Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1349,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bo (of order \(6\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{18} - 16 x^{16} + 87 x^{14} + 91 x^{12} - 1104 x^{10} + 819 x^{8} + 7047 x^{6} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1949.9 | ||
Root | \(-1.56233 - 0.747749i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1949 |
Dual form | 2100.2.bo.g.1349.9 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.42873 | + | 0.979142i | 0.824880 | + | 0.565308i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60608 | + | 0.456468i | −0.985004 | + | 0.172529i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.08256 | + | 2.79787i | 0.360854 | + | 0.932622i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.698384 | + | 0.403212i | 0.210571 | + | 0.121573i | 0.601577 | − | 0.798815i | \(-0.294539\pi\) |
−0.391006 | + | 0.920388i | \(0.627873\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.86649 | 1.07237 | 0.536186 | − | 0.844100i | \(-0.319864\pi\) | ||||
0.536186 | + | 0.844100i | \(0.319864\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.83578 | + | 1.05989i | 0.445242 | + | 0.257061i | 0.705819 | − | 0.708393i | \(-0.250579\pi\) |
−0.260577 | + | 0.965453i | \(0.583913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.70603 | + | 1.56233i | −0.620807 | + | 0.358423i | −0.777183 | − | 0.629275i | \(-0.783352\pi\) |
0.156376 | + | 0.987698i | \(0.450019\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.17034 | − | 1.89955i | −0.910042 | − | 0.414515i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.43635 | + | 4.21989i | 0.508015 | + | 0.879908i | 0.999957 | + | 0.00927994i | \(0.00295394\pi\) |
−0.491942 | + | 0.870628i | \(0.663713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.19282 | + | 5.05739i | −0.229558 | + | 0.973295i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.67701i | − | 1.23989i | −0.784645 | − | 0.619945i | \(-0.787155\pi\) | ||
0.784645 | − | 0.619945i | \(-0.212845\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65010 | + | 3.26209i | 1.01479 | + | 0.585888i | 0.912590 | − | 0.408876i | \(-0.134079\pi\) |
0.102198 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.603003 | + | 1.25990i | 0.104969 | + | 0.219320i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.75485 | + | 3.89991i | −1.11049 | + | 0.641142i | −0.938956 | − | 0.344036i | \(-0.888206\pi\) |
−0.171534 | + | 0.985178i | \(0.554872\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.52419 | + | 3.78585i | 0.884579 | + | 0.606221i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.44841 | −1.31942 | −0.659710 | − | 0.751520i | \(-0.729321\pi\) | ||||
−0.659710 | + | 0.751520i | \(0.729321\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.819076i | − | 0.124908i | −0.998048 | − | 0.0624540i | \(-0.980107\pi\) | ||
0.998048 | − | 0.0624540i | \(-0.0198927\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.40368 | − | 1.38776i | 0.350612 | − | 0.202426i | −0.314343 | − | 0.949310i | \(-0.601784\pi\) |
0.664955 | + | 0.746883i | \(0.268451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.58327 | − | 2.37918i | 0.940468 | − | 0.339883i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.58506 | + | 3.31179i | 0.221953 | + | 0.463743i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.67216 | + | 11.5565i | −0.916492 | + | 1.58741i | −0.111789 | + | 0.993732i | \(0.535658\pi\) |
−0.804703 | + | 0.593678i | \(0.797675\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.39594 | − | 0.417438i | −0.714710 | − | 0.0552910i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.86351 | + | 4.95974i | −0.372797 | + | 0.645703i | −0.989995 | − | 0.141105i | \(-0.954935\pi\) |
0.617198 | + | 0.786808i | \(0.288268\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.79397 | − | 1.03575i | 0.229694 | − | 0.132614i | −0.380737 | − | 0.924683i | \(-0.624330\pi\) |
0.610431 | + | 0.792070i | \(0.290996\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.09838 | − | 6.79730i | −0.516347 | − | 0.856380i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.44157 | + | 5.45110i | 1.15347 | + | 0.665957i | 0.949731 | − | 0.313067i | \(-0.101357\pi\) |
0.203741 | + | 0.979025i | \(0.434690\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.650969 | + | 8.41464i | −0.0783674 | + | 1.01300i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3850i | 1.23248i | 0.787559 | + | 0.616239i | \(0.211344\pi\) | ||||
−0.787559 | + | 0.616239i | \(0.788656\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.54270 | + | 2.67203i | −0.180559 | + | 0.312737i | −0.942071 | − | 0.335413i | \(-0.891124\pi\) |
0.761512 | + | 0.648151i | \(0.224457\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00410 | − | 0.732012i | −0.228388 | − | 0.0834205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.76342 | − | 11.7146i | −0.760944 | − | 1.31799i | −0.942364 | − | 0.334589i | \(-0.891403\pi\) |
0.181420 | − | 0.983406i | \(-0.441931\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.65612 | + | 6.05773i | −0.739569 | + | 0.673081i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.8948i | 1.41539i | 0.706519 | + | 0.707694i | \(0.250265\pi\) | ||||
−0.706519 | + | 0.707694i | \(0.749735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.53775 | − | 9.53968i | 0.700920 | − | 1.02276i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.60530 | + | 2.78046i | 0.170161 | + | 0.294728i | 0.938476 | − | 0.345344i | \(-0.112238\pi\) |
−0.768315 | + | 0.640072i | \(0.778904\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0764 | + | 1.76493i | −1.05629 | + | 0.185015i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.87844 | + | 10.1929i | 0.505871 | + | 1.05695i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01388 | 0.102944 | 0.0514721 | − | 0.998674i | \(-0.483609\pi\) | ||||
0.0514721 | + | 0.998674i | \(0.483609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.372090 | + | 2.39049i | −0.0373965 | + | 0.240253i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.27796 | + | 7.40965i | −0.425673 | + | 0.737288i | −0.996483 | − | 0.0837947i | \(-0.973296\pi\) |
0.570810 | + | 0.821082i | \(0.306629\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.88921 | + | 8.46835i | 0.481748 | + | 0.834411i | 0.999781 | − | 0.0209492i | \(-0.00666884\pi\) |
−0.518033 | + | 0.855361i | \(0.673336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.14150 | + | 15.8336i | 0.883743 | + | 1.53069i | 0.847148 | + | 0.531357i | \(0.178318\pi\) |
0.0365946 | + | 0.999330i | \(0.488349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.74840 | − | 15.1527i | 0.837945 | − | 1.45136i | −0.0536658 | − | 0.998559i | \(-0.517091\pi\) |
0.891610 | − | 0.452804i | \(-0.149576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.4695 | − | 1.04202i | −1.27846 | − | 0.0989039i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.96021 | 0.654761 | 0.327381 | − | 0.944893i | \(-0.393834\pi\) | ||||
