Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(25,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bj (of order \(6\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 11x^{14} + 88x^{12} - 303x^{10} + 758x^{8} - 968x^{6} + 867x^{4} - 30x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 142.8 | ||
Root | \(2.25575 - 1.30236i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.142 |
Dual form | 273.2.bj.c.25.8 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.25575 | + | 1.30236i | 1.59506 | + | 0.920907i | 0.992420 | + | 0.122892i | \(0.0392168\pi\) |
0.602637 | + | 0.798015i | \(0.294117\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 2.39228 | + | 4.14355i | 1.19614 | + | 2.07177i | ||||
\(5\) | −0.401974 | − | 0.232080i | −0.179768 | − | 0.103789i | 0.407415 | − | 0.913243i | \(-0.366430\pi\) |
−0.587184 | + | 0.809454i | \(0.699763\pi\) | |||||||
\(6\) | − | 2.60472i | − | 1.06337i | ||||||
\(7\) | 2.25575 | − | 1.38260i | 0.852594 | − | 0.522574i | ||||
\(8\) | 7.25298i | 2.56432i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.604503 | − | 1.04703i | −0.191161 | − | 0.331100i | ||||
\(11\) | −3.95602 | + | 2.28401i | −1.19279 | + | 0.688655i | −0.958937 | − | 0.283618i | \(-0.908465\pi\) |
−0.233849 | + | 0.972273i | \(0.575132\pi\) | |||||||
\(12\) | 2.39228 | − | 4.14355i | 0.690591 | − | 1.19614i | ||||
\(13\) | 3.57555 | + | 0.464160i | 0.991679 | + | 0.128735i | ||||
\(14\) | 6.88906 | − | 0.181004i | 1.84118 | − | 0.0483754i | ||||
\(15\) | 0.464160i | 0.119846i | ||||||||
\(16\) | −4.66143 | + | 8.07383i | −1.16536 | + | 2.01846i | ||||
\(17\) | −2.16465 | − | 3.74928i | −0.525005 | − | 0.909335i | −0.999576 | − | 0.0291177i | \(-0.990730\pi\) |
0.474571 | − | 0.880217i | \(-0.342603\pi\) | |||||||
\(18\) | −2.25575 | + | 1.30236i | −0.531686 | + | 0.306969i | ||||
\(19\) | −2.65773 | − | 1.53444i | −0.609724 | − | 0.352024i | 0.163133 | − | 0.986604i | \(-0.447840\pi\) |
−0.772858 | + | 0.634580i | \(0.781173\pi\) | |||||||
\(20\) | − | 2.22080i | − | 0.496586i | ||||||
\(21\) | −2.32524 | − | 1.26224i | −0.507410 | − | 0.275443i | ||||
\(22\) | −11.8984 | −2.53675 | ||||||||
\(23\) | 1.87366 | − | 3.24527i | 0.390684 | − | 0.676685i | −0.601856 | − | 0.798605i | \(-0.705572\pi\) |
0.992540 | + | 0.121920i | \(0.0389051\pi\) | |||||||
\(24\) | 6.28127 | − | 3.62649i | 1.28216 | − | 0.740254i | ||||
\(25\) | −2.39228 | − | 4.14355i | −0.478456 | − | 0.828709i | ||||
\(26\) | 7.46105 | + | 5.70368i | 1.46323 | + | 1.11858i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 11.1253 | + | 6.03925i | 2.10248 | + | 1.14131i | ||||
\(29\) | −5.57555 | −1.03535 | −0.517677 | − | 0.855576i | \(-0.673203\pi\) | ||||
−0.517677 | + | 0.855576i | \(0.673203\pi\) | |||||||
\(30\) | −0.604503 | + | 1.04703i | −0.110367 | + | 0.191161i | ||||
\(31\) | −8.13504 | + | 4.69677i | −1.46110 | + | 0.843565i | −0.999062 | − | 0.0432970i | \(-0.986214\pi\) |
−0.462035 | + | 0.886862i | \(0.652880\pi\) | |||||||
\(32\) | −8.46753 | + | 4.88873i | −1.49686 | + | 0.864213i | ||||
\(33\) | 3.95602 | + | 2.28401i | 0.688655 | + | 0.397595i | ||||
\(34\) | − | 11.2766i | − | 1.93392i | ||||||
\(35\) | −1.22763 | + | 0.0322549i | −0.207507 | + | 0.00545208i | ||||
\(36\) | −4.78456 | −0.797426 | ||||||||
\(37\) | 6.35076 | + | 3.66661i | 1.04406 | + | 0.602787i | 0.920980 | − | 0.389610i | \(-0.127390\pi\) |
0.123078 | + | 0.992397i | \(0.460723\pi\) | |||||||
\(38\) | −3.99678 | − | 6.92263i | −0.648363 | − | 1.12300i | ||||
\(39\) | −1.38580 | − | 3.32860i | −0.221906 | − | 0.533002i | ||||
\(40\) | 1.68327 | − | 2.91551i | 0.266149 | − | 0.460983i | ||||
\(41\) | − | 4.95194i | − | 0.773363i | −0.922213 | − | 0.386682i | \(-0.873621\pi\) | ||
0.922213 | − | 0.386682i | \(-0.126379\pi\) | |||||||
\(42\) | −3.60128 | − | 5.87560i | −0.555690 | − | 0.906624i | ||||
\(43\) | 8.16532 | 1.24520 | 0.622600 | − | 0.782540i | \(-0.286076\pi\) | ||||
0.622600 | + | 0.782540i | \(0.286076\pi\) | |||||||
\(44\) | −18.9278 | − | 10.9280i | −2.85348 | − | 1.64745i | ||||
\(45\) | 0.401974 | − | 0.232080i | 0.0599228 | − | 0.0345964i | ||||
\(46\) | 8.45300 | − | 4.88034i | 1.24633 | − | 0.719567i | ||||
\(47\) | 1.67480 | + | 0.966946i | 0.244295 | + | 0.141044i | 0.617149 | − | 0.786846i | \(-0.288288\pi\) |
−0.372854 | + | 0.927890i | \(0.621621\pi\) | |||||||
\(48\) | 9.32286 | 1.34564 | ||||||||
\(49\) | 3.17683 | − | 6.23761i | 0.453833 | − | 0.891087i | ||||
\(50\) | − | 12.4624i | − | 1.76245i | ||||||
\(51\) | −2.16465 | + | 3.74928i | −0.303112 | + | 0.525005i | ||||
\(52\) | 6.63044 | + | 15.9259i | 0.919477 | + | 2.20852i | ||||
\(53\) | 3.31351 | + | 5.73917i | 0.455145 | + | 0.788335i | 0.998697 | − | 0.0510411i | \(-0.0162539\pi\) |
−0.543551 | + | 0.839376i | \(0.682921\pi\) | |||||||
\(54\) | 2.25575 | + | 1.30236i | 0.306969 | + | 0.177229i | ||||
\(55\) | 2.12029 | 0.285900 | ||||||||
\(56\) | 10.0280 | + | 16.3609i | 1.34004 | + | 2.18632i | ||||
\(57\) | 3.06888i | 0.406483i | ||||||||
\(58\) | −12.5771 | − | 7.26137i | −1.65145 | − | 0.953464i | ||||
\(59\) | −6.00330 | + | 3.46601i | −0.781563 | + | 0.451236i | −0.836984 | − | 0.547227i | \(-0.815683\pi\) |
0.0554207 | + | 0.998463i | \(0.482350\pi\) | |||||||
\(60\) | −1.92327 | + | 1.11040i | −0.248293 | + | 0.143352i | ||||
\(61\) | 2.41090 | − | 4.17580i | 0.308684 | − | 0.534657i | −0.669391 | − | 0.742911i | \(-0.733445\pi\) |
0.978075 | + | 0.208254i | \(0.0667781\pi\) | |||||||
\(62\) | −24.4675 | −3.10738 | ||||||||
\(63\) | 0.0694910 | + | 2.64484i | 0.00875504 | + | 0.333218i | ||||
\(64\) | −6.82180 | −0.852725 | ||||||||
\(65\) | −1.32956 | − | 1.01639i | −0.164911 | − | 0.126068i | ||||
\(66\) | 5.94921 | + | 10.3043i | 0.732297 | + | 1.26837i | ||||
\(67\) | −4.89895 | + | 2.82841i | −0.598503 | + | 0.345546i | −0.768452 | − | 0.639907i | \(-0.778973\pi\) |
0.169950 | + | 0.985453i | \(0.445639\pi\) | |||||||
\(68\) | 10.3569 | − | 17.9387i | 1.25596 | − | 2.17538i | ||||
\(69\) | −3.74731 | −0.451123 | ||||||||
\(70\) | −2.81123 | − | 1.52605i | −0.336007 | − | 0.182398i | ||||
\(71\) | 8.37533i | 0.993968i | 0.867760 | + | 0.496984i | \(0.165559\pi\) | ||||
−0.867760 | + | 0.496984i | \(0.834441\pi\) | |||||||
\(72\) | −6.28127 | − | 3.62649i | −0.740254 | − | 0.427386i | ||||
\(73\) | −2.95857 | + | 1.70813i | −0.346275 | + | 0.199922i | −0.663043 | − | 0.748581i | \(-0.730735\pi\) |
0.316769 | + | 0.948503i | \(0.397402\pi\) | |||||||
\(74\) | 9.55049 | + | 16.5419i | 1.11022 | + | 1.92296i | ||||
\(75\) | −2.39228 | + | 4.14355i | −0.276236 | + | 0.478456i | ||||
\(76\) | − | 14.6832i | − | 1.68428i | ||||||
\(77\) | −5.76593 | + | 10.6218i | −0.657089 | + | 1.21046i | ||||
\(78\) | 1.20901 | − | 9.31330i | 0.136893 | − | 1.05452i | ||||
\(79\) | −2.93341 | + | 5.08082i | −0.330035 | + | 0.571637i | −0.982518 | − | 0.186166i | \(-0.940394\pi\) |
0.652483 | + | 0.757803i | \(0.273727\pi\) | |||||||
\(80\) | 3.74755 | − | 2.16365i | 0.418989 | − | 0.241903i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 6.44921 | − | 11.1704i | 0.712196 | − | 1.23356i | ||||
\(83\) | 0.731307i | 0.0802714i | 0.999194 | + | 0.0401357i | \(0.0127790\pi\) | ||||
−0.999194 | + | 0.0401357i | \(0.987221\pi\) | |||||||
\(84\) | −0.332483 | − | 12.6544i | −0.0362769 | − | 1.38071i | ||||
\(85\) | 2.00949i | 0.217960i | ||||||||
\(86\) | 18.4189 | + | 10.6342i | 1.98617 | + | 1.14671i | ||||
\(87\) | 2.78777 | + | 4.82857i | 0.298881 | + | 0.517677i | ||||
\(88\) | −16.5659 | − | 28.6930i | −1.76593 | − | 3.05868i | ||||
\(89\) | −2.72722 | − | 1.57456i | −0.289084 | − | 0.166903i | 0.348444 | − | 0.937329i | \(-0.386710\pi\) |
−0.637529 | + | 0.770426i | \(0.720043\pi\) | |||||||
\(90\) | 1.20901 | 0.127440 | ||||||||
\(91\) | 8.70730 | − | 3.89653i | 0.912773 | − | 0.408467i | ||||
\(92\) | 17.9292 | 1.86925 | ||||||||
\(93\) | 8.13504 | + | 4.69677i | 0.843565 | + | 0.487032i | ||||
\(94\) | 2.51862 | + | 4.36238i | 0.259776 | + | 0.449945i | ||||
\(95\) | 0.712225 | + | 1.23361i | 0.0730728 | + | 0.126566i | ||||
\(96\) | 8.46753 | + | 4.88873i | 0.864213 | + | 0.498954i | ||||
\(97\) | 1.96330i | 0.199343i | 0.995020 | + | 0.0996717i | \(0.0317793\pi\) | ||||
−0.995020 | + | 0.0996717i | \(0.968221\pi\) | |||||||
\(98\) | 15.2897 | − | 9.93311i | 1.54450 | − | 1.00340i | ||||
\(99\) | − | 4.56802i | − | 0.459104i | ||||||
\(100\) | 11.4460 | − | 19.8250i | 1.14460 | − | 1.98250i | ||||
\(101\) | 7.82608 | + | 13.5552i | 0.778724 | + | 1.34879i | 0.932677 | + | 0.360711i | \(0.117466\pi\) |
−0.153953 | + | 0.988078i | \(0.549201\pi\) | |||||||
\(102\) | −9.76582 | + | 5.63830i | −0.966961 | + | 0.558275i | ||||
\(103\) | −2.22763 | + | 3.85837i | −0.219495 | + | 0.380176i | −0.954654 | − | 0.297719i | \(-0.903774\pi\) |
0.735159 | + | 0.677895i | \(0.237108\pi\) | |||||||
\(104\) | −3.36654 | + | 25.9334i | −0.330117 | + | 2.54298i | ||||
\(105\) | 0.641748 | + | 1.04703i | 0.0626282 | + | 0.102180i | ||||
\(106\) | 17.2615i | 1.67659i | ||||||||
\(107\) | 5.29167 | − | 9.16544i | 0.511565 | − | 0.886056i | −0.488345 | − | 0.872650i | \(-0.662399\pi\) |
0.999910 | − | 0.0134057i | \(-0.00426730\pi\) | |||||||
\(108\) | 2.39228 | + | 4.14355i | 0.230197 | + | 0.398713i | ||||
\(109\) | 17.2504 | − | 9.95954i | 1.65229 | − | 0.953951i | 0.676164 | − | 0.736751i | \(-0.263641\pi\) |
0.976127 | − | 0.217199i | \(-0.0696922\pi\) | |||||||
\(110\) | 4.78286 | + | 2.76138i | 0.456027 | + | 0.263288i | ||||
\(111\) | − | 7.33322i | − | 0.696039i | ||||||
\(112\) | 0.647855 | + | 24.6575i | 0.0612165 | + | 2.32991i | ||||
\(113\) | −5.20257 | −0.489416 | −0.244708 | − | 0.969597i | \(-0.578692\pi\) | ||||
−0.244708 | + | 0.969597i | \(0.578692\pi\) | |||||||
\(114\) | −3.99678 | + | 6.92263i | −0.374333 | + | 0.648363i | ||||
