Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(257,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.bc (of order \(6\), 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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.353 |
Dual form | 672.2.bc.a.257.1 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73205 | −1.00000 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | 0.732294 | − | 0.680989i | \(-0.238450\pi\) |
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.33013 | − | 2.50000i | −1.30558 | − | 0.753778i | −0.324227 | − | 0.945979i | \(-0.605104\pi\) |
−0.981356 | + | 0.192201i | \(0.938437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.866025 | + | 1.50000i | 0.223607 | + | 0.387298i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.500000 | + | 0.866025i | −0.121268 | + | 0.210042i | −0.920268 | − | 0.391289i | \(-0.872029\pi\) |
0.799000 | + | 0.601331i | \(0.205363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.866025 | − | 0.500000i | 0.198680 | − | 0.114708i | −0.397360 | − | 0.917663i | \(-0.630073\pi\) |
0.596040 | + | 0.802955i | \(0.296740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | + | 3.46410i | −0.654654 | + | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.33013 | + | 2.50000i | −0.902894 | + | 0.521286i | −0.878138 | − | 0.478407i | \(-0.841214\pi\) |
−0.0247559 | + | 0.999694i | \(0.507881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.46410i | − | 0.643268i | −0.946864 | − | 0.321634i | \(-0.895768\pi\) | ||
0.946864 | − | 0.321634i | \(-0.104232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.79423 | − | 4.50000i | −1.39988 | − | 0.808224i | −0.405505 | − | 0.914093i | \(-0.632904\pi\) |
−0.994380 | + | 0.105869i | \(0.966238\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.50000 | + | 4.33013i | 1.30558 | + | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.59808 | − | 0.500000i | −0.439155 | − | 0.0845154i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | − | 2.59808i | −0.246598 | − | 0.427121i | 0.715981 | − | 0.698119i | \(-0.245980\pi\) |
−0.962580 | + | 0.270998i | \(0.912646\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.00000i | − | 0.960769i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | − | 2.59808i | −0.223607 | − | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.866025 | − | 1.50000i | −0.126323 | − | 0.218797i | 0.795926 | − | 0.605393i | \(-0.206984\pi\) |
−0.922249 | + | 0.386596i | \(0.873651\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.866025 | − | 1.50000i | 0.121268 | − | 0.210042i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5000 | − | 6.06218i | −1.44229 | − | 0.832704i | −0.444284 | − | 0.895886i | \(-0.646542\pi\) |
−0.998002 | + | 0.0631819i | \(0.979875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000i | 0.674200i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.50000 | + | 0.866025i | −0.198680 | + | 0.114708i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.33013 | + | 7.50000i | −0.563735 | + | 0.976417i | 0.433432 | + | 0.901186i | \(0.357303\pi\) |
−0.997166 | + | 0.0752304i | \(0.976031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5000 | + | 6.06218i | −1.34439 | + | 0.776182i | −0.987448 | − | 0.157945i | \(-0.949513\pi\) |
−0.356939 | + | 0.934128i | \(0.616180\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.19615 | − | 6.00000i | 0.654654 | − | 0.755929i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 1.73205i | 0.372104 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.06218 | − | 10.5000i | 0.740613 | − | 1.28278i | −0.211604 | − | 0.977356i | \(-0.567869\pi\) |
0.952217 | − | 0.305424i | \(-0.0987981\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.50000 | − | 4.33013i | 0.902894 | − | 0.521286i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000i | 0.237356i | 0.992933 | + | 0.118678i | \(0.0378657\pi\) | ||||
−0.992933 | + | 0.118678i | \(0.962134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.50000 | + | 4.33013i | 0.877809 | + | 0.506803i | 0.869935 | − | 0.493166i | \(-0.164160\pi\) |
0.00787336 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.46410 | + | 6.00000i | −0.400000 | + | 0.692820i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.5000 | + | 4.33013i | −1.42451 | + | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.866025 | + | 1.50000i | 0.0974355 | + | 0.168763i | 0.910622 | − | 0.413239i | \(-0.135603\pi\) |
−0.813187 | + | 0.582003i | \(0.802269\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.8564 | 1.52094 | 0.760469 | − | 0.649374i | \(-0.224969\pi\) | ||||
0.760469 | + | 0.649374i | \(0.224969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.00000i | 0.643268i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.50000 | + | 11.2583i | 0.688999 | + | 1.19338i | 0.972162 | + | 0.234309i | \(0.0752827\pi\) |
−0.283164 | + | 0.959072i | \(0.591384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.92820 | + | 6.00000i | 0.726273 | + | 0.628971i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.5000 | + | 7.79423i | 1.39988 | + | 0.808224i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.866025 | − | 0.500000i | −0.0888523 | − | 0.0512989i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.46410i | − | 0.351726i | −0.984415 | − | 0.175863i | \(-0.943728\pi\) | ||
0.984415 | − | 0.175863i | \(-0.0562716\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.9904 | − | 7.50000i | −1.30558 | − | 0.753778i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.50000 | − | 6.06218i | 0.348263 | − | 0.603209i | −0.637678 | − | 0.770303i | \(-0.720105\pi\) |
0.985941 | + | 0.167094i | \(0.0534383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.79423 | + | 4.50000i | −0.767988 | + | 0.443398i | −0.832156 | − | 0.554541i | \(-0.812894\pi\) |
0.0641683 | + | 0.997939i | \(0.479561\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.50000 | + | 0.866025i | 0.439155 | + | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.2583 | − | 6.50000i | 1.08838 | − | 0.628379i | 0.155238 | − | 0.987877i | \(-0.450386\pi\) |
0.933146 | + | 0.359498i | \(0.117052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | + | 4.33013i | −0.239457 | + | 0.414751i | −0.960558 | − | 0.278078i | \(-0.910303\pi\) |
0.721102 | + | 0.692829i | \(0.243636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.59808 | + | 4.50000i | 0.246598 | + | 0.427121i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 17.3205i | − | 1.62938i | −0.579899 | − | 0.814688i | \(-0.696908\pi\) | ||
0.579899 | − | 0.814688i | \(-0.303092\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.33013 | + | 2.50000i | 0.403786 | + | 0.233126i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.3923i | 0.960769i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.866025 | + | 2.50000i | 0.0793884 | + | 0.229175i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | + | 12.1244i | 0.636364 | + | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.8564 | 1.24939 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59808 | − | 4.50000i | −0.226995 | − | 0.393167i | 0.729921 | − | 0.683531i | \(-0.239557\pi\) |
