Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,3,Mod(31,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.92371580679\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.3 | ||
Root | \(2.06288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.79 |
Dual form | 144.3.o.a.31.3 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.456412 | + | 2.96508i | −0.152137 | + | 0.988359i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.61660 | + | 7.99619i | 0.923321 | + | 1.59924i | 0.794240 | + | 0.607604i | \(0.207869\pi\) |
0.129080 | + | 0.991634i | \(0.458797\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.33093 | − | 3.07781i | −0.761561 | − | 0.439687i | 0.0682950 | − | 0.997665i | \(-0.478244\pi\) |
−0.829856 | + | 0.557978i | \(0.811577\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.58338 | − | 2.70659i | −0.953709 | − | 0.300732i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.70016 | − | 2.13629i | −0.336378 | − | 0.194208i | 0.322291 | − | 0.946641i | \(-0.395547\pi\) |
−0.658669 | + | 0.752433i | \(0.728880\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.869235 | + | 1.50556i | 0.0668642 | + | 0.115812i | 0.897519 | − | 0.440975i | \(-0.145367\pi\) |
−0.830655 | + | 0.556787i | \(0.812034\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −25.8164 | + | 10.0390i | −1.72109 | + | 0.669269i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.3476 | 0.726329 | 0.363164 | − | 0.931725i | \(-0.381696\pi\) | ||||
0.363164 | + | 0.931725i | \(0.381696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33.9338i | 1.78599i | 0.450065 | + | 0.892996i | \(0.351401\pi\) | ||||
−0.450065 | + | 0.892996i | \(0.648599\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.5590 | − | 14.4019i | 0.550431 | − | 0.685803i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.35035 | + | 1.93433i | −0.145668 | + | 0.0841012i | −0.571062 | − | 0.820907i | \(-0.693469\pi\) |
0.425395 | + | 0.905008i | \(0.360135\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −30.1260 | + | 52.1798i | −1.20504 | + | 2.08719i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.9428 | − | 24.2151i | 0.442326 | − | 0.896854i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.8409 | − | 30.9014i | 0.615204 | − | 1.06556i | −0.375145 | − | 0.926966i | \(-0.622407\pi\) |
0.990349 | − | 0.138598i | \(-0.0442596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.8262 | − | 22.4163i | 1.25246 | − | 0.723107i | 0.280861 | − | 0.959748i | \(-0.409380\pi\) |
0.971597 | + | 0.236641i | \(0.0760466\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.02306 | − | 9.99624i | 0.243123 | − | 0.302916i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 56.8361i | − | 1.62389i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.7130 | −0.884134 | −0.442067 | − | 0.896982i | \(-0.645755\pi\) | ||||
−0.442067 | + | 0.896982i | \(0.645755\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.86083 | + | 1.89019i | −0.124637 | + | 0.0484665i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.8565 | + | 37.8565i | 0.533085 | + | 0.923330i | 0.999253 | + | 0.0386343i | \(0.0123007\pi\) |
−0.466168 | + | 0.884696i | \(0.654366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 33.9339 | + | 19.5918i | 0.789161 | + | 0.455622i | 0.839667 | − | 0.543102i | \(-0.182750\pi\) |
−0.0505063 | + | 0.998724i | \(0.516084\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17.9836 | − | 81.1296i | −0.399636 | − | 1.80288i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 39.8784 | + | 23.0238i | 0.848477 | + | 0.489868i | 0.860137 | − | 0.510064i | \(-0.170378\pi\) |
−0.0116600 | + | 0.999932i | \(0.503712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.55415 | − | 9.62007i | −0.113350 | − | 0.196328i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.63558 | + | 36.6116i | −0.110502 | + | 0.717874i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 46.3143 | 0.873854 | 0.436927 | − | 0.899497i | \(-0.356067\pi\) | ||||
0.436927 | + | 0.899497i | \(0.356067\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 39.4496i | − | 0.717265i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −100.617 | − | 15.4878i | −1.76520 | − | 0.271716i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 23.2710 | − | 13.4355i | 0.394423 | − | 0.227720i | −0.289652 | − | 0.957132i | \(-0.593539\pi\) |
0.684075 | + | 0.729412i | \(0.260206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.4545 | − | 40.6243i | 0.384500 | − | 0.665973i | −0.607200 | − | 0.794549i | \(-0.707707\pi\) |
0.991700 | + | 0.128576i | \(0.0410407\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 37.4270 | + | 40.8467i | 0.594079 | + | 0.648360i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.02582 | + | 13.9011i | −0.123474 | + | 0.213864i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −56.9984 | + | 32.9080i | −0.850722 | + | 0.491164i | −0.860894 | − | 0.508784i | \(-0.830095\pi\) |
0.0101725 | + | 0.999948i | \(0.496762\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.20629 | − | 10.8169i | −0.0609607 | − | 0.156767i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 96.7955i | − | 1.36332i | −0.731671 | − | 0.681658i | \(-0.761259\pi\) | ||
0.731671 | − | 0.681658i | \(-0.238741\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0622 | −0.192633 | −0.0963163 | − | 0.995351i | \(-0.530706\pi\) | ||||
−0.0963163 | + | 0.995351i | \(0.530706\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −140.967 | − | 113.142i | −1.87957 | − | 1.50855i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.1502 | + | 22.7768i | 0.170782 | + | 0.295803i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 34.3954 | + | 19.8582i | 0.435385 | + | 0.251369i | 0.701638 | − | 0.712534i | \(-0.252452\pi\) |
−0.266253 | + | 0.963903i | \(0.585786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 66.3487 | + | 46.4634i | 0.819120 | + | 0.573622i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 81.7202 | + | 47.1812i | 0.984581 | + | 0.568448i | 0.903650 | − | 0.428272i | \(-0.140877\pi\) |
0.0809306 | + | 0.996720i | \(0.474211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 57.0039 | + | 98.7336i | 0.670634 | + | 1.16157i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 83.4822 | + | 67.0034i | 0.959565 | + | 0.770154i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −81.8478 | −0.919639 | −0.459819 | − | 0.888012i | \(-0.652086\pi\) | ||||
−0.459819 | + | 0.888012i | \(0.652086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10.7014i | − | 0.117597i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 48.7454 | + | 125.354i | 0.524144 | + | 1.34789i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −271.341 | + | 156.659i | −2.85623 | + | 1.64904i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.99028 | + | 13.8396i | −0.0823741 | + | 0.142676i | −0.904269 | − | 0.426963i | \(-0.859584\pi\) |
0.821895 | + | 0.569639i | \(0.192917\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 25.9778 | + | 28.3514i | 0.262402 | + | 0.286378i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 50.6344 | − | 87.7014i | 0.501331 | − | 0.868330i | −0.498668 | − | 0.866793i | \(-0.666177\pi\) |
0.999999 | − | 0.00153723i | \(-0.000489314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −88.4092 | + | 51.0431i | −0.858341 | + | 0.495564i | −0.863456 | − | 0.504423i | \(-0.831705\pi\) |
0.00511517 | + | 0.999987i | \(0.498372\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 168.524 | + | 25.9407i | 1.60499 | + | 0.247054i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 73.1463i | 0.683610i | 0.939771 | + | 0.341805i | \(0.111038\pi\) | ||||
−0.939771 | + | 0.341805i | \(0.888962\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −33.9344 | −0.311325 | −0.155663 | − | 0.987810i | \(-0.549751\pi\) | ||||
−0.155663 | + | 0.987810i | \(0.549751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.9306 | − | 96.9965i | 0.134510 | − | 0.873842i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.9292 | − | 24.1262i | −0.123268 | − | 0.213506i | 0.797787 | − | 0.602940i | \(-0.206004\pi\) |
