Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7448,2,Mod(1,7448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7448.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7448.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: | \(59.4725794254\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 11 x^{12} + 114 x^{11} - 10 x^{10} - 806 x^{9} + 523 x^{8} + 2586 x^{7} - 2226 x^{6} - 3618 x^{5} + 3397 x^{4} + 1570 x^{3} - 1529 x^{2} + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.72076\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7448.1 |
$q$-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 | ||||||||
\(3\) | −1.72076 | −0.993479 | −0.496739 | − | 0.867900i | \(-0.665470\pi\) | ||||
−0.496739 | + | 0.867900i | \(0.665470\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.55524 | 0.695525 | 0.347762 | − | 0.937583i | \(-0.386942\pi\) | ||||
0.347762 | + | 0.937583i | \(0.386942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0389984 | −0.0129995 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.04360 | 1.82221 | 0.911107 | − | 0.412170i | \(-0.135229\pi\) | ||||
0.911107 | + | 0.412170i | \(0.135229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.93856 | −0.815009 | −0.407504 | − | 0.913203i | \(-0.633601\pi\) | ||||
−0.407504 | + | 0.913203i | \(0.633601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.67619 | −0.690989 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.38986 | −1.06470 | −0.532348 | − | 0.846525i | \(-0.678690\pi\) | ||||
−0.532348 | + | 0.846525i | \(0.678690\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.90354 | 0.396915 | 0.198458 | − | 0.980109i | \(-0.436407\pi\) | ||||
0.198458 | + | 0.980109i | \(0.436407\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.58123 | −0.516245 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.22938 | 1.00639 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.96246 | 0.735811 | 0.367905 | − | 0.929863i | \(-0.380075\pi\) | ||||
0.367905 | + | 0.929863i | \(0.380075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.21372 | −0.756807 | −0.378404 | − | 0.925641i | \(-0.623527\pi\) | ||||
−0.378404 | + | 0.925641i | \(0.623527\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.3996 | −1.81033 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.98959 | 0.655884 | 0.327942 | − | 0.944698i | \(-0.393645\pi\) | ||||
0.327942 | + | 0.944698i | \(0.393645\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.05654 | 0.809694 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.08103 | 1.10587 | 0.552935 | − | 0.833224i | \(-0.313508\pi\) | ||||
0.552935 | + | 0.833224i | \(0.313508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.81873 | −1.19234 | −0.596172 | − | 0.802856i | \(-0.703313\pi\) | ||||
−0.596172 | + | 0.802856i | \(0.703313\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0606520 | −0.00904146 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.40992 | −1.22671 | −0.613357 | − | 0.789806i | \(-0.710181\pi\) | ||||
−0.613357 | + | 0.789806i | \(0.710181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.55387 | 1.05775 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.95105 | −0.267998 | −0.133999 | − | 0.990981i | \(-0.542782\pi\) | ||||
−0.133999 | + | 0.990981i | \(0.542782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.39925 | 1.26740 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.72076 | 0.227920 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.02110 | −0.393314 | −0.196657 | − | 0.980472i | \(-0.563009\pi\) | ||||
−0.196657 | + | 0.980472i | \(0.563009\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.04678 | 0.902248 | 0.451124 | − | 0.892461i | \(-0.351023\pi\) | ||||
0.451124 | + | 0.892461i | \(0.351023\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.57016 | −0.566859 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.42678 | −0.540817 | −0.270409 | − | 0.962746i | \(-0.587159\pi\) | ||||
−0.270409 | + | 0.962746i | \(0.587159\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.27552 | −0.394327 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.33231 | −0.751507 | −0.375753 | − | 0.926720i | \(-0.622616\pi\) | ||||
−0.375753 | + | 0.926720i | \(0.622616\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.59721 | −0.421021 | −0.210511 | − | 0.977592i | \(-0.567513\pi\) | ||||
−0.210511 | + | 0.977592i | \(0.567513\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.44166 | 0.512879 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.562901 | 0.0633314 | 0.0316657 | − | 0.999499i | \(-0.489919\pi\) | ||||
0.0316657 | + | 0.999499i | \(0.489919\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.88148 | −0.986832 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.3232 | −1.57218 | −0.786089 | − | 0.618113i | \(-0.787897\pi\) | ||||
−0.786089 | + | 0.618113i | \(0.787897\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.82728 | −0.740523 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.81843 | −0.731013 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.68823 | −0.708951 | −0.354476 | − | 0.935065i | \(-0.615341\pi\) | ||||
−0.354476 | + | 0.935065i | \(0.615341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.25079 | 0.751872 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.55524 | −0.159564 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.98549 | −0.709269 | −0.354634 | − | 0.935005i | \(-0.615395\pi\) | ||||
−0.354634 | + | 0.935005i | \(0.615395\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.235691 | −0.0236878 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.03369 | −0.699878 | −0.349939 | − | 0.936772i | \(-0.613798\pi\) | ||||
−0.349939 | + | 0.936772i | \(0.613798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.01658 | 0.691364 | 0.345682 | − | 0.938352i | \(-0.387648\pi\) | ||||
