Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(26,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.p (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: | \(1.50917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.1 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.26 |
Dual form | 189.2.p.b.80.1 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.22474 | + | 2.12132i | −0.547723 | + | 0.948683i | 0.450708 | + | 0.892672i | \(0.351172\pi\) |
−0.998430 | + | 0.0560116i | \(0.982162\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.00000 | − | 1.73205i | 0.948683 | − | 0.547723i | ||||
\(11\) | 4.89898 | − | 2.82843i | 1.47710 | − | 0.852803i | 0.477432 | − | 0.878668i | \(-0.341568\pi\) |
0.999665 | + | 0.0258656i | \(0.00823419\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | −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 | \(-0.262668\pi\) |
−0.975458 | + | 0.220184i | \(0.929334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50000 | + | 0.866025i | 0.344124 | + | 0.198680i | 0.662094 | − | 0.749421i | \(-0.269668\pi\) |
−0.317970 | + | 0.948101i | \(0.603001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.00000 | −1.70561 | ||||||||
\(23\) | 6.12372 | + | 3.53553i | 1.27688 | + | 0.737210i | 0.976274 | − | 0.216537i | \(-0.0694763\pi\) |
0.300610 | + | 0.953747i | \(0.402810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 2.44949 | − | 4.24264i | 0.480384 | − | 0.832050i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41421i | 0.262613i | 0.991342 | + | 0.131306i | \(0.0419172\pi\) | ||||
−0.991342 | + | 0.131306i | \(0.958083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50000 | + | 2.59808i | −0.808224 | + | 0.466628i | −0.846339 | − | 0.532645i | \(-0.821198\pi\) |
0.0381148 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.46410i | 0.594089i | ||||||||
\(35\) | −4.89898 | + | 4.24264i | −0.828079 | + | 0.717137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | − | 3.46410i | 0.328798 | − | 0.569495i | −0.653476 | − | 0.756948i | \(-0.726690\pi\) |
0.982274 | + | 0.187453i | \(0.0600231\pi\) | |||||||
\(38\) | −1.22474 | − | 2.12132i | −0.198680 | − | 0.344124i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.00000 | − | 3.46410i | −0.948683 | − | 0.547723i | ||||
\(41\) | −2.44949 | −0.382546 | −0.191273 | − | 0.981537i | \(-0.561262\pi\) | ||||
−0.191273 | + | 0.981537i | \(0.561262\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.00000 | −1.06749 | −0.533745 | − | 0.845645i | \(-0.679216\pi\) | ||||
−0.533745 | + | 0.845645i | \(0.679216\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.00000 | − | 8.66025i | −0.737210 | − | 1.27688i | ||||
\(47\) | −3.67423 | + | 6.36396i | −0.535942 | + | 0.928279i | 0.463175 | + | 0.886267i | \(0.346710\pi\) |
−0.999117 | + | 0.0420122i | \(0.986623\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 1.41421i | 0.200000i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.22474 | − | 0.707107i | 0.168232 | − | 0.0971286i | −0.413520 | − | 0.910495i | \(-0.635701\pi\) |
0.581752 | + | 0.813366i | \(0.302368\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.8564i | 1.86840i | ||||||||
\(56\) | −2.44949 | + | 7.07107i | −0.327327 | + | 0.944911i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.00000 | − | 1.73205i | 0.131306 | − | 0.227429i | ||||
\(59\) | −7.34847 | − | 12.7279i | −0.956689 | − | 1.65703i | −0.730454 | − | 0.682962i | \(-0.760692\pi\) |
−0.226235 | − | 0.974073i | \(-0.572642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.50000 | − | 2.59808i | −0.576166 | − | 0.332650i | 0.183442 | − | 0.983030i | \(-0.441276\pi\) |
−0.759608 | + | 0.650381i | \(0.774609\pi\) | |||||||
\(62\) | 7.34847 | 0.933257 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −7.34847 | − | 4.24264i | −0.911465 | − | 0.526235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.00000 | − | 1.73205i | 1.07571 | − | 0.207020i | ||||
\(71\) | − | 2.82843i | − | 0.335673i | −0.985815 | − | 0.167836i | \(-0.946322\pi\) | ||
0.985815 | − | 0.167836i | \(-0.0536780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5000 | − | 6.06218i | 1.22893 | − | 0.709524i | 0.262126 | − | 0.965034i | \(-0.415577\pi\) |
0.966807 | + | 0.255510i | \(0.0822432\pi\) | |||||||
\(74\) | −4.89898 | + | 2.82843i | −0.569495 | + | 0.328798i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.6969 | − | 2.82843i | 1.67487 | − | 0.322329i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 4.89898 | + | 8.48528i | 0.547723 | + | 0.948683i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | + | 1.73205i | 0.331295 | + | 0.191273i | ||||
\(83\) | 9.79796 | 1.07547 | 0.537733 | − | 0.843115i | \(-0.319281\pi\) | ||||
0.537733 | + | 0.843115i | \(0.319281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | 8.57321 | + | 4.94975i | 0.924473 | + | 0.533745i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.00000 | + | 13.8564i | 0.852803 | + | 1.47710i | ||||
\(89\) | 1.22474 | − | 2.12132i | 0.129823 | − | 0.224860i | −0.793785 | − | 0.608198i | \(-0.791893\pi\) |
0.923608 | + | 0.383339i | \(0.125226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | + | 8.66025i | −0.314485 | + | 0.907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.00000 | − | 5.19615i | 0.928279 | − | 0.535942i | ||||
\(95\) | −3.67423 | + | 2.12132i | −0.376969 | + | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.66025i | − | 0.879316i | −0.898165 | − | 0.439658i | \(-0.855100\pi\) | ||
0.898165 | − | 0.439658i | \(-0.144900\pi\) | |||||||
\(98\) | −3.67423 | − | 9.19239i | −0.371154 | − | 0.928571i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.89898 | + | 8.48528i | 0.487467 | + | 0.844317i | 0.999896 | − | 0.0144123i | \(-0.00458773\pi\) |
−0.512429 | + | 0.858729i | \(0.671254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0000 | + | 6.92820i | 1.18240 | + | 0.682656i | 0.956567 | − | 0.291511i | \(-0.0941580\pi\) |
0.225828 | + | 0.974167i | \(0.427491\pi\) | |||||||
\(104\) | −9.79796 | −0.960769 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | −12.2474 | − | 7.07107i | −1.18401 | − | 0.683586i | −0.227068 | − | 0.973879i | \(-0.572914\pi\) |
−0.956938 | + | 0.290293i | \(0.906247\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.50000 | − | 14.7224i | −0.814152 | − | 1.41015i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.0957826 | − | 0.995402i | \(-0.469465\pi\) | |||||||
\(110\) | 9.79796 | − | 16.9706i | 0.934199 | − | 1.61808i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.00000 | − | 6.92820i | 0.755929 | − | 0.654654i | ||||
\(113\) | − | 2.82843i | − | 0.266076i | −0.991111 | − | 0.133038i | \(-0.957527\pi\) | ||
0.991111 | − | 0.133038i | \(-0.0424732\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.0000 | + | 8.66025i | −1.39876 | + | 0.807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.7846i | 1.91338i | ||||||||
\(119\) | −1.22474 | − | 6.36396i | −0.112272 | − | 0.583383i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5000 | − | 18.1865i | 0.954545 | − | 1.65332i | ||||
\(122\) | 3.67423 | + | 6.36396i | 0.332650 | + | 0.576166i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.00000 | + | 10.3923i | 0.526235 | + | 0.911465i | ||||
\(131\) | −8.57321 | + | 14.8492i | −0.749045 | + | 1.29738i | 0.199236 | + | 0.979952i | \(0.436154\pi\) |
