Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.75645.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 13x^{2} + 22x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.20386\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.20386 | 0.538381 | 0.269190 | − | 0.963087i | \(-0.413244\pi\) | ||||
0.269190 | + | 0.963087i | \(0.413244\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.02422 | −0.610325 | −0.305162 | − | 0.952300i | \(-0.598711\pi\) | ||||
−0.305162 | + | 0.952300i | \(0.598711\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.90542 | −1.08317 | −0.541584 | − | 0.840647i | \(-0.682175\pi\) | ||||
−0.541584 | + | 0.840647i | \(0.682175\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.20386 | 0.310834 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.70156 | 1.14030 | 0.570148 | − | 0.821542i | \(-0.306886\pi\) | ||||
0.570148 | + | 0.821542i | \(0.306886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.02422 | 0.923219 | 0.461609 | − | 0.887083i | \(-0.347272\pi\) | ||||
0.461609 | + | 0.887083i | \(0.347272\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.55073 | −0.710146 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.10927 | 0.948768 | 0.474384 | − | 0.880318i | \(-0.342671\pi\) | ||||
0.474384 | + | 0.880318i | \(0.342671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.10927 | 0.917653 | 0.458826 | − | 0.888526i | \(-0.348270\pi\) | ||||
0.458826 | + | 0.888526i | \(0.348270\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.02422 | −0.352371 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.20386 | 0.203489 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.70156 | −0.444134 | −0.222067 | − | 0.975031i | \(-0.571280\pi\) | ||||
−0.222067 | + | 0.975031i | \(0.571280\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.90542 | −0.625367 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.61651 | 0.252456 | 0.126228 | − | 0.992001i | \(-0.459713\pi\) | ||||
0.126228 | + | 0.992001i | \(0.459713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.55073 | 0.998977 | 0.499488 | − | 0.866321i | \(-0.333521\pi\) | ||||
0.499488 | + | 0.866321i | \(0.333521\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.20386 | 0.179460 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.13349 | −1.04053 | −0.520263 | − | 0.854006i | \(-0.674166\pi\) | ||||
−0.520263 | + | 0.854006i | \(0.674166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.70156 | 0.658350 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.69204 | −1.05658 | −0.528291 | − | 0.849063i | \(-0.677167\pi\) | ||||
−0.528291 | + | 0.849063i | \(0.677167\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.43687 | −0.328587 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.02422 | 0.533021 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.52651 | 0.589302 | 0.294651 | − | 0.955605i | \(-0.404797\pi\) | ||||
0.294651 | + | 0.955605i | \(0.404797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.58276 | 0.586763 | 0.293381 | − | 0.955996i | \(-0.405219\pi\) | ||||
0.293381 | + | 0.955996i | \(0.405219\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.70156 | −0.583157 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.96626 | 0.362386 | 0.181193 | − | 0.983448i | \(-0.442004\pi\) | ||||
0.181193 | + | 0.983448i | \(0.442004\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.14302 | 0.966398 | 0.483199 | − | 0.875510i | \(-0.339475\pi\) | ||||
0.483199 | + | 0.875510i | \(0.339475\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.34687 | 0.625804 | 0.312902 | − | 0.949785i | \(-0.398699\pi\) | ||||
0.312902 | + | 0.949785i | \(0.398699\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.55073 | −0.410003 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.02422 | −0.230681 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.46396 | 0.952270 | 0.476135 | − | 0.879372i | \(-0.342037\pi\) | ||||
0.476135 | + | 0.879372i | \(0.342037\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.51240 | −0.714829 | −0.357414 | − | 0.933946i | \(-0.616342\pi\) | ||||
−0.357414 | + | 0.933946i | \(0.616342\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.66000 | 0.613914 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.10927 | 0.547772 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.31313 | −0.245191 | −0.122596 | − | 0.992457i | \(-0.539122\pi\) | ||||
−0.122596 | + | 0.992457i | \(0.539122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.90542 | −0.409399 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.10927 | 0.529807 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.84458 | 0.497043 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.46396 | 0.453247 | 0.226623 | − | 0.973982i | \(-0.427231\pi\) | ||||
0.226623 | + | 0.973982i | \(0.427231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.02422 | −0.203442 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.87661 | −0.883256 | −0.441628 | − | 0.897198i | \(-0.645599\pi\) | ||||
−0.441628 | + | 0.897198i | \(0.645599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.08047 | −0.796192 | −0.398096 | − | 0.917344i | \(-0.630329\pi\) | ||||
−0.398096 | + | 0.917344i | \(0.630329\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.20386 | 0.117484 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.73531 | 0.554453 | 0.277226 | − | 0.960805i | \(-0.410585\pi\) | ||||
0.277226 | + | 0.960805i | \(0.410585\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.32094 | −0.605437 | −0.302718 | − | 0.953080i | \(-0.597894\pi\) | ||||
−0.302718 | + | 0.953080i | \(0.597894\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.70156 | −0.256421 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.84458 | 0.267596 | 0.133798 | − | 0.991009i | \(-0.457283\pi\) | ||||
0.133798 | + | 0.991009i | \(0.457283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.20386 | 0.112260 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.90542 | −0.361056 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.70156 | 0.430991 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.90254 | −0.627504 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.61651 | 0.145755 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.2938 | −0.920710 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2235 | 1.08466 | 0.542329 | − | 0.840166i | \(-0.317542\pi\) | ||||
