Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1274,2,Mod(459,1274)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1274.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1274 = 2 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1274.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.1729412175\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 459.3 | ||
Root | \(0.500000 - 3.15681i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1274.459 |
Dual form | 1274.2.o.e.569.6 |
$q$-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 \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(885\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.14539 | + | 1.98388i | 0.661293 | + | 1.14539i | 0.980276 | + | 0.197633i | \(0.0633254\pi\) |
−0.318983 | + | 0.947760i | \(0.603341\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.781015 | + | 0.450919i | −0.349281 | + | 0.201657i | −0.664368 | − | 0.747405i | \(-0.731299\pi\) |
0.315088 | + | 0.949063i | \(0.397966\pi\) | |||||||
\(6\) | 1.98388 | − | 1.14539i | 0.809915 | − | 0.467605i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.12385 | + | 1.94657i | −0.374617 | + | 0.648856i | ||||
\(10\) | 0.450919 | + | 0.781015i | 0.142593 | + | 0.246979i | ||||
\(11\) | 3.75609 | − | 2.16858i | 1.13251 | − | 0.653852i | 0.187941 | − | 0.982180i | \(-0.439819\pi\) |
0.944564 | + | 0.328328i | \(0.106485\pi\) | |||||||
\(12\) | −1.14539 | − | 1.98388i | −0.330647 | − | 0.572697i | ||||
\(13\) | 0.426876 | − | 3.58019i | 0.118394 | − | 0.992967i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.78914 | − | 1.03296i | −0.461954 | − | 0.266709i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.06592 | 1.22867 | 0.614333 | − | 0.789047i | \(-0.289425\pi\) | ||||
0.614333 | + | 0.789047i | \(0.289425\pi\) | |||||||
\(18\) | 1.94657 | + | 1.12385i | 0.458811 | + | 0.264894i | ||||
\(19\) | 5.34544 | + | 3.08619i | 1.22633 | + | 0.708021i | 0.966260 | − | 0.257570i | \(-0.0829217\pi\) |
0.260068 | + | 0.965590i | \(0.416255\pi\) | |||||||
\(20\) | 0.781015 | − | 0.450919i | 0.174640 | − | 0.100829i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.16858 | − | 3.75609i | −0.462343 | − | 0.800802i | ||||
\(23\) | −8.45117 | −1.76219 | −0.881096 | − | 0.472938i | \(-0.843193\pi\) | ||||
−0.881096 | + | 0.472938i | \(0.843193\pi\) | |||||||
\(24\) | −1.98388 | + | 1.14539i | −0.404958 | + | 0.233802i | ||||
\(25\) | −2.09334 | + | 3.62578i | −0.418669 | + | 0.725155i | ||||
\(26\) | −3.58019 | − | 0.426876i | −0.702133 | − | 0.0837173i | ||||
\(27\) | 1.72335 | 0.331659 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.09643 | − | 1.89907i | 0.203602 | − | 0.352649i | −0.746085 | − | 0.665851i | \(-0.768069\pi\) |
0.949686 | + | 0.313203i | \(0.101402\pi\) | |||||||
\(30\) | −1.03296 | + | 1.78914i | −0.188592 | + | 0.326651i | ||||
\(31\) | 0.756094 | + | 0.436531i | 0.135799 | + | 0.0784033i | 0.566360 | − | 0.824158i | \(-0.308351\pi\) |
−0.430562 | + | 0.902561i | \(0.641684\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 8.60441 | + | 4.96776i | 1.49784 | + | 0.864776i | ||||
\(34\) | − | 5.06592i | − | 0.868798i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.12385 | − | 1.94657i | 0.187309 | − | 0.324428i | ||||
\(37\) | − | 0.144306i | − | 0.0237238i | −0.999930 | − | 0.0118619i | \(-0.996224\pi\) | ||
0.999930 | − | 0.0118619i | \(-0.00377585\pi\) | |||||||
\(38\) | 3.08619 | − | 5.34544i | 0.500646 | − | 0.867145i | ||||
\(39\) | 7.59161 | − | 3.25386i | 1.21563 | − | 0.521034i | ||||
\(40\) | −0.450919 | − | 0.781015i | −0.0712966 | − | 0.123489i | ||||
\(41\) | 3.46110 | + | 1.99827i | 0.540533 | + | 0.312077i | 0.745295 | − | 0.666735i | \(-0.232309\pi\) |
−0.204762 | + | 0.978812i | \(0.565642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.85426 | + | 6.67577i | 0.587768 | + | 1.01804i | 0.994524 | + | 0.104508i | \(0.0333267\pi\) |
−0.406756 | + | 0.913537i | \(0.633340\pi\) | |||||||
\(44\) | −3.75609 | + | 2.16858i | −0.566253 | + | 0.326926i | ||||
\(45\) | − | 2.02707i | − | 0.302177i | ||||||
\(46\) | 8.45117i | 1.24606i | ||||||||
\(47\) | 2.52979 | − | 1.46057i | 0.369008 | − | 0.213047i | −0.304017 | − | 0.952667i | \(-0.598328\pi\) |
0.673025 | + | 0.739620i | \(0.264995\pi\) | |||||||
\(48\) | 1.14539 | + | 1.98388i | 0.165323 | + | 0.286348i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.62578 | + | 2.09334i | 0.512762 | + | 0.296043i | ||||
\(51\) | 5.80247 | + | 10.0502i | 0.812509 | + | 1.40731i | ||||
\(52\) | −0.426876 | + | 3.58019i | −0.0591970 | + | 0.496483i | ||||
\(53\) | −0.848493 | + | 1.46963i | −0.116549 | + | 0.201870i | −0.918398 | − | 0.395658i | \(-0.870517\pi\) |
0.801849 | + | 0.597527i | \(0.203850\pi\) | |||||||
\(54\) | − | 1.72335i | − | 0.234518i | ||||||
\(55\) | −1.95571 | + | 3.38739i | −0.263708 | + | 0.456756i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.1396i | 1.87284i | ||||||||
\(58\) | −1.89907 | − | 1.09643i | −0.249360 | − | 0.143968i | ||||
\(59\) | 8.54933i | 1.11303i | 0.830838 | + | 0.556514i | \(0.187861\pi\) | ||||
−0.830838 | + | 0.556514i | \(0.812139\pi\) | |||||||
\(60\) | 1.78914 | + | 1.03296i | 0.230977 | + | 0.133355i | ||||
\(61\) | 4.16720 | − | 7.21780i | 0.533555 | − | 0.924145i | −0.465676 | − | 0.884955i | \(-0.654189\pi\) |
0.999232 | − | 0.0391900i | \(-0.0124777\pi\) | |||||||
\(62\) | 0.436531 | − | 0.756094i | 0.0554395 | − | 0.0960241i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.28098 | + | 2.98867i | 0.158886 | + | 0.370699i | ||||
\(66\) | 4.96776 | − | 8.60441i | 0.611489 | − | 1.05913i | ||||
\(67\) | 8.99180 | − | 5.19142i | 1.09852 | − | 0.634233i | 0.162691 | − | 0.986677i | \(-0.447983\pi\) |
0.935833 | + | 0.352444i | \(0.114649\pi\) | |||||||
\(68\) | −5.06592 | −0.614333 | ||||||||
\(69\) | −9.67992 | − | 16.7661i | −1.16532 | − | 2.01840i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.83932 | + | 1.63928i | −0.336965 | + | 0.194547i | −0.658929 | − | 0.752205i | \(-0.728990\pi\) |
0.321964 | + | 0.946752i | \(0.395657\pi\) | |||||||
\(72\) | −1.94657 | − | 1.12385i | −0.229405 | − | 0.132447i | ||||
\(73\) | 0.466808 | + | 0.269511i | 0.0546357 | + | 0.0315439i | 0.527069 | − | 0.849822i | \(-0.323291\pi\) |
−0.472433 | + | 0.881366i | \(0.656624\pi\) | |||||||
\(74\) | −0.144306 | −0.0167753 | ||||||||
\(75\) | −9.59081 | −1.10745 | ||||||||
\(76\) | −5.34544 | − | 3.08619i | −0.613164 | − | 0.354010i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.25386 | − | 7.59161i | −0.368427 | − | 0.859581i | ||||
\(79\) | −3.26674 | − | 5.65817i | −0.367537 | − | 0.636593i | 0.621643 | − | 0.783301i | \(-0.286466\pi\) |
−0.989180 | + | 0.146708i | \(0.953132\pi\) | |||||||
\(80\) | −0.781015 | + | 0.450919i | −0.0873202 | + | 0.0504143i | ||||
\(81\) | 5.34547 | + | 9.25862i | 0.593941 | + | 1.02874i | ||||
\(82\) | 1.99827 | − | 3.46110i | 0.220672 | − | 0.382215i | ||||
\(83\) | 13.2348i | 1.45271i | 0.687319 | + | 0.726356i | \(0.258788\pi\) | ||||
−0.687319 | + | 0.726356i | \(0.741212\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.95656 | + | 2.28432i | −0.429149 | + | 0.247769i | ||||
\(86\) | 6.67577 | − | 3.85426i | 0.719866 | − | 0.415615i | ||||
\(87\) | 5.02337 | 0.538562 | ||||||||
\(88\) | 2.16858 | + | 3.75609i | 0.231172 | + | 0.400401i | ||||
\(89\) | − | 7.79180i | − | 0.825929i | −0.910747 | − | 0.412965i | \(-0.864493\pi\) | ||
0.910747 | − | 0.412965i | \(-0.135507\pi\) | |||||||
\(90\) | −2.02707 | −0.213672 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.45117 | 0.881096 | ||||||||
\(93\) | 2.00000i | 0.207390i | ||||||||
\(94\) | −1.46057 | − | 2.52979i | −0.150647 | − | 0.260928i | ||||
\(95\) | −5.56649 | −0.571110 | ||||||||
\(96\) | 1.98388 | − | 1.14539i | 0.202479 | − | 0.116901i | ||||
\(97\) | −10.1378 | + | 5.85305i | −1.02934 | + | 0.594287i | −0.916794 | − | 0.399360i | \(-0.869232\pi\) |
−0.112541 | + | 0.993647i | \(0.535899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.74866i | 0.979777i | ||||||||
\(100\) | 2.09334 | − | 3.62578i | 0.209334 | − | 0.362578i | ||||
\(101\) | 5.37145 | + | 9.30362i | 0.534479 | + | 0.925745i | 0.999188 | + | 0.0402814i | \(0.0128254\pi\) |
−0.464709 | + | 0.885463i | \(0.653841\pi\) | |||||||
\(102\) | 10.0502 | − | 5.80247i | 0.995116 | − | 0.574530i | ||||
\(103\) | 2.40550 | + | 4.16644i | 0.237021 | + | 0.410532i | 0.959858 | − | 0.280486i | \(-0.0904958\pi\) |
−0.722837 | + | 0.691018i | \(0.757162\pi\) | |||||||
\(104\) | 3.58019 | + | 0.426876i | 0.351067 | + | 0.0418586i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.46963 | + | 0.848493i | 0.142743 | + | 0.0824129i | ||||
\(107\) | 13.6530 | 1.31989 | 0.659944 | − | 0.751315i | \(-0.270580\pi\) | ||||
0.659944 | + | 0.751315i | \(0.270580\pi\) | |||||||
\(108\) | −1.72335 | −0.165829 | ||||||||
\(109\) | −4.43186 | − | 2.55874i | −0.424495 | − | 0.245082i | 0.272503 | − | 0.962155i | \(-0.412148\pi\) |
−0.696999 | + | 0.717072i | \(0.745482\pi\) | |||||||
\(110\) | 3.38739 | + | 1.95571i | 0.322975 | + | 0.186470i | ||||
\(111\) | 0.286286 | − | 0.165287i | 0.0271731 | − | 0.0156884i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.96603 | − | 15.5296i | −0.843453 | − | 1.46090i | −0.886958 | − | 0.461850i | \(-0.847186\pi\) |