−0.956916 | + | 0.290365i | \(0.906223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.500000 | − | 2.59808i | 0.0433555 | − | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.59808 | + | 4.50000i | 0.223607 | + | 0.387298i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.5000 | − | 11.2583i | −1.66600 | − | 0.961864i | −0.969763 | − | 0.244050i | \(-0.921524\pi\) |
−0.696235 | − | 0.717814i | \(-0.745143\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000i | 0.508913i | 0.967084 | + | 0.254457i | \(0.0818966\pi\) | ||||
−0.967084 | + | 0.254457i | \(0.918103\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.50000 | + | 2.59808i | 0.126323 | + | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.66025 | − | 15.0000i | 0.724207 | − | 1.25436i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00000 | + | 1.73205i | −0.249136 | + | 0.143839i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73205 | + | 12.0000i | 0.142857 | + | 0.989743i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5000 | − | 9.52628i | 1.35173 | − | 0.780423i | 0.363241 | − | 0.931695i | \(-0.381670\pi\) |
0.988492 | + | 0.151272i | \(0.0483370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.52628 | + | 16.5000i | −0.775238 | + | 1.34275i | 0.159423 | + | 0.987210i | \(0.449037\pi\) |
−0.934661 | + | 0.355541i | \(0.884297\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.50000 | + | 2.59808i | −0.121268 | + | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.00000i | 0.722897i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.50000 | + | 0.866025i | 0.119713 | + | 0.0691164i | 0.558661 | − | 0.829396i | \(-0.311315\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.1865 | + | 10.5000i | 1.44229 | + | 0.832704i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.50000 | + | 12.9904i | −0.197028 | + | 1.02379i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.33013 | + | 7.50000i | 0.339162 | + | 0.587445i | 0.984275 | − | 0.176641i | \(-0.0565233\pi\) |
−0.645114 | + | 0.764087i | \(0.723190\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 8.66025i | − | 0.674200i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.3923 | 0.804181 | 0.402090 | − | 0.915600i | \(-0.368284\pi\) | ||||
0.402090 | + | 0.915600i | \(0.368284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.59808 | − | 1.50000i | 0.198680 | − | 0.114708i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.500000 | + | 0.866025i | 0.0380143 | + | 0.0658427i | 0.884407 | − | 0.466717i | \(-0.154563\pi\) |
−0.846392 | + | 0.532560i | \(0.821230\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.46410 | − | 10.0000i | −0.261861 | − | 0.755929i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.50000 | − | 12.9904i | 0.563735 | − | 0.976417i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.06218 | + | 3.50000i | 0.453108 | + | 0.261602i | 0.709142 | − | 0.705066i | \(-0.249082\pi\) |
−0.256034 | + | 0.966668i | \(0.582416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.7846i | − | 1.54491i | −0.635071 | − | 0.772454i | \(-0.719029\pi\) | ||
0.635071 | − | 0.772454i | \(-0.280971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.1865 | − | 10.5000i | 1.34439 | − | 0.776182i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.50000 | + | 2.59808i | −0.110282 | + | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.33013 | − | 2.50000i | 0.316650 | − | 0.182818i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.00000 | + | 10.3923i | −0.654654 | + | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2583 | − | 6.50000i | 0.814624 | − | 0.470323i | −0.0339349 | − | 0.999424i | \(-0.510804\pi\) |
0.848559 | + | 0.529101i | \(0.177471\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50000 | − | 12.9904i | 0.539862 | − | 0.935068i | −0.459049 | − | 0.888411i | \(-0.651810\pi\) |
0.998911 | − | 0.0466572i | \(-0.0148568\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.19615 | + | 3.00000i | −0.372104 | + | 0.214834i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.3205i | 1.23404i | 0.786949 | + | 0.617018i | \(0.211659\pi\) | ||||
−0.786949 | + | 0.617018i | \(0.788341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7224 | − | 8.50000i | −1.04365 | − | 0.602549i | −0.122782 | − | 0.992434i | \(-0.539182\pi\) |
−0.920864 | + | 0.389885i | \(0.872515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.5000 | + | 18.1865i | −0.740613 | + | 1.28278i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.92820 | − | 6.00000i | −0.486265 | − | 0.421117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | + | 6.92820i | 0.279372 | + | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.9904 | + | 7.50000i | −0.902894 | + | 0.521286i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.00000 | −0.345857 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.92820 | 0.476957 | 0.238479 | − | 0.971148i | \(-0.423351\pi\) | ||||
0.238479 | + | 0.971148i | \(0.423351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.46410i | − | 0.237356i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.5000 | + | 7.79423i | −1.52740 | + | 0.529107i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.9904 | − | 7.50000i | −0.877809 | − | 0.506803i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 1.73205i | −0.201802 | − | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.00000i | − | 0.133930i | −0.997755 | − | 0.0669650i | \(-0.978668\pi\) | ||
0.997755 | − | 0.0669650i | \(-0.0213316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.00000 | − | 10.3923i | 0.400000 | − | 0.692820i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.866025 | − | 1.50000i | 0.0574801 | − | 0.0995585i | −0.835853 | − | 0.548953i | \(-0.815027\pi\) |
0.893334 | + | 0.449394i | \(0.148360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.50000 | + | 0.866025i | −0.0991228 | + | 0.0572286i | −0.548742 | − | 0.835992i | \(-0.684893\pi\) |
0.449619 | + | 0.893220i | \(0.351560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.6506 | − | 7.50000i | 1.42451 | − | 0.493464i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.50000 | − | 2.59808i | 0.294805 | − | 0.170206i | −0.345302 | − | 0.938492i | \(-0.612223\pi\) |
0.640107 | + | 0.768286i | \(0.278890\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.866025 | + | 1.50000i | −0.0564933 | + | 0.0978492i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.50000 | − | 2.59808i | −0.0974355 | − | 0.168763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.0000i | 1.81117i | 0.424165 | + | 0.905585i | \(0.360568\pi\) | ||||
−0.424165 | + | 0.905585i | \(0.639432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.5000 | − | 12.9904i | −1.44935 | − | 0.836784i | −0.450910 | − | 0.892570i | \(-0.648900\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.50000 | + | 4.33013i | −0.351382 | + | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.73205 | + | 3.00000i | 0.110208 | + | 0.190885i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.0000 | −1.52094 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.46410 | −0.218652 | −0.109326 | − | 0.994006i | \(-0.534869\pi\) | ||||
−0.109326 | + | 0.994006i | \(0.534869\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.0000 | 1.57174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.73205 | −0.108465 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.50000 | + | 9.52628i | 0.343081 | + | 0.594233i | 0.985003 | − | 0.172536i | \(-0.0551963\pi\) |
