Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(793,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.q (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: | \(12.0733807856\) |
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 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1369.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1369 |
Dual form | 1512.2.q.b.793.1 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 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 | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.573539 | − | 0.993399i | −0.996199 | − | 0.0871106i | \(-0.972237\pi\) |
0.422659 | − | 0.906289i | \(-0.361097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913434 | + | 0.406986i | \(0.133420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.50000 | − | 7.79423i | 0.835629 | − | 1.44735i | −0.0578882 | − | 0.998323i | \(-0.518437\pi\) |
0.893517 | − | 0.449029i | \(-0.148230\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 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 | 0.584002 | − | 0.811752i | \(-0.301486\pi\) |
−0.994999 | + | 0.0998840i | \(0.968153\pi\) | |||||||
\(38\) | 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 | −0.957437 | − | 0.288641i | \(-0.906796\pi\) |
0.728689 | + | 0.684844i | \(0.240130\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 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 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.50000 | − | 11.2583i | 0.760767 | − | 1.31769i | −0.181688 | − | 0.983356i | \(-0.558156\pi\) |
0.942455 | − | 0.334332i | \(-0.108511\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.50000 | − | 7.79423i | 0.170941 | − | 0.888235i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.50000 | + | 11.2583i | −0.713468 | + | 1.23576i | 0.250080 | + | 0.968225i | \(0.419543\pi\) |
−0.963548 | + | 0.267537i | \(0.913790\pi\) | |||||||
\(84\) | 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 | 0.522654 | − | 0.852545i | \(-0.324942\pi\) |
−0.999653 | + | 0.0263586i | \(0.991609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.500000 | − | 2.59808i | 0.0524142 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.00000 | −0.512989 | ||||||||
\(96\) | 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 | ||||||||
\(101\) | −3.50000 | − | 6.06218i | −0.348263 | − | 0.603209i | 0.637678 | − | 0.770303i | \(-0.279895\pi\) |
−0.985941 | + | 0.167094i | \(0.946562\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.50000 | + | 7.79423i | −0.443398 | + | 0.767988i | −0.997939 | − | 0.0641683i | \(-0.979561\pi\) |
0.554541 | + | 0.832156i | \(0.312894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.50000 | − | 6.06218i | −0.338358 | − | 0.586053i | 0.645766 | − | 0.763535i | \(-0.276538\pi\) |
−0.984124 | + | 0.177482i | \(0.943205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | + | 4.33013i | −0.239457 | + | 0.414751i | −0.960558 | − | 0.278078i | \(-0.910303\pi\) |
0.721102 | + | 0.692829i | \(0.243636\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −0.500000 | − | 0.866025i | −0.0466252 | − | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.50000 | − | 2.59808i | 0.687524 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 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 | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.50000 | − | 2.59808i | 0.131056 | − | 0.226995i | −0.793028 | − | 0.609185i | \(-0.791497\pi\) |
0.924084 | + | 0.382190i | \(0.124830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.50000 | − | 12.9904i | 0.216777 | − | 1.12641i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.50000 | + | 9.52628i | 0.469897 | + | 0.813885i | 0.999408 | − | 0.0344182i | \(-0.0109578\pi\) |
−0.529511 | + | 0.848303i | \(0.677624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | − | 4.33013i | −0.212047 | − | 0.367277i | 0.740308 | − | 0.672268i | \(-0.234680\pi\) |
−0.952355 | + | 0.304991i | \(0.901346\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | −7.50000 | + | 12.9904i | −0.614424 | + | 1.06421i | 0.376061 | + | 0.926595i | \(0.377278\pi\) |
−0.990485 | + | 0.137619i | \(0.956055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.50000 | + | 14.7224i | 0.691720 | + | 1.19809i | 0.971274 | + | 0.237964i | \(0.0764802\pi\) |