0.0435052 | − | 0.999053i | \(-0.486147\pi\) | |||||||
\(114\) | 14.1396 | 1.32430 | ||||||||
\(115\) | 6.60049 | − | 3.81080i | 0.615499 | − | 0.355359i | ||||
\(116\) | −1.09643 | + | 1.89907i | −0.101801 | + | 0.176324i | ||||
\(117\) | 6.48935 | + | 4.85455i | 0.599940 | + | 0.448803i | ||||
\(118\) | 8.54933 | 0.787030 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.03296 | − | 1.78914i | 0.0942959 | − | 0.163325i | ||||
\(121\) | 3.90550 | − | 6.76452i | 0.355045 | − | 0.614956i | ||||
\(122\) | −7.21780 | − | 4.16720i | −0.653469 | − | 0.377281i | ||||
\(123\) | 9.15521i | 0.825498i | ||||||||
\(124\) | −0.756094 | − | 0.436531i | −0.0678993 | − | 0.0392017i | ||||
\(125\) | − | 8.28491i | − | 0.741025i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.75681 | + | 16.8993i | −0.865777 | + | 1.49957i | 0.000496195 | 1.00000i | \(0.499842\pi\) | |
−0.866273 | + | 0.499570i | \(0.833491\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −8.82928 | + | 15.2928i | −0.777375 | + | 1.34645i | ||||
\(130\) | 2.98867 | − | 1.28098i | 0.262124 | − | 0.112350i | ||||
\(131\) | −10.3248 | − | 17.8831i | −0.902083 | − | 1.56245i | −0.824785 | − | 0.565446i | \(-0.808704\pi\) |
−0.0772984 | − | 0.997008i | \(-0.524629\pi\) | |||||||
\(132\) | −8.60441 | − | 4.96776i | −0.748918 | − | 0.432388i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.19142 | − | 8.99180i | −0.448470 | − | 0.776773i | ||||
\(135\) | −1.34596 | + | 0.777092i | −0.115842 | + | 0.0668814i | ||||
\(136\) | 5.06592i | 0.434399i | ||||||||
\(137\) | 3.18956i | 0.272503i | 0.990674 | + | 0.136251i | \(0.0435055\pi\) | ||||
−0.990674 | + | 0.136251i | \(0.956495\pi\) | |||||||
\(138\) | −16.7661 | + | 9.67992i | −1.42723 | + | 0.824009i | ||||
\(139\) | −0.297855 | − | 0.515900i | −0.0252637 | − | 0.0437581i | 0.853117 | − | 0.521719i | \(-0.174709\pi\) |
−0.878381 | + | 0.477961i | \(0.841376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.79521 | + | 3.34587i | 0.488045 | + | 0.281773i | ||||
\(142\) | 1.63928 | + | 2.83932i | 0.137565 | + | 0.238270i | ||||
\(143\) | −6.16055 | − | 14.3733i | −0.515171 | − | 1.20195i | ||||
\(144\) | −1.12385 | + | 1.94657i | −0.0936543 | + | 0.162214i | ||||
\(145\) | 1.97760i | 0.164231i | ||||||||
\(146\) | 0.269511 | − | 0.466808i | 0.0223049 | − | 0.0386333i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.144306i | 0.0118619i | ||||||||
\(149\) | −9.70783 | − | 5.60482i | −0.795297 | − | 0.459165i | 0.0465273 | − | 0.998917i | \(-0.485185\pi\) |
−0.841824 | + | 0.539752i | \(0.818518\pi\) | |||||||
\(150\) | 9.59081i | 0.783086i | ||||||||
\(151\) | 11.3216 | + | 6.53653i | 0.921339 | + | 0.531935i | 0.884062 | − | 0.467369i | \(-0.154798\pi\) |
0.0372772 | + | 0.999305i | \(0.488132\pi\) | |||||||
\(152\) | −3.08619 | + | 5.34544i | −0.250323 | + | 0.433572i | ||||
\(153\) | −5.69334 | + | 9.86116i | −0.460280 | + | 0.797228i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.787362 | −0.0632424 | ||||||||
\(156\) | −7.59161 | + | 3.25386i | −0.607815 | + | 0.260517i | ||||
\(157\) | 8.96225 | − | 15.5231i | 0.715266 | − | 1.23888i | −0.247591 | − | 0.968865i | \(-0.579639\pi\) |
0.962857 | − | 0.270012i | \(-0.0870276\pi\) | |||||||
\(158\) | −5.65817 | + | 3.26674i | −0.450139 | + | 0.259888i | ||||
\(159\) | −3.88743 | −0.308293 | ||||||||
\(160\) | 0.450919 | + | 0.781015i | 0.0356483 | + | 0.0617447i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.25862 | − | 5.34547i | 0.727426 | − | 0.419980i | ||||
\(163\) | −17.5958 | − | 10.1589i | −1.37821 | − | 0.795710i | −0.386266 | − | 0.922387i | \(-0.626235\pi\) |
−0.991944 | + | 0.126677i | \(0.959569\pi\) | |||||||
\(164\) | −3.46110 | − | 1.99827i | −0.270267 | − | 0.156038i | ||||
\(165\) | −8.96024 | −0.697553 | ||||||||
\(166\) | 13.2348 | 1.02722 | ||||||||
\(167\) | 2.79770 | + | 1.61525i | 0.216493 | + | 0.124992i | 0.604325 | − | 0.796738i | \(-0.293443\pi\) |
−0.387833 | + | 0.921730i | \(0.626776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6356 | − | 3.05660i | −0.971966 | − | 0.235123i | ||||
\(170\) | 2.28432 | + | 3.95656i | 0.175199 | + | 0.303454i | ||||
\(171\) | −12.0150 | + | 6.93684i | −0.918807 | + | 0.530474i | ||||
\(172\) | −3.85426 | − | 6.67577i | −0.293884 | − | 0.509022i | ||||
\(173\) | 4.58522 | − | 7.94183i | 0.348608 | − | 0.603806i | −0.637395 | − | 0.770538i | \(-0.719988\pi\) |
0.986002 | + | 0.166731i | \(0.0533212\pi\) | |||||||
\(174\) | − | 5.02337i | − | 0.380821i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.75609 | − | 2.16858i | 0.283126 | − | 0.163463i | ||||
\(177\) | −16.9608 | + | 9.79235i | −1.27486 | + | 0.736038i | ||||
\(178\) | −7.79180 | −0.584020 | ||||||||
\(179\) | −8.47747 | − | 14.6834i | −0.633636 | − | 1.09749i | −0.986802 | − | 0.161929i | \(-0.948228\pi\) |
0.353166 | − | 0.935561i | \(-0.385105\pi\) | |||||||
\(180\) | 2.02707i | 0.151089i | ||||||||
\(181\) | 2.65743 | 0.197525 | 0.0987626 | − | 0.995111i | \(-0.468512\pi\) | ||||
0.0987626 | + | 0.995111i | \(0.468512\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.0923 | 1.41135 | ||||||||
\(184\) | − | 8.45117i | − | 0.623029i | ||||||
\(185\) | 0.0650705 | + | 0.112705i | 0.00478408 | + | 0.00828627i | ||||
\(186\) | 2.00000 | 0.146647 | ||||||||
\(187\) | 19.0281 | − | 10.9859i | 1.39147 | − | 0.803366i | ||||
\(188\) | −2.52979 | + | 1.46057i | −0.184504 | + | 0.106523i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.56649i | 0.403836i | ||||||||
\(191\) | 12.2430 | − | 21.2056i | 0.885875 | − | 1.53438i | 0.0411671 | − | 0.999152i | \(-0.486892\pi\) |
0.844708 | − | 0.535228i | \(-0.179774\pi\) | |||||||
\(192\) | −1.14539 | − | 1.98388i | −0.0826616 | − | 0.143174i | ||||
\(193\) | −10.6009 | + | 6.12046i | −0.763072 | + | 0.440560i | −0.830398 | − | 0.557171i | \(-0.811887\pi\) |
0.0673254 | + | 0.997731i | \(0.478553\pi\) | |||||||
\(194\) | 5.85305 | + | 10.1378i | 0.420224 | + | 0.727850i | ||||
\(195\) | −4.46194 | + | 5.96452i | −0.319526 | + | 0.427128i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.72634 | + | 2.72876i | 0.336738 | + | 0.194416i | 0.658829 | − | 0.752293i | \(-0.271052\pi\) |
−0.322091 | + | 0.946709i | \(0.604386\pi\) | |||||||
\(198\) | 9.74866 | 0.692807 | ||||||||
\(199\) | −12.8166 | −0.908548 | −0.454274 | − | 0.890862i | \(-0.650101\pi\) | ||||
−0.454274 | + | 0.890862i | \(0.650101\pi\) | |||||||
\(200\) | −3.62578 | − | 2.09334i | −0.256381 | − | 0.148022i | ||||
\(201\) | 20.5983 | + | 11.8924i | 1.45289 | + | 0.838828i | ||||
\(202\) | 9.30362 | − | 5.37145i | 0.654600 | − | 0.377934i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.80247 | − | 10.0502i | −0.406254 | − | 0.703653i | ||||
\(205\) | −3.60423 | −0.251730 | ||||||||
\(206\) | 4.16644 | − | 2.40550i | 0.290290 | − | 0.167599i | ||||
\(207\) | 9.49787 | − | 16.4508i | 0.660147 | − | 1.14341i | ||||
\(208\) | 0.426876 | − | 3.58019i | 0.0295985 | − | 0.248242i | ||||
\(209\) | 26.7706 | 1.85176 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.65552 | − | 16.7239i | 0.664713 | − | 1.15132i | −0.314649 | − | 0.949208i | \(-0.601887\pi\) |
0.979363 | − | 0.202110i | \(-0.0647797\pi\) | |||||||
\(212\) | 0.848493 | − | 1.46963i | 0.0582747 | − | 0.100935i | ||||
\(213\) | −6.50427 | − | 3.75524i | −0.445665 | − | 0.257305i | ||||
\(214\) | − | 13.6530i | − | 0.933302i | ||||||
\(215\) | −6.02046 | − | 3.47592i | −0.410592 | − | 0.237056i | ||||
\(216\) | 1.72335i | 0.117259i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.55874 | + | 4.43186i | −0.173299 | + | 0.300163i | ||||
\(219\) | 1.23479i | 0.0834391i | ||||||||
\(220\) | 1.95571 | − | 3.38739i | 0.131854 | − | 0.228378i | ||||
\(221\) | 2.16252 | − | 18.1370i | 0.145467 | − | 1.22002i | ||||
\(222\) | −0.165287 | − | 0.286286i | −0.0110934 | − | 0.0192143i | ||||
\(223\) | 9.21079 | + | 5.31785i | 0.616800 | + | 0.356110i | 0.775622 | − | 0.631197i | \(-0.217436\pi\) |
−0.158822 | + | 0.987307i | \(0.550770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.70522 | − | 8.14967i | −0.313681 | − | 0.543312i | ||||
\(226\) | −15.5296 | + | 8.96603i | −1.03301 | + | 0.596411i | ||||
\(227\) | − | 22.7217i | − | 1.50809i | −0.656821 | − | 0.754047i | \(-0.728099\pi\) | ||
0.656821 | − | 0.754047i | \(-0.271901\pi\) | |||||||
\(228\) | − | 14.1396i | − | 0.936418i | ||||||
\(229\) | −17.5885 | + | 10.1547i | −1.16228 | + | 0.671042i | −0.951849 | − | 0.306567i | \(-0.900820\pi\) |
−0.210429 | + | 0.977609i | \(0.567486\pi\) | |||||||
\(230\) | −3.81080 | − | 6.60049i | −0.251277 | − | 0.435224i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.89907 | + | 1.09643i | 0.124680 | + | 0.0719841i | ||||
\(233\) | −5.32231 | − | 9.21851i | −0.348676 | − | 0.603925i | 0.637338 | − | 0.770584i | \(-0.280035\pi\) |
−0.986015 | + | 0.166659i | \(0.946702\pi\) | |||||||
\(234\) | 4.85455 | − | 6.48935i | 0.317352 | − | 0.424222i | ||||
\(235\) | −1.31720 | + | 2.28146i | −0.0859248 | + | 0.148826i | ||||
\(236\) | − | 8.54933i | − | 0.556514i | ||||||
\(237\) | 7.48341 | − | 12.9617i | 0.486100 | − | 0.841950i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 0.311564i | − | 0.0201534i | −0.999949 | − | 0.0100767i | \(-0.996792\pi\) | ||
0.999949 | − | 0.0100767i | \(-0.00320757\pi\) | |||||||
\(240\) | −1.78914 | − | 1.03296i | −0.115488 | − | 0.0666773i | ||||
