0.341555 + 0.286599i
\(768\) 0 0
\(769\) 0.558659 3.16831i 0.0201457 0.114252i −0.973077 0.230482i \(-0.925970\pi\)
0.993222 + 0.116230i \(0.0370809\pi\)
\(770\) 0.210323 1.19280i 0.00757950 0.0429855i
\(771\) 0 0
\(772\) 1.87211 1.57089i 0.0673788 0.0565375i
\(773\) 0.0922341 0.159754i 0.00331743 0.00574596i −0.864362 0.502870i \(-0.832277\pi\)
0.867679 + 0.497124i \(0.165611\pi\)
\(774\) 0 0
\(775\) 26.0526 + 45.1245i 0.935838 + 1.62092i
\(776\) 10.4168 + 3.79140i 0.373941 + 0.136103i
\(777\) 0 0
\(778\) −7.33228 6.15251i −0.262875 0.220578i
\(779\) 19.6027 7.13479i 0.702338 0.255630i
\(780\) 0 0
\(781\) −0.432257 2.45145i −0.0154674 0.0877197i
\(782\) −7.48576 −0.267690
\(783\) 0 0
\(784\) 0.0932736 0.00333120
\(785\) −8.32114 47.1915i −0.296994 1.68434i
\(786\) 0 0
\(787\) 0.449188 0.163491i 0.0160118 0.00582783i −0.334002 0.942572i \(-0.608399\pi\)
0.350014 + 0.936745i \(0.386177\pi\)
\(788\) −19.9145 16.7102i −0.709424 0.595277i
\(789\) 0 0
\(790\) −4.06670 1.48016i −0.144687 0.0526617i
\(791\) −2.52687 4.37667i −0.0898453 0.155617i
\(792\) 0 0
\(793\) 4.55896 7.89636i 0.161894 0.280408i
\(794\) 12.1977 10.2351i 0.432882 0.363231i
\(795\) 0 0
\(796\) 0.656879 3.72534i 0.0232824 0.132041i
\(797\) 2.51770 14.2786i 0.0891816 0.505774i −0.907194 0.420712i \(-0.861780\pi\)
0.996376 0.0850617i \(-0.0271087\pi\)
\(798\) 0 0
\(799\) 16.9991 14.2640i 0.601386 0.504623i
\(800\) 28.3307 49.0702i 1.00164 1.73489i
\(801\) 0 0
\(802\) 0.630415 + 1.09191i 0.0222607 + 0.0385567i
\(803\) −1.32547 0.482433i −0.0467750 0.0170247i
\(804\) 0 0
\(805\) −18.4231 15.4588i −0.649328 0.544851i
\(806\) −10.3319 + 3.76049i −0.363925 + 0.132458i
\(807\) 0 0
\(808\) −3.99788 22.6731i −0.140645 0.797638i
\(809\) −14.8743 −0.522954 −0.261477 0.965210i \(-0.584210\pi\)
−0.261477 + 0.965210i \(0.584210\pi\)
\(810\) 0 0
\(811\) 21.5963 0.758347 0.379174 0.925325i \(-0.376208\pi\)
0.379174 + 0.925325i \(0.376208\pi\)
\(812\) 3.12594 + 17.7281i 0.109699 + 0.622133i
\(813\) 0 0
\(814\) −0.891407 + 0.324446i −0.0312438 + 0.0113718i
\(815\) −40.8528 34.2796i −1.43101 1.20076i
\(816\) 0 0
\(817\) 21.0424 + 7.65879i 0.736179 + 0.267947i
\(818\) 3.78312 + 6.55255i 0.132274 + 0.229105i
\(819\) 0 0
\(820\) −13.8020 + 23.9058i −0.481987 + 0.834826i
\(821\) −2.51367 + 2.10922i −0.0877277 + 0.0736123i −0.685597 0.727981i \(-0.740459\pi\)
0.597869 + 0.801594i \(0.296014\pi\)