−0.948281 | + | 0.317433i | \(0.897179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | + | 3.46410i | 0.260133 | + | 0.300376i | ||||
\(134\) | 2.82843i | 0.244339i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | − | 3.46410i | 0.514496 | − | 0.297044i | ||||
\(137\) | −6.12372 | + | 3.53553i | −0.523185 | + | 0.302061i | −0.738237 | − | 0.674542i | \(-0.764341\pi\) |
0.215052 | + | 0.976603i | \(0.431008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.92820i | − | 0.587643i | −0.955860 | − | 0.293821i | \(-0.905073\pi\) | ||
0.955860 | − | 0.293821i | \(-0.0949270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.00000 | + | 3.46410i | −0.167836 | + | 0.290701i | ||||
\(143\) | 9.79796 | + | 16.9706i | 0.819346 | + | 1.41915i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00000 | − | 1.73205i | −0.249136 | − | 0.143839i | ||||
\(146\) | −17.1464 | −1.41905 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.57321 | − | 4.94975i | −0.702345 | − | 0.405499i | 0.105875 | − | 0.994379i | \(-0.466236\pi\) |
−0.808220 | + | 0.588880i | \(0.799569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.50000 | − | 9.52628i | −0.447584 | − | 0.775238i | 0.550645 | − | 0.834740i | \(-0.314382\pi\) |
−0.998228 | + | 0.0595022i | \(0.981049\pi\) | |||||||
\(152\) | −2.44949 | + | 4.24264i | −0.198680 | + | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −20.0000 | − | 6.92820i | −1.61165 | − | 0.558291i | ||||
\(155\) | − | 12.7279i | − | 1.02233i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | + | 5.19615i | −0.718278 | + | 0.414698i | −0.814119 | − | 0.580699i | \(-0.802779\pi\) |
0.0958404 | + | 0.995397i | \(0.469446\pi\) | |||||||
\(158\) | −4.89898 | + | 2.82843i | −0.389742 | + | 0.225018i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.2474 | + | 14.1421i | 0.965234 | + | 1.11456i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.5000 | + | 19.9186i | −0.900750 | + | 1.56014i | −0.0742262 | + | 0.997241i | \(0.523649\pi\) |
−0.826523 | + | 0.562902i | \(0.809685\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | − | 6.92820i | −0.931381 | − | 0.537733i | ||||
\(167\) | 4.89898 | 0.379094 | 0.189547 | − | 0.981872i | \(-0.439298\pi\) | ||||
0.189547 | + | 0.981872i | \(0.439298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −7.34847 | − | 4.24264i | −0.563602 | − | 0.325396i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.67423 | − | 6.36396i | 0.279347 | − | 0.483843i | −0.691876 | − | 0.722017i | \(-0.743215\pi\) |
0.971223 | + | 0.238174i | \(0.0765487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | − | 2.59808i | −0.0377964 | − | 0.196396i | ||||
\(176\) | − | 22.6274i | − | 1.70561i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | + | 1.73205i | −0.224860 | + | 0.129823i | ||||
\(179\) | 8.57321 | − | 4.94975i | 0.640792 | − | 0.369961i | −0.144127 | − | 0.989559i | \(-0.546038\pi\) |
0.784920 | + | 0.619598i | \(0.212704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.5885i | − | 1.15868i | −0.815086 | − | 0.579340i | \(-0.803310\pi\) | ||
0.815086 | − | 0.579340i | \(-0.196690\pi\) | |||||||
\(182\) | 9.79796 | − | 8.48528i | 0.726273 | − | 0.628971i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.0000 | + | 17.3205i | −0.737210 | + | 1.27688i | ||||
\(185\) | 4.89898 | + | 8.48528i | 0.360180 | + | 0.623850i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | − | 6.92820i | −0.877527 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | −1.22474 | − | 0.707107i | −0.0886194 | − | 0.0511645i | 0.455035 | − | 0.890473i | \(-0.349627\pi\) |
−0.543655 | + | 0.839309i | \(0.682960\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | −6.12372 | + | 10.6066i | −0.439658 | + | 0.761510i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.82843i | − | 0.201517i | −0.994911 | − | 0.100759i | \(-0.967873\pi\) | ||
0.994911 | − | 0.100759i | \(-0.0321270\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | − | 0.866025i | 0.106332 | − | 0.0613909i | −0.445891 | − | 0.895087i | \(-0.647113\pi\) |
0.552223 | + | 0.833696i | \(0.313780\pi\) | |||||||
\(200\) | 2.44949 | − | 1.41421i | 0.173205 | − | 0.100000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 13.8564i | − | 0.974933i | ||||||
\(203\) | −1.22474 | + | 3.53553i | −0.0859602 | + | 0.248146i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | − | 5.19615i | 0.209529 | − | 0.362915i | ||||
\(206\) | −9.79796 | − | 16.9706i | −0.682656 | − | 1.18240i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.0000 | + | 6.92820i | 0.832050 | + | 0.480384i | ||||
\(209\) | 9.79796 | 0.677739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | −0.0688428 | −0.0344214 | − | 0.999407i | \(-0.510959\pi\) | ||||
−0.0344214 | + | 0.999407i | \(0.510959\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.0000 | + | 17.3205i | 0.683586 | + | 1.18401i | ||||
\(215\) | 8.57321 | − | 14.8492i | 0.584688 | − | 1.01271i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.5000 | + | 2.59808i | −0.916440 | + | 0.176369i | ||||
\(218\) | 24.0416i | 1.62830i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.34847 | − | 4.24264i | 0.494312 | − | 0.285391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.8564i | − | 0.927894i | −0.885863 | − | 0.463947i | \(-0.846433\pi\) | ||
0.885863 | − | 0.463947i | \(-0.153567\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.00000 | + | 3.46410i | −0.133038 | + | 0.230429i | ||||
\(227\) | 1.22474 | + | 2.12132i | 0.0812892 | + | 0.140797i | 0.903804 | − | 0.427947i | \(-0.140763\pi\) |
−0.822515 | + | 0.568744i | \(0.807430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.50000 | − | 0.866025i | −0.0991228 | − | 0.0572286i | 0.449619 | − | 0.893220i | \(-0.351560\pi\) |
−0.548742 | + | 0.835992i | \(0.684893\pi\) | |||||||
\(230\) | 24.4949 | 1.61515 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.00000 | −0.262613 | ||||||||
\(233\) | 13.4722 | + | 7.77817i | 0.882593 | + | 0.509565i | 0.871512 | − | 0.490373i | \(-0.163140\pi\) |
0.0110803 | + | 0.999939i | \(0.496473\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | − | 15.5885i | −0.587095 | − | 1.01688i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.00000 | + | 8.66025i | −0.194461 | + | 0.561361i | ||||
\(239\) | 9.89949i | 0.640345i | 0.947359 | + | 0.320173i | \(0.103741\pi\) | ||||
−0.947359 | + | 0.320173i | \(0.896259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5000 | + | 6.06218i | −0.676364 | + | 0.390499i | −0.798484 | − | 0.602016i | \(-0.794364\pi\) |
0.122119 | + | 0.992515i | \(0.461031\pi\) | |||||||
\(242\) | −25.7196 | + | 14.8492i | −1.65332 | + | 0.954545i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.9217 | + | 6.36396i | −1.01720 | + | 0.406579i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00000 | + | 5.19615i | −0.190885 | + | 0.330623i | ||||
\(248\) | −7.34847 | − | 12.7279i | −0.466628 | − | 0.808224i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | + | 6.92820i | 0.758947 | + | 0.438178i | ||||
\(251\) | 7.34847 | 0.463831 | 0.231916 | − | 0.972736i | \(-0.425501\pi\) | ||||
0.231916 | + | 0.972736i | \(0.425501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.0000 | 2.51478 | ||||||||
\(254\) | 1.22474 | + | 0.707107i | 0.0768473 | + | 0.0443678i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.79796 | − | 16.9706i | 0.611180 | − | 1.05859i | −0.379862 | − | 0.925043i | \(-0.624029\pi\) |
