Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.60787333789\) |
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 | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.67 |
Dual form | 1078.2.e.k.177.1 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | + | 5.19615i | −0.727607 | + | 1.26025i | 0.230285 | + | 0.973123i | \(0.426034\pi\) |
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | −1.00000 | + | 1.73205i | −0.235702 | + | 0.408248i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 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 | \(0.618211\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0.500000 | + | 0.866025i | 0.0980581 | + | 0.169842i | ||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.00000 | 1.67126 | 0.835629 | − | 0.549294i | \(-0.185103\pi\) | ||||
0.835629 | + | 0.549294i | \(0.185103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −1.00000 | − | 1.73205i | −0.164399 | − | 0.284747i | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | −1.00000 | + | 1.73205i | −0.162221 | + | 0.280976i | ||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | 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 | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 3.00000 | + | 5.19615i | 0.420084 | + | 0.727607i | ||||
\(52\) | −0.500000 | + | 0.866025i | −0.0693375 | + | 0.120096i | ||||
\(53\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(54\) | 2.50000 | + | 4.33013i | 0.340207 | + | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 4.50000 | + | 7.79423i | 0.590879 | + | 1.02343i | ||||
\(59\) | −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 | ||||||||
\(61\) | 5.50000 | + | 9.52628i | 0.704203 | + | 1.21972i | 0.966978 | + | 0.254858i | \(0.0820288\pi\) |
−0.262776 | + | 0.964857i | \(0.584638\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.500000 | − | 0.866025i | 0.0615457 | − | 0.106600i | ||||
\(67\) | −5.50000 | + | 9.52628i | −0.671932 | + | 1.16382i | 0.305424 | + | 0.952217i | \(0.401202\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | −3.00000 | − | 5.19615i | −0.363803 | − | 0.630126i | ||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −1.00000 | − | 1.73205i | −0.117851 | − | 0.204124i | ||||
\(73\) | 1.00000 | − | 1.73205i | 0.117041 | − | 0.202721i | −0.801553 | − | 0.597924i | \(-0.795992\pi\) |
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | −2.50000 | − | 4.33013i | −0.288675 | − | 0.500000i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −2.50000 | − | 4.33013i | −0.281272 | − | 0.487177i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.971698 | + | 0.236225i | \(0.924090\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.00000 | + | 5.19615i | 0.331295 | + | 0.573819i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 4.50000 | − | 7.79423i | 0.482451 | − | 0.835629i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −9.00000 | − | 15.5885i | −0.953998 | − | 1.65237i | −0.736644 | − | 0.676280i | \(-0.763591\pi\) |
−0.217354 | − | 0.976093i | \(-0.569742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | 2.00000 | + | 3.46410i | 0.207390 | + | 0.359211i | ||||
\(94\) | 3.00000 | − | 5.19615i | 0.309426 | − | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 13.0000 | 1.31995 | 0.659975 | − | 0.751288i | \(-0.270567\pi\) | ||||
0.659975 | + | 0.751288i | \(0.270567\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | −7.50000 | + | 12.9904i | −0.746278 | + | 1.29259i | 0.203317 | + | 0.979113i | \(0.434828\pi\) |
−0.949595 | + | 0.313478i | \(0.898506\pi\) | |||||||
\(102\) | −3.00000 | + | 5.19615i | −0.297044 | + | 0.514496i | ||||
\(103\) | −8.00000 | − | 13.8564i | −0.788263 | − | 1.36531i | −0.927030 | − | 0.374987i | \(-0.877647\pi\) |
0.138767 | − | 0.990325i | \(-0.455686\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | − | 10.3923i | −0.580042 | − | 1.00466i | −0.995474 | − | 0.0950377i | \(-0.969703\pi\) |
0.415432 | − | 0.909624i | \(-0.363630\pi\) | |||||||
\(108\) | −2.50000 | + | 4.33013i | −0.240563 | + | 0.416667i | ||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | 1.00000 | + | 1.73205i | 0.0936586 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.50000 | + | 7.79423i | −0.417815 | + | 0.723676i | ||||
\(117\) | 1.00000 | + | 1.73205i | 0.0924500 | + | 0.160128i | ||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −5.50000 | + | 9.52628i | −0.497947 | + | 0.862469i | ||||
\(123\) | 3.00000 | − | 5.19615i | 0.270501 | − | 0.468521i | ||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −2.00000 | + | 3.46410i | −0.176090 | + | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.0000 | −0.950255 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | − | 5.19615i | 0.257248 | − | 0.445566i | ||||
\(137\) | 4.50000 | − | 7.79423i | 0.384461 | − | 0.665906i | −0.607233 | − | 0.794524i | \(-0.707721\pi\) |
0.991694 | + | 0.128618i | \(0.0410540\pi\) | |||||||
\(138\) | 3.00000 | + | 5.19615i | 0.255377 | + | 0.442326i | ||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.500000 | − | 0.866025i | 0.0418121 | − | 0.0724207i | ||||
\(144\) | 1.00000 | − | 1.73205i | 0.0833333 | − | 0.144338i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 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 | \(0.912374\pi\) | |||||||
\(150\) | 2.50000 | − | 4.33013i | 0.204124 | − | 0.353553i | ||||
\(151\) | 9.50000 | − | 16.4545i | 0.773099 | − | 1.33905i | −0.162758 | − | 0.986666i | \(-0.552039\pi\) |
0.935857 | − | 0.352381i | \(-0.114628\pi\) | |||||||
\(152\) | −1.00000 | − | 1.73205i | −0.0811107 | − | 0.140488i | ||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.500000 | + | 0.866025i | 0.0400320 | + | 0.0693375i | ||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | 2.50000 | − | 4.33013i | 0.198889 | − | 0.344486i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −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 | ||||
\(167\) | −3.00000 | −0.232147 | −0.116073 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116073 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | + | 3.46410i | −0.152944 | + | 0.264906i | ||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | −10.5000 | − | 18.1865i | −0.798300 | − | 1.38270i | −0.920722 | − | 0.390218i | \(-0.872399\pi\) |
0.122422 | − | 0.992478i | \(-0.460934\pi\) | |||||||
