Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(79,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
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 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.508 |
Dual form | 637.2.e.c.79.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 1.00000 | − | 1.73205i | 0.577350 | − | 1.00000i | −0.418432 | − | 0.908248i | \(-0.637420\pi\) |
0.995782 | − | 0.0917517i | \(-0.0292466\pi\) | |||||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | 1.50000 | + | 2.59808i | 0.670820 | + | 1.16190i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | −2.00000 | − | 3.46410i | −0.577350 | − | 1.00000i | ||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.00000 | 1.54919 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | + | 6.06218i | 0.802955 | + | 1.39076i | 0.917663 | + | 0.397360i | \(0.130073\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 6.00000 | 1.34164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50000 | − | 2.59808i | −0.312772 | − | 0.541736i | 0.666190 | − | 0.745782i | \(-0.267924\pi\) |
−0.978961 | + | 0.204046i | \(0.934591\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | + | 4.33013i | −0.449013 | + | 0.777714i | −0.998322 | − | 0.0579057i | \(-0.981558\pi\) |
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −1.00000 | − | 1.73205i | −0.164399 | − | 0.284747i | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | − | 1.73205i | 0.160128 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 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 | \(-0.236880\pi\) |
−0.954441 | + | 0.298401i | \(0.903547\pi\) | |||||||
\(48\) | −8.00000 | −1.15470 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | − | 10.3923i | −0.840168 | − | 1.45521i | ||||
\(52\) | 1.00000 | − | 1.73205i | 0.138675 | − | 0.240192i | ||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.0000 | 1.85435 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 6.00000 | − | 10.3923i | 0.774597 | − | 1.34164i | ||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 1.50000 | + | 2.59808i | 0.186052 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | + | 12.1244i | −0.855186 | + | 1.48123i | 0.0212861 | + | 0.999773i | \(0.493224\pi\) |
−0.876472 | + | 0.481452i | \(0.840109\pi\) | |||||||
\(68\) | −6.00000 | − | 10.3923i | −0.727607 | − | 1.26025i | ||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.50000 | + | 9.52628i | −0.643726 | + | 1.11497i | 0.340868 | + | 0.940111i | \(0.389279\pi\) |
−0.984594 | + | 0.174855i | \(0.944054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.00000 | + | 6.92820i | 0.461880 | + | 0.800000i | ||||
\(76\) | 14.0000 | 1.60591 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 6.00000 | − | 10.3923i | 0.670820 | − | 1.16190i | ||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.00000 | 0.329293 | 0.164646 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164646 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.0000 | 1.95237 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.00000 | + | 15.5885i | −0.964901 | + | 1.67126i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.50000 | − | 12.9904i | −0.794998 | − | 1.37698i | −0.922840 | − | 0.385183i | \(-0.874138\pi\) |
0.127842 | − | 0.991795i | \(-0.459195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | 5.00000 | + | 8.66025i | 0.518476 | + | 0.898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.5000 | + | 18.1865i | −1.07728 | + | 1.86590i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | + | 6.92820i | 0.400000 | + | 0.692820i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 4.00000 | − | 6.92820i | 0.384900 | − | 0.666667i | ||||
\(109\) | 8.00000 | − | 13.8564i | 0.766261 | − | 1.32720i | −0.173316 | − | 0.984866i | \(-0.555448\pi\) |
0.939577 | − | 0.342337i | \(-0.111218\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | − | 7.79423i | 0.419627 | − | 0.726816i | ||||
\(116\) | −9.00000 | + | 15.5885i | −0.835629 | + | 1.44735i | ||||
\(117\) | −0.500000 | − | 0.866025i | −0.0462250 | − | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | + | 10.3923i | −0.541002 | + | 0.937043i | ||||
\(124\) | 5.00000 | + | 8.66025i | 0.449013 | + | 0.777714i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00000 | + | 1.73205i | −0.0880451 | + | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | + | 10.3923i | 0.524222 | + | 0.907980i | 0.999602 | + | 0.0281993i | \(0.00897729\pi\) |
−0.475380 | + | 0.879781i | \(0.657689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.00000 | + | 10.3923i | 0.516398 | + | 0.894427i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.00000 | + | 3.46410i | −0.166667 | + | 0.288675i | ||||
\(145\) | −13.5000 | − | 23.3827i | −1.12111 | − | 1.94183i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.0000 | −1.20483 | ||||||||
\(156\) | −2.00000 | − | 3.46410i | −0.160128 | − | 0.277350i | ||||
\(157\) | −7.00000 | + | 12.1244i | −0.558661 | + | 0.967629i | 0.438948 | + | 0.898513i | \(0.355351\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.00000 | − | 15.5885i | −0.713746 | − | 1.23625i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | + | 13.8564i | 0.626608 | + | 1.08532i | 0.988227 | + | 0.152992i | \(0.0488907\pi\) |
−0.361619 | + | 0.932326i | \(0.617776\pi\) | |||||||