\(241\) | 25.2995i | 1.62969i | 0.579682 | + | 0.814843i | \(0.303177\pi\) | ||||
−0.579682 | + | 0.814843i | \(0.696823\pi\) | |||||||
\(242\) | −6.76452 | − | 3.90550i | −0.434840 | − | 0.251055i | ||||
\(243\) | −9.66031 | + | 16.7321i | −0.619709 | + | 1.07337i | ||||
\(244\) | −4.16720 | + | 7.21780i | −0.266778 | + | 0.462073i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.15521 | 0.583715 | ||||||||
\(247\) | 13.3310 | − | 17.8203i | 0.848231 | − | 1.13388i | ||||
\(248\) | −0.436531 | + | 0.756094i | −0.0277198 | + | 0.0480120i | ||||
\(249\) | −26.2563 | + | 15.1591i | −1.66393 | + | 0.960669i | ||||
\(250\) | −8.28491 | −0.523984 | ||||||||
\(251\) | −4.02015 | − | 6.96311i | −0.253750 | − | 0.439507i | 0.710805 | − | 0.703389i | \(-0.248331\pi\) |
−0.964555 | + | 0.263881i | \(0.914997\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.7434 | + | 18.3271i | −1.99569 | + | 1.15221i | ||||
\(254\) | 16.8993 | + | 9.75681i | 1.06036 | + | 0.612197i | ||||
\(255\) | −9.06364 | − | 5.23289i | −0.567587 | − | 0.327697i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.9327 | −1.05623 | −0.528116 | − | 0.849172i | \(-0.677101\pi\) | ||||
−0.528116 | + | 0.849172i | \(0.677101\pi\) | |||||||
\(258\) | 15.2928 | + | 8.82928i | 0.952085 | + | 0.549687i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.28098 | − | 2.98867i | −0.0794431 | − | 0.185350i | ||||
\(261\) | 2.46445 | + | 4.26855i | 0.152545 | + | 0.264217i | ||||
\(262\) | −17.8831 | + | 10.3248i | −1.10482 | + | 0.637869i | ||||
\(263\) | −5.16045 | − | 8.93817i | −0.318207 | − | 0.551151i | 0.661907 | − | 0.749586i | \(-0.269747\pi\) |
−0.980114 | + | 0.198435i | \(0.936414\pi\) | |||||||
\(264\) | −4.96776 | + | 8.60441i | −0.305744 | + | 0.529565i | ||||
\(265\) | − | 1.53041i | − | 0.0940122i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.4580 | − | 8.92468i | 0.946014 | − | 0.546181i | ||||
\(268\) | −8.99180 | + | 5.19142i | −0.549262 | + | 0.317116i | ||||
\(269\) | 6.13999 | 0.374362 | 0.187181 | − | 0.982325i | \(-0.440065\pi\) | ||||
0.187181 | + | 0.982325i | \(0.440065\pi\) | |||||||
\(270\) | 0.777092 | + | 1.34596i | 0.0472923 | + | 0.0819127i | ||||
\(271\) | 10.6772i | 0.648594i | 0.945955 | + | 0.324297i | \(0.105128\pi\) | ||||
−0.945955 | + | 0.324297i | \(0.894872\pi\) | |||||||
\(272\) | 5.06592 | 0.307167 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.18956 | 0.192689 | ||||||||
\(275\) | 18.1583i | 1.09499i | ||||||||
\(276\) | 9.67992 | + | 16.7661i | 0.582662 | + | 1.00920i | ||||
\(277\) | −21.9090 | −1.31638 | −0.658191 | − | 0.752851i | \(-0.728678\pi\) | ||||
−0.658191 | + | 0.752851i | \(0.728678\pi\) | |||||||
\(278\) | −0.515900 | + | 0.297855i | −0.0309416 | + | 0.0178642i | ||||
\(279\) | −1.69948 | + | 0.981193i | −0.101745 | + | 0.0587425i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 25.7719i | − | 1.53743i | −0.639594 | − | 0.768713i | \(-0.720898\pi\) | ||
0.639594 | − | 0.768713i | \(-0.279102\pi\) | |||||||
\(282\) | 3.34587 | − | 5.79521i | 0.199243 | − | 0.345100i | ||||
\(283\) | 5.66344 | + | 9.80937i | 0.336657 | + | 0.583107i | 0.983802 | − | 0.179260i | \(-0.0573704\pi\) |
−0.647145 | + | 0.762367i | \(0.724037\pi\) | |||||||
\(284\) | 2.83932 | − | 1.63928i | 0.168482 | − | 0.0972733i | ||||
\(285\) | −6.37582 | − | 11.0432i | −0.377671 | − | 0.654146i | ||||
\(286\) | −14.3733 | + | 6.16055i | −0.849908 | + | 0.364281i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.94657 | + | 1.12385i | 0.114703 | + | 0.0662236i | ||||
\(289\) | 8.66355 | 0.509621 | ||||||||
\(290\) | 1.97760 | 0.116129 | ||||||||
\(291\) | −23.2235 | − | 13.4081i | −1.36139 | − | 0.785996i | ||||
\(292\) | −0.466808 | − | 0.269511i | −0.0273178 | − | 0.0157720i | ||||
\(293\) | −20.5646 | + | 11.8730i | −1.20140 | + | 0.693626i | −0.960865 | − | 0.277016i | \(-0.910655\pi\) |
−0.240530 | + | 0.970642i | \(0.577321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.85506 | − | 6.67716i | −0.224450 | − | 0.388759i | ||||
\(296\) | 0.144306 | 0.00838763 | ||||||||
\(297\) | 6.47306 | − | 3.73723i | 0.375605 | − | 0.216856i | ||||
\(298\) | −5.60482 | + | 9.70783i | −0.324678 | + | 0.562360i | ||||
\(299\) | −3.60760 | + | 30.2568i | −0.208633 | + | 1.74980i | ||||
\(300\) | 9.59081 | 0.553725 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.53653 | − | 11.3216i | 0.376135 | − | 0.651485i | ||||
\(303\) | −12.3048 | + | 21.3126i | −0.706894 | + | 1.22438i | ||||
\(304\) | 5.34544 | + | 3.08619i | 0.306582 | + | 0.177005i | ||||
\(305\) | 7.51629i | 0.430381i | ||||||||
\(306\) | 9.86116 | + | 5.69334i | 0.563725 | + | 0.325467i | ||||
\(307\) | 6.68810i | 0.381710i | 0.981618 | + | 0.190855i | \(0.0611261\pi\) | ||||
−0.981618 | + | 0.190855i | \(0.938874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.51048 | + | 9.54443i | −0.313480 | + | 0.542964i | ||||
\(310\) | 0.787362i | 0.0447191i | ||||||||
\(311\) | 4.59362 | − | 7.95639i | 0.260480 | − | 0.451165i | −0.705889 | − | 0.708322i | \(-0.749452\pi\) |
0.966370 | + | 0.257157i | \(0.0827857\pi\) | |||||||
\(312\) | 3.25386 | + | 7.59161i | 0.184213 | + | 0.429790i | ||||
\(313\) | −8.58157 | − | 14.8637i | −0.485059 | − | 0.840147i | 0.514793 | − | 0.857314i | \(-0.327869\pi\) |
−0.999853 | + | 0.0171671i | \(0.994535\pi\) | |||||||
\(314\) | −15.5231 | − | 8.96225i | −0.876018 | − | 0.505769i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.26674 | + | 5.65817i | 0.183769 | + | 0.318297i | ||||
\(317\) | −3.25840 | + | 1.88124i | −0.183010 | + | 0.105661i | −0.588706 | − | 0.808347i | \(-0.700362\pi\) |
0.405696 | + | 0.914008i | \(0.367029\pi\) | |||||||
\(318\) | 3.88743i | 0.217996i | ||||||||
\(319\) | − | 9.51078i | − | 0.532502i | ||||||
\(320\) | 0.781015 | − | 0.450919i | 0.0436601 | − | 0.0252072i | ||||
\(321\) | 15.6381 | + | 27.0860i | 0.872833 | + | 1.51179i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.0796 | + | 15.6344i | 1.50675 | + | 0.869921i | ||||
\(324\) | −5.34547 | − | 9.25862i | −0.296971 | − | 0.514368i | ||||
\(325\) | 12.0874 | + | 9.04233i | 0.670487 | + | 0.501578i | ||||
\(326\) | −10.1589 | + | 17.5958i | −0.562652 | + | 0.974542i | ||||
\(327\) | − | 11.7230i | − | 0.648285i | ||||||
\(328\) | −1.99827 | + | 3.46110i | −0.110336 | + | 0.191107i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 8.96024i | 0.493245i | ||||||||
\(331\) | 27.9083 | + | 16.1129i | 1.53398 | + | 0.885643i | 0.999173 | + | 0.0406683i | \(0.0129487\pi\) |
0.534806 | + | 0.844975i | \(0.320385\pi\) | |||||||
\(332\) | − | 13.2348i | − | 0.726356i | ||||||
\(333\) | 0.280902 | + | 0.162179i | 0.0153933 | + | 0.00888735i | ||||
\(334\) | 1.61525 | − | 2.79770i | 0.0883827 | − | 0.153083i | ||||
\(335\) | −4.68182 | + | 8.10916i | −0.255795 | + | 0.443051i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.01703 | −0.164348 | −0.0821740 | − | 0.996618i | \(-0.526186\pi\) | ||||
−0.0821740 | + | 0.996618i | \(0.526186\pi\) | |||||||
\(338\) | −3.05660 | + | 12.6356i | −0.166257 | + | 0.687284i | ||||
\(339\) | 20.5393 | − | 35.5750i | 1.11554 | − | 1.93217i | ||||
\(340\) | 3.95656 | − | 2.28432i | 0.214575 | − | 0.123885i | ||||
\(341\) | 3.78662 | 0.205057 | ||||||||
\(342\) | 6.93684 | + | 12.0150i | 0.375101 | + | 0.649695i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.67577 | + | 3.85426i | −0.359933 | + | 0.207808i | ||||
\(345\) | 15.1203 | + | 8.72972i | 0.814051 | + | 0.469993i | ||||
\(346\) | −7.94183 | − | 4.58522i | −0.426956 | − | 0.246503i | ||||
\(347\) | 0.468540 | 0.0251526 | 0.0125763 | − | 0.999921i | \(-0.495997\pi\) | ||||
0.0125763 | + | 0.999921i | \(0.495997\pi\) | |||||||
\(348\) | −5.02337 | −0.269281 | ||||||||
\(349\) | 27.9044 | + | 16.1106i | 1.49369 | + | 0.862380i | 0.999974 | − | 0.00724565i | \(-0.00230638\pi\) |
0.493712 | + | 0.869625i | \(0.335640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.735656 | − | 6.16992i | 0.0392664 | − | 0.329326i | ||||
\(352\) | −2.16858 | − | 3.75609i | −0.115586 | − | 0.200200i | ||||
\(353\) | −11.3583 | + | 6.55771i | −0.604540 | + | 0.349031i | −0.770826 | − | 0.637046i | \(-0.780156\pi\) |
0.166285 | + | 0.986078i | \(0.446823\pi\) | |||||||
\(354\) | 9.79235 | + | 16.9608i | 0.520457 | + | 0.901459i | ||||
\(355\) | 1.47837 | − | 2.56060i | 0.0784635 | − | 0.135903i | ||||
\(356\) | 7.79180i | 0.412965i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.6834 | + | 8.47747i | −0.776043 | + | 0.448048i | ||||
\(359\) | 3.79302 | − | 2.18990i | 0.200188 | − | 0.115579i | −0.396555 | − | 0.918011i | \(-0.629794\pi\) |
0.596743 | + | 0.802432i | \(0.296461\pi\) | |||||||
\(360\) | 2.02707 | 0.106836 | ||||||||
\(361\) | 9.54914 | + | 16.5396i | 0.502586 | + | 0.870505i | ||||
\(362\) | − | 2.65743i | − | 0.139671i | ||||||
\(363\) | 17.8933 | 0.939156 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.486112 | −0.0254443 | ||||||||
\(366\) | − | 19.0923i | − | 0.997972i | ||||||
\(367\) | 12.9094 | + | 22.3597i | 0.673865 | + | 1.16717i | 0.976799 | + | 0.214157i | \(0.0687004\pi\) |
−0.302934 | + | 0.953011i | \(0.597966\pi\) | |||||||
\(368\) | −8.45117 | −0.440548 | ||||||||
\(369\) | −7.77953 | + | 4.49151i | −0.404986 | + | 0.233819i | ||||
\(370\) | 0.112705 | − | 0.0650705i | 0.00585928 | − | 0.00338285i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 2.00000i | − | 0.103695i | ||||||
