Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), 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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.271 |
Dual form | 405.2.e.g.136.1 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | + | 3.46410i | −0.554700 | + | 0.960769i | 0.443227 | + | 0.896410i | \(0.353834\pi\) |
−0.997927 | + | 0.0643593i | \(0.979500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 1.00000 | + | 1.73205i | 0.223607 | + | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.00000 | + | 8.66025i | −1.06600 | + | 1.84637i | ||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −8.00000 | −1.56893 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.50000 | − | 4.33013i | −0.464238 | − | 0.804084i | 0.534928 | − | 0.844897i | \(-0.320339\pi\) |
−0.999167 | + | 0.0408130i | \(0.987005\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | − | 7.79423i | 0.808224 | − | 1.39988i | −0.105869 | − | 0.994380i | \(-0.533762\pi\) |
0.914093 | − | 0.405505i | \(-0.132904\pi\) | |||||||
\(32\) | −4.00000 | + | 6.92820i | −0.707107 | + | 1.22474i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | + | 6.92820i | 0.685994 | + | 1.18818i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0000 | −1.64399 | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | −5.00000 | − | 8.66025i | −0.811107 | − | 1.40488i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.50000 | − | 6.06218i | 0.546608 | − | 0.946753i | −0.451896 | − | 0.892071i | \(-0.649252\pi\) |
0.998504 | − | 0.0546823i | \(-0.0174146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | + | 1.73205i | 0.152499 | + | 0.264135i | 0.932145 | − | 0.362084i | \(-0.117935\pi\) |
−0.779647 | + | 0.626219i | \(0.784601\pi\) | |||||||
\(44\) | −10.0000 | −1.50756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.0000 | 1.76930 | ||||||||
\(47\) | 1.00000 | + | 1.73205i | 0.145865 | + | 0.252646i | 0.929695 | − | 0.368329i | \(-0.120070\pi\) |
−0.783830 | + | 0.620975i | \(0.786737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.50000 | − | 6.06218i | 0.500000 | − | 0.866025i | ||||
\(50\) | 1.00000 | − | 1.73205i | 0.141421 | − | 0.244949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | − | 6.92820i | −0.554700 | − | 0.960769i | ||||
\(53\) | −8.00000 | −1.09888 | −0.549442 | − | 0.835532i | \(-0.685160\pi\) | ||||
−0.549442 | + | 0.835532i | \(0.685160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.00000 | − | 8.66025i | 0.656532 | − | 1.13715i | ||||
\(59\) | −0.500000 | + | 0.866025i | −0.0650945 | + | 0.112747i | −0.896736 | − | 0.442566i | \(-0.854068\pi\) |
0.831641 | + | 0.555313i | \(0.187402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 18.0000 | 2.28600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.00000 | + | 3.46410i | 0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | + | 5.19615i | −0.366508 | + | 0.634811i | −0.989017 | − | 0.147802i | \(-0.952780\pi\) |
0.622509 | + | 0.782613i | \(0.286114\pi\) | |||||||
\(68\) | −4.00000 | + | 6.92820i | −0.485071 | + | 0.840168i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.00000 | −0.118678 | −0.0593391 | − | 0.998238i | \(-0.518899\pi\) | ||||
−0.0593391 | + | 0.998238i | \(0.518899\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.00000 | −0.936329 | −0.468165 | − | 0.883641i | \(-0.655085\pi\) | ||||
−0.468165 | + | 0.883641i | \(0.655085\pi\) | |||||||
\(74\) | −10.0000 | − | 17.3205i | −1.16248 | − | 2.01347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.00000 | − | 8.66025i | 0.573539 | − | 0.993399i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | − | 10.3923i | −0.675053 | − | 1.16923i | −0.976453 | − | 0.215728i | \(-0.930788\pi\) |
0.301401 | − | 0.953498i | \(-0.402546\pi\) | |||||||
\(80\) | 4.00000 | 0.447214 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.0000 | 1.54604 | ||||||||
\(83\) | 3.00000 | + | 5.19615i | 0.329293 | + | 0.570352i | 0.982372 | − | 0.186938i | \(-0.0598564\pi\) |
−0.653079 | + | 0.757290i | \(0.726523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | − | 3.46410i | 0.216930 | − | 0.375735i | ||||
\(86\) | −2.00000 | + | 3.46410i | −0.215666 | + | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | 0.953998 | 0.476999 | − | 0.878904i | \(-0.341725\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | + | 10.3923i | 0.625543 | + | 1.08347i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.00000 | + | 3.46410i | −0.206284 | + | 0.357295i | ||||
\(95\) | −2.50000 | + | 4.33013i | −0.256495 | + | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | − | 12.1244i | −0.710742 | − | 1.23104i | −0.964579 | − | 0.263795i | \(-0.915026\pi\) |
0.253837 | − | 0.967247i | \(-0.418307\pi\) | |||||||
\(98\) | 14.0000 | 1.41421 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.00000 | + | 1.73205i | −0.0985329 | + | 0.170664i | −0.911078 | − | 0.412235i | \(-0.864748\pi\) |
0.812545 | + | 0.582899i | \(0.198082\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.00000 | − | 13.8564i | −0.777029 | − | 1.34585i | ||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 5.00000 | + | 8.66025i | 0.476731 | + | 0.825723i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.00000 | + | 13.8564i | −0.752577 | + | 1.30350i | 0.193993 | + | 0.981003i | \(0.437856\pi\) |
−0.946570 | + | 0.322498i | \(0.895477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | − | 5.19615i | −0.279751 | − | 0.484544i | ||||
\(116\) | 10.0000 | 0.928477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00000 | −0.184115 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | −2.00000 | + | 3.46410i | −0.181071 | + | 0.313625i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.00000 | + | 15.5885i | 0.808224 | + | 1.39988i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.00000 | + | 6.92820i | −0.350823 | + | 0.607644i | ||||
\(131\) | 7.50000 | − | 12.9904i | 0.655278 | − | 1.13497i | −0.326546 | − | 0.945181i | \(-0.605885\pi\) |
0.981824 | − | 0.189794i | \(-0.0607819\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.50000 | − | 16.4545i | 0.805779 | − | 1.39565i | −0.109984 | − | 0.993933i | \(-0.535080\pi\) |
0.915764 | − | 0.401718i | \(-0.131587\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.00000 | − | 1.73205i | −0.0839181 | − | 0.145350i | ||||
\(143\) | −20.0000 | −1.67248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.00000 | −0.415227 | ||||||||