0.991042 | − | 0.133551i | \(-0.0426381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | − | 6.92820i | 0.497096 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.0000 | − | 12.1244i | 1.29738 | − | 0.749045i | ||||
\(263\) | −17.1464 | + | 9.89949i | −1.05729 | + | 0.610429i | −0.924683 | − | 0.380739i | \(-0.875670\pi\) |
−0.132612 | + | 0.991168i | \(0.542336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.46410i | 0.212798i | ||||||||
\(266\) | −1.22474 | − | 6.36396i | −0.0750939 | − | 0.390199i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.2474 | − | 21.2132i | −0.746740 | − | 1.29339i | −0.949377 | − | 0.314138i | \(-0.898285\pi\) |
0.202637 | − | 0.979254i | \(-0.435049\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5000 | + | 11.2583i | 1.18454 | + | 0.683895i | 0.957061 | − | 0.289888i | \(-0.0936180\pi\) |
0.227480 | + | 0.973783i | \(0.426951\pi\) | |||||||
\(272\) | −9.79796 | −0.594089 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | −4.89898 | − | 2.82843i | −0.295420 | − | 0.170561i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5000 | + | 21.6506i | 0.751052 | + | 1.30086i | 0.947313 | + | 0.320309i | \(0.103787\pi\) |
−0.196261 | + | 0.980552i | \(0.562880\pi\) | |||||||
\(278\) | −4.89898 | + | 8.48528i | −0.293821 | + | 0.508913i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.0000 | − | 13.8564i | −0.717137 | − | 0.828079i | ||||
\(281\) | 5.65685i | 0.337460i | 0.985662 | + | 0.168730i | \(0.0539665\pi\) | ||||
−0.985662 | + | 0.168730i | \(0.946033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.5000 | + | 12.9904i | −1.33749 | + | 0.772198i | −0.986434 | − | 0.164158i | \(-0.947509\pi\) |
−0.351052 | + | 0.936356i | \(0.614176\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 27.7128i | − | 1.63869i | ||||||
\(287\) | −6.12372 | − | 2.12132i | −0.361472 | − | 0.125218i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50000 | − | 9.52628i | 0.323529 | − | 0.560369i | ||||
\(290\) | 2.44949 | + | 4.24264i | 0.143839 | + | 0.249136i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.4949 | −1.43101 | −0.715504 | − | 0.698609i | \(-0.753803\pi\) | ||||
−0.715504 | + | 0.698609i | \(0.753803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.0000 | 2.09600 | ||||||||
\(296\) | 9.79796 | + | 5.65685i | 0.569495 | + | 0.328798i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.00000 | + | 12.1244i | 0.405499 | + | 0.702345i | ||||
\(299\) | −12.2474 | + | 21.2132i | −0.708288 | + | 1.22679i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.5000 | − | 6.06218i | −1.00868 | − | 0.349418i | ||||
\(302\) | 15.5563i | 0.895167i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.00000 | − | 3.46410i | 0.344124 | − | 0.198680i | ||||
\(305\) | 11.0227 | − | 6.36396i | 0.631158 | − | 0.364399i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.19615i | 0.296560i | 0.988945 | + | 0.148280i | \(0.0473737\pi\) | ||||
−0.988945 | + | 0.148280i | \(0.952626\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.00000 | + | 15.5885i | −0.511166 | + | 0.885365i | ||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50000 | + | 2.59808i | 0.254355 | + | 0.146852i | 0.621757 | − | 0.783210i | \(-0.286419\pi\) |
−0.367402 | + | 0.930062i | \(0.619753\pi\) | |||||||
\(314\) | 14.6969 | 0.829396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.44949 | + | 1.41421i | 0.137577 | + | 0.0794301i | 0.567209 | − | 0.823574i | \(-0.308023\pi\) |
−0.429632 | + | 0.903004i | \(0.641357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 9.79796 | − | 16.9706i | 0.547723 | − | 0.948683i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.00000 | − | 25.9808i | −0.278639 | − | 1.44785i | ||||
\(323\) | − | 4.24264i | − | 0.236067i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | − | 1.73205i | 0.166410 | − | 0.0960769i | ||||
\(326\) | 28.1691 | − | 16.2635i | 1.56014 | − | 0.900750i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.92820i | − | 0.382546i | ||||||
\(329\) | −14.6969 | + | 12.7279i | −0.810268 | + | 0.701713i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | + | 14.7224i | −0.467202 | + | 0.809218i | −0.999298 | − | 0.0374662i | \(-0.988071\pi\) |
0.532096 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.00000 | − | 3.46410i | −0.328305 | − | 0.189547i | ||||
\(335\) | 4.89898 | 0.267660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | −0.0544735 | −0.0272367 | − | 0.999629i | \(-0.508671\pi\) | ||||
−0.0272367 | + | 0.999629i | \(0.508671\pi\) | |||||||
\(338\) | −1.22474 | − | 0.707107i | −0.0666173 | − | 0.0384615i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.6969 | + | 25.4558i | −0.795884 | + | 1.37851i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | − | 19.7990i | − | 1.06749i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | + | 5.19615i | −0.483843 | + | 0.279347i | ||||
\(347\) | 26.9444 | − | 15.5563i | 1.44645 | − | 0.835109i | 0.448183 | − | 0.893942i | \(-0.352071\pi\) |
0.998268 | + | 0.0588334i | \(0.0187381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.73205i | 0.0927146i | 0.998925 | + | 0.0463573i | \(0.0147613\pi\) | ||||
−0.998925 | + | 0.0463573i | \(0.985239\pi\) | |||||||
\(350\) | −1.22474 | + | 3.53553i | −0.0654654 | + | 0.188982i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.1464 | − | 29.6985i | −0.912612 | − | 1.58069i | −0.810360 | − | 0.585932i | \(-0.800728\pi\) |
−0.102252 | − | 0.994758i | \(-0.532605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 3.46410i | 0.318447 | + | 0.183855i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.0000 | −0.739923 | ||||||||
\(359\) | 9.79796 | + | 5.65685i | 0.517116 | + | 0.298557i | 0.735754 | − | 0.677249i | \(-0.236828\pi\) |
−0.218638 | + | 0.975806i | \(0.570161\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | − | 13.8564i | −0.421053 | − | 0.729285i | ||||
\(362\) | −11.0227 | + | 19.0919i | −0.579340 | + | 1.00345i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.6985i | 1.55449i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.50000 | − | 4.33013i | 0.391497 | − | 0.226031i | −0.291312 | − | 0.956628i | \(-0.594092\pi\) |
0.682808 | + | 0.730597i | \(0.260758\pi\) | |||||||
\(368\) | 24.4949 | − | 14.1421i | 1.27688 | − | 0.737210i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 13.8564i | − | 0.720360i | ||||||
\(371\) | 3.67423 | − | 0.707107i | 0.190757 | − | 0.0367112i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.500000 | − | 0.866025i | 0.0258890 | − | 0.0448411i | −0.852791 | − | 0.522253i | \(-0.825092\pi\) |
0.878680 | + | 0.477412i | \(0.158425\pi\) | |||||||
\(374\) | 9.79796 | + | 16.9706i | 0.506640 | + | 0.877527i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.0000 | − | 10.3923i | −0.928279 | − | 0.535942i | ||||
\(377\) | −4.89898 | −0.252310 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0000 | −0.513665 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.00000 | + | 1.73205i | 0.0511645 | + | 0.0886194i | ||||
\(383\) | 17.1464 | − | 29.6985i | 0.876142 | − | 1.51752i | 0.0205998 | − | 0.999788i | \(-0.493442\pi\) |
0.855542 | − | 0.517734i | \(-0.173224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | + | 34.6410i | −0.611577 | + | 1.76547i | ||||
\(386\) | − | 5.65685i | − | 0.287926i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.2702 | − | 13.4350i | 1.17984 | − | 0.681183i | 0.223865 | − | 0.974620i | \(-0.428132\pi\) |
