Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(377,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.377");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.x (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 756) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 377.4 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.377 |
Dual form | 2268.2.x.j.1889.4 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.866025 | − | 1.50000i | 0.387298 | − | 0.670820i | −0.604787 | − | 0.796387i | \(-0.706742\pi\) |
0.992085 | + | 0.125567i | \(0.0400750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62132 | − | 0.358719i | 0.990766 | − | 0.135583i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.67423 | + | 2.12132i | −1.10782 | + | 0.639602i | −0.938265 | − | 0.345918i | \(-0.887568\pi\) |
−0.169559 | + | 0.985520i | \(0.554234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.12132 | + | 1.22474i | 0.588348 | + | 0.339683i | 0.764444 | − | 0.644690i | \(-0.223014\pi\) |
−0.176096 | + | 0.984373i | \(0.556347\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.73205 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44949i | 0.561951i | 0.959715 | + | 0.280976i | \(0.0906580\pi\) | ||||
−0.959715 | + | 0.280976i | \(0.909342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.34847 | + | 4.24264i | 1.53226 | + | 0.884652i | 0.999257 | + | 0.0385394i | \(0.0122705\pi\) |
0.533005 | + | 0.846112i | \(0.321063\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | + | 1.73205i | 0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.67423 | + | 2.12132i | −0.682288 | + | 0.393919i | −0.800717 | − | 0.599043i | \(-0.795548\pi\) |
0.118428 | + | 0.992963i | \(0.462214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.36396 | + | 3.67423i | 1.14300 | + | 0.659912i | 0.947172 | − | 0.320726i | \(-0.103927\pi\) |
0.195829 | + | 0.980638i | \(0.437260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.73205 | − | 4.24264i | 0.292770 | − | 0.717137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) | ||||
0.0821995 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.866025 | + | 1.50000i | −0.135250 | + | 0.234261i | −0.925693 | − | 0.378275i | \(-0.876517\pi\) |
0.790443 | + | 0.612536i | \(0.209851\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.50000 | − | 6.06218i | −0.533745 | − | 0.924473i | −0.999223 | − | 0.0394140i | \(-0.987451\pi\) |
0.465478 | − | 0.885059i | \(-0.345882\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.06218 | + | 10.5000i | 0.884260 | + | 1.53158i | 0.846560 | + | 0.532293i | \(0.178670\pi\) |
0.0376995 | + | 0.999289i | \(0.487997\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.34847i | 0.990867i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.33013 | − | 7.50000i | 0.563735 | − | 0.976417i | −0.433432 | − | 0.901186i | \(-0.642697\pi\) |
0.997166 | − | 0.0752304i | \(-0.0239692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.12132 | − | 1.22474i | 0.271607 | − | 0.156813i | −0.358011 | − | 0.933718i | \(-0.616545\pi\) |
0.629618 | + | 0.776905i | \(0.283211\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.67423 | − | 2.12132i | 0.455733 | − | 0.263117i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.00000 | − | 8.66025i | 0.610847 | − | 1.05802i | −0.380251 | − | 0.924883i | \(-0.624162\pi\) |
0.991098 | − | 0.133135i | \(-0.0425044\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.48528i | − | 1.00702i | −0.863990 | − | 0.503509i | \(-0.832042\pi\) | ||
0.863990 | − | 0.503509i | \(-0.167958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.79796i | 1.14676i | 0.819288 | + | 0.573382i | \(0.194369\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.87039 | + | 6.87868i | −1.01087 | + | 0.783898i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.50000 | − | 4.33013i | −0.281272 | − | 0.487177i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.971698 | + | 0.236225i | \(0.924090\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.06218 | − | 10.5000i | −0.665410 | − | 1.15252i | −0.979174 | − | 0.203024i | \(-0.934923\pi\) |
0.313763 | − | 0.949501i | \(-0.398410\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.50000 | + | 2.59808i | −0.162698 | + | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 2.44949i | 0.628971 | + | 0.256776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.67423 | + | 2.12132i | 0.376969 | + | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.12132 | + | 1.22474i | −0.215387 | + | 0.124354i | −0.603813 | − | 0.797126i | \(-0.706353\pi\) |
0.388425 | + | 0.921480i | \(0.373019\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.19615 | − | 9.00000i | −0.517036 | − | 0.895533i | −0.999804 | − | 0.0197851i | \(-0.993702\pi\) |
0.482768 | − | 0.875748i | \(-0.339632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9706 | + | 9.79796i | 1.67216 | + | 0.965422i | 0.966426 | + | 0.256943i | \(0.0827154\pi\) |
0.705733 | + | 0.708478i | \(0.250618\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.48528i | 0.820303i | 0.912017 | + | 0.410152i | \(0.134524\pi\) | ||||
−0.912017 | + | 0.410152i | \(0.865476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0000 | 1.24517 | 0.622587 | − | 0.782551i | \(-0.286082\pi\) | ||||
0.622587 | + | 0.782551i | \(0.286082\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.0227 | − | 6.36396i | −1.03693 | − | 0.598671i | −0.117967 | − | 0.993018i | \(-0.537638\pi\) |
