Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,2,Mod(25,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.i (of order \(3\), 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: | \(0.574922894553\) |
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 | 25.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.25 |
Dual form | 72.2.i.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.50000 | − | 2.59808i | 0.566947 | − | 0.981981i | −0.429919 | − | 0.902867i | \(-0.641458\pi\) |
0.996866 | − | 0.0791130i | \(-0.0252088\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.50000 | + | 4.33013i | −0.753778 | + | 1.30558i | 0.192201 | + | 0.981356i | \(0.438437\pi\) |
−0.945979 | + | 0.324227i | \(0.894896\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50000 | + | 4.33013i | 0.693375 | + | 1.20096i | 0.970725 | + | 0.240192i | \(0.0772105\pi\) |
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 0.866025i | 0.387298 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.50000 | − | 2.59808i | −0.981981 | − | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | 0.913434 | − | 0.406986i | \(-0.133420\pi\) |
−0.809177 | + | 0.587565i | \(0.800087\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.50000 | − | 7.79423i | 0.835629 | − | 1.44735i | −0.0578882 | − | 0.998323i | \(-0.518437\pi\) |
0.893517 | − | 0.449029i | \(-0.148230\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.0898027 | + | 0.155543i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.817625 | + | 0.575751i | \(0.804710\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.50000 | + | 4.33013i | 1.30558 | + | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.50000 | − | 4.33013i | 1.20096 | − | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | − | 2.59808i | −0.223607 | − | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.50000 | − | 2.59808i | 0.218797 | − | 0.378968i | −0.735643 | − | 0.677369i | \(-0.763120\pi\) |
0.954441 | + | 0.298401i | \(0.0964533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.46410i | 0.485071i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.92820i | 0.917663i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.50000 | − | 9.52628i | −0.716039 | − | 1.24022i | −0.962557 | − | 0.271078i | \(-0.912620\pi\) |
0.246518 | − | 0.969138i | \(-0.420713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.50000 | + | 7.79423i | −0.566947 | + | 0.981981i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.50000 | + | 4.33013i | −0.310087 | + | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.500000 | + | 0.866025i | 0.0610847 | + | 0.105802i | 0.894951 | − | 0.446165i | \(-0.147211\pi\) |
−0.833866 | + | 0.551967i | \(0.813877\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.50000 | − | 0.866025i | 0.180579 | − | 0.104257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.00000 | − | 3.46410i | −0.692820 | − | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.50000 | + | 12.9904i | 0.854704 | + | 1.48039i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.500000 | + | 0.866025i | −0.0548821 | + | 0.0950586i | −0.892161 | − | 0.451717i | \(-0.850812\pi\) |
0.837279 | + | 0.546776i | \(0.184145\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | − | 1.73205i | −0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.5000 | − | 7.79423i | −1.44735 | − | 0.835629i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.0000 | −1.90800 | −0.953998 | − | 0.299813i | \(-0.903076\pi\) | ||||
−0.953998 | + | 0.299813i | \(0.903076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.0000 | 1.57243 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50000 | − | 0.866025i | 0.155543 | − | 0.0898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | − | 3.46410i | −0.205196 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.50000 | − | 11.2583i | 0.659975 | − | 1.14311i | −0.320647 | − | 0.947199i | \(-0.603900\pi\) |
0.980622 | − | 0.195911i | \(-0.0627665\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.50000 | − | 12.9904i | 0.753778 | − | 1.30558i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.50000 | + | 4.33013i | 0.246332 | + | 0.426660i | 0.962505 | − | 0.271263i | \(-0.0874412\pi\) |
−0.716173 | + | 0.697923i | \(0.754108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 5.19615i | − | 0.507093i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3923i | 0.986394i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.50000 | + | 7.79423i | 0.423324 | + | 0.733219i | 0.996262 | − | 0.0863794i | \(-0.0275297\pi\) |
−0.572938 | + | 0.819599i | \(0.694196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.500000 | + | 0.866025i | −0.0466252 | + | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.50000 | − | 12.9904i | −0.693375 | − | 1.20096i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | + | 5.19615i | −0.275010 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.50000 | + | 2.59808i | −0.405751 | + | 0.234261i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.50000 | + | 0.866025i | 0.132068 | + | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.50000 | + | 4.33013i | 0.218426 | + | 0.378325i | 0.954327 | − | 0.298764i | \(-0.0965744\pi\) |
−0.735901 | + | 0.677089i | \(0.763241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 10.3923i | −0.520266 | + | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.50000 | + | 2.59808i | −0.387298 | + | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.50000 | + | 2.59808i | −0.128154 | + | 0.221969i | −0.922961 | − | 0.384893i | \(-0.874238\pi\) |
0.794808 | + | 0.606861i | \(0.207572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.50000 | − | 2.59808i | −0.127228 | − | 0.220366i | 0.795373 | − | 0.606120i | \(-0.207275\pi\) |
−0.922602 | + | 0.385754i | \(0.873941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.50000 | − | 2.59808i | −0.378968 | − | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.0000 | −2.09061 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | 0.747409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.00000 | + | 1.73205i | −0.247436 | + | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.50000 | − | 16.4545i | −0.778270 | − | 1.34800i | −0.932938 | − | 0.360037i | \(-0.882764\pi\) |
0.154668 | − | 0.987967i | \(-0.450569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.50000 | + | 14.7224i | −0.691720 | + | 1.19809i | 0.279554 | + | 0.960130i | \(0.409814\pi\) |