\(115\) | −1.50632 | + | 0.869676i | −0.140465 | + | 0.0810977i | ||||
\(116\) | −13.3383 | − | 23.1026i | −1.23843 | − | 2.14502i | ||||
\(117\) | −2.18975 | + | 2.86444i | −0.202442 | + | 0.264817i | ||||
\(118\) | −18.0559 | −1.66218 | ||||||||
\(119\) | −10.0667 | − | 5.46461i | −0.922810 | − | 0.500940i | ||||
\(120\) | −3.36654 | −0.307322 | ||||||||
\(121\) | 4.93341 | − | 8.54492i | 0.448492 | − | 0.776811i | ||||
\(122\) | 10.8768 | − | 6.27971i | 0.984738 | − | 0.568539i | ||||
\(123\) | −4.28851 | + | 2.47597i | −0.386682 | + | 0.223251i | ||||
\(124\) | −38.9226 | − | 22.4720i | −3.49535 | − | 2.01804i | ||||
\(125\) | 4.54160i | 0.406213i | ||||||||
\(126\) | −3.28777 | + | 6.05660i | −0.292898 | + | 0.539565i | ||||
\(127\) | −3.48684 | −0.309407 | −0.154703 | − | 0.987961i | \(-0.549442\pi\) | ||||
−0.154703 | + | 0.987961i | \(0.549442\pi\) | |||||||
\(128\) | 1.54677 | + | 0.893026i | 0.136716 | + | 0.0789331i | ||||
\(129\) | −4.08266 | − | 7.07138i | −0.359458 | − | 0.622600i | ||||
\(130\) | −1.67544 | − | 4.02429i | −0.146946 | − | 0.352954i | ||||
\(131\) | −9.88584 | + | 17.1228i | −0.863730 | + | 1.49602i | 0.00457315 | + | 0.999990i | \(0.498544\pi\) |
−0.868303 | + | 0.496034i | \(0.834789\pi\) | |||||||
\(132\) | 21.8560i | 1.90232i | ||||||||
\(133\) | −8.11669 | + | 0.213259i | −0.703806 | + | 0.0184919i | ||||
\(134\) | −14.7344 | −1.27286 | ||||||||
\(135\) | −0.401974 | − | 0.232080i | −0.0345964 | − | 0.0199743i | ||||
\(136\) | 27.1935 | − | 15.7002i | 2.33182 | − | 1.34628i | ||||
\(137\) | −2.71225 | + | 1.56592i | −0.231723 | + | 0.133785i | −0.611367 | − | 0.791348i | \(-0.709380\pi\) |
0.379644 | + | 0.925133i | \(0.376047\pi\) | |||||||
\(138\) | −8.45300 | − | 4.88034i | −0.719567 | − | 0.415442i | ||||
\(139\) | 10.5999 | 0.899073 | 0.449537 | − | 0.893262i | \(-0.351589\pi\) | ||||
0.449537 | + | 0.893262i | \(0.351589\pi\) | |||||||
\(140\) | −3.07048 | − | 5.00957i | −0.259503 | − | 0.423386i | ||||
\(141\) | − | 1.93389i | − | 0.162863i | ||||||
\(142\) | −10.9077 | + | 18.8927i | −0.915352 | + | 1.58544i | ||||
\(143\) | −15.2051 | + | 6.33037i | −1.27151 | + | 0.529372i | ||||
\(144\) | −4.66143 | − | 8.07383i | −0.388453 | − | 0.672819i | ||||
\(145\) | 2.24123 | + | 1.29397i | 0.186124 | + | 0.107459i | ||||
\(146\) | −8.89841 | −0.736438 | ||||||||
\(147\) | −6.99034 | + | 0.367585i | −0.576554 | + | 0.0303179i | ||||
\(148\) | 35.0862i | 2.88407i | ||||||||
\(149\) | 13.0885 | + | 7.55666i | 1.07225 | + | 0.619066i | 0.928796 | − | 0.370591i | \(-0.120845\pi\) |
0.143457 | + | 0.989657i | \(0.454178\pi\) | |||||||
\(150\) | −10.7928 | + | 6.23121i | −0.881226 | + | 0.508776i | ||||
\(151\) | −2.89569 | + | 1.67183i | −0.235648 | + | 0.136052i | −0.613175 | − | 0.789947i | \(-0.710108\pi\) |
0.377527 | + | 0.925999i | \(0.376775\pi\) | |||||||
\(152\) | 11.1293 | − | 19.2764i | 0.902702 | − | 1.56353i | ||||
\(153\) | 4.32930 | 0.350003 | ||||||||
\(154\) | −26.8399 | + | 16.4507i | −2.16282 | + | 1.32564i | ||||
\(155\) | 4.36011 | 0.350212 | ||||||||
\(156\) | 10.4770 | − | 13.7051i | 0.838829 | − | 1.09728i | ||||
\(157\) | 10.3755 | + | 17.9709i | 0.828056 | + | 1.43423i | 0.899561 | + | 0.436794i | \(0.143886\pi\) |
−0.0715057 | + | 0.997440i | \(0.522780\pi\) | |||||||
\(158\) | −13.2341 | + | 7.64072i | −1.05285 | + | 0.607863i | ||||
\(159\) | 3.31351 | − | 5.73917i | 0.262778 | − | 0.455145i | ||||
\(160\) | 4.53830 | 0.358785 | ||||||||
\(161\) | −0.260404 | − | 9.91103i | −0.0205227 | − | 0.781099i | ||||
\(162\) | − | 2.60472i | − | 0.204646i | ||||||
\(163\) | −7.08522 | − | 4.09065i | −0.554957 | − | 0.320405i | 0.196162 | − | 0.980572i | \(-0.437152\pi\) |
−0.751119 | + | 0.660167i | \(0.770485\pi\) | |||||||
\(164\) | 20.5186 | − | 11.8464i | 1.60223 | − | 0.925050i | ||||
\(165\) | −1.06015 | − | 1.83623i | −0.0825323 | − | 0.142950i | ||||
\(166\) | −0.952424 | + | 1.64965i | −0.0739225 | + | 0.128037i | ||||
\(167\) | − | 18.8241i | − | 1.45665i | −0.685229 | − | 0.728327i | \(-0.740298\pi\) | ||
0.685229 | − | 0.728327i | \(-0.259702\pi\) | |||||||
\(168\) | 9.15499 | − | 16.8649i | 0.706323 | − | 1.30116i | ||||
\(169\) | 12.5691 | + | 3.31925i | 0.966855 | + | 0.255327i | ||||
\(170\) | −2.61707 | + | 4.53290i | −0.200720 | + | 0.347658i | ||||
\(171\) | 2.65773 | − | 1.53444i | 0.203241 | − | 0.117341i | ||||
\(172\) | 19.5337 | + | 33.8334i | 1.48943 | + | 2.57977i | ||||
\(173\) | 4.32180 | − | 7.48558i | 0.328580 | − | 0.569118i | −0.653650 | − | 0.756797i | \(-0.726763\pi\) |
0.982230 | + | 0.187679i | \(0.0600965\pi\) | |||||||
\(174\) | 14.5227i | 1.10097i | ||||||||
\(175\) | −11.1253 | − | 6.03925i | −0.840990 | − | 0.456524i | ||||
\(176\) | − | 42.5870i | − | 3.21012i | ||||||
\(177\) | 6.00330 | + | 3.46601i | 0.451236 | + | 0.260521i | ||||
\(178\) | −4.10128 | − | 7.10363i | −0.307404 | − | 0.532440i | ||||
\(179\) | −9.96461 | − | 17.2592i | −0.744790 | − | 1.29001i | −0.950293 | − | 0.311357i | \(-0.899216\pi\) |
0.205503 | − | 0.978656i | \(-0.434117\pi\) | |||||||
\(180\) | 1.92327 | + | 1.11040i | 0.143352 | + | 0.0827643i | ||||
\(181\) | 0.259128 | 0.0192608 | 0.00963041 | − | 0.999954i | \(-0.496934\pi\) | ||||
0.00963041 | + | 0.999954i | \(0.496934\pi\) | |||||||
\(182\) | 24.7162 | + | 2.55044i | 1.83209 | + | 0.189051i | ||||
\(183\) | −4.82180 | −0.356438 | ||||||||
\(184\) | 23.5379 | + | 13.5896i | 1.73523 | + | 1.00184i | ||||
\(185\) | −1.70189 | − | 2.94777i | −0.125126 | − | 0.216724i | ||||
\(186\) | 12.2338 | + | 21.1895i | 0.897023 | + | 1.55369i | ||||
\(187\) | 17.1268 | + | 9.88817i | 1.25244 | + | 0.723094i | ||||
\(188\) | 9.25282i | 0.674831i | ||||||||
\(189\) | 2.25575 | − | 1.38260i | 0.164082 | − | 0.100569i | ||||
\(190\) | 3.71029i | 0.269173i | ||||||||
\(191\) | −9.81964 | + | 17.0081i | −0.710524 | + | 1.23066i | 0.254136 | + | 0.967168i | \(0.418209\pi\) |
−0.964661 | + | 0.263496i | \(0.915125\pi\) | |||||||
\(192\) | 3.41090 | + | 5.90785i | 0.246161 | + | 0.426363i | ||||
\(193\) | 21.2359 | − | 12.2606i | 1.52860 | − | 0.882536i | 0.529176 | − | 0.848512i | \(-0.322501\pi\) |
0.999421 | − | 0.0340235i | \(-0.0108321\pi\) | |||||||
\(194\) | −2.55693 | + | 4.42873i | −0.183577 | + | 0.317964i | ||||
\(195\) | −0.215444 | + | 1.65963i | −0.0154283 | + | 0.118848i | ||||
\(196\) | 33.4457 | − | 1.75873i | 2.38898 | − | 0.125624i | ||||
\(197\) | − | 21.3481i | − | 1.52099i | −0.649345 | − | 0.760494i | \(-0.724957\pi\) | ||
0.649345 | − | 0.760494i | \(-0.275043\pi\) | |||||||
\(198\) | 5.94921 | − | 10.3043i | 0.422792 | − | 0.732297i | ||||
\(199\) | −8.64175 | − | 14.9679i | −0.612597 | − | 1.06105i | −0.990801 | − | 0.135327i | \(-0.956791\pi\) |
0.378204 | − | 0.925722i | \(-0.376542\pi\) | |||||||
\(200\) | 30.0531 | − | 17.3511i | 2.12507 | − | 1.22691i | ||||
\(201\) | 4.89895 | + | 2.82841i | 0.345546 | + | 0.199501i | ||||
\(202\) | 40.7695i | 2.86853i | ||||||||
\(203\) | −12.5771 | + | 7.70876i | −0.882736 | + | 0.541049i | ||||
\(204\) | −20.7138 | −1.45025 | ||||||||
\(205\) | −1.14925 | + | 1.99055i | −0.0802669 | + | 0.139026i | ||||
\(206\) | −10.0500 | + | 5.80234i | −0.700213 | + | 0.404268i | ||||
\(207\) | 1.87366 | + | 3.24527i | 0.130228 | + | 0.225562i | ||||
\(208\) | −20.4147 | + | 26.7047i | −1.41551 | + | 1.85164i | ||||
\(209\) | 14.0187 | 0.969694 | ||||||||
\(210\) | 0.0840150 | + | 3.19763i | 0.00579758 | + | 0.220657i | ||||
\(211\) | −26.6701 | −1.83604 | −0.918022 | − | 0.396529i | \(-0.870215\pi\) | ||||
−0.918022 | + | 0.396529i | \(0.870215\pi\) | |||||||
\(212\) | −15.8537 | + | 27.4594i | −1.08883 | + | 1.88592i | ||||
\(213\) | 7.25325 | − | 4.18766i | 0.496984 | − | 0.286934i | ||||
\(214\) | 23.8734 | − | 13.7833i | 1.63195 | − | 0.942207i | ||||
\(215\) | −3.28225 | − | 1.89501i | −0.223848 | − | 0.129238i | ||||
\(216\) | 7.25298i | 0.493503i | ||||||||
\(217\) | −11.8569 | + | 21.8423i | −0.804898 | + | 1.48275i | ||||
\(218\) | 51.8836 | 3.51400 | ||||||||
\(219\) | 2.95857 | + | 1.70813i | 0.199922 | + | 0.115425i | ||||
\(220\) | 5.07233 | + | 8.78553i | 0.341976 | + | 0.592321i | ||||
\(221\) | −5.99954 | − | 14.4105i | −0.403573 | − | 0.969355i | ||||
\(222\) | 9.55049 | − | 16.5419i | 0.640987 | − | 1.11022i | ||||
\(223\) | − | 19.3807i | − | 1.29782i | −0.760863 | − | 0.648912i | \(-0.775224\pi\) | ||
0.760863 | − | 0.648912i | \(-0.224776\pi\) | |||||||
\(224\) | −12.3415 | + | 22.7350i | −0.824600 | + | 1.51904i | ||||
\(225\) | 4.78456 | 0.318970 | ||||||||
\(226\) | −11.7357 | − | 6.77561i | −0.780647 | − | 0.450707i | ||||
\(227\) | 3.42959 | − | 1.98008i | 0.227630 | − | 0.131422i | −0.381848 | − | 0.924225i | \(-0.624712\pi\) |
0.609478 | + | 0.792803i | \(0.291379\pi\) | |||||||
\(228\) | −12.7160 | + | 7.34161i | −0.842140 | + | 0.486210i | ||||
\(229\) | 3.60857 | + | 2.08341i | 0.238461 | + | 0.137675i | 0.614469 | − | 0.788941i | \(-0.289370\pi\) |
−0.376008 | + | 0.926616i | \(0.622704\pi\) | |||||||
\(230\) | −4.53052 | −0.298734 | ||||||||
\(231\) | 12.0817 | − | 0.317436i | 0.794916 | − | 0.0208858i | ||||
\(232\) | − | 40.4394i | − | 2.65497i | ||||||
\(233\) | 4.73376 | − | 8.19911i | 0.310119 | − | 0.537142i | −0.668269 | − | 0.743920i | \(-0.732964\pi\) |
0.978388 | + | 0.206778i | \(0.0662978\pi\) | |||||||
\(234\) | −8.67006 | + | 3.60962i | −0.566779 | + | 0.235968i | ||||
\(235\) | −0.448818 | − | 0.777375i | −0.0292776 | − | 0.0507104i | ||||
\(236\) | −28.7231 | − | 16.5833i | −1.86972 | − | 1.07948i | ||||
\(237\) | 5.86683 | 0.381092 | ||||||||
\(238\) | −15.5910 | − | 25.4372i | −1.01062 | − | 1.64885i | ||||
\(239\) | 1.82723i | 0.118194i | 0.998252 | + | 0.0590968i | \(0.0188221\pi\) | ||||
−0.998252 | + | 0.0590968i | \(0.981178\pi\) | |||||||
\(240\) | −3.74755 | − | 2.16365i | −0.241903 | − | 0.139663i | ||||
