Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,2,Mod(9,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.n (of order \(8\), degree \(4\), 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: | \(1.08596546749\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.121 |
Dual form | 136.2.n.a.9.1 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.70711 | + | 0.707107i | −0.985599 | + | 0.408248i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) |
−0.169102 | + | 0.985599i | \(0.554087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.292893 | + | 0.707107i | 0.130986 | + | 0.316228i | 0.975742 | − | 0.218924i | \(-0.0702546\pi\) |
−0.844756 | + | 0.535151i | \(0.820255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.70711 | + | 4.12132i | −0.645226 | + | 1.55771i | 0.174314 | + | 0.984690i | \(0.444229\pi\) |
−0.819540 | + | 0.573023i | \(0.805771\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.292893 | − | 0.292893i | 0.0976311 | − | 0.0976311i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.70711 | + | 0.707107i | 0.514712 | + | 0.213201i | 0.624892 | − | 0.780711i | \(-0.285143\pi\) |
−0.110180 | + | 0.993912i | \(0.535143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | − | 1.00000i | −0.258199 | − | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 4.00000i | 0.242536 | + | 0.970143i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.41421 | − | 4.41421i | −1.01269 | − | 1.01269i | −0.999918 | − | 0.0127716i | \(-0.995935\pi\) |
−0.0127716 | − | 0.999918i | \(-0.504065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 8.24264i | − | 1.79869i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.53553 | + | 1.87868i | 0.945724 | + | 0.391732i | 0.801622 | − | 0.597831i | \(-0.203971\pi\) |
0.144102 | + | 0.989563i | \(0.453971\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.12132 | − | 3.12132i | 0.624264 | − | 0.624264i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.82843 | − | 4.41421i | 0.351881 | − | 0.849516i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.878680 | − | 2.12132i | −0.163167 | − | 0.393919i | 0.821057 | − | 0.570846i | \(-0.193385\pi\) |
−0.984224 | + | 0.176926i | \(0.943385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.12132 | − | 2.12132i | 0.919816 | − | 0.381000i | 0.128010 | − | 0.991773i | \(-0.459141\pi\) |
0.791806 | + | 0.610772i | \(0.209141\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.41421 | −0.594338 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.41421 | −0.577107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.70711 | − | 0.707107i | 0.280647 | − | 0.116248i | −0.237920 | − | 0.971285i | \(-0.576466\pi\) |
0.518567 | + | 0.855037i | \(0.326466\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.70711 | + | 8.94975i | −0.578953 | + | 1.39772i | 0.314801 | + | 0.949158i | \(0.398062\pi\) |
−0.893754 | + | 0.448558i | \(0.851938\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.24264 | + | 1.24264i | −0.189501 | + | 0.189501i | −0.795480 | − | 0.605979i | \(-0.792781\pi\) |
0.605979 | + | 0.795480i | \(0.292781\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.292893 | + | 0.121320i | 0.0436619 | + | 0.0180854i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.17157i | 1.04608i | 0.852308 | + | 0.523041i | \(0.175202\pi\) | ||||
−0.852308 | + | 0.523041i | \(0.824798\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.12132 | − | 9.12132i | −1.30305 | − | 1.30305i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.53553 | − | 6.12132i | −0.635102 | − | 0.857156i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.82843 | + | 7.82843i | 1.07532 | + | 1.07532i | 0.996922 | + | 0.0783948i | \(0.0249795\pi\) |
0.0783948 | + | 0.996922i | \(0.475021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41421i | 0.190693i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.6569 | + | 4.41421i | 1.41153 | + | 0.584677i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.41421 | − | 8.41421i | 1.09544 | − | 1.09544i | 0.100500 | − | 0.994937i | \(-0.467956\pi\) |
0.994937 | − | 0.100500i | \(-0.0320443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.87868 | + | 11.7782i | −0.624651 | + | 1.50804i | 0.221535 | + | 0.975152i | \(0.428893\pi\) |
−0.846186 | + | 0.532888i | \(0.821107\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.707107 | + | 1.70711i | 0.0890871 | + | 0.215075i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.65685 | −0.202417 | −0.101208 | − | 0.994865i | \(-0.532271\pi\) | ||||
−0.101208 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.07107 | −1.09203 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.29289 | − | 0.949747i | 0.272116 | − | 0.112714i | −0.242453 | − | 0.970163i | \(-0.577952\pi\) |
0.514569 | + | 0.857449i | \(0.327952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.36396 | − | 12.9497i | −0.627804 | − | 1.51565i | −0.842345 | − | 0.538938i | \(-0.818826\pi\) |
0.214541 | − | 0.976715i | \(-0.431174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.12132 | + | 7.53553i | −0.360419 | + | 0.870129i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.82843 | + | 5.82843i | −0.664211 | + | 0.664211i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5355 | + | 5.19239i | 1.41036 | + | 0.584189i | 0.952418 | − | 0.304794i | \(-0.0985876\pi\) |
0.457939 | + | 0.888983i | \(0.348588\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.0711i | 1.11901i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.24264 | + | 1.24264i | 0.136398 | + | 0.136398i | 0.772009 | − | 0.635612i | \(-0.219252\pi\) |
−0.635612 | + | 0.772009i | \(0.719252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.53553 | + | 1.87868i | −0.275017 | + | 0.203771i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | + | 3.00000i | 0.321634 | + | 0.321634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.65685i | − | 1.02362i | −0.859097 | − | 0.511812i | \(-0.828974\pi\) | ||
0.859097 | − | 0.511812i | \(-0.171026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.24264 | + | 7.24264i | −0.751027 | + | 0.751027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.82843 | − | 4.41421i | 0.187593 | − | 0.452889i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.778175 | + | 1.87868i | 0.0790117 | + | 0.190751i | 0.958449 | − | 0.285263i | \(-0.0920810\pi\) |
−0.879438 | + | 0.476014i | \(0.842081\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.707107 | − | 0.292893i | 0.0710669 | − | 0.0294369i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6569 | −1.34565 | −0.672825 | − | 0.739802i | \(-0.734919\pi\) | ||||
−0.672825 | + | 0.739802i | \(0.734919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.82843 | − | 2.41421i | 0.568796 | − | 0.235603i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.636039 | − | 1.53553i | −0.0614882 | − | 0.148446i | 0.890149 | − | 0.455669i | \(-0.150600\pi\) |
−0.951637 | + | 0.307224i | \(0.900600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.77817 | − | 11.5355i | 0.457666 | − | 1.10490i | −0.511674 | − | 0.859180i | \(-0.670974\pi\) |
0.969340 | − | 0.245724i | \(-0.0790257\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.41421 | + | 2.41421i | −0.229147 | + | 0.229147i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.12132 | − | 0.464466i | −0.105485 | − | 0.0436933i | 0.329317 | − | 0.944219i | \(-0.393182\pi\) |