0.542329 | + | 0.840166i | \(0.317542\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.55073 | 0.576760 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5444 | 1.44549 | 0.722747 | − | 0.691113i | \(-0.242879\pi\) | ||||
0.722747 | + | 0.691113i | \(0.242879\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.02422 | 0.348944 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.20386 | 0.103611 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.5975 | 0.990837 | 0.495419 | − | 0.868654i | \(-0.335015\pi\) | ||||
0.495419 | + | 0.868654i | \(0.335015\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.65542 | −0.734143 | −0.367071 | − | 0.930193i | \(-0.619640\pi\) | ||||
−0.367071 | + | 0.930193i | \(0.619640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.13349 | −0.600748 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.90542 | 0.661084 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.15083 | 0.510799 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.84287 | 0.806359 | 0.403180 | − | 0.915121i | \(-0.367905\pi\) | ||||
0.403180 | + | 0.915121i | \(0.367905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.4726 | 1.50328 | 0.751638 | − | 0.659576i | \(-0.229264\pi\) | ||||
0.751638 | + | 0.659576i | \(0.229264\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.70156 | 0.380099 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.15083 | 0.494047 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0614 | 1.60108 | 0.800538 | − | 0.599282i | \(-0.204547\pi\) | ||||
0.800538 | + | 0.599282i | \(0.204547\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.69204 | −0.610018 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.23589 | 0.566759 | 0.283379 | − | 0.959008i | \(-0.408544\pi\) | ||||
0.283379 | + | 0.959008i | \(0.408544\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.43687 | −0.189710 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.1897 | 1.33018 | 0.665091 | − | 0.746762i | \(-0.268393\pi\) | ||||
0.665091 | + | 0.746762i | \(0.268393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.25229 | 0.173253 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.02422 | 0.307740 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.15771 | 0.544191 | 0.272095 | − | 0.962270i | \(-0.412283\pi\) | ||||
0.272095 | + | 0.962270i | \(0.412283\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.55073 | −0.268410 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.52651 | 0.340233 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.36938 | −0.326583 | −0.163291 | − | 0.986578i | \(-0.552211\pi\) | ||||
−0.163291 | + | 0.986578i | \(0.552211\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.7309 | −1.83824 | −0.919118 | − | 0.393981i | \(-0.871097\pi\) | ||||
−0.919118 | + | 0.393981i | \(0.871097\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.58276 | 0.338768 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.25229 | −0.239113 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.51699 | −0.695951 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.0118 | 1.08622 | 0.543108 | − | 0.839663i | \(-0.317247\pi\) | ||||
0.543108 | + | 0.839663i | \(0.317247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.08506 | −0.222067 | −0.111034 | − | 0.993817i | \(-0.535416\pi\) | ||||
−0.111034 | + | 0.993817i | \(0.535416\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.70156 | −0.336686 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.66782 | 0.118827 | 0.0594136 | − | 0.998233i | \(-0.481077\pi\) | ||||
0.0594136 | + | 0.998233i | \(0.481077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.764112 | −0.0541664 | −0.0270832 | − | 0.999633i | \(-0.508622\pi\) | ||||
−0.0270832 | + | 0.999633i | \(0.508622\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.96626 | 0.209224 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.10927 | 0.358601 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.94604 | 0.135917 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.14589 | −0.563463 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.95673 | −0.272393 | −0.136196 | − | 0.990682i | \(-0.543488\pi\) | ||||
−0.136196 | + | 0.990682i | \(0.543488\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.14302 | 0.557950 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.88614 | 0.537830 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.10927 | 0.346840 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.34687 | 0.361308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.3616 | −1.23513 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6600 | 0.780812 | 0.390406 | − | 0.920643i | \(-0.372335\pi\) | ||||
0.390406 | + | 0.920643i | \(0.372335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.55073 | −0.236715 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.6600 | 1.03939 | 0.519696 | − | 0.854352i | \(-0.326045\pi\) | ||||
0.519696 | + | 0.854352i | \(0.326045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.8419 | −1.37727 | −0.688637 | − | 0.725106i | \(-0.741791\pi\) | ||||
−0.688637 | + | 0.725106i | \(0.741791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.02422 | −0.133184 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.48989 | 0.621703 | 0.310852 | − | 0.950458i | \(-0.399386\pi\) | ||||
0.310852 | + | 0.950458i | \(0.399386\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.58770 | −0.560200 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.46396 | 0.549793 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.0925 | −1.62310 | −0.811550 | − | 0.584283i | \(-0.801376\pi\) | ||||
−0.811550 | + | 0.584283i | \(0.801376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.09170 | 0.263570 | 0.131785 | − | 0.991278i | \(-0.457929\pi\) | ||||