0.327381 | + | 0.944893i | \(0.393834\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.18572 | + | 10.8179i | 0.386970 | + | 1.00012i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.26799 | − | 1.92417i | −0.482916 | − | 0.176389i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.17484 | − | 8.96309i | −0.470440 | − | 0.814826i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.0705 | − | 8.27219i | −1.08836 | − | 0.745879i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.77139i | − | 0.689600i | −0.938676 | − | 0.344800i | \(-0.887947\pi\) | ||
0.938676 | − | 0.344800i | \(-0.112053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.801992 | − | 1.17024i | 0.0706114 | − | 0.103034i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.93761 | − | 10.2842i | −0.518772 | − | 0.898539i | −0.999762 | − | 0.0218131i | \(-0.993056\pi\) |
0.480990 | − | 0.876726i | \(-0.340277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.33898 | − | 5.30677i | 0.549659 | − | 0.460155i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.22915 | + | 2.12894i | −0.105013 | + | 0.181888i | −0.913744 | − | 0.406291i | \(-0.866822\pi\) |
0.808730 | + | 0.588179i | \(0.200155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.81335i | 0.238625i | 0.992857 | + | 0.119313i | \(0.0380691\pi\) | ||||
−0.992857 | + | 0.119313i | \(0.961931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.79303 | + | 0.370796i | 0.403646 | + | 0.0312267i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.70030 | + | 1.55902i | 0.225810 | + | 0.130372i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.7353 | + | 3.04674i | 0.967912 | + | 0.251291i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.8234 | − | 7.40357i | 1.05053 | − | 0.606524i | 0.127733 | − | 0.991809i | \(-0.459230\pi\) |
0.922798 | + | 0.385285i | \(0.125897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.427898 | − | 0.741141i | 0.0348218 | − | 0.0603132i | −0.848089 | − | 0.529853i | \(-0.822247\pi\) |
0.882911 | + | 0.469540i | \(0.155580\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.978080 | + | 6.28366i | −0.0790731 | + | 0.508004i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1845 | − | 21.1042i | 0.972428 | − | 1.68430i | 0.284256 | − | 0.958748i | \(-0.408254\pi\) |
0.688173 | − | 0.725547i | \(-0.258413\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.8482 | + | 9.97820i | −1.65337 | + | 0.791323i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.27557 | − | 9.88524i | −0.652207 | − | 0.779066i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.36728 | − | 0.789402i | 0.107094 | − | 0.0618307i | −0.445496 | − | 0.895284i | \(-0.646973\pi\) |
0.552590 | + | 0.833453i | \(0.313639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 16.9264i | − | 1.30980i | −0.755714 | − | 0.654902i | \(-0.772710\pi\) | ||
0.755714 | − | 0.654902i | \(-0.227290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.94978 | 0.149983 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.30064 | − | 5.87980i | −0.558294 | − | 0.449640i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.03633 | − | 2.33037i | 0.306876 | − | 0.177175i | −0.338652 | − | 0.940912i | \(-0.609971\pi\) |
0.645528 | + | 0.763737i | \(0.276637\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.94748 | + | 4.28237i | −0.672534 | + | 0.321883i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.11674 | − | 1.79945i | −0.232956 | − | 0.134497i | 0.378979 | − | 0.925405i | \(-0.376275\pi\) |
−0.611935 | + | 0.790908i | \(0.709609\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.5821i | − | 1.67851i | −0.543737 | − | 0.839256i | \(-0.682991\pi\) | ||
0.543737 | − | 0.839256i | \(-0.317009\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.57725 | + | 0.276741i | 0.264438 | + | 0.0204573i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.854719 | + | 1.48042i | 0.0625033 | + | 0.108259i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.800034 | − | 13.7244i | 0.0581939 | − | 0.998305i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.92355 | + | 1.68791i | −0.211541 | + | 0.122133i | −0.602027 | − | 0.798475i | \(-0.705640\pi\) |
0.390486 | + | 0.920609i | \(0.372307\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.60463 | + | 5.54524i | 0.691357 | + | 0.399155i | 0.804120 | − | 0.594467i | \(-0.202637\pi\) |
−0.112763 | + | 0.993622i | \(0.535970\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.2585 | −1.15837 | −0.579184 | − | 0.815197i | \(-0.696629\pi\) | ||||
−0.579184 | + | 0.815197i | \(0.696629\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.07964 | + | 0.623332i | 0.0765338 | + | 0.0441868i | 0.537779 | − | 0.843086i | \(-0.319264\pi\) |
−0.461245 | + | 0.887273i | \(0.652597\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.15210 | + | 17.0328i | 0.575005 | + | 1.20140i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.04784 | + | 17.4008i | 0.213917 | + | 1.22130i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.16919 | + | 11.3849i | −0.637303 | + | 0.791305i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.51980 | −0.174298 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.65466 | −0.526968 | −0.263484 | − | 0.964664i | \(-0.584872\pi\) | ||||
−0.263484 | + | 0.964664i | \(0.584872\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.1684 | + | 14.8375i | −0.696730 | + | 1.01665i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.2136 | − | 5.92216i | −1.10065 | − | 0.402022i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.82040 | + | 2.30710i | −0.325732 | + | 0.155899i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.09803 | + | 4.09805i | 0.477465 | + | 0.275665i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9369 | 1.40204 | 0.701019 | − | 0.713143i | \(-0.252729\pi\) | ||||
0.701019 | + | 0.713143i | \(0.252729\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.96818 | + | 2.29103i | 0.263377 | + | 0.152061i | 0.625874 | − | 0.779924i | \(-0.284742\pi\) |
−0.362497 | + | 0.931985i | \(0.618076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.845272 | + | 0.488018i | −0.0558572 | + | 0.0322492i | −0.527669 | − | 0.849450i | \(-0.676934\pi\) |
0.471811 | + | 0.881700i | \(0.343600\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.14658 | − | 3.00814i | −0.141234 | − | 0.197921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.95247 | − | 17.2382i | −0.652008 | − | 1.12931i | −0.982635 | − | 0.185550i | \(-0.940593\pi\) |
0.330627 | − | 0.943762i | \(-0.392740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.80712 | − | 23.3594i | 0.117385 | − | 1.51736i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.2703i | 1.82865i | 0.404977 | + | 0.914327i | \(0.367279\pi\) | ||||