−0.434802 | + | 0.900526i | \(0.643182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.75736i | 0.350376i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.1924 | − | 2.70711i | −1.66769 | − | 0.248160i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.36396 | − | 5.36396i | −0.487633 | − | 0.487633i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 17.8995i | − | 1.61394i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.65685 | + | 2.75736i | 0.595407 | + | 0.246626i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.24264 | − | 7.24264i | 0.642680 | − | 0.642680i | −0.308533 | − | 0.951214i | \(-0.599838\pi\) |
0.951214 | + | 0.308533i | \(0.0998381\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.24264 | − | 3.00000i | 0.109408 | − | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.636039 | − | 1.53553i | −0.0555710 | − | 0.134160i | 0.893656 | − | 0.448753i | \(-0.148132\pi\) |
−0.949227 | + | 0.314593i | \(0.898132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.7279 | − | 10.6569i | 2.23089 | − | 0.924066i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.65685 | 0.314732 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.0000 | 1.19610 | 0.598050 | − | 0.801459i | \(-0.295942\pi\) | ||||
0.598050 | + | 0.801459i | \(0.295942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.1924 | + | 7.53553i | −1.54306 | + | 0.639156i | −0.982044 | − | 0.188651i | \(-0.939589\pi\) |
−0.561014 | + | 0.827806i | \(0.689589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.07107 | − | 12.2426i | −0.427061 | − | 1.03102i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.24264 | − | 1.24264i | 0.103196 | − | 0.103196i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22.0208 | + | 9.12132i | 1.81625 | + | 0.752314i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 17.6569i | − | 1.44651i | −0.690583 | − | 0.723253i | \(-0.742646\pi\) | ||
0.690583 | − | 0.723253i | \(-0.257354\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0710678 | + | 0.0710678i | 0.00578342 | + | 0.00578342i | 0.709993 | − | 0.704209i | \(-0.248698\pi\) |
−0.704209 | + | 0.709993i | \(0.748698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.46447 | + | 0.878680i | 0.118395 | + | 0.0710370i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.00000 | + | 3.00000i | 0.240966 | + | 0.240966i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.31371i | − | 0.583697i | −0.956464 | − | 0.291849i | \(-0.905730\pi\) | ||
0.956464 | − | 0.291849i | \(-0.0942704\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.8995 | − | 7.82843i | −1.49883 | − | 0.620835i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.4853 | + | 15.4853i | −1.22041 | + | 1.22041i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.70711 | + | 13.7782i | −0.447015 | + | 1.07919i | 0.526420 | + | 0.850225i | \(0.323534\pi\) |
−0.973435 | + | 0.228965i | \(0.926466\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.00000 | − | 2.41421i | −0.0778499 | − | 0.187946i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.70711 | + | 0.707107i | −0.132100 | + | 0.0547176i | −0.447754 | − | 0.894157i | \(-0.647776\pi\) |
0.315654 | + | 0.948874i | \(0.397776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.58579 | −0.197740 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.7782 | + | 9.43503i | −1.73179 | + | 0.717332i | −0.732460 | + | 0.680810i | \(0.761628\pi\) |
−0.999333 | + | 0.0365215i | \(0.988372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.53553 | + | 18.1924i | 0.569633 | + | 1.37522i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.41421 | + | 20.3137i | −0.632451 | + | 1.52687i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.89949 | + | 6.89949i | −0.515692 | + | 0.515692i | −0.916265 | − | 0.400573i | \(-0.868811\pi\) |
0.400573 | + | 0.916265i | \(0.368811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.12132 | − | 0.464466i | −0.0833471 | − | 0.0345235i | 0.340620 | − | 0.940201i | \(-0.389363\pi\) |
−0.423967 | + | 0.905677i | \(0.639363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 23.5563i | − | 1.74134i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | + | 1.00000i | 0.0735215 | + | 0.0735215i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.12132 | + | 7.53553i | −0.0819991 | + | 0.551053i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.0711 | + | 15.0711i | 1.09626 | + | 1.09626i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.17157i | − | 0.229487i | −0.993395 | − | 0.114743i | \(-0.963395\pi\) | ||
0.993395 | − | 0.114743i | \(-0.0366046\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.70711 | + | 0.707107i | 0.122880 | + | 0.0508987i | 0.443276 | − | 0.896385i | \(-0.353816\pi\) |
−0.320396 | + | 0.947284i | \(0.603816\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.36396 | + | 3.29289i | −0.0971782 | + | 0.234609i | −0.964991 | − | 0.262282i | \(-0.915525\pi\) |
0.867813 | + | 0.496891i | \(0.165525\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.22183 | + | 12.6066i | 0.370165 | + | 0.893658i | 0.993722 | + | 0.111880i | \(0.0356872\pi\) |
−0.623556 | + | 0.781778i | \(0.714313\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.82843 | − | 1.17157i | 0.199502 | − | 0.0826364i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.2426 | 0.718892 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.41421 | −0.517831 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.87868 | − | 0.778175i | 0.130577 | − | 0.0540869i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.41421 | − | 10.6569i | −0.305338 | − | 0.737150i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.80761 | − | 14.0208i | 0.399812 | − | 0.965233i | −0.587898 | − | 0.808935i | \(-0.700044\pi\) |
0.987710 | − | 0.156297i | \(-0.0499558\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.24264 | + | 3.24264i | −0.222182 | + | 0.222182i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.24264 | − | 0.514719i | −0.0847474 | − | 0.0351035i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.7279i | 1.67864i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.3137 | + | 18.3137i | 1.23753 | + | 1.23753i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.58579 | − | 9.58579i | −0.641912 | − | 0.641912i | 0.309113 | − | 0.951025i | \(-0.399968\pi\) |
−0.951025 | + | 0.309113i | \(0.899968\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 1.82843i | − | 0.121895i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.3640 | + | 4.70711i | 0.754253 | + | 0.312422i | 0.726475 | − | 0.687192i | \(-0.241157\pi\) |
0.0277772 | + | 0.999614i | \(0.491157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 7.00000i | −0.462573 | + | 0.462573i | −0.899498 | − | 0.436925i | \(-0.856068\pi\) |
0.436925 | + | 0.899498i | \(0.356068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.82843 | − | 14.0711i | 0.383482 | − | 0.925808i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.53553 | − | 15.7782i | −0.428157 | − | 1.03366i | −0.979871 | − | 0.199629i | \(-0.936026\pi\) |
0.551714 | − | 0.834033i | \(-0.313974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.07107 | + | 2.10051i | −0.330800 | + | 0.137022i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −25.0711 | −1.62854 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.36396 | − | 3.05025i | 0.474354 | − | 0.196484i | −0.132681 | − | 0.991159i | \(-0.542359\pi\) |
