Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(505,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.505");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.r (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.508277025.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 505.2 | ||
Root | \(-0.577806 + 2.22188i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.505 |
Dual form | 1512.2.r.d.1009.2 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.81197 | − | 3.13842i | −0.810336 | − | 1.40354i | −0.912629 | − | 0.408788i | \(-0.865951\pi\) |
0.102294 | − | 0.994754i | \(-0.467382\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.95863 | − | 3.39245i | 0.590550 | − | 1.02286i | −0.403609 | − | 0.914932i | \(-0.632244\pi\) |
0.994158 | − | 0.107930i | \(-0.0344224\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.53644 | − | 4.39324i | −0.703481 | − | 1.21847i | −0.967237 | − | 0.253876i | \(-0.918295\pi\) |
0.263755 | − | 0.964590i | \(-0.415039\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.03225 | −0.250357 | −0.125178 | − | 0.992134i | \(-0.539950\pi\) | ||||
−0.125178 | + | 0.992134i | \(0.539950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50895 | −0.575592 | −0.287796 | − | 0.957692i | \(-0.592922\pi\) | ||||
−0.287796 | + | 0.957692i | \(0.592922\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.47895 | + | 4.29366i | 0.516896 | + | 0.895290i | 0.999807 | + | 0.0196209i | \(0.00624592\pi\) |
−0.482912 | + | 0.875669i | \(0.660421\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.06644 | + | 7.04328i | −0.813288 | + | 1.40866i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.60288 | + | 7.97242i | −0.854733 | + | 1.48044i | 0.0221599 | + | 0.999754i | \(0.492946\pi\) |
−0.876893 | + | 0.480686i | \(0.840388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.422194 | + | 0.731261i | 0.0758282 | + | 0.131338i | 0.901446 | − | 0.432891i | \(-0.142507\pi\) |
−0.825618 | + | 0.564230i | \(0.809173\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.62393 | 0.612556 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.84439 | 0.796412 | 0.398206 | − | 0.917296i | \(-0.369633\pi\) | ||||
0.398206 | + | 0.917296i | \(0.369633\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.07362 | − | 3.59161i | −0.323844 | − | 0.560915i | 0.657433 | − | 0.753513i | \(-0.271642\pi\) |
−0.981278 | + | 0.192598i | \(0.938309\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.20174 | − | 3.81352i | 0.335762 | − | 0.581557i | −0.647869 | − | 0.761752i | \(-0.724340\pi\) |
0.983631 | + | 0.180195i | \(0.0576729\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.93758 | + | 6.82008i | −0.574355 | + | 0.994812i | 0.421757 | + | 0.906709i | \(0.361414\pi\) |
−0.996111 | + | 0.0881025i | \(0.971920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.2786 | −1.68660 | −0.843300 | − | 0.537443i | \(-0.819390\pi\) | ||||
−0.843300 | + | 0.537443i | \(0.819390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.1959 | −1.91417 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.60288 | − | 9.70447i | −0.729432 | − | 1.26341i | −0.957123 | − | 0.289681i | \(-0.906451\pi\) |
0.227691 | − | 0.973733i | \(-0.426882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.208348 | + | 0.360870i | −0.0266763 | + | 0.0462047i | −0.879055 | − | 0.476720i | \(-0.841826\pi\) |
0.852379 | + | 0.522924i | \(0.175159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.19188 | + | 15.9208i | −1.14011 | + | 1.97473i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.02507 | − | 8.70368i | −0.613910 | − | 1.06332i | −0.990575 | − | 0.136974i | \(-0.956262\pi\) |
0.376665 | − | 0.926350i | \(-0.377071\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.05162 | 0.599517 | 0.299759 | − | 0.954015i | \(-0.403094\pi\) | ||||
0.299759 | + | 0.954015i | \(0.403094\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.20723 | 0.843543 | 0.421771 | − | 0.906702i | \(-0.361408\pi\) | ||||
0.421771 | + | 0.906702i | \(0.361408\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.95863 | + | 3.39245i | 0.223207 | + | 0.386606i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.56570 | + | 13.1042i | −0.851208 | + | 1.47433i | 0.0289116 | + | 0.999582i | \(0.490796\pi\) |
−0.880119 | + | 0.474753i | \(0.842537\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.932821 | − | 1.61569i | 0.102390 | − | 0.177345i | −0.810279 | − | 0.586045i | \(-0.800684\pi\) |
0.912669 | + | 0.408699i | \(0.134018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.87040 | + | 3.23963i | 0.202873 | + | 0.351387i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.669401 | 0.0709564 | 0.0354782 | − | 0.999370i | \(-0.488705\pi\) | ||||
0.0354782 | + | 0.999370i | \(0.488705\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.07288 | 0.531782 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.54612 | + | 7.87412i | 0.466423 | + | 0.807868i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.63513 | + | 13.2244i | −0.775230 | + | 1.34274i | 0.159436 | + | 0.987208i | \(0.449032\pi\) |
−0.934665 | + | 0.355529i | \(0.884301\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.87840 | + | 10.1817i | −0.584923 | + | 1.01312i | 0.409962 | + | 0.912103i | \(0.365542\pi\) |
−0.994885 | + | 0.101014i | \(0.967791\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.51538 | − | 9.55293i | −0.543447 | − | 0.941278i | −0.998703 | − | 0.0509171i | \(-0.983786\pi\) |
0.455256 | − | 0.890361i | \(-0.349548\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.842907 | 0.0814869 | 0.0407434 | − | 0.999170i | \(-0.487027\pi\) | ||||
0.0407434 | + | 0.999170i | \(0.487027\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.1875 | −1.64627 | −0.823133 | − | 0.567849i | \(-0.807776\pi\) | ||||