0.131785 | + | 0.991278i | \(0.457929\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.20386 | 0.0769116 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.7163 | −1.00000 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.51240 | −0.412707 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8108 | 1.37669 | 0.688344 | − | 0.725385i | \(-0.258338\pi\) | ||||
0.688344 | + | 0.725385i | \(0.258338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.02422 | −0.127261 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.66000 | 0.354443 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.3181 | 0.643623 | 0.321812 | − | 0.946804i | \(-0.395708\pi\) | ||||
0.321812 | + | 0.946804i | \(0.395708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.70156 | −0.167867 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.10927 | 0.316256 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.8835 | 1.84269 | 0.921347 | − | 0.388740i | \(-0.127090\pi\) | ||||
0.921347 | + | 0.388740i | \(0.127090\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.26011 | −0.568844 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.31313 | −0.141561 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.71625 | −0.470468 | −0.235234 | − | 0.971939i | \(-0.575586\pi\) | ||||
−0.235234 | + | 0.971939i | \(0.575586\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.45937 | 0.331633 | 0.165817 | − | 0.986157i | \(-0.446974\pi\) | ||||
0.165817 | + | 0.986157i | \(0.446974\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.90542 | −0.236367 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.18745 | 0.433420 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.62661 | 0.458239 | 0.229119 | − | 0.973398i | \(-0.426415\pi\) | ||||
0.229119 | + | 0.973398i | \(0.426415\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.10927 | 0.305884 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.5202 | −1.22413 | −0.612067 | − | 0.790806i | \(-0.709662\pi\) | ||||
−0.612067 | + | 0.790806i | \(0.709662\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.31636 | 0.0782493 | 0.0391246 | − | 0.999234i | \(-0.487543\pi\) | ||||
0.0391246 | + | 0.999234i | \(0.487543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.84458 | 0.286968 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.61651 | 0.0954193 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.10469 | 0.300276 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.46396 | 0.261682 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.1545 | −0.943755 | −0.471878 | − | 0.881664i | \(-0.656424\pi\) | ||||
−0.471878 | + | 0.881664i | \(0.656424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.44927 | 0.317269 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.02422 | −0.117457 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.90542 | −0.225856 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.55073 | 0.377578 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.87661 | −0.509948 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.51699 | 0.315902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.23095 | −0.0702541 | −0.0351271 | − | 0.999383i | \(-0.511184\pi\) | ||||
−0.0351271 | + | 0.999383i | \(0.511184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.08047 | −0.459682 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.2483 | −1.54511 | −0.772554 | − | 0.634949i | \(-0.781021\pi\) | ||||
−0.772554 | + | 0.634949i | \(0.781021\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.27422 | 0.0720232 | 0.0360116 | − | 0.999351i | \(-0.488535\pi\) | ||||
0.0360116 | + | 0.999351i | \(0.488535\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.20386 | 0.0678296 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.3694 | −0.582402 | −0.291201 | − | 0.956662i | \(-0.594055\pi\) | ||||
−0.291201 | + | 0.956662i | \(0.594055\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.3423 | −0.579057 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.73531 | 0.320114 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.9201 | 1.05274 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.8671 | 0.769208 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.32094 | −0.349549 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.13349 | −0.393282 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.12890 | −0.226945 | −0.113473 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113473 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.70156 | −0.148045 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.57095 | 0.195102 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8864 | −0.647492 | −0.323746 | − | 0.946144i | \(-0.604942\pi\) | ||||
−0.323746 | + | 0.946144i | \(0.604942\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.84458 | 0.154496 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.3423 | −0.560066 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.20386 | 0.0648134 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.8717 | 1.01308 | 0.506542 | − | 0.862215i | \(-0.330923\pi\) | ||||
0.506542 | + | 0.862215i | \(0.330923\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0776 | −0.860614 | −0.430307 | − | 0.902683i | \(-0.641595\pi\) | ||||
−0.430307 | + | 0.902683i | \(0.641595\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.90542 | −0.208456 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.5124 | 0.985316 | 0.492658 | − | 0.870223i | \(-0.336025\pi\) | ||||
0.492658 | + | 0.870223i | \(0.336025\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.80302 | 0.520290 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.70156 | 0.248833 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.1462 | 0.693832 | 0.346916 | − | 0.937896i | \(-0.387229\pi\) | ||||
0.346916 | + | 0.937896i | \(0.387229\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.80567 | −0.147667 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.90254 | −0.362289 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.43687 | 0.336921 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.8013 | −1.50342 | −0.751708 | − | 0.659496i | \(-0.770770\pi\) | ||||
−0.751708 | + | 0.659496i | \(0.770770\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.61651 | 0.0841519 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.69204 | −0.399351 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.9830 | −1.13824 | −0.569119 | − | 0.822255i | \(-0.692715\pi\) | ||||