\(373\) | −15.3143 | + | 26.5251i | −0.792942 | + | 1.37342i | 0.131196 | + | 0.991356i | \(0.458118\pi\) |
−0.924138 | + | 0.382059i | \(0.875215\pi\) | |||||||
\(374\) | −10.9859 | − | 19.0281i | −0.568065 | − | 0.983918i | ||||
\(375\) | 16.4363 | − | 9.48948i | 0.848765 | − | 0.490035i | ||||
\(376\) | 1.46057 | + | 2.52979i | 0.0753234 | + | 0.130464i | ||||
\(377\) | −6.33100 | − | 4.73609i | −0.326063 | − | 0.243921i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.0409 | − | 19.0762i | −1.69720 | − | 0.979877i | −0.948400 | − | 0.317076i | \(-0.897299\pi\) |
−0.748796 | − | 0.662801i | \(-0.769368\pi\) | |||||||
\(380\) | 5.56649 | 0.285555 | ||||||||
\(381\) | −44.7016 | −2.29013 | ||||||||
\(382\) | −21.2056 | − | 12.2430i | −1.08497 | − | 0.626408i | ||||
\(383\) | −27.6783 | − | 15.9801i | −1.41430 | − | 0.816544i | −0.418507 | − | 0.908214i | \(-0.637446\pi\) |
−0.995790 | + | 0.0916693i | \(0.970780\pi\) | |||||||
\(384\) | −1.98388 | + | 1.14539i | −0.101239 | + | 0.0584506i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.12046 | + | 10.6009i | 0.311523 | + | 0.539574i | ||||
\(387\) | −17.3265 | −0.880753 | ||||||||
\(388\) | 10.1378 | − | 5.85305i | 0.514668 | − | 0.297144i | ||||
\(389\) | −2.62292 | + | 4.54304i | −0.132988 | + | 0.230341i | −0.924827 | − | 0.380388i | \(-0.875790\pi\) |
0.791839 | + | 0.610729i | \(0.209124\pi\) | |||||||
\(390\) | 5.96452 | + | 4.46194i | 0.302025 | + | 0.225939i | ||||
\(391\) | −42.8130 | −2.16514 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.6520 | − | 40.9664i | 1.19308 | − | 2.06648i | ||||
\(394\) | 2.72876 | − | 4.72634i | 0.137473 | − | 0.238110i | ||||
\(395\) | 5.10275 | + | 2.94608i | 0.256747 | + | 0.148233i | ||||
\(396\) | − | 9.74866i | − | 0.489889i | ||||||
\(397\) | 21.2432 | + | 12.2648i | 1.06617 | + | 0.615552i | 0.927132 | − | 0.374736i | \(-0.122266\pi\) |
0.139035 | + | 0.990287i | \(0.455600\pi\) | |||||||
\(398\) | 12.8166i | 0.642440i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.09334 | + | 3.62578i | −0.104667 | + | 0.181289i | ||||
\(401\) | − | 4.27143i | − | 0.213305i | −0.994296 | − | 0.106652i | \(-0.965987\pi\) | ||
0.994296 | − | 0.106652i | \(-0.0340132\pi\) | |||||||
\(402\) | 11.8924 | − | 20.5983i | 0.593141 | − | 1.02735i | ||||
\(403\) | 1.88562 | − | 2.52062i | 0.0939296 | − | 0.125561i | ||||
\(404\) | −5.37145 | − | 9.30362i | −0.267239 | − | 0.462872i | ||||
\(405\) | −8.34979 | − | 4.82075i | −0.414904 | − | 0.239545i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.312940 | − | 0.542028i | −0.0155119 | − | 0.0268673i | ||||
\(408\) | −10.0502 | + | 5.80247i | −0.497558 | + | 0.287265i | ||||
\(409\) | 1.61647i | 0.0799293i | 0.999201 | + | 0.0399646i | \(0.0127245\pi\) | ||||
−0.999201 | + | 0.0399646i | \(0.987275\pi\) | |||||||
\(410\) | 3.60423i | 0.178000i | ||||||||
\(411\) | −6.32771 | + | 3.65330i | −0.312123 | + | 0.180204i | ||||
\(412\) | −2.40550 | − | 4.16644i | −0.118510 | − | 0.205266i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −16.4508 | − | 9.49787i | −0.808512 | − | 0.466795i | ||||
\(415\) | −5.96784 | − | 10.3366i | −0.292950 | − | 0.507404i | ||||
\(416\) | −3.58019 | − | 0.426876i | −0.175533 | − | 0.0209293i | ||||
\(417\) | 0.682322 | − | 1.18182i | 0.0334135 | − | 0.0578738i | ||||
\(418\) | − | 26.7706i | − | 1.30939i | ||||||
\(419\) | −13.0156 | + | 22.5437i | −0.635854 | + | 1.10133i | 0.350480 | + | 0.936570i | \(0.386018\pi\) |
−0.986334 | + | 0.164761i | \(0.947315\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.5391i | 1.82954i | 0.403971 | + | 0.914772i | \(0.367630\pi\) | ||||
−0.403971 | + | 0.914772i | \(0.632370\pi\) | |||||||
\(422\) | −16.7239 | − | 9.65552i | −0.814104 | − | 0.470023i | ||||
\(423\) | 6.56588i | 0.319244i | ||||||||
\(424\) | −1.46963 | − | 0.848493i | −0.0713717 | − | 0.0412064i | ||||
\(425\) | −10.6047 | + | 18.3679i | −0.514404 | + | 0.890974i | ||||
\(426\) | −3.75524 | + | 6.50427i | −0.181942 | + | 0.315133i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −13.6530 | −0.659944 | ||||||||
\(429\) | 21.4585 | − | 28.6848i | 1.03603 | − | 1.38492i | ||||
\(430\) | −3.47592 | + | 6.02046i | −0.167624 | + | 0.290333i | ||||
\(431\) | −18.6662 | + | 10.7769i | −0.899118 | + | 0.519106i | −0.876914 | − | 0.480647i | \(-0.840402\pi\) |
−0.0222041 | + | 0.999753i | \(0.507068\pi\) | |||||||
\(432\) | 1.72335 | 0.0829147 | ||||||||
\(433\) | −1.59958 | − | 2.77056i | −0.0768710 | − | 0.133145i | 0.825027 | − | 0.565093i | \(-0.191160\pi\) |
−0.901898 | + | 0.431948i | \(0.857826\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.92333 | + | 2.26513i | −0.188109 | + | 0.108605i | ||||
\(436\) | 4.43186 | + | 2.55874i | 0.212248 | + | 0.122541i | ||||
\(437\) | −45.1752 | − | 26.0819i | −2.16102 | − | 1.24767i | ||||
\(438\) | 1.23479 | 0.0590004 | ||||||||
\(439\) | 26.6227 | 1.27063 | 0.635317 | − | 0.772252i | \(-0.280870\pi\) | ||||
0.635317 | + | 0.772252i | \(0.280870\pi\) | |||||||
\(440\) | −3.38739 | − | 1.95571i | −0.161488 | − | 0.0932349i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.1370 | − | 2.16252i | −0.862688 | − | 0.102861i | ||||
\(443\) | −4.54933 | − | 7.87968i | −0.216145 | − | 0.374375i | 0.737481 | − | 0.675368i | \(-0.236015\pi\) |
−0.953626 | + | 0.300993i | \(0.902682\pi\) | |||||||
\(444\) | −0.286286 | + | 0.165287i | −0.0135865 | + | 0.00784420i | ||||
\(445\) | 3.51347 | + | 6.08551i | 0.166555 | + | 0.288481i | ||||
\(446\) | 5.31785 | − | 9.21079i | 0.251808 | − | 0.436144i | ||||
\(447\) | − | 25.6789i | − | 1.21457i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.08550 | − | 3.51346i | 0.287192 | − | 0.165811i | −0.349483 | − | 0.936943i | \(-0.613643\pi\) |
0.636675 | + | 0.771132i | \(0.280309\pi\) | |||||||
\(450\) | −8.14967 | + | 4.70522i | −0.384179 | + | 0.221806i | ||||
\(451\) | 17.3336 | 0.816209 | ||||||||
\(452\) | 8.96603 | + | 15.5296i | 0.421726 | + | 0.730452i | ||||
\(453\) | 29.9476i | 1.40706i | ||||||||
\(454\) | −22.7217 | −1.06638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.1396 | −0.662148 | ||||||||
\(457\) | 19.1511i | 0.895851i | 0.894071 | + | 0.447926i | \(0.147837\pi\) | ||||
−0.894071 | + | 0.447926i | \(0.852163\pi\) | |||||||
\(458\) | 10.1547 | + | 17.5885i | 0.474498 | + | 0.821855i | ||||
\(459\) | 8.73035 | 0.407498 | ||||||||
\(460\) | −6.60049 | + | 3.81080i | −0.307750 | + | 0.177679i | ||||
\(461\) | 2.82026 | − | 1.62828i | 0.131353 | − | 0.0758365i | −0.432884 | − | 0.901450i | \(-0.642504\pi\) |
0.564236 | + | 0.825613i | \(0.309171\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.2761i | 0.988786i | 0.869238 | + | 0.494393i | \(0.164610\pi\) | ||||
−0.869238 | + | 0.494393i | \(0.835390\pi\) | |||||||
\(464\) | 1.09643 | − | 1.89907i | 0.0509004 | − | 0.0881621i | ||||
\(465\) | −0.901839 | − | 1.56203i | −0.0418218 | − | 0.0724374i | ||||
\(466\) | −9.21851 | + | 5.32231i | −0.427039 | + | 0.246551i | ||||
\(467\) | −1.66586 | − | 2.88535i | −0.0770866 | − | 0.133518i | 0.824905 | − | 0.565271i | \(-0.191228\pi\) |
−0.901992 | + | 0.431753i | \(0.857895\pi\) | |||||||
\(468\) | −6.48935 | − | 4.85455i | −0.299970 | − | 0.224402i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.28146 | + | 1.31720i | 0.105236 | + | 0.0607580i | ||||
\(471\) | 41.0612 | 1.89200 | ||||||||
\(472\) | −8.54933 | −0.393515 | ||||||||
\(473\) | 28.9539 | + | 16.7165i | 1.33130 | + | 0.768627i | ||||
\(474\) | −12.9617 | − | 7.48341i | −0.595348 | − | 0.343725i | ||||
\(475\) | −22.3797 | + | 12.9209i | −1.02685 | + | 0.592852i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.90716 | − | 3.30330i | −0.0873229 | − | 0.151248i | ||||
\(478\) | −0.311564 | −0.0142506 | ||||||||
\(479\) | −0.160402 | + | 0.0926079i | −0.00732894 | + | 0.00423136i | −0.503660 | − | 0.863902i | \(-0.668014\pi\) |
0.496331 | + | 0.868133i | \(0.334680\pi\) | |||||||
\(480\) | −1.03296 | + | 1.78914i | −0.0471480 | + | 0.0816627i | ||||
\(481\) | −0.516644 | − | 0.0616009i | −0.0235569 | − | 0.00280876i | ||||
\(482\) | 25.2995 | 1.15236 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.90550 | + | 6.76452i | −0.177523 | + | 0.307478i | ||||
\(485\) | 5.27851 | − | 9.14264i | 0.239685 | − | 0.415146i | ||||
\(486\) | 16.7321 | + | 9.66031i | 0.758985 | + | 0.438200i | ||||
\(487\) | − | 31.2308i | − | 1.41520i | −0.706613 | − | 0.707601i | \(-0.749778\pi\) | ||
0.706613 | − | 0.707601i | \(-0.250222\pi\) | |||||||
\(488\) | 7.21780 | + | 4.16720i | 0.326735 | + | 0.188640i | ||||
\(489\) | − | 46.5440i | − | 2.10479i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4236 | − | 23.2504i | 0.605799 | − | 1.04927i | −0.386126 | − | 0.922446i | \(-0.626187\pi\) |
0.991925 | − | 0.126829i | \(-0.0404798\pi\) | |||||||
\(492\) | − | 9.15521i | − | 0.412749i | ||||||
\(493\) | 5.55442 | − | 9.62054i | 0.250159 | − | 0.433287i | ||||
\(494\) | −17.8203 | − | 13.3310i | −0.801772 | − | 0.599790i | ||||
\(495\) | −4.39586 | − | 7.61385i | −0.197579 | − | 0.342217i | ||||
\(496\) | 0.756094 | + | 0.436531i | 0.0339496 | + | 0.0196008i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.1591 | + | 26.2563i | 0.679295 | + | 1.17657i | ||||
