Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (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: | \(24.1467615712\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.289 |
Dual form | 3024.2.t.c.1873.1 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | 0.104257 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.50000 | − | 7.79423i | 0.835629 | − | 1.44735i | −0.0578882 | − | 0.998323i | \(-0.518437\pi\) |
0.893517 | − | 0.449029i | \(-0.148230\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.50000 | − | 0.866025i | −0.422577 | − | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50000 | + | 4.33013i | −0.410997 | + | 0.711868i | −0.994999 | − | 0.0998840i | \(-0.968153\pi\) |
0.584002 | + | 0.811752i | \(0.301486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.50000 | + | 6.06218i | 0.546608 | + | 0.946753i | 0.998504 | + | 0.0546823i | \(0.0174146\pi\) |
−0.451896 | + | 0.892071i | \(0.649252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.50000 | − | 2.59808i | 0.228748 | − | 0.396203i | −0.728689 | − | 0.684844i | \(-0.759870\pi\) |
0.957437 | + | 0.288641i | \(0.0932035\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | − | 6.92820i | −0.583460 | − | 1.01058i | −0.995066 | − | 0.0992202i | \(-0.968365\pi\) |
0.411606 | − | 0.911362i | \(-0.364968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | + | 7.79423i | 0.618123 | + | 1.07062i | 0.989828 | + | 0.142269i | \(0.0454398\pi\) |
−0.371706 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | − | 3.46410i | 0.260378 | − | 0.450988i | −0.705965 | − | 0.708247i | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.500000 | + | 0.866025i | 0.0620174 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | − | 10.3923i | 0.733017 | − | 1.26962i | −0.222571 | − | 0.974916i | \(-0.571445\pi\) |
0.955588 | − | 0.294706i | \(-0.0952216\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.50000 | + | 11.2583i | 0.760767 | + | 1.31769i | 0.942455 | + | 0.334332i | \(0.108511\pi\) |
−0.181688 | + | 0.983356i | \(0.558156\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.50000 | − | 2.59808i | −0.854704 | − | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.50000 | − | 11.2583i | 0.713468 | − | 1.23576i | −0.250080 | − | 0.968225i | \(-0.580457\pi\) |
0.963548 | − | 0.267537i | \(-0.0862098\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.50000 | − | 2.59808i | −0.162698 | − | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.50000 | + | 7.79423i | −0.476999 | + | 0.826187i | −0.999653 | − | 0.0263586i | \(-0.991609\pi\) |
0.522654 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.500000 | − | 2.59808i | −0.0524142 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.50000 | + | 4.33013i | −0.256495 | + | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.50000 | − | 14.7224i | 0.863044 | − | 1.49484i | −0.00593185 | − | 0.999982i | \(-0.501888\pi\) |
0.868976 | − | 0.494854i | \(-0.164778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.00000 | 0.696526 | 0.348263 | − | 0.937397i | \(-0.386772\pi\) | ||||
0.348263 | + | 0.937397i | \(0.386772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.00000 | −0.886796 | −0.443398 | − | 0.896325i | \(-0.646227\pi\) | ||||
−0.443398 | + | 0.896325i | \(0.646227\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.50000 | − | 6.06218i | 0.338358 | − | 0.586053i | −0.645766 | − | 0.763535i | \(-0.723462\pi\) |
0.984124 | + | 0.177482i | \(0.0567953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | − | 4.33013i | −0.239457 | − | 0.414751i | 0.721102 | − | 0.692829i | \(-0.243636\pi\) |
−0.960558 | + | 0.278078i | \(0.910303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.500000 | − | 0.866025i | −0.0470360 | − | 0.0814688i | 0.841549 | − | 0.540181i | \(-0.181644\pi\) |
−0.888585 | + | 0.458712i | \(0.848311\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50000 | + | 7.79423i | 0.137505 | + | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | 0.262111 | 0.131056 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131056 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0000 | − | 8.66025i | 0.867110 | − | 0.750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.0000 | −0.939793 | −0.469897 | − | 0.882721i | \(-0.655709\pi\) | ||||
−0.469897 | + | 0.882721i | \(0.655709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.50000 | + | 2.59808i | 0.125436 | + | 0.217262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.50000 | + | 7.79423i | −0.373705 | + | 0.647275i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.0000 | 1.22885 | 0.614424 | − | 0.788976i | \(-0.289388\pi\) | ||||
0.614424 | + | 0.788976i | \(0.289388\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0000 | 1.38344 | 0.691720 | − | 0.722166i | \(-0.256853\pi\) | ||||
