Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.991 |
Dual form | 1386.2.k.n.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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0.500000 | + | 2.59808i | 0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 2.50000 | + | 4.33013i | 0.490290 | + | 0.849208i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | + | 1.73205i | −0.377964 | + | 0.327327i | ||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | − | 1.73205i | −0.164399 | − | 0.284747i | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 1.00000 | − | 1.73205i | 0.162221 | − | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | −0.500000 | − | 0.866025i | −0.0753778 | − | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.50000 | + | 4.33013i | −0.346688 | + | 0.600481i | ||||
\(53\) | −6.00000 | + | 10.3923i | −0.824163 | + | 1.42749i | 0.0783936 | + | 0.996922i | \(0.475021\pi\) |
−0.902557 | + | 0.430570i | \(0.858312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.50000 | − | 0.866025i | −0.334077 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.50000 | − | 2.59808i | −0.196960 | − | 0.341144i | ||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.50000 | − | 11.2583i | 0.794101 | − | 1.37542i | −0.129307 | − | 0.991605i | \(-0.541275\pi\) |
0.923408 | − | 0.383819i | \(-0.125391\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | − | 8.66025i | 0.585206 | − | 1.01361i | −0.409644 | − | 0.912245i | \(-0.634347\pi\) |
0.994850 | − | 0.101361i | \(-0.0323196\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −2.00000 | + | 1.73205i | −0.227921 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | + | 5.19615i | 0.331295 | + | 0.573819i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.5000 | + | 4.33013i | 1.31036 | + | 0.453921i | ||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.0000 | −1.31995 | −0.659975 | − | 0.751288i | \(-0.729433\pi\) | ||||
−0.659975 | + | 0.751288i | \(0.729433\pi\) | |||||||
\(98\) | −1.00000 | + | 6.92820i | −0.101015 | + | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | 1.50000 | − | 2.59808i | 0.149256 | − | 0.258518i | −0.781697 | − | 0.623658i | \(-0.785646\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | −5.00000 | −0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | + | 12.1244i | −0.670478 | + | 1.16130i | 0.307290 | + | 0.951616i | \(0.400578\pi\) |
−0.977769 | + | 0.209687i | \(0.932756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.500000 | − | 2.59808i | −0.0472456 | − | 0.245495i | ||||
\(113\) | −9.00000 | −0.846649 | −0.423324 | − | 0.905978i | \(-0.639137\pi\) | ||||
−0.423324 | + | 0.905978i | \(0.639137\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.50000 | − | 2.59808i | 0.139272 | − | 0.241225i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | 12.0000 | − | 10.3923i | 1.10004 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −3.50000 | + | 6.06218i | −0.316875 | + | 0.548844i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.00000 | − | 6.92820i | −0.359211 | − | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | − | 5.19615i | −0.0867110 | − | 0.450564i | ||||
\(134\) | 13.0000 | 1.12303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | 7.50000 | − | 12.9904i | 0.640768 | − | 1.10984i | −0.344493 | − | 0.938789i | \(-0.611949\pi\) |
0.985262 | − | 0.171054i | \(-0.0547174\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | + | 10.3923i | 0.503509 | + | 0.872103i | ||||
\(143\) | −2.50000 | + | 4.33013i | −0.209061 | + | 0.362103i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.500000 | − | 0.866025i | 0.0406894 | − | 0.0704761i | −0.844963 | − | 0.534824i | \(-0.820378\pi\) |
0.885653 | + | 0.464348i | \(0.153711\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.50000 | − | 0.866025i | −0.201456 | − | 0.0697863i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | − | 3.46410i | 0.159617 | − | 0.276465i | −0.775113 | − | 0.631822i | \(-0.782307\pi\) |
0.934731 | + | 0.355357i | \(0.115641\pi\) | |||||||
\(158\) | −0.500000 | + | 0.866025i | −0.0397779 | + | 0.0688973i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.00000 | + | 15.5885i | 0.236433 | + | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.50000 | − | 14.7224i | −0.665771 | − | 1.15315i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.313304 | − | 0.949653i | \(-0.398564\pi\) | |||||||
\(164\) | −3.00000 | + | 5.19615i | −0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | − | 5.19615i | −0.232845 | − | 0.403300i | ||||
\(167\) | −9.00000 | −0.696441 | −0.348220 | − | 0.937413i | \(-0.613214\pi\) | ||||
−0.348220 | + | 0.937413i | \(0.613214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | −7.50000 | − | 12.9904i | −0.570214 | − | 0.987640i | −0.996544 | − | 0.0830722i | \(-0.973527\pi\) |
0.426329 | − | 0.904568i | \(-0.359807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | − | 8.66025i | 0.755929 | − | 0.654654i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | 4.50000 | − | 7.79423i | 0.336346 | − | 0.582568i | −0.647397 | − | 0.762153i | \(-0.724142\pi\) |
0.983742 | + | 0.179585i | \(0.0574756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 2.50000 | + | 12.9904i | 0.185312 | + | 0.962911i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | − | 15.5885i | −0.651217 | − | 1.12794i | −0.982828 | − | 0.184525i | \(-0.940925\pi\) |
0.331611 | − | 0.943416i | \(-0.392408\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0000 | − | 19.0526i | 0.791797 | − | 1.37143i | −0.133056 | − | 0.991109i | \(-0.542479\pi\) |
