Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8464,2,Mod(1,8464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8464, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8464.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8464 = 2^{4} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8464.a (trivial) |
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: | yes |
Analytic conductor: | \(67.5853802708\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 30 x^{13} + 28 x^{12} + 354 x^{11} - 302 x^{10} - 2111 x^{9} + 1596 x^{8} + 6777 x^{7} + \cdots - 419 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 184) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.67059\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8464.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.67059 | 0.964516 | 0.482258 | − | 0.876029i | \(-0.339817\pi\) | ||||
0.482258 | + | 0.876029i | \(0.339817\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.30085 | 1.47618 | 0.738092 | − | 0.674700i | \(-0.235727\pi\) | ||||
0.738092 | + | 0.674700i | \(0.235727\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.48378 | 0.560815 | 0.280408 | − | 0.959881i | \(-0.409530\pi\) | ||||
0.280408 | + | 0.959881i | \(0.409530\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.209129 | −0.0697095 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.77429 | 0.836480 | 0.418240 | − | 0.908336i | \(-0.362647\pi\) | ||||
0.418240 | + | 0.908336i | \(0.362647\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41846 | 0.948112 | 0.474056 | − | 0.880495i | \(-0.342789\pi\) | ||||
0.474056 | + | 0.880495i | \(0.342789\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.51436 | 1.42380 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.76631 | −0.913464 | −0.456732 | − | 0.889604i | \(-0.650980\pi\) | ||||
−0.456732 | + | 0.889604i | \(0.650980\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.514351 | −0.118000 | −0.0590001 | − | 0.998258i | \(-0.518791\pi\) | ||||
−0.0590001 | + | 0.998258i | \(0.518791\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.47878 | 0.540915 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.89559 | 1.17912 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.36114 | −1.03175 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.25504 | 1.34723 | 0.673614 | − | 0.739083i | \(-0.264741\pi\) | ||||
0.673614 | + | 0.739083i | \(0.264741\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.65695 | 1.37523 | 0.687614 | − | 0.726076i | \(-0.258658\pi\) | ||||
0.687614 | + | 0.726076i | \(0.258658\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.63470 | 0.806798 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.89772 | 0.827866 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.28450 | 0.539968 | 0.269984 | − | 0.962865i | \(-0.412982\pi\) | ||||
0.269984 | + | 0.962865i | \(0.412982\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.71085 | 0.914468 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.7718 | −1.68227 | −0.841137 | − | 0.540821i | \(-0.818113\pi\) | ||||
−0.841137 | + | 0.540821i | \(0.818113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.13046 | −0.934887 | −0.467443 | − | 0.884023i | \(-0.654825\pi\) | ||||
−0.467443 | + | 0.884023i | \(0.654825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.690301 | −0.102904 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.93322 | 1.30304 | 0.651522 | − | 0.758630i | \(-0.274131\pi\) | ||||
0.651522 | + | 0.758630i | \(0.274131\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.79840 | −0.685486 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.29196 | −0.881050 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.3758 | 1.56259 | 0.781294 | − | 0.624164i | \(-0.214560\pi\) | ||||
0.781294 | + | 0.624164i | \(0.214560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.15751 | 1.23480 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.859270 | −0.113813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.03410 | 0.264817 | 0.132409 | − | 0.991195i | \(-0.457729\pi\) | ||||
0.132409 | + | 0.991195i | \(0.457729\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.6262 | −1.36055 | −0.680273 | − | 0.732959i | \(-0.738139\pi\) | ||||
−0.680273 | + | 0.732959i | \(0.738139\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.310300 | −0.0390942 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.2838 | 1.39959 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.97360 | 0.729791 | 0.364896 | − | 0.931048i | \(-0.381105\pi\) | ||||
0.364896 | + | 0.931048i | \(0.381105\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.0664 | −1.55070 | −0.775349 | − | 0.631533i | \(-0.782426\pi\) | ||||
−0.775349 | + | 0.631533i | \(0.782426\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0288 | 1.17378 | 0.586892 | − | 0.809665i | \(-0.300351\pi\) | ||||
0.586892 | + | 0.809665i | \(0.300351\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.84911 | 1.13728 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.11643 | 0.469111 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.58909 | 0.853840 | 0.426920 | − | 0.904289i | \(-0.359599\pi\) | ||||
0.426920 | + | 0.904289i | \(0.359599\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.32888 | −0.925431 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.04453 | 0.883002 | 0.441501 | − | 0.897261i | \(-0.354446\pi\) | ||||
0.441501 | + | 0.897261i | \(0.354446\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.4320 | −1.34844 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.1202 | 1.29942 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.7531 | −1.66983 | −0.834915 | − | 0.550379i | \(-0.814483\pi\) | ||||
−0.834915 | + | 0.550379i | \(0.814483\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.07224 | 0.531716 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.7916 | 1.32643 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.69779 | −0.174190 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.14396 | −0.725359 | −0.362679 | − | 0.931914i | \(-0.618138\pi\) | ||||
−0.362679 | + | 0.931914i | \(0.618138\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.580184 | −0.0583107 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.54788 | −0.651538 | −0.325769 | − | 0.945449i | \(-0.605623\pi\) | ||||