−0.823133 | + | 0.567849i | \(0.807776\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.54538 | + | 7.87284i | 0.427594 | + | 0.740614i | 0.996659 | − | 0.0816784i | \(-0.0260280\pi\) |
−0.569065 | + | 0.822293i | \(0.692695\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.98353 | − | 15.5599i | 0.837718 | − | 1.45097i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.516124 | − | 0.893953i | 0.0473130 | − | 0.0819486i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.17248 | − | 3.76284i | −0.197498 | − | 0.342076i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3533 | 1.01547 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.4859 | −1.28541 | −0.642706 | − | 0.766113i | \(-0.722188\pi\) | ||||
−0.642706 | + | 0.766113i | \(0.722188\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.03476 | + | 6.98840i | 0.352518 | + | 0.610580i | 0.986690 | − | 0.162613i | \(-0.0519921\pi\) |
−0.634172 | + | 0.773192i | \(0.718659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.25447 | − | 2.17281i | 0.108777 | − | 0.188407i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.85792 | − | 17.0744i | 0.842219 | − | 1.45877i | −0.0457961 | − | 0.998951i | \(-0.514582\pi\) |
0.888015 | − | 0.459815i | \(-0.152084\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.35960 | − | 14.4792i | −0.709052 | − | 1.22811i | −0.965209 | − | 0.261479i | \(-0.915790\pi\) |
0.256157 | − | 0.966635i | \(-0.417543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.8718 | −1.66176 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33.3610 | 2.77048 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.16439 | + | 15.8732i | 0.750776 | + | 1.30038i | 0.947447 | + | 0.319912i | \(0.103653\pi\) |
−0.196671 | + | 0.980469i | \(0.563013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.23100 | − | 12.5245i | 0.588450 | − | 1.01923i | −0.405985 | − | 0.913880i | \(-0.633072\pi\) |
0.994436 | − | 0.105346i | \(-0.0335951\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.53000 | − | 2.65004i | 0.122893 | − | 0.212856i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.92387 | − | 3.33225i | −0.153542 | − | 0.265942i | 0.778985 | − | 0.627042i | \(-0.215735\pi\) |
−0.932527 | + | 0.361100i | \(0.882401\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.95789 | −0.390737 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.0322 | 1.02076 | 0.510382 | − | 0.859948i | \(-0.329504\pi\) | ||||
0.510382 | + | 0.859948i | \(0.329504\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.04538 | − | 5.27476i | −0.235659 | − | 0.408173i | 0.723805 | − | 0.690005i | \(-0.242391\pi\) |
−0.959464 | + | 0.281831i | \(0.909058\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.36704 | + | 11.0280i | −0.489772 | + | 0.848310i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.89855 | − | 10.2166i | 0.448458 | − | 0.776752i | −0.549828 | − | 0.835278i | \(-0.685307\pi\) |
0.998286 | + | 0.0585258i | \(0.0186400\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.06644 | − | 7.04328i | −0.307394 | − | 0.532422i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.06148 | −0.0793389 | −0.0396694 | − | 0.999213i | \(-0.512630\pi\) | ||||
−0.0396694 | + | 0.999213i | \(0.512630\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0384 | −1.19212 | −0.596062 | − | 0.802938i | \(-0.703269\pi\) | ||||
−0.596062 | + | 0.802938i | \(0.703269\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.77786 | − | 15.2037i | −0.645361 | − | 1.11780i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.02179 | + | 3.50185i | −0.147848 | + | 0.256081i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9676 | − | 20.7285i | 0.865944 | − | 1.49986i | −0.000163629 | − | 1.00000i | \(-0.500052\pi\) |
0.866107 | − | 0.499858i | \(-0.166615\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.60707 | − | 11.4438i | −0.475587 | − | 0.823741i | 0.524022 | − | 0.851705i | \(-0.324431\pi\) |
−0.999609 | + | 0.0279638i | \(0.991098\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.0403 | 1.78405 | 0.892023 | − | 0.451990i | \(-0.149286\pi\) | ||||
0.892023 | + | 0.451990i | \(0.149286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.28159 | 0.587066 | 0.293533 | − | 0.955949i | \(-0.405169\pi\) | ||||
0.293533 | + | 0.955949i | \(0.405169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.60288 | − | 7.97242i | −0.323059 | − | 0.559554i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.51464 | + | 13.0157i | −0.524845 | + | 0.909059i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.91410 | + | 8.51148i | −0.339916 | + | 0.588751i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.79752 | − | 3.11340i | −0.123747 | − | 0.214335i | 0.797496 | − | 0.603325i | \(-0.206158\pi\) |
−0.921242 | + | 0.388989i | \(0.872824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.9579 | −1.08832 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.844387 | −0.0573207 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.61823 | + | 4.53491i | 0.176121 | + | 0.305051i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.08601 | + | 8.80923i | −0.340585 | + | 0.589910i | −0.984541 | − | 0.175152i | \(-0.943958\pi\) |
0.643957 | + | 0.765062i | \(0.277292\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.95054 | − | 12.0387i | 0.461324 | − | 0.799036i | −0.537704 | − | 0.843134i | \(-0.680708\pi\) |
0.999027 | + | 0.0440980i | \(0.0140414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.84347 | + | 4.92504i | 0.187902 | + | 0.325456i | 0.944551 | − | 0.328366i | \(-0.106498\pi\) |
−0.756649 | + | 0.653822i | \(0.773165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.4775 | −1.27601 | −0.638006 | − | 0.770031i | \(-0.720241\pi\) | ||||