0.691720 | + | 0.722166i | \(0.256853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | + | 3.46410i | −0.160644 | + | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.50000 | + | 0.866025i | 0.197028 | + | 0.0682524i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.50000 | − | 14.7224i | 0.665771 | − | 1.15315i | −0.313304 | − | 0.949653i | \(-0.601436\pi\) |
0.979076 | − | 0.203497i | \(-0.0652307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.500000 | + | 0.866025i | 0.0386912 | + | 0.0670151i | 0.884723 | − | 0.466118i | \(-0.154348\pi\) |
−0.846031 | + | 0.533133i | \(0.821014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.00000 | − | 1.73205i | −0.0760286 | − | 0.131685i | 0.825505 | − | 0.564396i | \(-0.190891\pi\) |
−0.901533 | + | 0.432710i | \(0.857557\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | − | 3.46410i | −0.755929 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5000 | + | 18.1865i | 0.784807 | + | 1.35933i | 0.929114 | + | 0.369792i | \(0.120571\pi\) |
−0.144308 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.50000 | − | 4.33013i | 0.183804 | − | 0.318357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.50000 | − | 7.79423i | −0.329073 | − | 0.569970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00000 | − | 3.46410i | −0.144715 | − | 0.250654i | 0.784552 | − | 0.620063i | \(-0.212893\pi\) |
−0.929267 | + | 0.369410i | \(0.879560\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.00000 | − | 15.5885i | 0.647834 | − | 1.12208i | −0.335805 | − | 0.941932i | \(-0.609008\pi\) |
0.983639 | − | 0.180150i | \(-0.0576584\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.0000 | 1.56744 | 0.783718 | − | 0.621117i | \(-0.213321\pi\) | ||||
0.783718 | + | 0.621117i | \(0.213321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5000 | + | 18.1865i | 0.744325 | + | 1.28921i | 0.950509 | + | 0.310696i | \(0.100562\pi\) |
−0.206184 | + | 0.978513i | \(0.566105\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.0000 | − | 15.5885i | 1.26335 | − | 1.09410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.50000 | − | 6.06218i | −0.244451 | − | 0.423401i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.50000 | + | 12.9904i | −0.518786 | + | 0.898563i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5000 | − | 23.3827i | −0.929378 | − | 1.60973i | −0.784364 | − | 0.620301i | \(-0.787010\pi\) |
−0.145014 | − | 0.989430i | \(-0.546323\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.50000 | + | 2.59808i | −0.102299 | + | 0.177187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | − | 6.92820i | 0.543075 | − | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.50000 | − | 2.59808i | 0.100901 | − | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.50000 | − | 11.2583i | 0.435272 | − | 0.753914i | −0.562046 | − | 0.827106i | \(-0.689985\pi\) |
0.997318 | + | 0.0731927i | \(0.0233188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.0000 | −0.995585 | −0.497792 | − | 0.867296i | \(-0.665856\pi\) | ||||
−0.497792 | + | 0.867296i | \(0.665856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0000 | 1.38772 | 0.693860 | − | 0.720110i | \(-0.255909\pi\) | ||||
0.693860 | + | 0.720110i | \(0.255909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.50000 | − | 2.59808i | 0.0982683 | − | 0.170206i | −0.812700 | − | 0.582683i | \(-0.802003\pi\) |
0.910968 | + | 0.412477i | \(0.135336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | + | 6.92820i | 0.260931 | + | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.50000 | + | 7.79423i | 0.291081 | + | 0.504167i | 0.974066 | − | 0.226266i | \(-0.0726518\pi\) |
−0.682985 | + | 0.730433i | \(0.739318\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | −0.0322078 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322078 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.50000 | − | 4.33013i | −0.351382 | − | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | −0.318142 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.00000 | −0.188608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.0000 | 1.06043 | 0.530215 | − | 0.847863i | \(-0.322111\pi\) | ||||
0.530215 | + | 0.847863i | \(0.322111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0000 | + | 8.66025i | −0.621370 | + | 0.538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0000 | 0.678289 | 0.339145 | − | 0.940734i | \(-0.389862\pi\) | ||||
0.339145 | + | 0.940734i | \(0.389862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.50000 | − | 7.79423i | −0.276433 | − | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.50000 | − | 6.06218i | −0.213399 | − | 0.369618i | 0.739377 | − | 0.673291i | \(-0.235120\pi\) |
−0.952776 | + | 0.303674i | \(0.901787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.5000 | − | 26.8468i | 0.941558 | − | 1.63083i | 0.179057 | − | 0.983839i | \(-0.442695\pi\) |
0.762501 | − | 0.646988i | \(-0.223971\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0000 | 0.723627 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.0000 | −1.14160 | −0.570800 | − | 0.821089i | \(-0.693367\pi\) | ||||
