Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(199,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.k (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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 424.6 | ||
Root | \(-0.673288 + 0.180407i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.424 |
Dual form | 675.2.k.b.199.6 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.17731 | + | 1.25707i | 1.53959 | + | 0.888882i | 0.998863 | + | 0.0476826i | \(0.0151836\pi\) |
0.540726 | + | 0.841199i | \(0.318150\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.16044 | + | 3.74200i | 1.08022 | + | 1.87100i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.445256 | + | 0.257068i | 0.168291 | + | 0.0971627i | 0.581780 | − | 0.813346i | \(-0.302357\pi\) |
−0.413489 | + | 0.910509i | \(0.635690\pi\) | |||||||
\(8\) | 5.83502i | 2.06299i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.66044 | + | 2.87597i | −0.500642 | + | 0.867138i | 0.499358 | + | 0.866396i | \(0.333569\pi\) |
−1.00000 | 0.000741679i | \(0.999764\pi\) | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.14392 | − | 0.660442i | 0.317266 | − | 0.183174i | −0.332907 | − | 0.942960i | \(-0.608030\pi\) |
0.650173 | + | 0.759786i | \(0.274696\pi\) | |||||||
\(14\) | 0.646305 | + | 1.11943i | 0.172732 | + | 0.299181i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.01414 | + | 5.22064i | −0.753534 | + | 1.30516i | ||||
\(17\) | 3.32088i | 0.805433i | 0.915325 | + | 0.402716i | \(0.131934\pi\) | ||||
−0.915325 | + | 0.402716i | \(0.868066\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.32088 | 0.303032 | 0.151516 | − | 0.988455i | \(-0.451585\pi\) | ||||
0.151516 | + | 0.988455i | \(0.451585\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.23058 | + | 4.17458i | −1.54157 | + | 0.890023i | ||||
\(23\) | 3.57463 | − | 2.06382i | 0.745363 | − | 0.430335i | −0.0786532 | − | 0.996902i | \(-0.525062\pi\) |
0.824016 | + | 0.566567i | \(0.191729\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.32088 | 0.651279 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.22153i | 0.419829i | ||||||||
\(29\) | 0.693252 | − | 1.20075i | 0.128734 | − | 0.222973i | −0.794453 | − | 0.607326i | \(-0.792242\pi\) |
0.923186 | + | 0.384353i | \(0.125575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.36783 | − | 7.56531i | −0.784486 | − | 1.35877i | −0.929306 | − | 0.369311i | \(-0.879594\pi\) |
0.144820 | − | 0.989458i | \(-0.453740\pi\) | |||||||
\(32\) | −3.01885 | + | 1.74293i | −0.533662 | + | 0.308110i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.17458 | + | 7.23058i | −0.715934 | + | 1.24003i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.292611i | 0.0481049i | 0.999711 | + | 0.0240524i | \(0.00765687\pi\) | ||||
−0.999711 | + | 0.0240524i | \(0.992343\pi\) | |||||||
\(38\) | 2.87597 | + | 1.66044i | 0.466544 | + | 0.269359i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.67458 | − | 9.82866i | −0.886220 | − | 1.53498i | −0.844308 | − | 0.535857i | \(-0.819988\pi\) |
−0.0419119 | − | 0.999121i | \(-0.513345\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.96263 | + | 5.17458i | 1.36679 | + | 0.789116i | 0.990517 | − | 0.137393i | \(-0.0438724\pi\) |
0.376272 | + | 0.926509i | \(0.377206\pi\) | |||||||
\(44\) | −14.3492 | −2.16322 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.3774 | 1.53007 | ||||||||
\(47\) | −4.21174 | − | 2.43165i | −0.614345 | − | 0.354692i | 0.160319 | − | 0.987065i | \(-0.448748\pi\) |
−0.774664 | + | 0.632373i | \(0.782081\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.36783 | − | 5.83326i | −0.481119 | − | 0.833322i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.94274 | + | 2.85369i | 0.685435 | + | 0.395736i | ||||
\(53\) | − | 5.02827i | − | 0.690687i | −0.938476 | − | 0.345343i | \(-0.887762\pi\) | ||
0.938476 | − | 0.345343i | \(-0.112238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.50000 | + | 2.59808i | −0.200446 | + | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.01885 | − | 1.74293i | 0.396394 | − | 0.228858i | ||||
\(59\) | 2.51414 | + | 4.35461i | 0.327313 | + | 0.566922i | 0.981978 | − | 0.188997i | \(-0.0605236\pi\) |
−0.654665 | + | 0.755919i | \(0.727190\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.67458 | + | 6.36456i | −0.470482 | + | 0.814898i | −0.999430 | − | 0.0337558i | \(-0.989253\pi\) |
0.528948 | + | 0.848654i | \(0.322586\pi\) | |||||||
\(62\) | − | 21.9627i | − | 2.78926i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.29261 | 0.411576 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.18266 | − | 4.72426i | 0.999670 | − | 0.577160i | 0.0915197 | − | 0.995803i | \(-0.470828\pi\) |
0.908151 | + | 0.418643i | \(0.137494\pi\) | |||||||
\(68\) | −12.4267 | + | 7.17458i | −1.50696 | + | 0.870046i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.99093 | −1.06703 | −0.533513 | − | 0.845792i | \(-0.679129\pi\) | ||||
−0.533513 | + | 0.845792i | \(0.679129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.05655i | − | 0.708865i | −0.935082 | − | 0.354433i | \(-0.884674\pi\) | ||
0.935082 | − | 0.354433i | \(-0.115326\pi\) | |||||||
\(74\) | −0.367832 | + | 0.637103i | −0.0427596 | + | 0.0740617i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.85369 | + | 4.94274i | 0.327341 | + | 0.566972i | ||||
\(77\) | −1.47864 | + | 0.853695i | −0.168507 | + | 0.0972875i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.02827 | + | 6.97717i | −0.453216 | + | 0.784994i | −0.998584 | − | 0.0532036i | \(-0.983057\pi\) |
0.545367 | + | 0.838197i | \(0.316390\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 28.5333i | − | 3.15098i | ||||||
\(83\) | −1.33577 | − | 0.771205i | −0.146619 | − | 0.0846508i | 0.424896 | − | 0.905242i | \(-0.360311\pi\) |
−0.571515 | + | 0.820592i | \(0.693644\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 13.0096 | + | 22.5333i | 1.40286 | + | 2.42983i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −16.7813 | − | 9.68872i | −1.78890 | − | 1.03282i | ||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.679116 | 0.0711906 | ||||||||
\(92\) | 15.4456 | + | 8.91751i | 1.61031 | + | 0.929715i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.11350 | − | 10.5889i | −0.630559 | − | 1.09216i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6134 | + | 6.12763i | 1.07762 | + | 0.622167i | 0.930255 | − | 0.366915i | \(-0.119586\pi\) |
0.147370 | + | 0.989081i | \(0.452919\pi\) | |||||||
\(98\) | − | 16.9344i | − | 1.71063i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.83502 | − | 10.1066i | 0.580606 | − | 1.00564i | −0.414801 | − | 0.909912i | \(-0.636149\pi\) |
0.995408 | − | 0.0957276i | \(-0.0305178\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.253408 | + | 0.146305i | −0.0249691 | + | 0.0144159i | −0.512433 | − | 0.858727i | \(-0.671256\pi\) |
0.487464 | + | 0.873143i | \(0.337922\pi\) | |||||||
\(104\) | 3.85369 | + | 6.67479i | 0.377886 | + | 0.654517i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.32088 | − | 10.9481i | 0.613939 | − | 1.06337i | ||||
\(107\) | − | 1.87237i | − | 0.181009i | −0.995896 | − | 0.0905043i | \(-0.971152\pi\) | ||
0.995896 | − | 0.0905043i | \(-0.0288479\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.54787 | −0.531390 | −0.265695 | − | 0.964057i | \(-0.585601\pi\) | ||||