−0.325769 | + | 0.945449i | \(0.605623\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7901 | 1.26025 | 0.630123 | − | 0.776495i | \(-0.283004\pi\) | ||||
0.630123 | + | 0.776495i | \(0.283004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.18209 | 0.798490 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.69776 | 0.550823 | 0.275411 | − | 0.961326i | \(-0.411186\pi\) | ||||
0.275411 | + | 0.961326i | \(0.411186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.49751 | 0.143435 | 0.0717177 | − | 0.997425i | \(-0.477152\pi\) | ||||
0.0717177 | + | 0.997425i | \(0.477152\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.48705 | 0.520808 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5976 | 0.996936 | 0.498468 | − | 0.866908i | \(-0.333896\pi\) | ||||
0.498468 | + | 0.866908i | \(0.333896\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.714899 | −0.0660924 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.58837 | −0.512285 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.30331 | −0.300300 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.9953 | −1.62258 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.95620 | 0.264410 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3452 | 1.00673 | 0.503363 | − | 0.864075i | \(-0.332096\pi\) | ||||
0.503363 | + | 0.864075i | \(0.332096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.2415 | −0.901713 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.56164 | −0.136441 | −0.0682206 | − | 0.997670i | \(-0.521732\pi\) | ||||
−0.0682206 | + | 0.997670i | \(0.521732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.763183 | −0.0661763 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.6963 | −1.52305 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3690 | 0.885885 | 0.442942 | − | 0.896550i | \(-0.353935\pi\) | ||||
0.442942 | + | 0.896550i | \(0.353935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.2890 | −1.63607 | −0.818034 | − | 0.575169i | \(-0.804936\pi\) | ||||
−0.818034 | + | 0.575169i | \(0.804936\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.9237 | 1.25681 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.48382 | 0.793077 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.9478 | 1.98876 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.01616 | −0.661162 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.2893 | 1.00678 | 0.503391 | − | 0.864059i | \(-0.332086\pi\) | ||||
0.503391 | + | 0.864059i | \(0.332086\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.133912 | −0.0108976 | −0.00544881 | − | 0.999985i | \(-0.501734\pi\) | ||||
−0.00544881 | + | 0.999985i | \(0.501734\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.787643 | 0.0636772 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.2744 | 2.03009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.293633 | 0.0234345 | 0.0117172 | − | 0.999931i | \(-0.496270\pi\) | ||||
0.0117172 | + | 0.999931i | \(0.496270\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.0043 | 1.50714 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.15981 | 0.482474 | 0.241237 | − | 0.970466i | \(-0.422447\pi\) | ||||
0.241237 | + | 0.970466i | \(0.422447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.2984 | 1.19098 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.0160 | 1.16197 | 0.580986 | − | 0.813913i | \(-0.302667\pi\) | ||||
0.580986 | + | 0.813913i | \(0.302667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.31410 | −0.101084 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.107565 | 0.00822574 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.24346 | −0.0945387 | −0.0472694 | − | 0.998882i | \(-0.515052\pi\) | ||||
−0.0472694 | + | 0.998882i | \(0.515052\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.74774 | 0.661267 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.39815 | 0.255421 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.3294 | −1.29526 | −0.647630 | − | 0.761955i | \(-0.724240\pi\) | ||||
−0.647630 | + | 0.761955i | \(0.724240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4880 | −1.52286 | −0.761431 | − | 0.648246i | \(-0.775503\pi\) | ||||
−0.761431 | + | 0.648246i | \(0.775503\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.7520 | −1.31227 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8416 | 0.797092 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.4488 | −0.764095 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.95474 | −0.578622 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.21168 | −0.521819 | −0.260909 | − | 0.965363i | \(-0.584022\pi\) | ||||
−0.260909 | + | 0.965363i | \(0.584022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.65971 | 0.335413 | 0.167707 | − | 0.985837i | \(-0.446364\pi\) | ||||
0.167707 | + | 0.985837i | \(0.446364\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.8507 | 1.34992 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.13481 | −0.0808521 | −0.0404261 | − | 0.999183i | \(-0.512872\pi\) | ||||
−0.0404261 | + | 0.999183i | \(0.512872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.8557 | 1.12398 | 0.561989 | − | 0.827145i | \(-0.310036\pi\) | ||||
0.561989 | + | 0.827145i | \(0.310036\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.97944 | 0.703895 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.7649 | 0.755546 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.5561 | −2.48335 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.42696 | −0.0987049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5298 | −1.34449 | −0.672244 | − | 0.740329i | \(-0.734670\pi\) | ||||
−0.672244 | + | 0.740329i | \(0.734670\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.8286 | −1.49567 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.2357 | −1.38006 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3612 | 0.771249 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.7540 | 1.13213 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.8750 | −0.866066 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.9362 | −1.40199 | −0.700994 | − | 0.713167i | \(-0.747260\pi\) | ||||
−0.700994 | + | 0.713167i | \(0.747260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.23294 | −0.0821957 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.0685 | 1.53111 | 0.765555 | − | 0.643371i | \(-0.222465\pi\) | ||||