−0.279554 | + | 0.960130i | \(0.590186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | − | 3.46410i | 0.160644 | − | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 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 | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.313304 | − | 0.949653i | \(-0.398564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.500000 | − | 0.866025i | −0.0386912 | − | 0.0670151i | 0.846031 | − | 0.533133i | \(-0.178986\pi\) |
−0.884723 | + | 0.466118i | \(0.845652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000 | 0.152057 | 0.0760286 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760286 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 10.3923i | −0.151186 | + | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5000 | + | 18.1865i | −0.784807 | + | 1.35933i | 0.144308 | + | 0.989533i | \(0.453905\pi\) |
−0.929114 | + | 0.369792i | \(0.879429\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | −5.00000 | −0.367607 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | −0.658145 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.0000 | −1.29567 | −0.647834 | − | 0.761781i | \(-0.724325\pi\) | ||||
−0.647834 | + | 0.761781i | \(0.724325\pi\) | |||||||
\(194\) | 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 | 0.206184 | + | 0.978513i | \(0.433895\pi\) |
−0.950509 | + | 0.310696i | \(0.899438\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.5000 | − | 7.79423i | 1.57919 | − | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.00000 | 0.488901 | ||||||||
\(206\) | 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 | \(0.212990\pi\) |
0.145014 | + | 0.989430i | \(0.453677\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.50000 | + | 11.2583i | −0.435272 | + | 0.753914i | −0.997318 | − | 0.0731927i | \(-0.976681\pi\) |
0.562046 | + | 0.827106i | \(0.310015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.50000 | − | 12.9904i | −0.497792 | − | 0.862202i | 0.502204 | − | 0.864749i | \(-0.332523\pi\) |
−0.999997 | + | 0.00254715i | \(0.999189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5000 | + | 18.1865i | −0.693860 | + | 1.20180i | 0.276704 | + | 0.960955i | \(0.410758\pi\) |
−0.970564 | + | 0.240845i | \(0.922576\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.50000 | + | 2.59808i | 0.0982683 | + | 0.170206i | 0.910968 | − | 0.412477i | \(-0.135336\pi\) |
−0.812700 | + | 0.582683i | \(0.802003\pi\) | |||||||
\(234\) | 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 | 0.682985 | − | 0.730433i | \(-0.260682\pi\) |
−0.974066 | + | 0.226266i | \(0.927348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.50000 | + | 2.59808i | 0.415270 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.50000 | + | 4.33013i | −0.159071 | + | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.00000 | −0.188608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.50000 | + | 14.7224i | −0.530215 | + | 0.918360i | 0.469163 | + | 0.883112i | \(0.344556\pi\) |
−0.999379 | + | 0.0352486i | \(0.988778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50000 | − | 12.9904i | 0.155342 | − | 0.807183i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.50000 | + | 9.52628i | 0.339145 | + | 0.587416i | 0.984272 | − | 0.176659i | \(-0.0565291\pi\) |
−0.645128 | + | 0.764075i | \(0.723196\pi\) | |||||||
\(264\) | 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 | −0.952776 | − | 0.303674i | \(-0.901787\pi\) |
0.739377 | + | 0.673291i | \(0.235120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5000 | − | 26.8468i | −0.941558 | − | 1.63083i | −0.762501 | − | 0.646988i | \(-0.776029\pi\) |
−0.179057 | − | 0.983839i | \(-0.557305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.00000 | − | 10.3923i | 0.361814 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.50000 | + | 16.4545i | 0.570800 | + | 0.988654i | 0.996484 | + | 0.0837823i | \(0.0267000\pi\) |
−0.425684 | + | 0.904872i | \(0.639967\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −24.0000 | −1.42665 | −0.713326 | − | 0.700832i | \(-0.752812\pi\) | ||||
−0.713326 | + | 0.700832i | \(0.752812\pi\) | |||||||
\(284\) | 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 | ||||||||
\(299\) | −1.00000 | −0.0578315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.50000 | + | 2.59808i | −0.432293 | + | 0.149751i | ||||
\(302\) | 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 | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.0000 | −0.786318 | −0.393159 | − | 0.919470i | \(-0.628618\pi\) | ||||