−0.921054 | + | 0.389434i | \(0.872671\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −30.9345 | − | 17.8600i | −0.268996 | − | 0.155305i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.38604 | − | 15.2754i | −0.0289405 | − | 0.130559i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −65.8241 | − | 38.0035i | −0.553143 | − | 0.319358i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −51.3725 | − | 88.9798i | −0.424566 | − | 0.735371i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −122.223 | + | 47.5280i | −0.993684 | + | 0.386407i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −325.490 | −2.60392 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 117.905i | − | 0.928387i | −0.885734 | − | 0.464193i | \(-0.846344\pi\) | ||
0.885734 | − | 0.464193i | \(-0.153656\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −73.5789 | + | 91.6748i | −0.570379 | + | 0.710657i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 73.5214 | − | 42.4476i | 0.561232 | − | 0.324027i | −0.192408 | − | 0.981315i | \(-0.561630\pi\) |
0.753640 | + | 0.657288i | \(0.228296\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 104.442 | − | 180.899i | 0.785278 | − | 1.36014i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 248.763 | − | 16.2943i | 1.84269 | − | 0.120699i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.97975 | − | 6.89314i | 0.0290493 | − | 0.0503149i | −0.851135 | − | 0.524946i | \(-0.824085\pi\) |
0.880185 | + | 0.474632i | \(0.157419\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9239 | − | 10.3484i | 0.128949 | − | 0.0744488i | −0.434138 | − | 0.900846i | \(-0.642947\pi\) |
0.563087 | + | 0.826398i | \(0.309614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −86.4683 | + | 107.734i | −0.613251 | + | 0.764073i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 7.42775i | − | 0.0519423i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 329.458 | 2.27212 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 31.0592 | − | 12.0778i | 0.211287 | − | 0.0821617i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 65.6122 | + | 113.644i | 0.440350 | + | 0.762709i | 0.997715 | − | 0.0675588i | \(-0.0215210\pi\) |
−0.557365 | + | 0.830267i | \(0.688188\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −204.949 | − | 118.328i | −1.35728 | − | 0.783627i | −0.368025 | − | 0.929816i | \(-0.619966\pi\) |
−0.989257 | + | 0.146189i | \(0.953299\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −105.984 | − | 33.4199i | −0.692706 | − | 0.218431i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 358.490 | + | 206.974i | 2.31284 | + | 1.33532i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −74.8892 | − | 129.712i | −0.477001 | − | 0.826190i | 0.522651 | − | 0.852546i | \(-0.324943\pi\) |
−0.999653 | + | 0.0263562i | \(0.991610\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.1384 | + | 137.325i | −0.132946 | + | 0.863682i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.8140 | 0.147913 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 152.365i | 0.934756i | 0.884057 | + | 0.467378i | \(0.154801\pi\) | ||||
−0.884057 | + | 0.467378i | \(0.845199\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 116.971 | + | 18.0053i | 0.708916 | + | 0.109123i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.5631 | + | 12.4494i | −0.129120 | + | 0.0745476i | −0.563169 | − | 0.826342i | \(-0.690418\pi\) |
0.434049 | + | 0.900889i | \(0.357085\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 82.9889 | − | 143.741i | 0.491058 | − | 0.850538i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91.8451 | − | 291.267i | 0.537106 | − | 1.70332i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −54.0452 | + | 93.6091i | −0.312400 | + | 0.541093i | −0.978881 | − | 0.204429i | \(-0.934466\pi\) |
0.666481 | + | 0.745522i | \(0.267800\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 321.199 | − | 185.445i | 1.83543 | − | 1.05968i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.2162 | + | 75.1323i | 0.165063 | + | 0.424477i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 313.318i | − | 1.75038i | −0.483779 | − | 0.875190i | \(-0.660736\pi\) | ||
0.483779 | − | 0.875190i | \(-0.339264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.5886 | 0.113749 | 0.0568746 | − | 0.998381i | \(-0.481886\pi\) | ||||
0.0568746 | + | 0.998381i | \(0.481886\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 109.749 | + | 88.0858i | 0.599724 | + | 0.481343i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −151.023 | − | 261.579i | −0.816339 | − | 1.41394i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −45.6881 | − | 26.3780i | −0.244321 | − | 0.141059i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −138.196 | + | 92.3310i | −0.731194 | + | 0.488524i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.6619 | − | 13.6612i | −0.123884 | − | 0.0715247i | 0.436777 | − | 0.899570i | \(-0.356120\pi\) |
−0.560662 | + | 0.828045i | \(0.689453\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −65.7227 | − | 113.835i | −0.340532 | − | 0.589819i | 0.644000 | − | 0.765026i | \(-0.277274\pi\) |
−0.984532 | + | 0.175207i | \(0.943941\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −37.5549 | − | 30.1418i | −0.192589 | − | 0.154574i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −126.466 | −0.641961 | −0.320981 | − | 0.947086i | \(-0.604012\pi\) | ||||
−0.320981 | + | 0.947086i | \(0.604012\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 76.0070i | − | 0.381945i | −0.981595 | − | 0.190972i | \(-0.938836\pi\) | ||
0.981595 | − | 0.190972i | \(-0.0611641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −71.5601 | − | 184.024i | −0.356021 | − | 0.915543i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −190.217 | + | 109.822i | −0.937030 | + | 0.540995i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −201.805 | + | 349.537i | −0.984417 | + | 1.70506i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 33.9928 | − | 7.53502i | 0.164216 | − | 0.0364011i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 72.4925 | − | 125.561i | 0.346854 | − | 0.600769i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −91.8563 | + | 53.0332i | −0.435338 | + | 0.251342i | −0.701618 | − | 0.712553i | \(-0.747539\pi\) |
0.266280 | + | 0.963896i | \(0.414205\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 287.006 | + | 44.1786i | 1.34745 | + | 0.207411i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 361.789i | 1.68274i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −275.973 | −1.27176 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.41814 | − | 41.6954i | 0.0293066 | − | 0.190390i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.7330 | + | 18.5900i | 0.0485654 | + | 0.0841177i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 55.1700 | + | 31.8524i | 0.247399 | + | 0.142836i | 0.618573 | − | 0.785728i | \(-0.287711\pi\) |
−0.371174 | + | 0.928563i | \(0.621045\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 399.813 | − | 366.340i | 1.77695 | − | 1.62818i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −304.643 | − | 175.886i | −1.34204 | − | 0.774827i | −0.354933 | − | 0.934892i | \(-0.615496\pi\) |
−0.987106 | + | 0.160065i | \(0.948830\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 102.232 | + | 177.072i | 0.446429 | + | 0.773238i | 0.998151 | − | 0.0607903i | \(-0.0193621\pi\) |
−0.551721 | + | 0.834029i | \(0.686029\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −73.5369 | + | 28.5958i | −0.318342 | + | 0.123791i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 236.626 | 1.01556 | 0.507782 | − | 0.861486i | \(-0.330466\pi\) | ||||
0.507782 | + | 0.861486i | \(0.330466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 425.167i | 1.80922i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −74.5795 | + | 92.9215i | −0.314682 | + | 0.392074i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.1578 | − | 9.32873i | 0.0676060 | − | 0.0390324i | −0.465816 | − | 0.884882i | \(-0.654239\pi\) |
0.533422 | + | 0.845849i | \(0.320906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −37.2290 | + | 64.4826i | −0.154477 | + | 0.267562i | −0.932869 | − | 0.360217i | \(-0.882703\pi\) |
