Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(177,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(-1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.529 |
Dual form | 1232.2.q.g.177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.32288 | + | 2.29129i | −0.763763 | + | 1.32288i | 0.177136 | + | 0.984186i | \(0.443317\pi\) |
−0.940898 | + | 0.338689i | \(0.890016\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.82288 | − | 3.15731i | −0.815215 | − | 1.41199i | −0.909174 | − | 0.416417i | \(-0.863286\pi\) |
0.0939588 | − | 0.995576i | \(-0.470048\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.32288 | − | 2.29129i | −0.500000 | − | 0.866025i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | − | 3.46410i | −0.666667 | − | 1.15470i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.64575 | 2.49052 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | + | 5.19615i | −0.727607 | + | 1.26025i | 0.230285 | + | 0.973123i | \(0.426034\pi\) |
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.177124 | − | 0.306788i | −0.0406351 | − | 0.0703821i | 0.844993 | − | 0.534778i | \(-0.179605\pi\) |
−0.885628 | + | 0.464396i | \(0.846271\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.00000 | 1.52753 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.82288 | − | 3.15731i | −0.380096 | − | 0.658345i | 0.610980 | − | 0.791646i | \(-0.290776\pi\) |
−0.991076 | + | 0.133301i | \(0.957442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.14575 | + | 7.18065i | −0.829150 | + | 1.43613i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.64575 | 0.509175 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.29150 | −0.796912 | −0.398456 | − | 0.917187i | \(-0.630454\pi\) | ||||
−0.398456 | + | 0.917187i | \(0.630454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.32288 | + | 2.29129i | 0.230283 | + | 0.398862i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.82288 | + | 8.35347i | −0.815215 | + | 1.41199i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.822876 | + | 1.42526i | 0.135280 | + | 0.234312i | 0.925704 | − | 0.378248i | \(-0.123473\pi\) |
−0.790424 | + | 0.612560i | \(0.790140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.61438 | + | 11.4564i | −1.05915 | + | 1.83450i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.93725 | −0.771070 | −0.385535 | − | 0.922693i | \(-0.625983\pi\) | ||||
−0.385535 | + | 0.922693i | \(0.625983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.29150 | + | 12.6293i | −1.08695 | + | 1.88266i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.64575 | + | 11.5108i | 0.969382 | + | 1.67902i | 0.697349 | + | 0.716732i | \(0.254363\pi\) |
0.272034 | + | 0.962288i | \(0.412304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.93725 | − | 13.7477i | −1.11144 | − | 1.92507i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.82288 | − | 3.15731i | 0.250391 | − | 0.433690i | −0.713242 | − | 0.700918i | \(-0.752774\pi\) |
0.963634 | + | 0.267227i | \(0.0861074\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.64575 | −0.491593 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.937254 | 0.124142 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.322876 | + | 0.559237i | −0.0420348 | + | 0.0728065i | −0.886277 | − | 0.463155i | \(-0.846717\pi\) |
0.844243 | + | 0.535961i | \(0.180051\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.85425 | − | 3.21165i | −0.237412 | − | 0.411210i | 0.722559 | − | 0.691310i | \(-0.242966\pi\) |
−0.959971 | + | 0.280099i | \(0.909633\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.29150 | + | 9.16515i | −0.666667 | + | 1.15470i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.11438 | − | 15.7866i | −1.13050 | − | 1.95808i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.96863 | − | 3.40976i | 0.240506 | − | 0.416569i | −0.720352 | − | 0.693608i | \(-0.756020\pi\) |
0.960859 | + | 0.277039i | \(0.0893533\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.64575 | 1.16121 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.64575 | −1.14474 | −0.572370 | − | 0.819995i | \(-0.693976\pi\) | ||||
−0.572370 | + | 0.819995i | \(0.693976\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.82288 | + | 4.88936i | −0.330393 | + | 0.572257i | −0.982589 | − | 0.185793i | \(-0.940514\pi\) |
0.652196 | + | 0.758050i | \(0.273848\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.9686 | − | 18.9982i | −1.26655 | − | 2.19373i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.64575 | −0.301511 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.32288 | + | 2.29129i | 0.148835 | + | 0.257790i | 0.930797 | − | 0.365536i | \(-0.119114\pi\) |
−0.781962 | + | 0.623326i | \(0.785781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.50000 | − | 4.33013i | 0.277778 | − | 0.481125i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.2915 | −1.45893 | −0.729466 | − | 0.684017i | \(-0.760231\pi\) | ||||
−0.729466 | + | 0.684017i | \(0.760231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.8745 | 2.37262 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.67712 | − | 9.83307i | 0.608652 | − | 1.05422i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.29150 | + | 12.6293i | 0.772898 | + | 1.33870i | 0.935968 | + | 0.352084i | \(0.114527\pi\) |
−0.163071 | + | 0.986614i | \(0.552140\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.61438 | − | 11.4564i | −0.693375 | − | 1.20096i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.29150 | − | 9.16515i | −0.548703 | − | 0.950382i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.645751 | + | 1.11847i | −0.0662527 | + | 0.114753i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.70850 | −0.579610 | −0.289805 | − | 0.957086i | \(-0.593590\pi\) | ||||
−0.289805 | + | 0.957086i | \(0.593590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.46863 | + | 11.2040i | 0.637373 | + | 1.10396i | 0.986007 | + | 0.166703i | \(0.0533122\pi\) |
−0.348634 | + | 0.937259i | \(0.613354\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.7601 | − | 22.1012i | −1.24526 | − | 2.15686i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.46863 | + | 4.27579i | 0.238651 | + | 0.413356i | 0.960327 | − | 0.278875i | \(-0.0899614\pi\) |
−0.721676 | + | 0.692231i | \(0.756628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.29150 | + | 9.16515i | −0.506834 | + | 0.877862i | 0.493135 | + | 0.869953i | \(0.335851\pi\) |
−0.999969 | + | 0.00790932i | \(0.997482\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.35425 | −0.413287 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.70850 | −0.725154 | −0.362577 | − | 0.931954i | \(-0.618103\pi\) | ||||
−0.362577 | + | 0.931954i | \(0.618103\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.64575 | + | 11.5108i | −0.619720 | + | 1.07339i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.0000 | − | 17.3205i | −0.924500 | − | 1.60128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.8745 | 1.45521 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.53137 | − | 11.3127i | 0.588914 | − | 1.02003i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0627461 | −0.00556781 | −0.00278391 | − | 0.999996i | \(-0.500886\pi\) | ||||
−0.00278391 | + | 0.999996i | \(0.500886\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.29150 | + | 9.16515i | −0.465891 | + | 0.806947i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.82288 | + | 13.5496i | 0.683488 | + | 1.18384i | 0.973909 | + | 0.226937i | \(0.0728711\pi\) |