−0.393159 | + | 0.919470i | \(0.628618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.0000 | −1.51171 | ||||||||
\(320\) | 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 | ||||||||
\(329\) | −16.0000 | − | 13.8564i | −0.882109 | − | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 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 | ||||||||
\(347\) | 28.0000 | 1.50312 | 0.751559 | − | 0.659665i | \(-0.229302\pi\) | ||||
0.751559 | + | 0.659665i | \(0.229302\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | 15.5000 | + | 26.8468i | 0.824982 | + | 1.42891i | 0.901933 | + | 0.431875i | \(0.142148\pi\) |
−0.0769515 | + | 0.997035i | \(0.524519\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | + | 6.92820i | −0.212298 | + | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.5000 | + | 23.3827i | 0.712503 | + | 1.23409i | 0.963915 | + | 0.266211i | \(0.0857717\pi\) |
−0.251412 | + | 0.967880i | \(0.580895\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | −5.50000 | − | 9.52628i | −0.287098 | − | 0.497268i | 0.686018 | − | 0.727585i | \(-0.259357\pi\) |
−0.973116 | + | 0.230317i | \(0.926024\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.5000 | − | 7.79423i | 1.16814 | − | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.50000 | + | 11.2583i | −0.336557 | + | 0.582934i | −0.983783 | − | 0.179364i | \(-0.942596\pi\) |
0.647225 | + | 0.762299i | \(0.275929\pi\) | |||||||
\(374\) | 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 | \(-0.192934\pi\) | ||||
0.821865 | + | 0.569683i | \(0.192934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.5000 | + | 30.3109i | −0.894208 | + | 1.54881i | −0.0594268 | + | 0.998233i | \(0.518927\pi\) |
−0.834781 | + | 0.550581i | \(0.814406\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 5.19615i | −0.305788 | − | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.5000 | + | 32.0429i | 0.937987 | + | 1.62464i | 0.769218 | + | 0.638986i | \(0.220646\pi\) |
0.168769 | + | 0.985656i | \(0.446021\pi\) | |||||||
\(390\) | 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 | −0.988080 | − | 0.153941i | \(-0.950803\pi\) |
0.360723 | − | 0.932673i | \(-0.382530\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.50000 | + | 11.2583i | −0.324595 | + | 0.562214i | −0.981430 | − | 0.191820i | \(-0.938561\pi\) |
0.656836 | + | 0.754034i | \(0.271895\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.50000 | + | 12.9904i | −0.371761 | + | 0.643909i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 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 | \(0.00478389\pi\) |
−0.486928 | + | 0.873442i | \(0.661883\pi\) | |||||||
\(420\) | 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 | ||||||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.00000 | + | 3.46410i | 0.193574 | + | 0.167640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.50000 | + | 12.9904i | −0.361262 | + | 0.625725i | −0.988169 | − | 0.153370i | \(-0.950987\pi\) |
0.626907 | + | 0.779094i | \(0.284321\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | −5.00000 | −0.239182 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.0000 | 1.14546 | 0.572729 | − | 0.819745i | \(-0.305885\pi\) | ||||
0.572729 | + | 0.819745i | \(0.305885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.0000 | −0.760183 | −0.380091 | − | 0.924949i | \(-0.624107\pi\) | ||||
−0.380091 | + | 0.924949i | \(0.624107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | −0.426641 | ||||||||
\(446\) | 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 | ||||||||
\(455\) | −2.00000 | − | 1.73205i | −0.0937614 | − | 0.0811998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.0000 | −1.21623 | −0.608114 | − | 0.793849i | \(-0.708074\pi\) | ||||
−0.608114 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(458\) | 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 | 0.877410 | − | 0.479741i | \(-0.159269\pi\) |
−0.854173 | + | 0.519989i | \(0.825936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.50000 | + | 11.2583i | 0.300784 | + | 0.520973i | 0.976314 | − | 0.216359i | \(-0.0694183\pi\) |
−0.675530 | + | 0.737333i | \(0.736085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0000 | + | 20.7846i | 1.10822 | + | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.00000 | 0.413820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0000 | − | 17.3205i | 0.458831 | − | 0.794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.5000 | − | 18.1865i | −0.479757 | − | 0.830964i | 0.519973 | − | 0.854183i | \(-0.325942\pi\) |
