Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(129,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.g (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8x^{14} + 32x^{12} - 64x^{10} + 127x^{8} - 576x^{6} + 2592x^{4} - 5832x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 641.3 | ||
Root | \(1.50947 - 0.849413i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.641 |
Dual form | 1024.2.g.h.385.3 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.59352 | + | 0.660056i | 0.920017 | + | 0.381083i | 0.791883 | − | 0.610673i | \(-0.209101\pi\) |
0.128134 | + | 0.991757i | \(0.459101\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.212292 | − | 0.512517i | −0.0949397 | − | 0.229205i | 0.869274 | − | 0.494330i | \(-0.164587\pi\) |
−0.964214 | + | 0.265125i | \(0.914587\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.69883 | + | 1.69883i | −0.642096 | + | 0.642096i | −0.951070 | − | 0.308974i | \(-0.900014\pi\) |
0.308974 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0177021 | − | 0.0177021i | −0.00590068 | − | 0.00590068i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.44127 | − | 1.42542i | 1.03758 | − | 0.429781i | 0.202139 | − | 0.979357i | \(-0.435211\pi\) |
0.835444 | + | 0.549576i | \(0.185211\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.34094 | + | 5.65154i | −0.649261 | + | 1.56746i | 0.164577 | + | 0.986364i | \(0.447374\pi\) |
−0.813839 | + | 0.581091i | \(0.802626\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.956828i | − | 0.247052i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.26768i | 1.27760i | 0.769373 | + | 0.638799i | \(0.220569\pi\) | ||||
−0.769373 | + | 0.638799i | \(0.779431\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.57436 | + | 3.80083i | −0.361182 | + | 0.871970i | 0.633946 | + | 0.773377i | \(0.281434\pi\) |
−0.995128 | + | 0.0985928i | \(0.968566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.82843 | + | 1.58579i | −0.835431 | + | 0.346047i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.31195 | + | 4.31195i | 0.899104 | + | 0.899104i | 0.995357 | − | 0.0962527i | \(-0.0306857\pi\) |
−0.0962527 | + | 0.995357i | \(0.530686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.31793 | − | 3.31793i | 0.663586 | − | 0.663586i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.99669 | − | 4.82044i | −0.384263 | − | 0.927694i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.23733 | + | 0.512517i | 0.229766 | + | 0.0951721i | 0.494596 | − | 0.869123i | \(-0.335316\pi\) |
−0.264830 | + | 0.964295i | \(0.585316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.53073 | 0.274928 | 0.137464 | − | 0.990507i | \(-0.456105\pi\) | ||||
0.137464 | + | 0.990507i | \(0.456105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.42458 | 1.11838 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.23132 | + | 0.510031i | 0.208132 | + | 0.0862110i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.49785 | + | 3.61614i | 0.246245 | + | 0.594489i | 0.997879 | − | 0.0650915i | \(-0.0207339\pi\) |
−0.751634 | + | 0.659581i | \(0.770734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.46066 | + | 7.46066i | −1.19466 | + | 1.19466i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.69226 | + | 8.69226i | 1.35750 | + | 1.35750i | 0.876985 | + | 0.480518i | \(0.159551\pi\) |
0.480518 | + | 0.876985i | \(0.340449\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.511123 | + | 0.211714i | −0.0779456 | + | 0.0322861i | −0.421316 | − | 0.906914i | \(-0.638432\pi\) |
0.343370 | + | 0.939200i | \(0.388432\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.00531461 | + | 0.0128306i | −0.000792255 | + | 0.00191267i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.73339i | − | 1.41976i | −0.704322 | − | 0.709881i | \(-0.748749\pi\) | ||
0.704322 | − | 0.709881i | \(-0.251251\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.22798i | 0.175425i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.47696 | + | 8.39412i | −0.486872 | + | 1.17541i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.73012 | + | 2.78771i | −0.924454 | + | 0.382921i | −0.793572 | − | 0.608477i | \(-0.791781\pi\) |
−0.130882 | + | 0.991398i | \(0.541781\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.46111 | − | 1.46111i | −0.197016 | − | 0.197016i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.01752 | + | 5.01752i | −0.664587 | + | 0.664587i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.14517 | − | 2.76469i | −0.149089 | − | 0.359933i | 0.831637 | − | 0.555319i | \(-0.187404\pi\) |
−0.980726 | + | 0.195387i | \(0.937404\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.40138 | − | 3.06575i | −0.947650 | − | 0.392529i | −0.145303 | − | 0.989387i | \(-0.546416\pi\) |
−0.802347 | + | 0.596858i | \(0.796416\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0601454 | 0.00757761 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.39347 | 0.420909 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.33529 | − | 2.20995i | −0.651810 | − | 0.269988i | 0.0321778 | − | 0.999482i | \(-0.489756\pi\) |
−0.683987 | + | 0.729494i | \(0.739756\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.02503 | + | 9.71729i | 0.484557 | + | 1.16982i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.45315 | − | 9.45315i | 1.12188 | − | 1.12188i | 0.130424 | − | 0.991458i | \(-0.458366\pi\) |
0.991458 | − | 0.130424i | \(-0.0416338\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.69977 | + | 1.69977i | 0.198944 | + | 0.198944i | 0.799547 | − | 0.600603i | \(-0.205073\pi\) |
−0.600603 | + | 0.799547i | \(0.705073\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.47719 | − | 3.09715i | 0.863391 | − | 0.357628i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.42458 | + | 8.26768i | −0.390267 | + | 0.942189i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.8332i | − | 1.44385i | −0.691973 | − | 0.721923i | \(-0.743258\pi\) | ||
0.691973 | − | 0.721923i | \(-0.256742\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 8.92427i | − | 0.991586i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.360647 | − | 0.870678i | 0.0395861 | − | 0.0955693i | −0.902850 | − | 0.429956i | \(-0.858529\pi\) |
0.942436 | + | 0.334387i | \(0.108529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.69977 | − | 1.11828i | 0.292832 | − | 0.121295i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.63341 | + | 1.63341i | 0.175120 | + | 0.175120i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.14939 | − | 1.14939i | 0.121835 | − | 0.121835i | −0.643560 | − | 0.765396i | \(-0.722543\pi\) |
0.765396 | + | 0.643560i | \(0.222543\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.62413 | − | 13.5778i | −0.589569 | − | 1.42334i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.43925 | + | 1.01037i | 0.252938 | + | 0.104770i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.28221 | 0.234150 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.83880 | −0.186702 | −0.0933508 | − | 0.995633i | \(-0.529758\pi\) | ||||
−0.0933508 | + | 0.995633i | \(0.529758\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0861505 | − | 0.0356847i | −0.00865845 | − | 0.00358645i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.730123 | − | 1.76267i | −0.0726500 | − | 0.175393i | 0.883383 | − | 0.468652i | \(-0.155260\pi\) |
−0.956033 | + | 0.293259i | \(0.905260\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.36725 | + | 5.36725i | −0.528851 | + | 0.528851i | −0.920230 | − | 0.391379i | \(-0.871998\pi\) |
0.391379 | + | 0.920230i | \(0.371998\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.62549 | + | 1.62549i | 0.158631 | + | 0.158631i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.3787 | + | 7.19848i | −1.68006 | + | 0.695904i | −0.999329 | − | 0.0366299i | \(-0.988338\pi\) |
−0.680731 | + | 0.732534i | \(0.738338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.61614 | − | 6.31591i | 0.250580 | − | 0.604954i | −0.747671 | − | 0.664070i | \(-0.768828\pi\) |