\(146\) | −8.00000 | − | 13.8564i | −0.662085 | − | 1.14676i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.0000 | − | 17.3205i | 0.821995 | − | 1.42374i | ||||
\(149\) | −1.00000 | + | 1.73205i | −0.0819232 | + | 0.141895i | −0.904076 | − | 0.427372i | \(-0.859440\pi\) |
0.822153 | + | 0.569267i | \(0.192773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | + | 4.33013i | 0.203447 | + | 0.352381i | 0.949637 | − | 0.313353i | \(-0.101452\pi\) |
−0.746190 | + | 0.665733i | \(0.768119\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.50000 | − | 7.79423i | −0.361449 | − | 0.626048i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | + | 1.73205i | −0.0798087 | + | 0.138233i | −0.903167 | − | 0.429289i | \(-0.858764\pi\) |
0.823359 | + | 0.567521i | \(0.192098\pi\) | |||||||
\(158\) | 12.0000 | − | 20.7846i | 0.954669 | − | 1.65353i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.00000 | + | 6.92820i | 0.316228 | + | 0.547723i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 7.00000 | + | 12.1244i | 0.546608 | + | 0.946753i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | 8.00000 | 0.613572 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.0000 | + | 17.3205i | −0.753778 | + | 1.30558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.00000 | + | 15.5885i | 0.674579 | + | 1.16840i | ||||
\(179\) | −23.0000 | −1.71910 | −0.859550 | − | 0.511051i | \(-0.829256\pi\) | ||||
−0.859550 | + | 0.511051i | \(0.829256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.0000 | −1.85824 | −0.929118 | − | 0.369784i | \(-0.879432\pi\) | ||||
−0.929118 | + | 0.369784i | \(0.879432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.00000 | + | 8.66025i | −0.367607 | + | 0.636715i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0000 | + | 17.3205i | 0.731272 | + | 1.26660i | ||||
\(188\) | −4.00000 | −0.291730 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.0000 | −0.725476 | ||||||||
\(191\) | 0.500000 | + | 0.866025i | 0.0361787 | + | 0.0626634i | 0.883548 | − | 0.468341i | \(-0.155148\pi\) |
−0.847369 | + | 0.531004i | \(0.821815\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.0000 | + | 22.5167i | −0.935760 | + | 1.62078i | −0.162488 | + | 0.986710i | \(0.551952\pi\) |
−0.773272 | + | 0.634074i | \(0.781381\pi\) | |||||||
\(194\) | 14.0000 | − | 24.2487i | 1.00514 | − | 1.74096i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.00000 | + | 12.1244i | 0.500000 | + | 0.866025i | ||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.00000 | − | 5.19615i | 0.211079 | − | 0.365600i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.50000 | − | 6.06218i | −0.244451 | − | 0.423401i | ||||
\(206\) | −4.00000 | −0.278693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.0000 | −1.10940 | ||||||||
\(209\) | −12.5000 | − | 21.6506i | −0.864643 | − | 1.49761i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.50000 | + | 9.52628i | −0.378636 | + | 0.655816i | −0.990864 | − | 0.134865i | \(-0.956940\pi\) |
0.612228 | + | 0.790681i | \(0.290273\pi\) | |||||||
\(212\) | 8.00000 | − | 13.8564i | 0.549442 | − | 0.951662i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.00000 | − | 1.73205i | −0.0677285 | − | 0.117309i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.00000 | + | 8.66025i | −0.337100 | + | 0.583874i | ||||
\(221\) | −8.00000 | + | 13.8564i | −0.538138 | + | 0.932083i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | − | 6.92820i | −0.267860 | − | 0.463947i | 0.700449 | − | 0.713702i | \(-0.252983\pi\) |
−0.968309 | + | 0.249756i | \(0.919650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32.0000 | −2.12861 | ||||||||
\(227\) | 2.00000 | + | 3.46410i | 0.132745 | + | 0.229920i | 0.924734 | − | 0.380615i | \(-0.124288\pi\) |
−0.791989 | + | 0.610535i | \(0.790954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.00000 | + | 5.19615i | −0.198246 | + | 0.343371i | −0.947960 | − | 0.318390i | \(-0.896858\pi\) |
0.749714 | + | 0.661762i | \(0.230191\pi\) | |||||||
\(230\) | 6.00000 | − | 10.3923i | 0.395628 | − | 0.685248i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | −1.00000 | − | 1.73205i | −0.0650945 | − | 0.112747i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | + | 13.8564i | −0.517477 | + | 0.896296i | 0.482317 | + | 0.875997i | \(0.339795\pi\) |
−0.999794 | + | 0.0202996i | \(0.993538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.50000 | + | 9.52628i | 0.354286 | + | 0.613642i | 0.986996 | − | 0.160748i | \(-0.0513906\pi\) |
−0.632709 | + | 0.774389i | \(0.718057\pi\) | |||||||
\(242\) | −28.0000 | −1.79991 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | −3.50000 | − | 6.06218i | −0.223607 | − | 0.387298i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0000 | − | 17.3205i | 0.636285 | − | 1.10208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | − | 1.73205i | −0.0632456 | − | 0.109545i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0000 | 1.88608 | ||||||||
\(254\) | 16.0000 | + | 27.7128i | 1.00393 | + | 1.73886i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −3.00000 | + | 5.19615i | −0.187135 | + | 0.324127i | −0.944294 | − | 0.329104i | \(-0.893253\pi\) |
0.757159 | + | 0.653231i | \(0.226587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.00000 | −0.496139 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 30.0000 | 1.85341 | ||||||||
\(263\) | 5.00000 | + | 8.66025i | 0.308313 | + | 0.534014i | 0.977993 | − | 0.208635i | \(-0.0669022\pi\) |
−0.669680 | + | 0.742650i | \(0.733569\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | + | 6.92820i | −0.245718 | + | 0.425596i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.00000 | − | 10.3923i | −0.366508 | − | 0.634811i | ||||
\(269\) | 31.0000 | 1.89010 | 0.945052 | − | 0.326921i | \(-0.106011\pi\) | ||||
0.945052 | + | 0.326921i | \(0.106011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 8.00000 | + | 13.8564i | 0.485071 | + | 0.840168i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | + | 20.7846i | −0.724947 | + | 1.25564i | ||||
\(275\) | 2.50000 | − | 4.33013i | 0.150756 | − | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.00000 | + | 15.5885i | 0.540758 | + | 0.936620i | 0.998861 | + | 0.0477206i | \(0.0151957\pi\) |
−0.458103 | + | 0.888899i | \(0.651471\pi\) | |||||||
\(278\) | 38.0000 | 2.27909 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | + | 5.19615i | 0.178965 | + | 0.309976i | 0.941526 | − | 0.336939i | \(-0.109392\pi\) |
−0.762561 | + | 0.646916i | \(0.776058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.00000 | + | 5.19615i | −0.178331 | + | 0.308879i | −0.941309 | − | 0.337546i | \(-0.890403\pi\) |