−0.404977 | + | 0.914327i | \(0.632721\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0949 | + | 6.40567i | 0.714688 | + | 0.412625i | 0.812794 | − | 0.582551i | \(-0.197945\pi\) |
−0.0981065 | + | 0.995176i | \(0.531279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4412 | + | 2.13760i | −0.990553 | + | 0.137127i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.4629 | + | 6.04074i | −0.665736 | + | 0.384363i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.6258 | + | 18.4232i | −0.800130 | + | 1.16753i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.3349 | −0.652335 | −0.326167 | − | 0.945312i | \(-0.605757\pi\) | ||||
−0.326167 | + | 0.945312i | \(0.605757\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.92947i | 0.247044i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.4185 | + | 15.2527i | −1.64794 | + | 0.951439i | −0.670052 | + | 0.742315i | \(0.733728\pi\) |
−0.977889 | + | 0.209124i | \(0.932939\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8235 | − | 13.2469i | 0.983223 | − | 0.823119i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.6814 | − | 7.22828i | 1.15635 | − | 0.447419i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.3377 | − | 17.9054i | 0.637447 | − | 1.10409i | −0.348543 | − | 0.937293i | \(-0.613324\pi\) |
0.985991 | − | 0.166799i | \(-0.0533430\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.428919 | + | 5.54435i | −0.0262494 | + | 0.339309i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.4095 | − | 21.4938i | 0.756618 | − | 1.31050i | −0.187948 | − | 0.982179i | \(-0.560184\pi\) |
0.944566 | − | 0.328322i | \(-0.106483\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8571 | − | 10.8871i | 1.14548 | − | 0.661346i | 0.197702 | − | 0.980262i | \(-0.436652\pi\) |
0.947783 | + | 0.318916i | \(0.103319\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.1246 | − | 7.34459i | −0.975905 | − | 0.444515i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.1831 | + | 7.61126i | 0.792095 | + | 0.457316i | 0.840699 | − | 0.541502i | \(-0.182144\pi\) |
−0.0486048 | + | 0.998818i | \(0.515477\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.01030 | + | 19.3396i | −0.180222 | + | 1.15783i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.9488i | 1.07073i | 0.844619 | + | 0.535367i | \(0.179827\pi\) | ||||
−0.844619 | + | 0.535367i | \(0.820173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4944 | − | 23.3730i | 0.802159 | − | 1.38938i | −0.116033 | − | 0.993245i | \(-0.537018\pi\) |
0.918192 | − | 0.396135i | \(-0.129649\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.0172 | − | 3.85643i | 1.29963 | − | 0.227638i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.25328 | − | 10.8310i | −0.367840 | − | 0.637117i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.44857 | + | 0.992735i | 0.0849166 | + | 0.0581951i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.4450i | − | 0.843887i | −0.906622 | − | 0.421944i | \(-0.861348\pi\) | ||
0.906622 | − | 0.421944i | \(-0.138652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.87224 | + | 3.05104i | −0.166665 | + | 0.177039i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.42015 | + | 16.3162i | 0.544782 | + | 0.943589i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.373882 | + | 2.13457i | 0.0215502 | + | 0.123035i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.3672 | + | 6.39768i | −0.767924 | + | 0.367537i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.34543 | −0.533372 | −0.266686 | − | 0.963783i | \(-0.585929\pi\) | ||||
−0.266686 | + | 0.963783i | \(0.585929\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.30635 | + | 16.8862i | −0.0743154 | + | 0.960625i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.6664 | − | 25.4029i | 0.831654 | − | 1.44047i | −0.0650722 | − | 0.997881i | \(-0.520728\pi\) |
0.896726 | − | 0.442586i | \(-0.145939\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.51790 | + | 9.55728i | 0.311890 | + | 0.540209i | 0.978772 | − | 0.204954i | \(-0.0657046\pi\) |
−0.666881 | + | 0.745164i | \(0.732371\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.48631 | + | 14.6987i | 0.476639 | + | 0.825563i | 0.999642 | − | 0.0267682i | \(-0.00852159\pi\) |
−0.523003 | + | 0.852331i | \(0.675188\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.69225 | − | 4.66312i | 0.150737 | − | 0.261085i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.44252 | + | 31.5728i | −0.136328 | + | 1.76222i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.62357 | −0.368546 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.3357 | − | 13.0832i | 1.51167 | − | 0.723503i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.63070 | + | 4.71382i | −0.310430 | + | 0.259881i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.82739 | + | 10.0933i | 0.320302 | + | 0.554780i | 0.980550 | − | 0.196268i | \(-0.0628822\pi\) |
−0.660248 | + | 0.751048i | \(0.729549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.2240 | − | 14.6773i | −0.998668 | − | 0.804310i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.1753i | − | 0.554286i | −0.960829 | − | 0.277143i | \(-0.910612\pi\) | ||
0.960829 | − | 0.277143i | \(-0.0893875\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.94428 | + | 6.81503i | 0.540099 | + | 0.370142i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.63063 | + | 4.55638i | 0.142456 | + | 0.246742i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0705 | + | 9.20538i | −0.867725 | + | 0.497044i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.796887 | − | 1.38025i | 0.0427791 | − | 0.0740956i | −0.843843 | − | 0.536590i | \(-0.819712\pi\) |
0.886622 | + | 0.462494i | \(0.153045\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.4812i | − | 0.828690i | −0.910120 | − | 0.414345i | \(-0.864011\pi\) | ||
0.910120 | − | 0.414345i | \(-0.135989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.61202 | + | 19.5544i | −0.246171 | + | 1.04374i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.0861 | − | 6.40056i | −0.590054 | − | 0.340668i | 0.175065 | − | 0.984557i | \(-0.443986\pi\) |
−0.765119 | + | 0.643889i | \(0.777320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.64251 | − | 7.90724i | −0.298633 | − | 0.418496i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.66697 | + | 3.27183i | −0.299091 | + | 0.172680i | −0.642035 | − | 0.766676i | \(-0.721909\pi\) |
0.342943 | + | 0.939356i | \(0.388576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.61826 | + | 7.99906i | −0.243066 | + | 0.421003i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.38266 | − | 17.8728i | 0.0725710 | − | 0.938077i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.66046 | + | 15.0004i | −0.452072 | + | 0.783012i | −0.998515 | − | 0.0544847i | \(-0.982648\pi\) |