−0.290422 | + | 0.956899i | \(0.593796\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.468627 | + | 0.811686i | −0.0406351 | + | 0.0703821i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.82288 | − | 8.35347i | −0.415087 | − | 0.718952i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.43725 | + | 16.3458i | −0.806279 | + | 1.39652i | 0.109145 | + | 0.994026i | \(0.465189\pi\) |
−0.915424 | + | 0.402490i | \(0.868145\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −35.1660 | −2.96151 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.50000 | − | 4.33013i | 0.209061 | − | 0.362103i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.82288 | + | 13.5496i | 0.649654 | + | 1.12523i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.26013 | − | 16.0390i | −0.763763 | − | 1.32288i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.35425 | + | 4.07768i | 0.192868 | + | 0.334056i | 0.946199 | − | 0.323584i | \(-0.104888\pi\) |
−0.753332 | + | 0.657641i | \(0.771555\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.67712 | + | 2.90486i | −0.136482 | + | 0.236395i | −0.926163 | − | 0.377124i | \(-0.876913\pi\) |
0.789680 | + | 0.613519i | \(0.210246\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 24.0000 | 1.94029 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.5830 | 1.17134 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5830 | − | 18.3303i | 0.844616 | − | 1.46292i | −0.0413387 | − | 0.999145i | \(-0.513162\pi\) |
0.885954 | − | 0.463772i | \(-0.153504\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.82288 | + | 8.35347i | 0.382479 | + | 0.662473i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.82288 | + | 8.35347i | −0.380096 | + | 0.658345i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.32288 | − | 4.02334i | −0.181942 | − | 0.315132i | 0.760600 | − | 0.649221i | \(-0.224905\pi\) |
−0.942542 | + | 0.334089i | \(0.891572\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.82288 | − | 8.35347i | 0.375460 | − | 0.650316i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.2288 | −1.17844 | −0.589218 | − | 0.807974i | \(-0.700564\pi\) | ||||
−0.589218 | + | 0.807974i | \(0.700564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.708497 | + | 1.22715i | −0.0541801 | + | 0.0938428i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.14575 | − | 8.91270i | −0.391224 | − | 0.677620i | 0.601387 | − | 0.798958i | \(-0.294615\pi\) |
−0.992611 | + | 0.121338i | \(0.961282\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.9373 | 1.65830 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.854249 | − | 1.47960i | −0.0642093 | − | 0.111214i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.03137 | + | 3.51844i | −0.151832 | + | 0.262981i | −0.931901 | − | 0.362713i | \(-0.881851\pi\) |
0.780069 | + | 0.625693i | \(0.215184\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.81176 | 0.725306 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.50000 | − | 6.06218i | −0.254588 | − | 0.440959i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.64575 | − | 11.5108i | −0.480870 | − | 0.832891i | 0.518889 | − | 0.854841i | \(-0.326346\pi\) |
−0.999759 | + | 0.0219507i | \(0.993012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.76013 | − | 9.97684i | 0.414623 | − | 0.718148i | −0.580766 | − | 0.814071i | \(-0.697247\pi\) |
0.995389 | + | 0.0959224i | \(0.0305801\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 48.2288 | 3.45373 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.8745 | 1.34475 | 0.672377 | − | 0.740209i | \(-0.265274\pi\) | ||||
0.672377 | + | 0.740209i | \(0.265274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.1144 | + | 19.2507i | −0.787877 | + | 1.36464i | 0.139388 | + | 0.990238i | \(0.455487\pi\) |
−0.927265 | + | 0.374406i | \(0.877847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.20850 | + | 9.02138i | 0.367379 | + | 0.636319i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.67712 | + | 9.83307i | 0.398456 | + | 0.690146i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 15.5885i | 0.628587 | + | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.29150 | + | 12.6293i | −0.506794 | + | 0.877794i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.354249 | −0.0245039 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9373 | 1.02832 | 0.514161 | − | 0.857693i | \(-0.328103\pi\) | ||||
0.514161 | + | 0.857693i | \(0.328103\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.7601 | − | 22.1012i | 0.874310 | − | 1.51435i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.29150 | − | 12.6293i | −0.497276 | − | 0.861308i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.5830 | 0.718421 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.46863 | − | 12.9360i | −0.504683 | − | 0.874137i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0000 | + | 25.9808i | −1.00901 | + | 1.74766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3542 | 0.827302 | 0.413651 | − | 0.910436i | \(-0.364253\pi\) | ||||
0.413651 | + | 0.910436i | \(0.364253\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 33.1660 | 2.21107 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.64575 | + | 11.5108i | −0.441094 | + | 0.763997i | −0.997771 | − | 0.0667318i | \(-0.978743\pi\) |
0.556677 | + | 0.830729i | \(0.312076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | + | 13.8564i | 0.528655 | + | 0.915657i | 0.999442 | + | 0.0334101i | \(0.0106368\pi\) |
−0.470787 | + | 0.882247i | \(0.656030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.50000 | − | 6.06218i | 0.230283 | − | 0.398862i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.46863 | − | 14.6681i | −0.554798 | − | 0.960939i | −0.997919 | − | 0.0644769i | \(-0.979462\pi\) |
0.443121 | − | 0.896462i | \(-0.353871\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.2288 | − | 41.9654i | 1.58051 | − | 2.73752i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.00000 | −0.454699 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.22876 | −0.596959 | −0.298479 | − | 0.954416i | \(-0.596479\pi\) | ||||
−0.298479 | + | 0.954416i | \(0.596479\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4059 | + | 19.7556i | −0.734717 | + | 1.27257i | 0.220130 | + | 0.975471i | \(0.429352\pi\) |
−0.954847 | + | 0.297097i | \(0.903981\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.5830 | + | 18.3303i | 0.678900 | + | 1.17589i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.5203 | 1.63043 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.885622 | − | 1.53394i | −0.0563508 | − | 0.0976024i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.5830 | − | 30.4547i | 1.11428 | − | 1.92999i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.29150 | −0.460236 | −0.230118 | − | 0.973163i | \(-0.573911\pi\) | ||||
−0.230118 | + | 0.973163i | \(0.573911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.64575 | −0.229206 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −28.9373 | + | 50.1208i | −1.81212 | + | 3.13869i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.208497 | + | 0.361128i | 0.0130057 | + | 0.0225265i | 0.872455 | − | 0.488694i | \(-0.162527\pi\) |