0.998251 | + | 0.0591151i | \(0.0188279\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.75103i | 0.640780i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.60045i | 0.620918i | 0.950587 | + | 0.310459i | \(0.100483\pi\) | ||||
−0.950587 | + | 0.310459i | \(0.899517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.29456 | − | 3.12534i | 0.120718 | − | 0.291440i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.141483 | − | 0.0586043i | 0.0130801 | − | 0.00541797i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.94887 | − | 8.94887i | −0.820341 | − | 0.820341i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.03237 | − | 2.03237i | 0.184761 | − | 0.184761i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.11387 | + | 19.5886i | 0.731603 | + | 1.76625i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.96745 | − | 2.05758i | −0.444302 | − | 0.184036i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.36789 | 0.387588 | 0.193794 | − | 0.981042i | \(-0.437921\pi\) | ||||
0.193794 | + | 0.981042i | \(0.437921\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.954226 | −0.0840149 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.29212 | + | 2.60628i | 0.549745 | + | 0.227712i | 0.640226 | − | 0.768186i | \(-0.278841\pi\) |
−0.0904813 | + | 0.995898i | \(0.528841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.78239 | − | 9.13151i | −0.327975 | − | 0.791802i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.04668 | + | 2.04668i | −0.176150 | + | 0.176150i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.47465 | − | 5.47465i | −0.467731 | − | 0.467731i | 0.433448 | − | 0.901179i | \(-0.357297\pi\) |
−0.901179 | + | 0.433448i | \(0.857297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7259 | − | 4.44282i | 0.909760 | − | 0.376835i | 0.121795 | − | 0.992555i | \(-0.461135\pi\) |
0.787965 | + | 0.615721i | \(0.211135\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.42458 | − | 15.5103i | 0.541048 | − | 1.30620i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.7853i | 1.90541i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.742954i | − | 0.0616990i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.810533 | + | 1.95680i | −0.0668516 | + | 0.161394i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.76267 | + | 1.97276i | −0.390173 | + | 0.161615i | −0.569141 | − | 0.822240i | \(-0.692724\pi\) |
0.178968 | + | 0.983855i | \(0.442724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.9603 | + | 13.9603i | 1.13607 | + | 1.13607i | 0.989148 | + | 0.146924i | \(0.0469374\pi\) |
0.146924 | + | 0.989148i | \(0.453063\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0932487 | − | 0.0932487i | 0.00753871 | − | 0.00753871i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.324962 | − | 0.784527i | −0.0261016 | − | 0.0630148i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0332 | + | 6.64117i | 1.27959 | + | 0.530023i | 0.915866 | − | 0.401484i | \(-0.131506\pi\) |
0.363723 | + | 0.931507i | \(0.381506\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.5646 | −0.996438 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.6505 | −1.15462 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.71513 | − | 1.95307i | −0.369317 | − | 0.152976i | 0.190303 | − | 0.981725i | \(-0.439053\pi\) |
−0.559620 | + | 0.828749i | \(0.689053\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.36388 | − | 3.29271i | −0.106178 | − | 0.256337i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.52743 | − | 3.52743i | 0.272960 | − | 0.272960i | −0.557330 | − | 0.830291i | \(-0.688174\pi\) |
0.830291 | + | 0.557330i | \(0.188174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.2675 | − | 17.2675i | −1.32827 | − | 1.32827i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0951518 | − | 0.0394132i | 0.00727644 | − | 0.00301400i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.29491 | + | 15.1973i | −0.478593 | + | 1.15543i | 0.481676 | + | 0.876350i | \(0.340028\pi\) |
−0.960269 | + | 0.279077i | \(0.909972\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2732i | 0.852171i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.16146i | − | 0.387959i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.65959 | − | 20.9061i | 0.647248 | − | 1.56260i | −0.169455 | − | 0.985538i | \(-0.554201\pi\) |
0.816704 | − | 0.577057i | \(-0.195799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7830 | − | 8.60862i | 1.54479 | − | 0.639874i | 0.562427 | − | 0.826847i | \(-0.309868\pi\) |
0.982365 | + | 0.186974i | \(0.0598679\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.77065 | − | 9.77065i | −0.722267 | − | 0.722267i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.53535 | − | 1.53535i | 0.112881 | − | 0.112881i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.50866 | + | 18.1275i | 0.549088 | + | 1.32562i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.5811 | + | 4.79706i | 0.842403 | + | 0.348935i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4366 | −0.755168 | −0.377584 | − | 0.925975i | \(-0.623245\pi\) | ||||
−0.377584 | + | 0.925975i | \(0.623245\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.81806 | −0.274830 | −0.137415 | − | 0.990514i | \(-0.543879\pi\) | ||||
−0.137415 | + | 0.990514i | \(0.543879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.40755 | + | 2.23988i | 0.387243 | + | 0.160401i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.08042 | − | 14.6794i | −0.433212 | − | 1.04587i | −0.978245 | − | 0.207452i | \(-0.933483\pi\) |
0.545033 | − | 0.838414i | \(-0.316517\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0244 | − | 16.0244i | 1.13594 | − | 1.13594i | 0.146771 | − | 0.989171i | \(-0.453112\pi\) |
0.989171 | − | 0.146771i | \(-0.0468879\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.04318 | − | 7.04318i | −0.496788 | − | 0.496788i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.97268 | + | 1.23132i | −0.208641 | + | 0.0864220i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.60964 | − | 6.30023i | 0.182265 | − | 0.440027i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.152661i | − | 0.0106107i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.3238i | 1.05997i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.50184 | − | 13.2826i | 0.378762 | − | 0.914413i | −0.613436 | − | 0.789744i | \(-0.710213\pi\) |
0.992198 | − | 0.124669i | \(-0.0397868\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.3033 | − | 8.82413i | 1.45968 | − | 0.604620i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.217014 | + | 0.217014i | 0.0148003 | + | 0.0148003i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.60045 | + | 2.60045i | −0.176530 | + | 0.176530i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.58667 | + | 3.83056i | 0.107217 | + | 0.258845i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.7705 | − | 12.3313i | −2.00258 | − | 0.829495i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.3670 | 1.09602 | 0.548008 | − | 0.836473i | \(-0.315386\pi\) | ||||
0.548008 | + | 0.836473i | \(0.315386\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.117468 | −0.00783122 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.19652 | + | 2.15247i | 0.344905 | + | 0.142864i | 0.548410 | − | 0.836210i | \(-0.315233\pi\) |
−0.203505 | + | 0.979074i | \(0.565233\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.04072 | − | 12.1694i | −0.333100 | − | 0.804175i | −0.998343 | − | 0.0575475i | \(-0.981672\pi\) |
0.665243 | − | 0.746627i | \(-0.268328\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.9143 | + | 10.9143i | −0.718105 | + | 0.718105i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.74984 | − | 1.74984i | −0.114636 | − | 0.114636i | 0.647462 | − | 0.762098i | \(-0.275831\pi\) |
−0.762098 | + | 0.647462i | \(0.775831\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.98853 | + | 2.06632i | −0.325416 | + | 0.134792i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.47062 | − | 20.4499i | 0.550226 | − | 1.32836i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7565i | 0.825152i | 0.910923 | + | 0.412576i | \(0.135371\pi\) | ||||