0.546442 | + | 0.837497i | \(0.315982\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.14593 | − | 23.6375i | −0.476118 | − | 1.23052i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.1130 | − | 33.1628i | 0.628875 | − | 1.72173i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.862445 | + | 0.497933i | −0.0446557 | + | 0.0257820i | −0.522162 | − | 0.852847i | \(-0.674874\pi\) |
0.477506 | + | 0.878629i | \(0.341541\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 25.8166i | − | 1.32962i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.2985 | 1.04266 | 0.521331 | − | 0.853355i | \(-0.325436\pi\) | ||||
0.521331 | + | 0.853355i | \(0.325436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.60930 | − | 11.1033i | 0.389836 | − | 0.568837i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.2120 | − | 9.93736i | 0.879493 | − | 0.507776i | 0.00900178 | − | 0.999959i | \(-0.497135\pi\) |
0.870491 | + | 0.492184i | \(0.163801\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.29167 | − | 0.886700i | 0.116492 | − | 0.0450735i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.56923 | + | 0.905994i | 0.0795630 | + | 0.0459357i | 0.539254 | − | 0.842143i | \(-0.318706\pi\) |
−0.459691 | + | 0.888079i | \(0.652040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3291i | 0.522363i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.58647 | − | 20.5072i | 0.0800268 | − | 1.03445i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.3967 | + | 30.1320i | 0.873116 | + | 1.51228i | 0.858757 | + | 0.512384i | \(0.171237\pi\) |
0.0143590 | + | 0.999897i | \(0.495429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.2528 | − | 1.37520i | 0.713532 | − | 0.0688461i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.5121 | − | 18.7709i | 1.62358 | − | 0.937374i | 0.637627 | − | 0.770345i | \(-0.279916\pi\) |
0.985952 | − | 0.167029i | \(-0.0534173\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.8461 | + | 12.6128i | 1.08823 | + | 0.628290i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.28997 | −0.311782 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.24769 | − | 1.87505i | −0.160588 | − | 0.0927154i | 0.417552 | − | 0.908653i | \(-0.362888\pi\) |
−0.578140 | + | 0.815937i | \(0.696221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.84066 | + | 1.83819i | −0.189446 | + | 0.0906710i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.19856 | − | 14.2326i | 0.255804 | − | 0.700339i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.75467 | + | 4.01953i | −0.134897 | + | 0.196837i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0547 | −1.46827 | −0.734134 | − | 0.679005i | \(-0.762411\pi\) | ||||
−0.734134 | + | 0.679005i | \(0.762411\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5447 | 1.00129 | 0.500643 | − | 0.865654i | \(-0.333097\pi\) | ||||
0.500643 | + | 0.865654i | \(0.333097\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.48491 | + | 5.22283i | 0.315307 | + | 0.253943i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.20243 | + | 3.51813i | −0.203370 | + | 0.170254i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.33151 | + | 4.87140i | 0.112566 | + | 0.235193i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.7400 | + | 18.3251i | 1.52886 | + | 0.882688i | 0.999410 | + | 0.0343478i | \(0.0109354\pi\) |
0.529451 | + | 0.848340i | \(0.322398\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.4397 | −1.75118 | −0.875589 | − | 0.483057i | \(-0.839526\pi\) | ||||
−0.875589 | + | 0.483057i | \(0.839526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.1857 | − | 7.61278i | −0.630758 | − | 0.364168i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.96135 | − | 4.59649i | 0.379975 | − | 0.219378i | −0.297833 | − | 0.954618i | \(-0.596264\pi\) |
0.677807 | + | 0.735240i | \(0.262930\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.7834 | + | 15.8435i | 0.656354 | + | 0.754453i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.9703 | − | 20.7332i | −0.568727 | − | 0.985063i | −0.996692 | − | 0.0812683i | \(-0.974103\pi\) |
0.427966 | − | 0.903795i | \(-0.359230\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.5703 | + | 1.97816i | 1.20943 | + | 0.0935636i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 24.0126i | − | 1.13322i | −0.823985 | − | 0.566611i | \(-0.808254\pi\) | ||
0.823985 | − | 0.566611i | \(-0.191746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.90023 | − | 3.40650i | −0.277831 | − | 0.160406i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.33703 | − | 0.639920i | 0.0628193 | − | 0.0300661i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.77786 | + | 3.33585i | −0.270277 | + | 0.156044i | −0.629013 | − | 0.777394i | \(-0.716541\pi\) |
0.358737 | + | 0.933439i | \(0.383208\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.55001 | + | 8.02000i | −0.352404 | + | 0.374342i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.6895 | −1.24305 | −0.621527 | − | 0.783393i | \(-0.713487\pi\) | ||||
−0.621527 | + | 0.783393i | \(0.713487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9550i | 0.509123i | 0.967057 | + | 0.254562i | \(0.0819312\pi\) | ||||
−0.967057 | + | 0.254562i | \(0.918069\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.952153 | + | 0.549726i | −0.0440604 | + | 0.0254383i | −0.521868 | − | 0.853026i | \(-0.674765\pi\) |
0.477808 | + | 0.878464i | \(0.341431\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.0937 | − | 9.89620i | −1.25107 | − | 0.456964i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.0724 | − | 18.2219i | 1.75428 | − | 0.839620i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.330261 | − | 0.572029i | 0.0151854 | − | 0.0263019i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −39.5566 | − | 6.15717i | −1.81117 | − | 0.281917i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.91657 | − | 11.9798i | 0.316026 | − | 0.547373i | −0.663629 | − | 0.748062i | \(-0.730985\pi\) |
0.979655 | + | 0.200689i | \(0.0643180\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1176 | + | 15.0790i | −1.19086 | + | 0.687543i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.14454 | − | 22.2263i | −0.0975799 | − | 1.01133i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.4385 | − | 15.8416i | −1.24336 | − | 0.717854i | −0.273582 | − | 0.961849i | \(-0.588209\pi\) |
−0.969776 | + | 0.243995i | \(0.921542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.72642 | + | 0.210920i | 0.123293 | + | 0.00953813i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.3388i | 1.68508i | 0.538636 | + | 0.842538i | \(0.318940\pi\) | ||||
−0.538636 | + | 0.842538i | \(0.681060\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.07689 | − | 12.2575i | 0.318727 | − | 0.552051i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.74044 | − | 27.0642i | −0.212638 | − | 1.21400i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.50065 | − | 9.52740i | −0.246243 | − | 0.426505i | 0.716237 | − | 0.697857i | \(-0.245863\pi\) |