0.607035 | + | 0.794675i | \(0.292359\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.63604 | − | 3.94975i | −0.104952 | − | 0.253376i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.77817 | − | 9.12132i | 0.241379 | − | 0.582740i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.00000 | − | 1.24264i | −0.190117 | − | 0.0787492i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.82843i | − | 0.304768i | −0.988321 | − | 0.152384i | \(-0.951305\pi\) | ||
0.988321 | − | 0.152384i | \(-0.0486950\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.41421 | + | 6.41421i | 0.403258 | + | 0.403258i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.00000 | − | 5.00000i | 0.187867 | − | 0.313112i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.171573 | − | 0.171573i | −0.0107024 | − | 0.0107024i | 0.701735 | − | 0.712438i | \(-0.252409\pi\) |
−0.712438 | + | 0.701735i | \(0.752409\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.24264i | 0.512173i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.878680 | − | 0.363961i | −0.0543889 | − | 0.0225286i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.2426 | − | 11.2426i | 0.693251 | − | 0.693251i | −0.269695 | − | 0.962946i | \(-0.586923\pi\) |
0.962946 | + | 0.269695i | \(0.0869228\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.24264 | + | 7.82843i | −0.199194 | + | 0.480896i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.82843 | + | 16.4853i | 0.417893 | + | 1.00888i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.36396 | − | 3.05025i | 0.448989 | − | 0.185977i | −0.146720 | − | 0.989178i | \(-0.546871\pi\) |
0.595708 | + | 0.803201i | \(0.296871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.3137 | 0.687259 | 0.343629 | − | 0.939105i | \(-0.388344\pi\) | ||||
0.343629 | + | 0.939105i | \(0.388344\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.53553 | − | 3.12132i | 0.454410 | − | 0.188223i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.46447 | + | 3.53553i | 0.0879912 | + | 0.212430i | 0.961749 | − | 0.273931i | \(-0.0883241\pi\) |
−0.873758 | + | 0.486361i | \(0.838324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.878680 | − | 2.12132i | 0.0526052 | − | 0.127000i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.3137 | − | 20.3137i | 1.21181 | − | 1.21181i | 0.241385 | − | 0.970429i | \(-0.422398\pi\) |
0.970429 | − | 0.241385i | \(-0.0776016\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.9497 | − | 8.26346i | −1.18589 | − | 0.491211i | −0.299475 | − | 0.954104i | \(-0.596812\pi\) |
−0.886414 | + | 0.462893i | \(0.846812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.82843i | 0.522951i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.5563 | − | 30.5563i | −1.80368 | − | 1.80368i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | + | 8.00000i | −0.882353 | + | 0.470588i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.65685 | − | 2.65685i | −0.155748 | − | 0.155748i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.3137i | 0.894636i | 0.894375 | + | 0.447318i | \(0.147621\pi\) | ||||
−0.894375 | + | 0.447318i | \(0.852379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.41421 | + | 3.48528i | 0.489894 | + | 0.202921i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.24264 | − | 6.24264i | 0.362235 | − | 0.362235i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | − | 7.24264i | −0.172917 | − | 0.417459i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.0711 | + | 7.07107i | −0.980707 | + | 0.406222i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.75736 | −0.558705 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6274 | 1.06312 | 0.531561 | − | 0.847020i | \(-0.321605\pi\) | ||||
0.531561 | + | 0.847020i | \(0.321605\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.3137 | − | 9.65685i | 1.32627 | − | 0.549359i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.29289 | − | 5.53553i | −0.130018 | − | 0.313891i | 0.845442 | − | 0.534067i | \(-0.179337\pi\) |
−0.975460 | + | 0.220176i | \(0.929337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.94975 | − | 14.3640i | 0.336300 | − | 0.811899i | −0.661765 | − | 0.749711i | \(-0.730192\pi\) |
0.998064 | − | 0.0621876i | \(-0.0198077\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | + | 1.00000i | −0.0563436 | + | 0.0563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.9497 | − | 6.60660i | −0.895827 | − | 0.371064i | −0.113213 | − | 0.993571i | \(-0.536114\pi\) |
−0.782614 | + | 0.622507i | \(0.786114\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.24264i | − | 0.237542i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.17157 | + | 2.17157i | 0.121205 | + | 0.121205i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.2426 | − | 22.0711i | 0.736840 | − | 1.22807i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.0711i | 1.27583i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.5563 | − | 12.2426i | −1.62949 | − | 0.674959i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.7279 | − | 15.7279i | 0.864485 | − | 0.864485i | −0.127370 | − | 0.991855i | \(-0.540654\pi\) |
0.991855 | + | 0.127370i | \(0.0406537\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.292893 | − | 0.707107i | 0.0160504 | − | 0.0387492i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.485281 | − | 1.17157i | −0.0265138 | − | 0.0640099i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.94975 | + | 1.63604i | −0.215156 | + | 0.0891207i | −0.487658 | − | 0.873034i | \(-0.662149\pi\) |
0.272502 | + | 0.962155i | \(0.412149\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.24264 | 0.121804 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2426 | 0.554670 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.3137 | − | 10.0711i | 1.31282 | − | 0.543787i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.65685 | − | 6.41421i | −0.143040 | − | 0.345330i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.36396 | + | 17.7782i | −0.395318 | + | 0.954382i | 0.593443 | + | 0.804876i | \(0.297768\pi\) |
−0.988761 | + | 0.149506i | \(0.952232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.48528 | − | 1.48528i | 0.0795053 | − | 0.0795053i | −0.666236 | − | 0.745741i | \(-0.732096\pi\) |
0.745741 | + | 0.666236i | \(0.232096\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.97056i | 0.477455i | 0.971087 | + | 0.238727i | \(0.0767302\pi\) | ||||
−0.971087 | + | 0.238727i | \(0.923270\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.34315 | + | 1.34315i | 0.0712868 | + | 0.0712868i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.9706 | − | 8.24264i | 1.74499 | − | 0.436247i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.72792 | + | 9.72792i | 0.513420 | + | 0.513420i | 0.915573 | − | 0.402153i | \(-0.131738\pi\) |
−0.402153 | + | 0.915573i | \(0.631738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.9706i | 1.05108i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.9497 | + | 5.36396i | 0.679685 | + | 0.281535i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.58579 | − | 7.58579i | 0.397058 | − | 0.397058i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.94975 | − | 19.1924i | 0.414973 | − | 1.00183i | −0.568809 | − | 0.822470i | \(-0.692596\pi\) |