−0.569119 | + | 0.822255i | \(0.692715\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.2938 | −0.531572 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.9539 | −1.02768 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.4516 | 1.10189 | 0.550946 | − | 0.834541i | \(-0.314267\pi\) | ||||
0.550946 | + | 0.834541i | \(0.314267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.2235 | 0.626228 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.9731 | −1.02058 | −0.510290 | − | 0.860003i | \(-0.670462\pi\) | ||||
−0.510290 | + | 0.860003i | \(0.670462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.43687 | −0.124194 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.55073 | 0.332992 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.881549 | 0.0446963 | 0.0223482 | − | 0.999750i | \(-0.492886\pi\) | ||||
0.0223482 | + | 0.999750i | \(0.492886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.70156 | 0.237768 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.5444 | 0.834556 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.1894 | 0.512684 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.4561 | 0.725533 | 0.362767 | − | 0.931880i | \(-0.381832\pi\) | ||||
0.362767 | + | 0.931880i | \(0.381832\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.02422 | 0.201463 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.72901 | 0.286093 | 0.143046 | − | 0.989716i | \(-0.454310\pi\) | ||||
0.143046 | + | 0.989716i | \(0.454310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.9539 | −0.993972 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.20386 | 0.0598201 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.46855 | 0.271066 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.8187 | 1.17776 | 0.588878 | − | 0.808222i | \(-0.299570\pi\) | ||||
0.588878 | + | 0.808222i | \(0.299570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.5975 | 0.572060 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.52651 | 0.222735 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.83999 | −0.384850 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.65542 | −0.423858 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.3583 | 1.14113 | 0.570565 | − | 0.821253i | \(-0.306724\pi\) | ||||
0.570565 | + | 0.821253i | \(0.306724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.9302 | −1.31250 | −0.656249 | − | 0.754544i | \(-0.727858\pi\) | ||||
−0.656249 | + | 0.754544i | \(0.727858\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.13349 | −0.346842 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.6940 | −0.809777 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.58276 | 0.221775 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.90542 | 0.381677 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.2765 | −0.832180 | −0.416090 | − | 0.909323i | \(-0.636600\pi\) | ||||
−0.416090 | + | 0.909323i | \(0.636600\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.01298 | −0.288965 | −0.144483 | − | 0.989507i | \(-0.546152\pi\) | ||||
−0.144483 | + | 0.989507i | \(0.546152\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.15083 | 0.294910 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.02422 | 0.192504 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.63291 | −0.0779345 | −0.0389673 | − | 0.999240i | \(-0.512407\pi\) | ||||
−0.0389673 | + | 0.999240i | \(0.512407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.9031 | −1.08816 | −0.544080 | − | 0.839033i | \(-0.683121\pi\) | ||||
−0.544080 | + | 0.839033i | \(0.683121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.78468 | −0.132006 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.84287 | 0.465552 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.4865 | 0.730852 | 0.365426 | − | 0.930840i | \(-0.380923\pi\) | ||||
0.365426 | + | 0.930840i | \(0.380923\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.27216 | −0.154080 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.4726 | 0.867916 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.70156 | −0.220413 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.0925 | −1.26733 | −0.633667 | − | 0.773606i | \(-0.718451\pi\) | ||||
−0.633667 | + | 0.773606i | \(0.718451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.70156 | 0.219450 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.9022 | −0.694064 | −0.347032 | − | 0.937853i | \(-0.612811\pi\) | ||||
−0.347032 | + | 0.937853i | \(0.612811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.2519 | −0.848240 | −0.424120 | − | 0.905606i | \(-0.639416\pi\) | ||||
−0.424120 | + | 0.905606i | \(0.639416\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.15083 | 0.285238 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.0216 | −1.01904 | −0.509518 | − | 0.860460i | \(-0.670176\pi\) | ||||
−0.509518 | + | 0.860460i | \(0.670176\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.96626 | 0.136969 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.0614 | 0.924381 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.2601 | −0.609700 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.2889 | −0.655620 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.69204 | −0.352194 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.3324 | −0.472100 | −0.236050 | − | 0.971741i | \(-0.575853\pi\) | ||||
−0.236050 | + | 0.971741i | \(0.575853\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5507 | 0.481072 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.37397 | 0.244019 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.8480 | 0.536886 | 0.268443 | − | 0.963296i | \(-0.413491\pi\) | ||||
0.268443 | + | 0.963296i | \(0.413491\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.23589 | 0.327218 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4821 | 0.788955 | 0.394478 | − | 0.918906i | \(-0.370926\pi\) | ||||