−0.962480 | + | 0.271352i | \(0.912529\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.5734 | − | 24.1833i | 0.740443 | − | 1.08043i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.2246i | − | 0.901772i | −0.892582 | − | 0.450886i | \(-0.851108\pi\) | ||
0.892582 | − | 0.450886i | \(-0.148892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.78572 | + | 1.90911i | 0.123718 | + | 0.0847867i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.24557 | + | 9.08560i | 0.232506 | + | 0.402712i | 0.958545 | − | 0.284941i | \(-0.0919742\pi\) |
−0.726039 | + | 0.687654i | \(0.758641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.80069 | − | 7.66771i | 0.123895 | − | 0.339199i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.67351 | − | 15.5490i | −0.206340 | − | 0.686507i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.23825 | 0.0984383 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.04860 | + | 0.622652i | 0.353295 | + | 0.0273314i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00130 | − | 10.3946i | 0.262922 | − | 0.455394i | −0.704095 | − | 0.710105i | \(-0.748647\pi\) |
0.967017 | + | 0.254712i | \(0.0819806\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.46891 | − | 7.74038i | −0.195412 | − | 0.338463i | 0.751624 | − | 0.659592i | \(-0.229271\pi\) |
−0.947035 | + | 0.321129i | \(0.895938\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.91489 | + | 11.9769i | 0.301217 | + | 0.521724i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.371651 | + | 0.643719i | −0.0161587 | + | 0.0279878i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.9766 | − | 2.64249i | −0.736723 | − | 0.114674i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.6657 | −1.41491 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.69107 | − | 5.62266i | −0.116128 | − | 0.242636i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.55697 | + | 0.992874i | 0.239356 | + | 0.0427661i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9695 | − | 27.6599i | −0.686581 | − | 1.18919i | −0.972937 | − | 0.231069i | \(-0.925778\pi\) |
0.286357 | − | 0.958123i | \(-0.407556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.1110 | − | 32.2638i | 0.948876 | − | 1.38457i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.6313i | 1.43797i | 0.695026 | + | 0.718984i | \(0.255393\pi\) | ||||
−0.695026 | + | 0.718984i | \(0.744607\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.83996 | + | 3.89802i | 0.206565 | + | 0.166363i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.4317 | + | 18.0682i | 0.444405 | + | 0.769732i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.9733 | + | 27.4418i | 0.976926 | + | 1.16695i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.30000 | − | 9.17988i | 0.224568 | − | 0.388964i | −0.731621 | − | 0.681711i | \(-0.761236\pi\) |
0.956190 | + | 0.292747i | \(0.0945695\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.16695i | − | 0.133948i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.228372 | + | 2.95201i | −0.00964188 | + | 0.124634i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.98833 | − | 1.14796i | −0.0837980 | − | 0.0483808i | 0.457515 | − | 0.889202i | \(-0.348739\pi\) |
−0.541313 | + | 0.840821i | \(0.682073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.5812 | − | 18.8252i | 0.612353 | − | 0.790585i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.1648 | − | 13.9515i | 1.01304 | − | 0.584878i | 0.100959 | − | 0.994891i | \(-0.467809\pi\) |
0.912080 | + | 0.410012i | \(0.134476\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.11649 | − | 5.39791i | 0.130421 | − | 0.225896i | −0.793418 | − | 0.608677i | \(-0.791700\pi\) |
0.923839 | + | 0.382782i | \(0.125034\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.82969 | − | 0.450993i | −0.243539 | − | 0.0188405i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.62662 | − | 11.4776i | 0.275870 | − | 0.477820i | −0.694484 | − | 0.719508i | \(-0.744368\pi\) |
0.970354 | + | 0.241687i | \(0.0777008\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.29289 | + | 17.3270i | 0.344641 | + | 0.720084i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.88606 | − | 33.6048i | −0.244195 | − | 1.39416i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.31946 | + | 5.38059i | −0.385973 | + | 0.222841i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18.6209i | − | 0.768568i | −0.923215 | − | 0.384284i | \(-0.874448\pi\) | ||
0.923215 | − | 0.384284i | \(-0.125552\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.3858 | −0.839982 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.2290 | − | 15.9193i | −0.955514 | − | 0.654834i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.38715 | − | 1.37822i | 0.0980284 | − | 0.0565967i | −0.450184 | − | 0.892936i | \(-0.648642\pi\) |
0.548213 | + | 0.836339i | \(0.315308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.932191 | + | 1.94770i | 0.0381520 | + | 0.0797140i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.2530 | − | 9.38368i | −0.664080 | − | 0.383407i | 0.129750 | − | 0.991547i | \(-0.458583\pi\) |
−0.793830 | + | 0.608140i | \(0.791916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 16.5669i | − | 0.675779i | −0.941186 | − | 0.337890i | \(-0.890287\pi\) | ||
0.941186 | − | 0.337890i | \(-0.109713\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.03035 | + | 32.3174i | −0.204852 | + | 1.31607i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.7301 | − | 28.9773i | −0.679053 | − | 1.17615i | −0.975266 | − | 0.221032i | \(-0.929057\pi\) |
0.296213 | − | 0.955122i | \(-0.404276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.6833 | + | 27.8454i | −0.513954 | + | 1.12835i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.29381 | − | 5.36578i | 0.375987 | − | 0.217076i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.5231 | + | 18.7772i | 1.31359 | + | 0.758404i | 0.982690 | − | 0.185260i | \(-0.0593128\pi\) |
0.330905 | + | 0.943664i | \(0.392646\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.5088 | −0.906172 | −0.453086 | − | 0.891467i | \(-0.649677\pi\) | ||||
−0.453086 | + | 0.891467i | \(0.649677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.3812 | + | 13.4991i | 0.939770 | + | 0.542576i | 0.889888 | − | 0.456179i | \(-0.150782\pi\) |
0.0498816 | + | 0.998755i | \(0.484116\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.2478 | + | 7.28804i | −0.973029 | + | 0.292459i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.45272 | − | 6.51332i | −0.218459 | − | 0.260951i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.60012 | − | 2.46724i | −0.143775 | − | 0.0985322i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.5339 | −0.659249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.17965 | 0.365436 | 0.182718 | − | 0.983165i | \(-0.441510\pi\) | ||||