−0.999730 | + | 0.0232187i | \(0.992609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.50000 | + | 4.33013i | −0.113990 | + | 0.197437i | ||||
\(482\) | 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 | 0.0529875 | + | 0.998595i | \(0.483126\pi\) |
−0.891303 | + | 0.453409i | \(0.850208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.50000 | + | 7.79423i | 0.203082 | + | 0.351749i | 0.949520 | − | 0.313707i | \(-0.101571\pi\) |
−0.746438 | + | 0.665455i | \(0.768237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.5000 | − | 23.3827i | −0.608009 | − | 1.05310i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | − | 13.8564i | −0.717698 | − | 0.621545i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.5000 | − | 25.1147i | 0.649109 | − | 1.12429i | −0.334227 | − | 0.942493i | \(-0.608475\pi\) |
0.983336 | − | 0.181797i | \(-0.0581915\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.00000 | −0.311496 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5000 | − | 28.5788i | 0.731350 | − | 1.26673i | −0.224957 | − | 0.974369i | \(-0.572224\pi\) |
0.956306 | − | 0.292366i | \(-0.0944425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.5000 | − | 11.2583i | 1.43772 | − | 0.498039i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.50000 | + | 7.79423i | 0.198294 | + | 0.343455i | ||||
\(516\) | 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 | −0.831295 | − | 0.555831i | \(-0.812400\pi\) |
0.897011 | + | 0.442007i | \(0.145733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5000 | − | 28.5788i | −0.721495 | − | 1.24967i | −0.960401 | − | 0.278623i | \(-0.910122\pi\) |
0.238906 | − | 0.971043i | \(-0.423211\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.50000 | − | 6.06218i | 0.151602 | − | 0.262582i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.00000 | −0.302636 | ||||||||
\(536\) | 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 | 0.959697 | − | 0.281037i | \(-0.0906783\pi\) |
−0.723234 | + | 0.690604i | \(0.757345\pi\) | |||||||
\(542\) | 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 | −0.807617 | − | 0.589707i | \(-0.799243\pi\) |
0.914510 | + | 0.404564i | \(0.132577\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45.0000 | −1.91706 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | + | 13.8564i | 0.680389 | + | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.5000 | + | 33.7750i | −0.826242 | + | 1.43109i | 0.0747252 | + | 0.997204i | \(0.476192\pi\) |
−0.900967 | + | 0.433888i | \(0.857141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.00000 | 0.126886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.00000 | −0.0420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.0000 | 1.76073 | 0.880366 | − | 0.474295i | \(-0.157297\pi\) | ||||
0.880366 | + | 0.474295i | \(0.157297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 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 | −0.895558 | − | 0.444945i | \(-0.853223\pi\) |
0.833112 | + | 0.553104i | \(0.186557\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.5000 | + | 11.2583i | −1.34833 | + | 0.467074i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.0000 | −1.11823 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.50000 | − | 12.9904i | 0.309558 | − | 0.536170i | −0.668708 | − | 0.743525i | \(-0.733152\pi\) |
0.978266 | + | 0.207355i | \(0.0664855\pi\) | |||||||
\(588\) | 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 | 0.565792 | − | 0.824548i | \(-0.308570\pi\) |
−0.996976 | + | 0.0777165i | \(0.975237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.50000 | − | 7.79423i | 0.0614940 | − | 0.319532i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5000 | − | 19.9186i | 0.466771 | − | 0.808470i | −0.532509 | − | 0.846424i | \(-0.678751\pi\) |
0.999279 | + | 0.0379540i | \(0.0120840\pi\) | |||||||
\(608\) | 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 | −0.912086 | − | 0.409998i | \(-0.865529\pi\) |
0.811112 | + | 0.584891i | \(0.198863\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | −10.5000 | − | 18.1865i | −0.422031 | − | 0.730978i | 0.574107 | − | 0.818780i | \(-0.305349\pi\) |
