Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(577,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.i (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: | \(13.7981494693\) |
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: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.577 |
Dual form | 1728.2.i.g.1153.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | − | 2.59808i | −0.566947 | − | 0.981981i | −0.996866 | − | 0.0791130i | \(-0.974791\pi\) |
0.429919 | − | 0.902867i | \(-0.358542\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 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 | ||||||||
\(13\) | −2.50000 | + | 4.33013i | −0.693375 | + | 1.20096i | 0.277350 | + | 0.960769i | \(0.410544\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913434 | + | 0.406986i | \(0.133420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.50000 | + | 7.79423i | 0.835629 | + | 1.44735i | 0.893517 | + | 0.449029i | \(0.148230\pi\) |
−0.0578882 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.500000 | + | 0.866025i | −0.0898027 | + | 0.155543i | −0.907428 | − | 0.420208i | \(-0.861957\pi\) |
0.817625 | + | 0.575751i | \(0.195290\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.50000 | + | 2.59808i | 0.218797 | + | 0.378968i | 0.954441 | − | 0.298401i | \(-0.0964533\pi\) |
−0.735643 | + | 0.677369i | \(0.763120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 1.73205i | −0.142857 | + | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.50000 | − | 9.52628i | 0.716039 | − | 1.24022i | −0.246518 | − | 0.969138i | \(-0.579287\pi\) |
0.962557 | − | 0.271078i | \(-0.0873801\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.50000 | + | 4.33013i | 0.310087 | + | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.500000 | − | 0.866025i | 0.0610847 | − | 0.105802i | −0.833866 | − | 0.551967i | \(-0.813877\pi\) |
0.894951 | + | 0.446165i | \(0.147211\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.500000 | + | 0.866025i | 0.0548821 | + | 0.0950586i | 0.892161 | − | 0.451717i | \(-0.149188\pi\) |
−0.837279 | + | 0.546776i | \(0.815855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | − | 1.73205i | 0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.0000 | 1.90800 | 0.953998 | − | 0.299813i | \(-0.0969242\pi\) | ||||
0.953998 | + | 0.299813i | \(0.0969242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.0000 | 1.57243 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | + | 3.46410i | −0.205196 | + | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.50000 | + | 11.2583i | 0.659975 | + | 1.14311i | 0.980622 | + | 0.195911i | \(0.0627665\pi\) |
−0.320647 | + | 0.947199i | \(0.603900\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −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 | ||||||||
\(103\) | −2.50000 | + | 4.33013i | −0.246332 | + | 0.426660i | −0.962505 | − | 0.271263i | \(-0.912559\pi\) |
0.716173 | + | 0.697923i | \(0.245892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.50000 | + | 7.79423i | −0.423324 | + | 0.733219i | −0.996262 | − | 0.0863794i | \(-0.972470\pi\) |
0.572938 | + | 0.819599i | \(0.305804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.500000 | − | 0.866025i | −0.0466252 | − | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.50000 | + | 4.33013i | −0.218426 | + | 0.378325i | −0.954327 | − | 0.298764i | \(-0.903426\pi\) |
0.735901 | + | 0.677089i | \(0.236759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | + | 10.3923i | 0.520266 | + | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.50000 | + | 2.59808i | 0.128154 | + | 0.221969i | 0.922961 | − | 0.384893i | \(-0.125762\pi\) |
−0.794808 | + | 0.606861i | \(0.792428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.50000 | + | 2.59808i | −0.127228 | + | 0.220366i | −0.922602 | − | 0.385754i | \(-0.873941\pi\) |
0.795373 | + | 0.606120i | \(0.207275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.0000 | −2.09061 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | 0.747409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.50000 | + | 16.4545i | −0.778270 | + | 1.34800i | 0.154668 | + | 0.987967i | \(0.450569\pi\) |
−0.932938 | + | 0.360037i | \(0.882764\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.50000 | + | 14.7224i | 0.691720 | + | 1.19809i | 0.971274 | + | 0.237964i | \(0.0764802\pi\) |