0.924853 | − | 0.380325i | \(-0.124188\pi\) | |||||||
\(194\) | −6.50000 | − | 11.2583i | −0.466673 | − | 0.808301i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | + | 12.1244i | −0.496217 | + | 0.859473i | −0.999990 | − | 0.00436292i | \(-0.998611\pi\) |
0.503774 | + | 0.863836i | \(0.331945\pi\) | |||||||
\(200\) | −2.50000 | + | 4.33013i | −0.176777 | + | 0.306186i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.00000 | 0.211079 | ||||||||
\(203\) | −7.50000 | − | 2.59808i | −0.526397 | − | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | + | 3.46410i | −0.139347 | + | 0.241355i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.50000 | − | 4.33013i | −0.173344 | − | 0.300240i | ||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0000 | 1.78991 | 0.894957 | − | 0.446153i | \(-0.147206\pi\) | ||||
0.894957 | + | 0.446153i | \(0.147206\pi\) | |||||||
\(212\) | −6.00000 | − | 10.3923i | −0.412082 | − | 0.713746i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | + | 13.8564i | −1.08615 | + | 0.940634i | ||||
\(218\) | −14.0000 | −0.948200 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.0000 | − | 25.9808i | 1.00901 | − | 1.74766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0000 | −0.669650 | −0.334825 | − | 0.942280i | \(-0.608677\pi\) | ||||
−0.334825 | + | 0.942280i | \(0.608677\pi\) | |||||||
\(224\) | 2.00000 | − | 1.73205i | 0.133631 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.50000 | − | 7.79423i | −0.299336 | − | 0.518464i | ||||
\(227\) | −3.00000 | + | 5.19615i | −0.199117 | + | 0.344881i | −0.948242 | − | 0.317547i | \(-0.897141\pi\) |
0.749125 | + | 0.662428i | \(0.230474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | − | 17.3205i | −0.660819 | − | 1.14457i | −0.980401 | − | 0.197013i | \(-0.936876\pi\) |
0.319582 | − | 0.947559i | \(-0.396457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | −15.0000 | − | 25.9808i | −0.982683 | − | 1.70206i | −0.651813 | − | 0.758380i | \(-0.725991\pi\) |
−0.330870 | − | 0.943676i | \(-0.607342\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.50000 | − | 2.59808i | −0.0976417 | − | 0.169120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.0000 | + | 5.19615i | 0.972306 | + | 0.336817i | ||||
\(239\) | −21.0000 | −1.35838 | −0.679189 | − | 0.733964i | \(-0.737668\pi\) | ||||
−0.679189 | + | 0.733964i | \(0.737668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 0.500000 | − | 0.866025i | 0.0321412 | − | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.00000 | −0.448129 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | − | 8.66025i | −0.318142 | − | 0.551039i | ||||
\(248\) | 4.00000 | − | 6.92820i | 0.254000 | − | 0.439941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | −6.50000 | − | 11.2583i | −0.407846 | − | 0.706410i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 13.5000 | + | 23.3827i | 0.842107 | + | 1.45857i | 0.888110 | + | 0.459631i | \(0.152018\pi\) |
−0.0460033 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | − | 5.19615i | −0.0621370 | − | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.00000 | + | 5.19615i | −0.185341 | + | 0.321019i | ||||
\(263\) | −1.50000 | + | 2.59808i | −0.0924940 | + | 0.160204i | −0.908560 | − | 0.417755i | \(-0.862817\pi\) |
0.816066 | + | 0.577959i | \(0.196151\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.00000 | − | 3.46410i | 0.245256 | − | 0.212398i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.50000 | + | 11.2583i | 0.397051 | + | 0.687712i | ||||
\(269\) | −12.0000 | + | 20.7846i | −0.731653 | + | 1.26726i | 0.224523 | + | 0.974469i | \(0.427917\pi\) |
−0.956176 | + | 0.292791i | \(0.905416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5000 | + | 21.6506i | 0.759321 | + | 1.31518i | 0.943197 | + | 0.332233i | \(0.107802\pi\) |
−0.183876 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.0000 | 0.906183 | ||||||||
\(275\) | 2.50000 | + | 4.33013i | 0.150756 | + | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | −2.00000 | − | 3.46410i | −0.119952 | − | 0.207763i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0000 | − | 19.0526i | 0.653882 | − | 1.13256i | −0.328291 | − | 0.944577i | \(-0.606473\pi\) |
0.982173 | − | 0.187980i | \(-0.0601941\pi\) | |||||||
\(284\) | −6.00000 | + | 10.3923i | −0.356034 | + | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.00000 | −0.295656 | ||||||||
\(287\) | 15.0000 | + | 5.19615i | 0.885422 | + | 0.306719i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.00000 | + | 8.66025i | 0.292603 | + | 0.506803i | ||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000 | + | 1.73205i | 0.0581238 | + | 0.100673i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | 15.0000 | + | 25.9808i | 0.867472 | + | 1.50251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | − | 3.46410i | −0.576390 | − | 0.199667i | ||||
\(302\) | 1.00000 | 0.0575435 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | + | 1.73205i | −0.0573539 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.0000 | 1.82634 | 0.913168 | − | 0.407583i | \(-0.133628\pi\) | ||||
0.913168 | + | 0.407583i | \(0.133628\pi\) | |||||||
\(308\) | −0.500000 | − | 2.59808i | −0.0284901 | − | 0.148039i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.50000 | + | 6.06218i | 0.197832 | + | 0.342655i | 0.947825 | − | 0.318791i | \(-0.103277\pi\) |
−0.749993 | + | 0.661445i | \(0.769943\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00000 | −0.0562544 | ||||||||
