Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(16,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.i (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: | \(0.838429221223\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.16 |
Dual form | 105.2.i.a.46.1 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 1.00000 | − | 1.73205i | 0.288675 | − | 0.500000i | ||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | −2.00000 | − | 1.73205i | −0.436436 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.00000 | + | 3.46410i | 0.755929 | + | 0.654654i | ||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | − | 2.59808i | 0.0845154 | − | 0.439155i | ||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 3.50000 | − | 6.06218i | 0.575396 | − | 0.996616i | −0.420602 | − | 0.907245i | \(-0.638181\pi\) |
0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.0000 | 1.87409 | 0.937043 | − | 0.349215i | \(-0.113552\pi\) | ||||
0.937043 | + | 0.349215i | \(0.113552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 5.19615i | −0.437595 | + | 0.757937i | −0.997503 | − | 0.0706177i | \(-0.977503\pi\) |
0.559908 | + | 0.828554i | \(0.310836\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | + | 5.19615i | −0.420084 | + | 0.727607i | ||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | + | 5.19615i | 0.390567 | + | 0.676481i | 0.992524 | − | 0.122047i | \(-0.0389457\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(60\) | −1.00000 | − | 1.73205i | −0.129099 | − | 0.223607i | ||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.500000 | + | 2.59808i | −0.0629941 | + | 0.327327i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.0620174 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | + | 6.06218i | 0.427593 | + | 0.740613i | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | 6.00000 | − | 10.3923i | 0.727607 | − | 1.26025i | ||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.50000 | − | 9.52628i | −0.643726 | − | 1.11497i | −0.984594 | − | 0.174855i | \(-0.944054\pi\) |
0.340868 | − | 0.940111i | \(-0.389279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | −10.0000 | −1.14708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | 2.00000 | + | 3.46410i | 0.223607 | + | 0.387298i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 1.00000 | − | 5.19615i | 0.109109 | − | 0.566947i | ||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | + | 5.19615i | 0.321634 | + | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | + | 0.866025i | −0.262071 | + | 0.0907841i | ||||
\(92\) | −12.0000 | −1.25109 | ||||||||
\(93\) | −2.50000 | + | 4.33013i | −0.259238 | + | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.50000 | + | 4.33013i | 0.256495 | + | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | − | 1.73205i | 0.100000 | − | 0.173205i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.500000 | − | 0.866025i | 0.0492665 | − | 0.0853320i | −0.840341 | − | 0.542059i | \(-0.817645\pi\) |
0.889607 | + | 0.456727i | \(0.150978\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.50000 | + | 0.866025i | −0.243975 | + | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.00000 | + | 15.5885i | −0.870063 | + | 1.50699i | −0.00813215 | + | 0.999967i | \(0.502589\pi\) |
−0.861931 | + | 0.507026i | \(0.830745\pi\) | |||||||
\(108\) | 1.00000 | + | 1.73205i | 0.0962250 | + | 0.166667i | ||||
\(109\) | 3.50000 | + | 6.06218i | 0.335239 | + | 0.580651i | 0.983531 | − | 0.180741i | \(-0.0578495\pi\) |
−0.648292 | + | 0.761392i | \(0.724516\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.00000 | −0.664411 | ||||||||
\(112\) | −2.00000 | + | 10.3923i | −0.188982 | + | 0.981981i | ||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | + | 5.19615i | 0.279751 | + | 0.484544i | ||||
\(116\) | −6.00000 | − | 10.3923i | −0.557086 | − | 0.964901i | ||||
\(117\) | 0.500000 | − | 0.866025i | 0.0462250 | − | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.0000 | − | 10.3923i | −1.10004 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | − | 10.3923i | −0.541002 | − | 0.937043i | ||||
\(124\) | 5.00000 | − | 8.66025i | 0.449013 | − | 0.777714i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0000 | 0.976092 | 0.488046 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488046 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.500000 | + | 0.866025i | 0.0440225 | + | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | − | 5.19615i | 0.262111 | − | 0.453990i | −0.704692 | − | 0.709514i | \(-0.748915\pi\) |
0.966803 | + | 0.255524i | \(0.0822479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50000 | + | 12.9904i | −0.216777 | + | 1.12641i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | − | 5.19615i | −0.256307 | − | 0.443937i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | 0.424094 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(140\) | 5.00000 | − | 1.73205i | 0.422577 | − | 0.146385i | ||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.00000 | − | 3.46410i | −0.166667 | − | 0.288675i | ||||
\(145\) | −3.00000 | + | 5.19615i | −0.249136 | + | 0.431517i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.50000 | − | 2.59808i | −0.536111 | − | 0.214286i | ||||
\(148\) | 14.0000 | 1.15079 | ||||||||
\(149\) | 12.0000 | − | 20.7846i | 0.983078 | − | 1.70274i | 0.332896 | − | 0.942964i | \(-0.391974\pi\) |
0.650183 | − | 0.759778i | \(-0.274692\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.00000 | −0.401610 | ||||||||
\(156\) | −1.00000 | + | 1.73205i | −0.0800641 | + | 0.138675i | ||||
\(157\) | 5.00000 | + | 8.66025i | 0.399043 | + | 0.691164i | 0.993608 | − | 0.112884i | \(-0.0360089\pi\) |
−0.594565 | + | 0.804048i | \(0.702676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | + | 15.5885i | −0.236433 | + | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | − | 3.46410i | 0.156652 | − | 0.271329i | −0.777007 | − | 0.629492i | \(-0.783263\pi\) |
0.933659 | + | 0.358162i | \(0.116597\pi\) | |||||||