−0.910923 | + | 0.412576i | \(0.864629\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.9660i | − | 1.22171i | −0.791743 | − | 0.610854i | \(-0.790826\pi\) | ||
0.791743 | − | 0.610854i | \(-0.209174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.0995586 | + | 0.240356i | −0.00638669 | + | 0.0154188i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.629359 | − | 0.260689i | 0.0402083 | − | 0.0166548i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.7951 | − | 17.7951i | −1.13227 | − | 1.13227i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.14939 | − | 1.14939i | 0.0728398 | − | 0.0728398i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.77199 | + | 9.10639i | 0.238086 | + | 0.574790i | 0.997085 | − | 0.0763018i | \(-0.0243113\pi\) |
−0.758999 | + | 0.651092i | \(0.774311\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.9850 | + | 8.69226i | 1.31931 | + | 0.546478i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.04026 | 0.315633 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.06510 | −0.128817 | −0.0644087 | − | 0.997924i | \(-0.520516\pi\) | ||||
−0.0644087 | + | 0.997924i | \(0.520516\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.68778 | − | 3.59860i | −0.539832 | − | 0.223606i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0128306 | − | 0.0309758i | −0.000794194 | − | 0.00191736i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.8612 | − | 17.8612i | 1.10137 | − | 1.10137i | 0.107120 | − | 0.994246i | \(-0.465837\pi\) |
0.994246 | − | 0.107120i | \(-0.0341629\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.85750 | + | 2.85750i | 0.175535 | + | 0.175535i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.59024 | − | 1.07291i | 0.158520 | − | 0.0656611i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.65583 | − | 13.6544i | 0.344842 | − | 0.832523i | −0.652370 | − | 0.757901i | \(-0.726225\pi\) |
0.997212 | − | 0.0746220i | \(-0.0237750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.39655i | 0.145580i | 0.997347 | + | 0.0727901i | \(0.0231903\pi\) | ||||
−0.997347 | + | 0.0727901i | \(0.976810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 25.3487i | − | 1.53418i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.68845 | − | 16.1473i | 0.403329 | − | 0.973722i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.24018 | + | 3.82741i | −0.555189 | + | 0.229967i | −0.642595 | − | 0.766206i | \(-0.722142\pi\) |
0.0874063 | + | 0.996173i | \(0.472142\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.0270971 | − | 0.0270971i | −0.00162226 | − | 0.00162226i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.8667 | + | 19.8667i | −1.18515 | + | 1.18515i | −0.206754 | + | 0.978393i | \(0.566290\pi\) |
−0.978393 | + | 0.206754i | \(0.933710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.97378 | − | 4.76511i | −0.117329 | − | 0.283257i | 0.854295 | − | 0.519788i | \(-0.173989\pi\) |
−0.971624 | + | 0.236532i | \(0.923989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.63674 | + | 1.50639i | 0.215422 | + | 0.0892307i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.5333 | −1.74329 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.7484 | −0.632259 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.93015 | − | 1.21371i | −0.171769 | − | 0.0711488i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.38983 | + | 20.2548i | 0.490139 | + | 1.18330i | 0.954649 | + | 0.297733i | \(0.0962305\pi\) |
−0.464510 | + | 0.885568i | \(0.653770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17384 | + | 1.17384i | −0.0683438 | + | 0.0683438i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.7423 | − | 13.7423i | −0.797411 | − | 0.797411i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −34.4632 | + | 14.2751i | −1.99306 | + | 0.825552i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.508644 | − | 1.22798i | 0.0293178 | − | 0.0707793i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.29077i | − | 0.189050i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.44417i | 0.254472i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.25751 | + | 19.9354i | −0.471281 | + | 1.13777i | 0.492317 | + | 0.870416i | \(0.336150\pi\) |
−0.963598 | + | 0.267356i | \(0.913850\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0955 | + | 5.01011i | −0.688088 | + | 0.285015i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4798 | + | 15.4798i | 0.877779 | + | 0.877779i | 0.993304 | − | 0.115526i | \(-0.0368553\pi\) |
−0.115526 | + | 0.993304i | \(0.536855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0918 | − | 14.0918i | 0.796516 | − | 0.796516i | −0.186028 | − | 0.982544i | \(-0.559562\pi\) |
0.982544 | + | 0.186028i | \(0.0595616\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0127684 | − | 0.0308256i | −0.000719416 | − | 0.00173682i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.37983 | − | 3.05683i | −0.414492 | − | 0.171688i | 0.165685 | − | 0.986179i | \(-0.447017\pi\) |
−0.580177 | + | 0.814490i | \(0.697017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.98853 | 0.279304 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.4446 | −1.81088 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0215 | − | 8.29319i | −1.11403 | − | 0.461445i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.9843 | + | 26.5185i | 0.609300 | + | 1.47098i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.33771 | − | 8.33771i | 0.461076 | − | 0.461076i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.5354 | + | 16.5354i | 0.911623 | + | 0.911623i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.47564 | − | 2.68230i | 0.355934 | − | 0.147433i | −0.197550 | − | 0.980293i | \(-0.563298\pi\) |
0.553483 | + | 0.832860i | \(0.313298\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0374980 | − | 0.0905281i | 0.00205488 | − | 0.00496091i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.20358i | 0.175030i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.82843i | − | 0.154074i | −0.997028 | − | 0.0770371i | \(-0.975454\pi\) | ||
0.997028 | − | 0.0770371i | \(-0.0245460\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.35667 | + | 10.5179i | −0.236622 | + | 0.571255i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.26768 | − | 2.18194i | 0.285261 | − | 0.118159i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.9779 | − | 13.9779i | −0.754736 | − | 0.754736i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.12580 | − | 4.12580i | 0.222126 | − | 0.222126i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.39235 | − | 10.6041i | −0.235794 | − | 0.569256i | 0.761046 | − | 0.648698i | \(-0.224686\pi\) |
−0.996840 | + | 0.0794417i | \(0.974686\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.7580 | − | 8.18404i | −1.05762 | − | 0.438081i | −0.215015 | − | 0.976611i | \(-0.568980\pi\) |
−0.842607 | + | 0.538529i | \(0.818980\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 31.9170 | 1.70361 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.0563 | 1.38684 | 0.693418 | − | 0.720535i | \(-0.256104\pi\) | ||||
0.693418 | + | 0.720535i | \(0.256104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.85172 | − | 2.83808i | −0.363652 | − | 0.150629i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.35341 | − | 20.1669i | −0.442109 | − | 1.06735i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.77460 | − | 6.77460i | 0.357550 | − | 0.357550i | −0.505359 | − | 0.862909i | \(-0.668640\pi\) |
0.862909 | + | 0.505359i | \(0.168640\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.46732 | + | 1.46732i | 0.0772274 | + | 0.0772274i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.58008 | − | 1.89713i | 0.240392 | − | 0.0995737i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.510316 | − | 1.23201i | 0.0267112 | − | 0.0644864i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 19.2892i | − | 1.00689i | −0.864028 | − | 0.503444i | \(-0.832066\pi\) | ||
0.864028 | − | 0.503444i | \(-0.167934\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.307742i | − | 0.0160204i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.69748 | − | 16.1691i | 0.347716 | − | 0.839460i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.81560 | − | 2.82311i | 0.352898 | − | 0.146175i | −0.199190 | − | 0.979961i | \(-0.563831\pi\) |