\(822\) 0 0
\(823\) 2.38444 13.5228i 0.0831163 0.471376i −0.914631 0.404290i \(-0.867519\pi\)
0.997747 0.0670860i \(-0.0213702\pi\)
\(824\) 9.18732 52.1039i 0.320055 1.81512i
\(825\) 0 0
\(826\) −7.53643 + 6.32381i −0.262226 + 0.220034i
\(827\) −10.1163 + 17.5220i −0.351779 + 0.609300i −0.986561 0.163392i \(-0.947757\pi\)
0.634782 + 0.772691i \(0.281090\pi\)
\(828\) 0 0
\(829\) −12.7638 22.1076i −0.443306 0.767828i 0.554627 0.832099i \(-0.312861\pi\)
−0.997932 + 0.0642710i \(0.979528\pi\)
\(830\) −27.1707 9.88933i −0.943109 0.343264i
\(831\) 0 0
\(832\) 9.31386 + 7.81526i 0.322900 + 0.270945i
\(833\) 6.27719 2.28471i 0.217492 0.0791605i
\(834\) 0 0
\(835\) −2.50387 14.2002i −0.0866500 0.491417i
\(836\) −0.716881 −0.0247939
\(837\) 0 0
\(838\) 10.8265 0.373994
\(839\) 3.01801 + 17.1160i 0.104193 + 0.590909i 0.991539 + 0.129805i \(0.0414353\pi\)
−0.887346 + 0.461104i \(0.847454\pi\)
\(840\) 0 0
\(841\) −15.1446 + 5.51217i −0.522226 + 0.190075i
\(842\) −7.48861 6.28369i −0.258074 0.216550i
\(843\) 0 0
\(844\) 1.16163 + 0.422797i 0.0399848 + 0.0145533i
\(845\) 13.9363 + 24.1384i 0.479423 + 0.830385i
\(846\) 0 0
\(847\) −11.9875 + 20.7630i −0.411896 + 0.713424i
\(848\) −0.0450442 + 0.0377966i −0.00154683 + 0.00129794i
\(849\) 0 0
\(850\) −4.60385 + 26.1097i −0.157911 + 0.895555i
\(851\) −3.27079 + 18.5496i −0.112121 + 0.635872i
\(852\) 0 0
\(853\) 10.1905 8.55082i 0.348915 0.292775i −0.451439 0.892302i \(-0.649089\pi\)
0.800354 + 0.599527i \(0.204645\pi\)
\(854\) 3.63223 6.29120i 0.124292 0.215280i
\(855\) 0 0
\(856\) −10.7772 18.6666i −0.368357 0.638013i
\(857\) 18.7199 + 6.81348i 0.639459 + 0.232744i 0.641343 0.767254i \(-0.278378\pi\)
−0.00188429 + 0.999998i \(0.500600\pi\)
\(858\) 0 0
\(859\) 20.1811 + 16.9340i 0.688572 + 0.577780i 0.918497 0.395428i \(-0.129404\pi\)
−0.229925 + 0.973208i \(0.573848\pi\)
\(860\) −27.8444 + 10.1345i −0.949485 + 0.345584i
\(861\) 0 0
\(862\) 5.63412 + 31.9527i 0.191899 + 1.08831i
\(863\) 38.2995 1.30373 0.651866 0.758334i \(-0.273987\pi\)
0.651866 + 0.758334i \(0.273987\pi\)
\(864\) 0 0
\(865\) −6.04963 −0.205694
\(866\) 5.80247 + 32.9074i 0.197176 + 1.11824i
\(867\) 0 0
\(868\) 13.0575 4.75253i 0.443200 0.161311i
\(869\) −0.157918 0.132509i −0.00535701 0.00449506i
\(870\) 0 0
\(871\) 13.2900 + 4.83716i 0.450314 + 0.163901i
\(872\) 22.1866 + 38.4283i 0.751333 + 1.30135i
\(873\) 0 0