0.983783 | − | 0.179365i | \(-0.0574043\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.53553 | + | 3.70711i | 0.0799367 | + | 0.192984i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −45.6274 | + | 18.8995i | −2.36886 | + | 0.981213i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.9411 | −1.65385 | −0.826924 | − | 0.562313i | \(-0.809912\pi\) | ||||
−0.826924 | + | 0.562313i | \(0.809912\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.3137 | −0.687517 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.05025 | + | 9.77817i | 0.208047 | + | 0.502271i | 0.993116 | − | 0.117138i | \(-0.0373721\pi\) |
−0.785068 | + | 0.619409i | \(0.787372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.24264 | + | 17.4853i | −0.371052 | + | 0.895798i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.4142 | + | 10.4142i | −0.532141 | + | 0.532141i | −0.921209 | − | 0.389068i | \(-0.872797\pi\) |
0.389068 | + | 0.921209i | \(0.372797\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.82843 | − | 2.41421i | −0.297044 | − | 0.123040i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.727922i | 0.0370024i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.31371 | − | 2.31371i | −0.117310 | − | 0.117310i | 0.646015 | − | 0.763325i | \(-0.276434\pi\) |
−0.763325 | + | 0.646015i | \(0.776434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.97918 | + | 20.0208i | −0.150664 | + | 1.01250i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.17157 | + | 2.17157i | 0.109541 | + | 0.109541i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.3848i | 0.522515i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.87868 | + | 2.84924i | 0.345231 | + | 0.142999i | 0.548560 | − | 0.836111i | \(-0.315176\pi\) |
−0.203329 | + | 0.979110i | \(0.565176\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −36.3848 | + | 36.3848i | −1.82152 | + | 1.82152i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.979185 | − | 2.36396i | 0.0488982 | − | 0.118051i | −0.897543 | − | 0.440927i | \(-0.854650\pi\) |
0.946441 | + | 0.322876i | \(0.104650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.12132 | + | 2.94975i | −0.353861 | + | 0.146574i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.41421 | 0.169236 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.8995 | + | 9.89949i | −1.17888 | + | 0.488306i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.3137 | + | 49.0416i | 0.999572 | + | 2.41318i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.514719 | + | 1.24264i | −0.0252665 | + | 0.0609988i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.7279 | − | 25.7279i | 1.25990 | − | 1.25990i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.53553 | + | 1.87868i | 0.221575 | + | 0.0917795i | 0.490710 | − | 0.871323i | \(-0.336738\pi\) |
−0.269134 | + | 0.963103i | \(0.586738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3137i | 0.551396i | 0.961244 | + | 0.275698i | \(0.0889090\pi\) | ||||
−0.961244 | + | 0.275698i | \(0.911091\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.10051 | + | 2.10051i | 0.102130 | + | 0.102130i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.6066 | + | 9.36396i | 0.757031 | + | 0.454219i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.2132 | − | 40.2132i | −1.94605 | − | 1.94605i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.12132 | − | 2.12132i | −0.246685 | − | 0.102180i | 0.255915 | − | 0.966699i | \(-0.417623\pi\) |
−0.502600 | + | 0.864519i | \(0.667623\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.82843 | + | 1.82843i | −0.0878686 | + | 0.0878686i | −0.749675 | − | 0.661806i | \(-0.769790\pi\) |
0.661806 | + | 0.749675i | \(0.269790\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.24264 | + | 3.00000i | −0.0595801 | + | 0.143839i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.7279 | − | 28.3137i | −0.561023 | − | 1.35443i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6066 | − | 7.29289i | 0.840317 | − | 0.348071i | 0.0793386 | − | 0.996848i | \(-0.474719\pi\) |
0.760979 | + | 0.648777i | \(0.224719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.34315 | −0.254436 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.2843 | 0.773689 | 0.386845 | − | 0.922145i | \(-0.373565\pi\) | ||||
0.386845 | + | 0.922145i | \(0.373565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.82843 | − | 2.82843i | 0.323698 | − | 0.134080i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4853 | + | 30.1421i | 0.590534 | + | 1.42567i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.46447 | − | 22.8492i | 0.446656 | − | 1.07832i | −0.526911 | − | 0.849920i | \(-0.676650\pi\) |
0.973567 | − | 0.228402i | \(-0.0733501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.6569 | + | 12.6569i | −0.595988 | + | 0.595988i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.171573 | − | 0.0710678i | −0.00806120 | − | 0.00333906i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.4853 | + | 13.4853i | 0.630815 | + | 0.630815i | 0.948272 | − | 0.317458i | \(-0.102829\pi\) |
−0.317458 | + | 0.948272i | \(0.602829\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.4853 | + | 2.89949i | 0.909495 | + | 0.135337i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.4853 | − | 19.4853i | −0.907520 | − | 0.907520i | 0.0885516 | − | 0.996072i | \(-0.471776\pi\) |
−0.996072 | + | 0.0885516i | \(0.971776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.14214i | − | 0.192501i | −0.995357 | − | 0.0962507i | \(-0.969315\pi\) | ||
0.995357 | − | 0.0962507i | \(-0.0306850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.24264 | − | 3.00000i | −0.335869 | − | 0.139122i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.4142 | − | 12.4142i | 0.574461 | − | 0.574461i | −0.358911 | − | 0.933372i | \(-0.616852\pi\) |
0.933372 | + | 0.358911i | \(0.116852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.82843 | − | 6.82843i | 0.130605 | − | 0.315307i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.17157 | + | 12.4853i | 0.238293 | + | 0.575291i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00000 | + | 1.24264i | −0.137940 | + | 0.0571367i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.5563 | −1.26437 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.58579 | 0.209969 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.46447 | − | 3.09188i | 0.341060 | − | 0.141272i | −0.205578 | − | 0.978641i | \(-0.565907\pi\) |
0.546638 | + | 0.837369i | \(0.315907\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.4853 | − | 37.3848i | 0.704605 | − | 1.70107i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.10051 | + | 1.10051i | −0.0499714 | + | 0.0499714i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.2635 | − | 16.2635i | −1.77920 | − | 0.736968i | −0.992876 | − | 0.119149i | \(-0.961983\pi\) |
−0.786321 | − | 0.617819i | \(-0.788017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 27.5563i | − | 1.24614i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.5858 | + | 11.5858i | 0.522859 | + | 0.522859i | 0.918434 | − | 0.395575i | \(-0.129455\pi\) |
−0.395575 | + | 0.918434i | \(0.629455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.60660 | − | 5.63604i | 0.342584 | − | 0.253834i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.414214 | + | 0.414214i | 0.0186175 | + | 0.0186175i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.0711i | 0.496605i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.4350 | − | 8.46447i | −0.914798 | − | 0.378922i | −0.124906 | − | 0.992169i | \(-0.539863\pi\) |