\(164\) | 12.0000 | + | 20.7846i | 0.937043 | + | 1.62301i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.50000 | − | 4.33013i | −0.191180 | − | 0.331133i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | − | 1.73205i | −0.151186 | − | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.00000 | − | 5.19615i | 0.225494 | − | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.00000 | − | 15.5885i | −0.672692 | − | 1.16514i | −0.977138 | − | 0.212607i | \(-0.931805\pi\) |
0.304446 | − | 0.952529i | \(-0.401529\pi\) | |||||||
\(180\) | −1.00000 | + | 1.73205i | −0.0745356 | + | 0.129099i | ||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.50000 | − | 6.06218i | −0.257325 | − | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.0000 | −0.875190 | ||||||||
\(189\) | 2.50000 | − | 0.866025i | 0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | − | 5.19615i | 0.217072 | − | 0.375980i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.953912 | + | 0.300088i | \(0.0970159\pi\) | |||||||
\(192\) | 4.00000 | + | 6.92820i | 0.288675 | + | 0.500000i | ||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 13.0000 | + | 5.19615i | 0.928571 | + | 0.371154i | ||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | + | 13.8564i | 0.567105 | + | 0.982255i | 0.996850 | + | 0.0793045i | \(0.0252700\pi\) |
−0.429745 | + | 0.902950i | \(0.641397\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | − | 6.06218i | 0.246871 | − | 0.427593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.0000 | + | 5.19615i | −1.05279 | + | 0.364698i | ||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | 6.00000 | − | 10.3923i | 0.419058 | − | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.00000 | − | 5.19615i | −0.208514 | − | 0.361158i | ||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | − | 10.3923i | −0.411113 | − | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.500000 | + | 0.866025i | −0.0340997 | + | 0.0590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0000 | − | 8.66025i | −0.678844 | − | 0.587896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.50000 | + | 9.52628i | −0.371656 | + | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | − | 10.3923i | −0.398234 | − | 0.689761i | 0.595274 | − | 0.803523i | \(-0.297043\pi\) |
−0.993508 | + | 0.113761i | \(0.963710\pi\) | |||||||
\(228\) | 5.00000 | + | 8.66025i | 0.331133 | + | 0.573539i | ||||
\(229\) | −14.5000 | + | 25.1147i | −0.958187 | + | 1.65963i | −0.231287 | + | 0.972886i | \(0.574293\pi\) |
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | + | 5.19615i | 0.195698 | + | 0.338960i | ||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | −13.0000 | −0.844441 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 2.00000 | − | 3.46410i | 0.129099 | − | 0.223607i | ||||
\(241\) | −1.00000 | − | 1.73205i | −0.0644157 | − | 0.111571i | 0.832019 | − | 0.554747i | \(-0.187185\pi\) |
−0.896435 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | −1.00000 | − | 6.92820i | −0.0638877 | − | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.50000 | − | 4.33013i | 0.159071 | − | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | + | 10.3923i | 0.380235 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | −5.00000 | + | 1.73205i | −0.314970 | + | 0.109109i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.00000 | + | 5.19615i | 0.187867 | + | 0.325396i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 6.00000 | − | 10.3923i | 0.374270 | − | 0.648254i | −0.615948 | − | 0.787787i | \(-0.711227\pi\) |
0.990217 | + | 0.139533i | \(0.0445601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.50000 | − | 18.1865i | 0.217479 | − | 1.13006i | ||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000 | 0.367194 | ||||||||
\(268\) | −7.00000 | + | 12.1244i | −0.427593 | + | 0.740613i | ||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 24.0000 | 1.45521 | ||||||||
\(273\) | 2.00000 | + | 1.73205i | 0.121046 | + | 0.104828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | + | 10.3923i | 0.361158 | + | 0.625543i | ||||
\(277\) | −11.5000 | − | 19.9186i | −0.690968 | − | 1.19679i | −0.971521 | − | 0.236953i | \(-0.923851\pi\) |
0.280553 | − | 0.959839i | \(-0.409482\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0000 | −1.43172 | −0.715860 | − | 0.698244i | \(-0.753965\pi\) | ||||
−0.715860 | + | 0.698244i | \(0.753965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.50000 | − | 9.52628i | −0.326941 | − | 0.566279i | 0.654962 | − | 0.755662i | \(-0.272685\pi\) |
−0.981903 | + | 0.189383i | \(0.939351\pi\) | |||||||
\(284\) | 12.0000 | + | 20.7846i | 0.712069 | + | 1.23334i | ||||
\(285\) | 2.50000 | − | 4.33013i | 0.148087 | − | 0.256495i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.0000 | − | 10.3923i | 1.77084 | − | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | + | 8.66025i | 0.293105 | + | 0.507673i | ||||
\(292\) | 11.0000 | − | 19.0526i | 0.643726 | − | 1.11497i | ||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | −2.50000 | + | 0.866025i | −0.144098 | + | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.0000 | − | 17.3205i | −0.573539 | − | 0.993399i | ||||
\(305\) | 1.00000 | + | 1.73205i | 0.0572598 | + | 0.0991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.00000 | −0.399511 | −0.199756 | − | 0.979846i | \(-0.564015\pi\) | ||||
−0.199756 | + | 0.979846i | \(0.564015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | − | 10.3923i | −0.340229 | − | 0.589294i | 0.644246 | − | 0.764818i | \(-0.277171\pi\) |
−0.984475 | + | 0.175525i | \(0.943838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.50000 | + | 14.7224i | −0.480448 | + | 0.832161i | −0.999748 | − | 0.0224310i | \(-0.992859\pi\) |
0.519300 | + | 0.854592i | \(0.326193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.00000 | + | 1.73205i | 0.112687 | + | 0.0975900i | ||||
\(316\) | 26.0000 | 1.46261 | ||||||||
\(317\) | −3.00000 | + | 5.19615i | −0.168497 | + | 0.291845i | −0.937892 | − | 0.346929i | \(-0.887225\pi\) |
0.769395 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.00000 | + | 6.92820i | −0.223607 | + | 0.387298i | ||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.0000 | 1.66924 | ||||||||