−0.859449 | + | 0.511221i | \(0.829193\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.17712 | − | 3.77089i | 0.135280 | − | 0.234312i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.58301 | + | 14.8662i | 0.531275 | + | 0.920195i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.03137 | − | 3.51844i | 0.125260 | − | 0.216956i | −0.796575 | − | 0.604540i | \(-0.793357\pi\) |
0.921834 | + | 0.387584i | \(0.126690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.2915 | −0.816491 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −38.5830 | −2.36124 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.2915 | + | 23.0216i | −0.810397 | + | 1.40365i | 0.102189 | + | 0.994765i | \(0.467415\pi\) |
−0.912586 | + | 0.408884i | \(0.865918\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.96863 | − | 15.5341i | −0.544805 | − | 0.943630i | −0.998619 | − | 0.0525339i | \(-0.983270\pi\) |
0.453814 | − | 0.891097i | \(-0.350063\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 35.0000 | 2.11830 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.14575 | + | 7.18065i | 0.249998 | + | 0.433010i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.85425 | − | 10.1399i | 0.351748 | − | 0.609245i | −0.634808 | − | 0.772670i | \(-0.718921\pi\) |
0.986556 | + | 0.163425i | \(0.0522542\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.0000 | 0.957895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.06275 | −0.421328 | −0.210664 | − | 0.977559i | \(-0.567563\pi\) | ||||
−0.210664 | + | 0.977559i | \(0.567563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.82288 | + | 6.62141i | −0.227246 | + | 0.393602i | −0.956991 | − | 0.290118i | \(-0.906306\pi\) |
0.729745 | + | 0.683720i | \(0.239639\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.70850 | − | 2.95920i | −0.101203 | − | 0.175288i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.53137 | + | 11.3127i | 0.385535 | + | 0.667766i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.55163 | − | 13.0798i | 0.442685 | − | 0.766752i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.35425 | 0.137070 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.32288 | − | 2.29129i | 0.0767610 | − | 0.132954i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.11438 | − | 15.7866i | −0.527098 | − | 0.912961i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.29150 | − | 9.16515i | −0.304997 | − | 0.528271i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.96863 | − | 6.87386i | −0.227992 | − | 0.394893i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.76013 | + | 11.7089i | −0.387084 | + | 0.670449i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.22876 | 0.241348 | 0.120674 | − | 0.992692i | \(-0.461494\pi\) | ||||
0.120674 | + | 0.992692i | \(0.461494\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.2288 | −1.94721 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.46863 | − | 14.6681i | 0.480212 | − | 0.831751i | −0.519531 | − | 0.854452i | \(-0.673893\pi\) |
0.999742 | + | 0.0227007i | \(0.00722647\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.20850 | − | 2.09318i | −0.0683083 | − | 0.118313i | 0.829848 | − | 0.557989i | \(-0.188427\pi\) |
−0.898157 | + | 0.439675i | \(0.855093\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 38.5830 | 2.17391 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00000 | − | 10.3923i | −0.336994 | − | 0.583690i | 0.646872 | − | 0.762598i | \(-0.276077\pi\) |
−0.983866 | + | 0.178908i | \(0.942743\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.14575 | + | 3.71655i | −0.120139 | + | 0.208087i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.0627 | −0.729091 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.12549 | 0.118266 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.7288 | + | 35.9033i | −1.14982 | + | 1.99155i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.0000 | − | 24.2487i | −0.774202 | − | 1.34096i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.5830 | − | 30.4547i | 0.969382 | − | 1.67902i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.67712 | − | 13.2972i | −0.421973 | − | 0.730879i | 0.574159 | − | 0.818743i | \(-0.305329\pi\) |
−0.996132 | + | 0.0878650i | \(0.971996\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.29150 | − | 5.70105i | 0.180373 | − | 0.312416i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.3542 | −0.784256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.9373 | 1.35842 | 0.679209 | − | 0.733945i | \(-0.262323\pi\) | ||||
0.679209 | + | 0.733945i | \(0.262323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.1974 | − | 17.6624i | 0.553846 | − | 0.959289i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | + | 3.46410i | 0.108306 | + | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.5830 | − | 30.4547i | −0.946637 | − | 1.63962i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.4059 | − | 23.2197i | 0.719665 | − | 1.24650i | −0.241467 | − | 0.970409i | \(-0.577629\pi\) |
0.961132 | − | 0.276088i | \(-0.0890381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.8745 | 1.59915 | 0.799573 | − | 0.600569i | \(-0.205059\pi\) | ||||
0.799573 | + | 0.600569i | \(0.205059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.2288 | 0.706099 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5830 | − | 30.4547i | 0.935849 | − | 1.62094i | 0.162736 | − | 0.986670i | \(-0.447968\pi\) |
0.773113 | − | 0.634268i | \(-0.218699\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.5830 | + | 30.4547i | 0.933209 | + | 1.61637i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.0000 | + | 36.3731i | −1.11144 | + | 1.92507i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.03137 | − | 8.71459i | −0.265546 | − | 0.459939i | 0.702161 | − | 0.712018i | \(-0.252219\pi\) |
−0.967706 | + | 0.252080i | \(0.918885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.43725 | − | 16.3458i | 0.496698 | − | 0.860305i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.64575 | 0.138866 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.5830 | 1.07736 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.88562 | + | 8.46215i | −0.255027 | + | 0.441720i | −0.964903 | − | 0.262607i | \(-0.915418\pi\) |
0.709876 | + | 0.704327i | \(0.248751\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.87451 | + | 17.1031i | 0.514046 | + | 0.890354i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.64575 | −0.500782 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.43725 | + | 9.41760i | 0.281530 | + | 0.487625i | 0.971762 | − | 0.235964i | \(-0.0758247\pi\) |
−0.690232 | + | 0.723589i | \(0.742491\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.8745 | + | 27.4955i | −0.819756 | + | 1.41986i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.4575 | −1.10512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.9373 | −1.12684 | −0.563421 | − | 0.826170i | \(-0.690515\pi\) | ||||
−0.563421 | + | 0.826170i | \(0.690515\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0830052 | − | 0.143769i | 0.00425249 | − | 0.00736552i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.0516 | − | 29.5343i | −0.871298 | − | 1.50913i | −0.860655 | − | 0.509189i | \(-0.829946\pi\) |