\(317\) | −12.0000 | − | 20.7846i | −0.673987 | − | 1.16738i | −0.976764 | − | 0.214318i | \(-0.931247\pi\) |
0.302777 | − | 0.953062i | \(-0.402086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.50000 | − | 2.59808i | 0.0839839 | − | 0.145464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | + | 10.3923i | −0.668734 | + | 0.579141i | ||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5000 | − | 21.6506i | 0.693375 | − | 1.20096i | ||||
\(326\) | 8.50000 | − | 14.7224i | 0.470771 | − | 0.815400i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 3.00000 | + | 15.5885i | 0.165395 | + | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.50000 | + | 11.2583i | 0.357272 | + | 0.618814i | 0.987504 | − | 0.157593i | \(-0.0503735\pi\) |
−0.630232 | + | 0.776407i | \(0.717040\pi\) | |||||||
\(332\) | 3.00000 | − | 5.19615i | 0.164646 | − | 0.285176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.50000 | − | 7.79423i | −0.246229 | − | 0.426481i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | 6.00000 | + | 10.3923i | 0.326357 | + | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | − | 6.92820i | −0.216612 | − | 0.375183i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.50000 | − | 12.9904i | 0.403202 | − | 0.698367i | ||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | 12.5000 | + | 4.33013i | 0.668153 | + | 0.231455i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | 15.0000 | − | 25.9808i | 0.798369 | − | 1.38282i | −0.122308 | − | 0.992492i | \(-0.539030\pi\) |
0.920677 | − | 0.390324i | \(-0.127637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.00000 | 0.475665 | ||||||||
\(359\) | −4.50000 | − | 7.79423i | −0.237501 | − | 0.411364i | 0.722496 | − | 0.691375i | \(-0.242995\pi\) |
−0.959997 | + | 0.280012i | \(0.909662\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −5.00000 | − | 8.66025i | −0.262794 | − | 0.455173i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.0000 | + | 8.66025i | −0.524142 | + | 0.453921i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.0000 | + | 32.9090i | −0.991792 | + | 1.71783i | −0.385164 | + | 0.922848i | \(0.625855\pi\) |
−0.606628 | + | 0.794986i | \(0.707478\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0000 | + | 20.7846i | −1.24602 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50000 | − | 9.52628i | −0.284779 | − | 0.493252i | 0.687776 | − | 0.725923i | \(-0.258587\pi\) |
−0.972556 | + | 0.232671i | \(0.925254\pi\) | |||||||
\(374\) | −3.00000 | + | 5.19615i | −0.155126 | + | 0.268687i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | −15.0000 | −0.772539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0000 | −1.28416 | −0.642082 | − | 0.766636i | \(-0.721929\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.00000 | − | 15.5885i | 0.460480 | − | 0.797575i | ||||
\(383\) | 6.00000 | + | 10.3923i | 0.306586 | + | 0.531022i | 0.977613 | − | 0.210411i | \(-0.0674801\pi\) |
−0.671027 | + | 0.741433i | \(0.734147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.0000 | 1.11977 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.50000 | − | 11.2583i | 0.329988 | − | 0.571555i | ||||
\(389\) | 6.00000 | − | 10.3923i | 0.304212 | − | 0.526911i | −0.672874 | − | 0.739758i | \(-0.734940\pi\) |
0.977086 | + | 0.212847i | \(0.0682735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0000 | 1.82060 | ||||||||
\(392\) | −5.50000 | − | 4.33013i | −0.277792 | − | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.50000 | + | 7.79423i | 0.226707 | + | 0.392668i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00000 | − | 1.73205i | −0.0501886 | − | 0.0869291i | 0.839840 | − | 0.542834i | \(-0.182649\pi\) |
−0.890028 | + | 0.455905i | \(0.849316\pi\) | |||||||
\(398\) | −14.0000 | −0.701757 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −4.50000 | − | 7.79423i | −0.224719 | − | 0.389225i | 0.731516 | − | 0.681824i | \(-0.238813\pi\) |
−0.956235 | + | 0.292599i | \(0.905480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.0000 | + | 34.6410i | −0.996271 | + | 1.72559i | ||||
\(404\) | 1.50000 | + | 2.59808i | 0.0746278 | + | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.50000 | − | 7.79423i | −0.0744438 | − | 0.386821i | ||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.00000 | − | 3.46410i | 0.0988936 | − | 0.171289i | −0.812333 | − | 0.583193i | \(-0.801803\pi\) |
0.911227 | + | 0.411905i | \(0.135136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | −6.00000 | + | 5.19615i | −0.295241 | + | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.50000 | − | 4.33013i | 0.122573 | − | 0.212302i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.00000 | + | 1.73205i | 0.0489116 | + | 0.0847174i | ||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | −0.779792 | −0.389896 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389896 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(422\) | 13.0000 | + | 22.5167i | 0.632830 | + | 1.09609i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | − | 10.3923i | 0.291386 | − | 0.504695i | ||||
\(425\) | −15.0000 | − | 25.9808i | −0.727607 | − | 1.26025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.50000 | + | 18.1865i | 0.169377 | + | 0.880108i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.50000 | − | 12.9904i | 0.361262 | − | 0.625725i | −0.626907 | − | 0.779094i | \(-0.715679\pi\) |
0.988169 | + | 0.153370i | \(0.0490126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | −20.0000 | − | 6.92820i | −0.960031 | − | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | 6.00000 | − | 10.3923i | 0.287019 | − | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.50000 | + | 16.4545i | 0.453410 | + | 0.785330i | 0.998595 | − | 0.0529862i | \(-0.0168739\pi\) |
