Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(269,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.ch (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.4857532416.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 7x^{6} - 2x^{5} + 98x^{4} - 98x^{3} + 67x^{2} - 30x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(0.0386042 - 0.555062i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.269 |
Dual form | 504.2.ch.a.341.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.866025 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | 2.87228 | − | 1.65831i | 1.28452 | − | 0.741620i | 0.306851 | − | 0.951757i | \(-0.400725\pi\) |
0.977672 | + | 0.210138i | \(0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.34521 | + | 4.06202i | −0.741620 | + | 1.28452i | ||||
\(11\) | −2.87228 | + | 4.97494i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.69042 | 1.30089 | 0.650444 | − | 0.759555i | \(-0.274583\pi\) | ||||
0.650444 | + | 0.759555i | \(0.274583\pi\) | |||||||
\(14\) | −2.44949 | + | 2.82843i | −0.654654 | + | 0.755929i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 1.22474 | − | 2.12132i | 0.297044 | − | 0.514496i | −0.678414 | − | 0.734680i | \(-0.737332\pi\) |
0.975458 | + | 0.220184i | \(0.0706658\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.34521 | − | 4.06202i | −0.538028 | − | 0.931891i | −0.999010 | − | 0.0444819i | \(-0.985836\pi\) |
0.460983 | − | 0.887409i | \(-0.347497\pi\) | |||||||
\(20\) | − | 6.63325i | − | 1.48324i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 8.12404i | − | 1.73205i | ||||||
\(23\) | 1.22474 | − | 0.707107i | 0.255377 | − | 0.147442i | −0.366847 | − | 0.930281i | \(-0.619563\pi\) |
0.622224 | + | 0.782839i | \(0.286229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 5.19615i | 0.600000 | − | 1.03923i | ||||
\(26\) | −5.74456 | + | 3.31662i | −1.12660 | + | 0.650444i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | − | 5.19615i | 0.188982 | − | 0.981981i | ||||
\(29\) | −5.74456 | −1.06674 | −0.533369 | − | 0.845883i | \(-0.679074\pi\) | ||||
−0.533369 | + | 0.845883i | \(0.679074\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | + | 2.59808i | 0.808224 | + | 0.466628i | 0.846339 | − | 0.532645i | \(-0.178802\pi\) |
−0.0381148 | + | 0.999273i | \(0.512135\pi\) | |||||||
\(32\) | 4.89898 | + | 2.82843i | 0.866025 | + | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.46410i | 0.594089i | ||||||||
\(35\) | 5.74456 | − | 6.63325i | 0.971008 | − | 1.12122i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.03562 | + | 4.06202i | −1.15665 | + | 0.667792i | −0.950499 | − | 0.310728i | \(-0.899427\pi\) |
−0.206151 | + | 0.978520i | \(0.566094\pi\) | |||||||
\(38\) | 5.74456 | + | 3.31662i | 0.931891 | + | 0.538028i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.69042 | + | 8.12404i | 0.741620 | + | 1.28452i | ||||
\(41\) | 9.79796 | 1.53018 | 0.765092 | − | 0.643921i | \(-0.222693\pi\) | ||||
0.765092 | + | 0.643921i | \(0.222693\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.12404i | 1.23890i | 0.785034 | + | 0.619452i | \(0.212645\pi\) | ||||
−0.785034 | + | 0.619452i | \(0.787355\pi\) | |||||||
\(44\) | 5.74456 | + | 9.94987i | 0.866025 | + | 1.50000i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | + | 1.73205i | −0.147442 | + | 0.255377i | ||||
\(47\) | −3.67423 | − | 6.36396i | −0.535942 | − | 0.928279i | −0.999117 | − | 0.0420122i | \(-0.986623\pi\) |
0.463175 | − | 0.886267i | \(-0.346710\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 8.48528i | 1.20000i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.69042 | − | 8.12404i | 0.650444 | − | 1.12660i | ||||
\(53\) | 2.87228 | − | 4.97494i | 0.394538 | − | 0.683360i | −0.598504 | − | 0.801120i | \(-0.704238\pi\) |
0.993042 | + | 0.117760i | \(0.0375713\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.0526i | 2.56905i | ||||||||
\(56\) | 2.44949 | + | 7.07107i | 0.327327 | + | 0.944911i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.03562 | − | 4.06202i | 0.923823 | − | 0.533369i | ||||
\(59\) | −2.87228 | − | 1.65831i | −0.373939 | − | 0.215894i | 0.301239 | − | 0.953549i | \(-0.402600\pi\) |
−0.675178 | + | 0.737655i | \(0.735933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.34521 | − | 4.06202i | −0.300273 | − | 0.520088i | 0.675925 | − | 0.736971i | \(-0.263744\pi\) |
−0.976198 | + | 0.216883i | \(0.930411\pi\) | |||||||
\(62\) | −7.34847 | −0.933257 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 13.4722 | − | 7.77817i | 1.67102 | − | 0.964764i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | −2.44949 | − | 4.24264i | −0.297044 | − | 0.514496i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.34521 | + | 12.1861i | −0.280306 | + | 1.45651i | ||||
\(71\) | 1.41421i | 0.167836i | 0.996473 | + | 0.0839181i | \(0.0267434\pi\) | ||||
−0.996473 | + | 0.0839181i | \(0.973257\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | − | 1.73205i | −0.351123 | − | 0.202721i | 0.314057 | − | 0.949404i | \(-0.398312\pi\) |
−0.665180 | + | 0.746683i | \(0.731645\pi\) | |||||||
\(74\) | 5.74456 | − | 9.94987i | 0.667792 | − | 1.15665i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.38083 | −1.07606 | ||||||||
\(77\) | −2.87228 | + | 14.9248i | −0.327327 | + | 1.70084i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.50000 | + | 6.06218i | 0.393781 | + | 0.682048i | 0.992945 | − | 0.118578i | \(-0.0378336\pi\) |
−0.599164 | + | 0.800626i | \(0.704500\pi\) | |||||||
\(80\) | −11.4891 | − | 6.63325i | −1.28452 | − | 0.741620i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.0000 | + | 6.92820i | −1.32518 | + | 0.765092i | ||||
\(83\) | 3.31662i | 0.364047i | 0.983294 | + | 0.182023i | \(0.0582647\pi\) | ||||
−0.983294 | + | 0.182023i | \(0.941735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 8.12404i | − | 0.881176i | ||||||
\(86\) | −5.74456 | − | 9.94987i | −0.619452 | − | 1.07292i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −14.0712 | − | 8.12404i | −1.50000 | − | 0.866025i | ||||
\(89\) | −4.89898 | − | 8.48528i | −0.519291 | − | 0.899438i | −0.999749 | − | 0.0224202i | \(-0.992863\pi\) |
0.480458 | − | 0.877018i | \(-0.340471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.7260 | − | 4.06202i | 1.22922 | − | 0.425815i | ||||
\(92\) | − | 2.82843i | − | 0.294884i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.00000 | + | 5.19615i | 0.928279 | + | 0.535942i | ||||
\(95\) | −13.4722 | − | 7.77817i | −1.38222 | − | 0.798024i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.73205i | − | 0.175863i | −0.996127 | − | 0.0879316i | \(-0.971974\pi\) | ||
0.996127 | − | 0.0879316i | \(-0.0280257\pi\) | |||||||
\(98\) | −3.67423 | + | 9.19239i | −0.371154 | + | 0.928571i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.00000 | − | 10.3923i | −0.600000 | − | 1.03923i | ||||
\(101\) | 5.74456 | + | 3.31662i | 0.571605 | + | 0.330017i | 0.757790 | − | 0.652498i | \(-0.226279\pi\) |
−0.186185 | + | 0.982515i | \(0.559612\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | + | 3.46410i | −0.591198 | + | 0.341328i | −0.765571 | − | 0.643352i | \(-0.777543\pi\) |
0.174373 | + | 0.984680i | \(0.444210\pi\) | |||||||
\(104\) | 13.2665i | 1.30089i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.12404i | 0.789076i | ||||||||
\(107\) | −2.87228 | − | 4.97494i | −0.277674 | − | 0.480945i | 0.693132 | − | 0.720810i | \(-0.256230\pi\) |
−0.970806 | + | 0.239865i | \(0.922897\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0712 | + | 8.12404i | 1.34778 | + | 0.778142i | 0.987935 | − | 0.154870i | \(-0.0494958\pi\) |
0.359846 | + | 0.933012i | \(0.382829\pi\) | |||||||
\(110\) | −13.4722 | − | 23.3345i | −1.28452 | − | 2.22486i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.00000 | − | 6.92820i | −0.755929 | − | 0.654654i | ||||
\(113\) | 14.1421i | 1.33038i | 0.746674 | + | 0.665190i | \(0.231650\pi\) | ||||
−0.746674 | + | 0.665190i | \(0.768350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.34521 | − | 4.06202i | 0.218692 | − | 0.378785i | ||||
\(116\) | −5.74456 | + | 9.94987i | −0.533369 | + | 0.923823i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.69042 | 0.431788 | ||||||||