0.552088 | + | 0.833786i | \(0.313831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.55759 | − | 6.55759i | −0.338632 | − | 0.338632i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.79302 | + | 5.79302i | −0.298356 | + | 0.298356i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.30491 | − | 12.8072i | −0.272495 | − | 0.657861i | 0.727094 | − | 0.686538i | \(-0.240870\pi\) |
−0.999589 | + | 0.0286774i | \(0.990870\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.96030 | + | 2.88305i | 0.356587 | + | 0.147703i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.78803 | −0.193559 | −0.0967797 | − | 0.995306i | \(-0.530854\pi\) | ||||
−0.0967797 | + | 0.995306i | \(0.530854\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.96434 | 0.253006 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0127957 | + | 0.00530016i | 0.000650442 | + | 0.000269422i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.93103 | − | 19.1472i | −0.402119 | − | 0.970801i | −0.987151 | − | 0.159791i | \(-0.948918\pi\) |
0.585032 | − | 0.811010i | \(-0.301082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.7140 | + | 22.7140i | −1.14869 | + | 1.14869i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.30630 | + | 8.30630i | 0.418997 | + | 0.418997i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.57723 | + | 2.72438i | −0.330936 | + | 0.137078i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.65594 | − | 6.41201i | 0.133298 | − | 0.321810i | −0.843111 | − | 0.537740i | \(-0.819278\pi\) |
0.976409 | + | 0.215930i | \(0.0692783\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 17.0478i | − | 0.853457i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0373i | 1.05055i | 0.850931 | + | 0.525277i | \(0.176038\pi\) | ||||
−0.850931 | + | 0.525277i | \(0.823962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.58336 | + | 8.65100i | −0.178500 | + | 0.430937i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.57384 | + | 1.89455i | −0.227276 | + | 0.0941408i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3090 | + | 10.3090i | 0.511000 | + | 0.511000i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.106839 | − | 0.106839i | 0.00528285 | − | 0.00528285i | −0.704460 | − | 0.709743i | \(-0.748811\pi\) |
0.709743 | + | 0.704460i | \(0.248811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.11037 | − | 12.3375i | −0.252076 | − | 0.608565i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.64219 | + | 2.75128i | 0.326841 | + | 0.135382i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.522800 | −0.0256632 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.0244 | 0.980599 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.7318 | + | 7.75898i | 0.915110 | + | 0.379051i | 0.790011 | − | 0.613093i | \(-0.210075\pi\) |
0.125099 | + | 0.992144i | \(0.460075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.08471 | + | 12.2756i | 0.247814 | + | 0.598275i | 0.998018 | − | 0.0629310i | \(-0.0200448\pi\) |
−0.750204 | + | 0.661206i | \(0.770045\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.172301 | + | 0.172301i | −0.00837756 | + | 0.00837756i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.4778 | + | 17.4778i | 0.847796 | + | 0.847796i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.7819 | − | 7.36548i | 0.860524 | − | 0.356441i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.0396 | + | 36.3088i | −0.726118 | + | 1.75300i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.96851i | − | 0.431998i | −0.976394 | − | 0.215999i | \(-0.930699\pi\) | ||
0.976394 | − | 0.215999i | \(-0.0693008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.14680i | − | 0.151225i | −0.997137 | − | 0.0756127i | \(-0.975909\pi\) | ||
0.997137 | − | 0.0756127i | \(-0.0240913\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.490391 | − | 1.18391i | 0.0235125 | − | 0.0567641i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.1775 | + | 9.60045i | −1.10873 | + | 0.459252i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.35602 | + | 5.35602i | 0.255629 | + | 0.255629i | 0.823274 | − | 0.567645i | \(-0.192145\pi\) |
−0.567645 | + | 0.823274i | \(0.692145\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0217377 | − | 0.0217377i | 0.00103513 | − | 0.00103513i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.13988 | + | 17.2372i | 0.339226 | + | 0.818964i | 0.997790 | + | 0.0664397i | \(0.0211640\pi\) |
−0.658564 | + | 0.752524i | \(0.728836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.833089 | − | 0.345077i | −0.0394922 | − | 0.0163582i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.89153 | −0.420555 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.0511 | 1.65416 | 0.827082 | − | 0.562081i | \(-0.189999\pi\) | ||||
0.827082 | + | 0.562081i | \(0.189999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.3026 | + | 17.5223i | 1.99195 | + | 0.825093i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.0314 | + | 31.4605i | 0.612267 | + | 1.47814i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.76492 | + | 5.76492i | −0.270264 | + | 0.270264i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.65659 | − | 9.65659i | −0.451716 | − | 0.451716i | 0.444207 | − | 0.895924i | \(-0.353485\pi\) |
−0.895924 | + | 0.444207i | \(0.853485\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.3925 | − | 10.5179i | 1.18522 | − | 0.490935i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.64976 | + | 23.2966i | −0.449434 | + | 1.08503i | 0.523100 | + | 0.852271i | \(0.324775\pi\) |
−0.972534 | + | 0.232759i | \(0.925225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.57747i | − | 0.0733113i | −0.999328 | − | 0.0366556i | \(-0.988330\pi\) | ||
0.999328 | − | 0.0366556i | \(-0.0116705\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1.46465i | − | 0.0679215i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.79289 | + | 23.6421i | −0.453161 | + | 1.09403i | 0.517953 | + | 0.855409i | \(0.326694\pi\) |
−0.971114 | + | 0.238618i | \(0.923306\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8181 | − | 5.30941i | 0.591883 | − | 0.245166i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.1656 | + | 21.1656i | 0.975260 | + | 0.975260i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.45713 | + | 1.45713i | −0.0669991 | + | 0.0669991i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.38728 | + | 17.8345i | 0.338952 | + | 0.818302i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.168485 | + | 0.0697888i | 0.00771441 | + | 0.00319541i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.1963 | −1.15125 | −0.575623 | − | 0.817715i | \(-0.695240\pi\) | ||||
−0.575623 | + | 0.817715i | \(0.695240\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.9431 | −1.09171 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23.3458 | − | 9.67016i | −1.06227 | − | 0.440008i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.390361 | + | 0.942415i | 0.0177254 | + | 0.0427929i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.4256 | + | 15.4256i | −0.699001 | + | 0.699001i | −0.964195 | − | 0.265194i | \(-0.914564\pi\) |
0.265194 | + | 0.964195i | \(0.414564\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.22450 | − | 6.22450i | −0.281481 | − | 0.281481i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.8199 | − | 11.9376i | 1.30062 | − | 0.538736i | 0.378489 | − | 0.925606i | \(-0.376444\pi\) |
0.922134 | + | 0.386870i | \(0.126444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.69977 | + | 6.51783i | −0.121592 | + | 0.293548i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0517292i | 0.00232505i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.1185i | 1.44071i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.6102 | + | 35.2722i | −0.654043 | + | 1.57900i | 0.152814 | + | 0.988255i | \(0.451166\pi\) |