\(164\) | −6.00000 | + | 10.3923i | −0.468521 | + | 0.811503i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.0000 | −1.16073 | −0.580367 | − | 0.814355i | \(-0.697091\pi\) | ||||
−0.580367 | + | 0.814355i | \(0.697091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.50000 | − | 6.06218i | 0.267652 | − | 0.463586i | ||||
\(172\) | −1.00000 | + | 1.73205i | −0.0762493 | + | 0.132068i | ||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.50000 | + | 12.9904i | −0.560576 | + | 0.970947i | 0.436870 | + | 0.899525i | \(0.356087\pi\) |
−0.997446 | + | 0.0714220i | \(0.977246\pi\) | |||||||
\(180\) | −3.00000 | − | 5.19615i | −0.223607 | − | 0.387298i | ||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.0000 | 1.47844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | − | 20.7846i | −0.868290 | − | 1.50392i | −0.863743 | − | 0.503932i | \(-0.831886\pi\) |
−0.00454614 | − | 0.999990i | \(-0.501447\pi\) | |||||||
\(192\) | −8.00000 | + | 13.8564i | −0.577350 | + | 1.00000i | ||||
\(193\) | 11.0000 | − | 19.0526i | 0.791797 | − | 1.37143i | −0.133056 | − | 0.991109i | \(-0.542479\pi\) |
0.924853 | − | 0.380325i | \(-0.124188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.00000 | 0.429669 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00000 | + | 1.73205i | −0.0708881 | + | 0.122782i | −0.899291 | − | 0.437351i | \(-0.855917\pi\) |
0.828403 | + | 0.560133i | \(0.189250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.0000 | + | 24.2487i | 0.987484 | + | 1.71037i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −24.0000 | −1.68034 | ||||||||
\(205\) | −9.00000 | − | 15.5885i | −0.628587 | − | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.50000 | + | 2.59808i | −0.104257 | + | 0.180579i | ||||
\(208\) | −2.00000 | − | 3.46410i | −0.138675 | − | 0.240192i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0000 | 1.58339 | 0.791693 | − | 0.610920i | \(-0.209200\pi\) | ||||
0.791693 | + | 0.610920i | \(0.209200\pi\) | |||||||
\(212\) | −9.00000 | − | 15.5885i | −0.618123 | − | 1.07062i | ||||
\(213\) | −6.00000 | + | 10.3923i | −0.411113 | + | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.50000 | − | 2.59808i | −0.102299 | − | 0.177187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.0000 | + | 19.0526i | 0.743311 | + | 1.28745i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | − | 5.19615i | 0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | −0.0334825 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334825 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.0000 | + | 20.7846i | −0.796468 | + | 1.37952i | 0.125435 | + | 0.992102i | \(0.459967\pi\) |
−0.921903 | + | 0.387421i | \(0.873366\pi\) | |||||||
\(228\) | 14.0000 | − | 24.2487i | 0.927173 | − | 1.60591i | ||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.50000 | + | 7.79423i | 0.294805 | + | 0.510617i | 0.974939 | − | 0.222470i | \(-0.0714120\pi\) |
−0.680135 | + | 0.733087i | \(0.738079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.50000 | − | 7.79423i | 0.293548 | − | 0.508439i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000 | 0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | −12.0000 | − | 20.7846i | −0.774597 | − | 1.34164i | ||||
\(241\) | 0.500000 | − | 0.866025i | 0.0322078 | − | 0.0557856i | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.00000 | − | 8.66025i | −0.320750 | − | 0.555556i | ||||
\(244\) | 20.0000 | 1.28037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.50000 | + | 6.06218i | 0.222700 | + | 0.385727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.0000 | − | 31.1769i | 1.12720 | − | 1.95237i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 12.0000 | + | 20.7846i | 0.748539 | + | 1.29651i | 0.948523 | + | 0.316709i | \(0.102578\pi\) |
−0.199983 | + | 0.979799i | \(0.564089\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 4.50000 | + | 7.79423i | 0.278543 | + | 0.482451i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.50000 | + | 7.79423i | −0.277482 | + | 0.480613i | −0.970758 | − | 0.240059i | \(-0.922833\pi\) |
0.693276 | + | 0.720672i | \(0.256167\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.0000 | 1.65860 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −30.0000 | −1.83597 | ||||||||
\(268\) | 14.0000 | + | 24.2487i | 0.855186 | + | 1.48123i | ||||
\(269\) | 12.0000 | − | 20.7846i | 0.731653 | − | 1.26726i | −0.224523 | − | 0.974469i | \(-0.572083\pi\) |
0.956176 | − | 0.292791i | \(-0.0945841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | −24.0000 | −1.45521 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | ||||
\(277\) | 9.50000 | − | 16.4545i | 0.570800 | − | 0.988654i | −0.425684 | − | 0.904872i | \(-0.639967\pi\) |
0.996484 | − | 0.0837823i | \(-0.0267000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | −6.00000 | + | 10.3923i | −0.356034 | + | 0.616670i | ||||
\(285\) | 21.0000 | + | 36.3731i | 1.24393 | + | 2.15455i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00000 | + | 1.73205i | −0.0586210 | + | 0.101535i | ||||
\(292\) | 11.0000 | + | 19.0526i | 0.643726 | + | 1.11497i | ||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.50000 | − | 2.59808i | −0.0867472 | − | 0.150251i | ||||
\(300\) | 16.0000 | 0.923760 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.0000 | − | 24.2487i | 0.802955 | − | 1.39076i | ||||
\(305\) | −15.0000 | + | 25.9808i | −0.858898 | + | 1.48765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0000 | 0.627803 | 0.313902 | − | 0.949456i | \(-0.398364\pi\) | ||||