−0.265695 | + | 0.964057i | \(0.585601\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.68412 | + | 1.54968i | −0.253626 | + | 0.146431i | ||||
\(113\) | 6.75611 | − | 3.90064i | 0.635561 | − | 0.366942i | −0.147341 | − | 0.989086i | \(-0.547072\pi\) |
0.782903 | + | 0.622144i | \(0.213738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.99093 | 0.556244 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.6418i | 1.16377i | ||||||||
\(119\) | −0.853695 | + | 1.47864i | −0.0782581 | + | 0.135547i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0141369 | − | 0.0244859i | −0.00128518 | − | 0.00222599i | ||||
\(122\) | −16.0014 | + | 9.23840i | −1.44870 | + | 0.836405i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.8729 | − | 32.6888i | 1.69484 | − | 2.93554i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8916i | 1.58762i | 0.608166 | + | 0.793810i | \(0.291906\pi\) | ||||
−0.608166 | + | 0.793810i | \(0.708094\pi\) | |||||||
\(128\) | 13.2067 | + | 7.62490i | 1.16732 | + | 0.673952i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | − | 5.19615i | −0.262111 | − | 0.453990i | 0.704692 | − | 0.709514i | \(-0.251085\pi\) |
−0.966803 | + | 0.255524i | \(0.917752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.588131 | + | 0.339558i | 0.0509974 | + | 0.0294434i | ||||
\(134\) | 23.7549 | 2.05211 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19.3774 | −1.66160 | ||||||||
\(137\) | 4.91040 | + | 2.83502i | 0.419524 | + | 0.242212i | 0.694874 | − | 0.719132i | \(-0.255460\pi\) |
−0.275350 | + | 0.961344i | \(0.588794\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | + | 6.92820i | 0.339276 | + | 0.587643i | 0.984297 | − | 0.176522i | \(-0.0564848\pi\) |
−0.645021 | + | 0.764165i | \(0.723151\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −19.5760 | − | 11.3022i | −1.64278 | − | 0.948460i | ||||
\(143\) | 4.38650i | 0.366818i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.61350 | − | 13.1870i | 0.630097 | − | 1.09136i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.09495 | + | 0.632168i | −0.0900042 | + | 0.0519639i | ||||
\(149\) | −8.83049 | − | 15.2948i | −0.723422 | − | 1.25300i | −0.959620 | − | 0.281298i | \(-0.909235\pi\) |
0.236199 | − | 0.971705i | \(-0.424098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.632168 | + | 1.09495i | −0.0514451 | + | 0.0891056i | −0.890601 | − | 0.454785i | \(-0.849716\pi\) |
0.839156 | + | 0.543891i | \(0.183049\pi\) | |||||||
\(152\) | 7.70739i | 0.625152i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.29261 | −0.345908 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.5707 | + | 7.83502i | −1.08306 | + | 0.625303i | −0.931719 | − | 0.363179i | \(-0.881691\pi\) |
−0.151337 | + | 0.988482i | \(0.548358\pi\) | |||||||
\(158\) | −17.5416 | + | 10.1276i | −1.39553 | + | 0.805711i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.12217 | 0.167250 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.7074i | − | 1.23030i | −0.788411 | − | 0.615149i | \(-0.789096\pi\) | ||
0.788411 | − | 0.615149i | \(-0.210904\pi\) | |||||||
\(164\) | 24.5192 | − | 42.4685i | 1.91463 | − | 3.31623i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.93892 | − | 3.35830i | −0.150489 | − | 0.260655i | ||||
\(167\) | −5.33903 | + | 3.08249i | −0.413146 | + | 0.238530i | −0.692141 | − | 0.721763i | \(-0.743332\pi\) |
0.278994 | + | 0.960293i | \(0.409999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.62763 | + | 9.74734i | −0.432895 | + | 0.749796i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 44.7175i | 3.40968i | ||||||||
\(173\) | −7.43502 | − | 4.29261i | −0.565274 | − | 0.326361i | 0.189986 | − | 0.981787i | \(-0.439156\pi\) |
−0.755260 | + | 0.655426i | \(0.772489\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.0096 | − | 17.3371i | −0.754502 | − | 1.30684i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.53192 | − | 3.77121i | −0.489588 | − | 0.282664i | ||||
\(179\) | −1.06562 | −0.0796482 | −0.0398241 | − | 0.999207i | \(-0.512680\pi\) | ||||
−0.0398241 | + | 0.999207i | \(0.512680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6700 | −0.941757 | −0.470878 | − | 0.882198i | \(-0.656063\pi\) | ||||
−0.470878 | + | 0.882198i | \(0.656063\pi\) | |||||||
\(182\) | 1.47864 | + | 0.853695i | 0.109604 | + | 0.0632801i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.0424 | + | 20.8581i | 0.887778 | + | 1.53768i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.55077 | − | 5.51414i | −0.698421 | − | 0.403234i | ||||
\(188\) | − | 21.0137i | − | 1.53258i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.46719 | + | 14.6656i | −0.612664 | + | 1.06117i | 0.378125 | + | 0.925754i | \(0.376569\pi\) |
−0.990789 | + | 0.135411i | \(0.956764\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.1380 | + | 13.3588i | −1.66551 | + | 0.961585i | −0.695502 | + | 0.718524i | \(0.744818\pi\) |
−0.970011 | + | 0.243060i | \(0.921849\pi\) | |||||||
\(194\) | 15.4057 | + | 26.6835i | 1.10607 | + | 1.91576i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.5520 | − | 25.2048i | 1.03943 | − | 1.80034i | ||||
\(197\) | 14.2553i | 1.01565i | 0.861462 | + | 0.507823i | \(0.169550\pi\) | ||||
−0.861462 | + | 0.507823i | \(0.830450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.6610 | 1.74817 | 0.874085 | − | 0.485773i | \(-0.161462\pi\) | ||||
0.874085 | + | 0.485773i | \(0.161462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 25.4093 | − | 14.6700i | 1.78779 | − | 1.03218i | ||||
\(203\) | 0.617349 | − | 0.356427i | 0.0433294 | − | 0.0250162i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.735663 | −0.0512561 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.96265i | 0.552111i | ||||||||
\(209\) | −2.19325 | + | 3.79882i | −0.151710 | + | 0.262770i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.68872 | + | 4.65699i | 0.185099 | + | 0.320601i | 0.943610 | − | 0.331060i | \(-0.107406\pi\) |
−0.758511 | + | 0.651660i | \(0.774073\pi\) | |||||||
\(212\) | 18.8158 | − | 10.8633i | 1.29227 | − | 0.746094i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.35369 | − | 4.07672i | 0.160895 | − | 0.278679i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.49133i | − | 0.304891i | ||||||
\(218\) | −12.0794 | − | 6.97406i | −0.818122 | − | 0.472343i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.19325 | + | 3.79882i | 0.147534 | + | 0.255537i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.50375 | + | 4.33229i | 0.502488 | + | 0.290112i | 0.729740 | − | 0.683724i | \(-0.239641\pi\) |
−0.227252 | + | 0.973836i | \(0.572974\pi\) | |||||||
\(224\) | −1.79221 | −0.119747 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.6135 | 1.30467 | ||||||||
\(227\) | 2.87597 | + | 1.66044i | 0.190885 | + | 0.110207i | 0.592397 | − | 0.805646i | \(-0.298182\pi\) |
−0.401512 | + | 0.915854i | \(0.631515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.6559 | − | 21.9207i | −0.836326 | − | 1.44856i | −0.892946 | − | 0.450163i | \(-0.851366\pi\) |
0.0566206 | − | 0.998396i | \(-0.481967\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.00639 | + | 4.04514i | 0.459992 | + | 0.265577i | ||||
\(233\) | 27.6327i | 1.81028i | 0.425116 | + | 0.905139i | \(0.360233\pi\) | ||||
−0.425116 | + | 0.905139i | \(0.639767\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.8633 | + | 18.8158i | −0.707140 | + | 1.22480i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.71751 | + | 2.14631i | −0.240970 | + | 0.139124i | ||||
