Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(289,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.j (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.447703281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(1.19003 + 0.764088i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.529 |
Dual form | 546.2.j.c.289.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.924396 | − | 1.60110i | −0.413402 | − | 0.716034i | 0.581857 | − | 0.813291i | \(-0.302326\pi\) |
−0.995259 | + | 0.0972573i | \(0.968993\pi\) | |||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 2.61442 | − | 0.405935i | 0.988160 | − | 0.153429i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.924396 | − | 1.60110i | −0.292320 | − | 0.506312i | ||||
\(11\) | −0.357690 | − | 0.619538i | −0.107848 | − | 0.186798i | 0.807050 | − | 0.590483i | \(-0.201063\pi\) |
−0.914898 | + | 0.403685i | \(0.867729\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −2.81454 | − | 2.25352i | −0.780613 | − | 0.625015i | ||||
\(14\) | 2.61442 | − | 0.405935i | 0.698734 | − | 0.108491i | ||||
\(15\) | −0.924396 | + | 1.60110i | −0.238678 | + | 0.413402i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.31156 | 1.04571 | 0.522853 | − | 0.852423i | \(-0.324868\pi\) | ||||
0.522853 | + | 0.852423i | \(0.324868\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 3.43786 | − | 5.95456i | 0.788700 | − | 1.36607i | −0.138063 | − | 0.990423i | \(-0.544088\pi\) |
0.926763 | − | 0.375645i | \(-0.122579\pi\) | |||||||
\(20\) | −0.924396 | − | 1.60110i | −0.206701 | − | 0.358017i | ||||
\(21\) | −1.65876 | − | 2.06119i | −0.361972 | − | 0.449789i | ||||
\(22\) | −0.357690 | − | 0.619538i | −0.0762599 | − | 0.132086i | ||||
\(23\) | −7.16035 | −1.49304 | −0.746518 | − | 0.665365i | \(-0.768276\pi\) | ||||
−0.746518 | + | 0.665365i | \(0.768276\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0.790985 | − | 1.37003i | 0.158197 | − | 0.274005i | ||||
\(26\) | −2.81454 | − | 2.25352i | −0.551977 | − | 0.441952i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.61442 | − | 0.405935i | 0.494080 | − | 0.0767145i | ||||
\(29\) | −4.63798 | + | 8.03322i | −0.861251 | + | 1.49173i | 0.00947068 | + | 0.999955i | \(0.496985\pi\) |
−0.870722 | + | 0.491776i | \(0.836348\pi\) | |||||||
\(30\) | −0.924396 | + | 1.60110i | −0.168771 | + | 0.292320i | ||||
\(31\) | 1.11104 | − | 1.92438i | 0.199549 | − | 0.345629i | −0.748833 | − | 0.662759i | \(-0.769386\pi\) |
0.948382 | + | 0.317129i | \(0.102719\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.357690 | + | 0.619538i | −0.0622659 | + | 0.107848i | ||||
\(34\) | 4.31156 | 0.739426 | ||||||||
\(35\) | −3.06671 | − | 3.81071i | −0.518368 | − | 0.644128i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 2.13341 | 0.350731 | 0.175365 | − | 0.984503i | \(-0.443889\pi\) | ||||
0.175365 | + | 0.984503i | \(0.443889\pi\) | |||||||
\(38\) | 3.43786 | − | 5.95456i | 0.557695 | − | 0.965956i | ||||
\(39\) | −0.544337 | + | 3.56422i | −0.0871637 | + | 0.570733i | ||||
\(40\) | −0.924396 | − | 1.60110i | −0.146160 | − | 0.253156i | ||||
\(41\) | 2.23138 | − | 3.86487i | 0.348483 | − | 0.603591i | −0.637497 | − | 0.770453i | \(-0.720030\pi\) |
0.985980 | + | 0.166862i | \(0.0533634\pi\) | |||||||
\(42\) | −1.65876 | − | 2.06119i | −0.255953 | − | 0.318049i | ||||
\(43\) | −0.0979721 | − | 0.169693i | −0.0149406 | − | 0.0258779i | 0.858458 | − | 0.512883i | \(-0.171423\pi\) |
−0.873399 | + | 0.487005i | \(0.838089\pi\) | |||||||
\(44\) | −0.357690 | − | 0.619538i | −0.0539239 | − | 0.0933989i | ||||
\(45\) | 1.84879 | 0.275602 | ||||||||
\(46\) | −7.16035 | −1.05574 | ||||||||
\(47\) | 4.60553 | + | 7.97700i | 0.671785 | + | 1.16357i | 0.977398 | + | 0.211410i | \(0.0678054\pi\) |
−0.305613 | + | 0.952156i | \(0.598861\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 6.67043 | − | 2.12257i | 0.952919 | − | 0.303225i | ||||
\(50\) | 0.790985 | − | 1.37003i | 0.111862 | − | 0.193751i | ||||
\(51\) | −2.15578 | − | 3.73392i | −0.301869 | − | 0.522853i | ||||
\(52\) | −2.81454 | − | 2.25352i | −0.390307 | − | 0.312507i | ||||
\(53\) | 3.80147 | − | 6.58434i | 0.522172 | − | 0.904429i | −0.477495 | − | 0.878634i | \(-0.658455\pi\) |
0.999667 | − | 0.0257942i | \(-0.00821145\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.661295 | + | 1.14540i | −0.0891690 | + | 0.154445i | ||||
\(56\) | 2.61442 | − | 0.405935i | 0.349367 | − | 0.0542453i | ||||
\(57\) | −6.87573 | −0.910712 | ||||||||
\(58\) | −4.63798 | + | 8.03322i | −0.608997 | + | 1.05481i | ||||
\(59\) | −2.48056 | −0.322942 | −0.161471 | − | 0.986877i | \(-0.551624\pi\) | ||||
−0.161471 | + | 0.986877i | \(0.551624\pi\) | |||||||
\(60\) | −0.924396 | + | 1.60110i | −0.119339 | + | 0.206701i | ||||
\(61\) | −4.31156 | + | 7.46783i | −0.552038 | + | 0.956158i | 0.446089 | + | 0.894989i | \(0.352816\pi\) |
−0.998127 | + | 0.0611697i | \(0.980517\pi\) | |||||||
\(62\) | 1.11104 | − | 1.92438i | 0.141103 | − | 0.244397i | ||||
\(63\) | −0.955663 | + | 2.46713i | −0.120402 | + | 0.310829i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00637 | + | 6.58951i | −0.124824 | + | 0.817328i | ||||
\(66\) | −0.357690 | + | 0.619538i | −0.0440287 | + | 0.0762599i | ||||
\(67\) | 6.96322 | + | 12.0606i | 0.850692 | + | 1.47344i | 0.880585 | + | 0.473889i | \(0.157150\pi\) |
−0.0298923 | + | 0.999553i | \(0.509516\pi\) | |||||||
\(68\) | 4.31156 | 0.522853 | ||||||||
\(69\) | 3.58017 | + | 6.20104i | 0.431002 | + | 0.746518i | ||||
\(70\) | −3.06671 | − | 3.81071i | −0.366541 | − | 0.455467i | ||||
\(71\) | 7.50874 | + | 13.0055i | 0.891124 | + | 1.54347i | 0.838530 | + | 0.544855i | \(0.183415\pi\) |
0.0525935 | + | 0.998616i | \(0.483251\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −0.989914 | + | 1.71458i | −0.115861 | + | 0.200676i | −0.918123 | − | 0.396294i | \(-0.870296\pi\) |
0.802263 | + | 0.596971i | \(0.203629\pi\) | |||||||
\(74\) | 2.13341 | 0.248004 | ||||||||
\(75\) | −1.58197 | −0.182670 | ||||||||
\(76\) | 3.43786 | − | 5.95456i | 0.394350 | − | 0.683034i | ||||
\(77\) | −1.18665 | − | 1.47454i | −0.135231 | − | 0.168039i | ||||
\(78\) | −0.544337 | + | 3.56422i | −0.0616341 | + | 0.403569i | ||||
\(79\) | 7.37533 | + | 12.7744i | 0.829790 | + | 1.43724i | 0.898203 | + | 0.439581i | \(0.144873\pi\) |
−0.0684137 | + | 0.997657i | \(0.521794\pi\) | |||||||
\(80\) | −0.924396 | − | 1.60110i | −0.103351 | − | 0.179008i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.23138 | − | 3.86487i | 0.246415 | − | 0.426803i | ||||
\(83\) | −9.71538 | −1.06640 | −0.533201 | − | 0.845989i | \(-0.679011\pi\) | ||||
−0.533201 | + | 0.845989i | \(0.679011\pi\) | |||||||
\(84\) | −1.65876 | − | 2.06119i | −0.180986 | − | 0.224894i | ||||
\(85\) | −3.98558 | − | 6.90323i | −0.432297 | − | 0.748761i | ||||
\(86\) | −0.0979721 | − | 0.169693i | −0.0105646 | − | 0.0182984i | ||||
\(87\) | 9.27596 | 0.994487 | ||||||||
\(88\) | −0.357690 | − | 0.619538i | −0.0381299 | − | 0.0660430i | ||||
\(89\) | −4.46953 | −0.473769 | −0.236885 | − | 0.971538i | \(-0.576126\pi\) | ||||
−0.236885 | + | 0.971538i | \(0.576126\pi\) | |||||||
\(90\) | 1.84879 | 0.194880 | ||||||||
\(91\) | −8.27319 | − | 4.74914i | −0.867266 | − | 0.497846i | ||||
\(92\) | −7.16035 | −0.746518 | ||||||||
\(93\) | −2.22209 | −0.230419 | ||||||||
\(94\) | 4.60553 | + | 7.97700i | 0.475024 | + | 0.822765i | ||||
\(95\) | −12.7118 | −1.30420 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 1.39194 | + | 2.41091i | 0.141330 | + | 0.244791i | 0.927998 | − | 0.372586i | \(-0.121529\pi\) |
−0.786668 | + | 0.617377i | \(0.788195\pi\) | |||||||
\(98\) | 6.67043 | − | 2.12257i | 0.673816 | − | 0.214412i | ||||
\(99\) | 0.715381 | 0.0718985 | ||||||||
\(100\) | 0.790985 | − | 1.37003i | 0.0790985 | − | 0.137003i | ||||
\(101\) | −2.67775 | − | 4.63800i | −0.266446 | − | 0.461498i | 0.701496 | − | 0.712674i | \(-0.252516\pi\) |
−0.967941 | + | 0.251176i | \(0.919183\pi\) | |||||||
\(102\) | −2.15578 | − | 3.73392i | −0.213454 | − | 0.369713i | ||||
\(103\) | 3.26429 | + | 5.65391i | 0.321640 | + | 0.557097i | 0.980827 | − | 0.194883i | \(-0.0624326\pi\) |
−0.659187 | + | 0.751979i | \(0.729099\pi\) | |||||||
\(104\) | −2.81454 | − | 2.25352i | −0.275988 | − | 0.220976i | ||||
\(105\) | −1.76682 | + | 4.56120i | −0.172424 | + | 0.445128i | ||||
\(106\) | 3.80147 | − | 6.58434i | 0.369231 | − | 0.639528i | ||||
\(107\) | −4.61994 | −0.446627 | −0.223313 | − | 0.974747i | \(-0.571687\pi\) | ||||
−0.223313 | + | 0.974747i | \(0.571687\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 4.95093 | − | 8.57527i | 0.474214 | − | 0.821362i | −0.525351 | − | 0.850886i | \(-0.676066\pi\) |
0.999564 | + | 0.0295240i | \(0.00939913\pi\) | |||||||
\(110\) | −0.661295 | + | 1.14540i | −0.0630520 | + | 0.109209i | ||||
\(111\) | −1.06671 | − | 1.84759i | −0.101247 | − | 0.175365i | ||||
\(112\) | 2.61442 | − | 0.405935i | 0.247040 | − | 0.0383572i | ||||
\(113\) | 1.50417 | + | 2.60530i | 0.141501 | + | 0.245086i | 0.928062 | − | 0.372426i | \(-0.121474\pi\) |
−0.786561 | + | 0.617512i | \(0.788141\pi\) | |||||||
\(114\) | −6.87573 | −0.643971 | ||||||||
\(115\) | 6.61899 | + | 11.4644i | 0.617224 | + | 1.06906i | ||||
\(116\) | −4.63798 | + | 8.03322i | −0.430626 | + | 0.745865i | ||||
\(117\) | 3.35888 | − | 1.31070i | 0.310528 | − | 0.121174i | ||||
\(118\) | −2.48056 | −0.228354 | ||||||||
\(119\) | 11.2722 | − | 1.75021i | 1.03332 | − | 0.160442i | ||||
\(120\) | −0.924396 | + | 1.60110i | −0.0843854 | + | 0.146160i | ||||
\(121\) | 5.24412 | − | 9.08307i | 0.476738 | − | 0.825734i | ||||
\(122\) | −4.31156 | + | 7.46783i | −0.390350 | + | 0.676106i | ||||