0.778391 | + | 0.627779i | \(0.216036\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −168.050 | + | 175.523i | −0.691564 | + | 0.722316i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 51.2826 | − | 88.8241i | 0.209317 | − | 0.362547i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −51.0894 | + | 29.4965i | −0.206840 | + | 0.119419i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −177.194 | + | 220.773i | −0.711622 | + | 0.886637i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 206.637i | − | 0.823257i | −0.911352 | − | 0.411628i | \(-0.864960\pi\) | ||
0.911352 | − | 0.411628i | \(-0.135040\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.5291 | 0.0653325 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −318.770 | + | 123.958i | −1.25008 | + | 0.486109i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 148.678 | + | 257.517i | 0.578513 | + | 1.00201i | 0.995650 | + | 0.0931698i | \(0.0296999\pi\) |
−0.417138 | + | 0.908843i | \(0.636967\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 174.390 | + | 100.684i | 0.673322 | + | 0.388743i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −236.773 | + | 216.950i | −0.907175 | + | 0.831226i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 123.730 | + | 71.4357i | 0.470457 | + | 0.271619i | 0.716431 | − | 0.697658i | \(-0.245774\pi\) |
−0.245974 | + | 0.969276i | \(0.579108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 213.815 | + | 370.338i | 0.806847 | + | 1.39750i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 37.3563 | − | 242.685i | 0.139911 | − | 0.908934i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 370.517 | 1.37738 | 0.688692 | − | 0.725054i | \(-0.258185\pi\) | ||||
0.688692 | + | 0.725054i | \(0.258185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 368.022i | − | 1.35801i | −0.734132 | − | 0.679007i | \(-0.762411\pi\) | ||
0.734132 | − | 0.679007i | \(-0.237589\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 31.7304 | + | 4.88423i | 0.116229 | + | 0.0178909i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 222.942 | − | 128.716i | 0.810700 | − | 0.468058i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.3234 | + | 26.5409i | −0.0553191 | + | 0.0958154i | −0.892359 | − | 0.451327i | \(-0.850951\pi\) |
0.837040 | + | 0.547142i | \(0.184284\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −393.932 | + | 87.3210i | −1.41194 | + | 0.312979i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −231.041 | + | 400.176i | −0.822212 | + | 1.42411i | 0.0818203 | + | 0.996647i | \(0.473927\pi\) |
−0.904032 | + | 0.427465i | \(0.859407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −422.693 | + | 244.042i | −1.49361 | + | 0.862339i | −0.999973 | − | 0.00732653i | \(-0.997668\pi\) |
−0.493642 | + | 0.869665i | \(0.664335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −340.663 | − | 876.050i | −1.19531 | − | 3.07386i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 269.081i | − | 0.937563i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −136.537 | −0.472447 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −37.3886 | − | 30.0084i | −0.128483 | − | 0.103122i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 215.030 | + | 372.442i | 0.733890 | + | 1.27113i | 0.955209 | + | 0.295933i | \(0.0956305\pi\) |
−0.221319 | + | 0.975201i | \(0.571036\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 214.866 | + | 124.053i | 0.728358 | + | 0.420518i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −95.9207 | + | 64.0863i | −0.322965 | + | 0.215779i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.82449 | − | 3.36277i | −0.0194799 | − | 0.0112467i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −120.599 | − | 208.884i | −0.400663 | − | 0.693968i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 236.931 | + | 190.163i | 0.781951 | + | 0.627600i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 433.120 | 1.42007 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 276.184i | − | 0.899621i | −0.893124 | − | 0.449810i | \(-0.851492\pi\) | ||
0.893124 | − | 0.449810i | \(-0.148508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −110.996 | − | 285.437i | −0.359209 | − | 0.923743i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 172.998 | − | 99.8806i | 0.556264 | − | 0.321159i | −0.195380 | − | 0.980728i | \(-0.562594\pi\) |
0.751645 | + | 0.659568i | \(0.229261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 59.3385 | − | 102.777i | 0.189580 | − | 0.328362i | −0.755530 | − | 0.655114i | \(-0.772621\pi\) |
0.945110 | + | 0.326752i | \(0.105954\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −153.832 | + | 487.846i | −0.488356 | + | 1.54872i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 193.261 | − | 334.738i | 0.609657 | − | 1.05596i | −0.381640 | − | 0.924311i | \(-0.624641\pi\) |
0.991297 | − | 0.131645i | \(-0.0420260\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −132.028 | + | 76.2267i | −0.413882 | + | 0.238955i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −216.884 | − | 33.3848i | −0.675652 | − | 0.104003i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 419.001i | 1.29722i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −104.746 | −0.322297 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.4881 | − | 100.618i | 0.0473641 | − | 0.307701i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −141.726 | − | 245.476i | −0.430778 | − | 0.746129i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 282.733 | + | 163.236i | 0.854179 | + | 0.493161i | 0.862059 | − | 0.506808i | \(-0.169175\pi\) |
−0.00787942 | + | 0.999969i | \(0.502508\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 280.788 | + | 88.5407i | 0.843206 | + | 0.265888i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −526.278 | − | 303.847i | −1.57098 | − | 0.907005i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 57.4906 | + | 99.5766i | 0.170595 | + | 0.295479i | 0.938628 | − | 0.344931i | \(-0.112098\pi\) |
−0.768033 | + | 0.640410i | \(0.778764\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 77.8934 | − | 30.2898i | 0.229774 | − | 0.0893506i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −191.551 | −0.561733 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 370.004i | 1.07873i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 67.0753 | − | 83.5717i | 0.194421 | − | 0.242237i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 502.945 | − | 290.375i | 1.44941 | − | 0.836817i | 0.450963 | − | 0.892543i | \(-0.351081\pi\) |
0.998446 | + | 0.0557260i | \(0.0177473\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −175.463 | + | 303.912i | −0.502761 | + | 0.870807i | 0.497234 | + | 0.867616i | \(0.334349\pi\) |
−0.999995 | + | 0.00319067i | \(0.998984\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 46.8383 | − | 3.06797i | 0.133442 | − | 0.00874066i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −67.7870 | + | 117.411i | −0.192031 | + | 0.332608i | −0.945923 | − | 0.324390i | \(-0.894841\pi\) |
0.753892 | + | 0.656998i | \(0.228174\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 773.995 | − | 446.866i | 2.18027 | − | 1.25878i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 142.726 | − | 177.828i | 0.399794 | − | 0.498118i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 108.852i | 0.303210i | 0.988441 | + | 0.151605i | \(0.0484441\pi\) | ||||
−0.988441 | + | 0.151605i | \(0.951556\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −790.506 | −2.18977 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 287.279 | − | 111.712i | 0.791403 | − | 0.307747i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −64.9195 | − | 112.444i | −0.177862 | − | 0.308065i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6619 | + | 8.46503i | 0.0399506 | + | 0.0230655i | 0.519842 | − | 0.854262i | \(-0.325991\pi\) |
−0.479892 | + | 0.877328i | \(0.659324\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −85.1402 | − | 384.094i | −0.230732 | − | 1.04090i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −246.898 | − | 142.547i | −0.665493 | − | 0.384223i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5300 | − | 32.0949i | −0.0496783 | − | 0.0860454i | 0.840117 | − | 0.542405i | \(-0.182486\pi\) |