−0.918962 | + | 0.394346i | \(0.870971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.7279 | − | 7.34847i | 1.18688 | − | 0.685248i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.54026 | + | 0.621320i | −0.416205 | + | 0.0569563i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.19615 | − | 9.00000i | 0.453990 | − | 0.786334i | −0.544640 | − | 0.838670i | \(-0.683334\pi\) |
0.998630 | + | 0.0523366i | \(0.0166669\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.878680 | + | 6.42090i | 0.0761912 | + | 0.556762i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3712 | − | 10.6066i | 1.56956 | − | 0.906183i | 0.573335 | − | 0.819321i | \(-0.305649\pi\) |
0.996220 | − | 0.0868620i | \(-0.0276839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6066 | + | 6.12372i | 0.899640 | + | 0.519408i | 0.877083 | − | 0.480338i | \(-0.159486\pi\) |
0.0225568 | + | 0.999746i | \(0.492819\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.3923 | −0.869048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.34847i | 0.610257i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.0227 | − | 6.36396i | −0.903015 | − | 0.521356i | −0.0248379 | − | 0.999691i | \(-0.507907\pi\) |
−0.878177 | + | 0.478335i | \(0.841240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | + | 4.33013i | 0.203447 | + | 0.352381i | 0.949637 | − | 0.313353i | \(-0.101452\pi\) |
−0.746190 | + | 0.665733i | \(0.768119\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.0227 | − | 6.36396i | 0.885365 | − | 0.511166i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.36396 | + | 3.67423i | 0.507899 | + | 0.293236i | 0.731970 | − | 0.681337i | \(-0.238601\pi\) |
−0.224070 | + | 0.974573i | \(0.571935\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.7846 | + | 8.48528i | 1.63806 | + | 0.668734i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | −0.0783260 | −0.0391630 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391630 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.52628 | + | 16.5000i | −0.737166 | + | 1.27681i | 0.216601 | + | 0.976260i | \(0.430503\pi\) |
−0.953767 | + | 0.300548i | \(0.902830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.50000 | − | 6.06218i | −0.269231 | − | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.3923 | + | 18.0000i | 0.790112 | + | 1.36851i | 0.925897 | + | 0.377776i | \(0.123311\pi\) |
−0.135785 | + | 0.990738i | \(0.543356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.24264 | + | 4.18154i | 0.245121 | + | 0.316095i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.24264i | 0.317110i | 0.987350 | + | 0.158555i | \(0.0506835\pi\) | ||||
−0.987350 | + | 0.158555i | \(0.949317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.89898i | 0.364138i | 0.983286 | + | 0.182069i | \(0.0582795\pi\) | ||||
−0.983286 | + | 0.182069i | \(0.941721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.866025 | − | 1.50000i | 0.0636715 | − | 0.110282i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.36396 | − | 3.67423i | 0.465379 | − | 0.268687i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.34847 | + | 4.24264i | −0.531717 | + | 0.306987i | −0.741715 | − | 0.670715i | \(-0.765987\pi\) |
0.209999 | + | 0.977702i | \(0.432654\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.50000 | + | 6.06218i | −0.251936 | + | 0.436365i | −0.964059 | − | 0.265689i | \(-0.914400\pi\) |
0.712123 | + | 0.702055i | \(0.247734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.2132i | 1.51138i | 0.654931 | + | 0.755689i | \(0.272698\pi\) | ||||
−0.654931 | + | 0.755689i | \(0.727302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.79796i | − | 0.694559i | −0.937762 | − | 0.347279i | \(-0.887106\pi\) | ||
0.937762 | − | 0.347279i | \(-0.112894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.87039 | + | 6.87868i | −0.622579 | + | 0.482789i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.50000 | + | 2.59808i | 0.104765 | + | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.19615 | − | 9.00000i | −0.359425 | − | 0.622543i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | − | 6.92820i | 0.275371 | − | 0.476957i | −0.694857 | − | 0.719148i | \(-0.744533\pi\) |
0.970229 | + | 0.242190i | \(0.0778659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.1244 | −0.826874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | + | 7.34847i | 1.22192 | + | 0.498847i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.67423 | − | 2.12132i | −0.247156 | − | 0.142695i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0919 | − | 11.0227i | 1.27849 | − | 0.738135i | 0.301917 | − | 0.953334i | \(-0.402373\pi\) |
0.976570 | + | 0.215199i | \(0.0690401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.7279 | − | 7.34847i | −0.841085 | − | 0.485601i | 0.0165480 | − | 0.999863i | \(-0.494732\pi\) |
−0.857633 | + | 0.514263i | \(0.828066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.24264i | − | 0.277945i | −0.990296 | − | 0.138972i | \(-0.955620\pi\) | ||
0.990296 | − | 0.138972i | \(-0.0443799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.0000 | 1.36989 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3712 | + | 10.6066i | 1.18833 | + | 0.686084i | 0.957927 | − | 0.287011i | \(-0.0926616\pi\) |
0.230405 | + | 0.973095i | \(0.425995\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.3345 | + | 13.4722i | −1.50311 | + | 0.867820i | −0.503115 | + | 0.864219i | \(0.667813\pi\) |
−0.999994 | + | 0.00360098i | \(0.998854\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.01834 | − | 11.7426i | 0.192835 | − | 0.750210i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00000 | + | 5.19615i | −0.190885 | + | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.0526 | 1.20259 | 0.601293 | − | 0.799028i | \(-0.294652\pi\) | ||||