\(239\) | 2.09936 | + | 3.63620i | 0.135796 | + | 0.235206i | 0.925901 | − | 0.377765i | \(-0.123307\pi\) |
−0.790105 | + | 0.612971i | \(0.789974\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.80221 | + | 3.12152i | −0.116091 | + | 0.201075i | −0.918215 | − | 0.396082i | \(-0.870370\pi\) |
0.802125 | + | 0.597157i | \(0.203703\pi\) | |||||||
\(242\) | − | 0.0710844i | − | 0.00456948i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −31.7549 | −2.03290 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.51099 | − | 0.872368i | 0.0961417 | − | 0.0555074i | ||||
\(248\) | 44.1437 | − | 25.4864i | 2.80313 | − | 1.61839i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.87783 | 0.434125 | 0.217062 | − | 0.976158i | \(-0.430352\pi\) | ||||
0.217062 | + | 0.976158i | \(0.430352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.7074i | 0.861776i | ||||||||
\(254\) | −22.4909 | + | 38.9554i | −1.41121 | + | 2.44428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.8774 | + | 27.5005i | 0.992340 | + | 1.71878i | ||||
\(257\) | 15.5885 | − | 9.00000i | 0.972381 | − | 0.561405i | 0.0724199 | − | 0.997374i | \(-0.476928\pi\) |
0.899961 | + | 0.435970i | \(0.143595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0752210 | + | 0.130287i | −0.00467400 | + | 0.00809561i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 15.0848i | − | 0.931943i | ||||||
\(263\) | −5.40059 | − | 3.11803i | −0.333015 | − | 0.192266i | 0.324164 | − | 0.946001i | \(-0.394917\pi\) |
−0.657179 | + | 0.753735i | \(0.728250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.853695 | + | 1.47864i | 0.0523434 | + | 0.0906614i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 35.3563 | + | 20.4130i | 2.15973 | + | 1.24692i | ||||
\(269\) | 9.92345 | 0.605044 | 0.302522 | − | 0.953142i | \(-0.402172\pi\) | ||||
0.302522 | + | 0.953142i | \(0.402172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.60442 | 0.401190 | 0.200595 | − | 0.979674i | \(-0.435712\pi\) | ||||
0.200595 | + | 0.979674i | \(0.435712\pi\) | |||||||
\(272\) | −17.3371 | − | 10.0096i | −1.05122 | − | 0.606921i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.12763 | + | 12.3454i | 0.430596 | + | 0.745814i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.6250 | − | 11.3305i | −1.17915 | − | 0.680783i | −0.223333 | − | 0.974742i | \(-0.571694\pi\) |
−0.955818 | + | 0.293959i | \(0.905027\pi\) | |||||||
\(278\) | 20.1131i | 1.20630i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.77394 | + | 13.4649i | −0.463754 | + | 0.803246i | −0.999144 | − | 0.0413590i | \(-0.986831\pi\) |
0.535390 | + | 0.844605i | \(0.320165\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.558913 | + | 0.322689i | −0.0332240 | + | 0.0191819i | −0.516520 | − | 0.856275i | \(-0.672773\pi\) |
0.483296 | + | 0.875457i | \(0.339439\pi\) | |||||||
\(284\) | −19.4244 | − | 33.6440i | −1.15262 | − | 1.99640i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.51414 | + | 9.55077i | −0.326058 | + | 0.564749i | ||||
\(287\) | − | 5.83502i | − | 0.344430i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.97173 | 0.351278 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 22.6636 | − | 13.0848i | 1.32629 | − | 0.765731i | ||||
\(293\) | −1.19289 | + | 0.688716i | −0.0696895 | + | 0.0402352i | −0.534440 | − | 0.845207i | \(-0.679477\pi\) |
0.464750 | + | 0.885442i | \(0.346144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.70739 | −0.0992400 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 44.4021i | − | 2.57214i | ||||||
\(299\) | 2.72606 | − | 4.72168i | 0.157652 | − | 0.273062i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.66044 | + | 4.60802i | 0.153345 | + | 0.265602i | ||||
\(302\) | −2.75285 | + | 1.58936i | −0.158409 | + | 0.0914573i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.98133 | + | 6.89586i | −0.228345 | + | 0.395505i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.98546i | − | 0.455754i | −0.973690 | − | 0.227877i | \(-0.926822\pi\) | ||
0.973690 | − | 0.227877i | \(-0.0731785\pi\) | |||||||
\(308\) | −6.38904 | − | 3.68872i | −0.364050 | − | 0.210184i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.81635 | + | 8.34216i | 0.273110 | + | 0.473040i | 0.969657 | − | 0.244471i | \(-0.0786143\pi\) |
−0.696547 | + | 0.717512i | \(0.745281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2496 | − | 12.2685i | −1.20110 | − | 0.693455i | −0.240300 | − | 0.970699i | \(-0.577246\pi\) |
−0.960800 | + | 0.277244i | \(0.910579\pi\) | |||||||
\(314\) | −39.3966 | −2.22328 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −34.8114 | −1.95829 | ||||||||
\(317\) | −17.6229 | − | 10.1746i | −0.989800 | − | 0.571461i | −0.0845855 | − | 0.996416i | \(-0.526957\pi\) |
−0.905215 | + | 0.424955i | \(0.860290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.30221 | + | 3.98755i | 0.128899 | + | 0.223260i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.62061 | + | 2.66771i | 0.257497 | + | 0.148666i | ||||
\(323\) | 4.38650i | 0.244072i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.7453 | − | 34.1998i | 1.09359 | − | 1.89415i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 57.3504 | − | 33.1113i | 3.16665 | − | 1.82827i | ||||
\(329\) | −1.25020 | − | 2.16541i | −0.0689257 | − | 0.119383i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.22153 | + | 14.2401i | −0.451896 | + | 0.782707i | −0.998504 | − | 0.0546819i | \(-0.982586\pi\) |
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(332\) | − | 6.66458i | − | 0.365766i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.4996 | −0.848100 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.24096 | − | 2.44852i | 0.231020 | − | 0.133379i | −0.380023 | − | 0.924977i | \(-0.624084\pi\) |
0.611042 | + | 0.791598i | \(0.290751\pi\) | |||||||
\(338\) | −24.5062 | + | 14.1486i | −1.33296 | + | 0.769584i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.0101 | 1.57099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.06201i | − | 0.381313i | ||||||
\(344\) | −30.1938 | + | 52.2972i | −1.62794 | + | 2.81967i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.7922 | − | 18.6927i | −0.580193 | − | 1.00492i | ||||
\(347\) | −19.2903 | + | 11.1372i | −1.03556 | + | 0.597878i | −0.918571 | − | 0.395256i | \(-0.870656\pi\) |
−0.116984 | + | 0.993134i | \(0.537323\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.47173 | + | 2.54910i | −0.0787797 | + | 0.136450i | −0.902724 | − | 0.430221i | \(-0.858436\pi\) |
0.823944 | + | 0.566671i | \(0.191769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 11.5761i | − | 0.617011i | ||||||
\(353\) | −16.3069 | − | 9.41478i | −0.867927 | − | 0.501098i | −0.00126845 | − | 0.999999i | \(-0.500404\pi\) |
−0.866659 | + | 0.498901i | \(0.833737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.48133 | − | 11.2260i | −0.343510 | − | 0.594976i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.32018 | − | 1.33956i | −0.122625 | − | 0.0707978i | ||||
\(359\) | −31.8770 | −1.68241 | −0.841203 | − | 0.540720i | \(-0.818152\pi\) | ||||
−0.841203 | + | 0.540720i | \(0.818152\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2553 | −0.908172 | ||||||||
\(362\) | −27.5866 | − | 15.9271i | −1.44992 | − | 0.837110i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.46719 | + | 2.54125i | 0.0769016 | + | 0.133198i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.8908 | + | 9.17458i | 0.829495 | + | 0.478909i | 0.853680 | − | 0.520798i | \(-0.174366\pi\) |
