Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(99,1225)]
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([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1225.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.78167424761\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.4227136.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 22x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 175) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.6 | ||
Root | \(2.19869i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.99 |
Dual form | 1225.2.b.l.99.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.19869i | 1.55471i | 0.629062 | + | 0.777355i | \(0.283439\pi\) | ||||
−0.629062 | + | 0.777355i | \(0.716561\pi\) | |||||||
\(3\) | 2.83424i | 1.63635i | 0.574969 | + | 0.818176i | \(0.305014\pi\) | ||||
−0.574969 | + | 0.818176i | \(0.694986\pi\) | |||||||
\(4\) | −2.83424 | −1.41712 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.23163 | −2.54405 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.83424i | − 0.648503i | ||||||||
\(9\) | −5.03293 | −1.67764 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56314 | −0.772816 | −0.386408 | − | 0.922328i | \(-0.626284\pi\) | ||||
−0.386408 | + | 0.922328i | \(0.626284\pi\) | |||||||
\(12\) | − 8.03293i | − 2.31891i | ||||||||
\(13\) | − 0.563139i | − 0.156187i | −0.996946 | − | 0.0780934i | \(-0.975117\pi\) | ||||
0.996946 | − | 0.0780934i | \(-0.0248832\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.63555 | −0.408888 | ||||||||
\(17\) | − 5.19869i | − 1.26087i | −0.776243 | − | 0.630434i | \(-0.782877\pi\) | ||||
0.776243 | − | 0.630434i | \(-0.217123\pi\) | |||||||
\(18\) | − 11.0659i | − 2.60825i | ||||||||
\(19\) | −0.469795 | −0.107778 | −0.0538892 | − | 0.998547i | \(-0.517162\pi\) | ||||
−0.0538892 | + | 0.998547i | \(0.517162\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 5.63555i | − 1.20150i | ||||||||
\(23\) | 4.03293i | 0.840925i | 0.907310 | + | 0.420462i | \(0.138132\pi\) | ||||
−0.907310 | + | 0.420462i | \(0.861868\pi\) | |||||||
\(24\) | 5.19869 | 1.06118 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.23817 | 0.242825 | ||||||||
\(27\) | − 5.76183i | − 1.10886i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.86718 | −0.532422 | −0.266211 | − | 0.963915i | \(-0.585772\pi\) | ||||
−0.266211 | + | 0.963915i | \(0.585772\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.86718 | −0.694566 | −0.347283 | − | 0.937760i | \(-0.612896\pi\) | ||||
−0.347283 | + | 0.937760i | \(0.612896\pi\) | |||||||
\(32\) | − 7.26456i | − 1.28420i | ||||||||
\(33\) | − 7.26456i | − 1.26460i | ||||||||
\(34\) | 11.4303 | 1.96028 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 14.2646 | 2.37743 | ||||||||
\(37\) | − 2.23163i | − 0.366877i | −0.983031 | − | 0.183439i | \(-0.941277\pi\) | ||||
0.983031 | − | 0.183439i | \(-0.0587228\pi\) | |||||||
\(38\) | − 1.03293i | − 0.167564i | ||||||||
\(39\) | 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 | ||||||||
\(43\) | 10.4303i | 1.59061i | 0.606211 | + | 0.795304i | \(0.292689\pi\) | ||||
−0.606211 | + | 0.795304i | \(0.707311\pi\) | |||||||
\(44\) | 7.26456 | 1.09517 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.86718 | −1.30739 | ||||||||
\(47\) | − 9.36445i | − 1.36595i | −0.730444 | − | 0.682973i | \(-0.760687\pi\) | ||||
0.730444 | − | 0.682973i | \(-0.239313\pi\) | |||||||
\(48\) | − 4.63555i | − 0.669084i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.7344 | 2.06322 | ||||||||
\(52\) | 1.59607i | 0.221336i | ||||||||
\(53\) | 10.7014i | 1.46995i | 0.678092 | + | 0.734977i | \(0.262807\pi\) | ||||
−0.678092 | + | 0.734977i | \(0.737193\pi\) | |||||||
\(54\) | 12.6685 | 1.72396 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 1.33151i | − 0.176363i | ||||||||
\(58\) | − 6.30404i | − 0.827761i | ||||||||
\(59\) | −3.96052 | −0.515616 | −0.257808 | − | 0.966196i | \(-0.583000\pi\) | ||||
−0.257808 | + | 0.966196i | \(0.583000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.86718 | −0.495141 | −0.247571 | − | 0.968870i | \(-0.579632\pi\) | ||||
−0.247571 | + | 0.968870i | \(0.579632\pi\) | |||||||
\(62\) | − 8.50273i | − 1.07985i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.7014 | 1.58768 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.9725 | 1.96608 | ||||||||
\(67\) | 7.66849i | 0.936855i | 0.883502 | + | 0.468427i | \(0.155179\pi\) | ||||
−0.883502 | + | 0.468427i | \(0.844821\pi\) | |||||||
\(68\) | 14.7344i | 1.78680i | ||||||||
\(69\) | −11.4303 | −1.37605 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.73436 | −1.03658 | −0.518289 | − | 0.855206i | \(-0.673431\pi\) | ||||
−0.518289 | + | 0.855206i | \(0.673431\pi\) | |||||||
\(72\) | 9.23163i | 1.08796i | ||||||||
\(73\) | − 11.3370i | − 1.32689i | −0.748224 | − | 0.663446i | \(-0.769093\pi\) | ||||
0.748224 | − | 0.663446i | \(-0.230907\pi\) | |||||||
\(74\) | 4.90666 | 0.570387 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.33151 | 0.152735 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.50927i | 0.397347i | ||||||||
\(79\) | −5.15921 | −0.580457 | −0.290228 | − | 0.956957i | \(-0.593731\pi\) | ||||
−0.290228 | + | 0.956957i | \(0.593731\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.23163 | 0.136847 | ||||||||
\(82\) | 7.26456i | 0.802236i | ||||||||
\(83\) | 3.13282i | 0.343872i | 0.985108 | + | 0.171936i | \(0.0550022\pi\) | ||||
−0.985108 | + | 0.171936i | \(0.944998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −22.9330 | −2.47293 | ||||||||
\(87\) | − 8.12628i | − 0.871229i | ||||||||
\(88\) | 4.70142i | 0.501173i | ||||||||
\(89\) | 5.57514 | 0.590964 | 0.295482 | − | 0.955348i | \(-0.404520\pi\) | ||||
0.295482 | + | 0.955348i | \(0.404520\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 11.4303i | − 1.19169i | ||||||||
\(93\) | − 10.9605i | − 1.13655i | ||||||||
\(94\) | 20.5895 | 2.12365 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 20.5895 | 2.10141 | ||||||||
\(97\) | 15.2975i | 1.55323i | 0.629978 | + | 0.776613i | \(0.283064\pi\) | ||||
−0.629978 | + | 0.776613i | \(0.716936\pi\) | |||||||
\(98\) | 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 | \(0.420084\pi\) | |||||||
\(102\) | 32.3963i | 3.20771i | ||||||||
\(103\) | 20.0264i | 1.97326i | 0.162980 | + | 0.986629i | \(0.447890\pi\) | ||||
−0.162980 | + | 0.986629i | \(0.552110\pi\) | |||||||
\(104\) | −1.03293 | −0.101288 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23.5291 | −2.28535 | ||||||||
\(107\) | 11.3699i | 1.09917i | 0.835438 | + | 0.549585i | \(0.185214\pi\) | ||||
−0.835438 | + | 0.549585i | \(0.814786\pi\) | |||||||