−0.806858 | + | 0.590746i | \(0.798834\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.94930 | − | 3.29271i | 0.355149 | − | 0.147107i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.18240 | − | 2.18240i | −0.0973084 | − | 0.0973084i | 0.656777 | − | 0.754085i | \(-0.271919\pi\) |
−0.754085 | + | 0.656777i | \(0.771919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.748402 | + | 0.748402i | −0.0333034 | + | 0.0333034i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.1185 | − | 38.9135i | −0.715848 | − | 1.72821i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.44742 | − | 3.08482i | −0.330101 | − | 0.136732i | 0.211477 | − | 0.977383i | \(-0.432173\pi\) |
−0.541578 | + | 0.840651i | \(0.682173\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.77524 | −0.255482 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.4652 | 0.947710 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.89023 | + | 1.61139i | 0.171424 | + | 0.0710061i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.8742 | − | 33.4953i | −0.610187 | − | 1.47312i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.0621 | + | 20.0621i | −0.880627 | + | 0.880627i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.94553 | + | 6.94553i | 0.304289 | + | 0.304289i | 0.842689 | − | 0.538400i | \(-0.180971\pi\) |
−0.538400 | + | 0.842689i | \(0.680971\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.24673 | − | 0.930625i | 0.0982425 | − | 0.0406934i | −0.333021 | − | 0.942919i | \(-0.608068\pi\) |
0.431263 | + | 0.902226i | \(0.358068\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.44092 | + | 17.9640i | −0.324748 | + | 0.784012i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.06341i | 0.351248i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.1859i | 0.616777i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0286688 | + | 0.0692127i | −0.00124412 | + | 0.00300358i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −69.4727 | + | 28.7765i | −3.00920 | + | 1.24645i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.37869 | + | 7.37869i | 0.319009 | + | 0.319009i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.5984 | − | 27.5984i | 1.19096 | − | 1.19096i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.75038 | + | 4.22580i | 0.0753944 | + | 0.182018i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.4120 | + | 10.5260i | 1.09255 | + | 0.452548i | 0.854894 | − | 0.518802i | \(-0.173622\pi\) |
0.237653 | + | 0.971350i | \(0.423622\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 38.8003 | 1.66508 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.79240 | −0.162448 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.52591 | − | 1.04627i | −0.108000 | − | 0.0447351i | 0.328029 | − | 0.944668i | \(-0.393616\pi\) |
−0.436029 | + | 0.899932i | \(0.643616\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0767495 | + | 0.185290i | 0.00327559 | + | 0.00790798i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.89598 | + | 3.89598i | −0.165974 | + | 0.165974i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.8014 | + | 21.8014i | 0.927088 | + | 0.927088i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.46002 | − | 1.43319i | 0.146870 | − | 0.0608354i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.61495 | + | 20.7983i | −0.365027 | + | 0.881254i | 0.629522 | + | 0.776983i | \(0.283251\pi\) |
−0.994549 | + | 0.104271i | \(0.966749\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.38425i | − | 0.143138i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33.8426i | 1.42884i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.66534 | − | 20.9200i | 0.365201 | − | 0.881672i | −0.629321 | − | 0.777145i | \(-0.716667\pi\) |
0.994522 | − | 0.104527i | \(-0.0333329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.38285 | − | 1.40122i | 0.142317 | − | 0.0589498i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.1608 | + | 15.1608i | 0.636693 | + | 0.636693i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.276633 | − | 0.276633i | 0.0115970 | − | 0.0115970i | −0.701284 | − | 0.712882i | \(-0.747390\pi\) |
0.712882 | + | 0.701284i | \(0.247390\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.2460 | − | 31.9788i | −0.554329 | − | 1.33827i | −0.914198 | − | 0.405267i | \(-0.867179\pi\) |
0.359869 | − | 0.933003i | \(-0.382821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.6309 | − | 6.88876i | −0.694767 | − | 0.287782i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.6135 | 1.19327 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.0407 | 1.25061 | 0.625306 | − | 0.780379i | \(-0.284974\pi\) | ||||
0.625306 | + | 0.780379i | \(0.284974\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.08413 | − | 2.52013i | −0.252848 | − | 0.104733i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.866455 | + | 2.09181i | 0.0359466 | + | 0.0867828i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.1865 | + | 19.1865i | −0.794625 | + | 0.794625i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0600715 | − | 0.0600715i | −0.00248365 | − | 0.00248365i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.7941 | + | 13.5838i | −1.35356 | + | 0.560662i | −0.937281 | − | 0.348575i | \(-0.886665\pi\) |
−0.416277 | + | 0.909238i | \(0.636665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.40992 | + | 5.81806i | −0.0992990 | + | 0.239729i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 27.4053i | − | 1.12730i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.66555i | 0.109461i | 0.998501 | + | 0.0547306i | \(0.0174300\pi\) | ||||
−0.998501 | + | 0.0547306i | \(0.982570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.68668 | + | 6.48622i | −0.110143 | + | 0.265909i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.1122 | − | 14.9582i | 1.47797 | − | 0.612197i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.9077 | − | 11.9077i | −0.486534 | − | 0.486534i | 0.420677 | − | 0.907211i | \(-0.361793\pi\) |
−0.907211 | + | 0.420677i | \(0.861793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.86501 | − | 1.86501i | 0.0760755 | − | 0.0760755i | −0.668045 | − | 0.744121i | \(-0.732869\pi\) |
0.744121 | + | 0.668045i | \(0.232869\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.0553250 | + | 0.133566i | 0.00225301 | + | 0.00543924i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.47308 | − | 0.610169i | −0.0598891 | − | 0.0248069i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.47275 | −0.343898 | −0.171949 | − | 0.985106i | \(-0.555006\pi\) | ||||
−0.171949 | + | 0.985106i | \(0.555006\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.54976 | −0.224887 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 55.0087 | + | 22.7853i | 2.22541 | + | 0.921796i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.67657 | + | 23.3613i | 0.390833 | + | 0.943555i | 0.989759 | + | 0.142750i | \(0.0455945\pi\) |
−0.598926 | + | 0.800805i | \(0.704405\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.31700 | − | 8.31700i | 0.335374 | − | 0.335374i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.91738 | + | 8.91738i | 0.359000 | + | 0.359000i | 0.863444 | − | 0.504444i | \(-0.168303\pi\) |
−0.504444 | + | 0.863444i | \(0.668303\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.56774 | − | 2.30623i | 0.223786 | − | 0.0926953i | −0.267973 | − | 0.963426i | \(-0.586354\pi\) |
0.491760 | + | 0.870731i | \(0.336354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.1759 | − | 29.3951i | 0.488601 | − | 1.17959i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.90524i | 0.156460i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 20.4786i | − | 0.819143i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.1146 | + | 24.4187i | −0.403937 | + | 0.975191i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.0486 | + | 7.89020i | −0.759519 | + | 0.314603i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4932 | + | 33.4932i | 1.33334 | + | 1.33334i | 0.902361 | + | 0.430981i | \(0.141833\pi\) |