−0.570800 | + | 0.821089i | \(0.693367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.5000 | − | 23.3827i | 0.805342 | − | 1.39489i | −0.110717 | − | 0.993852i | \(-0.535315\pi\) |
0.916060 | − | 0.401042i | \(-0.131352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0000 | + | 20.7846i | −0.713326 | + | 1.23552i | 0.250276 | + | 0.968175i | \(0.419479\pi\) |
−0.963602 | + | 0.267342i | \(0.913855\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.50000 | + | 18.1865i | 0.206598 | + | 1.07352i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.500000 | + | 0.866025i | 0.0292103 | + | 0.0505937i | 0.880261 | − | 0.474490i | \(-0.157367\pi\) |
−0.851051 | + | 0.525084i | \(0.824034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | + | 3.46410i | −0.116445 | + | 0.201688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.500000 | − | 0.866025i | −0.0289157 | − | 0.0500835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | − | 5.19615i | 0.345834 | − | 0.299501i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.00000 | + | 1.73205i | 0.0572598 | + | 0.0991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | + | 20.7846i | −0.680458 | + | 1.17859i | 0.294384 | + | 0.955687i | \(0.404886\pi\) |
−0.974841 | + | 0.222900i | \(0.928448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.00000 | − | 5.19615i | −0.169570 | − | 0.293704i | 0.768699 | − | 0.639611i | \(-0.220905\pi\) |
−0.938269 | + | 0.345907i | \(0.887571\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.00000 | + | 12.1244i | 0.393159 | + | 0.680972i | 0.992864 | − | 0.119249i | \(-0.0380488\pi\) |
−0.599705 | + | 0.800221i | \(0.704715\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.5000 | + | 23.3827i | −0.755855 | + | 1.30918i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0000 | 0.834622 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | + | 3.46410i | 0.110940 | + | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.00000 | − | 20.7846i | −0.220527 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.00000 | + | 10.3923i | −0.327815 | + | 0.567792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.50000 | − | 12.9904i | −0.408551 | − | 0.707631i | 0.586177 | − | 0.810183i | \(-0.300632\pi\) |
−0.994728 | + | 0.102552i | \(0.967299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | + | 10.3923i | −0.324918 | + | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.0000 | − | 24.2487i | 0.751559 | − | 1.30174i | −0.195507 | − | 0.980702i | \(-0.562635\pi\) |
0.947067 | − | 0.321037i | \(-0.104031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.50000 | + | 14.7224i | −0.454995 | + | 0.788074i | −0.998688 | − | 0.0512103i | \(-0.983692\pi\) |
0.543693 | + | 0.839284i | \(0.317025\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.0000 | −1.64996 | −0.824982 | − | 0.565159i | \(-0.808815\pi\) | ||||
−0.824982 | + | 0.565159i | \(0.808815\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.5000 | + | 23.3827i | −0.712503 | + | 1.23409i | 0.251412 | + | 0.967880i | \(0.419105\pi\) |
−0.963915 | + | 0.266211i | \(0.914228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.50000 | − | 11.2583i | −0.340226 | − | 0.589288i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0000 | −0.574195 | −0.287098 | − | 0.957901i | \(-0.592690\pi\) | ||||
−0.287098 | + | 0.957901i | \(0.592690\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.50000 | + | 23.3827i | 0.233628 | + | 1.21397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0000 | 0.673114 | 0.336557 | − | 0.941663i | \(-0.390737\pi\) | ||||
0.336557 | + | 0.941663i | \(0.390737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.00000 | −0.463524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.0000 | −1.64373 | −0.821865 | − | 0.569683i | \(-0.807066\pi\) | ||||
−0.821865 | + | 0.569683i | \(0.807066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.0000 | −1.78842 | −0.894208 | − | 0.447651i | \(-0.852261\pi\) | ||||
−0.894208 | + | 0.447651i | \(0.852261\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.50000 | + | 2.59808i | 0.382235 | + | 0.132410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.0000 | −1.87597 | −0.937987 | − | 0.346670i | \(-0.887312\pi\) | ||||
−0.937987 | + | 0.346670i | \(0.887312\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.50000 | + | 2.59808i | 0.0758583 | + | 0.131390i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.00000 | − | 6.92820i | −0.201262 | − | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5000 | + | 21.6506i | −0.627357 | + | 1.08661i | 0.360723 | + | 0.932673i | \(0.382530\pi\) |
−0.988080 | + | 0.153941i | \(0.950803\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0000 | 0.649189 | 0.324595 | − | 0.945853i | \(-0.394772\pi\) | ||||
0.324595 | + | 0.945853i | \(0.394772\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.50000 | − | 12.9904i | 0.371761 | − | 0.643909i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | + | 8.66025i | −0.247234 | + | 0.428222i | −0.962757 | − | 0.270367i | \(-0.912855\pi\) |