\(499\) | −13.2389 | + | 7.64346i | −0.592653 | + | 0.342168i | −0.766146 | − | 0.642667i | \(-0.777828\pi\) |
0.173493 | + | 0.984835i | \(0.444495\pi\) | |||||||
\(500\) | 8.28491i | 0.370512i | ||||||||
\(501\) | 7.40040i | 0.330625i | ||||||||
\(502\) | −6.96311 | + | 4.02015i | −0.310779 | + | 0.179428i | ||||
\(503\) | −13.0551 | − | 22.6121i | −0.582097 | − | 1.00822i | −0.995230 | − | 0.0975513i | \(-0.968899\pi\) |
0.413133 | − | 0.910671i | \(-0.364434\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.39036 | − | 4.84418i | −0.373366 | − | 0.215563i | ||||
\(506\) | 18.3271 | + | 31.7434i | 0.814737 | + | 1.41117i | ||||
\(507\) | −8.40876 | − | 28.5684i | −0.373446 | − | 1.26877i | ||||
\(508\) | 9.75681 | − | 16.8993i | 0.432889 | − | 0.749785i | ||||
\(509\) | 17.0271i | 0.754715i | 0.926068 | + | 0.377357i | \(0.123167\pi\) | ||||
−0.926068 | + | 0.377357i | \(0.876833\pi\) | |||||||
\(510\) | −5.23289 | + | 9.06364i | −0.231716 | + | 0.401345i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 9.21206 | + | 5.31858i | 0.406722 | + | 0.234821i | ||||
\(514\) | 16.9327i | 0.746868i | ||||||||
\(515\) | −3.75746 | − | 2.16937i | −0.165573 | − | 0.0955939i | ||||
\(516\) | 8.82928 | − | 15.2928i | 0.388687 | − | 0.673226i | ||||
\(517\) | 6.33475 | − | 10.9721i | 0.278602 | − | 0.482553i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.0075 | 0.922128 | ||||||||
\(520\) | −2.98867 | + | 1.28098i | −0.131062 | + | 0.0561748i | ||||
\(521\) | −9.38802 | + | 16.2605i | −0.411297 | + | 0.712387i | −0.995032 | − | 0.0995575i | \(-0.968257\pi\) |
0.583735 | + | 0.811944i | \(0.301591\pi\) | |||||||
\(522\) | 4.26855 | − | 2.46445i | 0.186829 | − | 0.107866i | ||||
\(523\) | 3.03247 | 0.132601 | 0.0663004 | − | 0.997800i | \(-0.478880\pi\) | ||||
0.0663004 | + | 0.997800i | \(0.478880\pi\) | |||||||
\(524\) | 10.3248 | + | 17.8831i | 0.451042 | + | 0.781227i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.93817 | + | 5.16045i | −0.389723 | + | 0.225006i | ||||
\(527\) | 3.83031 | + | 2.21143i | 0.166851 | + | 0.0963315i | ||||
\(528\) | 8.60441 | + | 4.96776i | 0.374459 | + | 0.216194i | ||||
\(529\) | 48.4223 | 2.10532 | ||||||||
\(530\) | −1.53041 | −0.0664766 | ||||||||
\(531\) | −16.6419 | − | 9.60818i | −0.722195 | − | 0.416960i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.63164 | − | 11.5384i | 0.373878 | − | 0.499783i | ||||
\(534\) | −8.92468 | − | 15.4580i | −0.386209 | − | 0.668933i | ||||
\(535\) | −10.6632 | + | 6.15642i | −0.461011 | + | 0.266165i | ||||
\(536\) | 5.19142 | + | 8.99180i | 0.224235 | + | 0.388387i | ||||
\(537\) | 19.4201 | − | 33.6366i | 0.838038 | − | 1.45153i | ||||
\(538\) | − | 6.13999i | − | 0.264714i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.34596 | − | 0.777092i | 0.0579210 | − | 0.0334407i | ||||
\(541\) | 5.29873 | − | 3.05922i | 0.227810 | − | 0.131526i | −0.381751 | − | 0.924265i | \(-0.624679\pi\) |
0.609561 | + | 0.792739i | \(0.291346\pi\) | |||||||
\(542\) | 10.6772 | 0.458625 | ||||||||
\(543\) | 3.04380 | + | 5.27202i | 0.130622 | + | 0.226244i | ||||
\(544\) | − | 5.06592i | − | 0.217200i | ||||||
\(545\) | 4.61513 | 0.197691 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.4754 | −1.60233 | −0.801166 | − | 0.598442i | \(-0.795786\pi\) | ||||
−0.801166 | + | 0.598442i | \(0.795786\pi\) | |||||||
\(548\) | − | 3.18956i | − | 0.136251i | ||||||
\(549\) | 9.36663 | + | 16.2235i | 0.399758 | + | 0.692402i | ||||
\(550\) | 18.1583 | 0.774275 | ||||||||
\(551\) | 11.7218 | − | 6.76758i | 0.499365 | − | 0.288308i | ||||
\(552\) | 16.7661 | − | 9.67992i | 0.713613 | − | 0.412005i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.9090i | 0.930823i | ||||||||
\(555\) | −0.149063 | + | 0.258184i | −0.00632736 | + | 0.0109593i | ||||
\(556\) | 0.297855 | + | 0.515900i | 0.0126319 | + | 0.0218790i | ||||
\(557\) | 7.69941 | − | 4.44526i | 0.326234 | − | 0.188352i | −0.327934 | − | 0.944701i | \(-0.606352\pi\) |
0.654168 | + | 0.756349i | \(0.273019\pi\) | |||||||
\(558\) | 0.981193 | + | 1.69948i | 0.0415372 | + | 0.0719446i | ||||
\(559\) | 25.5458 | − | 10.9493i | 1.08047 | − | 0.463104i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 43.5893 | + | 25.1663i | 1.84034 | + | 1.06252i | ||||
\(562\) | −25.7719 | −1.08712 | ||||||||
\(563\) | 17.7920 | 0.749841 | 0.374921 | − | 0.927057i | \(-0.377670\pi\) | ||||
0.374921 | + | 0.927057i | \(0.377670\pi\) | |||||||
\(564\) | −5.79521 | − | 3.34587i | −0.244022 | − | 0.140886i | ||||
\(565\) | 14.0052 | + | 8.08591i | 0.589204 | + | 0.340177i | ||||
\(566\) | 9.80937 | − | 5.66344i | 0.412319 | − | 0.238052i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.63928 | − | 2.83932i | −0.0687826 | − | 0.119135i | ||||
\(569\) | −11.1737 | −0.468425 | −0.234212 | − | 0.972185i | \(-0.575251\pi\) | ||||
−0.234212 | + | 0.972185i | \(0.575251\pi\) | |||||||
\(570\) | −11.0432 | + | 6.37582i | −0.462551 | + | 0.267054i | ||||
\(571\) | 8.36194 | − | 14.4833i | 0.349936 | − | 0.606108i | −0.636301 | − | 0.771441i | \(-0.719537\pi\) |
0.986238 | + | 0.165333i | \(0.0528698\pi\) | |||||||
\(572\) | 6.16055 | + | 14.3733i | 0.257586 | + | 0.600976i | ||||
\(573\) | 56.0924 | 2.34329 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.6912 | − | 30.6421i | 0.737774 | − | 1.27786i | ||||
\(576\) | 1.12385 | − | 1.94657i | 0.0468272 | − | 0.0811070i | ||||
\(577\) | 0.691857 | + | 0.399444i | 0.0288024 | + | 0.0166291i | 0.514332 | − | 0.857591i | \(-0.328040\pi\) |
−0.485530 | + | 0.874220i | \(0.661373\pi\) | |||||||
\(578\) | − | 8.66355i | − | 0.360356i | ||||||
\(579\) | −24.2845 | − | 14.0207i | −1.00923 | − | 0.582679i | ||||
\(580\) | − | 1.97760i | − | 0.0821155i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.4081 | + | 23.2235i | −0.555783 | + | 0.962645i | ||||
\(583\) | 7.36010i | 0.304824i | ||||||||
\(584\) | −0.269511 | + | 0.466808i | −0.0111525 | + | 0.0193166i | ||||
\(585\) | −7.25729 | − | 0.865306i | −0.300052 | − | 0.0357760i | ||||
\(586\) | 11.8730 | + | 20.5646i | 0.490468 | + | 0.849515i | ||||
\(587\) | −6.94921 | − | 4.01213i | −0.286825 | − | 0.165598i | 0.349684 | − | 0.936868i | \(-0.386289\pi\) |
−0.636509 | + | 0.771269i | \(0.719622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.69444 | + | 4.66690i | 0.111022 | + | 0.192296i | ||||
\(590\) | −6.67716 | + | 3.85506i | −0.274894 | + | 0.158710i | ||||
\(591\) | 12.5020i | 0.514263i | ||||||||
\(592\) | − | 0.144306i | − | 0.00593095i | ||||||
\(593\) | 4.27055 | − | 2.46560i | 0.175370 | − | 0.101250i | −0.409745 | − | 0.912200i | \(-0.634382\pi\) |
0.585116 | + | 0.810950i | \(0.301049\pi\) | |||||||
\(594\) | −3.73723 | − | 6.47306i | −0.153340 | − | 0.265593i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.70783 | + | 5.60482i | 0.397648 | + | 0.229582i | ||||
\(597\) | −14.6801 | − | 25.4267i | −0.600816 | − | 1.04064i | ||||
\(598\) | 30.2568 | + | 3.60760i | 1.23729 | + | 0.147526i | ||||
\(599\) | 8.91246 | − | 15.4368i | 0.364153 | − | 0.630732i | −0.624487 | − | 0.781035i | \(-0.714692\pi\) |
0.988640 | + | 0.150304i | \(0.0480251\pi\) | |||||||
\(600\) | − | 9.59081i | − | 0.391543i | ||||||
\(601\) | −0.0809165 | + | 0.140152i | −0.00330065 | + | 0.00571690i | −0.867671 | − | 0.497139i | \(-0.834384\pi\) |
0.864370 | + | 0.502856i | \(0.167717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.3375i | 0.950378i | ||||||||
\(604\) | −11.3216 | − | 6.53653i | −0.460670 | − | 0.265968i | ||||
\(605\) | 7.04426i | 0.286390i | ||||||||
\(606\) | 21.3126 | + | 12.3048i | 0.865765 | + | 0.499850i | ||||
\(607\) | 3.09423 | − | 5.35937i | 0.125591 | − | 0.217530i | −0.796373 | − | 0.604806i | \(-0.793251\pi\) |
0.921964 | + | 0.387276i | \(0.126584\pi\) | |||||||
\(608\) | 3.08619 | − | 5.34544i | 0.125162 | − | 0.216786i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.51629 | 0.304326 | ||||||||
\(611\) | −4.14923 | − | 9.68062i | −0.167860 | − | 0.391636i | ||||
\(612\) | 5.69334 | − | 9.86116i | 0.230140 | − | 0.398614i | ||||
\(613\) | −32.2269 | + | 18.6062i | −1.30163 | + | 0.751497i | −0.980684 | − | 0.195600i | \(-0.937335\pi\) |
−0.320947 | + | 0.947097i | \(0.604001\pi\) | |||||||
\(614\) | 6.68810 | 0.269910 | ||||||||
\(615\) | −4.12826 | − | 7.15036i | −0.166468 | − | 0.288330i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.78536 | + | 3.34018i | −0.232910 | + | 0.134471i | −0.611914 | − | 0.790924i | \(-0.709600\pi\) |
0.379004 | + | 0.925395i | \(0.376267\pi\) | |||||||
\(618\) | 9.54443 | + | 5.51048i | 0.383933 | + | 0.221664i | ||||
\(619\) | −20.5546 | − | 11.8672i | −0.826158 | − | 0.476982i | 0.0263776 | − | 0.999652i | \(-0.491603\pi\) |
−0.852535 | + | 0.522670i | \(0.824936\pi\) | |||||||
\(620\) | 0.787362 | 0.0316212 | ||||||||
\(621\) | −14.5643 | −0.584446 | ||||||||
\(622\) | −7.95639 | − | 4.59362i | −0.319022 | − | 0.184187i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.59161 | − | 3.25386i | 0.303908 | − | 0.130259i | ||||
\(625\) | −6.73089 | − | 11.6582i | −0.269236 | − | 0.466330i | ||||
\(626\) | −14.8637 | + | 8.58157i | −0.594074 | + | 0.342989i | ||||
\(627\) | 30.6629 | + | 53.1097i | 1.22456 | + | 2.12100i | ||||
\(628\) | −8.96225 | + | 15.5231i | −0.357633 | + | 0.619438i | ||||
\(629\) | − | 0.731044i | − | 0.0291486i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.9348 | − | 11.5093i | 0.793590 | − | 0.458180i | −0.0476346 | − | 0.998865i | \(-0.515168\pi\) |