−0.996138 | + | 0.0878015i | \(0.972016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.50000 | − | 23.3827i | 0.180289 | − | 0.936808i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 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 | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | − | 6.92820i | 0.158735 | − | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.50000 | − | 4.33013i | 0.217918 | − | 0.171566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.50000 | − | 4.33013i | −0.0987441 | − | 0.171030i | 0.812421 | − | 0.583071i | \(-0.198149\pi\) |
−0.911165 | + | 0.412042i | \(0.864816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.5000 | − | 32.0429i | −0.729569 | − | 1.26365i | −0.957066 | − | 0.289871i | \(-0.906387\pi\) |
0.227497 | − | 0.973779i | \(-0.426946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.5000 | − | 35.5070i | 0.805938 | − | 1.39593i | −0.109718 | − | 0.993963i | \(-0.534995\pi\) |
0.915656 | − | 0.401963i | \(-0.131672\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | − | 10.3923i | −0.235521 | − | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.50000 | + | 2.59808i | −0.0586995 | + | 0.101671i | −0.893882 | − | 0.448303i | \(-0.852029\pi\) |
0.835182 | + | 0.549973i | \(0.185362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.50000 | − | 2.59808i | −0.0586098 | − | 0.101515i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.50000 | − | 12.9904i | 0.292159 | − | 0.506033i | −0.682161 | − | 0.731202i | \(-0.738960\pi\) |
0.974320 | + | 0.225168i | \(0.0722932\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.0000 | 1.47803 | 0.739014 | − | 0.673690i | \(-0.235292\pi\) | ||||
0.739014 | + | 0.673690i | \(0.235292\pi\) | |||||||
\(662\) | 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 | ||||||||
\(677\) | −38.0000 | −1.46046 | −0.730229 | − | 0.683202i | \(-0.760587\pi\) | ||||
−0.730229 | + | 0.683202i | \(0.760587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.5000 | − | 14.7224i | 1.63100 | − | 0.564995i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5000 | − | 26.8468i | 0.593091 | − | 1.02726i | −0.400722 | − | 0.916200i | \(-0.631241\pi\) |
0.993813 | − | 0.111064i | \(-0.0354259\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.0000 | 0.420288 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.00000 | −0.342873 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.00000 | −0.189661 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.0000 | 0.795432 | ||||||||
\(698\) | 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 | ||||||||
\(707\) | 3.50000 | − | 18.1865i | 0.131631 | − | 0.683975i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0000 | −0.676004 | −0.338002 | − | 0.941145i | \(-0.609751\pi\) | ||||
−0.338002 | + | 0.941145i | \(0.609751\pi\) | |||||||
\(710\) | 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 | \(-0.0513892\pi\) |
−0.632706 | + | 0.774392i | \(0.718056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.5000 | + | 7.79423i | −0.837944 | + | 0.290272i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 36.0000 | 1.33701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.50000 | + | 14.7224i | −0.315248 | + | 0.546025i | −0.979490 | − | 0.201492i | \(-0.935421\pi\) |
0.664243 | + | 0.747517i | \(0.268754\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.50000 | + | 7.79423i | 0.166439 | + | 0.288280i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.5000 | − | 37.2391i | 0.794121 | − | 1.37546i | −0.129275 | − | 0.991609i | \(-0.541265\pi\) |
0.923396 | − | 0.383849i | \(-0.125402\pi\) | |||||||
\(734\) | 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 | \(-0.732107\pi\) |
0.978941 | + | 0.204143i | \(0.0654407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.500000 | − | 0.866025i | −0.0183432 | − | 0.0317714i | 0.856708 | − | 0.515802i | \(-0.172506\pi\) |
−0.875051 | + | 0.484030i | \(0.839172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.50000 | + | 12.9904i | 0.274779 | + | 0.475931i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.50000 | − | 18.1865i | 0.127887 | − | 0.664521i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.50000 | − | 12.9904i | 0.273679 | − | 0.474026i | −0.696122 | − | 0.717923i | \(-0.745093\pi\) |
0.969801 | + | 0.243898i | \(0.0784261\pi\) | |||||||
\(752\) | 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 | ||||||||