−0.0241848 | + | 0.999708i | \(0.507699\pi\) | |||||||
\(368\) | 24.8825i | 1.29709i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.29261 | − | 2.23887i | 0.0671090 | − | 0.116236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.90414 | − | 1.09936i | 0.0985929 | − | 0.0569226i | −0.449893 | − | 0.893083i | \(-0.648538\pi\) |
0.548486 | + | 0.836160i | \(0.315205\pi\) | |||||||
\(374\) | −13.8633 | − | 24.0119i | −0.716854 | − | 1.24163i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.1887 | − | 24.5756i | 0.731727 | − | 1.26739i | ||||
\(377\) | − | 1.83141i | − | 0.0943226i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.4713 | −0.794709 | −0.397354 | − | 0.917665i | \(-0.630072\pi\) | ||||
−0.397354 | + | 0.917665i | \(0.630072\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −36.8713 | + | 21.2877i | −1.88650 | + | 1.08917i | ||||
\(383\) | 6.67479 | − | 3.85369i | 0.341066 | − | 0.196915i | −0.319677 | − | 0.947526i | \(-0.603574\pi\) |
0.660743 | + | 0.750612i | \(0.270241\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −67.1715 | −3.41894 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 52.9536i | 2.68831i | ||||||||
\(389\) | 12.3163 | − | 21.3325i | 0.624464 | − | 1.08160i | −0.364181 | − | 0.931328i | \(-0.618651\pi\) |
0.988644 | − | 0.150274i | \(-0.0480157\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.85369 | + | 11.8709i | 0.346606 | + | 0.600340i | ||||
\(392\) | 34.0372 | − | 19.6514i | 1.71914 | − | 0.992544i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.9198 | + | 31.0381i | −0.902789 | + | 1.56368i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 6.77301i | − | 0.339928i | −0.985450 | − | 0.169964i | \(-0.945635\pi\) | ||
0.985450 | − | 0.169964i | \(-0.0543651\pi\) | |||||||
\(398\) | 53.6945 | + | 31.0005i | 2.69146 | + | 1.55392i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.24980 | − | 16.0211i | −0.461913 | − | 0.800057i | 0.537143 | − | 0.843491i | \(-0.319503\pi\) |
−0.999056 | + | 0.0434343i | \(0.986170\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.99290 | − | 5.76940i | −0.497782 | − | 0.287394i | ||||
\(404\) | 50.4249 | 2.50873 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.79221 | 0.0889459 | ||||||||
\(407\) | −0.841540 | − | 0.485863i | −0.0417136 | − | 0.0240833i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.70739 | − | 11.6175i | −0.331659 | − | 0.574450i | 0.651178 | − | 0.758925i | \(-0.274275\pi\) |
−0.982837 | + | 0.184474i | \(0.940942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.09495 | − | 0.632168i | −0.0539442 | − | 0.0311447i | ||||
\(413\) | 2.58522i | 0.127210i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.30221 | + | 3.98755i | −0.112875 | + | 0.195506i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.55077 | + | 5.51414i | −0.467143 | + | 0.269705i | ||||
\(419\) | 16.5575 | + | 28.6784i | 0.808886 | + | 1.40103i | 0.913636 | + | 0.406532i | \(0.133262\pi\) |
−0.104751 | + | 0.994499i | \(0.533404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.34916 | − | 12.7291i | 0.358176 | − | 0.620379i | −0.629480 | − | 0.777017i | \(-0.716732\pi\) |
0.987656 | + | 0.156637i | \(0.0500654\pi\) | |||||||
\(422\) | 13.5196i | 0.658124i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 29.3401 | 1.42488 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.27225 | + | 1.88924i | −0.158355 | + | 0.0914266i | ||||
\(428\) | 7.00639 | − | 4.04514i | 0.338667 | − | 0.195529i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.7549 | 1.57775 | 0.788873 | − | 0.614556i | \(-0.210665\pi\) | ||||
0.788873 | + | 0.614556i | \(0.210665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8314i | 0.568581i | 0.958738 | + | 0.284291i | \(0.0917581\pi\) | ||||
−0.958738 | + | 0.284291i | \(0.908242\pi\) | |||||||
\(434\) | 5.64591 | − | 9.77900i | 0.271012 | − | 0.469407i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.9859 | − | 20.7601i | −0.574019 | − | 0.994230i | ||||
\(437\) | 4.72168 | − | 2.72606i | 0.225869 | − | 0.130405i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.15591 | − | 7.19824i | 0.198351 | − | 0.343553i | −0.749643 | − | 0.661842i | \(-0.769775\pi\) |
0.947994 | + | 0.318289i | \(0.103108\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.0283i | 0.524561i | ||||||||
\(443\) | 25.2664 | + | 14.5876i | 1.20044 | + | 0.693076i | 0.960654 | − | 0.277750i | \(-0.0895885\pi\) |
0.239789 | + | 0.970825i | \(0.422922\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.8920 | + | 18.8654i | 0.515750 | + | 0.893305i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.46605 | + | 0.846426i | 0.0692645 | + | 0.0399899i | ||||
\(449\) | 18.9717 | 0.895331 | 0.447666 | − | 0.894201i | \(-0.352256\pi\) | ||||
0.447666 | + | 0.894201i | \(0.352256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.6892 | 1.77472 | ||||||||
\(452\) | 29.1924 | + | 16.8542i | 1.37309 | + | 0.792756i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.17458 | + | 7.23058i | 0.195923 | + | 0.339348i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.1223 | + | 11.6176i | 0.941283 | + | 0.543450i | 0.890362 | − | 0.455253i | \(-0.150451\pi\) |
0.0509206 | + | 0.998703i | \(0.483784\pi\) | |||||||
\(458\) | − | 63.6374i | − | 2.97358i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.21285 | − | 3.83277i | 0.103063 | − | 0.178510i | −0.809882 | − | 0.586592i | \(-0.800469\pi\) |
0.912945 | + | 0.408082i | \(0.133802\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.8950 | − | 9.75434i | 0.785178 | − | 0.453322i | −0.0530845 | − | 0.998590i | \(-0.516905\pi\) |
0.838262 | + | 0.545268i | \(0.183572\pi\) | |||||||
\(464\) | 4.17912 | + | 7.23844i | 0.194011 | + | 0.336036i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −34.7362 | + | 60.1648i | −1.60912 | + | 2.78708i | ||||
\(467\) | 24.5935i | 1.13805i | 0.822320 | + | 0.569026i | \(0.192679\pi\) | ||||
−0.822320 | + | 0.569026i | \(0.807321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.85783 | 0.224314 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.4093 | + | 14.6700i | −1.16956 | + | 0.675243i | ||||
\(473\) | −29.7639 | + | 17.1842i | −1.36854 | + | 0.790129i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.37743 | −0.338144 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.5561i | 0.482827i | ||||||||
\(479\) | −16.3774 | + | 28.3665i | −0.748304 | + | 1.29610i | 0.200331 | + | 0.979728i | \(0.435798\pi\) |
−0.948635 | + | 0.316372i | \(0.897535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.193252 | + | 0.334723i | 0.00881155 | + | 0.0152621i | ||||
\(482\) | −7.84793 | + | 4.53101i | −0.357464 | + | 0.206382i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0610840 | − | 0.105801i | 0.00277655 | − | 0.00480912i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.03735i | − | 0.273578i | −0.990600 | − | 0.136789i | \(-0.956322\pi\) | ||
0.990600 | − | 0.136789i | \(-0.0436783\pi\) | |||||||
\(488\) | −37.1373 | − | 21.4412i | −1.68113 | − | 0.970600i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.22153 | + | 12.5081i | 0.325903 | + | 0.564480i | 0.981695 | − | 0.190461i | \(-0.0609984\pi\) |
−0.655792 | + | 0.754942i | \(0.727665\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.98755 | + | 2.30221i | 0.179590 | + | 0.103686i | ||||