0.313902 | + | 0.949456i | \(0.398364\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.00000 | − | 10.3923i | 0.340229 | − | 0.589294i | −0.644246 | − | 0.764818i | \(-0.722829\pi\) |
0.984475 | + | 0.175525i | \(0.0561621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.00000 | − | 6.92820i | −0.226093 | − | 0.391605i | 0.730554 | − | 0.682855i | \(-0.239262\pi\) |
−0.956647 | + | 0.291250i | \(0.905929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −6.00000 | − | 10.3923i | −0.336994 | − | 0.583690i | 0.646872 | − | 0.762598i | \(-0.276077\pi\) |
−0.983866 | + | 0.178908i | \(0.942743\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −12.0000 | − | 20.7846i | −0.670820 | − | 1.16190i | ||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.0000 | 2.33694 | ||||||||
\(324\) | −11.0000 | − | 19.0526i | −0.611111 | − | 1.05848i | ||||
\(325\) | −2.00000 | + | 3.46410i | −0.110940 | + | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.0000 | − | 27.7128i | −0.884802 | − | 1.53252i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | − | 22.5167i | −0.714545 | − | 1.23763i | −0.963135 | − | 0.269019i | \(-0.913301\pi\) |
0.248590 | − | 0.968609i | \(-0.420033\pi\) | |||||||
\(332\) | 3.00000 | − | 5.19615i | 0.164646 | − | 0.285176i | ||||
\(333\) | −1.00000 | + | 1.73205i | −0.0547997 | + | 0.0949158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −42.0000 | −2.29471 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.00000 | − | 15.5885i | 0.488813 | − | 0.846649i | ||||
\(340\) | 18.0000 | − | 31.1769i | 0.976187 | − | 1.69081i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.00000 | − | 15.5885i | −0.484544 | − | 0.839254i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 18.0000 | + | 31.1769i | 0.964901 | + | 1.67126i | ||||
\(349\) | −1.00000 | −0.0535288 | −0.0267644 | − | 0.999642i | \(-0.508520\pi\) | ||||
−0.0267644 | + | 0.999642i | \(0.508520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | − | 15.5885i | 0.479022 | − | 0.829690i | −0.520689 | − | 0.853746i | \(-0.674325\pi\) |
0.999711 | + | 0.0240566i | \(0.00765819\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.00000 | − | 15.5885i | −0.477670 | − | 0.827349i | ||||
\(356\) | −30.0000 | −1.59000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.00000 | − | 15.5885i | −0.475002 | − | 0.822727i | 0.524588 | − | 0.851356i | \(-0.324219\pi\) |
−0.999590 | + | 0.0286287i | \(0.990886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.0000 | 1.15470 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.0000 | −1.72730 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0000 | − | 24.2487i | 0.730794 | − | 1.26577i | −0.225750 | − | 0.974185i | \(-0.572483\pi\) |
0.956544 | − | 0.291587i | \(-0.0941834\pi\) | |||||||
\(368\) | −6.00000 | + | 10.3923i | −0.312772 | + | 0.541736i | ||||
\(369\) | 3.00000 | + | 5.19615i | 0.156174 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 20.0000 | 1.03695 | ||||||||
\(373\) | −7.00000 | − | 12.1244i | −0.362446 | − | 0.627775i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.00000 | − | 5.19615i | 0.154919 | − | 0.268328i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.00000 | −0.463524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 21.0000 | + | 36.3731i | 1.07728 | + | 1.86590i | ||||
\(381\) | −16.0000 | + | 27.7128i | −0.819705 | + | 1.41977i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.500000 | + | 0.866025i | 0.0254164 | + | 0.0440225i | ||||
\(388\) | −1.00000 | + | 1.73205i | −0.0507673 | + | 0.0879316i | ||||
\(389\) | 3.00000 | − | 5.19615i | 0.152106 | − | 0.263455i | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.50000 | + | 2.59808i | −0.0754732 | + | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.50000 | − | 9.52628i | −0.276037 | − | 0.478110i | 0.694359 | − | 0.719629i | \(-0.255688\pi\) |
−0.970396 | + | 0.241518i | \(0.922355\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0000 | 0.800000 | ||||||||
\(401\) | −6.00000 | − | 10.3923i | −0.299626 | − | 0.518967i | 0.676425 | − | 0.736512i | \(-0.263528\pi\) |
−0.976050 | + | 0.217545i | \(0.930195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.50000 | + | 4.33013i | −0.124534 | + | 0.215699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 33.0000 | 1.63978 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5000 | + | 19.9186i | −0.568638 | + | 0.984911i | 0.428063 | + | 0.903749i | \(0.359196\pi\) |
−0.996701 | + | 0.0811615i | \(0.974137\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | + | 10.3923i | 0.295958 | + | 0.512615i | ||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.50000 | + | 7.79423i | 0.220896 | + | 0.382604i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | + | 6.92820i | −0.195881 | + | 0.339276i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.50000 | + | 2.59808i | −0.0729325 | + | 0.126323i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | + | 20.7846i | 0.582086 | + | 1.00820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.0000 | 1.16008 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | − | 25.9808i | 0.722525 | − | 1.25145i | −0.237460 | − | 0.971397i | \(-0.576315\pi\) |
0.959985 | − | 0.280052i | \(-0.0903517\pi\) | |||||||
\(432\) | −8.00000 | − | 13.8564i | −0.384900 | − | 0.666667i | ||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −54.0000 | −2.58910 | ||||||||
