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 | 80.2 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.80 |
Dual form | 189.2.p.b.26.2 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | \(0.166667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22474 | + | 2.12132i | 0.547723 | + | 0.948683i | 0.998430 | + | 0.0560116i | \(0.0178384\pi\) |
−0.450708 | + | 0.892672i | \(0.648828\pi\) | |||||||
\(6\) | 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 | \(-0.658432\pi\) |
−0.999665 | + | 0.0258656i | \(0.991766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 1.50000 | − | 0.866025i | 0.344124 | − | 0.198680i | −0.317970 | − | 0.948101i | \(-0.603001\pi\) |
0.662094 | + | 0.749421i | \(0.269668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.00000 | −1.70561 | ||||||||
\(23\) | −6.12372 | + | 3.53553i | −1.27688 | + | 0.737210i | −0.976274 | − | 0.216537i | \(-0.930524\pi\) |
−0.300610 | + | 0.953747i | \(0.597190\pi\) | |||||||
\(24\) | 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 | 0.0381148 | − | 0.999273i | \(-0.487865\pi\) |
−0.846339 | + | 0.532645i | \(0.821198\pi\) | |||||||
\(32\) | 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 | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | 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 | \(-0.438738\pi\) | ||||
0.191273 | + | 0.981537i | \(0.438738\pi\) | |||||||
\(42\) | 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 | 0.999117 | + | 0.0420122i | \(0.0133768\pi\) |
−0.463175 | + | 0.886267i | \(0.653290\pi\) | |||||||
\(48\) | 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 | \(-0.364299\pi\) |
−0.581752 | + | 0.813366i | \(0.697632\pi\) | |||||||
\(54\) | 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 | 0.226235 | − | 0.974073i | \(-0.427358\pi\) |
0.730454 | − | 0.682962i | \(-0.239308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.50000 | + | 2.59808i | −0.576166 | + | 0.332650i | −0.759608 | − | 0.650381i | \(-0.774609\pi\) |
0.183442 | + | 0.983030i | \(0.441276\pi\) | |||||||
\(62\) | −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 | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 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 | 0.966807 | − | 0.255510i | \(-0.0822432\pi\) |
0.262126 | + | 0.965034i | \(0.415577\pi\) | |||||||
\(74\) | 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 | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | −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 | \(-0.680719\pi\) | ||||
−0.537733 | + | 0.843115i | \(0.680719\pi\) | |||||||
\(84\) | 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 | \(-0.208107\pi\) |
−0.923608 | + | 0.383339i | \(0.874774\pi\) | |||||||
\(90\) | 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 | \(0.144900\pi\) | ||||
−0.898165 | + | 0.439658i | \(0.855100\pi\) | |||||||
\(98\) | 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 | \(-0.995412\pi\) |
0.512429 | + | 0.858729i | \(0.328746\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0000 | − | 6.92820i | 1.18240 | − | 0.682656i | 0.225828 | − | 0.974167i | \(-0.427491\pi\) |
0.956567 | + | 0.291511i | \(0.0941580\pi\) | |||||||
\(104\) | 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 | \(-0.427086\pi\) |
0.956938 | + | 0.290293i | \(0.0937528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.50000 | + | 14.7224i | −0.814152 | + | 1.41015i | 0.0957826 | + | 0.995402i | \(0.469465\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | −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 | 0.948281 | + | 0.317433i | \(0.102821\pi\) |
−0.199236 | + | 0.979952i | \(0.563846\pi\) | |||||||
\(132\) | 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 | \(-0.235659\pi\) |
−0.215052 | + | 0.976603i | \(0.568992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.92820i | 0.587643i | 0.955860 | + | 0.293821i | \(0.0949270\pi\) | ||||