0.601293 | + | 0.799028i | \(0.294652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36.0000 | −2.26330 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.19615 | − | 9.00000i | 0.324127 | − | 0.561405i | −0.657208 | − | 0.753709i | \(-0.728263\pi\) |
0.981335 | + | 0.192304i | \(0.0615961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.62132 | − | 0.358719i | 0.162881 | − | 0.0222897i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.3712 | + | 10.6066i | −1.13282 | + | 0.654031i | −0.944641 | − | 0.328105i | \(-0.893590\pi\) |
−0.188174 | + | 0.982136i | \(0.560257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.73205 | 0.105605 | 0.0528025 | − | 0.998605i | \(-0.483185\pi\) | ||||
0.0528025 | + | 0.998605i | \(0.483185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.89898i | 0.297592i | 0.988868 | + | 0.148796i | \(0.0475397\pi\) | ||||
−0.988868 | + | 0.148796i | \(0.952460\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.34847 | − | 4.24264i | −0.443129 | − | 0.255841i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.50000 | + | 6.06218i | 0.210295 | + | 0.364241i | 0.951807 | − | 0.306699i | \(-0.0992243\pi\) |
−0.741512 | + | 0.670940i | \(0.765891\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.34847 | + | 4.24264i | −0.438373 | + | 0.253095i | −0.702907 | − | 0.711282i | \(-0.748115\pi\) |
0.264534 | + | 0.964376i | \(0.414782\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.36396 | − | 3.67423i | −0.378298 | − | 0.218411i | 0.298779 | − | 0.954322i | \(-0.403421\pi\) |
−0.677078 | + | 0.735912i | \(0.736754\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.73205 | + | 4.24264i | −0.102240 | + | 0.250435i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.33013 | − | 7.50000i | 0.252969 | − | 0.438155i | −0.711373 | − | 0.702815i | \(-0.751926\pi\) |
0.964342 | + | 0.264660i | \(0.0852597\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.50000 | − | 12.9904i | −0.436667 | − | 0.756329i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.3923 | + | 18.0000i | 0.601003 | + | 1.04097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.3492 | − | 14.6354i | −0.654159 | − | 0.843570i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4.24264i | − | 0.242933i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.3939i | − | 1.67760i | −0.544442 | − | 0.838799i | \(-0.683259\pi\) | ||
0.544442 | − | 0.838799i | \(-0.316741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.2583 | − | 19.5000i | 0.638401 | − | 1.10574i | −0.347382 | − | 0.937724i | \(-0.612929\pi\) |
0.985784 | − | 0.168020i | \(-0.0537373\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2132 | + | 12.2474i | −1.19904 | + | 0.692267i | −0.960341 | − | 0.278827i | \(-0.910054\pi\) |
−0.238700 | + | 0.971093i | \(0.576721\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.24264i | − | 0.236067i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.89898i | 0.271746i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.6575 | + | 25.3492i | 1.08375 | + | 1.39755i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.50000 | − | 11.2583i | −0.357272 | − | 0.618814i | 0.630232 | − | 0.776407i | \(-0.282960\pi\) |
−0.987504 | + | 0.157593i | \(0.949627\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.66025 | − | 15.0000i | −0.473160 | − | 0.819538i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.5000 | + | 21.6506i | −0.680918 | + | 1.17939i | 0.293783 | + | 0.955872i | \(0.405086\pi\) |
−0.974701 | + | 0.223513i | \(0.928247\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.1769 | −1.68832 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.3712 | − | 10.6066i | −0.986216 | − | 0.569392i | −0.0820751 | − | 0.996626i | \(-0.526155\pi\) |
−0.904141 | + | 0.427234i | \(0.859488\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.9706 | + | 9.79796i | −0.908413 | + | 0.524473i | −0.879920 | − | 0.475121i | \(-0.842404\pi\) |
−0.0284931 | + | 0.999594i | \(0.509071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.866025 | + | 1.50000i | 0.0460939 | + | 0.0798369i | 0.888152 | − | 0.459550i | \(-0.151989\pi\) |
−0.842058 | + | 0.539387i | \(0.818656\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.7279 | − | 7.34847i | −0.675528 | − | 0.390016i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 33.9411i | − | 1.79134i | −0.444715 | − | 0.895672i | \(-0.646695\pi\) | ||
0.444715 | − | 0.895672i | \(-0.353305\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6969 | + | 8.48528i | 0.769273 | + | 0.444140i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.24264 | − | 2.44949i | 0.221464 | − | 0.127862i | −0.385164 | − | 0.922848i | \(-0.625855\pi\) |
0.606628 | + | 0.794986i | \(0.292522\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50000 | + | 9.52628i | −0.284779 | + | 0.493252i | −0.972556 | − | 0.232671i | \(-0.925254\pi\) |
0.687776 | + | 0.725923i | \(0.258587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.3923 | −0.535231 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.0000 | −1.79783 | −0.898915 | − | 0.438124i | \(-0.855643\pi\) | ||||
−0.898915 | + | 0.438124i | \(0.855643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.52628 | − | 16.5000i | 0.486770 | − | 0.843111i | −0.513114 | − | 0.858320i | \(-0.671508\pi\) |
0.999884 | + | 0.0152097i | \(0.00484160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.63604 | + | 19.2627i | 0.134345 | + | 0.981718i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.7196 | + | 14.8492i | −1.30404 | + | 0.752886i | −0.981094 | − | 0.193532i | \(-0.938006\pi\) |