0.394478 | + | 0.918906i | \(0.370926\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.0216 | 1.08188 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.43687 | −0.109529 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.14302 | 0.365264 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.32437 | 0.104053 | 0.0520265 | − | 0.998646i | \(-0.483432\pi\) | ||||
0.0520265 | + | 0.998646i | \(0.483432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.1897 | 0.767981 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0135 | 1.07071 | 0.535355 | − | 0.844627i | \(-0.320178\pi\) | ||||
0.535355 | + | 0.844627i | \(0.320178\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.6862 | −0.475528 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.25229 | 0.100028 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.26963 | 0.189248 | 0.0946240 | − | 0.995513i | \(-0.469835\pi\) | ||||
0.0946240 | + | 0.995513i | \(0.469835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.34687 | 0.236532 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.02422 | 0.177674 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.72772 | −0.428655 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.4397 | 0.635059 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.15771 | 0.314189 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.47636 | 0.327545 | 0.163773 | − | 0.986498i | \(-0.447634\pi\) | ||||
0.163773 | + | 0.986498i | \(0.447634\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.2742 | −0.667895 | −0.333947 | − | 0.942592i | \(-0.608381\pi\) | ||||
−0.333947 | + | 0.942592i | \(0.608381\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.55073 | −0.154967 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.0216 | 1.04640 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.52651 | 0.196434 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.31313 | −0.273452 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.90448 | 0.298507 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.36938 | −0.188553 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.02422 | −0.0871892 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.4974 | 0.924243 | 0.462122 | − | 0.886817i | \(-0.347088\pi\) | ||||
0.462122 | + | 0.886817i | \(0.347088\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.7309 | −1.06131 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.60951 | −0.325956 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.84917 | 0.0790647 | 0.0395324 | − | 0.999218i | \(-0.487413\pi\) | ||||
0.0395324 | + | 0.999218i | \(0.487413\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.58276 | 0.195588 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.5608 | 0.875921 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.46396 | 0.359924 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.25229 | −0.138052 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.3448 | 1.62472 | 0.812361 | − | 0.583155i | \(-0.198182\pi\) | ||||
0.812361 | + | 0.583155i | \(0.198182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.5833 | −1.08206 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.51699 | −0.401808 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.4394 | −1.28287 | −0.641434 | − | 0.767179i | \(-0.721660\pi\) | ||||
−0.641434 | + | 0.767179i | \(0.721660\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.42447 | 0.144068 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.0084 | −0.964562 | −0.482281 | − | 0.876017i | \(-0.660192\pi\) | ||||
−0.482281 | + | 0.876017i | \(0.660192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.4876 | −1.77805 | −0.889025 | − | 0.457858i | \(-0.848617\pi\) | ||||
−0.889025 | + | 0.457858i | \(0.848617\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.0118 | 0.627128 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.55073 | −0.148076 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.4279 | −0.517381 | −0.258691 | − | 0.965960i | \(-0.583291\pi\) | ||||
−0.258691 | + | 0.965960i | \(0.583291\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.08506 | −0.128211 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.51240 | −0.270180 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.5704 | 0.644858 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.70156 | −0.194386 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.2384 | 1.86719 | 0.933594 | − | 0.358331i | \(-0.116654\pi\) | ||||
0.933594 | + | 0.358331i | \(0.116654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.5608 | 0.847194 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.66782 | 0.0686049 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.00459 | 0.287644 | 0.143822 | − | 0.989604i | \(-0.454061\pi\) | ||||
0.143822 | + | 0.989604i | \(0.454061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.66000 | 0.232038 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.764112 | −0.0312730 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.42563 | 0.0991086 | 0.0495543 | − | 0.998771i | \(-0.484220\pi\) | ||||
0.0495543 | + | 0.998771i | \(0.484220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.3301 | 1.27798 | 0.638991 | − | 0.769214i | \(-0.279352\pi\) | ||||
0.638991 | + | 0.769214i | \(0.279352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.96626 | 0.120795 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.30967 | −0.337836 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.517922 | −0.0210218 | −0.0105109 | − | 0.999945i | \(-0.503346\pi\) | ||||
−0.0105109 | + | 0.999945i | \(0.503346\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.10927 | 0.207038 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.8593 | 1.12707 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.8526 | 0.599892 | 0.299946 | − | 0.953956i | \(-0.403031\pi\) | ||||
0.299946 | + | 0.953956i | \(0.403031\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.94604 | 0.0784719 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.32759 | −0.0534469 | −0.0267234 | − | 0.999643i | \(-0.508507\pi\) | ||||
−0.0267234 | + | 0.999643i | \(0.508507\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5992 | −0.667177 | −0.333588 | − | 0.942719i | \(-0.608260\pi\) | ||||