0.765555 | + | 0.643371i | \(0.222465\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.93760 | −0.524532 | −0.262266 | − | 0.964996i | \(-0.584470\pi\) | ||||
−0.262266 | + | 0.964996i | \(0.584470\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.87687 | 0.452465 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.7867 | −0.903196 | −0.451598 | − | 0.892221i | \(-0.649146\pi\) | ||||
−0.451598 | + | 0.892221i | \(0.649146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.4872 | 1.92353 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.6783 | 0.823542 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6236 | 0.816553 | 0.408276 | − | 0.912858i | \(-0.366130\pi\) | ||||
0.408276 | + | 0.912858i | \(0.366130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.14683 | 0.589199 | 0.294599 | − | 0.955621i | \(-0.404814\pi\) | ||||
0.294599 | + | 0.955621i | \(0.404814\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.16927 | 0.139159 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.8388 | −1.01190 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.75829 | −0.111877 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.4391 | 0.851670 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.31248 | −0.587799 | −0.293899 | − | 0.955836i | \(-0.594953\pi\) | ||||
−0.293899 | + | 0.955836i | \(0.594953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.7688 | −1.30059 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.0638 | −1.43868 | −0.719339 | − | 0.694659i | \(-0.755555\pi\) | ||||
−0.719339 | + | 0.694659i | \(0.755555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.87347 | 0.302823 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.51724 | −0.0939146 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.7098 | 1.64699 | 0.823497 | − | 0.567320i | \(-0.192020\pi\) | ||||
0.823497 | + | 0.567320i | \(0.192020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.5498 | 2.30667 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −26.3171 | −1.61058 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.85330 | −0.478824 | −0.239412 | − | 0.970918i | \(-0.576955\pi\) | ||||
−0.239412 | + | 0.970918i | \(0.576955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.7118 | 1.07591 | 0.537957 | − | 0.842972i | \(-0.319196\pi\) | ||||
0.537957 | + | 0.842972i | \(0.319196\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.47364 | 0.512848 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.3561 | 0.986309 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.46981 | −0.148396 | −0.0741982 | − | 0.997244i | \(-0.523640\pi\) | ||||
−0.0741982 | + | 0.997244i | \(0.523640\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.60129 | −0.0958666 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.4632 | −0.683837 | −0.341918 | − | 0.939730i | \(-0.611077\pi\) | ||||
−0.341918 | + | 0.939730i | \(0.611077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.9149 | 1.36215 | 0.681074 | − | 0.732215i | \(-0.261513\pi\) | ||||
0.681074 | + | 0.732215i | \(0.261513\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.83632 | −0.168009 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.9830 | −0.943446 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.81492 | −0.165584 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.9346 | −0.699620 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.8559 | −1.80262 | −0.901310 | − | 0.433176i | \(-0.857393\pi\) | ||||
−0.901310 | + | 0.433176i | \(0.857393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.71425 | 0.390919 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.8734 | −0.863040 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.09625 | −0.524299 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.9388 | −0.628419 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −35.0755 | −2.00842 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.14371 | −0.464786 | −0.232393 | − | 0.972622i | \(-0.574656\pi\) | ||||
−0.232393 | + | 0.972622i | \(0.574656\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.3670 | 1.21553 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.4868 | 0.821471 | 0.410736 | − | 0.911754i | \(-0.365272\pi\) | ||||
0.410736 | + | 0.911754i | \(0.365272\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.71085 | −0.153226 | −0.0766132 | − | 0.997061i | \(-0.524411\pi\) | ||||
−0.0766132 | + | 0.997061i | \(0.524411\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.02425 | −0.0577102 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.2198 | −0.798663 | −0.399331 | − | 0.916807i | \(-0.630758\pi\) | ||||
−0.399331 | + | 0.916807i | \(0.630758\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.1276 | 1.12693 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.51862 | 0.531277 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.93720 | 0.107789 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.1539 | 1.11793 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.50172 | 0.138346 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.2549 | 0.730767 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.6231 | −1.62823 | −0.814116 | − | 0.580702i | \(-0.802778\pi\) | ||||
−0.814116 | + | 0.580702i | \(0.802778\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.686883 | −0.0376409 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.7179 | 1.07731 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.9791 | −1.19728 | −0.598638 | − | 0.801019i | \(-0.704291\pi\) | ||||
−0.598638 | + | 0.801019i | \(0.704291\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.7042 | 0.961560 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.2426 | 1.15035 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.5062 | −0.945247 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.71737 | 0.467973 | 0.233986 | − | 0.972240i | \(-0.424823\pi\) | ||||
0.233986 | + | 0.972240i | \(0.424823\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.36899 | 0.126809 | 0.0634047 | − | 0.997988i | \(-0.479804\pi\) | ||||
0.0634047 | + | 0.997988i | \(0.479804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.3269 | −0.978216 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.94446 | 0.369616 | 0.184808 | − | 0.982775i | \(-0.440834\pi\) | ||||