−0.0106427 | − | 0.999943i | \(-0.503388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.82288 | + | 8.35347i | 0.245797 | + | 0.425732i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.00000 | − | 13.8564i | −0.406663 | − | 0.704361i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.4059 | − | 18.0235i | 0.527599 | − | 0.913828i | −0.471883 | − | 0.881661i | \(-0.656426\pi\) |
0.999482 | − | 0.0321675i | \(-0.0102410\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.8745 | 1.10624 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −41.3948 | −2.08809 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.82288 | − | 8.35347i | 0.242665 | − | 0.420308i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5830 | − | 26.9906i | −0.782089 | − | 1.35462i | −0.930723 | − | 0.365725i | \(-0.880821\pi\) |
0.148634 | − | 0.988892i | \(-0.452512\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.23987 | − | 2.14752i | −0.0620712 | − | 0.107510i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.208497 | − | 0.361128i | −0.0104119 | − | 0.0180339i | 0.860773 | − | 0.508990i | \(-0.169981\pi\) |
−0.871184 | + | 0.490956i | \(0.836648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0000 | + | 17.3205i | −0.498135 | + | 0.862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.2288 | −0.905794 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.64575 | 0.0815769 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.46863 | + | 16.4001i | −0.468193 | + | 0.810935i | −0.999339 | − | 0.0363456i | \(-0.988428\pi\) |
0.531146 | + | 0.847280i | \(0.321762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.9686 | − | 43.2469i | −1.23161 | − | 2.13321i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.70850 | 0.0840697 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.2288 | + | 41.9654i | 1.18934 | + | 2.06000i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.29150 | + | 9.16515i | −0.259126 | + | 0.448819i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.8745 | −1.06864 | −0.534320 | − | 0.845282i | \(-0.679432\pi\) | ||||
−0.534320 | + | 0.845282i | \(0.679432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.1660 | −1.61641 | −0.808206 | − | 0.588900i | \(-0.799561\pi\) | ||||
−0.808206 | + | 0.588900i | \(0.799561\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.5830 | − | 46.0431i | 1.29251 | − | 2.23869i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.8745 | − | 43.0839i | −1.20659 | − | 2.08988i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.90588 | + | 8.49723i | −0.237412 | + | 0.411210i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.61438 | + | 11.4564i | 0.319345 | + | 0.553122i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.38562 | − | 2.39997i | 0.0667430 | − | 0.115602i | −0.830723 | − | 0.556686i | \(-0.812073\pi\) |
0.897466 | + | 0.441084i | \(0.145406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −41.3948 | −1.98473 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.645751 | + | 1.11847i | −0.0308905 | + | 0.0535039i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.96863 | − | 10.3380i | −0.284867 | − | 0.493404i | 0.687710 | − | 0.725986i | \(-0.258616\pi\) |
−0.972577 | + | 0.232581i | \(0.925283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 28.0000 | 1.33333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.22876 | − | 15.9847i | −0.438471 | − | 0.759455i | 0.559100 | − | 0.829100i | \(-0.311147\pi\) |
−0.997572 | + | 0.0696451i | \(0.977813\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.5830 | − | 46.0431i | 1.26016 | − | 2.18265i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.4575 | −0.589220 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.87451 | 0.466007 | 0.233003 | − | 0.972476i | \(-0.425145\pi\) | ||||
0.233003 | + | 0.972476i | \(0.425145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.46863 | + | 4.27579i | −0.116243 | + | 0.201339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.43725 | − | 7.68555i | −0.208480 | − | 0.361099i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.1144 | + | 41.7673i | −1.13050 | + | 1.95808i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5830 | + | 33.9188i | 0.916054 | + | 1.58665i | 0.805350 | + | 0.592799i | \(0.201977\pi\) |
0.110704 | + | 0.993853i | \(0.464689\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.93725 | + | 13.7477i | −0.370479 | + | 0.641689i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.1660 | −1.49812 | −0.749060 | − | 0.662502i | \(-0.769495\pi\) | ||||
−0.749060 | + | 0.662502i | \(0.769495\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4575 | 1.04369 | 0.521845 | − | 0.853041i | \(-0.325244\pi\) | ||||
0.521845 | + | 0.853041i | \(0.325244\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.2915 | + | 33.4139i | −0.894622 | + | 1.54953i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.35425 | + | 9.27383i | 0.247765 | + | 0.429142i | 0.962905 | − | 0.269839i | \(-0.0869706\pi\) |
−0.715140 | + | 0.698981i | \(0.753637\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.4170 | −0.481012 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.0000 | + | 48.4974i | 1.29017 | + | 2.23464i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.00000 | − | 3.46410i | 0.0919601 | − | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.93725 | 0.134770 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.5830 | −0.667710 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.9686 | + | 22.4623i | −0.592552 | + | 1.02633i | 0.401336 | + | 0.915931i | \(0.368546\pi\) |
−0.993887 | + | 0.110399i | \(0.964787\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.11438 | + | 7.12631i | 0.187600 | + | 0.324932i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.7601 | − | 22.1012i | −0.580606 | − | 1.00564i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.4059 | + | 18.0235i | 0.472507 | + | 0.818406i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.2915 | + | 26.4857i | −0.692924 | + | 1.20018i | 0.277951 | + | 0.960595i | \(0.410345\pi\) |
−0.970875 | + | 0.239585i | \(0.922989\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.2915 | 0.555841 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7085 | −0.483268 | −0.241634 | − | 0.970367i | \(-0.577683\pi\) | ||||
−0.241634 | + | 0.970367i | \(0.577683\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.8745 | − | 22.2993i | 0.579839 | − | 1.00431i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.29150 | + | 12.6293i | 0.327729 | + | 0.567643i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7601 | + | 22.1012i | 0.572370 | + | 0.991374i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.93725 | + | 15.4798i | 0.400086 | + | 0.692970i | 0.993736 | − | 0.111754i | \(-0.0356468\pi\) |
−0.593650 | + | 0.804724i | \(0.702313\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.1458 | − | 34.8935i | 0.900046 | − | 1.55893i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.9373 | 0.888958 | 0.444479 | − | 0.895789i | \(-0.353389\pi\) | ||||
0.444479 | + | 0.895789i | \(0.353389\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9373 | 0.486701 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.8745 | + | 27.4955i | −0.705012 | + | 1.22112i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.2915 | − | 17.8254i | −0.456163 | − | 0.790097i | 0.542591 | − | 0.839997i | \(-0.317443\pi\) |