−0.971274 | + | 0.237964i | \(0.923520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.500000 | + | 0.866025i | −0.0401610 | + | 0.0695608i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.50000 | − | 6.06218i | −0.279330 | − | 0.483814i | 0.691888 | − | 0.722005i | \(-0.256779\pi\) |
−0.971219 | + | 0.238190i | \(0.923446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 3.46410i | − | 0.274721i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.00000 | 0.236433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.66025i | 0.674200i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.5000 | + | 18.1865i | 0.812514 | + | 1.40732i | 0.911099 | + | 0.412188i | \(0.135235\pi\) |
−0.0985846 | + | 0.995129i | \(0.531432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | + | 10.3923i | −0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.0000 | 0.917663 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.50000 | + | 2.59808i | −0.114043 | + | 0.197528i | −0.917397 | − | 0.397974i | \(-0.869713\pi\) |
0.803354 | + | 0.595502i | \(0.203047\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.00000 | − | 10.3923i | −0.453557 | − | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.5000 | + | 9.52628i | −1.24022 | + | 0.716039i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.5000 | + | 6.06218i | 0.776182 | + | 0.448129i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | − | 5.19615i | −0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.00000 | − | 8.66025i | 0.365636 | − | 0.633300i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.5000 | + | 7.79423i | 0.981981 | + | 0.566947i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5000 | − | 23.3827i | 0.976826 | − | 1.69191i | 0.303052 | − | 0.952974i | \(-0.401994\pi\) |
0.673774 | − | 0.738938i | \(-0.264672\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50000 | + | 11.2583i | 0.467880 | + | 0.810392i | 0.999326 | − | 0.0366998i | \(-0.0116845\pi\) |
−0.531446 | + | 0.847092i | \(0.678351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.50000 | + | 4.33013i | 0.537086 | + | 0.310087i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.50000 | − | 0.866025i | 0.105802 | − | 0.0610847i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.5000 | − | 23.3827i | −0.947514 | − | 1.64114i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.50000 | − | 2.59808i | 0.104765 | − | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.50000 | − | 2.59808i | −0.104257 | − | 0.180579i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0000 | − | 17.3205i | 0.691714 | − | 1.19808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.50000 | − | 6.06218i | −0.240950 | − | 0.417338i | 0.720035 | − | 0.693938i | \(-0.244126\pi\) |
−0.960985 | + | 0.276600i | \(0.910792\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 6.92820i | − | 0.474713i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.00000 | 0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.46410i | 0.234082i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00000 | − | 8.66025i | −0.336336 | − | 0.582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.50000 | − | 9.52628i | 0.368307 | − | 0.637927i | −0.620994 | − | 0.783815i | \(-0.713271\pi\) |
0.989301 | + | 0.145889i | \(0.0466041\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | + | 10.3923i | −0.400000 | + | 0.692820i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5000 | + | 18.1865i | −0.696909 | + | 1.20708i | 0.272623 | + | 0.962121i | \(0.412109\pi\) |
−0.969533 | + | 0.244962i | \(0.921225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.50000 | + | 14.7224i | 0.561696 | + | 0.972886i | 0.997349 | + | 0.0727709i | \(0.0231842\pi\) |
−0.435653 | + | 0.900115i | \(0.643482\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.5000 | − | 12.9904i | 1.48039 | − | 0.854704i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.0000 | 1.70332 | 0.851658 | − | 0.524097i | \(-0.175597\pi\) | ||||
0.851658 | + | 0.524097i | \(0.175597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.50000 | + | 0.866025i | 0.0974355 | + | 0.0562544i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.50000 | + | 14.7224i | 0.549819 | + | 0.952315i | 0.998286 | + | 0.0585157i | \(0.0186368\pi\) |
−0.448467 | + | 0.893799i | \(0.648030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | + | 12.9904i | −0.483117 | + | 0.836784i | −0.999812 | − | 0.0193858i | \(-0.993829\pi\) |
0.516695 | + | 0.856170i | \(0.327162\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0000 | − | 17.3205i | −0.636285 | − | 1.10208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.50000 | + | 0.866025i | 0.0950586 | + | 0.0548821i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.0000 | −1.26239 | −0.631194 | − | 0.775625i | \(-0.717435\pi\) | ||||
−0.631194 | + | 0.775625i | \(0.717435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.00000 | −0.314347 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.00000 | + | 1.73205i | −0.187867 | + | 0.108465i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.50000 | − | 6.06218i | −0.218324 | − | 0.378148i | 0.735972 | − | 0.677012i | \(-0.236726\pi\) |
−0.954296 | + | 0.298864i | \(0.903392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.00000 | + | 15.5885i | −0.559233 | + | 0.968620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.5000 | + | 23.3827i | −0.835629 | + | 1.44735i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.50000 | − | 6.06218i | 0.215819 | − | 0.373810i | −0.737706 | − | 0.675122i | \(-0.764091\pi\) |
0.953526 | + | 0.301312i | \(0.0974245\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.00000 | + | 1.73205i | 0.0614295 | + | 0.106399i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 31.1769i | 1.90800i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 25.9808i | − | 1.57243i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0000 | + | 17.3205i | 0.603023 | + | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.5000 | − | 25.1147i | 0.871221 | − | 1.50900i | 0.0104855 | − | 0.999945i | \(-0.496662\pi\) |
0.860735 | − | 0.509053i | \(-0.170004\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.50000 | − | 2.59808i | −0.0898027 | − | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.50000 | + | 16.4545i | −0.566722 | + | 0.981592i | 0.430165 | + | 0.902750i | \(0.358455\pi\) |