\(174\) | 9.00000 | 0.682288 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 1.50000 | + | 2.59808i | 0.112747 | + | 0.195283i | ||||
\(178\) | 9.00000 | − | 15.5885i | 0.674579 | − | 1.16840i | ||||
\(179\) | 7.50000 | − | 12.9904i | 0.560576 | − | 0.970947i | −0.436870 | − | 0.899525i | \(-0.643913\pi\) |
0.997446 | − | 0.0714220i | \(-0.0227537\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0000 | 0.813143 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.00000 | + | 3.46410i | −0.146647 | + | 0.254000i | ||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | − | 5.19615i | −0.217072 | − | 0.375980i | 0.736839 | − | 0.676068i | \(-0.236317\pi\) |
−0.953912 | + | 0.300088i | \(0.902984\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −7.00000 | + | 12.1244i | −0.503871 | + | 0.872730i | 0.496119 | + | 0.868255i | \(0.334758\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | 6.50000 | + | 11.2583i | 0.466673 | + | 0.808301i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | 1.00000 | + | 1.73205i | 0.0710669 | + | 0.123091i | ||||
\(199\) | 7.00000 | − | 12.1244i | 0.496217 | − | 0.859473i | −0.503774 | − | 0.863836i | \(-0.668055\pi\) |
0.999990 | + | 0.00436292i | \(0.00138876\pi\) | |||||||
\(200\) | −2.50000 | + | 4.33013i | −0.176777 | + | 0.306186i | ||||
\(201\) | 5.50000 | + | 9.52628i | 0.387940 | + | 0.671932i | ||||
\(202\) | −15.0000 | −1.05540 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.00000 | − | 13.8564i | 0.557386 | − | 0.965422i | ||||
\(207\) | −6.00000 | + | 10.3923i | −0.417029 | + | 0.722315i | ||||
\(208\) | −0.500000 | − | 0.866025i | −0.0346688 | − | 0.0600481i | ||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | −0.688428 | −0.344214 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344214 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | −1.00000 | − | 1.73205i | −0.0675737 | − | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | −1.00000 | − | 1.73205i | −0.0671156 | − | 0.116248i | ||||
\(223\) | −26.0000 | −1.74109 | −0.870544 | − | 0.492090i | \(-0.836233\pi\) | ||||
−0.870544 | + | 0.492090i | \(0.836233\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.0000 | 0.666667 | ||||||||
\(226\) | 4.50000 | + | 7.79423i | 0.299336 | + | 0.518464i | ||||
\(227\) | 9.00000 | − | 15.5885i | 0.597351 | − | 1.03464i | −0.395860 | − | 0.918311i | \(-0.629553\pi\) |
0.993210 | − | 0.116331i | \(-0.0371134\pi\) | |||||||
\(228\) | −1.00000 | + | 1.73205i | −0.0662266 | + | 0.114708i | ||||
\(229\) | −8.00000 | − | 13.8564i | −0.528655 | − | 0.915657i | −0.999442 | − | 0.0334101i | \(-0.989363\pi\) |
0.470787 | − | 0.882247i | \(-0.343970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.00000 | −0.590879 | ||||||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | −1.00000 | + | 1.73205i | −0.0653720 | + | 0.113228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.50000 | − | 2.59808i | −0.0976417 | − | 0.169120i | ||||
\(237\) | −5.00000 | −0.324785 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.00000 | −0.582162 | −0.291081 | − | 0.956698i | \(-0.594015\pi\) | ||||
−0.291081 | + | 0.956698i | \(0.594015\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0000 | − | 22.5167i | 0.837404 | − | 1.45043i | −0.0546547 | − | 0.998505i | \(-0.517406\pi\) |
0.892058 | − | 0.451920i | \(-0.149261\pi\) | |||||||
\(242\) | 0.500000 | − | 0.866025i | 0.0321412 | − | 0.0556702i | ||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | −11.0000 | −0.704203 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | 1.00000 | + | 1.73205i | 0.0636285 | + | 0.110208i | ||||
\(248\) | 2.00000 | − | 3.46410i | 0.127000 | − | 0.219971i | ||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | −3.50000 | − | 6.06218i | −0.219610 | − | 0.380375i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.50000 | + | 2.59808i | 0.0935674 | + | 0.162064i | 0.909010 | − | 0.416775i | \(-0.136840\pi\) |
−0.815442 | + | 0.578838i | \(0.803506\pi\) | |||||||
\(258\) | −4.00000 | −0.249029 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00000 | + | 15.5885i | 0.557086 | + | 0.964901i | ||||
\(262\) | −9.00000 | + | 15.5885i | −0.556022 | + | 0.963058i | ||||
\(263\) | 4.50000 | − | 7.79423i | 0.277482 | − | 0.480613i | −0.693276 | − | 0.720672i | \(-0.743833\pi\) |
0.970758 | + | 0.240059i | \(0.0771668\pi\) | |||||||
\(264\) | 0.500000 | + | 0.866025i | 0.0307729 | + | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.0000 | −1.10158 | ||||||||
\(268\) | −5.50000 | − | 9.52628i | −0.335966 | − | 0.581910i | ||||
\(269\) | 6.00000 | − | 10.3923i | 0.365826 | − | 0.633630i | −0.623082 | − | 0.782157i | \(-0.714120\pi\) |
0.988908 | + | 0.148527i | \(0.0474530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5000 | + | 25.1147i | 0.880812 | + | 1.52561i | 0.850439 | + | 0.526073i | \(0.176336\pi\) |
0.0303728 | + | 0.999539i | \(0.490331\pi\) | |||||||
\(272\) | 6.00000 | 0.363803 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | −2.50000 | − | 4.33013i | −0.150756 | − | 0.261116i | ||||
\(276\) | −3.00000 | + | 5.19615i | −0.180579 | + | 0.312772i | ||||
\(277\) | −14.5000 | + | 25.1147i | −0.871221 | + | 1.50900i | −0.0104855 | + | 0.999945i | \(0.503338\pi\) |
−0.860735 | + | 0.509053i | \(0.829996\pi\) | |||||||
\(278\) | −4.00000 | − | 6.92820i | −0.239904 | − | 0.415526i | ||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | −3.00000 | − | 5.19615i | −0.178647 | − | 0.309426i | ||||
\(283\) | −5.00000 | + | 8.66025i | −0.297219 | + | 0.514799i | −0.975499 | − | 0.220005i | \(-0.929393\pi\) |
0.678280 | + | 0.734804i | \(0.262726\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.00000 | 0.0591312 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.00000 | 0.117851 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.50000 | − | 11.2583i | 0.381037 | − | 0.659975i | ||||
\(292\) | 1.00000 | + | 1.73205i | 0.0585206 | + | 0.101361i | ||||
\(293\) | 30.0000 | 1.75262 | 0.876309 | − | 0.481749i | \(-0.159998\pi\) | ||||
0.876309 | + | 0.481749i | \(0.159998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000 | + | 1.73205i | 0.0581238 | + | 0.100673i | ||||
\(297\) | 2.50000 | − | 4.33013i | 0.145065 | − | 0.251259i | ||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 5.00000 | 0.288675 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.0000 | 1.09333 | ||||||||
