Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(9,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.g (of order \(3\), degree \(2\), 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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 9.2 | ||
Root | \(-1.02197 + 1.77010i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.9 |
Dual form | 91.2.g.b.81.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.777343 | − | 1.34640i | −0.549665 | − | 0.952047i | −0.998297 | − | 0.0583310i | \(-0.981422\pi\) |
0.448632 | − | 0.893716i | \(-0.351911\pi\) | |||||||
\(3\) | −0.489252 | −0.282470 | −0.141235 | − | 0.989976i | \(-0.545107\pi\) | ||||
−0.141235 | + | 0.989976i | \(0.545107\pi\) | |||||||
\(4\) | −0.208526 | + | 0.361177i | −0.104263 | + | 0.180588i | ||||
\(5\) | 0.595756 | − | 1.03188i | 0.266430 | − | 0.461470i | −0.701507 | − | 0.712662i | \(-0.747489\pi\) |
0.967937 | + | 0.251192i | \(0.0808225\pi\) | |||||||
\(6\) | 0.380316 | + | 0.658727i | 0.155264 | + | 0.268924i | ||||
\(7\) | 0.337371 | − | 2.62415i | 0.127514 | − | 0.991837i | ||||
\(8\) | −2.46099 | −0.870091 | ||||||||
\(9\) | −2.76063 | −0.920211 | ||||||||
\(10\) | −1.85243 | −0.585789 | ||||||||
\(11\) | 2.11614 | 0.638040 | 0.319020 | − | 0.947748i | \(-0.396646\pi\) | ||||
0.319020 | + | 0.947748i | \(0.396646\pi\) | |||||||
\(12\) | 0.102021 | − | 0.176706i | 0.0294511 | − | 0.0510107i | ||||
\(13\) | 2.86133 | + | 2.19381i | 0.793590 | + | 0.608453i | ||||
\(14\) | −3.79541 | + | 1.58563i | −1.01437 | + | 0.423778i | ||||
\(15\) | −0.291474 | + | 0.504848i | −0.0752584 | + | 0.130351i | ||||
\(16\) | 2.33009 | + | 4.03583i | 0.582521 | + | 1.00896i | ||||
\(17\) | 0.453151 | − | 0.784881i | 0.109905 | − | 0.190362i | −0.805826 | − | 0.592152i | \(-0.798279\pi\) |
0.915732 | + | 0.401790i | \(0.131612\pi\) | |||||||
\(18\) | 2.14596 | + | 3.71691i | 0.505808 | + | 0.876084i | ||||
\(19\) | 6.69028 | 1.53486 | 0.767428 | − | 0.641135i | \(-0.221536\pi\) | ||||
0.767428 | + | 0.641135i | \(0.221536\pi\) | |||||||
\(20\) | 0.248461 | + | 0.430346i | 0.0555575 | + | 0.0962284i | ||||
\(21\) | −0.165059 | + | 1.28387i | −0.0360189 | + | 0.280164i | ||||
\(22\) | −1.64497 | − | 2.84917i | −0.350708 | − | 0.607444i | ||||
\(23\) | −1.79866 | − | 3.11538i | −0.375048 | − | 0.649601i | 0.615287 | − | 0.788303i | \(-0.289040\pi\) |
−0.990334 | + | 0.138702i | \(0.955707\pi\) | |||||||
\(24\) | 1.20404 | 0.245774 | ||||||||
\(25\) | 1.79015 | + | 3.10063i | 0.358030 | + | 0.620126i | ||||
\(26\) | 0.729501 | − | 5.55783i | 0.143067 | − | 1.08998i | ||||
\(27\) | 2.81840 | 0.542401 | ||||||||
\(28\) | 0.877433 | + | 0.669054i | 0.165819 | + | 0.126439i | ||||
\(29\) | −4.25772 | + | 7.37459i | −0.790639 | + | 1.36943i | 0.134932 | + | 0.990855i | \(0.456918\pi\) |
−0.925572 | + | 0.378573i | \(0.876415\pi\) | |||||||
\(30\) | 0.906303 | 0.165467 | ||||||||
\(31\) | 2.64390 | + | 4.57937i | 0.474859 | + | 0.822479i | 0.999585 | − | 0.0287913i | \(-0.00916583\pi\) |
−0.524727 | + | 0.851271i | \(0.675832\pi\) | |||||||
\(32\) | 1.16156 | − | 2.01189i | 0.205337 | − | 0.355655i | ||||
\(33\) | −1.03532 | −0.180227 | ||||||||
\(34\) | −1.40902 | −0.241644 | ||||||||
\(35\) | −2.50682 | − | 1.91148i | −0.423730 | − | 0.323099i | ||||
\(36\) | 0.575663 | − | 0.997077i | 0.0959438 | − | 0.166180i | ||||
\(37\) | −2.49579 | − | 4.32284i | −0.410306 | − | 0.710670i | 0.584617 | − | 0.811309i | \(-0.301245\pi\) |
−0.994923 | + | 0.100639i | \(0.967911\pi\) | |||||||
\(38\) | −5.20065 | − | 9.00778i | −0.843656 | − | 1.46126i | ||||
\(39\) | −1.39991 | − | 1.07332i | −0.224165 | − | 0.171869i | ||||
\(40\) | −1.46615 | + | 2.53944i | −0.231818 | + | 0.401521i | ||||
\(41\) | −0.768181 | + | 1.33053i | −0.119970 | + | 0.207794i | −0.919755 | − | 0.392492i | \(-0.871613\pi\) |
0.799786 | + | 0.600286i | \(0.204946\pi\) | |||||||
\(42\) | 1.85691 | − | 0.775773i | 0.286527 | − | 0.119704i | ||||
\(43\) | −2.71636 | − | 4.70488i | −0.414242 | − | 0.717488i | 0.581107 | − | 0.813827i | \(-0.302620\pi\) |
−0.995349 | + | 0.0963397i | \(0.969286\pi\) | |||||||
\(44\) | −0.441269 | + | 0.764301i | −0.0665238 | + | 0.115223i | ||||
\(45\) | −1.64466 | + | 2.84864i | −0.245172 | + | 0.424650i | ||||
\(46\) | −2.79636 | + | 4.84344i | −0.412301 | + | 0.714126i | ||||
\(47\) | 1.59337 | − | 2.75979i | 0.232416 | − | 0.402557i | −0.726102 | − | 0.687587i | \(-0.758670\pi\) |
0.958519 | + | 0.285030i | \(0.0920035\pi\) | |||||||
\(48\) | −1.14000 | − | 1.97453i | −0.164545 | − | 0.284999i | ||||
\(49\) | −6.77236 | − | 1.77063i | −0.967480 | − | 0.252947i | ||||
\(50\) | 2.78312 | − | 4.82051i | 0.393593 | − | 0.681723i | ||||
\(51\) | −0.221705 | + | 0.384004i | −0.0310449 | + | 0.0537714i | ||||
\(52\) | −1.38901 | + | 0.575982i | −0.192621 | + | 0.0798743i | ||||
\(53\) | 1.41239 | + | 2.44632i | 0.194006 | + | 0.336029i | 0.946574 | − | 0.322486i | \(-0.104518\pi\) |
−0.752568 | + | 0.658514i | \(0.771185\pi\) | |||||||
\(54\) | −2.19086 | − | 3.79469i | −0.298139 | − | 0.516391i | ||||
\(55\) | 1.26070 | − | 2.18360i | 0.169993 | − | 0.294436i | ||||
\(56\) | −0.830268 | + | 6.45801i | −0.110949 | + | 0.862988i | ||||
\(57\) | −3.27323 | −0.433550 | ||||||||
\(58\) | 13.2389 | 1.73835 | ||||||||
\(59\) | 5.12298 | − | 8.87327i | 0.666956 | − | 1.15520i | −0.311795 | − | 0.950149i | \(-0.600930\pi\) |
0.978751 | − | 0.205052i | \(-0.0657363\pi\) | |||||||
\(60\) | −0.121560 | − | 0.210548i | −0.0156933 | − | 0.0271816i | ||||
\(61\) | −8.26845 | −1.05867 | −0.529333 | − | 0.848414i | \(-0.677558\pi\) | ||||
−0.529333 | + | 0.848414i | \(0.677558\pi\) | |||||||
\(62\) | 4.11044 | − | 7.11949i | 0.522026 | − | 0.904176i | ||||
\(63\) | −0.931359 | + | 7.24432i | −0.117340 | + | 0.912699i | ||||
\(64\) | 5.70861 | 0.713576 | ||||||||
\(65\) | 3.96840 | − | 1.64557i | 0.492219 | − | 0.204108i | ||||
\(66\) | 0.804802 | + | 1.39396i | 0.0990643 | + | 0.171584i | ||||
\(67\) | −3.74363 | −0.457358 | −0.228679 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228679 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(68\) | 0.188987 | + | 0.327336i | 0.0229181 | + | 0.0396953i | ||||
\(69\) | 0.880000 | + | 1.52420i | 0.105939 | + | 0.183493i | ||||
\(70\) | −0.624956 | + | 4.86105i | −0.0746965 | + | 0.581007i | ||||
\(71\) | 1.26510 | + | 2.19122i | 0.150140 | + | 0.260050i | 0.931279 | − | 0.364307i | \(-0.118694\pi\) |
−0.781139 | + | 0.624357i | \(0.785361\pi\) | |||||||
\(72\) | 6.79389 | 0.800668 | ||||||||
\(73\) | 2.86522 | + | 4.96271i | 0.335349 | + | 0.580841i | 0.983552 | − | 0.180627i | \(-0.0578125\pi\) |
−0.648203 | + | 0.761468i | \(0.724479\pi\) | |||||||
\(74\) | −3.88018 | + | 6.72066i | −0.451061 | + | 0.781261i | ||||
\(75\) | −0.875834 | − | 1.51699i | −0.101133 | − | 0.175167i | ||||
\(76\) | −1.39510 | + | 2.41638i | −0.160028 | + | 0.277177i | ||||
\(77\) | 0.713925 | − | 5.55307i | 0.0813593 | − | 0.632831i | ||||
\(78\) | −0.356910 | + | 2.71918i | −0.0404121 | + | 0.307886i | ||||
\(79\) | −3.03620 | + | 5.25885i | −0.341599 | + | 0.591667i | −0.984730 | − | 0.174089i | \(-0.944302\pi\) |
0.643131 | + | 0.765756i | \(0.277635\pi\) | |||||||
\(80\) | 5.55265 | 0.620805 | ||||||||
\(81\) | 6.90299 | 0.766999 | ||||||||
\(82\) | 2.38856 | 0.263773 | ||||||||
\(83\) | −11.6309 | −1.27665 | −0.638327 | − | 0.769766i | \(-0.720373\pi\) | ||||
−0.638327 | + | 0.769766i | \(0.720373\pi\) | |||||||
\(84\) | −0.429286 | − | 0.327336i | −0.0468389 | − | 0.0357153i | ||||
\(85\) | −0.539935 | − | 0.935195i | −0.0585642 | − | 0.101436i | ||||
\(86\) | −4.22310 | + | 7.31462i | −0.455388 | + | 0.788755i | ||||
\(87\) | 2.08310 | − | 3.60803i | 0.223331 | − | 0.386821i | ||||
\(88\) | −5.20780 | −0.555153 | ||||||||
\(89\) | 8.87557 | + | 15.3729i | 0.940808 | + | 1.62953i | 0.763934 | + | 0.645295i | \(0.223265\pi\) |
0.176875 | + | 0.984233i | \(0.443401\pi\) | |||||||
\(90\) | 5.11387 | 0.539049 | ||||||||
\(91\) | 6.72222 | − | 6.76844i | 0.704680 | − | 0.709525i | ||||
\(92\) | 1.50027 | 0.156414 | ||||||||
\(93\) | −1.29353 | − | 2.24046i | −0.134133 | − | 0.232325i | ||||
\(94\) | −4.95437 | −0.511004 | ||||||||
\(95\) | 3.98577 | − | 6.90356i | 0.408932 | − | 0.708291i | ||||
\(96\) | −0.568297 | + | 0.984319i | −0.0580015 | + | 0.100462i | ||||
\(97\) | −3.10217 | − | 5.37312i | −0.314978 | − | 0.545557i | 0.664455 | − | 0.747328i | \(-0.268664\pi\) |
−0.979433 | + | 0.201771i | \(0.935330\pi\) | |||||||
\(98\) | 2.88048 | + | 10.4947i | 0.290972 | + | 1.06012i | ||||
\(99\) | −5.84188 | −0.587131 | ||||||||
\(100\) | −1.49317 | −0.149317 | ||||||||
\(101\) | −7.22266 | −0.718682 | −0.359341 | − | 0.933206i | \(-0.616999\pi\) | ||||
−0.359341 | + | 0.933206i | \(0.616999\pi\) | |||||||
\(102\) | 0.689364 | 0.0682572 | ||||||||
\(103\) | −4.96322 | + | 8.59656i | −0.489041 | + | 0.847044i | −0.999921 | − | 0.0126084i | \(-0.995987\pi\) |
0.510879 | + | 0.859652i | \(0.329320\pi\) | |||||||
\(104\) | −7.04170 | − | 5.39894i | −0.690496 | − | 0.529409i | ||||
\(105\) | 1.22646 | + | 0.935195i | 0.119691 | + | 0.0912657i | ||||
\(106\) | 2.19582 | − | 3.80327i | 0.213277 | − | 0.369406i | ||||
\(107\) | 1.10003 | + | 1.90531i | 0.106344 | + | 0.184193i | 0.914287 | − | 0.405068i | \(-0.132752\pi\) |
−0.807942 | + | 0.589261i | \(0.799419\pi\) | |||||||
\(108\) | −0.587708 | + | 1.01794i | −0.0565523 | + | 0.0979514i | ||||
\(109\) | −6.87291 | − | 11.9042i | −0.658305 | − | 1.14022i | −0.981054 | − | 0.193734i | \(-0.937940\pi\) |
0.322749 | − | 0.946485i | \(-0.395393\pi\) | |||||||
\(110\) | −3.91999 | −0.373757 | ||||||||
\(111\) | 1.22107 | + | 2.11496i | 0.115899 | + | 0.200743i | ||||
\(112\) | 11.3767 | − | 4.75293i | 1.07500 | − | 0.449110i | ||||
\(113\) | 8.04736 | + | 13.9384i | 0.757032 | + | 1.31122i | 0.944358 | + | 0.328920i | \(0.106685\pi\) |
−0.187326 | + | 0.982298i | \(0.559982\pi\) | |||||||
\(114\) | 2.54442 | + | 4.40707i | 0.238307 | + | 0.412760i | ||||