−0.996887 | + | 0.0788417i | \(0.974878\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.50000 | + | 11.2583i | 0.386385 | + | 0.669238i | 0.991960 | − | 0.126550i | \(-0.0403903\pi\) |
−0.605575 | + | 0.795788i | \(0.707057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.00000 | + | 3.46410i | −0.355409 | + | 0.205196i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.00000 | −0.531253 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.5000 | − | 11.2583i | −1.14311 | − | 0.659975i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.50000 | + | 7.79423i | 0.262893 | + | 0.455344i | 0.967009 | − | 0.254741i | \(-0.0819901\pi\) |
−0.704117 | + | 0.710084i | \(0.748657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.50000 | − | 9.52628i | 0.320222 | − | 0.554641i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.5000 | − | 12.9904i | −1.30558 | − | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.50000 | + | 4.33013i | −0.144579 | + | 0.250418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.50000 | + | 2.59808i | 0.0864586 | + | 0.149751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.50000 | + | 2.59808i | 0.258518 | + | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.00000 | −0.400819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.50000 | − | 4.33013i | 0.426660 | − | 0.246332i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.50000 | + | 7.79423i | 0.255172 | + | 0.441970i | 0.964942 | − | 0.262463i | \(-0.0845347\pi\) |
−0.709771 | + | 0.704433i | \(0.751201\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50000 | − | 7.79423i | 0.254355 | − | 0.440556i | −0.710365 | − | 0.703833i | \(-0.751470\pi\) |
0.964720 | + | 0.263278i | \(0.0848035\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.00000 | −0.507093 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.50000 | + | 12.9904i | −0.421242 | + | 0.729612i | −0.996061 | − | 0.0886679i | \(-0.971739\pi\) |
0.574819 | + | 0.818280i | \(0.305072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.5000 | + | 38.9711i | 1.25976 | + | 2.18197i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 20.7846i | − | 1.16008i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.0000 | 1.10940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 17.3205i | − | 0.957826i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.50000 | − | 7.79423i | −0.248093 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50000 | − | 16.4545i | 0.522167 | − | 0.904420i | −0.477500 | − | 0.878632i | \(-0.658457\pi\) |
0.999667 | − | 0.0257885i | \(-0.00820965\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.0000 | 0.986394 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.500000 | + | 0.866025i | −0.0273179 | + | 0.0473160i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50000 | + | 7.79423i | 0.245131 | + | 0.424579i | 0.962168 | − | 0.272456i | \(-0.0878358\pi\) |
−0.717038 | + | 0.697034i | \(0.754502\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.5000 | − | 7.79423i | 0.733219 | − | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.00000 | −0.270765 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.50000 | + | 0.866025i | 0.0807573 | + | 0.0466252i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.50000 | + | 7.79423i | 0.241573 | + | 0.418416i | 0.961162 | − | 0.275983i | \(-0.0890035\pi\) |
−0.719590 | + | 0.694399i | \(0.755670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.5000 | − | 18.1865i | 0.562052 | − | 0.973503i | −0.435265 | − | 0.900302i | \(-0.643345\pi\) |
0.997317 | − | 0.0732005i | \(-0.0233213\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.5000 | + | 12.9904i | −1.20096 | + | 0.693375i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.50000 | − | 4.33013i | 0.133062 | − | 0.230469i | −0.791794 | − | 0.610789i | \(-0.790853\pi\) |
0.924855 | + | 0.380319i | \(0.124186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00000 | + | 3.46410i | 0.106149 | + | 0.183855i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.00000 | + | 5.19615i | 0.476331 | + | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.0000 | + | 12.1244i | −1.10221 | + | 0.636364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.00000 | − | 1.73205i | −0.0523424 | − | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5000 | − | 19.9186i | 0.600295 | − | 1.03974i | −0.392481 | − | 0.919760i | \(-0.628383\pi\) |
0.992776 | − | 0.119982i | \(-0.0382835\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.50000 | + | 7.79423i | 0.234261 | + | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.00000 | − | 5.19615i | 0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.5000 | − | 30.3109i | −0.906116 | − | 1.56944i | −0.819413 | − | 0.573204i | \(-0.805700\pi\) |
−0.0867031 | − | 0.996234i | \(-0.527633\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 15.5885i | − | 0.804984i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 45.0000 | 2.31762 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 27.7128i | − | 1.41977i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.5000 | − | 23.3827i | −0.689818 | − | 1.19480i | −0.971897 | − | 0.235408i | \(-0.924357\pi\) |
0.282079 | − | 0.959391i | \(-0.408976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.50000 | + | 12.9904i | −0.382235 | + | 0.662051i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.50000 | − | 2.59808i | 0.0762493 | − | 0.132068i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.5000 | + | 30.3109i | −0.887285 | + | 1.53682i | −0.0442134 | + | 0.999022i | \(0.514078\pi\) |
−0.843072 | + | 0.537801i | \(0.819255\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | − | 1.73205i | −0.0505722 | − | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.50000 | − | 4.33013i | 0.378325 | − | 0.218426i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.00000 | −0.0503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.0000 | + | 10.3923i | 0.901127 | + | 0.520266i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.5000 | + | 18.1865i | 0.524345 | + | 0.908192i | 0.999598 | + | 0.0283431i | \(0.00902310\pi\) |
−0.475253 | + | 0.879849i | \(0.657644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.50000 | + | 4.33013i | −0.124534 | + | 0.215699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.50000 | + | 7.79423i | 0.223607 | + | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.0000 | − | 25.9808i | 0.743522 | − | 1.28782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5000 | + | 28.5788i | 0.815872 | + | 1.41313i | 0.908700 | + | 0.417450i | \(0.137076\pi\) |