\(303\) | 7.50000 | + | 12.9904i | 0.430864 | + | 0.746278i | ||||
\(304\) | 1.00000 | − | 1.73205i | 0.0573539 | − | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.00000 | − | 10.3923i | −0.342997 | − | 0.594089i | ||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.0000 | −0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | −0.500000 | + | 0.866025i | −0.0283069 | + | 0.0490290i | ||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | 0.281272 | ||||||||
\(317\) | −6.00000 | − | 10.3923i | −0.336994 | − | 0.583690i | 0.646872 | − | 0.762598i | \(-0.276077\pi\) |
−0.983866 | + | 0.178908i | \(0.942743\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | − | 7.79423i | 0.251952 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 2.50000 | − | 4.33013i | 0.138675 | − | 0.240192i | ||||
\(326\) | 8.50000 | − | 14.7224i | 0.470771 | − | 0.815400i | ||||
\(327\) | 1.00000 | + | 1.73205i | 0.0553001 | + | 0.0957826i | ||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.5000 | − | 30.3109i | −0.961887 | − | 1.66604i | −0.717756 | − | 0.696295i | \(-0.754831\pi\) |
−0.244131 | − | 0.969742i | \(-0.578503\pi\) | |||||||
\(332\) | −3.00000 | + | 5.19615i | −0.164646 | + | 0.285176i | ||||
\(333\) | 2.00000 | − | 3.46410i | 0.109599 | − | 0.189832i | ||||
\(334\) | −1.50000 | − | 2.59808i | −0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 4.50000 | − | 7.79423i | 0.244406 | − | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | + | 3.46410i | 0.108306 | + | 0.187592i | ||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5000 | − | 18.1865i | 0.564483 | − | 0.977714i | ||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 4.50000 | + | 7.79423i | 0.241225 | + | 0.417815i | ||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | −9.00000 | + | 15.5885i | −0.479022 | + | 0.829690i | −0.999711 | − | 0.0240566i | \(-0.992342\pi\) |
0.520689 | + | 0.853746i | \(0.325675\pi\) | |||||||
\(354\) | −1.50000 | + | 2.59808i | −0.0797241 | + | 0.138086i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.0000 | 0.953998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.0000 | 0.792775 | ||||||||
\(359\) | 1.50000 | + | 2.59808i | 0.0791670 | + | 0.137121i | 0.902891 | − | 0.429870i | \(-0.141441\pi\) |
−0.823724 | + | 0.566991i | \(0.808107\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −1.00000 | − | 1.73205i | −0.0525588 | − | 0.0910346i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.50000 | + | 9.52628i | 0.287490 | + | 0.497947i | ||||
\(367\) | −5.00000 | + | 8.66025i | −0.260998 | + | 0.452062i | −0.966507 | − | 0.256639i | \(-0.917385\pi\) |
0.705509 | + | 0.708700i | \(0.250718\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 6.00000 | + | 10.3923i | 0.312348 | + | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.00000 | −0.207390 | ||||||||
\(373\) | 15.5000 | + | 26.8468i | 0.802560 | + | 1.39007i | 0.917926 | + | 0.396751i | \(0.129862\pi\) |
−0.115367 | + | 0.993323i | \(0.536804\pi\) | |||||||
\(374\) | −3.00000 | + | 5.19615i | −0.155126 | + | 0.268687i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | + | 5.19615i | 0.154713 | + | 0.267971i | ||||
\(377\) | 9.00000 | 0.463524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0000 | 1.18143 | 0.590715 | − | 0.806880i | \(-0.298846\pi\) | ||||
0.590715 | + | 0.806880i | \(0.298846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.50000 | + | 6.06218i | −0.179310 | + | 0.310575i | ||||
\(382\) | 3.00000 | − | 5.19615i | 0.153493 | − | 0.265858i | ||||
\(383\) | −18.0000 | − | 31.1769i | −0.919757 | − | 1.59307i | −0.799783 | − | 0.600289i | \(-0.795052\pi\) |
−0.119974 | − | 0.992777i | \(-0.538281\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | −4.00000 | − | 6.92820i | −0.203331 | − | 0.352180i | ||||
\(388\) | −6.50000 | + | 11.2583i | −0.329988 | + | 0.571555i | ||||
\(389\) | −6.00000 | + | 10.3923i | −0.304212 | + | 0.526911i | −0.977086 | − | 0.212847i | \(-0.931726\pi\) |
0.672874 | + | 0.739758i | \(0.265060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.0000 | −1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | −1.50000 | − | 2.59808i | −0.0755689 | − | 0.130889i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | + | 1.73205i | −0.0502519 | + | 0.0870388i | ||||
\(397\) | −11.0000 | − | 19.0526i | −0.552074 | − | 0.956221i | −0.998125 | − | 0.0612128i | \(-0.980503\pi\) |
0.446051 | − | 0.895008i | \(-0.352830\pi\) | |||||||
\(398\) | 14.0000 | 0.701757 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 16.5000 | + | 28.5788i | 0.823971 | + | 1.42716i | 0.902703 | + | 0.430263i | \(0.141579\pi\) |
−0.0787327 | + | 0.996896i | \(0.525087\pi\) | |||||||
\(402\) | −5.50000 | + | 9.52628i | −0.274315 | + | 0.475128i | ||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | −7.50000 | − | 12.9904i | −0.373139 | − | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.00000 | −0.0991363 | ||||||||
\(408\) | −3.00000 | − | 5.19615i | −0.148522 | − | 0.257248i | ||||
\(409\) | −2.00000 | + | 3.46410i | −0.0988936 | + | 0.171289i | −0.911227 | − | 0.411905i | \(-0.864864\pi\) |
0.812333 | + | 0.583193i | \(0.198197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.50000 | − | 7.79423i | −0.221969 | − | 0.384461i | ||||
\(412\) | 16.0000 | 0.788263 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.0000 | −0.589768 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | − | 0.866025i | 0.0245145 | − | 0.0424604i | ||||
\(417\) | −4.00000 | + | 6.92820i | −0.195881 | + | 0.339276i | ||||
\(418\) | 1.00000 | + | 1.73205i | 0.0489116 | + | 0.0847174i | ||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0000 | −1.36464 | −0.682318 | − | 0.731055i | \(-0.739028\pi\) | ||||
−0.682318 | + | 0.731055i | \(0.739028\pi\) | |||||||
\(422\) | −5.00000 | − | 8.66025i | −0.243396 | − | 0.421575i | ||||
\(423\) | 6.00000 | − | 10.3923i | 0.291730 | − | 0.505291i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.0000 | + | 25.9808i | 0.727607 | + | 1.26025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | −0.500000 | − | 0.866025i | −0.0241402 | − | 0.0418121i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.50000 | − | 2.59808i | 0.0722525 | − | 0.125145i | −0.827636 | − | 0.561266i | \(-0.810315\pi\) |
