Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + x^{18} + 4x^{16} + 8x^{12} + 4x^{10} + 32x^{8} + 256x^{4} + 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.13 | ||
Root | \(0.725842 - 1.21374i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.e.757.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.725842 | − | 1.21374i | 0.513248 | − | 0.858241i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.946308 | − | 1.76196i | −0.473154 | − | 0.880980i | ||||
\(5\) | − | 3.06888i | − | 1.37244i | −0.727392 | − | 0.686222i | \(-0.759268\pi\) | ||
0.727392 | − | 0.686222i | \(-0.240732\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.82542 | − | 0.130337i | −0.998938 | − | 0.0460809i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.72481 | − | 2.22752i | −1.17789 | − | 0.704403i | ||||
\(11\) | 5.80820i | 1.75124i | 0.483001 | + | 0.875620i | \(0.339547\pi\) | ||||
−0.483001 | + | 0.875620i | \(0.660453\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.52392i | 0.977359i | 0.872463 | + | 0.488680i | \(0.162521\pi\) | ||||
−0.872463 | + | 0.488680i | \(0.837479\pi\) | |||||||
\(14\) | −0.725842 | + | 1.21374i | −0.193989 | + | 0.324384i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.20900 | + | 3.33471i | −0.552251 | + | 0.833678i | ||||
\(17\) | −6.79736 | −1.64860 | −0.824301 | − | 0.566151i | \(-0.808432\pi\) | ||||
−0.824301 | + | 0.566151i | \(0.808432\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.28617i | − | 1.21273i | −0.795186 | − | 0.606365i | \(-0.792627\pi\) | ||
0.795186 | − | 0.606365i | \(-0.207373\pi\) | |||||||
\(20\) | −5.40724 | + | 2.90410i | −1.20910 | + | 0.649377i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.04962 | + | 4.21584i | 1.50298 | + | 0.898819i | ||||
\(23\) | −5.65085 | −1.17828 | −0.589141 | − | 0.808030i | \(-0.700534\pi\) | ||||
−0.589141 | + | 0.808030i | \(0.700534\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41801 | −0.883601 | ||||||||
\(26\) | 4.27711 | + | 2.55781i | 0.838809 | + | 0.501627i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.946308 | + | 1.76196i | 0.178835 | + | 0.332979i | ||||
\(29\) | − | 1.21394i | − | 0.225422i | −0.993628 | − | 0.112711i | \(-0.964047\pi\) | ||
0.993628 | − | 0.112711i | \(-0.0359534\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.107385 | 0.0192868 | 0.00964342 | − | 0.999954i | \(-0.496930\pi\) | ||||
0.00964342 | + | 0.999954i | \(0.496930\pi\) | |||||||
\(32\) | 2.44407 | + | 5.10162i | 0.432055 | + | 0.901847i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.93381 | + | 8.25020i | −0.846141 | + | 1.41490i | ||||
\(35\) | 3.06888i | 0.518735i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.90235i | 0.805942i | 0.915213 | + | 0.402971i | \(0.132022\pi\) | ||||
−0.915213 | + | 0.402971i | \(0.867978\pi\) | |||||||
\(38\) | −6.41601 | − | 3.83692i | −1.04081 | − | 0.622431i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.399987 | + | 8.67087i | −0.0632435 | + | 1.37099i | ||||
\(41\) | −11.6855 | −1.82497 | −0.912485 | − | 0.409111i | \(-0.865839\pi\) | ||||
−0.912485 | + | 0.409111i | \(0.865839\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.85684i | 0.283165i | 0.989926 | + | 0.141583i | \(0.0452191\pi\) | ||||
−0.989926 | + | 0.141583i | \(0.954781\pi\) | |||||||
\(44\) | 10.2338 | − | 5.49635i | 1.54281 | − | 0.828606i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.10162 | + | 6.85863i | −0.604751 | + | 1.01125i | ||||
\(47\) | 6.76459 | 0.986717 | 0.493359 | − | 0.869826i | \(-0.335769\pi\) | ||||
0.493359 | + | 0.869826i | \(0.335769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.20677 | + | 5.36229i | −0.453506 | + | 0.758343i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.20900 | − | 3.33471i | 0.861034 | − | 0.462441i | ||||
\(53\) | − | 11.4861i | − | 1.57773i | −0.614566 | − | 0.788865i | \(-0.710669\pi\) | ||
0.614566 | − | 0.788865i | \(-0.289331\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.8247 | 2.40348 | ||||||||
\(56\) | 2.82542 | + | 0.130337i | 0.377563 | + | 0.0174170i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.47340 | − | 0.881125i | −0.193466 | − | 0.115697i | ||||
\(59\) | 7.85494i | 1.02263i | 0.859394 | + | 0.511313i | \(0.170841\pi\) | ||||
−0.859394 | + | 0.511313i | \(0.829159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.0556i | − | 1.54356i | −0.635890 | − | 0.771779i | \(-0.719367\pi\) | ||
0.635890 | − | 0.771779i | \(-0.280633\pi\) | |||||||
\(62\) | 0.0779442 | − | 0.130337i | 0.00989893 | − | 0.0165528i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.96602 | + | 0.736512i | 0.995753 | + | 0.0920639i | ||||
\(65\) | 10.8145 | 1.34137 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.66942i | 0.814800i | 0.913250 | + | 0.407400i | \(0.133564\pi\) | ||||
−0.913250 | + | 0.407400i | \(0.866436\pi\) | |||||||
\(68\) | 6.43240 | + | 11.9767i | 0.780043 | + | 1.45239i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.72481 | + | 2.22752i | 0.445199 | + | 0.266239i | ||||
\(71\) | 1.98478 | 0.235550 | 0.117775 | − | 0.993040i | \(-0.462424\pi\) | ||||
0.117775 | + | 0.993040i | \(0.462424\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.52879 | −0.764137 | −0.382068 | − | 0.924134i | \(-0.624788\pi\) | ||||
−0.382068 | + | 0.924134i | \(0.624788\pi\) | |||||||
\(74\) | 5.95016 | + | 3.55833i | 0.691692 | + | 0.413648i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.31402 | + | 5.00234i | −1.06839 | + | 0.573808i | ||||
\(77\) | − | 5.80820i | − | 0.661906i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.30741 | 0.259604 | 0.129802 | − | 0.991540i | \(-0.458566\pi\) | ||||
0.129802 | + | 0.991540i | \(0.458566\pi\) | |||||||
\(80\) | 10.2338 | + | 6.77916i | 1.14418 | + | 0.757933i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.48183 | + | 14.1831i | −0.936661 | + | 1.56626i | ||||
\(83\) | − | 12.5795i | − | 1.38078i | −0.723436 | − | 0.690391i | \(-0.757438\pi\) | ||
0.723436 | − | 0.690391i | \(-0.242562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.8603i | 2.26261i | ||||||||
\(86\) | 2.25371 | + | 1.34777i | 0.243024 | + | 0.145334i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.757021 | − | 16.4106i | 0.0806987 | − | 1.74938i | ||||
\(89\) | −7.79151 | −0.825898 | −0.412949 | − | 0.910754i | \(-0.635501\pi\) | ||||
−0.412949 | + | 0.910754i | \(0.635501\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.52392i | − | 0.369407i | ||||||
\(92\) | 5.34744 | + | 9.95656i | 0.557509 | + | 1.03804i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.91002 | − | 8.21043i | 0.506430 | − | 0.846841i | ||||
\(95\) | −16.2226 | −1.66440 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.05981 | 0.412212 | 0.206106 | − | 0.978530i | \(-0.433921\pi\) | ||||
0.206106 | + | 0.978530i | \(0.433921\pi\) | |||||||
\(98\) | 0.725842 | − | 1.21374i | 0.0733211 | − | 0.122606i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.18079 | + | 7.78435i | 0.418079 | + | 0.778435i | ||||
\(101\) | 10.3336i | 1.02823i | 0.857721 | + | 0.514116i | \(0.171880\pi\) | ||||
−0.857721 | + | 0.514116i | \(0.828120\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.94679 | 0.881554 | 0.440777 | − | 0.897617i | \(-0.354703\pi\) | ||||
0.440777 | + | 0.897617i | \(0.354703\pi\) | |||||||
\(104\) | 0.459295 | − | 9.95656i | 0.0450376 | − | 0.976321i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.9410 | − | 8.33705i | −1.35407 | − | 0.809766i | ||||
\(107\) | − | 17.8845i | − | 1.72896i | −0.502669 | − | 0.864479i | \(-0.667649\pi\) | ||
0.502669 | − | 0.864479i | \(-0.332351\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9610i | 1.14566i | 0.819676 | + | 0.572828i | \(0.194154\pi\) | ||||
−0.819676 | + | 0.572828i | \(0.805846\pi\) | |||||||
\(110\) | 12.9379 | − | 21.6344i | 1.23358 | − | 2.06276i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.20900 | − | 3.33471i | 0.208731 | − | 0.315101i | ||||
\(113\) | −13.3192 | −1.25297 | −0.626484 | − | 0.779434i | \(-0.715507\pi\) | ||||