0.182718 | + | 0.983165i | \(0.441510\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.9365 | − | 7.49499i | −0.434686 | − | 0.297899i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.4542 | − | 9.19909i | 1.00853 | − | 0.364481i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.0560 | + | 11.2425i | −1.14944 | + | 0.444745i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.6664 | + | 15.3959i | 1.05326 | + | 0.608100i | 0.923560 | − | 0.383453i | \(-0.125265\pi\) |
0.129700 | + | 0.991553i | \(0.458599\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.42929 | −0.135238 | −0.0676189 | − | 0.997711i | \(-0.521540\pi\) | ||||
−0.0676189 | + | 0.997711i | \(0.521540\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.8152 | + | 25.2967i | 1.72255 | + | 0.994516i | 0.913567 | + | 0.406689i | \(0.133317\pi\) |
0.808986 | + | 0.587828i | \(0.200017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.99966 | + | 2.30920i | −0.157000 | + | 0.0906441i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.3663 | − | 24.3366i | −0.680640 | − | 0.953828i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.64220 | + | 4.57643i | 0.103397 | + | 0.179090i | 0.913082 | − | 0.407775i | \(-0.133695\pi\) |
−0.809685 | + | 0.586865i | \(0.800362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.14605 | − | 1.42362i | −0.356821 | − | 0.0555408i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.0502i | 1.01477i | 0.861719 | + | 0.507385i | \(0.169388\pi\) | ||||
−0.861719 | + | 0.507385i | \(0.830612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.3751 | − | 16.3823i | −1.10366 | − | 0.637199i | −0.166481 | − | 0.986045i | \(-0.553241\pi\) |
−0.937180 | + | 0.348845i | \(0.886574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.12863 | + | 12.8050i | 0.238016 | + | 0.497305i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.1763 | − | 16.2676i | 1.09099 | − | 0.629883i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.9132 | + | 20.5002i | 1.15651 | + | 0.792583i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.67050 | 0.0644891 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 38.5194i | − | 1.48481i | −0.669950 | − | 0.742406i | \(-0.733685\pi\) | ||
0.669950 | − | 0.742406i | \(-0.266315\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5938 | − | 9.58044i | 0.637752 | − | 0.368206i | −0.145996 | − | 0.989285i | \(-0.546639\pi\) |
0.783748 | + | 0.621079i | \(0.213305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.64225 | + | 0.462805i | −0.101400 | + | 0.0177608i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.42623 | + | 7.15868i | 0.131293 | + | 0.274321i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.4812 | + | 25.0821i | −0.554107 | + | 0.959741i | 0.443866 | + | 0.896093i | \(0.353607\pi\) |
−0.997972 | + | 0.0636479i | \(0.979727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.68551 | − | 0.130393i | −0.0643062 | − | 0.00497482i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.7979 | + | 44.6832i | −0.982821 | + | 1.70230i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.4572 | − | 22.7806i | 1.50102 | − | 0.866616i | 0.501024 | − | 0.865433i | \(-0.332957\pi\) |
0.999999 | − | 0.00118303i | \(-0.000376571\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.121486 | − | 6.39964i | −0.00461485 | − | 0.243102i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.5094 | − | 8.95437i | −0.587461 | − | 0.339171i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.65920 | − | 34.3737i | 0.100580 | − | 1.30013i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.2878i | 1.48388i | 0.670466 | + | 0.741940i | \(0.266094\pi\) | ||||
−0.670466 | + | 0.741940i | \(0.733906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.1859 | − | 21.1066i | 0.459600 | − | 0.796050i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.76643 | − | 21.2629i | 0.292087 | − | 0.799672i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.88537 | + | 17.1220i | 0.371253 | + | 0.643029i | 0.989759 | − | 0.142752i | \(-0.0455950\pi\) |
−0.618506 | + | 0.785780i | \(0.712262\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.4540 | − | 31.6049i | 0.954601 | − | 1.18528i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.7904i | 1.19056i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.6806 | + | 40.3907i | −1.03375 | + | 1.50842i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.740641 | + | 1.28283i | 0.0276212 | + | 0.0478414i | 0.879506 | − | 0.475889i | \(-0.157873\pi\) |
−0.851884 | + | 0.523730i | \(0.824540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.6072 | − | 19.8374i | −0.618484 | − | 0.738784i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.57966 | + | 20.0155i | 0.356271 | + | 0.744385i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.35193 | 0.235580 | 0.117790 | − | 0.993039i | \(-0.462419\pi\) | ||||
0.117790 | + | 0.993039i | \(0.462419\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.1544 | − | 12.0651i | −0.894607 | − | 0.446855i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.868129 | − | 1.50364i | 0.0321089 | − | 0.0556142i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.6357 | − | 34.0100i | −0.725261 | − | 1.25619i | −0.958866 | − | 0.283857i | \(-0.908386\pi\) |
0.233605 | − | 0.972331i | \(-0.424948\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.39590 | + | 7.61392i | 0.161925 | + | 0.280462i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.2904 | + | 19.5555i | −0.415324 | + | 0.719362i | −0.995462 | − | 0.0951558i | \(-0.969665\pi\) |
0.580139 | + | 0.814518i | \(0.302998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.8634 | − | 1.61402i | −0.766436 | − | 0.0592926i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.6330 | 0.977070 | 0.488535 | − | 0.872544i | \(-0.337532\pi\) | ||||
0.488535 | + | 0.872544i | \(0.337532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.0779 | + | 13.9594i | −1.32002 | + | 0.510748i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.0510 | − | 37.0906i | −1.13458 | − | 1.35526i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.62709 | + | 14.9426i | 0.314807 | + | 0.545262i | 0.979396 | − | 0.201947i | \(-0.0647268\pi\) |
−0.664589 | + | 0.747209i | \(0.731393\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.7659 | − | 10.1194i | −0.538098 | − | 0.368770i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.1712i | − | 0.914863i | −0.889245 | − | 0.457431i | \(-0.848770\pi\) | ||
0.889245 | − | 0.457431i | \(-0.151230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.84751 | + | 5.61417i | −0.139656 | + | 0.203781i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.00796126 | − | 0.0137893i | −0.000288596 | − | 0.000499862i | 0.865881 | − | 0.500250i | \(-0.166759\pi\) |
−0.866170 | + | 0.499750i | \(0.833425\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.8823 | + | 43.4824i | −0.574977 | + | 1.57417i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.0717 | + | 19.1768i | −0.399777 | + | 0.692435i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.0356i | − | 0.470075i | −0.971986 | − | 0.235037i | \(-0.924479\pi\) | ||