\(123\) | −4.46276 | −0.402394 | ||||||||
\(124\) | 1.11104 | − | 1.92438i | 0.0997746 | − | 0.172815i | ||||
\(125\) | −12.1687 | −1.08840 | ||||||||
\(126\) | −0.955663 | + | 2.46713i | −0.0851372 | + | 0.219789i | ||||
\(127\) | −7.58356 | + | 13.1351i | −0.672932 | + | 1.16555i | 0.304137 | + | 0.952628i | \(0.401632\pi\) |
−0.977069 | + | 0.212924i | \(0.931701\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.0979721 | + | 0.169693i | −0.00862596 | + | 0.0149406i | ||||
\(130\) | −1.00637 | + | 6.58951i | −0.0882642 | + | 0.577938i | ||||
\(131\) | 9.69444 | + | 16.7913i | 0.847007 | + | 1.46706i | 0.883867 | + | 0.467739i | \(0.154931\pi\) |
−0.0368595 | + | 0.999320i | \(0.511735\pi\) | |||||||
\(132\) | −0.357690 | + | 0.619538i | −0.0311330 | + | 0.0539239i | ||||
\(133\) | 6.57088 | − | 16.9633i | 0.569767 | − | 1.47090i | ||||
\(134\) | 6.96322 | + | 12.0606i | 0.601530 | + | 1.04188i | ||||
\(135\) | −0.924396 | − | 1.60110i | −0.0795593 | − | 0.137801i | ||||
\(136\) | 4.31156 | 0.369713 | ||||||||
\(137\) | −4.74829 | −0.405673 | −0.202837 | − | 0.979213i | \(-0.565016\pi\) | ||||
−0.202837 | + | 0.979213i | \(0.565016\pi\) | |||||||
\(138\) | 3.58017 | + | 6.20104i | 0.304765 | + | 0.527868i | ||||
\(139\) | −7.69027 | − | 13.3199i | −0.652280 | − | 1.12978i | −0.982568 | − | 0.185902i | \(-0.940479\pi\) |
0.330288 | − | 0.943880i | \(-0.392854\pi\) | |||||||
\(140\) | −3.06671 | − | 3.81071i | −0.259184 | − | 0.322064i | ||||
\(141\) | 4.60553 | − | 7.97700i | 0.387855 | − | 0.671785i | ||||
\(142\) | 7.50874 | + | 13.0055i | 0.630120 | + | 1.09140i | ||||
\(143\) | −0.389409 | + | 2.54978i | −0.0325640 | + | 0.213223i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 17.1493 | 1.42417 | ||||||||
\(146\) | −0.989914 | + | 1.71458i | −0.0819258 | + | 0.141900i | ||||
\(147\) | −5.17342 | − | 4.71548i | −0.426696 | − | 0.388926i | ||||
\(148\) | 2.13341 | 0.175365 | ||||||||
\(149\) | 5.82384 | − | 10.0872i | 0.477107 | − | 0.826374i | −0.522548 | − | 0.852610i | \(-0.675019\pi\) |
0.999656 | + | 0.0262354i | \(0.00835195\pi\) | |||||||
\(150\) | −1.58197 | −0.129167 | ||||||||
\(151\) | −4.09544 | + | 7.09351i | −0.333282 | + | 0.577262i | −0.983153 | − | 0.182783i | \(-0.941489\pi\) |
0.649871 | + | 0.760044i | \(0.274823\pi\) | |||||||
\(152\) | 3.43786 | − | 5.95456i | 0.278848 | − | 0.482978i | ||||
\(153\) | −2.15578 | + | 3.73392i | −0.174284 | + | 0.301869i | ||||
\(154\) | −1.18665 | − | 1.47454i | −0.0956227 | − | 0.118822i | ||||
\(155\) | −4.10817 | −0.329976 | ||||||||
\(156\) | −0.544337 | + | 3.56422i | −0.0435819 | + | 0.285366i | ||||
\(157\) | 11.4353 | − | 19.8066i | 0.912639 | − | 1.58074i | 0.102317 | − | 0.994752i | \(-0.467374\pi\) |
0.810322 | − | 0.585985i | \(-0.199292\pi\) | |||||||
\(158\) | 7.37533 | + | 12.7744i | 0.586750 | + | 1.01628i | ||||
\(159\) | −7.60294 | −0.602952 | ||||||||
\(160\) | −0.924396 | − | 1.60110i | −0.0730799 | − | 0.126578i | ||||
\(161\) | −18.7202 | + | 2.90663i | −1.47536 | + | 0.229075i | ||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −9.01923 | + | 15.6218i | −0.706440 | + | 1.22359i | 0.259729 | + | 0.965682i | \(0.416367\pi\) |
−0.966169 | + | 0.257909i | \(0.916967\pi\) | |||||||
\(164\) | 2.23138 | − | 3.86487i | 0.174242 | − | 0.301795i | ||||
\(165\) | 1.32259 | 0.102964 | ||||||||
\(166\) | −9.71538 | −0.754060 | ||||||||
\(167\) | 3.86936 | − | 6.70193i | 0.299420 | − | 0.518611i | −0.676583 | − | 0.736366i | \(-0.736540\pi\) |
0.976003 | + | 0.217755i | \(0.0698734\pi\) | |||||||
\(168\) | −1.65876 | − | 2.06119i | −0.127976 | − | 0.159024i | ||||
\(169\) | 2.84327 | + | 12.6853i | 0.218713 | + | 0.975789i | ||||
\(170\) | −3.98558 | − | 6.90323i | −0.305680 | − | 0.529454i | ||||
\(171\) | 3.43786 | + | 5.95456i | 0.262900 | + | 0.455356i | ||||
\(172\) | −0.0979721 | − | 0.169693i | −0.00747030 | − | 0.0129389i | ||||
\(173\) | −6.01212 | + | 10.4133i | −0.457093 | + | 0.791709i | −0.998806 | − | 0.0488550i | \(-0.984443\pi\) |
0.541713 | + | 0.840564i | \(0.317776\pi\) | |||||||
\(174\) | 9.27596 | 0.703209 | ||||||||
\(175\) | 1.51183 | − | 3.90292i | 0.114284 | − | 0.295033i | ||||
\(176\) | −0.357690 | − | 0.619538i | −0.0269619 | − | 0.0466994i | ||||
\(177\) | 1.24028 | + | 2.14823i | 0.0932253 | + | 0.161471i | ||||
\(178\) | −4.46953 | −0.335005 | ||||||||
\(179\) | −5.65742 | − | 9.79893i | −0.422855 | − | 0.732407i | 0.573362 | − | 0.819302i | \(-0.305639\pi\) |
−0.996217 | + | 0.0868953i | \(0.972305\pi\) | |||||||
\(180\) | 1.84879 | 0.137801 | ||||||||
\(181\) | −2.49725 | −0.185619 | −0.0928095 | − | 0.995684i | \(-0.529585\pi\) | ||||
−0.0928095 | + | 0.995684i | \(0.529585\pi\) | |||||||
\(182\) | −8.27319 | − | 4.74914i | −0.613249 | − | 0.352030i | ||||
\(183\) | 8.62311 | 0.637439 | ||||||||
\(184\) | −7.16035 | −0.527868 | ||||||||
\(185\) | −1.97212 | − | 3.41580i | −0.144993 | − | 0.251135i | ||||
\(186\) | −2.22209 | −0.162931 | ||||||||
\(187\) | −1.54220 | − | 2.67117i | −0.112777 | − | 0.195336i | ||||
\(188\) | 4.60553 | + | 7.97700i | 0.335892 | + | 0.581783i | ||||
\(189\) | 2.61442 | − | 0.405935i | 0.190171 | − | 0.0295274i | ||||
\(190\) | −12.7118 | −0.922210 | ||||||||
\(191\) | 2.66349 | − | 4.61330i | 0.192723 | − | 0.333807i | −0.753428 | − | 0.657530i | \(-0.771601\pi\) |
0.946152 | + | 0.323723i | \(0.104935\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −4.86186 | − | 8.42099i | −0.349964 | − | 0.606156i | 0.636278 | − | 0.771460i | \(-0.280473\pi\) |
−0.986243 | + | 0.165303i | \(0.947140\pi\) | |||||||
\(194\) | 1.39194 | + | 2.41091i | 0.0999356 | + | 0.173093i | ||||
\(195\) | 6.20986 | − | 2.42321i | 0.444698 | − | 0.173530i | ||||
\(196\) | 6.67043 | − | 2.12257i | 0.476460 | − | 0.151612i | ||||
\(197\) | −3.08593 | + | 5.34499i | −0.219863 | + | 0.380815i | −0.954766 | − | 0.297358i | \(-0.903895\pi\) |
0.734903 | + | 0.678173i | \(0.237228\pi\) | |||||||
\(198\) | 0.715381 | 0.0508399 | ||||||||
\(199\) | 5.41454 | 0.383827 | 0.191913 | − | 0.981412i | \(-0.438531\pi\) | ||||
0.191913 | + | 0.981412i | \(0.438531\pi\) | |||||||
\(200\) | 0.790985 | − | 1.37003i | 0.0559311 | − | 0.0968755i | ||||
\(201\) | 6.96322 | − | 12.0606i | 0.491147 | − | 0.850692i | ||||
\(202\) | −2.67775 | − | 4.63800i | −0.188406 | − | 0.326328i | ||||
\(203\) | −8.86469 | + | 22.8850i | −0.622179 | + | 1.60621i | ||||
\(204\) | −2.15578 | − | 3.73392i | −0.150935 | − | 0.261426i | ||||
\(205\) | −8.25072 | −0.576255 | ||||||||
\(206\) | 3.26429 | + | 5.65391i | 0.227434 | + | 0.393927i | ||||
\(207\) | 3.58017 | − | 6.20104i | 0.248839 | − | 0.431002i | ||||
\(208\) | −2.81454 | − | 2.25352i | −0.195153 | − | 0.156254i | ||||
\(209\) | −4.91877 | −0.340238 | ||||||||
\(210\) | −1.76682 | + | 4.56120i | −0.121922 | + | 0.314753i | ||||
\(211\) | 13.6366 | − | 23.6193i | 0.938785 | − | 1.62602i | 0.171043 | − | 0.985264i | \(-0.445286\pi\) |
0.767742 | − | 0.640759i | \(-0.221380\pi\) | |||||||
\(212\) | 3.80147 | − | 6.58434i | 0.261086 | − | 0.452214i | ||||
\(213\) | 7.50874 | − | 13.0055i | 0.514490 | − | 0.891124i | ||||
\(214\) | −4.61994 | −0.315813 | ||||||||
\(215\) | −0.181130 | + | 0.313726i | −0.0123530 | + | 0.0213960i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.12356 | − | 5.48216i | 0.144157 | − | 0.372153i | ||||
\(218\) | 4.95093 | − | 8.57527i | 0.335320 | − | 0.580791i | ||||
\(219\) | 1.97983 | 0.133784 | ||||||||
\(220\) | −0.661295 | + | 1.14540i | −0.0445845 | + | 0.0772226i | ||||
\(221\) | −12.1350 | − | 9.71619i | −0.816292 | − | 0.653582i | ||||
\(222\) | −1.06671 | − | 1.84759i | −0.0715926 | − | 0.124002i | ||||
\(223\) | −2.88502 | + | 4.99700i | −0.193195 | + | 0.334624i | −0.946307 | − | 0.323268i | \(-0.895218\pi\) |
0.753112 | + | 0.657892i | \(0.228552\pi\) | |||||||
\(224\) | 2.61442 | − | 0.405935i | 0.174684 | − | 0.0271227i | ||||
\(225\) | 0.790985 | + | 1.37003i | 0.0527324 | + | 0.0913351i | ||||
\(226\) | 1.50417 | + | 2.60530i | 0.100056 | + | 0.173302i | ||||
\(227\) | 16.9846 | 1.12731 | 0.563653 | − | 0.826012i | \(-0.309396\pi\) | ||||
0.563653 | + | 0.826012i | \(0.309396\pi\) | |||||||
\(228\) | −6.87573 | −0.455356 | ||||||||
\(229\) | 0.460390 | + | 0.797420i | 0.0304235 | + | 0.0526950i | 0.880836 | − | 0.473421i | \(-0.156981\pi\) |
−0.850413 | + | 0.526116i | \(0.823648\pi\) | |||||||
\(230\) | 6.61899 | + | 11.4644i | 0.436444 | + | 0.755942i | ||||
\(231\) | −0.683663 | + | 1.76493i | −0.0449817 | + | 0.116124i | ||||
\(232\) | −4.63798 | + | 8.03322i | −0.304498 | + | 0.527407i | ||||
\(233\) | −2.50283 | − | 4.33502i | −0.163966 | − | 0.283997i | 0.772322 | − | 0.635231i | \(-0.219095\pi\) |
−0.936287 | + | 0.351235i | \(0.885762\pi\) | |||||||
\(234\) | 3.35888 | − | 1.31070i | 0.219577 | − | 0.0856833i | ||||
\(235\) | 8.51466 | − | 14.7478i | 0.555435 | − | 0.962041i | ||||
\(236\) | −2.48056 | −0.161471 | ||||||||
\(237\) | 7.37533 | − | 12.7744i | 0.479079 | − | 0.829790i | ||||
\(238\) | 11.2722 | − | 1.75021i | 0.730671 | − | 0.113449i | ||||
\(239\) | 13.8239 | 0.894195 | 0.447097 | − | 0.894485i | \(-0.352458\pi\) | ||||
0.447097 | + | 0.894485i | \(0.352458\pi\) | |||||||
\(240\) | −0.924396 | + | 1.60110i | −0.0596695 | + | 0.103351i | ||||
\(241\) | 10.7589 | 0.693041 | 0.346521 | − | 0.938042i | \(-0.387363\pi\) | ||||
0.346521 | + | 0.938042i | \(0.387363\pi\) | |||||||
\(242\) | 5.24412 | − | 9.08307i | 0.337104 | − | 0.583882i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −4.31156 | + | 7.46783i | −0.276019 | + | 0.478079i | ||||
\(245\) | −9.56457 | − | 8.71794i | −0.611058 | − | 0.556969i | ||||