0.762978 | + | 0.646425i | \(0.223737\pi\) | |||||||
\(284\) | 1.00000 | − | 1.73205i | 0.0593391 | − | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.0000 | − | 34.6410i | −1.18262 | − | 2.04837i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −5.00000 | − | 8.66025i | −0.293610 | − | 0.508548i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.00000 | − | 13.8564i | 0.468165 | − | 0.810885i | ||||
\(293\) | 9.00000 | − | 15.5885i | 0.525786 | − | 0.910687i | −0.473763 | − | 0.880652i | \(-0.657105\pi\) |
0.999549 | − | 0.0300351i | \(-0.00956192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.500000 | + | 0.866025i | 0.0291111 | + | 0.0504219i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.00000 | −0.231714 | ||||||||
\(299\) | 12.0000 | + | 20.7846i | 0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.00000 | + | 8.66025i | −0.287718 | + | 0.498342i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.0000 | − | 17.3205i | −0.573539 | − | 0.993399i | ||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000 | 0.570730 | 0.285365 | − | 0.958419i | \(-0.407885\pi\) | ||||
0.285365 | + | 0.958419i | \(0.407885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00000 | − | 15.5885i | 0.511166 | − | 0.885365i | ||||
\(311\) | −4.50000 | + | 7.79423i | −0.255172 | + | 0.441970i | −0.964942 | − | 0.262463i | \(-0.915465\pi\) |
0.709771 | + | 0.704433i | \(0.248799\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000 | + | 3.46410i | 0.113047 | + | 0.195803i | 0.916997 | − | 0.398894i | \(-0.130606\pi\) |
−0.803951 | + | 0.594696i | \(0.797272\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.0000 | 1.35011 | ||||||||
\(317\) | −1.00000 | − | 1.73205i | −0.0561656 | − | 0.0972817i | 0.836576 | − | 0.547852i | \(-0.184554\pi\) |
−0.892741 | + | 0.450570i | \(0.851221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5000 | − | 21.6506i | 0.699866 | − | 1.21220i | ||||
\(320\) | −4.00000 | + | 6.92820i | −0.223607 | + | 0.387298i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0000 | −1.11283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | 8.00000 | + | 13.8564i | 0.443079 | + | 0.767435i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.5000 | + | 18.1865i | 0.577132 | + | 0.999622i | 0.995806 | + | 0.0914858i | \(0.0291616\pi\) |
−0.418674 | + | 0.908137i | \(0.637505\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.0000 | 1.31322 | ||||||||
\(335\) | 3.00000 | + | 5.19615i | 0.163908 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.00000 | − | 6.92820i | 0.217894 | − | 0.377403i | −0.736270 | − | 0.676688i | \(-0.763415\pi\) |
0.954164 | + | 0.299285i | \(0.0967480\pi\) | |||||||
\(338\) | 3.00000 | − | 5.19615i | 0.163178 | − | 0.282633i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | + | 6.92820i | 0.216930 | + | 0.375735i | ||||
\(341\) | 45.0000 | 2.43689 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | − | 10.3923i | 0.322562 | − | 0.558694i | ||||
\(347\) | 10.0000 | − | 17.3205i | 0.536828 | − | 0.929814i | −0.462244 | − | 0.886753i | \(-0.652956\pi\) |
0.999072 | − | 0.0430610i | \(-0.0137110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.50000 | − | 11.2583i | −0.347937 | − | 0.602645i | 0.637946 | − | 0.770081i | \(-0.279784\pi\) |
−0.985883 | + | 0.167437i | \(0.946451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −40.0000 | −2.13201 | ||||||||
\(353\) | −9.00000 | − | 15.5885i | −0.479022 | − | 0.829690i | 0.520689 | − | 0.853746i | \(-0.325675\pi\) |
−0.999711 | + | 0.0240566i | \(0.992342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.500000 | + | 0.866025i | −0.0265372 | + | 0.0459639i | ||||
\(356\) | −9.00000 | + | 15.5885i | −0.476999 | + | 0.826187i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.0000 | − | 39.8372i | −1.21559 | − | 2.10546i | ||||
\(359\) | 27.0000 | 1.42501 | 0.712503 | − | 0.701669i | \(-0.247562\pi\) | ||||
0.712503 | + | 0.701669i | \(0.247562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | −25.0000 | − | 43.3013i | −1.31397 | − | 2.27586i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | + | 6.92820i | −0.209370 | + | 0.362639i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.00000 | − | 15.5885i | −0.469796 | − | 0.813711i | 0.529607 | − | 0.848243i | \(-0.322339\pi\) |
−0.999404 | + | 0.0345320i | \(0.989006\pi\) | |||||||
\(368\) | 24.0000 | 1.25109 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.0000 | −1.03975 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.00000 | + | 13.8564i | −0.414224 | + | 0.717458i | −0.995347 | − | 0.0963587i | \(-0.969280\pi\) |
0.581122 | + | 0.813816i | \(0.302614\pi\) | |||||||
\(374\) | −20.0000 | + | 34.6410i | −1.03418 | + | 1.79124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.0000 | 1.03005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | −5.00000 | − | 8.66025i | −0.256495 | − | 0.444262i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.00000 | + | 1.73205i | −0.0511645 | + | 0.0886194i | ||||
\(383\) | −18.0000 | + | 31.1769i | −0.919757 | + | 1.59307i | −0.119974 | + | 0.992777i | \(0.538281\pi\) |
−0.799783 | + | 0.600289i | \(0.795052\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −52.0000 | −2.64673 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.0000 | 1.42148 | ||||||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | − | 20.7846i | 0.606866 | − | 1.05112i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.0000 | − | 20.7846i | −0.604551 | − | 1.04711i | ||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.0000 | −1.90717 | −0.953583 | − | 0.301131i | \(-0.902636\pi\) | ||||
−0.953583 | + | 0.301131i | \(0.902636\pi\) | |||||||
\(398\) | 16.0000 | + | 27.7128i | 0.802008 | + | 1.38912i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | − | 3.46410i | 0.100000 | − | 0.173205i | ||||
\(401\) | 15.0000 | − | 25.9808i | 0.749064 | − | 1.29742i | −0.199207 | − | 0.979957i | \(-0.563837\pi\) |
0.948272 | − | 0.317460i | \(-0.102830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0000 | + | 31.1769i | 0.896644 | + | 1.55303i | ||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.0000 | − | 43.3013i | −1.23920 | − | 2.14636i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00000 | + | 12.1244i | −0.346128 | + | 0.599511i | −0.985558 | − | 0.169338i | \(-0.945837\pi\) |
0.639430 | + | 0.768849i | \(0.279170\pi\) | |||||||