0.715523 | + | 0.698589i | \(0.246188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | − | 6.92820i | 0.393654 | − | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.50000 | + | 11.2583i | −0.319072 | + | 0.552650i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5000 | − | 18.1865i | −0.512959 | − | 0.888470i | −0.999887 | − | 0.0150285i | \(-0.995216\pi\) |
0.486928 | − | 0.873442i | \(-0.338117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.50000 | − | 2.59808i | 0.0731055 | − | 0.126622i | −0.827155 | − | 0.561973i | \(-0.810042\pi\) |
0.900261 | + | 0.435351i | \(0.143376\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | − | 10.3923i | −0.291043 | − | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.00000 | − | 5.19615i | −0.0483934 | − | 0.251459i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.50000 | + | 12.9904i | 0.361262 | + | 0.625725i | 0.988169 | − | 0.153370i | \(-0.0490126\pi\) |
−0.626907 | + | 0.779094i | \(0.715679\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.50000 | − | 4.33013i | 0.119591 | − | 0.207138i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | + | 20.7846i | 0.572729 | + | 0.991995i | 0.996284 | + | 0.0861252i | \(0.0274485\pi\) |
−0.423556 | + | 0.905870i | \(0.639218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.00000 | − | 13.8564i | −0.380091 | − | 0.658338i | 0.610984 | − | 0.791643i | \(-0.290774\pi\) |
−0.991075 | + | 0.133306i | \(0.957441\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.50000 | − | 7.79423i | 0.213320 | − | 0.369482i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5000 | − | 18.1865i | −0.494426 | − | 0.856370i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.500000 | + | 2.59808i | 0.0234404 | + | 0.121800i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0000 | + | 22.5167i | 0.608114 | + | 1.05328i | 0.991551 | + | 0.129718i | \(0.0414071\pi\) |
−0.383437 | + | 0.923567i | \(0.625260\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.5000 | + | 23.3827i | −0.628758 | + | 1.08904i | 0.359044 | + | 0.933321i | \(0.383103\pi\) |
−0.987801 | + | 0.155719i | \(0.950230\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.500000 | − | 0.866025i | −0.0232370 | − | 0.0402476i | 0.854173 | − | 0.519989i | \(-0.174064\pi\) |
−0.877410 | + | 0.479741i | \(0.840731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.50000 | + | 11.2583i | −0.300784 | + | 0.520973i | −0.976314 | − | 0.216359i | \(-0.930582\pi\) |
0.675530 | + | 0.737333i | \(0.263915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0000 | − | 20.7846i | 1.10822 | − | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.50000 | + | 7.79423i | −0.206910 | + | 0.358379i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0000 | + | 17.3205i | −0.458831 | + | 0.794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.0000 | −0.959514 | −0.479757 | − | 0.877401i | \(-0.659275\pi\) | ||||
−0.479757 | + | 0.877401i | \(0.659275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | 0.227980 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.50000 | + | 14.7224i | −0.385965 | + | 0.668511i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5000 | + | 32.0429i | 0.838315 | + | 1.45200i | 0.891303 | + | 0.453409i | \(0.149792\pi\) |
−0.0529875 | + | 0.998595i | \(0.516874\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.50000 | − | 7.79423i | −0.203082 | − | 0.351749i | 0.746438 | − | 0.665455i | \(-0.231763\pi\) |
−0.949520 | + | 0.313707i | \(0.898429\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0000 | 1.21602 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.0000 | + | 6.92820i | 0.897123 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.0000 | 1.29822 | 0.649109 | − | 0.760695i | \(-0.275142\pi\) | ||||
0.649109 | + | 0.760695i | \(0.275142\pi\) | |||||||
\(500\) | 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 | ||||||||
\(505\) | −7.00000 | −0.311496 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.0000 | −1.46270 | −0.731350 | − | 0.682003i | \(-0.761109\pi\) | ||||
−0.731350 | + | 0.682003i | \(0.761109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.50000 | + | 33.7750i | 0.287543 | + | 1.49412i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.00000 | 0.396587 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000 | + | 20.7846i | 0.527759 | + | 0.914106i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50000 | + | 2.59808i | 0.0657162 | + | 0.113824i | 0.897011 | − | 0.442007i | \(-0.145733\pi\) |
−0.831295 | + | 0.555831i | \(0.812400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.5000 | − | 28.5788i | 0.721495 | − | 1.24967i | −0.238906 | − | 0.971043i | \(-0.576789\pi\) |