\(119\) | 1.22474 | − | 6.36396i | 0.112272 | − | 0.583383i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | − | 19.0526i | −1.00000 | − | 1.73205i | ||||
\(122\) | 5.74456 | + | 3.31662i | 0.520088 | + | 0.300273i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.00000 | − | 5.19615i | 0.808224 | − | 0.466628i | ||||
\(125\) | − | 3.31662i | − | 0.296648i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.866025 | − | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.0000 | + | 19.0526i | −0.964764 | + | 1.67102i | ||||
\(131\) | 2.87228 | − | 1.65831i | 0.250952 | − | 0.144887i | −0.369248 | − | 0.929331i | \(-0.620385\pi\) |
0.620200 | + | 0.784444i | \(0.287051\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.38083 | − | 8.12404i | −0.813421 | − | 0.704443i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | + | 3.46410i | 0.514496 | + | 0.297044i | ||||
\(137\) | −12.2474 | − | 7.07107i | −1.04637 | − | 0.604122i | −0.124739 | − | 0.992190i | \(-0.539809\pi\) |
−0.921631 | + | 0.388067i | \(0.873143\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.38083 | −0.795672 | −0.397836 | − | 0.917457i | \(-0.630239\pi\) | ||||
−0.397836 | + | 0.917457i | \(0.630239\pi\) | |||||||
\(140\) | −5.74456 | − | 16.5831i | −0.485504 | − | 1.40153i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.00000 | − | 1.73205i | −0.0839181 | − | 0.145350i | ||||
\(143\) | −13.4722 | + | 23.3345i | −1.12660 | + | 1.95133i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.5000 | + | 9.52628i | −1.37025 | + | 0.791114i | ||||
\(146\) | 4.89898 | 0.405442 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.2481i | 1.33558i | ||||||||
\(149\) | −5.74456 | − | 9.94987i | −0.470613 | − | 0.815125i | 0.528822 | − | 0.848733i | \(-0.322634\pi\) |
−0.999435 | + | 0.0336072i | \(0.989300\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.500000 | − | 0.866025i | 0.0406894 | − | 0.0704761i | −0.844963 | − | 0.534824i | \(-0.820378\pi\) |
0.885653 | + | 0.464348i | \(0.153711\pi\) | |||||||
\(152\) | 11.4891 | − | 6.63325i | 0.931891 | − | 0.538028i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.03562 | − | 20.3101i | −0.566947 | − | 1.63663i | ||||
\(155\) | 17.2337 | 1.38424 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.38083 | + | 16.2481i | −0.748672 | + | 1.29674i | 0.199788 | + | 0.979839i | \(0.435975\pi\) |
−0.948459 | + | 0.316898i | \(0.897359\pi\) | |||||||
\(158\) | −8.57321 | − | 4.94975i | −0.682048 | − | 0.393781i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.7617 | 1.48324 | ||||||||
\(161\) | 2.44949 | − | 2.82843i | 0.193047 | − | 0.222911i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.03562 | + | 4.06202i | −0.551073 | + | 0.318162i | −0.749554 | − | 0.661943i | \(-0.769732\pi\) |
0.198482 | + | 0.980105i | \(0.436399\pi\) | |||||||
\(164\) | 9.79796 | − | 16.9706i | 0.765092 | − | 1.32518i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.34521 | − | 4.06202i | −0.182023 | − | 0.315274i | ||||
\(167\) | −4.89898 | −0.379094 | −0.189547 | − | 0.981872i | \(-0.560702\pi\) | ||||
−0.189547 | + | 0.981872i | \(0.560702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 5.74456 | + | 9.94987i | 0.440588 | + | 0.763121i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.0712 | + | 8.12404i | 1.07292 | + | 0.619452i | ||||
\(173\) | −5.74456 | + | 3.31662i | −0.436751 | + | 0.252158i | −0.702219 | − | 0.711961i | \(-0.747807\pi\) |
0.265467 | + | 0.964120i | \(0.414474\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.00000 | − | 15.5885i | 0.226779 | − | 1.17838i | ||||
\(176\) | 22.9783 | 1.73205 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.0000 | + | 6.92820i | 0.899438 | + | 0.519291i | ||||
\(179\) | −5.74456 | + | 9.94987i | −0.429369 | + | 0.743689i | −0.996817 | − | 0.0797204i | \(-0.974597\pi\) |
0.567448 | + | 0.823409i | \(0.307931\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.38083 | −0.697272 | −0.348636 | − | 0.937258i | \(-0.613355\pi\) | ||||
−0.348636 | + | 0.937258i | \(0.613355\pi\) | |||||||
\(182\) | −11.4891 | + | 13.2665i | −0.851631 | + | 0.983378i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.00000 | + | 3.46410i | 0.147442 | + | 0.255377i | ||||
\(185\) | −13.4722 | + | 23.3345i | −0.990495 | + | 1.71559i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.03562 | + | 12.1861i | 0.514496 | + | 0.891133i | ||||
\(188\) | −14.6969 | −1.07188 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 22.0000 | 1.59605 | ||||||||
\(191\) | 4.89898 | − | 2.82843i | 0.354478 | − | 0.204658i | −0.312178 | − | 0.950024i | \(-0.601059\pi\) |
0.666656 | + | 0.745366i | \(0.267725\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.500000 | − | 0.866025i | 0.0359908 | − | 0.0623379i | −0.847469 | − | 0.530845i | \(-0.821875\pi\) |
0.883460 | + | 0.468507i | \(0.155208\pi\) | |||||||
\(194\) | 1.22474 | + | 2.12132i | 0.0879316 | + | 0.152302i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.00000 | − | 13.8564i | −0.142857 | − | 0.989743i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.00000 | + | 3.46410i | 0.425329 | + | 0.245564i | 0.697355 | − | 0.716726i | \(-0.254360\pi\) |
−0.272026 | + | 0.962290i | \(0.587694\pi\) | |||||||
\(200\) | 14.6969 | + | 8.48528i | 1.03923 | + | 0.600000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.38083 | −0.660033 | ||||||||
\(203\) | −14.3614 | + | 4.97494i | −1.00797 | + | 0.349172i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.1425 | − | 16.2481i | 1.96556 | − | 1.13481i | ||||
\(206\) | 4.89898 | − | 8.48528i | 0.341328 | − | 0.591198i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.38083 | − | 16.2481i | −0.650444 | − | 1.12660i | ||||
\(209\) | 26.9444 | 1.86378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.12404i | − | 0.559282i | −0.960105 | − | 0.279641i | \(-0.909785\pi\) | ||
0.960105 | − | 0.279641i | \(-0.0902154\pi\) | |||||||
\(212\) | −5.74456 | − | 9.94987i | −0.394538 | − | 0.683360i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.03562 | + | 4.06202i | 0.480945 | + | 0.277674i | ||||
\(215\) | 13.4722 | + | 23.3345i | 0.918796 | + | 1.59140i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.5000 | + | 2.59808i | 0.916440 | + | 0.176369i | ||||
\(218\) | −22.9783 | −1.55628 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 33.0000 | + | 19.0526i | 2.22486 | + | 1.28452i | ||||
\(221\) | 5.74456 | − | 9.94987i | 0.386421 | − | 0.669301i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0526i | 1.27585i | 0.770097 | + | 0.637927i | \(0.220208\pi\) | ||||
−0.770097 | + | 0.637927i | \(0.779792\pi\) | |||||||
\(224\) | 14.6969 | + | 2.82843i | 0.981981 | + | 0.188982i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.0000 | − | 17.3205i | −0.665190 | − | 1.15214i | ||||
\(227\) | −20.1060 | − | 11.6082i | −1.33448 | − | 0.770462i | −0.348497 | − | 0.937310i | \(-0.613308\pi\) |
−0.985983 | + | 0.166847i | \(0.946641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.69042 | + | 8.12404i | 0.309951 | + | 0.536852i | 0.978351 | − | 0.206950i | \(-0.0663539\pi\) |
−0.668400 | + | 0.743802i | \(0.733021\pi\) | |||||||
\(230\) | 6.63325i | 0.437384i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 16.2481i | − | 1.06674i | ||||||
\(233\) | −6.12372 | + | 3.53553i | −0.401179 | + | 0.231621i | −0.686992 | − | 0.726665i | \(-0.741069\pi\) |
0.285814 | + | 0.958285i | \(0.407736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.1069 | − | 12.1861i | −1.37686 | − | 0.794931i | ||||
\(236\) | −5.74456 | + | 3.31662i | −0.373939 | + | 0.215894i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.00000 | + | 8.66025i | 0.194461 | + | 0.561361i | ||||
\(239\) | 1.41421i | 0.0914779i | 0.998953 | + | 0.0457389i | \(0.0145642\pi\) | ||||
−0.998953 | + | 0.0457389i | \(0.985436\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5000 | − | 6.06218i | −0.676364 | − | 0.390499i | 0.122119 | − | 0.992515i | \(-0.461031\pi\) |
−0.798484 | + | 0.602016i | \(0.794364\pi\) | |||||||
\(242\) | 26.9444 | + | 15.5563i | 1.73205 | + | 1.00000i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.38083 | −0.600546 | ||||||||