0.345682 | + | 0.938352i | \(0.387648\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.07461 | −0.200560 | −0.100280 | − | 0.994959i | \(-0.531974\pi\) | ||||
−0.100280 | + | 0.994959i | \(0.531974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.6130 | 1.78280 | 0.891402 | − | 0.453214i | \(-0.149723\pi\) | ||||
0.891402 | + | 0.453214i | \(0.149723\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.86511 | −0.651607 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.02528 | 0.849027 | 0.424513 | − | 0.905422i | \(-0.360445\pi\) | ||||
0.424513 | + | 0.905422i | \(0.360445\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.96046 | 0.276064 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.114599 | 0.0105947 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.5251 | 2.32047 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.1847 | −1.09866 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7906 | −1.05459 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.8080 | −1.49147 | −0.745734 | − | 0.666244i | \(-0.767901\pi\) | ||||
−0.745734 | + | 0.666244i | \(0.767901\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.4541 | 1.18457 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.34309 | 0.816310 | 0.408155 | − | 0.912913i | \(-0.366172\pi\) | ||||
0.408155 | + | 0.912913i | \(0.366172\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.13294 | 0.699972 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.1516 | −1.63623 | −0.818114 | − | 0.575056i | \(-0.804980\pi\) | ||||
−0.818114 | + | 0.575056i | \(0.804980\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7380 | 1.50452 | 0.752261 | − | 0.658865i | \(-0.228963\pi\) | ||||
0.752261 | + | 0.658865i | \(0.228963\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.4714 | 1.21871 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.7595 | −1.48512 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.16258 | 0.511775 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.8408 | 1.54350 | 0.771750 | − | 0.635926i | \(-0.219382\pi\) | ||||
0.771750 | + | 0.635926i | \(0.219382\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0381565 | 0.00310513 | 0.00155256 | − | 0.999999i | \(-0.499506\pi\) | ||||
0.00155256 | + | 0.999999i | \(0.499506\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.171198 | 0.0138405 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.55336 | −0.526378 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.01333 | −0.160682 | −0.0803408 | − | 0.996767i | \(-0.525601\pi\) | ||||
−0.0803408 | + | 0.996767i | \(0.525601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.35729 | 0.266250 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0606 | 1.10131 | 0.550657 | − | 0.834732i | \(-0.314377\pi\) | ||||
0.550657 | + | 0.834732i | \(0.314377\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.1738 | −1.25913 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.6333 | −1.28712 | −0.643560 | − | 0.765396i | \(-0.722543\pi\) | ||||
−0.643560 | + | 0.765396i | \(0.722543\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.36489 | −0.335761 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0389984 | 0.00298229 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.9559 | 1.51722 | 0.758608 | − | 0.651548i | \(-0.225880\pi\) | ||||
0.758608 | + | 0.651548i | \(0.225880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.19858 | 0.390749 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.7482 | −1.55079 | −0.775397 | − | 0.631473i | \(-0.782450\pi\) | ||||
−0.775397 | + | 0.631473i | \(0.782450\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.957746 | −0.0711887 | −0.0355943 | − | 0.999366i | \(-0.511332\pi\) | ||||
−0.0355943 | + | 0.999366i | \(0.511332\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.1258 | −0.896364 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.20477 | 0.456184 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.5305 | −1.94011 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.91976 | −0.500696 | −0.250348 | − | 0.968156i | \(-0.580545\pi\) | ||||
−0.250348 | + | 0.968156i | \(0.580545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0552 | 1.08370 | 0.541849 | − | 0.840476i | \(-0.317725\pi\) | ||||
0.541849 | + | 0.840476i | \(0.317725\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.86413 | 0.563162 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.95441 | −0.495481 | −0.247741 | − | 0.968826i | \(-0.579688\pi\) | ||||
−0.247741 | + | 0.968826i | \(0.579688\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.3426 | −1.01672 | −0.508361 | − | 0.861144i | \(-0.669749\pi\) | ||||
−0.508361 | + | 0.861144i | \(0.669749\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.61741 | 0.537291 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0127 | 0.769160 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0742350 | −0.00515969 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.04360 | −0.418045 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2034 | 1.25317 | 0.626587 | − | 0.779352i | \(-0.284451\pi\) | ||||
0.626587 | + | 0.779352i | \(0.284451\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.8964 | 0.746606 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.1600 | −0.829305 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.18992 | 0.418276 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.8998 | 0.867737 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.15231 | −0.345024 | −0.172512 | − | 0.985007i | \(-0.555188\pi\) | ||||
−0.172512 | + | 0.985007i | \(0.555188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.100664 | 0.00671092 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.6722 | −0.708342 | −0.354171 | − | 0.935181i | \(-0.615237\pi\) | ||||