0.899888 | + | 0.436121i | \(0.143648\pi\) | |||||||
\(432\) | −2.50000 | − | 4.33013i | −0.120281 | − | 0.208333i | ||||
\(433\) | 34.0000 | 1.63394 | 0.816968 | − | 0.576683i | \(-0.195653\pi\) | ||||
0.816968 | + | 0.576683i | \(0.195653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | −6.00000 | + | 10.3923i | −0.287019 | + | 0.497131i | ||||
\(438\) | 1.00000 | − | 1.73205i | 0.0477818 | − | 0.0827606i | ||||
\(439\) | −0.500000 | − | 0.866025i | −0.0238637 | − | 0.0413331i | 0.853847 | − | 0.520524i | \(-0.174263\pi\) |
−0.877711 | + | 0.479191i | \(0.840930\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | 1.00000 | − | 1.73205i | 0.0474579 | − | 0.0821995i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.0000 | − | 22.5167i | −0.615568 | − | 1.06619i | ||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 5.00000 | + | 8.66025i | 0.235702 | + | 0.408248i | ||||
\(451\) | 3.00000 | − | 5.19615i | 0.141264 | − | 0.244677i | ||||
\(452\) | −4.50000 | + | 7.79423i | −0.211662 | + | 0.366610i | ||||
\(453\) | −9.50000 | − | 16.4545i | −0.446349 | − | 0.773099i | ||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 11.0000 | + | 19.0526i | 0.514558 | + | 0.891241i | 0.999857 | + | 0.0168929i | \(0.00537742\pi\) |
−0.485299 | + | 0.874348i | \(0.661289\pi\) | |||||||
\(458\) | 8.00000 | − | 13.8564i | 0.373815 | − | 0.647467i | ||||
\(459\) | −15.0000 | + | 25.9808i | −0.700140 | + | 1.21268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.0000 | −0.978068 | −0.489034 | − | 0.872265i | \(-0.662651\pi\) | ||||
−0.489034 | + | 0.872265i | \(0.662651\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.0000 | −1.02243 | −0.511213 | − | 0.859454i | \(-0.670804\pi\) | ||||
−0.511213 | + | 0.859454i | \(0.670804\pi\) | |||||||
\(464\) | −4.50000 | − | 7.79423i | −0.208907 | − | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | 6.00000 | + | 10.3923i | 0.277647 | + | 0.480899i | 0.970799 | − | 0.239892i | \(-0.0771121\pi\) |
−0.693153 | + | 0.720791i | \(0.743779\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.00000 | + | 3.46410i | 0.0921551 | + | 0.159617i | ||||
\(472\) | 1.50000 | − | 2.59808i | 0.0690431 | − | 0.119586i | ||||
\(473\) | −2.00000 | + | 3.46410i | −0.0919601 | + | 0.159280i | ||||
\(474\) | −2.50000 | − | 4.33013i | −0.114829 | − | 0.198889i | ||||
\(475\) | 10.0000 | 0.458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.50000 | − | 7.79423i | −0.205825 | − | 0.356500i | ||||
\(479\) | 7.50000 | − | 12.9904i | 0.342684 | − | 0.593546i | −0.642246 | − | 0.766498i | \(-0.721997\pi\) |
0.984930 | + | 0.172953i | \(0.0553307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00000 | − | 1.73205i | −0.0455961 | − | 0.0789747i | ||||
\(482\) | 26.0000 | 1.18427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.00000 | + | 13.8564i | −0.362887 | + | 0.628539i | ||||
\(487\) | −10.0000 | + | 17.3205i | −0.453143 | + | 0.784867i | −0.998579 | − | 0.0532853i | \(-0.983031\pi\) |
0.545436 | + | 0.838152i | \(0.316364\pi\) | |||||||
\(488\) | −5.50000 | − | 9.52628i | −0.248973 | − | 0.431234i | ||||
\(489\) | −17.0000 | −0.768767 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.0000 | 1.89543 | 0.947717 | − | 0.319113i | \(-0.103385\pi\) | ||||
0.947717 | + | 0.319113i | \(0.103385\pi\) | |||||||
\(492\) | 3.00000 | + | 5.19615i | 0.135250 | + | 0.234261i | ||||
\(493\) | −27.0000 | + | 46.7654i | −1.21602 | + | 2.10621i | ||||
\(494\) | −1.00000 | + | 1.73205i | −0.0449921 | + | 0.0779287i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.00000 | 0.268866 | ||||||||
\(499\) | 20.0000 | + | 34.6410i | 0.895323 | + | 1.55074i | 0.833404 | + | 0.552664i | \(0.186389\pi\) |
0.0619186 | + | 0.998081i | \(0.480278\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.50000 | + | 2.59808i | −0.0670151 | + | 0.116073i | ||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | 33.0000 | 1.47140 | 0.735699 | − | 0.677309i | \(-0.236854\pi\) | ||||
0.735699 | + | 0.677309i | \(0.236854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00000 | + | 5.19615i | 0.133366 | + | 0.230997i | ||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | 3.50000 | − | 6.06218i | 0.155287 | − | 0.268966i | ||||
\(509\) | −3.00000 | − | 5.19615i | −0.132973 | − | 0.230315i | 0.791849 | − | 0.610718i | \(-0.209119\pi\) |
−0.924821 | + | 0.380402i | \(0.875786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.00000 | + | 8.66025i | 0.220755 | + | 0.382360i | ||||
\(514\) | −1.50000 | + | 2.59808i | −0.0661622 | + | 0.114596i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.00000 | − | 3.46410i | −0.0880451 | − | 0.152499i | ||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.0000 | −0.921798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0000 | + | 36.3731i | −0.920027 | + | 1.59353i | −0.120656 | + | 0.992694i | \(0.538500\pi\) |
−0.799370 | + | 0.600839i | \(0.794833\pi\) | |||||||
\(522\) | −9.00000 | + | 15.5885i | −0.393919 | + | 0.682288i | ||||
\(523\) | −8.00000 | − | 13.8564i | −0.349816 | − | 0.605898i | 0.636401 | − | 0.771358i | \(-0.280422\pi\) |
−0.986216 | + | 0.165460i | \(0.947089\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.00000 | 0.392419 | ||||||||
\(527\) | −12.0000 | − | 20.7846i | −0.522728 | − | 0.905392i | ||||
\(528\) | −0.500000 | + | 0.866025i | −0.0217597 | + | 0.0376889i | ||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | 0.259889 | ||||||||
\(534\) | −9.00000 | − | 15.5885i | −0.389468 | − | 0.674579i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.50000 | − | 9.52628i | 0.237564 | − | 0.411473i | ||||
\(537\) | −7.50000 | − | 12.9904i | −0.323649 | − | 0.560576i | ||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | + | 21.6506i | 0.537417 | + | 0.930834i | 0.999042 | + | 0.0437584i | \(0.0139332\pi\) |
−0.461625 | + | 0.887075i | \(0.652733\pi\) | |||||||
\(542\) | −14.5000 | + | 25.1147i | −0.622828 | + | 1.07877i | ||||
\(543\) | −1.00000 | + | 1.73205i | −0.0429141 | + | 0.0743294i | ||||
\(544\) | 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 | \(0.704275\pi\) | |||||||
\(548\) | 4.50000 | + | 7.79423i | 0.192230 | + | 0.332953i | ||||
\(549\) | −11.0000 | + | 19.0526i | −0.469469 | + | 0.813143i | ||||
\(550\) | 2.50000 | − | 4.33013i | 0.106600 | − | 0.184637i | ||||