\(436\) | −16.0000 | − | 27.7128i | −0.766261 | − | 1.32720i | ||||
\(437\) | 10.5000 | − | 18.1865i | 0.502283 | − | 0.869980i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.00000 | + | 8.66025i | 0.238637 | + | 0.413331i | 0.960323 | − | 0.278889i | \(-0.0899661\pi\) |
−0.721686 | + | 0.692220i | \(0.756633\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5000 | − | 33.7750i | −0.926473 | − | 1.60470i | −0.789175 | − | 0.614168i | \(-0.789492\pi\) |
−0.137298 | − | 0.990530i | \(-0.543842\pi\) | |||||||
\(444\) | −4.00000 | + | 6.92820i | −0.189832 | + | 0.328798i | ||||
\(445\) | 22.5000 | − | 38.9711i | 1.06660 | − | 1.84741i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.0000 | −1.13263 | −0.566315 | − | 0.824189i | \(-0.691631\pi\) | ||||
−0.566315 | + | 0.824189i | \(0.691631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.00000 | − | 15.5885i | 0.423324 | − | 0.733219i | ||||
\(453\) | −10.0000 | − | 17.3205i | −0.469841 | − | 0.813788i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000 | + | 8.66025i | 0.233890 | + | 0.405110i | 0.958950 | − | 0.283577i | \(-0.0915211\pi\) |
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.0000 | − | 20.7846i | 0.560112 | − | 0.970143i | ||||
\(460\) | −9.00000 | − | 15.5885i | −0.419627 | − | 0.726816i | ||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | 18.0000 | + | 31.1769i | 0.835629 | + | 1.44735i | ||||
\(465\) | −15.0000 | + | 25.9808i | −0.695608 | + | 1.20483i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0000 | + | 31.1769i | 0.832941 | + | 1.44270i | 0.895696 | + | 0.444667i | \(0.146678\pi\) |
−0.0627555 | + | 0.998029i | \(0.519989\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.0000 | + | 24.2487i | 0.645086 | + | 1.11732i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.0000 | −1.28473 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | −0.412082 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.50000 | + | 7.79423i | −0.205610 | + | 0.356127i | −0.950327 | − | 0.311253i | \(-0.899251\pi\) |
0.744717 | + | 0.667381i | \(0.232585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00000 | − | 1.73205i | −0.0455961 | − | 0.0789747i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | −1.50000 | − | 2.59808i | −0.0681115 | − | 0.117973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00000 | + | 1.73205i | −0.0453143 | + | 0.0784867i | −0.887793 | − | 0.460243i | \(-0.847762\pi\) |
0.842479 | + | 0.538730i | \(0.181096\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.0000 | 1.44709 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 12.0000 | + | 20.7846i | 0.541002 | + | 0.937043i | ||||
\(493\) | −27.0000 | + | 46.7654i | −1.21602 | + | 2.10621i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.00000 | − | 12.1244i | −0.313363 | − | 0.542761i | 0.665725 | − | 0.746197i | \(-0.268122\pi\) |
−0.979088 | + | 0.203436i | \(0.934789\pi\) | |||||||
\(500\) | 3.00000 | − | 5.19615i | 0.134164 | − | 0.232379i | ||||
\(501\) | −15.0000 | + | 25.9808i | −0.670151 | + | 1.16073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | − | 1.73205i | 0.0444116 | − | 0.0769231i | ||||
\(508\) | −16.0000 | + | 27.7128i | −0.709885 | + | 1.22956i | ||||
\(509\) | −10.5000 | − | 18.1865i | −0.465404 | − | 0.806104i | 0.533815 | − | 0.845601i | \(-0.320758\pi\) |
−0.999220 | + | 0.0394971i | \(0.987424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.0000 | + | 24.2487i | 0.618115 | + | 1.07061i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.00000 | + | 10.3923i | −0.264392 | + | 0.457940i | ||||
\(516\) | 2.00000 | + | 3.46410i | 0.0880451 | + | 0.152499i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.00000 | − | 1.73205i | −0.0437269 | − | 0.0757373i | 0.843334 | − | 0.537390i | \(-0.180590\pi\) |
−0.887061 | + | 0.461653i | \(0.847256\pi\) | |||||||
\(524\) | 24.0000 | 1.04844 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.0000 | + | 25.9808i | 0.653410 | + | 1.13174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.00000 | −0.259889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | + | 31.1769i | −0.778208 | + | 1.34790i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.0000 | + | 25.9808i | 0.647298 | + | 1.12115i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 24.0000 | 1.03280 | ||||||||
\(541\) | 17.0000 | + | 29.4449i | 0.730887 | + | 1.26593i | 0.956504 | + | 0.291718i | \(0.0942267\pi\) |
−0.225617 | + | 0.974216i | \(0.572440\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.0000 | + | 27.7128i | −0.686626 | + | 1.18927i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 48.0000 | 2.05609 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0000 | 0.726868 | 0.363434 | − | 0.931620i | \(-0.381604\pi\) | ||||
0.363434 | + | 0.931620i | \(0.381604\pi\) | |||||||
\(548\) | 6.00000 | + | 10.3923i | 0.256307 | + | 0.443937i | ||||
\(549\) | 5.00000 | − | 8.66025i | 0.213395 | − | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.5000 | − | 54.5596i | −1.34195 | − | 2.32432i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.00000 | − | 10.3923i | −0.254686 | − | 0.441129i | ||||
\(556\) | −4.00000 | + | 6.92820i | −0.169638 | + | 0.293821i | ||||
\(557\) | 6.00000 | − | 10.3923i | 0.254228 | − | 0.440336i | −0.710457 | − | 0.703740i | \(-0.751512\pi\) |