−0.279554 | + | 0.960130i | \(0.590186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 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 | \(-0.743221\pi\) |
0.971219 | + | 0.238190i | \(0.0765542\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.5000 | − | 18.1865i | 0.812514 | − | 1.40732i | −0.0985846 | − | 0.995129i | \(-0.531432\pi\) |
0.911099 | − | 0.412188i | \(-0.135235\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.50000 | − | 2.59808i | −0.114043 | − | 0.197528i | 0.803354 | − | 0.595502i | \(-0.203047\pi\) |
−0.917397 | + | 0.397974i | \(0.869713\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.00000 | − | 10.3923i | 0.453557 | − | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5000 | + | 23.3827i | 0.976826 | + | 1.69191i | 0.673774 | + | 0.738938i | \(0.264672\pi\) |
0.303052 | + | 0.952974i | \(0.401994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50000 | − | 11.2583i | 0.467880 | − | 0.810392i | −0.531446 | − | 0.847092i | \(-0.678351\pi\) |
0.999326 | + | 0.0366998i | \(0.0116845\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0000 | − | 17.3205i | −0.691714 | − | 1.19808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.50000 | + | 6.06218i | −0.240950 | + | 0.417338i | −0.960985 | − | 0.276600i | \(-0.910792\pi\) |
0.720035 | + | 0.693938i | \(0.244126\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.00000 | 0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | \(-0.286729\pi\) |
−0.989301 | + | 0.145889i | \(0.953396\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5000 | + | 18.1865i | 0.696909 | + | 1.20708i | 0.969533 | + | 0.244962i | \(0.0787754\pi\) |
−0.272623 | + | 0.962121i | \(0.587891\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.50000 | + | 14.7224i | −0.561696 | + | 0.972886i | 0.435653 | + | 0.900115i | \(0.356518\pi\) |
−0.997349 | + | 0.0727709i | \(0.976816\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.0000 | −1.70332 | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||||
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.50000 | − | 14.7224i | 0.549819 | − | 0.952315i | −0.448467 | − | 0.893799i | \(-0.648030\pi\) |
0.998286 | − | 0.0585157i | \(-0.0186368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | − | 12.9904i | −0.483117 | − | 0.836784i | 0.516695 | − | 0.856170i | \(-0.327162\pi\) |
−0.999812 | + | 0.0193858i | \(0.993829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 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 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.0000 | 1.26239 | 0.631194 | − | 0.775625i | \(-0.282565\pi\) | ||||
0.631194 | + | 0.775625i | \(0.282565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.00000 | 0.314347 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.50000 | − | 6.06218i | 0.218324 | − | 0.378148i | −0.735972 | − | 0.677012i | \(-0.763274\pi\) |
0.954296 | + | 0.298864i | \(0.0966077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.00000 | − | 15.5885i | −0.559233 | − | 0.968620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.50000 | + | 6.06218i | 0.215819 | + | 0.373810i | 0.953526 | − | 0.301312i | \(-0.0974245\pi\) |
−0.737706 | + | 0.675122i | \(0.764091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.00000 | − | 1.73205i | 0.0614295 | − | 0.106399i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.0000 | + | 17.3205i | −0.603023 | + | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.5000 | − | 25.1147i | −0.871221 | − | 1.50900i | −0.860735 | − | 0.509053i | \(-0.829996\pi\) |
−0.0104855 | − | 0.999945i | \(-0.503338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.50000 | + | 16.4545i | 0.566722 | + | 0.981592i | 0.996887 | + | 0.0788417i | \(0.0251222\pi\) |
−0.430165 | + | 0.902750i | \(0.641545\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.50000 | − | 11.2583i | 0.386385 | − | 0.669238i | −0.605575 | − | 0.795788i | \(-0.707057\pi\) |
0.991960 | + | 0.126550i | \(0.0403903\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.00000 | −0.531253 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.50000 | − | 7.79423i | 0.262893 | − | 0.455344i | −0.704117 | − | 0.710084i | \(-0.748657\pi\) |
0.967009 | + | 0.254741i | \(0.0819901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.50000 | − | 9.52628i | −0.320222 | − | 0.554641i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.50000 | − | 7.79423i | 0.255172 | − | 0.441970i | −0.709771 | − | 0.704433i | \(-0.751201\pi\) |