−0.641923 | + | 0.766769i | \(0.721863\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.79423 | − | 1.50000i | −0.484310 | − | 0.0932055i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 10.3923i | − | 0.643268i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.52628 | − | 5.50000i | −0.587416 | − | 0.339145i | 0.176659 | − | 0.984272i | \(-0.443471\pi\) |
−0.764075 | + | 0.645128i | \(0.776804\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1244i | 0.744793i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.2583 | − | 19.5000i | −0.688999 | − | 1.19338i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.500000 | − | 0.866025i | 0.0304855 | − | 0.0528025i | −0.850380 | − | 0.526169i | \(-0.823628\pi\) |
0.880866 | + | 0.473366i | \(0.156961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9904 | − | 7.50000i | 0.789109 | − | 0.455593i | −0.0505395 | − | 0.998722i | \(-0.516094\pi\) |
0.839649 | + | 0.543130i | \(0.182761\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | − | 10.3923i | −0.726273 | − | 0.628971i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.3205 | + | 10.0000i | −1.04447 | + | 0.603023i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.5000 | − | 18.1865i | 0.630884 | − | 1.09272i | −0.356488 | − | 0.934300i | \(-0.616026\pi\) |
0.987371 | − | 0.158423i | \(-0.0506409\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.3827 | − | 13.5000i | −1.39988 | − | 0.808224i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.3205i | − | 1.03325i | −0.856210 | − | 0.516627i | \(-0.827187\pi\) | ||
0.856210 | − | 0.516627i | \(-0.172813\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.8468 | + | 15.5000i | 1.59588 | + | 0.921379i | 0.992270 | + | 0.124096i | \(0.0396032\pi\) |
0.603606 | + | 0.797283i | \(0.293730\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.50000 | + | 0.866025i | 0.0888523 | + | 0.0512989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.8564 | + | 16.0000i | −0.817918 | + | 0.944450i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | + | 13.8564i | 0.470588 | + | 0.815083i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000i | 0.351726i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.66025 | 0.504219 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.5000 | + | 12.9904i | 1.30558 | + | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.66025 | − | 15.0000i | −0.500835 | − | 0.867472i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.06218 | + | 10.5000i | −0.348263 | + | 0.603209i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.5000 | + | 6.06218i | 0.601228 | + | 0.347119i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.0000i | − | 1.48390i | −0.670456 | − | 0.741949i | \(-0.733902\pi\) | ||
0.670456 | − | 0.741949i | \(-0.266098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.5000 | − | 7.79423i | 0.767988 | − | 0.443398i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.52628 | − | 16.5000i | 0.540186 | − | 0.935629i | −0.458707 | − | 0.888587i | \(-0.651687\pi\) |
0.998893 | − | 0.0470417i | \(-0.0149794\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.50000 | − | 0.866025i | 0.0847850 | − | 0.0489506i | −0.457008 | − | 0.889463i | \(-0.651079\pi\) |
0.541793 | + | 0.840512i | \(0.317746\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.79423 | − | 1.50000i | −0.439155 | − | 0.0845154i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.5000 | − | 7.79423i | 0.758236 | − | 0.437767i | −0.0704263 | − | 0.997517i | \(-0.522436\pi\) |
0.828662 | + | 0.559749i | \(0.189103\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.66025 | + | 15.0000i | −0.484881 | + | 0.839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.5000 | + | 11.2583i | −1.08838 | + | 0.628379i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.00000i | 0.0556415i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0000 | + | 6.92820i | 0.665640 | + | 0.384308i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.33013 | − | 7.50000i | 0.239457 | − | 0.414751i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.50000 | − | 0.866025i | −0.248093 | − | 0.0477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9904 | − | 22.5000i | −0.714016 | − | 1.23671i | −0.963338 | − | 0.268291i | \(-0.913541\pi\) |
0.249322 | − | 0.968421i | \(-0.419792\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.50000 | − | 7.79423i | −0.246598 | − | 0.427121i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.1244 | −0.662424 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.0000 | −0.871576 | −0.435788 | − | 0.900049i | \(-0.643530\pi\) | ||||
−0.435788 | + | 0.900049i | \(0.643530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 30.0000i | 1.62938i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.5000 | + | 38.9711i | 1.21844 | + | 2.11041i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.50000 | − | 4.33013i | −0.403786 | − | 0.233126i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.2583 | + | 6.50000i | 0.604379 | + | 0.348938i | 0.770762 | − | 0.637123i | \(-0.219876\pi\) |
−0.166383 | + | 0.986061i | \(0.553209\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.3205i | 0.927146i | 0.886059 | + | 0.463573i | \(0.153433\pi\) | ||||
−0.886059 | + | 0.463573i | \(0.846567\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 18.0000i | − | 0.960769i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.50000 | − | 16.4545i | 0.505634 | − | 0.875784i | −0.494345 | − | 0.869266i | \(-0.664592\pi\) |
0.999979 | − | 0.00651782i | \(-0.00207470\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.73205 | − | 1.00000i | 0.0919277 | − | 0.0530745i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.50000 | − | 4.33013i | −0.0793884 | − | 0.229175i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.4545 | + | 9.50000i | −0.868434 | + | 0.501391i | −0.866828 | − | 0.498608i | \(-0.833845\pi\) |
−0.00160673 | + | 0.999999i | \(0.500511\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | + | 15.5885i | −0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.1244 | − | 21.0000i | −0.636364 | − | 1.10221i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8.66025i | − | 0.453298i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.06218 | − | 3.50000i | −0.316443 | − | 0.182699i | 0.333363 | − | 0.942799i | \(-0.391817\pi\) |
−0.649806 | + | 0.760100i | \(0.725150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.0000 | −1.24939 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −30.3109 | + | 10.5000i | −1.57366 | + | 0.545133i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.500000 | + | 0.866025i | 0.0258890 | + | 0.0448411i | 0.878680 | − | 0.477412i | \(-0.158425\pi\) |
−0.852791 | + | 0.522253i | \(0.825092\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.5885 | 0.804984 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.2487 | −1.24557 | −0.622786 | − | 0.782392i | \(-0.713999\pi\) | ||||
−0.622786 | + | 0.782392i | \(0.713999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.7224 | − | 25.5000i | −0.752281 | − | 1.30299i | −0.946715 | − | 0.322073i | \(-0.895620\pi\) |