\(324\) | 1.00000 | − | 1.73205i | 0.0555556 | − | 0.0962250i | ||||
\(325\) | 0.500000 | + | 0.866025i | 0.0277350 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.50000 | − | 6.06218i | 0.193550 | − | 0.335239i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00000 | + | 15.5885i | −0.165395 | + | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.5000 | + | 19.9186i | −0.632097 | + | 1.09482i | 0.355025 | + | 0.934857i | \(0.384472\pi\) |
−0.987122 | + | 0.159968i | \(0.948861\pi\) | |||||||
\(332\) | −12.0000 | − | 20.7846i | −0.658586 | − | 1.14070i | ||||
\(333\) | 3.50000 | + | 6.06218i | 0.191799 | + | 0.332205i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.00000 | 0.382451 | ||||||||
\(336\) | 10.0000 | − | 3.46410i | 0.545545 | − | 0.188982i | ||||
\(337\) | −13.0000 | −0.708155 | −0.354078 | − | 0.935216i | \(-0.615205\pi\) | ||||
−0.354078 | + | 0.935216i | \(0.615205\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.00000 | − | 15.5885i | −0.488813 | − | 0.846649i | ||||
\(340\) | −6.00000 | − | 10.3923i | −0.325396 | − | 0.563602i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.00000 | − | 5.19615i | 0.161515 | − | 0.279751i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000 | + | 20.7846i | 0.644194 | + | 1.11578i | 0.984487 | + | 0.175457i | \(0.0561403\pi\) |
−0.340293 | + | 0.940319i | \(0.610526\pi\) | |||||||
\(348\) | −6.00000 | + | 10.3923i | −0.321634 | + | 0.557086i | ||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | − | 10.3923i | 0.318447 | − | 0.551566i | ||||
\(356\) | −12.0000 | −0.635999 | ||||||||
\(357\) | −3.00000 | + | 15.5885i | −0.158777 | + | 0.825029i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.00000 | − | 5.19615i | 0.158334 | − | 0.274242i | −0.775934 | − | 0.630814i | \(-0.782721\pi\) |
0.934268 | + | 0.356572i | \(0.116054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | −4.00000 | − | 3.46410i | −0.209657 | − | 0.181568i | ||||
\(365\) | −11.0000 | −0.575766 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.50000 | + | 16.4545i | 0.495896 | + | 0.858917i | 0.999989 | − | 0.00473247i | \(-0.00150640\pi\) |
−0.504093 | + | 0.863649i | \(0.668173\pi\) | |||||||
\(368\) | −12.0000 | − | 20.7846i | −0.625543 | − | 1.08347i | ||||
\(369\) | −6.00000 | + | 10.3923i | −0.312348 | + | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.0000 | −0.518476 | ||||||||
\(373\) | −8.50000 | + | 14.7224i | −0.440113 | + | 0.762299i | −0.997697 | − | 0.0678218i | \(-0.978395\pi\) |
0.557584 | + | 0.830120i | \(0.311728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000 | 0.309016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0000 | −1.28416 | −0.642082 | − | 0.766636i | \(-0.721929\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(380\) | −5.00000 | + | 8.66025i | −0.256495 | + | 0.444262i | ||||
\(381\) | −5.50000 | − | 9.52628i | −0.281774 | − | 0.488046i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.500000 | − | 0.866025i | 0.0254164 | − | 0.0440225i | ||||
\(388\) | −10.0000 | − | 17.3205i | −0.507673 | − | 0.879316i | ||||
\(389\) | −6.00000 | − | 10.3923i | −0.304212 | − | 0.526911i | 0.672874 | − | 0.739758i | \(-0.265060\pi\) |
−0.977086 | + | 0.212847i | \(0.931726\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0000 | 1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | −0.302660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.50000 | − | 11.2583i | −0.327050 | − | 0.566468i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.5000 | + | 25.1147i | −0.727734 | + | 1.26047i | 0.230105 | + | 0.973166i | \(0.426093\pi\) |
−0.957839 | + | 0.287307i | \(0.907240\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.5000 | − | 4.33013i | 0.625783 | − | 0.216777i | ||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | −12.0000 | + | 20.7846i | −0.599251 | + | 1.03793i | 0.393680 | + | 0.919247i | \(0.371202\pi\) |
−0.992932 | + | 0.118686i | \(0.962132\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.50000 | + | 4.33013i | 0.124534 | + | 0.215699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50000 | − | 4.33013i | −0.123617 | − | 0.214111i | 0.797574 | − | 0.603220i | \(-0.206116\pi\) |
−0.921192 | + | 0.389109i | \(0.872783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00000 | + | 5.19615i | −0.147979 | + | 0.256307i | ||||
\(412\) | 2.00000 | 0.0985329 | ||||||||
\(413\) | 12.0000 | + | 10.3923i | 0.590481 | + | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | + | 10.3923i | −0.294528 | + | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.50000 | − | 4.33013i | −0.122426 | − | 0.212047i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0000 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(420\) | −4.00000 | − | 3.46410i | −0.195180 | − | 0.169031i | ||||
\(421\) | −7.00000 | −0.341159 | −0.170580 | − | 0.985344i | \(-0.554564\pi\) | ||||
−0.170580 | + | 0.985344i | \(0.554564\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | − | 5.19615i | −0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | + | 5.19615i | −0.145521 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.00000 | + | 5.19615i | −0.0483934 | + | 0.251459i | ||||
\(428\) | −36.0000 | −1.74013 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | −2.00000 | + | 3.46410i | −0.0962250 | + | 0.166667i | ||||
\(433\) | 29.0000 | 1.39365 | 0.696826 | − | 0.717241i | \(-0.254595\pi\) | ||||
0.696826 | + | 0.717241i | \(0.254595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.00000 | 0.287678 | ||||||||
\(436\) | −7.00000 | + | 12.1244i | −0.335239 | + | 0.580651i | ||||
\(437\) | −15.0000 | − | 25.9808i | −0.717547 | − | 1.24283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | − | 24.2487i | 0.668184 | − | 1.15733i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
0.978412 | − | 0.206666i | \(-0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0000 | − | 31.1769i | 0.855206 | − | 1.48126i | −0.0212481 | − | 0.999774i | \(-0.506764\pi\) |