0.960401 | − | 0.278623i | \(-0.0898779\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | 0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.50000 | − | 6.06218i | 0.151602 | − | 0.262582i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.50000 | + | 6.06218i | −0.151318 | + | 0.262091i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.5000 | − | 12.9904i | −0.710705 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.50000 | − | 9.52628i | 0.236463 | − | 0.409567i | −0.723234 | − | 0.690604i | \(-0.757345\pi\) |
0.959697 | + | 0.281037i | \(0.0906783\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.50000 | + | 4.33013i | 0.107088 | + | 0.185482i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.50000 | + | 4.33013i | −0.106892 | + | 0.185143i | −0.914510 | − | 0.404564i | \(-0.867423\pi\) |
0.807617 | + | 0.589707i | \(0.200757\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.5000 | − | 38.9711i | −0.958532 | − | 1.66023i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | + | 20.7846i | 0.170097 | + | 0.883852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.5000 | − | 33.7750i | −0.826242 | − | 1.43109i | −0.900967 | − | 0.433888i | \(-0.857141\pi\) |
0.0747252 | − | 0.997204i | \(-0.476192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.00000 | −0.126886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.00000 | − | 10.3923i | 0.252870 | − | 0.437983i | −0.711445 | − | 0.702742i | \(-0.751959\pi\) |
0.964315 | + | 0.264758i | \(0.0852922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.500000 | + | 0.866025i | 0.0210352 | + | 0.0364340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.0000 | − | 36.3731i | −0.880366 | − | 1.52484i | −0.850935 | − | 0.525271i | \(-0.823964\pi\) |
−0.0294311 | − | 0.999567i | \(-0.509370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.50000 | − | 2.59808i | −0.0624458 | − | 0.108159i | 0.833112 | − | 0.553104i | \(-0.186557\pi\) |
−0.895558 | + | 0.444945i | \(0.853223\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.0000 | − | 22.5167i | 1.07866 | − | 0.934148i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.5000 | − | 23.3827i | −0.559113 | − | 0.968412i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.50000 | + | 12.9904i | −0.309558 | + | 0.536170i | −0.978266 | − | 0.207355i | \(-0.933514\pi\) |
0.668708 | + | 0.743525i | \(0.266848\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0000 | − | 17.3205i | −0.412043 | − | 0.713679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.5000 | + | 18.1865i | −0.431183 | + | 0.746831i | −0.996976 | − | 0.0777165i | \(-0.975237\pi\) |
0.565792 | + | 0.824548i | \(0.308570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.50000 | − | 7.79423i | −0.0614940 | − | 0.319532i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.5000 | + | 19.9186i | −0.469095 | + | 0.812496i | −0.999376 | − | 0.0353259i | \(-0.988753\pi\) |
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.00000 | 0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.0000 | 0.933541 | 0.466771 | − | 0.884378i | \(-0.345417\pi\) | ||||
0.466771 | + | 0.884378i | \(0.345417\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | + | 6.92820i | −0.161823 | + | 0.280285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.50000 | − | 4.33013i | −0.100974 | − | 0.174892i | 0.811112 | − | 0.584891i | \(-0.198863\pi\) |
−0.912086 | + | 0.409998i | \(0.865529\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50000 | + | 2.59808i | 0.0603877 | + | 0.104595i | 0.894639 | − | 0.446790i | \(-0.147433\pi\) |
−0.834251 | + | 0.551385i | \(0.814100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.0000 | −0.844061 | −0.422031 | − | 0.906582i | \(-0.638683\pi\) | ||||
−0.422031 | + | 0.906582i | \(0.638683\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.0000 | + | 15.5885i | −0.721155 | + | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.0000 | −0.598089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.00000 | 0.317470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | − | 6.92820i | 0.0396214 | − | 0.274505i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.00000 | 0.197488 | 0.0987441 | − | 0.995113i | \(-0.468517\pi\) | ||||
0.0987441 | + | 0.995113i | \(0.468517\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5000 | + | 32.0429i | 0.729569 | + | 1.26365i | 0.957066 | + | 0.289871i | \(0.0936125\pi\) |
−0.227497 | + | 0.973779i | \(0.573054\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.5000 | − | 35.5070i | −0.805938 | − | 1.39593i | −0.915656 | − | 0.401963i | \(-0.868328\pi\) |
0.109718 | − | 0.993963i | \(-0.465005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | + | 10.3923i | −0.235521 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.00000 | 0.117399 | 0.0586995 | − | 0.998276i | \(-0.481305\pi\) | ||||
0.0586995 | + | 0.998276i | \(0.481305\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | −0.117220 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.50000 | + | 12.9904i | −0.292159 | + | 0.506033i | −0.974320 | − | 0.225168i | \(-0.927707\pi\) |