0.430981 | + | 0.902361i | \(0.358167\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.5345 | − | 17.5345i | 0.696935 | − | 0.696935i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.927266 | − | 2.23862i | −0.0367974 | − | 0.0888369i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.93995 | − | 2.87462i | −0.274971 | − | 0.113897i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.334680 | −0.0132397 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.8508 | −1.06054 | −0.530272 | − | 0.847827i | \(-0.677910\pi\) | ||||
−0.530272 | + | 0.847827i | \(0.677910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.4666 | − | 13.0339i | −1.24092 | − | 0.514006i | −0.336918 | − | 0.941534i | \(-0.609384\pi\) |
−0.904002 | + | 0.427528i | \(0.859384\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.202574 | + | 0.489057i | 0.00797635 | + | 0.0192566i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.43000 | − | 6.43000i | 0.252789 | − | 0.252789i | −0.569324 | − | 0.822113i | \(-0.692795\pi\) |
0.822113 | + | 0.569324i | \(0.192795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.88172 | − | 7.88172i | −0.309384 | − | 0.309384i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.86030 | + | 2.42742i | −0.229683 | + | 0.0951380i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.23125 | + | 12.6294i | −0.204715 | + | 0.494225i | −0.992576 | − | 0.121628i | \(-0.961188\pi\) |
0.787861 | + | 0.615853i | \(0.211188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.77811i | − | 0.147623i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.0601790i | − | 0.00234781i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.94335 | + | 14.3485i | −0.231520 | + | 0.558939i | −0.996357 | − | 0.0852857i | \(-0.972820\pi\) |
0.764837 | + | 0.644224i | \(0.222820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.2370 | + | 8.79664i | −0.826022 | + | 0.342150i | −0.755327 | − | 0.655348i | \(-0.772522\pi\) |
−0.0706953 | + | 0.997498i | \(0.522522\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −39.3003 | − | 39.3003i | −1.52630 | − | 1.52630i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.87708 | + | 3.87708i | −0.150347 | + | 0.150347i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.12534 | + | 7.54524i | 0.121014 | + | 0.292153i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.0811 | + | 10.8031i | 1.00835 | + | 0.417673i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.8402 | −1.15197 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.6959 | 1.53017 | 0.765083 | − | 0.643932i | \(-0.222698\pi\) | ||||
0.765083 | + | 0.643932i | \(0.222698\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.6187 | − | 9.36899i | −0.870596 | − | 0.360613i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.16911 | + | 19.7220i | 0.313964 | + | 0.757977i | 0.999550 | + | 0.0299855i | \(0.00954612\pi\) |
−0.685586 | + | 0.727992i | \(0.740454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.12380 | − | 3.12380i | 0.119880 | − | 0.119880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.85998 | + | 6.85998i | 0.262875 | + | 0.262875i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.6783 | − | 9.39365i | 0.867760 | − | 0.359438i | 0.0960227 | − | 0.995379i | \(-0.469388\pi\) |
0.771738 | + | 0.635941i | \(0.219388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.64363 | + | 3.96808i | −0.0627999 | + | 0.151612i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 22.7192i | − | 0.866793i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 44.5614i | − | 1.69766i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.63891 | + | 13.6135i | −0.214514 | + | 0.517883i | −0.994107 | − | 0.108404i | \(-0.965426\pi\) |
0.779593 | + | 0.626287i | \(0.215426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.206977 | − | 0.0857327i | 0.00786241 | − | 0.00325671i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.55404 | − | 4.55404i | −0.172745 | − | 0.172745i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −45.7880 | + | 45.7880i | −1.73434 | + | 1.73434i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.63341 | − | 3.94340i | −0.0617812 | − | 0.149153i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.5832 | − | 17.6385i | −1.60835 | − | 0.666199i | −0.615781 | − | 0.787917i | \(-0.711160\pi\) |
−0.992565 | + | 0.121718i | \(0.961160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.1025 | −0.607316 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.31319 | −0.350755 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.23483 | + | 1.75412i | 0.159267 | + | 0.0659706i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1294 | + | 26.8688i | 0.417974 | + | 1.00908i | 0.982934 | + | 0.183960i | \(0.0588916\pi\) |
−0.564960 | + | 0.825118i | \(0.691108\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.227174 | + | 0.227174i | −0.00851968 | + | 0.00851968i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.60045 | + | 6.60045i | 0.247189 | + | 0.247189i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.6779 | − | 4.83714i | 0.436728 | − | 0.180899i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.42003 | + | 20.3277i | −0.314452 | + | 0.759154i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.82423i | 0.0680323i | 0.999421 | + | 0.0340162i | \(0.0108298\pi\) | ||||
−0.999421 | + | 0.0340162i | \(0.989170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 18.2360i | − | 0.679146i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.5186 | − | 30.2226i | 0.465573 | − | 1.12399i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.80585 | − | 2.40486i | 0.215624 | − | 0.0893144i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.1795 | − | 20.1795i | −0.748416 | − | 0.748416i | 0.225765 | − | 0.974182i | \(-0.427512\pi\) |
−0.974182 | + | 0.225765i | \(0.927512\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.2485 | + | 19.2485i | −0.712909 | + | 0.712909i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.11524 | − | 2.69243i | −0.0412487 | − | 0.0995832i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.2520 | − | 4.66073i | −0.415602 | − | 0.172148i | 0.165077 | − | 0.986281i | \(-0.447213\pi\) |
−0.580679 | + | 0.814133i | \(0.697213\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.17496 | 0.0433391 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.5103 | −0.792343 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.6586 | − | 9.38552i | −0.833512 | − | 0.345252i | −0.0752197 | − | 0.997167i | \(-0.523966\pi\) |
−0.758292 | + | 0.651915i | \(0.773966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.6110 | − | 40.1024i | −0.610219 | − | 1.47320i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.4077 | − | 30.4077i | 1.11555 | − | 1.11555i | 0.123164 | − | 0.992386i | \(-0.460696\pi\) |
0.992386 | − | 0.123164i | \(-0.0393041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.02215 | + | 2.02215i | 0.0740859 | + | 0.0740859i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0217970 | + | 0.00902860i | −0.000797510 | + | 0.000330339i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.2944 | − | 41.7523i | 0.631923 | − | 1.52560i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 5.81357i | − | 0.212140i | −0.994359 | − | 0.106070i | \(-0.966173\pi\) | ||
0.994359 | − | 0.106070i | \(-0.0338268\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.0009i | 0.619547i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.19124 | − | 10.1185i | 0.152535 | − | 0.368251i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.65558 | + | 1.09998i | −0.0965185 | + | 0.0399793i | −0.430420 | − | 0.902629i | \(-0.641635\pi\) |
0.333902 | + | 0.942608i | \(0.391635\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.7025 | + | 27.7025i | 1.00554 | + | 1.00554i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.9432 | + | 17.9432i | −0.650442 | + | 0.650442i | −0.953099 | − | 0.302658i | \(-0.902126\pi\) |
0.302658 | + | 0.953099i | \(0.402126\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.28528 | + | 15.1740i | 0.227542 | + | 0.549336i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0675875 | − | 0.0279956i | −0.00244363 | − | 0.00101218i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.3056 | 0.660976 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.98104 | −0.107499 | −0.0537495 | − | 0.998554i | \(-0.517117\pi\) | ||||