−0.354171 | + | 0.935181i | \(0.615237\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.54146 | 0.300108 | 0.150054 | − | 0.988678i | \(-0.452055\pi\) | ||||
0.150054 | + | 0.988678i | \(0.452055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.78977 | 0.313788 | 0.156894 | − | 0.987615i | \(-0.449852\pi\) | ||||
0.156894 | + | 0.987615i | \(0.449852\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.0795 | −0.853210 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.968616 | −0.0629184 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.36268 | −0.346883 | −0.173441 | − | 0.984844i | \(-0.555489\pi\) | ||||
−0.173441 | + | 0.984844i | \(0.555489\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0096 | −1.09568 | −0.547842 | − | 0.836582i | \(-0.684551\pi\) | ||||
−0.547842 | + | 0.836582i | \(0.684551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.405258 | −0.0259973 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.93856 | 0.186976 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 24.6468 | 1.56193 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.05059 | −0.445029 | −0.222515 | − | 0.974929i | \(-0.571427\pi\) | ||||
−0.222515 | + | 0.974929i | \(0.571427\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5042 | 0.723264 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.7481 | 0.735694 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.67823 | 0.291820 | 0.145910 | − | 0.989298i | \(-0.453389\pi\) | ||||
0.145910 | + | 0.989298i | \(0.453389\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.154530 | −0.00956516 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.7009 | 1.21481 | 0.607406 | − | 0.794392i | \(-0.292210\pi\) | ||||
0.607406 | + | 0.794392i | \(0.292210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.03436 | −0.186399 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.5088 | 0.704328 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.92147 | −0.422009 | −0.211005 | − | 0.977485i | \(-0.567674\pi\) | ||||
−0.211005 | + | 0.977485i | \(0.567674\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.8271 | −1.69037 | −0.845187 | − | 0.534470i | \(-0.820511\pi\) | ||||
−0.845187 | + | 0.534470i | \(0.820511\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.5999 | −0.940710 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.7666 | −0.827155 | −0.413577 | − | 0.910469i | \(-0.635721\pi\) | ||||
−0.413577 | + | 0.910469i | \(0.635721\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.164329 | 0.00983810 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.14705 | 0.366702 | 0.183351 | − | 0.983047i | \(-0.441305\pi\) | ||||
0.183351 | + | 0.983047i | \(0.441305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.7018 | 0.933376 | 0.466688 | − | 0.884422i | \(-0.345447\pi\) | ||||
0.466688 | + | 0.884422i | \(0.345447\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.67619 | 0.158524 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.27084 | 0.133579 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0203 | 0.704644 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.6428 | −1.67333 | −0.836666 | − | 0.547714i | \(-0.815498\pi\) | ||||
−0.836666 | + | 0.547714i | \(0.815498\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.69854 | −0.273560 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.6043 | 1.83387 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.59365 | −0.323489 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.1033 | 0.695314 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.9594 | 0.627536 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7028 | 0.839131 | 0.419565 | − | 0.907725i | \(-0.362182\pi\) | ||||
0.419565 | + | 0.907725i | \(0.362182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0738 | −0.686856 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.7626 | −1.17734 | −0.588669 | − | 0.808374i | \(-0.700348\pi\) | ||||
−0.588669 | + | 0.808374i | \(0.700348\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.95015 | −0.562416 | −0.281208 | − | 0.959647i | \(-0.590735\pi\) | ||||
−0.281208 | + | 0.959647i | \(0.590735\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.1038 | 0.735981 | 0.367990 | − | 0.929830i | \(-0.380046\pi\) | ||||
0.367990 | + | 0.929830i | \(0.380046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.9475 | 1.34081 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.56989 | 0.199252 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.38986 | 0.244258 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.58508 | 0.420744 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −32.0285 | −1.77118 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.3836 | −1.12038 | −0.560191 | − | 0.828364i | \(-0.689272\pi\) | ||||
−0.560191 | + | 0.828364i | \(0.689272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.155588 | −0.00852616 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.88471 | −0.376152 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.4997 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.5303 | −0.843490 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.4661 | −1.37906 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.09423 | −0.274264 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0859 | −1.29300 | −0.646499 | − | 0.762915i | \(-0.723768\pi\) | ||||
−0.646499 | + | 0.762915i | \(0.723768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.4912 | −0.829223 | −0.414612 | − | 0.909998i | \(-0.636083\pi\) | ||||
−0.414612 | + | 0.909998i | \(0.636083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.3668 | −0.820220 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.9658 | 0.743324 | 0.371662 | − | 0.928368i | \(-0.378788\pi\) | ||||