−0.545185 | + | 0.838316i | \(0.683541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | 6.00000 | + | 10.3923i | 0.285069 | + | 0.493753i | 0.972626 | − | 0.232377i | \(-0.0746503\pi\) |
−0.687557 | + | 0.726130i | \(0.741317\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.00000 | − | 8.66025i | −0.236757 | − | 0.410075i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.50000 | + | 0.866025i | 0.118114 | + | 0.0409159i | ||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.00000 | + | 5.19615i | −0.141264 | + | 0.244677i | ||||
\(452\) | 4.50000 | − | 7.79423i | 0.211662 | − | 0.366610i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0000 | + | 19.0526i | 0.514558 | + | 0.891241i | 0.999857 | + | 0.0168929i | \(0.00537742\pi\) |
−0.485299 | + | 0.874348i | \(0.661289\pi\) | |||||||
\(458\) | 10.0000 | − | 17.3205i | 0.467269 | − | 0.809334i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.0000 | −1.81641 | −0.908206 | − | 0.418524i | \(-0.862547\pi\) | ||||
−0.908206 | + | 0.418524i | \(0.862547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | 1.50000 | + | 2.59808i | 0.0696358 | + | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.0000 | − | 25.9808i | 0.694862 | − | 1.20354i | ||||
\(467\) | −6.00000 | − | 10.3923i | −0.277647 | − | 0.480899i | 0.693153 | − | 0.720791i | \(-0.256221\pi\) |
−0.970799 | + | 0.239892i | \(0.922888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.0000 | − | 22.5167i | 1.20057 | − | 1.03972i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.50000 | − | 2.59808i | 0.0690431 | − | 0.119586i | ||||
\(473\) | 2.00000 | − | 3.46410i | 0.0919601 | − | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0000 | −0.458831 | ||||||||
\(476\) | 3.00000 | + | 15.5885i | 0.137505 | + | 0.714496i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.5000 | − | 18.1865i | −0.480259 | − | 0.831833i | ||||
\(479\) | −1.50000 | + | 2.59808i | −0.0685367 | + | 0.118709i | −0.898257 | − | 0.439470i | \(-0.855166\pi\) |
0.829721 | + | 0.558179i | \(0.188500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00000 | − | 8.66025i | −0.227980 | − | 0.394874i | ||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000 | − | 3.46410i | 0.0906287 | − | 0.156973i | −0.817147 | − | 0.576429i | \(-0.804446\pi\) |
0.907776 | + | 0.419456i | \(0.137779\pi\) | |||||||
\(488\) | −3.50000 | − | 6.06218i | −0.158438 | − | 0.274422i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0000 | 1.35388 | 0.676941 | − | 0.736038i | \(-0.263305\pi\) | ||||
0.676941 | + | 0.736038i | \(0.263305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | + | 15.5885i | −0.405340 | + | 0.702069i | ||||
\(494\) | 5.00000 | − | 8.66025i | 0.224961 | − | 0.389643i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 30.0000 | + | 10.3923i | 1.34568 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | − | 6.92820i | −0.179065 | − | 0.310149i | 0.762496 | − | 0.646993i | \(-0.223974\pi\) |
−0.941560 | + | 0.336844i | \(0.890640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.00000 | − | 10.3923i | −0.267793 | − | 0.463831i | ||||
\(503\) | −21.0000 | −0.936344 | −0.468172 | − | 0.883637i | \(-0.655087\pi\) | ||||
−0.468172 | + | 0.883637i | \(0.655087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.00000 | − | 5.19615i | −0.133366 | − | 0.230997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.50000 | − | 11.2583i | 0.288391 | − | 0.499508i | ||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | − | 17.3205i | 0.884748 | − | 0.766214i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.5000 | + | 23.3827i | −0.595459 | + | 1.03137i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | 4.00000 | − | 3.46410i | 0.175750 | − | 0.152204i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | + | 15.5885i | −0.394297 | + | 0.682943i | −0.993011 | − | 0.118020i | \(-0.962345\pi\) |
0.598714 | + | 0.800963i | \(0.295679\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.00000 | + | 13.8564i | 0.349816 | + | 0.605898i | 0.986216 | − | 0.165460i | \(-0.0529109\pi\) |
−0.636401 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | −0.130806 | ||||||||
\(527\) | 24.0000 | + | 41.5692i | 1.04546 | + | 1.81078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.00000 | + | 1.73205i | 0.216777 | + | 0.0750939i | ||||
\(533\) | 30.0000 | 1.29944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.50000 | + | 11.2583i | −0.280757 | + | 0.486286i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.0000 | −1.03471 | ||||||||
\(539\) | −6.50000 | + | 2.59808i | −0.279975 | + | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.50000 | − | 4.33013i | −0.107483 | − | 0.186167i | 0.807267 | − | 0.590187i | \(-0.200946\pi\) |
−0.914750 | + | 0.404020i | \(0.867613\pi\) | |||||||
\(542\) | −12.5000 | + | 21.6506i | −0.536921 | + | 0.929974i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.00000 | − | 5.19615i | −0.128624 | − | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 7.50000 | + | 12.9904i | 0.320384 | + | 0.554922i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.50000 | + | 4.33013i | −0.106600 | + | 0.184637i | ||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.500000 | + | 2.59808i | 0.0212622 | + | 0.110481i | ||||
\(554\) | 1.00000 | 0.0424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | ||||