0.876454 | − | 0.481486i | \(-0.159903\pi\) | |||||||
\(444\) | −7.00000 | − | 12.1244i | −0.332205 | − | 0.575396i | ||||
\(445\) | 3.00000 | + | 5.19615i | 0.142214 | + | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.0000 | −1.13516 | ||||||||
\(448\) | −20.0000 | + | 6.92820i | −0.944911 | + | 0.327327i | ||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 18.0000 | + | 31.1769i | 0.846649 | + | 1.46644i | ||||
\(453\) | 8.00000 | − | 13.8564i | 0.375873 | − | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.500000 | + | 2.59808i | −0.0234404 | + | 0.121800i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.50000 | + | 9.52628i | −0.257279 | + | 0.445621i | −0.965512 | − | 0.260358i | \(-0.916159\pi\) |
0.708233 | + | 0.705979i | \(0.249493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.00000 | − | 5.19615i | −0.140028 | − | 0.242536i | ||||
\(460\) | −6.00000 | + | 10.3923i | −0.279751 | + | 0.484544i | ||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.00000 | −0.325318 | −0.162659 | − | 0.986682i | \(-0.552007\pi\) | ||||
−0.162659 | + | 0.986682i | \(0.552007\pi\) | |||||||
\(464\) | 12.0000 | − | 20.7846i | 0.557086 | − | 0.964901i | ||||
\(465\) | 2.50000 | + | 4.33013i | 0.115935 | + | 0.200805i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.0000 | + | 25.9808i | −0.694117 | + | 1.20225i | 0.276360 | + | 0.961054i | \(0.410872\pi\) |
−0.970477 | + | 0.241192i | \(0.922462\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | 14.0000 | + | 12.1244i | 0.646460 | + | 0.559851i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | − | 8.66025i | 0.230388 | − | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.00000 | 0.229416 | ||||||||
\(476\) | 6.00000 | − | 31.1769i | 0.275010 | − | 1.42899i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.50000 | + | 6.06218i | −0.159586 | + | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.0000 | − | 5.19615i | 0.682524 | − | 0.236433i | ||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | −5.00000 | + | 8.66025i | −0.227038 | + | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.50000 | + | 6.06218i | 0.158600 | + | 0.274703i | 0.934364 | − | 0.356320i | \(-0.115969\pi\) |
−0.775764 | + | 0.631023i | \(0.782635\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 12.0000 | − | 20.7846i | 0.541002 | − | 0.937043i | ||||
\(493\) | 18.0000 | + | 31.1769i | 0.810679 | + | 1.40414i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | 30.0000 | − | 10.3923i | 1.34568 | − | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.50000 | + | 14.7224i | −0.380512 | + | 0.659067i | −0.991136 | − | 0.132855i | \(-0.957586\pi\) |
0.610623 | + | 0.791921i | \(0.290919\pi\) | |||||||
\(500\) | −1.00000 | − | 1.73205i | −0.0447214 | − | 0.0774597i | ||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | + | 10.3923i | 0.266469 | + | 0.461538i | ||||
\(508\) | 11.0000 | + | 19.0526i | 0.488046 | + | 0.845321i | ||||
\(509\) | 9.00000 | − | 15.5885i | 0.398918 | − | 0.690946i | −0.594675 | − | 0.803966i | \(-0.702719\pi\) |
0.993593 | + | 0.113020i | \(0.0360525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.0000 | − | 19.0526i | −0.973223 | − | 0.842836i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.50000 | + | 4.33013i | −0.110378 | + | 0.191180i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.500000 | − | 0.866025i | −0.0220326 | − | 0.0381616i | ||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | + | 20.7846i | 0.525730 | + | 0.910590i | 0.999551 | + | 0.0299693i | \(0.00954094\pi\) |
−0.473821 | + | 0.880621i | \(0.657126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.5000 | − | 37.2391i | 0.940129 | − | 1.62835i | 0.174908 | − | 0.984585i | \(-0.444037\pi\) |
0.765222 | − | 0.643767i | \(-0.222629\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | −0.500000 | + | 2.59808i | −0.0218218 | + | 0.113389i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.0000 | + | 25.9808i | −0.653410 | + | 1.13174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | −25.0000 | + | 8.66025i | −1.08389 | + | 0.375470i | ||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00000 | + | 15.5885i | 0.389104 | + | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.00000 | + | 15.5885i | −0.388379 | + | 0.672692i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.00000 | 0.0860663 | ||||||||
\(541\) | 9.50000 | − | 16.4545i | 0.408437 | − | 0.707433i | −0.586278 | − | 0.810110i | \(-0.699407\pi\) |
0.994715 | + | 0.102677i | \(0.0327407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.50000 | + | 6.06218i | 0.150199 | + | 0.260153i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.00000 | 0.299847 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 6.00000 | − | 10.3923i | 0.256307 | − | 0.443937i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0000 | − | 25.9808i | 0.639021 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.50000 | − | 33.7750i | 0.276408 | − | 1.43626i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.50000 | + | 6.06218i | −0.148567 | + | 0.257325i | ||||
\(556\) | 5.00000 | + | 8.66025i | 0.212047 | + | 0.367277i | ||||
\(557\) | −9.00000 | − | 15.5885i | −0.381342 | − | 0.660504i | 0.609912 | − | 0.792469i | \(-0.291205\pi\) |
−0.991254 | + | 0.131965i | \(0.957871\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00000 | 0.0422955 | ||||||||
\(560\) | 8.00000 | + | 6.92820i | 0.338062 | + | 0.292770i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.00000 | + | 15.5885i | 0.379305 | + | 0.656975i | 0.990961 | − | 0.134148i | \(-0.0428299\pi\) |
−0.611656 | + | 0.791123i | \(0.709497\pi\) | |||||||
\(564\) | 6.00000 | + | 10.3923i | 0.252646 | + | 0.437595i | ||||
\(565\) | 9.00000 | − | 15.5885i | 0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | − | 1.73205i | −0.0839921 | − | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0000 | − | 20.7846i | 0.503066 | − | 0.871336i | −0.496928 | − | 0.867792i | \(-0.665539\pi\) |