0.964942 | + | 0.262463i | \(0.0845347\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50000 | + | 7.79423i | 0.254355 | + | 0.440556i | 0.964720 | − | 0.263278i | \(-0.0848035\pi\) |
−0.710365 | + | 0.703833i | \(0.751470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.50000 | − | 12.9904i | −0.421242 | − | 0.729612i | 0.574819 | − | 0.818280i | \(-0.305072\pi\) |
−0.996061 | + | 0.0886679i | \(0.971739\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5000 | + | 38.9711i | −1.25976 | + | 2.18197i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.0000 | −1.10940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50000 | − | 7.79423i | 0.248093 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50000 | + | 16.4545i | 0.522167 | + | 0.904420i | 0.999667 | + | 0.0257885i | \(0.00820965\pi\) |
−0.477500 | + | 0.878632i | \(0.658457\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.500000 | − | 0.866025i | −0.0273179 | − | 0.0473160i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50000 | − | 7.79423i | 0.245131 | − | 0.424579i | −0.717038 | − | 0.697034i | \(-0.754502\pi\) |
0.962168 | + | 0.272456i | \(0.0878358\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.00000 | −0.270765 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.50000 | + | 7.79423i | −0.241573 | + | 0.418416i | −0.961162 | − | 0.275983i | \(-0.910997\pi\) |
0.719590 | + | 0.694399i | \(0.244330\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.5000 | − | 18.1865i | −0.562052 | − | 0.973503i | −0.997317 | − | 0.0732005i | \(-0.976679\pi\) |
0.435265 | − | 0.900302i | \(-0.356655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.50000 | − | 4.33013i | −0.133062 | − | 0.230469i | 0.791794 | − | 0.610789i | \(-0.209147\pi\) |
−0.924855 | + | 0.380319i | \(0.875814\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00000 | − | 3.46410i | 0.106149 | − | 0.183855i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.00000 | + | 1.73205i | −0.0523424 | + | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5000 | − | 19.9186i | −0.600295 | − | 1.03974i | −0.992776 | − | 0.119982i | \(-0.961716\pi\) |
0.392481 | − | 0.919760i | \(-0.371617\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.5000 | − | 30.3109i | 0.906116 | − | 1.56944i | 0.0867031 | − | 0.996234i | \(-0.472367\pi\) |
0.819413 | − | 0.573204i | \(-0.194300\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.5000 | + | 23.3827i | −0.689818 | + | 1.19480i | 0.282079 | + | 0.959391i | \(0.408976\pi\) |
−0.971897 | + | 0.235408i | \(0.924357\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.50000 | − | 12.9904i | −0.382235 | − | 0.662051i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.5000 | − | 30.3109i | −0.887285 | − | 1.53682i | −0.843072 | − | 0.537801i | \(-0.819255\pi\) |
−0.0442134 | − | 0.999022i | \(-0.514078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00000 | − | 1.73205i | 0.0505722 | − | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.00000 | 0.0503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0000 | 1.10415 | 0.552074 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5000 | + | 18.1865i | −0.524345 | + | 0.908192i | 0.475253 | + | 0.879849i | \(0.342356\pi\) |
−0.999598 | + | 0.0283431i | \(0.990977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.50000 | − | 4.33013i | −0.124534 | − | 0.215699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.0000 | + | 25.9808i | 0.743522 | + | 1.28782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5000 | − | 28.5788i | 0.815872 | − | 1.41313i | −0.0928272 | − | 0.995682i | \(-0.529590\pi\) |
0.908700 | − | 0.417450i | \(-0.137076\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.0000 | −1.62382 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.00000 | 0.0490881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.50000 | − | 12.9904i | 0.366399 | − | 0.634622i | −0.622601 | − | 0.782540i | \(-0.713924\pi\) |
0.989000 | + | 0.147918i | \(0.0472572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.500000 | − | 0.866025i | −0.0243685 | − | 0.0422075i | 0.853584 | − | 0.520955i | \(-0.174424\pi\) |
−0.877952 | + | 0.478748i | \(0.841091\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 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 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00000 | + | 3.46410i | −0.0956730 | + | 0.165710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.5000 | + | 28.5788i | 0.787502 | + | 1.36399i | 0.927493 | + | 0.373841i | \(0.121959\pi\) |