−0.638006 | + | 0.770031i | \(0.720241\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.5390 | 1.86168 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.50000 | + | 4.33013i | 0.161712 | + | 0.280093i | 0.935483 | − | 0.353373i | \(-0.114965\pi\) |
−0.773771 | + | 0.633465i | \(0.781632\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.14080 | + | 8.90412i | −0.331148 | + | 0.573565i | −0.982737 | − | 0.185007i | \(-0.940769\pi\) |
0.651589 | + | 0.758572i | \(0.274103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.81197 | + | 3.13842i | −0.115762 | + | 0.200506i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.36379 | + | 11.0224i | 0.404918 | + | 0.701339i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.829685 | 0.0523693 | 0.0261846 | − | 0.999657i | \(-0.491664\pi\) | ||||
0.0261846 | + | 0.999657i | \(0.491664\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.4214 | 1.22101 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.87516 | − | 11.9081i | −0.428860 | − | 0.742808i | 0.567912 | − | 0.823089i | \(-0.307751\pi\) |
−0.996772 | + | 0.0802814i | \(0.974418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.42219 | + | 4.19536i | −0.150508 | + | 0.260687i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.9285 | − | 22.3929i | 0.797208 | − | 1.38081i | −0.124219 | − | 0.992255i | \(-0.539643\pi\) |
0.921427 | − | 0.388550i | \(-0.127024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.2485 | + | 38.5355i | 1.36671 | + | 2.36721i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.32410 | −0.568500 | −0.284250 | − | 0.958750i | \(-0.591745\pi\) | ||||
−0.284250 | + | 0.958750i | \(0.591745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.7421 | 1.56372 | 0.781861 | − | 0.623453i | \(-0.214271\pi\) | ||||
0.781861 | + | 0.623453i | \(0.214271\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.9293 | + | 27.5904i | 0.960574 | + | 1.66376i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.06570 | − | 8.77405i | 0.304368 | − | 0.527181i | −0.672752 | − | 0.739868i | \(-0.734888\pi\) |
0.977120 | + | 0.212686i | \(0.0682213\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.47969 | + | 6.02699i | −0.207581 | + | 0.359540i | −0.950952 | − | 0.309339i | \(-0.899892\pi\) |
0.743371 | + | 0.668879i | \(0.233226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.95920 | + | 6.85753i | 0.235350 | + | 0.407638i | 0.959374 | − | 0.282136i | \(-0.0910430\pi\) |
−0.724024 | + | 0.689774i | \(0.757710\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.14723 | 0.244803 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9345 | −0.937321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.63128 | − | 9.75367i | −0.328983 | − | 0.569815i | 0.653327 | − | 0.757076i | \(-0.273373\pi\) |
−0.982310 | + | 0.187260i | \(0.940039\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.3044 | + | 35.1683i | −1.18217 | + | 2.04758i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.5754 | − | 21.7812i | 0.727253 | − | 1.25964i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.20174 | + | 3.81352i | 0.126906 | + | 0.219808i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.51008 | 0.0864669 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0142 | 1.31349 | 0.656744 | − | 0.754113i | \(-0.271933\pi\) | ||||
0.656744 | + | 0.754113i | \(0.271933\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.78832 | − | 11.7577i | −0.384930 | − | 0.666719i | 0.606829 | − | 0.794832i | \(-0.292441\pi\) |
−0.991760 | + | 0.128114i | \(0.959108\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.92362 | − | 15.4562i | 0.504393 | − | 0.873634i | −0.495595 | − | 0.868554i | \(-0.665050\pi\) |
0.999987 | − | 0.00507958i | \(-0.00161689\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.69755 | + | 16.7966i | −0.544669 | + | 0.943394i | 0.453959 | + | 0.891022i | \(0.350011\pi\) |
−0.998628 | + | 0.0523711i | \(0.983322\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0307 | + | 31.2301i | 1.00952 | + | 1.74855i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.58986 | 0.144103 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 41.2571 | 2.28853 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.93758 | − | 6.82008i | −0.217086 | − | 0.376003i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.28729 | + | 12.6220i | −0.400546 | + | 0.693765i | −0.993792 | − | 0.111256i | \(-0.964513\pi\) |
0.593246 | + | 0.805021i | \(0.297846\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.2105 | + | 31.5415i | −0.994946 | + | 1.72330i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8962 | − | 24.0689i | −0.756975 | − | 1.31112i | −0.944387 | − | 0.328837i | \(-0.893343\pi\) |
0.187412 | − | 0.982281i | \(-0.439990\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.30769 | 0.179121 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.45604 | + | 12.9142i | 0.400261 | + | 0.693273i | 0.993757 | − | 0.111564i | \(-0.0355861\pi\) |
−0.593496 | + | 0.804837i | \(0.702253\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.9579 | − | 18.9796i | 0.586562 | − | 1.01596i | −0.408116 | − | 0.912930i | \(-0.633814\pi\) |
0.994679 | − | 0.103026i | \(-0.0328525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.73100 | − | 13.3905i | 0.411480 | − | 0.712703i | −0.583572 | − | 0.812061i | \(-0.698346\pi\) |
0.995052 | + | 0.0993578i | \(0.0316788\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.15337 | − | 15.8541i | −0.485810 | − | 0.841448i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.56506 | −0.399269 | −0.199634 | − | 0.979870i | \(-0.563975\pi\) | ||||
−0.199634 | + | 0.979870i | \(0.563975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.7052 | −0.668694 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.0593 | − | 22.6193i | −0.683553 | − | 1.18395i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.5046 | − | 25.1227i | 0.757133 | − | 1.31139i | −0.187174 | − | 0.982327i | \(-0.559933\pi\) |