\(115\) | −4.28626 | −0.399696 | ||||||||
\(116\) | −1.77569 | − | 3.07558i | −0.164869 | − | 0.285561i | ||||
\(117\) | −7.89908 | − | 6.05630i | −0.730270 | − | 0.559905i | ||||
\(118\) | −15.9293 | −1.46641 | ||||||||
\(119\) | −1.90677 | − | 1.45394i | −0.174793 | − | 0.133282i | ||||
\(120\) | 0.717315 | − | 1.24243i | 0.0654816 | − | 0.113418i | ||||
\(121\) | −6.52196 | −0.592905 | ||||||||
\(122\) | 6.42743 | + | 11.1326i | 0.581912 | + | 1.00790i | ||||
\(123\) | 0.375834 | − | 0.650963i | 0.0338878 | − | 0.0586954i | ||||
\(124\) | −2.20528 | −0.198040 | ||||||||
\(125\) | 10.2235 | 0.914420 | ||||||||
\(126\) | 10.4777 | − | 4.37735i | 0.933430 | − | 0.389965i | ||||
\(127\) | 7.83921 | − | 13.5779i | 0.695617 | − | 1.20484i | −0.274355 | − | 0.961628i | \(-0.588464\pi\) |
0.969972 | − | 0.243216i | \(-0.0782023\pi\) | |||||||
\(128\) | −6.76067 | − | 11.7098i | −0.597565 | − | 1.03501i | ||||
\(129\) | 1.32899 | + | 2.30187i | 0.117011 | + | 0.202668i | ||||
\(130\) | −5.30041 | − | 4.06387i | −0.464876 | − | 0.356425i | ||||
\(131\) | 4.76884 | − | 8.25988i | 0.416656 | − | 0.721669i | −0.578945 | − | 0.815367i | \(-0.696535\pi\) |
0.995601 | + | 0.0936976i | \(0.0298687\pi\) | |||||||
\(132\) | 0.215892 | − | 0.373935i | 0.0187910 | − | 0.0325469i | ||||
\(133\) | 2.25711 | − | 17.5563i | 0.195716 | − | 1.52233i | ||||
\(134\) | 2.91009 | + | 5.04042i | 0.251393 | + | 0.435426i | ||||
\(135\) | 1.67908 | − | 2.90825i | 0.144512 | − | 0.250302i | ||||
\(136\) | −1.11520 | + | 1.93158i | −0.0956277 | + | 0.165632i | ||||
\(137\) | 1.38231 | − | 2.39422i | 0.118098 | − | 0.204552i | −0.800916 | − | 0.598777i | \(-0.795654\pi\) |
0.919014 | + | 0.394225i | \(0.128987\pi\) | |||||||
\(138\) | 1.36812 | − | 2.36966i | 0.116462 | − | 0.201719i | ||||
\(139\) | 11.3983 | + | 19.7425i | 0.966795 | + | 1.67454i | 0.704714 | + | 0.709492i | \(0.251075\pi\) |
0.262081 | + | 0.965046i | \(0.415591\pi\) | |||||||
\(140\) | 1.21312 | − | 0.506812i | 0.102527 | − | 0.0428335i | ||||
\(141\) | −0.779557 | + | 1.35023i | −0.0656505 | + | 0.113710i | ||||
\(142\) | 1.96684 | − | 3.40666i | 0.165053 | − | 0.285881i | ||||
\(143\) | 6.05497 | + | 4.64240i | 0.506342 | + | 0.388217i | ||||
\(144\) | −6.43251 | − | 11.1414i | −0.536043 | − | 0.928453i | ||||
\(145\) | 5.07312 | + | 8.78691i | 0.421300 | + | 0.729713i | ||||
\(146\) | 4.45452 | − | 7.71546i | 0.368659 | − | 0.638536i | ||||
\(147\) | 3.31339 | + | 0.866283i | 0.273284 | + | 0.0714498i | ||||
\(148\) | 2.08175 | 0.171119 | ||||||||
\(149\) | −14.4116 | −1.18065 | −0.590323 | − | 0.807167i | \(-0.701000\pi\) | ||||
−0.590323 | + | 0.807167i | \(0.701000\pi\) | |||||||
\(150\) | −1.36165 | + | 2.35844i | −0.111178 | + | 0.192566i | ||||
\(151\) | −7.62901 | − | 13.2138i | −0.620840 | − | 1.07533i | −0.989330 | − | 0.145695i | \(-0.953458\pi\) |
0.368489 | − | 0.929632i | \(-0.379875\pi\) | |||||||
\(152\) | −16.4647 | −1.33546 | ||||||||
\(153\) | −1.25098 | + | 2.16677i | −0.101136 | + | 0.175173i | ||||
\(154\) | −8.03161 | + | 3.35542i | −0.647206 | + | 0.270387i | ||||
\(155\) | 6.30048 | 0.506067 | ||||||||
\(156\) | 0.679577 | − | 0.281800i | 0.0544097 | − | 0.0225621i | ||||
\(157\) | 5.70745 | + | 9.88559i | 0.455504 | + | 0.788956i | 0.998717 | − | 0.0506387i | \(-0.0161257\pi\) |
−0.543213 | + | 0.839595i | \(0.682792\pi\) | |||||||
\(158\) | 9.44068 | 0.751060 | ||||||||
\(159\) | −0.691012 | − | 1.19687i | −0.0548008 | − | 0.0949178i | ||||
\(160\) | −1.38402 | − | 2.39719i | −0.109416 | − | 0.189514i | ||||
\(161\) | −8.78205 | + | 3.66893i | −0.692122 | + | 0.289152i | ||||
\(162\) | −5.36600 | − | 9.29418i | −0.421592 | − | 0.730220i | ||||
\(163\) | −14.4077 | −1.12850 | −0.564249 | − | 0.825605i | \(-0.690834\pi\) | ||||
−0.564249 | + | 0.825605i | \(0.690834\pi\) | |||||||
\(164\) | −0.320371 | − | 0.554899i | −0.0250168 | − | 0.0433303i | ||||
\(165\) | −0.616800 | + | 1.06833i | −0.0480178 | + | 0.0831693i | ||||
\(166\) | 9.04118 | + | 15.6598i | 0.701731 | + | 1.21543i | ||||
\(167\) | −3.88595 | + | 6.73066i | −0.300704 | + | 0.520834i | −0.976296 | − | 0.216442i | \(-0.930555\pi\) |
0.675592 | + | 0.737276i | \(0.263888\pi\) | |||||||
\(168\) | 0.406210 | − | 3.15959i | 0.0313398 | − | 0.243768i | ||||
\(169\) | 3.37442 | + | 12.5544i | 0.259571 | + | 0.965724i | ||||
\(170\) | −0.839430 | + | 1.45394i | −0.0643813 | + | 0.111512i | ||||
\(171\) | −18.4694 | −1.41239 | ||||||||
\(172\) | 2.26573 | 0.172760 | ||||||||
\(173\) | 6.09461 | 0.463365 | 0.231682 | − | 0.972791i | \(-0.425577\pi\) | ||||
0.231682 | + | 0.972791i | \(0.425577\pi\) | |||||||
\(174\) | −6.47713 | −0.491030 | ||||||||
\(175\) | 8.74048 | − | 3.65156i | 0.660718 | − | 0.276032i | ||||
\(176\) | 4.93078 | + | 8.54037i | 0.371672 | + | 0.643754i | ||||
\(177\) | −2.50643 | + | 4.34126i | −0.188395 | + | 0.326309i | ||||
\(178\) | 13.7987 | − | 23.9001i | 1.03426 | − | 1.79139i | ||||
\(179\) | 18.5298 | 1.38498 | 0.692490 | − | 0.721428i | \(-0.256514\pi\) | ||||
0.692490 | + | 0.721428i | \(0.256514\pi\) | |||||||
\(180\) | −0.685909 | − | 1.18803i | −0.0511246 | − | 0.0885504i | ||||
\(181\) | −5.60520 | −0.416631 | −0.208316 | − | 0.978062i | \(-0.566798\pi\) | ||||
−0.208316 | + | 0.978062i | \(0.566798\pi\) | |||||||
\(182\) | −14.3385 | − | 3.78938i | −1.06284 | − | 0.280887i | ||||
\(183\) | 4.04535 | 0.299041 | ||||||||
\(184\) | 4.42650 | + | 7.66692i | 0.326326 | + | 0.565212i | ||||
\(185\) | −5.94753 | −0.437271 | ||||||||
\(186\) | −2.01104 | + | 3.48322i | −0.147456 | + | 0.255402i | ||||
\(187\) | 0.958931 | − | 1.66092i | 0.0701240 | − | 0.121458i | ||||
\(188\) | 0.664516 | + | 1.15097i | 0.0484648 | + | 0.0839435i | ||||
\(189\) | 0.950847 | − | 7.39591i | 0.0691640 | − | 0.537973i | ||||
\(190\) | −12.3933 | −0.899102 | ||||||||
\(191\) | 0.503703 | 0.0364466 | 0.0182233 | − | 0.999834i | \(-0.494199\pi\) | ||||
0.0182233 | + | 0.999834i | \(0.494199\pi\) | |||||||
\(192\) | −2.79294 | −0.201563 | ||||||||
\(193\) | −3.71244 | −0.267227 | −0.133614 | − | 0.991033i | \(-0.542658\pi\) | ||||
−0.133614 | + | 0.991033i | \(0.542658\pi\) | |||||||
\(194\) | −4.82290 | + | 8.35351i | −0.346264 | + | 0.599747i | ||||
\(195\) | −1.94154 | + | 0.805100i | −0.139037 | + | 0.0576544i | ||||
\(196\) | 2.05172 | − | 2.07680i | 0.146552 | − | 0.148343i | ||||
\(197\) | 3.72225 | − | 6.44713i | 0.265200 | − | 0.459339i | −0.702416 | − | 0.711766i | \(-0.747895\pi\) |
0.967616 | + | 0.252427i | \(0.0812288\pi\) | |||||||
\(198\) | 4.54115 | + | 7.86550i | 0.322725 | + | 0.558977i | ||||
\(199\) | −3.75278 | + | 6.50001i | −0.266028 | + | 0.460773i | −0.967832 | − | 0.251596i | \(-0.919045\pi\) |
0.701805 | + | 0.712369i | \(0.252378\pi\) | |||||||
\(200\) | −4.40554 | − | 7.63062i | −0.311519 | − | 0.539566i | ||||
\(201\) | 1.83158 | 0.129190 | ||||||||
\(202\) | 5.61449 | + | 9.72458i | 0.395034 | + | 0.684219i | ||||
\(203\) | 17.9156 | + | 13.6609i | 1.25743 | + | 0.958807i | ||||
\(204\) | −0.0924624 | − | 0.160149i | −0.00647366 | − | 0.0112127i | ||||
\(205\) | 0.915297 | + | 1.58534i | 0.0639271 | + | 0.110725i | ||||
\(206\) | 15.4325 | 1.07523 | ||||||||
\(207\) | 4.96545 | + | 8.60042i | 0.345123 | + | 0.597770i | ||||
\(208\) | −2.18668 | + | 16.6596i | −0.151619 | + | 1.15513i | ||||
\(209\) | 14.1576 | 0.979299 | ||||||||
\(210\) | 0.305761 | − | 2.37828i | 0.0210995 | − | 0.164117i | ||||
\(211\) | −1.89531 | + | 3.28278i | −0.130479 | + | 0.225996i | −0.923861 | − | 0.382728i | \(-0.874985\pi\) |
0.793383 | + | 0.608723i | \(0.208318\pi\) | |||||||
\(212\) | −1.17807 | −0.0809105 | ||||||||
\(213\) | −0.618953 | − | 1.07206i | −0.0424100 | − | 0.0734562i | ||||
\(214\) | 1.71020 | − | 2.96216i | 0.116907 | − | 0.202489i | ||||
\(215\) | −6.47316 | −0.441466 | ||||||||
\(216\) | −6.93605 | −0.471938 | ||||||||
\(217\) | 12.9089 | − | 5.39305i | 0.876317 | − | 0.366104i | ||||
\(218\) | −10.6852 | + | 18.5073i | −0.723695 | + | 1.25348i | ||||
\(219\) | −1.40181 | − | 2.42801i | −0.0947258 | − | 0.164070i | ||||
\(220\) | 0.525777 | + | 0.910673i | 0.0354479 | + | 0.0613975i | ||||
\(221\) | 3.01849 | − | 1.25168i | 0.203046 | − | 0.0841970i | ||||
\(222\) | 1.89838 | − | 3.28809i | 0.127411 | − | 0.220682i | ||||
\(223\) | −2.43440 | + | 4.21650i | −0.163019 | + | 0.282358i | −0.935950 | − | 0.352133i | \(-0.885457\pi\) |
0.772931 | + | 0.634490i | \(0.218790\pi\) | |||||||
\(224\) | −4.88762 | − | 3.72687i | −0.326568 | − | 0.249012i | ||||
\(225\) | −4.94195 | − | 8.55971i | −0.329463 | − | 0.570647i | ||||
\(226\) | 12.5111 | − | 21.6699i | 0.832228 | − | 1.44146i | ||||
\(227\) | −12.0884 | + | 20.9376i | −0.802332 | + | 1.38968i | 0.115745 | + | 0.993279i | \(0.463075\pi\) |
−0.918077 | + | 0.396402i | \(0.870259\pi\) | |||||||
\(228\) | 0.682552 | − | 1.18222i | 0.0452031 | − | 0.0782941i | ||||
\(229\) | 10.8561 | − | 18.8034i | 0.717394 | − | 1.24256i | −0.244635 | − | 0.969615i | \(-0.578668\pi\) |
0.962029 | − | 0.272947i | \(-0.0879985\pi\) | |||||||
\(230\) | 3.33190 | + | 5.77101i | 0.219699 | + | 0.380529i | ||||
\(231\) | −0.349289 | + | 2.71685i | −0.0229815 | + | 0.178756i | ||||
\(232\) | 10.4782 | − | 18.1488i | 0.687928 | − | 1.19153i | ||||
\(233\) | −1.89842 | + | 3.28816i | −0.124370 | + | 0.215414i | −0.921486 | − | 0.388411i | \(-0.873024\pi\) |
0.797117 | + | 0.603825i | \(0.206358\pi\) | |||||||
\(234\) | −2.01389 | + | 15.3431i | −0.131652 | + | 1.00301i | ||||
\(235\) | −1.89851 | − | 3.28832i | −0.123845 | − | 0.214507i | ||||
\(236\) | 2.13655 | + | 3.70061i | 0.139077 | + | 0.240889i | ||||
\(237\) | 1.48547 | − | 2.57290i | 0.0964914 | − | 0.167128i | ||||
\(238\) | −0.475362 | + | 3.69748i | −0.0308131 | + | 0.239672i | ||||
\(239\) | 21.9100 | 1.41724 | 0.708619 | − | 0.705592i | \(-0.249319\pi\) | ||||
0.708619 | + | 0.705592i | \(0.249319\pi\) | |||||||
\(240\) | −2.71664 | −0.175358 | ||||||||
\(241\) | 10.3744 | − | 17.9690i | 0.668273 | − | 1.15748i | −0.310114 | − | 0.950699i | \(-0.600367\pi\) |