\(245\) | 8.61684 | − | 21.5581i | 0.550510 | − | 1.37729i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.0000 | − | 19.0526i | −0.699913 | − | 1.21229i | ||||
\(248\) | −7.34847 | + | 12.7279i | −0.466628 | + | 0.808224i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.34521 | + | 4.06202i | 0.148324 | + | 0.256905i | ||||
\(251\) | 3.31662i | 0.209344i | 0.994507 | + | 0.104672i | \(0.0333792\pi\) | ||||
−0.994507 | + | 0.104672i | \(0.966621\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.12404i | 0.510754i | ||||||||
\(254\) | 15.9217 | − | 9.19239i | 0.999015 | − | 0.576782i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 4.89898 | + | 8.48528i | 0.305590 | + | 0.529297i | 0.977393 | − | 0.211433i | \(-0.0678130\pi\) |
−0.671803 | + | 0.740730i | \(0.734480\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.0712 | + | 16.2481i | −0.874345 | + | 1.00961i | ||||
\(260\) | − | 31.1127i | − | 1.92953i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.34521 | + | 4.06202i | −0.144887 | + | 0.250952i | ||||
\(263\) | −8.57321 | − | 4.94975i | −0.528647 | − | 0.305215i | 0.211818 | − | 0.977309i | \(-0.432061\pi\) |
−0.740465 | + | 0.672095i | \(0.765395\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 19.0526i | − | 1.17039i | ||||||
\(266\) | 17.2337 | + | 3.31662i | 1.05667 | + | 0.203355i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.3614 | + | 8.29156i | 0.875630 | + | 0.505545i | 0.869215 | − | 0.494434i | \(-0.164625\pi\) |
0.00641522 | + | 0.999979i | \(0.497958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.50000 | − | 0.866025i | 0.0911185 | − | 0.0526073i | −0.453748 | − | 0.891130i | \(-0.649914\pi\) |
0.544867 | + | 0.838523i | \(0.316580\pi\) | |||||||
\(272\) | −9.79796 | −0.594089 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.0000 | 1.20824 | ||||||||
\(275\) | 17.2337 | + | 29.8496i | 1.03923 | + | 1.80000i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0712 | − | 8.12404i | −0.845459 | − | 0.488126i | 0.0136569 | − | 0.999907i | \(-0.495653\pi\) |
−0.859116 | + | 0.511781i | \(0.828986\pi\) | |||||||
\(278\) | 11.4891 | − | 6.63325i | 0.689072 | − | 0.397836i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 18.7617 | + | 16.2481i | 1.12122 | + | 0.971008i | ||||
\(281\) | 22.6274i | 1.34984i | 0.737892 | + | 0.674919i | \(0.235822\pi\) | ||||
−0.737892 | + | 0.674919i | \(0.764178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.7260 | − | 20.3101i | 0.697041 | − | 1.20731i | −0.272447 | − | 0.962171i | \(-0.587833\pi\) |
0.969488 | − | 0.245139i | \(-0.0788337\pi\) | |||||||
\(284\) | 2.44949 | + | 1.41421i | 0.145350 | + | 0.0839181i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 38.1051i | − | 2.25320i | ||||||
\(287\) | 24.4949 | − | 8.48528i | 1.44589 | − | 0.500870i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50000 | + | 9.52628i | 0.323529 | + | 0.560369i | ||||
\(290\) | 13.4722 | − | 23.3345i | 0.791114 | − | 1.37025i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | + | 3.46410i | −0.351123 | + | 0.202721i | ||||
\(293\) | 3.31662i | 0.193759i | 0.995296 | + | 0.0968796i | \(0.0308862\pi\) | ||||
−0.995296 | + | 0.0968796i | \(0.969114\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.0000 | −0.640445 | ||||||||
\(296\) | −11.4891 | − | 19.8997i | −0.667792 | − | 1.15665i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.0712 | + | 8.12404i | 0.815125 | + | 0.470613i | ||||
\(299\) | 5.74456 | − | 3.31662i | 0.332217 | − | 0.191805i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.03562 | + | 20.3101i | 0.405527 | + | 1.17065i | ||||
\(302\) | 1.41421i | 0.0813788i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.38083 | + | 16.2481i | −0.538028 | + | 0.931891i | ||||
\(305\) | −13.4722 | − | 7.77817i | −0.771416 | − | 0.445377i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.8329 | 1.87387 | 0.936937 | − | 0.349499i | \(-0.113648\pi\) | ||||
0.936937 | + | 0.349499i | \(0.113648\pi\) | |||||||
\(308\) | 22.9783 | + | 19.8997i | 1.30931 | + | 1.13389i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −21.1069 | + | 12.1861i | −1.19879 | + | 0.692122i | ||||
\(311\) | −14.6969 | + | 25.4558i | −0.833387 | + | 1.44347i | 0.0619501 | + | 0.998079i | \(0.480268\pi\) |
−0.895337 | + | 0.445389i | \(0.853065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.5000 | + | 12.9904i | −1.27178 | + | 0.734260i | −0.975322 | − | 0.220788i | \(-0.929137\pi\) |
−0.296453 | + | 0.955047i | \(0.595804\pi\) | |||||||
\(314\) | − | 26.5330i | − | 1.49734i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | 8.61684 | + | 14.9248i | 0.483970 | + | 0.838261i | 0.999830 | − | 0.0184118i | \(-0.00586098\pi\) |
−0.515860 | + | 0.856673i | \(0.672528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.5000 | − | 28.5788i | 0.923823 | − | 1.60011i | ||||
\(320\) | −22.9783 | + | 13.2665i | −1.28452 | + | 0.741620i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.00000 | + | 5.19615i | −0.0557278 | + | 0.289570i | ||||
\(323\) | −11.4891 | −0.639272 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0712 | − | 24.3721i | 0.780532 | − | 1.35192i | ||||
\(326\) | 5.74456 | − | 9.94987i | 0.318162 | − | 0.551073i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 27.7128i | 1.53018i | ||||||||
\(329\) | −14.6969 | − | 12.7279i | −0.810268 | − | 0.701713i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | 5.74456 | + | 3.31662i | 0.315274 | + | 0.182023i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.00000 | − | 3.46410i | 0.328305 | − | 0.189547i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.0000 | 1.57973 | 0.789865 | − | 0.613280i | \(-0.210150\pi\) | ||||
0.789865 | + | 0.613280i | \(0.210150\pi\) | |||||||
\(338\) | −11.0227 | + | 6.36396i | −0.599556 | + | 0.346154i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.0712 | − | 8.12404i | −0.763121 | − | 0.440588i | ||||
\(341\) | −25.8505 | + | 14.9248i | −1.39988 | + | 0.808224i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | −22.9783 | −1.23890 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.69042 | − | 8.12404i | 0.252158 | − | 0.436751i | ||||
\(347\) | 17.2337 | − | 29.8496i | 0.925153 | − | 1.60241i | 0.133838 | − | 0.991003i | \(-0.457270\pi\) |
0.791315 | − | 0.611408i | \(-0.209397\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.38083 | −0.502144 | −0.251072 | − | 0.967968i | \(-0.580783\pi\) | ||||
−0.251072 | + | 0.967968i | \(0.580783\pi\) | |||||||
\(350\) | 7.34847 | + | 21.2132i | 0.392792 | + | 1.13389i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −28.1425 | + | 16.2481i | −1.50000 | + | 0.866025i | ||||
\(353\) | −4.89898 | + | 8.48528i | −0.260746 | + | 0.451626i | −0.966440 | − | 0.256891i | \(-0.917302\pi\) |
0.705694 | + | 0.708517i | \(0.250635\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.34521 | + | 4.06202i | 0.124471 | + | 0.215590i | ||||
\(356\) | −19.5959 | −1.03858 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 16.2481i | − | 0.858738i | ||||||
\(359\) | 4.89898 | − | 2.82843i | 0.258558 | − | 0.149279i | −0.365118 | − | 0.930961i | \(-0.618972\pi\) |
0.623677 | + | 0.781682i | \(0.285638\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.50000 | + | 2.59808i | −0.0789474 | + | 0.136741i | ||||
\(362\) | 11.4891 | − | 6.63325i | 0.603855 | − | 0.348636i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.69042 | − | 24.3721i | 0.245845 | − | 1.27745i | ||||
\(365\) | −11.4891 | −0.601368 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.5000 | − | 11.2583i | −1.01789 | − | 0.587680i | −0.104399 | − | 0.994535i | \(-0.533292\pi\) |
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(368\) | −4.89898 | − | 2.82843i | −0.255377 | − | 0.147442i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 38.1051i | − | 1.98099i | ||||||
\(371\) | 2.87228 | − | 14.9248i | 0.149121 | − | 0.774858i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0712 | + | 8.12404i | −0.728582 | + | 0.420647i | −0.817903 | − | 0.575356i | \(-0.804863\pi\) |
0.0893215 | + | 0.996003i | \(0.471530\pi\) | |||||||
\(374\) | −17.2337 | − | 9.94987i | −0.891133 | − | 0.514496i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.0000 | − | 10.3923i | 0.928279 | − | 0.535942i | ||||