−0.955860 | + | 0.293821i | \(0.905073\pi\) | |||||||
\(140\) | 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 | \(-0.533764\pi\) |
0.808220 | + | 0.588880i | \(0.200431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.50000 | + | 9.52628i | −0.447584 | + | 0.775238i | −0.998228 | − | 0.0595022i | \(-0.981049\pi\) |
0.550645 | + | 0.834740i | \(0.314382\pi\) | |||||||
\(152\) | 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 | 0.0958404 | − | 0.995397i | \(-0.469446\pi\) |
−0.814119 | + | 0.580699i | \(0.802779\pi\) | |||||||
\(158\) | 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 | −0.826523 | − | 0.562902i | \(-0.809685\pi\) |
−0.0742262 | − | 0.997241i | \(-0.523649\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | + | 6.92820i | −0.931381 | + | 0.537733i | ||||
\(167\) | −4.89898 | −0.379094 | −0.189547 | − | 0.981872i | \(-0.560702\pi\) | ||||
−0.189547 | + | 0.981872i | \(0.560702\pi\) | |||||||
\(168\) | 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 | \(-0.256785\pi\) |
−0.971223 | + | 0.238174i | \(0.923451\pi\) | |||||||
\(174\) | 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 | \(-0.453962\pi\) |
−0.784920 | + | 0.619598i | \(0.787296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5885i | 1.15868i | 0.815086 | + | 0.579340i | \(0.196690\pi\) | ||||
−0.815086 | + | 0.579340i | \(0.803310\pi\) | |||||||
\(182\) | −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 | \(-0.650373\pi\) |
0.543655 | + | 0.839309i | \(0.317040\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | − | 3.46410i | 0.143963 | − | 0.249351i | −0.785022 | − | 0.619467i | \(-0.787349\pi\) |
0.928986 | + | 0.370116i | \(0.120682\pi\) | |||||||
\(194\) | 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 | 0.552223 | − | 0.833696i | \(-0.313780\pi\) |
−0.445891 | + | 0.895087i | \(0.647113\pi\) | |||||||
\(200\) | −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 | \(0.153567\pi\) | ||||
−0.885863 | + | 0.463947i | \(0.846433\pi\) | |||||||
\(224\) | 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 | \(-0.859237\pi\) |
0.822515 | + | 0.568744i | \(0.192570\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.50000 | + | 0.866025i | −0.0991228 | + | 0.0572286i | −0.548742 | − | 0.835992i | \(-0.684893\pi\) |
0.449619 | + | 0.893220i | \(0.351560\pi\) | |||||||
\(230\) | −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 | \(-0.836860\pi\) |
−0.0110803 | + | 0.999939i | \(0.503527\pi\) | |||||||
\(234\) | 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 | 0.122119 | − | 0.992515i | \(-0.461031\pi\) |
−0.798484 | + | 0.602016i | \(0.794364\pi\) | |||||||
\(242\) | 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 | \(-0.574499\pi\) | ||||
−0.231916 | + | 0.972736i | \(0.574499\pi\) | |||||||
\(252\) | 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 | −0.991042 | − | 0.133551i | \(-0.957362\pi\) |
0.379862 | − | 0.925043i | \(-0.375971\pi\) | |||||||
\(258\) | 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 | \(-0.124330\pi\) |
0.132612 | + | 0.991168i | \(0.457664\pi\) | |||||||
\(264\) | 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 | −0.202637 | − | 0.979254i | \(-0.564951\pi\) |
0.949377 | − | 0.314138i | \(-0.101715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5000 | − | 11.2583i | 1.18454 | − | 0.683895i | 0.227480 | − | 0.973783i | \(-0.426951\pi\) |
0.957061 | + | 0.289888i | \(0.0936180\pi\) | |||||||
\(272\) | 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 | −0.196261 | − | 0.980552i | \(-0.562880\pi\) |
0.947313 | − | 0.320309i | \(-0.103787\pi\) | |||||||
\(278\) | 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 | −0.351052 | − | 0.936356i | \(-0.614176\pi\) |
−0.986434 | + | 0.164158i | \(0.947509\pi\) | |||||||