0.978387 | − | 0.206783i | \(-0.0662994\pi\) | |||||||
\(242\) | 5.06980 | + | 8.78115i | 0.325899 | + | 0.564474i | ||||
\(243\) | −11.8325 | −0.759055 | ||||||||
\(244\) | 1.72418 | − | 2.98637i | 0.110380 | − | 0.191183i | ||||
\(245\) | −5.86175 | + | 5.93340i | −0.374493 | + | 0.379071i | ||||
\(246\) | −1.16861 | −0.0745077 | ||||||||
\(247\) | 19.1431 | + | 14.6772i | 1.21805 | + | 0.933887i | ||||
\(248\) | −6.50661 | − | 11.2698i | −0.413170 | − | 0.715632i | ||||
\(249\) | 5.69042 | 0.360616 | ||||||||
\(250\) | −7.94719 | − | 13.7649i | −0.502624 | − | 0.870571i | ||||
\(251\) | −6.62891 | − | 11.4816i | −0.418413 | − | 0.724713i | 0.577367 | − | 0.816485i | \(-0.304080\pi\) |
−0.995780 | + | 0.0917718i | \(0.970747\pi\) | |||||||
\(252\) | −2.42227 | − | 1.84701i | −0.152589 | − | 0.116351i | ||||
\(253\) | −3.80622 | − | 6.59257i | −0.239295 | − | 0.414472i | ||||
\(254\) | −24.3750 | −1.52943 | ||||||||
\(255\) | 0.264164 | + | 0.457546i | 0.0165426 | + | 0.0286526i | ||||
\(256\) | −4.80213 | + | 8.31753i | −0.300133 | + | 0.519845i | ||||
\(257\) | 6.58555 | + | 11.4065i | 0.410795 | + | 0.711518i | 0.994977 | − | 0.100105i | \(-0.0319178\pi\) |
−0.584182 | + | 0.811623i | \(0.698584\pi\) | |||||||
\(258\) | 2.06616 | − | 3.57869i | 0.128633 | − | 0.222799i | ||||
\(259\) | −12.1858 | + | 5.09094i | −0.757189 | + | 0.316336i | ||||
\(260\) | −0.233169 | + | 1.77644i | −0.0144605 | + | 0.110170i | ||||
\(261\) | 11.7540 | − | 20.3585i | 0.727555 | − | 1.26016i | ||||
\(262\) | −14.8281 | −0.916084 | ||||||||
\(263\) | −19.1406 | −1.18026 | −0.590129 | − | 0.807309i | \(-0.700923\pi\) | ||||
−0.590129 | + | 0.807309i | \(0.700923\pi\) | |||||||
\(264\) | 2.54792 | 0.156814 | ||||||||
\(265\) | 3.36575 | 0.206756 | ||||||||
\(266\) | −25.3924 | + | 10.6083i | −1.55691 | + | 0.650438i | ||||
\(267\) | −4.34239 | − | 7.52123i | −0.265750 | − | 0.460292i | ||||
\(268\) | 0.780643 | − | 1.35211i | 0.0476854 | − | 0.0825935i | ||||
\(269\) | 14.2411 | − | 24.6663i | 0.868296 | − | 1.50393i | 0.00455867 | − | 0.999990i | \(-0.498549\pi\) |
0.863737 | − | 0.503943i | \(-0.168118\pi\) | |||||||
\(270\) | −5.22088 | −0.317732 | ||||||||
\(271\) | −8.97371 | − | 15.5429i | −0.545114 | − | 0.944165i | −0.998600 | − | 0.0529014i | \(-0.983153\pi\) |
0.453486 | − | 0.891263i | \(-0.350180\pi\) | |||||||
\(272\) | 4.22353 | 0.256089 | ||||||||
\(273\) | −3.28885 | + | 3.31147i | −0.199051 | + | 0.200419i | ||||
\(274\) | −4.29811 | −0.259658 | ||||||||
\(275\) | 3.78821 | + | 6.56137i | 0.228437 | + | 0.395665i | ||||
\(276\) | −0.734010 | −0.0441822 | ||||||||
\(277\) | −6.71943 | + | 11.6384i | −0.403732 | + | 0.699284i | −0.994173 | − | 0.107797i | \(-0.965620\pi\) |
0.590441 | + | 0.807081i | \(0.298954\pi\) | |||||||
\(278\) | 17.7209 | − | 30.6934i | 1.06283 | − | 1.84087i | ||||
\(279\) | −7.29884 | − | 12.6420i | −0.436970 | − | 0.756855i | ||||
\(280\) | 6.16925 | + | 4.70413i | 0.368683 | + | 0.281126i | ||||
\(281\) | −29.9530 | −1.78685 | −0.893424 | − | 0.449214i | \(-0.851704\pi\) | ||||
−0.893424 | + | 0.449214i | \(0.851704\pi\) | |||||||
\(282\) | 2.42393 | 0.144343 | ||||||||
\(283\) | −9.89122 | −0.587972 | −0.293986 | − | 0.955810i | \(-0.594982\pi\) | ||||
−0.293986 | + | 0.955810i | \(0.594982\pi\) | |||||||
\(284\) | −1.05523 | −0.0626161 | ||||||||
\(285\) | −1.95005 | + | 3.37758i | −0.115511 | + | 0.200070i | ||||
\(286\) | 1.54373 | − | 11.7611i | 0.0912824 | − | 0.695451i | ||||
\(287\) | 3.23235 | + | 2.46471i | 0.190800 | + | 0.145487i | ||||
\(288\) | −3.20665 | + | 5.55408i | −0.188954 | + | 0.327277i | ||||
\(289\) | 8.08931 | + | 14.0111i | 0.475842 | + | 0.824182i | ||||
\(290\) | 7.88712 | − | 13.6609i | 0.463148 | − | 0.802195i | ||||
\(291\) | 1.51774 | + | 2.62881i | 0.0889716 | + | 0.154103i | ||||
\(292\) | −2.38989 | −0.139858 | ||||||||
\(293\) | −3.95529 | − | 6.85076i | −0.231071 | − | 0.400226i | 0.727053 | − | 0.686581i | \(-0.240889\pi\) |
−0.958123 | + | 0.286356i | \(0.907556\pi\) | |||||||
\(294\) | −1.40928 | − | 5.13454i | −0.0821908 | − | 0.299452i | ||||
\(295\) | −6.10409 | − | 10.5726i | −0.355394 | − | 0.615561i | ||||
\(296\) | 6.14212 | + | 10.6385i | 0.357003 | + | 0.618348i | ||||
\(297\) | 5.96412 | 0.346073 | ||||||||
\(298\) | 11.2028 | + | 19.4038i | 0.648959 | + | 1.12403i | ||||
\(299\) | 1.68797 | − | 12.8601i | 0.0976175 | − | 0.743716i | ||||
\(300\) | 0.730535 | 0.0421775 | ||||||||
\(301\) | −13.2628 | + | 5.54086i | −0.764452 | + | 0.319370i | ||||
\(302\) | −11.8607 | + | 20.5434i | −0.682508 | + | 1.18214i | ||||
\(303\) | 3.53370 | 0.203006 | ||||||||
\(304\) | 15.5889 | + | 27.0008i | 0.894086 | + | 1.54860i | ||||
\(305\) | −4.92598 | + | 8.53204i | −0.282061 | + | 0.488543i | ||||
\(306\) | 3.88978 | 0.222364 | ||||||||
\(307\) | 1.27238 | 0.0726187 | 0.0363094 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363094 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(308\) | 1.85677 | + | 1.41581i | 0.105799 | + | 0.0806733i | ||||
\(309\) | 2.42827 | − | 4.20588i | 0.138139 | − | 0.239264i | ||||
\(310\) | −4.89763 | − | 8.48295i | −0.278167 | − | 0.481799i | ||||
\(311\) | −12.3817 | − | 21.4458i | −0.702103 | − | 1.21608i | −0.967727 | − | 0.252002i | \(-0.918911\pi\) |
0.265624 | − | 0.964077i | \(-0.414422\pi\) | |||||||
\(312\) | 3.44516 | + | 2.64144i | 0.195044 | + | 0.149542i | ||||
\(313\) | −1.18826 | + | 2.05812i | −0.0671642 | + | 0.116332i | −0.897652 | − | 0.440705i | \(-0.854728\pi\) |
0.830488 | + | 0.557037i | \(0.188062\pi\) | |||||||
\(314\) | 8.87330 | − | 15.3690i | 0.500749 | − | 0.867323i | ||||
\(315\) | 6.92040 | + | 5.27690i | 0.389921 | + | 0.297319i | ||||
\(316\) | −1.26625 | − | 2.19321i | −0.0712322 | − | 0.123378i | ||||
\(317\) | 9.88979 | − | 17.1296i | 0.555466 | − | 0.962096i | −0.442401 | − | 0.896817i | \(-0.645873\pi\) |
0.997867 | − | 0.0652782i | \(-0.0207935\pi\) | |||||||
\(318\) | −1.07431 | + | 1.86076i | −0.0602442 | + | 0.104346i | ||||
\(319\) | −9.00993 | + | 15.6057i | −0.504459 | + | 0.873749i | ||||
\(320\) | 3.40093 | − | 5.89059i | 0.190118 | − | 0.329294i | ||||
\(321\) | −0.538192 | − | 0.932176i | −0.0300390 | − | 0.0520290i | ||||
\(322\) | 11.7665 | + | 8.97212i | 0.655722 | + | 0.499997i | ||||
\(323\) | 3.03171 | − | 5.25108i | 0.168689 | − | 0.292178i | ||||
\(324\) | −1.43945 | + | 2.49320i | −0.0799695 | + | 0.138511i | ||||
\(325\) | −1.67997 | + | 12.7992i | −0.0931882 | + | 0.709970i | ||||
\(326\) | 11.1997 | + | 19.3985i | 0.620295 | + | 1.07438i | ||||
\(327\) | 3.36258 | + | 5.82416i | 0.185951 | + | 0.322077i | ||||
\(328\) | 1.89049 | − | 3.27442i | 0.104385 | − | 0.180799i | ||||
\(329\) | −6.70456 | − | 5.11231i | −0.369634 | − | 0.281851i | ||||
\(330\) | 1.91786 | 0.105575 | ||||||||
\(331\) | 3.92773 | 0.215888 | 0.107944 | − | 0.994157i | \(-0.465573\pi\) | ||||
0.107944 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(332\) | 2.42533 | − | 4.20080i | 0.133107 | − | 0.230549i | ||||
\(333\) | 6.88997 | + | 11.9338i | 0.377568 | + | 0.653967i | ||||
\(334\) | 12.0829 | 0.661145 | ||||||||
\(335\) | −2.23029 | + | 3.86298i | −0.121854 | + | 0.211057i | ||||
\(336\) | −5.56608 | + | 2.32538i | −0.303655 | + | 0.126860i | ||||
\(337\) | −7.14099 | −0.388995 | −0.194497 | − | 0.980903i | \(-0.562308\pi\) | ||||
−0.194497 | + | 0.980903i | \(0.562308\pi\) | |||||||
\(338\) | 14.2802 | − | 14.3024i | 0.776738 | − | 0.777948i | ||||
\(339\) | −3.93718 | − | 6.81940i | −0.213838 | − | 0.370379i | ||||
\(340\) | 0.450361 | 0.0244243 | ||||||||
\(341\) | 5.59486 | + | 9.69059i | 0.302979 | + | 0.524775i | ||||
\(342\) | 14.3571 | + | 24.8672i | 0.776342 | + | 1.34466i | ||||
\(343\) | −6.93120 | + | 17.1744i | −0.374250 | + | 0.927328i | ||||
\(344\) | 6.68494 | + | 11.5787i | 0.360428 | + | 0.624280i | ||||
\(345\) | 2.09706 | 0.112902 | ||||||||
\(346\) | −4.73761 | − | 8.20578i | −0.254695 | − | 0.441145i | ||||
\(347\) | −5.03498 | + | 8.72085i | −0.270292 | + | 0.468160i | −0.968937 | − | 0.247309i | \(-0.920454\pi\) |
0.698644 | + | 0.715469i | \(0.253787\pi\) | |||||||
\(348\) | 0.868758 | + | 1.50473i | 0.0465703 | + | 0.0806622i | ||||
\(349\) | 3.14418 | − | 5.44588i | 0.168304 | − | 0.291512i | −0.769520 | − | 0.638623i | \(-0.779504\pi\) |
0.937824 | + | 0.347112i | \(0.112838\pi\) | |||||||
\(350\) | −11.7108 | − | 8.92964i | −0.625969 | − | 0.477310i | ||||
\(351\) | 8.06437 | + | 6.18302i | 0.430444 | + | 0.330025i | ||||
\(352\) | 2.45803 | − | 4.25743i | 0.131013 | − | 0.226922i | ||||
\(353\) | 34.1672 | 1.81854 | 0.909269 | − | 0.416210i | \(-0.136642\pi\) | ||||
0.909269 | + | 0.416210i | \(0.136642\pi\) | |||||||
\(354\) | 7.79342 | 0.414216 | ||||||||
\(355\) | 3.01477 | 0.160007 | ||||||||
\(356\) | −7.40313 | −0.392365 | ||||||||
\(357\) | 0.932889 | + | 0.711340i | 0.0493737 | + | 0.0376481i | ||||
\(358\) | −14.4040 | − | 24.9484i | −0.761274 | − | 1.31857i | ||||
\(359\) | −9.34327 | + | 16.1830i | −0.493119 | + | 0.854107i | −0.999969 | − | 0.00792750i | \(-0.997477\pi\) |
0.506850 | + | 0.862034i | \(0.330810\pi\) | |||||||
\(360\) | 4.04750 | − | 7.01047i | 0.213322 | − | 0.369484i | ||||
\(361\) | 25.7599 | 1.35578 | ||||||||
\(362\) | 4.35716 | + | 7.54683i | 0.229007 | + | 0.396653i | ||||
\(363\) | 3.19088 | 0.167478 | ||||||||
\(364\) | 1.04285 | + | 3.83930i | 0.0546602 | + | 0.201234i | ||||
\(365\) | 6.82788 | 0.357388 | ||||||||
\(366\) | −3.14463 | − | 5.44666i | −0.164372 | − | 0.284701i | ||||
\(367\) | −31.0611 | −1.62137 | −0.810687 | − | 0.585479i | \(-0.800906\pi\) | ||||
−0.810687 | + | 0.585479i | \(0.800906\pi\) | |||||||
\(368\) | 8.38209 | − | 14.5182i | 0.436946 | − | 0.756813i | ||||
\(369\) | 2.12067 | − | 3.67310i | 0.110397 | − | 0.191214i | ||||
\(370\) | 4.62327 | + | 8.00775i | 0.240353 | + | 0.416303i | ||||
\(371\) | 6.89603 | − | 2.88100i | 0.358024 | − | 0.149574i | ||||
\(372\) | 1.07894 | 0.0559404 | ||||||||