0.184808 | + | 0.982775i | \(0.440834\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.1302 | −2.28911 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.33587 | −0.494107 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.8278 | −0.677028 | −0.338514 | − | 0.940961i | \(-0.609924\pi\) | ||||
−0.338514 | + | 0.940961i | \(0.609924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7354 | −0.986076 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.51847 | −0.289645 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.1036 | 1.73272 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5274 | 0.862724 | 0.431362 | − | 0.902179i | \(-0.358033\pi\) | ||||
0.431362 | + | 0.902179i | \(0.358033\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.25269 | 0.117271 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.8792 | 0.876323 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2405 | 0.530231 | 0.265115 | − | 0.964217i | \(-0.414590\pi\) | ||||
0.265115 | + | 0.964217i | \(0.414590\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.93859 | 0.255028 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.8011 | 1.27732 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.8829 | 1.22678 | 0.613390 | − | 0.789780i | \(-0.289805\pi\) | ||||
0.613390 | + | 0.789780i | \(0.289805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.9532 | 0.971003 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.9381 | 0.712204 | 0.356102 | − | 0.934447i | \(-0.384106\pi\) | ||||
0.356102 | + | 0.934447i | \(0.384106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.5877 | 0.692494 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.28206 | 0.0651705 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.7222 | 0.543640 | 0.271820 | − | 0.962348i | \(-0.412375\pi\) | ||||
0.271820 | + | 0.962348i | \(0.412375\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.60886 | −0.131600 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.0504 | 1.26042 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.8056 | 0.642695 | 0.321348 | − | 0.946961i | \(-0.395864\pi\) | ||||
0.321348 | + | 0.946961i | \(0.395864\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.27497 | −0.0638281 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.0322 | 1.34992 | 0.674961 | − | 0.737853i | \(-0.264160\pi\) | ||||
0.674961 | + | 0.737853i | \(0.264160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.1750 | 1.30387 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.4924 | −1.36611 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.11216 | 0.451673 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.55832 | 0.373735 | 0.186867 | − | 0.982385i | \(-0.440167\pi\) | ||||
0.186867 | + | 0.982385i | \(0.440167\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.3224 | 0.854450 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.01815 | 0.148514 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.5538 | 1.30347 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −32.2240 | −1.57801 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.18896 | 0.0580844 | 0.0290422 | − | 0.999578i | \(-0.490754\pi\) | ||||
0.0290422 | + | 0.999578i | \(0.490754\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.5074 | −1.43810 | −0.719051 | − | 0.694957i | \(-0.755423\pi\) | ||||
−0.719051 | + | 0.694957i | \(0.755423\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.86819 | −0.0908346 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.2046 | −1.07708 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.7669 | −0.763015 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.8436 | 0.764935 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.7495 | 0.806795 | 0.403398 | − | 0.915025i | \(-0.367829\pi\) | ||||
0.403398 | + | 0.915025i | \(0.367829\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.1801 | −1.45036 | −0.725182 | − | 0.688557i | \(-0.758244\pi\) | ||||
−0.725182 | + | 0.688557i | \(0.758244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 40.0069 | 1.91819 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.0215 | −0.907848 | −0.453924 | − | 0.891040i | \(-0.649976\pi\) | ||||
−0.453924 | + | 0.891040i | \(0.649976\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00348 | 0.0477849 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.1089 | −1.62056 | −0.810281 | − | 0.586041i | \(-0.800686\pi\) | ||||
−0.810281 | + | 0.586041i | \(0.800686\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −51.9987 | −2.46498 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.5305 | 0.971057 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.75986 | 0.366211 | 0.183105 | − | 0.983093i | \(-0.441385\pi\) | ||||
0.183105 | + | 0.983093i | \(0.441385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.8842 | −1.40719 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.223712 | −0.0105109 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.7427 | 0.784910 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.26466 | −0.105937 | −0.0529683 | − | 0.998596i | \(-0.516868\pi\) | ||||
−0.0529683 | + | 0.998596i | \(0.516868\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.1917 | 0.942468 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.3135 | 0.992668 | 0.496334 | − | 0.868132i | \(-0.334679\pi\) | ||||
0.496334 | + | 0.868132i | \(0.334679\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.493172 | 0.0229196 | 0.0114598 | − | 0.999934i | \(-0.496352\pi\) | ||||
0.0114598 | + | 0.999934i | \(0.496352\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 42.2232 | 1.95805 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.0616 | 0.928338 | 0.464169 | − | 0.885747i | \(-0.346353\pi\) | ||||
0.464169 | + | 0.885747i | \(0.346353\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.86350 | 0.409278 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.490540 | 0.0226029 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.0077 | −0.782015 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.03240 | −0.139136 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.37901 | −0.108927 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.71347 | −0.169673 | −0.0848363 | − | 0.996395i | \(-0.527037\pi\) | ||||