−0.889795 | + | 0.456360i | \(0.849153\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 148.557 | − | 965.102i | 0.396153 | − | 2.57361i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 62.0318 | 0.164540 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 531.193i | − | 1.40156i | −0.713375 | − | 0.700782i | \(-0.752834\pi\) | ||
0.713375 | − | 0.700782i | \(-0.247166\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 349.598 | + | 53.8133i | 0.917580 | + | 0.141242i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 324.004 | − | 187.064i | 0.845963 | − | 0.488417i | −0.0133235 | − | 0.999911i | \(-0.504241\pi\) |
0.859287 | + | 0.511494i | \(0.170908\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −121.418 | + | 210.303i | −0.315373 | + | 0.546241i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −238.241 | − | 260.009i | −0.615609 | − | 0.671857i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 271.593 | − | 470.412i | 0.698182 | − | 1.20929i | −0.270915 | − | 0.962603i | \(-0.587326\pi\) |
0.969096 | − | 0.246683i | \(-0.0793406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.3688 | + | 23.8843i | −0.105802 | + | 0.0610851i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 92.3044 | + | 237.370i | 0.234871 | + | 0.603995i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 366.709i | 0.928378i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 606.097 | 1.52669 | 0.763346 | − | 0.645990i | \(-0.223555\pi\) | ||||
0.763346 | + | 0.645990i | \(0.223555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 488.711 | + | 392.243i | 1.22484 | + | 0.983065i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −293.529 | − | 508.408i | −0.731994 | − | 1.26785i | −0.956030 | − | 0.293269i | \(-0.905257\pi\) |
0.224036 | − | 0.974581i | \(-0.428077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 67.4982 | + | 38.9701i | 0.167489 | + | 0.0967000i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −65.2245 | + | 745.040i | −0.161048 | + | 1.83961i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 121.043 | + | 69.8844i | 0.297404 | + | 0.171706i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 129.882 | + | 224.961i | 0.317559 | + | 0.550028i | 0.979978 | − | 0.199105i | \(-0.0638036\pi\) |
−0.662419 | + | 0.749133i | \(0.730470\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.6223 | + | 14.9464i | 0.0453097 | + | 0.0363659i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −165.408 | −0.400503 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 871.267i | 2.09944i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.5031 | + | 57.8689i | 0.0539642 | + | 0.138774i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −297.997 | + | 172.049i | −0.711210 | + | 0.410617i | −0.811509 | − | 0.584340i | \(-0.801353\pi\) |
0.100299 | + | 0.994957i | \(0.468020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 153.263 | − | 265.460i | 0.364046 | − | 0.630546i | −0.624576 | − | 0.780964i | \(-0.714728\pi\) |
0.988623 | + | 0.150417i | \(0.0480617\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −279.975 | − | 305.557i | −0.661880 | − | 0.722356i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −371.984 | + | 644.295i | −0.875256 | + | 1.51599i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −250.068 | + | 144.377i | −0.585640 | + | 0.338119i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.0239 | + | 3.39011i | 0.0513376 | + | 0.00790235i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 208.029i | − | 0.482667i | −0.970442 | − | 0.241333i | \(-0.922415\pi\) | ||
0.970442 | − | 0.241333i | \(-0.0775847\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 353.874 | 0.817260 | 0.408630 | − | 0.912700i | \(-0.366007\pi\) | ||||
0.408630 | + | 0.912700i | \(0.366007\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −150.368 | + | 976.867i | −0.345674 | + | 2.24567i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −65.6392 | − | 113.690i | −0.150204 | − | 0.260161i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −200.356 | − | 115.675i | −0.456391 | − | 0.263497i | 0.254135 | − | 0.967169i | \(-0.418209\pi\) |
−0.710525 | + | 0.703672i | \(0.751543\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.6358 | + | 97.6055i | 0.0490607 | + | 0.221328i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 221.434 | + | 127.845i | 0.499851 | + | 0.288589i | 0.728652 | − | 0.684884i | \(-0.240147\pi\) |
−0.228801 | + | 0.973473i | \(0.573480\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −377.859 | − | 654.471i | −0.849121 | − | 1.47072i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −366.908 | + | 142.677i | −0.820824 | + | 0.319188i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 323.060 | 0.719509 | 0.359755 | − | 0.933047i | \(-0.382860\pi\) | ||||
0.359755 | + | 0.933047i | \(0.382860\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 186.767i | − | 0.414118i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 444.392 | − | 553.685i | 0.980998 | − | 1.22226i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 85.5702 | − | 49.4039i | 0.188066 | − | 0.108580i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 277.264 | − | 480.235i | 0.606704 | − | 1.05084i | −0.385076 | − | 0.922885i | \(-0.625825\pi\) |
0.991780 | − | 0.127957i | \(-0.0408418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 147.465 | − | 298.998i | 0.321274 | − | 0.651411i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −368.753 | + | 638.699i | −0.799898 | + | 1.38546i | 0.119784 | + | 0.992800i | \(0.461780\pi\) |
−0.919682 | + | 0.392664i | \(0.871553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −116.461 | + | 67.2386i | −0.251535 | + | 0.145224i | −0.620467 | − | 0.784233i | \(-0.713057\pi\) |
0.368932 | + | 0.929456i | \(0.379724\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −777.315 | + | 968.486i | −1.67164 | + | 2.08277i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 595.000i | 1.27409i | 0.770827 | + | 0.637045i | \(0.219844\pi\) | ||||
−0.770827 | + | 0.637045i | \(0.780156\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 405.139 | 0.863835 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 418.786 | − | 162.850i | 0.889143 | − | 0.345754i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −83.7073 | − | 144.985i | −0.176971 | − | 0.306523i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1770.66 | − | 1022.29i | −3.72771 | − | 2.15219i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −397.533 | − | 125.354i | −0.833402 | − | 0.262796i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −388.924 | − | 224.545i | −0.811950 | − | 0.468779i | 0.0356829 | − | 0.999363i | \(-0.488639\pi\) |
−0.847632 | + | 0.530584i | \(0.821973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.4352 | − | 49.2513i | −0.0591169 | − | 0.102394i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.8690 | + | 70.6103i | −0.0225031 | + | 0.146191i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −147.552 | −0.304231 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 120.044i | − | 0.246497i | −0.992376 | − | 0.123249i | \(-0.960669\pi\) | ||
0.992376 | − | 0.123249i | \(-0.0393312\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −451.775 | − | 69.5413i | −0.923875 | − | 0.142211i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −372.302 | + | 214.949i | −0.758252 | + | 0.437777i | −0.828668 | − | 0.559741i | \(-0.810901\pi\) |
0.0704158 | + | 0.997518i | \(0.477567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 220.292 | − | 381.557i | 0.446840 | − | 0.773950i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −106.774 | + | 338.611i | −0.215705 | + | 0.684062i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −297.918 | + | 516.010i | −0.599433 | + | 1.03825i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 639.117 | − | 368.994i | 1.28080 | − | 0.739467i | 0.303802 | − | 0.952735i | \(-0.401744\pi\) |