\(373\) | −2.93704 | −0.152074 | −0.0760371 | − | 0.997105i | \(-0.524227\pi\) | ||||
−0.0760371 | + | 0.997105i | \(0.524227\pi\) | |||||||
\(374\) | −2.98168 | −0.154179 | ||||||||
\(375\) | −5.00188 | −0.258296 | ||||||||
\(376\) | −3.92126 | + | 6.79182i | −0.202223 | + | 0.350261i | ||||
\(377\) | −28.3612 | + | 11.7605i | −1.46068 | + | 0.605698i | ||||
\(378\) | −10.6970 | + | 4.46894i | −0.550193 | + | 0.229858i | ||||
\(379\) | −5.04254 | + | 8.73394i | −0.259018 | + | 0.448632i | −0.965979 | − | 0.258620i | \(-0.916732\pi\) |
0.706961 | + | 0.707252i | \(0.250066\pi\) | |||||||
\(380\) | 1.66227 | + | 2.87914i | 0.0852727 | + | 0.147697i | ||||
\(381\) | −3.83534 | + | 6.64301i | −0.196491 | + | 0.340332i | ||||
\(382\) | −0.391550 | − | 0.678184i | −0.0200334 | − | 0.0346989i | ||||
\(383\) | 3.68931 | 0.188515 | 0.0942576 | − | 0.995548i | \(-0.469952\pi\) | ||||
0.0942576 | + | 0.995548i | \(0.469952\pi\) | |||||||
\(384\) | 3.30767 | + | 5.72905i | 0.168794 | + | 0.292360i | ||||
\(385\) | −5.30477 | − | 4.04496i | −0.270356 | − | 0.206150i | ||||
\(386\) | 2.88584 | + | 4.99842i | 0.146885 | + | 0.254413i | ||||
\(387\) | 7.49888 | + | 12.9884i | 0.381190 | + | 0.660240i | ||||
\(388\) | 2.58753 | 0.131362 | ||||||||
\(389\) | −11.3333 | − | 19.6299i | −0.574623 | − | 0.995277i | −0.996082 | − | 0.0884295i | \(-0.971815\pi\) |
0.421459 | − | 0.906847i | \(-0.361518\pi\) | |||||||
\(390\) | 2.59323 | + | 1.98825i | 0.131313 | + | 0.100679i | ||||
\(391\) | −3.26027 | −0.164879 | ||||||||
\(392\) | 16.6667 | + | 4.35750i | 0.841796 | + | 0.220087i | ||||
\(393\) | −2.33316 | + | 4.04116i | −0.117693 | + | 0.203849i | ||||
\(394\) | −11.5739 | −0.583084 | ||||||||
\(395\) | 3.61767 | + | 6.26598i | 0.182025 | + | 0.315276i | ||||
\(396\) | 1.21818 | − | 2.10995i | 0.0612160 | − | 0.106029i | ||||
\(397\) | −29.1360 | −1.46229 | −0.731146 | − | 0.682221i | \(-0.761014\pi\) | ||||
−0.731146 | + | 0.682221i | \(0.761014\pi\) | |||||||
\(398\) | 11.6688 | 0.584904 | ||||||||
\(399\) | −1.10429 | + | 8.58946i | −0.0552839 | + | 0.430011i | ||||
\(400\) | −8.34241 | + | 14.4495i | −0.417120 | + | 0.722474i | ||||
\(401\) | −4.06026 | − | 7.03258i | −0.202760 | − | 0.351190i | 0.746657 | − | 0.665209i | \(-0.231658\pi\) |
−0.949417 | + | 0.314019i | \(0.898324\pi\) | |||||||
\(402\) | −1.42377 | − | 2.46603i | −0.0710110 | − | 0.122995i | ||||
\(403\) | −2.48118 | + | 18.9033i | −0.123596 | + | 0.941641i | ||||
\(404\) | 1.50611 | − | 2.60866i | 0.0749318 | − | 0.129786i | ||||
\(405\) | 4.11250 | − | 7.12305i | 0.204352 | − | 0.353947i | ||||
\(406\) | 4.46641 | − | 34.7408i | 0.221664 | − | 1.72416i | ||||
\(407\) | −5.28144 | − | 9.14773i | −0.261791 | − | 0.453436i | ||||
\(408\) | 0.545614 | − | 0.945031i | 0.0270119 | − | 0.0467860i | ||||
\(409\) | 4.16131 | − | 7.20759i | 0.205763 | − | 0.356393i | −0.744612 | − | 0.667497i | \(-0.767366\pi\) |
0.950376 | + | 0.311105i | \(0.100699\pi\) | |||||||
\(410\) | 1.42300 | − | 2.46471i | 0.0702769 | − | 0.121723i | ||||
\(411\) | −0.676295 | + | 1.17138i | −0.0333592 | + | 0.0577798i | ||||
\(412\) | −2.06992 | − | 3.58520i | −0.101978 | − | 0.176630i | ||||
\(413\) | −21.5565 | − | 16.4371i | −1.06072 | − | 0.808816i | ||||
\(414\) | 7.71973 | − | 13.3710i | 0.379404 | − | 0.657147i | ||||
\(415\) | −6.92915 | + | 12.0016i | −0.340139 | + | 0.589138i | ||||
\(416\) | 7.73731 | − | 3.20843i | 0.379353 | − | 0.157306i | ||||
\(417\) | −5.57666 | − | 9.65905i | −0.273090 | − | 0.473006i | ||||
\(418\) | −11.0053 | − | 19.0617i | −0.538286 | − | 0.932339i | ||||
\(419\) | 6.50832 | − | 11.2727i | 0.317952 | − | 0.550710i | −0.662108 | − | 0.749408i | \(-0.730338\pi\) |
0.980061 | + | 0.198699i | \(0.0636715\pi\) | |||||||
\(420\) | −0.593520 | + | 0.247959i | −0.0289608 | + | 0.0120991i | ||||
\(421\) | −8.89681 | −0.433604 | −0.216802 | − | 0.976216i | \(-0.569563\pi\) | ||||
−0.216802 | + | 0.976216i | \(0.569563\pi\) | |||||||
\(422\) | 5.89323 | 0.286878 | ||||||||
\(423\) | −4.39870 | + | 7.61877i | −0.213872 | + | 0.370437i | ||||
\(424\) | −3.47587 | − | 6.02038i | −0.168803 | − | 0.292376i | ||||
\(425\) | 3.24484 | 0.157398 | ||||||||
\(426\) | −0.962279 | + | 1.66672i | −0.0466225 | + | 0.0807526i | ||||
\(427\) | −2.78954 | + | 21.6977i | −0.134995 | + | 1.05002i | ||||
\(428\) | −0.917539 | −0.0443509 | ||||||||
\(429\) | −2.96240 | − | 2.27130i | −0.143026 | − | 0.109659i | ||||
\(430\) | 5.03187 | + | 8.71545i | 0.242658 | + | 0.420296i | ||||
\(431\) | −8.95743 | −0.431464 | −0.215732 | − | 0.976453i | \(-0.569214\pi\) | ||||
−0.215732 | + | 0.976453i | \(0.569214\pi\) | |||||||
\(432\) | 6.56711 | + | 11.3746i | 0.315960 | + | 0.547259i | ||||
\(433\) | 0.0864547 | + | 0.149744i | 0.00415475 | + | 0.00719624i | 0.868095 | − | 0.496398i | \(-0.165344\pi\) |
−0.863941 | + | 0.503594i | \(0.832011\pi\) | |||||||
\(434\) | −17.2959 | − | 13.1883i | −0.830229 | − | 0.633060i | ||||
\(435\) | −2.48203 | − | 4.29901i | −0.119004 | − | 0.206122i | ||||
\(436\) | 5.73271 | 0.274547 | ||||||||
\(437\) | −12.0336 | − | 20.8428i | −0.575644 | − | 0.997045i | ||||
\(438\) | −2.17938 | + | 3.77480i | −0.104135 | + | 0.180367i | ||||
\(439\) | −4.77080 | − | 8.26327i | −0.227698 | − | 0.394384i | 0.729428 | − | 0.684058i | \(-0.239787\pi\) |
−0.957125 | + | 0.289674i | \(0.906453\pi\) | |||||||
\(440\) | −3.10257 | + | 5.37382i | −0.147909 | + | 0.256187i | ||||
\(441\) | 18.6960 | + | 4.88806i | 0.890286 | + | 0.232765i | ||||
\(442\) | −4.03166 | − | 3.09111i | −0.191767 | − | 0.147029i | ||||
\(443\) | 6.93676 | − | 12.0148i | 0.329576 | − | 0.570842i | −0.652852 | − | 0.757485i | \(-0.726428\pi\) |
0.982428 | + | 0.186644i | \(0.0597610\pi\) | |||||||
\(444\) | −1.01850 | −0.0483358 | ||||||||
\(445\) | 21.1507 | 1.00264 | ||||||||
\(446\) | 7.56945 | 0.358424 | ||||||||
\(447\) | 7.05091 | 0.333496 | ||||||||
\(448\) | 1.92592 | − | 14.9803i | 0.0909912 | − | 0.707751i | ||||
\(449\) | 10.6456 | + | 18.4388i | 0.502398 | + | 0.870180i | 0.999996 | + | 0.00277167i | \(0.000882252\pi\) |
−0.497598 | + | 0.867408i | \(0.665784\pi\) | |||||||
\(450\) | −7.68318 | + | 13.3077i | −0.362189 | + | 0.627329i | ||||
\(451\) | −1.62558 | + | 2.81558i | −0.0765455 | + | 0.132581i | ||||
\(452\) | −6.71232 | −0.315721 | ||||||||
\(453\) | 3.73251 | + | 6.46489i | 0.175368 | + | 0.303747i | ||||
\(454\) | 37.5872 | 1.76406 | ||||||||
\(455\) | −2.97941 | − | 10.9689i | −0.139677 | − | 0.514228i | ||||
\(456\) | 8.05539 | 0.377228 | ||||||||
\(457\) | −4.84282 | − | 8.38801i | −0.226538 | − | 0.392375i | 0.730242 | − | 0.683189i | \(-0.239407\pi\) |
−0.956780 | + | 0.290814i | \(0.906074\pi\) | |||||||
\(458\) | −33.7558 | −1.57730 | ||||||||
\(459\) | 1.27716 | − | 2.21211i | 0.0596128 | − | 0.103252i | ||||
\(460\) | 0.893795 | − | 1.54810i | 0.0416734 | − | 0.0721804i | ||||
\(461\) | 0.687178 | + | 1.19023i | 0.0320051 | + | 0.0554344i | 0.881584 | − | 0.472027i | \(-0.156477\pi\) |
−0.849579 | + | 0.527461i | \(0.823144\pi\) | |||||||
\(462\) | 3.92948 | − | 1.64164i | 0.182816 | − | 0.0763761i | ||||
\(463\) | 31.7710 | 1.47653 | 0.738263 | − | 0.674513i | \(-0.235646\pi\) | ||||
0.738263 | + | 0.674513i | \(0.235646\pi\) | |||||||
\(464\) | −39.6834 | −1.84226 | ||||||||
\(465\) | −3.08252 | −0.142948 | ||||||||
\(466\) | 5.90290 | 0.273446 | ||||||||
\(467\) | 14.5605 | − | 25.2195i | 0.673778 | − | 1.16702i | −0.303046 | − | 0.952976i | \(-0.598004\pi\) |
0.976824 | − | 0.214042i | \(-0.0686629\pi\) | |||||||
\(468\) | 3.83456 | − | 1.59007i | 0.177252 | − | 0.0735012i | ||||
\(469\) | −1.26299 | + | 9.82387i | −0.0583197 | + | 0.453624i | ||||
\(470\) | −2.95160 | + | 5.11231i | −0.136147 | + | 0.235813i | ||||
\(471\) | −2.79238 | − | 4.83654i | −0.128666 | − | 0.222856i | ||||
\(472\) | −12.6076 | + | 21.8370i | −0.580312 | + | 1.00513i | ||||
\(473\) | −5.74820 | − | 9.95618i | −0.264303 | − | 0.457786i | ||||
\(474\) | −4.61887 | −0.212152 | ||||||||
\(475\) | 11.9766 | + | 20.7441i | 0.549525 | + | 0.951804i | ||||
\(476\) | 0.922738 | − | 0.385498i | 0.0422936 | − | 0.0176693i | ||||
\(477\) | −3.89908 | − | 6.75341i | −0.178527 | − | 0.309217i | ||||
\(478\) | −17.0316 | − | 29.4995i | −0.779005 | − | 1.34928i | ||||
\(479\) | 9.72184 | 0.444202 | 0.222101 | − | 0.975024i | \(-0.428708\pi\) | ||||
0.222101 | + | 0.975024i | \(0.428708\pi\) | |||||||
\(480\) | 0.677132 | + | 1.17283i | 0.0309067 | + | 0.0535320i | ||||
\(481\) | 2.34219 | − | 17.8444i | 0.106795 | − | 0.813633i | ||||
\(482\) | −32.2578 | −1.46930 | ||||||||
\(483\) | 4.29663 | − | 1.79503i | 0.195503 | − | 0.0816767i | ||||
\(484\) | 1.36000 | − | 2.35558i | 0.0618180 | − | 0.107072i | ||||
\(485\) | −7.39254 | −0.335678 | ||||||||
\(486\) | 9.19791 | + | 15.9313i | 0.417226 | + | 0.722656i | ||||
\(487\) | 8.55666 | − | 14.8206i | 0.387739 | − | 0.671584i | −0.604406 | − | 0.796676i | \(-0.706589\pi\) |
0.992145 | + | 0.125093i | \(0.0399228\pi\) | |||||||
\(488\) | 20.3486 | 0.921137 | ||||||||
\(489\) | 7.04899 | 0.318766 | ||||||||
\(490\) | 12.5453 | + | 3.27996i | 0.566739 | + | 0.148174i | ||||
\(491\) | 12.8607 | − | 22.2753i | 0.580394 | − | 1.00527i | −0.415038 | − | 0.909804i | \(-0.636232\pi\) |
0.995432 | − | 0.0954681i | \(-0.0304348\pi\) | |||||||
\(492\) | 0.156742 | + | 0.271485i | 0.00706647 | + | 0.0122395i | ||||
\(493\) | 3.85879 | + | 6.68361i | 0.173791 | + | 0.301015i | ||||
\(494\) | 4.88057 | − | 37.1835i | 0.219587 | − | 1.67296i | ||||
\(495\) | −3.48033 | + | 6.02812i | −0.156429 | + | 0.270944i | ||||
\(496\) | −12.3210 | + | 21.3407i | −0.553231 | + | 0.958224i | ||||
\(497\) | 6.17691 | − | 2.58057i | 0.277072 | − | 0.115754i | ||||
\(498\) | −4.42341 | − | 7.66157i | −0.198218 | − | 0.343323i | ||||
\(499\) | −2.70198 | + | 4.67996i | −0.120957 | + | 0.209504i | −0.920145 | − | 0.391577i | \(-0.871930\pi\) |
0.799188 | + | 0.601081i | \(0.205263\pi\) | |||||||
\(500\) | −2.13187 | + | 3.69250i | −0.0953400 | + | 0.165134i | ||||