\(410\) | 7.00000 | − | 12.1244i | 0.345705 | − | 0.598779i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.00000 | − | 3.46410i | −0.0985329 | − | 0.170664i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −16.0000 | − | 27.7128i | −0.784465 | − | 1.35873i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.0000 | − | 43.3013i | 1.22279 | − | 2.11793i | ||||
\(419\) | 8.00000 | − | 13.8564i | 0.390826 | − | 0.676930i | −0.601733 | − | 0.798697i | \(-0.705523\pi\) |
0.992559 | + | 0.121768i | \(0.0388562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.50000 | − | 11.2583i | −0.316791 | − | 0.548697i | 0.663026 | − | 0.748596i | \(-0.269272\pi\) |
−0.979817 | + | 0.199899i | \(0.935939\pi\) | |||||||
\(422\) | −22.0000 | −1.07094 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | − | 3.46410i | −0.0970143 | − | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.00000 | + | 10.3923i | −0.290021 | + | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | + | 3.46410i | 0.0964486 | + | 0.167054i | ||||
\(431\) | −3.00000 | −0.144505 | −0.0722525 | − | 0.997386i | \(-0.523019\pi\) | ||||
−0.0722525 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | −15.0000 | + | 25.9808i | −0.717547 | + | 1.24283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5000 | + | 25.1147i | 0.692047 | + | 1.19866i | 0.971166 | + | 0.238404i | \(0.0766244\pi\) |
−0.279119 | + | 0.960257i | \(0.590042\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −32.0000 | −1.52208 | ||||||||
\(443\) | 3.00000 | + | 5.19615i | 0.142534 | + | 0.246877i | 0.928450 | − | 0.371457i | \(-0.121142\pi\) |
−0.785916 | + | 0.618333i | \(0.787808\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.50000 | − | 7.79423i | 0.213320 | − | 0.369482i | ||||
\(446\) | 8.00000 | − | 13.8564i | 0.378811 | − | 0.656120i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.0000 | −0.802280 | −0.401140 | − | 0.916017i | \(-0.631386\pi\) | ||||
−0.401140 | + | 0.916017i | \(0.631386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.0000 | 1.64809 | ||||||||
\(452\) | −16.0000 | − | 27.7128i | −0.752577 | − | 1.30350i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.00000 | + | 6.92820i | −0.187729 | + | 0.325157i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0000 | + | 32.9090i | 0.888783 | + | 1.53942i | 0.841316 | + | 0.540544i | \(0.181781\pi\) |
0.0474665 | + | 0.998873i | \(0.484885\pi\) | |||||||
\(458\) | −12.0000 | −0.560723 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.0000 | 0.559503 | ||||||||
\(461\) | −7.50000 | − | 12.9904i | −0.349310 | − | 0.605022i | 0.636817 | − | 0.771015i | \(-0.280251\pi\) |
−0.986127 | + | 0.165992i | \(0.946917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.00000 | − | 5.19615i | 0.139422 | − | 0.241486i | −0.787856 | − | 0.615859i | \(-0.788809\pi\) |
0.927278 | + | 0.374374i | \(0.122142\pi\) | |||||||
\(464\) | 10.0000 | − | 17.3205i | 0.464238 | − | 0.804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | − | 10.3923i | −0.277945 | − | 0.481414i | ||||
\(467\) | −4.00000 | −0.185098 | −0.0925490 | − | 0.995708i | \(-0.529501\pi\) | ||||
−0.0925490 | + | 0.995708i | \(0.529501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.00000 | + | 3.46410i | 0.0922531 | + | 0.159787i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.00000 | + | 8.66025i | −0.229900 | + | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | + | 4.33013i | 0.114708 | + | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −32.0000 | −1.46365 | ||||||||
\(479\) | −7.50000 | − | 12.9904i | −0.342684 | − | 0.593546i | 0.642246 | − | 0.766498i | \(-0.278003\pi\) |
−0.984930 | + | 0.172953i | \(0.944669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | − | 34.6410i | 0.911922 | − | 1.57949i | ||||
\(482\) | −11.0000 | + | 19.0526i | −0.501036 | + | 0.867820i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.0000 | − | 24.2487i | −0.636364 | − | 1.10221i | ||||
\(485\) | −14.0000 | −0.635707 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | 0.362515 | 0.181257 | − | 0.983436i | \(-0.441983\pi\) | ||||
0.181257 | + | 0.983436i | \(0.441983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.00000 | − | 12.1244i | 0.316228 | − | 0.547723i | ||||
\(491\) | 21.5000 | − | 37.2391i | 0.970281 | − | 1.68058i | 0.275581 | − | 0.961278i | \(-0.411130\pi\) |
0.694701 | − | 0.719299i | \(-0.255537\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0000 | − | 17.3205i | −0.450377 | − | 0.780076i | ||||
\(494\) | 40.0000 | 1.79969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.0000 | 1.61645 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50000 | + | 6.06218i | −0.156682 | + | 0.271380i | −0.933670 | − | 0.358134i | \(-0.883413\pi\) |
0.776989 | + | 0.629515i | \(0.216746\pi\) | |||||||
\(500\) | 1.00000 | − | 1.73205i | 0.0447214 | − | 0.0774597i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000 | + | 20.7846i | 0.535586 | + | 0.927663i | ||||
\(503\) | 20.0000 | 0.891756 | 0.445878 | − | 0.895094i | \(-0.352892\pi\) | ||||
0.445878 | + | 0.895094i | \(0.352892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | 30.0000 | + | 51.9615i | 1.33366 | + | 2.30997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.0000 | + | 27.7128i | −0.709885 | + | 1.22956i | ||||
\(509\) | 1.00000 | − | 1.73205i | 0.0443242 | − | 0.0767718i | −0.843012 | − | 0.537895i | \(-0.819220\pi\) |
0.887336 | + | 0.461123i | \(0.152553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −32.0000 | −1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.0000 | −0.529297 | ||||||||
\(515\) | 1.00000 | + | 1.73205i | 0.0440653 | + | 0.0763233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.00000 | + | 8.66025i | −0.219900 | + | 0.380878i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | 0.699631 | 0.349816 | − | 0.936819i | \(-0.386244\pi\) | ||||
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(524\) | 15.0000 | + | 25.9808i | 0.655278 | + | 1.13497i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.0000 | + | 17.3205i | −0.436021 | + | 0.755210i | ||||
\(527\) | 18.0000 | − | 31.1769i | 0.784092 | − | 1.35809i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | −16.0000 | −0.694996 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.0000 | + | 24.2487i | 0.606407 | + | 1.05033i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | − | 5.19615i | 0.129701 | − | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.0000 | + | 53.6936i | 1.33650 | + | 2.31489i | ||||