0.371662 | + | 0.928368i | \(0.378788\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.84826 | −0.522692 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.7918 | 1.36124 | 0.680621 | − | 0.732636i | \(-0.261710\pi\) | ||||
0.680621 | + | 0.732636i | \(0.261710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −43.9225 | −2.30533 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.59452 | −0.292831 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.9061 | −1.92648 | −0.963242 | − | 0.268633i | \(-0.913428\pi\) | ||||
−0.963242 | + | 0.268633i | \(0.913428\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.276149 | −0.0143757 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.9966 | 1.65672 | 0.828359 | − | 0.560197i | \(-0.189275\pi\) | ||||
0.828359 | + | 0.560197i | \(0.189275\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.2888 | 1.04771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.6439 | −0.599692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.3529 | −1.61049 | −0.805245 | − | 0.592943i | \(-0.797966\pi\) | ||||
−0.805245 | + | 0.592943i | \(0.797966\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.9224 | 1.48174 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.28405 | 0.321100 | 0.160550 | − | 0.987028i | \(-0.448673\pi\) | ||||
0.160550 | + | 0.987028i | \(0.448673\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.304918 | 0.0154999 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.2715 | −0.977105 | −0.488553 | − | 0.872534i | \(-0.662475\pi\) | ||||
−0.488553 | + | 0.872534i | \(0.662475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.35626 | −0.422594 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.0772 | −0.810986 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.875447 | 0.0440485 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.6728 | −1.08773 | −0.543863 | − | 0.839174i | \(-0.683039\pi\) | ||||
−0.543863 | + | 0.839174i | \(0.683039\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5694 | −0.627688 | −0.313844 | − | 0.949475i | \(-0.601617\pi\) | ||||
−0.313844 | + | 0.949475i | \(0.601617\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.3823 | 0.616804 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.8128 | −0.686366 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.1115 | 1.19516 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.79037 | 0.137975 | 0.0689874 | − | 0.997618i | \(-0.478023\pi\) | ||||
0.0689874 | + | 0.997618i | \(0.478023\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.9552 | 1.62556 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.2761 | −1.09349 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.5229 | −1.49471 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.8393 | −1.40889 | −0.704445 | − | 0.709759i | \(-0.748804\pi\) | ||||
−0.704445 | + | 0.709759i | \(0.748804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.7241 | −0.863819 | −0.431909 | − | 0.901917i | \(-0.642160\pi\) | ||||
−0.431909 | + | 0.901917i | \(0.642160\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.327974 | 0.0159466 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.3312 | 0.549645 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 30.5597 | 1.47544 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.4231 | −0.791072 | −0.395536 | − | 0.918451i | \(-0.629441\pi\) | ||||
−0.395536 | + | 0.918451i | \(0.629441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.6537 | 0.608099 | 0.304050 | − | 0.952656i | \(-0.401661\pi\) | ||||
0.304050 | + | 0.952656i | \(0.401661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.6043 | −0.508437 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.90354 | −0.0910586 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.1568 | −1.39158 | −0.695790 | − | 0.718245i | \(-0.744946\pi\) | ||||
−0.695790 | + | 0.718245i | \(0.744946\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.1636 | −1.57565 | −0.787825 | − | 0.615899i | \(-0.788793\pi\) | ||||
−0.787825 | + | 0.615899i | \(0.788793\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.4018 | −0.493093 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.4204 | −1.53343 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.4179 | 1.71867 | 0.859334 | − | 0.511415i | \(-0.170879\pi\) | ||||
0.859334 | + | 0.511415i | \(0.170879\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.7949 | 2.01513 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.0656580 | −0.00308488 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.13478 | −0.146639 | −0.0733194 | − | 0.997309i | \(-0.523359\pi\) | ||||
−0.0733194 | + | 0.997309i | \(0.523359\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.9562 | −1.07150 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.0172 | 1.07202 | 0.536009 | − | 0.844212i | \(-0.319931\pi\) | ||||
0.536009 | + | 0.844212i | \(0.319931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.8814 | 1.20281 | 0.601406 | − | 0.798944i | \(-0.294608\pi\) | ||||
0.601406 | + | 0.798944i | \(0.294608\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.2767 | 0.522946 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.2749 | −0.753111 | −0.376556 | − | 0.926394i | \(-0.622892\pi\) | ||||
−0.376556 | + | 0.926394i | \(0.622892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.46446 | 0.159634 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −47.2533 | −2.17271 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.58123 | 0.118435 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.0760880 | 0.00348383 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.55561 | 0.299533 | 0.149767 | − | 0.988721i | \(-0.452148\pi\) | ||||