0.976994 | + | 0.213268i | \(0.0684107\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.0719 | − | 69.6182i | −0.0540358 | − | 0.138959i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 951.782i | 1.89221i | 0.323859 | + | 0.946105i | \(0.395020\pi\) | ||||
−0.323859 | + | 0.946105i | \(0.604980\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 935.036 | 1.85156 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 388.326 | + | 311.673i | 0.765929 | + | 0.614741i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.8898 | + | 65.6271i | 0.0744398 | + | 0.128933i | 0.900843 | − | 0.434146i | \(-0.142950\pi\) |
−0.826403 | + | 0.563079i | \(0.809616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 74.9644 | + | 43.2807i | 0.146701 | + | 0.0846981i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 821.710 | + | 405.265i | 1.60177 | + | 0.789991i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −816.300 | − | 471.291i | −1.58505 | − | 0.915128i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −98.3710 | − | 170.384i | −0.190273 | − | 0.329562i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −252.891 | − | 202.973i | −0.487267 | − | 0.391084i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.6152 | 0.0472461 | 0.0236230 | − | 0.999721i | \(-0.492480\pi\) | ||||
0.0236230 | + | 0.999721i | \(0.492480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 165.798i | 0.317013i | 0.987358 | + | 0.158506i | \(0.0506678\pi\) | ||||
−0.987358 | + | 0.158506i | \(0.949332\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 403.259 | + | 1037.02i | 0.768111 | + | 1.97528i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 479.410 | − | 276.787i | 0.909696 | − | 0.525213i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −257.017 | + | 445.166i | −0.485854 | + | 0.841524i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −236.108 | + | 52.3369i | −0.444648 | + | 0.0985630i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.9968 | + | 65.8124i | −0.0712886 | + | 0.123476i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −584.892 | + | 337.687i | −1.09326 | + | 0.631191i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 929.013 | + | 143.002i | 1.73001 | + | 0.266298i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 47.4611i | 0.0880539i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −184.323 | −0.340708 | −0.170354 | − | 0.985383i | \(-0.554491\pi\) | ||||
−0.170354 | + | 0.985383i | \(0.554491\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.39688 | + | 61.0469i | −0.0173055 | + | 0.112425i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −156.662 | − | 271.346i | −0.287453 | − | 0.497883i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 803.354 | + | 463.817i | 1.46865 | + | 0.847928i | 0.999383 | − | 0.0351259i | \(-0.0111832\pi\) |
0.469272 | + | 0.883054i | \(0.344517\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −311.272 | + | 285.212i | −0.566980 | + | 0.519512i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1048.60 | + | 605.411i | 1.90309 | + | 1.09875i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −122.240 | − | 211.725i | −0.221048 | − | 0.382866i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 844.531 | − | 328.407i | 1.52168 | − | 0.591724i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −492.087 | −0.883459 | −0.441730 | − | 0.897148i | \(-0.645635\pi\) | ||||
−0.441730 | + | 0.897148i | \(0.645635\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 68.1193i | 0.121859i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 99.0654 | − | 123.429i | 0.176587 | − | 0.220017i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −626.453 | + | 361.683i | −1.11271 | + | 0.642421i | −0.939529 | − | 0.342470i | \(-0.888736\pi\) |
−0.173177 | + | 0.984891i | \(0.555403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 128.612 | − | 222.762i | 0.227631 | − | 0.394269i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −210.695 | − | 451.902i | −0.371595 | − | 0.797005i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 435.816 | − | 754.855i | 0.765933 | − | 1.32664i | −0.173819 | − | 0.984778i | \(-0.555611\pi\) |
0.939752 | − | 0.341857i | \(-0.111056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −210.649 | + | 121.618i | −0.368912 | + | 0.212991i | −0.672983 | − | 0.739658i | \(-0.734987\pi\) |
0.304071 | + | 0.952649i | \(0.401654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 51.3061 | − | 63.9243i | 0.0895395 | − | 0.111561i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 233.094i | − | 0.405382i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −201.625 | −0.349436 | −0.174718 | − | 0.984619i | \(-0.555901\pi\) | ||||
−0.174718 | + | 0.984619i | \(0.555901\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 367.526 | − | 142.917i | 0.634761 | − | 0.246835i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −290.430 | − | 503.039i | −0.499879 | − | 0.865815i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −171.370 | − | 98.9406i | −0.293945 | − | 0.169710i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 106.513 | − | 97.5960i | 0.182074 | − | 0.166831i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −688.983 | − | 397.784i | −1.17374 | − | 0.677656i | −0.219178 | − | 0.975685i | \(-0.570338\pi\) |
−0.954557 | + | 0.298029i | \(0.903671\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 760.672 | + | 1317.52i | 1.29146 | + | 2.23688i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 57.7207 | − | 374.983i | 0.0976662 | − | 0.634489i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1078.05 | −1.81796 | −0.908980 | − | 0.416839i | \(-0.863138\pi\) | ||||
−0.908980 | + | 0.416839i | \(0.863138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 701.789i | − | 1.17948i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 225.367 | + | 34.6905i | 0.377499 | + | 0.0581080i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 209.699 | − | 121.070i | 0.350082 | − | 0.202120i | −0.314639 | − | 0.949211i | \(-0.601883\pi\) |
0.664722 | + | 0.747091i | \(0.268550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 135.406 | − | 234.529i | 0.225300 | − | 0.390232i | −0.731109 | − | 0.682261i | \(-0.760997\pi\) |
0.956410 | + | 0.292029i | \(0.0943303\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 578.307 | − | 128.191i | 0.959050 | − | 0.212588i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 474.333 | − | 821.569i | 0.784022 | − | 1.35797i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 335.657 | − | 193.792i | 0.552977 | − | 0.319261i | −0.197345 | − | 0.980334i | \(-0.563232\pi\) |
0.750322 | + | 0.661073i | \(0.229899\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −238.813 | − | 614.133i | −0.392140 | − | 1.00843i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 80.0524i | 0.131019i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1120.09 | −1.82722 | −0.913610 | − | 0.406591i | \(-0.866718\pi\) | ||||
−0.913610 | + | 0.406591i | \(0.866718\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −944.299 | − | 757.902i | −1.53545 | − | 1.23236i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −266.289 | − | 461.226i | −0.431587 | − | 0.747530i | 0.565423 | − | 0.824801i | \(-0.308713\pi\) |
−0.997010 | + | 0.0772706i | \(0.975379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 761.814 | + | 439.833i | 1.23072 | + | 0.710555i | 0.967179 | − | 0.254095i | \(-0.0817774\pi\) |
0.263537 | + | 0.964649i | \(0.415111\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.82723 | + | 104.230i | 0.0109939 | + | 0.167843i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 436.325 | + | 251.912i | 0.700361 | + | 0.404354i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −749.506 | − | 1298.18i | −1.19921 | − | 2.07709i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 339.211 | + | 272.253i | 0.541006 | + | 0.434216i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −403.926 | −0.642172 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 310.499i | − | 0.492075i | −0.969260 | − | 0.246037i | \(-0.920871\pi\) | ||