−0.333588 | + | 0.942719i | \(0.608260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.31313 | −0.0926736 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.36134 | 0.214453 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.14589 | −0.325316 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.7016 | −0.506444 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.2500 | 1.36347 | 0.681735 | − | 0.731599i | \(-0.261226\pi\) | ||||
0.681735 | + | 0.731599i | \(0.261226\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.95673 | −0.157266 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.7153 | 0.583960 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.90542 | −0.154738 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.14302 | 0.322133 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0919 | 0.477603 | 0.238801 | − | 0.971068i | \(-0.423246\pi\) | ||||
0.238801 | + | 0.971068i | \(0.423246\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.8826 | −0.468603 | −0.234301 | − | 0.972164i | \(-0.575280\pi\) | ||||
−0.234301 | + | 0.972164i | \(0.575280\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.88614 | 0.310516 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.93803 | 0.351390 | 0.175695 | − | 0.984445i | \(-0.443783\pi\) | ||||
0.175695 | + | 0.984445i | \(0.443783\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.16265 | −0.359665 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.10927 | 0.200248 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.45133 | −0.369859 | −0.184930 | − | 0.982752i | \(-0.559206\pi\) | ||||
−0.184930 | + | 0.982752i | \(0.559206\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.9171 | 0.778226 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.34687 | 0.208601 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.85721 | 0.383982 | 0.191991 | − | 0.981397i | \(-0.438505\pi\) | ||||
0.191991 | + | 0.981397i | \(0.438505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0917 | 0.548104 | 0.274052 | − | 0.961715i | \(-0.411636\pi\) | ||||
0.274052 | + | 0.961715i | \(0.411636\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.3616 | −0.713104 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.84458 | 0.187865 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.10927 | 0.197832 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.6600 | 0.450802 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.27651 | −0.358116 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.0674 | 0.812087 | 0.406044 | − | 0.913854i | \(-0.366908\pi\) | ||||
0.406044 | + | 0.913854i | \(0.366908\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.55073 | −0.136668 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.88520 | 0.187754 | 0.0938768 | − | 0.995584i | \(-0.470074\pi\) | ||||
0.0938768 | + | 0.995584i | \(0.470074\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.46396 | 0.171311 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.6600 | 0.600093 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.604690 | −0.0231378 | −0.0115689 | − | 0.999933i | \(-0.503683\pi\) | ||||
−0.0115689 | + | 0.999933i | \(0.503683\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.9617 | 0.533448 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.8419 | −0.795169 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.0406 | 1.14446 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.84781 | 0.0702938 | 0.0351469 | − | 0.999382i | \(-0.488810\pi\) | ||||
0.0351469 | + | 0.999382i | \(0.488810\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.02422 | −0.0768937 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.4199 | −0.395248 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.60010 | 0.287874 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.48989 | 0.358941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.5403 | 1.38011 | 0.690053 | − | 0.723758i | \(-0.257587\pi\) | ||||
0.690053 | + | 0.723758i | \(0.257587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.8717 | −0.410033 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.58770 | −0.323431 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.87661 | −0.333839 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.3524 | −1.74080 | −0.870400 | − | 0.492345i | \(-0.836140\pi\) | ||||
−0.870400 | + | 0.492345i | \(0.836140\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.46396 | 0.317423 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.10927 | 0.191344 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.51699 | 0.355915 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.0925 | −0.937097 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.3088 | −1.54056 | −0.770279 | − | 0.637707i | \(-0.779883\pi\) | ||||
−0.770279 | + | 0.637707i | \(0.779883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.08047 | −0.300932 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.09170 | 0.152172 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.1417 | −0.673764 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5398 | 0.724693 | 0.362346 | − | 0.932044i | \(-0.381976\pi\) | ||||
0.362346 | + | 0.932044i | \(0.381976\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.7987 | 1.13913 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.7048 | 0.432326 | 0.216163 | − | 0.976357i | \(-0.430646\pi\) | ||||
0.216163 | + | 0.976357i | \(0.430646\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.20386 | 0.0444049 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.00435 | −0.221173 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.6184 | −1.86203 | −0.931015 | − | 0.364981i | \(-0.881075\pi\) | ||||
−0.931015 | + | 0.364981i | \(0.881075\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.7163 | −0.577351 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.68216 | 0.0617126 | 0.0308563 | − | 0.999524i | \(-0.490177\pi\) | ||||
0.0308563 | + | 0.999524i | \(0.490177\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8494 | 0.434128 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.51240 | −0.238276 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.73531 | 0.209563 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.9125 | −1.41994 | −0.709969 | − | 0.704233i | \(-0.751291\pi\) | ||||