\(494\) | 4.38650 | 0.197358 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 52.6610 | 2.36455 | ||||||||
\(497\) | −4.00326 | − | 2.31128i | −0.179571 | − | 0.103675i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.4859 | + | 18.1620i | 0.469412 | + | 0.813045i | 0.999388 | − | 0.0349673i | \(-0.0111327\pi\) |
−0.529977 | + | 0.848012i | \(0.677799\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.9751 | + | 8.64591i | 0.668374 | + | 0.385886i | ||||
\(503\) | − | 5.31728i | − | 0.237086i | −0.992949 | − | 0.118543i | \(-0.962178\pi\) | ||
0.992949 | − | 0.118543i | \(-0.0378223\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −17.2311 | + | 29.8452i | −0.766017 | + | 1.32678i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −66.9502 | + | 38.6537i | −2.97043 | + | 1.71498i | ||||
\(509\) | −9.11350 | − | 15.7850i | −0.403949 | − | 0.699659i | 0.590250 | − | 0.807221i | \(-0.299029\pi\) |
−0.994198 | + | 0.107561i | \(0.965696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.55695 | − | 2.69671i | 0.0688753 | − | 0.119296i | ||||
\(512\) | 49.3365i | 2.18038i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 45.2545 | 1.99609 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.9867 | − | 8.07522i | 0.615134 | − | 0.355148i | ||||
\(518\) | −0.327558 | + | 0.189116i | −0.0143921 | + | 0.00830927i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.1232 | −1.75783 | −0.878915 | − | 0.476978i | \(-0.841732\pi\) | ||||
−0.878915 | + | 0.476978i | \(0.841732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18.9873i | − | 0.830257i | −0.909763 | − | 0.415129i | \(-0.863737\pi\) | ||
0.909763 | − | 0.415129i | \(-0.136263\pi\) | |||||||
\(524\) | 12.9627 | − | 22.4520i | 0.566276 | − | 0.980819i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.83916 | − | 13.5778i | −0.341804 | − | 0.592021i | ||||
\(527\) | 25.1235 | − | 14.5051i | 1.09440 | − | 0.631851i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.98133 | + | 5.16381i | −0.129623 | + | 0.224513i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.93438i | 0.127221i | ||||||||
\(533\) | −12.9825 | − | 7.49546i | −0.562336 | − | 0.324665i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 27.5661 | + | 47.7460i | 1.19068 | + | 2.06231i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.6064 | + | 12.4745i | 0.931518 | + | 0.537812i | ||||
\(539\) | 22.3684 | 0.963473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5279 | 0.710589 | 0.355294 | − | 0.934754i | \(-0.384381\pi\) | ||||
0.355294 | + | 0.934754i | \(0.384381\pi\) | |||||||
\(542\) | 14.3799 | + | 8.30221i | 0.617668 | + | 0.356611i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.78807 | − | 10.0252i | −0.248162 | − | 0.429829i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.3058 | − | 8.83683i | −0.654430 | − | 0.377835i | 0.135721 | − | 0.990747i | \(-0.456665\pi\) |
−0.790151 | + | 0.612912i | \(0.789998\pi\) | |||||||
\(548\) | 24.4996i | 1.04657i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.915706 | − | 1.58605i | 0.0390104 | − | 0.0675680i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.58722 | + | 2.07108i | −0.152544 | + | 0.0880715i | ||||
\(554\) | −28.4864 | − | 49.3399i | −1.21027 | − | 2.09625i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.2835 | + | 29.9360i | −0.732985 | + | 1.26957i | ||||
\(557\) | − | 17.3401i | − | 0.734723i | −0.930078 | − | 0.367362i | \(-0.880261\pi\) | ||
0.930078 | − | 0.367362i | \(-0.119739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.6700 | 0.578181 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −33.8525 | + | 19.5447i | −1.42798 | + | 0.824445i | ||||
\(563\) | 11.2536 | − | 6.49727i | 0.474283 | − | 0.273827i | −0.243748 | − | 0.969839i | \(-0.578377\pi\) |
0.718031 | + | 0.696011i | \(0.245044\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.62257 | −0.0682016 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 52.4623i | − | 2.20127i | ||||||
\(569\) | 8.34009 | − | 14.4455i | 0.349635 | − | 0.605585i | −0.636550 | − | 0.771236i | \(-0.719639\pi\) |
0.986184 | + | 0.165651i | \(0.0529724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | −16.4143 | + | 9.47679i | −0.686316 | + | 0.396245i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.33502 | − | 12.7046i | 0.306158 | − | 0.530281i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 23.5953i | − | 0.982287i | −0.871079 | − | 0.491144i | \(-0.836579\pi\) | ||
0.871079 | − | 0.491144i | \(-0.163421\pi\) | |||||||
\(578\) | 13.0023 | + | 7.50687i | 0.540823 | + | 0.312245i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.396505 | − | 0.686767i | −0.0164498 | − | 0.0284919i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.4612 | + | 8.34916i | 0.598920 | + | 0.345787i | ||||
\(584\) | 35.3401 | 1.46238 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.46305 | −0.143057 | ||||||||
\(587\) | 24.3592 | + | 14.0638i | 1.00541 | + | 0.580476i | 0.909846 | − | 0.414947i | \(-0.136200\pi\) |
0.0955681 | + | 0.995423i | \(0.469533\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.76940 | − | 9.99290i | −0.237724 | − | 0.411750i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.52761 | − | 0.881969i | −0.0627846 | − | 0.0362487i | ||||
\(593\) | − | 9.17872i | − | 0.376925i | −0.982080 | − | 0.188462i | \(-0.939650\pi\) | ||
0.982080 | − | 0.188462i | \(-0.0603503\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 38.1555 | − | 66.0873i | 1.56291 | − | 2.70704i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.8709 | − | 6.85369i | 0.485439 | − | 0.280268i | ||||
\(599\) | 15.7357 | + | 27.2550i | 0.642942 | + | 1.11361i | 0.984773 | + | 0.173846i | \(0.0556196\pi\) |
−0.341831 | + | 0.939761i | \(0.611047\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.6327 | − | 25.3446i | 0.596880 | − | 1.03383i | −0.396398 | − | 0.918079i | \(-0.629740\pi\) |
0.993279 | − | 0.115748i | \(-0.0369265\pi\) | |||||||
\(602\) | 13.3774i | 0.545223i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.46305 | −0.222288 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.2813 | + | 22.1017i | −1.55379 | + | 0.897080i | −0.555960 | + | 0.831209i | \(0.687649\pi\) |
−0.997828 | + | 0.0658708i | \(0.979017\pi\) | |||||||
\(608\) | −3.98755 | + | 2.30221i | −0.161716 | + | 0.0933670i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.42385 | −0.259881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.1715i | 1.42056i | 0.703918 | + | 0.710282i | \(0.251432\pi\) | ||||
−0.703918 | + | 0.710282i | \(0.748568\pi\) | |||||||
\(614\) | 10.0383 | − | 17.3868i | 0.405112 | − | 0.701674i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.98133 | − | 8.62791i | −0.200703 | − | 0.347628i | ||||
\(617\) | 6.43085 | − | 3.71285i | 0.258896 | − | 0.149474i | −0.364935 | − | 0.931033i | \(-0.618909\pi\) |
0.623831 | + | 0.781559i | \(0.285575\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.27394 | − | 7.40268i | 0.171784 | − | 0.297539i | −0.767260 | − | 0.641337i | \(-0.778380\pi\) |
0.939044 | + | 0.343798i | \(0.111714\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.2179i | 0.971050i | ||||||||
\(623\) | −1.33577 | − | 0.771205i | −0.0535164 | − | 0.0308977i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30.8446 | − | 53.4245i | −1.23280 | − | 2.13527i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −58.6372 | − | 33.8542i | −2.33988 | − | 1.35093i | ||||