\(108\) | 16.3304i | 1.57140i | ||||||||
\(109\) | −8.96052 | −0.858262 | −0.429131 | − | 0.903242i | \(-0.641180\pi\) | ||||
−0.429131 | + | 0.903242i | \(0.641180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.32497 | 0.600340 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 11.8672i | − 1.11637i | −0.829716 | − | 0.558185i | \(-0.811498\pi\) | ||||
0.829716 | − | 0.558185i | \(-0.188502\pi\) | |||||||
\(114\) | 2.92759 | 0.274194 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.12628 | 0.754506 | ||||||||
\(117\) | 2.83424i | 0.262026i | ||||||||
\(118\) | − 8.70796i | − 0.801633i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43032 | −0.402756 | ||||||||
\(122\) | − 8.50273i | − 0.769801i | ||||||||
\(123\) | 9.36445i | 0.844364i | ||||||||
\(124\) | 10.9605 | 0.984284 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4303i | 1.10301i | 0.834171 | + | 0.551506i | \(0.185947\pi\) | ||||
−0.834171 | + | 0.551506i | \(0.814053\pi\) | |||||||
\(128\) | 13.3974i | 1.18417i | ||||||||
\(129\) | −29.5621 | −2.60279 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.99346 | 0.436280 | 0.218140 | − | 0.975917i | \(-0.430001\pi\) | ||||
0.218140 | + | 0.975917i | \(0.430001\pi\) | |||||||
\(132\) | 20.5895i | 1.79209i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −16.8606 | −1.45654 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.53566 | −0.817676 | ||||||||
\(137\) | − 0.509273i | − 0.0435102i | −0.999763 | − | 0.0217551i | \(-0.993075\pi\) | ||||
0.999763 | − | 0.0217551i | \(-0.00692540\pi\) | |||||||
\(138\) | − 25.1317i | − 2.13936i | ||||||||
\(139\) | −22.2975 | −1.89125 | −0.945624 | − | 0.325261i | \(-0.894548\pi\) | ||||
−0.945624 | + | 0.325261i | \(0.894548\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.5411 | 2.23517 | ||||||||
\(142\) | − 19.2042i | − 1.61158i | ||||||||
\(143\) | 1.44340i | 0.120704i | ||||||||
\(144\) | 8.23163 | 0.685969 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 24.9265 | 2.06293 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.32497i | 0.519909i | ||||||||
\(149\) | −10.4698 | −0.857719 | −0.428860 | − | 0.903371i | \(-0.641084\pi\) | ||||
−0.428860 | + | 0.903371i | \(0.641084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.99346 | 0.813256 | 0.406628 | − | 0.913594i | \(-0.366705\pi\) | ||||
0.406628 | + | 0.913594i | \(0.366705\pi\) | |||||||
\(152\) | 0.861719i | 0.0698946i | ||||||||
\(153\) | 26.1647i | 2.11529i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.52366 | −0.362183 | ||||||||
\(157\) | 6.62355i | 0.528617i | 0.964438 | + | 0.264308i | \(0.0851437\pi\) | ||||
−0.964438 | + | 0.264308i | \(0.914856\pi\) | |||||||
\(158\) | − 11.3435i | − 0.902442i | ||||||||
\(159\) | −30.3304 | −2.40536 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.70796i | 0.212758i | ||||||||
\(163\) | − 7.21962i | − 0.565484i | −0.959196 | − | 0.282742i | \(-0.908756\pi\) | ||||
0.959196 | − | 0.282742i | \(-0.0912441\pi\) | |||||||
\(164\) | −9.36445 | −0.731241 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.88811 | −0.534621 | ||||||||
\(167\) | − 21.1712i | − 1.63828i | −0.573595 | − | 0.819139i | \(-0.694452\pi\) | ||||
0.573595 | − | 0.819139i | \(-0.305548\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6829 | 0.975606 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.36445 | 0.180814 | ||||||||
\(172\) | − 29.5621i | − 2.25409i | ||||||||
\(173\) | 7.46980i | 0.567918i | 0.958836 | + | 0.283959i | \(0.0916480\pi\) | ||||
−0.958836 | + | 0.283959i | \(0.908352\pi\) | |||||||
\(174\) | 17.8672 | 1.35451 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.19215 | 0.315995 | ||||||||
\(177\) | − 11.2251i | − 0.843729i | ||||||||
\(178\) | 12.2580i | 0.918777i | ||||||||
\(179\) | 0.728896 | 0.0544803 | 0.0272401 | − | 0.999629i | \(-0.491328\pi\) | ||||
0.0272401 | + | 0.999629i | \(0.491328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00654 | −0.149145 | −0.0745726 | − | 0.997216i | \(-0.523759\pi\) | ||||
−0.0745726 | + | 0.997216i | \(0.523759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 10.9605i | − 0.810225i | ||||||||
\(184\) | 7.39738 | 0.545342 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 24.0988 | 1.76701 | ||||||||
\(187\) | 13.3250i | 0.974418i | ||||||||
\(188\) | 26.5411i | 1.93571i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.12628 | 0.153852 | 0.0769261 | − | 0.997037i | \(-0.475489\pi\) | ||||
0.0769261 | + | 0.997037i | \(0.475489\pi\) | |||||||
\(192\) | 35.9989i | 2.59800i | ||||||||
\(193\) | − 2.64101i | − 0.190104i | −0.995472 | − | 0.0950521i | \(-0.969698\pi\) | ||||
0.995472 | − | 0.0950521i | \(-0.0303018\pi\) | |||||||
\(194\) | −33.6345 | −2.41481 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 6.17122i | − 0.439681i | −0.975536 | − | 0.219840i | \(-0.929446\pi\) | ||||
0.975536 | − | 0.219840i | \(-0.0705537\pi\) | |||||||
\(198\) | 28.3634i | 2.01570i | ||||||||
\(199\) | 22.7673 | 1.61393 | 0.806965 | − | 0.590599i | \(-0.201108\pi\) | ||||
0.806965 | + | 0.590599i | \(0.201108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.7344 | −1.53302 | ||||||||
\(202\) | 10.9791i | 0.772485i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −41.7607 | −2.92384 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −44.0318 | −3.06784 | ||||||||
\(207\) | − 20.2975i | − 1.41077i | ||||||||
\(208\) | 0.921044i | 0.0638629i | ||||||||
\(209\) | 1.20415 | 0.0832928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8672 | −1.09234 | −0.546171 | − | 0.837674i | \(-0.683915\pi\) | ||||
−0.546171 | + | 0.837674i | \(0.683915\pi\) | |||||||
\(212\) | − 30.3304i | − 2.08310i | ||||||||
\(213\) | − 24.7553i | − 1.69620i | ||||||||
\(214\) | −24.9989 | −1.70889 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.5686 | −0.719102 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 19.7014i | − 1.33435i | ||||||||
\(219\) | 32.1317 | 2.17126 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.92759 | −0.196931 | ||||||||
\(222\) | 13.9067i | 0.933354i | ||||||||
\(223\) | 7.56314i | 0.506465i | 0.967405 | + | 0.253233i | \(0.0814938\pi\) | ||||
−0.967405 | + | 0.253233i | \(0.918506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 26.0923 | 1.73563 | ||||||||
\(227\) | − 13.3250i | − 0.884409i | −0.896914 | − | 0.442205i | \(-0.854196\pi\) | ||||
0.896914 | − | 0.442205i | \(-0.145804\pi\) | |||||||
\(228\) | 3.77383i | 0.249928i | ||||||||
\(229\) | 12.8212 | 0.847246 | 0.423623 | − | 0.905839i | \(-0.360758\pi\) | ||||
0.423623 | + | 0.905839i | \(0.360758\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.25910i | 0.345277i | ||||||||