\(246\) | −4.46276 | −0.284535 | ||||||||
\(247\) | −23.0947 | + | 9.01203i | −1.46948 | + | 0.573422i | ||||
\(248\) | 1.11104 | − | 1.92438i | 0.0705513 | − | 0.122198i | ||||
\(249\) | 4.85769 | + | 8.41377i | 0.307844 | + | 0.533201i | ||||
\(250\) | −12.1687 | −0.769616 | ||||||||
\(251\) | −11.8267 | − | 20.4844i | −0.746492 | − | 1.29296i | −0.949494 | − | 0.313784i | \(-0.898403\pi\) |
0.203002 | − | 0.979178i | \(-0.434930\pi\) | |||||||
\(252\) | −0.955663 | + | 2.46713i | −0.0602011 | + | 0.155414i | ||||
\(253\) | 2.56119 | + | 4.43611i | 0.161021 | + | 0.278896i | ||||
\(254\) | −7.58356 | + | 13.1351i | −0.475835 | + | 0.824170i | ||||
\(255\) | −3.98558 | + | 6.90323i | −0.249587 | + | 0.432297i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.1940 | −1.19729 | −0.598646 | − | 0.801014i | \(-0.704294\pi\) | ||||
−0.598646 | + | 0.801014i | \(0.704294\pi\) | |||||||
\(258\) | −0.0979721 | + | 0.169693i | −0.00609948 | + | 0.0105646i | ||||
\(259\) | 5.57764 | − | 0.866025i | 0.346578 | − | 0.0538122i | ||||
\(260\) | −1.00637 | + | 6.58951i | −0.0624122 | + | 0.408664i | ||||
\(261\) | −4.63798 | − | 8.03322i | −0.287084 | − | 0.497244i | ||||
\(262\) | 9.69444 | + | 16.7913i | 0.598925 | + | 1.03737i | ||||
\(263\) | −5.49567 | − | 9.51878i | −0.338878 | − | 0.586953i | 0.645344 | − | 0.763892i | \(-0.276714\pi\) |
−0.984222 | + | 0.176939i | \(0.943381\pi\) | |||||||
\(264\) | −0.357690 | + | 0.619538i | −0.0220143 | + | 0.0381299i | ||||
\(265\) | −14.0562 | −0.863469 | ||||||||
\(266\) | 6.57088 | − | 16.9633i | 0.402886 | − | 1.04009i | ||||
\(267\) | 2.23476 | + | 3.87073i | 0.136765 | + | 0.236885i | ||||
\(268\) | 6.96322 | + | 12.0606i | 0.425346 | + | 0.736721i | ||||
\(269\) | 16.5175 | 1.00709 | 0.503546 | − | 0.863968i | \(-0.332028\pi\) | ||||
0.503546 | + | 0.863968i | \(0.332028\pi\) | |||||||
\(270\) | −0.924396 | − | 1.60110i | −0.0562569 | − | 0.0974399i | ||||
\(271\) | −18.1906 | −1.10500 | −0.552499 | − | 0.833514i | \(-0.686326\pi\) | ||||
−0.552499 | + | 0.833514i | \(0.686326\pi\) | |||||||
\(272\) | 4.31156 | 0.261426 | ||||||||
\(273\) | 0.0237134 | + | 9.53936i | 0.00143520 | + | 0.577348i | ||||
\(274\) | −4.74829 | −0.286854 | ||||||||
\(275\) | −1.13171 | −0.0682448 | ||||||||
\(276\) | 3.58017 | + | 6.20104i | 0.215501 | + | 0.373259i | ||||
\(277\) | 16.4894 | 0.990751 | 0.495376 | − | 0.868679i | \(-0.335030\pi\) | ||||
0.495376 | + | 0.868679i | \(0.335030\pi\) | |||||||
\(278\) | −7.69027 | − | 13.3199i | −0.461232 | − | 0.798877i | ||||
\(279\) | 1.11104 | + | 1.92438i | 0.0665164 | + | 0.115210i | ||||
\(280\) | −3.06671 | − | 3.81071i | −0.183271 | − | 0.227734i | ||||
\(281\) | 15.2768 | 0.911335 | 0.455667 | − | 0.890150i | \(-0.349401\pi\) | ||||
0.455667 | + | 0.890150i | \(0.349401\pi\) | |||||||
\(282\) | 4.60553 | − | 7.97700i | 0.274255 | − | 0.475024i | ||||
\(283\) | 4.57838 | + | 7.92998i | 0.272156 | + | 0.471388i | 0.969414 | − | 0.245432i | \(-0.0789299\pi\) |
−0.697257 | + | 0.716821i | \(0.745597\pi\) | |||||||
\(284\) | 7.50874 | + | 13.0055i | 0.445562 | + | 0.771736i | ||||
\(285\) | 6.35589 | + | 11.0087i | 0.376491 | + | 0.652101i | ||||
\(286\) | −0.389409 | + | 2.54978i | −0.0230262 | + | 0.150772i | ||||
\(287\) | 4.26490 | − | 11.0102i | 0.251749 | − | 0.649912i | ||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | 1.58952 | 0.0935010 | ||||||||
\(290\) | 17.1493 | 1.00704 | ||||||||
\(291\) | 1.39194 | − | 2.41091i | 0.0815971 | − | 0.141330i | ||||
\(292\) | −0.989914 | + | 1.71458i | −0.0579303 | + | 0.100338i | ||||
\(293\) | 5.93488 | + | 10.2795i | 0.346719 | + | 0.600536i | 0.985665 | − | 0.168717i | \(-0.0539623\pi\) |
−0.638945 | + | 0.769252i | \(0.720629\pi\) | |||||||
\(294\) | −5.17342 | − | 4.71548i | −0.301720 | − | 0.275012i | ||||
\(295\) | 2.29302 | + | 3.97163i | 0.133505 | + | 0.231237i | ||||
\(296\) | 2.13341 | 0.124002 | ||||||||
\(297\) | −0.357690 | − | 0.619538i | −0.0207553 | − | 0.0359492i | ||||
\(298\) | 5.82384 | − | 10.0872i | 0.337366 | − | 0.584335i | ||||
\(299\) | 20.1531 | + | 16.1360i | 1.16548 | + | 0.933169i | ||||
\(300\) | −1.58197 | −0.0913351 | ||||||||
\(301\) | −0.325025 | − | 0.403878i | −0.0187341 | − | 0.0232792i | ||||
\(302\) | −4.09544 | + | 7.09351i | −0.235666 | + | 0.408186i | ||||
\(303\) | −2.67775 | + | 4.63800i | −0.153833 | + | 0.266446i | ||||
\(304\) | 3.43786 | − | 5.95456i | 0.197175 | − | 0.341517i | ||||
\(305\) | 15.9423 | 0.912855 | ||||||||
\(306\) | −2.15578 | + | 3.73392i | −0.123238 | + | 0.213454i | ||||
\(307\) | −28.0679 | −1.60192 | −0.800959 | − | 0.598719i | \(-0.795677\pi\) | ||||
−0.800959 | + | 0.598719i | \(0.795677\pi\) | |||||||
\(308\) | −1.18665 | − | 1.47454i | −0.0676155 | − | 0.0840195i | ||||
\(309\) | 3.26429 | − | 5.65391i | 0.185699 | − | 0.321640i | ||||
\(310\) | −4.10817 | −0.233328 | ||||||||
\(311\) | −12.7326 | + | 22.0536i | −0.722001 | + | 1.25054i | 0.238195 | + | 0.971217i | \(0.423444\pi\) |
−0.960196 | + | 0.279325i | \(0.909889\pi\) | |||||||
\(312\) | −0.544337 | + | 3.56422i | −0.0308170 | + | 0.201784i | ||||
\(313\) | −8.82204 | − | 15.2802i | −0.498651 | − | 0.863689i | 0.501348 | − | 0.865246i | \(-0.332838\pi\) |
−0.999999 | + | 0.00155673i | \(0.999504\pi\) | |||||||
\(314\) | 11.4353 | − | 19.8066i | 0.645333 | − | 1.11775i | ||||
\(315\) | 4.83353 | − | 0.750489i | 0.272338 | − | 0.0422852i | ||||
\(316\) | 7.37533 | + | 12.7744i | 0.414895 | + | 0.718619i | ||||
\(317\) | −14.8710 | − | 25.7573i | −0.835239 | − | 1.44668i | −0.893836 | − | 0.448394i | \(-0.851996\pi\) |
0.0585974 | − | 0.998282i | \(-0.481337\pi\) | |||||||
\(318\) | −7.60294 | −0.426352 | ||||||||
\(319\) | 6.63585 | 0.371536 | ||||||||
\(320\) | −0.924396 | − | 1.60110i | −0.0516753 | − | 0.0895042i | ||||
\(321\) | 2.30997 | + | 4.00099i | 0.128930 | + | 0.223313i | ||||
\(322\) | −18.7202 | + | 2.90663i | −1.04324 | + | 0.161980i | ||||
\(323\) | 14.8225 | − | 25.6734i | 0.824748 | − | 1.42851i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −5.31365 | + | 2.07349i | −0.294748 | + | 0.115017i | ||||
\(326\) | −9.01923 | + | 15.6218i | −0.499529 | + | 0.865209i | ||||
\(327\) | −9.90187 | −0.547575 | ||||||||
\(328\) | 2.23138 | − | 3.86487i | 0.123207 | − | 0.213402i | ||||
\(329\) | 15.2789 | + | 18.9857i | 0.842355 | + | 1.04672i | ||||
\(330\) | 1.32259 | 0.0728062 | ||||||||
\(331\) | −12.0197 | + | 20.8187i | −0.660661 | + | 1.14430i | 0.319781 | + | 0.947491i | \(0.396391\pi\) |
−0.980442 | + | 0.196807i | \(0.936943\pi\) | |||||||
\(332\) | −9.71538 | −0.533201 | ||||||||
\(333\) | −1.06671 | + | 1.84759i | −0.0584551 | + | 0.101247i | ||||
\(334\) | 3.86936 | − | 6.70193i | 0.211722 | − | 0.366713i | ||||
\(335\) | 12.8735 | − | 22.2976i | 0.703356 | − | 1.21825i | ||||
\(336\) | −1.65876 | − | 2.06119i | −0.0904929 | − | 0.112447i | ||||
\(337\) | −2.21939 | −0.120898 | −0.0604490 | − | 0.998171i | \(-0.519253\pi\) | ||||
−0.0604490 | + | 0.998171i | \(0.519253\pi\) | |||||||
\(338\) | 2.84327 | + | 12.6853i | 0.154654 | + | 0.689987i | ||||
\(339\) | 1.50417 | − | 2.60530i | 0.0816954 | − | 0.141501i | ||||
\(340\) | −3.98558 | − | 6.90323i | −0.216149 | − | 0.374380i | ||||
\(341\) | −1.58964 | −0.0860837 | ||||||||
\(342\) | 3.43786 | + | 5.95456i | 0.185898 | + | 0.321985i | ||||
\(343\) | 16.5777 | − | 8.25707i | 0.895113 | − | 0.445840i | ||||
\(344\) | −0.0979721 | − | 0.169693i | −0.00528230 | − | 0.00914921i | ||||
\(345\) | 6.61899 | − | 11.4644i | 0.356355 | − | 0.617224i | ||||
\(346\) | −6.01212 | + | 10.4133i | −0.323214 | + | 0.559823i | ||||
\(347\) | −2.01895 | −0.108383 | −0.0541916 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541916 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(348\) | 9.27596 | 0.497244 | ||||||||
\(349\) | −16.8191 | + | 29.1316i | −0.900306 | + | 1.55938i | −0.0732096 | + | 0.997317i | \(0.523324\pi\) |
−0.827097 | + | 0.562060i | \(0.810009\pi\) | |||||||
\(350\) | 1.51183 | − | 3.90292i | 0.0808107 | − | 0.208620i | ||||
\(351\) | −2.81454 | − | 2.25352i | −0.150229 | − | 0.120284i | ||||
\(352\) | −0.357690 | − | 0.619538i | −0.0190650 | − | 0.0330215i | ||||
\(353\) | −11.6388 | − | 20.1590i | −0.619472 | − | 1.07296i | −0.989582 | − | 0.143970i | \(-0.954013\pi\) |
0.370110 | − | 0.928988i | \(-0.379320\pi\) | |||||||
\(354\) | 1.24028 | + | 2.14823i | 0.0659202 | + | 0.114177i | ||||
\(355\) | 13.8821 | − | 24.0445i | 0.736785 | − | 1.27615i | ||||
\(356\) | −4.46953 | −0.236885 | ||||||||
\(357\) | −7.15185 | − | 8.88694i | −0.378516 | − | 0.470347i | ||||
\(358\) | −5.65742 | − | 9.79893i | −0.299004 | − | 0.517890i | ||||
\(359\) | 5.44896 | + | 9.43787i | 0.287585 | + | 0.498112i | 0.973233 | − | 0.229822i | \(-0.0738143\pi\) |
−0.685648 | + | 0.727933i | \(0.740481\pi\) | |||||||
\(360\) | 1.84879 | 0.0974399 | ||||||||
\(361\) | −14.1378 | − | 24.4874i | −0.744096 | − | 1.28881i | ||||
\(362\) | −2.49725 | −0.131252 | ||||||||
\(363\) | −10.4882 | −0.550489 | ||||||||
\(364\) | −8.27319 | − | 4.74914i | −0.433633 | − | 0.248923i | ||||
\(365\) | 3.66029 | 0.191588 | ||||||||
\(366\) | 8.62311 | 0.450737 | ||||||||
\(367\) | −2.44394 | − | 4.23302i | −0.127573 | − | 0.220962i | 0.795163 | − | 0.606396i | \(-0.207385\pi\) |
−0.922736 | + | 0.385434i | \(0.874052\pi\) | |||||||
\(368\) | −7.16035 | −0.373259 | ||||||||
\(369\) | 2.23138 | + | 3.86487i | 0.116161 | + | 0.201197i | ||||
\(370\) | −1.97212 | − | 3.41580i | −0.102525 | − | 0.177579i | ||||
\(371\) | 7.26584 | − | 18.7574i | 0.377224 | − | 0.973836i | ||||
\(372\) | −2.22209 | −0.115210 | ||||||||