0.194434 | − | 0.980916i | \(-0.437713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.0000 | + | 8.66025i | 0.509647 | + | 0.441367i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.50000 | − | 0.866025i | −0.0760530 | − | 0.0439092i | 0.461491 | − | 0.887145i | \(-0.347315\pi\) |
−0.537544 | + | 0.843236i | \(0.680648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.00000i | − | 0.252861i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.50000 | + | 7.79423i | 0.226995 | + | 0.393167i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.866025 | − | 1.50000i | 0.0435745 | − | 0.0754732i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.50000 | + | 4.33013i | −0.376414 | + | 0.217323i | −0.676257 | − | 0.736666i | \(-0.736399\pi\) |
0.299843 | + | 0.953989i | \(0.403066\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.866025 | + | 4.50000i | −0.0433555 | + | 0.225282i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5000 | − | 9.52628i | 0.823971 | − | 0.475720i | −0.0278131 | − | 0.999613i | \(-0.508854\pi\) |
0.851784 | + | 0.523893i | \(0.175521\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.5885 | − | 27.0000i | 0.776516 | − | 1.34497i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.50000 | − | 7.79423i | −0.223607 | − | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.0000i | 0.743522i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.50000 | − | 4.33013i | −0.370851 | − | 0.214111i | 0.302979 | − | 0.952997i | \(-0.402019\pi\) |
−0.673830 | + | 0.738886i | \(0.735352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 33.7750 | + | 19.5000i | 1.66600 | + | 0.961864i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.50000 | + | 21.6506i | 0.369051 | + | 1.06536i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.92820 | − | 12.0000i | −0.340092 | − | 0.589057i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 10.3923i | − | 0.508913i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8564 | 0.676930 | 0.338465 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338465 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0000 | −0.584844 | −0.292422 | − | 0.956289i | \(-0.594461\pi\) | ||||
−0.292422 | + | 0.956289i | \(0.594461\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.59808 | − | 4.50000i | −0.126323 | − | 0.218797i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | + | 3.46410i | 0.0970143 | + | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.06218 | + | 31.5000i | −0.293369 | + | 1.52439i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.0000 | + | 25.9808i | −0.724207 | + | 1.25436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.6506 | − | 12.5000i | −1.04287 | − | 0.602104i | −0.122228 | − | 0.992502i | \(-0.539004\pi\) |
−0.920646 | + | 0.390398i | \(0.872337\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 31.1769i | − | 1.49827i | −0.662419 | − | 0.749133i | \(-0.730470\pi\) | ||
0.662419 | − | 0.749133i | \(-0.269530\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.19615 | − | 3.00000i | 0.249136 | − | 0.143839i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.50000 | + | 4.33013i | −0.119591 | + | 0.207138i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.06218 | + | 3.50000i | −0.289332 | + | 0.167046i | −0.637641 | − | 0.770334i | \(-0.720089\pi\) |
0.348309 | + | 0.937380i | \(0.386756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.6506 | − | 12.5000i | 1.02865 | − | 0.593893i | 0.112054 | − | 0.993702i | \(-0.464257\pi\) |
0.916598 | + | 0.399809i | \(0.130924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.50000 | − | 11.2583i | 0.308130 | − | 0.533696i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.5788 | + | 16.5000i | −1.35173 | + | 0.780423i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.1769i | 1.47133i | 0.677346 | + | 0.735665i | \(0.263130\pi\) | ||||
−0.677346 | + | 0.735665i | \(0.736870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.6410 | + | 20.0000i | 1.63118 | + | 0.941763i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.5000 | − | 28.5788i | 0.775238 | − | 1.34275i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.73205 | − | 9.00000i | 0.0811998 | − | 0.421927i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.50000 | + | 11.2583i | 0.304057 | + | 0.526642i | 0.977051 | − | 0.213006i | \(-0.0683253\pi\) |
−0.672994 | + | 0.739648i | \(0.734992\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.59808 | − | 4.50000i | 0.121268 | − | 0.210042i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.00000 | −0.372597 | −0.186299 | − | 0.982493i | \(-0.559649\pi\) | ||||
−0.186299 | + | 0.982493i | \(0.559649\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8564 | 0.643962 | 0.321981 | − | 0.946746i | \(-0.395651\pi\) | ||||
0.321981 | + | 0.946746i | \(0.395651\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 15.5885i | − | 0.722897i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.06218 | − | 10.5000i | −0.280524 | − | 0.485882i | 0.690990 | − | 0.722865i | \(-0.257175\pi\) |
−0.971514 | + | 0.236982i | \(0.923842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.5000 | − | 30.3109i | −0.484845 | − | 1.39963i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.59808 | − | 1.50000i | −0.119713 | − | 0.0691164i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.00000i | − | 0.183533i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.5000 | − | 18.1865i | −1.44229 | − | 0.832704i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.79423 | + | 13.5000i | −0.356127 | + | 0.616831i | −0.987310 | − | 0.158803i | \(-0.949236\pi\) |
0.631183 | + | 0.775634i | \(0.282570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.00000 | − | 5.19615i | 0.410365 | − | 0.236924i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.33013 | − | 22.5000i | 0.197028 | − | 1.02379i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.00000 | + | 1.73205i | −0.136223 | + | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.79423 | + | 13.5000i | −0.353190 | + | 0.611743i | −0.986807 | − | 0.161904i | \(-0.948236\pi\) |
0.633616 | + | 0.773647i | \(0.281570\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.50000 | − | 12.9904i | −0.339162 | − | 0.587445i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.00000i | − | 0.361035i | −0.983572 | − | 0.180517i | \(-0.942223\pi\) | ||
0.983572 | − | 0.180517i | \(-0.0577772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00000 | + | 1.73205i | 0.135113 | + | 0.0780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.0000i | 0.674200i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000 | + | 3.46410i | 0.179425 | + | 0.155386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.06218 | − | 10.5000i | −0.271380 | − | 0.470045i | 0.697835 | − | 0.716258i | \(-0.254147\pi\) |
−0.969216 | + | 0.246214i | \(0.920813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0000 | −0.804181 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.6410 | 1.54457 | 0.772283 | − | 0.635278i | \(-0.219115\pi\) | ||||
0.772283 | + | 0.635278i | \(0.219115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.00000 | −0.311496 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.73205 | −0.0769231 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.50000 | − | 4.33013i | −0.110811 | − | 0.191930i | 0.805287 | − | 0.592886i | \(-0.202011\pi\) |