−0.789891 | + | 0.613247i | \(0.789863\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.41421 | − | 2.41421i | 0.107859 | − | 0.107859i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.70711 | + | 4.12132i | −0.0761161 | + | 0.183761i | −0.957357 | − | 0.288906i | \(-0.906708\pi\) |
0.881241 | + | 0.472667i | \(0.156708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.92893 | + | 7.07107i | 0.130336 | + | 0.314658i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.1924 | + | 9.19239i | −0.985599 | + | 0.408248i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.2843 | 0.810436 | 0.405218 | − | 0.914220i | \(-0.367196\pi\) | ||||
0.405218 | + | 0.914220i | \(0.367196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 62.5269 | 2.76603 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.5563 | + | 11.4142i | −1.21664 | + | 0.503950i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.00000 | − | 9.65685i | −0.176261 | − | 0.425532i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.07107 | + | 12.2426i | −0.223025 | + | 0.538431i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.2132 | − | 32.2132i | 1.41400 | − | 1.41400i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.02082 | + | 3.73654i | 0.395209 | + | 0.163701i | 0.571432 | − | 0.820649i | \(-0.306388\pi\) |
−0.176223 | + | 0.984350i | \(0.556388\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.1421i | − | 1.05566i | −0.849349 | − | 0.527831i | \(-0.823005\pi\) | ||
0.849349 | − | 0.527831i | \(-0.176995\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −25.7279 | − | 25.7279i | −1.12286 | − | 1.12286i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.6066 | + | 18.3640i | 0.592713 | + | 0.799947i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.778175 | + | 0.778175i | 0.0338337 | + | 0.0338337i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4.92893i | − | 0.213897i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.899495 | − | 0.899495i | 0.0388886 | − | 0.0388886i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.89949 | − | 16.6569i | 0.297735 | − | 0.718796i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.12132 | − | 22.0208i | −0.392883 | − | 0.948504i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.0502525 | − | 0.0208153i | 0.00216053 | − | 0.000894919i | −0.381603 | − | 0.924326i | \(-0.624628\pi\) |
0.383763 | + | 0.923431i | \(0.374628\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.24264 | 0.0962409 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.55635 | 0.409349 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.2635 | − | 6.32233i | 0.652618 | − | 0.270323i | −0.0317103 | − | 0.999497i | \(-0.510095\pi\) |
0.684329 | + | 0.729174i | \(0.260095\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.02082 | + | 4.87868i | 0.0862463 | + | 0.208217i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.48528 | + | 13.2426i | −0.233681 | + | 0.564155i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −42.7990 | + | 42.7990i | −1.82000 | + | 1.82000i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.41421 | − | 1.00000i | −0.102478 | − | 0.0424476i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 16.0000i | − | 0.677942i | −0.940797 | − | 0.338971i | \(-0.889921\pi\) | ||
0.940797 | − | 0.338971i | \(-0.110079\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.41421 | − | 13.6569i | −0.144148 | − | 0.576593i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.5858 | + | 15.5858i | 0.656863 | + | 0.656863i | 0.954636 | − | 0.297774i | \(-0.0962441\pi\) |
−0.297774 | + | 0.954636i | \(0.596244\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.928932i | − | 0.0390805i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −41.5061 | − | 17.1924i | −1.74309 | − | 0.722012i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.6569 | + | 32.6569i | −1.36905 | + | 1.36905i | −0.507244 | + | 0.861802i | \(0.669336\pi\) |
−0.861802 | + | 0.507244i | \(0.830664\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.150758 | − | 0.363961i | 0.00630901 | − | 0.0152313i | −0.920694 | − | 0.390286i | \(-0.872376\pi\) |
0.927003 | + | 0.375055i | \(0.122376\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.24264 | + | 5.41421i | 0.0936877 | + | 0.226182i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.0208 | − | 8.29289i | 0.834926 | − | 0.345838i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.41421 | −0.141890 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.24264 | + | 3.00000i | −0.300475 | + | 0.124461i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.82843 | + | 18.8995i | 0.324220 | + | 0.782737i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.7279 | − | 31.7279i | 1.30955 | − | 1.30955i | 0.387814 | − | 0.921738i | \(-0.373230\pi\) |
0.921738 | − | 0.387814i | \(-0.126770\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.9706 | − | 13.2426i | −1.31732 | − | 0.545654i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 6.58579i | − | 0.270903i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.6569 | + | 26.6569i | 1.09467 | + | 1.09467i | 0.995023 | + | 0.0996425i | \(0.0317699\pi\) |
0.0996425 | + | 0.995023i | \(0.468230\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.41421 | − | 13.6569i | −0.139969 | − | 0.559876i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.8284 | − | 17.8284i | −0.729669 | − | 0.729669i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.1716i | 1.60051i | 0.599662 | + | 0.800254i | \(0.295302\pi\) | ||||
−0.599662 | + | 0.800254i | \(0.704698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.60660 | − | 3.97918i | −0.391861 | − | 0.162314i | 0.178048 | − | 0.984022i | \(-0.443022\pi\) |
−0.569910 | + | 0.821707i | \(0.693022\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.485281 | + | 0.485281i | −0.0197622 | + | 0.0197622i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.22183 | − | 5.36396i | 0.0903300 | − | 0.218076i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.09188 | − | 5.05025i | −0.0849069 | − | 0.204983i | 0.875723 | − | 0.482813i | \(-0.160385\pi\) |
−0.960630 | + | 0.277830i | \(0.910385\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.4853 | + | 7.24264i | −0.708539 | + | 0.293487i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.68629 | −0.270057 | −0.135028 | − | 0.990842i | \(-0.543113\pi\) | ||||
−0.135028 | + | 0.990842i | \(0.543113\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.6569 | − | 5.24264i | 0.510374 | − | 0.211404i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.22183 | − | 17.4350i | −0.290740 | − | 0.701908i | 0.709256 | − | 0.704951i | \(-0.249031\pi\) |
−0.999995 | + | 0.00304356i | \(0.999031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.94975 | − | 19.1924i | 0.319527 | − | 0.771407i | −0.679752 | − | 0.733442i | \(-0.737912\pi\) |
0.999279 | − | 0.0379649i | \(-0.0120875\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.5858 | − | 16.5858i | 0.665565 | − | 0.665565i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.7990 | + | 16.4853i | 1.59451 | + | 0.660469i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 16.5563i | − | 0.662254i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.0711 | + | 15.0711i | 0.601880 | + | 0.601880i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.53553 | + | 6.12132i | 0.180844 | + | 0.244073i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.3848 | + | 19.3848i | 0.771696 | + | 0.771696i | 0.978403 | − | 0.206707i | \(-0.0662747\pi\) |