0.944307 | − | 0.329066i | \(-0.106734\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.13932 | − | 10.6336i | 0.318737 | − | 0.552069i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.655525 | − | 1.13540i | −0.0339418 | − | 0.0587889i | 0.848556 | − | 0.529106i | \(-0.177473\pi\) |
−0.882497 | + | 0.470317i | \(0.844139\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 46.6997 | 2.40515 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7015 | −0.806531 | −0.403265 | − | 0.915083i | \(-0.632125\pi\) | ||||
−0.403265 | + | 0.915083i | \(0.632125\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.4804 | − | 18.1525i | −0.535522 | − | 0.927551i | −0.999138 | − | 0.0415148i | \(-0.986782\pi\) |
0.463616 | − | 0.886036i | \(-0.346552\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.09795 | − | 12.2940i | 0.361745 | − | 0.626561i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.80937 | − | 10.0621i | 0.294547 | − | 0.510170i | −0.680333 | − | 0.732904i | \(-0.738165\pi\) |
0.974879 | + | 0.222733i | \(0.0714980\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.55889 | − | 4.43212i | −0.129409 | − | 0.224142i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 54.8351 | 2.75906 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.5217 | −1.78278 | −0.891390 | − | 0.453237i | \(-0.850269\pi\) | ||||
−0.891390 | + | 0.453237i | \(0.850269\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.45388 | − | 4.25024i | −0.122541 | − | 0.212247i | 0.798228 | − | 0.602355i | \(-0.205771\pi\) |
−0.920769 | + | 0.390108i | \(0.872438\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.14174 | − | 3.70960i | 0.106687 | − | 0.184788i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.48837 | − | 16.4343i | 0.470321 | − | 0.814620i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.21561 | − | 3.83756i | −0.109555 | − | 0.189755i | 0.806035 | − | 0.591868i | \(-0.201609\pi\) |
−0.915590 | + | 0.402113i | \(0.868276\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.2058 | 0.551399 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.76096 | −0.331882 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.7719 | + | 30.7819i | 0.868216 | + | 1.50379i | 0.863818 | + | 0.503803i | \(0.168066\pi\) |
0.00439727 | + | 0.999990i | \(0.498600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.81923 | − | 3.15100i | 0.0886639 | − | 0.153570i | −0.818283 | − | 0.574816i | \(-0.805074\pi\) |
0.906947 | + | 0.421246i | \(0.138407\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.19757 | − | 7.27041i | 0.203612 | − | 0.352667i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.208348 | − | 0.360870i | −0.0100827 | − | 0.0174637i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.9303 | −0.526495 | −0.263247 | − | 0.964728i | \(-0.584794\pi\) | ||||
−0.263247 | + | 0.964728i | \(0.584794\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3189 | 0.736180 | 0.368090 | − | 0.929790i | \(-0.380012\pi\) | ||||
0.368090 | + | 0.929790i | \(0.380012\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.21954 | − | 10.7726i | −0.297521 | − | 0.515322i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.30117 | + | 9.18189i | −0.253011 | + | 0.438228i | −0.964353 | − | 0.264618i | \(-0.914754\pi\) |
0.711343 | + | 0.702846i | \(0.248087\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0680 | + | 17.4383i | −0.478347 | + | 0.828521i | −0.999692 | − | 0.0248251i | \(-0.992097\pi\) |
0.521345 | + | 0.853346i | \(0.325430\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.21293 | − | 2.10086i | −0.0574985 | − | 0.0995903i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.74616 | 0.129599 | 0.0647997 | − | 0.997898i | \(-0.479359\pi\) | ||||
0.0647997 | + | 0.997898i | \(0.479359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.2458 | −0.764985 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.19188 | − | 15.9208i | −0.430922 | − | 0.746379i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.7715 | + | 22.1208i | −0.597423 | + | 1.03477i | 0.395777 | + | 0.918347i | \(0.370475\pi\) |
−0.993200 | + | 0.116421i | \(0.962858\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.82316 | + | 15.2822i | −0.410936 | + | 0.711761i | −0.994992 | − | 0.0999516i | \(-0.968131\pi\) |
0.584057 | + | 0.811713i | \(0.301465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2501 | − | 22.9499i | −0.615785 | − | 1.06657i | −0.990246 | − | 0.139328i | \(-0.955506\pi\) |
0.374461 | − | 0.927242i | \(-0.377828\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.1735 | −0.933519 | −0.466759 | − | 0.884384i | \(-0.654579\pi\) | ||||
−0.466759 | + | 0.884384i | \(0.654579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0501 | 0.464072 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.62479 | − | 14.9386i | −0.396568 | − | 0.686876i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.2025 | − | 17.6712i | 0.468122 | − | 0.810811i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.92470 | + | 8.52984i | −0.225015 | + | 0.389738i | −0.956324 | − | 0.292309i | \(-0.905577\pi\) |
0.731309 | + | 0.682047i | \(0.238910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.2875 | − | 21.2826i | −0.560261 | − | 0.970401i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 55.3383 | 2.51278 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0278 | 0.454403 | 0.227202 | − | 0.973848i | \(-0.427042\pi\) | ||||
0.227202 | + | 0.973848i | \(0.427042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.610055 | − | 1.05665i | −0.0275314 | − | 0.0476858i | 0.851931 | − | 0.523653i | \(-0.175431\pi\) |