−0.322944 | + | 0.946418i | \(0.604672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7279 | − | 7.34847i | −0.643679 | − | 0.371628i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.66025 | −0.435745 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 29.3939i | − | 1.47524i | −0.675218 | − | 0.737618i | \(-0.735950\pi\) | ||
0.675218 | − | 0.737618i | \(-0.264050\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.34847 | + | 4.24264i | 0.366965 | + | 0.211867i | 0.672132 | − | 0.740432i | \(-0.265379\pi\) |
−0.305167 | + | 0.952299i | \(0.598712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.00000 | + | 15.5885i | 0.448322 | + | 0.776516i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.67423 | + | 2.12132i | −0.182125 | + | 0.105150i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.9411 | − | 19.5959i | −1.67828 | − | 0.968956i | −0.962757 | − | 0.270367i | \(-0.912855\pi\) |
−0.715523 | − | 0.698589i | \(-0.753812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.66025 | − | 21.2132i | 0.426143 | − | 1.04383i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.0000 | −1.03085 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.7224 | + | 25.5000i | −0.719238 | + | 1.24576i | 0.242064 | + | 0.970260i | \(0.422176\pi\) |
−0.961302 | + | 0.275496i | \(0.911158\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | − | 17.3205i | −0.487370 | − | 0.844150i | 0.512524 | − | 0.858673i | \(-0.328710\pi\) |
−0.999895 | + | 0.0145228i | \(0.995377\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.73205 | − | 3.00000i | −0.0840168 | − | 0.145521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.12132 | − | 3.97141i | 0.247838 | − | 0.192190i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16.9706i | − | 0.817443i | −0.912659 | − | 0.408722i | \(-0.865975\pi\) | ||
0.912659 | − | 0.408722i | \(-0.134025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.0454i | 1.05943i | 0.848174 | + | 0.529717i | \(0.177702\pi\) | ||||
−0.848174 | + | 0.529717i | \(0.822298\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.3923 | + | 18.0000i | −0.497131 | + | 0.861057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4558 | − | 14.6969i | 1.21494 | − | 0.701447i | 0.251110 | − | 0.967959i | \(-0.419205\pi\) |
0.963832 | + | 0.266512i | \(0.0858712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0227 | − | 6.36396i | 0.523704 | − | 0.302361i | −0.214745 | − | 0.976670i | \(-0.568892\pi\) |
0.738449 | + | 0.674309i | \(0.235559\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 21.2132i | − | 1.00111i | −0.865704 | − | 0.500556i | \(-0.833129\pi\) | ||
0.865704 | − | 0.500556i | \(-0.166871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.34847i | − | 0.346026i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.87039 | − | 6.87868i | 0.415850 | − | 0.322477i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.00000 | + | 6.92820i | 0.187112 | + | 0.324088i | 0.944286 | − | 0.329125i | \(-0.106754\pi\) |
−0.757174 | + | 0.653213i | \(0.773421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.7224 | + | 25.5000i | 0.685692 | + | 1.18765i | 0.973219 | + | 0.229881i | \(0.0738336\pi\) |
−0.287527 | + | 0.957773i | \(0.592833\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5000 | + | 25.1147i | −0.673872 | + | 1.16718i | 0.302925 | + | 0.953014i | \(0.402037\pi\) |
−0.976797 | + | 0.214166i | \(0.931297\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.7846 | 0.961797 | 0.480899 | − | 0.876776i | \(-0.340311\pi\) | ||||
0.480899 | + | 0.876776i | \(0.340311\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0000 | − | 24.4949i | 0.461757 | − | 1.13107i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.7196 | + | 14.8492i | 1.18259 | + | 0.682769i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.24264 | + | 2.44949i | −0.194666 | + | 0.112390i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.9186 | + | 34.5000i | 0.910103 | + | 1.57635i | 0.813916 | + | 0.580982i | \(0.197331\pi\) |
0.0961869 | + | 0.995363i | \(0.469335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.12132 | + | 1.22474i | 0.0967239 | + | 0.0558436i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.24264i | 0.192648i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0000 | 0.996915 | 0.498458 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.0227 | − | 6.36396i | −0.497448 | − | 0.287202i | 0.230211 | − | 0.973141i | \(-0.426058\pi\) |
−0.727659 | + | 0.685939i | \(0.759392\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.36396 | − | 3.67423i | 0.286618 | − | 0.165479i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.04384 | − | 22.2426i | −0.136535 | − | 0.997719i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.50000 | + | 16.4545i | −0.425278 | + | 0.736604i | −0.996446 | − | 0.0842294i | \(-0.973157\pi\) |
0.571168 | + | 0.820833i | \(0.306490\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.73205 | 0.0772283 | 0.0386142 | − | 0.999254i | \(-0.487706\pi\) | ||||
0.0386142 | + | 0.999254i | \(0.487706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.52628 | − | 16.5000i | 0.422245 | − | 0.731350i | −0.573914 | − | 0.818916i | \(-0.694576\pi\) |
0.996159 | + | 0.0875661i | \(0.0279089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.51472 | + | 25.6836i | 0.155482 | + | 1.13618i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.3939 | − | 16.9706i | 1.29525 | − | 0.747812i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44.5477 | − | 25.7196i | −1.95921 | − | 1.13115i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.73205 | 0.0758825 | 0.0379413 | − | 0.999280i | \(-0.487920\pi\) | ||||