0.955978 | + | 0.293437i | \(0.0947991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.3205i | − | 0.875936i | ||||||
\(392\) | −12.2474 | + | 15.5563i | −0.618590 | + | 0.785714i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.00000 | + | 3.46410i | −0.100759 | + | 0.174519i | ||||
\(395\) | 4.89898 | + | 8.48528i | 0.246494 | + | 0.426941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5000 | − | 9.52628i | −0.828111 | − | 0.478110i | 0.0250943 | − | 0.999685i | \(-0.492011\pi\) |
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | −2.44949 | −0.122782 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −19.5959 | − | 11.3137i | −0.978573 | − | 0.564980i | −0.0767343 | − | 0.997052i | \(-0.524449\pi\) |
−0.901839 | + | 0.432072i | \(0.857783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00000 | − | 15.5885i | −0.448322 | − | 0.776516i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | − | 3.46410i | 0.198517 | − | 0.171920i | ||||
\(407\) | − | 22.6274i | − | 1.12160i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.00000 | + | 5.19615i | −0.445021 | + | 0.256933i | −0.705725 | − | 0.708486i | \(-0.749379\pi\) |
0.260704 | + | 0.965419i | \(0.416045\pi\) | |||||||
\(410\) | −7.34847 | + | 4.24264i | −0.362915 | + | 0.209529i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.34847 | − | 38.1838i | −0.361595 | − | 1.87890i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | + | 20.7846i | −0.589057 | + | 1.02028i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.0000 | − | 6.92820i | −0.586939 | − | 0.338869i | ||||
\(419\) | −2.44949 | −0.119665 | −0.0598327 | − | 0.998208i | \(-0.519057\pi\) | ||||
−0.0598327 | + | 0.998208i | \(0.519057\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | 0.536107 | 0.268054 | − | 0.963404i | \(-0.413620\pi\) | ||||
0.268054 | + | 0.963404i | \(0.413620\pi\) | |||||||
\(422\) | 1.22474 | + | 0.707107i | 0.0596196 | + | 0.0344214i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.00000 | + | 3.46410i | 0.0971286 | + | 0.168232i | ||||
\(425\) | −1.22474 | + | 2.12132i | −0.0594089 | + | 0.102899i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.00000 | − | 10.3923i | −0.435541 | − | 0.502919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.0000 | + | 12.1244i | −1.01271 | + | 0.584688i | ||||
\(431\) | −24.4949 | + | 14.1421i | −1.17988 | + | 0.681203i | −0.955986 | − | 0.293411i | \(-0.905209\pi\) |
−0.223891 | + | 0.974614i | \(0.571876\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.19615i | 0.249711i | 0.992175 | + | 0.124856i | \(0.0398468\pi\) | ||||
−0.992175 | + | 0.124856i | \(0.960153\pi\) | |||||||
\(434\) | 18.3712 | + | 6.36396i | 0.881845 | + | 0.305480i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.12372 | + | 10.6066i | 0.292937 | + | 0.507383i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.0000 | + | 10.3923i | 0.859093 | + | 0.495998i | 0.863708 | − | 0.503992i | \(-0.168136\pi\) |
−0.00461537 | + | 0.999989i | \(0.501469\pi\) | |||||||
\(440\) | −39.1918 | −1.86840 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | 13.4722 | + | 7.77817i | 0.640083 | + | 0.369552i | 0.784647 | − | 0.619943i | \(-0.212844\pi\) |
−0.144563 | + | 0.989496i | \(0.546178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | + | 5.19615i | 0.142214 | + | 0.246321i | ||||
\(446\) | −9.79796 | + | 16.9706i | −0.463947 | + | 0.803579i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.0000 | − | 6.92820i | −0.944911 | − | 0.327327i | ||||
\(449\) | 35.3553i | 1.66852i | 0.551370 | + | 0.834261i | \(0.314105\pi\) | ||||
−0.551370 | + | 0.834261i | \(0.685895\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | + | 6.92820i | −0.565058 | + | 0.326236i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 3.46410i | − | 0.162578i | ||||||
\(455\) | −14.6969 | − | 16.9706i | −0.689003 | − | 0.795592i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.50000 | + | 4.33013i | −0.116945 | + | 0.202555i | −0.918556 | − | 0.395292i | \(-0.870643\pi\) |
0.801611 | + | 0.597847i | \(0.203977\pi\) | |||||||
\(458\) | 1.22474 | + | 2.12132i | 0.0572286 | + | 0.0991228i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.4949 | 1.14084 | 0.570421 | − | 0.821353i | \(-0.306780\pi\) | ||||
0.570421 | + | 0.821353i | \(0.306780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00000 | −0.0464739 | −0.0232370 | − | 0.999730i | \(-0.507397\pi\) | ||||
−0.0232370 | + | 0.999730i | \(0.507397\pi\) | |||||||
\(464\) | 4.89898 | + | 2.82843i | 0.227429 | + | 0.131306i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.0000 | − | 19.0526i | −0.509565 | − | 0.882593i | ||||
\(467\) | −2.44949 | + | 4.24264i | −0.113349 | + | 0.196326i | −0.917119 | − | 0.398615i | \(-0.869491\pi\) |
0.803770 | + | 0.594941i | \(0.202824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.00000 | − | 5.19615i | −0.0461757 | − | 0.239936i | ||||
\(470\) | 25.4558i | 1.17419i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 36.0000 | − | 20.7846i | 1.65703 | − | 0.956689i | ||||
\(473\) | −34.2929 | + | 19.7990i | −1.57679 | + | 0.910359i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.73205i | − | 0.0794719i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.00000 | − | 12.1244i | 0.320173 | − | 0.554555i | ||||
\(479\) | 1.22474 | + | 2.12132i | 0.0559600 | + | 0.0969256i | 0.892648 | − | 0.450754i | \(-0.148845\pi\) |
−0.836688 | + | 0.547679i | \(0.815511\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | + | 6.92820i | 0.547153 | + | 0.315899i | ||||
\(482\) | 17.1464 | 0.780998 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.3712 | + | 10.6066i | 0.834192 | + | 0.481621i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.50000 | + | 11.2583i | 0.294543 | + | 0.510164i | 0.974879 | − | 0.222737i | \(-0.0714992\pi\) |
−0.680335 | + | 0.732901i | \(0.738166\pi\) | |||||||
\(488\) | 7.34847 | − | 12.7279i | 0.332650 | − | 0.576166i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 24.0000 | + | 3.46410i | 1.08421 | + | 0.156492i | ||||
\(491\) | 5.65685i | 0.255290i | 0.991820 | + | 0.127645i | \(0.0407419\pi\) | ||||
−0.991820 | + | 0.127645i | \(0.959258\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00000 | − | 1.73205i | 0.135113 | − | 0.0780076i | ||||
\(494\) | 7.34847 | − | 4.24264i | 0.330623 | − | 0.190885i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.7846i | 0.933257i | ||||||||
\(497\) | 2.44949 | − | 7.07107i | 0.109875 | − | 0.317181i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5000 | − | 21.6506i | 0.559577 | − | 0.969216i | −0.437955 | − | 0.898997i | \(-0.644297\pi\) |
0.997532 | − | 0.0702185i | \(-0.0223697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.00000 | − | 5.19615i | −0.401690 | − | 0.231916i | ||||
\(503\) | −22.0454 | −0.982956 | −0.491478 | − | 0.870890i | \(-0.663543\pi\) | ||||
−0.491478 | + | 0.870890i | \(0.663543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.0000 | −1.06799 | ||||||||
\(506\) | −48.9898 | − | 28.2843i | −2.17786 | − | 1.25739i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.79796 | − | 16.9706i | 0.434287 | − | 0.752207i | −0.562950 | − | 0.826491i | \(-0.690334\pi\) |
