Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(1,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.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: | \(9.78167424761\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 175) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.19869\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.19869 | −1.55471 | −0.777355 | − | 0.629062i | \(-0.783439\pi\) | ||||
−0.777355 | + | 0.629062i | \(0.783439\pi\) | |||||||
\(3\) | 2.83424 | 1.63635 | 0.818176 | − | 0.574969i | \(-0.194986\pi\) | ||||
0.818176 | + | 0.574969i | \(0.194986\pi\) | |||||||
\(4\) | 2.83424 | 1.41712 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.23163 | −2.54405 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.83424 | −0.648503 | ||||||||
\(9\) | 5.03293 | 1.67764 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56314 | −0.772816 | −0.386408 | − | 0.922328i | \(-0.626284\pi\) | ||||
−0.386408 | + | 0.922328i | \(0.626284\pi\) | |||||||
\(12\) | 8.03293 | 2.31891 | ||||||||
\(13\) | −0.563139 | −0.156187 | −0.0780934 | − | 0.996946i | \(-0.524883\pi\) | ||||
−0.0780934 | + | 0.996946i | \(0.524883\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.63555 | −0.408888 | ||||||||
\(17\) | 5.19869 | 1.26087 | 0.630434 | − | 0.776243i | \(-0.282877\pi\) | ||||
0.630434 | + | 0.776243i | \(0.282877\pi\) | |||||||
\(18\) | −11.0659 | −2.60825 | ||||||||
\(19\) | 0.469795 | 0.107778 | 0.0538892 | − | 0.998547i | \(-0.482838\pi\) | ||||
0.0538892 | + | 0.998547i | \(0.482838\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.63555 | 1.20150 | ||||||||
\(23\) | 4.03293 | 0.840925 | 0.420462 | − | 0.907310i | \(-0.361868\pi\) | ||||
0.420462 | + | 0.907310i | \(0.361868\pi\) | |||||||
\(24\) | −5.19869 | −1.06118 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.23817 | 0.242825 | ||||||||
\(27\) | 5.76183 | 1.10886 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.86718 | 0.532422 | 0.266211 | − | 0.963915i | \(-0.414228\pi\) | ||||
0.266211 | + | 0.963915i | \(0.414228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.86718 | −0.694566 | −0.347283 | − | 0.937760i | \(-0.612896\pi\) | ||||
−0.347283 | + | 0.937760i | \(0.612896\pi\) | |||||||
\(32\) | 7.26456 | 1.28420 | ||||||||
\(33\) | −7.26456 | −1.26460 | ||||||||
\(34\) | −11.4303 | −1.96028 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 14.2646 | 2.37743 | ||||||||
\(37\) | 2.23163 | 0.366877 | 0.183439 | − | 0.983031i | \(-0.441277\pi\) | ||||
0.183439 | + | 0.983031i | \(0.441277\pi\) | |||||||
\(38\) | −1.03293 | −0.167564 | ||||||||
\(39\) | −1.59607 | −0.255576 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.30404 | 0.516004 | 0.258002 | − | 0.966144i | \(-0.416936\pi\) | ||||
0.258002 | + | 0.966144i | \(0.416936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4303 | 1.59061 | 0.795304 | − | 0.606211i | \(-0.207311\pi\) | ||||
0.795304 | + | 0.606211i | \(0.207311\pi\) | |||||||
\(44\) | −7.26456 | −1.09517 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.86718 | −1.30739 | ||||||||
\(47\) | 9.36445 | 1.36595 | 0.682973 | − | 0.730444i | \(-0.260687\pi\) | ||||
0.682973 | + | 0.730444i | \(0.260687\pi\) | |||||||
\(48\) | −4.63555 | −0.669084 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.7344 | 2.06322 | ||||||||
\(52\) | −1.59607 | −0.221336 | ||||||||
\(53\) | 10.7014 | 1.46995 | 0.734977 | − | 0.678092i | \(-0.237193\pi\) | ||||
0.734977 | + | 0.678092i | \(0.237193\pi\) | |||||||
\(54\) | −12.6685 | −1.72396 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.33151 | 0.176363 | ||||||||
\(58\) | −6.30404 | −0.827761 | ||||||||
\(59\) | 3.96052 | 0.515616 | 0.257808 | − | 0.966196i | \(-0.417000\pi\) | ||||
0.257808 | + | 0.966196i | \(0.417000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.86718 | −0.495141 | −0.247571 | − | 0.968870i | \(-0.579632\pi\) | ||||
−0.247571 | + | 0.968870i | \(0.579632\pi\) | |||||||
\(62\) | 8.50273 | 1.07985 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.7014 | −1.58768 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.9725 | 1.96608 | ||||||||
\(67\) | −7.66849 | −0.936855 | −0.468427 | − | 0.883502i | \(-0.655179\pi\) | ||||
−0.468427 | + | 0.883502i | \(0.655179\pi\) | |||||||
\(68\) | 14.7344 | 1.78680 | ||||||||
\(69\) | 11.4303 | 1.37605 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.73436 | −1.03658 | −0.518289 | − | 0.855206i | \(-0.673431\pi\) | ||||
−0.518289 | + | 0.855206i | \(0.673431\pi\) | |||||||
\(72\) | −9.23163 | −1.08796 | ||||||||
\(73\) | −11.3370 | −1.32689 | −0.663446 | − | 0.748224i | \(-0.730907\pi\) | ||||
−0.663446 | + | 0.748224i | \(0.730907\pi\) | |||||||
\(74\) | −4.90666 | −0.570387 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.33151 | 0.152735 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.50927 | 0.397347 | ||||||||
\(79\) | 5.15921 | 0.580457 | 0.290228 | − | 0.956957i | \(-0.406269\pi\) | ||||
0.290228 | + | 0.956957i | \(0.406269\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.23163 | 0.136847 | ||||||||
\(82\) | −7.26456 | −0.802236 | ||||||||
\(83\) | 3.13282 | 0.343872 | 0.171936 | − | 0.985108i | \(-0.444998\pi\) | ||||
0.171936 | + | 0.985108i | \(0.444998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −22.9330 | −2.47293 | ||||||||
\(87\) | 8.12628 | 0.871229 | ||||||||
\(88\) | 4.70142 | 0.501173 | ||||||||
\(89\) | −5.57514 | −0.590964 | −0.295482 | − | 0.955348i | \(-0.595480\pi\) | ||||
−0.295482 | + | 0.955348i | \(0.595480\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 11.4303 | 1.19169 | ||||||||
\(93\) | −10.9605 | −1.13655 | ||||||||
\(94\) | −20.5895 | −2.12365 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 20.5895 | 2.10141 | ||||||||
\(97\) | −15.2975 | −1.55323 | −0.776613 | − | 0.629978i | \(-0.783064\pi\) | ||||
−0.776613 | + | 0.629978i | \(0.783064\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.9001 | −1.29651 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.99346 | 0.496867 | 0.248434 | − | 0.968649i | \(-0.420084\pi\) | ||||
0.248434 | + | 0.968649i | \(0.420084\pi\) | |||||||
\(102\) | −32.3963 | −3.20771 | ||||||||
\(103\) | 20.0264 | 1.97326 | 0.986629 | − | 0.162980i | \(-0.0521104\pi\) | ||||
0.986629 | + | 0.162980i | \(0.0521104\pi\) | |||||||
\(104\) | 1.03293 | 0.101288 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23.5291 | −2.28535 | ||||||||
\(107\) | −11.3699 | −1.09917 | −0.549585 | − | 0.835438i | \(-0.685214\pi\) | ||||
−0.549585 | + | 0.835438i | \(0.685214\pi\) | |||||||
\(108\) | 16.3304 | 1.57140 | ||||||||
\(109\) | 8.96052 | 0.858262 | 0.429131 | − | 0.903242i | \(-0.358820\pi\) | ||||