−0.879463 | + | 0.475968i | \(0.842098\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.75131 | − | 8.22951i | 0.213988 | − | 0.370639i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.52581 | + | 4.37483i | −0.113298 | + | 0.196238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.3222 | − | 17.8786i | −0.462086 | − | 0.800356i | 0.536979 | − | 0.843596i | \(-0.319566\pi\) |
−0.999065 | + | 0.0432393i | \(0.986232\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.85094 | −0.394644 | −0.197322 | − | 0.980339i | \(-0.563224\pi\) | ||||
−0.197322 | + | 0.980339i | \(0.563224\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.6059 | 1.89594 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.8460 | − | 22.2499i | −0.569388 | − | 0.986209i | −0.996627 | − | 0.0820702i | \(-0.973847\pi\) |
0.427238 | − | 0.904139i | \(-0.359487\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.60362 | + | 6.24165i | −0.159415 | + | 0.276114i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.9874 | + | 34.6191i | −0.880749 | + | 1.52550i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.4245 | + | 26.7161i | 0.678370 | + | 1.17497i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.6797 | 0.643129 | 0.321565 | − | 0.946888i | \(-0.395791\pi\) | ||||
0.321565 | + | 0.946888i | \(0.395791\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.7922 | 0.909182 | 0.454591 | − | 0.890700i | \(-0.349786\pi\) | ||||
0.454591 | + | 0.890700i | \(0.349786\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.435809 | − | 0.754843i | −0.0189841 | − | 0.0328815i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.790345 | + | 1.36892i | −0.0343628 | + | 0.0595181i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.5192 | + | 18.2198i | −0.455637 | + | 0.789187i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.52732 | − | 2.64539i | −0.0660317 | − | 0.114370i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.91726 | −0.168728 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.9593 | −1.33104 | −0.665521 | − | 0.746379i | \(-0.731791\pi\) | ||||
−0.665521 | + | 0.746379i | \(0.731791\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.1432 | + | 53.9416i | 1.33403 | + | 2.31060i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.80535 | − | 10.0552i | 0.248219 | − | 0.429928i | −0.714813 | − | 0.699316i | \(-0.753488\pi\) |
0.963032 | + | 0.269388i | \(0.0868214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5484 | − | 20.0024i | 0.491977 | − | 0.852130i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.56570 | − | 13.1042i | −0.321726 | − | 0.557246i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.0116 | −0.805546 | −0.402773 | − | 0.915300i | \(-0.631954\pi\) | ||||
−0.402773 | + | 0.915300i | \(0.631954\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.3383 | −0.944809 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.7959 | − | 18.6990i | −0.454992 | − | 0.788069i | 0.543696 | − | 0.839282i | \(-0.317024\pi\) |
−0.998688 | + | 0.0512136i | \(0.983691\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.4722 | − | 28.5306i | 0.692989 | − | 1.20029i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.28858 | − | 16.0883i | 0.389397 | − | 0.674456i | −0.602971 | − | 0.797763i | \(-0.706017\pi\) |
0.992369 | + | 0.123307i | \(0.0393500\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.42902 | + | 7.67130i | 0.185349 | + | 0.321034i | 0.943694 | − | 0.330820i | \(-0.107325\pi\) |
−0.758345 | + | 0.651853i | \(0.773992\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −40.3219 | −1.68154 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.76684 | −0.156816 | −0.0784078 | − | 0.996921i | \(-0.524984\pi\) | ||||
−0.0784078 | + | 0.996921i | \(0.524984\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.932821 | + | 1.61569i | 0.0386999 | + | 0.0670302i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.0493 | + | 41.6546i | −0.996021 | + | 1.72516i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.37616 | − | 14.5079i | 0.345721 | − | 0.598806i | −0.639763 | − | 0.768572i | \(-0.720968\pi\) |
0.985484 | + | 0.169766i | \(0.0543010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.05926 | − | 1.83469i | −0.0436461 | − | 0.0755973i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.3776 | −1.24746 | −0.623729 | − | 0.781640i | \(-0.714383\pi\) | ||||
−0.623729 | + | 0.781640i | \(0.714383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.74080 | −0.153358 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.97578 | + | 15.5465i | 0.366741 | + | 0.635213i | 0.989054 | − | 0.147555i | \(-0.0471403\pi\) |
−0.622313 | + | 0.782768i | \(0.713807\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.66678 | − | 4.61900i | 0.108780 | − | 0.188413i | −0.806496 | − | 0.591239i | \(-0.798639\pi\) |
0.915276 | + | 0.402826i | \(0.131972\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.87291 | + | 13.6363i | −0.320079 | + | 0.554393i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.11826 | + | 15.7933i | 0.370099 | + | 0.641030i | 0.989580 | − | 0.143981i | \(-0.0459905\pi\) |
−0.619482 | + | 0.785011i | \(0.712657\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.9497 | 1.61619 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.2030 | 0.977550 | 0.488775 | − | 0.872410i | \(-0.337444\pi\) | ||||
0.488775 | + | 0.872410i | \(0.337444\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.15635 | − | 5.46696i | −0.127070 | − | 0.220092i | 0.795470 | − | 0.605993i | \(-0.207224\pi\) |
−0.922540 | + | 0.385901i | \(0.873891\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.03450 | + | 12.1841i | −0.282740 | + | 0.489721i | −0.972059 | − | 0.234738i | \(-0.924577\pi\) |