−0.626484 | + | 0.779434i | \(0.715507\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.3417i | 1.61713i | ||||||||
\(116\) | −2.13890 | + | 1.14876i | −0.198592 | + | 0.106659i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.53382 | + | 5.70144i | 0.877659 | + | 0.524860i | ||||
\(119\) | 6.79736 | 0.623113 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −22.7352 | −2.06684 | ||||||||
\(122\) | −14.6323 | − | 8.75044i | −1.32474 | − | 0.792228i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.101619 | − | 0.189207i | −0.00912565 | − | 0.0169913i | ||||
\(125\) | − | 1.78606i | − | 0.159750i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.42140 | −0.658543 | −0.329271 | − | 0.944235i | \(-0.606803\pi\) | ||||
−0.329271 | + | 0.944235i | \(0.606803\pi\) | |||||||
\(128\) | 6.67600 | − | 9.13406i | 0.590081 | − | 0.807344i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.84960 | − | 13.1259i | 0.688455 | − | 1.15122i | ||||
\(131\) | − | 4.82695i | − | 0.421733i | −0.977515 | − | 0.210866i | \(-0.932372\pi\) | ||
0.977515 | − | 0.210866i | \(-0.0676285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.28617i | 0.458369i | ||||||||
\(134\) | 8.09492 | + | 4.84095i | 0.699294 | + | 0.418194i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.2054 | + | 0.885945i | 1.64685 | + | 0.0759691i | ||||
\(137\) | −14.8496 | −1.26868 | −0.634342 | − | 0.773052i | \(-0.718729\pi\) | ||||
−0.634342 | + | 0.773052i | \(0.718729\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.99694i | 0.423835i | 0.977288 | + | 0.211918i | \(0.0679708\pi\) | ||||
−0.977288 | + | 0.211918i | \(0.932029\pi\) | |||||||
\(140\) | 5.40724 | − | 2.90410i | 0.456995 | − | 0.245441i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.44063 | − | 2.40899i | 0.120895 | − | 0.202158i | ||||
\(143\) | −20.4676 | −1.71159 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.72542 | −0.309379 | ||||||||
\(146\) | −4.73886 | + | 7.92422i | −0.392191 | + | 0.655813i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.63775 | − | 4.63914i | 0.710019 | − | 0.381335i | ||||
\(149\) | 9.54688i | 0.782111i | 0.920367 | + | 0.391055i | \(0.127890\pi\) | ||||
−0.920367 | + | 0.391055i | \(0.872110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4778 | −0.934052 | −0.467026 | − | 0.884244i | \(-0.654675\pi\) | ||||
−0.467026 | + | 0.884244i | \(0.654675\pi\) | |||||||
\(152\) | −0.688981 | + | 14.9357i | −0.0558837 | + | 1.21144i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.04962 | − | 4.21584i | −0.568075 | − | 0.339722i | ||||
\(155\) | − | 0.329550i | − | 0.0264701i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.38325i | − | 0.110396i | −0.998475 | − | 0.0551979i | \(-0.982421\pi\) | ||
0.998475 | − | 0.0551979i | \(-0.0175790\pi\) | |||||||
\(158\) | 1.67482 | − | 2.80059i | 0.133241 | − | 0.222803i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.6562 | − | 7.50055i | 1.23773 | − | 0.592971i | ||||
\(161\) | 5.65085 | 0.445349 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0101i | 0.784050i | 0.919955 | + | 0.392025i | \(0.128225\pi\) | ||||
−0.919955 | + | 0.392025i | \(0.871775\pi\) | |||||||
\(164\) | 11.0581 | + | 20.5894i | 0.863491 | + | 1.60776i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.2682 | − | 9.13074i | −1.18504 | − | 0.708683i | ||||
\(167\) | 1.63373 | 0.126422 | 0.0632110 | − | 0.998000i | \(-0.479866\pi\) | ||||
0.0632110 | + | 0.998000i | \(0.479866\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.581993 | 0.0447687 | ||||||||
\(170\) | 25.3188 | + | 15.1413i | 1.94187 | + | 1.16128i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.27167 | − | 1.75714i | 0.249463 | − | 0.133981i | ||||
\(173\) | − | 3.93513i | − | 0.299182i | −0.988748 | − | 0.149591i | \(-0.952204\pi\) | ||
0.988748 | − | 0.149591i | \(-0.0477957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.41801 | 0.333970 | ||||||||
\(176\) | −19.3687 | − | 12.8303i | −1.45997 | − | 0.967124i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.65540 | + | 9.45683i | −0.423890 | + | 0.708819i | ||||
\(179\) | 0.199235i | 0.0148915i | 0.999972 | + | 0.00744577i | \(0.00237008\pi\) | ||||
−0.999972 | + | 0.00744577i | \(0.997630\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.14783i | − | 0.531294i | −0.964070 | − | 0.265647i | \(-0.914414\pi\) | ||
0.964070 | − | 0.265647i | \(-0.0855855\pi\) | |||||||
\(182\) | −4.27711 | − | 2.55781i | −0.317040 | − | 0.189597i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.9660 | + | 0.736512i | 1.17703 | + | 0.0542964i | ||||
\(185\) | 15.0447 | 1.10611 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 39.4805i | − | 2.88710i | ||||||
\(188\) | −6.40139 | − | 11.9189i | −0.466869 | − | 0.869278i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.7750 | + | 19.6899i | −0.854251 | + | 1.42846i | ||||
\(191\) | −17.8761 | −1.29347 | −0.646733 | − | 0.762717i | \(-0.723865\pi\) | ||||
−0.646733 | + | 0.762717i | \(0.723865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.2993 | −1.02928 | −0.514642 | − | 0.857405i | \(-0.672075\pi\) | ||||
−0.514642 | + | 0.857405i | \(0.672075\pi\) | |||||||
\(194\) | 2.94678 | − | 4.92754i | 0.211567 | − | 0.353777i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.946308 | − | 1.76196i | −0.0675934 | − | 0.125854i | ||||
\(197\) | 4.13436i | 0.294561i | 0.989095 | + | 0.147280i | \(0.0470520\pi\) | ||||
−0.989095 | + | 0.147280i | \(0.952948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5173 | 1.02910 | 0.514550 | − | 0.857460i | \(-0.327959\pi\) | ||||
0.514550 | + | 0.857460i | \(0.327959\pi\) | |||||||
\(200\) | 12.4827 | + | 0.575828i | 0.882663 | + | 0.0407172i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.5423 | + | 7.50055i | 0.882470 | + | 0.527737i | ||||
\(203\) | 1.21394i | 0.0852015i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 35.8614i | 2.50467i | ||||||||
\(206\) | 6.49395 | − | 10.8590i | 0.452455 | − | 0.756585i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.7513 | − | 7.78435i | −0.814803 | − | 0.539748i | ||||
\(209\) | 30.7031 | 2.12378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 13.9076i | − | 0.957439i | −0.877968 | − | 0.478719i | \(-0.841101\pi\) | ||
0.877968 | − | 0.478719i | \(-0.158899\pi\) | |||||||
\(212\) | −20.2380 | + | 10.8693i | −1.38995 | + | 0.746509i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −21.7070 | − | 12.9813i | −1.48386 | − | 0.887383i | ||||
\(215\) | 5.69841 | 0.388628 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.107385 | −0.00728974 | ||||||||
\(218\) | 14.5175 | + | 8.68179i | 0.983248 | + | 0.588005i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −16.8676 | − | 31.4063i | −1.13721 | − | 2.11742i | ||||
\(221\) | − | 23.9534i | − | 1.61128i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1591 | −0.814231 | −0.407115 | − | 0.913377i | \(-0.633465\pi\) | ||||
−0.407115 | + | 0.913377i | \(0.633465\pi\) | |||||||
\(224\) | −2.44407 | − | 5.10162i | −0.163301 | − | 0.340866i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.66766 | + | 16.1660i | −0.643083 | + | 1.07535i | ||||
\(227\) | − | 24.4059i | − | 1.61987i | −0.586517 | − | 0.809937i | \(-0.699501\pi\) | ||
0.586517 | − | 0.809937i | \(-0.300499\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.95033i | 0.128881i | 0.997922 | + | 0.0644407i | \(0.0205263\pi\) | ||||
−0.997922 | + | 0.0644407i | \(0.979474\pi\) | |||||||
\(230\) | 21.0483 | + | 12.5874i | 1.38788 | + | 0.829986i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.158220 | + | 3.42988i | −0.0103877 | + | 0.225183i | ||||
\(233\) | 16.3094 | 1.06847 | 0.534233 | − | 0.845337i | \(-0.320600\pi\) | ||||
0.534233 | + | 0.845337i | \(0.320600\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 20.7597i | − | 1.35421i | ||||||
\(236\) | 13.8401 | − | 7.43319i | 0.900913 | − | 0.483860i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.93381 | − | 8.25020i | 0.319811 | − | 0.534781i | ||||