0.149767 | + | 0.988721i | \(0.452148\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.7236 | −0.534551 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.8641 | −0.493314 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.9218 | 0.902743 | 0.451372 | − | 0.892336i | \(-0.350935\pi\) | ||||
0.451372 | + | 0.892336i | \(0.350935\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.1949 | −1.09413 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.1248 | −1.67542 | −0.837709 | − | 0.546117i | \(-0.816105\pi\) | ||||
−0.837709 | + | 0.546117i | \(0.816105\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.3946 | −0.783415 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.366556 | −0.0164755 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.27794 | 0.191507 | 0.0957535 | − | 0.995405i | \(-0.469474\pi\) | ||||
0.0957535 | + | 0.995405i | \(0.469474\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.6218 | 1.27873 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.4931 | 1.00292 | 0.501458 | − | 0.865182i | \(-0.332797\pi\) | ||||
0.501458 | + | 0.865182i | \(0.332797\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9391 | −0.486783 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.51091 | 0.333571 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.718953 | 0.0318670 | 0.0159335 | − | 0.999873i | \(-0.494928\pi\) | ||||
0.0159335 | + | 0.999873i | \(0.494928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.22938 | −0.230883 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.9125 | 0.480861 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −50.8262 | −2.23533 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34.3392 | −1.50732 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.5791 | −0.507291 | −0.253646 | − | 0.967297i | \(-0.581630\pi\) | ||||
−0.253646 | + | 0.967297i | \(0.581630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.8967 | −0.913749 | −0.456875 | − | 0.889531i | \(-0.651031\pi\) | ||||
−0.456875 | + | 0.889531i | \(0.651031\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.4976 | 0.805770 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.3765 | −0.842458 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.117818 | 0.00511288 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.8080 | −0.901294 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.22651 | −0.139494 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 35.7026 | 1.54068 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.2267 | −1.72948 | −0.864741 | − | 0.502218i | \(-0.832518\pi\) | ||||
−0.864741 | + | 0.502218i | \(0.832518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.64805 | 0.0707245 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.9477 | 1.23998 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.3996 | −0.701196 | −0.350598 | − | 0.936526i | \(-0.614022\pi\) | ||||
−0.350598 | + | 0.936526i | \(0.614022\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.274813 | −0.0117288 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.96246 | −0.168807 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.6769 | −0.453209 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.4238 | −1.75518 | −0.877592 | − | 0.479408i | \(-0.840852\pi\) | ||||
−0.877592 | + | 0.479408i | \(0.840852\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.9758 | 0.971771 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 45.6526 | 1.92745 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.52573 | 0.232882 | 0.116441 | − | 0.993198i | \(-0.462851\pi\) | ||||
0.116441 | + | 0.993198i | \(0.462851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0365 | 0.590519 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.0308 | 0.923580 | 0.461790 | − | 0.886989i | \(-0.347207\pi\) | ||||
0.461790 | + | 0.886989i | \(0.347207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.98240 | 0.417750 | 0.208875 | − | 0.977942i | \(-0.433020\pi\) | ||||
0.208875 | + | 0.977942i | \(0.433020\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.9072 | 0.497431 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.91346 | −0.204906 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.26255 | 0.0941913 | 0.0470957 | − | 0.998890i | \(-0.485003\pi\) | ||||
0.0470957 | + | 0.998890i | \(0.485003\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.9063 | −1.07663 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.7914 | −0.488349 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.178229 | 0.00736887 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.8815 | −0.944419 | −0.472209 | − | 0.881486i | \(-0.656543\pi\) | ||||
−0.472209 | + | 0.881486i | \(0.656543\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.21372 | 0.173623 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.9668 | 0.492250 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.7867 | 1.67491 | 0.837455 | − | 0.546507i | \(-0.184043\pi\) | ||||
0.837455 | + | 0.546507i | \(0.184043\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.6802 | 1.01009 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.7013 | −1.09098 | −0.545492 | − | 0.838116i | \(-0.683657\pi\) | ||||
−0.545492 | + | 0.838116i | \(0.683657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.2174 | 1.55892 | 0.779459 | − | 0.626453i | \(-0.215494\pi\) | ||||
0.779459 | + | 0.626453i | \(0.215494\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.172637 | 0.00703034 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 39.6977 | 1.61394 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.00389 | 0.243690 | 0.121845 | − | 0.992549i | \(-0.461119\pi\) | ||||
0.121845 | + | 0.992549i | \(0.461119\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.7130 | 0.999782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.2793 | −1.78843 | −0.894213 | − | 0.447643i | \(-0.852264\pi\) | ||||