−0.998754 | + | 0.0498996i | \(0.984110\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.9373 | 0.660785 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.468627 | − | 0.811686i | −0.0206904 | − | 0.0358368i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.5830 | − | 40.8470i | 1.03919 | − | 1.79993i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2915 | 0.584560 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.2288 | 1.19521 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.06275 | − | 1.84073i | 0.0465598 | − | 0.0806439i | −0.841806 | − | 0.539780i | \(-0.818508\pi\) |
0.888366 | + | 0.459136i | \(0.151841\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.76013 | + | 13.4409i | 0.339327 | + | 0.587731i | 0.984306 | − | 0.176469i | \(-0.0564674\pi\) |
−0.644979 | + | 0.764200i | \(0.723134\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −29.0203 | + | 50.2646i | −1.26655 | + | 2.19373i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0000 | − | 20.7846i | −0.522728 | − | 0.905392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.85425 | − | 8.40781i | 0.211054 | − | 0.365557i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.58301 | 0.112093 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.6863 | −1.06928 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00000 | − | 15.5885i | 0.389104 | − | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.37451 | − | 9.30892i | −0.231927 | − | 0.401710i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.50000 | + | 6.06218i | 0.150756 | + | 0.261116i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.14575 | + | 7.18065i | 0.178240 | + | 0.308720i | 0.941278 | − | 0.337633i | \(-0.109626\pi\) |
−0.763038 | + | 0.646354i | \(0.776293\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.2288 | − | 22.9129i | 0.567700 | − | 0.983286i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.5830 | 1.65271 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.5203 | −1.17668 | −0.588341 | − | 0.808613i | \(-0.700219\pi\) | ||||
−0.588341 | + | 0.808613i | \(0.700219\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.41699 | + | 12.8466i | −0.316550 | + | 0.548280i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.760130 | + | 1.31658i | 0.0323826 | + | 0.0560883i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.50000 | − | 6.06218i | 0.148835 | − | 0.257790i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.93725 | + | 13.7477i | 0.336918 | + | 0.583559i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.8745 | + | 27.4955i | −0.672624 | + | 1.16502i | 0.304533 | + | 0.952502i | \(0.401500\pi\) |
−0.977157 | + | 0.212518i | \(0.931834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.0000 | 0.845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.8745 | −0.670222 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.53137 | − | 11.3127i | 0.275265 | − | 0.476772i | −0.694937 | − | 0.719070i | \(-0.744568\pi\) |
0.970202 | + | 0.242298i | \(0.0779012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0516 | + | 24.3381i | 0.591157 | + | 1.02391i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.2288 | −0.555556 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.5830 | + | 35.6508i | 0.862884 | + | 1.49456i | 0.869133 | + | 0.494579i | \(0.164678\pi\) |
−0.00624806 | + | 0.999980i | \(0.501989\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.4686 | + | 38.9168i | −0.940283 | + | 1.62862i | −0.175351 | + | 0.984506i | \(0.556106\pi\) |
−0.764932 | + | 0.644112i | \(0.777227\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 35.1660 | 1.46908 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.2288 | 1.26063 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.7288 | − | 22.0469i | 0.529905 | − | 0.917823i | −0.469486 | − | 0.882940i | \(-0.655561\pi\) |
0.999391 | − | 0.0348828i | \(-0.0111058\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.2399 | + | 26.3962i | 0.633347 | + | 1.09699i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.5830 | + | 30.4547i | 0.729466 | + | 1.26347i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.82288 | − | 3.15731i | −0.0754958 | − | 0.130763i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −36.4575 | + | 63.1463i | −1.50733 | + | 2.61078i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.93725 | 0.327606 | 0.163803 | − | 0.986493i | \(-0.447624\pi\) | ||||
0.163803 | + | 0.986493i | \(0.447624\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.41699 | 0.0583863 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.9686 | + | 43.2469i | −1.02707 | + | 1.77894i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.4686 | − | 19.8642i | −0.470960 | − | 0.815727i | 0.528488 | − | 0.848941i | \(-0.322759\pi\) |
−0.999448 | + | 0.0332139i | \(0.989426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.9373 | − | 50.1208i | −1.18631 | − | 2.05475i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.4059 | − | 50.9325i | −1.20350 | − | 2.08453i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.87451 | + | 17.1031i | −0.403461 | + | 0.698816i | −0.994141 | − | 0.108090i | \(-0.965526\pi\) |
0.590680 | + | 0.806906i | \(0.298860\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.5830 | −1.00276 | −0.501381 | − | 0.865227i | \(-0.667174\pi\) | ||||
−0.501381 | + | 0.865227i | \(0.667174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.7490 | −0.641350 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.82288 | + | 3.15731i | −0.0741104 | + | 0.128363i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.6458 | + | 18.4390i | 0.432098 | + | 0.748415i | 0.997054 | − | 0.0767058i | \(-0.0244402\pi\) |
−0.564956 | + | 0.825121i | \(0.691107\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.0405 | −1.21730 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.2288 | + | 57.5539i | 1.34429 | + | 2.32838i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −47.6235 | −1.92037 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.2915 | −0.655871 | −0.327936 | − | 0.944700i | \(-0.606353\pi\) | ||||
−0.327936 | + | 0.944700i | \(0.606353\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.2915 | − | 29.9498i | 0.695004 | − | 1.20378i | −0.275175 | − | 0.961394i | \(-0.588736\pi\) |
0.970179 | − | 0.242388i | \(-0.0779308\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.82288 | − | 8.35347i | −0.193535 | − | 0.335213i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.2915 | − | 33.4139i | 0.772898 | − | 1.33870i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.14575 | − | 1.98450i | −0.0458301 | − | 0.0793800i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.468627 | − | 0.811686i | 0.0187152 | − | 0.0324156i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.87451 | −0.393722 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.8118 | −1.38583 | −0.692917 | − | 0.721017i | \(-0.743675\pi\) | ||||
−0.692917 | + | 0.721017i | \(0.743675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.7601 | + | 34.2255i | −0.785395 | + | 1.36034i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.114378 | + | 0.198109i | 0.00453896 | + | 0.00786172i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.5000 | + | 30.3109i | −0.693375 | + | 1.20096i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.2915 | + | 33.4139i | 0.763160 | + | 1.32183i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.43725 | − | 16.3458i | 0.372749 | − | 0.645620i | −0.617238 | − | 0.786776i | \(-0.711749\pi\) |