\(629\) | −0.971726 | −0.0387453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.36836 | −0.0942829 | −0.0471415 | − | 0.998888i | \(-0.515011\pi\) | ||||
−0.0471415 | + | 0.998888i | \(0.515011\pi\) | |||||||
\(632\) | −40.7120 | − | 23.5051i | −1.61944 | − | 0.934981i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −25.5803 | − | 44.3064i | −1.01592 | − | 1.75963i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.70506 | − | 4.44852i | −0.305285 | − | 0.176257i | ||||
\(638\) | 11.5761i | 0.458304i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.0665480 | + | 0.115265i | −0.00262849 | + | 0.00455268i | −0.867337 | − | 0.497722i | \(-0.834170\pi\) |
0.864708 | + | 0.502275i | \(0.167503\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.6124 | − | 11.3232i | 0.773437 | − | 0.446544i | −0.0606623 | − | 0.998158i | \(-0.519321\pi\) |
0.834099 | + | 0.551614i | \(0.185988\pi\) | |||||||
\(644\) | 4.58482 | + | 7.94114i | 0.180667 | + | 0.312925i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.51414 | + | 9.55077i | −0.216951 | + | 0.375770i | ||||
\(647\) | − | 46.3912i | − | 1.82383i | −0.410385 | − | 0.911913i | \(-0.634606\pi\) | ||
0.410385 | − | 0.911913i | \(-0.365394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.6983 | −0.655466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 58.7770 | − | 33.9349i | 2.30188 | − | 1.32899i | ||||
\(653\) | 31.5283 | − | 18.2029i | 1.23380 | − | 0.712333i | 0.265977 | − | 0.963979i | \(-0.414305\pi\) |
0.967819 | + | 0.251647i | \(0.0809721\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 68.4158 | 2.67119 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 6.28635i | − | 0.245067i | ||||||
\(659\) | −9.57068 | + | 16.5769i | −0.372821 | + | 0.645745i | −0.989998 | − | 0.141079i | \(-0.954943\pi\) |
0.617177 | + | 0.786824i | \(0.288276\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.9536 | − | 34.5606i | −0.776104 | − | 1.34425i | −0.934172 | − | 0.356824i | \(-0.883860\pi\) |
0.158067 | − | 0.987428i | \(-0.449474\pi\) | |||||||
\(662\) | −35.8016 | + | 20.6700i | −1.39147 | + | 0.803364i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.50000 | − | 7.79423i | 0.174634 | − | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 5.72298i | − | 0.221595i | ||||||
\(668\) | −23.0693 | − | 13.3191i | −0.892579 | − | 0.515331i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.2029 | − | 21.1360i | −0.471086 | − | 0.815945i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.4822 | + | 11.8254i | 0.789532 | + | 0.455836i | 0.839798 | − | 0.542899i | \(-0.182674\pi\) |
−0.0502658 | + | 0.998736i | \(0.516007\pi\) | |||||||
\(674\) | 12.3118 | 0.474233 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −48.6327 | −1.87049 | ||||||||
\(677\) | −12.8199 | − | 7.40157i | −0.492709 | − | 0.284465i | 0.232989 | − | 0.972479i | \(-0.425149\pi\) |
−0.725697 | + | 0.688014i | \(0.758483\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.15044 | + | 5.45673i | 0.120903 | + | 0.209410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 63.1639 | + | 36.4677i | 2.41867 | + | 1.39642i | ||||
\(683\) | − | 4.95252i | − | 0.189503i | −0.995501 | − | 0.0947515i | \(-0.969794\pi\) | ||
0.995501 | − | 0.0947515i | \(-0.0302057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.87743 | − | 15.3762i | 0.338942 | − | 0.587065i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −54.0292 | + | 31.1938i | −2.05984 | + | 1.18925i | ||||
\(689\) | −3.32088 | − | 5.75194i | −0.126516 | − | 0.219131i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.60442 | − | 16.6353i | 0.365369 | − | 0.632838i | −0.623466 | − | 0.781851i | \(-0.714276\pi\) |
0.988835 | + | 0.149012i | \(0.0476093\pi\) | |||||||
\(692\) | − | 37.0957i | − | 1.41017i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −56.0011 | −2.12577 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.6398 | − | 18.8446i | 1.23632 | − | 0.713791i | ||||
\(698\) | −6.40880 | + | 3.70012i | −0.242577 | + | 0.140052i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3492 | 1.10850 | 0.554251 | − | 0.832349i | \(-0.313005\pi\) | ||||
0.554251 | + | 0.832349i | \(0.313005\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.386505i | 0.0145773i | ||||||||
\(704\) | −5.46719 | + | 9.46945i | −0.206052 | + | 0.356893i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.6700 | − | 40.9977i | −0.890834 | − | 1.54297i | ||||
\(707\) | 5.19615 | − | 3.00000i | 0.195421 | − | 0.112827i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.3633 | − | 33.5382i | 0.727204 | − | 1.25955i | −0.230857 | − | 0.972988i | \(-0.574153\pi\) |
0.958060 | − | 0.286566i | \(-0.0925138\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 17.5051i | − | 0.656030i | ||||||
\(713\) | −31.2268 | − | 18.0288i | −1.16945 | − | 0.675184i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.30221 | − | 3.98755i | −0.0860377 | − | 0.149022i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −69.4061 | − | 40.0716i | −2.59021 | − | 1.49546i | ||||
\(719\) | −15.0848 | −0.562569 | −0.281284 | − | 0.959624i | \(-0.590760\pi\) | ||||
−0.281284 | + | 0.959624i | \(0.590760\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.150442 | −0.00560275 | ||||||||
\(722\) | −37.5700 | − | 21.6910i | −1.39821 | − | 0.807257i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.3729 | − | 47.4112i | −1.01731 | − | 1.76203i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.6916 | − | 6.17277i | −0.396528 | − | 0.228936i | 0.288457 | − | 0.957493i | \(-0.406858\pi\) |
−0.684985 | + | 0.728557i | \(0.740191\pi\) | |||||||
\(728\) | 3.96265i | 0.146866i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.1842 | + | 29.7639i | −0.635580 | + | 1.10086i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.0526 | − | 11.0000i | 0.703722 | − | 0.406294i | −0.105010 | − | 0.994471i | \(-0.533487\pi\) |
0.808732 | + | 0.588177i | \(0.200154\pi\) | |||||||
\(734\) | 23.0661 | + | 39.9517i | 0.851387 | + | 1.47465i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.19418 | + | 12.4607i | −0.265181 | + | 0.459307i | ||||
\(737\) | 31.3774i | 1.15580i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.7266 | −1.09351 | −0.546755 | − | 0.837293i | \(-0.684137\pi\) | ||||
−0.546755 | + | 0.837293i | \(0.684137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.62882 | − | 3.24980i | 0.206640 | − | 0.119304i | ||||
\(743\) | 41.8851 | − | 24.1824i | 1.53662 | − | 0.887165i | 0.537582 | − | 0.843212i | \(-0.319338\pi\) |
0.999034 | − | 0.0439537i | \(-0.0139954\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.52787 | 0.202390 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 47.6519i | − | 1.74233i | ||||||
\(749\) | 0.481327 | − | 0.833682i | 0.0175873 | − | 0.0304621i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9102 | + | 27.5573i | 0.580573 | + | 1.00558i | 0.995411 | + | 0.0956869i | \(0.0305047\pi\) |
−0.414838 | + | 0.909895i | \(0.636162\pi\) | |||||||
\(752\) | 25.3895 | − | 14.6586i | 0.925860 | − | 0.534546i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.30221 | − | 3.98755i | 0.0838416 | − | 0.145218i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.94531i | 0.179740i | 0.995953 | + | 0.0898701i | \(0.0286452\pi\) | ||||
−0.995953 | + | 0.0898701i | \(0.971355\pi\) | |||||||