−0.0537495 | + | 0.998554i | \(0.517117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.29077 | − | 1.36308i | −0.118514 | − | 0.0490902i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.20933 | + | 17.4049i | 0.259302 | + | 0.626009i | 0.998893 | − | 0.0470471i | \(-0.0149811\pi\) |
−0.739591 | + | 0.673056i | \(0.764981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.07886 | − | 5.07886i | 0.182438 | − | 0.182438i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.4688 | − | 11.4688i | −0.411442 | − | 0.411442i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −46.7225 | + | 19.3531i | −1.67401 | + | 0.693396i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.0561 | − | 46.0056i | 0.681882 | − | 1.64621i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.98779i | − | 0.249723i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 9.62716i | − | 0.343608i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3060 | − | 32.1235i | 0.474307 | − | 1.14508i | −0.487934 | − | 0.872881i | \(-0.662249\pi\) |
0.962241 | − | 0.272198i | \(-0.0877507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 40.2514 | − | 16.6727i | 1.43299 | − | 0.593563i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2130 | − | 11.2130i | −0.398689 | − | 0.398689i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.6525 | − | 34.6525i | 1.23054 | − | 1.23054i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.66736 | + | 6.43957i | 0.0946015 | + | 0.228388i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.5225 | + | 6.84385i | 0.585258 | + | 0.242422i | 0.655609 | − | 0.755101i | \(-0.272412\pi\) |
−0.0703512 | + | 0.997522i | \(0.522412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.2724 | 1.81389 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0406932 | −0.00143782 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.27229 | + | 3.42649i | 0.291923 | + | 0.120918i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.11018 | + | 7.50864i | 0.109620 | + | 0.264645i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0253 | − | 18.0253i | 0.634521 | − | 0.634521i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.5558 | + | 10.5558i | 0.371123 | + | 0.371123i | 0.867886 | − | 0.496763i | \(-0.165478\pi\) |
−0.496763 | + | 0.867886i | \(0.665478\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.31304 | + | 1.78652i | −0.151451 | + | 0.0627333i | −0.457122 | − | 0.889404i | \(-0.651120\pi\) |
0.305670 | + | 0.952138i | \(0.401120\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.58186 | + | 3.81894i | −0.0554782 | + | 0.133936i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.83121i | 0.0991728i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.27601i | − | 0.0796274i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.140797 | + | 0.339914i | −0.00491985 | + | 0.0118776i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.4218 | − | 10.5300i | 0.887225 | − | 0.367501i | 0.107931 | − | 0.994158i | \(-0.465578\pi\) |
0.779295 | + | 0.626658i | \(0.215578\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.1280 | − | 28.1280i | −0.980479 | − | 0.980479i | 0.0193343 | − | 0.999813i | \(-0.493845\pi\) |
−0.999813 | + | 0.0193343i | \(0.993845\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.3163 | − | 21.3163i | 0.742138 | − | 0.742138i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.05658 | − | 14.6219i | −0.210608 | − | 0.508453i | 0.782909 | − | 0.622136i | \(-0.213735\pi\) |
−0.993517 | + | 0.113683i | \(0.963735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.3516 | + | 11.7436i | 0.984691 | + | 0.407872i | 0.816161 | − | 0.577824i | \(-0.196098\pi\) |
0.168530 | + | 0.985697i | \(0.446098\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.2507 | −0.598419 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.46858 | −0.224123 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.55671 | − | 1.05902i | −0.0884786 | − | 0.0366490i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.05640 | − | 7.37881i | −0.105645 | − | 0.255049i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2678 | + | 19.2678i | −0.665199 | + | 0.665199i | −0.956601 | − | 0.291401i | \(-0.905878\pi\) |
0.291401 | + | 0.956601i | \(0.405878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.2378 | − | 19.2378i | −0.663372 | − | 0.663372i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44.7710 | + | 18.5448i | −1.54199 | + | 0.638715i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.18414 | + | 12.5156i | −0.178340 | + | 0.430551i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.90528i | 0.237268i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 8.89609i | − | 0.305313i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.13394 | + | 22.0513i | −0.313107 | + | 0.755908i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.3619 | − | 5.53470i | 0.457504 | − | 0.189504i | −0.142016 | − | 0.989864i | \(-0.545358\pi\) |
0.599520 | + | 0.800360i | \(0.295358\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0403999 | − | 0.0403999i | −0.00138165 | − | 0.00138165i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.2115 | − | 16.2115i | 0.553775 | − | 0.553775i | −0.373753 | − | 0.927528i | \(-0.621929\pi\) |
0.927528 | + | 0.373753i | \(0.121929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.6184 | + | 25.6351i | 0.362295 | + | 0.874658i | 0.994964 | + | 0.100235i | \(0.0319595\pi\) |
−0.632669 | + | 0.774423i | \(0.718040\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −47.0617 | − | 19.4936i | −1.60386 | − | 0.664341i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.8195 | −1.38951 | −0.694755 | − | 0.719246i | \(-0.744487\pi\) | ||||
−0.694755 | + | 0.719246i | \(0.744487\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.12521 | 0.310267 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.1277 | − | 7.09454i | −0.581689 | − | 0.240943i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.2927 | − | 44.1625i | −0.620538 | − | 1.49811i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.9792 | − | 24.9792i | 0.846389 | − | 0.846389i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.0325505 | + | 0.0325505i | 0.00110167 | + | 0.00110167i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.9343 | − | 4.94336i | 0.403454 | − | 0.167116i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.1786 | − | 43.8869i | 0.613846 | − | 1.48196i | −0.244896 | − | 0.969549i | \(-0.578754\pi\) |
0.858743 | − | 0.512407i | \(-0.171246\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 37.8142i | 1.27544i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.849166i | 0.0286091i | 0.999898 | + | 0.0143046i | \(0.00455344\pi\) | ||||
−0.999898 | + | 0.0143046i | \(0.995447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.6785 | − | 49.9223i | 0.695886 | − | 1.68002i | −0.0366838 | − | 0.999327i | \(-0.511679\pi\) |
0.732570 | − | 0.680692i | \(-0.238321\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.64534 | + | 1.09574i | −0.0889221 | + | 0.0368327i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.8530 | + | 17.8530i | 0.599446 | + | 0.599446i | 0.940165 | − | 0.340719i | \(-0.110671\pi\) |
−0.340719 | + | 0.940165i | \(0.610671\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.42029 | + | 7.42029i | −0.248868 | + | 0.248868i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.7209 | − | 30.7109i | −0.426165 | − | 1.02885i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.9950 | + | 15.3238i | 1.23799 | + | 0.512792i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.5531 | −0.419604 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −64.3400 | −2.14825 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.89402 | + | 0.784527i | 0.0631690 | + | 0.0261655i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.6847 | − | 35.4521i | −0.489220 | − | 1.18108i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.62107 | − | 1.62107i | 0.0539457 | − | 0.0539457i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.82413 | − | 8.82413i | −0.293324 | − | 0.293324i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2527 | + | 4.24679i | −0.340434 | + | 0.141012i | −0.546349 | − | 0.837558i | \(-0.683983\pi\) |