\(239\) | 1.65345 | 0.106953 | 0.0534764 | − | 0.998569i | \(-0.482970\pi\) | ||||
0.0534764 | + | 0.998569i | \(0.482970\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.63938 | 0.234433 | 0.117217 | − | 0.993106i | \(-0.462603\pi\) | ||||
0.117217 | + | 0.993106i | \(0.462603\pi\) | |||||||
\(242\) | −16.5022 | + | 27.5946i | −1.06080 | + | 1.77385i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −21.2414 | + | 11.4083i | −1.35984 | + | 0.730341i | ||||
\(245\) | − | 3.06888i | − | 0.196063i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.6280 | 1.18527 | ||||||||
\(248\) | −0.303407 | − | 0.0139961i | −0.0192664 | − | 0.000888756i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.16781 | − | 1.29640i | −0.137104 | − | 0.0819916i | ||||
\(251\) | 25.2386i | 1.59305i | 0.604607 | + | 0.796524i | \(0.293330\pi\) | ||||
−0.604607 | + | 0.796524i | \(0.706670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 32.8213i | − | 2.06346i | ||||||
\(254\) | −5.38676 | + | 9.00762i | −0.337996 | + | 0.565188i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.24061 | − | 14.7328i | −0.390038 | − | 0.920799i | ||||
\(257\) | −14.2051 | −0.886087 | −0.443044 | − | 0.896500i | \(-0.646101\pi\) | ||||
−0.443044 | + | 0.896500i | \(0.646101\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.90235i | − | 0.304617i | ||||||
\(260\) | −10.2338 | − | 19.0547i | −0.634675 | − | 1.18172i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.85864 | − | 3.50360i | −0.361948 | − | 0.216453i | ||||
\(263\) | −16.3785 | −1.00994 | −0.504971 | − | 0.863137i | \(-0.668497\pi\) | ||||
−0.504971 | + | 0.863137i | \(0.668497\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.2493 | −2.16535 | ||||||||
\(266\) | 6.41601 | + | 3.83692i | 0.393391 | + | 0.235257i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.7513 | − | 6.31133i | 0.717822 | − | 0.385526i | ||||
\(269\) | − | 4.73448i | − | 0.288666i | −0.989529 | − | 0.144333i | \(-0.953896\pi\) | ||
0.989529 | − | 0.144333i | \(-0.0461037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3680 | 1.23727 | 0.618634 | − | 0.785679i | \(-0.287686\pi\) | ||||
0.618634 | + | 0.785679i | \(0.287686\pi\) | |||||||
\(272\) | 15.0154 | − | 22.6672i | 0.910442 | − | 1.37440i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.7784 | + | 18.0234i | −0.651149 | + | 1.08884i | ||||
\(275\) | − | 25.6607i | − | 1.54740i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 29.0135i | − | 1.74325i | −0.490170 | − | 0.871627i | \(-0.663065\pi\) | ||
0.490170 | − | 0.871627i | \(-0.336935\pi\) | |||||||
\(278\) | 6.06497 | + | 3.62699i | 0.363753 | + | 0.217532i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.399987 | − | 8.67087i | 0.0239038 | − | 0.518184i | ||||
\(281\) | −16.5849 | −0.989373 | −0.494687 | − | 0.869071i | \(-0.664717\pi\) | ||||
−0.494687 | + | 0.869071i | \(0.664717\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 21.8603i | − | 1.29946i | −0.760165 | − | 0.649730i | \(-0.774882\pi\) | ||
0.760165 | − | 0.649730i | \(-0.225118\pi\) | |||||||
\(284\) | −1.87821 | − | 3.49709i | −0.111451 | − | 0.207514i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.8563 | + | 24.8423i | −0.878470 | + | 1.46896i | ||||
\(287\) | 11.6855 | 0.689774 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.2041 | 1.71789 | ||||||||
\(290\) | −2.70406 | + | 4.52167i | −0.158788 | + | 0.265522i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.17824 | + | 11.5035i | 0.361554 | + | 0.673189i | ||||
\(293\) | 3.59022i | 0.209743i | 0.994486 | + | 0.104872i | \(0.0334431\pi\) | ||||
−0.994486 | + | 0.104872i | \(0.966557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.1059 | 1.40350 | ||||||||
\(296\) | 0.638956 | − | 13.8512i | 0.0371386 | − | 0.805086i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.5874 | + | 6.92952i | 0.671239 | + | 0.401416i | ||||
\(299\) | − | 19.9131i | − | 1.15161i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.85684i | − | 0.107026i | ||||||
\(302\) | −8.33108 | + | 13.9310i | −0.479400 | + | 0.801641i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.6279 | + | 11.6772i | 1.01103 | + | 0.669731i | ||||
\(305\) | −36.9971 | −2.11845 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.1418i | − | 0.978333i | −0.872191 | − | 0.489166i | \(-0.837301\pi\) | ||
0.872191 | − | 0.489166i | \(-0.162699\pi\) | |||||||
\(308\) | −10.2338 | + | 5.49635i | −0.583126 | + | 0.313184i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.399987 | − | 0.239201i | −0.0227177 | − | 0.0135857i | ||||
\(311\) | 21.2814 | 1.20676 | 0.603379 | − | 0.797454i | \(-0.293820\pi\) | ||||
0.603379 | + | 0.797454i | \(0.293820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.14361 | −0.403781 | −0.201890 | − | 0.979408i | \(-0.564708\pi\) | ||||
−0.201890 | + | 0.979408i | \(0.564708\pi\) | |||||||
\(314\) | −1.67891 | − | 1.00402i | −0.0947461 | − | 0.0566604i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.18352 | − | 4.06556i | −0.122833 | − | 0.228706i | ||||
\(317\) | 31.4066i | 1.76397i | 0.471277 | + | 0.881986i | \(0.343793\pi\) | ||||
−0.471277 | + | 0.881986i | \(0.656207\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.05078 | 0.394768 | ||||||||
\(320\) | 2.26026 | − | 24.4468i | 0.126353 | − | 1.36661i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.10162 | − | 6.85863i | 0.228574 | − | 0.382217i | ||||
\(323\) | 35.9320i | 1.99931i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 15.5687i | − | 0.863596i | ||||||
\(326\) | 12.1496 | + | 7.26574i | 0.672904 | + | 0.402412i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 33.0165 | + | 1.52305i | 1.82303 | + | 0.0840963i | ||||
\(329\) | −6.76459 | −0.372944 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6712i | 0.641506i | 0.947163 | + | 0.320753i | \(0.103936\pi\) | ||||
−0.947163 | + | 0.320753i | \(0.896064\pi\) | |||||||
\(332\) | −22.1646 | + | 11.9041i | −1.21644 | + | 0.653322i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.18583 | − | 1.98292i | 0.0648858 | − | 0.108500i | ||||
\(335\) | 20.4676 | 1.11827 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4008 | 1.11130 | 0.555652 | − | 0.831415i | \(-0.312469\pi\) | ||||
0.555652 | + | 0.831415i | \(0.312469\pi\) | |||||||
\(338\) | 0.422435 | − | 0.706385i | 0.0229774 | − | 0.0384223i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 36.7550 | − | 19.7402i | 1.99332 | − | 1.07056i | ||||
\(341\) | 0.623712i | 0.0337759i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.242014 | − | 5.24635i | 0.0130485 | − | 0.282864i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.77620 | − | 2.85628i | −0.256770 | − | 0.153554i | ||||
\(347\) | 12.5903i | 0.675881i | 0.941167 | + | 0.337940i | \(0.109730\pi\) | ||||
−0.941167 | + | 0.337940i | \(0.890270\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.8022i | 0.685286i | 0.939466 | + | 0.342643i | \(0.111322\pi\) | ||||
−0.939466 | + | 0.342643i | \(0.888678\pi\) | |||||||
\(350\) | 3.20677 | − | 5.36229i | 0.171409 | − | 0.286627i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −29.6312 | + | 14.1957i | −1.57935 | + | 0.756631i | ||||
\(353\) | 17.2495 | 0.918099 | 0.459050 | − | 0.888411i | \(-0.348190\pi\) | ||||
0.459050 | + | 0.888411i | \(0.348190\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 6.09103i | − | 0.323278i | ||||||
\(356\) | 7.37317 | + | 13.7283i | 0.390777 | + | 0.727600i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.241819 | + | 0.144613i | 0.0127805 | + | 0.00764304i | ||||
\(359\) | 1.52892 | 0.0806935 | 0.0403468 | − | 0.999186i | \(-0.487154\pi\) | ||||
0.0403468 | + | 0.999186i | \(0.487154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.94358 | −0.470715 | ||||||||
\(362\) | −8.67557 | − | 5.18819i | −0.455978 | − | 0.272685i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.20900 | + | 3.33471i | −0.325440 | + | 0.174786i | ||||