\(761\) | −22.5000 | + | 38.9711i | −0.815624 | + | 1.41270i | 0.0932544 | + | 0.995642i | \(0.470273\pi\) |
−0.908879 | + | 0.417061i | \(0.863060\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.5000 | + | 4.33013i | −0.452530 | + | 0.156761i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.00000 | − | 3.46410i | −0.0722158 | − | 0.125081i | ||||
\(768\) | 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 | −0.922079 | − | 0.387002i | \(-0.873511\pi\) |
0.796193 | + | 0.605043i | \(0.206844\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | + | 13.8564i | 0.287368 | + | 0.497737i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.5000 | − | 30.3109i | 0.627003 | − | 1.08600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | + | 20.7846i | 0.429394 | + | 0.743732i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.00000 | − | 12.1244i | 0.249841 | − | 0.432737i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | 0.712923 | 0.356462 | − | 0.934310i | \(-0.383983\pi\) | ||||
0.356462 | + | 0.934310i | \(0.383983\pi\) | |||||||
\(788\) | 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 | ||||||||
\(803\) | −39.0000 | −1.37628 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.500000 | − | 2.59808i | 0.0176227 | − | 0.0915702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.5000 | − | 47.6314i | 0.966849 | − | 1.67463i | 0.262284 | − | 0.964991i | \(-0.415524\pi\) |
0.704564 | − | 0.709640i | \(-0.251142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.0000 | −0.595484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.0000 | 0.524784 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.0000 | −1.46581 | −0.732905 | − | 0.680331i | \(-0.761836\pi\) | ||||
−0.732905 | + | 0.680331i | \(0.761836\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.0000 | −1.39431 | −0.697156 | − | 0.716919i | \(-0.745552\pi\) | ||||
−0.697156 | + | 0.716919i | \(0.745552\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.0000 | 1.39094 | 0.695468 | − | 0.718557i | \(-0.255197\pi\) | ||||
0.695468 | + | 0.718557i | \(0.255197\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.50000 | + | 4.33013i | −0.0868286 | + | 0.150392i | −0.906169 | − | 0.422916i | \(-0.861007\pi\) |
0.819340 | + | 0.573307i | \(0.194340\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.5000 | + | 7.79423i | 0.675635 | + | 0.270054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.00000 | −0.0346064 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.5000 | − | 38.9711i | 0.776786 | − | 1.34543i | −0.156999 | − | 0.987599i | \(-0.550182\pi\) |
0.933785 | − | 0.357834i | \(-0.116485\pi\) | |||||||
\(840\) | 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 | ||||||||
\(851\) | −5.00000 | −0.171398 | ||||||||
\(852\) | 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 | ||||||||
\(857\) | 3.50000 | + | 6.06218i | 0.119558 | + | 0.207080i | 0.919592 | − | 0.392874i | \(-0.128519\pi\) |
−0.800035 | + | 0.599954i | \(0.795186\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.50000 | + | 16.4545i | −0.324136 | + | 0.561420i | −0.981337 | − | 0.192295i | \(-0.938407\pi\) |
0.657201 | + | 0.753715i | \(0.271740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.50000 | + | 9.52628i | 0.187222 | + | 0.324278i | 0.944323 | − | 0.329020i | \(-0.106718\pi\) |
−0.757101 | + | 0.653298i | \(0.773385\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | −6.00000 | − | 10.3923i | −0.203302 | − | 0.352130i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.0000 | + | 15.5885i | 0.608511 | + | 0.526986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.5000 | − | 19.9186i | 0.388327 | − | 0.672603i | −0.603897 | − | 0.797062i | \(-0.706386\pi\) |
0.992225 | + | 0.124459i | \(0.0397196\pi\) | |||||||
\(878\) | 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 | \(-0.160881\pi\) | ||||
0.874970 | + | 0.484178i | \(0.160881\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.5000 | + | 23.3827i | −0.453286 | + | 0.785114i | −0.998588 | − | 0.0531258i | \(-0.983082\pi\) |
0.545302 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | + | 13.8564i | 0.536623 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.0000 | + | 34.6410i | 0.669274 | + | 1.15922i | ||||
\(894\) | 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 | ||||||||
\(905\) | −9.00000 | + | 15.5885i | −0.299170 | + | 0.518178i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.50000 | + | 6.06218i | 0.116216 | + | 0.201291i | 0.918265 | − | 0.395966i | \(-0.129590\pi\) |