−0.0928272 | + | 0.995682i | \(0.529590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.50000 | + | 2.59808i | 0.221969 | + | 0.128154i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.0000 | −1.62382 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.00000 | −0.0490881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.50000 | + | 2.59808i | −0.220366 | + | 0.127228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.50000 | − | 12.9904i | −0.366399 | − | 0.634622i | 0.622601 | − | 0.782540i | \(-0.286076\pi\) |
−0.989000 | + | 0.147918i | \(0.952743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.500000 | − | 0.866025i | 0.0243685 | − | 0.0422075i | −0.853584 | − | 0.520955i | \(-0.825576\pi\) |
0.877952 | + | 0.478748i | \(0.158909\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.50000 | + | 7.79423i | −0.218797 | + | 0.378968i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.00000 | + | 6.92820i | −0.194029 | + | 0.336067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.5000 | + | 18.1865i | 0.508131 | + | 0.880108i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 43.3013i | 2.09061i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.00000 | −0.385346 | −0.192673 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 15.5885i | − | 0.747409i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00000 | − | 3.46410i | −0.0956730 | − | 0.165710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5000 | + | 28.5788i | −0.787502 | + | 1.36399i | 0.139991 | + | 0.990153i | \(0.455293\pi\) |
−0.927493 | + | 0.373841i | \(0.878041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | + | 5.19615i | 0.142857 | + | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.5000 | − | 19.9186i | 0.546381 | − | 0.946360i | −0.452137 | − | 0.891948i | \(-0.649338\pi\) |
0.998519 | − | 0.0544120i | \(-0.0173284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | − | 15.5885i | −0.426641 | − | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.5000 | + | 16.4545i | −1.34800 | + | 0.778270i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0000 | 0.706322 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.5000 | + | 14.7224i | 1.19809 | + | 0.691720i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.50000 | + | 12.9904i | 0.351605 | + | 0.608998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.50000 | + | 9.52628i | −0.257279 | + | 0.445621i | −0.965512 | − | 0.260358i | \(-0.916159\pi\) |
0.708233 | + | 0.705979i | \(0.249493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 10.3923i | − | 0.485071i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.5000 | − | 21.6506i | 0.582183 | − | 1.00837i | −0.413037 | − | 0.910714i | \(-0.635532\pi\) |
0.995220 | − | 0.0976564i | \(-0.0311346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.5000 | − | 19.9186i | −0.534450 | − | 0.925695i | −0.999190 | − | 0.0402476i | \(-0.987185\pi\) |
0.464739 | − | 0.885448i | \(-0.346148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.50000 | + | 0.866025i | 0.0695608 | + | 0.0401610i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.00000 | 0.138527 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.5000 | + | 6.06218i | −0.483814 | + | 0.279330i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.50000 | − | 4.33013i | −0.114950 | − | 0.199099i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | + | 13.8564i | −0.367065 | + | 0.635776i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.500000 | + | 0.866025i | −0.0228456 | + | 0.0395697i | −0.877222 | − | 0.480085i | \(-0.840606\pi\) |
0.854377 | + | 0.519654i | \(0.173939\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.0000 | − | 25.9808i | −0.683941 | − | 1.18462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 5.19615i | − | 0.236433i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.0000 | 0.590300 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0000 | −1.45006 | −0.725029 | − | 0.688718i | \(-0.758174\pi\) | ||||
−0.725029 | + | 0.688718i | \(0.758174\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.7846i | 0.939913i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.5000 | − | 23.3827i | −0.609246 | − | 1.05525i | −0.991365 | − | 0.131132i | \(-0.958139\pi\) |
0.382118 | − | 0.924113i | \(-0.375195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | + | 15.5885i | −0.405340 | + | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.0000 | 0.674200 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.00000 | − | 10.3923i | 0.269137 | − | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.5000 | − | 23.3827i | −0.604343 | − | 1.04675i | −0.992155 | − | 0.125014i | \(-0.960102\pi\) |
0.387812 | − | 0.921739i | \(-0.373231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.5000 | − | 18.1865i | 1.40732 | − | 0.812514i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.0000 | + | 10.3923i | 0.799408 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.50000 | − | 2.59808i | −0.0664863 | − | 0.115158i | 0.830866 | − | 0.556473i | \(-0.187846\pi\) |
−0.897352 | + | 0.441315i | \(0.854512\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | + | 5.19615i | −0.132712 | + | 0.229864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 20.7846i | − | 0.917663i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.50000 | + | 4.33013i | −0.110163 | + | 0.190808i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.50000 | + | 12.9904i | 0.329850 | + | 0.571316i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.50000 | + | 2.59808i | 0.197528 | + | 0.114043i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.0000 | 1.74908 | 0.874539 | − | 0.484955i | \(-0.161164\pi\) | ||||
0.874539 | + | 0.484955i | \(0.161164\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.0000 | + | 10.3923i | −0.785584 | + | 0.453557i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.00000 | − | 1.73205i | −0.0435607 | − | 0.0754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.5000 | + | 28.5788i | 0.716039 | + | 1.24022i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.50000 | − | 12.9904i | 0.324861 | − | 0.562676i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | + | 10.3923i | 0.259403 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 20.7846i | − | 0.896922i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0000 | 0.430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3923i | 0.445976i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.00000 | + | 8.66025i | 0.214176 | + | 0.370965i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.50000 | − | 16.4545i | 0.406191 | − | 0.703543i | −0.588269 | − | 0.808666i | \(-0.700190\pi\) |