0.429131 | + | 0.903242i | \(0.358820\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.32497 | 0.600340 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.8672 | −1.11637 | −0.558185 | − | 0.829716i | \(-0.688502\pi\) | ||||
−0.558185 | + | 0.829716i | \(0.688502\pi\) | |||||||
\(114\) | −2.92759 | −0.274194 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.12628 | 0.754506 | ||||||||
\(117\) | −2.83424 | −0.262026 | ||||||||
\(118\) | −8.70796 | −0.801633 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43032 | −0.402756 | ||||||||
\(122\) | 8.50273 | 0.769801 | ||||||||
\(123\) | 9.36445 | 0.844364 | ||||||||
\(124\) | −10.9605 | −0.984284 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4303 | −1.10301 | −0.551506 | − | 0.834171i | \(-0.685947\pi\) | ||||
−0.551506 | + | 0.834171i | \(0.685947\pi\) | |||||||
\(128\) | 13.3974 | 1.18417 | ||||||||
\(129\) | 29.5621 | 2.60279 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.99346 | 0.436280 | 0.218140 | − | 0.975917i | \(-0.430001\pi\) | ||||
0.218140 | + | 0.975917i | \(0.430001\pi\) | |||||||
\(132\) | −20.5895 | −1.79209 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16.8606 | 1.45654 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.53566 | −0.817676 | ||||||||
\(137\) | 0.509273 | 0.0435102 | 0.0217551 | − | 0.999763i | \(-0.493075\pi\) | ||||
0.0217551 | + | 0.999763i | \(0.493075\pi\) | |||||||
\(138\) | −25.1317 | −2.13936 | ||||||||
\(139\) | 22.2975 | 1.89125 | 0.945624 | − | 0.325261i | \(-0.105452\pi\) | ||||
0.945624 | + | 0.325261i | \(0.105452\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.5411 | 2.23517 | ||||||||
\(142\) | 19.2042 | 1.61158 | ||||||||
\(143\) | 1.44340 | 0.120704 | ||||||||
\(144\) | −8.23163 | −0.685969 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 24.9265 | 2.06293 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.32497 | 0.519909 | ||||||||
\(149\) | 10.4698 | 0.857719 | 0.428860 | − | 0.903371i | \(-0.358916\pi\) | ||||
0.428860 | + | 0.903371i | \(0.358916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.99346 | 0.813256 | 0.406628 | − | 0.913594i | \(-0.366705\pi\) | ||||
0.406628 | + | 0.913594i | \(0.366705\pi\) | |||||||
\(152\) | −0.861719 | −0.0698946 | ||||||||
\(153\) | 26.1647 | 2.11529 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.52366 | −0.362183 | ||||||||
\(157\) | −6.62355 | −0.528617 | −0.264308 | − | 0.964438i | \(-0.585144\pi\) | ||||
−0.264308 | + | 0.964438i | \(0.585144\pi\) | |||||||
\(158\) | −11.3435 | −0.902442 | ||||||||
\(159\) | 30.3304 | 2.40536 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.70796 | −0.212758 | ||||||||
\(163\) | −7.21962 | −0.565484 | −0.282742 | − | 0.959196i | \(-0.591244\pi\) | ||||
−0.282742 | + | 0.959196i | \(0.591244\pi\) | |||||||
\(164\) | 9.36445 | 0.731241 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.88811 | −0.534621 | ||||||||
\(167\) | 21.1712 | 1.63828 | 0.819139 | − | 0.573595i | \(-0.194452\pi\) | ||||
0.819139 | + | 0.573595i | \(0.194452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6829 | −0.975606 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.36445 | 0.180814 | ||||||||
\(172\) | 29.5621 | 2.25409 | ||||||||
\(173\) | 7.46980 | 0.567918 | 0.283959 | − | 0.958836i | \(-0.408352\pi\) | ||||
0.283959 | + | 0.958836i | \(0.408352\pi\) | |||||||
\(174\) | −17.8672 | −1.35451 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.19215 | 0.315995 | ||||||||
\(177\) | 11.2251 | 0.843729 | ||||||||
\(178\) | 12.2580 | 0.918777 | ||||||||
\(179\) | −0.728896 | −0.0544803 | −0.0272401 | − | 0.999629i | \(-0.508672\pi\) | ||||
−0.0272401 | + | 0.999629i | \(0.508672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00654 | −0.149145 | −0.0745726 | − | 0.997216i | \(-0.523759\pi\) | ||||
−0.0745726 | + | 0.997216i | \(0.523759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.9605 | −0.810225 | ||||||||
\(184\) | −7.39738 | −0.545342 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 24.0988 | 1.76701 | ||||||||
\(187\) | −13.3250 | −0.974418 | ||||||||
\(188\) | 26.5411 | 1.93571 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.12628 | 0.153852 | 0.0769261 | − | 0.997037i | \(-0.475489\pi\) | ||||
0.0769261 | + | 0.997037i | \(0.475489\pi\) | |||||||
\(192\) | −35.9989 | −2.59800 | ||||||||
\(193\) | −2.64101 | −0.190104 | −0.0950521 | − | 0.995472i | \(-0.530302\pi\) | ||||
−0.0950521 | + | 0.995472i | \(0.530302\pi\) | |||||||
\(194\) | 33.6345 | 2.41481 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.17122 | 0.439681 | 0.219840 | − | 0.975536i | \(-0.429446\pi\) | ||||
0.219840 | + | 0.975536i | \(0.429446\pi\) | |||||||
\(198\) | 28.3634 | 2.01570 | ||||||||
\(199\) | −22.7673 | −1.61393 | −0.806965 | − | 0.590599i | \(-0.798892\pi\) | ||||
−0.806965 | + | 0.590599i | \(0.798892\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.7344 | −1.53302 | ||||||||
\(202\) | −10.9791 | −0.772485 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 41.7607 | 2.92384 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −44.0318 | −3.06784 | ||||||||
\(207\) | 20.2975 | 1.41077 | ||||||||
\(208\) | 0.921044 | 0.0638629 | ||||||||
\(209\) | −1.20415 | −0.0832928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8672 | −1.09234 | −0.546171 | − | 0.837674i | \(-0.683915\pi\) | ||||
−0.546171 | + | 0.837674i | \(0.683915\pi\) | |||||||
\(212\) | 30.3304 | 2.08310 | ||||||||
\(213\) | −24.7553 | −1.69620 | ||||||||
\(214\) | 24.9989 | 1.70889 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.5686 | −0.719102 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −19.7014 | −1.33435 | ||||||||
\(219\) | −32.1317 | −2.17126 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.92759 | −0.196931 | ||||||||
\(222\) | −13.9067 | −0.933354 | ||||||||
\(223\) | 7.56314 | 0.506465 | 0.253233 | − | 0.967405i | \(-0.418506\pi\) | ||||
0.253233 | + | 0.967405i | \(0.418506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 26.0923 | 1.73563 | ||||||||
\(227\) | 13.3250 | 0.884409 | 0.442205 | − | 0.896914i | \(-0.354196\pi\) | ||||
0.442205 | + | 0.896914i | \(0.354196\pi\) | |||||||
\(228\) | 3.77383 | 0.249928 | ||||||||
\(229\) | −12.8212 | −0.847246 | −0.423623 | − | 0.905839i | \(-0.639242\pi\) | ||||
−0.423623 | + | 0.905839i | \(0.639242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.25910 | −0.345277 | ||||||||
\(233\) | −20.6135 | −1.35044 | −0.675219 | − | 0.737617i | \(-0.735951\pi\) | ||||
−0.675219 | + | 0.737617i | \(0.735951\pi\) | |||||||
\(234\) | 6.23163 | 0.407374 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.2251 | 0.730691 | ||||||||