\(365\) | 20.0360i | 1.04873i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.04525 | −0.211160 | −0.105580 | − | 0.994411i | \(-0.533670\pi\) | ||||
−0.105580 | + | 0.994411i | \(0.533670\pi\) | |||||||
\(368\) | 12.4827 | − | 18.8439i | 0.650708 | − | 0.982308i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.9201 | − | 18.2603i | 0.567708 | − | 0.949309i | ||||
\(371\) | 11.4861i | 0.596326i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.1416i | 1.30178i | 0.759171 | + | 0.650891i | \(0.225605\pi\) | ||||
−0.759171 | + | 0.650891i | \(0.774395\pi\) | |||||||
\(374\) | −47.9188 | − | 28.6566i | −2.47782 | − | 1.48180i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.1128 | − | 0.881673i | −0.985669 | − | 0.0454688i | ||||
\(377\) | 4.27781 | 0.220318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.1885i | 0.523349i | 0.965156 | + | 0.261675i | \(0.0842747\pi\) | ||||
−0.965156 | + | 0.261675i | \(0.915725\pi\) | |||||||
\(380\) | 15.3516 | + | 28.5836i | 0.787519 | + | 1.46631i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.9752 | + | 21.6968i | −0.663868 | + | 1.11010i | ||||
\(383\) | −35.9423 | −1.83657 | −0.918284 | − | 0.395923i | \(-0.870425\pi\) | ||||
−0.918284 | + | 0.395923i | \(0.870425\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.8247 | −0.908429 | ||||||||
\(386\) | −10.3790 | + | 17.3555i | −0.528278 | + | 0.883373i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.84183 | − | 7.15323i | −0.195039 | − | 0.363150i | ||||
\(389\) | 6.81471i | 0.345519i | 0.984964 | + | 0.172760i | \(0.0552684\pi\) | ||||
−0.984964 | + | 0.172760i | \(0.944732\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.4108 | 1.94252 | ||||||||
\(392\) | −2.82542 | − | 0.130337i | −0.142705 | − | 0.00658299i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.01802 | + | 3.00089i | 0.252804 | + | 0.151183i | ||||
\(395\) | − | 7.08116i | − | 0.356292i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 11.1982i | − | 0.562021i | −0.959705 | − | 0.281010i | \(-0.909330\pi\) | ||
0.959705 | − | 0.281010i | \(-0.0906695\pi\) | |||||||
\(398\) | 10.5372 | − | 17.6201i | 0.528184 | − | 0.883216i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.75939 | − | 14.7328i | 0.487970 | − | 0.736639i | ||||
\(401\) | −29.9404 | −1.49515 | −0.747577 | − | 0.664175i | \(-0.768783\pi\) | ||||
−0.747577 | + | 0.664175i | \(0.768783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.378415i | 0.0188502i | ||||||||
\(404\) | 18.2074 | − | 9.77876i | 0.905851 | − | 0.486512i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.47340 | + | 0.881125i | 0.0731234 | + | 0.0437295i | ||||
\(407\) | −28.4739 | −1.41140 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0213 | −0.544968 | −0.272484 | − | 0.962160i | \(-0.587845\pi\) | ||||
−0.272484 | + | 0.962160i | \(0.587845\pi\) | |||||||
\(410\) | 43.5262 | + | 26.0297i | 2.14961 | + | 1.28551i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.46642 | − | 15.7639i | −0.417110 | − | 0.776631i | ||||
\(413\) | − | 7.85494i | − | 0.386516i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.6050 | −1.89505 | ||||||||
\(416\) | −17.9777 | + | 8.61271i | −0.881429 | + | 0.422273i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 22.2856 | − | 37.2655i | 1.09003 | − | 1.82272i | ||||
\(419\) | − | 14.0133i | − | 0.684594i | −0.939592 | − | 0.342297i | \(-0.888795\pi\) | ||
0.939592 | − | 0.342297i | \(-0.111205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 19.4716i | − | 0.948988i | −0.880259 | − | 0.474494i | \(-0.842631\pi\) | ||
0.880259 | − | 0.474494i | \(-0.157369\pi\) | |||||||
\(422\) | −16.8801 | − | 10.0947i | −0.821713 | − | 0.491403i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.49705 | + | 32.4529i | −0.0727033 | + | 1.57605i | ||||
\(425\) | 30.0308 | 1.45671 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0556i | 0.583410i | ||||||||
\(428\) | −31.5117 | + | 16.9242i | −1.52318 | + | 0.818063i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.13614 | − | 6.91636i | 0.199462 | − | 0.333536i | ||||
\(431\) | 37.2120 | 1.79244 | 0.896219 | − | 0.443612i | \(-0.146303\pi\) | ||||
0.896219 | + | 0.443612i | \(0.146303\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.4042 | −1.12474 | −0.562368 | − | 0.826887i | \(-0.690109\pi\) | ||||
−0.562368 | + | 0.826887i | \(0.690109\pi\) | |||||||
\(434\) | −0.0779442 | + | 0.130337i | −0.00374144 | + | 0.00625635i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.0748 | − | 11.3188i | 1.00930 | − | 0.542071i | ||||
\(437\) | 29.8713i | 1.42894i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7533 | 1.03823 | 0.519115 | − | 0.854705i | \(-0.326262\pi\) | ||||
0.519115 | + | 0.854705i | \(0.326262\pi\) | |||||||
\(440\) | −50.3622 | − | 2.32321i | −2.40092 | − | 0.110754i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −29.0730 | − | 17.3863i | −1.38286 | − | 0.826984i | ||||
\(443\) | − | 12.8369i | − | 0.609901i | −0.952368 | − | 0.304951i | \(-0.901360\pi\) | ||
0.952368 | − | 0.304951i | \(-0.0986400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.9112i | 1.13350i | ||||||||
\(446\) | −8.82555 | + | 14.7579i | −0.417902 | + | 0.698806i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.96602 | − | 0.736512i | −0.376359 | − | 0.0347969i | ||||
\(449\) | 11.7889 | 0.556353 | 0.278176 | − | 0.960530i | \(-0.410270\pi\) | ||||
0.278176 | + | 0.960530i | \(0.410270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 67.8718i | − | 3.19596i | ||||||
\(452\) | 12.6041 | + | 23.4680i | 0.592847 | + | 1.10384i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −29.6223 | − | 17.7148i | −1.39024 | − | 0.831397i | ||||
\(455\) | −10.8145 | −0.506990 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.5157 | −1.56780 | −0.783900 | − | 0.620888i | \(-0.786772\pi\) | ||||
−0.783900 | + | 0.620888i | \(0.786772\pi\) | |||||||
\(458\) | 2.36718 | + | 1.41563i | 0.110611 | + | 0.0661480i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 30.5555 | − | 16.4106i | 1.42466 | − | 0.765150i | ||||
\(461\) | 10.0902i | 0.469946i | 0.972002 | + | 0.234973i | \(0.0755002\pi\) | ||||
−0.972002 | + | 0.234973i | \(0.924500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.6131 | −1.09739 | −0.548697 | − | 0.836021i | \(-0.684876\pi\) | ||||
−0.548697 | + | 0.836021i | \(0.684876\pi\) | |||||||
\(464\) | 4.04812 | + | 2.68159i | 0.187929 | + | 0.124490i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.8381 | − | 19.7953i | 0.548388 | − | 0.917001i | ||||
\(467\) | 2.52944i | 0.117048i | 0.998286 | + | 0.0585242i | \(0.0186395\pi\) | ||||
−0.998286 | + | 0.0585242i | \(0.981361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.66942i | − | 0.307965i | ||||||
\(470\) | −25.1968 | − | 15.0683i | −1.16224 | − | 0.695047i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.02379 | − | 22.1935i | 0.0471236 | − | 1.02154i | ||||
\(473\) | −10.7849 | −0.495890 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.3543i | 1.07157i | ||||||||
\(476\) | −6.43240 | − | 11.9767i | −0.294828 | − | 0.548950i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.20014 | − | 2.00685i | 0.0548933 | − | 0.0917912i | ||||
\(479\) | −15.1106 | −0.690421 | −0.345210 | − | 0.938525i | \(-0.612192\pi\) | ||||
−0.345210 | + | 0.938525i | \(0.612192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.2755 | −0.787695 | ||||||||
\(482\) | 2.64161 | − | 4.41725i | 0.120322 | − | 0.201200i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.5145 | + | 40.0586i | 0.977933 | + | 1.82084i | ||||
\(485\) | − | 12.4591i | − | 0.565737i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.1541 | 1.86487 | 0.932436 | − | 0.361335i | \(-0.117679\pi\) | ||||
0.932436 | + | 0.361335i | \(0.117679\pi\) | |||||||
\(488\) | −1.57128 | + | 34.0621i | −0.0711286 | + | 1.54192i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.72481 | − | 2.22752i | −0.168270 | − | 0.100629i | ||||
\(491\) | 36.6868i | 1.65565i | 0.560984 | + | 0.827827i | \(0.310423\pi\) | ||||