0.994459 | + | 0.105123i | \(0.0335235\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.5000 | − | 18.1865i | 0.448129 | − | 0.776182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.0000 | + | 31.1769i | −0.766826 | + | 1.32818i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.50000 | + | 2.59808i | 0.0637865 | + | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.00000 | + | 5.19615i | −0.382029 | + | 0.220564i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.0000 | −0.932170 | −0.466085 | − | 0.884740i | \(-0.654336\pi\) | ||||
−0.466085 | + | 0.884740i | \(0.654336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00000 | −0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.0000 | − | 8.66025i | −0.633300 | − | 0.365636i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.500000 | + | 0.866025i | 0.0210725 | + | 0.0364986i | 0.876369 | − | 0.481640i | \(-0.159959\pi\) |
−0.855297 | + | 0.518138i | \(0.826625\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.50000 | + | 7.79423i | −0.189316 | + | 0.327906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.5000 | − | 23.3827i | 0.566947 | − | 0.981981i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.5000 | − | 21.6506i | 0.524027 | − | 0.907642i | −0.475581 | − | 0.879672i | \(-0.657762\pi\) |
0.999609 | − | 0.0279702i | \(-0.00890434\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.50000 | − | 12.9904i | −0.313865 | − | 0.543631i | 0.665330 | − | 0.746549i | \(-0.268291\pi\) |
−0.979196 | + | 0.202919i | \(0.934957\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.5000 | − | 23.3827i | −1.69191 | − | 0.976826i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.5000 | − | 11.2583i | 0.810392 | − | 0.467880i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.50000 | + | 2.59808i | 0.0622305 | + | 0.107786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.00000 | + | 8.66025i | −0.207079 | + | 0.358671i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.50000 | − | 12.9904i | 0.310087 | − | 0.537086i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.50000 | + | 14.7224i | −0.350833 | + | 0.607660i | −0.986396 | − | 0.164389i | \(-0.947435\pi\) |
0.635563 | + | 0.772049i | \(0.280768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | − | 3.46410i | −0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 10.3923i | − | 0.427482i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.0000 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | −0.245976 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.6410i | 1.41776i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5000 | + | 18.1865i | 0.429018 | + | 0.743082i | 0.996786 | − | 0.0801071i | \(-0.0255262\pi\) |
−0.567768 | + | 0.823189i | \(0.692193\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.50000 | + | 16.4545i | −0.387513 | + | 0.671192i | −0.992114 | − | 0.125336i | \(-0.959999\pi\) |
0.604601 | + | 0.796528i | \(0.293332\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.50000 | − | 2.59808i | −0.0610847 | − | 0.105802i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | − | 12.1244i | 0.284590 | − | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.50000 | + | 11.2583i | 0.263827 | + | 0.456962i | 0.967256 | − | 0.253804i | \(-0.0816819\pi\) |
−0.703429 | + | 0.710766i | \(0.748349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −40.5000 | + | 23.3827i | −1.64114 | + | 0.947514i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | 0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.50000 | − | 2.59808i | −0.181458 | − | 0.104765i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.50000 | − | 2.59808i | −0.0603877 | − | 0.104595i | 0.834251 | − | 0.551385i | \(-0.185900\pi\) |
−0.894639 | + | 0.446790i | \(0.852567\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.50000 | − | 9.52628i | 0.221064 | − | 0.382893i | −0.734068 | − | 0.679076i | \(-0.762380\pi\) |
0.955131 | + | 0.296183i | \(0.0957138\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.50000 | + | 2.59808i | −0.180579 | + | 0.104257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.0000 | + | 46.7654i | −1.08173 | + | 1.87362i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.0000 | − | 17.3205i | −1.19808 | − | 0.691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.5000 | + | 6.06218i | −0.417338 | + | 0.240950i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.00000 | + | 13.8564i | 0.317470 | + | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00000 | − | 8.66025i | 0.198107 | − | 0.343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.500000 | − | 0.866025i | 0.0197488 | − | 0.0342059i | −0.855982 | − | 0.517005i | \(-0.827047\pi\) |
0.875731 | + | 0.482800i | \(0.160380\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.50000 | − | 12.9904i | −0.295771 | − | 0.512291i | 0.679393 | − | 0.733775i | \(-0.262243\pi\) |
−0.975164 | + | 0.221484i | \(0.928910\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.73205i | 0.0681994i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.0000 | −1.25805 | −0.629025 | − | 0.777385i | \(-0.716546\pi\) | ||||
−0.629025 | + | 0.777385i | \(0.716546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.0000 | 2.15894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 5.19615i | − | 0.203653i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.5000 | + | 28.5788i | 0.645695 | + | 1.11838i | 0.984141 | + | 0.177390i | \(0.0567655\pi\) |
−0.338446 | + | 0.940986i | \(0.609901\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.50000 | + | 4.33013i | −0.0976831 | + | 0.169192i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.5000 | + | 18.1865i | −0.409022 | + | 0.708447i | −0.994780 | − | 0.102039i | \(-0.967463\pi\) |
0.585758 | + | 0.810486i | \(0.300797\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5000 | + | 21.6506i | 0.486194 | + | 0.842112i | 0.999874 | − | 0.0158695i | \(-0.00505163\pi\) |