\(373\) | 7.68366 | − | 13.3085i | 0.397845 | − | 0.689088i | −0.595615 | − | 0.803270i | \(-0.703092\pi\) |
0.993460 | + | 0.114182i | \(0.0364249\pi\) | |||||||
\(374\) | −1.54220 | − | 2.67117i | −0.0797454 | − | 0.138123i | ||||
\(375\) | 6.08435 | + | 10.5384i | 0.314194 | + | 0.544200i | ||||
\(376\) | 4.60553 | + | 7.97700i | 0.237512 | + | 0.411383i | ||||
\(377\) | 31.1568 | − | 12.1580i | 1.60466 | − | 0.626170i | ||||
\(378\) | 2.61442 | − | 0.405935i | 0.134472 | − | 0.0208790i | ||||
\(379\) | 8.66626 | − | 15.0104i | 0.445156 | − | 0.771033i | −0.552907 | − | 0.833243i | \(-0.686482\pi\) |
0.998063 | + | 0.0622101i | \(0.0198149\pi\) | |||||||
\(380\) | −12.7118 | −0.652101 | ||||||||
\(381\) | 15.1671 | 0.777035 | ||||||||
\(382\) | 2.66349 | − | 4.61330i | 0.136276 | − | 0.236037i | ||||
\(383\) | 5.99628 | − | 10.3859i | 0.306396 | − | 0.530693i | −0.671175 | − | 0.741298i | \(-0.734210\pi\) |
0.977571 | + | 0.210606i | \(0.0675436\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | −1.26395 | + | 3.26300i | −0.0644169 | + | 0.166298i | ||||
\(386\) | −4.86186 | − | 8.42099i | −0.247462 | − | 0.428617i | ||||
\(387\) | 0.195944 | 0.00996040 | ||||||||
\(388\) | 1.39194 | + | 2.41091i | 0.0706651 | + | 0.122396i | ||||
\(389\) | −8.89274 | + | 15.4027i | −0.450880 | + | 0.780947i | −0.998441 | − | 0.0558191i | \(-0.982223\pi\) |
0.547561 | + | 0.836766i | \(0.315556\pi\) | |||||||
\(390\) | 6.20986 | − | 2.42321i | 0.314449 | − | 0.122704i | ||||
\(391\) | −30.8722 | −1.56128 | ||||||||
\(392\) | 6.67043 | − | 2.12257i | 0.336908 | − | 0.107206i | ||||
\(393\) | 9.69444 | − | 16.7913i | 0.489020 | − | 0.847007i | ||||
\(394\) | −3.08593 | + | 5.34499i | −0.155467 | + | 0.269277i | ||||
\(395\) | 13.6354 | − | 23.6173i | 0.686074 | − | 1.18831i | ||||
\(396\) | 0.715381 | 0.0359492 | ||||||||
\(397\) | −7.02952 | + | 12.1755i | −0.352802 | + | 0.611070i | −0.986739 | − | 0.162314i | \(-0.948104\pi\) |
0.633938 | + | 0.773384i | \(0.281438\pi\) | |||||||
\(398\) | 5.41454 | 0.271406 | ||||||||
\(399\) | −17.9761 | + | 2.79110i | −0.899929 | + | 0.139730i | ||||
\(400\) | 0.790985 | − | 1.37003i | 0.0395493 | − | 0.0685013i | ||||
\(401\) | 4.13072 | 0.206278 | 0.103139 | − | 0.994667i | \(-0.467111\pi\) | ||||
0.103139 | + | 0.994667i | \(0.467111\pi\) | |||||||
\(402\) | 6.96322 | − | 12.0606i | 0.347294 | − | 0.601530i | ||||
\(403\) | −7.46371 | + | 2.91249i | −0.371794 | + | 0.145082i | ||||
\(404\) | −2.67775 | − | 4.63800i | −0.133223 | − | 0.230749i | ||||
\(405\) | −0.924396 | + | 1.60110i | −0.0459336 | + | 0.0795593i | ||||
\(406\) | −8.86469 | + | 22.8850i | −0.439947 | + | 1.13576i | ||||
\(407\) | −0.763101 | − | 1.32173i | −0.0378255 | − | 0.0655157i | ||||
\(408\) | −2.15578 | − | 3.73392i | −0.106727 | − | 0.184856i | ||||
\(409\) | −5.21490 | −0.257860 | −0.128930 | − | 0.991654i | \(-0.541154\pi\) | ||||
−0.128930 | + | 0.991654i | \(0.541154\pi\) | |||||||
\(410\) | −8.25072 | −0.407474 | ||||||||
\(411\) | 2.37414 | + | 4.11214i | 0.117108 | + | 0.202837i | ||||
\(412\) | 3.26429 | + | 5.65391i | 0.160820 | + | 0.278548i | ||||
\(413\) | −6.48525 | + | 1.00695i | −0.319118 | + | 0.0495486i | ||||
\(414\) | 3.58017 | − | 6.20104i | 0.175956 | − | 0.304765i | ||||
\(415\) | 8.98086 | + | 15.5553i | 0.440853 | + | 0.763580i | ||||
\(416\) | −2.81454 | − | 2.25352i | −0.137994 | − | 0.110488i | ||||
\(417\) | −7.69027 | + | 13.3199i | −0.376594 | + | 0.652280i | ||||
\(418\) | −4.91877 | −0.240585 | ||||||||
\(419\) | 3.69624 | − | 6.40207i | 0.180573 | − | 0.312762i | −0.761503 | − | 0.648162i | \(-0.775538\pi\) |
0.942076 | + | 0.335400i | \(0.108871\pi\) | |||||||
\(420\) | −1.76682 | + | 4.56120i | −0.0862120 | + | 0.222564i | ||||
\(421\) | 4.67144 | 0.227672 | 0.113836 | − | 0.993500i | \(-0.463686\pi\) | ||||
0.113836 | + | 0.993500i | \(0.463686\pi\) | |||||||
\(422\) | 13.6366 | − | 23.6193i | 0.663821 | − | 1.14977i | ||||
\(423\) | −9.21105 | −0.447857 | ||||||||
\(424\) | 3.80147 | − | 6.58434i | 0.184616 | − | 0.319764i | ||||
\(425\) | 3.41038 | − | 5.90695i | 0.165428 | − | 0.286529i | ||||
\(426\) | 7.50874 | − | 13.0055i | 0.363800 | − | 0.630120i | ||||
\(427\) | −8.24079 | + | 21.2743i | −0.398800 | + | 1.02954i | ||||
\(428\) | −4.61994 | −0.223313 | ||||||||
\(429\) | 2.40288 | − | 0.937651i | 0.116012 | − | 0.0452702i | ||||
\(430\) | −0.181130 | + | 0.313726i | −0.00873486 | + | 0.0151292i | ||||
\(431\) | 11.0089 | + | 19.0680i | 0.530280 | + | 0.918472i | 0.999376 | + | 0.0353247i | \(0.0112465\pi\) |
−0.469096 | + | 0.883147i | \(0.655420\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −12.5366 | − | 21.7141i | −0.602472 | − | 1.04351i | −0.992446 | − | 0.122686i | \(-0.960849\pi\) |
0.389973 | − | 0.920826i | \(-0.372484\pi\) | |||||||
\(434\) | 2.12356 | − | 5.48216i | 0.101934 | − | 0.263152i | ||||
\(435\) | −8.57466 | − | 14.8517i | −0.411123 | − | 0.712086i | ||||
\(436\) | 4.95093 | − | 8.57527i | 0.237107 | − | 0.410681i | ||||
\(437\) | −24.6163 | + | 42.6367i | −1.17756 | + | 2.03959i | ||||
\(438\) | 1.97983 | 0.0945998 | ||||||||
\(439\) | −13.9493 | −0.665764 | −0.332882 | − | 0.942969i | \(-0.608021\pi\) | ||||
−0.332882 | + | 0.942969i | \(0.608021\pi\) | |||||||
\(440\) | −0.661295 | + | 1.14540i | −0.0315260 | + | 0.0546046i | ||||
\(441\) | −1.49702 | + | 6.83805i | −0.0712865 | + | 0.325621i | ||||
\(442\) | −12.1350 | − | 9.71619i | −0.577205 | − | 0.462152i | ||||
\(443\) | 1.69137 | + | 2.92955i | 0.0803596 | + | 0.139187i | 0.903404 | − | 0.428789i | \(-0.141060\pi\) |
−0.823045 | + | 0.567976i | \(0.807726\pi\) | |||||||
\(444\) | −1.06671 | − | 1.84759i | −0.0506236 | − | 0.0876826i | ||||
\(445\) | 4.13161 | + | 7.15616i | 0.195857 | + | 0.339235i | ||||
\(446\) | −2.88502 | + | 4.99700i | −0.136610 | + | 0.236615i | ||||
\(447\) | −11.6477 | −0.550916 | ||||||||
\(448\) | 2.61442 | − | 0.405935i | 0.123520 | − | 0.0191786i | ||||
\(449\) | 7.51094 | + | 13.0093i | 0.354463 | + | 0.613948i | 0.987026 | − | 0.160561i | \(-0.0513304\pi\) |
−0.632563 | + | 0.774509i | \(0.717997\pi\) | |||||||
\(450\) | 0.790985 | + | 1.37003i | 0.0372874 | + | 0.0645837i | ||||
\(451\) | −3.19258 | −0.150333 | ||||||||
\(452\) | 1.50417 | + | 2.60530i | 0.0707503 | + | 0.122543i | ||||
\(453\) | 8.19088 | 0.384841 | ||||||||
\(454\) | 16.9846 | 0.797126 | ||||||||
\(455\) | 0.0438411 | + | 17.6363i | 0.00205530 | + | 0.826802i | ||||
\(456\) | −6.87573 | −0.321985 | ||||||||
\(457\) | −11.9647 | −0.559686 | −0.279843 | − | 0.960046i | \(-0.590282\pi\) | ||||
−0.279843 | + | 0.960046i | \(0.590282\pi\) | |||||||
\(458\) | 0.460390 | + | 0.797420i | 0.0215126 | + | 0.0372610i | ||||
\(459\) | 4.31156 | 0.201246 | ||||||||
\(460\) | 6.61899 | + | 11.4644i | 0.308612 | + | 0.534532i | ||||
\(461\) | 5.35595 | + | 9.27677i | 0.249451 | + | 0.432062i | 0.963374 | − | 0.268163i | \(-0.0864164\pi\) |
−0.713922 | + | 0.700225i | \(0.753083\pi\) | |||||||
\(462\) | −0.683663 | + | 1.76493i | −0.0318069 | + | 0.0821122i | ||||
\(463\) | −13.5305 | −0.628814 | −0.314407 | − | 0.949288i | \(-0.601806\pi\) | ||||
−0.314407 | + | 0.949288i | \(0.601806\pi\) | |||||||
\(464\) | −4.63798 | + | 8.03322i | −0.215313 | + | 0.372933i | ||||
\(465\) | 2.05409 | + | 3.55778i | 0.0952560 | + | 0.164988i | ||||
\(466\) | −2.50283 | − | 4.33502i | −0.115941 | − | 0.200816i | ||||
\(467\) | −13.9783 | − | 24.2112i | −0.646840 | − | 1.12036i | −0.983873 | − | 0.178867i | \(-0.942757\pi\) |
0.337034 | − | 0.941493i | \(-0.390576\pi\) | |||||||
\(468\) | 3.35888 | − | 1.31070i | 0.155264 | − | 0.0605872i | ||||
\(469\) | 23.1006 | + | 28.7050i | 1.06669 | + | 1.32548i | ||||
\(470\) | 8.51466 | − | 14.7478i | 0.392752 | − | 0.680266i | ||||
\(471\) | −22.8707 | −1.05382 | ||||||||
\(472\) | −2.48056 | −0.114177 | ||||||||
\(473\) | −0.0700874 | + | 0.121395i | −0.00322262 | + | 0.00558174i | ||||
\(474\) | 7.37533 | − | 12.7744i | 0.338760 | − | 0.586750i | ||||
\(475\) | −5.43860 | − | 9.41993i | −0.249540 | − | 0.432216i | ||||
\(476\) | 11.2722 | − | 1.75021i | 0.516662 | − | 0.0802208i | ||||
\(477\) | 3.80147 | + | 6.58434i | 0.174057 | + | 0.301476i | ||||
\(478\) | 13.8239 | 0.632291 | ||||||||
\(479\) | 5.79262 | + | 10.0331i | 0.264672 | + | 0.458425i | 0.967478 | − | 0.252957i | \(-0.0814031\pi\) |
−0.702806 | + | 0.711382i | \(0.748070\pi\) | |||||||
\(480\) | −0.924396 | + | 1.60110i | −0.0421927 | + | 0.0730799i | ||||
\(481\) | −6.00457 | − | 4.80769i | −0.273785 | − | 0.219212i | ||||
\(482\) | 10.7589 | 0.490054 | ||||||||
\(483\) | 11.8773 | + | 14.7588i | 0.540436 | + | 0.671551i | ||||
\(484\) | 5.24412 | − | 9.08307i | 0.238369 | − | 0.412867i | ||||
\(485\) | 2.57341 | − | 4.45728i | 0.116853 | − | 0.202394i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −8.48336 | −0.384418 | −0.192209 | − | 0.981354i | \(-0.561565\pi\) | ||||
−0.192209 | + | 0.981354i | \(0.561565\pi\) | |||||||
\(488\) | −4.31156 | + | 7.46783i | −0.195175 | + | 0.338053i | ||||
\(489\) | 18.0385 | 0.815727 | ||||||||
\(490\) | −9.56457 | − | 8.71794i | −0.432083 | − | 0.393836i | ||||
\(491\) | −14.8606 | + | 25.7394i | −0.670650 | + | 1.16160i | 0.307069 | + | 0.951687i | \(0.400652\pi\) |
−0.977720 | + | 0.209914i | \(0.932682\pi\) | |||||||
\(492\) | −4.46276 | −0.201197 | ||||||||
\(493\) | −19.9969 | + | 34.6357i | −0.900616 | + | 1.55991i | ||||
\(494\) | −23.0947 | + | 9.01203i | −1.03908 | + | 0.405471i | ||||
\(495\) | −0.661295 | − | 1.14540i | −0.0297230 | − | 0.0514818i | ||||
\(496\) | 1.11104 | − | 1.92438i | 0.0498873 | − | 0.0864073i | ||||
\(497\) | 24.9104 | + | 30.9539i | 1.11739 | + | 1.38847i | ||||