\(551\) | 9.00000 | + | 15.5885i | 0.383413 | + | 0.664091i | ||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −29.0000 | −1.23209 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.00000 | − | 6.92820i | 0.169638 | − | 0.293821i | ||||
\(557\) | 9.00000 | − | 15.5885i | 0.381342 | − | 0.660504i | −0.609912 | − | 0.792469i | \(-0.708795\pi\) |
0.991254 | + | 0.131965i | \(0.0421286\pi\) | |||||||
\(558\) | −4.00000 | − | 6.92820i | −0.169334 | − | 0.293294i | ||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.00000 | 0.253320 | ||||||||
\(562\) | 9.00000 | + | 15.5885i | 0.379642 | + | 0.657559i | ||||
\(563\) | −9.00000 | + | 15.5885i | −0.379305 | + | 0.656975i | −0.990961 | − | 0.134148i | \(-0.957170\pi\) |
0.611656 | + | 0.791123i | \(0.290503\pi\) | |||||||
\(564\) | 3.00000 | − | 5.19615i | 0.126323 | − | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.0000 | −0.420331 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.0000 | + | 31.1769i | 0.754599 | + | 1.30700i | 0.945573 | + | 0.325409i | \(0.105502\pi\) |
−0.190974 | + | 0.981595i | \(0.561165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | 0.500000 | + | 0.866025i | 0.0209061 | + | 0.0362103i | ||||
\(573\) | −6.00000 | −0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.0000 | 1.25109 | ||||||||
\(576\) | 1.00000 | + | 1.73205i | 0.0416667 | + | 0.0721688i | ||||
\(577\) | −3.50000 | + | 6.06218i | −0.145707 | + | 0.252372i | −0.929636 | − | 0.368478i | \(-0.879879\pi\) |
0.783930 | + | 0.620850i | \(0.213212\pi\) | |||||||
\(578\) | 9.50000 | − | 16.4545i | 0.395148 | − | 0.684416i | ||||
\(579\) | 7.00000 | + | 12.1244i | 0.290910 | + | 0.503871i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 13.0000 | 0.538867 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.00000 | + | 1.73205i | −0.0413803 | + | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.0000 | + | 25.9808i | 0.619644 | + | 1.07326i | ||||
\(587\) | −9.00000 | −0.371470 | −0.185735 | − | 0.982600i | \(-0.559467\pi\) | ||||
−0.185735 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.50000 | + | 2.59808i | −0.0617018 | + | 0.106871i | ||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | 18.0000 | + | 31.1769i | 0.739171 | + | 1.28028i | 0.952869 | + | 0.303383i | \(0.0981160\pi\) |
−0.213697 | + | 0.976900i | \(0.568551\pi\) | |||||||
\(594\) | 5.00000 | 0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | −7.00000 | − | 12.1244i | −0.286491 | − | 0.496217i | ||||
\(598\) | −3.00000 | + | 5.19615i | −0.122679 | + | 0.212486i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 2.50000 | + | 4.33013i | 0.102062 | + | 0.176777i | ||||
\(601\) | −2.00000 | −0.0815817 | −0.0407909 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407909 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.0000 | −0.895909 | ||||||||
\(604\) | 9.50000 | + | 16.4545i | 0.386550 | + | 0.669523i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.50000 | + | 12.9904i | −0.304667 | + | 0.527698i | ||||
\(607\) | −20.0000 | − | 34.6410i | −0.811775 | − | 1.40604i | −0.911621 | − | 0.411033i | \(-0.865168\pi\) |
0.0998457 | − | 0.995003i | \(-0.468165\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | − | 5.19615i | −0.121367 | − | 0.210214i | ||||
\(612\) | 6.00000 | − | 10.3923i | 0.242536 | − | 0.420084i | ||||
\(613\) | 5.00000 | − | 8.66025i | 0.201948 | − | 0.349784i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) |
0.949156 | + | 0.314806i | \(0.101939\pi\) | |||||||
\(614\) | −10.0000 | − | 17.3205i | −0.403567 | − | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.0000 | 0.845428 | 0.422714 | − | 0.906263i | \(-0.361077\pi\) | ||||
0.422714 | + | 0.906263i | \(0.361077\pi\) | |||||||
\(618\) | −8.00000 | − | 13.8564i | −0.321807 | − | 0.557386i | ||||
\(619\) | 10.0000 | − | 17.3205i | 0.401934 | − | 0.696170i | −0.592025 | − | 0.805919i | \(-0.701671\pi\) |
0.993959 | + | 0.109749i | \(0.0350048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0000 | + | 25.9808i | 0.601929 | + | 1.04257i | ||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −8.50000 | + | 14.7224i | −0.339728 | + | 0.588427i | ||||
\(627\) | 1.00000 | − | 1.73205i | 0.0399362 | − | 0.0691714i | ||||
\(628\) | −2.00000 | − | 3.46410i | −0.0798087 | − | 0.138233i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 2.50000 | + | 4.33013i | 0.0994447 | + | 0.172243i | ||||
\(633\) | −5.00000 | + | 8.66025i | −0.198732 | + | 0.344214i | ||||
\(634\) | 6.00000 | − | 10.3923i | 0.238290 | − | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.00000 | 0.356313 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | + | 7.79423i | −0.177739 | + | 0.307854i | −0.941106 | − | 0.338112i | \(-0.890212\pi\) |
0.763367 | + | 0.645966i | \(0.223545\pi\) | |||||||
\(642\) | −6.00000 | − | 10.3923i | −0.236801 | − | 0.410152i | ||||
\(643\) | −5.00000 | −0.197181 | −0.0985904 | − | 0.995128i | \(-0.531433\pi\) | ||||
−0.0985904 | + | 0.995128i | \(0.531433\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | −6.00000 | + | 10.3923i | −0.235884 | + | 0.408564i | −0.959529 | − | 0.281609i | \(-0.909132\pi\) |
0.723645 | + | 0.690172i | \(0.242465\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 1.50000 | + | 2.59808i | 0.0588802 | + | 0.101983i | ||||
\(650\) | 5.00000 | 0.196116 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.0000 | 0.665771 | ||||||||
\(653\) | −9.00000 | − | 15.5885i | −0.352197 | − | 0.610023i | 0.634437 | − | 0.772975i | \(-0.281232\pi\) |
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(654\) | −1.00000 | + | 1.73205i | −0.0391031 | + | 0.0677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | − | 5.19615i | −0.117130 | − | 0.202876i | ||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | − | 12.1244i | 0.272268 | − | 0.471583i | −0.697174 | − | 0.716902i | \(-0.745559\pi\) |
0.969442 | + | 0.245319i | \(0.0788928\pi\) | |||||||
\(662\) | 17.5000 | − | 30.3109i | 0.680157 | − | 1.17807i | ||||
\(663\) | 3.00000 | + | 5.19615i | 0.116510 | + | 0.201802i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | 27.0000 | + | 46.7654i | 1.04544 | + | 1.81076i | ||||
\(668\) | 1.50000 | − | 2.59808i | 0.0580367 | − | 0.100523i | ||||
\(669\) | −13.0000 | + | 22.5167i | −0.502609 | + | 0.870544i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.0000 | 0.424650 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0000 | −1.07932 | −0.539660 | − | 0.841883i | \(-0.681447\pi\) | ||||