\(237\) | 14.6225 | 0.949831 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4753 | −1.00101 | −0.500505 | − | 0.865733i | \(-0.666852\pi\) | ||||
−0.500505 | + | 0.865733i | \(0.666852\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0384 | 0.711045 | 0.355523 | − | 0.934668i | \(-0.384303\pi\) | ||||
0.355523 | + | 0.934668i | \(0.384303\pi\) | |||||||
\(242\) | 9.74090 | 0.626169 | ||||||||
\(243\) | −13.7948 | −0.884935 | ||||||||
\(244\) | −10.9605 | −0.701676 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.5895 | −1.31274 | ||||||||
\(247\) | −0.264560 | −0.0168336 | ||||||||
\(248\) | 7.09334 | 0.450428 | ||||||||
\(249\) | 8.87918 | 0.562695 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.8541 | −1.75813 | −0.879067 | − | 0.476698i | \(-0.841834\pi\) | ||||
−0.879067 | + | 0.476698i | \(0.841834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.3370 | −0.649880 | ||||||||
\(254\) | 27.3304 | 1.71486 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.05387 | −0.253367 | ||||||||
\(257\) | 14.5291 | 0.906302 | 0.453151 | − | 0.891434i | \(-0.350300\pi\) | ||||
0.453151 | + | 0.891434i | \(0.350300\pi\) | |||||||
\(258\) | −64.9978 | −4.04659 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.4303 | 0.893214 | ||||||||
\(262\) | −10.9791 | −0.678289 | ||||||||
\(263\) | −0.292035 | −0.0180077 | −0.00900384 | − | 0.999959i | \(-0.502866\pi\) | ||||
−0.00900384 | + | 0.999959i | \(0.502866\pi\) | |||||||
\(264\) | 13.3250 | 0.820095 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.8013 | −0.967024 | ||||||||
\(268\) | −21.7344 | −1.32764 | ||||||||
\(269\) | 8.53675 | 0.520495 | 0.260247 | − | 0.965542i | \(-0.416196\pi\) | ||||
0.260247 | + | 0.965542i | \(0.416196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.91211 | 0.176898 | 0.0884492 | − | 0.996081i | \(-0.471809\pi\) | ||||
0.0884492 | + | 0.996081i | \(0.471809\pi\) | |||||||
\(272\) | −8.50273 | −0.515554 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.11973 | −0.0676457 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 32.3963 | 1.95003 | ||||||||
\(277\) | −1.83970 | −0.110537 | −0.0552685 | − | 0.998472i | \(-0.517601\pi\) | ||||
−0.0552685 | + | 0.998472i | \(0.517601\pi\) | |||||||
\(278\) | −49.0253 | −2.94034 | ||||||||
\(279\) | −19.4633 | −1.16523 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.608077 | −0.0362748 | −0.0181374 | − | 0.999836i | \(-0.505774\pi\) | ||||
−0.0181374 | + | 0.999836i | \(0.505774\pi\) | |||||||
\(282\) | −58.3557 | −3.47503 | ||||||||
\(283\) | 11.6949 | 0.695188 | 0.347594 | − | 0.937645i | \(-0.386999\pi\) | ||||
0.347594 | + | 0.937645i | \(0.386999\pi\) | |||||||
\(284\) | −24.7553 | −1.46896 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.17360 | −0.187659 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 36.5621 | 2.15444 | ||||||||
\(289\) | 10.0264 | 0.589788 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −43.3568 | −2.54162 | ||||||||
\(292\) | −32.1317 | −1.88037 | ||||||||
\(293\) | −28.0253 | −1.63726 | −0.818628 | − | 0.574324i | \(-0.805265\pi\) | ||||
−0.818628 | + | 0.574324i | \(0.805265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.09334 | −0.237921 | ||||||||
\(297\) | −14.7684 | −0.856948 | ||||||||
\(298\) | −23.0198 | −1.33350 | ||||||||
\(299\) | −2.27110 | −0.131341 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −21.9725 | −1.26438 | ||||||||
\(303\) | 14.1527 | 0.813050 | ||||||||
\(304\) | −0.768374 | −0.0440693 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −57.5280 | −3.28866 | ||||||||
\(307\) | −5.55660 | −0.317132 | −0.158566 | − | 0.987348i | \(-0.550687\pi\) | ||||
−0.158566 | + | 0.987348i | \(0.550687\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 56.7597 | 3.22894 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.60808 | 0.374710 | 0.187355 | − | 0.982292i | \(-0.440009\pi\) | ||||
0.187355 | + | 0.982292i | \(0.440009\pi\) | |||||||
\(312\) | 2.92759 | 0.165742 | ||||||||
\(313\) | 11.9001 | 0.672634 | 0.336317 | − | 0.941749i | \(-0.390819\pi\) | ||||
0.336317 | + | 0.941749i | \(0.390819\pi\) | |||||||
\(314\) | 14.5631 | 0.821845 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.6225 | 0.822578 | ||||||||
\(317\) | −8.71035 | −0.489222 | −0.244611 | − | 0.969621i | \(-0.578660\pi\) | ||||
−0.244611 | + | 0.969621i | \(0.578660\pi\) | |||||||
\(318\) | −66.6872 | −3.73964 | ||||||||
\(319\) | −7.34898 | −0.411464 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.2251 | −1.79863 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.44232 | 0.135894 | ||||||||
\(324\) | 3.49073 | 0.193929 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.8737 | 0.879164 | ||||||||
\(327\) | 25.3963 | 1.40442 | ||||||||
\(328\) | −6.06041 | −0.334630 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.4687 | −0.685342 | −0.342671 | − | 0.939455i | \(-0.611332\pi\) | ||||
−0.342671 | + | 0.939455i | \(0.611332\pi\) | |||||||
\(332\) | 8.87918 | 0.487308 | ||||||||
\(333\) | 11.2316 | 0.615489 | ||||||||
\(334\) | −46.5490 | −2.54705 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.61462 | 0.196901 | 0.0984505 | − | 0.995142i | \(-0.468611\pi\) | ||||
0.0984505 | + | 0.995142i | \(0.468611\pi\) | |||||||
\(338\) | 27.8857 | 1.51678 | ||||||||
\(339\) | −33.6345 | −1.82677 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.91211 | 0.536771 | ||||||||
\(342\) | −5.19869 | −0.281113 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −19.1317 | −1.03151 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.4238 | −0.882948 | ||||||||
\(347\) | −21.8397 | −1.17242 | −0.586208 | − | 0.810160i | \(-0.699380\pi\) | ||||
−0.586208 | + | 0.810160i | \(0.699380\pi\) | |||||||
\(348\) | 23.0318 | 1.23464 | ||||||||
\(349\) | −3.69596 | −0.197840 | −0.0989201 | − | 0.995095i | \(-0.531539\pi\) | ||||
−0.0989201 | + | 0.995095i | \(0.531539\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.24471 | −0.173190 | ||||||||
\(352\) | −18.6201 | −0.992454 | ||||||||
\(353\) | 31.6434 | 1.68421 | 0.842104 | − | 0.539315i | \(-0.181317\pi\) | ||||
0.842104 | + | 0.539315i | \(0.181317\pi\) | |||||||
\(354\) | −24.6805 | −1.31175 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.8013 | −0.837468 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.60262 | 0.0847010 | ||||||||
\(359\) | −17.1383 | −0.904524 | −0.452262 | − | 0.891885i | \(-0.649383\pi\) | ||||
−0.452262 | + | 0.891885i | \(0.649383\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7793 | −0.988384 | ||||||||
\(362\) | 4.41177 | 0.231877 | ||||||||
\(363\) | −12.5566 | −0.659050 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 24.0988 | 1.25966 | ||||||||