\(377\) | −26.9444 | −1.38771 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | −26.9444 | + | 15.5563i | −1.38222 | + | 0.798024i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.00000 | + | 6.92820i | −0.204658 | + | 0.354478i | ||||
\(383\) | 4.89898 | + | 8.48528i | 0.250326 | + | 0.433578i | 0.963616 | − | 0.267292i | \(-0.0861288\pi\) |
−0.713289 | + | 0.700870i | \(0.752795\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.5000 | + | 47.6314i | 0.840918 | + | 2.42752i | ||||
\(386\) | 1.41421i | 0.0719816i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.00000 | − | 1.73205i | −0.152302 | − | 0.0879316i | ||||
\(389\) | −11.4891 | + | 19.8997i | −0.582522 | + | 1.00896i | 0.412658 | + | 0.910886i | \(0.364601\pi\) |
−0.995179 | + | 0.0980711i | \(0.968733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.46410i | − | 0.175187i | ||||||
\(392\) | 12.2474 | + | 15.5563i | 0.618590 | + | 0.785714i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.1060 | + | 11.6082i | 1.01164 | + | 0.584071i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.38083 | − | 16.2481i | −0.470810 | − | 0.815468i | 0.528632 | − | 0.848851i | \(-0.322705\pi\) |
−0.999443 | + | 0.0333834i | \(0.989372\pi\) | |||||||
\(398\) | −9.79796 | −0.491127 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −24.0000 | −1.20000 | ||||||||
\(401\) | 12.2474 | − | 7.07107i | 0.611608 | − | 0.353112i | −0.161986 | − | 0.986793i | \(-0.551790\pi\) |
0.773595 | + | 0.633681i | \(0.218457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.1069 | + | 12.1861i | 1.05141 | + | 0.607031i | ||||
\(404\) | 11.4891 | − | 6.63325i | 0.571605 | − | 0.330017i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.0712 | − | 16.2481i | 0.698344 | − | 0.806379i | ||||
\(407\) | − | 46.6690i | − | 2.31330i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.5000 | − | 12.9904i | −1.11255 | − | 0.642333i | −0.173064 | − | 0.984911i | \(-0.555367\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | −22.9783 | + | 39.7995i | −1.13481 | + | 1.96556i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.8564i | 0.682656i | ||||||||
\(413\) | −8.61684 | − | 1.65831i | −0.424007 | − | 0.0816002i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.50000 | + | 9.52628i | 0.269984 | + | 0.467627i | ||||
\(416\) | 22.9783 | + | 13.2665i | 1.12660 | + | 0.650444i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −33.0000 | + | 19.0526i | −1.61408 | + | 0.931891i | ||||
\(419\) | − | 26.5330i | − | 1.29622i | −0.761546 | − | 0.648111i | \(-0.775559\pi\) | ||
0.761546 | − | 0.648111i | \(-0.224441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.12404i | 0.395941i | 0.980208 | + | 0.197971i | \(0.0634351\pi\) | ||||
−0.980208 | + | 0.197971i | \(0.936565\pi\) | |||||||
\(422\) | 5.74456 | + | 9.94987i | 0.279641 | + | 0.484352i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.0712 | + | 8.12404i | 0.683360 | + | 0.394538i | ||||
\(425\) | −7.34847 | − | 12.7279i | −0.356453 | − | 0.617395i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.38083 | − | 8.12404i | −0.453970 | − | 0.393150i | ||||
\(428\) | −11.4891 | −0.555348 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −33.0000 | − | 19.0526i | −1.59140 | − | 0.918796i | ||||
\(431\) | 24.4949 | + | 14.1421i | 1.17988 | + | 0.681203i | 0.955986 | − | 0.293411i | \(-0.0947906\pi\) |
0.223891 | + | 0.974614i | \(0.428124\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.1769i | 1.49827i | 0.662419 | + | 0.749133i | \(0.269530\pi\) | ||||
−0.662419 | + | 0.749133i | \(0.730470\pi\) | |||||||
\(434\) | −18.3712 | + | 6.36396i | −0.881845 | + | 0.305480i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 28.1425 | − | 16.2481i | 1.34778 | − | 0.778142i | ||||
\(437\) | −5.74456 | − | 3.31662i | −0.274800 | − | 0.158656i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5000 | − | 12.9904i | 1.07387 | − | 0.619997i | 0.144631 | − | 0.989486i | \(-0.453800\pi\) |
0.929235 | + | 0.369489i | \(0.120467\pi\) | |||||||
\(440\) | −53.8888 | −2.56905 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.2481i | 0.772842i | ||||||||
\(443\) | −8.61684 | − | 14.9248i | −0.409399 | − | 0.709099i | 0.585424 | − | 0.810727i | \(-0.300928\pi\) |
−0.994822 | + | 0.101628i | \(0.967595\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.1425 | − | 16.2481i | −1.33408 | − | 0.770233i | ||||
\(446\) | −13.4722 | − | 23.3345i | −0.637927 | − | 1.10492i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.0000 | + | 6.92820i | −0.944911 | + | 0.327327i | ||||
\(449\) | − | 24.0416i | − | 1.13459i | −0.823513 | − | 0.567297i | \(-0.807989\pi\) | ||
0.823513 | − | 0.567297i | \(-0.192011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.1425 | + | 48.7442i | −1.32518 | + | 2.29528i | ||||
\(452\) | 24.4949 | + | 14.1421i | 1.15214 | + | 0.665190i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 32.8329 | 1.54092 | ||||||||
\(455\) | 26.9444 | − | 31.1127i | 1.26317 | − | 1.45859i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.5000 | + | 21.6506i | 0.584725 | + | 1.01277i | 0.994910 | + | 0.100771i | \(0.0321310\pi\) |
−0.410184 | + | 0.912003i | \(0.634536\pi\) | |||||||
\(458\) | −11.4891 | − | 6.63325i | −0.536852 | − | 0.309951i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.69042 | − | 8.12404i | −0.218692 | − | 0.378785i | ||||
\(461\) | − | 6.63325i | − | 0.308941i | −0.987997 | − | 0.154471i | \(-0.950633\pi\) | ||
0.987997 | − | 0.154471i | \(-0.0493672\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.0000 | −1.02243 | −0.511213 | − | 0.859454i | \(-0.670804\pi\) | ||||
−0.511213 | + | 0.859454i | \(0.670804\pi\) | |||||||
\(464\) | 11.4891 | + | 19.8997i | 0.533369 | + | 0.923823i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.00000 | − | 8.66025i | 0.231621 | − | 0.401179i | ||||
\(467\) | −5.74456 | + | 3.31662i | −0.265827 | + | 0.153475i | −0.626990 | − | 0.779028i | \(-0.715713\pi\) |
0.361163 | + | 0.932503i | \(0.382380\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 34.4674 | 1.58986 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.69042 | − | 8.12404i | 0.215894 | − | 0.373939i | ||||
\(473\) | −40.4166 | − | 23.3345i | −1.85836 | − | 1.07292i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.1425 | −1.29127 | ||||||||
\(476\) | −9.79796 | − | 8.48528i | −0.449089 | − | 0.388922i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.00000 | − | 1.73205i | −0.0457389 | − | 0.0792222i | ||||
\(479\) | 13.4722 | − | 23.3345i | 0.615560 | − | 1.06618i | −0.374726 | − | 0.927136i | \(-0.622263\pi\) |
0.990286 | − | 0.139046i | \(-0.0444036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.0000 | + | 19.0526i | −1.50467 | + | 0.868722i | ||||
\(482\) | 17.1464 | 0.780998 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −44.0000 | −2.00000 | ||||||||
\(485\) | −2.87228 | − | 4.97494i | −0.130424 | − | 0.225900i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5000 | − | 21.6506i | 0.566429 | − | 0.981084i | −0.430486 | − | 0.902597i | \(-0.641658\pi\) |
0.996915 | − | 0.0784867i | \(-0.0250088\pi\) | |||||||
\(488\) | 11.4891 | − | 6.63325i | 0.520088 | − | 0.300273i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.69042 | + | 32.4962i | 0.211891 | + | 1.46803i | ||||
\(491\) | −28.7228 | −1.29624 | −0.648121 | − | 0.761537i | \(-0.724445\pi\) | ||||
−0.648121 | + | 0.761537i | \(0.724445\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.03562 | + | 12.1861i | −0.316869 | + | 0.548832i | ||||
\(494\) | 26.9444 | + | 15.5563i | 1.21229 | + | 0.699913i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 20.7846i | − | 0.933257i | ||||||
\(497\) | 1.22474 | + | 3.53553i | 0.0549373 | + | 0.158590i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.1425 | − | 16.2481i | 1.25983 | − | 0.727364i | 0.286790 | − | 0.957994i | \(-0.407412\pi\) |
0.973042 | + | 0.230630i | \(0.0740786\pi\) | |||||||
\(500\) | −5.74456 | − | 3.31662i | −0.256905 | − | 0.148324i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.34521 | − | 4.06202i | −0.104672 | − | 0.181297i | ||||
\(503\) | −7.34847 | −0.327652 | −0.163826 | − | 0.986489i | \(-0.552384\pi\) | ||||