\(233\) | − 20.6135i | − 1.35044i | −0.737617 | − | 0.675219i | \(-0.764049\pi\) | ||||
0.737617 | − | 0.675219i | \(-0.235951\pi\) | |||||||
\(234\) | −6.23163 | −0.407374 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.2251 | 0.730691 | ||||||||
\(237\) | − 14.6225i | − 0.949831i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4753 | 1.00101 | 0.500505 | − | 0.865733i | \(-0.333148\pi\) | ||||
0.500505 | + | 0.865733i | \(0.333148\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0384 | 0.711045 | 0.355523 | − | 0.934668i | \(-0.384303\pi\) | ||||
0.355523 | + | 0.934668i | \(0.384303\pi\) | |||||||
\(242\) | − 9.74090i | − 0.626169i | ||||||||
\(243\) | − 13.7948i | − 0.884935i | ||||||||
\(244\) | 10.9605 | 0.701676 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.5895 | −1.31274 | ||||||||
\(247\) | 0.264560i | 0.0168336i | ||||||||
\(248\) | 7.09334i | 0.450428i | ||||||||
\(249\) | −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 | ||||||||
\(253\) | − 10.3370i | − 0.649880i | ||||||||
\(254\) | −27.3304 | −1.71486 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.05387 | −0.253367 | ||||||||
\(257\) | − 14.5291i | − 0.906302i | −0.891434 | − | 0.453151i | \(-0.850300\pi\) | ||||
0.891434 | − | 0.453151i | \(-0.149700\pi\) | |||||||
\(258\) | − 64.9978i | − 4.04659i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.4303 | 0.893214 | ||||||||
\(262\) | 10.9791i | 0.678289i | ||||||||
\(263\) | − 0.292035i | − 0.0180077i | −0.999959 | − | 0.00900384i | \(-0.997134\pi\) | ||||
0.999959 | − | 0.00900384i | \(-0.00286605\pi\) | |||||||
\(264\) | −13.3250 | −0.820095 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.8013i | 0.967024i | ||||||||
\(268\) | − 21.7344i | − 1.32764i | ||||||||
\(269\) | −8.53675 | −0.520495 | −0.260247 | − | 0.965542i | \(-0.583804\pi\) | ||||
−0.260247 | + | 0.965542i | \(0.583804\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.91211 | 0.176898 | 0.0884492 | − | 0.996081i | \(-0.471809\pi\) | ||||
0.0884492 | + | 0.996081i | \(0.471809\pi\) | |||||||
\(272\) | 8.50273i | 0.515554i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.11973 | 0.0676457 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 32.3963 | 1.95003 | ||||||||
\(277\) | 1.83970i | 0.110537i | 0.998472 | + | 0.0552685i | \(0.0176015\pi\) | ||||
−0.998472 | + | 0.0552685i | \(0.982399\pi\) | |||||||
\(278\) | − 49.0253i | − 2.94034i | ||||||||
\(279\) | 19.4633 | 1.16523 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.608077 | −0.0362748 | −0.0181374 | − | 0.999836i | \(-0.505774\pi\) | ||||
−0.0181374 | + | 0.999836i | \(0.505774\pi\) | |||||||
\(282\) | 58.3557i | 3.47503i | ||||||||
\(283\) | 11.6949i | 0.695188i | 0.937645 | + | 0.347594i | \(0.113001\pi\) | ||||
−0.937645 | + | 0.347594i | \(0.886999\pi\) | |||||||
\(284\) | 24.7553 | 1.46896 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.17360 | −0.187659 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 36.5621i | 2.15444i | ||||||||
\(289\) | −10.0264 | −0.589788 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −43.3568 | −2.54162 | ||||||||
\(292\) | 32.1317i | 1.88037i | ||||||||
\(293\) | − 28.0253i | − 1.63726i | −0.574324 | − | 0.818628i | \(-0.694735\pi\) | ||||
0.574324 | − | 0.818628i | \(-0.305265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.09334 | −0.237921 | ||||||||
\(297\) | 14.7684i | 0.856948i | ||||||||
\(298\) | − 23.0198i | − 1.33350i | ||||||||
\(299\) | 2.27110 | 0.131341 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 21.9725i | 1.26438i | ||||||||
\(303\) | 14.1527i | 0.813050i | ||||||||
\(304\) | 0.768374 | 0.0440693 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −57.5280 | −3.28866 | ||||||||
\(307\) | 5.55660i | 0.317132i | 0.987348 | + | 0.158566i | \(0.0506870\pi\) | ||||
−0.987348 | + | 0.158566i | \(0.949313\pi\) | |||||||
\(308\) | 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 | \(0.440009\pi\) | |||||||
\(312\) | − 2.92759i | − 0.165742i | ||||||||
\(313\) | 11.9001i | 0.672634i | 0.941749 | + | 0.336317i | \(0.109181\pi\) | ||||
−0.941749 | + | 0.336317i | \(0.890819\pi\) | |||||||
\(314\) | −14.5631 | −0.821845 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.6225 | 0.822578 | ||||||||
\(317\) | 8.71035i | 0.489222i | 0.969621 | + | 0.244611i | \(0.0786603\pi\) | ||||
−0.969621 | + | 0.244611i | \(0.921340\pi\) | |||||||
\(318\) | − 66.6872i | − 3.73964i | ||||||||
\(319\) | 7.34898 | 0.411464 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.2251 | −1.79863 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.44232i | 0.135894i | ||||||||
\(324\) | −3.49073 | −0.193929 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.8737 | 0.879164 | ||||||||
\(327\) | − 25.3963i | − 1.40442i | ||||||||
\(328\) | − 6.06041i | − 0.334630i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.4687 | −0.685342 | −0.342671 | − | 0.939455i | \(-0.611332\pi\) | ||||
−0.342671 | + | 0.939455i | \(0.611332\pi\) | |||||||
\(332\) | − 8.87918i | − 0.487308i | ||||||||
\(333\) | 11.2316i | 0.615489i | ||||||||
\(334\) | 46.5490 | 2.54705 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 3.61462i | − 0.196901i | −0.995142 | − | 0.0984505i | \(-0.968611\pi\) | ||||
0.995142 | − | 0.0984505i | \(-0.0313886\pi\) | |||||||
\(338\) | 27.8857i | 1.51678i | ||||||||
\(339\) | 33.6345 | 1.82677 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.91211 | 0.536771 | ||||||||
\(342\) | 5.19869i | 0.281113i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 19.1317 | 1.03151 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.4238 | −0.882948 | ||||||||
\(347\) | 21.8397i | 1.17242i | 0.810160 | + | 0.586208i | \(0.199380\pi\) | ||||
−0.810160 | + | 0.586208i | \(0.800620\pi\) | |||||||
\(348\) | 23.0318i | 1.23464i | ||||||||
\(349\) | 3.69596 | 0.197840 | 0.0989201 | − | 0.995095i | \(-0.468461\pi\) | ||||
0.0989201 | + | 0.995095i | \(0.468461\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.24471 | −0.173190 | ||||||||
\(352\) | 18.6201i | 0.992454i | ||||||||
\(353\) | 31.6434i | 1.68421i | 0.539315 | + | 0.842104i | \(0.318683\pi\) | ||||
−0.539315 | + | 0.842104i | \(0.681317\pi\) | |||||||
\(354\) | 24.6805 | 1.31175 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.8013 | −0.837468 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.60262i | 0.0847010i | ||||||||
\(359\) | 17.1383 | 0.904524 | 0.452262 | − | 0.891885i | \(-0.350617\pi\) | ||||
0.452262 | + | 0.891885i | \(0.350617\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7793 | −0.988384 | ||||||||
\(362\) | − 4.41177i | − 0.231877i | ||||||||
\(363\) | − 12.5566i | − 0.659050i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 24.0988 | 1.25966 | ||||||||