−0.539660 | + | 0.841883i | \(0.681447\pi\) | |||||||
\(674\) | 7.00000 | + | 12.1244i | 0.269630 | + | 0.467013i | ||||
\(675\) | 12.5000 | − | 21.6506i | 0.481125 | − | 0.833333i | ||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | 3.00000 | + | 5.19615i | 0.115299 | + | 0.199704i | 0.917899 | − | 0.396813i | \(-0.129884\pi\) |
−0.802600 | + | 0.596518i | \(0.796551\pi\) | |||||||
\(678\) | 9.00000 | 0.345643 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | − | 15.5885i | −0.344881 | − | 0.597351i | ||||
\(682\) | −2.00000 | + | 3.46410i | −0.0765840 | + | 0.132647i | ||||
\(683\) | 10.5000 | − | 18.1865i | 0.401771 | − | 0.695888i | −0.592168 | − | 0.805814i | \(-0.701728\pi\) |
0.993940 | + | 0.109926i | \(0.0350613\pi\) | |||||||
\(684\) | −2.00000 | − | 3.46410i | −0.0764719 | − | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.0000 | −0.610438 | ||||||||
\(688\) | 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 | \(-0.0995710\pi\) |
−0.742242 | + | 0.670132i | \(0.766238\pi\) | |||||||
\(692\) | 21.0000 | 0.798300 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.50000 | + | 7.79423i | −0.170572 | + | 0.295439i | ||||
\(697\) | −18.0000 | + | 31.1769i | −0.681799 | + | 1.18091i | ||||
\(698\) | −1.00000 | − | 1.73205i | −0.0378506 | − | 0.0655591i | ||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.0000 | 1.47301 | 0.736505 | − | 0.676432i | \(-0.236475\pi\) | ||||
0.736505 | + | 0.676432i | \(0.236475\pi\) | |||||||
\(702\) | 2.50000 | + | 4.33013i | 0.0943564 | + | 0.163430i | ||||
\(703\) | 2.00000 | − | 3.46410i | 0.0754314 | − | 0.130651i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0000 | −0.677439 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.00000 | −0.112747 | ||||||||
\(709\) | −13.0000 | − | 22.5167i | −0.488225 | − | 0.845631i | 0.511683 | − | 0.859174i | \(-0.329022\pi\) |
−0.999908 | + | 0.0135434i | \(0.995689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.00000 | − | 8.66025i | 0.187515 | − | 0.324785i | ||||
\(712\) | 9.00000 | + | 15.5885i | 0.337289 | + | 0.584202i | ||||
\(713\) | −24.0000 | −0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.50000 | + | 12.9904i | 0.280288 | + | 0.485473i | ||||
\(717\) | −4.50000 | + | 7.79423i | −0.168056 | + | 0.291081i | ||||
\(718\) | −1.50000 | + | 2.59808i | −0.0559795 | + | 0.0969593i | ||||
\(719\) | −21.0000 | − | 36.3731i | −0.783168 | − | 1.35649i | −0.930087 | − | 0.367338i | \(-0.880269\pi\) |
0.146920 | − | 0.989148i | \(-0.453064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.0000 | 0.558242 | ||||||||
\(723\) | −13.0000 | − | 22.5167i | −0.483475 | − | 0.837404i | ||||
\(724\) | 1.00000 | − | 1.73205i | 0.0371647 | − | 0.0643712i | ||||
\(725\) | 22.5000 | − | 38.9711i | 0.835629 | − | 1.44735i | ||||
\(726\) | −0.500000 | − | 0.866025i | −0.0185567 | − | 0.0321412i | ||||
\(727\) | −14.0000 | −0.519231 | −0.259616 | − | 0.965712i | \(-0.583596\pi\) | ||||
−0.259616 | + | 0.965712i | \(0.583596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | − | 20.7846i | 0.443836 | − | 0.768747i | ||||
\(732\) | −5.50000 | + | 9.52628i | −0.203286 | + | 0.352101i | ||||
\(733\) | −12.5000 | − | 21.6506i | −0.461698 | − | 0.799684i | 0.537348 | − | 0.843361i | \(-0.319426\pi\) |
−0.999046 | + | 0.0436764i | \(0.986093\pi\) | |||||||
\(734\) | −10.0000 | −0.369107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 5.50000 | + | 9.52628i | 0.202595 | + | 0.350905i | ||||
\(738\) | −6.00000 | + | 10.3923i | −0.220863 | + | 0.382546i | ||||
\(739\) | −25.0000 | + | 43.3013i | −0.919640 | + | 1.59286i | −0.119677 | + | 0.992813i | \(0.538186\pi\) |
−0.799962 | + | 0.600050i | \(0.795147\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00000 | 0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.0000 | −1.32071 | −0.660356 | − | 0.750953i | \(-0.729595\pi\) | ||||
−0.660356 | + | 0.750953i | \(0.729595\pi\) | |||||||
\(744\) | −2.00000 | − | 3.46410i | −0.0733236 | − | 0.127000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.5000 | + | 26.8468i | −0.567495 | + | 0.982931i | ||||
\(747\) | 6.00000 | + | 10.3923i | 0.219529 | + | 0.380235i | ||||
\(748\) | −6.00000 | −0.219382 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | + | 3.46410i | 0.0729810 | + | 0.126407i | 0.900207 | − | 0.435463i | \(-0.143415\pi\) |
−0.827225 | + | 0.561870i | \(0.810082\pi\) | |||||||
\(752\) | −3.00000 | + | 5.19615i | −0.109399 | + | 0.189484i | ||||
\(753\) | 6.00000 | − | 10.3923i | 0.218652 | − | 0.378717i | ||||
\(754\) | 4.50000 | + | 7.79423i | 0.163880 | + | 0.283849i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.0000 | −1.67190 | −0.835949 | − | 0.548807i | \(-0.815082\pi\) | ||||
−0.835949 | + | 0.548807i | \(0.815082\pi\) | |||||||
\(758\) | 11.5000 | + | 19.9186i | 0.417699 | + | 0.723476i | ||||
\(759\) | 3.00000 | − | 5.19615i | 0.108893 | − | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | − | 15.5885i | −0.326250 | − | 0.565081i | 0.655515 | − | 0.755182i | \(-0.272452\pi\) |
−0.981764 | + | 0.190101i | \(0.939118\pi\) | |||||||
\(762\) | −7.00000 | −0.253583 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0000 | − | 31.1769i | 0.650366 | − | 1.12647i | ||||
\(767\) | −1.50000 | + | 2.59808i | −0.0541619 | + | 0.0938111i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | 0.108042 | ||||||||
\(772\) | −7.00000 | − | 12.1244i | −0.251936 | − | 0.436365i | ||||
\(773\) | 12.0000 | − | 20.7846i | 0.431610 | − | 0.747570i | −0.565402 | − | 0.824815i | \(-0.691279\pi\) |
0.997012 | + | 0.0772449i | \(0.0246123\pi\) | |||||||
\(774\) | 4.00000 | − | 6.92820i | 0.143777 | − | 0.249029i | ||||
\(775\) | 10.0000 | + | 17.3205i | 0.359211 | + | 0.622171i | ||||
\(776\) | −13.0000 | −0.466673 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.0000 | −0.430221 | ||||||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.0000 | − | 31.1769i | −0.643679 | − | 1.11488i | ||||
\(783\) | 45.0000 | 1.60817 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.00000 | + | 15.5885i | 0.321019 | + | 0.556022i | ||||
\(787\) | 7.00000 | − | 12.1244i | 0.249523 | − | 0.432187i | −0.713871 | − | 0.700278i | \(-0.753059\pi\) |