−0.560984 | + | 0.827827i | \(0.689577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.25156i | 0.371631i | ||||||||
\(494\) | 13.5210 | − | 22.6095i | 0.608339 | − | 1.01725i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.237213 | + | 0.358097i | −0.0106512 | + | 0.0160790i | ||||
\(497\) | −1.98478 | −0.0890294 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.1824i | 0.903489i | 0.892147 | + | 0.451744i | \(0.149198\pi\) | ||||
−0.892147 | + | 0.451744i | \(0.850802\pi\) | |||||||
\(500\) | −3.14697 | + | 1.69017i | −0.140737 | + | 0.0755866i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30.6330 | + | 18.3192i | 1.36722 | + | 0.817628i | ||||
\(503\) | 10.5011 | 0.468222 | 0.234111 | − | 0.972210i | \(-0.424782\pi\) | ||||
0.234111 | + | 0.972210i | \(0.424782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.7125 | 1.41119 | ||||||||
\(506\) | −39.8363 | − | 23.8230i | −1.77094 | − | 1.05906i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.02293 | + | 13.0762i | 0.311592 | + | 0.580163i | ||||
\(509\) | − | 28.5910i | − | 1.26727i | −0.773630 | − | 0.633637i | \(-0.781561\pi\) | ||
0.773630 | − | 0.633637i | \(-0.218439\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.52879 | 0.288816 | ||||||||
\(512\) | −22.4114 | − | 3.11922i | −0.990453 | − | 0.137851i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.3106 | + | 17.2412i | −0.454782 | + | 0.760476i | ||||
\(515\) | − | 27.4566i | − | 1.20988i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.2901i | 1.72798i | ||||||||
\(518\) | −5.95016 | − | 3.55833i | −0.261435 | − | 0.156344i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −30.5555 | − | 1.40952i | −1.33995 | − | 0.0618116i | ||||
\(521\) | 10.8325 | 0.474578 | 0.237289 | − | 0.971439i | \(-0.423741\pi\) | ||||
0.237289 | + | 0.971439i | \(0.423741\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.77247i | 0.0775047i | 0.999249 | + | 0.0387523i | \(0.0123383\pi\) | ||||
−0.999249 | + | 0.0387523i | \(0.987662\pi\) | |||||||
\(524\) | −8.50489 | + | 4.56778i | −0.371538 | + | 0.199544i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.8882 | + | 19.8792i | −0.518350 | + | 0.866772i | ||||
\(527\) | −0.729932 | −0.0317963 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.93205 | 0.388350 | ||||||||
\(530\) | −25.5854 | + | 42.7833i | −1.11136 | + | 1.85839i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.31402 | − | 5.00234i | 0.403814 | − | 0.216879i | ||||
\(533\) | − | 41.1788i | − | 1.78365i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −54.8853 | −2.37290 | ||||||||
\(536\) | 0.869270 | − | 18.8439i | 0.0375467 | − | 0.813934i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.74641 | − | 3.43648i | −0.247745 | − | 0.148157i | ||||
\(539\) | 5.80820i | 0.250177i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 11.0556i | − | 0.475316i | −0.971349 | − | 0.237658i | \(-0.923620\pi\) | ||
0.971349 | − | 0.237658i | \(-0.0763797\pi\) | |||||||
\(542\) | 14.7840 | − | 24.7214i | 0.635025 | − | 1.06187i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.6132 | − | 34.6776i | −0.712287 | − | 1.48679i | ||||
\(545\) | 36.7068 | 1.57235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.55978i | 0.237719i | 0.992911 | + | 0.118859i | \(0.0379238\pi\) | ||||
−0.992911 | + | 0.118859i | \(0.962076\pi\) | |||||||
\(548\) | 14.0523 | + | 26.1643i | 0.600283 | + | 1.11769i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −31.1453 | − | 18.6256i | −1.32804 | − | 0.794198i | ||||
\(551\) | −6.41707 | −0.273376 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.30741 | −0.0981211 | ||||||||
\(554\) | −35.2147 | − | 21.0592i | −1.49613 | − | 0.894720i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.80441 | − | 4.72865i | 0.373390 | − | 0.200539i | ||||
\(557\) | − | 4.30560i | − | 0.182434i | −0.995831 | − | 0.0912171i | \(-0.970924\pi\) | ||
0.995831 | − | 0.0912171i | \(-0.0290757\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.54335 | −0.276754 | ||||||||
\(560\) | −10.2338 | − | 6.77916i | −0.432458 | − | 0.286472i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0380 | + | 20.1297i | −0.507793 | + | 0.849120i | ||||
\(563\) | 2.43447i | 0.102601i | 0.998683 | + | 0.0513003i | \(0.0163366\pi\) | ||||
−0.998683 | + | 0.0513003i | \(0.983663\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.8751i | 1.71963i | ||||||||
\(566\) | −26.5326 | − | 15.8671i | −1.11525 | − | 0.666944i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.60783 | − | 0.258689i | −0.235299 | − | 0.0108543i | ||||
\(569\) | 10.9163 | 0.457635 | 0.228818 | − | 0.973469i | \(-0.426514\pi\) | ||||
0.228818 | + | 0.973469i | \(0.426514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3442i | 0.474740i | 0.971419 | + | 0.237370i | \(0.0762854\pi\) | ||||
−0.971419 | + | 0.237370i | \(0.923715\pi\) | |||||||
\(572\) | 19.3687 | + | 36.0632i | 0.809845 | + | 1.50788i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.48183 | − | 14.1831i | 0.354025 | − | 0.591992i | ||||
\(575\) | 24.9655 | 1.04113 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.97962 | 0.332196 | 0.166098 | − | 0.986109i | \(-0.446883\pi\) | ||||
0.166098 | + | 0.986109i | \(0.446883\pi\) | |||||||
\(578\) | 21.1976 | − | 35.4461i | 0.881703 | − | 1.47436i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.52539 | + | 6.56404i | 0.146384 | + | 0.272557i | ||||
\(581\) | 12.5795i | 0.521887i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 66.7133 | 2.76298 | ||||||||
\(584\) | 18.4466 | + | 0.850939i | 0.763325 | + | 0.0352121i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.35758 | + | 2.60593i | 0.180010 | + | 0.107650i | ||||
\(587\) | 41.7410i | 1.72283i | 0.507898 | + | 0.861417i | \(0.330423\pi\) | ||||
−0.507898 | + | 0.861417i | \(0.669577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.567653i | − | 0.0233897i | ||||||
\(590\) | 17.4970 | − | 29.2581i | 0.720341 | − | 1.20454i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.3479 | − | 10.8293i | −0.671896 | − | 0.445082i | ||||
\(593\) | 4.43527 | 0.182135 | 0.0910673 | − | 0.995845i | \(-0.470972\pi\) | ||||
0.0910673 | + | 0.995845i | \(0.470972\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 20.8603i | − | 0.855188i | ||||||
\(596\) | 16.8212 | − | 9.03429i | 0.689024 | − | 0.370059i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.1693 | − | 14.4538i | −0.988355 | − | 0.591059i | ||||
\(599\) | 12.4875 | 0.510224 | 0.255112 | − | 0.966911i | \(-0.417888\pi\) | ||||
0.255112 | + | 0.966911i | \(0.417888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.1871 | 1.51690 | 0.758448 | − | 0.651734i | \(-0.225958\pi\) | ||||
0.758448 | + | 0.651734i | \(0.225958\pi\) | |||||||
\(602\) | −2.25371 | − | 1.34777i | −0.0918544 | − | 0.0549310i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.8615 | + | 20.2235i | 0.441950 | + | 0.822881i | ||||
\(605\) | 69.7716i | 2.83662i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.8403 | −0.886470 | −0.443235 | − | 0.896405i | \(-0.646169\pi\) | ||||
−0.443235 | + | 0.896405i | \(0.646169\pi\) | |||||||
\(608\) | 26.9680 | − | 12.9198i | 1.09370 | − | 0.523966i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −26.8540 | + | 44.9047i | −1.08729 | + | 1.81814i | ||||
\(611\) | 23.8379i | 0.964377i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 30.7687i | − | 1.24274i | −0.783519 | − | 0.621368i | \(-0.786577\pi\) | ||
0.783519 | − | 0.621368i | \(-0.213423\pi\) | |||||||
\(614\) | −20.8056 | − | 12.4422i | −0.839645 | − | 0.502127i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.757021 | + | 16.4106i | −0.0305013 | + | 0.661203i | ||||
\(617\) | 38.0402 | 1.53144 | 0.765721 | − | 0.643173i | \(-0.222383\pi\) | ||||
0.765721 | + | 0.643173i | \(0.222383\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.9005i | 0.598903i | 0.954111 | + | 0.299452i | \(0.0968037\pi\) | ||||
−0.954111 | + | 0.299452i | \(0.903196\pi\) | |||||||