\(539\) | 35.0000 | 1.50756 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.00000 | 0.128980 | 0.0644900 | − | 0.997918i | \(-0.479458\pi\) | ||||
0.0644900 | + | 0.997918i | \(0.479458\pi\) | |||||||
\(542\) | −8.00000 | − | 13.8564i | −0.343629 | − | 0.595184i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.0000 | + | 27.7128i | −0.685994 | + | 1.18818i | ||||
\(545\) | −0.500000 | + | 0.866025i | −0.0214176 | + | 0.0370965i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.0000 | − | 24.2487i | −0.598597 | − | 1.03680i | −0.993028 | − | 0.117875i | \(-0.962392\pi\) |
0.394432 | − | 0.918925i | \(-0.370941\pi\) | |||||||
\(548\) | −24.0000 | −1.02523 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.0000 | 0.426401 | ||||||||
\(551\) | 12.5000 | + | 21.6506i | 0.532518 | + | 0.922348i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.0000 | + | 31.1769i | −0.764747 | + | 1.32458i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.0000 | + | 32.9090i | 0.805779 | + | 1.39565i | ||||
\(557\) | 24.0000 | 1.01691 | 0.508456 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508456 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | + | 10.3923i | −0.253095 | + | 0.438373i | ||||
\(563\) | −9.00000 | + | 15.5885i | −0.379305 | + | 0.656975i | −0.990961 | − | 0.134148i | \(-0.957170\pi\) |
0.611656 | + | 0.791123i | \(0.290503\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.00000 | + | 13.8564i | 0.336563 | + | 0.582943i | ||||
\(566\) | −12.0000 | −0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.50000 | − | 2.59808i | −0.0628833 | − | 0.108917i | 0.832870 | − | 0.553469i | \(-0.186696\pi\) |
−0.895753 | + | 0.444552i | \(0.853363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50000 | + | 4.33013i | −0.104622 | + | 0.181210i | −0.913584 | − | 0.406651i | \(-0.866697\pi\) |
0.808962 | + | 0.587861i | \(0.200030\pi\) | |||||||
\(572\) | 20.0000 | − | 34.6410i | 0.836242 | − | 1.44841i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.0000 | −0.666089 | −0.333044 | − | 0.942911i | \(-0.608076\pi\) | ||||
−0.333044 | + | 0.942911i | \(0.608076\pi\) | |||||||
\(578\) | −1.00000 | − | 1.73205i | −0.0415945 | − | 0.0720438i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.00000 | − | 8.66025i | 0.207614 | − | 0.359597i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.0000 | − | 34.6410i | −0.828315 | − | 1.43468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.0000 | 1.48715 | ||||||||
\(587\) | 9.00000 | + | 15.5885i | 0.371470 | + | 0.643404i | 0.989792 | − | 0.142520i | \(-0.0455206\pi\) |
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.5000 | + | 38.9711i | −0.927096 | + | 1.60578i | ||||
\(590\) | −1.00000 | + | 1.73205i | −0.0411693 | + | 0.0713074i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.0000 | − | 34.6410i | −0.821995 | − | 1.42374i | ||||
\(593\) | 14.0000 | 0.574911 | 0.287456 | − | 0.957794i | \(-0.407191\pi\) | ||||
0.287456 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.00000 | − | 3.46410i | −0.0819232 | − | 0.141895i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.0000 | + | 41.5692i | −0.981433 | + | 1.69989i | ||||
\(599\) | −8.50000 | + | 14.7224i | −0.347301 | + | 0.601542i | −0.985769 | − | 0.168106i | \(-0.946235\pi\) |
0.638468 | + | 0.769648i | \(0.279568\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.50000 | + | 16.4545i | 0.387513 | + | 0.671192i | 0.992114 | − | 0.125336i | \(-0.0400009\pi\) |
−0.604601 | + | 0.796528i | \(0.706668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0000 | −0.406894 | ||||||||
\(605\) | 7.00000 | + | 12.1244i | 0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.0000 | + | 29.4449i | −0.690009 | + | 1.19513i | 0.281826 | + | 0.959466i | \(0.409060\pi\) |
−0.971834 | + | 0.235665i | \(0.924273\pi\) | |||||||
\(608\) | 20.0000 | − | 34.6410i | 0.811107 | − | 1.40488i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.00000 | + | 3.46410i | 0.0809776 | + | 0.140257i | ||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.00000 | 0.161558 | 0.0807792 | − | 0.996732i | \(-0.474259\pi\) | ||||
0.0807792 | + | 0.996732i | \(0.474259\pi\) | |||||||
\(614\) | 10.0000 | + | 17.3205i | 0.403567 | + | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | + | 20.7846i | −0.483102 | + | 0.836757i | −0.999812 | − | 0.0194037i | \(-0.993823\pi\) |
0.516710 | + | 0.856161i | \(0.327157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000 | + | 24.2487i | 0.562708 | + | 0.974638i | 0.997259 | + | 0.0739910i | \(0.0235736\pi\) |
−0.434551 | + | 0.900647i | \(0.643093\pi\) | |||||||
\(620\) | 18.0000 | 0.722897 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.0000 | −0.721734 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −4.00000 | + | 6.92820i | −0.159872 | + | 0.276907i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | − | 3.46410i | −0.0798087 | − | 0.138233i | ||||
\(629\) | −40.0000 | −1.59490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.0000 | −0.676759 | −0.338380 | − | 0.941010i | \(-0.609879\pi\) | ||||
−0.338380 | + | 0.941010i | \(0.609879\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.00000 | − | 3.46410i | 0.0794301 | − | 0.137577i | ||||
\(635\) | 8.00000 | − | 13.8564i | 0.317470 | − | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.0000 | + | 24.2487i | 0.554700 | + | 0.960769i | ||||
\(638\) | 50.0000 | 1.97952 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.50000 | + | 2.59808i | 0.0592464 | + | 0.102618i | 0.894127 | − | 0.447813i | \(-0.147797\pi\) |
−0.834881 | + | 0.550431i | \(0.814464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.00000 | + | 5.19615i | −0.118308 | + | 0.204916i | −0.919097 | − | 0.394030i | \(-0.871080\pi\) |
0.800789 | + | 0.598947i | \(0.204414\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.0000 | − | 34.6410i | −0.786889 | − | 1.36293i | ||||
\(647\) | 10.0000 | 0.393141 | 0.196570 | − | 0.980490i | \(-0.437020\pi\) | ||||
0.196570 | + | 0.980490i | \(0.437020\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.00000 | −0.196267 | ||||||||
\(650\) | 4.00000 | + | 6.92820i | 0.156893 | + | 0.271746i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.00000 | + | 13.8564i | −0.313304 | + | 0.542659i | ||||
\(653\) | −4.00000 | + | 6.92820i | −0.156532 | + | 0.271122i | −0.933616 | − | 0.358276i | \(-0.883365\pi\) |
0.777084 | + | 0.629397i | \(0.216698\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.50000 | − | 12.9904i | −0.293049 | − | 0.507576i | ||||