−0.163826 | + | 0.986489i | \(0.552384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0000 | 0.978987 | ||||||||
\(506\) | −5.74456 | − | 9.94987i | −0.255377 | − | 0.442326i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.0000 | + | 22.5167i | −0.576782 | + | 0.999015i | ||||
\(509\) | 37.3397 | − | 21.5581i | 1.65505 | − | 0.955544i | 0.680102 | − | 0.733118i | \(-0.261936\pi\) |
0.974949 | − | 0.222427i | \(-0.0713977\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.00000 | − | 1.73205i | −0.398137 | − | 0.0766214i | ||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.0000 | − | 6.92820i | −0.529297 | − | 0.305590i | ||||
\(515\) | −11.4891 | + | 19.8997i | −0.506271 | + | 0.876888i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42.2137 | 1.85656 | ||||||||
\(518\) | 5.74456 | − | 29.8496i | 0.252402 | − | 1.31152i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 22.0000 | + | 38.1051i | 0.964764 | + | 1.67102i | ||||
\(521\) | 8.57321 | − | 14.8492i | 0.375599 | − | 0.650557i | −0.614817 | − | 0.788670i | \(-0.710770\pi\) |
0.990417 | + | 0.138113i | \(0.0441036\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.34521 | − | 4.06202i | −0.102549 | − | 0.177620i | 0.810185 | − | 0.586174i | \(-0.199366\pi\) |
−0.912734 | + | 0.408554i | \(0.866033\pi\) | |||||||
\(524\) | − | 6.63325i | − | 0.289775i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.0000 | 0.610429 | ||||||||
\(527\) | 11.0227 | − | 6.36396i | 0.480157 | − | 0.277218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5000 | + | 18.1865i | −0.456522 | + | 0.790719i | ||||
\(530\) | 13.4722 | + | 23.3345i | 0.585195 | + | 1.01359i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −23.4521 | + | 8.12404i | −1.01678 | + | 0.352222i | ||||
\(533\) | 45.9565 | 1.99060 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.5000 | − | 9.52628i | −0.713357 | − | 0.411857i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −23.4521 | −1.01109 | ||||||||
\(539\) | 5.74456 | + | 39.7995i | 0.247436 | + | 1.71429i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.03562 | + | 4.06202i | −0.302485 | + | 0.174640i | −0.643559 | − | 0.765397i | \(-0.722543\pi\) |
0.341074 | + | 0.940037i | \(0.389209\pi\) | |||||||
\(542\) | −1.22474 | + | 2.12132i | −0.0526073 | + | 0.0911185i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.0000 | − | 6.92820i | 0.514496 | − | 0.297044i | ||||
\(545\) | 53.8888 | 2.30834 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 40.6202i | − | 1.73679i | −0.495870 | − | 0.868397i | \(-0.665151\pi\) | ||
0.495870 | − | 0.868397i | \(-0.334849\pi\) | |||||||
\(548\) | −24.4949 | + | 14.1421i | −1.04637 | + | 0.604122i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −42.2137 | − | 24.3721i | −1.80000 | − | 1.03923i | ||||
\(551\) | 13.4722 | + | 23.3345i | 0.573935 | + | 0.994084i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0000 | + | 12.1244i | 0.595341 | + | 0.515580i | ||||
\(554\) | 22.9783 | 0.976252 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.38083 | + | 16.2481i | −0.397836 | + | 0.689072i | ||||
\(557\) | 2.87228 | − | 4.97494i | 0.121702 | − | 0.210795i | −0.798737 | − | 0.601681i | \(-0.794498\pi\) |
0.920439 | + | 0.390886i | \(0.127831\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.1051i | 1.61167i | ||||||||
\(560\) | −34.4674 | − | 6.63325i | −1.45651 | − | 0.280306i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.0000 | − | 27.7128i | −0.674919 | − | 1.16899i | ||||
\(563\) | 31.5951 | + | 18.2414i | 1.33157 | + | 0.768785i | 0.985541 | − | 0.169437i | \(-0.0541950\pi\) |
0.346034 | + | 0.938222i | \(0.387528\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.4521 | + | 40.6202i | 0.986636 | + | 1.70890i | ||||
\(566\) | 33.1662i | 1.39408i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −13.4722 | + | 7.77817i | −0.564784 | + | 0.326078i | −0.755063 | − | 0.655652i | \(-0.772394\pi\) |
0.190280 | + | 0.981730i | \(0.439061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.1069 | + | 12.1861i | 0.883295 | + | 0.509971i | 0.871743 | − | 0.489963i | \(-0.162990\pi\) |
0.0115516 | + | 0.999933i | \(0.496323\pi\) | |||||||
\(572\) | 26.9444 | + | 46.6690i | 1.12660 | + | 1.95133i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −24.0000 | + | 27.7128i | −1.00174 | + | 1.15671i | ||||
\(575\) | − | 8.48528i | − | 0.353861i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5000 | + | 6.06218i | 0.437121 | + | 0.252372i | 0.702376 | − | 0.711807i | \(-0.252123\pi\) |
−0.265255 | + | 0.964178i | \(0.585456\pi\) | |||||||
\(578\) | −13.4722 | − | 7.77817i | −0.560369 | − | 0.323529i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 38.1051i | 1.58223i | ||||||||
\(581\) | 2.87228 | + | 8.29156i | 0.119162 | + | 0.343992i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.5000 | + | 28.5788i | 0.683360 | + | 1.18361i | ||||
\(584\) | 4.89898 | − | 8.48528i | 0.202721 | − | 0.351123i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.34521 | − | 4.06202i | −0.0968796 | − | 0.167800i | ||||
\(587\) | 23.2164i | 0.958242i | 0.877749 | + | 0.479121i | \(0.159045\pi\) | ||||
−0.877749 | + | 0.479121i | \(0.840955\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 24.3721i | − | 1.00424i | ||||||
\(590\) | 13.4722 | − | 7.77817i | 0.554641 | − | 0.320222i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 28.1425 | + | 16.2481i | 1.15665 | + | 0.667792i | ||||
\(593\) | −8.57321 | − | 14.8492i | −0.352060 | − | 0.609785i | 0.634550 | − | 0.772881i | \(-0.281185\pi\) |
−0.986610 | + | 0.163096i | \(0.947852\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.03562 | − | 20.3101i | −0.288432 | − | 0.832633i | ||||
\(596\) | −22.9783 | −0.941226 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.69042 | + | 8.12404i | −0.191805 | + | 0.332217i | ||||
\(599\) | −12.2474 | − | 7.07107i | −0.500417 | − | 0.288916i | 0.228469 | − | 0.973551i | \(-0.426628\pi\) |
−0.728886 | + | 0.684635i | \(0.759961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 43.3013i | − | 1.76630i | −0.469095 | − | 0.883148i | \(-0.655420\pi\) | ||
0.469095 | − | 0.883148i | \(-0.344580\pi\) | |||||||
\(602\) | −22.9783 | − | 19.8997i | −0.936524 | − | 0.811053i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.00000 | − | 1.73205i | −0.0406894 | − | 0.0704761i | ||||
\(605\) | −63.1902 | − | 36.4829i | −2.56905 | − | 1.48324i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.5000 | − | 19.9186i | 1.40031 | − | 0.808470i | 0.405887 | − | 0.913923i | \(-0.366962\pi\) |
0.994424 | + | 0.105453i | \(0.0336291\pi\) | |||||||
\(608\) | − | 26.5330i | − | 1.07606i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.0000 | 0.890754 | ||||||||
\(611\) | −17.2337 | − | 29.8496i | −0.697200 | − | 1.20759i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.1781 | + | 20.3101i | 1.42083 | + | 0.820317i | 0.996370 | − | 0.0851292i | \(-0.0271303\pi\) |
0.424461 | + | 0.905446i | \(0.360464\pi\) | |||||||
\(614\) | −40.2119 | + | 23.2164i | −1.62282 | + | 0.936937i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −42.2137 | − | 8.12404i | −1.70084 | − | 0.327327i | ||||
\(617\) | 18.3848i | 0.740143i | 0.929003 | + | 0.370072i | \(0.120667\pi\) | ||||
−0.929003 | + | 0.370072i | \(0.879333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.7260 | − | 20.3101i | 0.471309 | − | 0.816332i | −0.528152 | − | 0.849150i | \(-0.677115\pi\) |
0.999461 | + | 0.0328182i | \(0.0104482\pi\) | |||||||
\(620\) | 17.2337 | − | 29.8496i | 0.692122 | − | 1.19879i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 41.5692i | − | 1.66677i | ||||||
\(623\) | −19.5959 | − | 16.9706i | −0.785094 | − | 0.679911i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 18.3712 | − | 31.8198i | 0.734260 | − | 1.27178i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.7617 | + | 32.4962i | 0.748672 | + | 1.29674i | ||||
\(629\) | 19.8997i | 0.793455i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0000 | −1.23409 | −0.617045 | − | 0.786928i | \(-0.711670\pi\) | ||||
−0.617045 | + | 0.786928i | \(0.711670\pi\) | |||||||
\(632\) | −17.1464 | + | 9.89949i | −0.682048 | + | 0.393781i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.1069 | − | 12.1861i | −0.838261 | − | 0.483970i | ||||