0.989987 | + | 0.141156i | \(0.0450819\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.52026 | −0.257134 | −0.128567 | − | 0.991701i | \(-0.541038\pi\) | ||||
−0.128567 | + | 0.991701i | \(0.541038\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 38.5830 | 1.51920 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.4059 | − | 33.6120i | 0.762924 | − | 1.32142i | −0.178413 | − | 0.983956i | \(-0.557096\pi\) |
0.941337 | − | 0.337467i | \(-0.109570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.322876 | + | 0.559237i | 0.0126740 | + | 0.0219520i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.0000 | + | 24.2487i | −0.548703 | + | 0.950382i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.17712 | − | 2.03884i | −0.0460644 | − | 0.0797859i | 0.842074 | − | 0.539362i | \(-0.181335\pi\) |
−0.888138 | + | 0.459576i | \(0.848001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.5203 | − | 49.3985i | 1.11438 | − | 1.93016i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.5830 | 0.881047 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.5830 | −0.568073 | −0.284037 | − | 0.958813i | \(-0.591674\pi\) | ||||
−0.284037 | + | 0.958813i | \(0.591674\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.2915 | + | 24.7536i | −0.555875 | + | 0.962804i | 0.441960 | + | 0.897035i | \(0.354283\pi\) |
−0.997835 | + | 0.0657690i | \(0.979050\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −39.6863 | − | 68.7386i | −1.54129 | − | 2.66959i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.41699 | 0.132505 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.82288 | + | 13.5496i | 0.302903 | + | 0.524643i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.3431 | + | 28.3071i | −0.631862 | + | 1.09442i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.70850 | −0.143165 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.9373 | −0.575789 | −0.287894 | − | 0.957662i | \(-0.592955\pi\) | ||||
−0.287894 | + | 0.957662i | \(0.592955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.9686 | + | 18.9982i | −0.422183 | + | 0.731242i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.06275 | + | 1.84073i | 0.0408446 | + | 0.0707450i | 0.885725 | − | 0.464210i | \(-0.153662\pi\) |
−0.844880 | + | 0.534955i | \(0.820328\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.55163 | + | 13.0798i | 0.289805 | + | 0.501957i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.5830 | − | 30.4547i | −0.673782 | − | 1.16703i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.96863 | + | 12.0700i | −0.266647 | + | 0.461846i | −0.967994 | − | 0.250974i | \(-0.919249\pi\) |
0.701347 | + | 0.712820i | \(0.252582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 68.8118 | 2.62916 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −42.3320 | −1.61507 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.11438 | − | 15.7866i | 0.347230 | − | 0.601420i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.38562 | − | 16.2564i | −0.357046 | − | 0.618422i | 0.630420 | − | 0.776254i | \(-0.282883\pi\) |
−0.987466 | + | 0.157833i | \(0.949549\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.29150 | + | 9.16515i | 0.201008 | + | 0.348155i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.29150 | − | 12.6293i | −0.276582 | − | 0.479055i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.8118 | − | 25.6547i | 0.561035 | − | 0.971742i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 44.8118 | 1.69494 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.87451 | −0.259647 | −0.129823 | − | 0.991537i | \(-0.541441\pi\) | ||||
−0.129823 | + | 0.991537i | \(0.541441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.291503 | − | 0.504897i | 0.0109942 | − | 0.0190426i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 64.1033 | + | 111.030i | 2.41427 | + | 4.18164i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.93725 | 0.298511 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.40588 | + | 5.89916i | 0.127911 | + | 0.221548i | 0.922867 | − | 0.385119i | \(-0.125840\pi\) |
−0.794956 | + | 0.606667i | \(0.792506\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.29150 | − | 9.16515i | 0.198447 | − | 0.343720i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.5830 | 0.546138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.2288 | −0.681717 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.2085 | − | 21.1457i | 0.455935 | − | 0.789702i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.93725 | − | 3.35542i | −0.0722474 | − | 0.125136i | 0.827639 | − | 0.561261i | \(-0.189684\pi\) |
−0.899886 | + | 0.436125i | \(0.856350\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.1144 | − | 29.6430i | 0.637373 | − | 1.10396i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.1771 | − | 52.2683i | −1.12230 | − | 1.94388i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.7915 | − | 30.8158i | 0.660760 | − | 1.14447i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.2915 | 0.641306 | 0.320653 | − | 0.947197i | \(-0.396098\pi\) | ||||
0.320653 | + | 0.947197i | \(0.396098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.0000 | −1.51852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.7288 | − | 35.9033i | −0.765634 | − | 1.32612i | −0.939911 | − | 0.341420i | \(-0.889092\pi\) |
0.174277 | − | 0.984697i | \(-0.444241\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −33.7601 | + | 58.4743i | −1.24526 | + | 2.15686i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.96863 | − | 3.40976i | −0.0725153 | − | 0.125600i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.93725 | + | 6.81952i | −0.144834 | + | 0.250860i | −0.929311 | − | 0.369298i | \(-0.879598\pi\) |
0.784477 | + | 0.620158i | \(0.212932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.68627 | 0.172154 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.7085 | 1.27333 | 0.636666 | − | 0.771140i | \(-0.280313\pi\) | ||||
0.636666 | + | 0.771140i | \(0.280313\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.58301 | − | 14.8662i | 0.314457 | − | 0.544655i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.5830 | + | 46.0431i | 0.972621 | + | 1.68463i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.53137 | − | 11.3127i | 0.238651 | − | 0.413356i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.00000 | − | 13.8564i | −0.291924 | − | 0.505627i | 0.682341 | − | 0.731034i | \(-0.260962\pi\) |
−0.974265 | + | 0.225407i | \(0.927629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.64575 | − | 16.7069i | 0.351511 | − | 0.608834i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.2288 | 0.445050 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1660 | 0.696600 | 0.348300 | − | 0.937383i | \(-0.386759\pi\) | ||||
0.348300 | + | 0.937383i | \(0.386759\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.82288 | − | 8.35347i | 0.175059 | − | 0.303212i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.00000 | + | 5.19615i | 0.108750 | + | 0.188360i | 0.915264 | − | 0.402854i | \(-0.131982\pi\) |
−0.806514 | + | 0.591215i | \(0.798649\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.0000 | 1.01367 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −43.7490 | − | 75.7755i | −1.58175 | − | 2.73967i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.61438 | + | 2.79619i | −0.0582918 | + | 0.100964i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.1660 | −0.546900 | −0.273450 | − | 0.961886i | \(-0.588165\pi\) | ||||