0.964686 | + | 0.263404i | \(0.0848453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.00000 | −0.0422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | −6.00000 | + | 10.3923i | −0.252646 | + | 0.437595i | ||||
\(565\) | 13.5000 | + | 23.3827i | 0.567949 | + | 0.983717i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5000 | − | 23.3827i | −0.565949 | − | 0.980253i | −0.996961 | − | 0.0779066i | \(-0.975176\pi\) |
0.431011 | − | 0.902347i | \(-0.358157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.5000 | + | 19.9186i | −0.481260 | + | 0.833567i | −0.999769 | − | 0.0215055i | \(-0.993154\pi\) |
0.518509 | + | 0.855072i | \(0.326487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −48.0000 | −2.00523 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 4.00000 | + | 6.92820i | 0.166667 | + | 0.288675i | ||||
\(577\) | 17.0000 | − | 29.4449i | 0.707719 | − | 1.22581i | −0.257982 | − | 0.966150i | \(-0.583058\pi\) |
0.965701 | − | 0.259656i | \(-0.0836092\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.0000 | − | 38.1051i | −0.914289 | − | 1.58359i | ||||
\(580\) | −54.0000 | −2.24223 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.50000 | − | 2.59808i | 0.0620174 | − | 0.107417i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.00000 | −0.371470 | −0.185735 | − | 0.982600i | \(-0.559467\pi\) | ||||
−0.185735 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.0000 | −1.44215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | − | 10.3923i | 0.246807 | − | 0.427482i | ||||
\(592\) | −4.00000 | + | 6.92820i | −0.164399 | + | 0.284747i | ||||
\(593\) | −4.50000 | − | 7.79423i | −0.184793 | − | 0.320071i | 0.758714 | − | 0.651424i | \(-0.225828\pi\) |
−0.943507 | + | 0.331353i | \(0.892495\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.00000 | + | 3.46410i | 0.0818546 | + | 0.141776i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.50000 | + | 12.9904i | −0.306442 | + | 0.530773i | −0.977581 | − | 0.210558i | \(-0.932472\pi\) |
0.671140 | + | 0.741331i | \(0.265805\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0000 | 0.570124 | ||||||||
\(604\) | −10.0000 | − | 17.3205i | −0.406894 | − | 0.704761i | ||||
\(605\) | −16.5000 | + | 28.5788i | −0.670820 | + | 1.16190i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.00000 | + | 3.46410i | 0.0811775 | + | 0.140604i | 0.903756 | − | 0.428048i | \(-0.140799\pi\) |
−0.822578 | + | 0.568652i | \(0.807465\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.50000 | − | 2.59808i | −0.0606835 | − | 0.105107i | ||||
\(612\) | −6.00000 | + | 10.3923i | −0.242536 | + | 0.420084i | ||||
\(613\) | 8.00000 | − | 13.8564i | 0.323117 | − | 0.559655i | −0.658012 | − | 0.753007i | \(-0.728603\pi\) |
0.981129 | + | 0.193352i | \(0.0619359\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.0000 | −1.45166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000 | − | 24.2487i | 0.562708 | − | 0.974638i | −0.434551 | − | 0.900647i | \(-0.643093\pi\) |
0.997259 | − | 0.0739910i | \(-0.0235736\pi\) | |||||||
\(620\) | −15.0000 | + | 25.9808i | −0.602414 | + | 1.04341i | ||||
\(621\) | −6.00000 | − | 10.3923i | −0.240772 | − | 0.417029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.00000 | −0.320256 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | + | 24.2487i | 0.558661 | + | 0.967629i | ||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.0000 | − | 39.8372i | 0.914168 | − | 1.58339i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.0000 | − | 41.5692i | −0.952411 | − | 1.64962i | ||||
\(636\) | −36.0000 | −1.42749 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.00000 | + | 5.19615i | 0.118678 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5000 | − | 33.7750i | 0.770204 | − | 1.33403i | −0.167247 | − | 0.985915i | \(-0.553488\pi\) |
0.937451 | − | 0.348117i | \(-0.113179\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0000 | − | 41.5692i | 0.943537 | − | 1.63425i | 0.184884 | − | 0.982760i | \(-0.440809\pi\) |
0.758654 | − | 0.651494i | \(-0.225858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.0000 | 1.25322 | ||||||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0000 | + | 31.1769i | −0.703318 | + | 1.21818i | ||||
\(656\) | 12.0000 | + | 20.7846i | 0.468521 | + | 0.811503i | ||||
\(657\) | 11.0000 | 0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.00000 | −0.116863 | −0.0584317 | − | 0.998291i | \(-0.518610\pi\) | ||||
−0.0584317 | + | 0.998291i | \(0.518610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.50000 | − | 11.2583i | 0.252821 | − | 0.437898i | −0.711481 | − | 0.702706i | \(-0.751975\pi\) |
0.964301 | + | 0.264807i | \(0.0853084\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.00000 | − | 10.3923i | −0.233021 | − | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.5000 | + | 23.3827i | 0.522722 | + | 0.905381i | ||||
\(668\) | −15.0000 | + | 25.9808i | −0.580367 | + | 1.00523i | ||||
\(669\) | −1.00000 | + | 1.73205i | −0.0386622 | + | 0.0669650i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0000 | −0.732396 | −0.366198 | − | 0.930537i | \(-0.619341\pi\) | ||||
−0.366198 | + | 0.930537i | \(0.619341\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.00000 | + | 13.8564i | −0.307920 | + | 0.533333i | ||||
\(676\) | 1.00000 | − | 1.73205i | 0.0384615 | − | 0.0666173i | ||||
\(677\) | −6.00000 | − | 10.3923i | −0.230599 | − | 0.399409i | 0.727386 | − | 0.686229i | \(-0.240735\pi\) |