−0.513680 | + | 0.857982i | \(0.671718\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.0000 | + | 8.66025i | −0.582552 | + | 0.336336i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | −0.465340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | 0.348481 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.5000 | − | 9.52628i | −0.637927 | − | 0.368307i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.5000 | − | 30.3109i | −0.675580 | − | 1.17014i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.50000 | + | 16.4545i | −0.366198 | + | 0.634274i | −0.988968 | − | 0.148132i | \(-0.952674\pi\) |
0.622770 | + | 0.782405i | \(0.286007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.0000 | + | 10.3923i | 0.692820 | + | 0.400000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.5000 | + | 30.3109i | −0.672580 | + | 1.16494i | 0.304590 | + | 0.952483i | \(0.401480\pi\) |
−0.977170 | + | 0.212459i | \(0.931853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.5000 | − | 33.7750i | −0.748341 | − | 1.29617i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.5000 | + | 18.1865i | 1.20708 | + | 0.696909i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.00000 | −0.153056 | −0.0765279 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765279 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.00000 | −0.114624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.5000 | − | 14.7224i | 0.972886 | − | 0.561696i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.00000 | + | 8.66025i | 0.190485 | + | 0.329929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5000 | + | 35.5070i | −0.779857 | + | 1.35075i | 0.152167 | + | 0.988355i | \(0.451375\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.5000 | − | 38.9711i | −0.854704 | − | 1.48039i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.50000 | − | 2.59808i | 0.0568982 | − | 0.0985506i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | + | 5.19615i | 0.113633 | + | 0.196818i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 45.0333i | − | 1.70332i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | 0.905177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 5.19615i | − | 0.195698i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.50000 | + | 7.79423i | 0.169240 | + | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.50000 | + | 9.52628i | −0.206557 | + | 0.357767i | −0.950628 | − | 0.310334i | \(-0.899559\pi\) |
0.744071 | + | 0.668101i | \(0.232892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.50000 | − | 2.59808i | 0.0562544 | − | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.500000 | + | 0.866025i | −0.0187251 | + | 0.0324329i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.5000 | − | 21.6506i | −0.467473 | − | 0.809688i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.5000 | − | 14.7224i | 0.952315 | − | 0.549819i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.0000 | 1.19340 | 0.596699 | − | 0.802465i | \(-0.296479\pi\) | ||||
0.596699 | + | 0.802465i | \(0.296479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0000 | 0.558629 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.5000 | + | 12.9904i | 0.836784 | + | 0.483117i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0000 | − | 31.1769i | −0.668503 | − | 1.15788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5000 | − | 33.7750i | 0.723215 | − | 1.25265i | −0.236490 | − | 0.971634i | \(-0.575997\pi\) |
0.959705 | − | 0.281011i | \(-0.0906698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.00000 | − | 1.73205i | 0.0369863 | − | 0.0640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.50000 | + | 11.2583i | 0.240083 | + | 0.415836i | 0.960738 | − | 0.277458i | \(-0.0894920\pi\) |
−0.720655 | + | 0.693294i | \(0.756159\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.00000 | − | 1.73205i | −0.110657 | − | 0.0638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.00000 | −0.184177 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −30.0000 | + | 17.3205i | −1.10208 | + | 0.636285i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.50000 | − | 9.52628i | −0.201775 | − | 0.349485i | 0.747325 | − | 0.664459i | \(-0.231338\pi\) |
−0.949101 | + | 0.314973i | \(0.898004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.50000 | − | 16.4545i | 0.348053 | − | 0.602846i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.50000 | − | 2.59808i | 0.0548821 | − | 0.0950586i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | − | 31.1769i | 0.657706 | − | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.5000 | − | 23.3827i | −0.492622 | − | 0.853246i | 0.507342 | − | 0.861745i | \(-0.330628\pi\) |
−0.999964 | + | 0.00849853i | \(0.997295\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.6410i | 1.26239i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.0000 | −0.618693 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.66025i | 0.314347i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.50000 | + | 4.33013i | 0.0906249 | + | 0.156967i | 0.907774 | − | 0.419459i | \(-0.137780\pi\) |
−0.817149 | + | 0.576426i | \(0.804447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.0000 | − | 25.9808i | 0.543036 | − | 0.940567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.00000 | + | 5.19615i | 0.108465 | + | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.5000 | − | 47.6314i | 0.992967 | − | 1.71987i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.500000 | + | 0.866025i | 0.0180305 | + | 0.0312297i | 0.874900 | − | 0.484304i | \(-0.160927\pi\) |
−0.856869 | + | 0.515534i | \(0.827594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.5000 | + | 6.06218i | −0.378148 | + | 0.218324i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.0000 | 1.51064 | 0.755318 | − | 0.655359i | \(-0.227483\pi\) | ||||
0.755318 | + | 0.655359i | \(0.227483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.0000 | + | 15.5885i | 0.968620 | + | 0.559233i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0000 | + | 17.3205i | −0.357828 | + | 0.619777i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 40.5000 | + | 23.3827i | 1.44735 | + | 0.835629i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.50000 | − | 6.06218i | 0.124920 | − | 0.216368i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.5000 | + | 45.8993i | 0.944623 | + | 1.63614i | 0.756504 | + | 0.653989i | \(0.226906\pi\) |