\(241\) | −13.3006 | + | 7.67909i | −0.856765 | + | 0.494653i | −0.862928 | − | 0.505328i | \(-0.831372\pi\) |
0.00616275 | + | 0.999981i | \(0.498038\pi\) | |||||||
\(242\) | 22.2571 | − | 12.8502i | 1.43074 | − | 0.826039i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 23.0702 | 1.47692 | ||||||||
\(245\) | −2.72463 | + | 1.77008i | −0.174070 | + | 0.113086i | ||||
\(246\) | −12.8984 | −0.822373 | ||||||||
\(247\) | −8.79061 | − | 6.72007i | −0.559333 | − | 0.427588i | ||||
\(248\) | −34.0656 | − | 59.0033i | −2.16317 | − | 3.74671i | ||||
\(249\) | 0.633331 | − | 0.365654i | 0.0401357 | − | 0.0231724i | ||||
\(250\) | −5.91479 | + | 10.2447i | −0.374084 | + | 0.647933i | ||||
\(251\) | 20.7904 | 1.31228 | 0.656139 | − | 0.754640i | \(-0.272189\pi\) | ||||
0.656139 | + | 0.754640i | \(0.272189\pi\) | |||||||
\(252\) | −10.7928 | + | 6.61513i | −0.679881 | + | 0.416714i | ||||
\(253\) | 17.1178i | 1.07619i | ||||||||
\(254\) | −7.86544 | − | 4.54111i | −0.493522 | − | 0.284935i | ||||
\(255\) | 1.74027 | − | 1.00474i | 0.108980 | − | 0.0629195i | ||||
\(256\) | 9.14788 | + | 15.8446i | 0.571743 | + | 0.990287i | ||||
\(257\) | −4.05332 | + | 7.02056i | −0.252839 | + | 0.437930i | −0.964306 | − | 0.264789i | \(-0.914698\pi\) |
0.711467 | + | 0.702719i | \(0.248031\pi\) | |||||||
\(258\) | − | 21.2684i | − | 1.32411i | ||||||
\(259\) | 19.3952 | − | 0.509593i | 1.20516 | − | 0.0316646i | ||||
\(260\) | 1.03081 | − | 7.94058i | 0.0639279 | − | 0.492454i | ||||
\(261\) | 2.78777 | − | 4.82857i | 0.172559 | − | 0.298881i | ||||
\(262\) | −44.6000 | + | 25.7498i | −2.75540 | + | 1.59083i | ||||
\(263\) | 1.88584 | + | 3.26637i | 0.116286 | + | 0.201413i | 0.918293 | − | 0.395901i | \(-0.129568\pi\) |
−0.802007 | + | 0.597314i | \(0.796234\pi\) | |||||||
\(264\) | −16.5659 | + | 28.6930i | −1.01956 | + | 1.76593i | ||||
\(265\) | − | 3.07600i | − | 0.188957i | ||||||
\(266\) | −18.5870 | − | 10.0898i | −1.13964 | − | 0.618644i | ||||
\(267\) | 3.14912i | 0.192723i | ||||||||
\(268\) | −23.4393 | − | 13.5327i | −1.43178 | − | 0.826641i | ||||
\(269\) | −11.0337 | − | 19.1110i | −0.672738 | − | 1.16522i | −0.977125 | − | 0.212667i | \(-0.931785\pi\) |
0.304387 | − | 0.952548i | \(-0.401548\pi\) | |||||||
\(270\) | −0.604503 | − | 1.04703i | −0.0367889 | − | 0.0637202i | ||||
\(271\) | −10.3882 | − | 5.99763i | −0.631039 | − | 0.364330i | 0.150116 | − | 0.988668i | \(-0.452035\pi\) |
−0.781154 | + | 0.624338i | \(0.785369\pi\) | |||||||
\(272\) | 40.3615 | 2.44727 | ||||||||
\(273\) | −7.72814 | − | 5.59248i | −0.467728 | − | 0.338472i | ||||
\(274\) | −8.15754 | −0.492815 | ||||||||
\(275\) | 18.9278 | + | 10.9280i | 1.14139 | + | 0.658982i | ||||
\(276\) | −8.96461 | − | 15.5272i | −0.539606 | − | 0.934625i | ||||
\(277\) | −14.7151 | − | 25.4874i | −0.884147 | − | 1.53139i | −0.846688 | − | 0.532089i | \(-0.821407\pi\) |
−0.0374587 | − | 0.999298i | \(-0.511926\pi\) | |||||||
\(278\) | 23.9108 | + | 13.8049i | 1.43407 | + | 0.827963i | ||||
\(279\) | − | 9.39354i | − | 0.562377i | ||||||
\(280\) | −0.233944 | − | 8.90396i | −0.0139809 | − | 0.532114i | ||||
\(281\) | 10.3189i | 0.615572i | 0.951456 | + | 0.307786i | \(0.0995881\pi\) | ||||
−0.951456 | + | 0.307786i | \(0.900412\pi\) | |||||||
\(282\) | 2.51862 | − | 4.36238i | 0.149982 | − | 0.259776i | ||||
\(283\) | −5.49073 | − | 9.51022i | −0.326390 | − | 0.565324i | 0.655403 | − | 0.755280i | \(-0.272499\pi\) |
−0.981793 | + | 0.189956i | \(0.939166\pi\) | |||||||
\(284\) | −34.7036 | + | 20.0361i | −2.05928 | + | 1.18892i | ||||
\(285\) | 0.712225 | − | 1.23361i | 0.0421886 | − | 0.0730728i | ||||
\(286\) | −42.5434 | − | 5.52277i | −2.51564 | − | 0.326568i | ||||
\(287\) | −6.84656 | − | 11.1704i | −0.404139 | − | 0.659365i | ||||
\(288\) | − | 9.77746i | − | 0.576142i | ||||||
\(289\) | −0.871415 | + | 1.50934i | −0.0512597 | + | 0.0887844i | ||||
\(290\) | 3.37044 | + | 5.83777i | 0.197919 | + | 0.342805i | ||||
\(291\) | 1.70027 | − | 0.981652i | 0.0996717 | − | 0.0575455i | ||||
\(292\) | −14.1555 | − | 8.17266i | −0.828386 | − | 0.478269i | ||||
\(293\) | − | 14.7635i | − | 0.862490i | −0.902235 | − | 0.431245i | \(-0.858074\pi\) | ||
0.902235 | − | 0.431245i | \(-0.141926\pi\) | |||||||
\(294\) | −16.2472 | − | 8.27475i | −0.947556 | − | 0.482593i | ||||
\(295\) | 3.21756 | 0.187334 | ||||||||
\(296\) | −26.5939 | + | 46.0619i | −1.54574 | + | 2.67730i | ||||
\(297\) | −3.95602 | + | 2.28401i | −0.229552 | + | 0.132532i | ||||
\(298\) | 19.6830 | + | 34.0919i | 1.14020 | + | 1.97489i | ||||
\(299\) | 8.20567 | − | 10.7339i | 0.474546 | − | 0.620759i | ||||
\(300\) | −22.8920 | −1.32167 | ||||||||
\(301\) | 18.4189 | − | 11.2894i | 1.06165 | − | 0.650709i | ||||
\(302\) | −8.70929 | −0.501163 | ||||||||
\(303\) | 7.82608 | − | 13.5552i | 0.449597 | − | 0.778724i | ||||
\(304\) | 24.7776 | − | 14.3054i | 1.42109 | − | 0.820469i | ||||
\(305\) | −1.93824 | + | 1.11904i | −0.110983 | + | 0.0640762i | ||||
\(306\) | 9.76582 | + | 5.63830i | 0.558275 | + | 0.322320i | ||||
\(307\) | 12.8535i | 0.733585i | 0.930303 | + | 0.366793i | \(0.119544\pi\) | ||||
−0.930303 | + | 0.366793i | \(0.880456\pi\) | |||||||
\(308\) | −57.8055 | + | 1.51879i | −3.29377 | + | 0.0865412i | ||||
\(309\) | 4.45526 | 0.253451 | ||||||||
\(310\) | 9.83532 | + | 5.67842i | 0.558608 | + | 0.322513i | ||||
\(311\) | 6.19428 | + | 10.7288i | 0.351245 | + | 0.608374i | 0.986468 | − | 0.163955i | \(-0.0524250\pi\) |
−0.635223 | + | 0.772329i | \(0.719092\pi\) | |||||||
\(312\) | 24.1423 | − | 10.0512i | 1.36679 | − | 0.569036i | ||||
\(313\) | −14.6067 | + | 25.2996i | −0.825622 | + | 1.43002i | 0.0758211 | + | 0.997121i | \(0.475842\pi\) |
−0.901443 | + | 0.432898i | \(0.857491\pi\) | |||||||
\(314\) | 54.0505i | 3.05025i | ||||||||
\(315\) | 0.585881 | − | 1.07928i | 0.0330106 | − | 0.0608108i | ||||
\(316\) | −28.0702 | −1.57907 | ||||||||
\(317\) | −8.51369 | − | 4.91538i | −0.478176 | − | 0.276075i | 0.241480 | − | 0.970406i | \(-0.422367\pi\) |
−0.719656 | + | 0.694331i | \(0.755701\pi\) | |||||||
\(318\) | 14.9489 | − | 8.63076i | 0.838293 | − | 0.483989i | ||||
\(319\) | 22.0570 | − | 12.7346i | 1.23496 | − | 0.713002i | ||||
\(320\) | 2.74219 | + | 1.58320i | 0.153293 | + | 0.0885038i | ||||
\(321\) | −10.5833 | −0.590704 | ||||||||
\(322\) | 12.3203 | − | 22.6960i | 0.686584 | − | 1.26480i | ||||
\(323\) | 13.2861i | 0.739258i | ||||||||
\(324\) | 2.39228 | − | 4.14355i | 0.132904 | − | 0.230197i | ||||
\(325\) | −6.63044 | − | 15.9259i | −0.367791 | − | 0.883408i | ||||
\(326\) | −10.6550 | − | 18.4550i | −0.590125 | − | 1.02213i | ||||
\(327\) | −17.2504 | − | 9.95954i | −0.953951 | − | 0.550764i | ||||
\(328\) | 35.9163 | 1.98315 | ||||||||
\(329\) | 5.11483 | − | 0.134388i | 0.281990 | − | 0.00740905i | ||||
\(330\) | − | 5.52277i | − | 0.304018i | ||||||
\(331\) | 4.35183 | + | 2.51253i | 0.239198 | + | 0.138101i | 0.614808 | − | 0.788677i | \(-0.289233\pi\) |
−0.375610 | + | 0.926778i | \(0.622567\pi\) | |||||||
\(332\) | −3.03021 | + | 1.74949i | −0.166304 | + | 0.0960157i | ||||
\(333\) | −6.35076 | + | 3.66661i | −0.348019 | + | 0.200929i | ||||
\(334\) | 24.5158 | − | 42.4626i | 1.34144 | − | 2.32345i | ||||
\(335\) | 2.62567 | 0.143456 | ||||||||
\(336\) | 21.0301 | − | 12.8898i | 1.14728 | − | 0.703196i | ||||
\(337\) | 0.536185 | 0.0292078 | 0.0146039 | − | 0.999893i | \(-0.495351\pi\) | ||||
0.0146039 | + | 0.999893i | \(0.495351\pi\) | |||||||
\(338\) | 24.0299 | + | 23.8569i | 1.30706 | + | 1.29764i | ||||
\(339\) | 2.60128 | + | 4.50556i | 0.141282 | + | 0.244708i | ||||
\(340\) | −8.32640 | + | 4.80725i | −0.451563 | + | 0.260710i | ||||
\(341\) | 21.4550 | − | 37.1611i | 1.16185 | − | 2.01238i | ||||
\(342\) | 7.99356 | 0.432242 | ||||||||
\(343\) | −1.45797 | − | 18.4628i | −0.0787229 | − | 0.996897i | ||||
\(344\) | 59.2229i | 3.19309i | ||||||||
\(345\) | 1.50632 | + | 0.869676i | 0.0810977 | + | 0.0468218i | ||||
\(346\) | 19.4978 | − | 11.2571i | 1.04821 | − | 0.605184i | ||||
\(347\) | 13.8050 | + | 23.9110i | 0.741093 | + | 1.28361i | 0.951998 | + | 0.306104i | \(0.0990255\pi\) |
−0.210905 | + | 0.977507i | \(0.567641\pi\) | |||||||
\(348\) | −13.3383 | + | 23.1026i | −0.715006 | + | 1.23843i | ||||
\(349\) | 34.2310i | 1.83234i | 0.400785 | + | 0.916172i | \(0.368737\pi\) | ||||
−0.400785 | + | 0.916172i | \(0.631263\pi\) | |||||||
\(350\) | −17.2305 | − | 28.1121i | −0.921011 | − | 1.50266i | ||||
\(351\) | 3.57555 | + | 0.464160i | 0.190849 | + | 0.0247750i | ||||
\(352\) | 22.3318 | − | 38.6799i | 1.19029 | − | 2.06164i | ||||
\(353\) | 15.6891 | − | 9.05813i | 0.835048 | − | 0.482115i | −0.0205296 | − | 0.999789i | \(-0.506535\pi\) |
0.855578 | + | 0.517674i | \(0.173202\pi\) | |||||||
\(354\) | 9.02797 | + | 15.6369i | 0.479831 | + | 0.831092i | ||||
\(355\) | 1.94375 | − | 3.36667i | 0.103163 | − | 0.178684i | ||||
\(356\) | − | 15.0671i | − | 0.798557i | ||||||
\(357\) | 0.300847 | + | 11.4503i | 0.0159225 | + | 0.606014i | ||||
\(358\) | − | 51.9100i | − | 2.74353i | ||||||
\(359\) | −3.25320 | − | 1.87824i | −0.171697 | − | 0.0991296i | 0.411689 | − | 0.911325i | \(-0.364939\pi\) |
−0.583386 | + | 0.812195i | \(0.698272\pi\) | |||||||
\(360\) | 1.68327 | + | 2.91551i | 0.0887162 | + | 0.153661i | ||||
\(361\) | −4.79099 | − | 8.29825i | −0.252158 | − | 0.436750i | ||||
\(362\) | 0.584528 | + | 0.337478i | 0.0307221 | + | 0.0177374i | ||||
\(363\) | −9.86683 | −0.517874 | ||||||||
\(364\) | 36.9757 | + | 26.7575i | 1.93805 | + | 1.40248i | ||||
\(365\) | 1.58569 | 0.0829990 | ||||||||
\(366\) | −10.8768 | − | 6.27971i | −0.568539 | − | 0.328246i | ||||
\(367\) | 1.25697 | + | 2.17713i | 0.0656132 | + | 0.113645i | 0.896966 | − | 0.442100i | \(-0.145766\pi\) |
−0.831353 | + | 0.555745i | \(0.812433\pi\) | |||||||
\(368\) | 17.4678 | + | 30.2552i | 0.910573 | + | 1.57716i | ||||