−0.916097 | + | 0.400956i | \(0.868678\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.6506 | − | 7.50000i | 0.957768 | − | 0.331780i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.50000 | + | 2.59808i | −0.198680 | + | 0.114708i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.79423 | + | 4.50000i | 0.343455 | + | 0.198294i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.66025i | 0.380878i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.866025 | − | 1.50000i | −0.0380143 | − | 0.0658427i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.5000 | + | 30.3109i | −0.766689 | + | 1.32794i | 0.172660 | + | 0.984981i | \(0.444764\pi\) |
−0.939349 | + | 0.342963i | \(0.888570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9904 | + | 7.50000i | −0.568030 | + | 0.327952i | −0.756362 | − | 0.654153i | \(-0.773025\pi\) |
0.188332 | + | 0.982105i | \(0.439692\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.00000 | + | 17.3205i | 0.261861 | + | 0.755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.79423 | − | 4.50000i | 0.339522 | − | 0.196023i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | − | 1.73205i | 0.0434783 | − | 0.0753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.9904 | + | 22.5000i | −0.563735 | + | 0.976417i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 27.7128i | − | 1.20038i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.2583 | − | 6.50000i | −0.486740 | − | 0.281020i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.5000 | − | 6.06218i | −0.453108 | − | 0.261602i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.9904 | + | 32.5000i | −0.559535 | + | 1.39987i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.5000 | − | 18.1865i | −0.451430 | − | 0.781900i | 0.547045 | − | 0.837103i | \(-0.315753\pi\) |
−0.998475 | + | 0.0552031i | \(0.982419\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.0000i | 1.54491i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.00000 | 0.214176 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.3205 | −0.740571 | −0.370286 | − | 0.928918i | \(-0.620740\pi\) | ||||
−0.370286 | + | 0.928918i | \(0.620740\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −31.5000 | + | 18.1865i | −1.34439 | + | 0.776182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.73205 | − | 3.00000i | −0.0737878 | − | 0.127804i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.50000 | + | 0.866025i | 0.191359 | + | 0.0368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.59808 | − | 4.50000i | 0.110282 | − | 0.191014i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.5000 | + | 19.9186i | 1.46181 | + | 0.843978i | 0.999095 | − | 0.0425287i | \(-0.0135414\pi\) |
0.462717 | + | 0.886506i | \(0.346875\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.50000 | + | 4.33013i | −0.316650 | + | 0.182818i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.9904 | − | 22.5000i | 0.547479 | − | 0.948262i | −0.450967 | − | 0.892541i | \(-0.648921\pi\) |
0.998446 | − | 0.0557214i | \(-0.0177458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.0000 | + | 8.66025i | −0.631055 | + | 0.364340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.5885 | − | 18.0000i | 0.654654 | − | 0.755929i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5000 | − | 7.79423i | 0.565949 | − | 0.326751i | −0.189580 | − | 0.981865i | \(-0.560713\pi\) |
0.755530 | + | 0.655114i | \(0.227379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.06218 | + | 10.5000i | −0.253694 | + | 0.439411i | −0.964540 | − | 0.263937i | \(-0.914979\pi\) |
0.710846 | + | 0.703348i | \(0.248312\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.5000 | + | 11.2583i | −0.814624 | + | 0.470323i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.0000i | 0.834058i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.5000 | + | 14.7224i | 1.06158 | + | 0.612903i | 0.925869 | − | 0.377846i | \(-0.123335\pi\) |
0.135710 | + | 0.990749i | \(0.456668\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.9904 | + | 22.5000i | −0.539862 | + | 0.935068i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | − | 27.7128i | 0.995688 | − | 1.14972i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.3109 | + | 52.5000i | 1.25535 | + | 2.17433i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.00000 | − | 5.19615i | 0.372104 | − | 0.214834i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.7128 | 1.14383 | 0.571915 | − | 0.820313i | \(-0.306201\pi\) | ||||
0.571915 | + | 0.820313i | \(0.306201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | −0.370839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 30.0000i | − | 1.23404i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.500000 | − | 0.866025i | −0.0205325 | − | 0.0355634i | 0.855577 | − | 0.517676i | \(-0.173203\pi\) |
−0.876109 | + | 0.482113i | \(0.839870\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.73205 | − | 2.00000i | 0.0710072 | − | 0.0819920i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.5000 | + | 14.7224i | 1.04365 | + | 0.602549i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.866025 | + | 0.500000i | 0.0353848 | + | 0.0204294i | 0.517588 | − | 0.855630i | \(-0.326830\pi\) |
−0.482203 | + | 0.876059i | \(0.660163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.46410i | − | 0.141304i | −0.997501 | − | 0.0706518i | \(-0.977492\pi\) | ||
0.997501 | − | 0.0706518i | \(-0.0225079\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.1865 | − | 31.5000i | 0.740613 | − | 1.28278i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | − | 12.1244i | 0.284590 | − | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.0429 | − | 18.5000i | 1.30058 | − | 0.750892i | 0.320079 | − | 0.947391i | \(-0.396291\pi\) |
0.980504 | + | 0.196499i | \(0.0629573\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0000 | + | 10.3923i | 0.486265 | + | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.19615 | − | 3.00000i | 0.210214 | − | 0.121367i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.5000 | + | 42.4352i | −0.989546 | + | 1.71394i | −0.369875 | + | 0.929082i | \(0.620599\pi\) |
−0.619671 | + | 0.784862i | \(0.712734\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.92820 | − | 12.0000i | −0.279372 | − | 0.483887i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.2487i | 0.976216i | 0.872783 | + | 0.488108i | \(0.162313\pi\) | ||||
−0.872783 | + | 0.488108i | \(0.837687\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.3827 | − | 13.5000i | −0.939829 | − | 0.542611i | −0.0499226 | − | 0.998753i | \(-0.515897\pi\) |
−0.889907 | + | 0.456142i | \(0.849231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.5000 | − | 12.9904i | 0.902894 | − | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33.7750 | + | 6.50000i | 1.35317 | + | 0.260417i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.66025 | 0.345857 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.00000 | 0.119618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.7846 | 0.827422 | 0.413711 | − | 0.910408i | \(-0.364232\pi\) | ||||