0.682161 | + | 0.731202i | \(0.261040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0000 | + | 32.9090i | −0.739014 | + | 1.28001i | 0.213925 | + | 0.976850i | \(0.431375\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.0000 | + | 8.66025i | −0.387783 | + | 0.335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.50000 | − | 7.79423i | 0.174241 | − | 0.301794i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.00000 | + | 5.19615i | 0.115814 | + | 0.200595i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.5000 | + | 30.3109i | −0.674575 | + | 1.16840i | 0.302017 | + | 0.953302i | \(0.402340\pi\) |
−0.976593 | + | 0.215096i | \(0.930993\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.0000 | + | 32.9090i | 0.730229 | + | 1.26479i | 0.956785 | + | 0.290796i | \(0.0939201\pi\) |
−0.226556 | + | 0.973998i | \(0.572747\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.0000 | − | 29.4449i | 1.30480 | − | 1.12999i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.5000 | − | 26.8468i | −0.593091 | − | 1.02726i | −0.993813 | − | 0.111064i | \(-0.964574\pi\) |
0.400722 | − | 0.916200i | \(-0.368759\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.0000 | 0.420288 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.50000 | − | 7.79423i | 0.171436 | − | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.00000 | − | 10.3923i | −0.228251 | − | 0.395342i | 0.729039 | − | 0.684472i | \(-0.239967\pi\) |
−0.957290 | + | 0.289130i | \(0.906634\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.50000 | − | 4.33013i | −0.0948304 | − | 0.164251i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.5000 | + | 18.1865i | −0.397716 | + | 0.688864i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.5000 | + | 21.6506i | 0.471446 | + | 0.816569i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.5000 | + | 6.06218i | 0.658155 | + | 0.227992i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.00000 | + | 15.5885i | 0.338002 | + | 0.585437i | 0.984057 | − | 0.177854i | \(-0.0569156\pi\) |
−0.646055 | + | 0.763291i | \(0.723582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.00000 | − | 3.46410i | 0.0749006 | − | 0.129732i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.50000 | − | 2.59808i | −0.0560968 | − | 0.0971625i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.50000 | + | 16.4545i | −0.354290 | + | 0.613649i | −0.986996 | − | 0.160743i | \(-0.948611\pi\) |
0.632706 | + | 0.774392i | \(0.281944\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.5000 | − | 7.79423i | −0.837944 | − | 0.290272i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0000 | + | 31.1769i | −0.668503 | + | 1.15788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.50000 | − | 14.7224i | 0.315248 | − | 0.546025i | −0.664243 | − | 0.747517i | \(-0.731246\pi\) |
0.979490 | + | 0.201492i | \(0.0645791\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.00000 | 0.332877 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.0000 | −1.58824 | −0.794121 | − | 0.607760i | \(-0.792068\pi\) | ||||
−0.794121 | + | 0.607760i | \(0.792068\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.0000 | + | 31.1769i | −0.663039 | + | 1.14842i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.50000 | − | 14.7224i | −0.312678 | − | 0.541573i | 0.666264 | − | 0.745716i | \(-0.267893\pi\) |
−0.978941 | + | 0.204143i | \(0.934559\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.500000 | + | 0.866025i | 0.0183432 | + | 0.0317714i | 0.875051 | − | 0.484030i | \(-0.160828\pi\) |
−0.856708 | + | 0.515802i | \(0.827494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.0000 | −0.549557 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.0000 | − | 12.1244i | 0.511549 | − | 0.443014i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.0000 | 0.547358 | 0.273679 | − | 0.961821i | \(-0.411759\pi\) | ||||
0.273679 | + | 0.961821i | \(0.411759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.0000 | −0.618693 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.0000 | 0.508839 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.0000 | 1.63125 | 0.815624 | − | 0.578582i | \(-0.196394\pi\) | ||||
0.815624 | + | 0.578582i | \(0.196394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.50000 | − | 12.9904i | −0.0905061 | − | 0.470283i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | −0.144432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.5000 | + | 35.5070i | 0.739249 | + | 1.28042i | 0.952834 | + | 0.303492i | \(0.0981526\pi\) |
−0.213585 | + | 0.976924i | \(0.568514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.50000 | − | 6.06218i | −0.125886 | − | 0.218041i | 0.796193 | − | 0.605043i | \(-0.206844\pi\) |
−0.922079 | + | 0.387002i | \(0.873511\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | + | 13.8564i | −0.287368 | + | 0.497737i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.0000 | 1.25401 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.0000 | −0.858788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.00000 | − | 12.1244i | 0.249841 | − | 0.432737i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.0000 | − | 17.3205i | 0.356462 | − | 0.617409i | −0.630905 | − | 0.775860i | \(-0.717316\pi\) |