−0.894213 | + | 0.447643i | \(0.852264\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.9502 | −0.764145 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.2323 | −0.895039 | −0.447519 | − | 0.894274i | \(-0.647692\pi\) | ||||
−0.447519 | + | 0.894274i | \(0.647692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.3252 | 1.25907 | 0.629534 | − | 0.776973i | \(-0.283246\pi\) | ||||
0.629534 | + | 0.776973i | \(0.283246\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.95431 | 0.399453 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.43114 | −0.217246 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.3996 | 0.415319 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.5137 | −0.698318 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.2735 | 1.24498 | 0.622488 | − | 0.782629i | \(-0.286122\pi\) | ||||
0.622488 | + | 0.782629i | \(0.286122\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.3236 | −1.24500 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.1405 | −1.03735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.246950 | 0.00976920 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.36977 | −0.251591 | −0.125795 | − | 0.992056i | \(-0.540148\pi\) | ||||
−0.125795 | + | 0.992056i | \(0.540148\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.4825 | −0.847188 | −0.423594 | − | 0.905852i | \(-0.639232\pi\) | ||||
−0.423594 | + | 0.905852i | \(0.639232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.9244 | 0.823897 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.9963 | −1.06133 | −0.530667 | − | 0.847580i | \(-0.678059\pi\) | ||||
−0.530667 | + | 0.847580i | \(0.678059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.2583 | −0.716703 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.6716 | −0.965473 | −0.482737 | − | 0.875766i | \(-0.660357\pi\) | ||||
−0.482737 | + | 0.875766i | \(0.660357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5308 | 0.567764 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.140285 | 0.00547306 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.5236 | 1.53962 | 0.769810 | − | 0.638274i | \(-0.220351\pi\) | ||||
0.769810 | + | 0.638274i | \(0.220351\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.9541 | −0.503856 | −0.251928 | − | 0.967746i | \(-0.581065\pi\) | ||||
−0.251928 | + | 0.967746i | \(0.581065\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.1975 | −0.862078 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.54270 | 0.292054 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.86586 | 0.342774 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.5879 | 1.64409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6910 | −0.681937 | −0.340968 | − | 0.940075i | \(-0.610755\pi\) | ||||
−0.340968 | + | 0.940075i | \(0.610755\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.4982 | −0.519546 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.9395 | 1.03537 | 0.517685 | − | 0.855571i | \(-0.326794\pi\) | ||||
0.517685 | + | 0.855571i | \(0.326794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.3643 | 0.703723 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.5395 | 1.01551 | 0.507754 | − | 0.861502i | \(-0.330476\pi\) | ||||
0.507754 | + | 0.861502i | \(0.330476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.7853 | −1.13804 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.81475 | −0.298151 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.73328 | 0.218420 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.80182 | −0.372879 | −0.186439 | − | 0.982466i | \(-0.559695\pi\) | ||||
−0.186439 | + | 0.982466i | \(0.559695\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.5869 | 1.04643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.0847 | −1.17742 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.24202 | −0.311742 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.65378 | −0.364618 | −0.182309 | − | 0.983241i | \(-0.558357\pi\) | ||||
−0.182309 | + | 0.983241i | \(0.558357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.98959 | −0.150470 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.5066 | 0.847646 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.3356 | 0.651053 | 0.325526 | − | 0.945533i | \(-0.394459\pi\) | ||||
0.325526 | + | 0.945533i | \(0.394459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0219523 | −0.000823275 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.02098 | −0.300388 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.6202 | −1.03294 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.22786 | 0.344621 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.9661 | 1.30402 | 0.652008 | − | 0.758212i | \(-0.273927\pi\) | ||||
0.652008 | + | 0.758212i | \(0.273927\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.2694 | 1.08854 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.2280 | −0.379859 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.6942 | 1.24965 | 0.624825 | − | 0.780765i | \(-0.285170\pi\) | ||||
0.624825 | + | 0.780765i | \(0.285170\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.3418 | 1.01266 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.3231 | 1.26949 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.99072 | 0.0735288 | 0.0367644 | − | 0.999324i | \(-0.488295\pi\) | ||||
0.0367644 | + | 0.999324i | \(0.488295\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.7537 | −0.985485 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.565193 | −0.0207910 | −0.0103955 | − | 0.999946i | \(-0.503309\pi\) | ||||
−0.0103955 | + | 0.999946i | \(0.503309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.05654 | −0.185757 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.1044 | −0.407380 | −0.203690 | − | 0.979035i | \(-0.565293\pi\) | ||||