0.0379413 | + | 0.999280i | \(0.487920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 31.8434i | − | 1.39241i | −0.717841 | − | 0.696207i | \(-0.754870\pi\) | ||
0.717841 | − | 0.696207i | \(-0.245130\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.0227 | − | 6.36396i | −0.480157 | − | 0.277218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.5000 | + | 42.4352i | 1.06522 | + | 1.84501i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.67423 | + | 2.12132i | −0.159149 | + | 0.0918846i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.7279 | + | 7.34847i | 0.550276 | + | 0.317702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.7846 | + | 21.2132i | −0.895257 | + | 0.913717i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | 0.730887 | 0.365444 | − | 0.930834i | \(-0.380917\pi\) | ||||
0.365444 | + | 0.930834i | \(0.380917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.2583 | − | 19.5000i | 0.482254 | − | 0.835288i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.5000 | − | 35.5070i | −0.876517 | − | 1.51817i | −0.855138 | − | 0.518400i | \(-0.826528\pi\) |
−0.0213785 | − | 0.999771i | \(-0.506805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.19615 | − | 9.00000i | −0.221364 | − | 0.383413i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.10660 | − | 10.4539i | −0.344728 | − | 0.444543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.48528i | 0.359533i | 0.983709 | + | 0.179766i | \(0.0575342\pi\) | ||||
−0.983709 | + | 0.179766i | \(0.942466\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 17.1464i | − | 0.725217i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.3923 | + | 18.0000i | −0.437983 | + | 0.758610i | −0.997534 | − | 0.0701867i | \(-0.977640\pi\) |
0.559550 | + | 0.828796i | \(0.310974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.0919 | + | 11.0227i | −0.803202 | + | 0.463729i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.3939 | + | 16.9706i | −1.23226 | + | 0.711443i | −0.967500 | − | 0.252872i | \(-0.918625\pi\) |
−0.264756 | + | 0.964315i | \(0.585291\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.5000 | − | 21.6506i | 0.523109 | − | 0.906051i | −0.476530 | − | 0.879158i | \(-0.658105\pi\) |
0.999638 | − | 0.0268925i | \(-0.00856117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.9706i | 0.707721i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.5959i | − | 0.815789i | −0.913029 | − | 0.407894i | \(-0.866263\pi\) | ||
0.913029 | − | 0.407894i | \(-0.133737\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.6575 | − | 25.3492i | −0.815529 | − | 1.05166i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.7846 | − | 36.0000i | −0.857873 | − | 1.48588i | −0.873954 | − | 0.486008i | \(-0.838452\pi\) |
0.0160815 | − | 0.999871i | \(-0.494881\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | + | 15.5885i | −0.370839 | + | 0.642311i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.66025 | −0.355634 | −0.177817 | − | 0.984064i | \(-0.556904\pi\) | ||||
−0.177817 | + | 0.984064i | \(0.556904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.00000 | + | 7.34847i | −0.122988 | + | 0.301258i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.67423 | + | 2.12132i | 0.150125 | + | 0.0866748i | 0.573181 | − | 0.819429i | \(-0.305709\pi\) |
−0.423056 | + | 0.906104i | \(0.639043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0919 | + | 11.0227i | −0.778774 | + | 0.449625i | −0.835996 | − | 0.548736i | \(-0.815109\pi\) |
0.0572215 | + | 0.998362i | \(0.481776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.06218 | − | 10.5000i | −0.246463 | − | 0.426886i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.3345 | − | 13.4722i | −0.947119 | − | 0.546819i | −0.0549343 | − | 0.998490i | \(-0.517495\pi\) |
−0.892185 | + | 0.451671i | \(0.850828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.6985i | 1.20147i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00000 | −0.161558 | −0.0807792 | − | 0.996732i | \(-0.525741\pi\) | ||||
−0.0807792 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0454 | − | 12.7279i | −0.887515 | − | 0.512407i | −0.0143859 | − | 0.999897i | \(-0.504579\pi\) |
−0.873129 | + | 0.487490i | \(0.837913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.12132 | + | 1.22474i | −0.0852631 | + | 0.0492267i | −0.542025 | − | 0.840362i | \(-0.682342\pi\) |
0.456762 | + | 0.889589i | \(0.349009\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.2416 | + | 3.72792i | −1.09141 | + | 0.149356i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.73205 | −0.0690614 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.0000 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.2583 | + | 19.5000i | −0.446773 | + | 0.773834i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.6066 | + | 4.26858i | 0.657978 | + | 0.169127i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.3712 | − | 10.6066i | 0.725618 | − | 0.418936i | −0.0911991 | − | 0.995833i | \(-0.529070\pi\) |
0.816817 | + | 0.576897i | \(0.195737\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.7279 | + | 7.34847i | 0.501940 | + | 0.289795i | 0.729514 | − | 0.683965i | \(-0.239746\pi\) |
−0.227574 | + | 0.973761i | \(0.573079\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7846 | 0.817127 | 0.408564 | − | 0.912730i | \(-0.366030\pi\) | ||||