−0.273450 | + | 0.961886i | \(0.588165\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.10326 | −0.0397331 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.29150 | + | 2.23695i | −0.0464521 | + | 0.0804574i | −0.888317 | − | 0.459232i | \(-0.848125\pi\) |
0.841864 | + | 0.539689i | \(0.181458\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.5830 | − | 28.7226i | −0.595679 | − | 1.03175i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.76013 | + | 9.97684i | 0.206643 | + | 0.357917i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.874508 | + | 1.51469i | 0.0313325 | + | 0.0542695i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.82288 | + | 8.35347i | −0.172576 | + | 0.298911i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.3542 | −0.405768 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −77.1660 | −2.75417 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.405881 | + | 0.703006i | −0.0144681 | + | 0.0250595i | −0.873169 | − | 0.487418i | \(-0.837939\pi\) |
0.858701 | + | 0.512477i | \(0.171272\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.37451 | + | 9.30892i | 0.191338 | + | 0.331406i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.1974 | + | 17.6624i | 0.362577 | + | 0.628002i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.27124 | − | 16.0583i | −0.329232 | − | 0.570246i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.5830 | − | 30.4547i | 0.623605 | − | 1.08012i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.1660 | −1.24564 | −0.622822 | − | 0.782364i | \(-0.714014\pi\) | ||||
−0.622822 | + | 0.782364i | \(0.714014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −79.7490 | −2.82132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.1660 | − | 50.5170i | 1.03053 | − | 1.78493i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.82288 | + | 4.88936i | 0.0996171 | + | 0.172542i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.1660 | 1.23944 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35.1660 | − | 60.9093i | −1.23790 | − | 2.14411i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.2915 | + | 43.8062i | −0.889202 | + | 1.54014i | −0.0483813 | + | 0.998829i | \(0.515406\pi\) |
−0.840821 | + | 0.541314i | \(0.817927\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.7490 | −0.974400 | −0.487200 | − | 0.873290i | \(-0.661982\pi\) | ||||
−0.487200 | + | 0.873290i | \(0.661982\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.4575 | 1.66441 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.46863 | + | 14.6681i | −0.296643 | + | 0.513801i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.708497 | − | 1.22715i | −0.0247872 | − | 0.0429327i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26.4575 | + | 45.8258i | −0.924500 | + | 1.60128i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.85425 | + | 6.67575i | 0.134514 | + | 0.232985i | 0.925412 | − | 0.378963i | \(-0.123719\pi\) |
−0.790898 | + | 0.611949i | \(0.790386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.9373 | + | 37.9964i | −0.764685 | + | 1.32447i | 0.175729 | + | 0.984439i | \(0.443772\pi\) |
−0.940413 | + | 0.340034i | \(0.889561\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.9373 | −0.763757 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.3948 | 1.23080 | 0.615398 | − | 0.788216i | \(-0.288995\pi\) | ||||
0.615398 | + | 0.788216i | \(0.288995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.6974 | + | 37.5810i | −0.753581 | + | 1.30524i | 0.192495 | + | 0.981298i | \(0.438342\pi\) |
−0.946077 | + | 0.323943i | \(0.894991\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.4889 | + | 26.8275i | 0.537304 | + | 0.930637i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.0000 | − | 36.3731i | −0.727607 | − | 1.26025i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.7601 | + | 48.0820i | 0.960679 | + | 1.66394i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.29150 | + | 9.16515i | −0.182901 | + | 0.316794i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.8745 | −0.962335 | −0.481167 | − | 0.876629i | \(-0.659787\pi\) | ||||
−0.481167 | + | 0.876629i | \(0.659787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5830 | −0.364931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.34313 | − | 16.1828i | 0.321795 | − | 0.557365i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.8745 | − | 37.8878i | −0.752506 | − | 1.30338i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.32288 | + | 2.29129i | −0.0454545 | + | 0.0787296i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.1144 | − | 17.5186i | −0.347125 | − | 0.601237i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.00000 | − | 5.19615i | 0.102839 | − | 0.178122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.16601 | −0.108402 | −0.0542011 | − | 0.998530i | \(-0.517261\pi\) | ||||
−0.0542011 | + | 0.998530i | \(0.517261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.16601 | 0.176674 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0000 | + | 31.1769i | −0.614868 | + | 1.06498i | 0.375539 | + | 0.926806i | \(0.377458\pi\) |
−0.990408 | + | 0.138177i | \(0.955876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.9059 | + | 32.7459i | 0.645060 | + | 1.11728i | 0.984288 | + | 0.176573i | \(0.0565011\pi\) |
−0.339227 | + | 0.940704i | \(0.610166\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.5608 | −1.17783 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.7601 | − | 42.8858i | −0.842845 | − | 1.45985i | −0.887480 | − | 0.460846i | \(-0.847546\pi\) |
0.0446353 | − | 0.999003i | \(-0.485787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7601 | + | 32.4935i | −0.637864 | + | 1.10481i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 50.2693 | 1.70723 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.64575 | 0.0897510 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.84313 | − | 17.0488i | 0.333522 | − | 0.577677i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.4170 | + | 19.7748i | 0.386407 | + | 0.669276i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.8745 | − | 27.4955i | −0.536656 | − | 0.929516i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.43725 | − | 7.68555i | −0.149835 | − | 0.259523i | 0.781331 | − | 0.624117i | \(-0.214541\pi\) |
−0.931167 | + | 0.364594i | \(0.881208\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.8745 | + | 27.4955i | −0.535434 | + | 0.927399i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.87451 | 0.231608 | 0.115804 | − | 0.993272i | \(-0.463056\pi\) | ||||
0.115804 | + | 0.993272i | \(0.463056\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.06275 | −0.204028 | −0.102014 | − | 0.994783i | \(-0.532529\pi\) | ||||
−0.102014 | + | 0.994783i | \(0.532529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.11438 | + | 5.39426i | −0.104689 | + | 0.181326i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.55163 | − | 11.3478i | −0.219982 | − | 0.381020i | 0.734820 | − | 0.678262i | \(-0.237267\pi\) |