\(501\) | 1.90121 | − | 3.29299i | 0.0849396 | − | 0.147120i | ||||
\(502\) | −10.3059 | + | 17.8503i | −0.459974 | + | 0.796699i | ||||
\(503\) | 6.30847 | + | 10.9266i | 0.281281 | + | 0.487193i | 0.971700 | − | 0.236216i | \(-0.0759074\pi\) |
−0.690420 | + | 0.723409i | \(0.742574\pi\) | |||||||
\(504\) | 2.29206 | − | 17.8282i | 0.102097 | − | 0.794131i | ||||
\(505\) | −4.30294 | + | 7.45292i | −0.191478 | + | 0.331650i | ||||
\(506\) | −5.91749 | + | 10.2494i | −0.263064 | + | 0.455641i | ||||
\(507\) | −1.65094 | − | 6.14227i | −0.0733209 | − | 0.272788i | ||||
\(508\) | 3.26935 | + | 5.66268i | 0.145054 | + | 0.251241i | ||||
\(509\) | 0.979379 | + | 1.69633i | 0.0434102 | + | 0.0751887i | 0.886914 | − | 0.461934i | \(-0.152844\pi\) |
−0.843504 | + | 0.537123i | \(0.819511\pi\) | |||||||
\(510\) | 0.410692 | − | 0.711340i | 0.0181858 | − | 0.0314987i | ||||
\(511\) | 13.9895 | − | 5.84450i | 0.618861 | − | 0.258546i | ||||
\(512\) | −12.1111 | −0.535240 | ||||||||
\(513\) | 18.8559 | 0.832507 | ||||||||
\(514\) | 10.2385 | − | 17.7335i | 0.451599 | − | 0.782193i | ||||
\(515\) | 5.91374 | + | 10.2429i | 0.260590 | + | 0.451356i | ||||
\(516\) | −1.10851 | −0.0487994 | ||||||||
\(517\) | 3.37178 | − | 5.84010i | 0.148291 | − | 0.256847i | ||||
\(518\) | 16.3270 | + | 12.4495i | 0.717367 | + | 0.547001i | ||||
\(519\) | −2.98180 | −0.130886 | ||||||||
\(520\) | −9.76618 | + | 4.04974i | −0.428276 | + | 0.177593i | ||||
\(521\) | 19.5477 | + | 33.8576i | 0.856401 | + | 1.48333i | 0.875339 | + | 0.483509i | \(0.160638\pi\) |
−0.0189387 | + | 0.999821i | \(0.506029\pi\) | |||||||
\(522\) | −36.5476 | −1.59965 | ||||||||
\(523\) | 4.35634 | + | 7.54540i | 0.190489 | + | 0.329937i | 0.945413 | − | 0.325876i | \(-0.105659\pi\) |
−0.754923 | + | 0.655813i | \(0.772326\pi\) | |||||||
\(524\) | 1.98885 | + | 3.44479i | 0.0868834 | + | 0.150486i | ||||
\(525\) | −4.27629 | + | 1.78653i | −0.186633 | + | 0.0779707i | ||||
\(526\) | 14.8788 | + | 25.7708i | 0.648746 | + | 1.12366i | ||||
\(527\) | 4.79235 | 0.208758 | ||||||||
\(528\) | −2.41239 | − | 4.17839i | −0.104986 | − | 0.181841i | ||||
\(529\) | 5.02961 | − | 8.71154i | 0.218679 | − | 0.378763i | ||||
\(530\) | −2.61634 | − | 4.53164i | −0.113647 | − | 0.196842i | ||||
\(531\) | −14.1427 | + | 24.4958i | −0.613740 | + | 1.06303i | ||||
\(532\) | 5.87028 | + | 4.47616i | 0.254509 | + | 0.194066i | ||||
\(533\) | −5.11694 | + | 2.12184i | −0.221639 | + | 0.0919072i | ||||
\(534\) | −6.75105 | + | 11.6932i | −0.292147 | + | 0.506013i | ||||
\(535\) | 2.62140 | 0.113333 | ||||||||
\(536\) | 9.21304 | 0.397943 | ||||||||
\(537\) | −9.06571 | −0.391214 | ||||||||
\(538\) | −44.2809 | −1.90909 | ||||||||
\(539\) | −14.3313 | − | 3.74690i | −0.617291 | − | 0.161390i | ||||
\(540\) | 0.700261 | + | 1.21289i | 0.0301344 | + | 0.0521944i | ||||
\(541\) | 10.7497 | − | 18.6190i | 0.462165 | − | 0.800493i | −0.536904 | − | 0.843644i | \(-0.680406\pi\) |
0.999069 | + | 0.0431505i | \(0.0137395\pi\) | |||||||
\(542\) | −13.9513 | + | 24.1644i | −0.599260 | + | 1.03795i | ||||
\(543\) | 2.74235 | 0.117686 | ||||||||
\(544\) | −1.05273 | − | 1.82338i | −0.0451353 | − | 0.0781767i | ||||
\(545\) | −16.3783 | −0.701569 | ||||||||
\(546\) | 7.01513 | + | 1.85396i | 0.300220 | + | 0.0793421i | ||||
\(547\) | −30.2968 | −1.29540 | −0.647699 | − | 0.761896i | \(-0.724269\pi\) | ||||
−0.647699 | + | 0.761896i | \(0.724269\pi\) | |||||||
\(548\) | 0.576493 | + | 0.998514i | 0.0246265 | + | 0.0426544i | ||||
\(549\) | 22.8262 | 0.974197 | ||||||||
\(550\) | 5.88947 | − | 10.2009i | 0.251128 | − | 0.434967i | ||||
\(551\) | −28.4854 | + | 49.3381i | −1.21352 | + | 2.10187i | ||||
\(552\) | −2.16567 | − | 3.75105i | −0.0921770 | − | 0.159655i | ||||
\(553\) | 12.7757 | + | 9.74164i | 0.543278 | + | 0.414257i | ||||
\(554\) | 20.8932 | 0.887668 | ||||||||
\(555\) | 2.90984 | 0.123516 | ||||||||
\(556\) | −9.50738 | −0.403203 | ||||||||
\(557\) | −17.6840 | −0.749296 | −0.374648 | − | 0.927167i | \(-0.622236\pi\) | ||||
−0.374648 | + | 0.927167i | \(0.622236\pi\) | |||||||
\(558\) | −11.3474 | + | 19.6543i | −0.480374 | + | 0.832033i | ||||
\(559\) | 2.54918 | − | 19.4214i | 0.107819 | − | 0.821437i | ||||
\(560\) | 1.87330 | − | 14.5710i | 0.0791616 | − | 0.615737i | ||||
\(561\) | −0.469159 | + | 0.812606i | −0.0198079 | + | 0.0343083i | ||||
\(562\) | 23.2838 | + | 40.3287i | 0.982167 | + | 1.70116i | ||||
\(563\) | 20.8695 | − | 36.1471i | 0.879545 | − | 1.52342i | 0.0277042 | − | 0.999616i | \(-0.491180\pi\) |
0.851841 | − | 0.523801i | \(-0.175486\pi\) | |||||||
\(564\) | −0.325115 | − | 0.563116i | −0.0136898 | − | 0.0237115i | ||||
\(565\) | 19.1770 | 0.806784 | ||||||||
\(566\) | 7.68887 | + | 13.3175i | 0.323187 | + | 0.559777i | ||||
\(567\) | 2.32887 | − | 18.1145i | 0.0978035 | − | 0.760738i | ||||
\(568\) | −3.11340 | − | 5.39257i | −0.130636 | − | 0.226267i | ||||
\(569\) | −2.73388 | − | 4.73521i | −0.114610 | − | 0.198510i | 0.803014 | − | 0.595960i | \(-0.203229\pi\) |
−0.917624 | + | 0.397450i | \(0.869895\pi\) | |||||||
\(570\) | 6.06342 | 0.253969 | ||||||||
\(571\) | −4.67621 | − | 8.09944i | −0.195693 | − | 0.338951i | 0.751434 | − | 0.659808i | \(-0.229362\pi\) |
−0.947128 | + | 0.320857i | \(0.896029\pi\) | |||||||
\(572\) | −2.93934 | + | 1.21886i | −0.122900 | + | 0.0509630i | ||||
\(573\) | −0.246437 | −0.0102951 | ||||||||
\(574\) | 0.805833 | − | 6.26795i | 0.0336348 | − | 0.261619i | ||||
\(575\) | 6.43976 | − | 11.1540i | 0.268557 | − | 0.465154i | ||||
\(576\) | −15.7594 | −0.656640 | ||||||||
\(577\) | 1.68462 | + | 2.91786i | 0.0701318 | + | 0.121472i | 0.898959 | − | 0.438033i | \(-0.144325\pi\) |
−0.828827 | + | 0.559505i | \(0.810991\pi\) | |||||||
\(578\) | 12.5763 | − | 21.7829i | 0.523107 | − | 0.906048i | ||||
\(579\) | 1.81632 | 0.0754836 | ||||||||
\(580\) | −4.23151 | −0.175704 | ||||||||
\(581\) | −3.92392 | + | 30.5212i | −0.162792 | + | 1.26623i | ||||
\(582\) | 2.35961 | − | 4.08697i | 0.0978091 | − | 0.169410i | ||||
\(583\) | 2.98881 | + | 5.17676i | 0.123784 | + | 0.214400i | ||||
\(584\) | −7.05128 | − | 12.2132i | −0.291784 | − | 0.505385i | ||||
\(585\) | −10.9553 | + | 4.54283i | −0.452945 | + | 0.187823i | ||||
\(586\) | −6.14924 | + | 10.6508i | −0.254023 | + | 0.439980i | ||||
\(587\) | 6.57639 | − | 11.3906i | 0.271437 | − | 0.470142i | −0.697793 | − | 0.716299i | \(-0.745835\pi\) |
0.969230 | + | 0.246157i | \(0.0791679\pi\) | |||||||
\(588\) | −1.00381 | + | 1.01608i | −0.0413963 | + | 0.0419023i | ||||
\(589\) | 17.6884 | + | 30.6373i | 0.728840 | + | 1.26239i | ||||
\(590\) | −9.48995 | + | 16.4371i | −0.390695 | + | 0.676704i | ||||
\(591\) | −1.82112 | + | 3.15427i | −0.0749108 | + | 0.129749i | ||||
\(592\) | 11.6308 | − | 20.1452i | 0.478024 | − | 0.827961i | ||||
\(593\) | −19.2958 | + | 33.4213i | −0.792384 | + | 1.37245i | 0.132102 | + | 0.991236i | \(0.457827\pi\) |
−0.924487 | + | 0.381214i | \(0.875506\pi\) | |||||||
\(594\) | −4.63617 | − | 8.03008i | −0.190224 | − | 0.329478i | ||||
\(595\) | −2.63625 | + | 1.10136i | −0.108076 | + | 0.0451515i | ||||
\(596\) | 3.00519 | − | 5.20515i | 0.123097 | − | 0.213211i | ||||
\(597\) | 1.83605 | − | 3.18014i | 0.0751447 | − | 0.130154i | ||||
\(598\) | −18.6269 | + | 7.72400i | −0.761710 | + | 0.315858i | ||||
\(599\) | −9.20762 | − | 15.9481i | −0.376213 | − | 0.651620i | 0.614295 | − | 0.789077i | \(-0.289441\pi\) |
−0.990508 | + | 0.137457i | \(0.956107\pi\) | |||||||
\(600\) | 2.15542 | + | 3.73329i | 0.0879946 | + | 0.152411i | ||||
\(601\) | 20.7018 | − | 35.8566i | 0.844445 | − | 1.46262i | −0.0416571 | − | 0.999132i | \(-0.513264\pi\) |
0.886102 | − | 0.463490i | \(-0.153403\pi\) | |||||||
\(602\) | 17.7699 | + | 13.5498i | 0.724248 | + | 0.552248i | ||||
\(603\) | 10.3348 | 0.420865 | ||||||||
\(604\) | 6.36338 | 0.258922 | ||||||||
\(605\) | −3.88549 | + | 6.72987i | −0.157968 | + | 0.273608i | ||||
\(606\) | −2.74690 | − | 4.75777i | −0.111585 | − | 0.193271i | ||||
\(607\) | 12.3051 | 0.499449 | 0.249724 | − | 0.968317i | \(-0.419660\pi\) | ||||
0.249724 | + | 0.968317i | \(0.419660\pi\) | |||||||
\(608\) | 7.77119 | − | 13.4601i | 0.315163 | − | 0.545879i | ||||
\(609\) | −8.76525 | − | 6.68361i | −0.355186 | − | 0.270834i | ||||
\(610\) | 15.3167 | 0.620155 | ||||||||
\(611\) | 10.6136 | − | 4.40114i | 0.429380 | − | 0.178051i | ||||
\(612\) | −0.521725 | − | 0.903654i | −0.0210895 | − | 0.0365280i | ||||
\(613\) | 26.2224 | 1.05911 | 0.529556 | − | 0.848275i | \(-0.322358\pi\) | ||||
0.529556 | + | 0.848275i | \(0.322358\pi\) | |||||||
\(614\) | −0.989078 | − | 1.71313i | −0.0399160 | − | 0.0691365i | ||||
\(615\) | −0.447810 | − | 0.775630i | −0.0180575 | − | 0.0312764i | ||||
\(616\) | −1.75696 | + | 13.6661i | −0.0707900 | + | 0.550621i | ||||
\(617\) | 9.41259 | + | 16.3031i | 0.378936 | + | 0.656337i | 0.990908 | − | 0.134543i | \(-0.0429565\pi\) |
−0.611971 | + | 0.790880i | \(0.709623\pi\) | |||||||
\(618\) | −7.55038 | −0.303721 | ||||||||
\(619\) | 7.90415 | + | 13.6904i | 0.317695 | + | 0.550263i | 0.980007 | − | 0.198965i | \(-0.0637580\pi\) |
−0.662312 | + | 0.749228i | \(0.730425\pi\) | |||||||
\(620\) | −1.31381 | + | 2.27559i | −0.0527639 | + | 0.0913898i | ||||
\(621\) | −5.06935 | − | 8.78038i | −0.203426 | − | 0.352344i | ||||
\(622\) | −19.2497 | + | 33.3415i | −0.771843 | + | 1.33687i | ||||
\(623\) | 43.3353 | − | 18.1045i | 1.73619 | − | 0.725340i | ||||
\(624\) | 1.06984 | − | 8.15073i | 0.0428277 | − | 0.326290i | ||||
\(625\) | −2.86003 | + | 4.95371i | −0.114401 | + | 0.198149i | ||||
\(626\) | 3.69473 | 0.147671 | ||||||||
\(627\) | −6.92661 | −0.276622 | ||||||||
\(628\) | −4.76060 | −0.189969 | ||||||||
\(629\) | −4.52389 | −0.180379 | ||||||||
\(630\) | 1.72527 | − | 13.4196i | 0.0687366 | − | 0.534649i | ||||
\(631\) | 8.33817 | + | 14.4421i | 0.331937 | + | 0.574933i | 0.982892 | − | 0.184184i | \(-0.0589644\pi\) |
−0.650954 | + | 0.759117i | \(0.725631\pi\) | |||||||