0.997237 | + | 0.0742838i | \(0.0236671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.5000 | − | 6.06218i | 1.39348 | − | 0.268175i | ||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.0000 | + | 13.8564i | −1.05859 | + | 0.611180i | ||||
\(515\) | −29.3939 | + | 16.9706i | −1.29525 | + | 0.747812i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.5692i | 1.82821i | ||||||||
\(518\) | −14.6969 | + | 2.82843i | −0.645746 | + | 0.124274i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.0000 | − | 20.7846i | 0.526235 | − | 0.911465i | ||||
\(521\) | −12.2474 | − | 21.2132i | −0.536570 | − | 0.929367i | −0.999086 | − | 0.0427559i | \(-0.986386\pi\) |
0.462515 | − | 0.886611i | \(-0.346947\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.00000 | − | 1.73205i | −0.131181 | − | 0.0757373i | 0.432973 | − | 0.901407i | \(-0.357464\pi\) |
−0.564154 | + | 0.825669i | \(0.690798\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.0000 | 1.22086 | ||||||||
\(527\) | 11.0227 | + | 6.36396i | 0.480157 | + | 0.277218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.5000 | + | 23.3827i | 0.586957 | + | 1.01664i | ||||
\(530\) | 2.44949 | − | 4.24264i | 0.106399 | − | 0.184289i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.48528i | − | 0.367538i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.0000 | − | 17.3205i | 1.29701 | − | 0.748831i | ||||
\(536\) | 4.89898 | − | 2.82843i | 0.211604 | − | 0.122169i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.6410i | 1.49348i | ||||||||
\(539\) | 39.1918 | + | 5.65685i | 1.68811 | + | 0.243658i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.50000 | − | 11.2583i | 0.279457 | − | 0.484033i | −0.691793 | − | 0.722096i | \(-0.743179\pi\) |
0.971250 | + | 0.238062i | \(0.0765123\pi\) | |||||||
\(542\) | −15.9217 | − | 27.5772i | −0.683895 | − | 1.18454i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 41.6413 | 1.78372 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.0000 | −1.06892 | −0.534461 | − | 0.845193i | \(-0.679486\pi\) | ||||
−0.534461 | + | 0.845193i | \(0.679486\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.00000 | + | 6.92820i | 0.170561 | + | 0.295420i | ||||
\(551\) | −1.22474 | + | 2.12132i | −0.0521759 | + | 0.0903713i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | − | 6.92820i | 0.340195 | − | 0.294617i | ||||
\(554\) | − | 35.3553i | − | 1.50210i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.22474 | − | 0.707107i | 0.0518941 | − | 0.0299611i | −0.473828 | − | 0.880617i | \(-0.657128\pi\) |
0.525723 | + | 0.850656i | \(0.323795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 24.2487i | − | 1.02561i | ||||||
\(560\) | 4.89898 | + | 25.4558i | 0.207020 | + | 1.07571i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.00000 | − | 6.92820i | 0.168730 | − | 0.292249i | ||||
\(563\) | 11.0227 | + | 19.0919i | 0.464552 | + | 0.804627i | 0.999181 | − | 0.0404596i | \(-0.0128822\pi\) |
−0.534630 | + | 0.845087i | \(0.679549\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000 | + | 3.46410i | 0.252422 | + | 0.145736i | ||||
\(566\) | 36.7423 | 1.54440 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | 31.8434 | + | 18.3848i | 1.33494 | + | 0.770730i | 0.986053 | − | 0.166434i | \(-0.0532251\pi\) |
0.348891 | + | 0.937163i | \(0.386558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5000 | − | 35.5070i | −0.857898 | − | 1.48592i | −0.873930 | − | 0.486052i | \(-0.838437\pi\) |
0.0160316 | − | 0.999871i | \(-0.494897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.00000 | + | 6.92820i | 0.250435 | + | 0.289178i | ||||
\(575\) | − | 7.07107i | − | 0.294884i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.00000 | + | 1.73205i | −0.124892 | + | 0.0721062i | −0.561144 | − | 0.827718i | \(-0.689639\pi\) |
0.436253 | + | 0.899824i | \(0.356305\pi\) | |||||||
\(578\) | −13.4722 | + | 7.77817i | −0.560369 | + | 0.323529i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.4949 | + | 8.48528i | 1.01622 | + | 0.352029i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | 17.1464 | + | 29.6985i | 0.709524 | + | 1.22893i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.0000 | + | 17.3205i | 1.23929 | + | 0.715504i | ||||
\(587\) | −26.9444 | −1.11211 | −0.556057 | − | 0.831144i | \(-0.687686\pi\) | ||||
−0.556057 | + | 0.831144i | \(0.687686\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | −0.370839 | ||||||||
\(590\) | −44.0908 | − | 25.4558i | −1.81519 | − | 1.04800i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.00000 | − | 13.8564i | −0.328798 | − | 0.569495i | ||||
\(593\) | 4.89898 | − | 8.48528i | 0.201177 | − | 0.348449i | −0.747731 | − | 0.664002i | \(-0.768857\pi\) |
0.948908 | + | 0.315553i | \(0.102190\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0000 | + | 5.19615i | 0.614940 | + | 0.213021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 30.0000 | − | 17.3205i | 1.22679 | − | 0.708288i | ||||
\(599\) | −6.12372 | + | 3.53553i | −0.250209 | + | 0.144458i | −0.619860 | − | 0.784713i | \(-0.712811\pi\) |
0.369651 | + | 0.929171i | \(0.379477\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.5167i | 0.918474i | 0.888314 | + | 0.459237i | \(0.151877\pi\) | ||||
−0.888314 | + | 0.459237i | \(0.848123\pi\) | |||||||
\(602\) | 17.1464 | + | 19.7990i | 0.698836 | + | 0.806947i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.7196 | + | 44.5477i | 1.04565 | + | 1.81112i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.5000 | + | 14.7224i | 1.03501 | + | 0.597565i | 0.918417 | − | 0.395614i | \(-0.129468\pi\) |
0.116596 | + | 0.993179i | \(0.462802\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.0000 | −0.728799 | ||||||||
\(611\) | −22.0454 | − | 12.7279i | −0.891862 | − | 0.514917i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5000 | + | 26.8468i | 0.626039 | + | 1.08433i | 0.988339 | + | 0.152270i | \(0.0486583\pi\) |
−0.362300 | + | 0.932062i | \(0.618008\pi\) | |||||||
\(614\) | 3.67423 | − | 6.36396i | 0.148280 | − | 0.256829i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.00000 | + | 41.5692i | 0.322329 | + | 1.67487i | ||||
\(617\) | − | 45.2548i | − | 1.82189i | −0.412527 | − | 0.910946i | \(-0.635354\pi\) | ||
0.412527 | − | 0.910946i | \(-0.364646\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.0000 | − | 17.3205i | 1.20580 | − | 0.696170i | 0.243962 | − | 0.969785i | \(-0.421553\pi\) |
0.961839 | + | 0.273615i | \(0.0882193\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.89898 | − | 4.24264i | 0.196273 | − | 0.169978i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | −3.67423 | − | 6.36396i | −0.146852 | − | 0.254355i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.79796 | −0.390670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.0000 | 0.437903 | 0.218952 | − | 0.975736i | \(-0.429736\pi\) | ||||
0.218952 | + | 0.975736i | \(0.429736\pi\) | |||||||
\(632\) | 9.79796 | + | 5.65685i | 0.389742 | + | 0.225018i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.00000 | − | 3.46410i | −0.0794301 | − | 0.137577i | ||||
\(635\) | 1.22474 | − | 2.12132i | 0.0486025 | − | 0.0841820i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0000 | + | 19.0526i | −0.594322 | + | 0.754890i | ||||
\(638\) | − | 11.3137i | − | 0.447914i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.0000 | + | 13.8564i | −0.948683 | + | 0.547723i | ||||
\(641\) | −6.12372 | + | 3.53553i | −0.241873 | + | 0.139645i | −0.616037 | − | 0.787717i | \(-0.711263\pi\) |