−0.709969 | + | 0.704233i | \(0.751291\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.8108 | 0.794831 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.2383 | 0.809334 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.5719 | 0.493278 | 0.246639 | − | 0.969107i | \(-0.420674\pi\) | ||||
0.246639 | + | 0.969107i | \(0.420674\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.02422 | −0.0734745 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.3959 | 1.02935 | 0.514675 | − | 0.857385i | \(-0.327913\pi\) | ||||
0.514675 | + | 0.857385i | \(0.327913\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.32094 | −0.228834 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.66000 | 0.204638 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.6779 | −0.638313 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.1026 | 0.580676 | 0.290338 | − | 0.956924i | \(-0.406232\pi\) | ||||
0.290338 | + | 0.956924i | \(0.406232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3181 | 0.371596 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.0452 | 0.756944 | 0.378472 | − | 0.925613i | \(-0.376450\pi\) | ||||
0.378472 | + | 0.925613i | \(0.376450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.1417 | −0.651668 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.70156 | −0.0969180 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.50517 | 0.233072 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.4832 | −0.589817 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.10927 | 0.182591 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.1511 | 0.861988 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.4487 | −1.26361 | −0.631805 | − | 0.775128i | \(-0.717685\pi\) | ||||
−0.631805 | + | 0.775128i | \(0.717685\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.8835 | 1.06388 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.84458 | 0.101142 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.8976 | −0.635563 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.26011 | −0.328422 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.6327 | −0.730848 | −0.365424 | − | 0.930841i | \(-0.619076\pi\) | ||||
−0.365424 | + | 0.930841i | \(0.619076\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.5386 | −1.18651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.31313 | −0.0817305 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.8232 | −0.381944 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.20386 | 0.0424304 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.71625 | −0.271625 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.8910 | 0.734487 | 0.367243 | − | 0.930125i | \(-0.380302\pi\) | ||||
0.367243 | + | 0.930125i | \(0.380302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.1715 | −0.357169 | −0.178584 | − | 0.983925i | \(-0.557152\pi\) | ||||
−0.178584 | + | 0.983925i | \(0.557152\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.45937 | 0.191469 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.71097 | 0.305132 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.3616 | 0.922274 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.90542 | −0.136466 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.04385 | 0.176032 | 0.0880158 | − | 0.996119i | \(-0.471947\pi\) | ||||
0.0880158 | + | 0.996119i | \(0.471947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.9205 | −1.25211 | −0.626054 | − | 0.779779i | \(-0.715331\pi\) | ||||
−0.626054 | + | 0.779779i | \(0.715331\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.18745 | 0.250235 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.6078 | 0.994789 | 0.497395 | − | 0.867524i | \(-0.334290\pi\) | ||||
0.497395 | + | 0.867524i | \(0.334290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.1104 | −1.56675 | −0.783375 | − | 0.621549i | \(-0.786504\pi\) | ||||
−0.783375 | + | 0.621549i | \(0.786504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.62661 | 0.264564 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.70156 | 0.162899 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.6940 | 0.716145 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.10927 | 0.176602 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.1869 | −0.662404 | −0.331202 | − | 0.943560i | \(-0.607454\pi\) | ||||
−0.331202 | + | 0.943560i | \(0.607454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.89531 | −0.0998384 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.5202 | −0.706754 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.71144 | 0.0932762 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.90254 | −0.237174 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.31636 | 0.0451772 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.70156 | −0.0926084 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.1759 | 1.13592 | 0.567960 | − | 0.823056i | \(-0.307733\pi\) | ||||
0.567960 | + | 0.823056i | \(0.307733\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.84458 | 0.165681 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.2735 | 1.37572 | 0.687859 | − | 0.725845i | \(-0.258551\pi\) | ||||
0.687859 | + | 0.725845i | \(0.258551\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4527 | 0.561360 | 0.280680 | − | 0.959801i | \(-0.409440\pi\) | ||||
0.280680 | + | 0.959801i | \(0.409440\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.61651 | 0.0550904 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.71280 | −0.296587 | −0.148294 | − | 0.988943i | \(-0.547378\pi\) | ||||
−0.148294 | + | 0.988943i | \(0.547378\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.61685 | 0.292982 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.10469 | 0.173364 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.1329 | −0.581194 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.5845 | −0.392525 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.46396 | 0.151082 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.2938 | −0.347996 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.96797 | 0.0664536 | 0.0332268 | − | 0.999448i | \(-0.489422\pi\) | ||||