\(284\) | 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 | \(-0.246197\pi\) | ||||
0.715504 | + | 0.698609i | \(0.246197\pi\) | |||||||
\(294\) | 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 | \(-0.952626\pi\) | ||
0.988945 | − | 0.148280i | \(-0.0473737\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.00000 | − | 15.5885i | −0.511166 | − | 0.885365i | ||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50000 | − | 2.59808i | 0.254355 | − | 0.146852i | −0.367402 | − | 0.930062i | \(-0.619753\pi\) |
0.621757 | + | 0.783210i | \(0.286419\pi\) | |||||||
\(314\) | −14.6969 | −0.829396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.44949 | + | 1.41421i | −0.137577 | + | 0.0794301i | −0.567209 | − | 0.823574i | \(-0.691977\pi\) |
0.429632 | + | 0.903004i | \(0.358643\pi\) | |||||||
\(318\) | 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 | 0.532096 | − | 0.846684i | \(-0.321405\pi\) |
−0.999298 | + | 0.0374662i | \(0.988071\pi\) | |||||||
\(332\) | 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 | \(-0.647929\pi\) |
−0.998268 | + | 0.0588334i | \(0.981262\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.73205i | − | 0.0927146i | −0.998925 | − | 0.0463573i | \(-0.985239\pi\) | ||
0.998925 | − | 0.0463573i | \(-0.0147613\pi\) | |||||||
\(350\) | 1.22474 | + | 3.53553i | 0.0654654 | + | 0.188982i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.1464 | − | 29.6985i | 0.912612 | − | 1.58069i | 0.102252 | − | 0.994758i | \(-0.467395\pi\) |
0.810360 | − | 0.585932i | \(-0.199272\pi\) | |||||||
\(354\) | 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 | \(-0.763172\pi\) |
0.218638 | + | 0.975806i | \(0.429839\pi\) | |||||||
\(360\) | 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 | 0.682808 | − | 0.730597i | \(-0.260758\pi\) |
−0.291312 | + | 0.956628i | \(0.594092\pi\) | |||||||
\(368\) | −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 | 0.878680 | − | 0.477412i | \(-0.158425\pi\) |
−0.852791 | + | 0.522253i | \(0.825092\pi\) | |||||||
\(374\) | −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 | −0.855542 | − | 0.517734i | \(-0.826776\pi\) |
−0.0205998 | − | 0.999788i | \(-0.506558\pi\) | |||||||
\(384\) | 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 | \(-0.571868\pi\) |
−0.955978 | + | 0.293437i | \(0.905201\pi\) | |||||||
\(390\) | 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 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) |
0.0250943 | + | 0.999685i | \(0.492011\pi\) | |||||||
\(398\) | 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 | \(-0.475551\pi\) |
0.901839 | + | 0.432072i | \(0.142217\pi\) | |||||||
\(402\) | 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 | 0.260704 | − | 0.965419i | \(-0.416045\pi\) |
−0.705725 | + | 0.708486i | \(0.749379\pi\) | |||||||
\(410\) | 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 | \(-0.480943\pi\) | ||||
0.0598327 | + | 0.998208i | \(0.480943\pi\) | |||||||
\(420\) | 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 | \(-0.0947906\pi\) |
0.223891 | + | 0.974614i | \(0.428124\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.19615i | − | 0.249711i | −0.992175 | − | 0.124856i | \(-0.960153\pi\) | ||
0.992175 | − | 0.124856i | \(-0.0398468\pi\) | |||||||
\(434\) | −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 | −0.00461537 | − | 0.999989i | \(-0.501469\pi\) |
0.863708 | + | 0.503992i | \(0.168136\pi\) | |||||||
\(440\) | 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 | \(-0.787156\pi\) |
0.144563 | + | 0.989496i | \(0.453822\pi\) | |||||||
\(444\) | 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 | 0.801611 | − | 0.597847i | \(-0.203977\pi\) |
−0.918556 | + | 0.395292i | \(0.870643\pi\) | |||||||
\(458\) | −1.22474 | + | 2.12132i | −0.0572286 | + | 0.0991228i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.4949 | −1.14084 | −0.570421 | − | 0.821353i | \(-0.693220\pi\) | ||||