0.408564 | + | 0.912730i | \(0.366030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.7423i | 1.44226i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.7196 | + | 14.8492i | 1.00649 | + | 0.581096i | 0.910161 | − | 0.414254i | \(-0.135958\pi\) |
0.0963261 | + | 0.995350i | \(0.469291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.00000 | − | 15.5885i | −0.351659 | − | 0.609091i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.6969 | − | 8.48528i | 0.572511 | − | 0.330540i | −0.185640 | − | 0.982618i | \(-0.559436\pi\) |
0.758152 | + | 0.652078i | \(0.226103\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.6066 | − | 6.12372i | −0.412549 | − | 0.238185i | 0.279335 | − | 0.960194i | \(-0.409886\pi\) |
−0.691884 | + | 0.722008i | \(0.743219\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.3923 | + | 4.24264i | 0.402996 | + | 0.164523i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.0000 | −1.39393 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.19615 | + | 9.00000i | −0.200595 | + | 0.347441i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.00000 | − | 13.8564i | −0.308377 | − | 0.534125i | 0.669630 | − | 0.742695i | \(-0.266453\pi\) |
−0.978008 | + | 0.208569i | \(0.933119\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.5885 | − | 27.0000i | −0.599113 | − | 1.03769i | −0.992952 | − | 0.118515i | \(-0.962187\pi\) |
0.393839 | − | 0.919179i | \(-0.371147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.12132 | + | 3.97141i | −0.196538 | + | 0.152409i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.1838i | 1.46106i | 0.682880 | + | 0.730531i | \(0.260727\pi\) | ||||
−0.682880 | + | 0.730531i | \(0.739273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 36.7423i | − | 1.40385i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.0919 | + | 11.0227i | −0.726289 | + | 0.419323i | −0.817063 | − | 0.576548i | \(-0.804399\pi\) |
0.0907737 | + | 0.995872i | \(0.471066\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.3712 | − | 10.6066i | 0.696858 | − | 0.402331i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50000 | − | 2.59808i | 0.0568166 | − | 0.0984092i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12.7279i | − | 0.480727i | −0.970683 | − | 0.240363i | \(-0.922733\pi\) | ||
0.970683 | − | 0.240363i | \(-0.0772666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.44949i | 0.0923843i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.8493 | − | 21.7279i | −0.633681 | − | 0.817163i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.5000 | − | 42.4352i | −0.920117 | − | 1.59369i | −0.799232 | − | 0.601023i | \(-0.794760\pi\) |
−0.120885 | − | 0.992667i | \(-0.538573\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.1769 | + | 54.0000i | 1.16758 | + | 2.02232i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.00000 | + | 15.5885i | −0.336581 | + | 0.582975i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.9090 | 1.22730 | 0.613649 | − | 0.789579i | \(-0.289701\pi\) | ||||
0.613649 | + | 0.789579i | \(0.289701\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.0000 | + | 19.5959i | 1.78761 | + | 0.729790i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.34847 | − | 4.24264i | −0.272915 | − | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.36396 | + | 3.67423i | −0.236026 | + | 0.136270i | −0.613349 | − | 0.789812i | \(-0.710178\pi\) |
0.377323 | + | 0.926082i | \(0.376845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.06218 | + | 10.5000i | 0.224218 | + | 0.388357i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.4558 | − | 14.6969i | −0.940233 | − | 0.542844i | −0.0501997 | − | 0.998739i | \(-0.515986\pi\) |
−0.890033 | + | 0.455895i | \(0.849319\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.4264i | 1.56280i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.0000 | 1.39785 | 0.698926 | − | 0.715194i | \(-0.253662\pi\) | ||||
0.698926 | + | 0.715194i | \(0.253662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.3712 | − | 10.6066i | −0.673973 | − | 0.389118i | 0.123607 | − | 0.992331i | \(-0.460554\pi\) |
−0.797580 | + | 0.603213i | \(0.793887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.0919 | + | 11.0227i | −0.699472 | + | 0.403841i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.04384 | + | 22.2426i | 0.111219 | + | 0.812728i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.00000 | + | 8.66025i | −0.182453 | + | 0.316017i | −0.942715 | − | 0.333599i | \(-0.891737\pi\) |
0.760263 | + | 0.649616i | \(0.225070\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.66025 | 0.315179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.0000 | −1.92632 | −0.963159 | − | 0.268933i | \(-0.913329\pi\) | ||||
−0.963159 | + | 0.268933i | \(0.913329\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.2583 | + | 19.5000i | −0.408114 | + | 0.706874i | −0.994678 | − | 0.103028i | \(-0.967147\pi\) |
0.586564 | + | 0.809903i | \(0.300480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.0772 | − | 4.66335i | 1.23368 | − | 0.168825i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.3712 | − | 10.6066i | 0.663345 | − | 0.382982i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.24264 | + | 2.44949i | 0.152994 | + | 0.0883309i | 0.574542 | − | 0.818475i | \(-0.305180\pi\) |
−0.421549 | + | 0.906806i | \(0.638513\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.8372 | 1.43284 | 0.716422 | − | 0.697668i | \(-0.245779\pi\) | ||||