0.689318 | + | 0.724459i | \(0.257910\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.334701 | + | 0.579718i | −0.0134095 | + | 0.0232259i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.239656 | − | 0.415097i | −0.00958625 | − | 0.0166039i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.00061 | −0.199387 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.75345 | −0.0698036 | −0.0349018 | − | 0.999391i | \(-0.511112\pi\) | ||||
−0.0349018 | + | 0.999391i | \(0.511112\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26.2479 | + | 45.4627i | 1.04162 | + | 1.80413i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.53644 | + | 4.39324i | −0.100497 | + | 0.174066i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.6942 | − | 23.7191i | 0.540889 | − | 0.936847i | −0.457964 | − | 0.888971i | \(-0.651421\pi\) |
0.998853 | − | 0.0478765i | \(-0.0152454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.3323 | + | 36.9486i | 0.841263 | + | 1.45711i | 0.888827 | + | 0.458242i | \(0.151521\pi\) |
−0.0475644 | + | 0.998868i | \(0.515146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.7615 | −1.79907 | −0.899536 | − | 0.436847i | \(-0.856095\pi\) | ||||
−0.899536 | + | 0.436847i | \(0.856095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.8959 | −1.72306 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.388265 | − | 0.672494i | −0.0151940 | − | 0.0263167i | 0.858328 | − | 0.513101i | \(-0.171503\pi\) |
−0.873522 | + | 0.486784i | \(0.838170\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.6217 | − | 25.3255i | 0.571316 | − | 0.989549i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.97934 | + | 10.3565i | −0.232922 | + | 0.403433i | −0.958667 | − | 0.284531i | \(-0.908162\pi\) |
0.725745 | + | 0.687964i | \(0.241495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.31373 | − | 10.9357i | −0.245576 | − | 0.425350i | 0.716718 | − | 0.697364i | \(-0.245644\pi\) |
−0.962293 | + | 0.272014i | \(0.912310\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.09225 | −0.352582 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.6411 | −1.76723 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.816155 | + | 1.41362i | 0.0315073 | + | 0.0545723i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.5735 | + | 25.2421i | −0.561768 | + | 0.973011i | 0.435574 | + | 0.900153i | \(0.356545\pi\) |
−0.997342 | + | 0.0728584i | \(0.976788\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.92732 | + | 6.80232i | −0.150939 | + | 0.261435i | −0.931573 | − | 0.363554i | \(-0.881563\pi\) |
0.780634 | + | 0.624989i | \(0.214896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.63513 | − | 13.2244i | −0.293009 | − | 0.507507i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.87441 | −0.339570 | −0.169785 | − | 0.985481i | \(-0.554307\pi\) | ||||
−0.169785 | + | 0.985481i | \(0.554307\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −71.4488 | −2.72992 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.1440 | + | 53.9430i | 1.18649 | + | 2.05506i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.82008 | − | 3.15248i | 0.0692392 | − | 0.119926i | −0.829327 | − | 0.558763i | \(-0.811276\pi\) |
0.898567 | + | 0.438837i | \(0.144609\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.2946 | + | 52.4718i | −1.14914 | + | 1.99037i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.14049 | + | 3.70743i | 0.0810767 | + | 0.140429i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.1003 | −0.683638 | −0.341819 | − | 0.939766i | \(-0.611043\pi\) | ||||
−0.341819 | + | 0.939766i | \(0.611043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.1543 | −0.458408 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.87840 | − | 10.1817i | −0.221080 | − | 0.382922i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5624 | + | 30.4191i | −0.659572 | + | 1.14241i | 0.321155 | + | 0.947027i | \(0.395929\pi\) |
−0.980727 | + | 0.195385i | \(0.937404\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.09319 | + | 3.62551i | −0.0783906 | + | 0.135776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0070 | + | 62.3660i | 1.34659 | + | 2.33235i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.8092 | 0.887933 | 0.443966 | − | 0.896044i | \(-0.353571\pi\) | ||||
0.443966 | + | 0.896044i | \(0.353571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.0308 | 0.410807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −37.4346 | − | 64.8387i | −1.39029 | − | 2.40805i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.29251 | + | 2.23869i | −0.0479364 | + | 0.0830283i | −0.888998 | − | 0.457911i | \(-0.848598\pi\) |
0.841062 | + | 0.540939i | \(0.181931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.27274 | + | 3.93650i | −0.0840603 | + | 0.145597i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.7493 | + | 20.3505i | 0.433972 | + | 0.751661i | 0.997211 | − | 0.0746325i | \(-0.0237784\pi\) |
−0.563239 | + | 0.826294i | \(0.690445\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −39.3691 | −1.45018 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9236 | 0.622544 | 0.311272 | − | 0.950321i | \(-0.399245\pi\) | ||||
0.311272 | + | 0.950321i | \(0.399245\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.39163 | + | 7.60652i | 0.161113 | + | 0.279056i | 0.935268 | − | 0.353940i | \(-0.115158\pi\) |
−0.774155 | + | 0.632996i | \(0.781825\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.2111 | − | 57.5233i | 1.21676 | − | 2.10749i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.421453 | + | 0.729979i | −0.0153996 | + | 0.0266728i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.983876 | − | 1.70412i | −0.0359021 | − | 0.0621843i | 0.847516 | − | 0.530770i | \(-0.178097\pi\) |
−0.883418 | + | 0.468585i | \(0.844764\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −52.4093 | −1.90737 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.3423 | −0.375899 | −0.187949 | − | 0.982179i | \(-0.560184\pi\) | ||||