\(367\) | −11.7882 | −0.615340 | −0.307670 | − | 0.951493i | \(-0.599549\pi\) | ||||
−0.307670 | + | 0.951493i | \(0.599549\pi\) | |||||||
\(368\) | −6.59607 | −0.343844 | ||||||||
\(369\) | 16.6290 | 0.865672 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −31.0648 | −1.61063 | ||||||||
\(373\) | −9.40393 | −0.486917 | −0.243458 | − | 0.969911i | \(-0.578282\pi\) | ||||
−0.243458 | + | 0.969911i | \(0.578282\pi\) | |||||||
\(374\) | 29.2975 | 1.51494 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.1767 | −0.885819 | ||||||||
\(377\) | −1.61462 | −0.0831572 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3490 | −0.891157 | −0.445579 | − | 0.895243i | \(-0.647002\pi\) | ||||
−0.445579 | + | 0.895243i | \(0.647002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.2305 | −1.80492 | ||||||||
\(382\) | −4.67503 | −0.239195 | ||||||||
\(383\) | −5.82116 | −0.297447 | −0.148724 | − | 0.988879i | \(-0.547516\pi\) | ||||
−0.148724 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(384\) | 37.9714 | 1.93772 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.80677 | 0.295557 | ||||||||
\(387\) | 52.4951 | 2.66848 | ||||||||
\(388\) | −43.3568 | −2.20111 | ||||||||
\(389\) | −26.6279 | −1.35009 | −0.675045 | − | 0.737777i | \(-0.735876\pi\) | ||||
−0.675045 | + | 0.737777i | \(0.735876\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.9660 | 1.06030 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.1527 | 0.713908 | ||||||||
\(394\) | −13.5686 | −0.683576 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −36.5621 | −1.83731 | ||||||||
\(397\) | −35.2305 | −1.76817 | −0.884085 | − | 0.467326i | \(-0.845217\pi\) | ||||
−0.884085 | + | 0.467326i | \(0.845217\pi\) | |||||||
\(398\) | 50.0582 | 2.50919 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.4369 | −1.22032 | −0.610159 | − | 0.792279i | \(-0.708895\pi\) | ||||
−0.610159 | + | 0.792279i | \(0.708895\pi\) | |||||||
\(402\) | 47.7871 | 2.38341 | ||||||||
\(403\) | 2.17776 | 0.108482 | ||||||||
\(404\) | 14.1527 | 0.704122 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.71997 | −0.283528 | ||||||||
\(408\) | −27.0264 | −1.33801 | ||||||||
\(409\) | 29.4873 | 1.45805 | 0.729026 | − | 0.684487i | \(-0.239974\pi\) | ||||
0.729026 | + | 0.684487i | \(0.239974\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.44340 | 0.0711979 | ||||||||
\(412\) | 56.7597 | 2.79635 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −44.6279 | −2.19334 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.09096 | −0.200576 | ||||||||
\(417\) | 63.1965 | 3.09475 | ||||||||
\(418\) | 2.64755 | 0.129496 | ||||||||
\(419\) | 9.74090 | 0.475874 | 0.237937 | − | 0.971281i | \(-0.423529\pi\) | ||||
0.237937 | + | 0.971281i | \(0.423529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.68942 | −0.131074 | −0.0655371 | − | 0.997850i | \(-0.520876\pi\) | ||||
−0.0655371 | + | 0.997850i | \(0.520876\pi\) | |||||||
\(422\) | 34.8870 | 1.69827 | ||||||||
\(423\) | 47.1307 | 2.29157 | ||||||||
\(424\) | −19.6290 | −0.953269 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 54.4292 | 2.63710 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −32.2251 | −1.55766 | ||||||||
\(429\) | 4.09096 | 0.197513 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.43686 | −0.454558 | −0.227279 | − | 0.973830i | \(-0.572983\pi\) | ||||
−0.227279 | + | 0.973830i | \(0.572983\pi\) | |||||||
\(432\) | −9.42377 | −0.453401 | ||||||||
\(433\) | 20.8541 | 1.00218 | 0.501092 | − | 0.865394i | \(-0.332932\pi\) | ||||
0.501092 | + | 0.865394i | \(0.332932\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 25.3963 | 1.21626 | ||||||||
\(437\) | 1.89465 | 0.0906335 | ||||||||
\(438\) | 70.6478 | 3.37568 | ||||||||
\(439\) | −22.5621 | −1.07683 | −0.538414 | − | 0.842680i | \(-0.680976\pi\) | ||||
−0.538414 | + | 0.842680i | \(0.680976\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.43686 | 0.306170 | ||||||||
\(443\) | 30.5961 | 1.45366 | 0.726832 | − | 0.686816i | \(-0.240992\pi\) | ||||
0.726832 | + | 0.686816i | \(0.240992\pi\) | |||||||
\(444\) | 17.9265 | 0.850754 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.6290 | −0.787406 | ||||||||
\(447\) | 29.6739 | 1.40353 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.25256 | 0.0591118 | 0.0295559 | − | 0.999563i | \(-0.490591\pi\) | ||||
0.0295559 | + | 0.999563i | \(0.490591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.46871 | −0.398776 | ||||||||
\(452\) | −33.6345 | −1.58203 | ||||||||
\(453\) | 28.3239 | 1.33077 | ||||||||
\(454\) | −29.2975 | −1.37500 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.44232 | −0.114372 | ||||||||
\(457\) | −23.7618 | −1.11153 | −0.555766 | − | 0.831339i | \(-0.687575\pi\) | ||||
−0.555766 | + | 0.831339i | \(0.687575\pi\) | |||||||
\(458\) | 28.1898 | 1.31722 | ||||||||
\(459\) | 29.9540 | 1.39813 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.0833 | −1.44770 | −0.723848 | − | 0.689960i | \(-0.757628\pi\) | ||||
−0.723848 | + | 0.689960i | \(0.757628\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.8606 | 1.15537 | 0.577686 | − | 0.816259i | \(-0.303956\pi\) | ||||
0.577686 | + | 0.816259i | \(0.303956\pi\) | |||||||
\(464\) | −4.68942 | −0.217701 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 45.3228 | 2.09954 | ||||||||
\(467\) | −13.6674 | −0.632452 | −0.316226 | − | 0.948684i | \(-0.602416\pi\) | ||||
−0.316226 | + | 0.948684i | \(0.602416\pi\) | |||||||
\(468\) | −8.03293 | −0.371323 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.7727 | −0.865003 | ||||||||
\(472\) | −7.26456 | −0.334378 | ||||||||
\(473\) | −26.7344 | −1.22925 | ||||||||
\(474\) | −32.1503 | −1.47671 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 53.8595 | 2.46606 | ||||||||
\(478\) | 34.0253 | 1.55628 | ||||||||
\(479\) | −4.16576 | −0.190338 | −0.0951691 | − | 0.995461i | \(-0.530339\pi\) | ||||
−0.0951691 | + | 0.995461i | \(0.530339\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.25672 | −0.0573013 | ||||||||
\(482\) | −24.2700 | −1.10547 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.5566 | −0.570754 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 30.3304 | 1.37582 | ||||||||
\(487\) | −14.1801 | −0.642564 | −0.321282 | − | 0.946984i | \(-0.604114\pi\) | ||||
−0.321282 | + | 0.946984i | \(0.604114\pi\) | |||||||
\(488\) | 7.09334 | 0.321101 | ||||||||
\(489\) | −20.4622 | −0.925331 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.8737 | 0.851759 | 0.425880 | − | 0.904780i | \(-0.359965\pi\) | ||||
0.425880 | + | 0.904780i | \(0.359965\pi\) | |||||||
\(492\) | 26.5411 | 1.19657 | ||||||||
\(493\) | 14.9056 | 0.671313 | ||||||||