\(632\) | 7.47206 | − | 12.9420i | 0.297222 | − | 0.514804i | ||||
\(633\) | 0.927285 | − | 1.60610i | 0.0368563 | − | 0.0638369i | ||||
\(634\) | −30.7511 | −1.22128 | ||||||||
\(635\) | −9.34050 | − | 16.1782i | −0.370667 | − | 0.642013i | ||||
\(636\) | 0.576375 | 0.0228548 | ||||||||
\(637\) | −15.4935 | − | 19.9236i | −0.613877 | − | 0.789402i | ||||
\(638\) | 28.0152 | 1.10913 | ||||||||
\(639\) | −3.49248 | − | 6.04916i | −0.138161 | − | 0.239301i | ||||
\(640\) | −16.1108 | −0.636837 | ||||||||
\(641\) | −24.6232 | + | 42.6487i | −0.972559 | + | 1.68452i | −0.284792 | + | 0.958589i | \(0.591925\pi\) |
−0.687767 | + | 0.725932i | \(0.741409\pi\) | |||||||
\(642\) | −0.836720 | + | 1.44924i | −0.0330227 | + | 0.0571970i | ||||
\(643\) | −21.4355 | − | 37.1275i | −0.845335 | − | 1.46416i | −0.885330 | − | 0.464964i | \(-0.846067\pi\) |
0.0399940 | − | 0.999200i | \(-0.487266\pi\) | |||||||
\(644\) | 0.506149 | − | 3.93694i | 0.0199450 | − | 0.155137i | ||||
\(645\) | 3.16700 | 0.124701 | ||||||||
\(646\) | −9.42672 | −0.370889 | ||||||||
\(647\) | 4.25859 | 0.167422 | 0.0837112 | − | 0.996490i | \(-0.473323\pi\) | ||||
0.0837112 | + | 0.996490i | \(0.473323\pi\) | |||||||
\(648\) | −16.9882 | −0.667359 | ||||||||
\(649\) | 10.8409 | − | 18.7771i | 0.425544 | − | 0.737064i | ||||
\(650\) | 18.5387 | − | 7.68744i | 0.727148 | − | 0.301526i | ||||
\(651\) | −6.31572 | + | 2.63856i | −0.247533 | + | 0.103413i | ||||
\(652\) | 3.00437 | − | 5.20373i | 0.117660 | − | 0.203794i | ||||
\(653\) | 1.04776 | + | 1.81477i | 0.0410020 | + | 0.0710176i | 0.885798 | − | 0.464071i | \(-0.153612\pi\) |
−0.844796 | + | 0.535088i | \(0.820278\pi\) | |||||||
\(654\) | 5.22776 | − | 9.05475i | 0.204422 | − | 0.354069i | ||||
\(655\) | −5.68213 | − | 9.84174i | −0.222019 | − | 0.384549i | ||||
\(656\) | −7.15971 | −0.279540 | ||||||||
\(657\) | −7.90982 | − | 13.7002i | −0.308592 | − | 0.534496i | ||||
\(658\) | −1.67146 | + | 13.0010i | −0.0651604 | + | 0.506833i | ||||
\(659\) | −12.7259 | − | 22.0419i | −0.495732 | − | 0.858632i | 0.504256 | − | 0.863554i | \(-0.331767\pi\) |
−0.999988 | + | 0.00492170i | \(0.998433\pi\) | |||||||
\(660\) | −0.257237 | − | 0.445548i | −0.0100129 | − | 0.0173429i | ||||
\(661\) | 27.8108 | 1.08171 | 0.540857 | − | 0.841115i | \(-0.318100\pi\) | ||||
0.540857 | + | 0.841115i | \(0.318100\pi\) | |||||||
\(662\) | −3.05319 | − | 5.28829i | −0.118666 | − | 0.205535i | ||||
\(663\) | −1.47680 | + | 0.612385i | −0.0573543 | + | 0.0237831i | ||||
\(664\) | 28.6234 | 1.11080 | ||||||||
\(665\) | −16.7713 | − | 12.7883i | −0.650364 | − | 0.495911i | ||||
\(666\) | 10.7117 | − | 18.5533i | 0.415072 | − | 0.718925i | ||||
\(667\) | 30.6329 | 1.18611 | ||||||||
\(668\) | −1.62064 | − | 2.80703i | −0.0627044 | − | 0.108607i | ||||
\(669\) | 1.19103 | − | 2.06293i | 0.0460480 | − | 0.0797574i | ||||
\(670\) | 6.93481 | 0.267915 | ||||||||
\(671\) | −17.4972 | −0.675472 | ||||||||
\(672\) | 2.39128 | + | 1.82338i | 0.0922455 | + | 0.0703384i | ||||
\(673\) | −7.76033 | + | 13.4413i | −0.299139 | + | 0.518124i | −0.975939 | − | 0.218043i | \(-0.930033\pi\) |
0.676800 | + | 0.736167i | \(0.263366\pi\) | |||||||
\(674\) | 5.55100 | + | 9.61462i | 0.213817 | + | 0.370341i | ||||
\(675\) | 5.04536 | + | 8.73881i | 0.194196 | + | 0.336357i | ||||
\(676\) | −5.23802 | − | 1.39915i | −0.201462 | − | 0.0538136i | ||||
\(677\) | −17.2813 | + | 29.9321i | −0.664175 | + | 1.15038i | 0.315334 | + | 0.948981i | \(0.397884\pi\) |
−0.979508 | + | 0.201403i | \(0.935450\pi\) | |||||||
\(678\) | −6.12109 | + | 10.6020i | −0.235079 | + | 0.407169i | ||||
\(679\) | −15.1465 | + | 6.32783i | −0.581268 | + | 0.242840i | ||||
\(680\) | 1.32877 | + | 2.30150i | 0.0509562 | + | 0.0882587i | ||||
\(681\) | 5.91425 | − | 10.2438i | 0.226634 | − | 0.392542i | ||||
\(682\) | 8.69826 | − | 15.0658i | 0.333074 | − | 0.576900i | ||||
\(683\) | −23.5032 | + | 40.7087i | −0.899325 | + | 1.55768i | −0.0709661 | + | 0.997479i | \(0.522608\pi\) |
−0.828359 | + | 0.560198i | \(0.810725\pi\) | |||||||
\(684\) | 3.85135 | − | 6.67073i | 0.147260 | − | 0.255062i | ||||
\(685\) | −1.64703 | − | 2.85275i | −0.0629299 | − | 0.108998i | ||||
\(686\) | 28.5114 | − | 4.01821i | 1.08857 | − | 0.153416i | ||||
\(687\) | −5.31138 | + | 9.19958i | −0.202642 | + | 0.350986i | ||||
\(688\) | 12.6587 | − | 21.9255i | 0.482609 | − | 0.835904i | ||||
\(689\) | −1.32546 | + | 10.0982i | −0.0504960 | + | 0.384713i | ||||
\(690\) | −1.63013 | − | 2.82348i | −0.0620582 | − | 0.107488i | ||||
\(691\) | −9.50301 | − | 16.4597i | −0.361512 | − | 0.626156i | 0.626698 | − | 0.779262i | \(-0.284406\pi\) |
−0.988210 | + | 0.153106i | \(0.951073\pi\) | |||||||
\(692\) | −1.27088 | + | 2.20123i | −0.0483117 | + | 0.0836784i | ||||
\(693\) | −1.97088 | + | 15.3300i | −0.0748677 | + | 0.582338i | ||||
\(694\) | 15.6556 | 0.594280 | ||||||||
\(695\) | 27.1625 | 1.03033 | ||||||||
\(696\) | −5.12648 | + | 8.87933i | −0.194319 | + | 0.336570i | ||||
\(697\) | 0.696205 | + | 1.20586i | 0.0263706 | + | 0.0456753i | ||||
\(698\) | −9.77644 | −0.370044 | ||||||||
\(699\) | 0.928805 | − | 1.60874i | 0.0351306 | − | 0.0608480i | ||||
\(700\) | −0.503753 | + | 3.91830i | −0.0190401 | + | 0.148098i | ||||
\(701\) | −45.4648 | −1.71718 | −0.858591 | − | 0.512662i | \(-0.828659\pi\) | ||||
−0.858591 | + | 0.512662i | \(0.828659\pi\) | |||||||
\(702\) | 2.05603 | − | 15.6642i | 0.0775997 | − | 0.591207i | ||||
\(703\) | −16.6976 | − | 28.9210i | −0.629760 | − | 1.09078i | ||||
\(704\) | 12.0802 | 0.455290 | ||||||||
\(705\) | 0.928851 | + | 1.60882i | 0.0349826 | + | 0.0605916i | ||||
\(706\) | −26.5597 | − | 46.0027i | −0.999586 | − | 1.73133i | ||||
\(707\) | −2.43672 | + | 18.9534i | −0.0916423 | + | 0.712815i | ||||
\(708\) | −1.04531 | − | 1.81053i | −0.0392851 | − | 0.0680438i | ||||
\(709\) | −9.78779 | −0.367588 | −0.183794 | − | 0.982965i | \(-0.558838\pi\) | ||||
−0.183794 | + | 0.982965i | \(0.558838\pi\) | |||||||
\(710\) | −2.34351 | − | 4.05908i | −0.0879504 | − | 0.152334i | ||||
\(711\) | 8.38183 | − | 14.5178i | 0.314343 | − | 0.544459i | ||||
\(712\) | −21.8427 | − | 37.8326i | −0.818589 | − | 1.41784i | ||||
\(713\) | 9.51099 | − | 16.4735i | 0.356189 | − | 0.616938i | ||||
\(714\) | 0.232572 | − | 1.80900i | 0.00870377 | − | 0.0677000i | ||||
\(715\) | 8.39768 | − | 3.48226i | 0.314055 | − | 0.130229i | ||||
\(716\) | −3.86393 | + | 6.69252i | −0.144402 | + | 0.250111i | ||||
\(717\) | −10.7195 | −0.400326 | ||||||||
\(718\) | 29.0517 | 1.08420 | ||||||||
\(719\) | −27.8403 | −1.03827 | −0.519133 | − | 0.854693i | \(-0.673745\pi\) | ||||
−0.519133 | + | 0.854693i | \(0.673745\pi\) | |||||||
\(720\) | −15.3288 | −0.571271 | ||||||||
\(721\) | 20.8842 | + | 15.9245i | 0.777770 | + | 0.593059i | ||||
\(722\) | −20.0243 | − | 34.6830i | −0.745226 | − | 1.29077i | ||||
\(723\) | −5.07568 | + | 8.79134i | −0.188767 | + | 0.326953i | ||||
\(724\) | 1.16883 | − | 2.02447i | 0.0434391 | − | 0.0752388i | ||||
\(725\) | −30.4879 | −1.13229 | ||||||||
\(726\) | −2.48041 | − | 4.29619i | −0.0920566 | − | 0.159447i | ||||
\(727\) | −14.5650 | −0.540186 | −0.270093 | − | 0.962834i | \(-0.587055\pi\) | ||||
−0.270093 | + | 0.962834i | \(0.587055\pi\) | |||||||
\(728\) | −16.5433 | + | 16.6571i | −0.613136 | + | 0.617352i | ||||
\(729\) | −14.9199 | −0.552589 | ||||||||
\(730\) | −5.30761 | − | 9.19305i | −0.196444 | − | 0.340250i | ||||
\(731\) | −4.92370 | −0.182109 | ||||||||
\(732\) | −0.843560 | + | 1.46109i | −0.0311789 | + | 0.0540034i | ||||
\(733\) | −8.83030 | + | 15.2945i | −0.326155 | + | 0.564916i | −0.981745 | − | 0.190200i | \(-0.939086\pi\) |
0.655591 | + | 0.755116i | \(0.272420\pi\) | |||||||
\(734\) | 24.1451 | + | 41.8206i | 0.891213 | + | 1.54363i | ||||
\(735\) | 2.86787 | − | 2.90292i | 0.105783 | − | 0.107076i | ||||
\(736\) | −8.35705 | −0.308045 | ||||||||
\(737\) | −7.92205 | −0.291812 | ||||||||
\(738\) | −6.59394 | −0.242726 | ||||||||
\(739\) | 8.96559 | 0.329804 | 0.164902 | − | 0.986310i | \(-0.447269\pi\) | ||||
0.164902 | + | 0.986310i | \(0.447269\pi\) | |||||||
\(740\) | 1.24021 | − | 2.14811i | 0.0455911 | − | 0.0789661i | ||||
\(741\) | −9.36579 | − | 7.18084i | −0.344061 | − | 0.263795i | ||||
\(742\) | −9.23955 | − | 7.04528i | −0.339195 | − | 0.258640i | ||||
\(743\) | 13.1839 | − | 22.8352i | 0.483671 | − | 0.837743i | −0.516153 | − | 0.856497i | \(-0.672636\pi\) |
0.999824 | + | 0.0187532i | \(0.00596968\pi\) | |||||||
\(744\) | 3.18337 | + | 5.51376i | 0.116708 | + | 0.202144i | ||||
\(745\) | −8.58580 | + | 14.8710i | −0.314560 | + | 0.544833i | ||||
\(746\) | 2.28309 | + | 3.95442i | 0.0835898 | + | 0.144782i | ||||
\(747\) | 32.1086 | 1.17479 | ||||||||
\(748\) | 0.399923 | + | 0.692688i | 0.0146226 | + | 0.0253272i | ||||
\(749\) | 5.37095 | − | 2.24385i | 0.196250 | − | 0.0819887i | ||||
\(750\) | 3.88818 | + | 6.73452i | 0.141976 | + | 0.245910i | ||||
\(751\) | 10.1438 | + | 17.5696i | 0.370152 | + | 0.641123i | 0.989589 | − | 0.143924i | \(-0.0459721\pi\) |
−0.619436 | + | 0.785047i | \(0.712639\pi\) | |||||||
\(752\) | 14.8507 | 0.541550 | ||||||||
\(753\) | 3.24321 | + | 5.61740i | 0.118189 | + | 0.204709i | ||||
\(754\) | 37.8807 | + | 29.0435i | 1.37953 | + | 1.05770i | ||||
\(755\) | −18.1801 | −0.661642 | ||||||||
\(756\) | 2.47296 | + | 1.88566i | 0.0899406 | + | 0.0685808i | ||||
\(757\) | −12.4992 | + | 21.6493i | −0.454292 | + | 0.786857i | −0.998647 | − | 0.0519981i | \(-0.983441\pi\) |
0.544355 | + | 0.838855i | \(0.316774\pi\) | |||||||
\(758\) | 15.6791 | 0.569492 | ||||||||
\(759\) | 1.86220 | + | 3.22543i | 0.0675936 | + | 0.117076i | ||||
\(760\) | −9.80895 | + | 16.9896i | −0.355808 | + | 0.616277i | ||||
\(761\) | 20.1422 | 0.730154 | 0.365077 | − | 0.930977i | \(-0.381043\pi\) | ||||
0.365077 | + | 0.930977i | \(0.381043\pi\) | |||||||
\(762\) | 11.9255 | 0.432016 | ||||||||
\(763\) | −33.5572 | + | 14.0194i | −1.21485 | + | 0.507537i | ||||