0.716422 | + | 0.697668i | \(0.245779\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.6969i | 0.527930i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.67423 | − | 2.12132i | −0.131643 | − | 0.0760042i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | + | 31.1769i | 0.644091 | + | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0227 | − | 6.36396i | 0.393417 | − | 0.227140i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.24264 | − | 2.44949i | −0.151234 | − | 0.0873149i | 0.422473 | − | 0.906375i | \(-0.361162\pi\) |
−0.573707 | + | 0.819060i | \(0.694495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.1769 | − | 12.7279i | −1.10852 | − | 0.452553i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | 0.213066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.19615 | − | 9.00000i | 0.184057 | − | 0.318796i | −0.759201 | − | 0.650856i | \(-0.774410\pi\) |
0.943258 | + | 0.332060i | \(0.107744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.5000 | − | 18.1865i | −0.371463 | − | 0.643393i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.7846 | − | 36.0000i | −0.733473 | − | 1.27041i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.7279 | − | 23.8284i | 1.08302 | − | 0.839842i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 25.4558i | − | 0.894980i | −0.894289 | − | 0.447490i | \(-0.852318\pi\) | ||
0.894289 | − | 0.447490i | \(-0.147682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.4393i | 1.80628i | 0.429349 | + | 0.903139i | \(0.358743\pi\) | ||||
−0.429349 | + | 0.903139i | \(0.641257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.866025 | + | 1.50000i | −0.0303355 | + | 0.0525427i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.8492 | − | 8.57321i | 0.519509 | − | 0.299939i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0454 | − | 12.7279i | 0.769390 | − | 0.444208i | −0.0632669 | − | 0.997997i | \(-0.520152\pi\) |
0.832657 | + | 0.553789i | \(0.186819\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.5000 | − | 21.6506i | 0.435723 | − | 0.754694i | −0.561632 | − | 0.827387i | \(-0.689826\pi\) |
0.997354 | + | 0.0726937i | \(0.0231595\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.1838i | 1.32778i | 0.747830 | + | 0.663890i | \(0.231096\pi\) | ||||
−0.747830 | + | 0.663890i | \(0.768904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 31.8434i | − | 1.10597i | −0.833193 | − | 0.552983i | \(-0.813489\pi\) | ||
0.833193 | − | 0.552983i | \(-0.186511\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.6786 | + | 3.25736i | −0.404639 | + | 0.112861i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.5000 | + | 28.5788i | 0.571006 | + | 0.989011i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.866025 | + | 1.50000i | 0.0298985 | + | 0.0517858i | 0.880587 | − | 0.473884i | \(-0.157148\pi\) |
−0.850689 | + | 0.525669i | \(0.823815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.50000 | + | 9.52628i | −0.189655 | + | 0.328492i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.1244 | −0.417091 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000 | − | 17.1464i | 0.240523 | − | 0.589158i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.34847 | + | 4.24264i | 0.251902 | + | 0.145436i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9706 | − | 9.79796i | 0.581061 | − | 0.335476i | −0.180494 | − | 0.983576i | \(-0.557770\pi\) |
0.761555 | + | 0.648100i | \(0.224436\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.06218 | + | 10.5000i | 0.207080 | + | 0.358673i | 0.950793 | − | 0.309825i | \(-0.100271\pi\) |
−0.743713 | + | 0.668499i | \(0.766937\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.9411 | + | 19.5959i | 1.15806 | + | 0.668604i | 0.950837 | − | 0.309691i | \(-0.100225\pi\) |
0.207219 | + | 0.978295i | \(0.433559\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.9706i | 0.577685i | 0.957377 | + | 0.288842i | \(0.0932703\pi\) | ||||
−0.957377 | + | 0.288842i | \(0.906730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.0000 | 1.22404 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.3712 | + | 10.6066i | 0.623199 | + | 0.359804i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.2132 | − | 12.2474i | 0.718782 | − | 0.414989i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.7818 | − | 4.34924i | 1.07442 | − | 0.147031i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.50000 | − | 6.06218i | 0.118187 | − | 0.204705i | −0.800862 | − | 0.598848i | \(-0.795625\pi\) |
0.919049 | + | 0.394143i | \(0.128959\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.1769 | −1.05038 | −0.525188 | − | 0.850986i | \(-0.676005\pi\) | ||||
−0.525188 | + | 0.850986i | \(0.676005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0000 | −0.572096 | −0.286048 | − | 0.958215i | \(-0.592342\pi\) | ||||
−0.286048 | + | 0.958215i | \(0.592342\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.52628 | + | 16.5000i | −0.319861 | + | 0.554016i | −0.980459 | − | 0.196724i | \(-0.936970\pi\) |
0.660598 | + | 0.750740i | \(0.270303\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.0772 | + | 4.66335i | −1.14291 | + | 0.156404i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.7196 | + | 14.8492i | −0.860675 | + | 0.496911i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.36396 | + | 3.67423i | 0.212724 | + | 0.122816i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.1769 | −1.03981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.34847 | + | 4.24264i | 0.244271 | + | 0.141030i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.50000 | − | 11.2583i | −0.215829 | − | 0.373827i | 0.737700 | − | 0.675129i | \(-0.235912\pi\) |