\(635\) | −37.3397 | + | 21.5581i | −1.48178 | + | 0.855506i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.7973 | − | 20.3101i | 1.02213 | − | 0.804715i | ||||
\(638\) | 46.6690i | 1.84765i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.7617 | − | 32.4962i | 0.741620 | − | 1.28452i | ||||
\(641\) | 35.5176 | + | 20.5061i | 1.40286 | + | 0.809942i | 0.994685 | − | 0.102961i | \(-0.0328318\pi\) |
0.408176 | + | 0.912903i | \(0.366165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.5233 | −1.47978 | −0.739888 | − | 0.672730i | \(-0.765121\pi\) | ||||
−0.739888 | + | 0.672730i | \(0.765121\pi\) | |||||||
\(644\) | −2.44949 | − | 7.07107i | −0.0965234 | − | 0.278639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.0712 | − | 8.12404i | 0.553626 | − | 0.319636i | ||||
\(647\) | 1.22474 | − | 2.12132i | 0.0481497 | − | 0.0833977i | −0.840946 | − | 0.541119i | \(-0.818001\pi\) |
0.889096 | + | 0.457721i | \(0.151334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.5000 | − | 9.52628i | 0.647682 | − | 0.373939i | ||||
\(650\) | 39.7995i | 1.56106i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.2481i | 0.636324i | ||||||||
\(653\) | 2.87228 | + | 4.97494i | 0.112401 | + | 0.194684i | 0.916738 | − | 0.399489i | \(-0.130813\pi\) |
−0.804337 | + | 0.594174i | \(0.797479\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.50000 | − | 9.52628i | 0.214903 | − | 0.372223i | ||||
\(656\) | −19.5959 | − | 33.9411i | −0.765092 | − | 1.32518i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 27.0000 | + | 5.19615i | 1.05257 | + | 0.202567i | ||||
\(659\) | 11.4891 | 0.447553 | 0.223776 | − | 0.974641i | \(-0.428161\pi\) | ||||
0.223776 | + | 0.974641i | \(0.428161\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.7260 | − | 20.3101i | 0.456090 | − | 0.789971i | −0.542660 | − | 0.839952i | \(-0.682583\pi\) |
0.998750 | + | 0.0499812i | \(0.0159161\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.38083 | −0.364047 | ||||||||
\(665\) | −40.4166 | − | 7.77817i | −1.56729 | − | 0.301625i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.03562 | + | 4.06202i | −0.272420 | + | 0.157282i | ||||
\(668\) | −4.89898 | + | 8.48528i | −0.189547 | + | 0.328305i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.9444 | 1.04018 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0000 | 0.655302 | 0.327651 | − | 0.944799i | \(-0.393743\pi\) | ||||
0.327651 | + | 0.944799i | \(0.393743\pi\) | |||||||
\(674\) | −35.5176 | + | 20.5061i | −1.36809 | + | 0.789865i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.00000 | − | 15.5885i | 0.346154 | − | 0.599556i | ||||
\(677\) | 20.1060 | − | 11.6082i | 0.772735 | − | 0.446139i | −0.0611143 | − | 0.998131i | \(-0.519465\pi\) |
0.833849 | + | 0.551992i | \(0.186132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.50000 | − | 4.33013i | −0.0575647 | − | 0.166175i | ||||
\(680\) | 22.9783 | 0.881176 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 21.1069 | − | 36.5582i | 0.808224 | − | 1.39988i | ||||
\(683\) | 20.1060 | − | 34.8246i | 0.769334 | − | 1.33252i | −0.168591 | − | 0.985686i | \(-0.553922\pi\) |
0.937925 | − | 0.346839i | \(-0.112745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.9042 | −1.79212 | ||||||||
\(686\) | −1.22474 | + | 26.1630i | −0.0467610 | + | 0.998906i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.1425 | − | 16.2481i | 1.07292 | − | 0.619452i | ||||
\(689\) | 13.4722 | − | 23.3345i | 0.513250 | − | 0.888975i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.4521 | − | 40.6202i | −0.892159 | − | 1.54526i | −0.837282 | − | 0.546772i | \(-0.815857\pi\) |
−0.0548775 | − | 0.998493i | \(-0.517477\pi\) | |||||||
\(692\) | 13.2665i | 0.504317i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 48.7442i | 1.85031i | ||||||||
\(695\) | −26.9444 | + | 15.5563i | −1.02206 | + | 0.590086i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0000 | − | 20.7846i | 0.454532 | − | 0.787273i | ||||
\(698\) | 11.4891 | − | 6.63325i | 0.434870 | − | 0.251072i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24.0000 | − | 20.7846i | −0.907115 | − | 0.785584i | ||||
\(701\) | 17.2337 | 0.650907 | 0.325454 | − | 0.945558i | \(-0.394483\pi\) | ||||
0.325454 | + | 0.945558i | \(0.394483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.0000 | + | 19.0526i | 1.24462 | + | 0.718581i | ||||
\(704\) | 22.9783 | − | 39.7995i | 0.866025 | − | 1.50000i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 13.8564i | − | 0.521493i | ||||||
\(707\) | 17.2337 | + | 3.31662i | 0.648140 | + | 0.124735i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.2137 | + | 24.3721i | −1.58537 | + | 0.915314i | −0.591315 | + | 0.806441i | \(0.701391\pi\) |
−0.994056 | + | 0.108873i | \(0.965276\pi\) | |||||||
\(710\) | −5.74456 | − | 3.31662i | −0.215590 | − | 0.124471i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.0000 | − | 13.8564i | 0.899438 | − | 0.519291i | ||||
\(713\) | 7.34847 | 0.275202 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 89.3644i | 3.34204i | ||||||||
\(716\) | 11.4891 | + | 19.8997i | 0.429369 | + | 0.743689i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.00000 | + | 6.92820i | −0.149279 | + | 0.258558i | ||||
\(719\) | 17.1464 | + | 29.6985i | 0.639454 | + | 1.10757i | 0.985553 | + | 0.169369i | \(0.0541728\pi\) |
−0.346099 | + | 0.938198i | \(0.612494\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0000 | + | 13.8564i | −0.446903 | + | 0.516040i | ||||
\(722\) | − | 4.24264i | − | 0.157895i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.38083 | + | 16.2481i | −0.348636 | + | 0.603855i | ||||
\(725\) | −17.2337 | + | 29.8496i | −0.640043 | + | 1.10859i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.1244i | − | 0.449667i | −0.974397 | − | 0.224834i | \(-0.927816\pi\) | ||
0.974397 | − | 0.224834i | \(-0.0721839\pi\) | |||||||
\(728\) | 11.4891 | + | 33.1662i | 0.425815 | + | 1.22922i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.0712 | − | 8.12404i | 0.520800 | − | 0.300684i | ||||
\(731\) | 17.2337 | + | 9.94987i | 0.637411 | + | 0.368009i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.4165 | − | 28.4341i | −0.606356 | − | 1.05024i | −0.991836 | − | 0.127523i | \(-0.959297\pi\) |
0.385480 | − | 0.922716i | \(-0.374036\pi\) | |||||||
\(734\) | 31.8434 | 1.17536 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.0712 | + | 8.12404i | 0.517619 | + | 0.298848i | 0.735960 | − | 0.677025i | \(-0.236731\pi\) |
−0.218341 | + | 0.975873i | \(0.570064\pi\) | |||||||
\(740\) | 26.9444 | + | 46.6690i | 0.990495 | + | 1.71559i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.03562 | + | 20.3101i | 0.258286 | + | 0.745607i | ||||
\(743\) | − | 19.7990i | − | 0.726354i | −0.931720 | − | 0.363177i | \(-0.881692\pi\) | ||
0.931720 | − | 0.363177i | \(-0.118308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.0000 | − | 19.0526i | −1.20903 | − | 0.698032i | ||||
\(746\) | 11.4891 | − | 19.8997i | 0.420647 | − | 0.728582i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 28.1425 | 1.02899 | ||||||||
\(749\) | −11.4891 | − | 9.94987i | −0.419804 | − | 0.363560i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.50000 | − | 4.33013i | −0.0912263 | − | 0.158009i | 0.816801 | − | 0.576919i | \(-0.195745\pi\) |
−0.908027 | + | 0.418911i | \(0.862412\pi\) | |||||||
\(752\) | −14.6969 | + | 25.4558i | −0.535942 | + | 0.928279i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 33.0000 | − | 19.0526i | 1.20179 | − | 0.693853i | ||||
\(755\) | − | 3.31662i | − | 0.120704i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.3721i | 0.885820i | 0.896566 | + | 0.442910i | \(0.146054\pi\) | ||||
−0.896566 | + | 0.442910i | \(0.853946\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 22.0000 | − | 38.1051i | 0.798024 | − | 1.38222i | ||||
\(761\) | 8.57321 | + | 14.8492i | 0.310779 | + | 0.538285i | 0.978531 | − | 0.206099i | \(-0.0660768\pi\) |
−0.667752 | + | 0.744383i | \(0.732744\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.2137 | + | 8.12404i | 1.52824 | + | 0.294110i | ||||