0.413711 | + | 0.910408i | \(0.364232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0000 | − | 3.46410i | 0.950915 | − | 0.137253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000i | 0.237356i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.50000 | + | 4.33013i | 0.296232 | + | 0.171030i | 0.640749 | − | 0.767750i | \(-0.278624\pi\) |
−0.344517 | + | 0.938780i | \(0.611957\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.0000i | 1.02534i | 0.858586 | + | 0.512670i | \(0.171344\pi\) | ||||
−0.858586 | + | 0.512670i | \(0.828656\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.06218 | − | 10.5000i | 0.238329 | − | 0.412798i | −0.721906 | − | 0.691991i | \(-0.756734\pi\) |
0.960235 | + | 0.279193i | \(0.0900671\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.5000 | − | 21.6506i | 1.47200 | − | 0.849862i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 38.9711 | − | 13.5000i | 1.52740 | − | 0.529107i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.5000 | + | 16.4545i | −1.11529 | + | 0.643914i | −0.940195 | − | 0.340638i | \(-0.889357\pi\) |
−0.175097 | + | 0.984551i | \(0.556024\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.59808 | + | 4.50000i | −0.101515 | + | 0.175830i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.5000 | + | 12.9904i | 0.877809 | + | 0.506803i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.0000i | 1.32445i | 0.749304 | + | 0.662226i | \(0.230388\pi\) | ||||
−0.749304 | + | 0.662226i | \(0.769612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5000 | + | 11.2583i | 0.758462 | + | 0.437898i | 0.828743 | − | 0.559629i | \(-0.189056\pi\) |
−0.0702812 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.19615 | + | 3.00000i | 0.201802 | + | 0.116510i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.50000 | + | 0.866025i | −0.0969458 | + | 0.0335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.66025 | + | 15.0000i | 0.335326 | + | 0.580802i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.46410i | 0.133930i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 60.6218 | 2.34028 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.0000 | 1.38770 | 0.693849 | − | 0.720121i | \(-0.255914\pi\) | ||||
0.693849 | + | 0.720121i | \(0.255914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.3923 | + | 18.0000i | −0.400000 | + | 0.692820i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.5000 | − | 32.0429i | −0.711013 | − | 1.23151i | −0.964477 | − | 0.264166i | \(-0.914903\pi\) |
0.253465 | − | 0.967345i | \(-0.418430\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.92820 | − | 6.00000i | −0.265880 | − | 0.230259i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.50000 | + | 2.59808i | −0.0574801 | + | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.2583 | − | 6.50000i | −0.430788 | − | 0.248716i | 0.268894 | − | 0.963170i | \(-0.413342\pi\) |
−0.699682 | + | 0.714454i | \(0.746675\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.5167i | 0.860317i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.59808 | − | 1.50000i | 0.0991228 | − | 0.0572286i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.0000 | − | 36.3731i | 0.800036 | − | 1.38570i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5788 | + | 16.5000i | −1.08719 | + | 0.627690i | −0.932827 | − | 0.360325i | \(-0.882666\pi\) |
−0.154363 | + | 0.988014i | \(0.549333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −37.5000 | + | 12.9904i | −1.42451 | + | 0.493464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.19615 | − | 3.00000i | 0.197101 | − | 0.113796i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | − | 6.92820i | 0.151511 | − | 0.262424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.79423 | + | 4.50000i | −0.294805 | + | 0.170206i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7846i | 0.785024i | 0.919747 | + | 0.392512i | \(0.128394\pi\) | ||||
−0.919747 | + | 0.392512i | \(0.871606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.59808 | − | 1.50000i | −0.0979883 | − | 0.0565736i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.50000 | − | 2.59808i | 0.0564933 | − | 0.0978492i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.06218 | − | 17.5000i | −0.227992 | − | 0.658155i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.5000 | − | 26.8468i | −0.582115 | − | 1.00825i | −0.995228 | − | 0.0975728i | \(-0.968892\pi\) |
0.413114 | − | 0.910679i | \(-0.364441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.59808 | + | 4.50000i | 0.0974355 | + | 0.168763i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.0000 | 1.68526 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.3205 | −0.647750 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 48.4974i | − | 1.81117i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2583 | + | 19.5000i | 0.419865 | + | 0.727227i | 0.995926 | − | 0.0901797i | \(-0.0287441\pi\) |
−0.576061 | + | 0.817407i | \(0.695411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.50000 | + | 23.3827i | −0.167589 | + | 0.870817i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 38.9711 | + | 22.5000i | 1.44935 | + | 0.836784i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0000 | − | 6.92820i | −0.445669 | − | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.0000i | 1.11264i | 0.830969 | + | 0.556319i | \(0.187787\pi\) | ||||
−0.830969 | + | 0.556319i | \(0.812213\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.5000 | + | 19.9186i | −1.27429 | + | 0.735710i | −0.975792 | − | 0.218702i | \(-0.929818\pi\) |
−0.298495 | + | 0.954411i | \(0.596485\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.52628 | − | 7.50000i | 0.351382 | − | 0.276642i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −52.5000 | + | 30.3109i | −1.93386 | + | 1.11652i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.1865 | − | 31.5000i | 0.669002 | − | 1.15875i | −0.309181 | − | 0.951003i | \(-0.600055\pi\) |
0.978183 | − | 0.207743i | \(-0.0666118\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | − | 5.19615i | −0.110208 | − | 0.190885i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.0000i | 0.807102i | 0.914957 | + | 0.403551i | \(0.132224\pi\) | ||||
−0.914957 | + | 0.403551i | \(0.867776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.5000 | − | 9.52628i | −0.604513 | − | 0.349016i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 41.5692 | 1.52094 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.50000 | − | 33.7750i | 0.237505 | − | 1.23411i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6506 | − | 37.5000i | −0.790043 | − | 1.36839i | −0.925940 | − | 0.377671i | \(-0.876725\pi\) |
0.135897 | − | 0.990723i | \(-0.456608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.00000 | 0.218652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.0526 | 0.693394 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.00000 | −0.290765 | −0.145382 | − | 0.989376i | \(-0.546441\pi\) | ||||
−0.145382 | + | 0.989376i | \(0.546441\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −43.3013 | −1.57174 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.5000 | − | 32.0429i | −0.670624 | − | 1.16156i | −0.977727 | − | 0.209879i | \(-0.932693\pi\) |