\(369\) | 4.28851 | + | 2.47597i | 0.223251 | + | 0.128894i | ||||
\(370\) | − | 8.86591i | − | 0.460917i | ||||||
\(371\) | 15.4094 | + | 8.36488i | 0.800017 | + | 0.434283i | ||||
\(372\) | 44.9439i | 2.33023i | ||||||||
\(373\) | 3.04474 | − | 5.27365i | 0.157651 | − | 0.273059i | −0.776370 | − | 0.630277i | \(-0.782941\pi\) |
0.934021 | + | 0.357218i | \(0.116275\pi\) | |||||||
\(374\) | 25.7559 | + | 44.6105i | 1.33181 | + | 2.30675i | ||||
\(375\) | 3.93314 | − | 2.27080i | 0.203106 | − | 0.117264i | ||||
\(376\) | −7.01324 | + | 12.1473i | −0.361680 | + | 0.626449i | ||||
\(377\) | −19.9357 | − | 2.58795i | −1.02674 | − | 0.133286i | ||||
\(378\) | 6.88906 | − | 0.181004i | 0.354335 | − | 0.00930986i | ||||
\(379\) | − | 2.67232i | − | 0.137268i | −0.997642 | − | 0.0686339i | \(-0.978136\pi\) | ||
0.997642 | − | 0.0686339i | \(-0.0218640\pi\) | |||||||
\(380\) | −3.40768 | + | 5.90228i | −0.174810 | + | 0.302780i | ||||
\(381\) | 1.74342 | + | 3.01969i | 0.0893180 | + | 0.154703i | ||||
\(382\) | −44.3013 | + | 25.5774i | −2.26665 | + | 1.30865i | ||||
\(383\) | −13.3898 | − | 7.73061i | −0.684187 | − | 0.395016i | 0.117243 | − | 0.993103i | \(-0.462594\pi\) |
−0.801431 | + | 0.598087i | \(0.795928\pi\) | |||||||
\(384\) | − | 1.78605i | − | 0.0911440i | ||||||
\(385\) | 4.78286 | − | 2.93152i | 0.243757 | − | 0.149404i | ||||
\(386\) | 63.8707 | 3.25093 | ||||||||
\(387\) | −4.08266 | + | 7.07138i | −0.207533 | + | 0.359458i | ||||
\(388\) | −8.13504 | + | 4.69677i | −0.412994 | + | 0.238442i | ||||
\(389\) | 4.69224 | + | 8.12719i | 0.237906 | + | 0.412065i | 0.960113 | − | 0.279612i | \(-0.0902057\pi\) |
−0.722207 | + | 0.691677i | \(0.756872\pi\) | |||||||
\(390\) | −2.64742 | + | 3.46312i | −0.134057 | + | 0.175362i | ||||
\(391\) | −16.2232 | −0.820444 | ||||||||
\(392\) | 45.2412 | + | 23.0415i | 2.28503 | + | 1.16377i | ||||
\(393\) | 19.7717 | 0.997349 | ||||||||
\(394\) | 27.8029 | − | 48.1560i | 1.40069 | − | 2.42606i | ||||
\(395\) | 2.35831 | − | 1.36157i | 0.118660 | − | 0.0685082i | ||||
\(396\) | 18.9278 | − | 10.9280i | 0.951158 | − | 0.549152i | ||||
\(397\) | −4.52648 | − | 2.61336i | −0.227177 | − | 0.131161i | 0.382092 | − | 0.924124i | \(-0.375204\pi\) |
−0.609269 | + | 0.792963i | \(0.708537\pi\) | |||||||
\(398\) | − | 45.0186i | − | 2.25658i | ||||||
\(399\) | 4.24303 | + | 6.92263i | 0.212417 | + | 0.346565i | ||||
\(400\) | 44.6057 | 2.23029 | ||||||||
\(401\) | −13.1585 | − | 7.59704i | −0.657102 | − | 0.379378i | 0.134070 | − | 0.990972i | \(-0.457195\pi\) |
−0.791172 | + | 0.611594i | \(0.790529\pi\) | |||||||
\(402\) | 7.36722 | + | 12.7604i | 0.367443 | + | 0.636431i | ||||
\(403\) | −31.2673 | + | 13.0176i | −1.55754 | + | 0.648451i | ||||
\(404\) | −37.4443 | + | 64.8555i | −1.86292 | + | 3.22668i | ||||
\(405\) | 0.464160i | 0.0230643i | ||||||||
\(406\) | −38.4103 | + | 1.00920i | −1.90627 | + | 0.0500857i | ||||
\(407\) | −33.4983 | −1.66045 | ||||||||
\(408\) | −27.1935 | − | 15.7002i | −1.34628 | − | 0.777274i | ||||
\(409\) | −2.65415 | + | 1.53237i | −0.131239 | + | 0.0757710i | −0.564182 | − | 0.825650i | \(-0.690808\pi\) |
0.432943 | + | 0.901421i | \(0.357475\pi\) | |||||||
\(410\) | −5.18483 | + | 2.99346i | −0.256060 | + | 0.147837i | ||||
\(411\) | 2.71225 | + | 1.56592i | 0.133785 | + | 0.0772409i | ||||
\(412\) | −21.3164 | −1.05018 | ||||||||
\(413\) | −8.74986 | + | 16.1186i | −0.430552 | + | 0.793146i | ||||
\(414\) | 9.76069i | 0.479712i | ||||||||
\(415\) | 0.169722 | − | 0.293967i | 0.00833131 | − | 0.0144303i | ||||
\(416\) | −32.5452 | + | 13.5496i | −1.59566 | + | 0.664324i | ||||
\(417\) | −5.29996 | − | 9.17980i | −0.259540 | − | 0.449537i | ||||
\(418\) | 31.6227 | + | 18.2574i | 1.54672 | + | 0.892998i | ||||
\(419\) | 28.3394 | 1.38447 | 0.692236 | − | 0.721671i | \(-0.256626\pi\) | ||||
0.692236 | + | 0.721671i | \(0.256626\pi\) | |||||||
\(420\) | −2.80318 | + | 5.16390i | −0.136781 | + | 0.251972i | ||||
\(421\) | 20.3101i | 0.989854i | 0.868934 | + | 0.494927i | \(0.164805\pi\) | ||||
−0.868934 | + | 0.494927i | \(0.835195\pi\) | |||||||
\(422\) | −60.1611 | − | 34.7340i | −2.92860 | − | 1.69083i | ||||
\(423\) | −1.67480 | + | 0.966946i | −0.0814316 | + | 0.0470145i | ||||
\(424\) | −41.6261 | + | 24.0328i | −2.02154 | + | 1.16714i | ||||
\(425\) | −10.3569 | + | 17.9387i | −0.502383 | + | 0.870152i | ||||
\(426\) | 21.8154 | 1.05696 | ||||||||
\(427\) | −0.335072 | − | 12.7529i | −0.0162152 | − | 0.617155i | ||||
\(428\) | 50.6365 | 2.44761 | ||||||||
\(429\) | 13.0848 | + | 10.0028i | 0.631741 | + | 0.482941i | ||||
\(430\) | −4.93596 | − | 8.54934i | −0.238033 | − | 0.412286i | ||||
\(431\) | 7.08307 | − | 4.08941i | 0.341180 | − | 0.196980i | −0.319614 | − | 0.947548i | \(-0.603553\pi\) |
0.660794 | + | 0.750568i | \(0.270220\pi\) | |||||||
\(432\) | −4.66143 | + | 8.07383i | −0.224273 | + | 0.388453i | ||||
\(433\) | −1.45603 | −0.0699724 | −0.0349862 | − | 0.999388i | \(-0.511139\pi\) | ||||
−0.0349862 | + | 0.999388i | \(0.511139\pi\) | |||||||
\(434\) | −55.1927 | + | 33.8288i | −2.64933 | + | 1.62383i | ||||
\(435\) | − | 2.58795i | − | 0.124083i | ||||||
\(436\) | 82.5356 | + | 47.6520i | 3.95274 | + | 2.28212i | ||||
\(437\) | −9.95933 | + | 5.75002i | −0.476419 | + | 0.275061i | ||||
\(438\) | 4.44921 | + | 7.70625i | 0.212591 | + | 0.368219i | ||||
\(439\) | −10.7864 | + | 18.6826i | −0.514807 | + | 0.891672i | 0.485045 | + | 0.874489i | \(0.338803\pi\) |
−0.999852 | + | 0.0171831i | \(0.994530\pi\) | |||||||
\(440\) | 15.3784i | 0.733139i | ||||||||
\(441\) | 3.81351 | + | 5.87002i | 0.181596 | + | 0.279525i | ||||
\(442\) | 5.23415 | − | 40.3201i | 0.248963 | − | 1.91783i | ||||
\(443\) | 6.44696 | − | 11.1665i | 0.306305 | − | 0.530535i | −0.671246 | − | 0.741234i | \(-0.734241\pi\) |
0.977551 | + | 0.210699i | \(0.0675741\pi\) | |||||||
\(444\) | 30.3856 | − | 17.5431i | 1.44203 | − | 0.832559i | ||||
\(445\) | 0.730848 | + | 1.26587i | 0.0346455 | + | 0.0600078i | ||||
\(446\) | 25.2406 | − | 43.7179i | 1.19518 | − | 2.07010i | ||||
\(447\) | − | 15.1133i | − | 0.714835i | ||||||
\(448\) | −15.3883 | + | 9.43182i | −0.727028 | + | 0.445612i | ||||
\(449\) | 3.89008i | 0.183584i | 0.995778 | + | 0.0917921i | \(0.0292595\pi\) | ||||
−0.995778 | + | 0.0917921i | \(0.970740\pi\) | |||||||
\(450\) | 10.7928 | + | 6.23121i | 0.508776 | + | 0.293742i | ||||
\(451\) | 11.3103 | + | 19.5900i | 0.532581 | + | 0.922457i | ||||
\(452\) | −12.4460 | − | 21.5571i | −0.585410 | − | 1.01396i | ||||
\(453\) | 2.89569 | + | 1.67183i | 0.136052 | + | 0.0785494i | ||||
\(454\) | 10.3151 | 0.484111 | ||||||||
\(455\) | −4.40442 | − | 0.454487i | −0.206482 | − | 0.0213067i | ||||
\(456\) | −22.2585 | −1.04235 | ||||||||
\(457\) | −10.6036 | − | 6.12199i | −0.496016 | − | 0.286375i | 0.231051 | − | 0.972942i | \(-0.425784\pi\) |
−0.727067 | + | 0.686567i | \(0.759117\pi\) | |||||||
\(458\) | 5.42669 | + | 9.39930i | 0.253573 | + | 0.439201i | ||||
\(459\) | −2.16465 | − | 3.74928i | −0.101037 | − | 0.175002i | ||||
\(460\) | −7.20708 | − | 4.16101i | −0.336032 | − | 0.194008i | ||||
\(461\) | − | 30.7975i | − | 1.43438i | −0.696877 | − | 0.717190i | \(-0.745428\pi\) | ||
0.696877 | − | 0.717190i | \(-0.254572\pi\) | |||||||
\(462\) | 27.6667 | + | 15.0186i | 1.28717 | + | 0.698730i | ||||
\(463\) | 1.54997i | 0.0720334i | 0.999351 | + | 0.0360167i | \(0.0114670\pi\) | ||||
−0.999351 | + | 0.0360167i | \(0.988533\pi\) | |||||||
\(464\) | 25.9900 | − | 45.0161i | 1.20656 | − | 2.08982i | ||||
\(465\) | −2.18005 | − | 3.77596i | −0.101098 | − | 0.175106i | ||||
\(466\) | 21.3564 | − | 12.3301i | 0.989315 | − | 0.571181i | ||||
\(467\) | −6.53403 | + | 11.3173i | −0.302359 | + | 0.523701i | −0.976670 | − | 0.214747i | \(-0.931107\pi\) |
0.674311 | + | 0.738447i | \(0.264441\pi\) | |||||||
\(468\) | −17.1074 | − | 2.22080i | −0.790791 | − | 0.102656i | ||||
\(469\) | −7.14026 | + | 13.1535i | −0.329707 | + | 0.607372i | ||||
\(470\) | − | 2.33809i | − | 0.107848i | ||||||
\(471\) | 10.3755 | − | 17.9709i | 0.478078 | − | 0.828056i | ||||
\(472\) | −25.1389 | − | 43.5418i | −1.15711 | − | 2.00418i | ||||
\(473\) | −32.3022 | + | 18.6497i | −1.48526 | + | 0.857514i | ||||
\(474\) | 13.2341 | + | 7.64072i | 0.607863 | + | 0.350950i | ||||
\(475\) | 14.6832i | 0.673712i | ||||||||
\(476\) | −1.43942 | − | 54.7846i | −0.0659757 | − | 2.51105i | ||||
\(477\) | −6.62702 | −0.303430 | ||||||||
\(478\) | −2.37971 | + | 4.12177i | −0.108845 | + | 0.188526i | ||||
\(479\) | 8.73629 | − | 5.04390i | 0.399171 | − | 0.230462i | −0.286955 | − | 0.957944i | \(-0.592643\pi\) |
0.686126 | + | 0.727482i | \(0.259310\pi\) | |||||||
\(480\) | −2.26915 | − | 3.93029i | −0.103572 | − | 0.179392i | ||||
\(481\) | 21.0056 | + | 16.0579i | 0.957771 | + | 0.732178i | ||||
\(482\) | −40.0037 | −1.82212 | ||||||||
\(483\) | −8.45300 | + | 5.18103i | −0.384625 | + | 0.235745i | ||||
\(484\) | 47.2084 | 2.14584 | ||||||||
\(485\) | 0.455644 | − | 0.789198i | 0.0206897 | − | 0.0358356i | ||||
\(486\) | −2.25575 | + | 1.30236i | −0.102323 | + | 0.0590762i | ||||
\(487\) | −6.85704 | + | 3.95891i | −0.310722 | + | 0.179396i | −0.647250 | − | 0.762278i | \(-0.724081\pi\) |
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(488\) | 30.2870 | + | 17.4862i | 1.37103 | + | 0.791564i | ||||
\(489\) | 8.18130i | 0.369971i | ||||||||
\(490\) | −8.45136 | + | 0.444412i | −0.381794 | + | 0.0200765i | ||||
\(491\) | 8.55041 | 0.385874 | 0.192937 | − | 0.981211i | \(-0.438199\pi\) | ||||
0.192937 | + | 0.981211i | \(0.438199\pi\) | |||||||
\(492\) | −20.5186 | − | 11.8464i | −0.925050 | − | 0.534078i | ||||
\(493\) | 12.0691 | + | 20.9043i | 0.543565 | + | 0.941483i | ||||
\(494\) | −11.0775 | − | 26.6073i | −0.498399 | − | 1.19712i | ||||
\(495\) | −1.06015 | + | 1.83623i | −0.0476500 | + | 0.0825323i | ||||