−0.954802 | + | 0.297242i | \(0.903933\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0830052 | + | 0.143769i | 0.00278391 | + | 0.00482187i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.50000 | − | 4.33013i | −0.0837532 | − | 0.145065i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.35425 | − | 4.07768i | 0.0787819 | − | 0.136454i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.8118 | 0.495103 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 48.2288 | 1.61031 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.58301 | − | 14.8662i | 0.286259 | − | 0.495816i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.9373 | + | 18.9439i | 0.364373 | + | 0.631112i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.0000 | 0.931782 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.2288 | + | 31.5731i | 0.605944 | + | 1.04953i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.22876 | + | 9.05647i | −0.173618 | + | 0.300715i | −0.939682 | − | 0.342049i | \(-0.888879\pi\) |
0.766064 | + | 0.642764i | \(0.222212\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.29150 | 0.0427894 | 0.0213947 | − | 0.999771i | \(-0.493189\pi\) | ||||
0.0213947 | + | 0.999771i | \(0.493189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.64575 | + | 11.5108i | −0.219942 | + | 0.380951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.8856 | − | 30.9788i | −0.591280 | − | 1.02413i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.6974 | − | 35.8489i | 0.683488 | − | 1.18384i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.6458 | − | 30.5633i | −0.582080 | − | 1.00819i | −0.995233 | − | 0.0975298i | \(-0.968906\pi\) |
0.413153 | − | 0.910662i | \(-0.364427\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.59412 | + | 9.68930i | −0.184332 | + | 0.319273i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48.2288 | −1.58747 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.6458 | −0.448670 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.8745 | − | 44.8160i | 0.849830 | − | 1.47195i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.7915 | − | 30.8158i | −0.583720 | − | 1.01103i | −0.995034 | − | 0.0995392i | \(-0.968263\pi\) |
0.411313 | − | 0.911494i | \(-0.365070\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.47974 | 0.0812702 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.4059 | + | 38.8081i | 0.733536 | + | 1.27052i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.9373 | − | 18.9439i | 0.357686 | − | 0.619531i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.6863 | −1.52517 | −0.762587 | − | 0.646886i | \(-0.776071\pi\) | ||||
−0.762587 | + | 0.646886i | \(0.776071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.39477 | 0.208685 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.3118 | − | 38.6451i | 0.727343 | − | 1.25979i | −0.230660 | − | 0.973034i | \(-0.574088\pi\) |
0.958002 | − | 0.286760i | \(-0.0925782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | + | 15.5885i | 0.293080 | + | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.7601 | + | 22.1012i | −0.415087 | + | 0.718952i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.9373 | − | 29.3362i | −0.550387 | − | 0.953298i | −0.998246 | − | 0.0591941i | \(-0.981147\pi\) |
0.447860 | − | 0.894104i | \(-0.352186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.1144 | + | 24.4468i | −0.458172 | + | 0.793577i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.7490 | 1.02953 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.5203 | −0.826682 | −0.413341 | − | 0.910576i | \(-0.635638\pi\) | ||||
−0.413341 | + | 0.910576i | \(0.635638\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.2288 | + | 41.9654i | −0.784024 | + | 1.35797i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.67712 | − | 9.83307i | −0.183515 | − | 0.317858i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.9373 | 1.61256 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.87451 | − | 17.1031i | 0.318202 | − | 0.551141i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.0000 | −1.35203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.3320 | 0.846781 | 0.423390 | − | 0.905947i | \(-0.360840\pi\) | ||||
0.423390 | + | 0.905947i | \(0.360840\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.81176 | + | 4.87011i | −0.0903268 | + | 0.156451i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.9686 | − | 22.4623i | −0.416183 | − | 0.720850i | 0.579369 | − | 0.815066i | \(-0.303299\pi\) |
−0.995552 | + | 0.0942153i | \(0.969966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.29150 | − | 9.16515i | −0.169638 | − | 0.293821i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −54.8431 | − | 94.9911i | −1.75639 | − | 3.04215i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.2288 | + | 31.5731i | −0.583190 | + | 1.01011i | 0.411909 | + | 0.911225i | \(0.364862\pi\) |
−0.995098 | + | 0.0988890i | \(0.968471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.5830 | 0.466075 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.3320 | 1.35156 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.6458 | + | 32.2954i | −0.594707 | + | 1.03006i | 0.398881 | + | 0.917003i | \(0.369399\pi\) |
−0.993588 | + | 0.113060i | \(0.963935\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.4059 | − | 59.5927i | −1.09626 | − | 1.89878i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.5203 | + | 80.5755i | 1.48076 | + | 2.56474i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.29150 | − | 12.6293i | −0.231856 | − | 0.401587i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.3431 | − | 49.0917i | 0.900349 | − | 1.55945i | 0.0733083 | − | 0.997309i | \(-0.476644\pi\) |
0.827041 | − | 0.562141i | \(-0.190022\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.6235 | 1.28915 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 81.0405 | 2.56916 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2915 | − | 36.8780i | 0.674309 | − | 1.16794i | −0.302362 | − | 0.953193i | \(-0.597775\pi\) |
0.976670 | − | 0.214744i | \(-0.0688916\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.17712 | + | 3.77089i | 0.0688812 | + | 0.119306i |
(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 | 1232.2.q.g.529.1 | 4 | ||
4.3 | odd | 2 | 154.2.e.f.67.2 | yes | 4 | ||
7.2 | even | 3 | inner | 1232.2.q.g.177.1 | 4 | ||
7.3 | odd | 6 | 8624.2.a.bk.1.1 | 2 | |||
7.4 | even | 3 | 8624.2.a.ca.1.2 | 2 | |||
12.11 | even | 2 | 1386.2.k.s.991.2 | 4 | |||
28.3 | even | 6 | 1078.2.a.n.1.2 | 2 | |||
28.11 | odd | 6 | 1078.2.a.s.1.1 | 2 | |||
28.19 | even | 6 | 1078.2.e.v.177.1 | 4 | |||
28.23 | odd | 6 | 154.2.e.f.23.2 | ✓ | 4 | ||
28.27 | even | 2 | 1078.2.e.v.67.1 | 4 | |||
84.11 | even | 6 | 9702.2.a.cz.1.1 | 2 | |||
84.23 | even | 6 | 1386.2.k.s.793.2 | 4 | |||
84.59 | odd | 6 | 9702.2.a.dr.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.f.23.2 | ✓ | 4 | 28.23 | odd | 6 | ||
154.2.e.f.67.2 | yes | 4 | 4.3 | odd | 2 | ||
1078.2.a.n.1.2 | 2 | 28.3 | even | 6 | |||
1078.2.a.s.1.1 | 2 | 28.11 | odd | 6 | |||
1078.2.e.v.67.1 | 4 | 28.27 | even | 2 | |||
1078.2.e.v.177.1 | 4 | 28.19 | even | 6 | |||
1232.2.q.g.177.1 | 4 | 7.2 | even | 3 | inner | ||
1232.2.q.g.529.1 | 4 | 1.1 | even | 1 | trivial | ||
1386.2.k.s.793.2 | 4 | 84.23 | even | 6 | |||
1386.2.k.s.991.2 | 4 | 12.11 | even | 2 | |||
8624.2.a.bk.1.1 | 2 | 7.3 | odd | 6 | |||
8624.2.a.ca.1.2 | 2 | 7.4 | even | 3 | |||
9702.2.a.cz.1.1 | 2 | 84.11 | even | 6 | |||
9702.2.a.dr.1.2 | 2 | 84.59 | odd | 6 |