\(764\) | −0.105035 | + | 0.181926i | −0.00380003 | + | 0.00658184i | ||||
\(765\) | 1.49056 | + | 2.58173i | 0.0538914 | + | 0.0933426i | ||||
\(766\) | −2.86786 | − | 4.96729i | −0.103620 | − | 0.179475i | ||||
\(767\) | 34.1248 | − | 14.1505i | 1.23217 | − | 0.510945i | ||||
\(768\) | 2.34945 | − | 4.06936i | 0.0847784 | − | 0.146840i | ||||
\(769\) | −4.33610 | + | 7.51034i | −0.156364 | + | 0.270830i | −0.933555 | − | 0.358435i | \(-0.883311\pi\) |
0.777191 | + | 0.629265i | \(0.216644\pi\) | |||||||
\(770\) | −1.32249 | + | 10.2867i | −0.0476594 | + | 0.370706i | ||||
\(771\) | −3.22199 | − | 5.58065i | −0.116037 | − | 0.200982i | ||||
\(772\) | 0.774139 | − | 1.34085i | 0.0278619 | − | 0.0482582i | ||||
\(773\) | −1.17283 | + | 2.03141i | −0.0421839 | + | 0.0730647i | −0.886346 | − | 0.463023i | \(-0.846765\pi\) |
0.844163 | + | 0.536087i | \(0.180098\pi\) | |||||||
\(774\) | 11.6584 | − | 20.1930i | 0.419053 | − | 0.725821i | ||||
\(775\) | −9.46596 | + | 16.3955i | −0.340027 | + | 0.588945i | ||||
\(776\) | 7.63441 | + | 13.2232i | 0.274059 | + | 0.474685i | ||||
\(777\) | 5.96192 | − | 2.49075i | 0.213883 | − | 0.0893552i | ||||
\(778\) | −17.6198 | + | 30.5184i | −0.631701 | + | 1.09414i | ||||
\(779\) | −5.13935 | + | 8.90161i | −0.184136 | + | 0.318933i | ||||
\(780\) | 0.114078 | − | 0.869125i | 0.00408466 | − | 0.0311197i | ||||
\(781\) | 2.67713 | + | 4.63693i | 0.0957953 | + | 0.165922i | ||||
\(782\) | 2.53435 | + | 4.38962i | 0.0906281 | + | 0.156973i | ||||
\(783\) | −12.0000 | + | 20.7845i | −0.428844 | + | 0.742779i | ||||
\(784\) | −8.63423 | − | 31.4578i | −0.308365 | − | 1.12349i | ||||
\(785\) | 13.6010 | 0.485440 | ||||||||
\(786\) | 7.25468 | 0.258766 | ||||||||
\(787\) | 17.0583 | − | 29.5459i | 0.608063 | − | 1.05320i | −0.383496 | − | 0.923543i | \(-0.625280\pi\) |
0.991559 | − | 0.129654i | \(-0.0413866\pi\) | |||||||
\(788\) | 1.55237 | + | 2.68878i | 0.0553009 | + | 0.0957840i | ||||
\(789\) | 9.36455 | 0.333387 | ||||||||
\(790\) | 5.62434 | − | 9.74164i | 0.200105 | − | 0.346592i | ||||
\(791\) | 39.2915 | − | 16.4151i | 1.39705 | − | 0.583653i | ||||
\(792\) | 14.3768 | 0.510858 | ||||||||
\(793\) | −23.6588 | − | 18.1394i | −0.840148 | − | 0.644149i | ||||
\(794\) | 22.6486 | + | 39.2286i | 0.803770 | + | 1.39217i | ||||
\(795\) | −1.64670 | −0.0584024 | ||||||||
\(796\) | −1.56510 | − | 2.71084i | −0.0554736 | − | 0.0960830i | ||||
\(797\) | 17.0422 | + | 29.5180i | 0.603666 | + | 1.04558i | 0.992261 | + | 0.124172i | \(0.0396275\pi\) |
−0.388594 | + | 0.921409i | \(0.627039\pi\) | |||||||
\(798\) | 12.4232 | − | 5.19014i | 0.439778 | − | 0.183729i | ||||
\(799\) | −1.44407 | − | 2.50121i | −0.0510876 | − | 0.0884863i | ||||
\(800\) | 8.31749 | 0.294068 | ||||||||
\(801\) | −24.5022 | − | 42.4390i | −0.865742 | − | 1.49951i | ||||
\(802\) | −6.31243 | + | 10.9335i | −0.222900 | + | 0.386074i | ||||
\(803\) | 6.06320 | + | 10.5018i | 0.213966 | + | 0.370600i | ||||
\(804\) | −0.381931 | + | 0.661524i | −0.0134697 | + | 0.0233302i | ||||
\(805\) | −1.44606 | + | 11.2478i | −0.0509670 | + | 0.396433i | ||||
\(806\) | 27.3801 | − | 11.3537i | 0.964423 | − | 0.399917i | ||||
\(807\) | −6.96748 | + | 12.0680i | −0.245267 | + | 0.424815i | ||||
\(808\) | 17.7749 | 0.625319 | ||||||||
\(809\) | −26.5205 | −0.932413 | −0.466206 | − | 0.884676i | \(-0.654380\pi\) | ||||
−0.466206 | + | 0.884676i | \(0.654380\pi\) | |||||||
\(810\) | −12.7873 | −0.449300 | ||||||||
\(811\) | 52.5463 | 1.84515 | 0.922575 | − | 0.385818i | \(-0.126081\pi\) | ||||
0.922575 | + | 0.385818i | \(0.126081\pi\) | |||||||
\(812\) | −8.66987 | + | 3.62207i | −0.304253 | + | 0.127110i | ||||
\(813\) | 4.39040 | + | 7.60439i | 0.153978 | + | 0.266698i | ||||
\(814\) | −8.21099 | + | 14.2219i | −0.287795 | + | 0.498476i | ||||
\(815\) | −8.58347 | + | 14.8670i | −0.300666 | + | 0.520768i | ||||
\(816\) | −2.06637 | −0.0723373 | ||||||||
\(817\) | −18.1732 | − | 31.4770i | −0.635801 | − | 1.10124i | ||||
\(818\) | −12.9391 | −0.452403 | ||||||||
\(819\) | −18.5576 | + | 18.6852i | −0.648454 | + | 0.652913i | ||||
\(820\) | −0.763451 | −0.0266609 | ||||||||
\(821\) | 15.3773 | + | 26.6343i | 0.536671 | + | 0.929542i | 0.999080 | + | 0.0428753i | \(0.0136518\pi\) |
−0.462409 | + | 0.886667i | \(0.653015\pi\) | |||||||
\(822\) | 2.10286 | 0.0733455 | ||||||||
\(823\) | 14.8519 | − | 25.7243i | 0.517705 | − | 0.896691i | −0.482084 | − | 0.876125i | \(-0.660120\pi\) |
0.999789 | − | 0.0205659i | \(-0.00654678\pi\) | |||||||
\(824\) | 12.2144 | − | 21.1560i | 0.425510 | − | 0.737006i | ||||
\(825\) | −1.85339 | − | 3.21016i | −0.0645266 | − | 0.111763i | ||||
\(826\) | −5.37408 | + | 41.8008i | −0.186988 | + | 1.45444i | ||||
\(827\) | 14.8351 | 0.515866 | 0.257933 | − | 0.966163i | \(-0.416959\pi\) | ||||
0.257933 | + | 0.966163i | \(0.416959\pi\) | |||||||
\(828\) | −4.14170 | −0.143934 | ||||||||
\(829\) | 14.5849 | 0.506554 | 0.253277 | − | 0.967394i | \(-0.418492\pi\) | ||||
0.253277 | + | 0.967394i | \(0.418492\pi\) | |||||||
\(830\) | 21.5453 | 0.747849 | ||||||||
\(831\) | 3.28749 | − | 5.69411i | 0.114042 | − | 0.197526i | ||||
\(832\) | 16.3342 | + | 12.5236i | 0.566287 | + | 0.434177i | ||||
\(833\) | −4.45864 | + | 4.51314i | −0.154483 | + | 0.156371i | ||||
\(834\) | −8.66995 | + | 15.0168i | −0.300216 | + | 0.519989i | ||||
\(835\) | 4.63015 | + | 8.01966i | 0.160233 | + | 0.277532i | ||||
\(836\) | −2.95221 | + | 5.11339i | −0.102104 | + | 0.176850i | ||||
\(837\) | 7.45157 | + | 12.9065i | 0.257564 | + | 0.446114i | ||||
\(838\) | −20.2368 | −0.699069 | ||||||||
\(839\) | −18.4043 | − | 31.8772i | −0.635386 | − | 1.10052i | −0.986433 | − | 0.164164i | \(-0.947508\pi\) |
0.351047 | − | 0.936358i | \(-0.385826\pi\) | |||||||
\(840\) | −3.01832 | − | 2.30150i | −0.104142 | − | 0.0794095i | ||||
\(841\) | −21.7564 | − | 37.6832i | −0.750221 | − | 1.29942i | ||||
\(842\) | 6.91588 | + | 11.9787i | 0.238337 | + | 0.412812i | ||||
\(843\) | 14.6546 | 0.504730 | ||||||||
\(844\) | −0.790442 | − | 1.36909i | −0.0272082 | − | 0.0471259i | ||||
\(845\) | 14.9650 | + | 3.99737i | 0.514811 | + | 0.137514i | ||||
\(846\) | 13.6772 | 0.470232 | ||||||||
\(847\) | −2.20032 | + | 17.1146i | −0.0756040 | + | 0.588065i | ||||
\(848\) | −6.58196 | + | 11.4003i | −0.226025 | + | 0.391488i | ||||
\(849\) | 4.83929 | 0.166084 | ||||||||
\(850\) | −2.52235 | − | 4.36884i | −0.0865160 | − | 0.149850i | ||||
\(851\) | −8.97819 | + | 15.5507i | −0.307768 | + | 0.533070i | ||||
\(852\) | 0.516270 | 0.0176871 | ||||||||
\(853\) | −4.10728 | −0.140630 | −0.0703152 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703152 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(854\) | 31.3822 | − | 13.1107i | 1.07388 | − | 0.448640i | ||||
\(855\) | −11.0033 | + | 19.0582i | −0.376303 | + | 0.651777i | ||||
\(856\) | −2.70717 | − | 4.68895i | −0.0925291 | − | 0.160265i | ||||
\(857\) | 19.1656 | + | 33.1958i | 0.654684 | + | 1.13395i | 0.981973 | + | 0.189022i | \(0.0605318\pi\) |
−0.327288 | + | 0.944925i | \(0.606135\pi\) | |||||||
\(858\) | −0.755270 | + | 5.75416i | −0.0257845 | + | 0.196444i | ||||
\(859\) | 19.7185 | − | 34.1534i | 0.672785 | − | 1.16530i | −0.304326 | − | 0.952568i | \(-0.598431\pi\) |
0.977111 | − | 0.212730i | \(-0.0682356\pi\) | |||||||
\(860\) | 1.34982 | − | 2.33796i | 0.0460284 | − | 0.0797236i | ||||
\(861\) | −1.58143 | − | 1.20586i | −0.0538951 | − | 0.0410957i | ||||
\(862\) | 6.96300 | + | 12.0603i | 0.237161 | + | 0.410775i | ||||
\(863\) | 19.3220 | − | 33.4667i | 0.657728 | − | 1.13922i | −0.323474 | − | 0.946237i | \(-0.604851\pi\) |
0.981202 | − | 0.192982i | \(-0.0618159\pi\) | |||||||
\(864\) | 3.27375 | − | 5.67030i | 0.111375 | − | 0.192907i | ||||
\(865\) | 3.63090 | − | 6.28891i | 0.123454 | − | 0.213829i | ||||
\(866\) | 0.134410 | − | 0.232805i | 0.00456744 | − | 0.00791104i | ||||
\(867\) | −3.95771 | − | 6.85495i | −0.134411 | − | 0.232806i | ||||
\(868\) | −0.744000 | + | 5.78701i | −0.0252530 | + | 0.196424i | ||||
\(869\) | −6.42502 | + | 11.1285i | −0.217954 | + | 0.377507i | ||||
\(870\) | −3.85879 | + | 6.68361i | −0.130825 | + | 0.226596i | ||||
\(871\) | −10.7118 | − | 8.21281i | −0.362955 | − | 0.278280i | ||||
\(872\) | 16.9142 | + | 29.2962i | 0.572786 | + | 0.992094i | ||||
\(873\) | 8.56395 | + | 14.8332i | 0.289846 | + | 0.502028i | ||||
\(874\) | −18.7084 | + | 32.4040i | −0.632822 | + | 1.09608i | ||||
\(875\) | 3.44913 | − | 26.8281i | 0.116602 | − | 0.906955i | ||||
\(876\) | 1.16926 | 0.0395055 | ||||||||
\(877\) | −58.0741 | −1.96102 | −0.980512 | − | 0.196458i | \(-0.937056\pi\) | ||||
−0.980512 | + | 0.196458i | \(0.937056\pi\) | |||||||
\(878\) | −7.41710 | + | 12.8468i | −0.250315 | + | 0.433558i | ||||
\(879\) | 1.93513 | + | 3.35175i | 0.0652704 | + | 0.113052i | ||||
\(880\) | 11.7502 | 0.396098 | ||||||||
\(881\) | −10.8118 | + | 18.7266i | −0.364259 | + | 0.630916i | −0.988657 | − | 0.150191i | \(-0.952011\pi\) |
0.624398 | + | 0.781107i | \(0.285345\pi\) | |||||||
\(882\) | −7.95194 | − | 28.9720i | −0.267756 | − | 0.975537i | ||||
\(883\) | −22.7329 | −0.765022 | −0.382511 | − | 0.923951i | \(-0.624941\pi\) | ||||
−0.382511 | + | 0.923951i | \(0.624941\pi\) | |||||||
\(884\) | −0.177356 | + | 1.35122i | −0.00596513 | + | 0.0454464i | ||||
\(885\) | 2.98644 | + | 5.17266i | 0.100388 | + | 0.173877i | ||||
\(886\) | −21.5690 | −0.724624 | ||||||||
\(887\) | 8.16585 | + | 14.1437i | 0.274182 | + | 0.474898i | 0.969929 | − | 0.243390i | \(-0.0782595\pi\) |
−0.695746 | + | 0.718288i | \(0.744926\pi\) | |||||||
\(888\) | −3.00504 | − | 5.20488i | −0.100843 | − | 0.174664i | ||||
\(889\) | −32.9858 | − | 25.1521i | −1.10631 | − | 0.843574i | ||||
\(890\) | −16.4413 | − | 28.4772i | −0.551115 | − | 0.954559i | ||||
\(891\) | 14.6077 | 0.489376 | ||||||||
\(892\) | −1.01527 | − | 1.75850i | −0.0339937 | − | 0.0588788i | ||||
\(893\) | 10.6601 | − | 18.4638i | 0.356726 | − | 0.617867i | ||||
\(894\) | −5.48098 | − | 9.49333i | −0.183311 | − | 0.317504i | ||||