0.969260 | − | 0.246037i | \(-0.0791286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −115.323 | − | 296.566i | −0.182186 | − | 0.468509i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 942.792 | − | 544.321i | 1.48471 | − | 0.857199i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.65572 | − | 16.7242i | 0.0151581 | − | 0.0262546i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −261.986 | + | 830.832i | −0.409994 | + | 1.30021i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −275.610 | + | 477.371i | −0.429969 | + | 0.744728i | −0.996870 | − | 0.0790578i | \(-0.974809\pi\) |
0.566901 | + | 0.823786i | \(0.308142\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −352.044 | + | 203.253i | −0.547503 | + | 0.316101i | −0.748114 | − | 0.663570i | \(-0.769041\pi\) |
0.200611 | + | 0.979671i | \(0.435707\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1072.73 | − | 165.125i | −1.66315 | − | 0.256008i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 652.891i | − | 1.00910i | −0.863381 | − | 0.504552i | \(-0.831658\pi\) | ||
0.863381 | − | 0.504552i | \(-0.168342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −114.808 | −0.176900 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 125.957 | − | 818.281i | 0.193483 | − | 1.25696i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 513.767 | + | 889.870i | 0.786779 | + | 1.36274i | 0.927930 | + | 0.372754i | \(0.121586\pi\) |
−0.141151 | + | 0.989988i | \(0.545080\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 678.838 | + | 391.927i | 1.03639 | + | 0.598362i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 120.701 | + | 38.0606i | 0.183715 | + | 0.0579309i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.5780 | + | 11.8807i | 0.0312261 | + | 0.0180284i | 0.515532 | − | 0.856870i | \(-0.327594\pi\) |
−0.484306 | + | 0.874899i | \(0.660928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 328.164 | + | 568.396i | 0.496465 | + | 0.859903i | 0.999992 | − | 0.00407665i | \(-0.00129764\pi\) |
−0.503526 | + | 0.863980i | \(0.667964\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −60.0195 | + | 23.3393i | −0.0905271 | + | 0.0352026i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1928.67 | 2.90025 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 138.041i | 0.206957i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −119.625 | + | 149.046i | −0.178812 | + | 0.222789i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −173.571 | + | 100.211i | −0.258675 | + | 0.149346i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 405.169 | − | 701.773i | 0.602034 | − | 1.04275i | −0.390479 | − | 0.920612i | \(-0.627691\pi\) |
0.992513 | − | 0.122141i | \(-0.0389760\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 903.748 | + | 1352.68i | 1.33889 | + | 2.00397i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −199.580 | + | 345.683i | −0.294801 | + | 0.510610i | −0.974939 | − | 0.222474i | \(-0.928587\pi\) |
0.680138 | + | 0.733084i | \(0.261920\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 85.1912 | − | 49.1852i | 0.125466 | − | 0.0724377i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 660.557 | − | 823.014i | 0.969981 | − | 1.20854i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 203.612i | 0.298114i | 0.988829 | + | 0.149057i | \(0.0476238\pi\) | ||||
−0.988829 | + | 0.149057i | \(0.952376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 73.4918 | 0.107287 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −571.691 | + | 222.309i | −0.832156 | + | 0.323594i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.2580 | + | 69.7288i | 0.0584296 | + | 0.101203i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −255.646 | − | 147.597i | −0.369965 | − | 0.213599i | 0.303478 | − | 0.952838i | \(-0.401852\pi\) |
−0.673443 | + | 0.739239i | \(0.735185\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −51.2255 | − | 231.094i | −0.0739185 | − | 0.333469i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 165.495 | + | 95.5487i | 0.238123 | + | 0.137480i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 269.875 | + | 467.437i | 0.387195 | + | 0.670641i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −107.999 | + | 701.615i | −0.154505 | + | 1.00374i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 283.069 | 0.403808 | 0.201904 | − | 0.979405i | \(-0.435287\pi\) | ||||
0.201904 | + | 0.979405i | \(0.435287\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1110.08i | − | 1.57906i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1260.65 | − | 194.051i | −1.78816 | − | 0.275250i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −539.857 | + | 311.686i | −0.763588 | + | 0.440858i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −209.399 | + | 362.690i | −0.295344 | + | 0.511551i | −0.975065 | − | 0.221920i | \(-0.928768\pi\) |
0.679721 | + | 0.733471i | \(0.262101\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −241.481 | − | 263.545i | −0.339635 | − | 0.370667i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −86.7210 | + | 150.205i | −0.121628 | + | 0.210666i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 59.3937 | − | 34.2910i | 0.0830681 | − | 0.0479594i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.2858 | + | 52.1670i | 0.0282926 | + | 0.0727573i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 454.879i | − | 0.632655i | −0.948650 | − | 0.316328i | \(-0.897550\pi\) | ||
0.948650 | − | 0.316328i | \(-0.102450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 628.404 | 0.871572 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −174.204 | − | 139.818i | −0.240946 | − | 0.193385i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1074.95 | + | 1861.87i | 1.48269 | + | 2.56810i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −207.375 | − | 119.728i | −0.285247 | − | 0.164688i | 0.350549 | − | 0.936544i | \(-0.385995\pi\) |
−0.635797 | + | 0.771857i | \(0.719328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −443.739 | − | 578.392i | −0.608695 | − | 0.793404i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 419.002 | + | 241.911i | 0.573190 | + | 0.330931i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −210.973 | − | 365.416i | −0.287822 | − | 0.498522i | 0.685468 | − | 0.728103i | \(-0.259598\pi\) |
−0.973289 | + | 0.229581i | \(0.926264\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 239.964 | + | 192.597i | 0.326482 | + | 0.262037i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 281.204 | 0.381552 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 150.203i | − | 0.203251i | −0.994823 | − | 0.101626i | \(-0.967596\pi\) | ||
0.994823 | − | 0.101626i | \(-0.0324044\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −64.1416 | − | 164.947i | −0.0865608 | − | 0.222600i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 726.756 | − | 419.593i | 0.978137 | − | 0.564728i | 0.0764298 | − | 0.997075i | \(-0.475648\pi\) |
0.901707 | + | 0.432347i | \(0.142315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −605.810 | + | 1049.29i | −0.813168 | + | 1.40845i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −573.735 | − | 626.157i | −0.768052 | − | 0.838229i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 225.130 | − | 389.937i | 0.300575 | − | 0.520611i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −634.488 | + | 366.322i | −0.844858 | + | 0.487779i | −0.858912 | − | 0.512122i | \(-0.828859\pi\) |
0.0140549 | + | 0.999901i | \(0.495526\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 612.696 | + | 94.3117i | 0.813673 | + | 0.125248i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2185.09i | − | 2.89415i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1455.19 | −1.92231 | −0.961153 | − | 0.276015i | \(-0.910986\pi\) | ||||
−0.961153 | + | 0.276015i | \(0.910986\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.54409 | + | 49.0102i | −0.00993951 | + | 0.0645720i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 365.230 | + | 632.596i | 0.479934 | + | 0.831270i | 0.999735 | − | 0.0230176i | \(-0.00732737\pi\) |