\(656\) | 28.0000 | 1.09322 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0000 | + | 38.1051i | 0.856998 | + | 1.48436i | 0.874779 | + | 0.484523i | \(0.161007\pi\) |
−0.0177803 | + | 0.999842i | \(0.505660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.5000 | + | 21.6506i | −0.486194 | + | 0.842112i | −0.999874 | − | 0.0158695i | \(-0.994948\pi\) |
0.513680 | + | 0.857982i | \(0.328282\pi\) | |||||||
\(662\) | −21.0000 | + | 36.3731i | −0.816188 | + | 1.41368i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.0000 | −1.16160 | ||||||||
\(668\) | 12.0000 | + | 20.7846i | 0.464294 | + | 0.804181i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.00000 | + | 10.3923i | −0.231800 | + | 0.401490i | ||||
\(671\) | −5.00000 | + | 8.66025i | −0.193023 | + | 0.334325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0000 | − | 36.3731i | −0.809491 | − | 1.40208i | −0.913217 | − | 0.407473i | \(-0.866410\pi\) |
0.103727 | − | 0.994606i | \(-0.466923\pi\) | |||||||
\(674\) | 16.0000 | 0.616297 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | 0.230769 | ||||||||
\(677\) | 3.00000 | + | 5.19615i | 0.115299 | + | 0.199704i | 0.917899 | − | 0.396813i | \(-0.129884\pi\) |
−0.802600 | + | 0.596518i | \(0.796551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 45.0000 | + | 77.9423i | 1.72314 | + | 2.98456i | ||||
\(683\) | −48.0000 | −1.83667 | −0.918334 | − | 0.395805i | \(-0.870466\pi\) | ||||
−0.918334 | + | 0.395805i | \(0.870466\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.00000 | + | 6.92820i | −0.152499 | + | 0.264135i | ||||
\(689\) | 16.0000 | − | 27.7128i | 0.609551 | − | 1.05577i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.00000 | − | 3.46410i | −0.0760836 | − | 0.131781i | 0.825473 | − | 0.564441i | \(-0.190908\pi\) |
−0.901557 | + | 0.432660i | \(0.857575\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.0000 | 1.51838 | ||||||||
\(695\) | −9.50000 | − | 16.4545i | −0.360356 | − | 0.624154i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.0000 | − | 24.2487i | 0.530288 | − | 0.918485i | ||||
\(698\) | 13.0000 | − | 22.5167i | 0.492057 | − | 0.852268i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.0000 | −0.717620 | −0.358810 | − | 0.933411i | \(-0.616817\pi\) | ||||
−0.358810 | + | 0.933411i | \(0.616817\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.0000 | 1.88579 | ||||||||
\(704\) | −20.0000 | − | 34.6410i | −0.753778 | − | 1.30558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.0000 | − | 31.1769i | 0.677439 | − | 1.17336i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.0000 | − | 19.0526i | −0.413114 | − | 0.715534i | 0.582115 | − | 0.813107i | \(-0.302225\pi\) |
−0.995228 | + | 0.0975728i | \(0.968892\pi\) | |||||||
\(710\) | −2.00000 | −0.0750587 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.0000 | − | 46.7654i | −1.01116 | − | 1.75138i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0000 | + | 17.3205i | −0.373979 | + | 0.647750i | ||||
\(716\) | 23.0000 | − | 39.8372i | 0.859550 | − | 1.48878i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.0000 | + | 46.7654i | 1.00763 | + | 1.74527i | ||||
\(719\) | −27.0000 | −1.00693 | −0.503465 | − | 0.864016i | \(-0.667942\pi\) | ||||
−0.503465 | + | 0.864016i | \(0.667942\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.00000 | + | 10.3923i | 0.223297 | + | 0.386762i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 25.0000 | − | 43.3013i | 0.929118 | − | 1.60928i | ||||
\(725\) | −2.50000 | + | 4.33013i | −0.0928477 | + | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0000 | − | 38.1051i | −0.815935 | − | 1.41324i | −0.908655 | − | 0.417548i | \(-0.862889\pi\) |
0.0927199 | − | 0.995692i | \(-0.470444\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −16.0000 | −0.592187 | ||||||||
\(731\) | 4.00000 | + | 6.92820i | 0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0000 | − | 39.8372i | 0.849524 | − | 1.47142i | −0.0321090 | − | 0.999484i | \(-0.510222\pi\) |
0.881633 | − | 0.471935i | \(-0.156444\pi\) | |||||||
\(734\) | 18.0000 | − | 31.1769i | 0.664392 | − | 1.15076i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.0000 | + | 41.5692i | 0.884652 | + | 1.53226i | ||||
\(737\) | −30.0000 | −1.10506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.0000 | −1.28750 | −0.643748 | − | 0.765238i | \(-0.722621\pi\) | ||||
−0.643748 | + | 0.765238i | \(0.722621\pi\) | |||||||
\(740\) | −10.0000 | − | 17.3205i | −0.367607 | − | 0.636715i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.00000 | + | 3.46410i | −0.0733729 | + | 0.127086i | −0.900378 | − | 0.435110i | \(-0.856710\pi\) |
0.827005 | + | 0.562195i | \(0.190043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.00000 | + | 1.73205i | 0.0366372 | + | 0.0634574i | ||||
\(746\) | −32.0000 | −1.17160 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −40.0000 | −1.46254 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | − | 27.7128i | 0.583848 | − | 1.01125i | −0.411170 | − | 0.911559i | \(-0.634880\pi\) |
0.995018 | − | 0.0996961i | \(-0.0317870\pi\) | |||||||
\(752\) | −4.00000 | + | 6.92820i | −0.145865 | + | 0.252646i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20.0000 | + | 34.6410i | 0.728357 | + | 1.26155i | ||||
\(755\) | 5.00000 | 0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.0000 | 1.01768 | 0.508839 | − | 0.860862i | \(-0.330075\pi\) | ||||
0.508839 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(758\) | 4.00000 | + | 6.92820i | 0.145287 | + | 0.251644i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5000 | + | 23.3827i | −0.489375 | + | 0.847622i | −0.999925 | − | 0.0122260i | \(-0.996108\pi\) |
0.510551 | + | 0.859848i | \(0.329442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.00000 | −0.0723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −72.0000 | −2.60147 | ||||||||
\(767\) | −2.00000 | − | 3.46410i | −0.0722158 | − | 0.125081i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.50000 | + | 4.33013i | −0.0901523 | + | 0.156148i | −0.907575 | − | 0.419890i | \(-0.862069\pi\) |
0.817423 | + | 0.576038i | \(0.195402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26.0000 | − | 45.0333i | −0.935760 | − | 1.62078i | ||||
\(773\) | −18.0000 | −0.647415 | −0.323708 | − | 0.946157i | \(-0.604929\pi\) | ||||
−0.323708 | + | 0.946157i | \(0.604929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.00000 | −0.323290 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.00000 | + | 10.3923i | −0.215110 | + | 0.372582i | ||||