−0.0848363 | + | 0.996395i | \(0.527037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.2279 | 0.511950 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.5811 | −1.07076 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5390 | −0.840081 | −0.420041 | − | 0.907505i | \(-0.637984\pi\) | ||||
−0.420041 | + | 0.907505i | \(0.637984\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.2905 | 0.465354 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0340 | −1.62619 | −0.813096 | − | 0.582129i | \(-0.802220\pi\) | ||||
−0.813096 | + | 0.582129i | \(0.802220\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.3247 | −1.23064 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.91510 | −0.0860772 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.3877 | −0.869655 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7071 | −0.837446 | −0.418723 | − | 0.908114i | \(-0.637522\pi\) | ||||
−0.418723 | + | 0.908114i | \(0.637522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.0856 | 1.12074 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.9153 | −1.51221 | −0.756104 | − | 0.654452i | \(-0.772899\pi\) | ||||
−0.756104 | + | 0.654452i | \(0.772899\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.6135 | −0.961790 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.19532 | −0.0974975 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.0661 | −1.33266 | −0.666329 | − | 0.745658i | \(-0.732135\pi\) | ||||
−0.666329 | + | 0.745658i | \(0.732135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.8805 | 0.658276 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.75751 | 0.121747 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.2182 | 1.86036 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.7833 | 1.08997 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.07732 | −0.0911841 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.3843 | −0.498755 | −0.249378 | − | 0.968406i | \(-0.580226\pi\) | ||||
−0.249378 | + | 0.968406i | \(0.580226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.34956 | 0.408828 | 0.204414 | − | 0.978885i | \(-0.434471\pi\) | ||||
0.204414 | + | 0.978885i | \(0.434471\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.6139 | 0.637803 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.8384 | −1.25622 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.425389 | −0.0184603 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.8231 | −1.59498 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.8074 | 0.813116 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.9503 | −1.24930 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.3122 | −0.573396 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.01082 | 0.0434587 | 0.0217294 | − | 0.999764i | \(-0.493083\pi\) | ||||
0.0217294 | + | 0.999764i | \(0.493083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34.2271 | −1.46882 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.94305 | 0.211737 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9526 | 0.468300 | 0.234150 | − | 0.972201i | \(-0.424769\pi\) | ||||
0.234150 | + | 0.972201i | \(0.424769\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.22224 | 0.0948431 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.73164 | −0.158973 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.2605 | 0.478846 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.1119 | 0.768808 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.93193 | −0.124230 | −0.0621149 | − | 0.998069i | \(-0.519785\pi\) | ||||
−0.0621149 | + | 0.998069i | \(0.519785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.9568 | −0.886377 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.4557 | −0.736981 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.1366 | −0.722223 | −0.361112 | − | 0.932523i | \(-0.617603\pi\) | ||||
−0.361112 | + | 0.932523i | \(0.617603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.9810 | 1.47166 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.3582 | −0.518996 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.3739 | 1.60872 | 0.804360 | − | 0.594143i | \(-0.202509\pi\) | ||||
0.804360 | + | 0.594143i | \(0.202509\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.9152 | 0.707879 | 0.353939 | − | 0.935268i | \(-0.384842\pi\) | ||||
0.353939 | + | 0.935268i | \(0.384842\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0478 | −0.503303 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.2677 | 0.718866 | 0.359433 | − | 0.933171i | \(-0.382970\pi\) | ||||
0.359433 | + | 0.933171i | \(0.382970\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.78446 | 0.323511 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.9363 | 0.495201 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.5598 | 1.30707 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.35977 | −0.0975645 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.0512 | −1.32289 | −0.661447 | − | 0.749992i | \(-0.730057\pi\) | ||||
−0.661447 | + | 0.749992i | \(0.730057\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.93836 | −0.162277 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.89581 | −0.0779831 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.05933 | −0.125632 | −0.0628158 | − | 0.998025i | \(-0.520008\pi\) | ||||
−0.0628158 | + | 0.998025i | \(0.520008\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.4463 | −0.756226 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.4883 | 1.08409 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.8858 | 0.853370 | 0.426685 | − | 0.904400i | \(-0.359681\pi\) | ||||
0.426685 | + | 0.904400i | \(0.359681\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.6184 | 1.33053 | 0.665267 | − | 0.746606i | \(-0.268318\pi\) | ||||
0.665267 | + | 0.746606i | \(0.268318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.24925 | −0.0508734 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.9037 | −0.443299 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.7411 | 1.57245 | 0.786227 | − | 0.617938i | \(-0.212032\pi\) | ||||
0.786227 | + | 0.617938i | \(0.212032\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.9837 | 0.728736 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.5379 | 1.23543 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.5002 | −0.706825 | −0.353412 | − | 0.935468i | \(-0.614979\pi\) | ||||