\(557\) | −3.00000 | + | 5.19615i | −0.127114 | + | 0.220168i | −0.922557 | − | 0.385860i | \(-0.873905\pi\) |
0.795443 | + | 0.606028i | \(0.207238\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.0000 | −0.845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.00000 | + | 5.19615i | 0.126547 | + | 0.219186i | ||||
\(563\) | 9.00000 | − | 15.5885i | 0.379305 | − | 0.656975i | −0.611656 | − | 0.791123i | \(-0.709497\pi\) |
0.990961 | + | 0.134148i | \(0.0428299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.0000 | 0.924729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | −2.50000 | − | 4.33013i | −0.104530 | − | 0.181052i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.00000 | + | 15.5885i | 0.125218 | + | 0.650650i | ||||
\(575\) | 30.0000 | 1.25109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.50000 | − | 6.06218i | 0.145707 | − | 0.252372i | −0.783930 | − | 0.620850i | \(-0.786788\pi\) |
0.929636 | + | 0.368478i | \(0.120121\pi\) | |||||||
\(578\) | 9.50000 | − | 16.4545i | 0.395148 | − | 0.684416i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | − | 5.19615i | −0.622305 | − | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | −5.00000 | + | 8.66025i | −0.206901 | + | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | + | 15.5885i | 0.371787 | + | 0.643953i | ||||
\(587\) | −9.00000 | −0.371470 | −0.185735 | − | 0.982600i | \(-0.559467\pi\) | ||||
−0.185735 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | 12.0000 | + | 20.7846i | 0.492781 | + | 0.853522i | 0.999965 | − | 0.00831589i | \(-0.00264706\pi\) |
−0.507184 | + | 0.861838i | \(0.669314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.0000 | + | 25.9808i | −0.613396 | + | 1.06243i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | −2.00000 | − | 10.3923i | −0.0815139 | − | 0.423559i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.500000 | + | 0.866025i | 0.0203447 | + | 0.0352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | − | 6.92820i | −0.162355 | − | 0.281207i | 0.773358 | − | 0.633970i | \(-0.218576\pi\) |
−0.935713 | + | 0.352763i | \(0.885242\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | + | 25.9808i | 0.606835 | + | 1.05107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0000 | + | 22.5167i | −0.525065 | + | 0.909439i | 0.474509 | + | 0.880251i | \(0.342626\pi\) |
−0.999574 | + | 0.0291886i | \(0.990708\pi\) | |||||||
\(614\) | 16.0000 | + | 27.7128i | 0.645707 | + | 1.11840i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | − | 1.73205i | 0.0805823 | − | 0.0697863i | ||||
\(617\) | −21.0000 | −0.845428 | −0.422714 | − | 0.906263i | \(-0.638923\pi\) | ||||
−0.422714 | + | 0.906263i | \(0.638923\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.0000 | + | 38.1051i | −0.884255 | + | 1.53157i | −0.0376891 | + | 0.999290i | \(0.512000\pi\) |
−0.846566 | + | 0.532284i | \(0.821334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | 3.00000 | + | 15.5885i | 0.120192 | + | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −3.50000 | + | 6.06218i | −0.139888 | + | 0.242293i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.00000 | + | 3.46410i | 0.0798087 | + | 0.138233i | ||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | −0.500000 | − | 0.866025i | −0.0198889 | − | 0.0344486i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.0000 | − | 20.7846i | 0.476581 | − | 0.825462i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.5000 | + | 21.6506i | 1.08959 | + | 0.857829i | ||||
\(638\) | 3.00000 | 0.118771 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.50000 | − | 7.79423i | 0.177739 | − | 0.307854i | −0.763367 | − | 0.645966i | \(-0.776455\pi\) |
0.941106 | + | 0.338112i | \(0.109788\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.0000 | −0.749287 | −0.374643 | − | 0.927169i | \(-0.622235\pi\) | ||||
−0.374643 | + | 0.927169i | \(0.622235\pi\) | |||||||
\(644\) | −15.0000 | − | 5.19615i | −0.591083 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 18.0000 | − | 31.1769i | 0.707653 | − | 1.22569i | −0.258073 | − | 0.966126i | \(-0.583087\pi\) |
0.965726 | − | 0.259565i | \(-0.0835793\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.50000 | − | 2.59808i | −0.0588802 | − | 0.101983i | ||||
\(650\) | 25.0000 | 0.980581 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.0000 | 0.665771 | ||||||||
\(653\) | −15.0000 | − | 25.9808i | −0.586995 | − | 1.01671i | −0.994623 | − | 0.103558i | \(-0.966977\pi\) |
0.407628 | − | 0.913148i | \(-0.366356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | − | 5.19615i | −0.117130 | − | 0.202876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0000 | + | 10.3923i | −0.467809 | + | 0.405134i | ||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0000 | − | 29.4449i | 0.661223 | − | 1.14527i | −0.319071 | − | 0.947731i | \(-0.603371\pi\) |
0.980294 | − | 0.197542i | \(-0.0632958\pi\) | |||||||
\(662\) | −6.50000 | + | 11.2583i | −0.252630 | + | 0.437567i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | − | 15.5885i | −0.348481 | − | 0.603587i | ||||
\(668\) | 4.50000 | − | 7.79423i | 0.174110 | − | 0.301568i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.00000 | −0.270232 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.00000 | −0.154189 | −0.0770943 | − | 0.997024i | \(-0.524564\pi\) | ||||
−0.0770943 | + | 0.997024i | \(0.524564\pi\) | |||||||
\(674\) | −11.0000 | − | 19.0526i | −0.423704 | − | 0.733877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | 21.0000 | + | 36.3731i | 0.807096 | + | 1.39793i | 0.914867 | + | 0.403755i | \(0.132295\pi\) |