\(494\) | 0.581686 | 0.0261713 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.32497 | 0.284000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −19.5226 | −0.874828 | ||||||||
\(499\) | −10.5237 | −0.471104 | −0.235552 | − | 0.971862i | \(-0.575690\pi\) | ||||
−0.235552 | + | 0.971862i | \(0.575690\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 60.0044 | 2.68080 | ||||||||
\(502\) | 61.2425 | 2.73339 | ||||||||
\(503\) | 19.3854 | 0.864351 | 0.432176 | − | 0.901789i | \(-0.357746\pi\) | ||||
0.432176 | + | 0.901789i | \(0.357746\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22.7278 | 1.01037 | ||||||||
\(507\) | −35.9463 | −1.59643 | ||||||||
\(508\) | −35.2305 | −1.56310 | ||||||||
\(509\) | 19.0713 | 0.845322 | 0.422661 | − | 0.906288i | \(-0.361096\pi\) | ||||
0.422661 | + | 0.906288i | \(0.361096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −17.8816 | −0.790261 | ||||||||
\(513\) | 2.70688 | 0.119512 | ||||||||
\(514\) | −31.9450 | −1.40904 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 83.7861 | 3.68848 | ||||||||
\(517\) | −24.0024 | −1.05562 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.1712 | 0.929313 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.64448 | −0.422532 | −0.211266 | − | 0.977429i | \(-0.567759\pi\) | ||||
−0.211266 | + | 0.977429i | \(0.567759\pi\) | |||||||
\(522\) | −31.7278 | −1.38869 | ||||||||
\(523\) | −30.6135 | −1.33864 | −0.669318 | − | 0.742976i | \(-0.733414\pi\) | ||||
−0.669318 | + | 0.742976i | \(0.733414\pi\) | |||||||
\(524\) | 14.1527 | 0.618262 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.642096 | 0.0279967 | ||||||||
\(527\) | −20.1043 | −0.875755 | ||||||||
\(528\) | 11.8816 | 0.517079 | ||||||||
\(529\) | −6.73544 | −0.292845 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.9330 | 0.865021 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.86063 | −0.0805930 | ||||||||
\(534\) | 34.7422 | 1.50344 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.0659 | 0.607553 | ||||||||
\(537\) | −2.06587 | −0.0891488 | ||||||||
\(538\) | −18.7697 | −0.809218 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.6829 | −1.36215 | −0.681077 | − | 0.732212i | \(-0.738488\pi\) | ||||
−0.681077 | + | 0.732212i | \(0.738488\pi\) | |||||||
\(542\) | −6.40284 | −0.275026 | ||||||||
\(543\) | −5.68703 | −0.244054 | ||||||||
\(544\) | 37.7662 | 1.61921 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.91866 | −0.253064 | −0.126532 | − | 0.991963i | \(-0.540385\pi\) | ||||
−0.126532 | + | 0.991963i | \(0.540385\pi\) | |||||||
\(548\) | 1.44340 | 0.0616592 | ||||||||
\(549\) | −19.4633 | −0.830671 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.34699 | 0.0573835 | ||||||||
\(552\) | −20.9660 | −0.892371 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.04494 | 0.171853 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 63.1965 | 2.68013 | ||||||||
\(557\) | −31.5806 | −1.33811 | −0.669057 | − | 0.743212i | \(-0.733302\pi\) | ||||
−0.669057 | + | 0.743212i | \(0.733302\pi\) | |||||||
\(558\) | 42.7937 | 1.81160 | ||||||||
\(559\) | −5.87372 | −0.248432 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.7662 | −1.59449 | ||||||||
\(562\) | 1.33697 | 0.0563968 | ||||||||
\(563\) | −20.9320 | −0.882177 | −0.441089 | − | 0.897464i | \(-0.645408\pi\) | ||||
−0.441089 | + | 0.897464i | \(0.645408\pi\) | |||||||
\(564\) | 75.2240 | 3.16750 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.7134 | −1.08082 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.0209 | 0.672223 | ||||||||
\(569\) | 26.7224 | 1.12026 | 0.560130 | − | 0.828405i | \(-0.310751\pi\) | ||||
0.560130 | + | 0.828405i | \(0.310751\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.2844 | 0.974422 | 0.487211 | − | 0.873284i | \(-0.338014\pi\) | ||||
0.487211 | + | 0.873284i | \(0.338014\pi\) | |||||||
\(572\) | 4.09096 | 0.171052 | ||||||||
\(573\) | 6.02639 | 0.251756 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −63.9254 | −2.66356 | ||||||||
\(577\) | 14.7937 | 0.615869 | 0.307934 | − | 0.951408i | \(-0.400362\pi\) | ||||
0.307934 | + | 0.951408i | \(0.400362\pi\) | |||||||
\(578\) | −22.0449 | −0.916949 | ||||||||
\(579\) | −7.48527 | −0.311077 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 95.3283 | 3.95148 | ||||||||
\(583\) | −27.4292 | −1.13600 | ||||||||
\(584\) | 20.7948 | 0.860493 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 61.6190 | 2.54546 | ||||||||
\(587\) | −34.6334 | −1.42947 | −0.714736 | − | 0.699394i | \(-0.753453\pi\) | ||||
−0.714736 | + | 0.699394i | \(0.753453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.81678 | −0.0748592 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.4907 | 0.719472 | ||||||||
\(592\) | −3.64994 | −0.150012 | ||||||||
\(593\) | 5.85517 | 0.240443 | 0.120222 | − | 0.992747i | \(-0.461639\pi\) | ||||
0.120222 | + | 0.992747i | \(0.461639\pi\) | |||||||
\(594\) | 32.4711 | 1.33231 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 29.6739 | 1.21549 | ||||||||
\(597\) | −64.5280 | −2.64096 | ||||||||
\(598\) | 4.99346 | 0.204198 | ||||||||
\(599\) | 32.7267 | 1.33718 | 0.668589 | − | 0.743632i | \(-0.266899\pi\) | ||||
0.668589 | + | 0.743632i | \(0.266899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.9485 | 1.09925 | 0.549627 | − | 0.835410i | \(-0.314770\pi\) | ||||
0.549627 | + | 0.835410i | \(0.314770\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −38.5950 | −1.57171 | ||||||||
\(604\) | 28.3239 | 1.15248 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −31.1173 | −1.26406 | ||||||||
\(607\) | 15.4094 | 0.625448 | 0.312724 | − | 0.949844i | \(-0.398759\pi\) | ||||
0.312724 | + | 0.949844i | \(0.398759\pi\) | |||||||
\(608\) | 3.41285 | 0.138410 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.27349 | −0.213343 | ||||||||
\(612\) | 74.1570 | 2.99762 | ||||||||
\(613\) | 39.8726 | 1.61044 | 0.805220 | − | 0.592976i | \(-0.202047\pi\) | ||||
0.805220 | + | 0.592976i | \(0.202047\pi\) | |||||||
\(614\) | 12.2172 | 0.493048 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.7409 | 1.47913 | 0.739566 | − | 0.673084i | \(-0.235031\pi\) | ||||
0.739566 | + | 0.673084i | \(0.235031\pi\) | |||||||
\(618\) | −124.797 | −5.02007 | ||||||||
\(619\) | −25.7289 | −1.03413 | −0.517066 | − | 0.855946i | \(-0.672976\pi\) | ||||
−0.517066 | + | 0.855946i | \(0.672976\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.2371 | 0.932472 | ||||||||
\(622\) | −14.5291 | −0.582565 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.61046 | 0.104502 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −26.1647 | −1.04575 | ||||||||