−0.570421 | + | 0.821353i | \(0.693220\pi\) | |||||||
\(462\) | 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 | \(-0.130509\pi\) |
−0.803770 | + | 0.594941i | \(0.797176\pi\) | |||||||
\(468\) | 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 | \(-0.851155\pi\) |
0.836688 | + | 0.547679i | \(0.184489\pi\) | |||||||
\(480\) | 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 | −0.680335 | − | 0.732901i | \(-0.738166\pi\) |
0.974879 | + | 0.222737i | \(0.0714992\pi\) | |||||||
\(488\) | −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 | 0.997532 | + | 0.0702185i | \(0.0223697\pi\) |
−0.437955 | + | 0.898997i | \(0.644297\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.00000 | + | 5.19615i | −0.401690 | + | 0.231916i | ||||
\(503\) | 22.0454 | 0.982956 | 0.491478 | − | 0.870890i | \(-0.336457\pi\) | ||||
0.491478 | + | 0.870890i | \(0.336457\pi\) | |||||||
\(504\) | 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 | \(-0.309666\pi\) |
−0.997237 | + | 0.0742838i | \(0.976333\pi\) | |||||||
\(510\) | 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 | −0.462515 | − | 0.886611i | \(-0.653053\pi\) |
0.999086 | − | 0.0427559i | \(-0.0136138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.00000 | + | 1.73205i | −0.131181 | + | 0.0757373i | −0.564154 | − | 0.825669i | \(-0.690798\pi\) |
0.432973 | + | 0.901407i | \(0.357464\pi\) | |||||||
\(524\) | 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 | 0.971250 | − | 0.238062i | \(-0.0765123\pi\) |
−0.691793 | + | 0.722096i | \(0.743179\pi\) | |||||||
\(542\) | 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 | \(-0.342872\pi\) |
−0.525723 | + | 0.850656i | \(0.676205\pi\) | |||||||
\(558\) | 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 | \(-0.987118\pi\) |
0.534630 | + | 0.845087i | \(0.320451\pi\) | |||||||
\(564\) | 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 | \(-0.946775\pi\) |
−0.348891 | + | 0.937163i | \(0.613442\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5000 | + | 35.5070i | −0.857898 | + | 1.48592i | 0.0160316 | + | 0.999871i | \(0.494897\pi\) |
−0.873930 | + | 0.486052i | \(0.838437\pi\) | |||||||
\(572\) | 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 | 0.436253 | − | 0.899824i | \(-0.356305\pi\) |
−0.561144 | + | 0.827718i | \(0.689639\pi\) | |||||||
\(578\) | 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 | \(-0.312314\pi\) | ||||
0.556057 | + | 0.831144i | \(0.312314\pi\) | |||||||
\(588\) | 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 | \(-0.231143\pi\) |
−0.948908 | + | 0.315553i | \(0.897810\pi\) | |||||||
\(594\) | 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 | \(-0.287189\pi\) |
−0.369651 | + | 0.929171i | \(0.620523\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.5167i | − | 0.918474i | −0.888314 | − | 0.459237i | \(-0.848123\pi\) | ||
0.888314 | − | 0.459237i | \(-0.151877\pi\) | |||||||
\(602\) | −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 | 0.116596 | − | 0.993179i | \(-0.462802\pi\) |
0.918417 | + | 0.395614i | \(0.129468\pi\) | |||||||
\(608\) | 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 | −0.362300 | − | 0.932062i | \(-0.618008\pi\) |
0.988339 | − | 0.152270i | \(-0.0486583\pi\) | |||||||
\(614\) | −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 | 0.961839 | − | 0.273615i | \(-0.0882193\pi\) |
0.243962 | + | 0.969785i | \(0.421553\pi\) | |||||||
\(620\) | 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 | \(-0.288737\pi\) |
−0.374165 | + | 0.927362i | \(0.622070\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.5167i | 0.887970i | 0.896034 | + | 0.443985i | \(0.146436\pi\) | ||||
−0.896034 | + | 0.443985i | \(0.853564\pi\) | |||||||
\(644\) | 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 | \(-0.673427\pi\) |