−0.206707 | + | 0.978403i | \(0.566275\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.0416i | 1.11455i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.24264 | + | 3.00000i | 0.287415 | + | 0.119051i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.393398 | − | 0.949747i | 0.0155626 | − | 0.0375714i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.1213 | + | 36.5061i | 0.597256 | + | 1.44190i | 0.876366 | + | 0.481645i | \(0.159961\pi\) |
−0.279110 | + | 0.960259i | \(0.590039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.02082 | + | 3.73654i | −0.355746 | + | 0.147355i | −0.553397 | − | 0.832918i | \(-0.686669\pi\) |
0.197651 | + | 0.980272i | \(0.436669\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.48528 | 0.0978579 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.2548 | −1.77915 | −0.889576 | − | 0.456788i | \(-0.849000\pi\) | ||||
−0.889576 | + | 0.456788i | \(0.849000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3137 | − | 8.41421i | 0.797383 | − | 0.330287i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.4853 | − | 42.2132i | −0.685302 | − | 1.65447i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.6360 | − | 25.6777i | 0.416220 | − | 1.00484i | −0.567212 | − | 0.823572i | \(-0.691978\pi\) |
0.983433 | − | 0.181273i | \(-0.0580219\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.899495 | − | 0.899495i | 0.0351462 | − | 0.0351462i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.36396 | − | 2.22183i | −0.209268 | − | 0.0866817i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 50.7696i | 1.97770i | 0.148912 | + | 0.988850i | \(0.452423\pi\) | ||||
−0.148912 | + | 0.988850i | \(0.547577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.7990 | + | 20.7990i | 0.808987 | + | 0.808987i | 0.984481 | − | 0.175494i | \(-0.0561521\pi\) |
−0.175494 | + | 0.984481i | \(0.556152\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.0711 | + | 15.0711i | 0.584431 | + | 0.584431i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.2721i | − | 0.436457i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.1421 | + | 9.58579i | 0.894727 | + | 0.370608i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.6569 | + | 16.6569i | −0.643031 | + | 0.643031i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.19239 | + | 10.1213i | −0.161605 | + | 0.390148i | −0.983852 | − | 0.178981i | \(-0.942720\pi\) |
0.822248 | + | 0.569130i | \(0.192720\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.07107 | − | 19.4853i | −0.310656 | − | 0.749989i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.0919 | + | 17.4350i | −1.61772 | + | 0.670083i | −0.993777 | − | 0.111385i | \(-0.964471\pi\) |
−0.623945 | + | 0.781468i | \(0.714471\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.07107 | −0.348116 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.7279 | −0.870936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.0208 | + | 15.3345i | −1.41656 | + | 0.586759i | −0.953994 | − | 0.299825i | \(-0.903072\pi\) |
−0.462568 | + | 0.886584i | \(0.653072\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.10051 | + | 9.89949i | 0.156672 | + | 0.378240i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.00000 | − | 16.8995i | 0.267067 | − | 0.644756i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.6066 | − | 13.9203i | −1.27846 | − | 0.529554i | −0.362931 | − | 0.931816i | \(-0.618224\pi\) |
−0.915524 | + | 0.402262i | \(0.868224\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.41421i | 0.129695i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.6569 | − | 10.6569i | −0.404238 | − | 0.404238i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.5061 | − | 5.87868i | −1.49640 | − | 0.222671i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.3137 | + | 22.3137i | 0.843982 | + | 0.843982i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.3137i | 1.93809i | 0.246880 | + | 0.969046i | \(0.420595\pi\) | ||||
−0.246880 | + | 0.969046i | \(0.579405\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6569 | − | 4.41421i | −0.401931 | − | 0.166485i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.17157 | − | 7.17157i | 0.270097 | − | 0.270097i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.0711 | + | 41.2132i | −0.642024 | + | 1.54998i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.8076 | + | 38.1630i | 0.593667 | + | 1.43324i | 0.879937 | + | 0.475091i | \(0.157585\pi\) |
−0.286270 | + | 0.958149i | \(0.592415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.19239 | − | 2.15076i | 0.194730 | − | 0.0806597i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.2132 | 1.01914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.3137 | − | 8.00000i | 0.721284 | − | 0.298765i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.05025 | + | 19.4350i | 0.300224 | + | 0.724804i | 0.999946 | + | 0.0103893i | \(0.00330708\pi\) |
−0.699722 | + | 0.714415i | \(0.746693\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.3137 | − | 56.2843i | 0.868248 | − | 2.09614i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.4142 | + | 10.4142i | −0.387309 | + | 0.387309i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.36396 | − | 3.87868i | −0.347769 | − | 0.144051i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.7990i | 0.808480i | 0.914653 | + | 0.404240i | \(0.132464\pi\) | ||||
−0.914653 | + | 0.404240i | \(0.867536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.7782 | − | 15.7782i | −0.584377 | − | 0.584377i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.21320 | − | 3.72792i | −0.229804 | − | 0.137882i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.514719 | + | 0.514719i | 0.0190116 | + | 0.0190116i | 0.716549 | − | 0.697537i | \(-0.245721\pi\) |
−0.697537 | + | 0.716549i | \(0.745721\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.2426i | 0.672890i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.82843 | − | 1.17157i | −0.104186 | − | 0.0431554i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.58579 | + | 3.58579i | −0.131905 | + | 0.131905i | −0.769977 | − | 0.638072i | \(-0.779732\pi\) |
0.638072 | + | 0.769977i | \(0.279732\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.150758 | − | 0.363961i | −0.00553076 | − | 0.0133524i | 0.921090 | − | 0.389350i | \(-0.127300\pi\) |
−0.926621 | + | 0.375997i | \(0.877300\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4853 | − | 5.17157i | 0.457425 | − | 0.189472i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.727922 | 0.0266333 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.41421 | 0.270909 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.2635 | − | 9.63604i | 0.848896 | − | 0.351624i | 0.0845408 | − | 0.996420i | \(-0.473058\pi\) |
0.764355 | + | 0.644796i | \(0.223058\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.41421 | + | 8.24264i | 0.124421 | + | 0.300379i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.0294373 | + | 0.0710678i | −0.00107133 | + | 0.00258642i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.9706 | + | 23.9706i | −0.871225 | + | 0.871225i | −0.992606 | − | 0.121381i | \(-0.961268\pi\) |