0.999994 | − | 0.00354413i | \(-0.00112814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50000 | + | 6.06218i | 0.146470 | + | 0.253694i | 0.929921 | − | 0.367760i | \(-0.119875\pi\) |
−0.783450 | + | 0.621455i | \(0.786542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.00000 | −0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000 | 0.250217 | ||||||||
\(576\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(577\) | 3.50000 | + | 6.06218i | 0.145707 | + | 0.252372i | 0.929636 | − | 0.368478i | \(-0.120121\pi\) |
−0.783930 | + | 0.620850i | \(0.786788\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.50000 | + | 4.33013i | −0.103896 | + | 0.179954i | ||||
\(580\) | −12.0000 | −0.498273 | ||||||||
\(581\) | −30.0000 | + | 10.3923i | −1.24461 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | − | 0.866025i | −0.0206725 | − | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0000 | −0.742940 | −0.371470 | − | 0.928445i | \(-0.621146\pi\) | ||||
−0.371470 | + | 0.928445i | \(0.621146\pi\) | |||||||
\(588\) | −2.00000 | − | 13.8564i | −0.0824786 | − | 0.571429i | ||||
\(589\) | 25.0000 | 1.03011 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | − | 5.19615i | −0.123404 | − | 0.213741i | ||||
\(592\) | 14.0000 | + | 24.2487i | 0.575396 | + | 0.996616i | ||||
\(593\) | −18.0000 | + | 31.1769i | −0.739171 | + | 1.28028i | 0.213697 | + | 0.976900i | \(0.431449\pi\) |
−0.952869 | + | 0.303383i | \(0.901884\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.0000 | + | 5.19615i | −0.614940 | + | 0.213021i | ||||
\(596\) | 48.0000 | 1.96616 | ||||||||
\(597\) | 8.00000 | − | 13.8564i | 0.327418 | − | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.00000 | − | 10.3923i | −0.245153 | − | 0.424618i | 0.717021 | − | 0.697051i | \(-0.245505\pi\) |
−0.962175 | + | 0.272433i | \(0.912172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | −0.0407909 | −0.0203954 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203954 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.00000 | −0.285062 | ||||||||
\(604\) | −16.0000 | + | 27.7128i | −0.651031 | + | 1.12762i | ||||
\(605\) | −5.50000 | − | 9.52628i | −0.223607 | − | 0.387298i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.50000 | − | 16.4545i | 0.385593 | − | 0.667867i | −0.606258 | − | 0.795268i | \(-0.707330\pi\) |
0.991851 | + | 0.127401i | \(0.0406635\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0000 | + | 10.3923i | 0.486265 | + | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | − | 5.19615i | 0.121367 | − | 0.210214i | ||||
\(612\) | 6.00000 | + | 10.3923i | 0.242536 | + | 0.420084i | ||||
\(613\) | −19.0000 | − | 32.9090i | −0.767403 | − | 1.32918i | −0.938967 | − | 0.344008i | \(-0.888215\pi\) |
0.171564 | − | 0.985173i | \(-0.445118\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.0000 | −0.483887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.0000 | −1.69086 | −0.845428 | − | 0.534089i | \(-0.820655\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.5000 | − | 30.3109i | −0.703384 | − | 1.21830i | −0.967271 | − | 0.253744i | \(-0.918338\pi\) |
0.263887 | − | 0.964554i | \(-0.414995\pi\) | |||||||
\(620\) | −5.00000 | − | 8.66025i | −0.200805 | − | 0.347804i | ||||
\(621\) | −3.00000 | + | 5.19615i | −0.120386 | + | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.00000 | + | 15.5885i | −0.120192 | + | 0.624538i | ||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.0000 | + | 17.3205i | −0.399043 | + | 0.691164i | ||||
\(629\) | −42.0000 | −1.67465 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.00000 | + | 3.46410i | 0.0794929 | + | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.50000 | − | 9.52628i | 0.218261 | − | 0.378039i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.50000 | + | 4.33013i | −0.217918 | + | 0.171566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | + | 10.3923i | −0.237356 | + | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | + | 25.9808i | 0.592464 | + | 1.02618i | 0.993899 | + | 0.110291i | \(0.0351782\pi\) |
−0.401435 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0000 | −0.985904 | −0.492952 | − | 0.870057i | \(-0.664082\pi\) | ||||
−0.492952 | + | 0.870057i | \(0.664082\pi\) | |||||||
\(644\) | −30.0000 | + | 10.3923i | −1.18217 | + | 0.409514i | ||||
\(645\) | 1.00000 | 0.0393750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | + | 20.7846i | 0.471769 | + | 0.817127i | 0.999478 | − | 0.0322975i | \(-0.0102824\pi\) |
−0.527710 | + | 0.849425i | \(0.676949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.50000 | + | 12.9904i | −0.0979827 | + | 0.509133i | ||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | 12.0000 | − | 20.7846i | 0.469596 | − | 0.813365i | −0.529799 | − | 0.848123i | \(-0.677733\pi\) |
0.999396 | + | 0.0347583i | \(0.0110661\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | − | 5.19615i | −0.117220 | − | 0.203030i | ||||
\(656\) | −24.0000 | + | 41.5692i | −0.937043 | + | 1.62301i | ||||
\(657\) | 11.0000 | 0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.50000 | + | 11.2583i | 0.252821 | + | 0.437898i | 0.964301 | − | 0.264807i | \(-0.0853084\pi\) |
−0.711481 | + | 0.702706i | \(0.751975\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.00000 | − | 5.19615i | 0.116510 | − | 0.201802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.0000 | + | 8.66025i | 0.387783 | + | 0.335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0000 | − | 31.1769i | 0.696963 | − | 1.20717i | ||||
\(668\) | 12.0000 | + | 20.7846i | 0.464294 | + | 0.804181i | ||||
\(669\) | 2.00000 | + | 3.46410i | 0.0773245 | + | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.0000 | −1.19496 | −0.597481 | − | 0.801883i | \(-0.703832\pi\) | ||||
−0.597481 | + | 0.801883i | \(0.703832\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | −12.0000 | − | 20.7846i | −0.461538 | − | 0.799408i | ||||
\(677\) | 9.00000 | − | 15.5885i | 0.345898 | − | 0.599113i | −0.639618 | − | 0.768693i | \(-0.720908\pi\) |