−0.107772 | + | 0.994176i | \(0.534372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.5000 | − | 11.2583i | −1.24724 | − | 0.432055i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.00000 | − | 6.92820i | 0.153168 | − | 0.265295i | ||||
\(683\) | −22.5000 | + | 38.9711i | −0.860939 | + | 1.49119i | 0.0100856 | + | 0.999949i | \(0.496790\pi\) |
−0.871024 | + | 0.491240i | \(0.836544\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | −30.0000 | + | 51.9615i | −1.14291 | + | 1.97958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.5000 | − | 30.3109i | −0.665731 | − | 1.15308i | −0.979086 | − | 0.203445i | \(-0.934786\pi\) |
0.313355 | − | 0.949636i | \(-0.398547\pi\) | |||||||
\(692\) | 15.0000 | 0.570214 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | − | 31.1769i | 0.681799 | − | 1.18091i | ||||
\(698\) | −17.0000 | − | 29.4449i | −0.643459 | − | 1.11450i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.50000 | + | 12.9904i | 0.0944911 | + | 0.490990i | ||||
\(701\) | 3.00000 | 0.113308 | 0.0566542 | − | 0.998394i | \(-0.481957\pi\) | ||||
0.0566542 | + | 0.998394i | \(0.481957\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00000 | + | 3.46410i | −0.0754314 | + | 0.130651i | ||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.0000 | 1.12906 | ||||||||
\(707\) | 6.00000 | − | 5.19615i | 0.225653 | − | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | + | 8.66025i | 0.187779 | + | 0.325243i | 0.944509 | − | 0.328484i | \(-0.106538\pi\) |
−0.756730 | + | 0.653727i | \(0.773204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | − | 5.19615i | −0.112430 | − | 0.194734i | ||||
\(713\) | −48.0000 | −1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.50000 | + | 7.79423i | 0.168173 | + | 0.291284i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.50000 | − | 7.79423i | 0.167939 | − | 0.290878i | ||||
\(719\) | −3.00000 | − | 5.19615i | −0.111881 | − | 0.193784i | 0.804648 | − | 0.593753i | \(-0.202354\pi\) |
−0.916529 | + | 0.399969i | \(0.869021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.00000 | + | 10.3923i | 0.0744839 | + | 0.387030i | ||||
\(722\) | 15.0000 | 0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.00000 | − | 8.66025i | 0.185824 | − | 0.321856i | ||||
\(725\) | −7.50000 | + | 12.9904i | −0.278543 | + | 0.482451i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.0000 | 1.85440 | 0.927199 | − | 0.374570i | \(-0.122210\pi\) | ||||
0.927199 | + | 0.374570i | \(0.122210\pi\) | |||||||
\(728\) | −12.5000 | − | 4.33013i | −0.463281 | − | 0.160485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.5000 | + | 37.2391i | 0.794121 | + | 1.37546i | 0.923396 | + | 0.383849i | \(0.125402\pi\) |
−0.129275 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(734\) | −38.0000 | −1.40261 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 6.50000 | + | 11.2583i | 0.239431 | + | 0.414706i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00000 | + | 1.73205i | −0.0367856 | + | 0.0637145i | −0.883832 | − | 0.467804i | \(-0.845045\pi\) |
0.847046 | + | 0.531519i | \(0.178379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.0000 | − | 10.3923i | −1.10133 | − | 0.381514i | ||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.50000 | − | 9.52628i | 0.201369 | − | 0.348782i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.00000 | −0.219382 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 3.00000 | − | 5.19615i | 0.109399 | − | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.50000 | − | 12.9904i | −0.273134 | − | 0.473082i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | −12.5000 | − | 21.6506i | −0.454020 | − | 0.786386i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | + | 25.9808i | 0.543750 | + | 0.941802i | 0.998684 | + | 0.0512772i | \(0.0163292\pi\) |
−0.454935 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.0000 | + | 24.2487i | −1.01367 | + | 0.877862i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.00000 | + | 10.3923i | −0.216789 | + | 0.375489i | ||||
\(767\) | −7.50000 | + | 12.9904i | −0.270809 | + | 0.469055i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.0000 | + | 19.0526i | 0.395899 | + | 0.685717i | ||||
\(773\) | −12.0000 | + | 20.7846i | −0.431610 | + | 0.747570i | −0.997012 | − | 0.0772449i | \(-0.975388\pi\) |
0.565402 | + | 0.824815i | \(0.308721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.0000 | + | 34.6410i | 0.718421 | + | 1.24434i | ||||
\(776\) | 13.0000 | 0.466673 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.0000 | 0.430221 | ||||||||
\(779\) | −6.00000 | − | 10.3923i | −0.214972 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | + | 10.3923i | −0.214697 | + | 0.371866i | ||||
\(782\) | 18.0000 | + | 31.1769i | 0.643679 | + | 1.11488i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.00000 | + | 12.1244i | −0.249523 | + | 0.432187i | −0.963394 | − | 0.268091i | \(-0.913607\pi\) |
0.713871 | + | 0.700278i | \(0.246941\pi\) | |||||||
\(788\) | −4.50000 | + | 7.79423i | −0.160306 | + | 0.277658i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.5000 | − | 7.79423i | −0.800008 | − | 0.277131i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.5000 | + | 30.3109i | 0.621443 | + | 1.07637i | ||||
\(794\) | 1.00000 | − | 1.73205i | 0.0354887 | − | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.00000 | − | 12.1244i | −0.248108 | − | 0.429736i | ||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0000 | 1.27359 | ||||||||