\(496\) | − | 87.5747i | − | 3.93222i | ||||||
\(497\) | 11.5797 | + | 18.8927i | 0.519422 | + | 0.847452i | ||||
\(498\) | 1.90485 | 0.0853583 | ||||||||
\(499\) | −18.7110 | − | 10.8028i | −0.837619 | − | 0.483599i | 0.0188355 | − | 0.999823i | \(-0.494004\pi\) |
−0.856454 | + | 0.516223i | \(0.827337\pi\) | |||||||
\(500\) | −18.8183 | + | 10.8648i | −0.841581 | + | 0.485887i | ||||
\(501\) | −16.3022 | + | 9.41206i | −0.728327 | + | 0.420500i | ||||
\(502\) | 46.8979 | + | 27.0765i | 2.09316 | + | 1.20849i | ||||
\(503\) | 24.3890 | 1.08745 | 0.543725 | − | 0.839264i | \(-0.317014\pi\) | ||||
0.543725 | + | 0.839264i | \(0.317014\pi\) | |||||||
\(504\) | −19.1830 | + | 0.504017i | −0.854477 | + | 0.0224507i | ||||
\(505\) | − | 7.26511i | − | 0.323293i | ||||||
\(506\) | −22.2935 | + | 38.6135i | −0.991068 | + | 1.71658i | ||||
\(507\) | −3.41000 | − | 12.5448i | −0.151443 | − | 0.557134i | ||||
\(508\) | −8.34148 | − | 14.4479i | −0.370093 | − | 0.641021i | ||||
\(509\) | 19.7239 | + | 11.3876i | 0.874244 | + | 0.504745i | 0.868756 | − | 0.495240i | \(-0.164920\pi\) |
0.00548797 | + | 0.999985i | \(0.498253\pi\) | |||||||
\(510\) | 5.23415 | 0.231772 | ||||||||
\(511\) | −4.31214 | + | 7.94365i | −0.190758 | + | 0.351406i | ||||
\(512\) | 44.0832i | 1.94822i | ||||||||
\(513\) | −2.65773 | − | 1.53444i | −0.117341 | − | 0.0677471i | ||||
\(514\) | −18.2866 | + | 10.5578i | −0.806586 | + | 0.465683i | ||||
\(515\) | 1.79090 | − | 1.03398i | 0.0789164 | − | 0.0455624i | ||||
\(516\) | 19.5337 | − | 33.8334i | 0.859924 | − | 1.48943i | ||||
\(517\) | −8.83406 | −0.388522 | ||||||||
\(518\) | 44.4144 | + | 24.1100i | 1.95146 | + | 1.05933i | ||||
\(519\) | −8.64360 | −0.379412 | ||||||||
\(520\) | 7.37189 | − | 9.64325i | 0.323279 | − | 0.422885i | ||||
\(521\) | 5.05760 | + | 8.76002i | 0.221577 | + | 0.383783i | 0.955287 | − | 0.295680i | \(-0.0955461\pi\) |
−0.733710 | + | 0.679463i | \(0.762213\pi\) | |||||||
\(522\) | 12.5771 | − | 7.26137i | 0.550483 | − | 0.317821i | ||||
\(523\) | −8.30220 | + | 14.3798i | −0.363030 | + | 0.628786i | −0.988458 | − | 0.151496i | \(-0.951591\pi\) |
0.625428 | + | 0.780282i | \(0.284924\pi\) | |||||||
\(524\) | −94.5987 | −4.13256 | ||||||||
\(525\) | 0.332483 | + | 12.6544i | 0.0145108 | + | 0.552282i | ||||
\(526\) | 9.82416i | 0.428354i | ||||||||
\(527\) | 35.2190 | + | 20.3337i | 1.53417 | + | 0.885751i | ||||
\(528\) | −36.8815 | + | 21.2935i | −1.60506 | + | 0.926681i | ||||
\(529\) | 4.47883 | + | 7.75756i | 0.194732 | + | 0.337285i | ||||
\(530\) | 4.00605 | − | 6.93868i | 0.174012 | − | 0.301397i | ||||
\(531\) | − | 6.93202i | − | 0.300824i | ||||||
\(532\) | −20.3010 | − | 33.1217i | −0.880161 | − | 1.43601i | ||||
\(533\) | 2.29849 | − | 17.7059i | 0.0995588 | − | 0.766928i | ||||
\(534\) | −4.10128 | + | 7.10363i | −0.177480 | + | 0.307404i | ||||
\(535\) | −4.25423 | + | 2.45618i | −0.183926 | + | 0.106190i | ||||
\(536\) | −20.5144 | − | 35.5320i | −0.886088 | − | 1.53475i | ||||
\(537\) | −9.96461 | + | 17.2592i | −0.430005 | + | 0.744790i | ||||
\(538\) | − | 57.4795i | − | 2.47812i | ||||||
\(539\) | 1.67914 | + | 31.9320i | 0.0723255 | + | 1.37541i | ||||
\(540\) | − | 2.22080i | − | 0.0955680i | ||||||
\(541\) | −24.4034 | − | 14.0893i | −1.04918 | − | 0.605746i | −0.126763 | − | 0.991933i | \(-0.540459\pi\) |
−0.922421 | + | 0.386187i | \(0.873792\pi\) | |||||||
\(542\) | −15.6221 | − | 27.0584i | −0.671029 | − | 1.16226i | ||||
\(543\) | −0.129564 | − | 0.224411i | −0.00556012 | − | 0.00963041i | ||||
\(544\) | 36.6585 | + | 21.1648i | 1.57172 | + | 0.907432i | ||||
\(545\) | −9.24564 | −0.396040 | ||||||||
\(546\) | −10.1494 | − | 22.6801i | −0.434352 | − | 0.970617i | ||||
\(547\) | −28.7280 | −1.22832 | −0.614160 | − | 0.789181i | \(-0.710505\pi\) | ||||
−0.614160 | + | 0.789181i | \(0.710505\pi\) | |||||||
\(548\) | −12.9769 | − | 7.49221i | −0.554345 | − | 0.320051i | ||||
\(549\) | 2.41090 | + | 4.17580i | 0.102895 | + | 0.178219i | ||||
\(550\) | 28.4643 | + | 49.3016i | 1.21372 | + | 2.10223i | ||||
\(551\) | 14.8183 | + | 8.55534i | 0.631280 | + | 0.364470i | ||||
\(552\) | − | 27.1792i | − | 1.15682i | ||||||
\(553\) | 0.407692 | + | 15.5168i | 0.0173368 | + | 0.659842i | ||||
\(554\) | − | 76.6576i | − | 3.25687i | ||||||
\(555\) | −1.70189 | + | 2.94777i | −0.0722414 | + | 0.125126i | ||||
\(556\) | 25.3579 | + | 43.9213i | 1.07542 | + | 1.86268i | ||||
\(557\) | 23.6204 | − | 13.6373i | 1.00083 | − | 0.577829i | 0.0923362 | − | 0.995728i | \(-0.470567\pi\) |
0.908494 | + | 0.417898i | \(0.137233\pi\) | |||||||
\(558\) | 12.2338 | − | 21.1895i | 0.517896 | − | 0.897023i | ||||
\(559\) | 29.1955 | + | 3.79002i | 1.23484 | + | 0.160301i | ||||
\(560\) | 5.46208 | − | 10.0620i | 0.230815 | − | 0.425198i | ||||
\(561\) | − | 19.7763i | − | 0.834958i | ||||||
\(562\) | −13.4389 | + | 23.2768i | −0.566885 | + | 0.981873i | ||||
\(563\) | −4.35825 | − | 7.54871i | −0.183678 | − | 0.318140i | 0.759452 | − | 0.650563i | \(-0.225467\pi\) |
−0.943130 | + | 0.332423i | \(0.892134\pi\) | |||||||
\(564\) | 8.01317 | − | 4.62641i | 0.337416 | − | 0.194807i | ||||
\(565\) | 2.09130 | + | 1.20741i | 0.0879816 | + | 0.0507962i | ||||
\(566\) | − | 28.6036i | − | 1.20230i | ||||||
\(567\) | −2.32524 | − | 1.26224i | −0.0976510 | − | 0.0530090i | ||||
\(568\) | −60.7461 | −2.54885 | ||||||||
\(569\) | 16.6405 | − | 28.8221i | 0.697604 | − | 1.20829i | −0.271690 | − | 0.962385i | \(-0.587583\pi\) |
0.969295 | − | 0.245902i | \(-0.0790840\pi\) | |||||||
\(570\) | 3.21321 | − | 1.85515i | 0.134586 | − | 0.0777035i | ||||
\(571\) | −6.40807 | − | 11.0991i | −0.268169 | − | 0.464483i | 0.700220 | − | 0.713927i | \(-0.253085\pi\) |
−0.968389 | + | 0.249444i | \(0.919752\pi\) | |||||||
\(572\) | −62.6050 | − | 47.8591i | −2.61765 | − | 2.00109i | ||||
\(573\) | 19.6393 | 0.820443 | ||||||||
\(574\) | −0.896323 | − | 34.1142i | −0.0374118 | − | 1.42390i | ||||
\(575\) | −17.9292 | −0.747700 | ||||||||
\(576\) | 3.41090 | − | 5.90785i | 0.142121 | − | 0.246161i | ||||
\(577\) | 19.9802 | − | 11.5356i | 0.831788 | − | 0.480233i | −0.0226765 | − | 0.999743i | \(-0.507219\pi\) |
0.854464 | + | 0.519510i | \(0.173885\pi\) | |||||||
\(578\) | −3.93139 | + | 2.26979i | −0.163524 | + | 0.0944109i | ||||
\(579\) | −21.2359 | − | 12.2606i | −0.882536 | − | 0.509532i | ||||
\(580\) | 12.3822i | 0.514142i | ||||||||
\(581\) | 1.01111 | + | 1.64965i | 0.0419477 | + | 0.0684389i | ||||
\(582\) | 5.11385 | 0.211976 | ||||||||
\(583\) | −26.2166 | − | 15.1362i | −1.08578 | − | 0.626877i | ||||
\(584\) | −12.3891 | − | 21.4585i | −0.512663 | − | 0.887958i | ||||
\(585\) | 1.54500 | − | 0.643233i | 0.0638779 | − | 0.0265944i | ||||
\(586\) | 19.2273 | − | 33.3027i | 0.794273 | − | 1.37572i | ||||
\(587\) | 45.6950i | 1.88603i | 0.332745 | + | 0.943017i | \(0.392025\pi\) | ||||
−0.332745 | + | 0.943017i | \(0.607975\pi\) | |||||||
\(588\) | −18.2459 | − | 28.0854i | −0.752450 | − | 1.15822i | ||||
\(589\) | 28.8276 | 1.18782 | ||||||||
\(590\) | 7.25803 | + | 4.19042i | 0.298808 | + | 0.172517i | ||||
\(591\) | −18.4880 | + | 10.6740i | −0.760494 | + | 0.439071i | ||||
\(592\) | −59.2072 | + | 34.1833i | −2.43340 | + | 1.40493i | ||||
\(593\) | −21.0446 | − | 12.1501i | −0.864197 | − | 0.498945i | 0.00121818 | − | 0.999999i | \(-0.499612\pi\) |
−0.865416 | + | 0.501055i | \(0.832946\pi\) | |||||||
\(594\) | −11.8984 | −0.488198 | ||||||||
\(595\) | 2.77832 | + | 4.53290i | 0.113900 | + | 0.185831i | ||||
\(596\) | 72.3105i | 2.96195i | ||||||||
\(597\) | −8.64175 | + | 14.9679i | −0.353683 | + | 0.612597i | ||||
\(598\) | 32.4894 | − | 13.5264i | 1.32859 | − | 0.553134i | ||||
\(599\) | 15.6357 | + | 27.0818i | 0.638857 | + | 1.10653i | 0.985684 | + | 0.168604i | \(0.0539259\pi\) |
−0.346827 | + | 0.937929i | \(0.612741\pi\) | |||||||
\(600\) | −30.0531 | − | 17.3511i | −1.22691 | − | 0.708358i | ||||
\(601\) | −16.1139 | −0.657298 | −0.328649 | − | 0.944452i | \(-0.606593\pi\) | ||||
−0.328649 | + | 0.944452i | \(0.606593\pi\) | |||||||
\(602\) | 56.2514 | − | 1.47796i | 2.29264 | − | 0.0602371i | ||||
\(603\) | − | 5.65682i | − | 0.230364i | ||||||
\(604\) | −13.8546 | − | 7.99896i | −0.563736 | − | 0.325473i | ||||
\(605\) | −3.96621 | + | 2.28989i | −0.161249 | + | 0.0930974i | ||||
\(606\) | 35.3074 | − | 20.3847i | 1.43426 | − | 0.828073i | ||||
\(607\) | 2.70189 | − | 4.67982i | 0.109667 | − | 0.189948i | −0.805969 | − | 0.591958i | \(-0.798355\pi\) |
0.915635 | + | 0.402010i | \(0.131688\pi\) | |||||||
\(608\) | 30.0058 | 1.21690 | ||||||||
\(609\) | 12.9645 | + | 7.03767i | 0.525348 | + | 0.285181i | ||||
\(610\) | −5.82958 | −0.236033 | ||||||||
\(611\) | 5.53951 | + | 4.23474i | 0.224105 | + | 0.171319i | ||||
\(612\) | 10.3569 | + | 17.9387i | 0.418652 | + | 0.725127i | ||||
\(613\) | −15.1816 | + | 8.76508i | −0.613178 | + | 0.354018i | −0.774208 | − | 0.632931i | \(-0.781852\pi\) |
0.161030 | + | 0.986949i | \(0.448518\pi\) | |||||||
\(614\) | −16.7398 | + | 28.9942i | −0.675564 | + | 1.17011i | ||||
\(615\) | 2.29849 | 0.0926842 | ||||||||
\(616\) | −77.0394 | − | 41.8202i | −3.10401 | − | 1.68498i | ||||
\(617\) | 6.14240i | 0.247284i | 0.992327 | + | 0.123642i | \(0.0394574\pi\) | ||||
−0.992327 | + | 0.123642i | \(0.960543\pi\) | |||||||
\(618\) | 10.0500 | + | 5.80234i | 0.404268 | + | 0.233404i | ||||
\(619\) | 2.55396 | − | 1.47453i | 0.102652 | − | 0.0592663i | −0.447795 | − | 0.894136i | \(-0.647791\pi\) |
0.550447 | + | 0.834870i | \(0.314457\pi\) | |||||||
\(620\) | 10.4306 | + | 18.0663i | 0.418902 | + | 0.725560i | ||||
\(621\) | 1.87366 | − | 3.24527i | 0.0751872 | − | 0.130228i | ||||
\(622\) | 32.2687i | 1.29386i | ||||||||
\(623\) | −8.32891 | + | 0.218835i | −0.333691 | + | 0.00876745i | ||||
\(624\) | 33.3344 | + | 4.32730i | 1.33444 | + | 0.173231i | ||||