0.999775 | + | 0.0212354i | \(0.00675993\pi\) | |||||||
\(648\) | 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 | \(-0.765117\pi\) |
0.212671 | + | 0.977124i | \(0.431784\pi\) | |||||||
\(654\) | 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 | −0.995506 | − | 0.0946945i | \(-0.969813\pi\) |
−0.579761 | − | 0.814787i | \(-0.696854\pi\) | |||||||
\(662\) | −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 | \(-0.0755280\pi\) |
−0.689557 | + | 0.724232i | \(0.742195\pi\) | |||||||
\(678\) | 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 | \(-0.0849645\pi\) |
0.253866 | + | 0.967239i | \(0.418298\pi\) | |||||||
\(684\) | 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 | −0.583146 | − | 0.812367i | \(-0.698178\pi\) |
0.411958 | + | 0.911203i | \(0.364845\pi\) | |||||||
\(692\) | 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 | 0.815255 | − | 0.579102i | \(-0.196597\pi\) |
−0.909145 | + | 0.416481i | \(0.863263\pi\) | |||||||
\(710\) | 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 | \(-0.317654\pi\) |
−0.998787 | + | 0.0492373i | \(0.984321\pi\) | |||||||
\(720\) | 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 | \(-0.791064\pi\) | ||
0.792199 | − | 0.610263i | \(-0.208936\pi\) | |||||||
\(728\) | 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 | −0.992757 | − | 0.120137i | \(-0.961667\pi\) |
−0.392337 | + | 0.919822i | \(0.628333\pi\) | |||||||
\(734\) | 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 | −0.908337 | − | 0.418238i | \(-0.862648\pi\) |
0.816373 | + | 0.577524i | \(0.195981\pi\) | |||||||
\(740\) | 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 | 0.976447 | + | 0.215757i | \(0.0692219\pi\) |
−0.301373 | + | 0.953506i | \(0.597445\pi\) | |||||||
\(752\) | −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 | \(-0.109837\pi\) |
−0.763466 | + | 0.645848i | \(0.776504\pi\) | |||||||
\(762\) | 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 | \(-0.639376\pi\) | ||
0.424003 | − | 0.905661i | \(-0.360624\pi\) | |||||||
\(770\) | −39.1918 | − | 33.9411i | −1.41238 | − | 1.22315i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.8207 | + | 36.0624i | −0.748867 | + | 1.29708i | 0.199499 | + | 0.979898i | \(0.436069\pi\) |
−0.948366 | + | 0.317178i | \(0.897265\pi\) | |||||||
\(774\) | 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 | 0.0421450 | − | 0.999112i | \(-0.486581\pi\) |
−0.844183 | + | 0.536054i | \(0.819914\pi\) | |||||||
\(788\) | 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 | \(-0.255792\pi\) | ||||
0.694123 | + | 0.719856i | \(0.255792\pi\) | |||||||
\(798\) | 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 | \(-0.269602\pi\) |
−0.317773 | + | 0.948167i | \(0.602935\pi\) | |||||||
\(810\) | 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 | \(-0.423842\pi\) |
0.959847 | + | 0.280525i | \(0.0905084\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5000 | + | 19.9186i | −0.400865 | + | 0.694318i | −0.993831 | − | 0.110910i | \(-0.964624\pi\) |
0.592966 | + | 0.805228i | \(0.297957\pi\) | |||||||
\(824\) | 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 | 0.905228 | − | 0.424926i | \(-0.139700\pi\) |
0.0846177 | + | 0.996413i | \(0.473033\pi\) | |||||||
\(830\) | −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 | \(-0.638963\pi\) | ||||
−0.422829 | + | 0.906210i | \(0.638963\pi\) | |||||||
\(840\) | 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 | \(0.0473675\pi\) | ||||
−0.988948 | + | 0.148261i | \(0.952633\pi\) | |||||||
\(854\) | −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 | \(-0.806668\pi\) |
0.904825 | + | 0.425784i | \(0.140002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.5000 | − | 25.1147i | 1.48420 | − | 0.856904i | 0.484362 | − | 0.874868i | \(-0.339052\pi\) |
0.999839 | + | 0.0179638i | \(0.00571836\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.0000 | 1.36241 | ||||||||