−0.203690 | + | 0.979035i | \(0.565293\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.3020 | 1.07354 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.558584 | 0.0204375 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.12656 | 0.187071 | 0.0935354 | − | 0.995616i | \(-0.470183\pi\) | ||||
0.0935354 | + | 0.995616i | \(0.470183\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.1324 | 0.442127 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.0593425 | 0.00215969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.1635 | −0.660164 | −0.330082 | − | 0.943952i | \(-0.607076\pi\) | ||||
−0.330082 | + | 0.943952i | \(0.607076\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.7960 | −0.718548 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.00837 | −0.109053 | −0.0545266 | − | 0.998512i | \(-0.517365\pi\) | ||||
−0.0545266 | + | 0.998512i | \(0.517365\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.266253 | 0.00962641 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.87768 | 0.320554 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.5047 | −0.450930 | −0.225465 | − | 0.974251i | \(-0.572390\pi\) | ||||
−0.225465 | + | 0.974251i | \(0.572390\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.05009 | −0.289917 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.6308 | −0.526235 | −0.263117 | − | 0.964764i | \(-0.584751\pi\) | ||||
−0.263117 | + | 0.964764i | \(0.584751\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.8766 | 0.390698 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.08103 | −0.253704 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.2699 | −1.36941 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.7212 | 0.740516 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.13122 | −0.111758 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.5644 | −0.875625 | −0.437813 | − | 0.899066i | \(-0.644247\pi\) | ||||
−0.437813 | + | 0.899066i | \(0.644247\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −33.9005 | −1.20689 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.7074 | −0.735340 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.22139 | 0.185184 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.9870 | 0.566290 | 0.283145 | − | 0.959077i | \(-0.408622\pi\) | ||||
0.283145 | + | 0.959077i | \(0.408622\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.9184 | 1.30608 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.260831 | 0.00921600 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.7401 | −0.767191 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.9102 | 0.419257 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.9841 | −0.491655 | −0.245827 | − | 0.969314i | \(-0.579060\pi\) | ||||
−0.245827 | + | 0.969314i | \(0.579060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.5695 | 1.67039 | 0.835196 | − | 0.549953i | \(-0.185354\pi\) | ||||
0.835196 | + | 0.549953i | \(0.185354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.8836 | 1.67935 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.8677 | 0.765991 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.81873 | 0.273543 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.9428 | −1.18461 | −0.592306 | − | 0.805713i | \(-0.701782\pi\) | ||||
−0.592306 | + | 0.805713i | \(0.701782\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.3697 | −0.500897 | −0.250448 | − | 0.968130i | \(-0.580578\pi\) | ||||
−0.250448 | + | 0.968130i | \(0.580578\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.8436 | 0.934575 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.4511 | −0.815474 | −0.407737 | − | 0.913099i | \(-0.633682\pi\) | ||||
−0.407737 | + | 0.913099i | \(0.633682\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.1483 | 1.25548 | 0.627741 | − | 0.778422i | \(-0.283980\pi\) | ||||
0.627741 | + | 0.778422i | \(0.283980\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.6890 | 0.821761 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.8687 | −0.895224 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.0351 | −0.761646 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.6909 | 1.16314 | 0.581569 | − | 0.813497i | \(-0.302439\pi\) | ||||
0.581569 | + | 0.813497i | \(0.302439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2989 | −0.458582 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.5776 | −0.364311 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.78846 | −0.233530 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.0190 | −0.927289 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.59433 | 0.260330 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.1231 | −1.61347 | −0.806733 | − | 0.590917i | \(-0.798766\pi\) | ||||
−0.806733 | + | 0.590917i | \(0.798766\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0606520 | 0.00207425 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.80685 | −0.164199 | −0.0820994 | − | 0.996624i | \(-0.526162\pi\) | ||||
−0.0820994 | + | 0.996624i | \(0.526162\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.2753 | −0.657663 | −0.328832 | − | 0.944389i | \(-0.606655\pi\) | ||||
−0.328832 | + | 0.944389i | \(0.606655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.74668 | −0.0594577 | −0.0297288 | − | 0.999558i | \(-0.509464\pi\) | ||||
−0.0297288 | + | 0.999558i | \(0.509464\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.0362 | 1.05526 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.90756 | −0.132708 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.40195 | 0.115403 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.0083 | 0.440771 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.272423 | 0.00922013 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.0397 | 1.41958 | 0.709790 | − | 0.704413i | \(-0.248790\pi\) | ||||