0.985517 | + | 0.169580i | \(0.0542410\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.0000 | + | 8.66025i | −0.959412 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | + | 10.3923i | −0.229920 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.00000 | − | 15.5885i | −0.344375 | − | 0.596476i | 0.640865 | − | 0.767654i | \(-0.278576\pi\) |
−0.985240 | + | 0.171178i | \(0.945243\pi\) | |||||||
\(684\) | 5.00000 | − | 8.66025i | 0.191180 | − | 0.331133i | ||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.0000 | 1.10642 | ||||||||
\(688\) | 2.00000 | − | 3.46410i | 0.0762493 | − | 0.132068i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.50000 | + | 9.52628i | −0.209230 | + | 0.362397i | −0.951472 | − | 0.307735i | \(-0.900429\pi\) |
0.742242 | + | 0.670132i | \(0.233762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.50000 | − | 4.33013i | 0.0948304 | − | 0.164251i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.0000 | − | 62.3538i | −1.36360 | − | 2.36182i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 1.00000 | − | 5.19615i | 0.0377964 | − | 0.196396i | ||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.5000 | + | 30.3109i | 0.660025 | + | 1.14320i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.00000 | − | 5.19615i | 0.112987 | − | 0.195698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.0000 | 0.450988 | ||||||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.50000 | + | 11.2583i | 0.243769 | + | 0.422220i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.0000 | 1.12351 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.0000 | − | 31.1769i | 0.672692 | − | 1.16514i | ||||
\(717\) | 3.00000 | + | 5.19615i | 0.112037 | + | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | −4.00000 | −0.149071 | ||||||||
\(721\) | 0.500000 | − | 2.59808i | 0.0186210 | − | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.00000 | + | 1.73205i | −0.0371904 | + | 0.0644157i | ||||
\(724\) | −7.00000 | − | 12.1244i | −0.260153 | − | 0.450598i | ||||
\(725\) | 3.00000 | + | 5.19615i | 0.111417 | + | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.00000 | −0.259616 | −0.129808 | − | 0.991539i | \(-0.541436\pi\) | ||||
−0.129808 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | + | 5.19615i | 0.110959 | + | 0.192187i | ||||
\(732\) | 2.00000 | + | 3.46410i | 0.0739221 | + | 0.128037i | ||||
\(733\) | 6.50000 | − | 11.2583i | 0.240083 | − | 0.415836i | −0.720655 | − | 0.693294i | \(-0.756159\pi\) |
0.960738 | + | 0.277458i | \(0.0894920\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.50000 | + | 4.33013i | −0.202871 | + | 0.159719i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.50000 | + | 6.06218i | 0.128750 | + | 0.223001i | 0.923192 | − | 0.384338i | \(-0.125570\pi\) |
−0.794443 | + | 0.607339i | \(0.792237\pi\) | |||||||
\(740\) | 7.00000 | − | 12.1244i | 0.257325 | − | 0.445700i | ||||
\(741\) | −5.00000 | −0.183680 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0000 | − | 20.7846i | −0.439646 | − | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | − | 10.3923i | 0.219529 | − | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.00000 | + | 46.7654i | −0.328853 | + | 1.70877i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.50000 | − | 16.4545i | 0.346660 | − | 0.600433i | −0.638994 | − | 0.769212i | \(-0.720649\pi\) |
0.985654 | + | 0.168779i | \(0.0539825\pi\) | |||||||
\(752\) | −12.0000 | − | 20.7846i | −0.437595 | − | 0.757937i | ||||
\(753\) | 9.00000 | + | 15.5885i | 0.327978 | + | 0.568075i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 4.00000 | + | 3.46410i | 0.145479 | + | 0.125988i | ||||
\(757\) | 50.0000 | 1.81728 | 0.908640 | − | 0.417579i | \(-0.137121\pi\) | ||||
0.908640 | + | 0.417579i | \(0.137121\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | − | 36.3731i | 0.761249 | − | 1.31852i | −0.180957 | − | 0.983491i | \(-0.557920\pi\) |
0.942207 | − | 0.335032i | \(-0.108747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | + | 12.1244i | 0.506834 | + | 0.438931i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 3.00000 | − | 5.19615i | 0.108465 | − | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.00000 | − | 5.19615i | −0.108324 | − | 0.187622i | ||||
\(768\) | −8.00000 | + | 13.8564i | −0.288675 | + | 0.500000i | ||||
\(769\) | −13.0000 | −0.468792 | −0.234396 | − | 0.972141i | \(-0.575311\pi\) | ||||
−0.234396 | + | 0.972141i | \(0.575311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 5.00000 | − | 8.66025i | 0.179954 | − | 0.311689i | ||||
\(773\) | 12.0000 | + | 20.7846i | 0.431610 | + | 0.747570i | 0.997012 | − | 0.0772449i | \(-0.0246123\pi\) |
−0.565402 | + | 0.824815i | \(0.691279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.50000 | + | 4.33013i | −0.0898027 | + | 0.155543i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.5000 | + | 6.06218i | −0.627809 | + | 0.217479i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.0000 | + | 51.9615i | −1.07486 | + | 1.86171i | ||||
\(780\) | 1.00000 | + | 1.73205i | 0.0358057 | + | 0.0620174i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.00000 | −0.214423 | ||||||||
\(784\) | 4.00000 | + | 27.7128i | 0.142857 | + | 0.989743i | ||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0000 | + | 24.2487i | 0.499046 | + | 0.864373i | 0.999999 | − | 0.00110111i | \(-0.000350496\pi\) |
−0.500953 | + | 0.865474i | \(0.667017\pi\) | |||||||
\(788\) | 6.00000 | + | 10.3923i | 0.213741 | + | 0.370211i | ||||
\(789\) | 6.00000 | − | 10.3923i | 0.213606 | − | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.0000 | − | 15.5885i | 1.60002 | − | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | − | 1.73205i | 0.0355110 | − | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.0000 | + | 27.7128i | −0.567105 | + | 0.982255i | ||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0000 | 1.27359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 14.0000 | 0.493742 | ||||||||
\(805\) | 12.0000 | + | 10.3923i | 0.422944 | + | 0.366281i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.00000 | − | 15.5885i | 0.316815 | − | 0.548740i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.00000 | − | 15.5885i | −0.316423 | − | 0.548061i | 0.663316 | − | 0.748340i | \(-0.269149\pi\) |