−0.139991 | + | 0.990153i | \(0.544707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.5000 | − | 19.9186i | −0.546381 | − | 0.946360i | −0.998519 | − | 0.0544120i | \(-0.982672\pi\) |
0.452137 | − | 0.891948i | \(-0.350662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | − | 15.5885i | 0.426641 | − | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0000 | 0.706322 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.50000 | − | 12.9904i | 0.351605 | − | 0.608998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.50000 | − | 9.52628i | −0.257279 | − | 0.445621i | 0.708233 | − | 0.705979i | \(-0.249493\pi\) |
−0.965512 | + | 0.260358i | \(0.916159\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.5000 | + | 21.6506i | 0.582183 | + | 1.00837i | 0.995220 | + | 0.0976564i | \(0.0311346\pi\) |
−0.413037 | + | 0.910714i | \(0.635532\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.5000 | − | 19.9186i | 0.534450 | − | 0.925695i | −0.464739 | − | 0.885448i | \(-0.653852\pi\) |
0.999190 | − | 0.0402476i | \(-0.0128147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.00000 | −0.138527 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 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 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.500000 | − | 0.866025i | −0.0228456 | − | 0.0395697i | 0.854377 | − | 0.519654i | \(-0.173939\pi\) |
−0.877222 | + | 0.480085i | \(0.840606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.0000 | + | 25.9808i | −0.683941 | + | 1.18462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.0000 | 0.590300 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0000 | 1.45006 | 0.725029 | − | 0.688718i | \(-0.241826\pi\) | ||||
0.725029 | + | 0.688718i | \(0.241826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.5000 | − | 23.3827i | 0.609246 | − | 1.05525i | −0.382118 | − | 0.924113i | \(-0.624805\pi\) |
0.991365 | − | 0.131132i | \(-0.0418613\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | + | 15.5885i | 0.405340 | + | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | − | 10.3923i | −0.269137 | − | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.5000 | + | 23.3827i | −0.604343 | + | 1.04675i | 0.387812 | + | 0.921739i | \(0.373231\pi\) |
−0.992155 | + | 0.125014i | \(0.960102\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.50000 | + | 2.59808i | −0.0664863 | + | 0.115158i | −0.897352 | − | 0.441315i | \(-0.854512\pi\) |
0.830866 | + | 0.556473i | \(0.187846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | + | 5.19615i | 0.132712 | + | 0.229864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | 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 | ||||||||
\(523\) | 40.0000 | 1.74908 | 0.874539 | − | 0.484955i | \(-0.161164\pi\) | ||||
0.874539 | + | 0.484955i | \(0.161164\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 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 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.0000 | −0.430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.00000 | + | 8.66025i | −0.214176 | + | 0.370965i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.50000 | + | 16.4545i | 0.406191 | + | 0.703543i | 0.994459 | − | 0.105123i | \(-0.0335235\pi\) |
−0.588269 | + | 0.808666i | \(0.700190\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.500000 | + | 0.866025i | −0.0210725 | + | 0.0364986i | −0.876369 | − | 0.481640i | \(-0.840041\pi\) |
0.855297 | + | 0.518138i | \(0.173375\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.50000 | + | 7.79423i | 0.189316 | + | 0.327906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.5000 | − | 21.6506i | −0.524027 | − | 0.907642i | −0.999609 | − | 0.0279702i | \(-0.991096\pi\) |
0.475581 | − | 0.879672i | \(-0.342238\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.50000 | + | 12.9904i | −0.313865 | + | 0.543631i | −0.979196 | − | 0.202919i | \(-0.934957\pi\) |
0.665330 | + | 0.746549i | \(0.268291\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.50000 | + | 14.7224i | 0.350833 | + | 0.607660i | 0.986396 | − | 0.164389i | \(-0.0525653\pi\) |
−0.635563 | + | 0.772049i | \(0.719232\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | − | 3.46410i | 0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.0000 | 1.39621 | 0.698106 | − | 0.715994i | \(-0.254026\pi\) | ||||