\(874\) 4.48680 7.77136i 0.151768 0.262870i
\(875\) −32.7859 + 27.5106i −1.10836 + 0.930028i
\(876\) 0 0
\(877\) −4.69846 + 26.6463i −0.158656 + 0.899782i 0.796711 + 0.604360i \(0.206571\pi\)
−0.955367 + 0.295422i \(0.904540\pi\)
\(878\) −0.0308505 + 0.174962i −0.00104116 + 0.00590468i
\(879\) 0 0
\(880\) −0.0202293 + 0.0169744i −0.000681930 + 0.000572207i
\(881\) −15.2888 + 26.4810i −0.515093 + 0.892167i 0.484754 + 0.874651i \(0.338909\pi\)
−0.999847 + 0.0175162i \(0.994424\pi\)
\(882\) 0 0
\(883\) −22.0526 38.1963i −0.742130 1.28541i −0.951524 0.307575i \(-0.900482\pi\)
0.209394 0.977831i \(-0.432851\pi\)
\(884\) 8.33915 + 3.03520i 0.280476 + 0.102085i
\(885\) 0 0
\(886\) −14.3011 12.0001i −0.480456 0.403150i
\(887\) 7.40895 2.69664i 0.248768 0.0905442i −0.214627 0.976696i \(-0.568853\pi\)
0.463395 + 0.886152i \(0.346631\pi\)
\(888\) 0 0
\(889\) −0.0158921 0.0901285i −0.000533004 0.00302281i
\(890\) −26.3432 −0.883025
\(891\) 0 0
\(892\) −22.4287 −0.750969
\(893\) 4.61927 + 26.1972i 0.154578 + 0.876655i
\(894\) 0 0
\(895\) 44.4470 16.1774i 1.48570 0.540751i
\(896\) −11.4520 9.60938i −0.382585 0.321027i
\(897\) 0 0
\(898\) −27.4840 10.0033i −0.917152 0.333816i
\(899\) 17.4128 + 30.1599i 0.580750 + 1.00589i
\(900\) 0 0
\(901\) −2.10560 + 3.64701i −0.0701477 + 0.121499i
\(902\) 0.635001 0.532829i 0.0211432 0.0177413i
\(903\) 0 0
\(904\) −1.13975 + 6.46383i −0.0379075 + 0.214984i
\(905\) −11.3662 + 64.4608i −0.377825 + 2.14275i
\(906\) 0 0
\(907\) −9.88713 + 8.29628i −0.328297 + 0.275474i −0.792005 0.610514i \(-0.790963\pi\)
0.463709 + 0.885988i \(0.346518\pi\)
\(908\) −1.62226 + 2.80984i −0.0538367 + 0.0932479i
\(909\) 0 0
\(910\) −8.98680 15.5656i −0.297909 0.515994i
\(911\) −19.9081 7.24595i −0.659584 0.240069i −0.00952715 0.999955i \(-0.503033\pi\)
−0.650057 + 0.759886i \(0.725255\pi\)
\(912\) 0 0
\(913\) −1.05509 0.885328i −0.0349185 0.0293001i
\(914\) −0.0282185 + 0.0102707i −0.000933385 + 0.000339724i
\(915\) 0 0
\(916\) 0.737627 + 4.18329i 0.0243719 + 0.138220i
\(917\) −40.0871 −1.32379
\(918\) 0 0
\(919\) 31.4688 1.03806 0.519031 0.854756i \(-0.326293\pi\)
0.519031 + 0.854756i \(0.326293\pi\)
\(920\) 5.42380 + 30.7599i 0.178817 + 1.01412i
\(921\) 0 0
\(922\) −12.3840 + 4.50742i −0.407846 + 0.148444i
\(923\) −28.2973 23.7442i −0.931416 0.781550i
\(924\) 0 0
\(925\) 62.6878 + 22.8165i 2.06116 + 0.750202i
\(926\) −13.3853 23.1840i −0.439869 0.761875i