0.374165 | + | 0.927362i | \(0.377930\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 22.5167i | − | 0.887970i | −0.896034 | − | 0.443985i | \(-0.853564\pi\) | ||
0.896034 | − | 0.443985i | \(-0.146436\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.00000 | + | 5.19615i | −0.118033 | + | 0.204440i | ||||
\(647\) | −12.2474 | − | 21.2132i | −0.481497 | − | 0.833977i | 0.518278 | − | 0.855212i | \(-0.326573\pi\) |
−0.999775 | + | 0.0212354i | \(0.993240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −72.0000 | − | 41.5692i | −2.82625 | − | 1.63173i | ||||
\(650\) | −4.89898 | −0.192154 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.4722 | + | 7.77817i | 0.527208 | + | 0.304383i | 0.739879 | − | 0.672740i | \(-0.234883\pi\) |
−0.212671 | + | 0.977124i | \(0.568216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.0000 | − | 36.3731i | −0.820538 | − | 1.42121i | ||||
\(656\) | −4.89898 | + | 8.48528i | −0.191273 | + | 0.331295i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 27.0000 | − | 5.19615i | 1.05257 | − | 0.202567i | ||||
\(659\) | − | 7.07107i | − | 0.275450i | −0.990471 | − | 0.137725i | \(-0.956021\pi\) | ||
0.990471 | − | 0.137725i | \(-0.0439790\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.5000 | + | 23.3827i | −1.57527 | + | 0.909481i | −0.579761 | + | 0.814787i | \(0.696854\pi\) |
−0.995506 | + | 0.0946945i | \(0.969813\pi\) | |||||||
\(662\) | 20.8207 | − | 12.0208i | 0.809218 | − | 0.467202i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.7128i | 1.07547i | ||||||||
\(665\) | −11.0227 | + | 2.12132i | −0.427442 | + | 0.0822613i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.00000 | + | 8.66025i | −0.193601 | + | 0.335326i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.00000 | − | 3.46410i | −0.231800 | − | 0.133830i | ||||
\(671\) | −29.3939 | −1.13474 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0000 | −0.963679 | −0.481840 | − | 0.876259i | \(-0.660031\pi\) | ||||
−0.481840 | + | 0.876259i | \(0.660031\pi\) | |||||||
\(674\) | 1.22474 | + | 0.707107i | 0.0471754 | + | 0.0272367i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.34847 | + | 12.7279i | −0.282425 | + | 0.489174i | −0.971981 | − | 0.235058i | \(-0.924472\pi\) |
0.689557 | + | 0.724232i | \(0.257805\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.50000 | − | 21.6506i | 0.287824 | − | 0.830875i | ||||
\(680\) | 16.9706i | 0.650791i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 36.0000 | − | 20.7846i | 1.37851 | − | 0.795884i | ||||
\(683\) | −31.8434 | + | 18.3848i | −1.21845 | + | 0.703474i | −0.964587 | − | 0.263766i | \(-0.915035\pi\) |
−0.253866 | + | 0.967239i | \(0.581702\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 17.3205i | − | 0.661783i | ||||||
\(686\) | −1.22474 | − | 26.1630i | −0.0467610 | − | 0.998906i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.0000 | + | 24.2487i | −0.533745 | + | 0.924473i | ||||
\(689\) | 2.44949 | + | 4.24264i | 0.0933181 | + | 0.161632i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.50000 | − | 2.59808i | −0.171188 | − | 0.0988355i | 0.411958 | − | 0.911203i | \(-0.364845\pi\) |
−0.583146 | + | 0.812367i | \(0.698178\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −44.0000 | −1.67022 | ||||||||
\(695\) | 14.6969 | + | 8.48528i | 0.557487 | + | 0.321865i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | + | 5.19615i | 0.113633 | + | 0.196818i | ||||
\(698\) | 1.22474 | − | 2.12132i | 0.0463573 | − | 0.0802932i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.5563i | − | 0.587555i | −0.955874 | − | 0.293778i | \(-0.905087\pi\) | ||
0.955874 | − | 0.293778i | \(-0.0949125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000 | − | 3.46410i | 0.226294 | − | 0.130651i | ||||
\(704\) | −39.1918 | + | 22.6274i | −1.47710 | + | 0.852803i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 48.4974i | 1.82522i | ||||||||
\(707\) | 4.89898 | + | 25.4558i | 0.184245 | + | 0.957366i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.50000 | + | 4.33013i | −0.0938895 | + | 0.162621i | −0.909145 | − | 0.416481i | \(-0.863263\pi\) |
0.815255 | + | 0.579102i | \(0.196597\pi\) | |||||||
\(710\) | −4.89898 | − | 8.48528i | −0.183855 | − | 0.318447i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000 | + | 3.46410i | 0.224860 | + | 0.129823i | ||||
\(713\) | −36.7423 | −1.37601 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −48.0000 | −1.79510 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.00000 | − | 13.8564i | −0.298557 | − | 0.517116i | ||||
\(719\) | 12.2474 | − | 21.2132i | 0.456753 | − | 0.791119i | −0.542034 | − | 0.840356i | \(-0.682346\pi\) |
0.998787 | + | 0.0492373i | \(0.0156791\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0000 | + | 27.7128i | 0.893807 | + | 1.03208i | ||||
\(722\) | 22.6274i | 0.842105i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.22474 | − | 0.707107i | 0.0454859 | − | 0.0262613i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.9090i | 1.22053i | 0.792199 | + | 0.610263i | \(0.208936\pi\) | ||||
−0.792199 | + | 0.610263i | \(0.791064\pi\) | |||||||
\(728\) | −24.4949 | − | 8.48528i | −0.907841 | − | 0.314485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.0000 | − | 36.3731i | 0.777245 | − | 1.34623i | ||||
\(731\) | 8.57321 | + | 14.8492i | 0.317092 | + | 0.549219i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.5000 | − | 21.6506i | −1.38509 | − | 0.799684i | −0.392337 | − | 0.919822i | \(-0.628333\pi\) |
−0.992757 | + | 0.120137i | \(0.961667\pi\) | |||||||
\(734\) | −12.2474 | −0.452062 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.79796 | − | 5.65685i | −0.360912 | − | 0.208373i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.50000 | − | 4.33013i | −0.0919640 | − | 0.159286i | 0.816373 | − | 0.577524i | \(-0.195981\pi\) |
−0.908337 | + | 0.418238i | \(0.862648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.00000 | − | 1.73205i | −0.183556 | − | 0.0635856i | ||||
\(743\) | 35.3553i | 1.29706i | 0.761188 | + | 0.648531i | \(0.224616\pi\) | ||||
−0.761188 | + | 0.648531i | \(0.775384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.0000 | − | 12.1244i | 0.769380 | − | 0.444202i | ||||
\(746\) | −1.22474 | + | 0.707107i | −0.0448411 | + | 0.0258890i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.4949 | − | 28.2843i | −0.895024 | − | 1.03348i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.5000 | − | 32.0429i | 0.675075 | − | 1.16926i | −0.301373 | − | 0.953506i | \(-0.597445\pi\) |
0.976447 | − | 0.215757i | \(-0.0692219\pi\) | |||||||
\(752\) | 14.6969 | + | 25.4558i | 0.535942 | + | 0.928279i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000 | + | 3.46410i | 0.218507 | + | 0.126155i | ||||
\(755\) | 26.9444 | 0.980607 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.00000 | −0.254419 | −0.127210 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127210 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(758\) | 12.2474 | + | 7.07107i | 0.444847 | + | 0.256833i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.00000 | − | 10.3923i | −0.217643 | − | 0.376969i | ||||
\(761\) | −4.89898 | + | 8.48528i | −0.177588 | + | 0.307591i | −0.941054 | − | 0.338257i | \(-0.890163\pi\) |
0.763466 | + | 0.645848i | \(0.223496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.50000 | − | 44.1673i | −0.307721 | − | 1.59896i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.0000 | + | 24.2487i | −1.51752 | + | 0.876142i | ||||