0.698106 | + | 0.715994i | \(0.254026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | −0.245976 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5000 | − | 18.1865i | 0.429018 | − | 0.743082i | −0.567768 | − | 0.823189i | \(-0.692193\pi\) |
0.996786 | + | 0.0801071i | \(0.0255262\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.50000 | − | 16.4545i | −0.387513 | − | 0.671192i | 0.604601 | − | 0.796528i | \(-0.293332\pi\) |
−0.992114 | + | 0.125336i | \(0.959999\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | \(-0.918318\pi\) |
0.703429 | + | 0.710766i | \(0.251651\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | −0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.00000 | −0.0807792 | −0.0403896 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403896 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50000 | − | 2.59808i | 0.0603877 | − | 0.104595i | −0.834251 | − | 0.551385i | \(-0.814100\pi\) |
0.894639 | + | 0.446790i | \(0.147433\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.50000 | + | 9.52628i | 0.221064 | + | 0.382893i | 0.955131 | − | 0.296183i | \(-0.0957138\pi\) |
−0.734068 | + | 0.679076i | \(0.762380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 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 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 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 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.500000 | − | 0.866025i | −0.0197488 | − | 0.0342059i | 0.855982 | − | 0.517005i | \(-0.172953\pi\) |
−0.875731 | + | 0.482800i | \(0.839620\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.50000 | + | 12.9904i | −0.295771 | + | 0.512291i | −0.975164 | − | 0.221484i | \(-0.928910\pi\) |
0.679393 | + | 0.733775i | \(0.262243\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.5000 | − | 28.5788i | 0.645695 | − | 1.11838i | −0.338446 | − | 0.940986i | \(-0.609901\pi\) |
0.984141 | − | 0.177390i | \(-0.0567655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.50000 | + | 4.33013i | 0.0976831 | + | 0.169192i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5000 | + | 18.1865i | 0.409022 | + | 0.708447i | 0.994780 | − | 0.102039i | \(-0.0325366\pi\) |
−0.585758 | + | 0.810486i | \(0.699203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.5000 | + | 21.6506i | −0.486194 | + | 0.842112i | −0.999874 | − | 0.0158695i | \(-0.994948\pi\) |
0.513680 | + | 0.857982i | \(0.328282\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | 0.465340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | 0.348481 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.5000 | + | 30.3109i | −0.675580 | + | 1.17014i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.50000 | − | 16.4545i | −0.366198 | − | 0.634274i | 0.622770 | − | 0.782405i | \(-0.286007\pi\) |
−0.988968 | + | 0.148132i | \(0.952674\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.5000 | − | 30.3109i | −0.672580 | − | 1.16494i | −0.977170 | − | 0.212459i | \(-0.931853\pi\) |
0.304590 | − | 0.952483i | \(-0.401480\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.5000 | − | 33.7750i | 0.748341 | − | 1.29617i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.00000 | 0.153056 | 0.0765279 | − | 0.997067i | \(-0.475617\pi\) | ||||
0.0765279 | + | 0.997067i | \(0.475617\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.00000 | 0.114624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.00000 | + | 8.66025i | −0.190485 | + | 0.329929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5000 | − | 35.5070i | −0.779857 | − | 1.35075i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.152167 | − | 0.988355i | \(-0.451375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | \(-0.100441\pi\) |
−0.744071 | + | 0.668101i | \(0.767108\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0000 | + | 31.1769i | −0.668503 | + | 1.15788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.5000 | − | 33.7750i | −0.723215 | − | 1.25265i | −0.959705 | − | 0.281011i | \(-0.909330\pi\) |
0.236490 | − | 0.971634i | \(-0.424003\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | \(-0.910508\pi\) |
0.720655 | + | 0.693294i | \(0.243841\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.50000 | + | 9.52628i | −0.201775 | + | 0.349485i | −0.949101 | − | 0.314973i | \(-0.898004\pi\) |
0.747325 | + | 0.664459i | \(0.231338\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.50000 | + | 16.4545i | 0.348053 | + | 0.602846i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | \(-0.669372\pi\) |