0.188119 | + | 0.982146i | \(0.439761\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.5000 | − | 6.06218i | −0.373810 | − | 0.215819i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.0000 | 0.960009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.0000 | −1.24289 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.00000 | − | 1.73205i | 0.106399 | − | 0.0614295i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.50000 | + | 11.2583i | 0.230242 | + | 0.398791i | 0.957879 | − | 0.287171i | \(-0.0927150\pi\) |
−0.727637 | + | 0.685962i | \(0.759382\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.00000 | + | 5.19615i | −0.106132 | + | 0.183827i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 54.0000 | 1.90800 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.00000 | − | 8.66025i | 0.176446 | − | 0.305614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.50000 | + | 2.59808i | 0.0528681 | + | 0.0915702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.2487i | 0.853595i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.0000 | −1.75791 | −0.878953 | − | 0.476908i | \(-0.841757\pi\) | ||||
−0.878953 | + | 0.476908i | \(0.841757\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 13.8564i | − | 0.485965i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.00000 | − | 10.3923i | −0.210171 | − | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | − | 3.46410i | 0.0699711 | − | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −45.0000 | −1.57243 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5000 | − | 28.5788i | 0.575854 | − | 0.997408i | −0.420094 | − | 0.907480i | \(-0.638003\pi\) |
0.995948 | − | 0.0899279i | \(-0.0286637\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5000 | + | 42.4352i | 0.854016 | + | 1.47920i | 0.877555 | + | 0.479477i | \(0.159174\pi\) |
−0.0235383 | + | 0.999723i | \(0.507493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.0000 | − | 17.3205i | 1.04447 | − | 0.603023i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.0000 | −1.53003 | −0.765015 | − | 0.644013i | \(-0.777268\pi\) | ||||
−0.765015 | + | 0.644013i | \(0.777268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.5000 | − | 25.1147i | −1.50900 | − | 0.871221i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000 | + | 3.46410i | 0.0692959 | + | 0.120024i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5000 | + | 18.1865i | −0.363367 | + | 0.629371i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.50000 | + | 2.59808i | −0.155543 | + | 0.0898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.5000 | + | 18.1865i | −0.362500 | + | 0.627869i | −0.988372 | − | 0.152057i | \(-0.951410\pi\) |
0.625871 | + | 0.779926i | \(0.284743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | − | 45.0333i | −0.896552 | − | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.5000 | + | 16.4545i | 0.981592 | + | 0.566722i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −42.0000 | −1.44314 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.5000 | − | 11.2583i | 0.669238 | − | 0.386385i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00000 | − | 5.19615i | −0.102839 | − | 0.178122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.500000 | − | 0.866025i | 0.0171197 | − | 0.0296521i | −0.857339 | − | 0.514753i | \(-0.827884\pi\) |
0.874458 | + | 0.485101i | \(0.161217\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | + | 10.3923i | 0.205196 | + | 0.355409i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.5000 | + | 23.3827i | −0.461151 | + | 0.798737i | −0.999019 | − | 0.0442921i | \(-0.985897\pi\) |
0.537867 | + | 0.843029i | \(0.319230\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.50000 | + | 7.79423i | 0.153538 | + | 0.265936i | 0.932526 | − | 0.361104i | \(-0.117600\pi\) |
−0.778988 | + | 0.627039i | \(0.784267\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.5885i | 0.531253i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.0000 | 1.90626 | 0.953131 | − | 0.302558i | \(-0.0978405\pi\) | ||||
0.953131 | + | 0.302558i | \(0.0978405\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.00000 | −0.102003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.5167i | 0.764706i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.50000 | − | 4.33013i | −0.0848067 | − | 0.146889i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.50000 | + | 4.33013i | −0.0847093 | + | 0.146721i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.5000 | + | 33.7750i | −0.659975 | + | 1.14311i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.5000 | − | 23.3827i | 0.456383 | − | 0.790479i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.50000 | − | 2.59808i | −0.0506514 | − | 0.0877308i | 0.839588 | − | 0.543224i | \(-0.182796\pi\) |
−0.890239 | + | 0.455493i | \(0.849463\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.5000 | − | 7.79423i | 0.455344 | − | 0.262893i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.0000 | −0.875962 | −0.437981 | − | 0.898984i | \(-0.644306\pi\) | ||||
−0.437981 | + | 0.898984i | \(0.644306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.5000 | − | 9.52628i | −0.554641 | − | 0.320222i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.5000 | − | 47.6314i | −0.923360 | − | 1.59931i | −0.794178 | − | 0.607685i | \(-0.792098\pi\) |
−0.129181 | − | 0.991621i | \(-0.541235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.0000 | − | 41.5692i | 0.804934 | − | 1.39419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.5000 | + | 38.9711i | −0.753778 | + | 1.30558i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.00000 | + | 10.3923i | 0.200558 | + | 0.347376i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.50000 | + | 4.33013i | 0.250418 | + | 0.144579i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.00000 | 0.300167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.50000 | − | 2.59808i | 0.149751 | − | 0.0864586i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.00000 | − | 5.19615i | −0.0997234 | − | 0.172726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.5000 | + | 42.4352i | −0.813509 | + | 1.40904i | 0.0968843 | + | 0.995296i | \(0.469112\pi\) |
−0.910393 | + | 0.413744i | \(0.864221\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.50000 | − | 7.79423i | 0.149256 | − | 0.258518i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5000 | + | 35.5070i | −0.679195 | + | 1.17640i | 0.296028 | + | 0.955179i | \(0.404338\pi\) |