\(367\) | 11.7882i | 0.615340i | 0.951493 | + | 0.307670i | \(0.0995493\pi\) | ||||
−0.951493 | + | 0.307670i | \(0.900451\pi\) | |||||||
\(368\) | − 6.59607i | − 0.343844i | ||||||||
\(369\) | −16.6290 | −0.865672 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 31.0648i | 1.61063i | ||||||||
\(373\) | − 9.40393i | − 0.486917i | −0.969911 | − | 0.243458i | \(-0.921718\pi\) | ||||
0.969911 | − | 0.243458i | \(-0.0782819\pi\) | |||||||
\(374\) | −29.2975 | −1.51494 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.1767 | −0.885819 | ||||||||
\(377\) | 1.61462i | 0.0831572i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3490 | 0.891157 | 0.445579 | − | 0.895243i | \(-0.352998\pi\) | ||||
0.445579 | + | 0.895243i | \(0.352998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.2305 | −1.80492 | ||||||||
\(382\) | 4.67503i | 0.239195i | ||||||||
\(383\) | − 5.82116i | − 0.297447i | −0.988879 | − | 0.148724i | \(-0.952484\pi\) | ||||
0.988879 | − | 0.148724i | \(-0.0475165\pi\) | |||||||
\(384\) | −37.9714 | −1.93772 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.80677 | 0.295557 | ||||||||
\(387\) | − 52.4951i | − 2.66848i | ||||||||
\(388\) | − 43.3568i | − 2.20111i | ||||||||
\(389\) | 26.6279 | 1.35009 | 0.675045 | − | 0.737777i | \(-0.264124\pi\) | ||||
0.675045 | + | 0.737777i | \(0.264124\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.9660 | 1.06030 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.1527i | 0.713908i | ||||||||
\(394\) | 13.5686 | 0.683576 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −36.5621 | −1.83731 | ||||||||
\(397\) | 35.2305i | 1.76817i | 0.467326 | + | 0.884085i | \(0.345217\pi\) | ||||
−0.467326 | + | 0.884085i | \(0.654783\pi\) | |||||||
\(398\) | 50.0582i | 2.50919i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.4369 | −1.22032 | −0.610159 | − | 0.792279i | \(-0.708895\pi\) | ||||
−0.610159 | + | 0.792279i | \(0.708895\pi\) | |||||||
\(402\) | − 47.7871i | − 2.38341i | ||||||||
\(403\) | 2.17776i | 0.108482i | ||||||||
\(404\) | −14.1527 | −0.704122 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.71997i | 0.283528i | ||||||||
\(408\) | − 27.0264i | − 1.33801i | ||||||||
\(409\) | −29.4873 | −1.45805 | −0.729026 | − | 0.684487i | \(-0.760026\pi\) | ||||
−0.729026 | + | 0.684487i | \(0.760026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.44340 | 0.0711979 | ||||||||
\(412\) | − 56.7597i | − 2.79635i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 44.6279 | 2.19334 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.09096 | −0.200576 | ||||||||
\(417\) | − 63.1965i | − 3.09475i | ||||||||
\(418\) | 2.64755i | 0.129496i | ||||||||
\(419\) | −9.74090 | −0.475874 | −0.237937 | − | 0.971281i | \(-0.576471\pi\) | ||||
−0.237937 | + | 0.971281i | \(0.576471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.68942 | −0.131074 | −0.0655371 | − | 0.997850i | \(-0.520876\pi\) | ||||
−0.0655371 | + | 0.997850i | \(0.520876\pi\) | |||||||
\(422\) | − 34.8870i | − 1.69827i | ||||||||
\(423\) | 47.1307i | 2.29157i | ||||||||
\(424\) | 19.6290 | 0.953269 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 54.4292 | 2.63710 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 32.2251i | − 1.55766i | ||||||||
\(429\) | −4.09096 | −0.197513 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.43686 | −0.454558 | −0.227279 | − | 0.973830i | \(-0.572983\pi\) | ||||
−0.227279 | + | 0.973830i | \(0.572983\pi\) | |||||||
\(432\) | 9.42377i | 0.453401i | ||||||||
\(433\) | 20.8541i | 1.00218i | 0.865394 | + | 0.501092i | \(0.167068\pi\) | ||||
−0.865394 | + | 0.501092i | \(0.832932\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 25.3963 | 1.21626 | ||||||||
\(437\) | − 1.89465i | − 0.0906335i | ||||||||
\(438\) | 70.6478i | 3.37568i | ||||||||
\(439\) | 22.5621 | 1.07683 | 0.538414 | − | 0.842680i | \(-0.319024\pi\) | ||||
0.538414 | + | 0.842680i | \(0.319024\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 6.43686i | − 0.306170i | ||||||||
\(443\) | 30.5961i | 1.45366i | 0.686816 | + | 0.726832i | \(0.259008\pi\) | ||||
−0.686816 | + | 0.726832i | \(0.740992\pi\) | |||||||
\(444\) | −17.9265 | −0.850754 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.6290 | −0.787406 | ||||||||
\(447\) | − 29.6739i | − 1.40353i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.25256 | −0.0591118 | −0.0295559 | − | 0.999563i | \(-0.509409\pi\) | ||||
−0.0295559 | + | 0.999563i | \(0.509409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.46871 | −0.398776 | ||||||||
\(452\) | 33.6345i | 1.58203i | ||||||||
\(453\) | 28.3239i | 1.33077i | ||||||||
\(454\) | 29.2975 | 1.37500 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.44232 | −0.114372 | ||||||||
\(457\) | 23.7618i | 1.11153i | 0.831339 | + | 0.555766i | \(0.187575\pi\) | ||||
−0.831339 | + | 0.555766i | \(0.812425\pi\) | |||||||
\(458\) | 28.1898i | 1.31722i | ||||||||
\(459\) | −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 | ||||||||
\(463\) | 24.8606i | 1.15537i | 0.816259 | + | 0.577686i | \(0.196044\pi\) | ||||
−0.816259 | + | 0.577686i | \(0.803956\pi\) | |||||||
\(464\) | 4.68942 | 0.217701 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 45.3228 | 2.09954 | ||||||||
\(467\) | 13.6674i | 0.632452i | 0.948684 | + | 0.316226i | \(0.102416\pi\) | ||||
−0.948684 | + | 0.316226i | \(0.897584\pi\) | |||||||
\(468\) | − 8.03293i | − 0.371323i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.7727 | −0.865003 | ||||||||
\(472\) | 7.26456i | 0.334378i | ||||||||
\(473\) | − 26.7344i | − 1.22925i | ||||||||
\(474\) | 32.1503 | 1.47671 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 53.8595i | − 2.46606i | ||||||||
\(478\) | 34.0253i | 1.55628i | ||||||||
\(479\) | 4.16576 | 0.190338 | 0.0951691 | − | 0.995461i | \(-0.469661\pi\) | ||||
0.0951691 | + | 0.995461i | \(0.469661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.25672 | −0.0573013 | ||||||||
\(482\) | 24.2700i | 1.10547i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.5566 | 0.570754 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 30.3304 | 1.37582 | ||||||||
\(487\) | 14.1801i | 0.642564i | 0.946984 | + | 0.321282i | \(0.104114\pi\) | ||||
−0.946984 | + | 0.321282i | \(0.895886\pi\) | |||||||
\(488\) | 7.09334i | 0.321101i | ||||||||
\(489\) | 20.4622 | 0.925331 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.8737 | 0.851759 | 0.425880 | − | 0.904780i | \(-0.359965\pi\) | ||||
0.425880 | + | 0.904780i | \(0.359965\pi\) | |||||||
\(492\) | − 26.5411i | − 1.19657i | ||||||||
\(493\) | 14.9056i | 0.671313i | ||||||||