0.307103 | − | 0.951676i | \(-0.400640\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.33013 | + | 12.5000i | 0.156761 | + | 0.452530i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.00000 | 0.108465 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.9808 | − | 15.0000i | −0.938111 | − | 0.541619i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.3923i | 0.374756i | 0.982288 | + | 0.187378i | \(0.0599989\pi\) | ||||
−0.982288 | + | 0.187378i | \(0.940001\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.52628 | − | 16.5000i | −0.343081 | − | 0.594233i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.5000 | + | 42.4352i | −0.881204 | + | 1.52629i | −0.0311999 | + | 0.999513i | \(0.509933\pi\) |
−0.850004 | + | 0.526777i | \(0.823400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.1769 | + | 18.0000i | −1.11991 | + | 0.646579i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.5000 | + | 2.59808i | 0.484310 | + | 0.0932055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.92820 | + | 4.00000i | −0.248229 | + | 0.143315i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.00000 | − | 8.66025i | 0.178914 | − | 0.309888i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.0000i | 0.643268i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.73205i | − | 0.0618195i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.3827 | − | 13.5000i | −0.833503 | − | 0.481223i | 0.0215477 | − | 0.999768i | \(-0.493141\pi\) |
−0.855050 | + | 0.518545i | \(0.826474\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.5000 | + | 9.52628i | 0.587416 | + | 0.339145i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.6410 | − | 30.0000i | −1.23169 | − | 1.06668i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.0000 | − | 36.3731i | −0.745732 | − | 1.29165i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 21.0000i | − | 0.744793i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.0000 | −1.13350 | −0.566749 | − | 0.823890i | \(-0.691799\pi\) | ||||
−0.566749 | + | 0.823890i | \(0.691799\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.73205 | 0.0612756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.5000 | + | 33.7750i | 0.688999 | + | 1.19338i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.6506 | − | 37.5000i | −0.764034 | − | 1.32335i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.5000 | − | 4.33013i | 0.440567 | − | 0.152617i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.866025 | + | 1.50000i | −0.0304855 | + | 0.0528025i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.5000 | + | 14.7224i | 0.896532 | + | 0.517613i | 0.876074 | − | 0.482178i | \(-0.160154\pi\) |
0.0204587 | + | 0.999791i | \(0.493487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000i | 1.05344i | 0.850038 | + | 0.526721i | \(0.176579\pi\) | ||||
−0.850038 | + | 0.526721i | \(0.823421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.5000 | + | 12.9904i | −0.789109 | + | 0.455593i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.33013 | − | 7.50000i | 0.151678 | − | 0.262714i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.7846 | + | 18.0000i | 0.726273 | + | 0.628971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5000 | + | 7.79423i | −0.471153 | + | 0.272020i | −0.716722 | − | 0.697359i | \(-0.754359\pi\) |
0.245569 | + | 0.969379i | \(0.421025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.8468 | − | 46.5000i | 0.935820 | − | 1.62089i | 0.162655 | − | 0.986683i | \(-0.447994\pi\) |
0.773165 | − | 0.634205i | \(-0.218673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.0000 | − | 17.3205i | 1.04447 | − | 0.603023i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.00000i | 0.0695468i | 0.999395 | + | 0.0347734i | \(0.0110710\pi\) | ||||
−0.999395 | + | 0.0347734i | \(0.988929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.50000 | − | 0.866025i | −0.0520972 | − | 0.0300783i | 0.473725 | − | 0.880673i | \(-0.342909\pi\) |
−0.525822 | + | 0.850594i | \(0.676242\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.1865 | + | 31.5000i | −0.630884 | + | 1.09272i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.50000 | + | 2.59808i | 0.225212 | + | 0.0900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.19615 | − | 9.00000i | −0.179820 | − | 0.311458i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 40.5000 | + | 23.3827i | 1.39988 | + | 0.808224i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.7128 | −0.956753 | −0.478376 | − | 0.878155i | \(-0.658774\pi\) | ||||
−0.478376 | + | 0.878155i | \(0.658774\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0000 | 0.586207 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.0000i | 1.03325i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.500000 | − | 0.866025i | −0.0172005 | − | 0.0297922i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.3731 | + | 7.00000i | 1.24979 | + | 0.240523i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −46.5000 | − | 26.8468i | −1.59588 | − | 0.921379i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.9904 | + | 7.50000i | 0.445305 | + | 0.257097i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.0333i | 1.54191i | 0.636889 | + | 0.770956i | \(0.280221\pi\) | ||||
−0.636889 | + | 0.770956i | \(0.719779\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.59808 | − | 1.50000i | −0.0888523 | − | 0.0512989i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.50000 | + | 6.06218i | −0.119558 | + | 0.207080i | −0.919592 | − | 0.392874i | \(-0.871481\pi\) |
0.800035 | + | 0.599954i | \(0.204814\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.866025 | − | 0.500000i | 0.0295484 | − | 0.0170598i | −0.485153 | − | 0.874429i | \(-0.661236\pi\) |
0.514701 | + | 0.857369i | \(0.327903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.0000 | − | 27.7128i | 0.817918 | − | 0.944450i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.4545 | − | 9.50000i | 0.560117 | − | 0.323384i | −0.193075 | − | 0.981184i | \(-0.561846\pi\) |
0.753193 | + | 0.657800i | \(0.228513\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.500000 | − | 0.866025i | 0.0170005 | − | 0.0294457i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.8564 | − | 24.0000i | −0.470588 | − | 0.815083i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.66025i | − | 0.293779i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.3731 | + | 21.0000i | 1.23245 | + | 0.711558i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 10.3923i | − | 0.351726i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.5885 | + | 18.0000i | −0.526986 | + | 0.608511i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.5000 | − | 32.0429i | −0.624701 | − | 1.08201i | −0.988599 | − | 0.150574i | \(-0.951888\pi\) |
0.363898 | − | 0.931439i | \(-0.381446\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.2487 | −0.817889 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.0000 | −0.336909 | −0.168454 | − | 0.985709i | \(-0.553878\pi\) | ||||
−0.168454 | + | 0.985709i | \(0.553878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.92820 | −0.233153 | −0.116576 | − | 0.993182i | \(-0.537192\pi\) | ||||
−0.116576 | + | 0.993182i | \(0.537192\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.0000 | −0.504219 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.79423 | − | 13.5000i | −0.261705 | − | 0.453286i | 0.704990 | − | 0.709217i | \(-0.250951\pi\) |