0.999964 | + | 0.00849853i | \(0.00270520\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.0000 | 0.618693 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.50000 | + | 4.33013i | −0.0906249 | + | 0.156967i | −0.907774 | − | 0.419459i | \(-0.862220\pi\) |
0.817149 | + | 0.576426i | \(0.195553\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.0000 | + | 25.9808i | 0.543036 | + | 0.940567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.5000 | + | 47.6314i | 0.992967 | + | 1.71987i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.500000 | − | 0.866025i | 0.0180305 | − | 0.0312297i | −0.856869 | − | 0.515534i | \(-0.827594\pi\) |
0.874900 | + | 0.484304i | \(0.160927\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.50000 | − | 6.06218i | −0.124920 | − | 0.216368i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.5000 | − | 45.8993i | 0.944623 | − | 1.63614i | 0.188119 | − | 0.982146i | \(-0.439761\pi\) |
0.756504 | − | 0.653989i | \(-0.226906\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.0000 | 0.960009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.0000 | −1.24289 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.50000 | − | 11.2583i | 0.230242 | − | 0.398791i | −0.727637 | − | 0.685962i | \(-0.759382\pi\) |
0.957879 | + | 0.287171i | \(0.0927150\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.00000 | + | 5.19615i | 0.106132 | + | 0.183827i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 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 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.0000 | 1.75791 | 0.878953 | − | 0.476908i | \(-0.158243\pi\) | ||||
0.878953 | + | 0.476908i | \(0.158243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5000 | + | 28.5788i | 0.575854 | + | 0.997408i | 0.995948 | + | 0.0899279i | \(0.0286637\pi\) |
−0.420094 | + | 0.907480i | \(0.638003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.5000 | + | 42.4352i | −0.854016 | + | 1.47920i | 0.0235383 | + | 0.999723i | \(0.492507\pi\) |
−0.877555 | + | 0.479477i | \(0.840826\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.0000 | 1.53003 | 0.765015 | − | 0.644013i | \(-0.222732\pi\) | ||||
0.765015 | + | 0.644013i | \(0.222732\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0000 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 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 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.5000 | − | 18.1865i | −0.362500 | − | 0.627869i | 0.625871 | − | 0.779926i | \(-0.284743\pi\) |
−0.988372 | + | 0.152057i | \(0.951410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | + | 45.0333i | −0.896552 | + | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.0000 | 1.44314 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | \(-0.172116\pi\) |
−0.874458 | + | 0.485101i | \(0.838783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.5000 | + | 23.3827i | 0.461151 | + | 0.798737i | 0.999019 | − | 0.0442921i | \(-0.0141032\pi\) |
−0.537867 | + | 0.843029i | \(0.680770\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.50000 | − | 7.79423i | 0.153538 | − | 0.265936i | −0.778988 | − | 0.627039i | \(-0.784267\pi\) |
0.932526 | + | 0.361104i | \(0.117600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | \(-0.817204\pi\) |
0.890239 | + | 0.455493i | \(0.150537\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.0000 | 0.875962 | 0.437981 | − | 0.898984i | \(-0.355694\pi\) | ||||
0.437981 | + | 0.898984i | \(0.355694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.5000 | + | 47.6314i | −0.923360 | + | 1.59931i | −0.129181 | + | 0.991621i | \(0.541235\pi\) |
−0.794178 | + | 0.607685i | \(0.792098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.0000 | + | 41.5692i | 0.804934 | + | 1.39419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 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 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.00000 | −0.300167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.00000 | − | 5.19615i | 0.0997234 | − | 0.172726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.5000 | − | 42.4352i | −0.813509 | − | 1.40904i | −0.910393 | − | 0.413744i | \(-0.864221\pi\) |
0.0968843 | − | 0.995296i | \(-0.469112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5000 | − | 35.5070i | −0.679195 | − | 1.17640i | −0.975224 | − | 0.221222i | \(-0.928996\pi\) |