0.987367 | + | 0.158450i | \(0.0506498\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.500000 | − | 2.59808i | −0.0177780 | − | 0.0923770i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.00000 | + | 1.73205i | −0.0355110 | + | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.5000 | − | 33.7750i | −0.690725 | − | 1.19637i | −0.971601 | − | 0.236627i | \(-0.923958\pi\) |
0.280875 | − | 0.959744i | \(-0.409375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | − | 20.7846i | 0.424529 | − | 0.735307i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.5000 | − | 33.7750i | −0.688140 | − | 1.19189i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.50000 | − | 0.866025i | −0.0881134 | − | 0.0305234i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.5000 | + | 47.6314i | 0.966849 | + | 1.67463i | 0.704564 | + | 0.709640i | \(0.251142\pi\) |
0.262284 | + | 0.964991i | \(0.415524\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.50000 | + | 14.7224i | −0.297742 | + | 0.515704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.50000 | − | 12.9904i | −0.262392 | − | 0.454476i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0000 | + | 36.3731i | 0.732905 | + | 1.26943i | 0.955636 | + | 0.294549i | \(0.0951694\pi\) |
−0.222731 | + | 0.974880i | \(0.571497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | + | 34.6410i | −0.697156 | + | 1.20751i | 0.272292 | + | 0.962215i | \(0.412218\pi\) |
−0.969448 | + | 0.245295i | \(0.921115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.0000 | −1.39094 | −0.695468 | − | 0.718557i | \(-0.744803\pi\) | ||||
−0.695468 | + | 0.718557i | \(0.744803\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.50000 | − | 4.33013i | −0.0868286 | − | 0.150392i | 0.819340 | − | 0.573307i | \(-0.194340\pi\) |
−0.906169 | + | 0.422916i | \(0.861007\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.00000 | + | 20.7846i | −0.103944 | + | 0.720144i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.500000 | − | 0.866025i | −0.0173032 | − | 0.0299700i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.5000 | + | 38.9711i | −0.776786 | + | 1.34543i | 0.156999 | + | 0.987599i | \(0.449818\pi\) |
−0.933785 | + | 0.357834i | \(0.883515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | − | 45.0333i | −0.896552 | − | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | − | 1.73205i | −0.171802 | − | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.50000 | + | 4.33013i | −0.0856989 | + | 0.148435i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.5000 | + | 25.1147i | −0.496471 | + | 0.859912i | −0.999992 | − | 0.00407068i | \(-0.998704\pi\) |
0.503521 | + | 0.863983i | \(0.332038\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.00000 | −0.239115 | −0.119558 | − | 0.992827i | \(-0.538148\pi\) | ||||
−0.119558 | + | 0.992827i | \(0.538148\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0000 | −0.648272 | −0.324136 | − | 0.946011i | \(-0.605073\pi\) | ||||
−0.324136 | + | 0.946011i | \(0.605073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.50000 | + | 9.52628i | −0.187222 | + | 0.324278i | −0.944323 | − | 0.329020i | \(-0.893282\pi\) |
0.757101 | + | 0.653298i | \(0.226615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00000 | + | 1.73205i | 0.0340010 | + | 0.0588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | − | 20.7846i | −0.407072 | − | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | −0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.5000 | + | 7.79423i | 0.760639 | + | 0.263493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0000 | −0.776655 | −0.388327 | − | 0.921521i | \(-0.626947\pi\) | ||||
−0.388327 | + | 0.921521i | \(0.626947\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.0000 | −1.74994 | −0.874970 | − | 0.484178i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.0000 | −0.906571 | −0.453286 | − | 0.891365i | \(-0.649748\pi\) | ||||
−0.453286 | + | 0.891365i | \(0.649748\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0000 | − | 6.92820i | −0.670778 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40.0000 | −1.33855 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.5000 | − | 18.1865i | −0.350976 | − | 0.607909i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.0000 | − | 31.1769i | −0.600334 | − | 1.03981i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.5000 | + | 23.3827i | −0.449750 | + | 0.778990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.0000 | 0.598340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.00000 | 0.232431 | 0.116216 | − | 0.993224i | \(-0.462924\pi\) | ||||
0.116216 | + | 0.993224i | \(0.462924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.5000 | − | 23.3827i | 0.447275 | − | 0.774703i | −0.550933 | − | 0.834550i | \(-0.685728\pi\) |