−0.966695 | + | 0.255931i | \(0.917618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.9711 | − | 22.5000i | −1.30558 | − | 0.753778i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.50000 | − | 0.866025i | −0.0501956 | − | 0.0289804i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.00000i | − | 0.233984i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.0000 | + | 25.9808i | 0.500835 | + | 0.867472i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.5885 | + | 27.0000i | −0.519904 | + | 0.900500i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.5000 | − | 6.06218i | 0.349806 | − | 0.201960i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0000 | + | 10.3923i | −0.598340 | + | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.866025 | + | 1.50000i | −0.0287559 | + | 0.0498067i | −0.880045 | − | 0.474890i | \(-0.842488\pi\) |
0.851289 | + | 0.524697i | \(0.175821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.5000 | − | 18.1865i | 0.348263 | − | 0.603209i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 22.0000i | − | 0.728893i | −0.931224 | − | 0.364446i | \(-0.881258\pi\) | ||
0.931224 | − | 0.364446i | \(-0.118742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −60.0000 | − | 34.6410i | −1.98571 | − | 1.14645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.1865 | − | 10.5000i | −0.601228 | − | 0.347119i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.5000 | − | 2.59808i | −0.445809 | − | 0.0857960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.52628 | + | 16.5000i | 0.314243 | + | 0.544285i | 0.979276 | − | 0.202529i | \(-0.0649160\pi\) |
−0.665033 | + | 0.746814i | \(0.731583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.0333i | 1.48390i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.92820 | −0.228045 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | −0.394558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.3827 | + | 13.5000i | −0.767988 | + | 0.443398i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.5000 | − | 47.6314i | −0.902246 | − | 1.56274i | −0.824572 | − | 0.565757i | \(-0.808584\pi\) |
−0.0776734 | − | 0.996979i | \(-0.524749\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.33013 | − | 5.50000i | −0.141914 | − | 0.180255i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.5000 | + | 28.5788i | −0.540186 | + | 0.935629i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.33013 | − | 2.50000i | −0.141610 | − | 0.0817587i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 27.7128i | − | 0.905338i | −0.891679 | − | 0.452669i | \(-0.850472\pi\) | ||
0.891679 | − | 0.452669i | \(-0.149528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.59808 | + | 1.50000i | −0.0847850 | + | 0.0489506i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.5000 | − | 25.1147i | 0.472686 | − | 0.818717i | −0.526825 | − | 0.849974i | \(-0.676618\pi\) |
0.999511 | + | 0.0312568i | \(0.00995098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.6410 | − | 20.0000i | 1.12807 | − | 0.651290i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.5000 | + | 2.59808i | 0.439155 | + | 0.0845154i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.52628 | − | 5.50000i | 0.309562 | − | 0.178726i | −0.337168 | − | 0.941444i | \(-0.609469\pi\) |
0.646731 | + | 0.762718i | \(0.276136\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0000 | + | 25.9808i | −0.486921 | + | 0.843371i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.3827 | + | 13.5000i | −0.758236 | + | 0.437767i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.3205i | 0.561066i | 0.959844 | + | 0.280533i | \(0.0905113\pi\) | ||||
−0.959844 | + | 0.280533i | \(0.909489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.2583 | − | 6.50000i | −0.364311 | − | 0.210335i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.0000 | − | 25.9808i | 0.484881 | − | 0.839839i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −56.2917 | + | 19.5000i | −1.81775 | + | 0.629688i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0000 | + | 43.3013i | 0.806452 | + | 1.39682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33.7750 | − | 19.5000i | 1.08838 | − | 0.628379i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.0000 | −0.482867 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.92820 | −0.222796 | −0.111398 | − | 0.993776i | \(-0.535533\pi\) | ||||
−0.111398 | + | 0.993776i | \(0.535533\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.73205i | − | 0.0556415i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.33013 | + | 7.50000i | 0.138960 | + | 0.240686i | 0.927103 | − | 0.374806i | \(-0.122291\pi\) |
−0.788143 | + | 0.615492i | \(0.788957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | + | 10.3923i | 0.384702 | + | 0.333162i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.7846 | − | 12.0000i | −0.665640 | − | 0.384308i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.5000 | − | 14.7224i | −0.815817 | − | 0.471012i | 0.0331547 | − | 0.999450i | \(-0.489445\pi\) |
−0.848972 | + | 0.528438i | \(0.822778\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 65.0000i | − | 2.07741i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.50000 | + | 12.9904i | −0.239457 | + | 0.414751i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.59808 | + | 4.50000i | −0.0828658 | + | 0.143528i | −0.904480 | − | 0.426517i | \(-0.859741\pi\) |
0.821614 | + | 0.570044i | \(0.193074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.0000 | − | 8.66025i | 0.477940 | − | 0.275939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.79423 | + | 1.50000i | 0.248093 | + | 0.0477455i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.52628 | − | 16.5000i | 0.302612 | − | 0.524140i | −0.674115 | − | 0.738627i | \(-0.735475\pi\) |
0.976727 | + | 0.214487i | \(0.0688080\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.5000 | + | 38.9711i | 0.714016 | + | 1.23671i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.0000i | 0.538936i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.5000 | + | 11.2583i | 0.617571 | + | 0.356555i | 0.775923 | − | 0.630828i | \(-0.217285\pi\) |
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.79423 | + | 13.5000i | 0.246598 | + | 0.427121i |
(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 | 672.2.bc.a.353.1 | yes | 4 | |
3.2 | odd | 2 | 672.2.bc.b.353.1 | yes | 4 | ||
4.3 | odd | 2 | inner | 672.2.bc.a.353.2 | yes | 4 | |
7.5 | odd | 6 | 672.2.bc.b.257.1 | yes | 4 | ||
12.11 | even | 2 | 672.2.bc.b.353.2 | yes | 4 | ||
21.5 | even | 6 | inner | 672.2.bc.a.257.1 | ✓ | 4 | |
28.19 | even | 6 | 672.2.bc.b.257.2 | yes | 4 | ||
84.47 | odd | 6 | inner | 672.2.bc.a.257.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.bc.a.257.1 | ✓ | 4 | 21.5 | even | 6 | inner | |
672.2.bc.a.257.2 | yes | 4 | 84.47 | odd | 6 | inner | |
672.2.bc.a.353.1 | yes | 4 | 1.1 | even | 1 | trivial | |
672.2.bc.a.353.2 | yes | 4 | 4.3 | odd | 2 | inner | |
672.2.bc.b.257.1 | yes | 4 | 7.5 | odd | 6 | ||
672.2.bc.b.257.2 | yes | 4 | 28.19 | even | 6 | ||
672.2.bc.b.353.1 | yes | 4 | 3.2 | odd | 2 | ||
672.2.bc.b.353.2 | yes | 4 | 12.11 | even | 2 |