\(767\) | 44.0908 | − | 25.4558i | 1.59203 | − | 0.919157i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.2295i | 1.81132i | 0.424003 | + | 0.905661i | \(0.360624\pi\) | ||||
−0.424003 | + | 0.905661i | \(0.639376\pi\) | |||||||
\(770\) | 39.1918 | − | 33.9411i | 1.41238 | − | 1.22315i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.8207 | + | 36.0624i | 0.748867 | + | 1.29708i | 0.948366 | + | 0.317178i | \(0.102735\pi\) |
−0.199499 | + | 0.979898i | \(0.563931\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.50000 | + | 2.59808i | 0.161645 | + | 0.0933257i | ||||
\(776\) | 24.4949 | 0.879316 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.0000 | −1.36237 | ||||||||
\(779\) | −3.67423 | − | 2.12132i | −0.131643 | − | 0.0760042i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | − | 13.8564i | −0.286263 | − | 0.495821i | ||||
\(782\) | −12.2474 | + | 21.2132i | −0.437968 | + | 0.758583i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 26.0000 | − | 10.3923i | 0.928571 | − | 0.371154i | ||||
\(785\) | − | 25.4558i | − | 0.908558i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.5000 | + | 12.9904i | −0.802038 | + | 0.463057i | −0.844183 | − | 0.536054i | \(-0.819914\pi\) |
0.0421450 | + | 0.999112i | \(0.486581\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 13.8564i | − | 0.492989i | ||||||
\(791\) | 2.44949 | − | 7.07107i | 0.0870938 | − | 0.251418i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.00000 | − | 15.5885i | 0.319599 | − | 0.553562i | ||||
\(794\) | 13.4722 | + | 23.3345i | 0.478110 | + | 0.828111i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.1918 | −1.38825 | −0.694123 | − | 0.719856i | \(-0.744208\pi\) | ||||
−0.694123 | + | 0.719856i | \(0.744208\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.0000 | + | 27.7128i | 0.564980 | + | 0.978573i | ||||
\(803\) | 34.2929 | − | 59.3970i | 1.21017 | − | 2.09607i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45.0000 | + | 8.66025i | −1.58604 | + | 0.305234i | ||||
\(806\) | 25.4558i | 0.896644i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −24.0000 | + | 13.8564i | −0.844317 | + | 0.487467i | ||||
\(809\) | −9.79796 | + | 5.65685i | −0.344478 | + | 0.198884i | −0.662250 | − | 0.749283i | \(-0.730398\pi\) |
0.317773 | + | 0.948167i | \(0.397065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.0000 | + | 27.7128i | −0.560800 | + | 0.971334i | ||||
\(815\) | −28.1691 | − | 48.7904i | −0.986722 | − | 1.70905i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5000 | − | 6.06218i | −0.367348 | − | 0.212089i | ||||
\(818\) | 14.6969 | 0.513866 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.2929 | − | 19.7990i | −1.19683 | − | 0.690990i | −0.236982 | − | 0.971514i | \(-0.576158\pi\) |
−0.959847 | + | 0.280525i | \(0.909492\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5000 | − | 19.9186i | −0.400865 | − | 0.694318i | 0.592966 | − | 0.805228i | \(-0.297957\pi\) |
−0.993831 | + | 0.110910i | \(0.964624\pi\) | |||||||
\(824\) | −19.5959 | + | 33.9411i | −0.682656 | + | 1.18240i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0000 | + | 51.9615i | −0.626300 | + | 1.80797i | ||||
\(827\) | 22.6274i | 0.786832i | 0.919360 | + | 0.393416i | \(0.128707\pi\) | ||||
−0.919360 | + | 0.393416i | \(0.871293\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.5000 | − | 16.4545i | 0.989846 | − | 0.571488i | 0.0846177 | − | 0.996413i | \(-0.473033\pi\) |
0.905228 | + | 0.424926i | \(0.139700\pi\) | |||||||
\(830\) | 29.3939 | − | 16.9706i | 1.02028 | − | 0.589057i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 27.7128i | − | 0.960769i | ||||||
\(833\) | 2.44949 | − | 16.9706i | 0.0848698 | − | 0.587995i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | + | 10.3923i | −0.207639 | + | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.00000 | + | 1.73205i | 0.103633 | + | 0.0598327i | ||||
\(839\) | 24.4949 | 0.845658 | 0.422829 | − | 0.906210i | \(-0.361037\pi\) | ||||
0.422829 | + | 0.906210i | \(0.361037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | −13.4722 | − | 7.77817i | −0.464282 | − | 0.268054i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.22474 | + | 2.12132i | −0.0421325 | + | 0.0729756i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.0000 | − | 36.3731i | 1.44314 | − | 1.24979i | ||||
\(848\) | − | 5.65685i | − | 0.194257i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.00000 | − | 1.73205i | 0.102899 | − | 0.0594089i | ||||
\(851\) | 24.4949 | − | 14.1421i | 0.839674 | − | 0.484786i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.66025i | − | 0.296521i | −0.988948 | − | 0.148261i | \(-0.952633\pi\) | ||
0.988948 | − | 0.148261i | \(-0.0473675\pi\) | |||||||
\(854\) | 3.67423 | + | 19.0919i | 0.125730 | + | 0.653311i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.0000 | − | 34.6410i | 0.683586 | − | 1.18401i | ||||
\(857\) | −2.44949 | − | 4.24264i | −0.0836730 | − | 0.144926i | 0.821152 | − | 0.570710i | \(-0.193332\pi\) |
−0.904825 | + | 0.425784i | \(0.859998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.5000 | + | 25.1147i | 1.48420 | + | 0.856904i | 0.999839 | − | 0.0179638i | \(-0.00571836\pi\) |
0.484362 | + | 0.874868i | \(0.339052\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.0000 | 1.36241 | ||||||||
\(863\) | −1.22474 | − | 0.707107i | −0.0416908 | − | 0.0240702i | 0.479010 | − | 0.877810i | \(-0.340996\pi\) |
−0.520701 | + | 0.853739i | \(0.674329\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 3.67423 | − | 6.36396i | 0.124856 | − | 0.216256i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 22.6274i | − | 0.767583i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00000 | − | 3.46410i | 0.203302 | − | 0.117377i | ||||
\(872\) | 41.6413 | − | 24.0416i | 1.41015 | − | 0.814152i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 17.3205i | − | 0.585875i | ||||||
\(875\) | −24.4949 | − | 8.48528i | −0.828079 | − | 0.286855i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.5000 | + | 30.3109i | −0.590933 | + | 1.02353i | 0.403174 | + | 0.915123i | \(0.367907\pi\) |
−0.994107 | + | 0.108403i | \(0.965426\pi\) | |||||||
\(878\) | −14.6969 | − | 25.4558i | −0.495998 | − | 0.859093i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 48.0000 | + | 27.7128i | 1.61808 | + | 0.934199i | ||||
\(881\) | 36.7423 | 1.23788 | 0.618941 | − | 0.785438i | \(-0.287562\pi\) | ||||
0.618941 | + | 0.785438i | \(0.287562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.0000 | −1.24515 | −0.622575 | − | 0.782560i | \(-0.713913\pi\) | ||||
−0.622575 | + | 0.782560i | \(0.713913\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.0000 | − | 19.0526i | −0.369552 | − | 0.640083i | ||||
\(887\) | −26.9444 | + | 46.6690i | −0.904704 | + | 1.56699i | −0.0833899 | + | 0.996517i | \(0.526575\pi\) |
−0.821314 | + | 0.570476i | \(0.806759\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.50000 | − | 0.866025i | −0.0838473 | − | 0.0290456i | ||||
\(890\) | − | 8.48528i | − | 0.284427i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.0227 | + | 6.36396i | −0.368861 | + | 0.212962i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.2487i | 0.810545i | ||||||||