\(779\) | −17.5000 | + | 30.3109i | −0.627003 | + | 1.08600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.50000 | − | 4.33013i | −0.0894570 | − | 0.154944i | ||||
\(782\) | 48.0000 | 1.71648 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 1.00000 | + | 1.73205i | 0.0356915 | + | 0.0618195i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00000 | + | 3.46410i | −0.0712923 | + | 0.123482i | −0.899468 | − | 0.436987i | \(-0.856046\pi\) |
0.828176 | + | 0.560469i | \(0.189379\pi\) | |||||||
\(788\) | 12.0000 | − | 20.7846i | 0.427482 | − | 0.740421i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.0000 | − | 20.7846i | −0.426941 | − | 0.739483i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | −0.284088 | ||||||||
\(794\) | −38.0000 | − | 65.8179i | −1.34857 | − | 2.33579i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.0000 | + | 27.7128i | −0.567105 | + | 0.982255i | ||||
\(797\) | 2.00000 | − | 3.46410i | 0.0708436 | − | 0.122705i | −0.828428 | − | 0.560096i | \(-0.810764\pi\) |
0.899271 | + | 0.437391i | \(0.144098\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | + | 6.92820i | 0.141510 | + | 0.245102i | ||||
\(800\) | 8.00000 | 0.282843 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 60.0000 | 2.11867 | ||||||||
\(803\) | −20.0000 | − | 34.6410i | −0.705785 | − | 1.22245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.0000 | + | 62.3538i | −1.26805 | + | 2.19632i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.00000 | −0.246107 | −0.123053 | − | 0.992400i | \(-0.539269\pi\) | ||||
−0.123053 | + | 0.992400i | \(0.539269\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.0000 | −0.737410 | −0.368705 | − | 0.929547i | \(-0.620199\pi\) | ||||
−0.368705 | + | 0.929547i | \(0.620199\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 50.0000 | − | 86.6025i | 1.75250 | − | 3.03542i | ||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.00000 | − | 8.66025i | −0.174928 | − | 0.302984i | ||||
\(818\) | −28.0000 | −0.978997 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.0000 | 0.488901 | ||||||||
\(821\) | 1.50000 | + | 2.59808i | 0.0523504 | + | 0.0906735i | 0.891013 | − | 0.453978i | \(-0.149995\pi\) |
−0.838663 | + | 0.544651i | \(0.816662\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.0000 | − | 39.8372i | 0.801730 | − | 1.38864i | −0.116747 | − | 0.993162i | \(-0.537247\pi\) |
0.918477 | − | 0.395475i | \(-0.129420\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.0000 | −1.53003 | −0.765015 | − | 0.644013i | \(-0.777268\pi\) | ||||
−0.765015 | + | 0.644013i | \(0.777268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.0000 | 0.937749 | 0.468874 | − | 0.883265i | \(-0.344660\pi\) | ||||
0.468874 | + | 0.883265i | \(0.344660\pi\) | |||||||
\(830\) | 6.00000 | + | 10.3923i | 0.208263 | + | 0.360722i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.0000 | − | 27.7128i | 0.554700 | − | 0.960769i | ||||
\(833\) | 14.0000 | − | 24.2487i | 0.485071 | − | 0.840168i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | − | 10.3923i | −0.207639 | − | 0.359641i | ||||
\(836\) | 50.0000 | 1.72929 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 32.0000 | 1.10542 | ||||||||
\(839\) | 6.50000 | + | 11.2583i | 0.224405 | + | 0.388681i | 0.956141 | − | 0.292908i | \(-0.0946228\pi\) |
−0.731736 | + | 0.681588i | \(0.761290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | 13.0000 | − | 22.5167i | 0.448010 | − | 0.775975i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.0000 | − | 19.0526i | −0.378636 | − | 0.655816i | ||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.0000 | − | 27.7128i | −0.549442 | − | 0.951662i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.00000 | − | 6.92820i | 0.137199 | − | 0.237635i | ||||
\(851\) | −30.0000 | + | 51.9615i | −1.02839 | + | 1.78122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.0000 | + | 27.7128i | 0.546550 | + | 0.946652i | 0.998508 | + | 0.0546125i | \(0.0173923\pi\) |
−0.451958 | + | 0.892039i | \(0.649274\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.5000 | + | 47.6314i | −0.938288 | + | 1.62516i | −0.169625 | + | 0.985509i | \(0.554255\pi\) |
−0.768663 | + | 0.639654i | \(0.779078\pi\) | |||||||
\(860\) | −2.00000 | + | 3.46410i | −0.0681994 | + | 0.118125i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.00000 | − | 5.19615i | −0.102180 | − | 0.176982i | ||||
\(863\) | 44.0000 | 1.49778 | 0.748889 | − | 0.662696i | \(-0.230588\pi\) | ||||
0.748889 | + | 0.662696i | \(0.230588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | −26.0000 | − | 45.0333i | −0.883516 | − | 1.53029i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.0000 | − | 51.9615i | 1.01768 | − | 1.76267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | − | 20.7846i | −0.406604 | − | 0.704260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −60.0000 | −2.02953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.0000 | − | 20.7846i | 0.405211 | − | 0.701846i | −0.589135 | − | 0.808035i | \(-0.700531\pi\) |
0.994346 | + | 0.106188i | \(0.0338646\pi\) | |||||||
\(878\) | −29.0000 | + | 50.2295i | −0.978703 | + | 1.69516i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.0000 | + | 17.3205i | 0.337100 | + | 0.583874i | ||||
\(881\) | 25.0000 | 0.842271 | 0.421136 | − | 0.906998i | \(-0.361632\pi\) | ||||
0.421136 | + | 0.906998i | \(0.361632\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.0000 | −1.74994 | −0.874970 | − | 0.484178i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | −16.0000 | − | 27.7128i | −0.538138 | − | 0.932083i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | 3.00000 | − | 5.19615i | 0.100730 | − | 0.174470i | −0.811256 | − | 0.584692i | \(-0.801215\pi\) |
0.911986 | + | 0.410222i | \(0.134549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.0000 | 0.535720 | ||||||||
\(893\) | −5.00000 | − | 8.66025i | −0.167319 | − | 0.289804i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.5000 | + | 19.9186i | −0.384403 | + | 0.665805i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.0000 | − | 29.4449i | −0.567297 | − | 0.982588i | ||||
\(899\) | −45.0000 | −1.50083 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.0000 | −1.06607 | ||||||||
\(902\) | 35.0000 | + | 60.6218i | 1.16537 | + | 2.01848i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.5000 | + | 21.6506i | −0.415514 | + | 0.719691i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.00000 | + | 15.5885i | 0.298840 | + | 0.517606i | 0.975871 | − | 0.218348i | \(-0.0700669\pi\) |