−0.187949 | + | 0.982179i | \(0.560184\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.88205 | − | 13.6521i | −0.285724 | − | 0.494889i | 0.687060 | − | 0.726600i | \(-0.258901\pi\) |
−0.972785 | + | 0.231711i | \(0.925567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.59376 | − | 14.8848i | 0.311115 | − | 0.538867i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28.4227 | + | 49.2296i | −1.02628 | + | 1.77758i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.1895 | + | 38.4333i | 0.800172 | + | 1.38594i | 0.919502 | + | 0.393084i | \(0.128592\pi\) |
−0.119330 | + | 0.992855i | \(0.538075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.5222 | 0.917969 | 0.458984 | − | 0.888444i | \(-0.348213\pi\) | ||||
0.458984 | + | 0.888444i | \(0.348213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.86730 | −0.246681 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.20259 | + | 9.01116i | 0.186402 | + | 0.322858i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.89427 | − | 17.1374i | 0.354045 | − | 0.613223i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.97199 | + | 12.0758i | −0.248841 | + | 0.431005i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.2841 | − | 21.2767i | −0.437882 | − | 0.758434i | 0.559644 | − | 0.828733i | \(-0.310938\pi\) |
−0.997526 | + | 0.0702995i | \(0.977605\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.09077 | −0.323231 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.11385 | 0.0750650 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.6983 | − | 32.3864i | −0.662328 | − | 1.14719i | −0.980002 | − | 0.198986i | \(-0.936235\pi\) |
0.317674 | − | 0.948200i | \(-0.397098\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.06456 | − | 7.04002i | 0.143794 | − | 0.249058i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.1163 | − | 24.4502i | 0.498154 | − | 0.862828i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.98353 | + | 15.5599i | 0.316628 | + | 0.548415i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.6565 | −0.444980 | −0.222490 | − | 0.974935i | \(-0.571418\pi\) | ||||
−0.222490 | + | 0.974935i | \(0.571418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.2499 | −1.48360 | −0.741798 | − | 0.670624i | \(-0.766027\pi\) | ||||
−0.741798 | + | 0.670624i | \(0.766027\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.6140 | − | 40.9006i | −0.827162 | − | 1.43269i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.52404 | + | 9.56792i | −0.193262 | + | 0.334739i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.7218 | − | 34.1591i | 0.688295 | − | 1.19216i | −0.284094 | − | 0.958797i | \(-0.591693\pi\) |
0.972389 | − | 0.233366i | \(-0.0749740\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.33208 | + | 2.30723i | 0.0464334 | + | 0.0804249i | 0.888308 | − | 0.459248i | \(-0.151881\pi\) |
−0.841875 | + | 0.539673i | \(0.818548\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.13009 | 0.0740704 | 0.0370352 | − | 0.999314i | \(-0.488209\pi\) | ||||
0.0370352 | + | 0.999314i | \(0.488209\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.61167 | −0.264364 | −0.132182 | − | 0.991225i | \(-0.542198\pi\) | ||||
−0.132182 | + | 0.991225i | \(0.542198\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.516124 | + | 0.893953i | 0.0178826 | + | 0.0309736i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.0363 | + | 19.1154i | −0.381926 | + | 0.661515i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.9543 | − | 34.5618i | 0.688898 | − | 1.19321i | −0.283297 | − | 0.959032i | \(-0.591428\pi\) |
0.972195 | − | 0.234174i | \(-0.0752385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8730 | − | 48.2774i | −0.961136 | − | 1.66474i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 46.1474 | 1.58752 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.34495 | 0.149294 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0090 | + | 20.8002i | 0.411662 | + | 0.713020i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.1004 | − | 41.7431i | 0.825182 | − | 1.42926i | −0.0765985 | − | 0.997062i | \(-0.524406\pi\) |
0.901780 | − | 0.432195i | \(-0.142261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.3367 | − | 35.2242i | 0.694688 | − | 1.20324i | −0.275598 | − | 0.961273i | \(-0.588876\pi\) |
0.970286 | − | 0.241962i | \(-0.0777909\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.05826 | + | 8.76116i | 0.172586 | + | 0.298927i | 0.939323 | − | 0.343034i | \(-0.111455\pi\) |
−0.766737 | + | 0.641961i | \(0.778121\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.5930 | −0.564832 | −0.282416 | − | 0.959292i | \(-0.591136\pi\) | ||||
−0.282416 | + | 0.959292i | \(0.591136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.7518 | −1.45361 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.6368 | + | 51.3325i | 1.00536 | + | 1.74134i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.4916 | + | 44.1527i | −0.863749 | + | 1.49606i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.67667 | + | 9.83228i | −0.191906 | + | 0.332392i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.9649 | − | 32.8482i | −0.640399 | − | 1.10920i | −0.985344 | − | 0.170581i | \(-0.945436\pi\) |
0.344945 | − | 0.938623i | \(-0.387898\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.9737 | −0.706623 | −0.353312 | − | 0.935506i | \(-0.614944\pi\) | ||||
−0.353312 | + | 0.935506i | \(0.614944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.6536 | 1.33445 | 0.667225 | − | 0.744856i | \(-0.267482\pi\) | ||||
0.667225 | + | 0.744856i | \(0.267482\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.6160 | + | 20.1195i | 0.390028 | + | 0.675548i | 0.992453 | − | 0.122628i | \(-0.0391321\pi\) |