0.841225 | + | 0.540685i | \(0.181835\pi\) | |||||||
\(632\) | 5.65817 | − | 3.26674i | 0.225070 | − | 0.129944i | ||||
\(633\) | 44.2375 | 1.75828 | ||||||||
\(634\) | 1.88124 | + | 3.25840i | 0.0747135 | + | 0.129408i | ||||
\(635\) | − | 17.5981i | − | 0.698361i | ||||||
\(636\) | 3.88743 | 0.154147 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.51078 | −0.376536 | ||||||||
\(639\) | − | 7.36923i | − | 0.291522i | ||||||
\(640\) | −0.450919 | − | 0.781015i | −0.0178242 | − | 0.0308723i | ||||
\(641\) | −12.6508 | −0.499676 | −0.249838 | − | 0.968288i | \(-0.580377\pi\) | ||||
−0.249838 | + | 0.968288i | \(0.580377\pi\) | |||||||
\(642\) | 27.0860 | − | 15.6381i | 1.06900 | − | 0.617186i | ||||
\(643\) | 13.1971 | − | 7.61938i | 0.520445 | − | 0.300479i | −0.216672 | − | 0.976244i | \(-0.569520\pi\) |
0.737117 | + | 0.675766i | \(0.236187\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 15.9252i | − | 0.627053i | ||||||
\(646\) | 15.6344 | − | 27.0796i | 0.615127 | − | 1.06543i | ||||
\(647\) | 14.6821 | + | 25.4301i | 0.577213 | + | 0.999762i | 0.995797 | + | 0.0915840i | \(0.0291930\pi\) |
−0.418585 | + | 0.908178i | \(0.637474\pi\) | |||||||
\(648\) | −9.25862 | + | 5.34547i | −0.363713 | + | 0.209990i | ||||
\(649\) | 18.5399 | + | 32.1121i | 0.727756 | + | 1.26051i | ||||
\(650\) | 9.04233 | − | 12.0874i | 0.354669 | − | 0.474106i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.5958 | + | 10.1589i | 0.689105 | + | 0.397855i | ||||
\(653\) | −29.0211 | −1.13568 | −0.567842 | − | 0.823137i | \(-0.692222\pi\) | ||||
−0.567842 | + | 0.823137i | \(0.692222\pi\) | |||||||
\(654\) | −11.7230 | −0.458407 | ||||||||
\(655\) | 16.1277 | + | 9.31132i | 0.630161 | + | 0.363823i | ||||
\(656\) | 3.46110 | + | 1.99827i | 0.135133 | + | 0.0780192i | ||||
\(657\) | −1.04925 | + | 0.605782i | −0.0409350 | + | 0.0236338i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.98651 | − | 6.90484i | −0.155293 | − | 0.268975i | 0.777873 | − | 0.628422i | \(-0.216299\pi\) |
−0.933166 | + | 0.359447i | \(0.882965\pi\) | |||||||
\(660\) | 8.96024 | 0.348777 | ||||||||
\(661\) | 3.40668 | − | 1.96685i | 0.132505 | − | 0.0765015i | −0.432282 | − | 0.901738i | \(-0.642292\pi\) |
0.564787 | + | 0.825237i | \(0.308958\pi\) | |||||||
\(662\) | 16.1129 | − | 27.9083i | 0.626244 | − | 1.08469i | ||||
\(663\) | 38.4585 | − | 16.4838i | 1.49360 | − | 0.640177i | ||||
\(664\) | −13.2348 | −0.513611 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.162179 | − | 0.280902i | 0.00628430 | − | 0.0108847i | ||||
\(667\) | −9.26611 | + | 16.0494i | −0.358785 | + | 0.621434i | ||||
\(668\) | −2.79770 | − | 1.61525i | −0.108246 | − | 0.0624960i | ||||
\(669\) | 24.3641i | 0.941972i | ||||||||
\(670\) | 8.10916 | + | 4.68182i | 0.313284 | + | 0.180875i | ||||
\(671\) | − | 36.1477i | − | 1.39547i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.1599 | − | 31.4539i | 0.700014 | − | 1.21246i | −0.268447 | − | 0.963295i | \(-0.586510\pi\) |
0.968461 | − | 0.249166i | \(-0.0801563\pi\) | |||||||
\(674\) | 3.01703i | 0.116212i | ||||||||
\(675\) | −3.60756 | + | 6.24848i | −0.138855 | + | 0.240504i | ||||
\(676\) | 12.6356 | + | 3.05660i | 0.485983 | + | 0.117561i | ||||
\(677\) | −10.5534 | − | 18.2790i | −0.405600 | − | 0.702520i | 0.588791 | − | 0.808285i | \(-0.299604\pi\) |
−0.994391 | + | 0.105765i | \(0.966271\pi\) | |||||||
\(678\) | −35.5750 | − | 20.5393i | −1.36625 | − | 0.788805i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.28432 | − | 3.95656i | −0.0875997 | − | 0.151727i | ||||
\(681\) | 45.0771 | − | 26.0253i | 1.72736 | − | 0.997292i | ||||
\(682\) | − | 3.78662i | − | 0.144997i | ||||||
\(683\) | − | 26.4258i | − | 1.01115i | −0.862782 | − | 0.505577i | \(-0.831280\pi\) | ||
0.862782 | − | 0.505577i | \(-0.168720\pi\) | |||||||
\(684\) | 12.0150 | − | 6.93684i | 0.459404 | − | 0.265237i | ||||
\(685\) | −1.43824 | − | 2.49110i | −0.0549522 | − | 0.0951799i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.2914 | − | 23.2623i | −1.53721 | − | 0.887511i | ||||
\(688\) | 3.85426 | + | 6.67577i | 0.146942 | + | 0.254511i | ||||
\(689\) | 4.89937 | + | 3.66512i | 0.186651 | + | 0.139630i | ||||
\(690\) | 8.72972 | − | 15.1203i | 0.332335 | − | 0.575621i | ||||
\(691\) | 0.779759i | 0.0296634i | 0.999890 | + | 0.0148317i | \(0.00472125\pi\) | ||||
−0.999890 | + | 0.0148317i | \(0.995279\pi\) | |||||||
\(692\) | −4.58522 | + | 7.94183i | −0.174304 | + | 0.301903i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 0.468540i | − | 0.0177855i | ||||||
\(695\) | 0.465259 | + | 0.268617i | 0.0176483 | + | 0.0101892i | ||||
\(696\) | 5.02337i | 0.190410i | ||||||||
\(697\) | 17.5337 | + | 10.1231i | 0.664135 | + | 0.383438i | ||||
\(698\) | 16.1106 | − | 27.9044i | 0.609795 | − | 1.05620i | ||||
\(699\) | 12.1923 | − | 21.1176i | 0.461154 | − | 0.798742i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.5491 | 0.813899 | 0.406950 | − | 0.913451i | \(-0.366592\pi\) | ||||
0.406950 | + | 0.913451i | \(0.366592\pi\) | |||||||
\(702\) | −6.16992 | − | 0.735656i | −0.232869 | − | 0.0277656i | ||||
\(703\) | 0.445357 | − | 0.771380i | 0.0167969 | − | 0.0290932i | ||||
\(704\) | −3.75609 | + | 2.16858i | −0.141563 | + | 0.0817315i | ||||
\(705\) | −6.03486 | −0.227286 | ||||||||
\(706\) | 6.55771 | + | 11.3583i | 0.246803 | + | 0.427474i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 16.9608 | − | 9.79235i | 0.637428 | − | 0.368019i | ||||
\(709\) | 3.92952 | + | 2.26871i | 0.147576 | + | 0.0852031i | 0.571970 | − | 0.820275i | \(-0.306179\pi\) |
−0.424394 | + | 0.905478i | \(0.639513\pi\) | |||||||
\(710\) | −2.56060 | − | 1.47837i | −0.0960978 | − | 0.0554821i | ||||
\(711\) | 14.6853 | 0.550743 | ||||||||
\(712\) | 7.79180 | 0.292010 | ||||||||
\(713\) | −6.38988 | − | 3.68920i | −0.239303 | − | 0.138162i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.2927 | + | 8.44782i | 0.422322 | + | 0.315931i | ||||
\(716\) | 8.47747 | + | 14.6834i | 0.316818 | + | 0.548745i | ||||
\(717\) | 0.618106 | − | 0.356863i | 0.0230836 | − | 0.0133273i | ||||
\(718\) | −2.18990 | − | 3.79302i | −0.0817265 | − | 0.141554i | ||||
\(719\) | 7.30036 | − | 12.6446i | 0.272258 | − | 0.471564i | −0.697182 | − | 0.716894i | \(-0.745563\pi\) |
0.969440 | + | 0.245330i | \(0.0788964\pi\) | |||||||
\(720\) | − | 2.02707i | − | 0.0755443i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.5396 | − | 9.54914i | 0.615540 | − | 0.355382i | ||||
\(723\) | −50.1912 | + | 28.9779i | −1.86663 | + | 1.07770i | ||||
\(724\) | −2.65743 | −0.0987626 | ||||||||
\(725\) | 4.59040 | + | 7.95081i | 0.170483 | + | 0.295286i | ||||
\(726\) | − | 17.8933i | − | 0.664083i | ||||||
\(727\) | −30.6315 | −1.13606 | −0.568030 | − | 0.823008i | \(-0.692294\pi\) | ||||
−0.568030 | + | 0.823008i | \(0.692294\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.1866 | −0.451355 | ||||||||
\(730\) | 0.486112i | 0.0179918i | ||||||||
\(731\) | 19.5254 | + | 33.8189i | 0.722171 | + | 1.25084i | ||||
\(732\) | −19.0923 | −0.705673 | ||||||||
\(733\) | −15.3455 | + | 8.85973i | −0.566799 | + | 0.327242i | −0.755870 | − | 0.654722i | \(-0.772786\pi\) |
0.189071 | + | 0.981963i | \(0.439452\pi\) | |||||||
\(734\) | 22.3597 | − | 12.9094i | 0.825313 | − | 0.476495i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.45117i | 0.311514i | ||||||||
\(737\) | 22.5160 | − | 38.9989i | 0.829389 | − | 1.43654i | ||||
\(738\) | 4.49151 | + | 7.77953i | 0.165335 | + | 0.286368i | ||||
\(739\) | 9.05014 | − | 5.22510i | 0.332915 | − | 0.192208i | −0.324220 | − | 0.945982i | \(-0.605102\pi\) |
0.657134 | + | 0.753773i | \(0.271768\pi\) | |||||||
\(740\) | −0.0650705 | − | 0.112705i | −0.00239204 | − | 0.00414313i | ||||
\(741\) | 50.6225 | + | 6.03586i | 1.85966 | + | 0.221733i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.0103 | + | 24.2547i | 1.54121 | + | 0.889818i | 0.998763 | + | 0.0497278i | \(0.0158354\pi\) |
0.542447 | + | 0.840090i | \(0.317498\pi\) | |||||||
\(744\) | −2.00000 | −0.0733236 | ||||||||
\(745\) | 10.1093 | 0.370376 | ||||||||
\(746\) | 26.5251 | + | 15.3143i | 0.971152 | + | 0.560695i | ||||
\(747\) | −25.7625 | − | 14.8740i | −0.942601 | − | 0.544211i | ||||
\(748\) | −19.0281 | + | 10.9859i | −0.695735 | + | 0.401683i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.48948 | − | 16.4363i | −0.346507 | − | 0.600168i | ||||
\(751\) | −31.4555 | −1.14783 | −0.573914 | − | 0.818915i | \(-0.694576\pi\) | ||||
−0.573914 | + | 0.818915i | \(0.694576\pi\) | |||||||
\(752\) | 2.52979 | − | 1.46057i | 0.0922519 | − | 0.0532617i | ||||
\(753\) | 9.20931 | − | 15.9510i | 0.335606 | − | 0.581286i | ||||
\(754\) | −4.73609 | + | 6.33100i | −0.172478 | + | 0.230561i | ||||
\(755\) | −11.7898 | −0.429075 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.3442 | + | 42.1654i | −0.884805 | + | 1.53253i | −0.0388676 | + | 0.999244i | \(0.512375\pi\) |
−0.845937 | + | 0.533283i | \(0.820958\pi\) | |||||||
\(758\) | −19.0762 | + | 33.0409i | −0.692877 | + | 1.20010i | ||||
\(759\) | −72.7174 | − | 41.9834i | −2.63947 | − | 1.52390i | ||||
\(760\) | − | 5.56649i | − | 0.201918i | ||||||
\(761\) | −40.3350 | − | 23.2874i | −1.46214 | − | 0.844169i | −0.463033 | − | 0.886341i | \(-0.653239\pi\) |