0.0332268 | + | 0.999448i | \(0.489422\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.1545 | −0.544877 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.8684 | 1.37689 | 0.688446 | − | 0.725287i | \(-0.258293\pi\) | ||||
0.688446 | + | 0.725287i | \(0.258293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.2243 | −0.680601 | −0.340300 | − | 0.940317i | \(-0.610529\pi\) | ||||
−0.340300 | + | 0.940317i | \(0.610529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.44927 | 0.183175 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.1038 | −1.44728 | −0.723641 | − | 0.690176i | \(-0.757533\pi\) | ||||
−0.723641 | + | 0.690176i | \(0.757533\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.2235 | 0.409963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.02422 | −0.0678139 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.7067 | −0.960634 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.26011 | −0.175826 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.90542 | −0.130398 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.1047 | 0.870640 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.1646 | −1.20482 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.55073 | 0.217995 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.7725 | −0.989672 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.08793 | −0.168942 | −0.0844710 | − | 0.996426i | \(-0.526920\pi\) | ||||
−0.0844710 | + | 0.996426i | \(0.526920\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.87661 | −0.294419 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.27686 | 0.207962 | 0.103981 | − | 0.994579i | \(-0.466842\pi\) | ||||
0.103981 | + | 0.994579i | \(0.466842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.1825 | 0.436278 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.51699 | 0.182386 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.5444 | 0.546345 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.1779 | −1.42431 | −0.712154 | − | 0.702023i | \(-0.752280\pi\) | ||||
−0.712154 | + | 0.702023i | \(0.752280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.23095 | −0.0405612 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.8019 | −1.04677 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.59252 | 0.315400 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.08047 | −0.265397 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.7142 | −1.27017 | −0.635086 | − | 0.772442i | \(-0.719035\pi\) | ||||
−0.635086 | + | 0.772442i | \(0.719035\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.02422 | 0.131888 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.2483 | −0.892069 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.4571 | −0.374687 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.1459 | 1.67086 | 0.835432 | − | 0.549594i | \(-0.185218\pi\) | ||||
0.835432 | + | 0.549594i | \(0.185218\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.27422 | 0.0415826 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.8730 | −1.56062 | −0.780308 | − | 0.625395i | \(-0.784938\pi\) | ||||
−0.780308 | + | 0.625395i | \(0.784938\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.61651 | 0.0526407 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.20386 | 0.0391614 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.7342 | −0.511292 | −0.255646 | − | 0.966770i | \(-0.582288\pi\) | ||||
−0.255646 | + | 0.966770i | \(0.582288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.8818 | −0.677851 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.3694 | −0.336250 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.4524 | −0.921663 | −0.460831 | − | 0.887488i | \(-0.652449\pi\) | ||||
−0.460831 | + | 0.887488i | \(0.652449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.0721 | 0.584798 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.3423 | −0.334319 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.5975 | 0.374501 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.89531 | −0.157913 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.73531 | 0.184818 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.71396 | −0.119557 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.7433 | −1.82474 | −0.912371 | − | 0.409363i | \(-0.865751\pi\) | ||||
−0.912371 | + | 0.409363i | \(0.865751\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.9201 | 0.607802 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.9001 | 1.08791 | 0.543953 | − | 0.839115i | \(-0.316927\pi\) | ||||
0.543953 | + | 0.839115i | \(0.316927\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.65542 | −0.277480 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.8671 | 0.444102 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.43745 | 0.141967 | 0.0709834 | − | 0.997477i | \(-0.477386\pi\) | ||||
0.0709834 | + | 0.997477i | \(0.477386\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.68228 | 0.149646 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.32094 | −0.201812 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.0517 | −1.78777 | −0.893885 | − | 0.448296i | \(-0.852031\pi\) | ||||
−0.893885 | + | 0.448296i | \(0.852031\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.00781 | 0.0639743 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.13349 | −0.227062 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.55073 | 0.208301 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.4218 | 0.807551 | 0.403775 | − | 0.914858i | \(-0.367698\pi\) | ||||
0.403775 | + | 0.914858i | \(0.367698\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.12890 | −0.131027 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.919881 | −0.0291622 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.6474 | −1.16063 | −0.580317 | − | 0.814391i | \(-0.697071\pi\) | ||||
−0.580317 | + | 0.814391i | \(0.697071\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.70156 | −0.0854736 |
(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 | 7728.2.a.cc.1.3 | 4 | ||
4.3 | odd | 2 | 3864.2.a.s.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.s.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
7728.2.a.cc.1.3 | 4 | 1.1 | even | 1 | trivial |