−0.957984 | + | 0.286820i | \(0.907402\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0000 | + | 41.5692i | 0.919682 | + | 1.59294i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00000 | + | 10.3923i | −0.229584 | + | 0.397650i | −0.957685 | − | 0.287819i | \(-0.907070\pi\) |
0.728101 | + | 0.685470i | \(0.240403\pi\) | |||||||
\(684\) | −7.00000 | − | 12.1244i | −0.267652 | − | 0.463586i | ||||
\(685\) | −18.0000 | −0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.0000 | −1.06827 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | 4.50000 | − | 7.79423i | 0.171436 | − | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5000 | + | 32.0429i | 0.703773 | + | 1.21897i | 0.967132 | + | 0.254273i | \(0.0818362\pi\) |
−0.263359 | + | 0.964698i | \(0.584830\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | − | 10.3923i | −0.227593 | − | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | + | 31.1769i | −0.681799 | + | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.0000 | 0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.00000 | 0.339925 | 0.169963 | − | 0.985451i | \(-0.445635\pi\) | ||||
0.169963 | + | 0.985451i | \(0.445635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.00000 | − | 12.1244i | 0.264010 | − | 0.457279i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.00000 | − | 15.5885i | −0.338960 | − | 0.587095i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | − | 6.92820i | −0.150223 | − | 0.260194i | 0.781086 | − | 0.624423i | \(-0.214666\pi\) |
−0.931309 | + | 0.364229i | \(0.881333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.500000 | − | 0.866025i | 0.0187515 | − | 0.0324785i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.0000 | 0.561754 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.0000 | + | 25.9808i | 0.560576 | + | 0.970947i | ||||
\(717\) | −12.0000 | + | 20.7846i | −0.448148 | + | 0.776215i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.00000 | − | 10.3923i | −0.223762 | − | 0.387568i | 0.732185 | − | 0.681106i | \(-0.238501\pi\) |
−0.955947 | + | 0.293538i | \(0.905167\pi\) | |||||||
\(720\) | −12.0000 | −0.447214 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.00000 | − | 1.73205i | −0.0371904 | − | 0.0644157i | ||||
\(724\) | −16.0000 | + | 27.7128i | −0.594635 | + | 1.02994i | ||||
\(725\) | 18.0000 | − | 31.1769i | 0.668503 | − | 1.15788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.0000 | 0.964287 | 0.482143 | − | 0.876092i | \(-0.339858\pi\) | ||||
0.482143 | + | 0.876092i | \(0.339858\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.00000 | + | 5.19615i | −0.110959 | + | 0.192187i | ||||
\(732\) | 20.0000 | − | 34.6410i | 0.739221 | − | 1.28037i | ||||
\(733\) | 24.5000 | + | 42.4352i | 0.904928 | + | 1.56738i | 0.821014 | + | 0.570909i | \(0.193409\pi\) |
0.0839145 | + | 0.996473i | \(0.473258\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.0000 | + | 17.3205i | −0.367856 | + | 0.637145i | −0.989230 | − | 0.146369i | \(-0.953241\pi\) |
0.621374 | + | 0.783514i | \(0.286575\pi\) | |||||||
\(740\) | −6.00000 | − | 10.3923i | −0.220564 | − | 0.382029i | ||||
\(741\) | 14.0000 | 0.514303 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.0000 | 1.76095 | 0.880475 | − | 0.474093i | \(-0.157224\pi\) | ||||
0.880475 | + | 0.474093i | \(0.157224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.50000 | − | 2.59808i | −0.0548821 | − | 0.0950586i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.50000 | + | 11.2583i | 0.237188 | + | 0.410822i | 0.959906 | − | 0.280321i | \(-0.0904408\pi\) |
−0.722718 | + | 0.691143i | \(0.757107\pi\) | |||||||
\(752\) | −6.00000 | + | 10.3923i | −0.218797 | + | 0.378968i | ||||
\(753\) | 12.0000 | − | 20.7846i | 0.437304 | − | 0.757433i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.0000 | 1.09181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.0000 | −1.56286 | −0.781431 | − | 0.623992i | \(-0.785510\pi\) | ||||
−0.781431 | + | 0.623992i | \(0.785510\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5000 | + | 23.3827i | 0.489375 | + | 0.847622i | 0.999925 | − | 0.0122260i | \(-0.00389175\pi\) |
−0.510551 | + | 0.859848i | \(0.670558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −48.0000 | −1.73658 | ||||||||
\(765\) | −9.00000 | − | 15.5885i | −0.325396 | − | 0.563602i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 16.0000 | + | 27.7128i | 0.577350 | + | 1.00000i | ||||
\(769\) | 5.00000 | 0.180305 | 0.0901523 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901523 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 48.0000 | 1.72868 | ||||||||
\(772\) | −22.0000 | − | 38.1051i | −0.791797 | − | 1.37143i | ||||
\(773\) | −15.0000 | + | 25.9808i | −0.539513 | + | 0.934463i | 0.459418 | + | 0.888220i | \(0.348058\pi\) |
−0.998930 | + | 0.0462427i | \(0.985275\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0000 | − | 17.3205i | −0.359211 | − | 0.622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.0000 | − | 36.3731i | −0.752403 | − | 1.30320i | ||||
\(780\) | 6.00000 | − | 10.3923i | 0.214834 | − | 0.372104i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.0000 | −1.28654 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.0000 | −1.49904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.50000 | + | 4.33013i | −0.0891154 | + | 0.154352i | −0.907137 | − | 0.420834i | \(-0.861737\pi\) |
0.818022 | + | 0.575187i | \(0.195071\pi\) | |||||||