−0.353412 | + | 0.935468i | \(0.614979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −59.3997 | −2.39523 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5760 | −0.546547 | −0.273274 | − | 0.961936i | \(-0.588106\pi\) | ||||
−0.273274 | + | 0.961936i | \(0.588106\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.9992 | −1.64790 | −0.823948 | − | 0.566666i | \(-0.808233\pi\) | ||||
−0.823948 | + | 0.566666i | \(0.808233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.3742 | −0.936467 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.7200 | −0.788800 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.38386 | −0.0952024 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.3704 | −0.493242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.73600 | 0.228346 | 0.114173 | − | 0.993461i | \(-0.463578\pi\) | ||||
0.114173 | + | 0.993461i | \(0.463578\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.6263 | −1.29678 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.4488 | 1.48611 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.4032 | −0.649917 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.73256 | 0.108098 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.3019 | −0.722880 | −0.361440 | − | 0.932395i | \(-0.617715\pi\) | ||||
−0.361440 | + | 0.932395i | \(0.617715\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.0965 | −0.555913 | −0.277957 | − | 0.960594i | \(-0.589657\pi\) | ||||
−0.277957 | + | 0.960594i | \(0.589657\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.8056 | −1.33109 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.2770 | −1.22963 | −0.614813 | − | 0.788673i | \(-0.710768\pi\) | ||||
−0.614813 | + | 0.788673i | \(0.710768\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.64319 | 0.221515 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.9799 | 0.743882 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.0904533 | −0.00353971 | −0.00176986 | − | 0.999998i | \(-0.500563\pi\) | ||||
−0.00176986 | + | 0.999998i | \(0.500563\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.15473 | −0.201412 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.09731 | −0.0818240 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.6709 | −1.07790 | −0.538952 | − | 0.842336i | \(-0.681180\pi\) | ||||
−0.538952 | + | 0.842336i | \(0.681180\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.7434 | 0.456764 | 0.228382 | − | 0.973572i | \(-0.426656\pi\) | ||||
0.228382 | + | 0.973572i | \(0.426656\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.5088 | −0.835334 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.51915 | −0.0976884 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.9757 | −1.35224 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.4802 | −1.13807 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.5751 | 1.10149 | 0.550745 | − | 0.834673i | \(-0.314343\pi\) | ||||
0.550745 | + | 0.834673i | \(0.314343\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −31.6071 | −1.21656 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.6106 | −1.09959 | −0.549797 | − | 0.835299i | \(-0.685295\pi\) | ||||
−0.549797 | + | 0.835299i | \(0.685295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.6000 | −0.406792 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.5380 | 1.47678 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.1726 | −0.427509 | −0.213754 | − | 0.976887i | \(-0.568569\pi\) | ||||
−0.213754 | + | 0.976887i | \(0.568569\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.2265 | 1.30773 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.2605 | −0.505919 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.8878 | 1.48151 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.1688 | 0.995509 | 0.497755 | − | 0.867318i | \(-0.334158\pi\) | ||||
0.497755 | + | 0.867318i | \(0.334158\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.860864 | −0.0327015 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −63.6699 | −2.41514 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.5700 | 1.53670 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.0319 | −0.871147 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.417323 | 0.0157621 | 0.00788103 | − | 0.999969i | \(-0.497491\pi\) | ||||
0.00788103 | + | 0.999969i | \(0.497491\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.68939 | −0.0637164 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 49.2610 | 1.85528 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.71560 | −0.365393 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.56216 | 0.0962238 | 0.0481119 | − | 0.998842i | \(-0.484680\pi\) | ||||
0.0481119 | + | 0.998842i | \(0.484680\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.58710 | −0.0595208 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.3046 | 1.17073 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.0889 | 0.787578 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.9255 | −1.11603 | −0.558017 | − | 0.829829i | \(-0.688438\pi\) | ||||
−0.558017 | + | 0.829829i | \(0.688438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9777 | 0.706766 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.2806 | 0.568292 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 42.7727 | 1.58854 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.6701 | 0.469908 | 0.234954 | − | 0.972006i | \(-0.424506\pi\) | ||||
0.234954 | + | 0.972006i | \(0.424506\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.6106 | 1.05965 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.0892 | 0.853986 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.50625 | −0.203378 | −0.101689 | − | 0.994816i | \(-0.532425\pi\) | ||||
−0.101689 | + | 0.994816i | \(0.532425\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.4601 | −0.975997 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.5725 | 0.610456 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.7590 | −1.20506 | −0.602529 | − | 0.798097i | \(-0.705840\pi\) | ||||
−0.602529 | + | 0.798097i | \(0.705840\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.93738 | −0.107907 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.7451 | 0.981182 | 0.490591 | − | 0.871390i | \(-0.336781\pi\) | ||||