\(498\) | 4.85769 | + | 8.41377i | 0.217678 | + | 0.377030i | ||||
\(499\) | 17.7944 | + | 30.8208i | 0.796586 | + | 1.37973i | 0.921827 | + | 0.387601i | \(0.126696\pi\) |
−0.125241 | + | 0.992126i | \(0.539970\pi\) | |||||||
\(500\) | −12.1687 | −0.544200 | ||||||||
\(501\) | −7.73872 | −0.345741 | ||||||||
\(502\) | −11.8267 | − | 20.4844i | −0.527850 | − | 0.914263i | ||||
\(503\) | 13.5658 | + | 23.4966i | 0.604867 | + | 1.04766i | 0.992072 | + | 0.125667i | \(0.0401072\pi\) |
−0.387205 | + | 0.921994i | \(0.626560\pi\) | |||||||
\(504\) | −0.955663 | + | 2.46713i | −0.0425686 | + | 0.109895i | ||||
\(505\) | −4.95060 | + | 8.57469i | −0.220299 | + | 0.381568i | ||||
\(506\) | 2.56119 | + | 4.43611i | 0.113859 | + | 0.197209i | ||||
\(507\) | 9.56412 | − | 8.80498i | 0.424757 | − | 0.391043i | ||||
\(508\) | −7.58356 | + | 13.1351i | −0.336466 | + | 0.582776i | ||||
\(509\) | 7.21670 | 0.319875 | 0.159937 | − | 0.987127i | \(-0.448871\pi\) | ||||
0.159937 | + | 0.987127i | \(0.448871\pi\) | |||||||
\(510\) | −3.98558 | + | 6.90323i | −0.176485 | + | 0.305680i | ||||
\(511\) | −1.89205 | + | 4.88448i | −0.0836992 | + | 0.216077i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.43786 | − | 5.95456i | 0.151785 | − | 0.262900i | ||||
\(514\) | −19.1940 | −0.846613 | ||||||||
\(515\) | 6.03499 | − | 10.4529i | 0.265933 | − | 0.460610i | ||||
\(516\) | −0.0979721 | + | 0.169693i | −0.00431298 | + | 0.00747030i | ||||
\(517\) | 3.29471 | − | 5.70660i | 0.144901 | − | 0.250976i | ||||
\(518\) | 5.57764 | − | 0.866025i | 0.245067 | − | 0.0380510i | ||||
\(519\) | 12.0242 | 0.527806 | ||||||||
\(520\) | −1.00637 | + | 6.58951i | −0.0441321 | + | 0.288969i | ||||
\(521\) | 11.6165 | − | 20.1203i | 0.508926 | − | 0.881486i | −0.491020 | − | 0.871148i | \(-0.663376\pi\) |
0.999947 | − | 0.0103382i | \(-0.00329081\pi\) | |||||||
\(522\) | −4.63798 | − | 8.03322i | −0.202999 | − | 0.351604i | ||||
\(523\) | −39.7226 | −1.73695 | −0.868475 | − | 0.495734i | \(-0.834899\pi\) | ||||
−0.868475 | + | 0.495734i | \(0.834899\pi\) | |||||||
\(524\) | 9.69444 | + | 16.7913i | 0.423504 | + | 0.733530i | ||||
\(525\) | −4.13594 | + | 0.642177i | −0.180507 | + | 0.0280269i | ||||
\(526\) | −5.49567 | − | 9.51878i | −0.239623 | − | 0.415039i | ||||
\(527\) | 4.79032 | − | 8.29708i | 0.208670 | − | 0.361427i | ||||
\(528\) | −0.357690 | + | 0.619538i | −0.0155665 | + | 0.0269619i | ||||
\(529\) | 28.2706 | 1.22916 | ||||||||
\(530\) | −14.0562 | −0.610564 | ||||||||
\(531\) | 1.24028 | − | 2.14823i | 0.0538236 | − | 0.0932253i | ||||
\(532\) | 6.57088 | − | 16.9633i | 0.284884 | − | 0.735452i | ||||
\(533\) | −14.9899 | + | 5.84936i | −0.649284 | + | 0.253364i | ||||
\(534\) | 2.23476 | + | 3.87073i | 0.0967077 | + | 0.167503i | ||||
\(535\) | 4.27065 | + | 7.39699i | 0.184636 | + | 0.319800i | ||||
\(536\) | 6.96322 | + | 12.0606i | 0.300765 | + | 0.520940i | ||||
\(537\) | −5.65742 | + | 9.79893i | −0.244136 | + | 0.422855i | ||||
\(538\) | 16.5175 | 0.712122 | ||||||||
\(539\) | −3.70096 | − | 3.37336i | −0.159412 | − | 0.145301i | ||||
\(540\) | −0.924396 | − | 1.60110i | −0.0397797 | − | 0.0689004i | ||||
\(541\) | 17.6323 | + | 30.5400i | 0.758070 | + | 1.31302i | 0.943834 | + | 0.330421i | \(0.107191\pi\) |
−0.185764 | + | 0.982594i | \(0.559476\pi\) | |||||||
\(542\) | −18.1906 | −0.781352 | ||||||||
\(543\) | 1.24862 | + | 2.16268i | 0.0535836 | + | 0.0928095i | ||||
\(544\) | 4.31156 | 0.184856 | ||||||||
\(545\) | −18.3065 | −0.784164 | ||||||||
\(546\) | 0.0237134 | + | 9.53936i | 0.00101484 | + | 0.408247i | ||||
\(547\) | −37.3861 | −1.59851 | −0.799257 | − | 0.600990i | \(-0.794773\pi\) | ||||
−0.799257 | + | 0.600990i | \(0.794773\pi\) | |||||||
\(548\) | −4.74829 | −0.202837 | ||||||||
\(549\) | −4.31156 | − | 7.46783i | −0.184013 | − | 0.318719i | ||||
\(550\) | −1.13171 | −0.0482563 | ||||||||
\(551\) | 31.8895 | + | 55.2342i | 1.35854 | + | 2.35306i | ||||
\(552\) | 3.58017 | + | 6.20104i | 0.152382 | + | 0.263934i | ||||
\(553\) | 24.4678 | + | 30.4039i | 1.04048 | + | 1.29291i | ||||
\(554\) | 16.4894 | 0.700567 | ||||||||
\(555\) | −1.97212 | + | 3.41580i | −0.0837116 | + | 0.144993i | ||||
\(556\) | −7.69027 | − | 13.3199i | −0.326140 | − | 0.564891i | ||||
\(557\) | −16.6350 | − | 28.8127i | −0.704847 | − | 1.22083i | −0.966747 | − | 0.255736i | \(-0.917682\pi\) |
0.261899 | − | 0.965095i | \(-0.415651\pi\) | |||||||
\(558\) | 1.11104 | + | 1.92438i | 0.0470342 | + | 0.0814656i | ||||
\(559\) | −0.106660 | + | 0.698389i | −0.00451123 | + | 0.0295387i | ||||
\(560\) | −3.06671 | − | 3.81071i | −0.129592 | − | 0.161032i | ||||
\(561\) | −1.54220 | + | 2.67117i | −0.0651118 | + | 0.112777i | ||||
\(562\) | 15.2768 | 0.644411 | ||||||||
\(563\) | 14.6410 | 0.617045 | 0.308523 | − | 0.951217i | \(-0.400165\pi\) | ||||
0.308523 | + | 0.951217i | \(0.400165\pi\) | |||||||
\(564\) | 4.60553 | − | 7.97700i | 0.193928 | − | 0.335892i | ||||
\(565\) | 2.78090 | − | 4.81666i | 0.116993 | − | 0.202638i | ||||
\(566\) | 4.57838 | + | 7.92998i | 0.192444 | + | 0.333322i | ||||
\(567\) | −1.65876 | − | 2.06119i | −0.0696615 | − | 0.0865619i | ||||
\(568\) | 7.50874 | + | 13.0055i | 0.315060 | + | 0.545700i | ||||
\(569\) | 34.8196 | 1.45972 | 0.729858 | − | 0.683599i | \(-0.239586\pi\) | ||||
0.729858 | + | 0.683599i | \(0.239586\pi\) | |||||||
\(570\) | 6.35589 | + | 11.0087i | 0.266219 | + | 0.461105i | ||||
\(571\) | 17.3721 | − | 30.0894i | 0.727001 | − | 1.25920i | −0.231144 | − | 0.972920i | \(-0.574247\pi\) |
0.958145 | − | 0.286283i | \(-0.0924199\pi\) | |||||||
\(572\) | −0.389409 | + | 2.54978i | −0.0162820 | + | 0.106612i | ||||
\(573\) | −5.32698 | −0.222538 | ||||||||
\(574\) | 4.26490 | − | 11.0102i | 0.178013 | − | 0.459557i | ||||
\(575\) | −5.66373 | + | 9.80987i | −0.236194 | + | 0.409100i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −11.2007 | + | 19.4003i | −0.466293 | + | 0.807643i | −0.999259 | − | 0.0384934i | \(-0.987744\pi\) |
0.532966 | + | 0.846137i | \(0.321077\pi\) | |||||||
\(578\) | 1.58952 | 0.0661152 | ||||||||
\(579\) | −4.86186 | + | 8.42099i | −0.202052 | + | 0.349964i | ||||
\(580\) | 17.1493 | 0.712086 | ||||||||
\(581\) | −25.4001 | + | 3.94381i | −1.05378 | + | 0.163617i | ||||
\(582\) | 1.39194 | − | 2.41091i | 0.0576978 | − | 0.0999356i | ||||
\(583\) | −5.43900 | −0.225260 | ||||||||
\(584\) | −0.989914 | + | 1.71458i | −0.0409629 | + | 0.0709499i | ||||
\(585\) | −5.20350 | − | 4.16629i | −0.215138 | − | 0.172255i | ||||
\(586\) | 5.93488 | + | 10.2795i | 0.245168 | + | 0.424643i | ||||
\(587\) | −7.57505 | + | 13.1204i | −0.312656 | + | 0.541536i | −0.978936 | − | 0.204165i | \(-0.934552\pi\) |
0.666280 | + | 0.745701i | \(0.267885\pi\) | |||||||
\(588\) | −5.17342 | − | 4.71548i | −0.213348 | − | 0.194463i | ||||
\(589\) | −7.63923 | − | 13.2315i | −0.314769 | − | 0.545196i | ||||
\(590\) | 2.29302 | + | 3.97163i | 0.0944022 | + | 0.163509i | ||||
\(591\) | 6.17186 | 0.253876 | ||||||||
\(592\) | 2.13341 | 0.0876826 | ||||||||
\(593\) | −3.85455 | − | 6.67627i | −0.158287 | − | 0.274162i | 0.775964 | − | 0.630777i | \(-0.217264\pi\) |
−0.934251 | + | 0.356616i | \(0.883931\pi\) | |||||||
\(594\) | −0.357690 | − | 0.619538i | −0.0146762 | − | 0.0254200i | ||||
\(595\) | −13.2223 | − | 16.4301i | −0.542060 | − | 0.673568i | ||||
\(596\) | 5.82384 | − | 10.0872i | 0.238554 | − | 0.413187i | ||||
\(597\) | −2.70727 | − | 4.68913i | −0.110801 | − | 0.191913i | ||||
\(598\) | 20.1531 | + | 16.1360i | 0.824121 | + | 0.659850i | ||||
\(599\) | −8.99448 | + | 15.5789i | −0.367505 | + | 0.636537i | −0.989175 | − | 0.146743i | \(-0.953121\pi\) |
0.621670 | + | 0.783279i | \(0.286454\pi\) | |||||||
\(600\) | −1.58197 | −0.0645837 | ||||||||
\(601\) | 4.77657 | − | 8.27326i | 0.194840 | − | 0.337473i | −0.752008 | − | 0.659154i | \(-0.770914\pi\) |
0.946848 | + | 0.321681i | \(0.104248\pi\) | |||||||
\(602\) | −0.325025 | − | 0.403878i | −0.0132470 | − | 0.0164609i | ||||
\(603\) | −13.9264 | −0.567128 | ||||||||
\(604\) | −4.09544 | + | 7.09351i | −0.166641 | + | 0.288631i | ||||
\(605\) | −19.3905 | −0.788338 | ||||||||
\(606\) | −2.67775 | + | 4.63800i | −0.108776 | + | 0.188406i | ||||
\(607\) | −10.7619 | + | 18.6402i | −0.436813 | + | 0.756582i | −0.997442 | − | 0.0714855i | \(-0.977226\pi\) |
0.560629 | + | 0.828067i | \(0.310559\pi\) | |||||||
\(608\) | 3.43786 | − | 5.95456i | 0.139424 | − | 0.241489i | ||||
\(609\) | 24.2513 | − | 3.76543i | 0.982712 | − | 0.152583i | ||||
\(610\) | 15.9423 | 0.645486 | ||||||||
\(611\) | 5.01392 | − | 32.8303i | 0.202841 | − | 1.32817i | ||||
\(612\) | −2.15578 | + | 3.73392i | −0.0871422 | + | 0.150935i | ||||
\(613\) | 18.4945 | + | 32.0334i | 0.746985 | + | 1.29382i | 0.949262 | + | 0.314488i | \(0.101833\pi\) |
−0.202276 | + | 0.979328i | \(0.564834\pi\) | |||||||
\(614\) | −28.0679 | −1.13273 | ||||||||
\(615\) | 4.12536 | + | 7.14533i | 0.166351 | + | 0.288128i | ||||
\(616\) | −1.18665 | − | 1.47454i | −0.0478114 | − | 0.0594108i | ||||
\(617\) | 1.88766 | + | 3.26953i | 0.0759945 | + | 0.131626i | 0.901518 | − | 0.432741i | \(-0.142454\pi\) |
−0.825524 | + | 0.564367i | \(0.809120\pi\) | |||||||
\(618\) | 3.26429 | − | 5.65391i | 0.131309 | − | 0.227434i | ||||
\(619\) | −14.0117 | + | 24.2689i | −0.563177 | + | 0.975451i | 0.434040 | + | 0.900894i | \(0.357088\pi\) |
−0.997217 | + | 0.0745570i | \(0.976246\pi\) | |||||||
\(620\) | −4.10817 | −0.164988 | ||||||||
\(621\) | −7.16035 | −0.287335 | ||||||||
\(622\) | −12.7326 | + | 22.0536i | −0.510532 | + | 0.884267i | ||||
\(623\) | −11.6852 | + | 1.81434i | −0.468160 | + | 0.0726899i | ||||
\(624\) | −0.544337 | + | 3.56422i | −0.0217909 | + | 0.142683i | ||||