0.121381 | + | 0.992606i | \(0.461268\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.4853 | − | 6.41421i | −0.562080 | − | 0.232821i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 36.9706i | − | 1.34018i | −0.742279 | − | 0.670091i | \(-0.766255\pi\) | ||
0.742279 | − | 0.670091i | \(-0.233745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.3848 | + | 39.3848i | 1.42582 | + | 1.42582i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.192388 | + | 1.29289i | −0.00695581 | + | 0.0467447i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 35.5980i | − | 1.28370i | −0.766832 | − | 0.641848i | \(-0.778168\pi\) | ||
0.766832 | − | 0.641848i | \(-0.221832\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.414214 | + | 0.171573i | 0.0149175 | + | 0.00617905i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.2843 | − | 33.2843i | 1.19715 | − | 1.19715i | 0.222136 | − | 0.975016i | \(-0.428697\pi\) |
0.975016 | − | 0.222136i | \(-0.0713030\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.36396 | − | 22.6066i | 0.336363 | − | 0.812053i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.82843 | − | 14.0711i | −0.209094 | − | 0.504797i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 55.8701 | − | 23.1421i | 2.00175 | − | 0.829153i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.58579 | 0.164092 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.9706 | −0.392056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.17157 | − | 2.14214i | 0.184581 | − | 0.0764561i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4350 | − | 39.6777i | −0.585846 | − | 1.41436i | −0.887442 | − | 0.460920i | \(-0.847519\pi\) |
0.301596 | − | 0.953436i | \(-0.402481\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.2426 | + | 27.1421i | −0.400249 | + | 0.966286i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.82843 | − | 3.82843i | 0.136123 | − | 0.136123i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 15.6569i | − | 0.555291i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.48528 | − | 7.48528i | −0.265142 | − | 0.265142i | 0.561997 | − | 0.827139i | \(-0.310033\pi\) |
−0.827139 | + | 0.561997i | \(0.810033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.6863 | + | 7.17157i | −1.01485 | + | 0.253712i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.82843 | − | 2.82843i | −0.0999376 | − | 0.0999376i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 25.8995i | − | 0.913973i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.4853 | − | 6.41421i | −0.545784 | − | 0.226071i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.4142 | + | 10.4142i | −0.366598 | + | 0.366598i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.778175 | − | 1.87868i | 0.0273592 | − | 0.0660509i | −0.909609 | − | 0.415464i | \(-0.863619\pi\) |
0.936969 | + | 0.349413i | \(0.113619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.50610 | + | 3.63604i | 0.0528862 | + | 0.127679i | 0.948114 | − | 0.317929i | \(-0.102988\pi\) |
−0.895228 | + | 0.445608i | \(0.852988\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.3137 | + | 8.00000i | −0.677361 | + | 0.280572i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.4142 | −0.399822 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9706 | 0.383811 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.5650 | − | 42.4056i | −0.613022 | − | 1.47997i | −0.859665 | − | 0.510859i | \(-0.829327\pi\) |
0.246643 | − | 0.969106i | \(-0.420673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.77817 | − | 16.3640i | 0.236272 | − | 0.570412i | −0.760619 | − | 0.649198i | \(-0.775105\pi\) |
0.996892 | + | 0.0787865i | \(0.0251045\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.6569 | + | 10.6569i | −0.371024 | + | 0.371024i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.12132 | − | 0.464466i | −0.0389921 | − | 0.0161511i | 0.363102 | − | 0.931749i | \(-0.381718\pi\) |
−0.402094 | + | 0.915598i | \(0.631718\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 13.9411i | − | 0.484195i | −0.970252 | − | 0.242098i | \(-0.922165\pi\) | ||
0.970252 | − | 0.242098i | \(-0.0778354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.00000 | − | 5.00000i | −0.173448 | − | 0.173448i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.3640 | − | 45.6066i | 0.948105 | − | 1.58018i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.00000 | − | 1.00000i | −0.0346064 | − | 0.0346064i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 26.4853i | − | 0.915465i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.636039 | − | 0.263456i | −0.0219585 | − | 0.00909551i | 0.371677 | − | 0.928362i | \(-0.378783\pi\) |
−0.393636 | + | 0.919267i | \(0.628783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.7782 | − | 16.7782i | 0.578558 | − | 0.578558i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.3137 | + | 49.0416i | −0.699641 | + | 1.68908i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.80761 | + | 9.19239i | 0.130986 | + | 0.316228i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.2635 | − | 12.9497i | 1.07423 | − | 0.444959i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 39.8995 | 1.36935 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.07107 | 0.310952 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.9497 | + | 6.60660i | −0.546109 | + | 0.226206i | −0.638642 | − | 0.769504i | \(-0.720504\pi\) |
0.0925332 | + | 0.995710i | \(0.470504\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.757359 | − | 1.82843i | −0.0259011 | − | 0.0625309i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.36396 | + | 12.9497i | −0.183229 | + | 0.442355i | −0.988629 | − | 0.150378i | \(-0.951951\pi\) |
0.805399 | + | 0.592733i | \(0.201951\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.27208 | + | 4.27208i | −0.145761 | + | 0.145761i | −0.776222 | − | 0.630460i | \(-0.782866\pi\) |
0.630460 | + | 0.776222i | \(0.282866\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 73.7696 | + | 30.5563i | 2.51406 | + | 1.04136i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 44.1421i | − | 1.50262i | −0.659952 | − | 0.751308i | \(-0.729423\pi\) | ||
0.659952 | − | 0.751308i | \(-0.270577\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.3431 | − | 13.3431i | −0.453681 | − | 0.453681i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.9497 | − | 24.2635i | 0.677529 | − | 0.824030i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.7279 | + | 17.7279i | 0.601379 | + | 0.601379i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.778175 | + | 0.322330i | 0.0263372 | + | 0.0109092i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.7279 | + | 22.7279i | −0.768344 | + | 0.768344i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.77817 | − | 21.1924i | 0.296418 | − | 0.715616i | −0.703570 | − | 0.710626i | \(-0.748412\pi\) |
0.999988 | − | 0.00498980i | \(-0.00158831\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.8284 | − | 26.1421i | −0.365234 | − | 0.881752i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.2635 | + | 9.63604i | −0.783766 | + | 0.324646i | −0.738434 | − | 0.674326i | \(-0.764434\pi\) |
−0.0453316 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.2548 | −1.65756 | −0.828779 | − | 0.559577i | \(-0.810964\pi\) | ||||
−0.828779 | + | 0.559577i | \(0.810964\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.8284 | −0.565681 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.8492 | + | 9.87868i | −0.800779 | + | 0.331694i | −0.745268 | − | 0.666764i | \(-0.767679\pi\) |