0.998208 | + | 0.0598468i | \(0.0190612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.5000 | + | 33.7750i | −0.645356 | + | 1.11779i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.50000 | + | 2.59808i | 0.247672 | + | 0.0857960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.50000 | + | 11.2583i | −0.214415 | + | 0.371378i | −0.953092 | − | 0.302682i | \(-0.902118\pi\) |
0.738676 | + | 0.674060i | \(0.235451\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.00000 | − | 6.92820i | −0.131662 | − | 0.228045i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0000 | − | 17.3205i | 0.328798 | − | 0.569495i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.00000 | − | 15.5885i | −0.295280 | − | 0.511441i | 0.679770 | − | 0.733426i | \(-0.262080\pi\) |
−0.975050 | + | 0.221985i | \(0.928746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.5000 | − | 12.9904i | 1.06514 | − | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.50000 | + | 7.79423i | 0.147166 | + | 0.254899i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.0000 | + | 43.3013i | −0.814977 | + | 1.41158i | 0.0943679 | + | 0.995537i | \(0.469917\pi\) |
−0.909345 | + | 0.416044i | \(0.863416\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.50000 | + | 6.06218i | 0.113976 | + | 0.197412i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.0000 | + | 31.1769i | 0.584921 | + | 1.01311i | 0.994885 | + | 0.101012i | \(0.0322080\pi\) |
−0.409964 | + | 0.912102i | \(0.634459\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.50000 | − | 11.2583i | 0.210999 | − | 0.365461i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.00000 | + | 3.46410i | 0.0647185 | + | 0.112096i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.5000 | − | 9.52628i | −0.888021 | − | 0.307620i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.00000 | + | 15.5885i | −0.289720 | + | 0.501810i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5000 | + | 23.3827i | 0.434131 | + | 0.751936i | 0.997224 | − | 0.0744567i | \(-0.0237223\pi\) |
−0.563094 | + | 0.826393i | \(0.690389\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5000 | − | 37.2391i | 0.689968 | − | 1.19506i | −0.281880 | − | 0.959450i | \(-0.590958\pi\) |
0.971848 | − | 0.235610i | \(-0.0757087\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.50000 | + | 12.9904i | 0.0801463 | + | 0.416452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.0000 | − | 19.0526i | 0.351921 | − | 0.609545i | −0.634665 | − | 0.772787i | \(-0.718862\pi\) |
0.986586 | + | 0.163242i | \(0.0521952\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.5000 | − | 23.3827i | 0.431462 | − | 0.747314i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.0000 | −1.30770 | −0.653848 | − | 0.756626i | \(-0.726847\pi\) | ||||
−0.653848 | + | 0.756626i | \(0.726847\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.0000 | −0.700978 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.50000 | − | 2.59808i | 0.0476972 | − | 0.0826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.50000 | − | 12.9904i | −0.238245 | − | 0.412653i | 0.721966 | − | 0.691929i | \(-0.243239\pi\) |
−0.960211 | + | 0.279276i | \(0.909906\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.5000 | − | 18.1865i | −0.332872 | − | 0.576552i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0000 | 0.411714 | 0.205857 | − | 0.978582i | \(-0.434002\pi\) | ||||
0.205857 | + | 0.978582i | \(0.434002\pi\) | |||||||
\(998\) | 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 | 3024.2.t.c.289.1 | 2 | ||
3.2 | odd | 2 | 1008.2.t.e.961.1 | 2 | |||
4.3 | odd | 2 | 1512.2.t.a.289.1 | 2 | |||
7.4 | even | 3 | 3024.2.q.d.2881.1 | 2 | |||
9.4 | even | 3 | 3024.2.q.d.2305.1 | 2 | |||
9.5 | odd | 6 | 1008.2.q.b.625.1 | 2 | |||
12.11 | even | 2 | 504.2.t.a.457.1 | yes | 2 | ||
21.11 | odd | 6 | 1008.2.q.b.529.1 | 2 | |||
28.11 | odd | 6 | 1512.2.q.b.1369.1 | 2 | |||
36.23 | even | 6 | 504.2.q.a.121.1 | yes | 2 | ||
36.31 | odd | 6 | 1512.2.q.b.793.1 | 2 | |||
63.4 | even | 3 | inner | 3024.2.t.c.1873.1 | 2 | ||
63.32 | odd | 6 | 1008.2.t.e.193.1 | 2 | |||
84.11 | even | 6 | 504.2.q.a.25.1 | ✓ | 2 | ||
252.67 | odd | 6 | 1512.2.t.a.361.1 | 2 | |||
252.95 | even | 6 | 504.2.t.a.193.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.a.25.1 | ✓ | 2 | 84.11 | even | 6 | ||
504.2.q.a.121.1 | yes | 2 | 36.23 | even | 6 | ||
504.2.t.a.193.1 | yes | 2 | 252.95 | even | 6 | ||
504.2.t.a.457.1 | yes | 2 | 12.11 | even | 2 | ||
1008.2.q.b.529.1 | 2 | 21.11 | odd | 6 | |||
1008.2.q.b.625.1 | 2 | 9.5 | odd | 6 | |||
1008.2.t.e.193.1 | 2 | 63.32 | odd | 6 | |||
1008.2.t.e.961.1 | 2 | 3.2 | odd | 2 | |||
1512.2.q.b.793.1 | 2 | 36.31 | odd | 6 | |||
1512.2.q.b.1369.1 | 2 | 28.11 | odd | 6 | |||
1512.2.t.a.289.1 | 2 | 4.3 | odd | 2 | |||
1512.2.t.a.361.1 | 2 | 252.67 | odd | 6 | |||
3024.2.q.d.2305.1 | 2 | 9.4 | even | 3 | |||
3024.2.q.d.2881.1 | 2 | 7.4 | even | 3 | |||
3024.2.t.c.289.1 | 2 | 1.1 | even | 1 | trivial | ||
3024.2.t.c.1873.1 | 2 | 63.4 | even | 3 | inner |