\(896\) | 19.5959 | + | 22.6274i | 0.654654 | + | 0.755929i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.0000 | − | 43.3013i | 0.834261 | − | 1.44498i | ||||
\(899\) | −3.67423 | − | 6.36396i | −0.122543 | − | 0.212250i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.00000 | − | 1.73205i | −0.0999445 | − | 0.0577030i | ||||
\(902\) | 19.5959 | 0.652473 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.00000 | 0.266076 | ||||||||
\(905\) | 33.0681 | + | 19.0919i | 1.09922 | + | 0.634636i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00000 | + | 13.8564i | 0.265636 | + | 0.460094i | 0.967730 | − | 0.251990i | \(-0.0810849\pi\) |
−0.702094 | + | 0.712084i | \(0.747752\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.00000 | + | 31.1769i | 0.198898 | + | 1.03350i | ||||
\(911\) | 52.3259i | 1.73363i | 0.498626 | + | 0.866817i | \(0.333838\pi\) | ||||
−0.498626 | + | 0.866817i | \(0.666162\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.0000 | − | 27.7128i | 1.58857 | − | 0.917160i | ||||
\(914\) | 6.12372 | − | 3.53553i | 0.202555 | − | 0.116945i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.2929 | + | 29.6985i | −1.13245 | + | 0.980730i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.50000 | + | 4.33013i | −0.0824674 | + | 0.142838i | −0.904309 | − | 0.426878i | \(-0.859613\pi\) |
0.821842 | + | 0.569716i | \(0.192947\pi\) | |||||||
\(920\) | −24.4949 | − | 42.4264i | −0.807573 | − | 1.39876i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.0000 | − | 17.3205i | −0.987997 | − | 0.570421i | ||||
\(923\) | 9.79796 | 0.322504 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 1.22474 | + | 0.707107i | 0.0402476 | + | 0.0232370i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.0227 | + | 19.0919i | −0.361643 | + | 0.626384i | −0.988231 | − | 0.152966i | \(-0.951117\pi\) |
0.626588 | + | 0.779350i | \(0.284451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.50000 | + | 11.2583i | 0.147482 | + | 0.368977i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.00000 | − | 3.46410i | 0.196326 | − | 0.113349i | ||||
\(935\) | 29.3939 | − | 16.9706i | 0.961283 | − | 0.554997i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.3923i | 0.339502i | 0.985487 | + | 0.169751i | \(0.0542963\pi\) | ||||
−0.985487 | + | 0.169751i | \(0.945704\pi\) | |||||||
\(938\) | −2.44949 | + | 7.07107i | −0.0799787 | + | 0.230879i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.34847 | − | 12.7279i | −0.239553 | − | 0.414918i | 0.721033 | − | 0.692901i | \(-0.243668\pi\) |
−0.960586 | + | 0.277982i | \(0.910334\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.0000 | − | 8.66025i | −0.488467 | − | 0.282017i | ||||
\(944\) | −58.7878 | −1.91338 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 56.0000 | 1.82072 | ||||||||
\(947\) | −8.57321 | − | 4.94975i | −0.278592 | − | 0.160845i | 0.354194 | − | 0.935172i | \(-0.384755\pi\) |
−0.632786 | + | 0.774327i | \(0.718089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.0000 | + | 36.3731i | 0.681689 | + | 1.18072i | ||||
\(950\) | −1.22474 | + | 2.12132i | −0.0397360 | + | 0.0688247i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.0000 | − | 3.46410i | 0.583383 | − | 0.112272i | ||||
\(953\) | 18.3848i | 0.595541i | 0.954637 | + | 0.297771i | \(0.0962431\pi\) | ||||
−0.954637 | + | 0.297771i | \(0.903757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.00000 | − | 1.73205i | 0.0970777 | − | 0.0560478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 3.46410i | − | 0.111920i | ||||||
\(959\) | −18.3712 | + | 3.53553i | −0.593236 | + | 0.114168i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | + | 3.46410i | −0.0645161 | + | 0.111745i | ||||
\(962\) | −9.79796 | − | 16.9706i | −0.315899 | − | 0.547153i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.79796 | −0.315407 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.0000 | −1.09337 | −0.546683 | − | 0.837340i | \(-0.684110\pi\) | ||||
−0.546683 | + | 0.837340i | \(0.684110\pi\) | |||||||
\(968\) | 51.4393 | + | 29.6985i | 1.65332 | + | 0.954545i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.0000 | − | 25.9808i | −0.481621 | − | 0.834192i | ||||
\(971\) | −6.12372 | + | 10.6066i | −0.196520 | + | 0.340382i | −0.947398 | − | 0.320059i | \(-0.896297\pi\) |
0.750878 | + | 0.660441i | \(0.229631\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | − | 17.3205i | 0.192351 | − | 0.555270i | ||||
\(974\) | − | 18.3848i | − | 0.589086i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.0000 | + | 10.3923i | −0.576166 | + | 0.332650i | ||||
\(977\) | −31.8434 | + | 18.3848i | −1.01876 | + | 0.588181i | −0.913744 | − | 0.406290i | \(-0.866822\pi\) |
−0.105015 | + | 0.994471i | \(0.533489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 13.8564i | − | 0.442853i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.00000 | − | 6.92820i | 0.127645 | − | 0.221088i | ||||
\(983\) | −2.44949 | − | 4.24264i | −0.0781266 | − | 0.135319i | 0.824315 | − | 0.566131i | \(-0.191561\pi\) |
−0.902442 | + | 0.430812i | \(0.858227\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000 | + | 3.46410i | 0.191176 | + | 0.110375i | ||||
\(986\) | −4.89898 | −0.156015 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.8661 | − | 24.7487i | −1.36306 | − | 0.786964i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.0000 | + | 50.2295i | 0.921215 | + | 1.59559i | 0.797537 | + | 0.603269i | \(0.206136\pi\) |
0.123678 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.00000 | + | 6.92820i | −0.253745 | + | 0.219749i | ||||
\(995\) | 4.24264i | 0.134501i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.5000 | − | 19.9186i | 1.09263 | − | 0.630828i | 0.158352 | − | 0.987383i | \(-0.449382\pi\) |
0.934274 | + | 0.356555i | \(0.116049\pi\) | |||||||
\(998\) | −30.6186 | + | 17.6777i | −0.969216 | + | 0.559577i | ||||
\(999\) | 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 | 189.2.p.b.26.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 189.2.p.b.26.2 | yes | 4 | |
7.2 | even | 3 | 1323.2.c.c.1322.4 | 4 | |||
7.3 | odd | 6 | inner | 189.2.p.b.80.2 | yes | 4 | |
7.5 | odd | 6 | 1323.2.c.c.1322.3 | 4 | |||
9.2 | odd | 6 | 567.2.i.e.215.1 | 4 | |||
9.4 | even | 3 | 567.2.s.c.26.2 | 4 | |||
9.5 | odd | 6 | 567.2.s.c.26.1 | 4 | |||
9.7 | even | 3 | 567.2.i.e.215.2 | 4 | |||
21.2 | odd | 6 | 1323.2.c.c.1322.1 | 4 | |||
21.5 | even | 6 | 1323.2.c.c.1322.2 | 4 | |||
21.17 | even | 6 | inner | 189.2.p.b.80.1 | yes | 4 | |
63.31 | odd | 6 | 567.2.i.e.269.2 | 4 | |||
63.38 | even | 6 | 567.2.s.c.458.2 | 4 | |||
63.52 | odd | 6 | 567.2.s.c.458.1 | 4 | |||
63.59 | even | 6 | 567.2.i.e.269.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.b.26.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
189.2.p.b.26.2 | yes | 4 | 3.2 | odd | 2 | inner | |
189.2.p.b.80.1 | yes | 4 | 21.17 | even | 6 | inner | |
189.2.p.b.80.2 | yes | 4 | 7.3 | odd | 6 | inner | |
567.2.i.e.215.1 | 4 | 9.2 | odd | 6 | |||
567.2.i.e.215.2 | 4 | 9.7 | even | 3 | |||
567.2.i.e.269.1 | 4 | 63.59 | even | 6 | |||
567.2.i.e.269.2 | 4 | 63.31 | odd | 6 | |||
567.2.s.c.26.1 | 4 | 9.5 | odd | 6 | |||
567.2.s.c.26.2 | 4 | 9.4 | even | 3 | |||
567.2.s.c.458.1 | 4 | 63.52 | odd | 6 | |||
567.2.s.c.458.2 | 4 | 63.38 | even | 6 | |||
1323.2.c.c.1322.1 | 4 | 21.2 | odd | 6 | |||
1323.2.c.c.1322.2 | 4 | 21.5 | even | 6 | |||
1323.2.c.c.1322.3 | 4 | 7.5 | odd | 6 | |||
1323.2.c.c.1322.4 | 4 | 7.2 | even | 3 |