\(494\) | −0.581686 | −0.0261713 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.32497 | 0.284000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − 19.5226i | − 0.874828i | ||||||||
\(499\) | 10.5237 | 0.471104 | 0.235552 | − | 0.971862i | \(-0.424310\pi\) | ||||
0.235552 | + | 0.971862i | \(0.424310\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 60.0044 | 2.68080 | ||||||||
\(502\) | − 61.2425i | − 2.73339i | ||||||||
\(503\) | 19.3854i | 0.864351i | 0.901789 | + | 0.432176i | \(0.142254\pi\) | ||||
−0.901789 | + | 0.432176i | \(0.857746\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22.7278 | 1.01037 | ||||||||
\(507\) | 35.9463i | 1.59643i | ||||||||
\(508\) | − 35.2305i | − 1.56310i | ||||||||
\(509\) | −19.0713 | −0.845322 | −0.422661 | − | 0.906288i | \(-0.638904\pi\) | ||||
−0.422661 | + | 0.906288i | \(0.638904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 17.8816i | 0.790261i | ||||||||
\(513\) | 2.70688i | 0.119512i | ||||||||
\(514\) | 31.9450 | 1.40904 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 83.7861 | 3.68848 | ||||||||
\(517\) | 24.0024i | 1.05562i | ||||||||
\(518\) | 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 | \(0.567759\pi\) | |||||||
\(522\) | 31.7278i | 1.38869i | ||||||||
\(523\) | − 30.6135i | − 1.33864i | −0.742976 | − | 0.669318i | \(-0.766586\pi\) | ||||
0.742976 | − | 0.669318i | \(-0.233414\pi\) | |||||||
\(524\) | −14.1527 | −0.618262 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.642096 | 0.0279967 | ||||||||
\(527\) | 20.1043i | 0.875755i | ||||||||
\(528\) | 11.8816i | 0.517079i | ||||||||
\(529\) | 6.73544 | 0.292845 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.9330 | 0.865021 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.86063i | − 0.0805930i | ||||||||
\(534\) | −34.7422 | −1.50344 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.0659 | 0.607553 | ||||||||
\(537\) | 2.06587i | 0.0891488i | ||||||||
\(538\) | − 18.7697i | − 0.809218i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.6829 | −1.36215 | −0.681077 | − | 0.732212i | \(-0.738488\pi\) | ||||
−0.681077 | + | 0.732212i | \(0.738488\pi\) | |||||||
\(542\) | 6.40284i | 0.275026i | ||||||||
\(543\) | − 5.68703i | − 0.244054i | ||||||||
\(544\) | −37.7662 | −1.61921 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.91866i | 0.253064i | 0.991963 | + | 0.126532i | \(0.0403846\pi\) | ||||
−0.991963 | + | 0.126532i | \(0.959615\pi\) | |||||||
\(548\) | 1.44340i | 0.0616592i | ||||||||
\(549\) | 19.4633 | 0.830671 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.34699 | 0.0573835 | ||||||||
\(552\) | 20.9660i | 0.892371i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.04494 | −0.171853 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 63.1965 | 2.68013 | ||||||||
\(557\) | 31.5806i | 1.33811i | 0.743212 | + | 0.669057i | \(0.233302\pi\) | ||||
−0.743212 | + | 0.669057i | \(0.766698\pi\) | |||||||
\(558\) | 42.7937i | 1.81160i | ||||||||
\(559\) | 5.87372 | 0.248432 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.7662 | −1.59449 | ||||||||
\(562\) | − 1.33697i | − 0.0563968i | ||||||||
\(563\) | − 20.9320i | − 0.882177i | −0.897464 | − | 0.441089i | \(-0.854592\pi\) | ||||
0.897464 | − | 0.441089i | \(-0.145408\pi\) | |||||||
\(564\) | −75.2240 | −3.16750 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.7134 | −1.08082 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.0209i | 0.672223i | ||||||||
\(569\) | −26.7224 | −1.12026 | −0.560130 | − | 0.828405i | \(-0.689249\pi\) | ||||
−0.560130 | + | 0.828405i | \(0.689249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.2844 | 0.974422 | 0.487211 | − | 0.873284i | \(-0.338014\pi\) | ||||
0.487211 | + | 0.873284i | \(0.338014\pi\) | |||||||
\(572\) | − 4.09096i | − 0.171052i | ||||||||
\(573\) | 6.02639i | 0.251756i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −63.9254 | −2.66356 | ||||||||
\(577\) | − 14.7937i | − 0.615869i | −0.951408 | − | 0.307934i | \(-0.900362\pi\) | ||||
0.951408 | − | 0.307934i | \(-0.0996378\pi\) | |||||||
\(578\) | − 22.0449i | − 0.916949i | ||||||||
\(579\) | 7.48527 | 0.311077 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − 95.3283i | − 3.95148i | ||||||||
\(583\) | − 27.4292i | − 1.13600i | ||||||||
\(584\) | −20.7948 | −0.860493 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 61.6190 | 2.54546 | ||||||||
\(587\) | 34.6334i | 1.42947i | 0.699394 | + | 0.714736i | \(0.253453\pi\) | ||||
−0.699394 | + | 0.714736i | \(0.746547\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.81678 | 0.0748592 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.4907 | 0.719472 | ||||||||
\(592\) | 3.64994i | 0.150012i | ||||||||
\(593\) | 5.85517i | 0.240443i | 0.992747 | + | 0.120222i | \(0.0383605\pi\) | ||||
−0.992747 | + | 0.120222i | \(0.961639\pi\) | |||||||
\(594\) | −32.4711 | −1.33231 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 29.6739 | 1.21549 | ||||||||
\(597\) | 64.5280i | 2.64096i | ||||||||
\(598\) | 4.99346i | 0.204198i | ||||||||
\(599\) | −32.7267 | −1.33718 | −0.668589 | − | 0.743632i | \(-0.733101\pi\) | ||||
−0.668589 | + | 0.743632i | \(0.733101\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.9485 | 1.09925 | 0.549627 | − | 0.835410i | \(-0.314770\pi\) | ||||
0.549627 | + | 0.835410i | \(0.314770\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 38.5950i | − 1.57171i | ||||||||
\(604\) | −28.3239 | −1.15248 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −31.1173 | −1.26406 | ||||||||
\(607\) | − 15.4094i | − 0.625448i | −0.949844 | − | 0.312724i | \(-0.898759\pi\) | ||||
0.949844 | − | 0.312724i | \(-0.101241\pi\) | |||||||
\(608\) | 3.41285i | 0.138410i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.27349 | −0.213343 | ||||||||
\(612\) | − 74.1570i | − 2.99762i | ||||||||
\(613\) | 39.8726i | 1.61044i | 0.592976 | + | 0.805220i | \(0.297953\pi\) | ||||
−0.592976 | + | 0.805220i | \(0.702047\pi\) | |||||||
\(614\) | −12.2172 | −0.493048 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 36.7409i | − 1.47913i | −0.673084 | − | 0.739566i | \(-0.735031\pi\) | ||||
0.673084 | − | 0.739566i | \(-0.264969\pi\) | |||||||
\(618\) | − 124.797i | − 5.02007i | ||||||||
\(619\) | 25.7289 | 1.03413 | 0.517066 | − | 0.855946i | \(-0.327024\pi\) | ||||
0.517066 | + | 0.855946i | \(0.327024\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.2371 | 0.932472 | ||||||||
\(622\) | 14.5291i | 0.582565i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.61046 | −0.104502 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −26.1647 | −1.04575 | ||||||||
\(627\) | 3.41285i | 0.136296i | ||||||||
\(628\) | − 18.7727i | − 0.749114i | ||||||||