0.205915 | + | 0.978570i | \(0.433983\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.0182783 | + | 0.0441276i | −0.000606252 | + | 0.00146362i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.1022i | 0.931067i | 0.885030 | + | 0.465534i | \(0.154138\pi\) | ||||
−0.885030 | + | 0.465534i | \(0.845862\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3.51032i | − | 0.116174i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.93340 | + | 7.08185i | −0.0969752 | + | 0.234119i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.1168 | + | 6.26160i | −0.499202 | + | 0.206776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.17031 | + | 5.17031i | 0.170553 | + | 0.170553i | 0.787222 | − | 0.616669i | \(-0.211518\pi\) |
−0.616669 | + | 0.787222i | \(0.711518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.3169 | + | 26.3169i | −0.867172 | + | 0.867172i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.2955 | + | 75.5541i | 1.03011 | + | 2.48689i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.9678 | + | 7.02831i | 0.557899 | + | 0.231089i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.190023 | 0.00624116 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.6165 | −0.709215 | −0.354608 | − | 0.935015i | \(-0.615386\pi\) | ||||
−0.354608 | + | 0.935015i | \(0.615386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.66733 | − | 1.93327i | −0.152965 | − | 0.0633604i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.4498 | + | 34.8848i | 0.473064 | + | 1.14208i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.69664 | − | 7.69664i | 0.251707 | − | 0.251707i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.3267 | − | 32.3267i | −1.05607 | − | 1.05607i | −0.998332 | − | 0.0577344i | \(-0.981612\pi\) |
−0.0577344 | − | 0.998332i | \(-0.518388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.7569 | − | 13.1541i | 1.03635 | − | 0.429269i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.90288 | − | 23.9077i | 0.322825 | − | 0.779368i | −0.676263 | − | 0.736660i | \(-0.736402\pi\) |
0.999088 | − | 0.0427073i | \(-0.0135983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74.9612i | 2.44107i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 6.95390i | − | 0.226210i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.97880 | − | 21.6767i | 0.291772 | − | 0.704399i | −0.708227 | − | 0.705985i | \(-0.750505\pi\) |
0.999999 | + | 0.00158544i | \(0.000504662\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.5854 | + | 5.62726i | −0.441001 | + | 0.182669i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.74220 | − | 9.74220i | −0.315912 | − | 0.315912i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.00440 | + | 3.00440i | −0.0973222 | + | 0.0973222i | −0.754092 | − | 0.656769i | \(-0.771923\pi\) |
0.656769 | + | 0.754092i | \(0.271923\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.21561 | + | 5.34895i | 0.0716954 | + | 0.173088i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.94930 | + | 3.29271i | 0.256965 | + | 0.106438i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.6010 | 0.600657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6569 | −0.924415 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.435066 | + | 0.180210i | 0.0140198 | + | 0.00580720i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.810542 | + | 1.95682i | 0.0260923 | + | 0.0629923i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.1087 | + | 29.1087i | −0.936074 | + | 0.936074i | −0.998076 | − | 0.0620023i | \(-0.980251\pi\) |
0.0620023 | + | 0.998076i | \(0.480251\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.4307 | − | 26.4307i | −0.849075 | − | 0.849075i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.623957 | + | 0.258452i | −0.0200237 | + | 0.00829411i | −0.392673 | − | 0.919678i | \(-0.628450\pi\) |
0.372649 | + | 0.927972i | \(0.378450\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.6739 | + | 25.7690i | −0.342189 | + | 0.826117i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 49.5079i | 1.58552i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.1041i | 1.05909i | 0.848281 | + | 0.529546i | \(0.177638\pi\) | ||||
−0.848281 | + | 0.529546i | \(0.822362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.31700 | − | 5.59374i | 0.0740518 | − | 0.178777i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.158116 | + | 0.0654936i | −0.00504824 | + | 0.00209105i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.49880 | − | 1.49880i | −0.0478044 | − | 0.0478044i | 0.682800 | − | 0.730605i | \(-0.260762\pi\) |
−0.730605 | + | 0.682800i | \(0.760762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.23264 | + | 6.23264i | −0.198588 | + | 0.198588i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.4351 | + | 37.2636i | 0.491304 | + | 1.18611i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.11684 | − | 1.29104i | −0.0991098 | − | 0.0410526i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.9387 | −0.823970 | −0.411985 | − | 0.911191i | \(-0.635164\pi\) | ||||
−0.411985 | + | 0.911191i | \(0.635164\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0895 | 0.383649 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.6146 | − | 4.81094i | −0.368209 | − | 0.152517i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.47449 | − | 5.97395i | −0.0783679 | − | 0.189197i | 0.879840 | − | 0.475270i | \(-0.157650\pi\) |
−0.958208 | + | 0.286074i | \(0.907650\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.4406 | − | 14.4406i | 0.456881 | − | 0.456881i |
(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 | 1024.2.g.h.641.3 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.h.641.2 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.c.641.3 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.c.641.2 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.e.129.3 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.b.129.3 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.b.129.2 | ✓ | 16 | ||
16.13 | even | 4 | 1024.2.g.e.129.2 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.b.897.2 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.c.385.2 | yes | 16 | ||
32.11 | odd | 8 | inner | 1024.2.g.h.385.2 | yes | 16 | |
32.13 | even | 8 | 1024.2.g.e.897.2 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.e.897.3 | yes | 16 | ||
32.21 | even | 8 | inner | 1024.2.g.h.385.3 | yes | 16 | |
32.27 | odd | 8 | 1024.2.g.c.385.3 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.b.897.3 | yes | 16 | ||
64.11 | odd | 16 | 4096.2.a.o.1.4 | 8 | |||
64.21 | even | 16 | 4096.2.a.o.1.3 | 8 | |||
64.43 | odd | 16 | 4096.2.a.n.1.5 | 8 | |||
64.53 | even | 16 | 4096.2.a.n.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.b.129.2 | ✓ | 16 | 16.11 | odd | 4 | ||
1024.2.g.b.129.3 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.b.897.2 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.b.897.3 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.c.385.2 | yes | 16 | 32.5 | even | 8 | ||
1024.2.g.c.385.3 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.c.641.2 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.c.641.3 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.e.129.2 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.e.129.3 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.e.897.2 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.e.897.3 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.h.385.2 | yes | 16 | 32.11 | odd | 8 | inner | |
1024.2.g.h.385.3 | yes | 16 | 32.21 | even | 8 | inner | |
1024.2.g.h.641.2 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.h.641.3 | yes | 16 | 1.1 | even | 1 | trivial | |
4096.2.a.n.1.5 | 8 | 64.43 | odd | 16 | |||
4096.2.a.n.1.6 | 8 | 64.53 | even | 16 | |||
4096.2.a.o.1.3 | 8 | 64.21 | even | 16 | |||
4096.2.a.o.1.4 | 8 | 64.11 | odd | 16 |