−0.999110 | + | 0.0421718i | \(0.986572\pi\) | |||||||
\(762\) | 44.7016i | 1.61937i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.2430 | + | 21.2056i | −0.442937 | + | 0.767190i | ||||
\(765\) | − | 10.2690i | − | 0.371275i | ||||||
\(766\) | −15.9801 | + | 27.6783i | −0.577384 | + | 1.00006i | ||||
\(767\) | 30.6083 | + | 3.64950i | 1.10520 | + | 0.131776i | ||||
\(768\) | 1.14539 | + | 1.98388i | 0.0413308 | + | 0.0715871i | ||||
\(769\) | 24.1069 | + | 13.9181i | 0.869315 | + | 0.501899i | 0.867121 | − | 0.498098i | \(-0.165968\pi\) |
0.00219468 | + | 0.999998i | \(0.499301\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.3946 | − | 33.5924i | −0.698479 | − | 1.20980i | ||||
\(772\) | 10.6009 | − | 6.12046i | 0.381536 | − | 0.220280i | ||||
\(773\) | − | 28.4724i | − | 1.02408i | −0.858961 | − | 0.512040i | \(-0.828890\pi\) | ||
0.858961 | − | 0.512040i | \(-0.171110\pi\) | |||||||
\(774\) | 17.3265i | 0.622786i | ||||||||
\(775\) | −3.16553 | + | 1.82762i | −0.113709 | + | 0.0656500i | ||||
\(776\) | −5.85305 | − | 10.1378i | −0.210112 | − | 0.363925i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.54304 | + | 2.62292i | 0.162876 | + | 0.0940364i | ||||
\(779\) | 12.3341 | + | 21.3632i | 0.441914 | + | 0.765417i | ||||
\(780\) | 4.46194 | − | 5.96452i | 0.159763 | − | 0.213564i | ||||
\(781\) | −7.10982 | + | 12.3146i | −0.254409 | + | 0.440650i | ||||
\(782\) | 42.8130i | 1.53099i | ||||||||
\(783\) | 1.88953 | − | 3.27276i | 0.0675263 | − | 0.116959i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.1650i | 0.576954i | ||||||||
\(786\) | −40.9664 | − | 23.6520i | −1.46122 | − | 0.843637i | ||||
\(787\) | − | 15.1319i | − | 0.539393i | −0.962945 | − | 0.269697i | \(-0.913077\pi\) | ||
0.962945 | − | 0.269697i | \(-0.0869234\pi\) | |||||||
\(788\) | −4.72634 | − | 2.72876i | −0.168369 | − | 0.0972079i | ||||
\(789\) | 11.8215 | − | 20.4754i | 0.420856 | − | 0.728945i | ||||
\(790\) | 2.94608 | − | 5.10275i | 0.104817 | − | 0.181548i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −9.74866 | −0.346404 | ||||||||
\(793\) | −24.0622 | − | 18.0005i | −0.854475 | − | 0.639216i | ||||
\(794\) | 12.2648 | − | 21.2432i | 0.435261 | − | 0.753894i | ||||
\(795\) | 3.03614 | − | 1.75292i | 0.107681 | − | 0.0621696i | ||||
\(796\) | 12.8166 | 0.454274 | ||||||||
\(797\) | −6.97234 | − | 12.0764i | −0.246973 | − | 0.427770i | 0.715712 | − | 0.698396i | \(-0.246103\pi\) |
−0.962684 | + | 0.270626i | \(0.912769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.8157 | − | 7.39916i | 0.453387 | − | 0.261763i | ||||
\(800\) | 3.62578 | + | 2.09334i | 0.128191 | + | 0.0740109i | ||||
\(801\) | 15.1673 | + | 8.75683i | 0.535909 | + | 0.309407i | ||||
\(802\) | −4.27143 | −0.150829 | ||||||||
\(803\) | 2.33783 | 0.0825003 | ||||||||
\(804\) | −20.5983 | − | 11.8924i | −0.726446 | − | 0.419414i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.52062 | − | 1.88562i | −0.0887850 | − | 0.0664183i | ||||
\(807\) | 7.03270 | + | 12.1810i | 0.247563 | + | 0.428791i | ||||
\(808\) | −9.30362 | + | 5.37145i | −0.327300 | + | 0.188967i | ||||
\(809\) | 10.8714 | + | 18.8299i | 0.382220 | + | 0.662024i | 0.991379 | − | 0.131024i | \(-0.0418264\pi\) |
−0.609159 | + | 0.793048i | \(0.708493\pi\) | |||||||
\(810\) | −4.82075 | + | 8.34979i | −0.169384 | + | 0.293382i | ||||
\(811\) | − | 21.1256i | − | 0.741819i | −0.928669 | − | 0.370910i | \(-0.879046\pi\) | ||
0.928669 | − | 0.370910i | \(-0.120954\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.1823 | + | 12.2296i | −0.742895 | + | 0.428911i | ||||
\(814\) | −0.542028 | + | 0.312940i | −0.0189981 | + | 0.0109685i | ||||
\(815\) | 18.3235 | 0.641843 | ||||||||
\(816\) | 5.80247 | + | 10.0502i | 0.203127 | + | 0.351827i | ||||
\(817\) | 47.5799i | 1.66461i | ||||||||
\(818\) | 1.61647 | 0.0565185 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.60423 | 0.125865 | ||||||||
\(821\) | 16.2736i | 0.567951i | 0.958831 | + | 0.283976i | \(0.0916535\pi\) | ||||
−0.958831 | + | 0.283976i | \(0.908347\pi\) | |||||||
\(822\) | 3.65330 | + | 6.32771i | 0.127424 | + | 0.220704i | ||||
\(823\) | −18.6543 | −0.650246 | −0.325123 | − | 0.945672i | \(-0.605406\pi\) | ||||
−0.325123 | + | 0.945672i | \(0.605406\pi\) | |||||||
\(824\) | −4.16644 | + | 2.40550i | −0.145145 | + | 0.0837994i | ||||
\(825\) | −36.0240 | + | 20.7985i | −1.25419 | + | 0.724109i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.3361i | 1.64604i | 0.568015 | + | 0.823018i | \(0.307712\pi\) | ||||
−0.568015 | + | 0.823018i | \(0.692288\pi\) | |||||||
\(828\) | −9.49787 | + | 16.4508i | −0.330074 | + | 0.571704i | ||||
\(829\) | −0.460988 | − | 0.798454i | −0.0160108 | − | 0.0277315i | 0.857909 | − | 0.513802i | \(-0.171763\pi\) |
−0.873920 | + | 0.486070i | \(0.838430\pi\) | |||||||
\(830\) | −10.3366 | + | 5.96784i | −0.358789 | + | 0.207147i | ||||
\(831\) | −25.0944 | − | 43.4647i | −0.870515 | − | 1.50778i | ||||
\(832\) | −0.426876 | + | 3.58019i | −0.0147993 | + | 0.124121i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.18182 | − | 0.682322i | −0.0409230 | − | 0.0236269i | ||||
\(835\) | −2.91339 | −0.100822 | ||||||||
\(836\) | −26.7706 | −0.925881 | ||||||||
\(837\) | 1.30301 | + | 0.752296i | 0.0450388 | + | 0.0260032i | ||||
\(838\) | 22.5437 | + | 13.0156i | 0.778758 | + | 0.449616i | ||||
\(839\) | 14.3894 | − | 8.30775i | 0.496779 | − | 0.286815i | −0.230604 | − | 0.973048i | \(-0.574070\pi\) |
0.727382 | + | 0.686232i | \(0.240737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0957 | + | 20.9503i | 0.417093 | + | 0.722426i | ||||
\(842\) | 37.5391 | 1.29368 | ||||||||
\(843\) | 51.1284 | − | 29.5190i | 1.76096 | − | 1.01669i | ||||
\(844\) | −9.65552 | + | 16.7239i | −0.332357 | + | 0.575659i | ||||
\(845\) | 11.2468 | − | 3.31037i | 0.386903 | − | 0.113880i | ||||
\(846\) | 6.56588 | 0.225740 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.848493 | + | 1.46963i | −0.0291374 | + | 0.0504674i | ||||
\(849\) | −12.9737 | + | 22.4712i | −0.445258 | + | 0.771209i | ||||
\(850\) | 18.3679 | + | 10.6047i | 0.630014 | + | 0.363739i | ||||
\(851\) | 1.21956i | 0.0418059i | ||||||||
\(852\) | 6.50427 | + | 3.75524i | 0.222832 | + | 0.128652i | ||||
\(853\) | 26.3277i | 0.901445i | 0.892664 | + | 0.450722i | \(0.148834\pi\) | ||||
−0.892664 | + | 0.450722i | \(0.851166\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.25591 | − | 10.8356i | 0.213948 | − | 0.370568i | ||||
\(856\) | 13.6530i | 0.466651i | ||||||||
\(857\) | 7.05290 | − | 12.2160i | 0.240923 | − | 0.417290i | −0.720055 | − | 0.693917i | \(-0.755883\pi\) |
0.960977 | + | 0.276627i | \(0.0892167\pi\) | |||||||
\(858\) | −28.6848 | − | 21.4585i | −0.979284 | − | 0.732583i | ||||
\(859\) | 11.7359 | + | 20.3272i | 0.400425 | + | 0.693557i | 0.993777 | − | 0.111386i | \(-0.0355291\pi\) |
−0.593352 | + | 0.804943i | \(0.702196\pi\) | |||||||
\(860\) | 6.02046 | + | 3.47592i | 0.205296 | + | 0.118528i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.7769 | + | 18.6662i | 0.367063 | + | 0.635772i | ||||
\(863\) | 10.3476 | − | 5.97418i | 0.352236 | − | 0.203364i | −0.313434 | − | 0.949610i | \(-0.601479\pi\) |
0.665670 | + | 0.746247i | \(0.268146\pi\) | |||||||
\(864\) | − | 1.72335i | − | 0.0586295i | ||||||
\(865\) | 8.27026i | 0.281197i | ||||||||
\(866\) | −2.77056 | + | 1.59958i | −0.0941474 | + | 0.0543560i | ||||
\(867\) | 9.92317 | + | 17.1874i | 0.337009 | + | 0.583716i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.5404 | − | 14.1684i | −0.832476 | − | 0.480630i | ||||
\(870\) | 2.26513 | + | 3.92333i | 0.0767953 | + | 0.133013i | ||||
\(871\) | −14.7479 | − | 34.4085i | −0.499713 | − | 1.16589i | ||||
\(872\) | 2.55874 | − | 4.43186i | 0.0866497 | − | 0.150082i | ||||
\(873\) | − | 26.3118i | − | 0.890521i | ||||||
\(874\) | −26.0819 | + | 45.1752i | −0.882234 | + | 1.52807i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 1.23479i | − | 0.0417196i | ||||||
\(877\) | 28.3486 | + | 16.3671i | 0.957264 | + | 0.552677i | 0.895330 | − | 0.445403i | \(-0.146940\pi\) |
0.0619342 | + | 0.998080i | \(0.480273\pi\) | |||||||
\(878\) | − | 26.6227i | − | 0.898474i | ||||||
\(879\) | −47.1091 | − | 27.1984i | −1.58895 | − | 0.917380i | ||||
\(880\) | −1.95571 | + | 3.38739i | −0.0659270 | + | 0.114189i | ||||
\(881\) | 5.29540 | − | 9.17190i | 0.178407 | − | 0.309009i | −0.762928 | − | 0.646483i | \(-0.776239\pi\) |
0.941335 | + | 0.337474i | \(0.109572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.6713 | −1.30139 | −0.650696 | − | 0.759338i | \(-0.725523\pi\) | ||||
−0.650696 | + | 0.759338i | \(0.725523\pi\) | |||||||
\(884\) | −2.16252 | + | 18.1370i | −0.0727334 | + | 0.610012i | ||||
\(885\) | 8.83112 | − | 15.2959i | 0.296855 | − | 0.514168i | ||||
\(886\) | −7.87968 | + | 4.54933i | −0.264723 | + | 0.152838i | ||||
\(887\) | −4.72164 | −0.158537 | −0.0792685 | − | 0.996853i | \(-0.525258\pi\) | ||||
−0.0792685 | + | 0.996853i | \(0.525258\pi\) | |||||||
\(888\) | 0.165287 | + | 0.286286i | 0.00554668 | + | 0.00960714i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.08551 | − | 3.51347i | 0.203987 | − | 0.117772i | ||||
\(891\) | 40.1562 | + | 23.1842i | 1.34528 | + | 0.776699i | ||||
\(892\) | −9.21079 | − | 5.31785i | −0.308400 | − | 0.178055i | ||||
\(893\) | 18.0304 | 0.603366 | ||||||||