\(758\) | −33.6858 | − | 19.4485i | −1.22352 | − | 0.706402i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.7125 | + | 30.6789i | 0.642076 | + | 1.11211i | 0.984969 | + | 0.172734i | \(0.0552600\pi\) |
−0.342893 | + | 0.939375i | \(0.611407\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.47022 | − | 1.42618i | −0.0894281 | − | 0.0516313i | ||||
\(764\) | −73.1715 | −2.64725 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.3774 | 0.700135 | ||||||||
\(767\) | 5.75194 | + | 3.32088i | 0.207691 | + | 0.119910i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.7125 | + | 42.8032i | 0.891154 | + | 1.54352i | 0.838494 | + | 0.544911i | \(0.183437\pi\) |
0.0526602 | + | 0.998612i | \(0.483230\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −99.9768 | − | 57.7217i | −3.59825 | − | 2.07745i | ||||
\(773\) | 12.6599i | 0.455345i | 0.973738 | + | 0.227673i | \(0.0731116\pi\) | ||||
−0.973738 | + | 0.227673i | \(0.926888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −35.7549 | + | 61.9292i | −1.28352 | + | 2.22313i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 53.6329 | − | 30.9650i | 1.92283 | − | 1.11015i | ||||
\(779\) | −7.49546 | − | 12.9825i | −0.268553 | − | 0.465147i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.9289 | − | 25.8576i | 0.534199 | − | 0.925259i | ||||
\(782\) | 34.4623i | 1.23237i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 40.6044 | 1.45016 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.7900 | − | 15.4672i | 0.954959 | − | 0.551346i | 0.0603410 | − | 0.998178i | \(-0.480781\pi\) |
0.894618 | + | 0.446832i | \(0.147448\pi\) | |||||||
\(788\) | −53.3431 | + | 30.7977i | −1.90027 | + | 1.09712i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.01093 | 0.142612 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.70739i | 0.344720i | ||||||||
\(794\) | 8.51414 | − | 14.7469i | 0.302155 | − | 0.523349i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 53.2786 | + | 92.2812i | 1.88841 | + | 3.27082i | ||||
\(797\) | 26.4947 | − | 15.2967i | 0.938492 | − | 0.541839i | 0.0490047 | − | 0.998799i | \(-0.484395\pi\) |
0.889487 | + | 0.456960i | \(0.151062\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.07522 | − | 13.9867i | 0.285681 | − | 0.494814i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 46.5105i | − | 1.64234i | ||||||
\(803\) | 17.4185 | + | 10.0565i | 0.614684 | + | 0.354888i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.5051 | − | 25.1235i | −0.510919 | − | 0.884938i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 58.9720 | + | 34.0475i | 2.07463 | + | 1.19779i | ||||
\(809\) | −2.89703 | −0.101854 | −0.0509271 | − | 0.998702i | \(-0.516218\pi\) | ||||
−0.0509271 | + | 0.998702i | \(0.516218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.8861 | −0.522722 | −0.261361 | − | 0.965241i | \(-0.584171\pi\) | ||||
−0.261361 | + | 0.965241i | \(0.584171\pi\) | |||||||
\(812\) | 2.66749 | + | 1.54008i | 0.0936107 | + | 0.0540462i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.22153 | − | 2.11575i | −0.0428145 | − | 0.0741568i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.8386 | + | 6.83502i | 0.414180 | + | 0.239127i | ||||
\(818\) | − | 33.7266i | − | 1.17922i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.47586 | + | 7.75242i | −0.156209 | + | 0.270561i | −0.933498 | − | 0.358581i | \(-0.883261\pi\) |
0.777290 | + | 0.629143i | \(0.216594\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.59334 | + | 1.49727i | −0.0903983 | + | 0.0521915i | −0.544518 | − | 0.838749i | \(-0.683287\pi\) |
0.454119 | + | 0.890941i | \(0.349954\pi\) | |||||||
\(824\) | −0.853695 | − | 1.47864i | −0.0297399 | − | 0.0515110i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.24980 | + | 5.62882i | −0.113075 | + | 0.195852i | ||||
\(827\) | − | 31.9663i | − | 1.11158i | −0.831324 | − | 0.555788i | \(-0.812417\pi\) | ||
0.831324 | − | 0.555788i | \(-0.187583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.7458 | −0.789994 | −0.394997 | − | 0.918682i | \(-0.629254\pi\) | ||||
−0.394997 | + | 0.918682i | \(0.629254\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.76648 | − | 2.17458i | 0.130579 | − | 0.0753900i | ||||
\(833\) | 19.3716 | − | 11.1842i | 0.671185 | − | 0.387509i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.9536 | −0.655523 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 83.2555i | 2.87601i | ||||||||
\(839\) | 11.6322 | − | 20.1475i | 0.401587 | − | 0.695569i | −0.592331 | − | 0.805695i | \(-0.701792\pi\) |
0.993918 | + | 0.110126i | \(0.0351254\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5388 | + | 23.4499i | 0.466855 | + | 0.808617i | ||||
\(842\) | 32.0027 | − | 18.4768i | 1.10289 | − | 0.636752i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.6176 | + | 20.1223i | −0.399895 | + | 0.692639i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.0145366i | − | 0.000499485i | ||||||
\(848\) | 26.2508 | + | 15.1559i | 0.901456 | + | 0.520456i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.603895 | + | 1.04598i | 0.0207012 | + | 0.0358556i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.51842 | + | 5.49546i | 0.325905 | + | 0.188161i | 0.654021 | − | 0.756476i | \(-0.273081\pi\) |
−0.328117 | + | 0.944637i | \(0.606414\pi\) | |||||||
\(854\) | −9.49960 | −0.325070 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.9253 | 0.373419 | ||||||||
\(857\) | −13.9867 | − | 8.07522i | −0.477776 | − | 0.275844i | 0.241713 | − | 0.970348i | \(-0.422291\pi\) |
−0.719489 | + | 0.694503i | \(0.755624\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.2594 | + | 24.6980i | 0.486524 | + | 0.842685i | 0.999880 | − | 0.0154909i | \(-0.00493111\pi\) |
−0.513356 | + | 0.858176i | \(0.671598\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 71.3174 | + | 41.1751i | 2.42908 | + | 1.40243i | ||||
\(863\) | 12.2890i | 0.418322i | 0.977881 | + | 0.209161i | \(0.0670734\pi\) | ||||
−0.977881 | + | 0.209161i | \(0.932927\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.8729 | + | 25.7606i | −0.505402 | + | 0.875381i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.8065 | − | 9.70325i | 0.570451 | − | 0.329350i | ||||
\(869\) | −13.3774 | − | 23.1704i | −0.453798 | − | 0.786002i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.24020 | − | 10.8083i | 0.211441 | − | 0.366227i | ||||
\(872\) | − | 32.3720i | − | 1.09625i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.7074 | 0.463659 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.3814 | + | 19.8501i | −1.16098 | + | 0.670290i | −0.951538 | − | 0.307532i | \(-0.900497\pi\) |
−0.209438 | + | 0.977822i | \(0.567164\pi\) | |||||||
\(878\) | 18.0974 | − | 10.4485i | 0.610756 | − | 0.352620i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.1040 | −1.08161 | −0.540806 | − | 0.841147i | \(-0.681881\pi\) | ||||
−0.540806 | + | 0.841147i | \(0.681881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.5051i | − | 0.454482i | −0.973839 | − | 0.227241i | \(-0.927030\pi\) | ||
0.973839 | − | 0.227241i | \(-0.0729704\pi\) | |||||||
\(884\) | −9.47679 | + | 16.4143i | −0.318739 | + | 0.552072i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.6751 | + | 63.5231i | 1.23212 | + | 2.13410i | ||||
\(887\) | −30.4167 | + | 17.5611i | −1.02129 | + | 0.589643i | −0.914478 | − | 0.404635i | \(-0.867398\pi\) |