\(625\) | −10.9074 | + | 18.8921i | −0.436295 | + | 0.755685i | ||||
\(626\) | −65.8984 | + | 38.0464i | −2.63383 | + | 1.52064i | ||||
\(627\) | −7.00935 | − | 12.1406i | −0.279927 | − | 0.484847i | ||||
\(628\) | −49.6422 | + | 85.9828i | −1.98094 | + | 3.43109i | ||||
\(629\) | − | 31.7477i | − | 1.26586i | ||||||
\(630\) | 2.72722 | − | 1.67157i | 0.108655 | − | 0.0665970i | ||||
\(631\) | − | 16.2280i | − | 0.646028i | −0.946394 | − | 0.323014i | \(-0.895304\pi\) | ||
0.946394 | − | 0.323014i | \(-0.104696\pi\) | |||||||
\(632\) | −36.8511 | − | 21.2760i | −1.46586 | − | 0.846314i | ||||
\(633\) | 13.3350 | + | 23.0970i | 0.530020 | + | 0.918022i | ||||
\(634\) | −12.8032 | − | 22.1758i | −0.508479 | − | 0.880712i | ||||
\(635\) | 1.40162 | + | 0.809225i | 0.0556216 | + | 0.0321131i | ||||
\(636\) | 31.7073 | 1.25728 | ||||||||
\(637\) | 14.2542 | − | 20.8283i | 0.564771 | − | 0.825248i | ||||
\(638\) | 66.3402 | 2.62643 | ||||||||
\(639\) | −7.25325 | − | 4.18766i | −0.286934 | − | 0.165661i | ||||
\(640\) | −0.414507 | − | 0.717947i | −0.0163848 | − | 0.0283793i | ||||
\(641\) | 1.40622 | + | 2.43564i | 0.0555422 | + | 0.0962018i | 0.892460 | − | 0.451127i | \(-0.148978\pi\) |
−0.836917 | + | 0.547329i | \(0.815645\pi\) | |||||||
\(642\) | −23.8734 | − | 13.7833i | −0.942207 | − | 0.543983i | ||||
\(643\) | 29.0689i | 1.14637i | 0.819428 | + | 0.573183i | \(0.194292\pi\) | ||||
−0.819428 | + | 0.573183i | \(0.805708\pi\) | |||||||
\(644\) | 40.4439 | − | 24.7889i | 1.59371 | − | 0.976821i | ||||
\(645\) | 3.79002i | 0.149232i | ||||||||
\(646\) | −17.3033 | + | 29.9701i | −0.680788 | + | 1.17916i | ||||
\(647\) | −18.7051 | − | 32.3982i | −0.735373 | − | 1.27370i | −0.954559 | − | 0.298021i | \(-0.903674\pi\) |
0.219186 | − | 0.975683i | \(-0.429660\pi\) | |||||||
\(648\) | 6.28127 | − | 3.62649i | 0.246751 | − | 0.142462i | ||||
\(649\) | 15.8328 | − | 27.4232i | 0.621492 | − | 1.07646i | ||||
\(650\) | 5.78456 | − | 44.5600i | 0.226889 | − | 1.74779i | ||||
\(651\) | 24.8444 | − | 0.652766i | 0.973729 | − | 0.0255839i | ||||
\(652\) | − | 39.1439i | − | 1.53299i | ||||||
\(653\) | −3.77665 | + | 6.54135i | −0.147792 | + | 0.255983i | −0.930411 | − | 0.366518i | \(-0.880550\pi\) |
0.782619 | + | 0.622501i | \(0.213883\pi\) | |||||||
\(654\) | −25.9418 | − | 44.9325i | −1.01440 | − | 1.75700i | ||||
\(655\) | 7.94771 | − | 4.58861i | 0.310543 | − | 0.179292i | ||||
\(656\) | 39.9812 | + | 23.0831i | 1.56100 | + | 0.901245i | ||||
\(657\) | − | 3.41627i | − | 0.133281i | ||||||
\(658\) | 11.7128 | + | 6.35820i | 0.456613 | + | 0.247869i | ||||
\(659\) | −35.1269 | −1.36835 | −0.684175 | − | 0.729318i | \(-0.739837\pi\) | ||||
−0.684175 | + | 0.729318i | \(0.739837\pi\) | |||||||
\(660\) | 5.07233 | − | 8.78553i | 0.197440 | − | 0.341976i | ||||
\(661\) | −13.8292 | + | 7.98429i | −0.537893 | + | 0.310553i | −0.744225 | − | 0.667929i | \(-0.767181\pi\) |
0.206331 | + | 0.978482i | \(0.433848\pi\) | |||||||
\(662\) | 6.54444 | + | 11.3353i | 0.254357 | + | 0.440559i | ||||
\(663\) | −9.48008 | + | 12.4010i | −0.368176 | + | 0.481615i | ||||
\(664\) | −5.30416 | −0.205841 | ||||||||
\(665\) | 3.31219 | + | 1.79800i | 0.128441 | + | 0.0697233i | ||||
\(666\) | −19.1010 | −0.740148 | ||||||||
\(667\) | −10.4467 | + | 18.0941i | −0.404496 | + | 0.700608i | ||||
\(668\) | 77.9986 | − | 45.0325i | 3.01786 | − | 1.74236i | ||||
\(669\) | −16.7841 | + | 9.69033i | −0.648912 | + | 0.374650i | ||||
\(670\) | 5.92286 | + | 3.41957i | 0.228820 | + | 0.132109i | ||||
\(671\) | 22.0261i | 0.850308i | ||||||||
\(672\) | 25.8598 | − | 0.679445i | 0.997563 | − | 0.0262102i | ||||
\(673\) | 14.9364 | 0.575757 | 0.287879 | − | 0.957667i | \(-0.407050\pi\) | ||||
0.287879 | + | 0.957667i | \(0.407050\pi\) | |||||||
\(674\) | 1.20950 | + | 0.698305i | 0.0465882 | + | 0.0268977i | ||||
\(675\) | −2.39228 | − | 4.14355i | −0.0920788 | − | 0.159485i | ||||
\(676\) | 16.3153 | + | 60.0213i | 0.627512 | + | 2.30851i | ||||
\(677\) | −1.99065 | + | 3.44790i | −0.0765068 | + | 0.132514i | −0.901741 | − | 0.432278i | \(-0.857710\pi\) |
0.825234 | + | 0.564791i | \(0.191043\pi\) | |||||||
\(678\) | 13.5512i | 0.520431i | ||||||||
\(679\) | 2.71447 | + | 4.42873i | 0.104172 | + | 0.169959i | ||||
\(680\) | −14.5748 | −0.558917 | ||||||||
\(681\) | −3.42959 | − | 1.98008i | −0.131422 | − | 0.0758767i | ||||
\(682\) | 96.7941 | − | 55.8841i | 3.70644 | − | 2.13991i | ||||
\(683\) | 2.56232 | − | 1.47935i | 0.0980443 | − | 0.0566059i | −0.450176 | − | 0.892940i | \(-0.648639\pi\) |
0.548220 | + | 0.836334i | \(0.315305\pi\) | |||||||
\(684\) | 12.7160 | + | 7.34161i | 0.486210 | + | 0.280713i | ||||
\(685\) | 1.45367 | 0.0555419 | ||||||||
\(686\) | 20.7564 | − | 43.5463i | 0.792481 | − | 1.66260i | ||||
\(687\) | − | 4.16682i | − | 0.158974i | ||||||
\(688\) | −38.0621 | + | 65.9255i | −1.45110 | + | 2.51338i | ||||
\(689\) | 9.18372 | + | 22.0587i | 0.349872 | + | 0.840368i | ||||
\(690\) | 2.26526 | + | 3.92355i | 0.0862370 | + | 0.149367i | ||||
\(691\) | 18.1762 | + | 10.4941i | 0.691457 | + | 0.399213i | 0.804158 | − | 0.594416i | \(-0.202617\pi\) |
−0.112701 | + | 0.993629i | \(0.535950\pi\) | |||||||
\(692\) | 41.3558 | 1.57211 | ||||||||
\(693\) | −6.31575 | − | 10.3043i | −0.239915 | − | 0.391429i | ||||
\(694\) | 71.9164i | 2.72991i | ||||||||
\(695\) | −4.26089 | − | 2.46003i | −0.161625 | − | 0.0933142i | ||||
\(696\) | −35.0215 | + | 20.2197i | −1.32749 | + | 0.766425i | ||||
\(697\) | −18.5662 | + | 10.7192i | −0.703246 | + | 0.406019i | ||||
\(698\) | −44.5811 | + | 77.2167i | −1.68742 | + | 2.92269i | ||||
\(699\) | −9.46752 | −0.358095 | ||||||||
\(700\) | −1.59079 | − | 60.5456i | −0.0601260 | − | 2.28841i | ||||
\(701\) | −16.0616 | −0.606639 | −0.303319 | − | 0.952889i | \(-0.598095\pi\) | ||||
−0.303319 | + | 0.952889i | \(0.598095\pi\) | |||||||
\(702\) | 7.46105 | + | 5.70368i | 0.281599 | + | 0.215271i | ||||
\(703\) | −11.2524 | − | 19.4897i | −0.424392 | − | 0.735068i | ||||
\(704\) | 26.9872 | − | 15.5811i | 1.01712 | − | 0.587234i | ||||
\(705\) | −0.448818 | + | 0.777375i | −0.0169035 | + | 0.0292776i | ||||
\(706\) | 47.1877 | 1.77593 | ||||||||
\(707\) | 36.3951 | + | 19.7568i | 1.36878 | + | 0.743029i | ||||
\(708\) | 33.1666i | 1.24648i | ||||||||
\(709\) | −21.4558 | − | 12.3875i | −0.805788 | − | 0.465222i | 0.0397031 | − | 0.999212i | \(-0.487359\pi\) |
−0.845491 | + | 0.533990i | \(0.820692\pi\) | |||||||
\(710\) | 8.76922 | − | 5.06291i | 0.329103 | − | 0.190008i | ||||
\(711\) | −2.93341 | − | 5.08082i | −0.110012 | − | 0.190546i | ||||
\(712\) | 11.4203 | − | 19.7805i | 0.427992 | − | 0.741304i | ||||
\(713\) | 35.2005i | 1.31827i | ||||||||
\(714\) | −14.2338 | + | 26.2208i | −0.532685 | + | 0.981290i | ||||
\(715\) | 7.58121 | + | 0.984155i | 0.283521 | + | 0.0368053i | ||||
\(716\) | 47.6762 | − | 82.5776i | 1.78174 | − | 3.08607i | ||||
\(717\) | 1.58243 | − | 0.913614i | 0.0590968 | − | 0.0341195i | ||||
\(718\) | −4.89228 | − | 8.47367i | −0.182578 | − | 0.316235i | ||||
\(719\) | 15.8716 | − | 27.4904i | 0.591911 | − | 1.02522i | −0.402063 | − | 0.915612i | \(-0.631707\pi\) |
0.993975 | − | 0.109609i | \(-0.0349598\pi\) | |||||||
\(720\) | 4.32730i | 0.161269i | ||||||||
\(721\) | 0.309600 | + | 11.7834i | 0.0115301 | + | 0.438838i | ||||
\(722\) | − | 24.9584i | − | 0.928855i | ||||||
\(723\) | 13.3006 | + | 7.67909i | 0.494653 | + | 0.285588i | ||||
\(724\) | 0.619906 | + | 1.07371i | 0.0230386 | + | 0.0399041i | ||||
\(725\) | 13.3383 | + | 23.1026i | 0.495371 | + | 0.858007i | ||||
\(726\) | −22.2571 | − | 12.8502i | −0.826039 | − | 0.476914i | ||||
\(727\) | 36.4008 | 1.35003 | 0.675016 | − | 0.737803i | \(-0.264137\pi\) | ||||
0.675016 | + | 0.737803i | \(0.264137\pi\) | |||||||
\(728\) | 28.2614 | + | 63.1539i | 1.04744 | + | 2.34064i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.57693 | + | 2.06514i | 0.132388 | + | 0.0764344i | ||||
\(731\) | −17.6751 | − | 30.6141i | −0.653736 | − | 1.13230i | ||||
\(732\) | −11.5351 | − | 19.9794i | −0.426349 | − | 0.738458i | ||||
\(733\) | −14.2104 | − | 8.20439i | −0.524874 | − | 0.303036i | 0.214053 | − | 0.976822i | \(-0.431334\pi\) |
−0.738927 | + | 0.673786i | \(0.764667\pi\) | |||||||
\(734\) | 6.54810i | 0.241695i | ||||||||
\(735\) | 2.89525 | + | 1.47456i | 0.106793 | + | 0.0543899i | ||||
\(736\) | 36.6392i | 1.35054i | ||||||||
\(737\) | 12.9203 | − | 22.3785i | 0.475924 | − | 0.824324i | ||||
\(738\) | 6.44921 | + | 11.1704i | 0.237399 | + | 0.411186i | ||||
\(739\) | 32.8322 | − | 18.9557i | 1.20775 | − | 0.697296i | 0.245485 | − | 0.969400i | \(-0.421053\pi\) |
0.962268 | + | 0.272104i | \(0.0877195\pi\) | |||||||
\(740\) | 8.14281 | − | 14.1038i | 0.299336 | − | 0.518464i | ||||
\(741\) | −1.42445 | + | 10.9729i | −0.0523285 | + | 0.403100i | ||||
\(742\) | 23.8658 | + | 38.9377i | 0.876140 | + | 1.42945i | ||||
\(743\) | − | 33.6517i | − | 1.23456i | −0.786743 | − | 0.617280i | \(-0.788234\pi\) | ||
0.786743 | − | 0.617280i | \(-0.211766\pi\) | |||||||
\(744\) | −34.0656 | + | 59.0033i | −1.24890 | + | 2.16317i | ||||
\(745\) | −3.50750 | − | 6.07517i | −0.128505 | − | 0.222577i | ||||
\(746\) | 13.7364 | − | 7.93070i | 0.502924 | − | 0.290363i | ||||
\(747\) | −0.633331 | − | 0.365654i | −0.0231724 | − | 0.0133786i | ||||
\(748\) | 94.6210i | 3.45969i | ||||||||
\(749\) | −0.735446 | − | 27.9912i | −0.0268726 | − | 1.02278i | ||||
\(750\) | 11.8296 | 0.431955 | ||||||||
\(751\) | −2.85330 | + | 4.94206i | −0.104118 | + | 0.180338i | −0.913378 | − | 0.407113i | \(-0.866535\pi\) |
0.809259 | + | 0.587452i | \(0.199869\pi\) | |||||||
\(752\) | −15.6139 | + | 9.01471i | −0.569381 | + | 0.328732i | ||||
\(753\) | −10.3952 | − | 18.0050i | −0.378822 | − | 0.656139i | ||||
\(754\) | −41.5995 | − | 31.8011i | −1.51496 | − | 1.15813i | ||||