\(625\) | 7.29376 | + | 12.6332i | 0.291750 | + | 0.505326i | ||||
\(626\) | −8.82204 | − | 15.2802i | −0.352600 | − | 0.610721i | ||||
\(627\) | 2.45938 | + | 4.25978i | 0.0982183 | + | 0.170119i | ||||
\(628\) | 11.4353 | − | 19.8066i | 0.456319 | − | 0.790368i | ||||
\(629\) | 9.19832 | 0.366761 | ||||||||
\(630\) | 4.83353 | − | 0.750489i | 0.192572 | − | 0.0299002i | ||||
\(631\) | 6.85038 | + | 11.8652i | 0.272709 | + | 0.472346i | 0.969555 | − | 0.244875i | \(-0.0787470\pi\) |
−0.696845 | + | 0.717221i | \(0.745414\pi\) | |||||||
\(632\) | 7.37533 | + | 12.7744i | 0.293375 | + | 0.508140i | ||||
\(633\) | −27.2733 | −1.08402 | ||||||||
\(634\) | −14.8710 | − | 25.7573i | −0.590603 | − | 1.02295i | ||||
\(635\) | 28.0408 | 1.11277 | ||||||||
\(636\) | −7.60294 | −0.301476 | ||||||||
\(637\) | −23.5575 | − | 9.05791i | −0.933381 | − | 0.358887i | ||||
\(638\) | 6.63585 | 0.262716 | ||||||||
\(639\) | −15.0175 | −0.594082 | ||||||||
\(640\) | −0.924396 | − | 1.60110i | −0.0365399 | − | 0.0632890i | ||||
\(641\) | −6.40335 | −0.252917 | −0.126458 | − | 0.991972i | \(-0.540361\pi\) | ||||
−0.126458 | + | 0.991972i | \(0.540361\pi\) | |||||||
\(642\) | 2.30997 | + | 4.00099i | 0.0911673 | + | 0.157906i | ||||
\(643\) | 9.93369 | + | 17.2057i | 0.391747 | + | 0.678525i | 0.992680 | − | 0.120774i | \(-0.0385377\pi\) |
−0.600933 | + | 0.799299i | \(0.705204\pi\) | |||||||
\(644\) | −18.7202 | + | 2.90663i | −0.737679 | + | 0.114537i | ||||
\(645\) | 0.362260 | 0.0142640 | ||||||||
\(646\) | 14.8225 | − | 25.6734i | 0.583185 | − | 1.01011i | ||||
\(647\) | −15.2592 | − | 26.4297i | −0.599902 | − | 1.03906i | −0.992835 | − | 0.119494i | \(-0.961873\pi\) |
0.392933 | − | 0.919567i | \(-0.371460\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 0.887274 | + | 1.53680i | 0.0348285 | + | 0.0603248i | ||||
\(650\) | −5.31365 | + | 2.07349i | −0.208418 | + | 0.0813291i | ||||
\(651\) | −5.80947 | + | 0.902022i | −0.227691 | + | 0.0353530i | ||||
\(652\) | −9.01923 | + | 15.6218i | −0.353220 | + | 0.611795i | ||||
\(653\) | 3.65412 | 0.142997 | 0.0714984 | − | 0.997441i | \(-0.477222\pi\) | ||||
0.0714984 | + | 0.997441i | \(0.477222\pi\) | |||||||
\(654\) | −9.90187 | −0.387194 | ||||||||
\(655\) | 17.9230 | − | 31.0435i | 0.700309 | − | 1.21297i | ||||
\(656\) | 2.23138 | − | 3.86487i | 0.0871208 | − | 0.150898i | ||||
\(657\) | −0.989914 | − | 1.71458i | −0.0386202 | − | 0.0668922i | ||||
\(658\) | 15.2789 | + | 18.9857i | 0.595635 | + | 0.740141i | ||||
\(659\) | 4.12332 | + | 7.14181i | 0.160622 | + | 0.278205i | 0.935092 | − | 0.354405i | \(-0.115317\pi\) |
−0.774470 | + | 0.632611i | \(0.781983\pi\) | |||||||
\(660\) | 1.32259 | 0.0514818 | ||||||||
\(661\) | −23.0565 | − | 39.9351i | −0.896796 | − | 1.55330i | −0.831567 | − | 0.555425i | \(-0.812556\pi\) |
−0.0652290 | − | 0.997870i | \(-0.520778\pi\) | |||||||
\(662\) | −12.0197 | + | 20.8187i | −0.467158 | + | 0.809141i | ||||
\(663\) | −2.34694 | + | 15.3674i | −0.0911476 | + | 0.596819i | ||||
\(664\) | −9.71538 | −0.377030 | ||||||||
\(665\) | −33.2340 | + | 5.16016i | −1.28876 | + | 0.200102i | ||||
\(666\) | −1.06671 | + | 1.84759i | −0.0413340 | + | 0.0715926i | ||||
\(667\) | 33.2095 | − | 57.5206i | 1.28588 | − | 2.22721i | ||||
\(668\) | 3.86936 | − | 6.70193i | 0.149710 | − | 0.259306i | ||||
\(669\) | 5.77004 | 0.223083 | ||||||||
\(670\) | 12.8735 | − | 22.2976i | 0.497348 | − | 0.861432i | ||||
\(671\) | 6.16881 | 0.238144 | ||||||||
\(672\) | −1.65876 | − | 2.06119i | −0.0639881 | − | 0.0795122i | ||||
\(673\) | −3.98669 | + | 6.90515i | −0.153676 | + | 0.266174i | −0.932576 | − | 0.360974i | \(-0.882444\pi\) |
0.778900 | + | 0.627148i | \(0.215778\pi\) | |||||||
\(674\) | −2.21939 | −0.0854879 | ||||||||
\(675\) | 0.790985 | − | 1.37003i | 0.0304450 | − | 0.0527324i | ||||
\(676\) | 2.84327 | + | 12.6853i | 0.109357 | + | 0.487895i | ||||
\(677\) | −20.4979 | − | 35.5033i | −0.787797 | − | 1.36450i | −0.927314 | − | 0.374285i | \(-0.877888\pi\) |
0.139517 | − | 0.990220i | \(-0.455445\pi\) | |||||||
\(678\) | 1.50417 | − | 2.60530i | 0.0577674 | − | 0.100056i | ||||
\(679\) | 4.61780 | + | 5.73811i | 0.177215 | + | 0.220209i | ||||
\(680\) | −3.98558 | − | 6.90323i | −0.152840 | − | 0.264727i | ||||
\(681\) | −8.49229 | − | 14.7091i | −0.325425 | − | 0.563653i | ||||
\(682\) | −1.58964 | −0.0608704 | ||||||||
\(683\) | 35.2665 | 1.34944 | 0.674718 | − | 0.738076i | \(-0.264265\pi\) | ||||
0.674718 | + | 0.738076i | \(0.264265\pi\) | |||||||
\(684\) | 3.43786 | + | 5.95456i | 0.131450 | + | 0.227678i | ||||
\(685\) | 4.38930 | + | 7.60248i | 0.167706 | + | 0.290476i | ||||
\(686\) | 16.5777 | − | 8.25707i | 0.632940 | − | 0.315256i | ||||
\(687\) | 0.460390 | − | 0.797420i | 0.0175650 | − | 0.0304235i | ||||
\(688\) | −0.0979721 | − | 0.169693i | −0.00373515 | − | 0.00646947i | ||||
\(689\) | −25.5373 | + | 9.96519i | −0.972895 | + | 0.379644i | ||||
\(690\) | 6.61899 | − | 11.4644i | 0.251981 | − | 0.436444i | ||||
\(691\) | 40.7075 | 1.54859 | 0.774293 | − | 0.632827i | \(-0.218105\pi\) | ||||
0.774293 | + | 0.632827i | \(0.218105\pi\) | |||||||
\(692\) | −6.01212 | + | 10.4133i | −0.228547 | + | 0.395854i | ||||
\(693\) | 1.87031 | − | 0.290398i | 0.0710472 | − | 0.0110313i | ||||
\(694\) | −2.01895 | −0.0766384 | ||||||||
\(695\) | −14.2177 | + | 24.6258i | −0.539308 | + | 0.934109i | ||||
\(696\) | 9.27596 | 0.351604 | ||||||||
\(697\) | 9.62073 | − | 16.6636i | 0.364411 | − | 0.631179i | ||||
\(698\) | −16.8191 | + | 29.1316i | −0.636613 | + | 1.10265i | ||||
\(699\) | −2.50283 | + | 4.33502i | −0.0946656 | + | 0.163966i | ||||
\(700\) | 1.51183 | − | 3.90292i | 0.0571418 | − | 0.147517i | ||||
\(701\) | −33.7968 | −1.27649 | −0.638243 | − | 0.769835i | \(-0.720339\pi\) | ||||
−0.638243 | + | 0.769835i | \(0.720339\pi\) | |||||||
\(702\) | −2.81454 | − | 2.25352i | −0.106228 | − | 0.0850537i | ||||
\(703\) | 7.33438 | − | 12.7035i | 0.276621 | − | 0.479122i | ||||
\(704\) | −0.357690 | − | 0.619538i | −0.0134810 | − | 0.0233497i | ||||
\(705\) | −17.0293 | −0.641361 | ||||||||
\(706\) | −11.6388 | − | 20.1590i | −0.438033 | − | 0.758696i | ||||
\(707\) | −8.88349 | − | 11.0387i | −0.334098 | − | 0.415153i | ||||
\(708\) | 1.24028 | + | 2.14823i | 0.0466126 | + | 0.0807355i | ||||
\(709\) | 1.67680 | − | 2.90430i | 0.0629736 | − | 0.109073i | −0.832820 | − | 0.553544i | \(-0.813275\pi\) |
0.895793 | + | 0.444471i | \(0.146608\pi\) | |||||||
\(710\) | 13.8821 | − | 24.0445i | 0.520986 | − | 0.902374i | ||||
\(711\) | −14.7507 | −0.553193 | ||||||||
\(712\) | −4.46953 | −0.167503 | ||||||||
\(713\) | −7.95545 | + | 13.7792i | −0.297934 | + | 0.516037i | ||||
\(714\) | −7.15185 | − | 8.88694i | −0.267651 | − | 0.332585i | ||||
\(715\) | 4.44242 | − | 1.73352i | 0.166137 | − | 0.0648300i | ||||
\(716\) | −5.65742 | − | 9.79893i | −0.211428 | − | 0.366203i | ||||
\(717\) | −6.91196 | − | 11.9719i | −0.258132 | − | 0.447097i | ||||
\(718\) | 5.44896 | + | 9.43787i | 0.203353 | + | 0.352218i | ||||
\(719\) | 19.5541 | − | 33.8687i | 0.729245 | − | 1.26309i | −0.227958 | − | 0.973671i | \(-0.573205\pi\) |
0.957203 | − | 0.289419i | \(-0.0934619\pi\) | |||||||
\(720\) | 1.84879 | 0.0689004 | ||||||||
\(721\) | 10.8294 | + | 13.4566i | 0.403306 | + | 0.501151i | ||||
\(722\) | −14.1378 | − | 24.4874i | −0.526155 | − | 0.911328i | ||||
\(723\) | −5.37945 | − | 9.31748i | −0.200064 | − | 0.346521i | ||||
\(724\) | −2.49725 | −0.0928095 | ||||||||
\(725\) | 7.33715 | + | 12.7083i | 0.272495 | + | 0.471975i | ||||
\(726\) | −10.4882 | −0.389255 | ||||||||
\(727\) | −3.65073 | −0.135398 | −0.0676990 | − | 0.997706i | \(-0.521566\pi\) | ||||
−0.0676990 | + | 0.997706i | \(0.521566\pi\) | |||||||
\(728\) | −8.27319 | − | 4.74914i | −0.306625 | − | 0.176015i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.66029 | 0.135473 | ||||||||
\(731\) | −0.422412 | − | 0.731639i | −0.0156235 | − | 0.0270607i | ||||
\(732\) | 8.62311 | 0.318719 | ||||||||
\(733\) | 16.3999 | + | 28.4054i | 0.605744 | + | 1.04918i | 0.991933 | + | 0.126760i | \(0.0404577\pi\) |
−0.386190 | + | 0.922419i | \(0.626209\pi\) | |||||||
\(734\) | −2.44394 | − | 4.23302i | −0.0902074 | − | 0.156244i | ||||
\(735\) | −2.76767 | + | 12.6421i | −0.102087 | + | 0.466312i | ||||
\(736\) | −7.16035 | −0.263934 | ||||||||
\(737\) | 4.98135 | − | 8.62796i | 0.183490 | − | 0.317815i | ||||
\(738\) | 2.23138 | + | 3.86487i | 0.0821383 | + | 0.142268i | ||||
\(739\) | −5.11506 | − | 8.85954i | −0.188160 | − | 0.325903i | 0.756477 | − | 0.654021i | \(-0.226919\pi\) |
−0.944637 | + | 0.328118i | \(0.893586\pi\) | |||||||
\(740\) | −1.97212 | − | 3.41580i | −0.0724964 | − | 0.125567i | ||||
\(741\) | 19.3520 | + | 15.4946i | 0.710914 | + | 0.569209i | ||||
\(742\) | 7.26584 | − | 18.7574i | 0.266738 | − | 0.688606i | ||||
\(743\) | 17.1231 | − | 29.6581i | 0.628186 | − | 1.08805i | −0.359729 | − | 0.933057i | \(-0.617131\pi\) |
0.987915 | − | 0.154994i | \(-0.0495357\pi\) | |||||||
\(744\) | −2.22209 | −0.0814656 | ||||||||
\(745\) | −21.5341 | −0.788949 | ||||||||
\(746\) | 7.68366 | − | 13.3085i | 0.281319 | − | 0.487259i | ||||
\(747\) | 4.85769 | − | 8.41377i | 0.177734 | − | 0.307844i | ||||
\(748\) | −1.54220 | − | 2.67117i | −0.0563885 | − | 0.0976678i | ||||
\(749\) | −12.0785 | + | 1.87539i | −0.441338 | + | 0.0685254i | ||||
\(750\) | 6.08435 | + | 10.5384i | 0.222169 | + | 0.384808i | ||||
\(751\) | 11.7925 | 0.430316 | 0.215158 | − | 0.976579i | \(-0.430973\pi\) | ||||
0.215158 | + | 0.976579i | \(0.430973\pi\) | |||||||
\(752\) | 4.60553 | + | 7.97700i | 0.167946 | + | 0.290891i | ||||