\(627\) | −3.41285 | −0.136296 | ||||||||
\(628\) | −18.7727 | −0.749114 | ||||||||
\(629\) | 11.6015 | 0.462583 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.47525 | 0.0985383 | 0.0492692 | − | 0.998786i | \(-0.484311\pi\) | ||||
0.0492692 | + | 0.998786i | \(0.484311\pi\) | |||||||
\(632\) | −9.46325 | −0.376428 | ||||||||
\(633\) | −44.9714 | −1.78745 | ||||||||
\(634\) | 19.1514 | 0.760598 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 85.9638 | 3.40869 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.1581 | 0.639706 | ||||||||
\(639\) | −43.9594 | −1.73901 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.3359 | −1.39568 | −0.697842 | − | 0.716252i | \(-0.745856\pi\) | ||||
−0.697842 | + | 0.716252i | \(0.745856\pi\) | |||||||
\(642\) | 70.8530 | 2.79635 | ||||||||
\(643\) | 2.98691 | 0.117792 | 0.0588962 | − | 0.998264i | \(-0.481242\pi\) | ||||
0.0588962 | + | 0.998264i | \(0.481242\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.36991 | −0.211276 | ||||||||
\(647\) | 26.0275 | 1.02325 | 0.511623 | − | 0.859210i | \(-0.329045\pi\) | ||||
0.511623 | + | 0.859210i | \(0.329045\pi\) | |||||||
\(648\) | −2.25910 | −0.0887459 | ||||||||
\(649\) | −10.1514 | −0.398476 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.4622 | −0.801360 | ||||||||
\(653\) | 17.8936 | 0.700229 | 0.350115 | − | 0.936707i | \(-0.386143\pi\) | ||||
0.350115 | + | 0.936707i | \(0.386143\pi\) | |||||||
\(654\) | −55.8386 | −2.18346 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.40393 | −0.210988 | ||||||||
\(657\) | −57.0582 | −2.22605 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.2076 | −0.592405 | −0.296202 | − | 0.955125i | \(-0.595720\pi\) | ||||
−0.296202 | + | 0.955125i | \(0.595720\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.48180 | −0.213217 | −0.106609 | − | 0.994301i | \(-0.533999\pi\) | ||||
−0.106609 | + | 0.994301i | \(0.533999\pi\) | |||||||
\(662\) | 27.4148 | 1.06551 | ||||||||
\(663\) | −8.29749 | −0.322248 | ||||||||
\(664\) | −5.74636 | −0.223002 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.6949 | −0.956907 | ||||||||
\(667\) | 11.5631 | 0.447727 | ||||||||
\(668\) | 60.0044 | 2.32164 | ||||||||
\(669\) | 21.4358 | 0.828755 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.91211 | 0.382653 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.6763 | −1.18249 | −0.591243 | − | 0.806494i | \(-0.701363\pi\) | ||||
−0.591243 | + | 0.806494i | \(0.701363\pi\) | |||||||
\(674\) | −7.94743 | −0.306124 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −35.9463 | −1.38255 | ||||||||
\(677\) | −5.54112 | −0.212963 | −0.106481 | − | 0.994315i | \(-0.533958\pi\) | ||||
−0.106481 | + | 0.994315i | \(0.533958\pi\) | |||||||
\(678\) | 73.9518 | 2.84010 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.7662 | 1.44720 | ||||||||
\(682\) | −21.7937 | −0.834523 | ||||||||
\(683\) | −1.90666 | −0.0729562 | −0.0364781 | − | 0.999334i | \(-0.511614\pi\) | ||||
−0.0364781 | + | 0.999334i | \(0.511614\pi\) | |||||||
\(684\) | 6.70142 | 0.256235 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −36.3383 | −1.38639 | ||||||||
\(688\) | −17.0593 | −0.650381 | ||||||||
\(689\) | −6.02639 | −0.229587 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.905571 | −0.0344495 | −0.0172248 | − | 0.999852i | \(-0.505483\pi\) | ||||
−0.0172248 | + | 0.999852i | \(0.505483\pi\) | |||||||
\(692\) | 21.1712 | 0.804809 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 48.0188 | 1.82277 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −14.9056 | −0.564994 | ||||||||
\(697\) | 17.1767 | 0.650613 | ||||||||
\(698\) | 8.12628 | 0.307584 | ||||||||
\(699\) | −58.4238 | −2.20979 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.8541 | 1.39196 | 0.695980 | − | 0.718061i | \(-0.254970\pi\) | ||||
0.695980 | + | 0.718061i | \(0.254970\pi\) | |||||||
\(702\) | 7.13412 | 0.269260 | ||||||||
\(703\) | 1.04841 | 0.0395414 | ||||||||
\(704\) | 32.5555 | 1.22698 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −69.5741 | −2.61845 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 31.8146 | 1.19567 | ||||||||
\(709\) | −41.6818 | −1.56539 | −0.782696 | − | 0.622404i | \(-0.786156\pi\) | ||||
−0.782696 | + | 0.622404i | \(0.786156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.9660 | 0.973800 | ||||||||
\(712\) | 10.2262 | 0.383242 | ||||||||
\(713\) | −15.5961 | −0.584078 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.06587 | −0.0772051 | ||||||||
\(717\) | −43.8606 | −1.63801 | ||||||||
\(718\) | 37.6818 | 1.40627 | ||||||||
\(719\) | −44.8595 | −1.67298 | −0.836489 | − | 0.547983i | \(-0.815396\pi\) | ||||
−0.836489 | + | 0.547983i | \(0.815396\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 41.2899 | 1.53665 | ||||||||
\(723\) | 31.2855 | 1.16352 | ||||||||
\(724\) | −5.68703 | −0.211357 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 27.6081 | 1.02463 | ||||||||
\(727\) | 9.08134 | 0.336808 | 0.168404 | − | 0.985718i | \(-0.446139\pi\) | ||||
0.168404 | + | 0.985718i | \(0.446139\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.7926 | −1.58491 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.2240 | 2.00555 | ||||||||
\(732\) | −31.0648 | −1.14819 | ||||||||
\(733\) | 28.4203 | 1.04973 | 0.524864 | − | 0.851186i | \(-0.324116\pi\) | ||||
0.524864 | + | 0.851186i | \(0.324116\pi\) | |||||||
\(734\) | 25.9187 | 0.956675 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.2975 | 1.07992 | ||||||||
\(737\) | 19.6554 | 0.724016 | ||||||||
\(738\) | −36.5621 | −1.34587 | ||||||||
\(739\) | 5.41047 | 0.199027 | 0.0995137 | − | 0.995036i | \(-0.468271\pi\) | ||||
0.0995137 | + | 0.995036i | \(0.468271\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.749828 | −0.0275456 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.1712 | 1.10687 | 0.553437 | − | 0.832891i | \(-0.313316\pi\) | ||||
0.553437 | + | 0.832891i | \(0.313316\pi\) | |||||||
\(744\) | 20.1043 | 0.737058 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.6763 | 0.757014 | ||||||||
\(747\) | 15.7673 | 0.576895 | ||||||||
\(748\) | −37.7662 | −1.38087 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.9056 | 1.60214 | 0.801069 | − | 0.598573i | \(-0.204265\pi\) | ||||
0.801069 | + | 0.598573i | \(0.204265\pi\) | |||||||
\(752\) | −15.3160 | −0.558519 | ||||||||
\(753\) | −78.9453 | −2.87693 | ||||||||
\(754\) | 3.55005 | 0.129285 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.6914 | −1.40626 | −0.703132 | − | 0.711060i | \(-0.748216\pi\) | ||||
−0.703132 | + | 0.711060i | \(0.748216\pi\) | |||||||
\(758\) | 38.1450 | 1.38549 | ||||||||