\(755\) | 1.55199 | 0.0564828 | ||||||||
\(756\) | 11.1253 | + | 6.03925i | 0.404622 | + | 0.219645i | ||||
\(757\) | 10.4161 | 0.378578 | 0.189289 | − | 0.981921i | \(-0.439382\pi\) | ||||
0.189289 | + | 0.981921i | \(0.439382\pi\) | |||||||
\(758\) | 3.48032 | − | 6.02809i | 0.126411 | − | 0.218950i | ||||
\(759\) | 14.8244 | − | 8.55890i | 0.538093 | − | 0.310668i | ||||
\(760\) | −8.94735 | + | 5.16576i | −0.324555 | + | 0.187382i | ||||
\(761\) | −44.7324 | − | 25.8262i | −1.62155 | − | 0.936201i | −0.986507 | − | 0.163722i | \(-0.947650\pi\) |
−0.635041 | − | 0.772479i | \(-0.719017\pi\) | |||||||
\(762\) | 9.08223i | 0.329014i | ||||||||
\(763\) | 25.1426 | − | 46.3167i | 0.910224 | − | 1.67678i | ||||
\(764\) | −93.9652 | −3.39954 | ||||||||
\(765\) | −1.74027 | − | 1.00474i | −0.0629195 | − | 0.0363266i | ||||
\(766\) | −20.1361 | − | 34.8767i | −0.727546 | − | 1.26015i | ||||
\(767\) | −23.0739 | + | 9.60639i | −0.833150 | + | 0.346867i | ||||
\(768\) | 9.14788 | − | 15.8446i | 0.330096 | − | 0.571743i | ||||
\(769\) | − | 0.362142i | − | 0.0130592i | −0.999979 | − | 0.00652958i | \(-0.997922\pi\) | ||
0.999979 | − | 0.00652958i | \(-0.00207845\pi\) | |||||||
\(770\) | 14.6068 | − | 0.383782i | 0.526393 | − | 0.0138306i | ||||
\(771\) | 8.10664 | 0.291954 | ||||||||
\(772\) | 101.605 | + | 58.6614i | 3.65683 | + | 2.11127i | ||||
\(773\) | 11.6446 | − | 6.72303i | 0.418828 | − | 0.241811i | −0.275748 | − | 0.961230i | \(-0.588925\pi\) |
0.694576 | + | 0.719420i | \(0.255592\pi\) | |||||||
\(774\) | −18.4189 | + | 10.6342i | −0.662055 | + | 0.382238i | ||||
\(775\) | 38.9226 | + | 22.4720i | 1.39814 | + | 0.807216i | ||||
\(776\) | −14.2398 | −0.511179 | ||||||||
\(777\) | −10.1389 | − | 16.5419i | −0.363732 | − | 0.593438i | ||||
\(778\) | 24.4439i | 0.876356i | ||||||||
\(779\) | −7.59845 | + | 13.1609i | −0.272243 | + | 0.471538i | ||||
\(780\) | −7.39215 | + | 3.07758i | −0.264681 | + | 0.110195i | ||||
\(781\) | −19.1293 | − | 33.1330i | −0.684502 | − | 1.18559i | ||||
\(782\) | −36.5956 | − | 21.1285i | −1.30866 | − | 0.755552i | ||||
\(783\) | −5.57555 | −0.199254 | ||||||||
\(784\) | 35.5528 | + | 54.7254i | 1.26974 | + | 1.95448i | ||||
\(785\) | − | 9.63179i | − | 0.343773i | ||||||
\(786\) | 44.6000 | + | 25.7498i | 1.59083 | + | 0.918466i | ||||
\(787\) | 15.0347 | − | 8.68027i | 0.535928 | − | 0.309418i | −0.207499 | − | 0.978235i | \(-0.566532\pi\) |
0.743427 | + | 0.668817i | \(0.233199\pi\) | |||||||
\(788\) | 88.4568 | − | 51.0706i | 3.15114 | − | 1.81931i | ||||
\(789\) | 1.88584 | − | 3.26637i | 0.0671376 | − | 0.116286i | ||||
\(790\) | 7.09303 | 0.252359 | ||||||||
\(791\) | −11.7357 | + | 7.19307i | −0.417273 | + | 0.255756i | ||||
\(792\) | 33.1318 | 1.17729 | ||||||||
\(793\) | 10.5585 | − | 13.8117i | 0.374945 | − | 0.490469i | ||||
\(794\) | −6.80707 | − | 11.7902i | −0.241574 | − | 0.418418i | ||||
\(795\) | −2.66389 | + | 1.53800i | −0.0944785 | + | 0.0545472i | ||||
\(796\) | 41.3469 | − | 71.6150i | 1.46550 | − | 2.53833i | ||||
\(797\) | −35.1519 | −1.24514 | −0.622572 | − | 0.782563i | \(-0.713912\pi\) | ||||
−0.622572 | + | 0.782563i | \(0.713912\pi\) | |||||||
\(798\) | 0.555480 | + | 21.1417i | 0.0196638 | + | 0.748407i | ||||
\(799\) | − | 8.37240i | − | 0.296194i | ||||||
\(800\) | 40.5134 | + | 23.3904i | 1.43236 | + | 0.826975i | ||||
\(801\) | 2.72722 | − | 1.57456i | 0.0963615 | − | 0.0556343i | ||||
\(802\) | −19.7881 | − | 34.2741i | −0.698744 | − | 1.21026i | ||||
\(803\) | 7.80279 | − | 13.5148i | 0.275355 | − | 0.476928i | ||||
\(804\) | 27.0654i | 0.954523i | ||||||||
\(805\) | −2.19548 | + | 4.04442i | −0.0773804 | + | 0.142547i | ||||
\(806\) | −87.4848 | − | 11.3568i | −3.08152 | − | 0.400028i | ||||
\(807\) | −11.0337 | + | 19.1110i | −0.388405 | + | 0.672738i | ||||
\(808\) | −98.3154 | + | 56.7624i | −3.45872 | + | 1.99689i | ||||
\(809\) | −0.0546871 | − | 0.0947209i | −0.00192270 | − | 0.00333021i | 0.865062 | − | 0.501664i | \(-0.167279\pi\) |
−0.866985 | + | 0.498334i | \(0.833945\pi\) | |||||||
\(810\) | −0.604503 | + | 1.04703i | −0.0212401 | + | 0.0367889i | ||||
\(811\) | − | 11.0787i | − | 0.389026i | −0.980900 | − | 0.194513i | \(-0.937687\pi\) | ||
0.980900 | − | 0.194513i | \(-0.0623127\pi\) | |||||||
\(812\) | −62.0294 | − | 33.6721i | −2.17681 | − | 1.18166i | ||||
\(813\) | 11.9953i | 0.420692i | ||||||||
\(814\) | −75.5639 | − | 43.6268i | −2.64851 | − | 1.52912i | ||||
\(815\) | 1.89872 | + | 3.28867i | 0.0665091 | + | 0.115197i | ||||
\(816\) | −20.1807 | − | 34.9540i | −0.706467 | − | 1.22364i | ||||
\(817\) | −21.7012 | − | 12.5292i | −0.759229 | − | 0.438341i | ||||
\(818\) | −7.98280 | −0.279112 | ||||||||
\(819\) | −0.979160 | + | 9.48901i | −0.0342146 | + | 0.331573i | ||||
\(820\) | −10.9973 | −0.384041 | ||||||||
\(821\) | 3.52286 | + | 2.03392i | 0.122949 | + | 0.0709845i | 0.560213 | − | 0.828349i | \(-0.310719\pi\) |
−0.437264 | + | 0.899333i | \(0.644053\pi\) | |||||||
\(822\) | 4.07877 | + | 7.06464i | 0.142263 | + | 0.246407i | ||||
\(823\) | 14.4821 | + | 25.0836i | 0.504813 | + | 0.874361i | 0.999985 | + | 0.00556599i | \(0.00177172\pi\) |
−0.495172 | + | 0.868795i | \(0.664895\pi\) | |||||||
\(824\) | −27.9847 | − | 16.1569i | −0.974892 | − | 0.562854i | ||||
\(825\) | − | 21.8560i | − | 0.760927i | ||||||
\(826\) | −40.7297 | + | 24.9642i | −1.41717 | + | 0.868614i | ||||
\(827\) | 38.1072i | 1.32512i | 0.749009 | + | 0.662559i | \(0.230530\pi\) | ||||
−0.749009 | + | 0.662559i | \(0.769470\pi\) | |||||||
\(828\) | −8.96461 | + | 15.5272i | −0.311542 | + | 0.539606i | ||||
\(829\) | −4.76233 | − | 8.24859i | −0.165402 | − | 0.286485i | 0.771396 | − | 0.636356i | \(-0.219559\pi\) |
−0.936798 | + | 0.349870i | \(0.886226\pi\) | |||||||
\(830\) | 0.765700 | − | 0.442077i | 0.0265778 | − | 0.0153447i | ||||
\(831\) | −14.7151 | + | 25.4874i | −0.510462 | + | 0.884147i | ||||
\(832\) | −24.3917 | − | 3.16641i | −0.845630 | − | 0.109775i | ||||
\(833\) | −30.2633 | + | 1.59138i | −1.04856 | + | 0.0551382i | ||||
\(834\) | − | 27.6098i | − | 0.956049i | ||||||
\(835\) | −4.36870 | + | 7.56682i | −0.151185 | + | 0.261860i | ||||
\(836\) | 33.5366 | + | 58.0872i | 1.15989 | + | 2.00899i | ||||
\(837\) | −8.13504 | + | 4.69677i | −0.281188 | + | 0.162344i | ||||
\(838\) | 63.9268 | + | 36.9081i | 2.20831 | + | 1.27497i | ||||
\(839\) | − | 16.0315i | − | 0.553468i | −0.960947 | − | 0.276734i | \(-0.910748\pi\) | ||
0.960947 | − | 0.276734i | \(-0.0892521\pi\) | |||||||
\(840\) | −7.59409 | + | 4.65458i | −0.262021 | + | 0.160598i | ||||
\(841\) | 2.08675 | 0.0719570 | ||||||||
\(842\) | −26.4511 | + | 45.8146i | −0.911564 | + | 1.57887i | ||||
\(843\) | 8.93640 | − | 5.15944i | 0.307786 | − | 0.177700i | ||||
\(844\) | −63.8023 | − | 110.509i | −2.19616 | − | 3.80387i | ||||
\(845\) | −4.28213 | − | 4.25129i | −0.147310 | − | 0.146249i | ||||
\(846\) | −5.03724 | −0.173184 | ||||||||
\(847\) | −0.685655 | − | 26.0962i | −0.0235594 | − | 0.896675i | ||||
\(848\) | −61.7828 | −2.12163 | ||||||||
\(849\) | −5.49073 | + | 9.51022i | −0.188441 | + | 0.326390i | ||||
\(850\) | −46.7251 | + | 26.9768i | −1.60266 | + | 0.925295i | ||||
\(851\) | 23.7983 | − | 13.7399i | 0.815794 | − | 0.470999i | ||||
\(852\) | 34.7036 | + | 20.0361i | 1.18892 | + | 0.686426i | ||||
\(853\) | 51.0076i | 1.74647i | 0.487303 | + | 0.873233i | \(0.337981\pi\) | ||||
−0.487303 | + | 0.873233i | \(0.662019\pi\) | |||||||
\(854\) | 15.8530 | − | 29.2037i | 0.542478 | − | 0.999331i | ||||
\(855\) | −1.42445 | −0.0487152 | ||||||||
\(856\) | 66.4767 | + | 38.3804i | 2.27213 | + | 1.31181i | ||||
\(857\) | −11.5139 | − | 19.9427i | −0.393308 | − | 0.681229i | 0.599576 | − | 0.800318i | \(-0.295336\pi\) |
−0.992884 | + | 0.119089i | \(0.962003\pi\) | |||||||
\(858\) | 16.4888 | + | 39.6050i | 0.562919 | + | 1.35209i | ||||
\(859\) | 10.4701 | − | 18.1347i | 0.357234 | − | 0.618748i | −0.630264 | − | 0.776381i | \(-0.717053\pi\) |
0.987498 | + | 0.157634i | \(0.0503865\pi\) | |||||||
\(860\) | − | 18.1335i | − | 0.618349i | ||||||
\(861\) | −6.25053 | + | 11.5145i | −0.213017 | + | 0.392412i | ||||
\(862\) | 21.3035 | 0.725602 | ||||||||
\(863\) | 9.14389 | + | 5.27923i | 0.311262 | + | 0.179707i | 0.647491 | − | 0.762073i | \(-0.275818\pi\) |
−0.336229 | + | 0.941780i | \(0.609152\pi\) | |||||||
\(864\) | −8.46753 | + | 4.88873i | −0.288071 | + | 0.166318i | ||||
\(865\) | −3.47451 | + | 2.00601i | −0.118137 | + | 0.0682063i | ||||
\(866\) | −3.28444 | − | 1.89627i | −0.111610 | − | 0.0644380i | ||||
\(867\) | 1.74283 | 0.0591896 | ||||||||
\(868\) | −118.869 | + | 3.12320i | −4.03469 | + | 0.106008i | ||||
\(869\) | − | 26.7998i | − | 0.909121i | ||||||
\(870\) | 3.37044 | − | 5.83777i | 0.114268 | − | 0.197919i | ||||
\(871\) | −18.8293 | + | 7.83923i | −0.638006 | + | 0.265622i | ||||
\(872\) | 72.2363 | + | 125.117i | 2.44623 | + | 4.23700i | ||||
\(873\) | −1.70027 | − | 0.981652i | −0.0575455 | − | 0.0332239i | ||||
\(874\) | −29.9544 | −1.01322 | ||||||||
\(875\) | 6.27922 | + | 10.2447i | 0.212276 | + | 0.346335i | ||||
\(876\) | 16.3453i | 0.552257i | ||||||||
\(877\) | −32.2429 | − | 18.6154i | −1.08877 | − | 0.628599i | −0.155518 | − | 0.987833i | \(-0.549705\pi\) |
−0.933248 | + | 0.359234i | \(0.883038\pi\) | |||||||
\(878\) | −48.6629 | + | 28.0956i | −1.64229 | + | 0.948179i | ||||
\(879\) | −12.7855 | + | 7.38173i | −0.431245 | + | 0.248980i | ||||
\(880\) | −9.88360 | + | 17.1189i | −0.333176 | + | 0.577078i | ||||
\(881\) | −9.90917 | −0.333848 | −0.166924 | − | 0.985970i | \(-0.553384\pi\) | ||||
−0.166924 | + | 0.985970i | \(0.553384\pi\) | |||||||
\(882\) | 0.957455 | + | 18.2079i | 0.0322392 | + | 0.613091i | ||||
\(883\) | 7.93329 | 0.266977 | 0.133488 | − | 0.991050i | \(-0.457382\pi\) | ||||
0.133488 | + | 0.991050i | \(0.457382\pi\) | |||||||