\(927\) 0 0
\(928\) 18.9354 32.7971i 0.621585 1.07662i
\(929\) −1.78240 + 1.49561i −0.0584788 + 0.0490695i −0.671559 0.740951i \(-0.734375\pi\)
0.613080 + 0.790021i \(0.289930\pi\)
\(930\) 0 0
\(931\) −1.39053 + 7.88609i −0.0455728 + 0.258456i
\(932\) −1.30483 + 7.40008i −0.0427413 + 0.242398i
\(933\) 0 0
\(934\) 0.344055 0.288696i 0.0112578 0.00944643i
\(935\) −0.945622 + 1.63787i −0.0309252 + 0.0535639i
\(936\) 0 0
\(937\) 5.49912 + 9.52476i 0.179649 + 0.311160i 0.941760 0.336285i \(-0.109171\pi\)
−0.762112 + 0.647446i \(0.775837\pi\)
\(938\) 10.5884 + 3.85387i 0.345724 + 0.125833i
\(939\) 0 0
\(940\) −26.9650 22.6263i −0.879500 0.737989i
\(941\) 22.6501 8.24395i 0.738371 0.268745i 0.0546673 0.998505i \(-0.482590\pi\)
0.683704 + 0.729759i \(0.260368\pi\)
\(942\) 0 0
\(943\) −2.85814 16.2093i −0.0930737 0.527847i
\(944\) 0.214498 0.00698131
\(945\) 0 0
\(946\) 0.889814 0.0289304
\(947\) −2.06980 11.7384i −0.0672596 0.381448i −0.999793 0.0203634i \(-0.993518\pi\)
0.932533 0.361085i \(-0.117593\pi\)
\(948\) 0 0
\(949\) −19.6694 + 7.15906i −0.638495 + 0.232393i
\(950\) −24.3464 20.4291i −0.789902 0.662807i
\(951\) 0 0
\(952\) 17.4764 + 6.36090i 0.566414 + 0.206158i
\(953\) 18.4145 + 31.8948i 0.596503 + 1.03317i 0.993333 + 0.115281i \(0.0367770\pi\)
−0.396830 + 0.917892i \(0.629890\pi\)
\(954\) 0 0
\(955\) 33.8974 58.7120i 1.09689 1.89988i
\(956\) 27.2053 22.8280i 0.879883 0.738310i
\(957\) 0 0
\(958\) 2.35937 13.3807i 0.0762279 0.432310i
\(959\) −5.43020 + 30.7962i −0.175350 + 0.994460i
\(960\) 0 0
\(961\) −3.15451 + 2.64695i −0.101759 + 0.0853856i
\(962\) −7.03849 + 12.1910i −0.226930 + 0.393054i
\(963\) 0 0
\(964\) 13.6934 + 23.7177i 0.441035 + 0.763895i
\(965\) 7.26264 + 2.64339i 0.233793 + 0.0850936i
\(966\) 0 0
\(967\) 41.0296 + 34.4279i 1.31942 + 1.10713i 0.986427 + 0.164200i \(0.0525042\pi\)
0.332996 + 0.942928i \(0.391940\pi\)
\(968\) 29.2597 10.6497i 0.940443 0.342293i
\(969\) 0 0
\(970\) 2.31433 + 13.1252i 0.0743087 + 0.421425i
\(971\) 53.2327 1.70832 0.854159 0.520012i \(-0.174073\pi\)
0.854159 + 0.520012i \(0.174073\pi\)
\(972\) 0 0
\(973\) −22.9299 −0.735100
\(974\) −4.50640 25.5570i −0.144394 0.818901i
\(975\) 0 0
\(976\) −0.148833 + 0.0541709i −0.00476404 + 0.00173397i
\(977\) 10.3086 + 8.64998i 0.329803 + 0.276737i 0.792620 0.609717i \(-0.208717\pi\)
−0.462817 + 0.886454i \(0.653161\pi\)
\(978\) 0 0