\(759\) | −29.2975 | −1.06343 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3293 | −1.13569 | −0.567844 | − | 0.823136i | \(-0.692222\pi\) | ||||
−0.567844 | + | 0.823136i | \(0.692222\pi\) | |||||||
\(762\) | 77.4611 | 2.80612 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.02639 | 0.218027 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.7989 | 0.462444 | ||||||||
\(767\) | −2.23033 | −0.0805324 | ||||||||
\(768\) | −11.4896 | −0.414597 | ||||||||
\(769\) | 9.00654 | 0.324784 | 0.162392 | − | 0.986726i | \(-0.448079\pi\) | ||||
0.162392 | + | 0.986726i | \(0.448079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.1791 | 1.48303 | ||||||||
\(772\) | −7.48527 | −0.269401 | ||||||||
\(773\) | −15.7673 | −0.567110 | −0.283555 | − | 0.958956i | \(-0.591514\pi\) | ||||
−0.283555 | + | 0.958956i | \(0.591514\pi\) | |||||||
\(774\) | −115.421 | −4.14870 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 28.0593 | 1.00727 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 58.5466 | 2.09900 | ||||||||
\(779\) | 1.55222 | 0.0556141 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.3874 | 0.801083 | ||||||||
\(782\) | −46.0977 | −1.64845 | ||||||||
\(783\) | 16.5202 | 0.590383 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −31.1173 | −1.10992 | ||||||||
\(787\) | 35.6225 | 1.26980 | 0.634902 | − | 0.772593i | \(-0.281041\pi\) | ||||
0.634902 | + | 0.772593i | \(0.281041\pi\) | |||||||
\(788\) | 17.4907 | 0.623081 | ||||||||
\(789\) | −0.827699 | −0.0294669 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 23.6619 | 0.840791 | ||||||||
\(793\) | 2.17776 | 0.0773345 | ||||||||
\(794\) | 77.4611 | 2.74899 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −64.5280 | −2.28714 | ||||||||
\(797\) | 39.6268 | 1.40365 | 0.701827 | − | 0.712347i | \(-0.252368\pi\) | ||||
0.701827 | + | 0.712347i | \(0.252368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.6829 | 1.72228 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.0593 | −0.991428 | ||||||||
\(802\) | 53.7291 | 1.89724 | ||||||||
\(803\) | 29.0582 | 1.02544 | ||||||||
\(804\) | −61.6004 | −2.17248 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.78822 | −0.168658 | ||||||||
\(807\) | 24.1952 | 0.851712 | ||||||||
\(808\) | −9.15921 | −0.322220 | ||||||||
\(809\) | −6.82531 | −0.239965 | −0.119983 | − | 0.992776i | \(-0.538284\pi\) | ||||
−0.119983 | + | 0.992776i | \(0.538284\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.4303 | 1.63039 | 0.815194 | − | 0.579187i | \(-0.196630\pi\) | ||||
0.815194 | + | 0.579187i | \(0.196630\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.25364 | 0.289468 | ||||||||
\(814\) | 12.5764 | 0.440804 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −24.0988 | −0.843627 | ||||||||
\(817\) | 4.90011 | 0.171433 | ||||||||
\(818\) | −64.8334 | −2.26685 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.4491 | 1.34188 | 0.670941 | − | 0.741511i | \(-0.265890\pi\) | ||||
0.670941 | + | 0.741511i | \(0.265890\pi\) | |||||||
\(822\) | −3.17360 | −0.110692 | ||||||||
\(823\) | 22.5939 | 0.787574 | 0.393787 | − | 0.919202i | \(-0.371165\pi\) | ||||
0.393787 | + | 0.919202i | \(0.371165\pi\) | |||||||
\(824\) | −36.7333 | −1.27966 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.2460 | −0.530156 | −0.265078 | − | 0.964227i | \(-0.585398\pi\) | ||||
−0.265078 | + | 0.964227i | \(0.585398\pi\) | |||||||
\(828\) | 57.5280 | 1.99924 | ||||||||
\(829\) | 12.9671 | 0.450365 | 0.225182 | − | 0.974317i | \(-0.427702\pi\) | ||||
0.225182 | + | 0.974317i | \(0.427702\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.21416 | −0.180877 | ||||||||
\(832\) | 7.15267 | 0.247974 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −138.950 | −4.81143 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.41285 | −0.118036 | ||||||||
\(837\) | −22.2820 | −0.770179 | ||||||||
\(838\) | −21.4172 | −0.739846 | ||||||||
\(839\) | 19.4818 | 0.672586 | 0.336293 | − | 0.941757i | \(-0.390827\pi\) | ||||
0.336293 | + | 0.941757i | \(0.390827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7793 | −0.716527 | ||||||||
\(842\) | 5.91320 | 0.203782 | ||||||||
\(843\) | −1.72344 | −0.0593583 | ||||||||
\(844\) | −44.9714 | −1.54798 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −103.626 | −3.56273 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −17.5027 | −0.601046 | ||||||||
\(849\) | 33.1461 | 1.13757 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.00000 | 0.308516 | ||||||||
\(852\) | −70.1625 | −2.40373 | ||||||||
\(853\) | −20.0449 | −0.686326 | −0.343163 | − | 0.939276i | \(-0.611498\pi\) | ||||
−0.343163 | + | 0.939276i | \(0.611498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.8552 | 0.712815 | ||||||||
\(857\) | −50.3383 | −1.71952 | −0.859761 | − | 0.510696i | \(-0.829388\pi\) | ||||
−0.859761 | + | 0.510696i | \(0.829388\pi\) | |||||||
\(858\) | −8.99476 | −0.307076 | ||||||||
\(859\) | 38.1396 | 1.30131 | 0.650653 | − | 0.759375i | \(-0.274495\pi\) | ||||
0.650653 | + | 0.759375i | \(0.274495\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.7487 | 0.706705 | ||||||||
\(863\) | −0.864103 | −0.0294144 | −0.0147072 | − | 0.999892i | \(-0.504682\pi\) | ||||
−0.0147072 | + | 0.999892i | \(0.504682\pi\) | |||||||
\(864\) | 41.8572 | 1.42401 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −45.8517 | −1.55810 | ||||||||
\(867\) | 28.4172 | 0.965100 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.2238 | −0.448586 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.31843 | 0.146324 | ||||||||
\(872\) | −16.4358 | −0.556586 | ||||||||
\(873\) | −76.9913 | −2.60576 | ||||||||
\(874\) | −4.16576 | −0.140909 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −91.0692 | −3.07694 | ||||||||
\(877\) | 9.31297 | 0.314477 | 0.157238 | − | 0.987561i | \(-0.449741\pi\) | ||||
0.157238 | + | 0.987561i | \(0.449741\pi\) | |||||||
\(878\) | 49.6070 | 1.67415 | ||||||||
\(879\) | −79.4305 | −2.67913 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.4602 | −0.655630 | −0.327815 | − | 0.944742i | \(-0.606312\pi\) | ||||
−0.327815 | + | 0.944742i | \(0.606312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.1712 | −1.45283 | −0.726414 | − | 0.687258i | \(-0.758814\pi\) | ||||
−0.726414 | + | 0.687258i | \(0.758814\pi\) | |||||||
\(884\) | −8.29749 | −0.279075 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −67.2713 | −2.26002 | ||||||||
\(887\) | 17.4907 | 0.587281 | 0.293641 | − | 0.955916i | \(-0.405133\pi\) | ||||
0.293641 | + | 0.955916i | \(0.405133\pi\) | |||||||
\(888\) | −11.6015 | −0.389322 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.15683 | −0.105758 | ||||||||
\(892\) | 21.4358 | 0.717723 | ||||||||