−0.0555107 | + | 0.998458i | \(0.517679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.4853 | + | 42.2132i | 0.586438 | + | 1.41579i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.12132 | + | 17.1924i | −0.238573 | + | 0.575967i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31.6569 | − | 31.6569i | 1.05936 | − | 1.05936i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.89949 | − | 2.85786i | −0.230625 | − | 0.0955279i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.00000 | − | 9.00000i | −0.300167 | − | 0.300167i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.4853 | + | 39.1421i | −0.782408 | + | 1.30401i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.2426 | + | 10.2426i | 0.340854 | + | 0.340854i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 0.928932i | − | 0.0308788i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.0208 | + | 13.6777i | 1.09644 | + | 0.454160i | 0.856247 | − | 0.516566i | \(-0.172790\pi\) |
0.240191 | + | 0.970726i | \(0.422790\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.92893 | − | 2.92893i | 0.0971465 | − | 0.0971465i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9203 | − | 40.8492i | 0.560595 | − | 1.35340i | −0.348696 | − | 0.937236i | \(-0.613376\pi\) |
0.909291 | − | 0.416160i | \(-0.136624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.24264 | + | 3.00000i | 0.0411254 | + | 0.0992855i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.6569 | − | 6.89949i | 0.550659 | − | 0.228090i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.41421 | 0.244839 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.2843 | −0.405221 | −0.202610 | − | 0.979259i | \(-0.564942\pi\) | ||||
−0.202610 | + | 0.979259i | \(0.564942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.7990 | + | 13.1716i | −1.04781 | + | 0.434018i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.12132 | − | 7.53553i | 0.102628 | − | 0.247767i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | + | 4.00000i | −0.131377 | + | 0.131377i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3640 | + | 9.67767i | 0.766547 | + | 0.317514i | 0.731473 | − | 0.681871i | \(-0.238833\pi\) |
0.0350740 | + | 0.999385i | \(0.488833\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 80.5269i | 2.63916i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.82843 | + | 7.82843i | 0.256291 | + | 0.256291i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.65685 | + | 1.41421i | −0.184999 | + | 0.0462497i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.3137 | − | 22.3137i | −0.728957 | − | 0.728957i | 0.241455 | − | 0.970412i | \(-0.422375\pi\) |
−0.970412 | + | 0.241455i | \(0.922375\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.7279i | 0.937500i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.9203 | − | 11.9792i | −0.942775 | − | 0.390510i | −0.142264 | − | 0.989829i | \(-0.545438\pi\) |
−0.800511 | + | 0.599318i | \(0.795438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.6274 | + | 33.6274i | −1.09506 | + | 1.09506i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.24264 | + | 15.0711i | −0.203073 | + | 0.490262i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.49390 | − | 15.6777i | −0.211024 | − | 0.509456i | 0.782558 | − | 0.622578i | \(-0.213915\pi\) |
−0.993581 | + | 0.113122i | \(0.963915\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.8995 | 1.03441 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.0000 | −1.61966 | −0.809829 | − | 0.586665i | \(-0.800440\pi\) | ||||
−0.809829 | + | 0.586665i | \(0.800440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.24264 | − | 0.928932i | 0.0725701 | − | 0.0300595i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.00000 | + | 7.24264i | 0.0969762 | + | 0.234121i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.8995 | + | 57.6985i | −0.771755 | + | 1.86318i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.192388 | + | 0.192388i | −0.00620607 | + | 0.00620607i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.636039 | − | 0.263456i | −0.0204961 | − | 0.00848975i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.41421i | 0.0455251i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.5858 | − | 21.5858i | −0.694152 | − | 0.694152i | 0.268991 | − | 0.963143i | \(-0.413310\pi\) |
−0.963143 | + | 0.268991i | \(0.913310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.00000 | + | 47.0416i | −0.224872 | + | 1.51119i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.6985 | − | 20.6985i | −0.664246 | − | 0.664246i | 0.292132 | − | 0.956378i | \(-0.405635\pi\) |
−0.956378 | + | 0.292132i | \(0.905635\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 87.8406i | − | 2.81604i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.68629 | − | 1.68629i | 0.0539492 | − | 0.0539492i | −0.679617 | − | 0.733567i | \(-0.737854\pi\) |
0.733567 | + | 0.679617i | \(0.237854\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.82843 | − | 16.4853i | 0.218237 | − | 0.526872i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.97918 | − | 4.77817i | −0.0631905 | − | 0.152555i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.9203 | − | 11.9792i | 0.922415 | − | 0.382077i | 0.129619 | − | 0.991564i | \(-0.458625\pi\) |
0.792796 | + | 0.609487i | \(0.208625\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.72792 | −0.0869188 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 59.1127 | 1.88158 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.97056 | + | 3.30152i | −0.253449 | + | 0.104982i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.07969 | + | 7.43503i | 0.0978296 | + | 0.236181i | 0.965216 | − | 0.261454i | \(-0.0842019\pi\) |
−0.867386 | + | 0.497635i | \(0.834202\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.7279 | + | 37.9706i | −0.499111 | + | 1.20496i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.38478 | + | 7.38478i | −0.234113 | + | 0.234113i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.6777 | + | 16.0208i | 1.22493 | + | 0.507384i | 0.898975 | − | 0.438000i | \(-0.144313\pi\) |
0.325959 | + | 0.945384i | \(0.394313\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 8.82843i | − | 0.279319i |
(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 | 136.2.n.a.121.1 | yes | 4 | |
3.2 | odd | 2 | 1224.2.bq.a.937.1 | 4 | |||
4.3 | odd | 2 | 272.2.v.e.257.1 | 4 | |||
17.3 | odd | 16 | 2312.2.a.s.1.1 | 4 | |||
17.5 | odd | 16 | 2312.2.b.j.577.1 | 4 | |||
17.9 | even | 8 | inner | 136.2.n.a.9.1 | ✓ | 4 | |
17.12 | odd | 16 | 2312.2.b.j.577.4 | 4 | |||
17.14 | odd | 16 | 2312.2.a.s.1.4 | 4 | |||
51.26 | odd | 8 | 1224.2.bq.a.145.1 | 4 | |||
68.3 | even | 16 | 4624.2.a.bm.1.4 | 4 | |||
68.31 | even | 16 | 4624.2.a.bm.1.1 | 4 | |||
68.43 | odd | 8 | 272.2.v.e.145.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.2.n.a.9.1 | ✓ | 4 | 17.9 | even | 8 | inner | |
136.2.n.a.121.1 | yes | 4 | 1.1 | even | 1 | trivial | |
272.2.v.e.145.1 | 4 | 68.43 | odd | 8 | |||
272.2.v.e.257.1 | 4 | 4.3 | odd | 2 | |||
1224.2.bq.a.145.1 | 4 | 51.26 | odd | 8 | |||
1224.2.bq.a.937.1 | 4 | 3.2 | odd | 2 | |||
2312.2.a.s.1.1 | 4 | 17.3 | odd | 16 | |||
2312.2.a.s.1.4 | 4 | 17.14 | odd | 16 | |||
2312.2.b.j.577.1 | 4 | 17.5 | odd | 16 | |||
2312.2.b.j.577.4 | 4 | 17.12 | odd | 16 | |||
4624.2.a.bm.1.1 | 4 | 68.31 | even | 16 | |||
4624.2.a.bm.1.4 | 4 | 68.3 | even | 16 |