\(895\) | 11.0392 | − | 19.1205i | 0.369000 | − | 0.639127i | ||||
\(896\) | −33.0093 | + | 13.7905i | −1.10276 | + | 0.460708i | ||||
\(897\) | −0.825840 | + | 6.29180i | −0.0275740 | + | 0.210077i | ||||
\(898\) | 16.5506 | − | 28.6665i | 0.552301 | − | 0.956614i | ||||
\(899\) | −45.0280 | −1.50177 | ||||||||
\(900\) | 4.12209 | 0.137403 | ||||||||
\(901\) | 2.56010 | 0.0852893 | ||||||||
\(902\) | 5.05453 | 0.168297 | ||||||||
\(903\) | 6.48882 | − | 2.71088i | 0.215934 | − | 0.0902123i | ||||
\(904\) | −19.8045 | − | 34.3023i | −0.658687 | − | 1.14088i | ||||
\(905\) | −3.33933 | + | 5.78389i | −0.111003 | + | 0.192263i | ||||
\(906\) | 5.80288 | − | 10.0509i | 0.192788 | − | 0.333918i | ||||
\(907\) | 14.4096 | 0.478463 | 0.239232 | − | 0.970963i | \(-0.423105\pi\) | ||||
0.239232 | + | 0.970963i | \(0.423105\pi\) | |||||||
\(908\) | −5.04146 | − | 8.73207i | −0.167307 | − | 0.289784i | ||||
\(909\) | 19.9391 | 0.661339 | ||||||||
\(910\) | −12.4524 | + | 12.5380i | −0.412794 | + | 0.415632i | ||||
\(911\) | −1.32236 | −0.0438118 | −0.0219059 | − | 0.999760i | \(-0.506973\pi\) | ||||
−0.0219059 | + | 0.999760i | \(0.506973\pi\) | |||||||
\(912\) | −7.62691 | − | 13.2102i | −0.252552 | − | 0.437433i | ||||
\(913\) | −24.6125 | −0.814556 | ||||||||
\(914\) | −7.52907 | + | 13.0407i | −0.249039 | + | 0.431349i | ||||
\(915\) | 2.41004 | − | 4.17432i | 0.0796735 | − | 0.137999i | ||||
\(916\) | 4.52757 | + | 7.84197i | 0.149595 | + | 0.259106i | ||||
\(917\) | −20.0663 | − | 15.3008i | −0.662648 | − | 0.505278i | ||||
\(918\) | −3.97117 | −0.131068 | ||||||||
\(919\) | −27.4458 | −0.905354 | −0.452677 | − | 0.891675i | \(-0.649531\pi\) | ||||
−0.452677 | + | 0.891675i | \(0.649531\pi\) | |||||||
\(920\) | 10.5484 | 0.347772 | ||||||||
\(921\) | −0.622515 | −0.0205126 | ||||||||
\(922\) | 1.06835 | − | 1.85043i | 0.0351841 | − | 0.0609407i | ||||
\(923\) | −1.18724 | + | 9.04520i | −0.0390785 | + | 0.297726i | ||||
\(924\) | −0.908428 | − | 0.692688i | −0.0298851 | − | 0.0227878i | ||||
\(925\) | 8.93569 | − | 15.4771i | 0.293804 | − | 0.508883i | ||||
\(926\) | −24.6970 | − | 42.7765i | −0.811594 | − | 1.40572i | ||||
\(927\) | 13.7016 | − | 23.7319i | 0.450021 | − | 0.779459i | ||||
\(928\) | 9.89123 | + | 17.1321i | 0.324696 | + | 0.562389i | ||||
\(929\) | −28.6389 | −0.939611 | −0.469805 | − | 0.882770i | \(-0.655676\pi\) | ||||
−0.469805 | + | 0.882770i | \(0.655676\pi\) | |||||||
\(930\) | 2.39618 | + | 4.15030i | 0.0785737 | + | 0.136094i | ||||
\(931\) | −45.3090 | − | 11.8460i | −1.48494 | − | 0.388237i | ||||
\(932\) | −0.791738 | − | 1.37133i | −0.0259343 | − | 0.0449194i | ||||
\(933\) | 6.05778 | + | 10.4924i | 0.198323 | + | 0.343505i | ||||
\(934\) | −45.2739 | −1.48141 | ||||||||
\(935\) | −1.14258 | − | 1.97900i | −0.0373663 | − | 0.0647203i | ||||
\(936\) | 19.4396 | + | 14.9045i | 0.635402 | + | 0.487168i | ||||
\(937\) | 27.9990 | 0.914688 | 0.457344 | − | 0.889290i | \(-0.348801\pi\) | ||||
0.457344 | + | 0.889290i | \(0.348801\pi\) | |||||||
\(938\) | 14.2086 | − | 5.93602i | 0.463928 | − | 0.193818i | ||||
\(939\) | 0.581356 | − | 1.00694i | 0.0189718 | − | 0.0328602i | ||||
\(940\) | 1.58356 | 0.0516499 | ||||||||
\(941\) | −14.4502 | − | 25.0284i | −0.471062 | − | 0.815903i | 0.528390 | − | 0.849002i | \(-0.322796\pi\) |
−0.999452 | + | 0.0330983i | \(0.989463\pi\) | |||||||
\(942\) | −4.34127 | + | 7.51931i | −0.141446 | + | 0.244992i | ||||
\(943\) | 5.52680 | 0.179977 | ||||||||
\(944\) | 47.7480 | 1.55406 | ||||||||
\(945\) | −7.06521 | − | 5.38731i | −0.229831 | − | 0.175249i | ||||
\(946\) | −8.93666 | + | 15.4787i | −0.290556 | + | 0.503257i | ||||
\(947\) | −15.0617 | − | 26.0877i | −0.489441 | − | 0.847736i | 0.510486 | − | 0.859886i | \(-0.329466\pi\) |
−0.999926 | + | 0.0121504i | \(0.996132\pi\) | |||||||
\(948\) | 0.619515 | + | 1.07303i | 0.0201209 | + | 0.0348505i | ||||
\(949\) | −2.68888 | + | 20.4857i | −0.0872847 | + | 0.664993i | ||||
\(950\) | 18.6199 | − | 32.2506i | 0.604109 | − | 1.04635i | ||||
\(951\) | −4.83860 | + | 8.38070i | −0.156902 | + | 0.271763i | ||||
\(952\) | 4.69254 | + | 3.57812i | 0.152086 | + | 0.115968i | ||||
\(953\) | −2.46511 | − | 4.26969i | −0.0798527 | − | 0.138309i | 0.823334 | − | 0.567558i | \(-0.192112\pi\) |
−0.903186 | + | 0.429249i | \(0.858778\pi\) | |||||||
\(954\) | −6.06185 | + | 10.4994i | −0.196260 | + | 0.339932i | ||||
\(955\) | 0.300084 | − | 0.519760i | 0.00971048 | − | 0.0168190i | ||||
\(956\) | −4.56879 | + | 7.91337i | −0.147765 | + | 0.255937i | ||||
\(957\) | 4.40812 | − | 7.63509i | 0.142494 | − | 0.246808i | ||||
\(958\) | −7.55721 | − | 13.0895i | −0.244162 | − | 0.422902i | ||||
\(959\) | −5.81646 | − | 4.43513i | −0.187823 | − | 0.143218i | ||||
\(960\) | −1.66391 | + | 2.88198i | −0.0537025 | + | 0.0930155i | ||||
\(961\) | 1.51957 | − | 2.63197i | 0.0490184 | − | 0.0849024i | ||||
\(962\) | −25.8463 | + | 10.7177i | −0.833318 | + | 0.345552i | ||||
\(963\) | −3.03678 | − | 5.25986i | −0.0978590 | − | 0.169497i | ||||
\(964\) | 4.32665 | + | 7.49398i | 0.139352 | + | 0.241365i | ||||
\(965\) | −2.21171 | + | 3.83079i | −0.0711974 | + | 0.123317i | ||||
\(966\) | −5.75678 | − | 4.38962i | −0.185222 | − | 0.141234i | ||||
\(967\) | 29.1431 | 0.937180 | 0.468590 | − | 0.883416i | \(-0.344762\pi\) | ||||
0.468590 | + | 0.883416i | \(0.344762\pi\) | |||||||
\(968\) | 16.0505 | 0.515882 | ||||||||
\(969\) | −1.48327 | + | 2.56910i | −0.0476495 | + | 0.0825313i | ||||
\(970\) | 5.74654 | + | 9.95331i | 0.184510 | + | 0.319581i | ||||
\(971\) | 14.5769 | 0.467794 | 0.233897 | − | 0.972261i | \(-0.424852\pi\) | ||||
0.233897 | + | 0.972261i | \(0.424852\pi\) | |||||||
\(972\) | 2.46738 | − | 4.27362i | 0.0791412 | − | 0.137077i | ||||
\(973\) | 55.6528 | − | 23.2504i | 1.78415 | − | 0.745375i | ||||
\(974\) | −26.6058 | −0.852506 | ||||||||
\(975\) | 0.821930 | − | 6.26202i | 0.0263228 | − | 0.200545i | ||||
\(976\) | −19.2662 | − | 33.3700i | −0.616696 | − | 1.06815i | ||||
\(977\) | 52.5218 | 1.68032 | 0.840161 | − | 0.542337i | \(-0.182460\pi\) | ||||
0.840161 | + | 0.542337i | \(0.182460\pi\) | |||||||
\(978\) | −5.47948 | − | 9.49074i | −0.175215 | − | 0.303481i | ||||
\(979\) | 18.7819 | + | 32.5313i | 0.600273 | + | 1.03970i | ||||
\(980\) | −0.920681 | − | 3.35439i | −0.0294101 | − | 0.107152i | ||||
\(981\) | 18.9736 | + | 32.8632i | 0.605780 | + | 1.04924i | ||||
\(982\) | −39.9886 | −1.27609 | ||||||||
\(983\) | 3.01884 | + | 5.22879i | 0.0962862 | + | 0.166773i | 0.910145 | − | 0.414291i | \(-0.135970\pi\) |
−0.813858 | + | 0.581063i | \(0.802637\pi\) | |||||||
\(984\) | −0.924923 | + | 1.60201i | −0.0294855 | + | 0.0510703i | ||||
\(985\) | −4.43511 | − | 7.68183i | −0.141314 | − | 0.244764i | ||||
\(986\) | 5.99920 | − | 10.3909i | 0.191054 | − | 0.330914i | ||||
\(987\) | 3.28022 | + | 2.50121i | 0.104410 | + | 0.0796143i | ||||
\(988\) | −9.29289 | + | 3.85348i | −0.295646 | + | 0.122596i | ||||
\(989\) | −9.77166 | + | 16.9250i | −0.310721 | + | 0.538184i | ||||
\(990\) | 10.8217 | 0.343935 | ||||||||
\(991\) | 31.3484 | 0.995813 | 0.497907 | − | 0.867231i | \(-0.334102\pi\) | ||||
0.497907 | + | 0.867231i | \(0.334102\pi\) | |||||||
\(992\) | 12.2842 | 0.390025 | ||||||||
\(993\) | −1.92165 | −0.0609816 | ||||||||
\(994\) | −8.27605 | − | 6.31060i | −0.262500 | − | 0.200160i | ||||
\(995\) | 4.47148 | + | 7.74483i | 0.141755 | + | 0.245528i | ||||
\(996\) | −1.18660 | + | 2.05525i | −0.0375988 | + | 0.0651230i | ||||
\(997\) | −2.74017 | + | 4.74611i | −0.0867819 | + | 0.150311i | −0.906149 | − | 0.422958i | \(-0.860992\pi\) |
0.819367 | + | 0.573269i | \(0.194325\pi\) | |||||||
\(998\) | 8.40146 | 0.265944 | ||||||||
\(999\) | −7.03414 | − | 12.1835i | −0.222550 | − | 0.385468i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 91.2.g.b.9.2 | ✓ | 12 | |
3.2 | odd | 2 | 819.2.n.d.100.5 | 12 | |||
7.2 | even | 3 | 637.2.f.k.295.2 | 12 | |||
7.3 | odd | 6 | 637.2.h.l.165.5 | 12 | |||
7.4 | even | 3 | 91.2.h.b.74.5 | yes | 12 | ||
7.5 | odd | 6 | 637.2.f.j.295.2 | 12 | |||
7.6 | odd | 2 | 637.2.g.l.373.2 | 12 | |||
13.3 | even | 3 | 91.2.h.b.16.5 | yes | 12 | ||
13.4 | even | 6 | 1183.2.e.g.170.5 | 12 | |||
13.9 | even | 3 | 1183.2.e.h.170.2 | 12 | |||
21.11 | odd | 6 | 819.2.s.d.802.2 | 12 | |||
39.29 | odd | 6 | 819.2.s.d.289.2 | 12 | |||
91.3 | odd | 6 | 637.2.g.l.263.2 | 12 | |||
91.4 | even | 6 | 1183.2.e.g.508.5 | 12 | |||
91.9 | even | 3 | 8281.2.a.bz.1.5 | 6 | |||
91.16 | even | 3 | 637.2.f.k.393.2 | 12 | |||
91.30 | even | 6 | 8281.2.a.ce.1.2 | 6 | |||
91.55 | odd | 6 | 637.2.h.l.471.5 | 12 | |||
91.61 | odd | 6 | 8281.2.a.ca.1.5 | 6 | |||
91.68 | odd | 6 | 637.2.f.j.393.2 | 12 | |||
91.74 | even | 3 | 1183.2.e.h.508.2 | 12 | |||
91.81 | even | 3 | inner | 91.2.g.b.81.2 | yes | 12 | |
91.82 | odd | 6 | 8281.2.a.cf.1.2 | 6 | |||
273.263 | odd | 6 | 819.2.n.d.172.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
91.2.g.b.81.2 | yes | 12 | 91.81 | even | 3 | inner | |
91.2.h.b.16.5 | yes | 12 | 13.3 | even | 3 | ||
91.2.h.b.74.5 | yes | 12 | 7.4 | even | 3 | ||
637.2.f.j.295.2 | 12 | 7.5 | odd | 6 | |||
637.2.f.j.393.2 | 12 | 91.68 | odd | 6 | |||
637.2.f.k.295.2 | 12 | 7.2 | even | 3 | |||
637.2.f.k.393.2 | 12 | 91.16 | even | 3 | |||
637.2.g.l.263.2 | 12 | 91.3 | odd | 6 | |||
637.2.g.l.373.2 | 12 | 7.6 | odd | 2 | |||
637.2.h.l.165.5 | 12 | 7.3 | odd | 6 | |||
637.2.h.l.471.5 | 12 | 91.55 | odd | 6 | |||
819.2.n.d.100.5 | 12 | 3.2 | odd | 2 | |||
819.2.n.d.172.5 | 12 | 273.263 | odd | 6 | |||
819.2.s.d.289.2 | 12 | 39.29 | odd | 6 | |||
819.2.s.d.802.2 | 12 | 21.11 | odd | 6 | |||
1183.2.e.g.170.5 | 12 | 13.4 | even | 6 | |||
1183.2.e.g.508.5 | 12 | 91.4 | even | 6 | |||
1183.2.e.h.170.2 | 12 | 13.9 | even | 3 | |||
1183.2.e.h.508.2 | 12 | 91.74 | even | 3 | |||
8281.2.a.bz.1.5 | 6 | 91.9 | even | 3 | |||
8281.2.a.ca.1.5 | 6 | 91.61 | odd | 6 | |||
8281.2.a.ce.1.2 | 6 | 91.30 | even | 6 | |||
8281.2.a.cf.1.2 | 6 | 91.82 | odd | 6 |