−0.802049 | + | 0.597258i | \(0.796257\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5000 | + | 23.3827i | −0.447275 | + | 0.774703i | −0.998208 | − | 0.0598468i | \(-0.980939\pi\) |
0.550933 | + | 0.834550i | \(0.314272\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.0000 | 1.29071 | ||||||||
\(914\) | 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 | \(-0.0978821\pi\) |
−0.738676 | + | 0.674060i | \(0.764549\pi\) | |||||||
\(920\) | 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 | ||||||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.5000 | − | 21.6506i | 0.901276 | − | 0.709571i | ||||
\(932\) | 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 | ||||||||
\(941\) | 50.0000 | 1.62995 | 0.814977 | − | 0.579494i | \(-0.196750\pi\) | ||||
0.814977 | + | 0.579494i | \(0.196750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.00000 | 0.227951 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.0000 | 1.16984 | 0.584921 | − | 0.811090i | \(-0.301125\pi\) | ||||
0.584921 | + | 0.811090i | \(0.301125\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.0000 | −0.421998 | ||||||||
\(950\) | 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 | ||||||||
\(959\) | −5.50000 | + | 28.5788i | −0.177604 | + | 0.922859i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 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 | 0.563094 | − | 0.826393i | \(-0.309611\pi\) |
−0.997224 | + | 0.0744567i | \(0.976278\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.5000 | − | 37.2391i | −0.689968 | − | 1.19506i | −0.971848 | − | 0.235610i | \(-0.924291\pi\) |
0.281880 | − | 0.959450i | \(-0.409042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.50000 | − | 12.9904i | 0.0801463 | − | 0.416452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.0000 | −0.703842 | −0.351921 | − | 0.936030i | \(-0.614471\pi\) | ||||
−0.351921 | + | 0.936030i | \(0.614471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.5000 | + | 23.3827i | −0.431462 | + | 0.747314i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.5000 | − | 35.5070i | −0.653848 | − | 1.13250i | −0.982181 | − | 0.187937i | \(-0.939820\pi\) |
0.328333 | − | 0.944562i | \(-0.393513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.0000 | − | 19.0526i | 0.350489 | − | 0.607065i | ||||
\(986\) | 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 | \(-0.756761\pi\) |
0.960211 | + | 0.279276i | \(0.0900944\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.5000 | + | 18.1865i | 0.332872 | + | 0.576552i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.50000 | − | 11.2583i | −0.205857 | − | 0.356555i | 0.744548 | − | 0.667568i | \(-0.232665\pi\) |
−0.950405 | + | 0.311014i | \(0.899332\pi\) | |||||||
\(998\) | 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 | 1512.2.q.b.1369.1 | 2 | ||
3.2 | odd | 2 | 504.2.q.a.25.1 | ✓ | 2 | ||
4.3 | odd | 2 | 3024.2.q.d.2881.1 | 2 | |||
7.2 | even | 3 | 1512.2.t.a.289.1 | 2 | |||
9.4 | even | 3 | 1512.2.t.a.361.1 | 2 | |||
9.5 | odd | 6 | 504.2.t.a.193.1 | yes | 2 | ||
12.11 | even | 2 | 1008.2.q.b.529.1 | 2 | |||
21.2 | odd | 6 | 504.2.t.a.457.1 | yes | 2 | ||
28.23 | odd | 6 | 3024.2.t.c.289.1 | 2 | |||
36.23 | even | 6 | 1008.2.t.e.193.1 | 2 | |||
36.31 | odd | 6 | 3024.2.t.c.1873.1 | 2 | |||
63.23 | odd | 6 | 504.2.q.a.121.1 | yes | 2 | ||
63.58 | even | 3 | inner | 1512.2.q.b.793.1 | 2 | ||
84.23 | even | 6 | 1008.2.t.e.961.1 | 2 | |||
252.23 | even | 6 | 1008.2.q.b.625.1 | 2 | |||
252.247 | odd | 6 | 3024.2.q.d.2305.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.a.25.1 | ✓ | 2 | 3.2 | odd | 2 | ||
504.2.q.a.121.1 | yes | 2 | 63.23 | odd | 6 | ||
504.2.t.a.193.1 | yes | 2 | 9.5 | odd | 6 | ||
504.2.t.a.457.1 | yes | 2 | 21.2 | odd | 6 | ||
1008.2.q.b.529.1 | 2 | 12.11 | even | 2 | |||
1008.2.q.b.625.1 | 2 | 252.23 | even | 6 | |||
1008.2.t.e.193.1 | 2 | 36.23 | even | 6 | |||
1008.2.t.e.961.1 | 2 | 84.23 | even | 6 | |||
1512.2.q.b.793.1 | 2 | 63.58 | even | 3 | inner | ||
1512.2.q.b.1369.1 | 2 | 1.1 | even | 1 | trivial | ||
1512.2.t.a.289.1 | 2 | 7.2 | even | 3 | |||
1512.2.t.a.361.1 | 2 | 9.4 | even | 3 | |||
3024.2.q.d.2305.1 | 2 | 252.247 | odd | 6 | |||
3024.2.q.d.2881.1 | 2 | 4.3 | odd | 2 | |||
3024.2.t.c.289.1 | 2 | 28.23 | odd | 6 | |||
3024.2.t.c.1873.1 | 2 | 36.31 | odd | 6 |