0.709790 | + | 0.704413i | \(0.248790\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 49.2873 | 1.66242 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.6661 | 1.33639 | 0.668193 | − | 0.743988i | \(-0.267068\pi\) | ||||
0.668193 | + | 0.743988i | \(0.267068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.3442 | −0.381761 | −0.190881 | − | 0.981613i | \(-0.561134\pi\) | ||||
−0.190881 | + | 0.981613i | \(0.561134\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.08505 | 0.271776 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.09158 | 0.103805 | 0.0519025 | − | 0.998652i | \(-0.483472\pi\) | ||||
0.0519025 | + | 0.998652i | \(0.483472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −53.6761 | −1.79822 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.40992 | 0.281427 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.2685 | −1.07862 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.62531 | 0.321380 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.6967 | −0.556867 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.56484 | 0.285336 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.48953 | −0.0495135 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.2594 | 0.639499 | 0.319750 | − | 0.947502i | \(-0.396401\pi\) | ||||
0.319750 | + | 0.947502i | \(0.396401\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.274303 | 0.00909805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.7350 | −1.18395 | −0.591977 | − | 0.805955i | \(-0.701652\pi\) | ||||
−0.591977 | + | 0.805955i | \(0.701652\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −86.5639 | −2.86485 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.8585 | −0.623444 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.8292 | −1.34683 | −0.673416 | − | 0.739264i | \(-0.735174\pi\) | ||||
−0.673416 | + | 0.739264i | \(0.735174\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.2999 | −0.833659 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.6078 | 0.612484 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.2980 | −0.338597 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.273636 | −0.00898738 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.4124 | −0.833755 | −0.416877 | − | 0.908963i | \(-0.636876\pi\) | ||||
−0.416877 | + | 0.908963i | \(0.636876\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.7274 | 1.16966 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −41.2614 | −1.34939 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.7066 | 1.06848 | 0.534239 | − | 0.845333i | \(-0.320598\pi\) | ||||
0.534239 | + | 0.845333i | \(0.320598\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.1218 | 0.558748 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.5311 | 0.636695 | 0.318347 | − | 0.947974i | \(-0.396872\pi\) | ||||
0.318347 | + | 0.947974i | \(0.396872\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.4790 | 0.438937 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.60632 | 0.0846941 | 0.0423470 | − | 0.999103i | \(-0.486516\pi\) | ||||
0.0423470 | + | 0.999103i | \(0.486516\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5706 | 0.343136 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.5484 | −0.731182 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −57.7638 | −1.87115 | −0.935577 | − | 0.353123i | \(-0.885120\pi\) | ||||
−0.935577 | + | 0.353123i | \(0.885120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.7619 | −0.348246 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −41.2079 | −1.33206 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.2445 | −0.427243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0809064 | 0.00260717 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.4145 | 0.753738 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.7179 | −0.730557 | −0.365279 | − | 0.930898i | \(-0.619026\pi\) | ||||
−0.365279 | + | 0.930898i | \(0.619026\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.55387 | −0.242665 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.5521 | −1.59020 | −0.795101 | − | 0.606478i | \(-0.792582\pi\) | ||||
−0.795101 | + | 0.606478i | \(0.792582\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.0521 | −0.418001 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.0651 | −0.641940 | −0.320970 | − | 0.947089i | \(-0.604009\pi\) | ||||
−0.320970 | + | 0.947089i | \(0.604009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.4210 | −1.29186 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.725878 | −0.0231755 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.3692 | 0.904837 | 0.452419 | − | 0.891806i | \(-0.350561\pi\) | ||||
0.452419 | + | 0.891806i | \(0.350561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.8158 | −0.344620 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.8832 | −0.473260 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7050 | 0.562417 | 0.281209 | − | 0.959647i | \(-0.409265\pi\) | ||||
0.281209 | + | 0.959647i | \(0.409265\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35.0751 | 1.11308 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.3063 | −0.707156 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.2816 | −1.56077 | −0.780383 | − | 0.625302i | \(-0.784976\pi\) | ||||
−0.780383 | + | 0.625302i | \(0.784976\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.8631 | 0.660078 |
(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 | 7448.2.a.bu.1.5 | ✓ | 14 | |
7.6 | odd | 2 | 7448.2.a.bx.1.10 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7448.2.a.bu.1.5 | ✓ | 14 | 1.1 | even | 1 | trivial | |
7448.2.a.bx.1.10 | yes | 14 | 7.6 | odd | 2 |