−0.953529 | + | 0.301302i | \(0.902579\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.7196 | + | 14.8492i | −0.852130 | + | 0.491977i | −0.861369 | − | 0.507980i | \(-0.830392\pi\) |
0.00923912 | + | 0.999957i | \(0.497059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.5477 | + | 25.7196i | 1.47431 | + | 0.851196i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.3923 | − | 25.4558i | 0.343184 | − | 0.840626i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.00000 | −0.164935 | −0.0824674 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824674 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.3923 | − | 18.0000i | 0.342067 | − | 0.592477i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | + | 1.73205i | 0.0328798 | + | 0.0569495i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.9186 | − | 34.5000i | −0.653508 | − | 1.13191i | −0.982266 | − | 0.187494i | \(-0.939963\pi\) |
0.328758 | − | 0.944414i | \(-0.393370\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.60660 | + | 16.5160i | 0.150975 | + | 0.541291i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 12.7279i | − | 0.416248i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.44949i | 0.0800213i | 0.999199 | + | 0.0400107i | \(0.0127392\pi\) | ||||
−0.999199 | + | 0.0400107i | \(0.987261\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.8468 | + | 46.5000i | −0.875180 | + | 1.51586i | −0.0186097 | + | 0.999827i | \(0.505924\pi\) |
−0.856571 | + | 0.516030i | \(0.827409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.7279 | + | 7.34847i | −0.414478 | + | 0.239299i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.6969 | − | 8.48528i | 0.477586 | − | 0.275735i | −0.241824 | − | 0.970320i | \(-0.577746\pi\) |
0.719410 | + | 0.694586i | \(0.244412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | + | 20.7846i | −0.389536 | + | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 50.9117i | − | 1.64919i | −0.565723 | − | 0.824596i | \(-0.691403\pi\) | ||
0.565723 | − | 0.824596i | \(-0.308597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.6969i | 0.475582i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.3519 | − | 34.3934i | 1.43220 | − | 1.11062i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.5000 | + | 19.9186i | 0.370968 | + | 0.642535i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.06218 | + | 10.5000i | 0.195148 | + | 0.338007i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.0000 | − | 39.8372i | 0.739630 | − | 1.28108i | −0.213032 | − | 0.977045i | \(-0.568334\pi\) |
0.952662 | − | 0.304032i | \(-0.0983329\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.9090 | 1.05610 | 0.528049 | − | 0.849214i | \(-0.322924\pi\) | ||||
0.528049 | + | 0.849214i | \(0.322924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.0000 | + | 12.2474i | 0.961756 | + | 0.392635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.7423 | − | 21.2132i | −1.17549 | − | 0.678671i | −0.220524 | − | 0.975381i | \(-0.570777\pi\) |
−0.954967 | + | 0.296711i | \(0.904110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.1838 | − | 22.0454i | 1.22036 | − | 0.704574i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.866025 | − | 1.50000i | −0.0276219 | − | 0.0478426i | 0.851884 | − | 0.523731i | \(-0.175460\pi\) |
−0.879506 | + | 0.475888i | \(0.842127\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.8198 | + | 18.3712i | 1.01386 | + | 0.585354i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 59.3970i | − | 1.88871i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.0000 | 1.74713 | 0.873566 | − | 0.486705i | \(-0.161801\pi\) | ||||
0.873566 | + | 0.486705i | \(0.161801\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.6969 | − | 8.48528i | −0.465924 | − | 0.269002i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.8198 | − | 18.3712i | 1.00774 | − | 0.581821i | 0.0972132 | − | 0.995264i | \(-0.469007\pi\) |
0.910530 | + | 0.413443i | \(0.135674\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2268.2.x.j.377.4 | 8 | ||
3.2 | odd | 2 | inner | 2268.2.x.j.377.2 | 8 | ||
7.6 | odd | 2 | inner | 2268.2.x.j.377.1 | 8 | ||
9.2 | odd | 6 | inner | 2268.2.x.j.1889.1 | 8 | ||
9.4 | even | 3 | 756.2.f.d.377.2 | yes | 4 | ||
9.5 | odd | 6 | 756.2.f.d.377.4 | yes | 4 | ||
9.7 | even | 3 | inner | 2268.2.x.j.1889.3 | 8 | ||
21.20 | even | 2 | inner | 2268.2.x.j.377.3 | 8 | ||
36.23 | even | 6 | 3024.2.k.h.1889.3 | 4 | |||
36.31 | odd | 6 | 3024.2.k.h.1889.1 | 4 | |||
63.13 | odd | 6 | 756.2.f.d.377.3 | yes | 4 | ||
63.20 | even | 6 | inner | 2268.2.x.j.1889.4 | 8 | ||
63.34 | odd | 6 | inner | 2268.2.x.j.1889.2 | 8 | ||
63.41 | even | 6 | 756.2.f.d.377.1 | ✓ | 4 | ||
252.139 | even | 6 | 3024.2.k.h.1889.4 | 4 | |||
252.167 | odd | 6 | 3024.2.k.h.1889.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.f.d.377.1 | ✓ | 4 | 63.41 | even | 6 | ||
756.2.f.d.377.2 | yes | 4 | 9.4 | even | 3 | ||
756.2.f.d.377.3 | yes | 4 | 63.13 | odd | 6 | ||
756.2.f.d.377.4 | yes | 4 | 9.5 | odd | 6 | ||
2268.2.x.j.377.1 | 8 | 7.6 | odd | 2 | inner | ||
2268.2.x.j.377.2 | 8 | 3.2 | odd | 2 | inner | ||
2268.2.x.j.377.3 | 8 | 21.20 | even | 2 | inner | ||
2268.2.x.j.377.4 | 8 | 1.1 | even | 1 | trivial | ||
2268.2.x.j.1889.1 | 8 | 9.2 | odd | 6 | inner | ||
2268.2.x.j.1889.2 | 8 | 63.34 | odd | 6 | inner | ||
2268.2.x.j.1889.3 | 8 | 9.7 | even | 3 | inner | ||
2268.2.x.j.1889.4 | 8 | 63.20 | even | 6 | inner | ||
3024.2.k.h.1889.1 | 4 | 36.31 | odd | 6 | |||
3024.2.k.h.1889.2 | 4 | 252.167 | odd | 6 | |||
3024.2.k.h.1889.3 | 4 | 36.23 | even | 6 | |||
3024.2.k.h.1889.4 | 4 | 252.139 | even | 6 |