−0.979739 | + | 0.200279i | \(0.935815\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | −24.0000 | − | 20.7846i | −0.842235 | − | 0.729397i | ||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | −12.0000 | − | 20.7846i | −0.420084 | − | 0.727607i | ||||
\(817\) | 2.50000 | − | 4.33013i | 0.0874639 | − | 0.151492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.500000 | − | 2.59808i | 0.0174714 | − | 0.0907841i | ||||
\(820\) | 24.0000 | 0.838116 | ||||||||
\(821\) | 12.0000 | − | 20.7846i | 0.418803 | − | 0.725388i | −0.577016 | − | 0.816733i | \(-0.695783\pi\) |
0.995819 | + | 0.0913446i | \(0.0291165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | + | 34.6410i | 0.697156 | + | 1.20751i | 0.969448 | + | 0.245295i | \(0.0788849\pi\) |
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.00000 | −0.208640 | −0.104320 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104320 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(828\) | 6.00000 | − | 10.3923i | 0.208514 | − | 0.361158i | ||||
\(829\) | 9.50000 | + | 16.4545i | 0.329949 | + | 0.571488i | 0.982501 | − | 0.186256i | \(-0.0596352\pi\) |
−0.652553 | + | 0.757743i | \(0.726302\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.5000 | + | 19.9186i | −0.398931 | + | 0.690968i | ||||
\(832\) | 8.00000 | 0.277350 | ||||||||
\(833\) | −39.0000 | − | 15.5885i | −1.35127 | − | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.00000 | − | 10.3923i | 0.207639 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.50000 | − | 4.33013i | −0.0864126 | − | 0.149671i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.0000 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0000 | + | 20.7846i | 0.413302 | + | 0.715860i | ||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.50000 | − | 28.5788i | 0.188982 | − | 0.981981i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.50000 | + | 9.52628i | −0.188760 | + | 0.326941i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.0000 | + | 36.3731i | 0.719871 | + | 1.24685i | ||||
\(852\) | 12.0000 | − | 20.7846i | 0.411113 | − | 0.712069i | ||||
\(853\) | 17.0000 | 0.582069 | 0.291034 | − | 0.956713i | \(-0.406001\pi\) | ||||
0.291034 | + | 0.956713i | \(0.406001\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.00000 | −0.170996 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0000 | − | 36.3731i | −0.717346 | − | 1.24248i | −0.962048 | − | 0.272882i | \(-0.912023\pi\) |
0.244701 | − | 0.969599i | \(-0.421310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | − | 3.46410i | 0.0682391 | − | 0.118194i | −0.829887 | − | 0.557931i | \(-0.811595\pi\) |
0.898126 | + | 0.439738i | \(0.144929\pi\) | |||||||
\(860\) | −2.00000 | −0.0681994 | ||||||||
\(861\) | −24.0000 | − | 20.7846i | −0.817918 | − | 0.708338i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.00000 | − | 5.19615i | 0.102121 | − | 0.176879i | −0.810437 | − | 0.585826i | \(-0.800770\pi\) |
0.912558 | + | 0.408946i | \(0.134104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.0000 | 0.645274 | ||||||||
\(868\) | 5.00000 | − | 25.9808i | 0.169711 | − | 0.881845i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.50000 | − | 6.06218i | −0.118593 | − | 0.205409i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.00000 | − | 8.66025i | 0.169224 | − | 0.293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.50000 | + | 0.866025i | −0.0845154 | + | 0.0292770i | ||||
\(876\) | −22.0000 | −0.743311 | ||||||||
\(877\) | −1.00000 | + | 1.73205i | −0.0337676 | + | 0.0584872i | −0.882415 | − | 0.470471i | \(-0.844084\pi\) |
0.848648 | + | 0.528958i | \(0.177417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | − | 10.3923i | −0.202375 | − | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.0000 | −1.04323 | −0.521617 | − | 0.853180i | \(-0.674671\pi\) | ||||
−0.521617 | + | 0.853180i | \(0.674671\pi\) | |||||||
\(884\) | −6.00000 | + | 10.3923i | −0.201802 | + | 0.349531i | ||||
\(885\) | −3.00000 | − | 5.19615i | −0.100844 | − | 0.174667i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.00000 | + | 10.3923i | −0.201460 | + | 0.348939i | −0.948999 | − | 0.315279i | \(-0.897902\pi\) |
0.747539 | + | 0.664218i | \(0.231235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.5000 | − | 9.52628i | 0.922320 | − | 0.319501i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.00000 | − | 6.92820i | −0.133930 | − | 0.231973i | ||||
\(893\) | −15.0000 | − | 25.9808i | −0.501956 | − | 0.869413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.0000 | −0.601674 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.0000 | + | 25.9808i | 0.500278 | + | 0.866507i | ||||
\(900\) | 1.00000 | + | 1.73205i | 0.0333333 | + | 0.0577350i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.00000 | + | 1.73205i | 0.0665558 | + | 0.0576390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.50000 | + | 6.06218i | −0.116344 | + | 0.201514i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.5000 | + | 26.8468i | 0.514669 | + | 0.891433i | 0.999855 | + | 0.0170220i | \(0.00541854\pi\) |
−0.485186 | + | 0.874411i | \(0.661248\pi\) | |||||||
\(908\) | 12.0000 | − | 20.7846i | 0.398234 | − | 0.689761i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.0000 | −0.596367 | −0.298183 | − | 0.954509i | \(-0.596381\pi\) | ||||
−0.298183 | + | 0.954509i | \(0.596381\pi\) | |||||||
\(912\) | −10.0000 | + | 17.3205i | −0.331133 | + | 0.573539i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.00000 | − | 1.73205i | 0.0330590 | − | 0.0572598i | ||||
\(916\) | −58.0000 | −1.91637 | ||||||||
\(917\) | 3.00000 | − | 15.5885i | 0.0990687 | − | 0.514776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.5000 | + | 40.7032i | −0.775193 | + | 1.34267i | 0.159492 | + | 0.987199i | \(0.449014\pi\) |