\(894\) | −25.6789 | −0.858831 | ||||||||
\(895\) | 13.2421 | + | 7.64531i | 0.442634 | + | 0.255555i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −64.1580 | + | 27.4989i | −2.14217 | + | 0.918162i | ||||
\(898\) | −3.51346 | − | 6.08550i | −0.117246 | − | 0.203076i | ||||
\(899\) | 1.65801 | − | 0.957251i | 0.0552976 | − | 0.0319261i | ||||
\(900\) | 4.70522 | + | 8.14967i | 0.156841 | + | 0.271656i | ||||
\(901\) | −4.29840 | + | 7.44504i | −0.143200 | + | 0.248030i | ||||
\(902\) | − | 17.3336i | − | 0.577147i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.5296 | − | 8.96603i | 0.516507 | − | 0.298206i | ||||
\(905\) | −2.07549 | + | 1.19829i | −0.0689917 | + | 0.0398324i | ||||
\(906\) | 29.9476 | 0.994943 | ||||||||
\(907\) | −20.9654 | − | 36.3132i | −0.696146 | − | 1.20576i | −0.969793 | − | 0.243930i | \(-0.921563\pi\) |
0.273646 | − | 0.961830i | \(-0.411770\pi\) | |||||||
\(908\) | 22.7217i | 0.754047i | ||||||||
\(909\) | −24.1468 | −0.800900 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.1425 | −1.79382 | −0.896910 | − | 0.442213i | \(-0.854194\pi\) | ||||
−0.896910 | + | 0.442213i | \(0.854194\pi\) | |||||||
\(912\) | 14.1396i | 0.468209i | ||||||||
\(913\) | 28.7008 | + | 49.7113i | 0.949859 | + | 1.64520i | ||||
\(914\) | 19.1511 | 0.633462 | ||||||||
\(915\) | −14.9114 | + | 8.60910i | −0.492956 | + | 0.284608i | ||||
\(916\) | 17.5885 | − | 10.1547i | 0.581139 | − | 0.335521i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 8.73035i | − | 0.288145i | ||||||
\(919\) | 12.9117 | − | 22.3636i | 0.425916 | − | 0.737708i | −0.570589 | − | 0.821236i | \(-0.693285\pi\) |
0.996506 | + | 0.0835271i | \(0.0266185\pi\) | |||||||
\(920\) | 3.81080 | + | 6.60049i | 0.125638 | + | 0.217612i | ||||
\(921\) | −13.2684 | + | 7.66051i | −0.437208 | + | 0.252422i | ||||
\(922\) | −1.62828 | − | 2.82026i | −0.0536245 | − | 0.0928804i | ||||
\(923\) | 4.65690 | + | 10.8651i | 0.153284 | + | 0.357628i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.523222 | + | 0.302083i | 0.0172034 | + | 0.00993241i | ||||
\(926\) | 21.2761 | 0.699178 | ||||||||
\(927\) | −10.8137 | −0.355168 | ||||||||
\(928\) | −1.89907 | − | 1.09643i | −0.0623400 | − | 0.0359920i | ||||
\(929\) | 13.8843 | + | 8.01610i | 0.455529 | + | 0.263000i | 0.710162 | − | 0.704038i | \(-0.248621\pi\) |
−0.254633 | + | 0.967038i | \(0.581955\pi\) | |||||||
\(930\) | −1.56203 | + | 0.901839i | −0.0512210 | + | 0.0295725i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.32231 | + | 9.21851i | 0.174338 | + | 0.301962i | ||||
\(933\) | 21.0460 | 0.689016 | ||||||||
\(934\) | −2.88535 | + | 1.66586i | −0.0944115 | + | 0.0545085i | ||||
\(935\) | −9.90748 | + | 17.1603i | −0.324009 | + | 0.561200i | ||||
\(936\) | −4.85455 | + | 6.48935i | −0.158676 | + | 0.212111i | ||||
\(937\) | −47.0232 | −1.53618 | −0.768091 | − | 0.640340i | \(-0.778793\pi\) | ||||
−0.768091 | + | 0.640340i | \(0.778793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.6586 | − | 34.0496i | 0.641533 | − | 1.11117i | ||||
\(940\) | 1.31720 | − | 2.28146i | 0.0429624 | − | 0.0744131i | ||||
\(941\) | −45.7754 | − | 26.4284i | −1.49224 | − | 0.861542i | −0.492275 | − | 0.870440i | \(-0.663835\pi\) |
−0.999960 | + | 0.00889731i | \(0.997168\pi\) | |||||||
\(942\) | − | 41.0612i | − | 1.33785i | ||||||
\(943\) | −29.2504 | − | 16.8877i | −0.952523 | − | 0.549939i | ||||
\(944\) | 8.54933i | 0.278257i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.7165 | − | 28.9539i | 0.543502 | − | 0.941372i | ||||
\(947\) | 38.5704i | 1.25337i | 0.779273 | + | 0.626684i | \(0.215588\pi\) | ||||
−0.779273 | + | 0.626684i | \(0.784412\pi\) | |||||||
\(948\) | −7.48341 | + | 12.9617i | −0.243050 | + | 0.420975i | ||||
\(949\) | 1.16417 | − | 1.55621i | 0.0377906 | − | 0.0505168i | ||||
\(950\) | 12.9209 | + | 22.3797i | 0.419210 | + | 0.726093i | ||||
\(951\) | −7.46430 | − | 4.30951i | −0.242046 | − | 0.139746i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.6505 | + | 23.6433i | 0.442182 | + | 0.765882i | 0.997851 | − | 0.0655217i | \(-0.0208711\pi\) |
−0.555669 | + | 0.831404i | \(0.687538\pi\) | |||||||
\(954\) | −3.30330 | + | 1.90716i | −0.106948 | + | 0.0617466i | ||||
\(955\) | 22.0825i | 0.714572i | ||||||||
\(956\) | 0.311564i | 0.0100767i | ||||||||
\(957\) | 18.8683 | − | 10.8936i | 0.609924 | − | 0.352140i | ||||
\(958\) | 0.0926079 | + | 0.160402i | 0.00299203 | + | 0.00518234i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.78914 | + | 1.03296i | 0.0577442 | + | 0.0333386i | ||||
\(961\) | −15.1189 | − | 26.1867i | −0.487706 | − | 0.844731i | ||||
\(962\) | −0.0616009 | + | 0.516644i | −0.00198609 | + | 0.0166573i | ||||
\(963\) | −15.3440 | + | 26.5766i | −0.494453 | + | 0.856418i | ||||
\(964\) | − | 25.2995i | − | 0.814843i | ||||||
\(965\) | 5.51966 | − | 9.56034i | 0.177684 | − | 0.307758i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 25.2494i | − | 0.811966i | −0.913881 | − | 0.405983i | \(-0.866929\pi\) | ||
0.913881 | − | 0.405983i | \(-0.133071\pi\) | |||||||
\(968\) | 6.76452 | + | 3.90550i | 0.217420 | + | 0.125527i | ||||
\(969\) | 71.6301i | 2.30109i | ||||||||
\(970\) | −9.14264 | − | 5.27851i | −0.293553 | − | 0.169483i | ||||
\(971\) | −3.28682 | + | 5.69294i | −0.105479 | + | 0.182695i | −0.913934 | − | 0.405863i | \(-0.866971\pi\) |
0.808455 | + | 0.588558i | \(0.200304\pi\) | |||||||
\(972\) | 9.66031 | − | 16.7321i | 0.309854 | − | 0.536684i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.2308 | −1.00070 | ||||||||
\(975\) | −4.09408 | + | 34.3369i | −0.131116 | + | 1.09966i | ||||
\(976\) | 4.16720 | − | 7.21780i | 0.133389 | − | 0.231036i | ||||
\(977\) | −12.0773 | + | 6.97285i | −0.386388 | + | 0.223081i | −0.680594 | − | 0.732661i | \(-0.738278\pi\) |
0.294206 | + | 0.955742i | \(0.404945\pi\) | |||||||
\(978\) | −46.5440 | −1.48831 | ||||||||
\(979\) | −16.8972 | − | 29.2667i | −0.540036 | − | 0.935369i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.96151 | − | 5.75128i | 0.318047 | − | 0.183624i | ||||
\(982\) | −23.2504 | − | 13.4236i | −0.741949 | − | 0.428365i | ||||
\(983\) | 40.8235 | + | 23.5695i | 1.30207 | + | 0.751750i | 0.980759 | − | 0.195224i | \(-0.0625435\pi\) |
0.321310 | + | 0.946974i | \(0.395877\pi\) | |||||||
\(984\) | −9.15521 | −0.291857 | ||||||||
\(985\) | −4.92180 | −0.156821 | ||||||||
\(986\) | −9.62054 | − | 5.55442i | −0.306380 | − | 0.176889i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.3310 | + | 17.8203i | −0.424115 | + | 0.566939i | ||||
\(989\) | −32.5730 | − | 56.4180i | −1.03576 | − | 1.79399i | ||||
\(990\) | −7.61385 | + | 4.39586i | −0.241984 | + | 0.139710i | ||||
\(991\) | −4.70805 | − | 8.15458i | −0.149556 | − | 0.259039i | 0.781507 | − | 0.623896i | \(-0.214451\pi\) |
−0.931063 | + | 0.364857i | \(0.881118\pi\) | |||||||
\(992\) | 0.436531 | − | 0.756094i | 0.0138599 | − | 0.0240060i | ||||
\(993\) | 73.8223i | 2.34268i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0100 | − | 5.77927i | 0.317338 | − | 0.183215i | ||||
\(996\) | 26.2563 | − | 15.1591i | 0.831963 | − | 0.480334i | ||||
\(997\) | −40.5215 | −1.28333 | −0.641664 | − | 0.766986i | \(-0.721755\pi\) | ||||
−0.641664 | + | 0.766986i | \(0.721755\pi\) | |||||||
\(998\) | 7.64346 | + | 13.2389i | 0.241950 | + | 0.419069i | ||||
\(999\) | − | 0.248690i | − | 0.00786821i |
(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 | 1274.2.o.e.459.3 | 12 | ||
7.2 | even | 3 | 1274.2.v.d.667.1 | 12 | |||
7.3 | odd | 6 | 182.2.m.b.43.4 | ✓ | 12 | ||
7.4 | even | 3 | 1274.2.m.c.589.6 | 12 | |||
7.5 | odd | 6 | 1274.2.v.e.667.3 | 12 | |||
7.6 | odd | 2 | 1274.2.o.d.459.1 | 12 | |||
13.10 | even | 6 | 1274.2.v.d.361.1 | 12 | |||
21.17 | even | 6 | 1638.2.bj.g.1135.2 | 12 | |||
28.3 | even | 6 | 1456.2.cc.d.225.5 | 12 | |||
91.10 | odd | 6 | 182.2.m.b.127.4 | yes | 12 | ||
91.17 | odd | 6 | 2366.2.d.r.337.11 | 12 | |||
91.23 | even | 6 | inner | 1274.2.o.e.569.6 | 12 | ||
91.45 | even | 12 | 2366.2.a.bf.1.5 | 6 | |||
91.59 | even | 12 | 2366.2.a.bh.1.5 | 6 | |||
91.62 | odd | 6 | 1274.2.v.e.361.3 | 12 | |||
91.75 | odd | 6 | 1274.2.o.d.569.4 | 12 | |||
91.87 | odd | 6 | 2366.2.d.r.337.5 | 12 | |||
91.88 | even | 6 | 1274.2.m.c.491.6 | 12 | |||
273.101 | even | 6 | 1638.2.bj.g.127.2 | 12 | |||
364.283 | even | 6 | 1456.2.cc.d.673.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.m.b.43.4 | ✓ | 12 | 7.3 | odd | 6 | ||
182.2.m.b.127.4 | yes | 12 | 91.10 | odd | 6 | ||
1274.2.m.c.491.6 | 12 | 91.88 | even | 6 | |||
1274.2.m.c.589.6 | 12 | 7.4 | even | 3 | |||
1274.2.o.d.459.1 | 12 | 7.6 | odd | 2 | |||
1274.2.o.d.569.4 | 12 | 91.75 | odd | 6 | |||
1274.2.o.e.459.3 | 12 | 1.1 | even | 1 | trivial | ||
1274.2.o.e.569.6 | 12 | 91.23 | even | 6 | inner | ||
1274.2.v.d.361.1 | 12 | 13.10 | even | 6 | |||
1274.2.v.d.667.1 | 12 | 7.2 | even | 3 | |||
1274.2.v.e.361.3 | 12 | 91.62 | odd | 6 | |||
1274.2.v.e.667.3 | 12 | 7.5 | odd | 6 | |||
1456.2.cc.d.225.5 | 12 | 28.3 | even | 6 | |||
1456.2.cc.d.673.5 | 12 | 364.283 | even | 6 | |||
1638.2.bj.g.127.2 | 12 | 273.101 | even | 6 | |||
1638.2.bj.g.1135.2 | 12 | 21.17 | even | 6 | |||
2366.2.a.bf.1.5 | 6 | 91.45 | even | 12 | |||
2366.2.a.bh.1.5 | 6 | 91.59 | even | 12 | |||
2366.2.d.r.337.5 | 12 | 91.87 | odd | 6 | |||
2366.2.d.r.337.11 | 12 | 91.17 | odd | 6 |