\(764\) | − | 11.3137i | − | 0.409316i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.0000 | − | 6.92820i | −0.433578 | − | 0.250326i | ||||
\(767\) | −13.4722 | − | 7.77817i | −0.486453 | − | 0.280854i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 39.8372i | − | 1.43657i | −0.695752 | − | 0.718283i | \(-0.744929\pi\) | ||
0.695752 | − | 0.718283i | \(-0.255071\pi\) | |||||||
\(770\) | −53.8888 | − | 46.6690i | −1.94202 | − | 1.68184i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.00000 | − | 1.73205i | −0.0359908 | − | 0.0623379i | ||||
\(773\) | −11.4891 | − | 6.63325i | −0.413235 | − | 0.238581i | 0.278944 | − | 0.960307i | \(-0.410016\pi\) |
−0.692179 | + | 0.721726i | \(0.743349\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.0000 | − | 15.5885i | 0.969869 | − | 0.559954i | ||||
\(776\) | 4.89898 | 0.175863 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 32.4962i | − | 1.16504i | ||||||
\(779\) | −22.9783 | − | 39.7995i | −0.823281 | − | 1.42596i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.03562 | − | 4.06202i | −0.251754 | − | 0.145350i | ||||
\(782\) | 2.44949 | + | 4.24264i | 0.0875936 | + | 0.151717i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.0000 | − | 10.3923i | −0.928571 | − | 0.371154i | ||||
\(785\) | 62.2254i | 2.22092i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4165 | + | 28.4341i | −0.585183 | + | 1.01357i | 0.409669 | + | 0.912234i | \(0.365644\pi\) |
−0.994853 | + | 0.101333i | \(0.967689\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.8329 | −1.16814 | ||||||||
\(791\) | 12.2474 | + | 35.3553i | 0.435469 | + | 1.25709i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.0000 | − | 19.0526i | −0.390621 | − | 0.676576i | ||||
\(794\) | 22.9783 | + | 13.2665i | 0.815468 | + | 0.470810i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.0000 | − | 6.92820i | 0.425329 | − | 0.245564i | ||||
\(797\) | 3.31662i | 0.117481i | 0.998273 | + | 0.0587404i | \(0.0187084\pi\) | ||||
−0.998273 | + | 0.0587404i | \(0.981292\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | −0.636794 | ||||||||
\(800\) | 29.3939 | − | 16.9706i | 1.03923 | − | 0.600000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.0000 | + | 17.3205i | −0.353112 | + | 0.611608i | ||||
\(803\) | 17.2337 | − | 9.94987i | 0.608164 | − | 0.351123i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.34521 | − | 12.1861i | 0.0826577 | − | 0.429502i | ||||
\(806\) | −34.4674 | −1.21406 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.38083 | + | 16.2481i | −0.330017 | + | 0.571605i | ||||
\(809\) | −19.5959 | − | 11.3137i | −0.688956 | − | 0.397769i | 0.114265 | − | 0.993450i | \(-0.463549\pi\) |
−0.803221 | + | 0.595682i | \(0.796882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.9042 | 1.64703 | 0.823514 | − | 0.567296i | \(-0.192011\pi\) | ||||
0.823514 | + | 0.567296i | \(0.192011\pi\) | |||||||
\(812\) | −5.74456 | + | 29.8496i | −0.201595 | + | 1.04752i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.0000 | + | 57.1577i | 1.15665 | + | 2.00338i | ||||
\(815\) | −13.4722 | + | 23.3345i | −0.471910 | + | 0.817373i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.0000 | − | 19.0526i | 1.15452 | − | 0.666565i | ||||
\(818\) | 36.7423 | 1.28467 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 64.9923i | − | 2.26963i | ||||||
\(821\) | 8.61684 | + | 14.9248i | 0.300730 | + | 0.520880i | 0.976301 | − | 0.216415i | \(-0.0694364\pi\) |
−0.675572 | + | 0.737294i | \(0.736103\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.00000 | + | 12.1244i | −0.244005 | + | 0.422628i | −0.961851 | − | 0.273573i | \(-0.911795\pi\) |
0.717847 | + | 0.696201i | \(0.245128\pi\) | |||||||
\(824\) | −9.79796 | − | 16.9706i | −0.341328 | − | 0.591198i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.7260 | − | 4.06202i | 0.408001 | − | 0.141336i | ||||
\(827\) | −17.2337 | −0.599274 | −0.299637 | − | 0.954053i | \(-0.596866\pi\) | ||||
−0.299637 | + | 0.954053i | \(0.596866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7260 | − | 20.3101i | 0.407262 | − | 0.705399i | −0.587320 | − | 0.809355i | \(-0.699817\pi\) |
0.994582 | + | 0.103956i | \(0.0331502\pi\) | |||||||
\(830\) | −13.4722 | − | 7.77817i | −0.467627 | − | 0.269984i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.5233 | −1.30089 | ||||||||
\(833\) | −2.44949 | − | 16.9706i | −0.0848698 | − | 0.587995i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0712 | + | 8.12404i | −0.486956 | + | 0.281144i | ||||
\(836\) | 26.9444 | − | 46.6690i | 0.931891 | − | 1.61408i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.7617 | + | 32.4962i | 0.648111 | + | 1.12256i | ||||
\(839\) | −46.5403 | −1.60675 | −0.803375 | − | 0.595474i | \(-0.796964\pi\) | ||||
−0.803375 | + | 0.595474i | \(0.796964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.00000 | 0.137931 | ||||||||
\(842\) | −5.74456 | − | 9.94987i | −0.197971 | − | 0.342895i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.0712 | − | 8.12404i | −0.484352 | − | 0.279641i | ||||
\(845\) | 25.8505 | − | 14.9248i | 0.889285 | − | 0.513429i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.0000 | − | 38.1051i | −1.51186 | − | 1.30931i | ||||
\(848\) | −22.9783 | −0.789076 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.0000 | + | 10.3923i | 0.617395 | + | 0.356453i | ||||
\(851\) | −5.74456 | + | 9.94987i | −0.196921 | + | 0.341077i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.7617 | 0.642387 | 0.321194 | − | 0.947014i | \(-0.395916\pi\) | ||||
0.321194 | + | 0.947014i | \(0.395916\pi\) | |||||||
\(854\) | 17.2337 | + | 3.31662i | 0.589725 | + | 0.113493i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.0712 | − | 8.12404i | 0.480945 | − | 0.277674i | ||||
\(857\) | −8.57321 | + | 14.8492i | −0.292855 | + | 0.507240i | −0.974484 | − | 0.224458i | \(-0.927939\pi\) |
0.681628 | + | 0.731699i | \(0.261272\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.34521 | − | 4.06202i | −0.0800175 | − | 0.138594i | 0.823240 | − | 0.567694i | \(-0.192164\pi\) |
−0.903257 | + | 0.429100i | \(0.858831\pi\) | |||||||
\(860\) | 53.8888 | 1.83759 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −40.0000 | −1.36241 | ||||||||
\(863\) | −17.1464 | + | 9.89949i | −0.583671 | + | 0.336983i | −0.762591 | − | 0.646881i | \(-0.776073\pi\) |
0.178920 | + | 0.983864i | \(0.442740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0000 | + | 19.0526i | −0.374011 | + | 0.647806i | ||||
\(866\) | −22.0454 | − | 38.1838i | −0.749133 | − | 1.29754i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.0000 | − | 20.7846i | 0.610960 | − | 0.705476i | ||||
\(869\) | −40.2119 | −1.36410 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −22.9783 | + | 39.7995i | −0.778142 | + | 1.34778i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.38083 | 0.317311 | ||||||||
\(875\) | −2.87228 | − | 8.29156i | −0.0971008 | − | 0.280306i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.0712 | + | 8.12404i | −0.475152 | + | 0.274329i | −0.718394 | − | 0.695636i | \(-0.755122\pi\) |
0.243242 | + | 0.969966i | \(0.421789\pi\) | |||||||
\(878\) | −18.3712 | + | 31.8198i | −0.619997 | + | 1.07387i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 66.0000 | − | 38.1051i | 2.22486 | − | 1.28452i | ||||
\(881\) | 44.0908 | 1.48546 | 0.742729 | − | 0.669593i | \(-0.233531\pi\) | ||||
0.742729 | + | 0.669593i | \(0.233531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 48.7442i | − | 1.64037i | −0.572096 | − | 0.820187i | \(-0.693869\pi\) | ||
0.572096 | − | 0.820187i | \(-0.306131\pi\) | |||||||
\(884\) | −11.4891 | − | 19.8997i | −0.386421 | − | 0.669301i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.1069 | + | 12.1861i | 0.709099 | + | 0.409399i | ||||
\(887\) | −6.12372 | − | 10.6066i | −0.205615 | − | 0.356135i | 0.744714 | − | 0.667384i | \(-0.232586\pi\) |
−0.950328 | + | 0.311249i | \(0.899253\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.5000 | + | 11.2583i | −1.09002 | + | 0.377592i | ||||
\(890\) | 45.9565 | 1.54047 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 33.0000 | + | 19.0526i | 1.10492 | + | 0.637927i | ||||
\(893\) | −17.2337 | + | 29.8496i | −0.576703 | + | 0.998880i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.1051i | 1.27371i | ||||||||