\(620\) | −0.580654 | + | 0.311856i | −0.0233196 | + | 0.0125244i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.4469 | − | 25.8300i | 0.619366 | − | 1.03569i | ||||
\(623\) | 7.79151 | 0.312160 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.5712 | −1.10285 | ||||||||
\(626\) | −5.18513 | + | 8.67045i | −0.207239 | + | 0.346541i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.43724 | + | 1.30898i | −0.0972564 | + | 0.0522342i | ||||
\(629\) | − | 33.3231i | − | 1.32868i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.8787 | −1.07002 | −0.535011 | − | 0.844845i | \(-0.679693\pi\) | ||||
−0.535011 | + | 0.844845i | \(0.679693\pi\) | |||||||
\(632\) | −6.51941 | − | 0.300740i | −0.259328 | − | 0.0119628i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 38.1193 | + | 22.7962i | 1.51391 | + | 0.905354i | ||||
\(635\) | 22.7754i | 0.903813i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.52392i | 0.139623i | ||||||||
\(638\) | 5.11775 | − | 8.55779i | 0.202614 | − | 0.338806i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28.0313 | − | 20.4878i | −1.10803 | − | 0.809853i | ||||
\(641\) | −12.4910 | −0.493365 | −0.246682 | − | 0.969096i | \(-0.579340\pi\) | ||||
−0.246682 | + | 0.969096i | \(0.579340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.53414i | 0.139373i | 0.997569 | + | 0.0696864i | \(0.0221999\pi\) | ||||
−0.997569 | + | 0.0696864i | \(0.977800\pi\) | |||||||
\(644\) | −5.34744 | − | 9.95656i | −0.210719 | − | 0.392343i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 43.6119 | + | 26.0809i | 1.71589 | + | 1.02614i | ||||
\(647\) | 28.3282 | 1.11370 | 0.556848 | − | 0.830614i | \(-0.312010\pi\) | ||||
0.556848 | + | 0.830614i | \(0.312010\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −45.6231 | −1.79086 | ||||||||
\(650\) | −18.8963 | − | 11.3004i | −0.741173 | − | 0.443239i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.6374 | − | 9.47262i | 0.690732 | − | 0.370976i | ||||
\(653\) | − | 29.9962i | − | 1.17384i | −0.809644 | − | 0.586921i | \(-0.800340\pi\) | ||
0.809644 | − | 0.586921i | \(-0.199660\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.8133 | −0.578804 | ||||||||
\(656\) | 25.8133 | − | 38.9678i | 1.00784 | − | 1.52144i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.91002 | + | 8.21043i | −0.191413 | + | 0.320076i | ||||
\(659\) | − | 16.0647i | − | 0.625793i | −0.949787 | − | 0.312896i | \(-0.898701\pi\) | ||
0.949787 | − | 0.312896i | \(-0.101299\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 44.3984i | − | 1.72690i | −0.504435 | − | 0.863450i | \(-0.668299\pi\) | ||
0.504435 | − | 0.863450i | \(-0.331701\pi\) | |||||||
\(662\) | 14.1657 | + | 8.47143i | 0.550567 | + | 0.329252i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.63957 | + | 35.5425i | −0.0636277 | + | 1.37932i | ||||
\(665\) | 16.2226 | 0.629086 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.85976i | 0.265611i | ||||||||
\(668\) | −1.54601 | − | 2.87857i | −0.0598170 | − | 0.111375i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.8563 | − | 24.8423i | 0.573948 | − | 0.959742i | ||||
\(671\) | 70.0213 | 2.70314 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.0649 | −1.92986 | −0.964930 | − | 0.262508i | \(-0.915450\pi\) | ||||
−0.964930 | + | 0.262508i | \(0.915450\pi\) | |||||||
\(674\) | 14.8078 | − | 24.7612i | 0.570374 | − | 0.953767i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.550744 | − | 1.02545i | −0.0211825 | − | 0.0394403i | ||||
\(677\) | 30.1370i | 1.15826i | 0.815236 | + | 0.579129i | \(0.196607\pi\) | ||||
−0.815236 | + | 0.579129i | \(0.803393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.05981 | −0.155801 | ||||||||
\(680\) | 2.71886 | − | 58.9391i | 0.104263 | − | 2.26021i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.757021 | + | 0.452716i | 0.0289878 | + | 0.0173354i | ||||
\(683\) | 1.49520i | 0.0572124i | 0.999591 | + | 0.0286062i | \(0.00910688\pi\) | ||||
−0.999591 | + | 0.0286062i | \(0.990893\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45.5715i | 1.74120i | ||||||||
\(686\) | −0.725842 | + | 1.21374i | −0.0277128 | + | 0.0463406i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.19202 | − | 4.10176i | −0.236069 | − | 0.156378i | ||||
\(689\) | 40.4759 | 1.54201 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.438347i | 0.0166755i | 0.999965 | + | 0.00833774i | \(0.00265402\pi\) | ||||
−0.999965 | + | 0.00833774i | \(0.997346\pi\) | |||||||
\(692\) | −6.93353 | + | 3.72384i | −0.263573 | + | 0.141559i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.2813 | + | 9.13854i | 0.580068 | + | 0.346894i | ||||
\(695\) | 15.3350 | 0.581690 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 79.4306 | 3.00865 | ||||||||
\(698\) | 15.5385 | + | 9.29236i | 0.588140 | + | 0.351721i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.18079 | − | 7.78435i | −0.158019 | − | 0.294221i | ||||
\(701\) | − | 43.1330i | − | 1.62911i | −0.580084 | − | 0.814556i | \(-0.696980\pi\) | ||
0.580084 | − | 0.814556i | \(-0.303020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.9147 | 0.977390 | ||||||||
\(704\) | −4.27781 | + | 46.2683i | −0.161226 | + | 1.74380i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.5204 | − | 20.9364i | 0.471212 | − | 0.787950i | ||||
\(707\) | − | 10.3336i | − | 0.388635i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8542i | 1.15875i | 0.815060 | + | 0.579376i | \(0.196704\pi\) | ||||
−0.815060 | + | 0.579376i | \(0.803296\pi\) | |||||||
\(710\) | −7.39290 | − | 4.42113i | −0.277451 | − | 0.165922i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22.0143 | + | 1.01552i | 0.825021 | + | 0.0380582i | ||||
\(713\) | −0.606814 | −0.0227254 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.8127i | 2.34906i | ||||||||
\(716\) | 0.351044 | − | 0.188538i | 0.0131191 | − | 0.00704599i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.10976 | − | 1.85571i | 0.0414158 | − | 0.0692544i | ||||
\(719\) | 2.24406 | 0.0836895 | 0.0418447 | − | 0.999124i | \(-0.486677\pi\) | ||||
0.0418447 | + | 0.999124i | \(0.486677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.94679 | −0.333196 | ||||||||
\(722\) | −6.49162 | + | 10.8551i | −0.241593 | + | 0.403987i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.5942 | + | 6.76404i | −0.468059 | + | 0.251384i | ||||
\(725\) | 5.36317i | 0.199183i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.9794 | −0.629733 | −0.314866 | − | 0.949136i | \(-0.601960\pi\) | ||||
−0.314866 | + | 0.949136i | \(0.601960\pi\) | |||||||
\(728\) | −0.459295 | + | 9.95656i | −0.0170226 | + | 0.369015i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 24.3185 | + | 14.5430i | 0.900066 | + | 0.538260i | ||||
\(731\) | − | 12.6216i | − | 0.466827i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.0255i | − | 1.25676i | −0.777906 | − | 0.628380i | \(-0.783718\pi\) | ||
0.777906 | − | 0.628380i | \(-0.216282\pi\) | |||||||
\(734\) | −2.93621 | + | 4.90987i | −0.108378 | + | 0.181226i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.8111 | − | 28.8285i | −0.509083 | − | 1.06263i | ||||
\(737\) | −38.7374 | −1.42691 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 0.0107994i | − | 0.000397263i | −1.00000 | 0.000198632i | \(-0.999937\pi\) | |||
1.00000 | 0.000198632i | \(-6.32264e-5\pi\) | ||||||||
\(740\) | −14.2369 | − | 26.5082i | −0.523360 | − | 0.974461i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.9410 | + | 8.33705i | 0.511791 | + | 0.306063i | ||||
\(743\) | 45.6360 | 1.67422 | 0.837112 | − | 0.547032i | \(-0.184242\pi\) | ||||
0.837112 | + | 0.547032i | \(0.184242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.2982 | 1.07340 | ||||||||
\(746\) | 30.5152 | + | 18.2488i | 1.11724 | + | 0.668137i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −69.5630 | + | 37.3607i | −2.54347 | + | 1.36604i | ||||
\(749\) | 17.8845i | 0.653485i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.95000 | −0.144138 | −0.0720688 | − | 0.997400i | \(-0.522960\pi\) | ||||