\(629\) | −11.6015 | −0.462583 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.47525 | 0.0985383 | 0.0492692 | − | 0.998786i | \(-0.484311\pi\) | ||||
0.0492692 | + | 0.998786i | \(0.484311\pi\) | |||||||
\(632\) | 9.46325i | 0.376428i | ||||||||
\(633\) | − 44.9714i | − 1.78745i | ||||||||
\(634\) | −19.1514 | −0.760598 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 85.9638 | 3.40869 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.1581i | 0.639706i | ||||||||
\(639\) | 43.9594 | 1.73901 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.3359 | −1.39568 | −0.697842 | − | 0.716252i | \(-0.745856\pi\) | ||||
−0.697842 | + | 0.716252i | \(0.745856\pi\) | |||||||
\(642\) | − 70.8530i | − 2.79635i | ||||||||
\(643\) | 2.98691i | 0.117792i | 0.998264 | + | 0.0588962i | \(0.0187581\pi\) | ||||
−0.998264 | + | 0.0588962i | \(0.981242\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.36991 | −0.211276 | ||||||||
\(647\) | − 26.0275i | − 1.02325i | −0.859210 | − | 0.511623i | \(-0.829045\pi\) | ||||
0.859210 | − | 0.511623i | \(-0.170955\pi\) | |||||||
\(648\) | − 2.25910i | − 0.0887459i | ||||||||
\(649\) | 10.1514 | 0.398476 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.4622i | 0.801360i | ||||||||
\(653\) | 17.8936i | 0.700229i | 0.936707 | + | 0.350115i | \(0.113857\pi\) | ||||
−0.936707 | + | 0.350115i | \(0.886143\pi\) | |||||||
\(654\) | 55.8386 | 2.18346 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.40393 | −0.210988 | ||||||||
\(657\) | 57.0582i | 2.22605i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.2076 | 0.592405 | 0.296202 | − | 0.955125i | \(-0.404280\pi\) | ||||
0.296202 | + | 0.955125i | \(0.404280\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.48180 | −0.213217 | −0.106609 | − | 0.994301i | \(-0.533999\pi\) | ||||
−0.106609 | + | 0.994301i | \(0.533999\pi\) | |||||||
\(662\) | − 27.4148i | − 1.06551i | ||||||||
\(663\) | − 8.29749i | − 0.322248i | ||||||||
\(664\) | 5.74636 | 0.223002 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.6949 | −0.956907 | ||||||||
\(667\) | − 11.5631i | − 0.447727i | ||||||||
\(668\) | 60.0044i | 2.32164i | ||||||||
\(669\) | −21.4358 | −0.828755 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.91211 | 0.382653 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 30.6763i | − 1.18249i | −0.806494 | − | 0.591243i | \(-0.798637\pi\) | ||||
0.806494 | − | 0.591243i | \(-0.201363\pi\) | |||||||
\(674\) | 7.94743 | 0.306124 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −35.9463 | −1.38255 | ||||||||
\(677\) | 5.54112i | 0.212963i | 0.994315 | + | 0.106481i | \(0.0339584\pi\) | ||||
−0.994315 | + | 0.106481i | \(0.966042\pi\) | |||||||
\(678\) | 73.9518i | 2.84010i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.7662 | 1.44720 | ||||||||
\(682\) | 21.7937i | 0.834523i | ||||||||
\(683\) | − 1.90666i | − 0.0729562i | −0.999334 | − | 0.0364781i | \(-0.988386\pi\) | ||||
0.999334 | − | 0.0364781i | \(-0.0116139\pi\) | |||||||
\(684\) | −6.70142 | −0.256235 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.3383i | 1.38639i | ||||||||
\(688\) | − 17.0593i | − 0.650381i | ||||||||
\(689\) | 6.02639 | 0.229587 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.905571 | −0.0344495 | −0.0172248 | − | 0.999852i | \(-0.505483\pi\) | ||||
−0.0172248 | + | 0.999852i | \(0.505483\pi\) | |||||||
\(692\) | − 21.1712i | − 0.804809i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −48.0188 | −1.82277 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −14.9056 | −0.564994 | ||||||||
\(697\) | − 17.1767i | − 0.650613i | ||||||||
\(698\) | 8.12628i | 0.307584i | ||||||||
\(699\) | 58.4238 | 2.20979 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.8541 | 1.39196 | 0.695980 | − | 0.718061i | \(-0.254970\pi\) | ||||
0.695980 | + | 0.718061i | \(0.254970\pi\) | |||||||
\(702\) | − 7.13412i | − 0.269260i | ||||||||
\(703\) | 1.04841i | 0.0395414i | ||||||||
\(704\) | −32.5555 | −1.22698 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −69.5741 | −2.61845 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 31.8146i | 1.19567i | ||||||||
\(709\) | 41.6818 | 1.56539 | 0.782696 | − | 0.622404i | \(-0.213844\pi\) | ||||
0.782696 | + | 0.622404i | \(0.213844\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.9660 | 0.973800 | ||||||||
\(712\) | − 10.2262i | − 0.383242i | ||||||||
\(713\) | − 15.5961i | − 0.584078i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.06587 | −0.0772051 | ||||||||
\(717\) | 43.8606i | 1.63801i | ||||||||
\(718\) | 37.6818i | 1.40627i | ||||||||
\(719\) | 44.8595 | 1.67298 | 0.836489 | − | 0.547983i | \(-0.184604\pi\) | ||||
0.836489 | + | 0.547983i | \(0.184604\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 41.2899i | − 1.53665i | ||||||||
\(723\) | 31.2855i | 1.16352i | ||||||||
\(724\) | 5.68703 | 0.211357 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 27.6081 | 1.02463 | ||||||||
\(727\) | − 9.08134i | − 0.336808i | −0.985718 | − | 0.168404i | \(-0.946139\pi\) | ||||
0.985718 | − | 0.168404i | \(-0.0538614\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 42.7926 | 1.58491 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.2240 | 2.00555 | ||||||||
\(732\) | 31.0648i | 1.14819i | ||||||||
\(733\) | 28.4203i | 1.04973i | 0.851186 | + | 0.524864i | \(0.175884\pi\) | ||||
−0.851186 | + | 0.524864i | \(0.824116\pi\) | |||||||
\(734\) | −25.9187 | −0.956675 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.2975 | 1.07992 | ||||||||
\(737\) | − 19.6554i | − 0.724016i | ||||||||
\(738\) | − 36.5621i | − 1.34587i | ||||||||
\(739\) | −5.41047 | −0.199027 | −0.0995137 | − | 0.995036i | \(-0.531729\pi\) | ||||
−0.0995137 | + | 0.995036i | \(0.531729\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.749828 | −0.0275456 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.1712i | 1.10687i | 0.832891 | + | 0.553437i | \(0.186684\pi\) | ||||
−0.832891 | + | 0.553437i | \(0.813316\pi\) | |||||||
\(744\) | −20.1043 | −0.737058 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.6763 | 0.757014 | ||||||||
\(747\) | − 15.7673i | − 0.576895i | ||||||||
\(748\) | − 37.7662i | − 1.38087i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.9056 | 1.60214 | 0.801069 | − | 0.598573i | \(-0.204265\pi\) | ||||
0.801069 | + | 0.598573i | \(0.204265\pi\) | |||||||
\(752\) | 15.3160i | 0.558519i | ||||||||
\(753\) | − 78.9453i | − 2.87693i | ||||||||
\(754\) | −3.55005 | −0.129285 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.6914i | 1.40626i | 0.711060 | + | 0.703132i | \(0.248216\pi\) | ||||
−0.711060 | + | 0.703132i | \(0.751784\pi\) | |||||||
\(758\) | 38.1450i | 1.38549i | ||||||||