−0.519801 | + | 0.854287i | \(0.673994\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 180.902 | + | 104.444i | 0.237093 | + | 0.136886i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −222.054 | − | 1001.75i | −0.290267 | − | 1.30948i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.4559 | + | 23.3572i | 0.0527456 | + | 0.0304527i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 430.746 | + | 746.074i | 0.560138 | + | 0.970187i | 0.997484 | + | 0.0708938i | \(0.0225851\pi\) |
−0.437346 | + | 0.899293i | \(0.644082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −831.417 | + | 323.307i | −1.07836 | + | 0.419335i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −981.517 | −1.26975 | −0.634875 | − | 0.772615i | \(-0.718948\pi\) | ||||
−0.634875 | + | 0.772615i | \(0.718948\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2701.26i | 3.48550i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −378.131 | + | 471.128i | −0.486655 | + | 0.606342i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1284.62 | + | 741.675i | −1.64906 | + | 0.952085i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −206.783 | + | 358.159i | −0.264767 | + | 0.458590i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −535.208 | − | 801.068i | −0.683535 | − | 1.02308i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 691.467 | − | 1197.66i | 0.880850 | − | 1.52568i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 614.292 | − | 354.662i | 0.780549 | − | 0.450650i | −0.0560758 | − | 0.998427i | \(-0.517859\pi\) |
0.836625 | + | 0.547776i | \(0.184526\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −268.284 | + | 334.266i | −0.340031 | + | 0.423658i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 171.486i | 0.216797i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 81.5498 | 0.102837 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1195.67 | + | 464.950i | −1.50398 | + | 0.584843i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −591.856 | − | 1025.12i | −0.742605 | − | 1.28623i | −0.951306 | − | 0.308249i | \(-0.900257\pi\) |
0.208701 | − | 0.977980i | \(-0.433076\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 492.402 | + | 284.288i | 0.616273 | + | 0.355805i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 702.531 | + | 221.529i | 0.877067 | + | 0.276565i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 52.0323 | + | 30.0409i | 0.0647974 | + | 0.0374108i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 109.940 | + | 190.421i | 0.136571 | + | 0.236548i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −169.108 | + | 1098.61i | −0.209551 | + | 1.36135i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 522.491 | 0.645847 | 0.322924 | − | 0.946425i | \(-0.395334\pi\) | ||||
0.322924 | + | 0.946425i | \(0.395334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 115.368i | 0.142254i | 0.997467 | + | 0.0711271i | \(0.0226596\pi\) | ||||
−0.997467 | + | 0.0711271i | \(0.977340\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1091.21 | + | 167.969i | 1.34221 | + | 0.206604i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1218.34 | + | 703.410i | −1.49490 | + | 0.863080i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −664.823 | + | 1151.51i | −0.813737 | + | 1.40943i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.9642 | + | 91.8538i | −0.0353654 | + | 0.112154i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 417.973 | − | 723.951i | 0.509102 | − | 0.881791i | −0.490842 | − | 0.871249i | \(-0.663311\pi\) |
0.999944 | − | 0.0105427i | \(-0.00335589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −629.895 | + | 363.670i | −0.765364 | + | 0.441883i | −0.831218 | − | 0.555946i | \(-0.812356\pi\) |
0.0658543 | + | 0.997829i | \(0.479023\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 279.899 | + | 719.789i | 0.339272 | + | 0.872472i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1271.70i | 1.53773i | 0.639413 | + | 0.768864i | \(0.279178\pi\) | ||||
−0.639413 | + | 0.768864i | \(0.720822\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 577.896 | 0.697100 | 0.348550 | − | 0.937290i | \(-0.386674\pi\) | ||||
0.348550 | + | 0.937290i | \(0.386674\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −71.7020 | − | 57.5486i | −0.0862840 | − | 0.0692522i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −68.5803 | − | 118.785i | −0.0823293 | − | 0.142599i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −199.096 | − | 114.948i | −0.238439 | − | 0.137663i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −79.1186 | − | 1207.89i | −0.0945264 | − | 1.44312i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −620.279 | − | 358.118i | −0.739308 | − | 0.426839i | 0.0825099 | − | 0.996590i | \(-0.473706\pi\) |
−0.821818 | + | 0.569751i | \(0.807040\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −216.096 | − | 374.289i | −0.256951 | − | 0.445053i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1081.10 | − | 867.701i | −1.28245 | − | 1.02930i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1532.51 | 1.81362 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 632.460i | 0.746706i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −530.681 | − | 1364.70i | −0.625066 | − | 1.60742i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 109.600 | − | 63.2776i | 0.128790 | − | 0.0743567i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −522.638 | + | 905.235i | −0.612705 | + | 1.06124i | 0.378077 | + | 0.925774i | \(0.376585\pi\) |
−0.990782 | + | 0.135463i | \(0.956748\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2753.04 | − | 610.253i | 3.21993 | − | 0.713746i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −411.368 | + | 712.510i | −0.480009 | + | 0.831400i | −0.999737 | − | 0.0229317i | \(-0.992700\pi\) |
0.519728 | + | 0.854332i | \(0.326033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.7624 | − | 31.0397i | 0.0625871 | − | 0.0361347i | −0.468380 | − | 0.883527i | \(-0.655162\pi\) |
0.530967 | + | 0.847392i | \(0.321829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 797.845 | + | 122.811i | 0.926649 | + | 0.142638i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1250.20i | − | 1.44867i | −0.689448 | − | 0.724335i | \(-0.742147\pi\) | ||
0.689448 | − | 0.724335i | \(-0.257853\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −998.022 | −1.15378 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 62.3171 | − | 404.843i | 0.0718767 | − | 0.466947i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −84.8456 | − | 146.957i | −0.0976360 | − | 0.169110i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −99.0899 | − | 57.2096i | −0.113766 | − | 0.0656827i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 106.042 | − | 97.1639i | 0.121468 | − | 0.111299i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1735.16 | + | 1001.80i | 1.98304 | + | 1.14491i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −105.302 | − | 182.388i | −0.120071 | − | 0.207968i | 0.799725 | − | 0.600367i | \(-0.204979\pi\) |
−0.919795 | + | 0.392398i | \(0.871645\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1202.46 | + | 467.593i | −1.36799 | + | 0.531960i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −366.361 | −0.415846 | −0.207923 | − | 0.978145i | \(-0.566670\pi\) | ||||
−0.207923 | + | 0.978145i | \(0.566670\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 266.329i | 0.301619i | 0.988563 | + | 0.150809i | \(0.0481879\pi\) | ||||
−0.988563 | + | 0.150809i | \(0.951812\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −465.893 | + | 580.474i | −0.526433 | + | 0.655903i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −175.292 | + | 101.205i | −0.197623 | + | 0.114098i | −0.595546 | − | 0.803321i | \(-0.703064\pi\) |