0.963394 | + | 0.268091i | \(0.0863928\pi\) | |||||||
\(788\) | 1.50000 | − | 2.59808i | 0.0534353 | − | 0.0925526i | ||||
\(789\) | −4.50000 | − | 7.79423i | −0.160204 | − | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.00000 | −0.0710669 | ||||||||
\(793\) | 5.50000 | + | 9.52628i | 0.195311 | + | 0.338288i | ||||
\(794\) | 11.0000 | − | 19.0526i | 0.390375 | − | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.00000 | + | 12.1244i | 0.248108 | + | 0.429736i | ||||
\(797\) | 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 | ||||||||
\(800\) | −2.50000 | − | 4.33013i | −0.0883883 | − | 0.153093i | ||||
\(801\) | 18.0000 | − | 31.1769i | 0.635999 | − | 1.10158i | ||||
\(802\) | −16.5000 | + | 28.5788i | −0.582635 | + | 1.00915i | ||||
\(803\) | −1.00000 | − | 1.73205i | −0.0352892 | − | 0.0611227i | ||||
\(804\) | −11.0000 | −0.387940 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | −6.00000 | − | 10.3923i | −0.211210 | − | 0.365826i | ||||
\(808\) | 7.50000 | − | 12.9904i | 0.263849 | − | 0.457000i | ||||
\(809\) | 24.0000 | − | 41.5692i | 0.843795 | − | 1.46150i | −0.0428684 | − | 0.999081i | \(-0.513650\pi\) |
0.886664 | − | 0.462415i | \(-0.153017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.0000 | 1.01707 | ||||||||
\(814\) | −1.00000 | − | 1.73205i | −0.0350500 | − | 0.0607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | −4.00000 | − | 6.92820i | −0.139942 | − | 0.242387i | ||||
\(818\) | −4.00000 | −0.139857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 4.50000 | − | 7.79423i | 0.156956 | − | 0.271855i | ||||
\(823\) | 5.00000 | − | 8.66025i | 0.174289 | − | 0.301877i | −0.765626 | − | 0.643286i | \(-0.777571\pi\) |
0.939915 | + | 0.341409i | \(0.110904\pi\) | |||||||
\(824\) | 8.00000 | + | 13.8564i | 0.278693 | + | 0.482711i | ||||
\(825\) | −5.00000 | −0.174078 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.0000 | 1.04320 | 0.521601 | − | 0.853189i | \(-0.325335\pi\) | ||||
0.521601 | + | 0.853189i | \(0.325335\pi\) | |||||||
\(828\) | −6.00000 | − | 10.3923i | −0.208514 | − | 0.361158i | ||||
\(829\) | −26.0000 | + | 45.0333i | −0.903017 | + | 1.56407i | −0.0794606 | + | 0.996838i | \(0.525320\pi\) |
−0.823557 | + | 0.567234i | \(0.808014\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5000 | + | 25.1147i | 0.502999 | + | 0.871221i | ||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.00000 | −0.277017 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.00000 | + | 1.73205i | −0.0345857 | + | 0.0599042i | ||||
\(837\) | −10.0000 | + | 17.3205i | −0.345651 | + | 0.598684i | ||||
\(838\) | 6.00000 | + | 10.3923i | 0.207267 | + | 0.358996i | ||||
\(839\) | −6.00000 | −0.207143 | −0.103572 | − | 0.994622i | \(-0.533027\pi\) | ||||
−0.103572 | + | 0.994622i | \(0.533027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | −14.0000 | − | 24.2487i | −0.482472 | − | 0.835666i | ||||
\(843\) | 9.00000 | − | 15.5885i | 0.309976 | − | 0.536895i | ||||
\(844\) | 5.00000 | − | 8.66025i | 0.172107 | − | 0.298098i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.0000 | 0.412568 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.00000 | + | 8.66025i | 0.171600 | + | 0.297219i | ||||
\(850\) | −15.0000 | + | 25.9808i | −0.514496 | + | 0.891133i | ||||
\(851\) | 6.00000 | − | 10.3923i | 0.205677 | − | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.0000 | 1.57501 | 0.787505 | − | 0.616308i | \(-0.211372\pi\) | ||||
0.787505 | + | 0.616308i | \(0.211372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | + | 10.3923i | 0.205076 | + | 0.355202i | ||||
\(857\) | 18.0000 | − | 31.1769i | 0.614868 | − | 1.06498i | −0.375539 | − | 0.926806i | \(-0.622542\pi\) |
0.990408 | − | 0.138177i | \(-0.0441242\pi\) | |||||||
\(858\) | 0.500000 | − | 0.866025i | 0.0170697 | − | 0.0295656i | ||||
\(859\) | −18.5000 | − | 32.0429i | −0.631212 | − | 1.09329i | −0.987304 | − | 0.158840i | \(-0.949225\pi\) |
0.356092 | − | 0.934451i | \(-0.384109\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.00000 | 0.102180 | ||||||||
\(863\) | −15.0000 | − | 25.9808i | −0.510606 | − | 0.884395i | −0.999924 | − | 0.0122903i | \(-0.996088\pi\) |
0.489319 | − | 0.872105i | \(-0.337246\pi\) | |||||||
\(864\) | 2.50000 | − | 4.33013i | 0.0850517 | − | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.0000 | + | 29.4449i | 0.577684 | + | 1.00058i | ||||
\(867\) | −19.0000 | −0.645274 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.00000 | −0.169613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.50000 | + | 9.52628i | −0.186360 | + | 0.322786i | ||||
\(872\) | 1.00000 | − | 1.73205i | 0.0338643 | − | 0.0586546i | ||||
\(873\) | 13.0000 | + | 22.5167i | 0.439983 | + | 0.762073i | ||||
\(874\) | −12.0000 | −0.405906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | −8.50000 | − | 14.7224i | −0.287025 | − | 0.497141i | 0.686074 | − | 0.727532i | \(-0.259333\pi\) |
−0.973098 | + | 0.230391i | \(0.925999\pi\) | |||||||
\(878\) | 0.500000 | − | 0.866025i | 0.0168742 | − | 0.0292269i | ||||
\(879\) | 15.0000 | − | 25.9808i | 0.505937 | − | 0.876309i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.0000 | −1.11180 | −0.555899 | − | 0.831250i | \(-0.687626\pi\) | ||||
−0.555899 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | −3.00000 | − | 5.19615i | −0.100901 | − | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.00000 | − | 10.3923i | 0.201574 | − | 0.349136i | ||||
\(887\) | 1.50000 | + | 2.59808i | 0.0503651 | + | 0.0872349i | 0.890109 | − | 0.455748i | \(-0.150628\pi\) |
−0.839744 | + | 0.542983i | \(0.817295\pi\) | |||||||
\(888\) | 2.00000 | 0.0671156 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | 13.0000 | − | 22.5167i | 0.435272 | − | 0.753914i | ||||
\(893\) | 6.00000 | − | 10.3923i | 0.200782 | − | 0.347765i | ||||
\(894\) | −3.00000 | − | 5.19615i | −0.100335 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.00000 | 0.200334 | ||||||||
\(898\) | −9.00000 | − | 15.5885i | −0.300334 | − | 0.520194i | ||||
\(899\) | −18.0000 | + | 31.1769i | −0.600334 | + | 1.03981i | ||||
\(900\) | −5.00000 | + | 8.66025i | −0.166667 | + | 0.288675i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 6.00000 | 0.199778 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.00000 | −0.299336 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.50000 | − | 16.4545i | 0.315616 | − | 0.546664i | ||||