\(800\) | −2.50000 | − | 4.33013i | −0.0883883 | − | 0.153093i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.50000 | − | 7.79423i | 0.158901 | − | 0.275224i | ||||
\(803\) | 5.00000 | + | 8.66025i | 0.176446 | + | 0.305614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −40.0000 | −1.40894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.50000 | + | 2.59808i | −0.0527698 | + | 0.0914000i | ||||
\(809\) | 18.0000 | − | 31.1769i | 0.632846 | − | 1.09612i | −0.354121 | − | 0.935200i | \(-0.615220\pi\) |
0.986967 | − | 0.160922i | \(-0.0514468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | 6.00000 | − | 5.19615i | 0.210559 | − | 0.182349i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.00000 | + | 1.73205i | 0.0350500 | + | 0.0607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | + | 6.92820i | 0.139942 | + | 0.242387i | ||||
\(818\) | 4.00000 | 0.139857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.5000 | + | 23.3827i | 0.471153 | + | 0.816061i | 0.999456 | − | 0.0329950i | \(-0.0105045\pi\) |
−0.528302 | + | 0.849056i | \(0.677171\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0000 | + | 22.5167i | −0.453152 | + | 0.784881i | −0.998580 | − | 0.0532760i | \(-0.983034\pi\) |
0.545428 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(824\) | −2.00000 | − | 3.46410i | −0.0696733 | − | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.50000 | − | 2.59808i | −0.260958 | − | 0.0903986i | ||||
\(827\) | −42.0000 | −1.46048 | −0.730242 | − | 0.683189i | \(-0.760592\pi\) | ||||
−0.730242 | + | 0.683189i | \(0.760592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.00000 | − | 13.8564i | 0.277851 | − | 0.481253i | −0.692999 | − | 0.720938i | \(-0.743711\pi\) |
0.970851 | + | 0.239686i | \(0.0770444\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.00000 | 0.173344 | ||||||||
\(833\) | 39.0000 | − | 15.5885i | 1.35127 | − | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.00000 | + | 1.73205i | −0.0345857 | + | 0.0599042i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | − | 10.3923i | −0.207267 | − | 0.358996i | ||||
\(839\) | −30.0000 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −8.00000 | − | 13.8564i | −0.275698 | − | 0.477523i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.0000 | + | 22.5167i | −0.447478 | + | 0.775055i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.500000 | − | 2.59808i | −0.0171802 | − | 0.0892710i | ||||
\(848\) | 12.0000 | 0.412082 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.0000 | − | 25.9808i | 0.514496 | − | 0.891133i | ||||
\(851\) | 6.00000 | − | 10.3923i | 0.205677 | − | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −58.0000 | −1.98588 | −0.992941 | − | 0.118609i | \(-0.962157\pi\) | ||||
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | −14.0000 | + | 12.1244i | −0.479070 | + | 0.414887i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0000 | − | 41.5692i | 0.819824 | − | 1.41998i | −0.0859870 | − | 0.996296i | \(-0.527404\pi\) |
0.905811 | − | 0.423681i | \(-0.139262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.5000 | − | 30.3109i | −0.597092 | − | 1.03419i | −0.993248 | − | 0.116011i | \(-0.962989\pi\) |
0.396156 | − | 0.918183i | \(-0.370344\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.0000 | 0.510902 | ||||||||
\(863\) | 3.00000 | + | 5.19615i | 0.102121 | + | 0.176879i | 0.912558 | − | 0.408946i | \(-0.134104\pi\) |
−0.810437 | + | 0.585826i | \(0.800770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.00000 | + | 12.1244i | 0.237870 | + | 0.412002i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.00000 | − | 20.7846i | −0.135769 | − | 0.705476i | ||||
\(869\) | −1.00000 | −0.0339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.5000 | − | 56.2917i | 1.10122 | − | 1.90737i | ||||
\(872\) | 7.00000 | − | 12.1244i | 0.237050 | − | 0.410582i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.0000 | 0.405906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.5000 | + | 32.0429i | 0.624701 | + | 1.08201i | 0.988599 | + | 0.150574i | \(0.0481123\pi\) |
−0.363898 | + | 0.931439i | \(0.618554\pi\) | |||||||
\(878\) | −9.50000 | + | 16.4545i | −0.320609 | + | 0.555312i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | 15.0000 | + | 25.9808i | 0.504505 | + | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | 28.5000 | + | 49.3634i | 0.956936 | + | 1.65746i | 0.729873 | + | 0.683582i | \(0.239579\pi\) |
0.227063 | + | 0.973880i | \(0.427088\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.5000 | − | 11.2583i | −1.09002 | − | 0.377592i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.00000 | − | 8.66025i | 0.167412 | − | 0.289967i | ||||
\(893\) | 6.00000 | − | 10.3923i | 0.200782 | − | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | + | 2.59808i | 0.0167038 | + | 0.0867956i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.0000 | − | 25.9808i | −0.500556 | − | 0.866989i | ||||
\(899\) | 12.0000 | − | 20.7846i | 0.400222 | − | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | + | 62.3538i | 1.19933 | + | 2.07731i | ||||
\(902\) | −6.00000 | −0.199778 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.00000 | 0.299336 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | + | 38.1051i | −0.730498 | + | 1.26526i | 0.226173 | + | 0.974087i | \(0.427379\pi\) |
−0.956671 | + | 0.291172i | \(0.905955\pi\) | |||||||
\(908\) | −3.00000 | − | 5.19615i | −0.0995585 | − | 0.172440i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.00000 | − | 5.19615i | 0.0992855 | − | 0.171968i | ||||