\(979\) −1.17917 0.429182i −0.0376864 0.0137167i
\(980\) −5.29813 9.17664i −0.169243 0.293137i
\(981\) 0 0
\(982\) 0.948615 1.64305i 0.0302715 0.0524318i
\(983\) −7.84524 + 6.58294i −0.250224 + 0.209963i −0.759269 0.650777i \(-0.774443\pi\)
0.509045 + 0.860740i \(0.329999\pi\)
\(984\) 0 0
\(985\) 14.2763 80.9650i 0.454881 2.57976i
\(986\) −3.07708 + 17.4510i −0.0979941 + 0.555752i
\(987\) 0 0
\(988\) −8.14930 + 6.83807i −0.259264 + 0.217548i
\(989\) 8.83409 15.3011i 0.280908 0.486547i
\(990\) 0 0
\(991\) −1.00000 1.73205i −0.0317660 0.0550204i 0.849705 0.527258i \(-0.176780\pi\)
−0.881471 + 0.472237i \(0.843446\pi\)
\(992\) −27.4697 9.99816i −0.872165 0.317442i
\(993\) 0 0
\(994\) −22.5450 18.9175i −0.715085 0.600028i
\(995\) 11.2417 4.09164i 0.356386 0.129714i
\(996\) 0 0
\(997\) 6.68573 + 37.9166i 0.211739 + 1.20083i 0.886476 + 0.462774i \(0.153146\pi\)
−0.674737 + 0.738058i \(0.735743\pi\)
\(998\) −6.59121 −0.208641
\(999\) 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.c.82.1 6
3.2 odd 2 729.2.e.h.82.1 6
9.2 odd 6 729.2.e.g.325.1 6
9.4 even 3 729.2.e.i.568.1 6
9.5 odd 6 729.2.e.a.568.1 6
9.7 even 3 729.2.e.b.325.1 6
27.2 odd 18 729.2.e.h.649.1 6
27.4 even 9 243.2.c.e.163.3 6
27.5 odd 18 243.2.a.e.1.3 3
27.7 even 9 729.2.e.b.406.1 6
27.11 odd 18 729.2.e.a.163.1 6
27.13 even 9 243.2.c.e.82.3 6
27.14 odd 18 243.2.c.f.82.1 6
27.16 even 9 729.2.e.i.163.1 6
27.20 odd 18 729.2.e.g.406.1 6
27.22 even 9 243.2.a.f.1.1 yes 3
27.23 odd 18 243.2.c.f.163.1 6
27.25 even 9 inner 729.2.e.c.649.1 6
108.59 even 18 3888.2.a.bd.1.1 3
108.103 odd 18 3888.2.a.bk.1.3 3
135.49 even 18 6075.2.a.bq.1.3 3
135.59 odd 18 6075.2.a.bv.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.e.1.3 3 27.5 odd 18
243.2.a.f.1.1 yes 3 27.22 even 9
243.2.c.e.82.3 6 27.13 even 9
243.2.c.e.163.3 6 27.4 even 9
243.2.c.f.82.1 6 27.14 odd 18
243.2.c.f.163.1 6 27.23 odd 18
729.2.e.a.163.1 6 27.11 odd 18
729.2.e.a.568.1 6 9.5 odd 6
729.2.e.b.325.1 6 9.7 even 3
729.2.e.b.406.1 6 27.7 even 9
729.2.e.c.82.1 6 1.1 even 1 trivial
729.2.e.c.649.1 6 27.25 even 9 inner
729.2.e.g.325.1 6 9.2 odd 6
729.2.e.g.406.1 6 27.20 odd 18
729.2.e.h.82.1 6 3.2 odd 2
729.2.e.h.649.1 6 27.2 odd 18
729.2.e.i.163.1 6 27.16 even 9
729.2.e.i.568.1 6 9.4 even 3
3888.2.a.bd.1.1 3 108.59 even 18
3888.2.a.bk.1.3 3 108.103 odd 18
6075.2.a.bq.1.3 3 135.49 even 18
6075.2.a.bv.1.1 3 135.59 odd 18