\(884\) | 45.3580 | − | 59.3333i | 1.52555 | − | 1.99559i | ||||
\(885\) | −1.60878 | − | 2.78649i | −0.0540786 | − | 0.0936669i | ||||
\(886\) | 29.0855 | − | 16.7925i | 0.977147 | − | 0.564156i | ||||
\(887\) | 2.18406 | − | 3.78291i | 0.0733337 | − | 0.127018i | −0.827027 | − | 0.562163i | \(-0.809970\pi\) |
0.900360 | + | 0.435145i | \(0.143303\pi\) | |||||||
\(888\) | 53.1877 | 1.78486 | ||||||||
\(889\) | −7.86544 | + | 4.82090i | −0.263798 | + | 0.161688i | ||||
\(890\) | 3.80730i | 0.127621i | ||||||||
\(891\) | 3.95602 | + | 2.28401i | 0.132532 | + | 0.0765173i | ||||
\(892\) | 80.3046 | − | 46.3639i | 2.68880 | − | 1.55238i | ||||
\(893\) | −2.96744 | − | 5.13976i | −0.0993016 | − | 0.171995i | ||||
\(894\) | 19.6830 | − | 34.0919i | 0.658297 | − | 1.14020i | ||||
\(895\) | 9.25034i | 0.309205i | ||||||||
\(896\) | 4.72382 | − | 0.124114i | 0.157812 | − | 0.00414637i | ||||
\(897\) | −13.3987 | − | 1.73935i | −0.447369 | − | 0.0580753i | ||||
\(898\) | −5.06628 | + | 8.77505i | −0.169064 | + | 0.292827i | ||||
\(899\) | 45.3573 | − | 26.1871i | 1.51275 | − | 0.873388i | ||||
\(900\) | 11.4460 | + | 19.8250i | 0.381533 | + | 0.660834i | ||||
\(901\) | 14.3452 | − | 24.8466i | 0.477907 | − | 0.827759i | ||||
\(902\) | 58.9202i | 1.96183i | ||||||||
\(903\) | −18.9864 | − | 10.3066i | −0.631826 | − | 0.342982i | ||||
\(904\) | − | 37.7341i | − | 1.25502i | ||||||
\(905\) | −0.104163 | − | 0.0601384i | −0.00346249 | − | 0.00199907i | ||||
\(906\) | 4.35465 | + | 7.54247i | 0.144673 | + | 0.250582i | ||||
\(907\) | 14.4157 | + | 24.9687i | 0.478664 | + | 0.829071i | 0.999701 | − | 0.0244635i | \(-0.00778776\pi\) |
−0.521036 | + | 0.853534i | \(0.674454\pi\) | |||||||
\(908\) | 16.4091 | + | 9.47378i | 0.544554 | + | 0.314398i | ||||
\(909\) | −15.6522 | −0.519149 | ||||||||
\(910\) | −9.34337 | − | 6.76134i | −0.309730 | − | 0.224136i | ||||
\(911\) | 48.3751 | 1.60274 | 0.801369 | − | 0.598171i | \(-0.204106\pi\) | ||||
0.801369 | + | 0.598171i | \(0.204106\pi\) | |||||||
\(912\) | −24.7776 | − | 14.3054i | −0.820469 | − | 0.473698i | ||||
\(913\) | −1.67031 | − | 2.89307i | −0.0552793 | − | 0.0957466i | ||||
\(914\) | −15.9461 | − | 27.6194i | −0.527449 | − | 0.913568i | ||||
\(915\) | 1.93824 | + | 1.11904i | 0.0640762 | + | 0.0369944i | ||||
\(916\) | 19.9364i | 0.658716i | ||||||||
\(917\) | 1.37395 | + | 52.2929i | 0.0453719 | + | 1.72686i | ||||
\(918\) | − | 11.2766i | − | 0.372183i | ||||||
\(919\) | 15.5584 | − | 26.9479i | 0.513224 | − | 0.888930i | −0.486658 | − | 0.873592i | \(-0.661784\pi\) |
0.999882 | − | 0.0153377i | \(-0.00488233\pi\) | |||||||
\(920\) | −6.30774 | − | 10.9253i | −0.207960 | − | 0.360198i | ||||
\(921\) | 11.1314 | − | 6.42673i | 0.366793 | − | 0.211768i | ||||
\(922\) | 40.1093 | − | 69.4714i | 1.32093 | − | 2.28792i | ||||
\(923\) | −3.88749 | + | 29.9464i | −0.127958 | + | 0.985698i | ||||
\(924\) | 30.2181 | + | 49.3016i | 0.994101 | + | 1.62190i | ||||
\(925\) | − | 35.0862i | − | 1.15363i | ||||||
\(926\) | −2.01862 | + | 3.49636i | −0.0663360 | + | 0.114897i | ||||
\(927\) | −2.22763 | − | 3.85837i | −0.0731649 | − | 0.126725i | ||||
\(928\) | 47.2111 | − | 27.2574i | 1.54978 | − | 0.894766i | ||||
\(929\) | 46.0689 | + | 26.5979i | 1.51147 | + | 0.872649i | 0.999910 | + | 0.0134024i | \(0.00426625\pi\) |
0.511562 | + | 0.859246i | \(0.329067\pi\) | |||||||
\(930\) | − | 11.3568i | − | 0.372406i | ||||||
\(931\) | −18.0144 | + | 11.7032i | −0.590397 | + | 0.383557i | ||||
\(932\) | 45.2979 | 1.48378 | ||||||||
\(933\) | 6.19428 | − | 10.7288i | 0.202791 | − | 0.351245i | ||||
\(934\) | −29.4783 | + | 17.0193i | −0.964559 | + | 0.556888i | ||||
\(935\) | −4.58969 | − | 7.94958i | −0.150099 | − | 0.259979i | ||||
\(936\) | −20.7757 | − | 15.8822i | −0.679075 | − | 0.519126i | ||||
\(937\) | 12.7179 | 0.415474 | 0.207737 | − | 0.978185i | \(-0.433390\pi\) | ||||
0.207737 | + | 0.978185i | \(0.433390\pi\) | |||||||
\(938\) | −33.2372 | + | 20.3718i | −1.08523 | + | 0.665164i | ||||
\(939\) | 29.2135 | 0.953346 | ||||||||
\(940\) | 2.14739 | − | 3.71939i | 0.0700403 | − | 0.121313i | ||||
\(941\) | 46.7431 | − | 26.9871i | 1.52378 | − | 0.879755i | 0.524177 | − | 0.851609i | \(-0.324373\pi\) |
0.999604 | − | 0.0281461i | \(-0.00896036\pi\) | |||||||
\(942\) | 46.8091 | − | 27.0253i | 1.52512 | − | 0.880531i | ||||
\(943\) | −16.0704 | − | 9.27823i | −0.523323 | − | 0.302141i | ||||
\(944\) | − | 64.6262i | − | 2.10340i | ||||||
\(945\) | −1.22763 | + | 0.0322549i | −0.0399347 | + | 0.00104925i | ||||
\(946\) | −97.1544 | −3.15876 | ||||||||
\(947\) | −18.3509 | − | 10.5949i | −0.596324 | − | 0.344288i | 0.171270 | − | 0.985224i | \(-0.445213\pi\) |
−0.767594 | + | 0.640936i | \(0.778546\pi\) | |||||||
\(948\) | 14.0351 | + | 24.3095i | 0.455838 | + | 0.789535i | ||||
\(949\) | −11.3714 | + | 4.73426i | −0.369130 | + | 0.153681i | ||||
\(950\) | −19.1228 | + | 33.1217i | −0.620426 | + | 1.07461i | ||||
\(951\) | 9.83076i | 0.318784i | ||||||||
\(952\) | 39.6347 | − | 73.0134i | 1.28457 | − | 2.36638i | ||||
\(953\) | 25.8117 | 0.836122 | 0.418061 | − | 0.908419i | \(-0.362710\pi\) | ||||
0.418061 | + | 0.908419i | \(0.362710\pi\) | |||||||
\(954\) | −14.9489 | − | 8.63076i | −0.483989 | − | 0.279431i | ||||
\(955\) | 7.89449 | − | 4.55788i | 0.255460 | − | 0.147490i | ||||
\(956\) | −7.57120 | + | 4.37124i | −0.244870 | + | 0.141376i | ||||
\(957\) | −22.0570 | − | 12.7346i | −0.713002 | − | 0.411652i | ||||
\(958\) | 26.2759 | 0.848935 | ||||||||
\(959\) | −3.95312 | + | 7.28227i | −0.127653 | + | 0.235157i | ||||
\(960\) | − | 3.16641i | − | 0.102195i | ||||||
\(961\) | 28.6193 | − | 49.5701i | 0.923203 | − | 1.59903i | ||||
\(962\) | 26.4701 | + | 63.5795i | 0.853432 | + | 2.04988i | ||||
\(963\) | 5.29167 | + | 9.16544i | 0.170522 | + | 0.295352i | ||||
\(964\) | −63.6373 | − | 36.7410i | −2.04962 | − | 1.18335i | ||||
\(965\) | −11.3817 | −0.366391 | ||||||||
\(966\) | −25.8154 | + | 0.678280i | −0.830598 | + | 0.0218233i | ||||
\(967\) | − | 40.3935i | − | 1.29897i | −0.760375 | − | 0.649484i | \(-0.774985\pi\) | ||
0.760375 | − | 0.649484i | \(-0.225015\pi\) | |||||||
\(968\) | 61.9762 | + | 35.7820i | 1.99199 | + | 1.15008i | ||||
\(969\) | 11.5061 | − | 6.64305i | 0.369629 | − | 0.213405i | ||||
\(970\) | 2.05564 | − | 1.18682i | 0.0660026 | − | 0.0381066i | ||||
\(971\) | −7.28924 | + | 12.6253i | −0.233923 | + | 0.405166i | −0.958959 | − | 0.283544i | \(-0.908490\pi\) |
0.725036 | + | 0.688711i | \(0.241823\pi\) | |||||||
\(972\) | −4.78456 | −0.153465 | ||||||||
\(973\) | 23.9108 | − | 14.6554i | 0.766545 | − | 0.469832i | ||||
\(974\) | −20.6237 | −0.660826 | ||||||||
\(975\) | −10.4770 | + | 13.7051i | −0.335532 | + | 0.438913i | ||||
\(976\) | 22.4765 | + | 38.9304i | 0.719455 | + | 1.24613i | ||||
\(977\) | 6.97255 | − | 4.02560i | 0.223071 | − | 0.128790i | −0.384300 | − | 0.923208i | \(-0.625557\pi\) |
0.607372 | + | 0.794418i | \(0.292224\pi\) | |||||||
\(978\) | −10.6550 | + | 18.4550i | −0.340709 | + | 0.590125i | ||||
\(979\) | 14.3852 | 0.459754 | ||||||||
\(980\) | −13.8525 | − | 7.05511i | −0.442501 | − | 0.225367i | ||||
\(981\) | 19.9191i | 0.635967i | ||||||||
\(982\) | 19.2876 | + | 11.1357i | 0.615492 | + | 0.355354i | ||||
\(983\) | 37.8895 | − | 21.8755i | 1.20849 | − | 0.697720i | 0.246058 | − | 0.969255i | \(-0.420865\pi\) |
0.962428 | + | 0.271535i | \(0.0875314\pi\) | |||||||
\(984\) | −17.9582 | − | 31.1045i | −0.572486 | − | 0.991574i | ||||
\(985\) | −4.95446 | + | 8.58138i | −0.157862 | + | 0.273426i | ||||
\(986\) | 62.8733i | 2.00229i | ||||||||
\(987\) | −2.67380 | − | 4.36238i | −0.0851080 | − | 0.138856i | ||||
\(988\) | 6.81536 | − | 52.5006i | 0.216826 | − | 1.67027i | ||||
\(989\) | 15.2990 | − | 26.4986i | 0.486480 | − | 0.842608i | ||||
\(990\) | −4.78286 | + | 2.76138i | −0.152009 | + | 0.0877625i | ||||
\(991\) | −11.3285 | − | 19.6216i | −0.359862 | − | 0.623300i | 0.628075 | − | 0.778153i | \(-0.283843\pi\) |
−0.987938 | + | 0.154853i | \(0.950510\pi\) | |||||||
\(992\) | 45.9225 | − | 79.5401i | 1.45804 | − | 2.52540i | ||||
\(993\) | − | 5.02506i | − | 0.159466i | ||||||
\(994\) | 1.51597 | + | 57.6981i | 0.0480837 | + | 1.83007i | ||||
\(995\) | 8.02231i | 0.254324i | ||||||||
\(996\) | 3.03021 | + | 1.74949i | 0.0960157 | + | 0.0554347i | ||||
\(997\) | 22.8932 | + | 39.6521i | 0.725033 | + | 1.25579i | 0.958960 | + | 0.283540i | \(0.0915090\pi\) |
−0.233927 | + | 0.972254i | \(0.575158\pi\) | |||||||
\(998\) | −28.1382 | − | 48.7368i | −0.890700 | − | 1.54274i | ||||
\(999\) | 6.35076 | + | 3.66661i | 0.200929 | + | 0.116006i |
(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 | 273.2.bj.c.142.8 | yes | 16 | |
3.2 | odd | 2 | 819.2.dl.f.415.1 | 16 | |||
7.2 | even | 3 | 1911.2.c.n.883.1 | 8 | |||
7.4 | even | 3 | inner | 273.2.bj.c.25.1 | ✓ | 16 | |
7.5 | odd | 6 | 1911.2.c.k.883.1 | 8 | |||
13.12 | even | 2 | inner | 273.2.bj.c.142.1 | yes | 16 | |
21.11 | odd | 6 | 819.2.dl.f.298.8 | 16 | |||
39.38 | odd | 2 | 819.2.dl.f.415.8 | 16 | |||
91.12 | odd | 6 | 1911.2.c.k.883.8 | 8 | |||
91.25 | even | 6 | inner | 273.2.bj.c.25.8 | yes | 16 | |
91.51 | even | 6 | 1911.2.c.n.883.8 | 8 | |||
273.116 | odd | 6 | 819.2.dl.f.298.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bj.c.25.1 | ✓ | 16 | 7.4 | even | 3 | inner | |
273.2.bj.c.25.8 | yes | 16 | 91.25 | even | 6 | inner | |
273.2.bj.c.142.1 | yes | 16 | 13.12 | even | 2 | inner | |
273.2.bj.c.142.8 | yes | 16 | 1.1 | even | 1 | trivial | |
819.2.dl.f.298.1 | 16 | 273.116 | odd | 6 | |||
819.2.dl.f.298.8 | 16 | 21.11 | odd | 6 | |||
819.2.dl.f.415.1 | 16 | 3.2 | odd | 2 | |||
819.2.dl.f.415.8 | 16 | 39.38 | odd | 2 | |||
1911.2.c.k.883.1 | 8 | 7.5 | odd | 6 | |||
1911.2.c.k.883.8 | 8 | 91.12 | odd | 6 | |||
1911.2.c.n.883.1 | 8 | 7.2 | even | 3 | |||
1911.2.c.n.883.8 | 8 | 91.51 | even | 6 |