0.397923 | + | 0.917419i | \(0.369731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −362.890 | + | 628.544i | −0.408200 | + | 0.707023i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −146.242 | − | 313.662i | −0.164132 | − | 0.352034i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −781.286 | + | 1353.23i | −0.874901 | + | 1.51537i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2505.35 | − | 1446.47i | 2.79928 | − | 1.61616i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.6292 | − | 15.7353i | 0.0140794 | − | 0.0175421i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1599.71i | − | 1.77943i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 571.869 | 0.634705 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 674.401 | − | 262.250i | 0.746845 | − | 0.290420i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 95.0495 | + | 164.630i | 0.105027 | + | 0.181912i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1048.89 | − | 605.576i | −1.15644 | − | 0.667669i | −0.205989 | − | 0.978554i | \(-0.566041\pi\) |
−0.950448 | + | 0.310885i | \(0.899375\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −671.986 | + | 615.727i | −0.739258 | + | 0.677368i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −640.792 | − | 369.962i | −0.703394 | − | 0.406105i | 0.105216 | − | 0.994449i | \(-0.466447\pi\) |
−0.808610 | + | 0.588344i | \(0.799780\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −201.585 | − | 349.156i | −0.220794 | − | 0.382427i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −197.681 | + | 1284.23i | −0.216045 | + | 1.40353i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −522.583 | −0.569883 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1080.71i | − | 1.17596i | −0.808874 | − | 0.587982i | \(-0.799922\pi\) | ||
0.808874 | − | 0.587982i | \(-0.200078\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 818.906 | + | 126.053i | 0.889149 | + | 0.136866i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 145.731 | − | 84.1380i | 0.157889 | − | 0.0911571i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 985.512 | − | 1706.96i | 1.06542 | − | 1.84536i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 897.002 | − | 198.834i | 0.967640 | − | 0.214492i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 594.530 | − | 1029.76i | 0.639968 | − | 1.10846i | −0.345472 | − | 0.938429i | \(-0.612281\pi\) |
0.985439 | − | 0.170027i | \(-0.0543856\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 326.446 | − | 188.474i | 0.350640 | − | 0.202442i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 217.195 | + | 558.540i | 0.232792 | + | 0.598649i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 487.107i | − | 0.520970i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1165.30 | 1.24364 | 0.621822 | − | 0.783158i | \(-0.286393\pi\) | ||||
0.621822 | + | 0.783158i | \(0.286393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 277.660 | + | 222.852i | 0.295698 | + | 0.237329i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 431.742 | + | 747.800i | 0.458812 | + | 0.794686i | 0.998898 | − | 0.0469234i | \(-0.0149417\pi\) |
−0.540086 | + | 0.841610i | \(0.681608\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −146.454 | − | 84.5552i | −0.155306 | − | 0.0896662i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1376.29 | − | 678.783i | −1.45639 | − | 0.718289i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 994.656 | + | 574.265i | 1.05032 | + | 0.606404i | 0.922740 | − | 0.385423i | \(-0.125945\pi\) |
0.127583 | + | 0.991828i | \(0.459278\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.2233 | − | 21.1714i | −0.0128802 | − | 0.0223092i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 904.318 | + | 725.813i | 0.950913 | + | 0.763210i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1447.80 | −1.51920 | −0.759600 | − | 0.650391i | \(-0.774605\pi\) | ||||
−0.759600 | + | 0.650391i | \(0.774605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 252.274i | − | 0.264161i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −165.759 | − | 426.266i | −0.173207 | − | 0.445419i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −42.4316 | + | 24.4979i | −0.0442456 | + | 0.0255452i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 524.483 | − | 908.431i | 0.545768 | − | 0.945297i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 197.977 | − | 627.842i | 0.205584 | − | 0.651965i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 606.831 | − | 1051.06i | 0.628840 | − | 1.08918i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1318.80 | + | 761.408i | −1.36380 | + | 0.787392i | −0.990128 | − | 0.140168i | \(-0.955236\pi\) |
−0.373675 | + | 0.927560i | \(0.621903\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1242.37 | − | 191.237i | −1.28212 | − | 0.197355i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 266.782i | 0.274750i | 0.990519 | + | 0.137375i | \(0.0438666\pi\) | ||||
−0.990519 | + | 0.137375i | \(0.956133\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −127.401 | −0.130937 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 47.8075 | − | 310.581i | 0.0490333 | − | 0.318545i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 874.915 | + | 1515.40i | 0.895512 | + | 1.55107i | 0.833170 | + | 0.553017i | \(0.186524\pi\) |
0.0623423 | + | 0.998055i | \(0.480143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 302.850 | + | 174.851i | 0.309347 | + | 0.178601i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 291.272 | + | 91.8467i | 0.296913 | + | 0.0936256i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1127.06 | + | 650.711i | 1.14656 | + | 0.661964i | 0.948046 | − | 0.318135i | \(-0.103056\pi\) |
0.198510 | + | 0.980099i | \(0.436390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −583.845 | − | 1011.25i | −0.592736 | − | 1.02665i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 792.542 | − | 308.190i | 0.802981 | − | 0.312249i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −151.587 | −0.153273 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 136.009i | 0.137245i | 0.997643 | + | 0.0686223i | \(0.0218603\pi\) | ||||
−0.997643 | + | 0.0686223i | \(0.978140\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −613.051 | + | 763.824i | −0.617372 | + | 0.769208i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 607.766 | − | 350.894i | 0.610820 | − | 0.352657i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 637.348 | − | 1103.92i | 0.639266 | − | 1.10724i | −0.346328 | − | 0.938113i | \(-0.612572\pi\) |
0.985594 | − | 0.169128i | \(-0.0540950\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −390.685 | + | 792.147i | −0.391076 | + | 0.792940i |
(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 | 144.3.o.a.79.3 | yes | 8 | |
3.2 | odd | 2 | 432.3.o.b.127.1 | 8 | |||
4.3 | odd | 2 | 144.3.o.c.79.2 | yes | 8 | ||
8.3 | odd | 2 | 576.3.o.d.511.3 | 8 | |||
8.5 | even | 2 | 576.3.o.f.511.2 | 8 | |||
9.2 | odd | 6 | 1296.3.g.k.1135.8 | 8 | |||
9.4 | even | 3 | 144.3.o.c.31.2 | yes | 8 | ||
9.5 | odd | 6 | 432.3.o.a.415.1 | 8 | |||
9.7 | even | 3 | 1296.3.g.j.1135.2 | 8 | |||
12.11 | even | 2 | 432.3.o.a.127.1 | 8 | |||
24.5 | odd | 2 | 1728.3.o.f.127.4 | 8 | |||
24.11 | even | 2 | 1728.3.o.e.127.4 | 8 | |||
36.7 | odd | 6 | 1296.3.g.j.1135.1 | 8 | |||
36.11 | even | 6 | 1296.3.g.k.1135.7 | 8 | |||
36.23 | even | 6 | 432.3.o.b.415.1 | 8 | |||
36.31 | odd | 6 | inner | 144.3.o.a.31.3 | ✓ | 8 | |
72.5 | odd | 6 | 1728.3.o.e.1279.4 | 8 | |||
72.13 | even | 6 | 576.3.o.d.319.3 | 8 | |||
72.59 | even | 6 | 1728.3.o.f.1279.4 | 8 | |||
72.67 | odd | 6 | 576.3.o.f.319.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.o.a.31.3 | ✓ | 8 | 36.31 | odd | 6 | inner | |
144.3.o.a.79.3 | yes | 8 | 1.1 | even | 1 | trivial | |
144.3.o.c.31.2 | yes | 8 | 9.4 | even | 3 | ||
144.3.o.c.79.2 | yes | 8 | 4.3 | odd | 2 | ||
432.3.o.a.127.1 | 8 | 12.11 | even | 2 | |||
432.3.o.a.415.1 | 8 | 9.5 | odd | 6 | |||
432.3.o.b.127.1 | 8 | 3.2 | odd | 2 | |||
432.3.o.b.415.1 | 8 | 36.23 | even | 6 | |||
576.3.o.d.319.3 | 8 | 72.13 | even | 6 | |||
576.3.o.d.511.3 | 8 | 8.3 | odd | 2 | |||
576.3.o.f.319.2 | 8 | 72.67 | odd | 6 | |||
576.3.o.f.511.2 | 8 | 8.5 | even | 2 | |||
1296.3.g.j.1135.1 | 8 | 36.7 | odd | 6 | |||
1296.3.g.j.1135.2 | 8 | 9.7 | even | 3 | |||
1296.3.g.k.1135.7 | 8 | 36.11 | even | 6 | |||
1296.3.g.k.1135.8 | 8 | 9.2 | odd | 6 | |||
1728.3.o.e.127.4 | 8 | 24.11 | even | 2 | |||
1728.3.o.e.1279.4 | 8 | 72.5 | odd | 6 | |||
1728.3.o.f.127.4 | 8 | 24.5 | odd | 2 | |||
1728.3.o.f.1279.4 | 8 | 72.59 | even | 6 |