\(753\) | −11.8267 | + | 20.4844i | −0.430988 | + | 0.746492i | ||||
\(754\) | 31.1568 | − | 12.1580i | 1.13466 | − | 0.442769i | ||||
\(755\) | 15.1432 | 0.551118 | ||||||||
\(756\) | 2.61442 | − | 0.405935i | 0.0950857 | − | 0.0147637i | ||||
\(757\) | 24.1278 | − | 41.7906i | 0.876940 | − | 1.51890i | 0.0222575 | − | 0.999752i | \(-0.492915\pi\) |
0.854682 | − | 0.519152i | \(-0.173752\pi\) | |||||||
\(758\) | 8.66626 | − | 15.0104i | 0.314773 | − | 0.545203i | ||||
\(759\) | 2.56119 | − | 4.43611i | 0.0929652 | − | 0.161021i | ||||
\(760\) | −12.7118 | −0.461105 | ||||||||
\(761\) | −6.11899 | + | 10.5984i | −0.221813 | + | 0.384192i | −0.955359 | − | 0.295449i | \(-0.904531\pi\) |
0.733545 | + | 0.679641i | \(0.237864\pi\) | |||||||
\(762\) | 15.1671 | 0.549446 | ||||||||
\(763\) | 9.46285 | − | 24.4292i | 0.342578 | − | 0.884395i | ||||
\(764\) | 2.66349 | − | 4.61330i | 0.0963617 | − | 0.166903i | ||||
\(765\) | 7.97117 | 0.288198 | ||||||||
\(766\) | 5.99628 | − | 10.3859i | 0.216654 | − | 0.375256i | ||||
\(767\) | 6.98165 | + | 5.59000i | 0.252093 | + | 0.201843i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 0.357690 | − | 0.619538i | 0.0128986 | − | 0.0223411i | −0.859504 | − | 0.511129i | \(-0.829227\pi\) |
0.872403 | + | 0.488788i | \(0.162561\pi\) | |||||||
\(770\) | −1.26395 | + | 3.26300i | −0.0455496 | + | 0.117590i | ||||
\(771\) | 9.59702 | + | 16.6225i | 0.345628 | + | 0.598646i | ||||
\(772\) | −4.86186 | − | 8.42099i | −0.174982 | − | 0.303078i | ||||
\(773\) | 5.43066 | 0.195327 | 0.0976636 | − | 0.995219i | \(-0.468863\pi\) | ||||
0.0976636 | + | 0.995219i | \(0.468863\pi\) | |||||||
\(774\) | 0.195944 | 0.00704307 | ||||||||
\(775\) | −1.75764 | − | 3.04432i | −0.0631362 | − | 0.109355i | ||||
\(776\) | 1.39194 | + | 2.41091i | 0.0499678 | + | 0.0865467i | ||||
\(777\) | −3.53882 | − | 4.39737i | −0.126954 | − | 0.157755i | ||||
\(778\) | −8.89274 | + | 15.4027i | −0.318820 | + | 0.552213i | ||||
\(779\) | −15.3424 | − | 26.5738i | −0.549698 | − | 0.952105i | ||||
\(780\) | 6.20986 | − | 2.42321i | 0.222349 | − | 0.0867650i | ||||
\(781\) | 5.37161 | − | 9.30390i | 0.192211 | − | 0.332920i | ||||
\(782\) | −30.8722 | −1.10399 | ||||||||
\(783\) | −4.63798 | + | 8.03322i | −0.165748 | + | 0.287084i | ||||
\(784\) | 6.67043 | − | 2.12257i | 0.238230 | − | 0.0758061i | ||||
\(785\) | −42.2831 | −1.50915 | ||||||||
\(786\) | 9.69444 | − | 16.7913i | 0.345789 | − | 0.598925i | ||||
\(787\) | −5.17027 | −0.184300 | −0.0921501 | − | 0.995745i | \(-0.529374\pi\) | ||||
−0.0921501 | + | 0.995745i | \(0.529374\pi\) | |||||||
\(788\) | −3.08593 | + | 5.34499i | −0.109932 | + | 0.190407i | ||||
\(789\) | −5.49567 | + | 9.51878i | −0.195651 | + | 0.338878i | ||||
\(790\) | 13.6354 | − | 23.6173i | 0.485127 | − | 0.840265i | ||||
\(791\) | 4.99013 | + | 6.20077i | 0.177428 | + | 0.220474i | ||||
\(792\) | 0.715381 | 0.0254200 | ||||||||
\(793\) | 28.9640 | − | 11.3023i | 1.02854 | − | 0.401358i | ||||
\(794\) | −7.02952 | + | 12.1755i | −0.249468 | + | 0.432092i | ||||
\(795\) | 7.02812 | + | 12.1731i | 0.249262 | + | 0.431734i | ||||
\(796\) | 5.41454 | 0.191913 | ||||||||
\(797\) | 3.24073 | + | 5.61311i | 0.114793 | + | 0.198827i | 0.917697 | − | 0.397281i | \(-0.130046\pi\) |
−0.802904 | + | 0.596108i | \(0.796713\pi\) | |||||||
\(798\) | −17.9761 | + | 2.79110i | −0.636346 | + | 0.0988038i | ||||
\(799\) | 19.8570 | + | 34.3933i | 0.702490 | + | 1.21675i | ||||
\(800\) | 0.790985 | − | 1.37003i | 0.0279656 | − | 0.0484378i | ||||
\(801\) | 2.23476 | − | 3.87073i | 0.0789615 | − | 0.136765i | ||||
\(802\) | 4.13072 | 0.145861 | ||||||||
\(803\) | 1.41633 | 0.0499812 | ||||||||
\(804\) | 6.96322 | − | 12.0606i | 0.245574 | − | 0.425346i | ||||
\(805\) | 21.9587 | + | 27.2860i | 0.773942 | + | 0.961706i | ||||
\(806\) | −7.46371 | + | 2.91249i | −0.262898 | + | 0.102588i | ||||
\(807\) | −8.25877 | − | 14.3046i | −0.290723 | − | 0.503546i | ||||
\(808\) | −2.67775 | − | 4.63800i | −0.0942028 | − | 0.163164i | ||||
\(809\) | −23.2909 | − | 40.3409i | −0.818863 | − | 1.41831i | −0.906521 | − | 0.422161i | \(-0.861272\pi\) |
0.0876578 | − | 0.996151i | \(-0.472062\pi\) | |||||||
\(810\) | −0.924396 | + | 1.60110i | −0.0324800 | + | 0.0562569i | ||||
\(811\) | 44.2321 | 1.55320 | 0.776600 | − | 0.629994i | \(-0.216943\pi\) | ||||
0.776600 | + | 0.629994i | \(0.216943\pi\) | |||||||
\(812\) | −8.86469 | + | 22.8850i | −0.311090 | + | 0.803105i | ||||
\(813\) | 9.09528 | + | 15.7535i | 0.318985 | + | 0.552499i | ||||
\(814\) | −0.763101 | − | 1.32173i | −0.0267467 | − | 0.0463266i | ||||
\(815\) | 33.3493 | 1.16818 | ||||||||
\(816\) | −2.15578 | − | 3.73392i | −0.0754673 | − | 0.130713i | ||||
\(817\) | −1.34726 | −0.0471346 | ||||||||
\(818\) | −5.21490 | −0.182335 | ||||||||
\(819\) | 8.24947 | − | 4.79022i | 0.288260 | − | 0.167384i | ||||
\(820\) | −8.25072 | −0.288128 | ||||||||
\(821\) | −8.26567 | −0.288474 | −0.144237 | − | 0.989543i | \(-0.546073\pi\) | ||||
−0.144237 | + | 0.989543i | \(0.546073\pi\) | |||||||
\(822\) | 2.37414 | + | 4.11214i | 0.0828078 | + | 0.143427i | ||||
\(823\) | −51.2361 | −1.78598 | −0.892989 | − | 0.450078i | \(-0.851396\pi\) | ||||
−0.892989 | + | 0.450078i | \(0.851396\pi\) | |||||||
\(824\) | 3.26429 | + | 5.65391i | 0.113717 | + | 0.196963i | ||||
\(825\) | 0.565856 | + | 0.980091i | 0.0197006 | + | 0.0341224i | ||||
\(826\) | −6.48525 | + | 1.00695i | −0.225651 | + | 0.0350362i | ||||
\(827\) | −4.84895 | −0.168615 | −0.0843073 | − | 0.996440i | \(-0.526868\pi\) | ||||
−0.0843073 | + | 0.996440i | \(0.526868\pi\) | |||||||
\(828\) | 3.58017 | − | 6.20104i | 0.124420 | − | 0.215501i | ||||
\(829\) | −0.997594 | − | 1.72788i | −0.0346479 | − | 0.0600118i | 0.848181 | − | 0.529706i | \(-0.177698\pi\) |
−0.882829 | + | 0.469694i | \(0.844364\pi\) | |||||||
\(830\) | 8.98086 | + | 15.5553i | 0.311730 | + | 0.539932i | ||||
\(831\) | −8.24469 | − | 14.2802i | −0.286005 | − | 0.495376i | ||||
\(832\) | −2.81454 | − | 2.25352i | −0.0975766 | − | 0.0781268i | ||||
\(833\) | 28.7600 | − | 9.15159i | 0.996473 | − | 0.317084i | ||||
\(834\) | −7.69027 | + | 13.3199i | −0.266292 | + | 0.461232i | ||||
\(835\) | −14.3073 | −0.495124 | ||||||||
\(836\) | −4.91877 | −0.170119 | ||||||||
\(837\) | 1.11104 | − | 1.92438i | 0.0384032 | − | 0.0665164i | ||||
\(838\) | 3.69624 | − | 6.40207i | 0.127684 | − | 0.221156i | ||||
\(839\) | 11.0996 | + | 19.2251i | 0.383201 | + | 0.663724i | 0.991518 | − | 0.129971i | \(-0.0414883\pi\) |
−0.608317 | + | 0.793694i | \(0.708155\pi\) | |||||||
\(840\) | −1.76682 | + | 4.56120i | −0.0609611 | + | 0.157376i | ||||
\(841\) | −28.5217 | − | 49.4011i | −0.983507 | − | 1.70348i | ||||
\(842\) | 4.67144 | 0.160989 | ||||||||
\(843\) | −7.63838 | − | 13.2301i | −0.263080 | − | 0.455667i | ||||
\(844\) | 13.6366 | − | 23.6193i | 0.469392 | − | 0.813011i | ||||
\(845\) | 17.6821 | − | 16.2786i | 0.608281 | − | 0.560000i | ||||
\(846\) | −9.21105 | −0.316682 | ||||||||
\(847\) | 10.0232 | − | 25.8758i | 0.344402 | − | 0.889102i | ||||
\(848\) | 3.80147 | − | 6.58434i | 0.130543 | − | 0.226107i | ||||
\(849\) | 4.57838 | − | 7.92998i | 0.157129 | − | 0.272156i | ||||
\(850\) | 3.41038 | − | 5.90695i | 0.116975 | − | 0.202607i | ||||
\(851\) | −15.2760 | −0.523653 | ||||||||
\(852\) | 7.50874 | − | 13.0055i | 0.257245 | − | 0.445562i | ||||
\(853\) | −20.8901 | −0.715262 | −0.357631 | − | 0.933863i | \(-0.616415\pi\) | ||||
−0.357631 | + | 0.933863i | \(0.616415\pi\) | |||||||
\(854\) | −8.24079 | + | 21.2743i | −0.281994 | + | 0.727992i | ||||
\(855\) | 6.35589 | − | 11.0087i | 0.217367 | − | 0.376491i | ||||
\(856\) | −4.61994 | −0.157906 | ||||||||
\(857\) | 6.25195 | − | 10.8287i | 0.213563 | − | 0.369901i | −0.739264 | − | 0.673415i | \(-0.764827\pi\) |
0.952827 | + | 0.303514i | \(0.0981599\pi\) | |||||||
\(858\) | 2.40288 | − | 0.937651i | 0.0820329 | − | 0.0320109i | ||||
\(859\) | 4.94030 | + | 8.55685i | 0.168561 | + | 0.291956i | 0.937914 | − | 0.346868i | \(-0.112755\pi\) |
−0.769353 | + | 0.638824i | \(0.779421\pi\) | |||||||
\(860\) | −0.181130 | + | 0.313726i | −0.00617648 | + | 0.0106980i | ||||
\(861\) | −11.6676 | + | 1.81159i | −0.397629 | + | 0.0617389i | ||||
\(862\) | 11.0089 | + | 19.0680i | 0.374965 | + | 0.649458i | ||||
\(863\) | −20.2808 | − | 35.1274i | −0.690367 | − | 1.19575i | −0.971718 | − | 0.236146i | \(-0.924116\pi\) |
0.281350 | − | 0.959605i | \(-0.409218\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 22.2303 | 0.755854 | ||||||||
\(866\) | −12.5366 | − | 21.7141i | −0.426012 | − | 0.737875i | ||||
\(867\) | −0.794759 | − | 1.37656i | −0.0269914 | − | 0.0467505i | ||||
\(868\) | 2.12356 | − | 5.48216i | 0.0720784 | − | 0.186077i | ||||
\(869\) | 5.27617 | − | 9.13860i | 0.178982 | − | 0.310006i | ||||
\(870\) | −8.57466 | − | 14.8517i | −0.290708 | − | 0.503521i | ||||
\(871\) | 7.58068 | − | 49.6369i | 0.256861 | − | 1.68188i | ||||
\(872\) | 4.95093 | − | 8.57527i | 0.167660 | − | 0.290395i | ||||
\(873\) | −2.78388 | −0.0942202 | ||||||||
\(874\) | −24.6163 | + | 42.6367i | −0.832659 | + | 1.44221i | ||||
\(875\) | −31.8141 | + | 4.93969i | −1.07551 | + | 0.166992i | ||||
\(876\) | 1.97983 | 0.0668922 | ||||||||
\(877\) | 15.6174 | − | 27.0502i | 0.527363 | − | 0.913420i | −0.472128 | − | 0.881530i | \(-0.656514\pi\) |
0.999491 | − | 0.0318902i | \(-0.0101527\pi\) | |||||||
\(878\) | −13.9493 | −0.470766 | ||||||||
\(879\) | 5.93488 | − | 10.2795i | 0.200179 | − | 0.346719i | ||||
\(880\) | −0.661295 | + | 1.14540i | −0.0222923 | + | 0.0386113i | ||||
\(881\) | −19.0177 | + | 32.9396i | −0.640722 | + | 1.10976i | 0.344550 | + | 0.938768i | \(0.388031\pi\) |