0.971986 | − | 0.235037i | \(-0.0755213\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.6796 | − | 4.07537i | −1.89721 | − | 0.146771i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.4758 | − | 14.7085i | −0.916301 | − | 0.529027i | −0.0338481 | − | 0.999427i | \(-0.510776\pi\) |
−0.882453 | + | 0.470400i | \(0.844110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 35.5781 | − | 3.43280i | 1.27636 | − | 0.123151i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.8617 | − | 13.1992i | 0.819105 | − | 0.472910i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.18738 | + | 7.25275i | −0.149836 | + | 0.259524i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.7683 | + | 7.96445i | 1.20678 | + | 0.284626i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.13148 | − | 1.95977i | 0.0403327 | − | 0.0698584i | −0.845154 | − | 0.534522i | \(-0.820492\pi\) |
0.885487 | + | 0.464664i | \(0.153825\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.3017 | − | 15.4600i | 1.14997 | − | 0.550389i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.1388 | + | 3.17711i | −0.644943 | + | 0.112965i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.93636 | − | 4.00471i | 0.246318 | − | 0.142211i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 19.6277i | − | 0.695250i | −0.937634 | − | 0.347625i | \(-0.886988\pi\) | ||
0.937634 | − | 0.347625i | \(-0.113012\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.88350 | 0.208143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.04152 | + | 7.50143i | −0.213467 | + | 0.265050i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.15479 | + | 1.24407i | −0.0760409 | + | 0.0439022i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.7753 | − | 18.5583i | 1.36496 | − | 0.653284i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.2506 | + | 12.2690i | 0.747130 | + | 0.431356i | 0.824656 | − | 0.565635i | \(-0.191369\pi\) |
−0.0775260 | + | 0.996990i | \(0.524702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.7927i | 1.36220i | 0.732192 | + | 0.681098i | \(0.238497\pi\) | ||||
−0.732192 | + | 0.681098i | \(0.761503\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.6018 | + | 2.90893i | 1.31875 | + | 0.102021i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.27967 | + | 2.21645i | 0.0447698 | + | 0.0775436i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.8464 | − | 26.2817i | −0.553716 | − | 0.918358i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.8734 | − | 6.85513i | 0.414386 | − | 0.239246i | −0.278287 | − | 0.960498i | \(-0.589767\pi\) |
0.692672 | + | 0.721252i | \(0.256433\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.00040 | − | 4.04168i | −0.244019 | − | 0.140884i | 0.373004 | − | 0.927830i | \(-0.378328\pi\) |
−0.617022 | + | 0.786946i | \(0.711661\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.6581 | −1.30950 | −0.654751 | − | 0.755845i | \(-0.727226\pi\) | ||||
−0.654751 | + | 0.755845i | \(0.727226\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4475 | − | 8.91864i | −0.536515 | − | 0.309757i | 0.207150 | − | 0.978309i | \(-0.433581\pi\) |
−0.743665 | + | 0.668552i | \(0.766914\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.3826 | + | 23.7826i | 0.394859 | + | 0.825008i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.6071 | + | 2.60988i | 0.506106 | + | 0.0904269i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.2372 | + | 24.6837i | −0.803194 | + | 0.853193i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.49497 | −0.155183 | −0.0775917 | − | 0.996985i | \(-0.524723\pi\) | ||||
−0.0775917 | + | 0.996985i | \(0.524723\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.5825 | −0.537329 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.5744 | + | 25.6440i | −0.605295 | + | 0.883228i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.5774 | + | 20.9963i | 0.603966 | + | 0.721443i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 42.1654 | − | 20.1809i | 1.44711 | − | 0.692605i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.9144 | − | 19.0032i | −1.12829 | − | 0.651420i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.0503 | −1.13162 | −0.565811 | − | 0.824535i | \(-0.691437\pi\) | ||||
−0.565811 | + | 0.824535i | \(0.691437\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.365051 | + | 0.210762i | 0.0124699 | + | 0.00719949i | 0.506222 | − | 0.862403i | \(-0.331042\pi\) |
−0.493752 | + | 0.869603i | \(0.664375\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.0294 | − | 9.83192i | 0.581035 | − | 0.335461i | −0.180509 | − | 0.983573i | \(-0.557775\pi\) |
0.761545 | + | 0.648112i | \(0.224441\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.2327 | + | 16.0482i | 1.20073 | + | 0.546920i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.451820 | − | 0.782575i | −0.0153801 | − | 0.0266392i | 0.858233 | − | 0.513260i | \(-0.171563\pi\) |
−0.873613 | + | 0.486621i | \(0.838229\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.67081 | − | 21.5974i | 0.0567437 | − | 0.733488i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.9084i | − | 0.370041i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.5058 | + | 21.0766i | 1.23695 | + | 0.714154i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.09759 | + | 2.83671i | 0.0371478 | + | 0.0960080i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.2661 | − | 7.65916i | 0.447963 | − | 0.258632i | −0.259006 | − | 0.965876i | \(-0.583395\pi\) |
0.706970 | + | 0.707244i | \(0.250062\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.1437 | − | 20.6381i | 0.477056 | − | 0.696106i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.8614 | −1.47773 | −0.738863 | − | 0.673855i | \(-0.764637\pi\) | ||||
−0.738863 | + | 0.673855i | \(0.764637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.91300i | − | 0.0980304i | −0.998798 | − | 0.0490152i | \(-0.984392\pi\) | ||
0.998798 | − | 0.0490152i | \(-0.0156083\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.9001 | + | 7.44790i | −0.433145 | + | 0.250076i | −0.700685 | − | 0.713470i | \(-0.747122\pi\) |
0.267541 | + | 0.963547i | \(0.413789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.54739 | + | 20.2528i | 0.118976 | + | 0.679259i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.09108 | + | 1.54679i | −0.237560 | + | 0.0518195i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.33629 | + | 7.51067i | −0.145108 | + | 0.251335i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.51697 | + | 32.5352i | −0.0840391 | + | 1.08632i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.7810 | − | 37.7258i | 0.726437 | − | 1.25823i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.4972 | + | 14.1435i | −0.816121 | + | 0.471188i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.55587 | + | 3.41582i | −0.0517762 | + | 0.113671i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.5393 | + | 9.54899i | 0.549180 | + | 0.317069i | 0.748791 | − | 0.662806i | \(-0.230635\pi\) |