0.490591 | + | 0.871390i | \(0.336781\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.5652 | 1.48620 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.68234 | −0.0615537 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.45421 | 0.308910 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.0124 | −1.24113 | −0.620566 | − | 0.784154i | \(-0.713097\pi\) | ||||
−0.620566 | + | 0.784154i | \(0.713097\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.5573 | −0.566941 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.442023 | −0.0160869 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.6288 | 1.62206 | 0.811031 | − | 0.585003i | \(-0.198907\pi\) | ||||
0.811031 | + | 0.585003i | \(0.198907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.8091 | 0.645581 | 0.322791 | − | 0.946470i | \(-0.395379\pi\) | ||||
0.322791 | + | 0.946470i | \(0.395379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.22197 | 0.0804407 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.59989 | 0.0939992 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.95350 | 0.251076 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.9856 | −1.15343 | −0.576715 | − | 0.816946i | \(-0.695666\pi\) | ||||
−0.576715 | + | 0.816946i | \(0.695666\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.5301 | −1.38763 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.2306 | −0.727644 | −0.363822 | − | 0.931468i | \(-0.618528\pi\) | ||||
−0.363822 | + | 0.931468i | \(0.618528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.1422 | 1.62156 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.14157 | 0.292077 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.54049 | 0.198509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.2500 | −1.29713 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.8953 | −1.39000 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.969237 | 0.0345936 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.2923 | 0.972865 | 0.486432 | − | 0.873718i | \(-0.338298\pi\) | ||||
0.486432 | + | 0.873718i | \(0.338298\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 44.6211 | 1.58855 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.7244 | 0.559097 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.3253 | −1.28995 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 62.7303 | 2.22481 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.1405 | 1.81149 | 0.905744 | − | 0.423825i | \(-0.139313\pi\) | ||||
0.905744 | + | 0.423825i | \(0.139313\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.6452 | −1.19028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.29443 | 0.116403 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.8229 | 0.981848 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.1197 | −0.461834 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.690659 | 0.0242823 | 0.0121411 | − | 0.999926i | \(-0.496135\pi\) | ||||
0.0121411 | + | 0.999926i | \(0.496135\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.3309 | 1.13529 | 0.567645 | − | 0.823273i | \(-0.307855\pi\) | ||||
0.567645 | + | 0.823273i | \(0.307855\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.5891 | 1.03774 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.3326 | 0.712220 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.15321 | 0.110317 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.06075 | −0.0370656 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.09808 | 0.212824 | 0.106412 | − | 0.994322i | \(-0.466064\pi\) | ||||
0.106412 | + | 0.994322i | \(0.466064\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.6548 | −0.963986 | −0.481993 | − | 0.876175i | \(-0.660087\pi\) | ||||
−0.481993 | + | 0.876175i | \(0.660087\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 27.3243 | 0.951310 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.5955 | 0.611857 | 0.305929 | − | 0.952054i | \(-0.401033\pi\) | ||||
0.305929 | + | 0.952054i | \(0.401033\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.7911 | 0.930494 | 0.465247 | − | 0.885181i | \(-0.345965\pi\) | ||||
0.465247 | + | 0.885181i | \(0.345965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.12604 | −0.143131 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0723 | 0.626167 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.5655 | 1.71528 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −41.0500 | −1.41889 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.62747 | −0.194282 | −0.0971410 | − | 0.995271i | \(-0.530970\pi\) | ||||
−0.0971410 | + | 0.995271i | \(0.530970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.6356 | 0.815022 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.1503 | −0.659571 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.33763 | −0.149219 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.90137 | −0.168413 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 38.2814 | 1.31381 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.9685 | 0.444032 | 0.222016 | − | 0.975043i | \(-0.428736\pi\) | ||||
0.222016 | + | 0.975043i | \(0.428736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.355057 | 0.0121427 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.6700 | 0.398641 | 0.199321 | − | 0.979934i | \(-0.436127\pi\) | ||||
0.199321 | + | 0.979934i | \(0.436127\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.2591 | 1.40774 | 0.703871 | − | 0.710328i | \(-0.251453\pi\) | ||||
0.703871 | + | 0.710328i | \(0.251453\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26.7010 | −0.909968 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.67249 | −0.193094 | −0.0965468 | − | 0.995328i | \(-0.530780\pi\) | ||||
−0.0965468 | + | 0.995328i | \(0.530780\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.10448 | −0.139557 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.70258 | −0.159708 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0544 | 0.714220 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.4205 | 0.691924 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.49401 | 0.0505644 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.38634 | 0.148285 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.4440 | 0.724112 | 0.362056 | − | 0.932156i | \(-0.382075\pi\) | ||||
0.362056 | + | 0.932156i | \(0.382075\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −51.5475 | −1.73865 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.86932 | 0.298815 | 0.149407 | − | 0.988776i | \(-0.452263\pi\) | ||||