\(788\) | 6.00000 | − | 10.3923i | 0.213741 | − | 0.370211i | ||||
\(789\) | 9.00000 | + | 15.5885i | 0.320408 | + | 0.554964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.00000 | + | 8.66025i | 0.177555 | + | 0.307535i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.0000 | − | 46.7654i | 0.957591 | − | 1.65860i | ||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | 54.0000 | 1.91278 | 0.956389 | − | 0.292096i | \(-0.0943526\pi\) | ||||
0.956389 | + | 0.292096i | \(0.0943526\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | −0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.50000 | + | 12.9904i | −0.264999 | + | 0.458993i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 56.0000 | 1.97497 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.0000 | − | 41.5692i | −0.844840 | − | 1.46331i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.50000 | − | 2.59808i | 0.0527372 | − | 0.0913435i | −0.838452 | − | 0.544976i | \(-0.816539\pi\) |
0.891189 | + | 0.453632i | \(0.149872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.0000 | 1.12229 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.0000 | + | 41.5692i | −0.840683 | + | 1.45611i | ||||
\(816\) | −24.0000 | + | 41.5692i | −0.840168 | + | 1.45521i | ||||
\(817\) | −3.50000 | − | 6.06218i | −0.122449 | − | 0.212089i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36.0000 | −1.25717 | ||||||||
\(821\) | 27.0000 | + | 46.7654i | 0.942306 | + | 1.63212i | 0.761056 | + | 0.648686i | \(0.224681\pi\) |
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | + | 27.7128i | −0.557725 | + | 0.966008i | 0.439961 | + | 0.898017i | \(0.354992\pi\) |
−0.997686 | + | 0.0679910i | \(0.978341\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 3.00000 | + | 5.19615i | 0.104257 | + | 0.180579i | ||||
\(829\) | −10.0000 | + | 17.3205i | −0.347314 | + | 0.601566i | −0.985771 | − | 0.168091i | \(-0.946240\pi\) |
0.638457 | + | 0.769657i | \(0.279573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.0000 | − | 32.9090i | −0.659103 | − | 1.14160i | ||||
\(832\) | −8.00000 | −0.277350 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.5000 | − | 38.9711i | −0.778645 | − | 1.34865i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0000 | + | 17.3205i | −0.345651 | + | 0.598684i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0000 | − | 20.7846i | 0.413302 | − | 0.715860i | ||||
\(844\) | 23.0000 | − | 39.8372i | 0.791693 | − | 1.37125i | ||||
\(845\) | 1.50000 | + | 2.59808i | 0.0516016 | + | 0.0893765i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −36.0000 | −1.23625 | ||||||||
\(849\) | −4.00000 | − | 6.92820i | −0.137280 | − | 0.237775i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00000 | + | 5.19615i | −0.102839 | + | 0.178122i | ||||
\(852\) | 12.0000 | + | 20.7846i | 0.411113 | + | 0.712069i | ||||
\(853\) | 17.0000 | 0.582069 | 0.291034 | − | 0.956713i | \(-0.406001\pi\) | ||||
0.291034 | + | 0.956713i | \(0.406001\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.0000 | 0.718185 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | − | 36.3731i | 0.717346 | − | 1.24248i | −0.244701 | − | 0.969599i | \(-0.578690\pi\) |
0.962048 | − | 0.272882i | \(-0.0879768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.0000 | − | 43.3013i | −0.852989 | − | 1.47742i | −0.878498 | − | 0.477746i | \(-0.841454\pi\) |
0.0255092 | − | 0.999675i | \(-0.491879\pi\) | |||||||
\(860\) | −6.00000 | −0.204598 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | − | 15.5885i | 0.306009 | − | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38.0000 | −1.29055 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.00000 | + | 12.1244i | −0.237186 | + | 0.410818i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.500000 | + | 0.866025i | 0.0169224 | + | 0.0293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.0000 | 1.48662 | ||||||||
\(877\) | 11.0000 | + | 19.0526i | 0.371444 | + | 0.643359i | 0.989788 | − | 0.142548i | \(-0.0455296\pi\) |
−0.618344 | + | 0.785907i | \(0.712196\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.00000 | − | 15.5885i | 0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.00000 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | −6.00000 | − | 10.3923i | −0.201802 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000 | + | 20.7846i | 0.402921 | + | 0.697879i | 0.994077 | − | 0.108678i | \(-0.0346618\pi\) |
−0.591156 | + | 0.806557i | \(0.701328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | + | 1.73205i | −0.0334825 | + | 0.0579934i | ||||
\(893\) | 10.5000 | − | 18.1865i | 0.351369 | − | 0.608589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45.0000 | −1.50418 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.5000 | − | 38.9711i | 0.750417 | − | 1.29976i | ||||
\(900\) | 4.00000 | − | 6.92820i | 0.133333 | − | 0.230940i | ||||
\(901\) | −27.0000 | − | 46.7654i | −0.899500 | − | 1.55798i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.0000 | − | 41.5692i | −0.797787 | − | 1.38181i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5000 | − | 32.0429i | 0.614282 | − | 1.06397i | −0.376228 | − | 0.926527i | \(-0.622779\pi\) |
0.990510 | − | 0.137441i | \(-0.0438878\pi\) | |||||||
\(908\) | 24.0000 | + | 41.5692i | 0.796468 | + | 1.37952i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0000 | −0.496972 | −0.248486 | − | 0.968635i | \(-0.579933\pi\) | ||||
−0.248486 | + | 0.968635i | \(0.579933\pi\) | |||||||