−0.0720688 | + | 0.997400i | \(0.522960\pi\) | |||||||
\(752\) | −14.9430 | + | 22.5580i | −0.544915 | + | 0.822604i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.10501 | − | 5.19213i | 0.113078 | − | 0.189086i | ||||
\(755\) | 35.2240i | 1.28193i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.6412i | 0.677524i | 0.940872 | + | 0.338762i | \(0.110008\pi\) | ||||
−0.940872 | + | 0.338762i | \(0.889992\pi\) | |||||||
\(758\) | 12.3662 | + | 7.39525i | 0.449160 | + | 0.268608i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 45.8357 | + | 2.11440i | 1.66264 | + | 0.0766973i | ||||
\(761\) | 4.86842 | 0.176480 | 0.0882401 | − | 0.996099i | \(-0.471876\pi\) | ||||
0.0882401 | + | 0.996099i | \(0.471876\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 11.9610i | − | 0.433017i | ||||||
\(764\) | 16.9162 | + | 31.4969i | 0.612008 | + | 1.13952i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.0884 | + | 43.6245i | −0.942614 | + | 1.57622i | ||||
\(767\) | −27.6802 | −0.999473 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.48442 | −0.0535297 | −0.0267649 | − | 0.999642i | \(-0.508521\pi\) | ||||
−0.0267649 | + | 0.999642i | \(0.508521\pi\) | |||||||
\(770\) | −12.9379 | + | 21.6344i | −0.466249 | + | 0.779651i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.5315 | + | 25.1947i | 0.487010 | + | 0.906779i | ||||
\(773\) | 14.2868i | 0.513861i | 0.966430 | + | 0.256931i | \(0.0827112\pi\) | ||||
−0.966430 | + | 0.256931i | \(0.917289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.474426 | −0.0170419 | ||||||||
\(776\) | −11.4707 | − | 0.529142i | −0.411774 | − | 0.0189951i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.27125 | + | 4.94640i | 0.296539 | + | 0.177337i | ||||
\(779\) | 61.7716i | 2.21320i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.5280i | 0.412504i | ||||||||
\(782\) | 27.8802 | − | 46.6206i | 0.996993 | − | 1.66715i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.20900 | + | 3.33471i | −0.0788930 | + | 0.119097i | ||||
\(785\) | −4.24504 | −0.151512 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.3799i | 0.797758i | 0.917004 | + | 0.398879i | \(0.130601\pi\) | ||||
−0.917004 | + | 0.398879i | \(0.869399\pi\) | |||||||
\(788\) | 7.28458 | − | 3.91238i | 0.259502 | − | 0.139373i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.59466 | − | 5.13980i | −0.305784 | − | 0.182866i | ||||
\(791\) | 13.3192 | 0.473578 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.4829 | 1.50861 | ||||||||
\(794\) | −13.5916 | − | 8.12811i | −0.482349 | − | 0.288456i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.7378 | − | 25.5788i | −0.486923 | − | 0.906617i | ||||
\(797\) | − | 23.1872i | − | 0.821334i | −0.911785 | − | 0.410667i | \(-0.865296\pi\) | ||
0.911785 | − | 0.410667i | \(-0.134704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.9814 | −1.62670 | ||||||||
\(800\) | −10.7979 | − | 22.5390i | −0.381764 | − | 0.796874i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.7320 | + | 36.3398i | −0.767384 | + | 1.28320i | ||||
\(803\) | − | 37.9205i | − | 1.33819i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 17.3417i | − | 0.611216i | ||||||
\(806\) | 0.459295 | + | 0.274669i | 0.0161780 | + | 0.00967481i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.34685 | − | 29.1968i | 0.0473818 | − | 1.02714i | ||||
\(809\) | −44.8263 | −1.57601 | −0.788004 | − | 0.615670i | \(-0.788886\pi\) | ||||
−0.788004 | + | 0.615670i | \(0.788886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18.4358i | − | 0.647370i | −0.946165 | − | 0.323685i | \(-0.895078\pi\) | ||
0.946165 | − | 0.323685i | \(-0.104922\pi\) | |||||||
\(812\) | 2.13890 | − | 1.14876i | 0.0750608 | − | 0.0403134i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.6675 | + | 34.5598i | −0.724396 | + | 1.21132i | ||||
\(815\) | 30.7197 | 1.07606 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.81556 | 0.343403 | ||||||||
\(818\) | −7.99972 | + | 13.3769i | −0.279704 | + | 0.467714i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 63.1863 | − | 33.9359i | 2.20656 | − | 1.18509i | ||||
\(821\) | − | 21.0533i | − | 0.734764i | −0.930070 | − | 0.367382i | \(-0.880254\pi\) | ||
0.930070 | − | 0.367382i | \(-0.119746\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.3206 | −1.12663 | −0.563313 | − | 0.826244i | \(-0.690473\pi\) | ||||
−0.563313 | + | 0.826244i | \(0.690473\pi\) | |||||||
\(824\) | −25.2785 | − | 1.16609i | −0.880617 | − | 0.0406228i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.53382 | − | 5.70144i | −0.331724 | − | 0.198379i | ||||
\(827\) | 12.4599i | 0.433272i | 0.976252 | + | 0.216636i | \(0.0695085\pi\) | ||||
−0.976252 | + | 0.216636i | \(0.930492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.78073i | 0.235504i | 0.993043 | + | 0.117752i | \(0.0375689\pi\) | ||||
−0.993043 | + | 0.117752i | \(0.962431\pi\) | |||||||
\(830\) | −28.0211 | + | 46.8563i | −0.972628 | + | 1.62641i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.59541 | + | 28.0716i | −0.0899796 | + | 0.973209i | ||||
\(833\) | −6.79736 | −0.235515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.01372i | − | 0.173507i | ||||||
\(836\) | −29.0546 | − | 54.0977i | −1.00488 | − | 1.87101i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.0084 | − | 10.1714i | −0.587546 | − | 0.351366i | ||||
\(839\) | 23.6268 | 0.815687 | 0.407843 | − | 0.913052i | \(-0.366281\pi\) | ||||
0.407843 | + | 0.913052i | \(0.366281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.5264 | 0.949185 | ||||||||
\(842\) | −23.6334 | − | 14.1333i | −0.814460 | − | 0.487066i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.5046 | + | 13.1609i | −0.843484 | + | 0.453016i | ||||
\(845\) | − | 1.78606i | − | 0.0614425i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.7352 | 0.781192 | ||||||||
\(848\) | 38.3027 | + | 25.3727i | 1.31532 | + | 0.871303i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 21.7976 | − | 36.4494i | 0.747652 | − | 1.25021i | ||||
\(851\) | − | 27.7024i | − | 0.949628i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.7202i | − | 0.606727i | −0.952875 | − | 0.303363i | \(-0.901890\pi\) | ||
0.952875 | − | 0.303363i | \(-0.0981096\pi\) | |||||||
\(854\) | 14.6323 | + | 8.75044i | 0.500707 | + | 0.299434i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.33100 | + | 50.5312i | −0.0796720 | + | 1.72712i | ||||
\(857\) | 13.5262 | 0.462046 | 0.231023 | − | 0.972948i | \(-0.425793\pi\) | ||||
0.231023 | + | 0.972948i | \(0.425793\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.6249i | 0.942548i | 0.881987 | + | 0.471274i | \(0.156206\pi\) | ||||
−0.881987 | + | 0.471274i | \(0.843794\pi\) | |||||||
\(860\) | −5.39245 | − | 10.0404i | −0.183881 | − | 0.342374i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.0100 | − | 45.1655i | 0.919964 | − | 1.53834i | ||||
\(863\) | 39.9545 | 1.36007 | 0.680034 | − | 0.733181i | \(-0.261965\pi\) | ||||
0.680034 | + | 0.733181i | \(0.261965\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0764 | −0.410610 | ||||||||
\(866\) | −16.9878 | + | 28.4065i | −0.577268 | + | 0.965294i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.101619 | + | 0.189207i | 0.00344917 | + | 0.00642212i | ||||
\(869\) | 13.4019i | 0.454629i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.5025 | −0.796352 | ||||||||
\(872\) | 1.55895 | − | 33.7949i | 0.0527929 | − | 1.14444i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 36.2559 | + | 21.6819i | 1.22637 | + | 0.733400i | ||||
\(875\) | 1.78606i | 0.0603800i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3922i | 0.384687i | 0.981328 | + | 0.192343i | \(0.0616087\pi\) | ||||
−0.981328 | + | 0.192343i | \(0.938391\pi\) | |||||||
\(878\) | 15.7895 | − | 26.4028i | 0.532869 | − | 0.891051i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −39.3747 | + | 59.4401i | −1.32732 | + | 2.00373i | ||||
\(881\) | −36.3753 | −1.22551 | −0.612757 | − | 0.790271i | \(-0.709940\pi\) | ||||