\(896\) | 19.5959 | − | 22.6274i | 0.654654 | − | 0.755929i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.0000 | + | 29.4449i | 0.567297 | + | 0.982588i | ||||
\(899\) | −25.8505 | − | 14.9248i | −0.862164 | − | 0.497770i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.03562 | − | 12.1861i | −0.234391 | − | 0.405976i | ||||
\(902\) | − | 79.5990i | − | 2.65036i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −40.0000 | −1.33038 | ||||||||
\(905\) | −26.9444 | + | 15.5563i | −0.895662 | + | 0.517111i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.1781 | − | 20.3101i | −1.16807 | − | 0.674386i | −0.214845 | − | 0.976648i | \(-0.568925\pi\) |
−0.953225 | + | 0.302262i | \(0.902258\pi\) | |||||||
\(908\) | −40.2119 | + | 23.2164i | −1.33448 | + | 0.770462i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.0000 | + | 57.1577i | −0.364646 | + | 1.89476i | ||||
\(911\) | 35.3553i | 1.17137i | 0.810537 | + | 0.585687i | \(0.199175\pi\) | ||||
−0.810537 | + | 0.585687i | \(0.800825\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.5000 | − | 9.52628i | −0.546070 | − | 0.315274i | ||||
\(914\) | −30.6186 | − | 17.6777i | −1.01277 | − | 0.584725i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.7617 | 0.619903 | ||||||||
\(917\) | 5.74456 | − | 6.63325i | 0.189702 | − | 0.219049i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0000 | + | 29.4449i | 0.560778 | + | 0.971296i | 0.997429 | + | 0.0716652i | \(0.0228313\pi\) |
−0.436650 | + | 0.899631i | \(0.643835\pi\) | |||||||
\(920\) | 11.4891 | + | 6.63325i | 0.378785 | + | 0.218692i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.69042 | + | 8.12404i | 0.154471 | + | 0.267551i | ||||
\(923\) | 6.63325i | 0.218336i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.7442i | 1.60270i | ||||||||
\(926\) | 26.9444 | − | 15.5563i | 0.885448 | − | 0.511213i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28.1425 | − | 16.2481i | −0.923823 | − | 0.533369i | ||||
\(929\) | 3.67423 | + | 6.36396i | 0.120548 | + | 0.208795i | 0.919984 | − | 0.391956i | \(-0.128202\pi\) |
−0.799436 | + | 0.600751i | \(0.794868\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.4877 | − | 12.1861i | −0.999194 | − | 0.399382i | ||||
\(932\) | 14.1421i | 0.463241i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.69042 | − | 8.12404i | 0.153475 | − | 0.265827i | ||||
\(935\) | 40.4166 | + | 23.3345i | 1.32176 | + | 0.763121i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36.3731i | − | 1.18826i | −0.804370 | − | 0.594128i | \(-0.797497\pi\) | ||
0.804370 | − | 0.594128i | \(-0.202503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −42.2137 | + | 24.3721i | −1.37686 | + | 0.794931i | ||||
\(941\) | 31.5951 | + | 18.2414i | 1.02997 | + | 0.594654i | 0.916976 | − | 0.398942i | \(-0.130622\pi\) |
0.112994 | + | 0.993596i | \(0.463956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.0000 | − | 6.92820i | 0.390774 | − | 0.225613i | ||||
\(944\) | 13.2665i | 0.431788i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 66.0000 | 2.14585 | ||||||||
\(947\) | 17.2337 | + | 29.8496i | 0.560020 | + | 0.969982i | 0.997494 | + | 0.0707515i | \(0.0225397\pi\) |
−0.437474 | + | 0.899231i | \(0.644127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.0712 | − | 8.12404i | −0.456772 | − | 0.263717i | ||||
\(950\) | 34.4674 | − | 19.8997i | 1.11827 | − | 0.645633i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.0000 | + | 3.46410i | 0.583383 | + | 0.112272i | ||||
\(953\) | − | 7.07107i | − | 0.229054i | −0.993420 | − | 0.114527i | \(-0.963465\pi\) | ||
0.993420 | − | 0.114527i | \(-0.0365353\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.38083 | − | 16.2481i | 0.303557 | − | 0.525775i | ||||
\(956\) | 2.44949 | + | 1.41421i | 0.0792222 | + | 0.0457389i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 38.1051i | 1.23112i | ||||||||
\(959\) | −36.7423 | − | 7.07107i | −1.18647 | − | 0.228337i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | − | 3.46410i | −0.0645161 | − | 0.111745i | ||||
\(962\) | 26.9444 | − | 46.6690i | 0.868722 | − | 1.50467i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.0000 | + | 12.1244i | −0.676364 | + | 0.390499i | ||||
\(965\) | − | 3.31662i | − | 0.106766i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0000 | −0.418052 | −0.209026 | − | 0.977910i | \(-0.567029\pi\) | ||||
−0.209026 | + | 0.977910i | \(0.567029\pi\) | |||||||
\(968\) | 53.8888 | − | 31.1127i | 1.73205 | − | 1.00000i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.03562 | + | 4.06202i | 0.225900 | + | 0.130424i | ||||
\(971\) | 37.3397 | − | 21.5581i | 1.19829 | − | 0.691831i | 0.238114 | − | 0.971237i | \(-0.423471\pi\) |
0.960173 | + | 0.279406i | \(0.0901376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.4521 | + | 8.12404i | −0.751839 | + | 0.260445i | ||||
\(974\) | 35.3553i | 1.13286i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.38083 | + | 16.2481i | −0.300273 | + | 0.520088i | ||||
\(977\) | 20.8207 | + | 12.0208i | 0.666112 | + | 0.384580i | 0.794602 | − | 0.607131i | \(-0.207680\pi\) |
−0.128490 | + | 0.991711i | \(0.541013\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.2850 | 1.79888 | ||||||||
\(980\) | −28.7228 | − | 36.4829i | −0.917517 | − | 1.16540i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 35.1781 | − | 20.3101i | 1.12258 | − | 0.648121i | ||||
\(983\) | −4.89898 | + | 8.48528i | −0.156253 | + | 0.270638i | −0.933515 | − | 0.358539i | \(-0.883275\pi\) |
0.777261 | + | 0.629178i | \(0.216608\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 19.8997i | − | 0.633737i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −44.0000 | −1.39983 | ||||||||
\(989\) | 5.74456 | + | 9.94987i | 0.182666 | + | 0.316388i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5000 | + | 30.3109i | −0.555906 | + | 0.962857i | 0.441927 | + | 0.897051i | \(0.354295\pi\) |
−0.997832 | + | 0.0658059i | \(0.979038\pi\) | |||||||
\(992\) | 14.6969 | + | 25.4558i | 0.466628 | + | 0.808224i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.00000 | − | 3.46410i | −0.126872 | − | 0.109875i | ||||
\(995\) | 22.9783 | 0.728460 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.38083 | + | 16.2481i | −0.297094 | + | 0.514582i | −0.975470 | − | 0.220133i | \(-0.929351\pi\) |
0.678376 | + | 0.734715i | \(0.262684\pi\) | |||||||
\(998\) | −22.9783 | + | 39.7995i | −0.727364 | + | 1.25983i | ||||
\(999\) | 0 | 0 |
(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 | 504.2.ch.a.269.2 | yes | 8 | |
3.2 | odd | 2 | inner | 504.2.ch.a.269.3 | yes | 8 | |
4.3 | odd | 2 | 2016.2.cp.a.17.4 | 8 | |||
7.5 | odd | 6 | inner | 504.2.ch.a.341.4 | yes | 8 | |
8.3 | odd | 2 | 2016.2.cp.a.17.1 | 8 | |||
8.5 | even | 2 | inner | 504.2.ch.a.269.1 | ✓ | 8 | |
12.11 | even | 2 | 2016.2.cp.a.17.2 | 8 | |||
21.5 | even | 6 | inner | 504.2.ch.a.341.1 | yes | 8 | |
24.5 | odd | 2 | inner | 504.2.ch.a.269.4 | yes | 8 | |
24.11 | even | 2 | 2016.2.cp.a.17.3 | 8 | |||
28.19 | even | 6 | 2016.2.cp.a.593.3 | 8 | |||
56.5 | odd | 6 | inner | 504.2.ch.a.341.3 | yes | 8 | |
56.19 | even | 6 | 2016.2.cp.a.593.2 | 8 | |||
84.47 | odd | 6 | 2016.2.cp.a.593.1 | 8 | |||
168.5 | even | 6 | inner | 504.2.ch.a.341.2 | yes | 8 | |
168.131 | odd | 6 | 2016.2.cp.a.593.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.ch.a.269.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
504.2.ch.a.269.2 | yes | 8 | 1.1 | even | 1 | trivial | |
504.2.ch.a.269.3 | yes | 8 | 3.2 | odd | 2 | inner | |
504.2.ch.a.269.4 | yes | 8 | 24.5 | odd | 2 | inner | |
504.2.ch.a.341.1 | yes | 8 | 21.5 | even | 6 | inner | |
504.2.ch.a.341.2 | yes | 8 | 168.5 | even | 6 | inner | |
504.2.ch.a.341.3 | yes | 8 | 56.5 | odd | 6 | inner | |
504.2.ch.a.341.4 | yes | 8 | 7.5 | odd | 6 | inner | |
2016.2.cp.a.17.1 | 8 | 8.3 | odd | 2 | |||
2016.2.cp.a.17.2 | 8 | 12.11 | even | 2 | |||
2016.2.cp.a.17.3 | 8 | 24.11 | even | 2 | |||
2016.2.cp.a.17.4 | 8 | 4.3 | odd | 2 | |||
2016.2.cp.a.593.1 | 8 | 84.47 | odd | 6 | |||
2016.2.cp.a.593.2 | 8 | 56.19 | even | 6 | |||
2016.2.cp.a.593.3 | 8 | 28.19 | even | 6 | |||
2016.2.cp.a.593.4 | 8 | 168.131 | odd | 6 |