\(912\) | −28.0000 | − | 48.4974i | −0.927173 | − | 1.60591i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.0000 | + | 51.9615i | 0.991769 | + | 1.71780i | ||||
\(916\) | −28.0000 | −0.925146 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | + | 13.8564i | 0.263896 | + | 0.457081i | 0.967274 | − | 0.253735i | \(-0.0816592\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.0000 | − | 19.0526i | 0.362462 | − | 0.627803i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.00000 | −0.197492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.00000 | − | 3.46410i | 0.0656886 | − | 0.113776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.50000 | + | 2.59808i | 0.0492134 | + | 0.0852401i | 0.889583 | − | 0.456774i | \(-0.150995\pi\) |
−0.840369 | + | 0.542014i | \(0.817662\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18.0000 | 0.589610 | ||||||||
\(933\) | −12.0000 | − | 20.7846i | −0.392862 | − | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0000 | −0.522140 | ||||||||
\(940\) | −9.00000 | − | 15.5885i | −0.293548 | − | 0.508439i | ||||
\(941\) | −7.50000 | + | 12.9904i | −0.244493 | + | 0.423474i | −0.961989 | − | 0.273088i | \(-0.911955\pi\) |
0.717496 | + | 0.696563i | \(0.245288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | + | 15.5885i | 0.293080 | + | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.0000 | − | 46.7654i | −0.877382 | − | 1.51967i | −0.854203 | − | 0.519939i | \(-0.825955\pi\) |
−0.0231788 | − | 0.999731i | \(-0.507379\pi\) | |||||||
\(948\) | 2.00000 | − | 3.46410i | 0.0649570 | − | 0.112509i | ||||
\(949\) | −5.50000 | + | 9.52628i | −0.178538 | + | 0.309236i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.0000 | 0.680257 | 0.340128 | − | 0.940379i | \(-0.389529\pi\) | ||||
0.340128 | + | 0.940379i | \(0.389529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.0000 | − | 62.3538i | 1.16493 | − | 2.01772i | ||||
\(956\) | −12.0000 | + | 20.7846i | −0.388108 | + | 0.672222i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −48.0000 | −1.54919 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | −1.00000 | − | 1.73205i | −0.0322078 | − | 0.0557856i | ||||
\(965\) | 66.0000 | 2.12462 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42.0000 | − | 72.7461i | 1.34923 | − | 2.33694i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.00000 | + | 5.19615i | 0.0962746 | + | 0.166752i | 0.910140 | − | 0.414301i | \(-0.135974\pi\) |
−0.813865 | + | 0.581054i | \(0.802641\pi\) | |||||||
\(972\) | −20.0000 | −0.641500 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.00000 | + | 6.92820i | 0.128103 | + | 0.221880i | ||||
\(976\) | 20.0000 | − | 34.6410i | 0.640184 | − | 1.10883i | ||||
\(977\) | −24.0000 | + | 41.5692i | −0.767828 | + | 1.32992i | 0.170910 | + | 0.985287i | \(0.445329\pi\) |
−0.938738 | + | 0.344631i | \(0.888004\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.5000 | + | 49.3634i | −0.909009 | + | 1.57445i | −0.0935651 | + | 0.995613i | \(0.529826\pi\) |
−0.815444 | + | 0.578836i | \(0.803507\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.00000 | + | 15.5885i | 0.286764 | + | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.0000 | 0.445399 | ||||||||
\(989\) | 1.50000 | + | 2.59808i | 0.0476972 | + | 0.0826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | − | 13.8564i | 0.254128 | − | 0.440163i | −0.710530 | − | 0.703667i | \(-0.751545\pi\) |
0.964658 | + | 0.263504i | \(0.0848781\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −52.0000 | −1.65017 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.00000 | −0.190213 | ||||||||
\(996\) | −6.00000 | − | 10.3923i | −0.190117 | − | 0.329293i | ||||
\(997\) | −4.00000 | + | 6.92820i | −0.126681 | + | 0.219418i | −0.922389 | − | 0.386263i | \(-0.873766\pi\) |
0.795708 | + | 0.605681i | \(0.207099\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.00000 | − | 6.92820i | −0.126554 | − | 0.219199i |
(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 | 637.2.e.c.508.1 | 2 | ||
7.2 | even | 3 | inner | 637.2.e.c.79.1 | 2 | ||
7.3 | odd | 6 | 637.2.a.b.1.1 | 1 | |||
7.4 | even | 3 | 91.2.a.b.1.1 | ✓ | 1 | ||
7.5 | odd | 6 | 637.2.e.b.79.1 | 2 | |||
7.6 | odd | 2 | 637.2.e.b.508.1 | 2 | |||
21.11 | odd | 6 | 819.2.a.c.1.1 | 1 | |||
21.17 | even | 6 | 5733.2.a.f.1.1 | 1 | |||
28.11 | odd | 6 | 1456.2.a.k.1.1 | 1 | |||
35.4 | even | 6 | 2275.2.a.d.1.1 | 1 | |||
56.11 | odd | 6 | 5824.2.a.f.1.1 | 1 | |||
56.53 | even | 6 | 5824.2.a.bd.1.1 | 1 | |||
91.18 | odd | 12 | 1183.2.c.a.337.2 | 2 | |||
91.25 | even | 6 | 1183.2.a.a.1.1 | 1 | |||
91.38 | odd | 6 | 8281.2.a.h.1.1 | 1 | |||
91.60 | odd | 12 | 1183.2.c.a.337.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.b.1.1 | ✓ | 1 | 7.4 | even | 3 | ||
637.2.a.b.1.1 | 1 | 7.3 | odd | 6 | |||
637.2.e.b.79.1 | 2 | 7.5 | odd | 6 | |||
637.2.e.b.508.1 | 2 | 7.6 | odd | 2 | |||
637.2.e.c.79.1 | 2 | 7.2 | even | 3 | inner | ||
637.2.e.c.508.1 | 2 | 1.1 | even | 1 | trivial | ||
819.2.a.c.1.1 | 1 | 21.11 | odd | 6 | |||
1183.2.a.a.1.1 | 1 | 91.25 | even | 6 | |||
1183.2.c.a.337.1 | 2 | 91.60 | odd | 12 | |||
1183.2.c.a.337.2 | 2 | 91.18 | odd | 12 | |||
1456.2.a.k.1.1 | 1 | 28.11 | odd | 6 | |||
2275.2.a.d.1.1 | 1 | 35.4 | even | 6 | |||
5733.2.a.f.1.1 | 1 | 21.17 | even | 6 | |||
5824.2.a.f.1.1 | 1 | 56.11 | odd | 6 | |||
5824.2.a.bd.1.1 | 1 | 56.53 | even | 6 | |||
8281.2.a.h.1.1 | 1 | 91.38 | odd | 6 |