−0.612757 | + | 0.790271i | \(0.709940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.0983i | 1.75325i | 0.481177 | + | 0.876624i | \(0.340210\pi\) | ||||
−0.481177 | + | 0.876624i | \(0.659790\pi\) | |||||||
\(884\) | −42.2048 | + | 22.6672i | −1.41950 | + | 0.762382i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.5807 | − | 9.31759i | −0.523442 | − | 0.313030i | ||||
\(887\) | −45.0095 | −1.51127 | −0.755635 | − | 0.654992i | \(-0.772672\pi\) | ||||
−0.755635 | + | 0.654992i | \(0.772672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.42140 | 0.248906 | ||||||||
\(890\) | 29.0219 | + | 17.3557i | 0.972815 | + | 0.581766i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.5062 | + | 21.4238i | 0.385256 | + | 0.717321i | ||||
\(893\) | − | 35.7588i | − | 1.19662i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.611428 | 0.0204378 | ||||||||
\(896\) | −6.67600 | + | 9.13406i | −0.223030 | + | 0.305147i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.55688 | − | 14.3086i | 0.285547 | − | 0.477485i | ||||
\(899\) | − | 0.130358i | − | 0.00434768i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 78.0748i | 2.60105i | ||||||||
\(902\) | −82.3784 | − | 49.2642i | −2.74290 | − | 1.64032i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.6325 | + | 1.73598i | 1.25164 | + | 0.0577379i | ||||
\(905\) | −21.9358 | −0.729171 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 7.96941i | − | 0.264620i | −0.991208 | − | 0.132310i | \(-0.957761\pi\) | ||
0.991208 | − | 0.132310i | \(-0.0422394\pi\) | |||||||
\(908\) | −43.0022 | + | 23.0955i | −1.42708 | + | 0.766450i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.84960 | + | 13.1259i | −0.260212 | + | 0.435120i | ||||
\(911\) | 47.8457 | 1.58520 | 0.792600 | − | 0.609742i | \(-0.208727\pi\) | ||||
0.792600 | + | 0.609742i | \(0.208727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73.0645 | 2.41808 | ||||||||
\(914\) | −24.3271 | + | 40.6792i | −0.804669 | + | 1.34555i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.43640 | − | 1.84561i | 0.113542 | − | 0.0609807i | ||||
\(917\) | 4.82695i | 0.159400i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2279 | 1.19505 | 0.597525 | − | 0.801851i | \(-0.296151\pi\) | ||||
0.597525 | + | 0.801851i | \(0.296151\pi\) | |||||||
\(920\) | 2.26026 | − | 48.9978i | 0.0745187 | − | 1.61541i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.2468 | + | 7.32387i | 0.403327 | + | 0.241199i | ||||
\(923\) | 6.99419i | 0.230217i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 21.6586i | − | 0.712132i | ||||||
\(926\) | −17.1394 | + | 28.6601i | −0.563235 | + | 0.941828i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.19303 | − | 2.96694i | 0.203296 | − | 0.0973947i | ||||
\(929\) | −9.44479 | −0.309874 | −0.154937 | − | 0.987924i | \(-0.549517\pi\) | ||||
−0.154937 | + | 0.987924i | \(0.549517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5.28617i | − | 0.173247i | ||||||
\(932\) | −15.4337 | − | 28.7366i | −0.505549 | − | 0.941297i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.07007 | + | 1.83597i | 0.100456 | + | 0.0600748i | ||||
\(935\) | −121.161 | −3.96238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2959 | −0.499695 | −0.249847 | − | 0.968285i | \(-0.580380\pi\) | ||||
−0.249847 | + | 0.968285i | \(0.580380\pi\) | |||||||
\(938\) | −8.09492 | − | 4.84095i | −0.264308 | − | 0.158062i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −36.5778 | + | 19.6451i | −1.19303 | + | 0.640751i | ||||
\(941\) | − | 29.2847i | − | 0.954654i | −0.878726 | − | 0.477327i | \(-0.841606\pi\) | ||
0.878726 | − | 0.477327i | \(-0.158394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 66.0330 | 2.15033 | ||||||||
\(944\) | −26.1940 | − | 17.3516i | −0.852541 | − | 0.564746i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.82812 | + | 13.0900i | −0.254514 | + | 0.425593i | ||||
\(947\) | − | 23.0133i | − | 0.747832i | −0.927463 | − | 0.373916i | \(-0.878015\pi\) | ||
0.927463 | − | 0.373916i | \(-0.121985\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 23.0069i | − | 0.746836i | ||||||
\(950\) | 28.3460 | + | 16.9515i | 0.919665 | + | 0.549981i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −19.2054 | − | 0.885945i | −0.622451 | − | 0.0287136i | ||||
\(953\) | 4.48602 | 0.145316 | 0.0726582 | − | 0.997357i | \(-0.476852\pi\) | ||||
0.0726582 | + | 0.997357i | \(0.476852\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.8594i | 1.77521i | ||||||||
\(956\) | −1.56467 | − | 2.91331i | −0.0506051 | − | 0.0942232i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.9679 | + | 18.3403i | −0.354357 | + | 0.592547i | ||||
\(959\) | 14.8496 | 0.479518 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9885 | −0.999628 | ||||||||
\(962\) | −12.5393 | + | 20.9679i | −0.404283 | + | 0.676032i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.44397 | − | 6.41244i | −0.110923 | − | 0.206531i | ||||
\(965\) | 43.8827i | 1.41263i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.4520 | −0.593376 | −0.296688 | − | 0.954974i | \(-0.595882\pi\) | ||||
−0.296688 | + | 0.954974i | \(0.595882\pi\) | |||||||
\(968\) | 64.2366 | + | 2.96323i | 2.06464 | + | 0.0952419i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.1220 | − | 9.04331i | −0.485539 | − | 0.290363i | ||||
\(971\) | 21.1370i | 0.678317i | 0.940729 | + | 0.339159i | \(0.110142\pi\) | ||||
−0.940729 | + | 0.339159i | \(0.889858\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4.99694i | − | 0.160195i | ||||||
\(974\) | 29.8714 | − | 49.9502i | 0.957141 | − | 1.60051i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 40.2019 | + | 26.6308i | 1.28683 | + | 0.852432i | ||||
\(977\) | 52.4783 | 1.67893 | 0.839465 | − | 0.543414i | \(-0.182869\pi\) | ||||
0.839465 | + | 0.543414i | \(0.182869\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 45.2547i | − | 1.44635i | ||||||
\(980\) | −5.40724 | + | 2.90410i | −0.172728 | + | 0.0927681i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 44.5281 | + | 26.6288i | 1.42095 | + | 0.849760i | ||||
\(983\) | −29.7453 | −0.948727 | −0.474364 | − | 0.880329i | \(-0.657322\pi\) | ||||
−0.474364 | + | 0.880329i | \(0.657322\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.6878 | 0.404268 | ||||||||
\(986\) | 10.0152 | + | 5.98932i | 0.318949 | + | 0.190739i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.6279 | − | 32.8218i | −0.560817 | − | 1.04420i | ||||
\(989\) | − | 10.4927i | − | 0.333649i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.11149 | 0.289436 | 0.144718 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144718 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(992\) | 0.262456 | + | 0.547835i | 0.00833298 | + | 0.0173938i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.44063 | + | 2.40899i | −0.0456941 | + | 0.0764086i | ||||
\(995\) | − | 44.5517i | − | 1.41238i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 4.52824i | − | 0.143411i | −0.997426 | − | 0.0717054i | \(-0.977156\pi\) | ||
0.997426 | − | 0.0717054i | \(-0.0228442\pi\) | |||||||
\(998\) | 24.4961 | + | 14.6492i | 0.775411 | + | 0.463713i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.c.e.757.13 | yes | 20 | |
3.2 | odd | 2 | inner | 1512.2.c.e.757.8 | yes | 20 | |
4.3 | odd | 2 | 6048.2.c.e.3025.6 | 20 | |||
8.3 | odd | 2 | 6048.2.c.e.3025.15 | 20 | |||
8.5 | even | 2 | inner | 1512.2.c.e.757.14 | yes | 20 | |
12.11 | even | 2 | 6048.2.c.e.3025.16 | 20 | |||
24.5 | odd | 2 | inner | 1512.2.c.e.757.7 | ✓ | 20 | |
24.11 | even | 2 | 6048.2.c.e.3025.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.e.757.7 | ✓ | 20 | 24.5 | odd | 2 | inner | |
1512.2.c.e.757.8 | yes | 20 | 3.2 | odd | 2 | inner | |
1512.2.c.e.757.13 | yes | 20 | 1.1 | even | 1 | trivial | |
1512.2.c.e.757.14 | yes | 20 | 8.5 | even | 2 | inner | |
6048.2.c.e.3025.5 | 20 | 24.11 | even | 2 | |||
6048.2.c.e.3025.6 | 20 | 4.3 | odd | 2 | |||
6048.2.c.e.3025.15 | 20 | 8.3 | odd | 2 | |||
6048.2.c.e.3025.16 | 20 | 12.11 | even | 2 |