−0.677031 | + | 0.735955i | \(0.736734\pi\) | |||||||
\(908\) | −8.00000 | −0.265489 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.5000 | − | 42.4352i | −0.811721 | − | 1.40594i | −0.911658 | − | 0.410949i | \(-0.865198\pi\) |
0.0999373 | − | 0.994994i | \(-0.468136\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.0000 | + | 25.9808i | −0.496428 | + | 0.859838i | ||||
\(914\) | −38.0000 | + | 65.8179i | −1.25693 | + | 2.17706i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.00000 | − | 10.3923i | −0.198246 | − | 0.343371i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.0000 | −0.362857 | −0.181428 | − | 0.983404i | \(-0.558072\pi\) | ||||
−0.181428 | + | 0.983404i | \(0.558072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.0000 | − | 25.9808i | 0.493999 | − | 0.855631i | ||||
\(923\) | 2.00000 | − | 3.46410i | 0.0658308 | − | 0.114022i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00000 | + | 8.66025i | 0.164399 | + | 0.284747i | ||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 40.0000 | 1.31306 | ||||||||
\(929\) | 0.500000 | + | 0.866025i | 0.0164045 | + | 0.0284134i | 0.874111 | − | 0.485726i | \(-0.161445\pi\) |
−0.857707 | + | 0.514139i | \(0.828111\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.5000 | + | 30.3109i | −0.573539 | + | 0.993399i | ||||
\(932\) | 6.00000 | − | 10.3923i | 0.196537 | − | 0.340411i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.00000 | − | 6.92820i | −0.130884 | − | 0.226698i | ||||
\(935\) | 20.0000 | 0.654070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0000 | 1.37208 | 0.686040 | − | 0.727564i | \(-0.259347\pi\) | ||||
0.686040 | + | 0.727564i | \(0.259347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.00000 | + | 3.46410i | −0.0652328 | + | 0.112987i | ||||
\(941\) | 23.0000 | − | 39.8372i | 0.749779 | − | 1.29865i | −0.198150 | − | 0.980172i | \(-0.563493\pi\) |
0.947929 | − | 0.318483i | \(-0.103173\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.0000 | − | 36.3731i | −0.683854 | − | 1.18447i | ||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.0000 | −0.650256 | ||||||||
\(947\) | 9.00000 | + | 15.5885i | 0.292461 | + | 0.506557i | 0.974391 | − | 0.224860i | \(-0.0721926\pi\) |
−0.681930 | + | 0.731417i | \(0.738859\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.0000 | − | 27.7128i | 0.519382 | − | 0.899596i | ||||
\(950\) | −5.00000 | + | 8.66025i | −0.162221 | + | 0.280976i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.0000 | 0.518291 | 0.259145 | − | 0.965838i | \(-0.416559\pi\) | ||||
0.259145 | + | 0.965838i | \(0.416559\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.00000 | 0.0323592 | ||||||||
\(956\) | −16.0000 | − | 27.7128i | −0.517477 | − | 0.896296i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.0000 | − | 25.9808i | 0.484628 | − | 0.839400i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0000 | − | 43.3013i | −0.806452 | − | 1.39682i | ||||
\(962\) | 80.0000 | 2.57930 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.0000 | −0.708572 | ||||||||
\(965\) | 13.0000 | + | 22.5167i | 0.418485 | + | 0.724837i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0000 | − | 34.6410i | 0.643157 | − | 1.11398i | −0.341567 | − | 0.939857i | \(-0.610958\pi\) |
0.984724 | − | 0.174123i | \(-0.0557089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.0000 | − | 24.2487i | −0.449513 | − | 0.778579i | ||||
\(971\) | 27.0000 | 0.866471 | 0.433236 | − | 0.901281i | \(-0.357372\pi\) | ||||
0.433236 | + | 0.901281i | \(0.357372\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.00000 | + | 13.8564i | 0.256337 | + | 0.443988i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | + | 6.92820i | −0.128037 | + | 0.221766i | ||||
\(977\) | −14.0000 | + | 24.2487i | −0.447900 | + | 0.775785i | −0.998249 | − | 0.0591494i | \(-0.981161\pi\) |
0.550349 | + | 0.834934i | \(0.314494\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.5000 | + | 38.9711i | 0.719103 | + | 1.24552i | ||||
\(980\) | 14.0000 | 0.447214 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 86.0000 | 2.74437 | ||||||||
\(983\) | 24.0000 | + | 41.5692i | 0.765481 | + | 1.32585i | 0.939992 | + | 0.341197i | \(0.110832\pi\) |
−0.174511 | + | 0.984655i | \(0.555834\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | + | 10.3923i | −0.191176 | + | 0.331126i | ||||
\(986\) | 20.0000 | − | 34.6410i | 0.636930 | − | 1.10319i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.0000 | + | 34.6410i | 0.636285 | + | 1.10208i | ||||
\(989\) | 12.0000 | 0.381578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.00000 | −0.0317660 | −0.0158830 | − | 0.999874i | \(-0.505056\pi\) | ||||
−0.0158830 | + | 0.999874i | \(0.505056\pi\) | |||||||
\(992\) | 36.0000 | + | 62.3538i | 1.14300 | + | 1.97974i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.00000 | − | 13.8564i | 0.253617 | − | 0.439278i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.0000 | − | 41.5692i | −0.760088 | − | 1.31651i | −0.942805 | − | 0.333345i | \(-0.891823\pi\) |
0.182717 | − | 0.983165i | \(-0.441511\pi\) | |||||||
\(998\) | −14.0000 | −0.443162 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.2.e.g.271.1 | 2 | ||
3.2 | odd | 2 | 405.2.e.a.271.1 | 2 | |||
9.2 | odd | 6 | 405.2.e.a.136.1 | 2 | |||
9.4 | even | 3 | 405.2.a.a.1.1 | ✓ | 1 | ||
9.5 | odd | 6 | 405.2.a.f.1.1 | yes | 1 | ||
9.7 | even | 3 | inner | 405.2.e.g.136.1 | 2 | ||
36.23 | even | 6 | 6480.2.a.r.1.1 | 1 | |||
36.31 | odd | 6 | 6480.2.a.f.1.1 | 1 | |||
45.4 | even | 6 | 2025.2.a.f.1.1 | 1 | |||
45.13 | odd | 12 | 2025.2.b.a.649.2 | 2 | |||
45.14 | odd | 6 | 2025.2.a.a.1.1 | 1 | |||
45.22 | odd | 12 | 2025.2.b.a.649.1 | 2 | |||
45.23 | even | 12 | 2025.2.b.b.649.1 | 2 | |||
45.32 | even | 12 | 2025.2.b.b.649.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.a.a.1.1 | ✓ | 1 | 9.4 | even | 3 | ||
405.2.a.f.1.1 | yes | 1 | 9.5 | odd | 6 | ||
405.2.e.a.136.1 | 2 | 9.2 | odd | 6 | |||
405.2.e.a.271.1 | 2 | 3.2 | odd | 2 | |||
405.2.e.g.136.1 | 2 | 9.7 | even | 3 | inner | ||
405.2.e.g.271.1 | 2 | 1.1 | even | 1 | trivial | ||
2025.2.a.a.1.1 | 1 | 45.14 | odd | 6 | |||
2025.2.a.f.1.1 | 1 | 45.4 | even | 6 | |||
2025.2.b.a.649.1 | 2 | 45.22 | odd | 12 | |||
2025.2.b.a.649.2 | 2 | 45.13 | odd | 12 | |||
2025.2.b.b.649.1 | 2 | 45.23 | even | 12 | |||
2025.2.b.b.649.2 | 2 | 45.32 | even | 12 | |||
6480.2.a.f.1.1 | 1 | 36.31 | odd | 6 | |||
6480.2.a.r.1.1 | 1 | 36.23 | even | 6 |