\(759\) | 29.2975 | 1.06343 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3293 | −1.13569 | −0.567844 | − | 0.823136i | \(-0.692222\pi\) | ||||
−0.567844 | + | 0.823136i | \(0.692222\pi\) | |||||||
\(762\) | − 77.4611i | − 2.80612i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.02639 | −0.218027 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.7989 | 0.462444 | ||||||||
\(767\) | 2.23033i | 0.0805324i | ||||||||
\(768\) | − 11.4896i | − 0.414597i | ||||||||
\(769\) | −9.00654 | −0.324784 | −0.162392 | − | 0.986726i | \(-0.551921\pi\) | ||||
−0.162392 | + | 0.986726i | \(0.551921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.1791 | 1.48303 | ||||||||
\(772\) | 7.48527i | 0.269401i | ||||||||
\(773\) | − 15.7673i | − 0.567110i | −0.958956 | − | 0.283555i | \(-0.908486\pi\) | ||||
0.958956 | − | 0.283555i | \(-0.0915139\pi\) | |||||||
\(774\) | 115.421 | 4.14870 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 28.0593 | 1.00727 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 58.5466i | 2.09900i | ||||||||
\(779\) | −1.55222 | −0.0556141 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.3874 | 0.801083 | ||||||||
\(782\) | 46.0977i | 1.64845i | ||||||||
\(783\) | 16.5202i | 0.590383i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −31.1173 | −1.10992 | ||||||||
\(787\) | − 35.6225i | − 1.26980i | −0.772593 | − | 0.634902i | \(-0.781041\pi\) | ||||
0.772593 | − | 0.634902i | \(-0.218959\pi\) | |||||||
\(788\) | 17.4907i | 0.623081i | ||||||||
\(789\) | 0.827699 | 0.0294669 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − 23.6619i | − 0.840791i | ||||||||
\(793\) | 2.17776i | 0.0773345i | ||||||||
\(794\) | −77.4611 | −2.74899 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −64.5280 | −2.28714 | ||||||||
\(797\) | − 39.6268i | − 1.40365i | −0.712347 | − | 0.701827i | \(-0.752368\pi\) | ||||
0.712347 | − | 0.701827i | \(-0.247632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.6829 | −1.72228 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.0593 | −0.991428 | ||||||||
\(802\) | − 53.7291i | − 1.89724i | ||||||||
\(803\) | 29.0582i | 1.02544i | ||||||||
\(804\) | 61.6004 | 2.17248 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.78822 | −0.168658 | ||||||||
\(807\) | − 24.1952i | − 0.851712i | ||||||||
\(808\) | − 9.15921i | − 0.322220i | ||||||||
\(809\) | 6.82531 | 0.239965 | 0.119983 | − | 0.992776i | \(-0.461716\pi\) | ||||
0.119983 | + | 0.992776i | \(0.461716\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.4303 | 1.63039 | 0.815194 | − | 0.579187i | \(-0.196630\pi\) | ||||
0.815194 | + | 0.579187i | \(0.196630\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.25364i | 0.289468i | ||||||||
\(814\) | −12.5764 | −0.440804 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −24.0988 | −0.843627 | ||||||||
\(817\) | − 4.90011i | − 0.171433i | ||||||||
\(818\) | − 64.8334i | − 2.26685i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.4491 | 1.34188 | 0.670941 | − | 0.741511i | \(-0.265890\pi\) | ||||
0.670941 | + | 0.741511i | \(0.265890\pi\) | |||||||
\(822\) | 3.17360i | 0.110692i | ||||||||
\(823\) | 22.5939i | 0.787574i | 0.919202 | + | 0.393787i | \(0.128835\pi\) | ||||
−0.919202 | + | 0.393787i | \(0.871165\pi\) | |||||||
\(824\) | 36.7333 | 1.27966 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.2460i | 0.530156i | 0.964227 | + | 0.265078i | \(0.0853977\pi\) | ||||
−0.964227 | + | 0.265078i | \(0.914602\pi\) | |||||||
\(828\) | 57.5280i | 1.99924i | ||||||||
\(829\) | −12.9671 | −0.450365 | −0.225182 | − | 0.974317i | \(-0.572298\pi\) | ||||
−0.225182 | + | 0.974317i | \(0.572298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.21416 | −0.180877 | ||||||||
\(832\) | − 7.15267i | − 0.247974i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 138.950 | 4.81143 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.41285 | −0.118036 | ||||||||
\(837\) | 22.2820i | 0.770179i | ||||||||
\(838\) | − 21.4172i | − 0.739846i | ||||||||
\(839\) | −19.4818 | −0.672586 | −0.336293 | − | 0.941757i | \(-0.609173\pi\) | ||||
−0.336293 | + | 0.941757i | \(0.609173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7793 | −0.716527 | ||||||||
\(842\) | − 5.91320i | − 0.203782i | ||||||||
\(843\) | − 1.72344i | − 0.0593583i | ||||||||
\(844\) | 44.9714 | 1.54798 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −103.626 | −3.56273 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 17.5027i | − 0.601046i | ||||||||
\(849\) | −33.1461 | −1.13757 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.00000 | 0.308516 | ||||||||
\(852\) | 70.1625i | 2.40373i | ||||||||
\(853\) | − 20.0449i | − 0.686326i | −0.939276 | − | 0.343163i | \(-0.888502\pi\) | ||||
0.939276 | − | 0.343163i | \(-0.111498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.8552 | 0.712815 | ||||||||
\(857\) | 50.3383i | 1.71952i | 0.510696 | + | 0.859761i | \(0.329388\pi\) | ||||
−0.510696 | + | 0.859761i | \(0.670612\pi\) | |||||||
\(858\) | − 8.99476i | − 0.307076i | ||||||||
\(859\) | −38.1396 | −1.30131 | −0.650653 | − | 0.759375i | \(-0.725505\pi\) | ||||
−0.650653 | + | 0.759375i | \(0.725505\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 20.7487i | − 0.706705i | ||||||||
\(863\) | − 0.864103i | − 0.0294144i | −0.999892 | − | 0.0147072i | \(-0.995318\pi\) | ||||
0.999892 | − | 0.0147072i | \(-0.00468162\pi\) | |||||||
\(864\) | −41.8572 | −1.42401 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −45.8517 | −1.55810 | ||||||||
\(867\) | − 28.4172i | − 0.965100i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.2238 | 0.448586 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.31843 | 0.146324 | ||||||||
\(872\) | 16.4358i | 0.556586i | ||||||||
\(873\) | − 76.9913i | − 2.60576i | ||||||||
\(874\) | 4.16576 | 0.140909 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −91.0692 | −3.07694 | ||||||||
\(877\) | − 9.31297i | − 0.314477i | −0.987561 | − | 0.157238i | \(-0.949741\pi\) | ||||
0.987561 | − | 0.157238i | \(-0.0502591\pi\) | |||||||
\(878\) | 49.6070i | 1.67415i | ||||||||
\(879\) | 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 | ||||||||
\(883\) | − 43.1712i | − 1.45283i | −0.687258 | − | 0.726414i | \(-0.741186\pi\) | ||||
0.687258 | − | 0.726414i | \(-0.258814\pi\) | |||||||
\(884\) | 8.29749 | 0.279075 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −67.2713 | −2.26002 | ||||||||
\(887\) | − 17.4907i | − 0.587281i | −0.955916 | − | 0.293641i | \(-0.905133\pi\) | ||||
0.955916 | − | 0.293641i | \(-0.0948669\pi\) | |||||||
\(888\) | − 11.6015i | − 0.389322i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.15683 | −0.105758 | ||||||||