−0.985272 | + | 0.170994i | \(0.945302\pi\) | |||||||
\(882\) | −1.49702 | + | 6.83805i | −0.0504071 | + | 0.230249i | ||||
\(883\) | 22.5813 | 0.759921 | 0.379961 | − | 0.925003i | \(-0.375938\pi\) | ||||
0.379961 | + | 0.925003i | \(0.375938\pi\) | |||||||
\(884\) | −12.1350 | − | 9.71619i | −0.408146 | − | 0.326791i | ||||
\(885\) | 2.29302 | − | 3.97163i | 0.0770791 | − | 0.133505i | ||||
\(886\) | 1.69137 | + | 2.92955i | 0.0568228 | + | 0.0984201i | ||||
\(887\) | 7.73646 | 0.259765 | 0.129882 | − | 0.991529i | \(-0.458540\pi\) | ||||
0.129882 | + | 0.991529i | \(0.458540\pi\) | |||||||
\(888\) | −1.06671 | − | 1.84759i | −0.0357963 | − | 0.0620010i | ||||
\(889\) | −14.4946 | + | 37.4192i | −0.486135 | + | 1.25500i | ||||
\(890\) | 4.13161 | + | 7.15616i | 0.138492 | + | 0.239875i | ||||
\(891\) | −0.357690 | + | 0.619538i | −0.0119831 | + | 0.0207553i | ||||
\(892\) | −2.88502 | + | 4.99700i | −0.0965976 | + | 0.167312i | ||||
\(893\) | 63.3327 | 2.11935 | ||||||||
\(894\) | −11.6477 | −0.389557 | ||||||||
\(895\) | −10.4594 | + | 18.1162i | −0.349619 | + | 0.605557i | ||||
\(896\) | 2.61442 | − | 0.405935i | 0.0873418 | − | 0.0135613i | ||||
\(897\) | 3.89765 | − | 25.5211i | 0.130139 | − | 0.852124i | ||||
\(898\) | 7.51094 | + | 13.0093i | 0.250643 | + | 0.434127i | ||||
\(899\) | 10.3060 | + | 17.8505i | 0.343724 | + | 0.595347i | ||||
\(900\) | 0.790985 | + | 1.37003i | 0.0263662 | + | 0.0456676i | ||||
\(901\) | 16.3903 | − | 28.3887i | 0.546038 | − | 0.945766i | ||||
\(902\) | −3.19258 | −0.106301 | ||||||||
\(903\) | −0.187257 | + | 0.483419i | −0.00623151 | + | 0.0160872i | ||||
\(904\) | 1.50417 | + | 2.60530i | 0.0500280 | + | 0.0866510i | ||||
\(905\) | 2.30845 | + | 3.99835i | 0.0767353 | + | 0.132909i | ||||
\(906\) | 8.19088 | 0.272124 | ||||||||
\(907\) | 20.3205 | + | 35.1961i | 0.674731 | + | 1.16867i | 0.976548 | + | 0.215302i | \(0.0690735\pi\) |
−0.301817 | + | 0.953366i | \(0.597593\pi\) | |||||||
\(908\) | 16.9846 | 0.563653 | ||||||||
\(909\) | 5.35550 | 0.177631 | ||||||||
\(910\) | 0.0438411 | + | 17.6363i | 0.00145332 | + | 0.584637i | ||||
\(911\) | 2.41059 | 0.0798664 | 0.0399332 | − | 0.999202i | \(-0.487285\pi\) | ||||
0.0399332 | + | 0.999202i | \(0.487285\pi\) | |||||||
\(912\) | −6.87573 | −0.227678 | ||||||||
\(913\) | 3.47510 | + | 6.01905i | 0.115009 | + | 0.199201i | ||||
\(914\) | −11.9647 | −0.395758 | ||||||||
\(915\) | −7.97117 | − | 13.8065i | −0.263519 | − | 0.456428i | ||||
\(916\) | 0.460390 | + | 0.797420i | 0.0152117 | + | 0.0263475i | ||||
\(917\) | 32.1615 | + | 39.9642i | 1.06207 | + | 1.31973i | ||||
\(918\) | 4.31156 | 0.142303 | ||||||||
\(919\) | −6.62695 | + | 11.4782i | −0.218603 | + | 0.378631i | −0.954381 | − | 0.298591i | \(-0.903483\pi\) |
0.735778 | + | 0.677223i | \(0.236817\pi\) | |||||||
\(920\) | 6.61899 | + | 11.4644i | 0.218222 | + | 0.377971i | ||||
\(921\) | 14.0339 | + | 24.3075i | 0.462434 | + | 0.800959i | ||||
\(922\) | 5.35595 | + | 9.27677i | 0.176389 | + | 0.305514i | ||||
\(923\) | 8.17458 | − | 53.5257i | 0.269069 | − | 1.76182i | ||||
\(924\) | −0.683663 | + | 1.76493i | −0.0224909 | + | 0.0580621i | ||||
\(925\) | 1.68750 | − | 2.92283i | 0.0554845 | − | 0.0961020i | ||||
\(926\) | −13.5305 | −0.444639 | ||||||||
\(927\) | −6.52858 | −0.214427 | ||||||||
\(928\) | −4.63798 | + | 8.03322i | −0.152249 | + | 0.263703i | ||||
\(929\) | 12.3258 | − | 21.3489i | 0.404397 | − | 0.700436i | −0.589854 | − | 0.807510i | \(-0.700815\pi\) |
0.994251 | + | 0.107074i | \(0.0341481\pi\) | |||||||
\(930\) | 2.05409 | + | 3.55778i | 0.0673561 | + | 0.116664i | ||||
\(931\) | 10.2931 | − | 47.0166i | 0.337342 | − | 1.54091i | ||||
\(932\) | −2.50283 | − | 4.33502i | −0.0819828 | − | 0.141998i | ||||
\(933\) | 25.4653 | 0.833695 | ||||||||
\(934\) | −13.9783 | − | 24.2112i | −0.457385 | − | 0.792214i | ||||
\(935\) | −2.85121 | + | 4.93844i | −0.0932446 | + | 0.161504i | ||||
\(936\) | 3.35888 | − | 1.31070i | 0.109788 | − | 0.0428416i | ||||
\(937\) | −26.6818 | −0.871656 | −0.435828 | − | 0.900030i | \(-0.643544\pi\) | ||||
−0.435828 | + | 0.900030i | \(0.643544\pi\) | |||||||
\(938\) | 23.1006 | + | 28.7050i | 0.754263 | + | 0.937253i | ||||
\(939\) | −8.82204 | + | 15.2802i | −0.287896 | + | 0.498651i | ||||
\(940\) | 8.51466 | − | 14.7478i | 0.277717 | − | 0.481021i | ||||
\(941\) | −20.1805 | + | 34.9536i | −0.657865 | + | 1.13946i | 0.323303 | + | 0.946296i | \(0.395207\pi\) |
−0.981167 | + | 0.193159i | \(0.938127\pi\) | |||||||
\(942\) | −22.8707 | −0.745166 | ||||||||
\(943\) | −15.9775 | + | 27.6738i | −0.520298 | + | 0.901183i | ||||
\(944\) | −2.48056 | −0.0807355 | ||||||||
\(945\) | −3.06671 | − | 3.81071i | −0.0997599 | − | 0.123962i | ||||
\(946\) | −0.0700874 | + | 0.121395i | −0.00227874 | + | 0.00394689i | ||||
\(947\) | 5.51853 | 0.179328 | 0.0896641 | − | 0.995972i | \(-0.471421\pi\) | ||||
0.0896641 | + | 0.995972i | \(0.471421\pi\) | |||||||
\(948\) | 7.37533 | − | 12.7744i | 0.239540 | − | 0.414895i | ||||
\(949\) | 6.65000 | − | 2.59496i | 0.215868 | − | 0.0842361i | ||||
\(950\) | −5.43860 | − | 9.41993i | −0.176451 | − | 0.305623i | ||||
\(951\) | −14.8710 | + | 25.7573i | −0.482225 | + | 0.835239i | ||||
\(952\) | 11.2722 | − | 1.75021i | 0.365335 | − | 0.0567246i | ||||
\(953\) | −2.92091 | − | 5.05916i | −0.0946175 | − | 0.163882i | 0.814831 | − | 0.579698i | \(-0.196829\pi\) |
−0.909449 | + | 0.415816i | \(0.863496\pi\) | |||||||
\(954\) | 3.80147 | + | 6.58434i | 0.123077 | + | 0.213176i | ||||
\(955\) | −9.84847 | −0.318689 | ||||||||
\(956\) | 13.8239 | 0.447097 | ||||||||
\(957\) | −3.31792 | − | 5.74681i | −0.107253 | − | 0.185768i | ||||
\(958\) | 5.79262 | + | 10.0331i | 0.187151 | + | 0.324155i | ||||
\(959\) | −12.4140 | + | 1.92749i | −0.400870 | + | 0.0622420i | ||||
\(960\) | −0.924396 | + | 1.60110i | −0.0298347 | + | 0.0516753i | ||||
\(961\) | 13.0312 | + | 22.5706i | 0.420360 | + | 0.728085i | ||||
\(962\) | −6.00457 | − | 4.80769i | −0.193595 | − | 0.155006i | ||||
\(963\) | 2.30997 | − | 4.00099i | 0.0744378 | − | 0.128930i | ||||
\(964\) | 10.7589 | 0.346521 | ||||||||
\(965\) | −8.98857 | + | 15.5687i | −0.289352 | + | 0.501173i | ||||
\(966\) | 11.8773 | + | 14.7588i | 0.382146 | + | 0.474858i | ||||
\(967\) | 4.98537 | 0.160319 | 0.0801594 | − | 0.996782i | \(-0.474457\pi\) | ||||
0.0801594 | + | 0.996782i | \(0.474457\pi\) | |||||||
\(968\) | 5.24412 | − | 9.08307i | 0.168552 | − | 0.291941i | ||||
\(969\) | −29.6451 | −0.952338 | ||||||||
\(970\) | 2.57341 | − | 4.45728i | 0.0826272 | − | 0.143115i | ||||
\(971\) | 1.37240 | − | 2.37707i | 0.0440424 | − | 0.0762837i | −0.843164 | − | 0.537657i | \(-0.819310\pi\) |
0.887206 | + | 0.461373i | \(0.152643\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | −25.5127 | − | 31.7022i | −0.817898 | − | 1.01633i | ||||
\(974\) | −8.48336 | −0.271824 | ||||||||
\(975\) | 4.45252 | + | 3.56501i | 0.142595 | + | 0.114172i | ||||
\(976\) | −4.31156 | + | 7.46783i | −0.138010 | + | 0.239040i | ||||
\(977\) | 8.19729 | + | 14.1981i | 0.262255 | + | 0.454238i | 0.966841 | − | 0.255380i | \(-0.0822007\pi\) |
−0.704586 | + | 0.709618i | \(0.748867\pi\) | |||||||
\(978\) | 18.0385 | 0.576806 | ||||||||
\(979\) | 1.59871 | + | 2.76904i | 0.0510949 | + | 0.0884990i | ||||
\(980\) | −9.56457 | − | 8.71794i | −0.305529 | − | 0.278484i | ||||
\(981\) | 4.95093 | + | 8.57527i | 0.158071 | + | 0.273787i | ||||
\(982\) | −14.8606 | + | 25.7394i | −0.474221 | + | 0.821376i | ||||
\(983\) | 15.1127 | − | 26.1760i | 0.482021 | − | 0.834884i | −0.517766 | − | 0.855522i | \(-0.673236\pi\) |
0.999787 | + | 0.0206379i | \(0.00656971\pi\) | |||||||
\(984\) | −4.46276 | −0.142268 | ||||||||
\(985\) | 11.4105 | 0.363568 | ||||||||
\(986\) | −19.9969 | + | 34.6357i | −0.636831 | + | 1.10302i | ||||
\(987\) | 8.80266 | − | 22.7248i | 0.280192 | − | 0.723339i | ||||
\(988\) | −23.0947 | + | 9.01203i | −0.734741 | + | 0.286711i | ||||
\(989\) | 0.701514 | + | 1.21506i | 0.0223069 | + | 0.0386366i | ||||
\(990\) | −0.661295 | − | 1.14540i | −0.0210173 | − | 0.0364031i | ||||
\(991\) | −10.0272 | − | 17.3677i | −0.318525 | − | 0.551702i | 0.661655 | − | 0.749808i | \(-0.269854\pi\) |
−0.980181 | + | 0.198106i | \(0.936521\pi\) | |||||||
\(992\) | 1.11104 | − | 1.92438i | 0.0352756 | − | 0.0610992i | ||||
\(993\) | 24.0394 | 0.762866 | ||||||||
\(994\) | 24.9104 | + | 30.9539i | 0.790111 | + | 0.981798i | ||||
\(995\) | −5.00518 | − | 8.66922i | −0.158675 | − | 0.274833i | ||||
\(996\) | 4.85769 | + | 8.41377i | 0.153922 | + | 0.266600i | ||||
\(997\) | −43.4877 | −1.37727 | −0.688635 | − | 0.725108i | \(-0.741790\pi\) | ||||
−0.688635 | + | 0.725108i | \(0.741790\pi\) | |||||||
\(998\) | 17.7944 | + | 30.8208i | 0.563272 | + | 0.975615i | ||||
\(999\) | 2.13341 | 0.0674981 |
(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 | 546.2.j.c.529.1 | yes | 8 | |
3.2 | odd | 2 | 1638.2.m.h.1621.4 | 8 | |||
7.2 | even | 3 | 546.2.k.c.373.1 | yes | 8 | ||
13.3 | even | 3 | 546.2.k.c.445.1 | yes | 8 | ||
21.2 | odd | 6 | 1638.2.p.h.919.4 | 8 | |||
39.29 | odd | 6 | 1638.2.p.h.991.4 | 8 | |||
91.16 | even | 3 | inner | 546.2.j.c.289.1 | ✓ | 8 | |
273.107 | odd | 6 | 1638.2.m.h.289.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.c.289.1 | ✓ | 8 | 91.16 | even | 3 | inner | |
546.2.j.c.529.1 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.k.c.373.1 | yes | 8 | 7.2 | even | 3 | ||
546.2.k.c.445.1 | yes | 8 | 13.3 | even | 3 | ||
1638.2.m.h.289.4 | 8 | 273.107 | odd | 6 | |||
1638.2.m.h.1621.4 | 8 | 3.2 | odd | 2 | |||
1638.2.p.h.919.4 | 8 | 21.2 | odd | 6 | |||
1638.2.p.h.991.4 | 8 | 39.29 | odd | 6 |