−0.934686 | + | 0.355475i | \(0.884319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.50000 | + | 6.06218i | 0.115329 | + | 0.199756i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.0000 | −0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | −0.230159 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.500000 | + | 0.866025i | 0.0164222 | + | 0.0284440i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00000 | − | 10.3923i | 0.196854 | − | 0.340960i | −0.750653 | − | 0.660697i | \(-0.770261\pi\) |
0.947507 | + | 0.319736i | \(0.103594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | + | 34.6410i | 0.163868 | + | 1.13531i | ||||
\(932\) | −12.0000 | −0.393073 | ||||||||
\(933\) | −6.00000 | + | 10.3923i | −0.196431 | + | 0.340229i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.0000 | 0.947389 | 0.473694 | − | 0.880689i | \(-0.342920\pi\) | ||||
0.473694 | + | 0.880689i | \(0.342920\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.0000 | 0.554774 | ||||||||
\(940\) | −6.00000 | + | 10.3923i | −0.195698 | + | 0.338960i | ||||
\(941\) | 15.0000 | + | 25.9808i | 0.488986 | + | 0.846949i | 0.999920 | − | 0.0126715i | \(-0.00403357\pi\) |
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0000 | + | 62.3538i | −1.17232 | + | 2.03052i | ||||
\(944\) | −24.0000 | −0.781133 | ||||||||
\(945\) | 0.500000 | − | 2.59808i | 0.0162650 | − | 0.0845154i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.0000 | + | 41.5692i | −0.779895 | + | 1.35082i | 0.152106 | + | 0.988364i | \(0.451394\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(948\) | −13.0000 | − | 22.5167i | −0.422220 | − | 0.731307i | ||||
\(949\) | 5.50000 | + | 9.52628i | 0.178538 | + | 0.309236i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000 | 0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.0000 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.00000 | − | 5.19615i | −0.0970777 | − | 0.168144i | ||||
\(956\) | −6.00000 | − | 10.3923i | −0.194054 | − | 0.336111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.0000 | − | 10.3923i | −0.387500 | − | 0.335585i | ||||
\(960\) | 8.00000 | 0.258199 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.00000 | − | 15.5885i | −0.290021 | − | 0.502331i | ||||
\(964\) | 2.00000 | − | 3.46410i | 0.0644157 | − | 0.111571i | ||||
\(965\) | −5.00000 | −0.160956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.0000 | −1.76868 | −0.884340 | − | 0.466843i | \(-0.845391\pi\) | ||||
−0.884340 | + | 0.466843i | \(0.845391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.0000 | − | 25.9808i | −0.481869 | − | 0.834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | − | 20.7846i | 0.385098 | − | 0.667010i | −0.606685 | − | 0.794943i | \(-0.707501\pi\) |
0.991783 | + | 0.127933i | \(0.0408342\pi\) | |||||||
\(972\) | −2.00000 | −0.0641500 | ||||||||
\(973\) | 12.5000 | − | 4.33013i | 0.400732 | − | 0.138817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.500000 | − | 0.866025i | 0.0160128 | − | 0.0277350i | ||||
\(976\) | −4.00000 | − | 6.92820i | −0.128037 | − | 0.221766i | ||||
\(977\) | 6.00000 | + | 10.3923i | 0.191957 | + | 0.332479i | 0.945899 | − | 0.324462i | \(-0.105183\pi\) |
−0.753942 | + | 0.656941i | \(0.771850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 11.0000 | − | 8.66025i | 0.351382 | − | 0.276642i | ||||
\(981\) | −7.00000 | −0.223493 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.00000 | − | 15.5885i | −0.287055 | − | 0.497195i | 0.686050 | − | 0.727554i | \(-0.259343\pi\) |
−0.973106 | + | 0.230360i | \(0.926010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | − | 5.19615i | 0.0955879 | − | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.0000 | − | 5.19615i | 0.477455 | − | 0.165395i | ||||
\(988\) | 10.0000 | 0.318142 | ||||||||
\(989\) | 3.00000 | − | 5.19615i | 0.0953945 | − | 0.165228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5000 | + | 37.2391i | 0.682970 | + | 1.18294i | 0.974070 | + | 0.226246i | \(0.0726454\pi\) |
−0.291100 | + | 0.956693i | \(0.594021\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.0000 | 0.729883 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | −12.0000 | + | 20.7846i | −0.380235 | + | 0.658586i | ||||
\(997\) | 15.5000 | + | 26.8468i | 0.490890 | + | 0.850246i | 0.999945 | − | 0.0104877i | \(-0.00333839\pi\) |
−0.509055 | + | 0.860734i | \(0.670005\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.50000 | − | 6.06218i | 0.110735 | − | 0.191799i |
(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 | 105.2.i.a.16.1 | ✓ | 2 | |
3.2 | odd | 2 | 315.2.j.b.226.1 | 2 | |||
4.3 | odd | 2 | 1680.2.bg.m.961.1 | 2 | |||
5.2 | odd | 4 | 525.2.r.b.499.1 | 4 | |||
5.3 | odd | 4 | 525.2.r.b.499.2 | 4 | |||
5.4 | even | 2 | 525.2.i.c.226.1 | 2 | |||
7.2 | even | 3 | 735.2.a.e.1.1 | 1 | |||
7.3 | odd | 6 | 735.2.i.c.361.1 | 2 | |||
7.4 | even | 3 | inner | 105.2.i.a.46.1 | yes | 2 | |
7.5 | odd | 6 | 735.2.a.d.1.1 | 1 | |||
7.6 | odd | 2 | 735.2.i.c.226.1 | 2 | |||
21.2 | odd | 6 | 2205.2.a.f.1.1 | 1 | |||
21.5 | even | 6 | 2205.2.a.d.1.1 | 1 | |||
21.11 | odd | 6 | 315.2.j.b.46.1 | 2 | |||
28.11 | odd | 6 | 1680.2.bg.m.1201.1 | 2 | |||
35.4 | even | 6 | 525.2.i.c.151.1 | 2 | |||
35.9 | even | 6 | 3675.2.a.h.1.1 | 1 | |||
35.18 | odd | 12 | 525.2.r.b.424.1 | 4 | |||
35.19 | odd | 6 | 3675.2.a.i.1.1 | 1 | |||
35.32 | odd | 12 | 525.2.r.b.424.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.a.16.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
105.2.i.a.46.1 | yes | 2 | 7.4 | even | 3 | inner | |
315.2.j.b.46.1 | 2 | 21.11 | odd | 6 | |||
315.2.j.b.226.1 | 2 | 3.2 | odd | 2 | |||
525.2.i.c.151.1 | 2 | 35.4 | even | 6 | |||
525.2.i.c.226.1 | 2 | 5.4 | even | 2 | |||
525.2.r.b.424.1 | 4 | 35.18 | odd | 12 | |||
525.2.r.b.424.2 | 4 | 35.32 | odd | 12 | |||
525.2.r.b.499.1 | 4 | 5.2 | odd | 4 | |||
525.2.r.b.499.2 | 4 | 5.3 | odd | 4 | |||
735.2.a.d.1.1 | 1 | 7.5 | odd | 6 | |||
735.2.a.e.1.1 | 1 | 7.2 | even | 3 | |||
735.2.i.c.226.1 | 2 | 7.6 | odd | 2 | |||
735.2.i.c.361.1 | 2 | 7.3 | odd | 6 | |||
1680.2.bg.m.961.1 | 2 | 4.3 | odd | 2 | |||
1680.2.bg.m.1201.1 | 2 | 28.11 | odd | 6 | |||
2205.2.a.d.1.1 | 1 | 21.5 | even | 6 | |||
2205.2.a.f.1.1 | 1 | 21.2 | odd | 6 | |||
3675.2.a.h.1.1 | 1 | 35.9 | even | 6 | |||
3675.2.a.i.1.1 | 1 | 35.19 | odd | 6 |