−0.602425 | + | 0.798175i | \(0.705799\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.24293 | − | 12.5451i | 0.242920 | − | 0.420750i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.87917 | − | 17.1112i | 0.330594 | − | 0.572605i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.92337 | + | 3.33137i | 0.0642911 | + | 0.111355i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.77322 | −0.259251 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6746 | 0.422252 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.0610 | + | 50.3352i | 0.966021 | + | 1.67320i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.1911 | − | 36.7041i | 0.703640 | − | 1.21874i | −0.263540 | − | 0.964649i | \(-0.584890\pi\) |
0.967180 | − | 0.254092i | \(-0.0817766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.66820 | − | 16.7458i | 0.320322 | − | 0.554814i | −0.660233 | − | 0.751061i | \(-0.729542\pi\) |
0.980554 | + | 0.196248i | \(0.0628756\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.65411 | − | 6.32910i | −0.120933 | − | 0.209463i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.06951 | −0.266479 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.4866 | 0.939685 | 0.469842 | − | 0.882750i | \(-0.344311\pi\) | ||||
0.469842 | + | 0.882750i | \(0.344311\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.8131 | − | 22.1930i | −0.421749 | − | 0.730491i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.6994 | + | 34.1204i | −0.647712 | + | 1.12187i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.5930 | + | 21.8117i | −0.413163 | + | 0.715620i | −0.995234 | − | 0.0975184i | \(-0.968910\pi\) |
0.582070 | + | 0.813139i | \(0.302243\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.25447 | + | 2.17281i | 0.0411137 | + | 0.0712110i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.6537 | 0.479227 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.4922 | −0.571445 | −0.285722 | − | 0.958312i | \(-0.592234\pi\) | ||||
−0.285722 | + | 0.958312i | \(0.592234\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.9577 | − | 27.6396i | −0.520207 | − | 0.901025i | −0.999724 | − | 0.0234921i | \(-0.992522\pi\) |
0.479517 | − | 0.877532i | \(-0.340812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.2808 | − | 17.8068i | 0.334788 | − | 0.579869i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.04820 | + | 13.9399i | −0.261531 | + | 0.452986i | −0.966649 | − | 0.256105i | \(-0.917561\pi\) |
0.705118 | + | 0.709090i | \(0.250894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.2807 | − | 31.6631i | −0.593417 | − | 1.02783i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.0358 | −0.778595 | −0.389298 | − | 0.921112i | \(-0.627282\pi\) | ||||
−0.389298 | + | 0.921112i | \(0.627282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −86.7394 | −2.80682 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.85792 | + | 17.0744i | 0.318329 | + | 0.551362i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1435 | − | 26.2293i | 0.488500 | − | 0.846107i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.9436 | + | 41.4715i | −0.770770 | + | 1.33501i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.29484 | + | 10.9030i | 0.202428 | + | 0.350616i | 0.949310 | − | 0.314340i | \(-0.101783\pi\) |
−0.746882 | + | 0.664957i | \(0.768450\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.7939 | −0.988223 | −0.494112 | − | 0.869398i | \(-0.664507\pi\) | ||||
−0.494112 | + | 0.869398i | \(0.664507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.7192 | 0.535993 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.78282 | − | 6.55204i | −0.121023 | − | 0.209618i | 0.799148 | − | 0.601134i | \(-0.205284\pi\) |
−0.920171 | + | 0.391516i | \(0.871951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.31111 | − | 2.27091i | 0.0419033 | − | 0.0725786i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.3823 | − | 23.1789i | 0.426830 | − | 0.739292i | −0.569759 | − | 0.821812i | \(-0.692964\pi\) |
0.996589 | + | 0.0825201i | \(0.0262969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −45.3721 | − | 78.5868i | −1.44568 | − | 2.50398i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.8320 | 0.694216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.6851 | −1.54653 | −0.773266 | − | 0.634082i | \(-0.781378\pi\) | ||||
−0.773266 | + | 0.634082i | \(0.781378\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.0060 | − | 25.9911i | −0.475721 | − | 0.823973i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.0635 | + | 29.5548i | −0.540406 | + | 0.936011i | 0.458474 | + | 0.888708i | \(0.348396\pi\) |
−0.998881 | + | 0.0473036i | \(0.984937\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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.r.d.505.2 | 8 | ||
3.2 | odd | 2 | 504.2.r.d.169.4 | ✓ | 8 | ||
4.3 | odd | 2 | 3024.2.r.l.2017.2 | 8 | |||
9.2 | odd | 6 | 4536.2.a.x.1.2 | 4 | |||
9.4 | even | 3 | inner | 1512.2.r.d.1009.2 | 8 | ||
9.5 | odd | 6 | 504.2.r.d.337.4 | yes | 8 | ||
9.7 | even | 3 | 4536.2.a.ba.1.3 | 4 | |||
12.11 | even | 2 | 1008.2.r.m.673.1 | 8 | |||
36.7 | odd | 6 | 9072.2.a.cl.1.3 | 4 | |||
36.11 | even | 6 | 9072.2.a.ce.1.2 | 4 | |||
36.23 | even | 6 | 1008.2.r.m.337.1 | 8 | |||
36.31 | odd | 6 | 3024.2.r.l.1009.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.d.169.4 | ✓ | 8 | 3.2 | odd | 2 | ||
504.2.r.d.337.4 | yes | 8 | 9.5 | odd | 6 | ||
1008.2.r.m.337.1 | 8 | 36.23 | even | 6 | |||
1008.2.r.m.673.1 | 8 | 12.11 | even | 2 | |||
1512.2.r.d.505.2 | 8 | 1.1 | even | 1 | trivial | ||
1512.2.r.d.1009.2 | 8 | 9.4 | even | 3 | inner | ||
3024.2.r.l.1009.2 | 8 | 36.31 | odd | 6 | |||
3024.2.r.l.2017.2 | 8 | 4.3 | odd | 2 | |||
4536.2.a.x.1.2 | 4 | 9.2 | odd | 6 | |||
4536.2.a.ba.1.3 | 4 | 9.7 | even | 3 | |||
9072.2.a.ce.1.2 | 4 | 36.11 | even | 6 | |||
9072.2.a.cl.1.3 | 4 | 36.7 | odd | 6 |