0.296028 | − | 0.955179i | \(-0.404338\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.50000 | + | 4.33013i | −0.0827379 | + | 0.143306i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.0000 | 0.495344 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.5000 | − | 25.1147i | −0.475730 | − | 0.823988i | 0.523884 | − | 0.851790i | \(-0.324483\pi\) |
−0.999613 | + | 0.0278019i | \(0.991149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | − | 6.92820i | 0.131095 | − | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.5000 | − | 28.5788i | 0.537885 | − | 0.931644i | −0.461133 | − | 0.887331i | \(-0.652557\pi\) |
0.999018 | − | 0.0443125i | \(-0.0141097\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.50000 | − | 2.59808i | −0.0488467 | − | 0.0846050i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.5000 | − | 23.3827i | −0.438691 | − | 0.759835i | 0.558898 | − | 0.829237i | \(-0.311224\pi\) |
−0.997589 | + | 0.0694014i | \(0.977891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.00000 | − | 8.66025i | 0.162307 | − | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.0000 | −0.971795 | −0.485898 | − | 0.874016i | \(-0.661507\pi\) | ||||
−0.485898 | + | 0.874016i | \(0.661507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.0000 | 0.873699 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | \(-0.965009\pi\) |
0.591991 | + | 0.805945i | \(0.298342\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.5000 | − | 33.7750i | 0.623860 | − | 1.08056i | −0.364900 | − | 0.931047i | \(-0.618897\pi\) |
0.988760 | − | 0.149511i | \(-0.0477699\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.0000 | + | 77.9423i | 1.43821 | + | 2.49105i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.50000 | + | 12.9904i | 0.239213 | + | 0.414329i | 0.960489 | − | 0.278319i | \(-0.0897773\pi\) |
−0.721276 | + | 0.692648i | \(0.756444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | − | 5.19615i | 0.0955879 | − | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.00000 | −0.0317982 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 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 | \(-0.0693903\pi\) |
−0.675465 | + | 0.737392i | \(0.736057\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1728.2.i.g.577.1 | 2 | ||
3.2 | odd | 2 | 576.2.i.c.193.1 | 2 | |||
4.3 | odd | 2 | 1728.2.i.h.577.1 | 2 | |||
8.3 | odd | 2 | 216.2.i.a.145.1 | 2 | |||
8.5 | even | 2 | 432.2.i.a.145.1 | 2 | |||
9.2 | odd | 6 | 576.2.i.c.385.1 | 2 | |||
9.4 | even | 3 | 5184.2.a.n.1.1 | 1 | |||
9.5 | odd | 6 | 5184.2.a.x.1.1 | 1 | |||
9.7 | even | 3 | inner | 1728.2.i.g.1153.1 | 2 | ||
12.11 | even | 2 | 576.2.i.d.193.1 | 2 | |||
24.5 | odd | 2 | 144.2.i.b.49.1 | 2 | |||
24.11 | even | 2 | 72.2.i.a.49.1 | yes | 2 | ||
36.7 | odd | 6 | 1728.2.i.h.1153.1 | 2 | |||
36.11 | even | 6 | 576.2.i.d.385.1 | 2 | |||
36.23 | even | 6 | 5184.2.a.s.1.1 | 1 | |||
36.31 | odd | 6 | 5184.2.a.i.1.1 | 1 | |||
72.5 | odd | 6 | 1296.2.a.e.1.1 | 1 | |||
72.11 | even | 6 | 72.2.i.a.25.1 | ✓ | 2 | ||
72.13 | even | 6 | 1296.2.a.i.1.1 | 1 | |||
72.29 | odd | 6 | 144.2.i.b.97.1 | 2 | |||
72.43 | odd | 6 | 216.2.i.a.73.1 | 2 | |||
72.59 | even | 6 | 648.2.a.a.1.1 | 1 | |||
72.61 | even | 6 | 432.2.i.a.289.1 | 2 | |||
72.67 | odd | 6 | 648.2.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.i.a.25.1 | ✓ | 2 | 72.11 | even | 6 | ||
72.2.i.a.49.1 | yes | 2 | 24.11 | even | 2 | ||
144.2.i.b.49.1 | 2 | 24.5 | odd | 2 | |||
144.2.i.b.97.1 | 2 | 72.29 | odd | 6 | |||
216.2.i.a.73.1 | 2 | 72.43 | odd | 6 | |||
216.2.i.a.145.1 | 2 | 8.3 | odd | 2 | |||
432.2.i.a.145.1 | 2 | 8.5 | even | 2 | |||
432.2.i.a.289.1 | 2 | 72.61 | even | 6 | |||
576.2.i.c.193.1 | 2 | 3.2 | odd | 2 | |||
576.2.i.c.385.1 | 2 | 9.2 | odd | 6 | |||
576.2.i.d.193.1 | 2 | 12.11 | even | 2 | |||
576.2.i.d.385.1 | 2 | 36.11 | even | 6 | |||
648.2.a.a.1.1 | 1 | 72.59 | even | 6 | |||
648.2.a.c.1.1 | 1 | 72.67 | odd | 6 | |||
1296.2.a.e.1.1 | 1 | 72.5 | odd | 6 | |||
1296.2.a.i.1.1 | 1 | 72.13 | even | 6 | |||
1728.2.i.g.577.1 | 2 | 1.1 | even | 1 | trivial | ||
1728.2.i.g.1153.1 | 2 | 9.7 | even | 3 | inner | ||
1728.2.i.h.577.1 | 2 | 4.3 | odd | 2 | |||
1728.2.i.h.1153.1 | 2 | 36.7 | odd | 6 | |||
5184.2.a.i.1.1 | 1 | 36.31 | odd | 6 | |||
5184.2.a.n.1.1 | 1 | 9.4 | even | 3 | |||
5184.2.a.s.1.1 | 1 | 36.23 | even | 6 | |||
5184.2.a.x.1.1 | 1 | 9.5 | odd | 6 |