\(863\) | 1.22474 | − | 0.707107i | 0.0416908 | − | 0.0240702i | −0.479010 | − | 0.877810i | \(-0.659004\pi\) |
0.520701 | + | 0.853739i | \(0.325671\pi\) | |||||||
\(864\) | 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 | −0.994107 | − | 0.108403i | \(-0.965426\pi\) |
0.403174 | − | 0.915123i | \(-0.367907\pi\) | |||||||
\(878\) | 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 | \(-0.712438\pi\) | ||||
−0.618941 | + | 0.785438i | \(0.712438\pi\) | |||||||
\(882\) | 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 | 0.821314 | + | 0.570476i | \(0.193241\pi\) |
0.0833899 | + | 0.996517i | \(0.473425\pi\) | |||||||
\(888\) | 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 | −0.702094 | − | 0.712084i | \(-0.747752\pi\) |
0.967730 | + | 0.251990i | \(0.0810849\pi\) | |||||||
\(908\) | 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 | 0.821842 | − | 0.569716i | \(-0.192947\pi\) |
−0.904309 | + | 0.426878i | \(0.859613\pi\) | |||||||
\(920\) | 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 | \(-0.0488825\pi\) |
−0.626588 | + | 0.779350i | \(0.715549\pi\) | |||||||
\(930\) | 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 | \(-0.945704\pi\) | ||
0.985487 | − | 0.169751i | \(-0.0542963\pi\) | |||||||
\(938\) | 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 | \(-0.756332\pi\) |
0.960586 | + | 0.277982i | \(0.0896657\pi\) | |||||||
\(942\) | 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 | \(-0.615245\pi\) |
0.632786 | + | 0.774327i | \(0.281911\pi\) | |||||||
\(948\) | 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 | \(-0.103703\pi\) |
−0.750878 | + | 0.660441i | \(0.770369\pi\) | |||||||
\(972\) | 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 | \(-0.133178\pi\) |
0.105015 | + | 0.994471i | \(0.466511\pi\) | |||||||
\(978\) | 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 | \(-0.808439\pi\) |
0.902442 | + | 0.430812i | \(0.141773\pi\) | |||||||
\(984\) | 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 | 0.123678 | − | 0.992322i | \(-0.460531\pi\) |
0.797537 | − | 0.603269i | \(-0.206136\pi\) | |||||||
\(992\) | 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 | 0.934274 | − | 0.356555i | \(-0.116049\pi\) |
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | 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.80.2 | yes | 4 | |
3.2 | odd | 2 | inner | 189.2.p.b.80.1 | yes | 4 | |
7.3 | odd | 6 | 1323.2.c.c.1322.4 | 4 | |||
7.4 | even | 3 | 1323.2.c.c.1322.3 | 4 | |||
7.5 | odd | 6 | inner | 189.2.p.b.26.1 | ✓ | 4 | |
9.2 | odd | 6 | 567.2.s.c.458.2 | 4 | |||
9.4 | even | 3 | 567.2.i.e.269.2 | 4 | |||
9.5 | odd | 6 | 567.2.i.e.269.1 | 4 | |||
9.7 | even | 3 | 567.2.s.c.458.1 | 4 | |||
21.5 | even | 6 | inner | 189.2.p.b.26.2 | yes | 4 | |
21.11 | odd | 6 | 1323.2.c.c.1322.2 | 4 | |||
21.17 | even | 6 | 1323.2.c.c.1322.1 | 4 | |||
63.5 | even | 6 | 567.2.s.c.26.1 | 4 | |||
63.40 | odd | 6 | 567.2.s.c.26.2 | 4 | |||
63.47 | even | 6 | 567.2.i.e.215.1 | 4 | |||
63.61 | odd | 6 | 567.2.i.e.215.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.b.26.1 | ✓ | 4 | 7.5 | odd | 6 | inner | |
189.2.p.b.26.2 | yes | 4 | 21.5 | even | 6 | inner | |
189.2.p.b.80.1 | yes | 4 | 3.2 | odd | 2 | inner | |
189.2.p.b.80.2 | yes | 4 | 1.1 | even | 1 | trivial | |
567.2.i.e.215.1 | 4 | 63.47 | even | 6 | |||
567.2.i.e.215.2 | 4 | 63.61 | odd | 6 | |||
567.2.i.e.269.1 | 4 | 9.5 | odd | 6 | |||
567.2.i.e.269.2 | 4 | 9.4 | even | 3 | |||
567.2.s.c.26.1 | 4 | 63.5 | even | 6 | |||
567.2.s.c.26.2 | 4 | 63.40 | odd | 6 | |||
567.2.s.c.458.1 | 4 | 9.7 | even | 3 | |||
567.2.s.c.458.2 | 4 | 9.2 | odd | 6 | |||
1323.2.c.c.1322.1 | 4 | 21.17 | even | 6 | |||
1323.2.c.c.1322.2 | 4 | 21.11 | odd | 6 | |||
1323.2.c.c.1322.3 | 4 | 7.4 | even | 3 | |||
1323.2.c.c.1322.4 | 4 | 7.3 | odd | 6 |