−0.199611 | + | 0.979875i | \(0.563968\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25.3624 | − | 3.94777i | −0.841217 | − | 0.130939i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.16915i | 0.204393i | 0.994764 | + | 0.102197i | \(0.0325871\pi\) | ||||
−0.994764 | + | 0.102197i | \(0.967413\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.19934 | + | 9.00552i | −0.172073 | + | 0.298039i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.1683 | + | 24.0912i | 0.666016 | + | 0.795562i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.8318 | + | 25.6894i | 0.489255 | + | 0.847415i | 0.999924 | − | 0.0123630i | \(-0.00393538\pi\) |
−0.510668 | + | 0.859778i | \(0.670602\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.3521 | − | 9.15051i | −0.439968 | − | 0.301519i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.1537i | 1.32168i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.4005 | + | 22.8469i | −0.604350 | + | 0.750389i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.8256 | − | 29.1428i | −0.552030 | − | 0.956144i | −0.998128 | − | 0.0611601i | \(-0.980520\pi\) |
0.446098 | − | 0.894984i | \(-0.352813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.0975 | + | 16.7234i | −0.462027 | + | 0.548087i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 45.8274 | − | 21.9335i | 1.50032 | − | 0.718072i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.99276 | −0.261112 | −0.130556 | − | 0.991441i | \(-0.541676\pi\) | ||||
−0.130556 | + | 0.991441i | \(0.541676\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.47433 | + | 19.0576i | −0.0481128 | + | 0.621922i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.69431 | + | 15.0590i | −0.283426 | + | 0.490909i | −0.972226 | − | 0.234043i | \(-0.924804\pi\) |
0.688800 | + | 0.724951i | \(0.258138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.5833 | − | 35.6514i | −0.670285 | − | 1.16097i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.1485 | + | 36.6302i | 0.687233 | + | 1.19032i | 0.972729 | + | 0.231943i | \(0.0745083\pi\) |
−0.285496 | + | 0.958380i | \(0.592158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.96483 | + | 10.3314i | −0.193627 | + | 0.335371i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.26746 | + | 29.3099i | −0.0735273 | + | 0.950438i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.5612 | 1.31391 | 0.656953 | − | 0.753932i | \(-0.271845\pi\) | ||||
0.656953 | + | 0.753932i | \(0.271845\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.41237 | − | 4.02626i | 0.271933 | − | 0.130150i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.23145 | − | 6.10926i | 0.0720574 | − | 0.197278i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.78241 | + | 10.0154i | 0.186529 | + | 0.323078i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.4039 | + | 42.7175i | −1.10865 | + | 1.37655i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.6713i | 1.21143i | 0.795682 | + | 0.605714i | \(0.207112\pi\) | ||||
−0.795682 | + | 0.605714i | \(0.792888\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.46333 | − | 6.48542i | −0.304006 | − | 0.208342i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.5452 | − | 37.3173i | −0.691418 | − | 1.19757i | −0.971373 | − | 0.237558i | \(-0.923653\pi\) |
0.279956 | − | 0.960013i | \(-0.409680\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.28420 | − | 7.33180i | −0.0411697 | − | 0.235047i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.3970 | + | 19.7402i | −0.364622 | + | 0.631545i | −0.988716 | − | 0.149805i | \(-0.952135\pi\) |
0.624093 | + | 0.781350i | \(0.285469\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.58910i | 0.0827481i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 51.8658 | + | 8.07315i | 1.65595 | + | 0.257756i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.1321 | + | 22.5929i | 1.24812 | + | 0.720602i | 0.970734 | − | 0.240157i | \(-0.0771990\pi\) |
0.277385 | + | 0.960759i | \(0.410532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.6603 | + | 1.22154i | −0.402981 | + | 0.0388822i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.45641 | − | 1.99556i | 0.109907 | − | 0.0634551i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.2760 | + | 43.7793i | −0.802919 | + | 1.39070i | 0.114768 | + | 0.993392i | \(0.463388\pi\) |
−0.917687 | + | 0.397304i | \(0.869946\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.55702 | + | 20.1265i | −0.0494105 | + | 0.638696i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0271 | + | 22.5635i | −0.412571 | + | 0.714595i | −0.995170 | − | 0.0981654i | \(-0.968703\pi\) |
0.582599 | + | 0.812760i | \(0.302036\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.6661 | − | 38.8138i | −0.369099 | − | 1.22801i |
(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 | 2100.2.bo.g.1949.9 | 20 | ||
3.2 | odd | 2 | 2100.2.bo.h.1949.3 | 20 | |||
5.2 | odd | 4 | 420.2.bh.b.101.4 | yes | 10 | ||
5.3 | odd | 4 | 2100.2.bi.j.101.2 | 10 | |||
5.4 | even | 2 | inner | 2100.2.bo.g.1949.2 | 20 | ||
7.5 | odd | 6 | 2100.2.bo.h.1349.8 | 20 | |||
15.2 | even | 4 | 420.2.bh.a.101.2 | ✓ | 10 | ||
15.8 | even | 4 | 2100.2.bi.k.101.4 | 10 | |||
15.14 | odd | 2 | 2100.2.bo.h.1949.8 | 20 | |||
21.5 | even | 6 | inner | 2100.2.bo.g.1349.2 | 20 | ||
35.12 | even | 12 | 420.2.bh.a.341.2 | yes | 10 | ||
35.17 | even | 12 | 2940.2.d.b.881.10 | 10 | |||
35.19 | odd | 6 | 2100.2.bo.h.1349.3 | 20 | |||
35.32 | odd | 12 | 2940.2.d.a.881.1 | 10 | |||
35.33 | even | 12 | 2100.2.bi.k.1601.4 | 10 | |||
105.17 | odd | 12 | 2940.2.d.a.881.2 | 10 | |||
105.32 | even | 12 | 2940.2.d.b.881.9 | 10 | |||
105.47 | odd | 12 | 420.2.bh.b.341.4 | yes | 10 | ||
105.68 | odd | 12 | 2100.2.bi.j.1601.2 | 10 | |||
105.89 | even | 6 | inner | 2100.2.bo.g.1349.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.2 | ✓ | 10 | 15.2 | even | 4 | ||
420.2.bh.a.341.2 | yes | 10 | 35.12 | even | 12 | ||
420.2.bh.b.101.4 | yes | 10 | 5.2 | odd | 4 | ||
420.2.bh.b.341.4 | yes | 10 | 105.47 | odd | 12 | ||
2100.2.bi.j.101.2 | 10 | 5.3 | odd | 4 | |||
2100.2.bi.j.1601.2 | 10 | 105.68 | odd | 12 | |||
2100.2.bi.k.101.4 | 10 | 15.8 | even | 4 | |||
2100.2.bi.k.1601.4 | 10 | 35.33 | even | 12 | |||
2100.2.bo.g.1349.2 | 20 | 21.5 | even | 6 | inner | ||
2100.2.bo.g.1349.9 | 20 | 105.89 | even | 6 | inner | ||
2100.2.bo.g.1949.2 | 20 | 5.4 | even | 2 | inner | ||
2100.2.bo.g.1949.9 | 20 | 1.1 | even | 1 | trivial | ||
2100.2.bo.h.1349.3 | 20 | 35.19 | odd | 6 | |||
2100.2.bo.h.1349.8 | 20 | 7.5 | odd | 6 | |||
2100.2.bo.h.1949.3 | 20 | 3.2 | odd | 2 | |||
2100.2.bo.h.1949.8 | 20 | 15.14 | odd | 2 | |||
2940.2.d.a.881.1 | 10 | 35.32 | odd | 12 | |||
2940.2.d.a.881.2 | 10 | 105.17 | odd | 12 | |||
2940.2.d.b.881.9 | 10 | 105.32 | even | 12 | |||
2940.2.d.b.881.10 | 10 | 35.17 | even | 12 |