−0.975224 | + | 0.221222i | \(0.928996\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.50000 | − | 4.33013i | −0.0827379 | − | 0.143306i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.1244i | 0.400819i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.0000 | 0.495344 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.7846i | 0.684876i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.0000 | + | 17.3205i | 0.329154 | + | 0.570111i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | + | 20.7846i | −0.394558 | + | 0.683394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.50000 | − | 12.9904i | −0.246332 | − | 0.426660i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.5000 | − | 25.1147i | 0.475730 | − | 0.823988i | −0.523884 | − | 0.851790i | \(-0.675517\pi\) |
0.999613 | + | 0.0278019i | \(0.00885076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | + | 6.92820i | 0.131095 | + | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.5000 | − | 7.79423i | 0.441970 | − | 0.255172i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.0000 | 0.327035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.0000 | −1.37208 | −0.686040 | − | 0.727564i | \(-0.740653\pi\) | ||||
−0.686040 | + | 0.727564i | \(0.740653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.5000 | − | 7.79423i | −0.440556 | − | 0.254355i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.5000 | + | 28.5788i | 0.537885 | + | 0.931644i | 0.999018 | + | 0.0443125i | \(0.0141097\pi\) |
−0.461133 | + | 0.887331i | \(0.652557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.50000 | − | 2.59808i | 0.0488467 | − | 0.0846050i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.5885i | 0.507093i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5000 | − | 23.3827i | 0.438691 | − | 0.759835i | −0.558898 | − | 0.829237i | \(-0.688776\pi\) |
0.997589 | + | 0.0694014i | \(0.0221089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.00000 | − | 8.66025i | −0.162307 | − | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.5000 | + | 12.9904i | 0.729612 | + | 0.421242i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.0000 | 0.873699 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 67.5000 | − | 38.9711i | 2.18197 | − | 1.25976i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.50000 | + | 7.79423i | 0.145313 | + | 0.251689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.0000 | −1.16008 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.50000 | + | 11.2583i | −0.209242 | + | 0.362418i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.5000 | + | 21.6506i | 0.401973 | + | 0.696237i | 0.993964 | − | 0.109707i | \(-0.0349913\pi\) |
−0.591991 | + | 0.805945i | \(0.701658\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 13.8564i | − | 0.445132i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.00000 | −0.288527 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 34.6410i | − | 1.10940i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5000 | − | 33.7750i | −0.623860 | − | 1.08056i | −0.988760 | − | 0.149511i | \(-0.952230\pi\) |
0.364900 | − | 0.931047i | \(-0.381103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.0000 | − | 77.9423i | 1.43821 | − | 2.49105i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.0000 | −0.957826 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.50000 | − | 12.9904i | 0.239213 | − | 0.414329i | −0.721276 | − | 0.692648i | \(-0.756444\pi\) |
0.960489 | + | 0.278319i | \(0.0897773\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | + | 5.19615i | 0.0955879 | + | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.5000 | + | 7.79423i | −0.429710 | + | 0.248093i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.00000 | −0.0317982 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000 | 1.27064 | 0.635321 | − | 0.772248i | \(-0.280868\pi\) | ||||
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.5000 | − | 16.4545i | −0.904420 | − | 0.522167i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.0000 | − | 17.3205i | −0.317021 | − | 0.549097i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.50000 | + | 16.4545i | −0.300868 | + | 0.521119i | −0.976333 | − | 0.216274i | \(-0.930610\pi\) |
0.675465 | + | 0.737392i | \(0.263943\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 31.1769i | − | 0.986394i |
(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 | 72.2.i.a.25.1 | ✓ | 2 | |
3.2 | odd | 2 | 216.2.i.a.73.1 | 2 | |||
4.3 | odd | 2 | 144.2.i.b.97.1 | 2 | |||
8.3 | odd | 2 | 576.2.i.c.385.1 | 2 | |||
8.5 | even | 2 | 576.2.i.d.385.1 | 2 | |||
9.2 | odd | 6 | 648.2.a.c.1.1 | 1 | |||
9.4 | even | 3 | inner | 72.2.i.a.49.1 | yes | 2 | |
9.5 | odd | 6 | 216.2.i.a.145.1 | 2 | |||
9.7 | even | 3 | 648.2.a.a.1.1 | 1 | |||
12.11 | even | 2 | 432.2.i.a.289.1 | 2 | |||
24.5 | odd | 2 | 1728.2.i.h.1153.1 | 2 | |||
24.11 | even | 2 | 1728.2.i.g.1153.1 | 2 | |||
36.7 | odd | 6 | 1296.2.a.e.1.1 | 1 | |||
36.11 | even | 6 | 1296.2.a.i.1.1 | 1 | |||
36.23 | even | 6 | 432.2.i.a.145.1 | 2 | |||
36.31 | odd | 6 | 144.2.i.b.49.1 | 2 | |||
72.5 | odd | 6 | 1728.2.i.h.577.1 | 2 | |||
72.11 | even | 6 | 5184.2.a.n.1.1 | 1 | |||
72.13 | even | 6 | 576.2.i.d.193.1 | 2 | |||
72.29 | odd | 6 | 5184.2.a.i.1.1 | 1 | |||
72.43 | odd | 6 | 5184.2.a.x.1.1 | 1 | |||
72.59 | even | 6 | 1728.2.i.g.577.1 | 2 | |||
72.61 | even | 6 | 5184.2.a.s.1.1 | 1 | |||
72.67 | odd | 6 | 576.2.i.c.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.i.a.25.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
72.2.i.a.49.1 | yes | 2 | 9.4 | even | 3 | inner | |
144.2.i.b.49.1 | 2 | 36.31 | odd | 6 | |||
144.2.i.b.97.1 | 2 | 4.3 | odd | 2 | |||
216.2.i.a.73.1 | 2 | 3.2 | odd | 2 | |||
216.2.i.a.145.1 | 2 | 9.5 | odd | 6 | |||
432.2.i.a.145.1 | 2 | 36.23 | even | 6 | |||
432.2.i.a.289.1 | 2 | 12.11 | even | 2 | |||
576.2.i.c.193.1 | 2 | 72.67 | odd | 6 | |||
576.2.i.c.385.1 | 2 | 8.3 | odd | 2 | |||
576.2.i.d.193.1 | 2 | 72.13 | even | 6 | |||
576.2.i.d.385.1 | 2 | 8.5 | even | 2 | |||
648.2.a.a.1.1 | 1 | 9.7 | even | 3 | |||
648.2.a.c.1.1 | 1 | 9.2 | odd | 6 | |||
1296.2.a.e.1.1 | 1 | 36.7 | odd | 6 | |||
1296.2.a.i.1.1 | 1 | 36.11 | even | 6 | |||
1728.2.i.g.577.1 | 2 | 72.59 | even | 6 | |||
1728.2.i.g.1153.1 | 2 | 24.11 | even | 2 | |||
1728.2.i.h.577.1 | 2 | 72.5 | odd | 6 | |||
1728.2.i.h.1153.1 | 2 | 24.5 | odd | 2 | |||
5184.2.a.i.1.1 | 1 | 72.29 | odd | 6 | |||
5184.2.a.n.1.1 | 1 | 72.11 | even | 6 | |||
5184.2.a.s.1.1 | 1 | 72.61 | even | 6 | |||
5184.2.a.x.1.1 | 1 | 72.43 | odd | 6 |