0.149407 | + | 0.988776i | \(0.452263\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.1229 | −1.58581 | −0.792905 | − | 0.609345i | \(-0.791432\pi\) | ||||
−0.792905 | + | 0.609345i | \(0.791432\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.2168 | 0.377048 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.75358 | −0.226763 | −0.113382 | − | 0.993552i | \(-0.536168\pi\) | ||||
−0.113382 | + | 0.993552i | \(0.536168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.8338 | 0.564587 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.1067 | −0.774105 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.59481 | −0.153759 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −57.2017 | −1.91204 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55.5515 | 1.85275 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.8448 | −1.42737 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.1961 | −0.505695 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −67.6278 | −2.24802 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0399 | 0.565800 | 0.282900 | − | 0.959149i | \(-0.408704\pi\) | ||||
0.282900 | + | 0.959149i | \(0.408704\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.36935 | 0.0454184 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.1556 | −0.402734 | −0.201367 | − | 0.979516i | \(-0.564538\pi\) | ||||
−0.201367 | + | 0.979516i | \(0.564538\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.3179 | 0.738614 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −58.5968 | −1.93715 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.31713 | −0.0765183 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.52112 | 0.0501772 | 0.0250886 | − | 0.999685i | \(-0.492013\pi\) | ||||
0.0250886 | + | 0.999685i | \(0.492013\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.6048 | −0.448293 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −44.6671 | −1.47023 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.3641 | 0.636686 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.67478 | −0.0878512 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.04569 | −0.132735 | −0.0663673 | − | 0.997795i | \(-0.521141\pi\) | ||||
−0.0663673 | + | 0.997795i | \(0.521141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.46806 | 0.0808875 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.2015 | 0.792322 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −34.4900 | −1.12794 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.7638 | 1.20102 | 0.600511 | − | 0.799616i | \(-0.294964\pi\) | ||||
0.600511 | + | 0.799616i | \(0.294964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.52872 | −0.147789 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0727 | 0.328360 | 0.164180 | − | 0.986430i | \(-0.447502\pi\) | ||||
0.164180 | + | 0.986430i | \(0.447502\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −26.2574 | −0.854152 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.3978 | 0.597849 | 0.298925 | − | 0.954277i | \(-0.403372\pi\) | ||||
0.298925 | + | 0.954277i | \(0.403372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.2832 | 1.11288 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.7554 | −0.770323 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.3556 | −1.04810 | −0.524050 | − | 0.851687i | \(-0.675580\pi\) | ||||
−0.524050 | + | 0.851687i | \(0.675580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.8047 | −0.770300 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.6250 | 1.08694 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.3853 | 0.496818 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.6289 | 0.891254 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.19156 | −0.0383976 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.3810 | 0.495131 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.5187 | 1.68889 | 0.844443 | − | 0.535645i | \(-0.179932\pi\) | ||||
0.844443 | + | 0.535645i | \(0.179932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.23627 | 0.103964 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.2023 | 0.712505 | 0.356252 | − | 0.934390i | \(-0.384054\pi\) | ||||
0.356252 | + | 0.934390i | \(0.384054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.6205 | −0.917532 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 33.6688 | 1.07827 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.58787 | 0.274750 | 0.137375 | − | 0.990519i | \(-0.456133\pi\) | ||||
0.137375 | + | 0.990519i | \(0.456133\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.7038 | −1.39678 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.313172 | −0.00999881 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0356 | 0.575246 | 0.287623 | − | 0.957744i | \(-0.407135\pi\) | ||||
0.287623 | + | 0.957744i | \(0.407135\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.74585 | −0.119353 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.1435 | 0.704836 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.2791 | 1.02538 | 0.512689 | − | 0.858574i | \(-0.328649\pi\) | ||||
0.512689 | + | 0.858574i | \(0.328649\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −49.4880 | −1.57046 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.3371 | 1.65920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.1217 | 1.27067 | 0.635333 | − | 0.772238i | \(-0.280863\pi\) | ||||
0.635333 | + | 0.772238i | \(0.280863\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.6087 | −0.557113 |
(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 | 8464.2.a.ch.1.11 | 15 | ||
4.3 | odd | 2 | 4232.2.a.ba.1.5 | 15 | |||
23.7 | odd | 22 | 368.2.m.e.49.3 | 30 | |||
23.10 | odd | 22 | 368.2.m.e.353.3 | 30 | |||
23.22 | odd | 2 | 8464.2.a.cg.1.11 | 15 | |||
92.7 | even | 22 | 184.2.i.b.49.1 | ✓ | 30 | ||
92.79 | even | 22 | 184.2.i.b.169.1 | yes | 30 | ||
92.91 | even | 2 | 4232.2.a.bb.1.5 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
184.2.i.b.49.1 | ✓ | 30 | 92.7 | even | 22 | ||
184.2.i.b.169.1 | yes | 30 | 92.79 | even | 22 | ||
368.2.m.e.49.3 | 30 | 23.7 | odd | 22 | |||
368.2.m.e.353.3 | 30 | 23.10 | odd | 22 | |||
4232.2.a.ba.1.5 | 15 | 4.3 | odd | 2 | |||
4232.2.a.bb.1.5 | 15 | 92.91 | even | 2 | |||
8464.2.a.cg.1.11 | 15 | 23.22 | odd | 2 | |||
8464.2.a.ch.1.11 | 15 | 1.1 | even | 1 | trivial |