\(914\) | −11.0000 | + | 19.0526i | −0.363848 | + | 0.630203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | 3.00000 | + | 15.5885i | 0.0990687 | + | 0.514776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | + | 13.8564i | 0.263896 | + | 0.457081i | 0.967274 | − | 0.253735i | \(-0.0816592\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.5000 | − | 33.7750i | −0.642198 | − | 1.11232i | ||||
\(923\) | 60.0000 | 1.97492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 13.0000 | + | 22.5167i | 0.427207 | + | 0.739943i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.50000 | + | 2.59808i | −0.0492399 | + | 0.0852860i | ||||
\(929\) | 7.50000 | + | 12.9904i | 0.246067 | + | 0.426201i | 0.962431 | − | 0.271526i | \(-0.0875283\pi\) |
−0.716364 | + | 0.697727i | \(0.754195\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | − | 13.8564i | 0.0655474 | − | 0.454125i | ||||
\(932\) | 30.0000 | 0.982683 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.00000 | − | 10.3923i | 0.196326 | − | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.0000 | −1.69877 | −0.849383 | − | 0.527777i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527777i | \(0.823026\pi\) | |||||||
\(938\) | 32.5000 | + | 11.2583i | 1.06116 | + | 0.367598i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5000 | + | 23.3827i | −0.440087 | + | 0.762254i | −0.997695 | − | 0.0678506i | \(-0.978386\pi\) |
0.557608 | + | 0.830104i | \(0.311719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0000 | + | 31.1769i | 0.586161 | + | 1.01526i | ||||
\(944\) | 3.00000 | 0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | −12.0000 | − | 20.7846i | −0.389948 | − | 0.675409i | 0.602494 | − | 0.798123i | \(-0.294174\pi\) |
−0.992442 | + | 0.122714i | \(0.960840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.0000 | − | 43.3013i | 0.811534 | − | 1.40562i | ||||
\(950\) | −5.00000 | − | 8.66025i | −0.162221 | − | 0.280976i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.0000 | + | 10.3923i | −0.388922 | + | 0.336817i | ||||
\(953\) | −24.0000 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.5000 | − | 18.1865i | 0.339594 | − | 0.588195i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.00000 | −0.0969256 | ||||||||
\(959\) | 30.0000 | − | 25.9808i | 0.968751 | − | 0.838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 5.00000 | − | 8.66025i | 0.161206 | − | 0.279218i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.00000 | + | 8.66025i | 0.161039 | + | 0.278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 0.500000 | + | 0.866025i | 0.0160706 | + | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.5000 | − | 28.5788i | −0.529510 | − | 0.917139i | −0.999408 | − | 0.0344175i | \(-0.989042\pi\) |
0.469897 | − | 0.882721i | \(-0.344291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0000 | − | 3.46410i | −0.320585 | − | 0.111054i | ||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.50000 | − | 6.06218i | 0.112032 | − | 0.194046i | ||||
\(977\) | −9.00000 | + | 15.5885i | −0.287936 | + | 0.498719i | −0.973317 | − | 0.229465i | \(-0.926302\pi\) |
0.685381 | + | 0.728184i | \(0.259636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.0000 | + | 25.9808i | 0.478669 | + | 0.829079i | ||||
\(983\) | −3.00000 | + | 5.19615i | −0.0956851 | + | 0.165732i | −0.909894 | − | 0.414840i | \(-0.863838\pi\) |
0.814209 | + | 0.580572i | \(0.197171\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.0000 | −0.573237 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.0000 | 0.318142 | ||||||||
\(989\) | −12.0000 | − | 20.7846i | −0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | − | 13.8564i | 0.254128 | − | 0.440163i | −0.710530 | − | 0.703667i | \(-0.751545\pi\) |
0.964658 | + | 0.263504i | \(0.0848781\pi\) | |||||||
\(992\) | 4.00000 | + | 6.92820i | 0.127000 | + | 0.219971i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000 | + | 31.1769i | 0.190308 | + | 0.988872i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.0000 | − | 39.8372i | 0.728417 | − | 1.26166i | −0.229135 | − | 0.973395i | \(-0.573590\pi\) |
0.957552 | − | 0.288261i | \(-0.0930771\pi\) | |||||||
\(998\) | 4.00000 | − | 6.92820i | 0.126618 | − | 0.219308i | ||||
\(999\) | 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 | 1386.2.k.n.991.1 | 2 | ||
3.2 | odd | 2 | 154.2.e.b.67.1 | yes | 2 | ||
7.2 | even | 3 | inner | 1386.2.k.n.793.1 | 2 | ||
7.3 | odd | 6 | 9702.2.a.l.1.1 | 1 | |||
7.4 | even | 3 | 9702.2.a.o.1.1 | 1 | |||
12.11 | even | 2 | 1232.2.q.c.529.1 | 2 | |||
21.2 | odd | 6 | 154.2.e.b.23.1 | ✓ | 2 | ||
21.5 | even | 6 | 1078.2.e.d.177.1 | 2 | |||
21.11 | odd | 6 | 1078.2.a.k.1.1 | 1 | |||
21.17 | even | 6 | 1078.2.a.i.1.1 | 1 | |||
21.20 | even | 2 | 1078.2.e.d.67.1 | 2 | |||
84.11 | even | 6 | 8624.2.a.l.1.1 | 1 | |||
84.23 | even | 6 | 1232.2.q.c.177.1 | 2 | |||
84.59 | odd | 6 | 8624.2.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.b.23.1 | ✓ | 2 | 21.2 | odd | 6 | ||
154.2.e.b.67.1 | yes | 2 | 3.2 | odd | 2 | ||
1078.2.a.i.1.1 | 1 | 21.17 | even | 6 | |||
1078.2.a.k.1.1 | 1 | 21.11 | odd | 6 | |||
1078.2.e.d.67.1 | 2 | 21.20 | even | 2 | |||
1078.2.e.d.177.1 | 2 | 21.5 | even | 6 | |||
1232.2.q.c.177.1 | 2 | 84.23 | even | 6 | |||
1232.2.q.c.529.1 | 2 | 12.11 | even | 2 | |||
1386.2.k.n.793.1 | 2 | 7.2 | even | 3 | inner | ||
1386.2.k.n.991.1 | 2 | 1.1 | even | 1 | trivial | ||
8624.2.a.l.1.1 | 1 | 84.11 | even | 6 | |||
8624.2.a.t.1.1 | 1 | 84.59 | odd | 6 | |||
9702.2.a.l.1.1 | 1 | 7.3 | odd | 6 | |||
9702.2.a.o.1.1 | 1 | 7.4 | even | 3 |