\(893\) | 4.39937 | 0.147219 | ||||||||
\(894\) | −65.2438 | −2.18208 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.43686 | −0.214921 | ||||||||
\(898\) | −2.75399 | −0.0919017 | ||||||||
\(899\) | −11.0879 | −0.369802 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.6334 | 1.85342 | ||||||||
\(902\) | 18.6201 | 0.619981 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.7673 | 0.723969 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −62.2755 | −2.06896 | ||||||||
\(907\) | −16.7453 | −0.556018 | −0.278009 | − | 0.960579i | \(-0.589674\pi\) | ||||
−0.278009 | + | 0.960579i | \(0.589674\pi\) | |||||||
\(908\) | 37.7662 | 1.25332 | ||||||||
\(909\) | 25.1317 | 0.833567 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.9485 | −0.925976 | −0.462988 | − | 0.886365i | \(-0.653223\pi\) | ||||
−0.462988 | + | 0.886365i | \(0.653223\pi\) | |||||||
\(912\) | −2.17776 | −0.0721128 | ||||||||
\(913\) | −8.02986 | −0.265750 | ||||||||
\(914\) | 52.2449 | 1.72811 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.3383 | −1.20065 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −65.8595 | −2.17369 | ||||||||
\(919\) | 23.2940 | 0.768399 | 0.384199 | − | 0.923250i | \(-0.374477\pi\) | ||||
0.384199 | + | 0.923250i | \(0.374477\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.7487 | −0.518939 | ||||||||
\(922\) | 68.3426 | 2.25075 | ||||||||
\(923\) | 4.91866 | 0.161900 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −54.6609 | −1.79627 | ||||||||
\(927\) | 100.792 | 3.31043 | ||||||||
\(928\) | 20.8288 | 0.683738 | ||||||||
\(929\) | −39.6949 | −1.30235 | −0.651173 | − | 0.758929i | \(-0.725723\pi\) | ||||
−0.651173 | + | 0.758929i | \(0.725723\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −58.4238 | −1.91373 | ||||||||
\(933\) | 18.7289 | 0.613157 | ||||||||
\(934\) | 30.0504 | 0.983279 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.19869 | 0.169925 | ||||||||
\(937\) | −2.00654 | −0.0655509 | −0.0327755 | − | 0.999463i | \(-0.510435\pi\) | ||||
−0.0327755 | + | 0.999463i | \(0.510435\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.7278 | 1.10067 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.0318 | −1.43540 | −0.717699 | − | 0.696354i | \(-0.754804\pi\) | ||||
−0.717699 | + | 0.696354i | \(0.754804\pi\) | |||||||
\(942\) | 41.2755 | 1.34483 | ||||||||
\(943\) | 13.3250 | 0.433921 | ||||||||
\(944\) | −6.47764 | −0.210829 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58.7806 | 1.91112 | ||||||||
\(947\) | −24.6609 | −0.801370 | −0.400685 | − | 0.916216i | \(-0.631228\pi\) | ||||
−0.400685 | + | 0.916216i | \(0.631228\pi\) | |||||||
\(948\) | 41.4436 | 1.34603 | ||||||||
\(949\) | 6.38429 | 0.207243 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.6872 | −0.800539 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.5435 | 1.15137 | 0.575684 | − | 0.817673i | \(-0.304736\pi\) | ||||
0.575684 | + | 0.817673i | \(0.304736\pi\) | |||||||
\(954\) | −118.421 | −3.83401 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −43.8606 | −1.41855 | ||||||||
\(957\) | −20.8288 | −0.673299 | ||||||||
\(958\) | 9.15921 | 0.295921 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0449 | −0.517579 | ||||||||
\(962\) | 2.76313 | 0.0890869 | ||||||||
\(963\) | −57.2240 | −1.84402 | ||||||||
\(964\) | 31.2855 | 1.00764 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.3228 | 1.23238 | 0.616189 | − | 0.787598i | \(-0.288676\pi\) | ||||
0.616189 | + | 0.787598i | \(0.288676\pi\) | |||||||
\(968\) | 8.12628 | 0.261188 | ||||||||
\(969\) | 6.92213 | 0.222371 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.5819 | −1.52698 | −0.763488 | − | 0.645822i | \(-0.776515\pi\) | ||||
−0.763488 | + | 0.645822i | \(0.776515\pi\) | |||||||
\(972\) | −39.0977 | −1.25406 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31.1778 | 0.999000 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.32497 | 0.202457 | ||||||||
\(977\) | −10.4842 | −0.335419 | −0.167709 | − | 0.985836i | \(-0.553637\pi\) | ||||
−0.167709 | + | 0.985836i | \(0.553637\pi\) | |||||||
\(978\) | 44.9900 | 1.43862 | ||||||||
\(979\) | 14.2899 | 0.456706 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.0977 | 1.43986 | ||||||||
\(982\) | −41.4975 | −1.32424 | ||||||||
\(983\) | 10.2262 | 0.326164 | 0.163082 | − | 0.986613i | \(-0.447856\pi\) | ||||
0.163082 | + | 0.986613i | \(0.447856\pi\) | |||||||
\(984\) | −17.1767 | −0.547572 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −32.7727 | −1.04370 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.749828 | −0.0238552 | ||||||||
\(989\) | 42.0648 | 1.33758 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.27873 | 0.0406203 | 0.0203101 | − | 0.999794i | \(-0.493535\pi\) | ||||
0.0203101 | + | 0.999794i | \(0.493535\pi\) | |||||||
\(992\) | −28.0933 | −0.891965 | ||||||||
\(993\) | −35.3394 | −1.12146 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 25.1658 | 0.797408 | ||||||||
\(997\) | −27.7200 | −0.877900 | −0.438950 | − | 0.898511i | \(-0.644650\pi\) | ||||
−0.438950 | + | 0.898511i | \(0.644650\pi\) | |||||||
\(998\) | 23.1383 | 0.732430 | ||||||||
\(999\) | 12.8582 | 0.406817 |
(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 | 1225.2.a.x.1.1 | 3 | ||
5.2 | odd | 4 | 1225.2.b.l.99.1 | 6 | |||
5.3 | odd | 4 | 1225.2.b.l.99.6 | 6 | |||
5.4 | even | 2 | 1225.2.a.y.1.3 | 3 | |||
7.2 | even | 3 | 175.2.e.e.151.3 | yes | 6 | ||
7.4 | even | 3 | 175.2.e.e.51.3 | yes | 6 | ||
7.6 | odd | 2 | 1225.2.a.w.1.1 | 3 | |||
35.2 | odd | 12 | 175.2.k.b.74.1 | 12 | |||
35.4 | even | 6 | 175.2.e.d.51.1 | ✓ | 6 | ||
35.9 | even | 6 | 175.2.e.d.151.1 | yes | 6 | ||
35.13 | even | 4 | 1225.2.b.m.99.6 | 6 | |||
35.18 | odd | 12 | 175.2.k.b.149.1 | 12 | |||
35.23 | odd | 12 | 175.2.k.b.74.6 | 12 | |||
35.27 | even | 4 | 1225.2.b.m.99.1 | 6 | |||
35.32 | odd | 12 | 175.2.k.b.149.6 | 12 | |||
35.34 | odd | 2 | 1225.2.a.z.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.e.d.51.1 | ✓ | 6 | 35.4 | even | 6 | ||
175.2.e.d.151.1 | yes | 6 | 35.9 | even | 6 | ||
175.2.e.e.51.3 | yes | 6 | 7.4 | even | 3 | ||
175.2.e.e.151.3 | yes | 6 | 7.2 | even | 3 | ||
175.2.k.b.74.1 | 12 | 35.2 | odd | 12 | |||
175.2.k.b.74.6 | 12 | 35.23 | odd | 12 | |||
175.2.k.b.149.1 | 12 | 35.18 | odd | 12 | |||
175.2.k.b.149.6 | 12 | 35.32 | odd | 12 | |||
1225.2.a.w.1.1 | 3 | 7.6 | odd | 2 | |||
1225.2.a.x.1.1 | 3 | 1.1 | even | 1 | trivial | ||
1225.2.a.y.1.3 | 3 | 5.4 | even | 2 | |||
1225.2.a.z.1.3 | 3 | 35.34 | odd | 2 | |||
1225.2.b.l.99.1 | 6 | 5.2 | odd | 4 | |||
1225.2.b.l.99.6 | 6 | 5.3 | odd | 4 | |||
1225.2.b.m.99.1 | 6 | 35.27 | even | 4 | |||
1225.2.b.m.99.6 | 6 | 35.13 | even | 4 |