−0.106814 | + | 0.994279i | \(0.534065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.59936 | + | 7.96632i | −0.154258 | + | 0.267182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 37.4386i | 1.25354i | ||||||||
\(893\) | −5.56322 | − | 3.21193i | −0.186166 | − | 0.107483i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.92024 | + | 6.79006i | 0.130966 | + | 0.226840i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41.3073 | + | 23.8488i | 1.37844 | + | 0.795843i | ||||
\(899\) | −12.1120 | −0.403959 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.6983 | 0.556302 | ||||||||
\(902\) | 82.0610 | + | 47.3780i | 2.73233 | + | 1.57751i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.7603 | + | 39.4220i | 0.756997 | + | 1.31116i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0931 | − | 7.55928i | −0.434748 | − | 0.251002i | 0.266619 | − | 0.963802i | \(-0.414093\pi\) |
−0.701367 | + | 0.712800i | \(0.747427\pi\) | |||||||
\(908\) | 14.3492i | 0.476194i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.2781 | − | 45.5150i | 0.870631 | − | 1.50798i | 0.00928675 | − | 0.999957i | \(-0.497044\pi\) |
0.861345 | − | 0.508021i | \(-0.169623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.43593 | − | 2.56108i | 0.146808 | − | 0.0847595i | ||||
\(914\) | 29.2083 | + | 50.5903i | 0.966125 | + | 1.67338i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 54.6847 | − | 94.7167i | 1.80683 | − | 3.12953i | ||||
\(917\) | − | 3.08482i | − | 0.101870i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.5489 | 1.79940 | 0.899702 | − | 0.436505i | \(-0.143784\pi\) | ||||
0.899702 | + | 0.436505i | \(0.143784\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.63612 | − | 5.56342i | 0.317349 | − | 0.183221i | ||||
\(923\) | −10.2849 | + | 5.93799i | −0.338532 | + | 0.195451i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 49.0475 | 1.61180 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.83317i | 0.158656i | ||||||||
\(929\) | −10.1896 | + | 17.6490i | −0.334311 | + | 0.579044i | −0.983352 | − | 0.181709i | \(-0.941837\pi\) |
0.649041 | + | 0.760753i | \(0.275170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.44852 | − | 7.70506i | −0.145794 | − | 0.252523i | ||||
\(932\) | −103.401 | + | 59.6988i | −3.38703 | + | 1.95550i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −30.9157 | + | 53.5476i | −1.01159 | + | 1.75213i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.1979i | 1.60723i | 0.595152 | + | 0.803613i | \(0.297092\pi\) | ||||
−0.595152 | + | 0.803613i | \(0.702908\pi\) | |||||||
\(938\) | 10.5770 | + | 6.10663i | 0.345351 | + | 0.199388i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6186 | − | 20.1239i | −0.378754 | − | 0.656022i | 0.612127 | − | 0.790759i | \(-0.290314\pi\) |
−0.990881 | + | 0.134738i | \(0.956981\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −40.5691 | − | 23.4226i | −1.32111 | − | 0.762744i | ||||
\(944\) | −30.3118 | −0.986565 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −86.4068 | −2.80933 | ||||||||
\(947\) | 32.1851 | + | 18.5821i | 1.04588 | + | 0.603837i | 0.921492 | − | 0.388397i | \(-0.126971\pi\) |
0.124384 | + | 0.992234i | \(0.460305\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | − | 6.92820i | −0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.62791 | − | 4.98133i | −0.279632 | − | 0.161446i | ||||
\(953\) | − | 23.5761i | − | 0.763706i | −0.924223 | − | 0.381853i | \(-0.875286\pi\) | ||
0.924223 | − | 0.381853i | \(-0.124714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.07108 | + | 15.7116i | −0.293380 | + | 0.508149i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −71.3174 | + | 41.1751i | −2.30416 | + | 1.33031i | ||||
\(959\) | 1.45759 | + | 2.52462i | 0.0470680 | + | 0.0815242i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.6559 | + | 39.2412i | −0.730836 | + | 1.26584i | ||||
\(962\) | 0.971726i | 0.0313297i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.5743 | −0.501614 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.25980 | − | 4.19145i | 0.233459 | − | 0.134788i | −0.378708 | − | 0.925516i | \(-0.623631\pi\) |
0.612167 | + | 0.790729i | \(0.290298\pi\) | |||||||
\(968\) | 0.142876 | − | 0.0824893i | 0.00459220 | − | 0.00265131i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.2078 | −0.423858 | −0.211929 | − | 0.977285i | \(-0.567975\pi\) | ||||
−0.211929 | + | 0.977285i | \(0.567975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.11310i | 0.131860i | ||||||||
\(974\) | 7.58936 | − | 13.1452i | 0.243179 | − | 0.421198i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.1514 | − | 38.3673i | −0.709048 | − | 1.22811i | ||||
\(977\) | 12.4110 | − | 7.16551i | 0.397064 | − | 0.229245i | −0.288153 | − | 0.957585i | \(-0.593041\pi\) |
0.685216 | + | 0.728340i | \(0.259708\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.98133 | − | 8.62791i | 0.159204 | − | 0.275749i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.3118i | 1.15876i | ||||||||
\(983\) | 27.9797 | + | 16.1541i | 0.892415 | + | 0.515236i | 0.874732 | − | 0.484608i | \(-0.161038\pi\) |
0.0176831 | + | 0.999844i | \(0.494371\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.78807 | + | 10.0252i | 0.184330 | + | 0.319269i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.52879 | + | 3.76940i | 0.207709 | + | 0.119921i | ||||
\(989\) | 42.7175 | 1.35834 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.6700 | −1.26016 | −0.630080 | − | 0.776530i | \(-0.716978\pi\) | ||||
−0.630080 | + | 0.776530i | \(0.716978\pi\) | |||||||
\(992\) | 26.3716 | + | 15.2257i | 0.837300 | + | 0.483415i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.81088 | − | 10.0647i | −0.184310 | − | 0.319234i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.5043 | − | 19.3437i | −1.06109 | − | 0.612621i | −0.135357 | − | 0.990797i | \(-0.543218\pi\) |
−0.925734 | + | 0.378176i | \(0.876551\pi\) | |||||||
\(998\) | 52.7258i | 1.66901i | ||||||||
\(999\) | 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 twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.1 | ✓ | 6 | 15.8 | even | 4 | ||
45.2.e.b.31.1 | yes | 6 | 45.23 | even | 12 | ||
135.2.e.b.46.3 | 6 | 5.3 | odd | 4 | |||
135.2.e.b.91.3 | 6 | 45.13 | odd | 12 | |||
225.2.e.b.76.3 | 6 | 45.32 | even | 12 | |||
225.2.e.b.151.3 | 6 | 15.2 | even | 4 | |||
225.2.k.b.49.1 | 12 | 45.14 | odd | 6 | |||
225.2.k.b.49.6 | 12 | 9.5 | odd | 6 | |||
225.2.k.b.124.1 | 12 | 3.2 | odd | 2 | |||
225.2.k.b.124.6 | 12 | 15.14 | odd | 2 | |||
405.2.a.i.1.1 | 3 | 45.43 | odd | 12 | |||
405.2.a.j.1.3 | 3 | 45.38 | even | 12 | |||
675.2.e.b.226.1 | 6 | 45.22 | odd | 12 | |||
675.2.e.b.451.1 | 6 | 5.2 | odd | 4 | |||
675.2.k.b.199.1 | 12 | 9.4 | even | 3 | inner | ||
675.2.k.b.199.6 | 12 | 45.4 | even | 6 | inner | ||
675.2.k.b.424.1 | 12 | 5.4 | even | 2 | inner | ||
675.2.k.b.424.6 | 12 | 1.1 | even | 1 | trivial | ||
720.2.q.i.241.1 | 6 | 60.23 | odd | 4 | |||
720.2.q.i.481.1 | 6 | 180.23 | odd | 12 | |||
2025.2.a.n.1.1 | 3 | 45.2 | even | 12 | |||
2025.2.a.o.1.3 | 3 | 45.7 | odd | 12 | |||
2025.2.b.l.649.1 | 6 | 45.29 | odd | 6 | |||
2025.2.b.l.649.6 | 6 | 9.2 | odd | 6 | |||
2025.2.b.m.649.1 | 6 | 9.7 | even | 3 | |||
2025.2.b.m.649.6 | 6 | 45.34 | even | 6 | |||
2160.2.q.k.721.1 | 6 | 20.3 | even | 4 | |||
2160.2.q.k.1441.1 | 6 | 180.103 | even | 12 | |||
6480.2.a.bs.1.3 | 3 | 180.43 | even | 12 | |||
6480.2.a.bv.1.3 | 3 | 180.83 | odd | 12 |