\(907\) | 14.0000 | − | 24.2487i | 0.464862 | − | 0.805165i | −0.534333 | − | 0.845274i | \(-0.679437\pi\) |
0.999195 | + | 0.0401089i | \(0.0127705\pi\) | |||||||
\(908\) | 9.00000 | + | 15.5885i | 0.298675 | + | 0.517321i | ||||
\(909\) | −30.0000 | −0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | −1.00000 | − | 1.73205i | −0.0331133 | − | 0.0573539i | ||||
\(913\) | 3.00000 | − | 5.19615i | 0.0992855 | − | 0.171968i | ||||
\(914\) | −11.0000 | + | 19.0526i | −0.363848 | + | 0.630203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.0000 | 0.528655 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −30.0000 | −0.990148 | ||||||||
\(919\) | −16.0000 | − | 27.7128i | −0.527791 | − | 0.914161i | −0.999475 | − | 0.0323936i | \(-0.989687\pi\) |
0.471684 | − | 0.881768i | \(-0.343646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | + | 17.3205i | −0.329511 | + | 0.570730i | ||||
\(922\) | −10.5000 | − | 18.1865i | −0.345799 | − | 0.598942i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | −11.0000 | − | 19.0526i | −0.361482 | − | 0.626106i | ||||
\(927\) | 16.0000 | − | 27.7128i | 0.525509 | − | 0.910208i | ||||
\(928\) | 4.50000 | − | 7.79423i | 0.147720 | − | 0.255858i | ||||
\(929\) | 19.5000 | + | 33.7750i | 0.639774 | + | 1.10812i | 0.985482 | + | 0.169779i | \(0.0543055\pi\) |
−0.345708 | + | 0.938342i | \(0.612361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | −12.0000 | − | 20.7846i | −0.392862 | − | 0.680458i | ||||
\(934\) | −6.00000 | + | 10.3923i | −0.196326 | + | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00000 | − | 1.73205i | −0.0326860 | − | 0.0566139i | ||||
\(937\) | −8.00000 | −0.261349 | −0.130674 | − | 0.991425i | \(-0.541714\pi\) | ||||
−0.130674 | + | 0.991425i | \(0.541714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.0000 | 0.554774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.50000 | − | 12.9904i | 0.244493 | − | 0.423474i | −0.717496 | − | 0.696563i | \(-0.754712\pi\) |
0.961989 | + | 0.273088i | \(0.0880451\pi\) | |||||||
\(942\) | −2.00000 | + | 3.46410i | −0.0651635 | + | 0.112867i | ||||
\(943\) | 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 | \(0.960840\pi\) | |||||||
\(948\) | 2.50000 | − | 4.33013i | 0.0811962 | − | 0.140636i | ||||
\(949\) | 1.00000 | − | 1.73205i | 0.0324614 | − | 0.0562247i | ||||
\(950\) | 5.00000 | + | 8.66025i | 0.162221 | + | 0.280976i | ||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.50000 | − | 7.79423i | 0.145540 | − | 0.252083i | ||||
\(957\) | −4.50000 | − | 7.79423i | −0.145464 | − | 0.251952i | ||||
\(958\) | 15.0000 | 0.484628 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 1.00000 | − | 1.73205i | 0.0322413 | − | 0.0558436i | ||||
\(963\) | 12.0000 | − | 20.7846i | 0.386695 | − | 0.669775i | ||||
\(964\) | 13.0000 | + | 22.5167i | 0.418702 | + | 0.725213i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.0000 | −1.28631 | −0.643157 | − | 0.765735i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765735i | \(0.722376\pi\) | |||||||
\(968\) | 0.500000 | + | 0.866025i | 0.0160706 | + | 0.0278351i | ||||
\(969\) | −6.00000 | + | 10.3923i | −0.192748 | + | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.50000 | + | 12.9904i | 0.240686 | + | 0.416881i | 0.960910 | − | 0.276861i | \(-0.0892941\pi\) |
−0.720224 | + | 0.693742i | \(0.755961\pi\) | |||||||
\(972\) | −16.0000 | −0.513200 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −20.0000 | −0.640841 | ||||||||
\(975\) | −2.50000 | − | 4.33013i | −0.0800641 | − | 0.138675i | ||||
\(976\) | 5.50000 | − | 9.52628i | 0.176051 | − | 0.304929i | ||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | −8.50000 | − | 14.7224i | −0.271800 | − | 0.470771i | ||||
\(979\) | −18.0000 | −0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | 21.0000 | + | 36.3731i | 0.670137 | + | 1.16071i | ||||
\(983\) | −3.00000 | + | 5.19615i | −0.0956851 | + | 0.165732i | −0.909894 | − | 0.414840i | \(-0.863838\pi\) |
0.814209 | + | 0.580572i | \(0.197171\pi\) | |||||||
\(984\) | −3.00000 | + | 5.19615i | −0.0956365 | + | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −54.0000 | −1.71971 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.00000 | −0.0636285 | ||||||||
\(989\) | −12.0000 | − | 20.7846i | −0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | − | 34.6410i | 0.635321 | − | 1.10041i | −0.351126 | − | 0.936328i | \(-0.614201\pi\) |
0.986447 | − | 0.164080i | \(-0.0524655\pi\) | |||||||
\(992\) | 2.00000 | + | 3.46410i | 0.0635001 | + | 0.109985i | ||||
\(993\) | −35.0000 | −1.11069 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.00000 | + | 5.19615i | 0.0950586 | + | 0.164646i | ||||
\(997\) | −17.0000 | + | 29.4449i | −0.538395 | + | 0.932528i | 0.460595 | + | 0.887610i | \(0.347636\pi\) |
−0.998991 | + | 0.0449179i | \(0.985697\pi\) | |||||||
\(998\) | −20.0000 | + | 34.6410i | −0.633089 | + | 1.09654i | ||||
\(999\) | −5.00000 | − | 8.66025i | −0.158193 | − | 0.273998i |
(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 | 1078.2.e.k.67.1 | 2 | ||
7.2 | even | 3 | inner | 1078.2.e.k.177.1 | 2 | ||
7.3 | odd | 6 | 1078.2.a.e.1.1 | 1 | |||
7.4 | even | 3 | 1078.2.a.c.1.1 | 1 | |||
7.5 | odd | 6 | 154.2.e.c.23.1 | ✓ | 2 | ||
7.6 | odd | 2 | 154.2.e.c.67.1 | yes | 2 | ||
21.5 | even | 6 | 1386.2.k.e.793.1 | 2 | |||
21.11 | odd | 6 | 9702.2.a.bs.1.1 | 1 | |||
21.17 | even | 6 | 9702.2.a.br.1.1 | 1 | |||
21.20 | even | 2 | 1386.2.k.e.991.1 | 2 | |||
28.3 | even | 6 | 8624.2.a.k.1.1 | 1 | |||
28.11 | odd | 6 | 8624.2.a.u.1.1 | 1 | |||
28.19 | even | 6 | 1232.2.q.d.177.1 | 2 | |||
28.27 | even | 2 | 1232.2.q.d.529.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.c.23.1 | ✓ | 2 | 7.5 | odd | 6 | ||
154.2.e.c.67.1 | yes | 2 | 7.6 | odd | 2 | ||
1078.2.a.c.1.1 | 1 | 7.4 | even | 3 | |||
1078.2.a.e.1.1 | 1 | 7.3 | odd | 6 | |||
1078.2.e.k.67.1 | 2 | 1.1 | even | 1 | trivial | ||
1078.2.e.k.177.1 | 2 | 7.2 | even | 3 | inner | ||
1232.2.q.d.177.1 | 2 | 28.19 | even | 6 | |||
1232.2.q.d.529.1 | 2 | 28.27 | even | 2 | |||
1386.2.k.e.793.1 | 2 | 21.5 | even | 6 | |||
1386.2.k.e.991.1 | 2 | 21.20 | even | 2 | |||
8624.2.a.k.1.1 | 1 | 28.3 | even | 6 | |||
8624.2.a.u.1.1 | 1 | 28.11 | odd | 6 | |||
9702.2.a.br.1.1 | 1 | 21.17 | even | 6 | |||
9702.2.a.bs.1.1 | 1 | 21.11 | odd | 6 |