\(892\) | − 21.4358i | − 0.717723i | ||||||||
\(893\) | 4.39937i | 0.147219i | ||||||||
\(894\) | 65.2438 | 2.18208 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.43686i | 0.214921i | ||||||||
\(898\) | − 2.75399i | − 0.0919017i | ||||||||
\(899\) | 11.0879 | 0.369802 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.6334 | 1.85342 | ||||||||
\(902\) | − 18.6201i | − 0.619981i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.7673 | −0.723969 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −62.2755 | −2.06896 | ||||||||
\(907\) | 16.7453i | 0.556018i | 0.960579 | + | 0.278009i | \(0.0896745\pi\) | ||||
−0.960579 | + | 0.278009i | \(0.910326\pi\) | |||||||
\(908\) | 37.7662i | 1.25332i | ||||||||
\(909\) | −25.1317 | −0.833567 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.9485 | −0.925976 | −0.462988 | − | 0.886365i | \(-0.653223\pi\) | ||||
−0.462988 | + | 0.886365i | \(0.653223\pi\) | |||||||
\(912\) | 2.17776i | 0.0721128i | ||||||||
\(913\) | − 8.02986i | − 0.265750i | ||||||||
\(914\) | −52.2449 | −1.72811 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.3383 | −1.20065 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − 65.8595i | − 2.17369i | ||||||||
\(919\) | −23.2940 | −0.768399 | −0.384199 | − | 0.923250i | \(-0.625523\pi\) | ||||
−0.384199 | + | 0.923250i | \(0.625523\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.7487 | −0.518939 | ||||||||
\(922\) | − 68.3426i | − 2.25075i | ||||||||
\(923\) | 4.91866i | 0.161900i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −54.6609 | −1.79627 | ||||||||
\(927\) | − 100.792i | − 3.31043i | ||||||||
\(928\) | 20.8288i | 0.683738i | ||||||||
\(929\) | 39.6949 | 1.30235 | 0.651173 | − | 0.758929i | \(-0.274277\pi\) | ||||
0.651173 | + | 0.758929i | \(0.274277\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 58.4238i | 1.91373i | ||||||||
\(933\) | 18.7289i | 0.613157i | ||||||||
\(934\) | −30.0504 | −0.983279 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.19869 | 0.169925 | ||||||||
\(937\) | 2.00654i | 0.0655509i | 0.999463 | + | 0.0327755i | \(0.0104346\pi\) | ||||
−0.999463 | + | 0.0327755i | \(0.989565\pi\) | |||||||
\(938\) | 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 | \(0.754804\pi\) | |||||||
\(942\) | − 41.2755i | − 1.34483i | ||||||||
\(943\) | 13.3250i | 0.433921i | ||||||||
\(944\) | 6.47764 | 0.210829 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58.7806 | 1.91112 | ||||||||
\(947\) | 24.6609i | 0.801370i | 0.916216 | + | 0.400685i | \(0.131228\pi\) | ||||
−0.916216 | + | 0.400685i | \(0.868772\pi\) | |||||||
\(948\) | 41.4436i | 1.34603i | ||||||||
\(949\) | −6.38429 | −0.207243 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.6872 | −0.800539 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.5435i | 1.15137i | 0.817673 | + | 0.575684i | \(0.195264\pi\) | ||||
−0.817673 | + | 0.575684i | \(0.804736\pi\) | |||||||
\(954\) | 118.421 | 3.83401 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −43.8606 | −1.41855 | ||||||||
\(957\) | 20.8288i | 0.673299i | ||||||||
\(958\) | 9.15921i | 0.295921i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0449 | −0.517579 | ||||||||
\(962\) | − 2.76313i | − 0.0890869i | ||||||||
\(963\) | − 57.2240i | − 1.84402i | ||||||||
\(964\) | −31.2855 | −1.00764 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 38.3228i | − 1.23238i | −0.787598 | − | 0.616189i | \(-0.788676\pi\) | ||||
0.787598 | − | 0.616189i | \(-0.211324\pi\) | |||||||
\(968\) | 8.12628i | 0.261188i | ||||||||
\(969\) | −6.92213 | −0.222371 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.5819 | −1.52698 | −0.763488 | − | 0.645822i | \(-0.776515\pi\) | ||||
−0.763488 | + | 0.645822i | \(0.776515\pi\) | |||||||
\(972\) | 39.0977i | 1.25406i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.1778 | −0.999000 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.32497 | 0.202457 | ||||||||
\(977\) | 10.4842i | 0.335419i | 0.985836 | + | 0.167709i | \(0.0536370\pi\) | ||||
−0.985836 | + | 0.167709i | \(0.946363\pi\) | |||||||
\(978\) | 44.9900i | 1.43862i | ||||||||
\(979\) | −14.2899 | −0.456706 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.0977 | 1.43986 | ||||||||
\(982\) | 41.4975i | 1.32424i | ||||||||
\(983\) | 10.2262i | 0.326164i | 0.986613 | + | 0.163082i | \(0.0521435\pi\) | ||||
−0.986613 | + | 0.163082i | \(0.947856\pi\) | |||||||
\(984\) | 17.1767 | 0.547572 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −32.7727 | −1.04370 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 0.749828i | − 0.0238552i | ||||||||
\(989\) | −42.0648 | −1.33758 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.27873 | 0.0406203 | 0.0203101 | − | 0.999794i | \(-0.493535\pi\) | ||||
0.0203101 | + | 0.999794i | \(0.493535\pi\) | |||||||
\(992\) | 28.0933i | 0.891965i | ||||||||
\(993\) | − 35.3394i | − 1.12146i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 25.1658 | 0.797408 | ||||||||
\(997\) | 27.7200i | 0.877900i | 0.898511 | + | 0.438950i | \(0.144650\pi\) | ||||
−0.898511 | + | 0.438950i | \(0.855350\pi\) | |||||||
\(998\) | 23.1383i | 0.732430i | ||||||||
\(999\) | −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.b.l.99.6 | 6 | ||
5.2 | odd | 4 | 1225.2.a.x.1.1 | 3 | |||
5.3 | odd | 4 | 1225.2.a.y.1.3 | 3 | |||
5.4 | even | 2 | inner | 1225.2.b.l.99.1 | 6 | ||
7.2 | even | 3 | 175.2.k.b.74.6 | 12 | |||
7.4 | even | 3 | 175.2.k.b.149.1 | 12 | |||
7.6 | odd | 2 | 1225.2.b.m.99.6 | 6 | |||
35.2 | odd | 12 | 175.2.e.e.151.3 | yes | 6 | ||
35.4 | even | 6 | 175.2.k.b.149.6 | 12 | |||
35.9 | even | 6 | 175.2.k.b.74.1 | 12 | |||
35.13 | even | 4 | 1225.2.a.z.1.3 | 3 | |||
35.18 | odd | 12 | 175.2.e.d.51.1 | ✓ | 6 | ||
35.23 | odd | 12 | 175.2.e.d.151.1 | yes | 6 | ||
35.27 | even | 4 | 1225.2.a.w.1.1 | 3 | |||
35.32 | odd | 12 | 175.2.e.e.51.3 | yes | 6 | ||
35.34 | odd | 2 | 1225.2.b.m.99.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.e.d.51.1 | ✓ | 6 | 35.18 | odd | 12 | ||
175.2.e.d.151.1 | yes | 6 | 35.23 | odd | 12 | ||
175.2.e.e.51.3 | yes | 6 | 35.32 | odd | 12 | ||
175.2.e.e.151.3 | yes | 6 | 35.2 | odd | 12 | ||
175.2.k.b.74.1 | 12 | 35.9 | even | 6 | |||
175.2.k.b.74.6 | 12 | 7.2 | even | 3 | |||
175.2.k.b.149.1 | 12 | 7.4 | even | 3 | |||
175.2.k.b.149.6 | 12 | 35.4 | even | 6 | |||
1225.2.a.w.1.1 | 3 | 35.27 | even | 4 | |||
1225.2.a.x.1.1 | 3 | 5.2 | odd | 4 | |||
1225.2.a.y.1.3 | 3 | 5.3 | odd | 4 | |||
1225.2.a.z.1.3 | 3 | 35.13 | even | 4 | |||
1225.2.b.l.99.1 | 6 | 5.4 | even | 2 | inner | ||
1225.2.b.l.99.6 | 6 | 1.1 | even | 1 | trivial | ||
1225.2.b.m.99.1 | 6 | 35.34 | odd | 2 | |||
1225.2.b.m.99.6 | 6 | 7.6 | odd | 2 |