Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (of order \(3\), degree \(2\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1768034304.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - x^{6} - 6x^{5} + 14x^{4} + 18x^{3} - 31x^{2} - 14x + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.1 | ||
Root | \(-0.885685 + 1.90520i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.277 |
Dual form | 966.2.i.l.415.1 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.914214 | − | 1.58346i | −0.408849 | − | 0.708147i | 0.585912 | − | 0.810374i | \(-0.300736\pi\) |
−0.994761 | + | 0.102228i | \(0.967403\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.75255 | − | 1.98206i | −0.662401 | − | 0.749150i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.914214 | + | 1.58346i | −0.289100 | + | 0.500735i | ||||
\(11\) | −2.07397 | + | 3.59222i | −0.625325 | + | 1.08310i | 0.363153 | + | 0.931730i | \(0.381700\pi\) |
−0.988478 | + | 0.151366i | \(0.951633\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −2.18558 | −0.606172 | −0.303086 | − | 0.952963i | \(-0.598017\pi\) | ||||
−0.303086 | + | 0.952963i | \(0.598017\pi\) | |||||||
\(14\) | −0.840244 | + | 2.50878i | −0.224565 | + | 0.670500i | ||||
\(15\) | 1.82843 | 0.472098 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.67858 | − | 2.90738i | 0.407115 | − | 0.705144i | −0.587450 | − | 0.809260i | \(-0.699868\pi\) |
0.994565 | + | 0.104117i | \(0.0332015\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 3.66676 | + | 6.35102i | 0.841213 | + | 1.45702i | 0.888870 | + | 0.458159i | \(0.151491\pi\) |
−0.0476575 | + | 0.998864i | \(0.515176\pi\) | |||||||
\(20\) | 1.82843 | 0.408849 | ||||||||
\(21\) | 2.59279 | − | 0.526718i | 0.565793 | − | 0.114939i | ||||
\(22\) | 4.14794 | 0.884344 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | ||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0.828427 | − | 1.43488i | 0.165685 | − | 0.286976i | ||||
\(26\) | 1.09279 | + | 1.89277i | 0.214314 | + | 0.371203i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.59279 | − | 0.526718i | 0.489992 | − | 0.0995404i | ||||
\(29\) | 5.18558 | 0.962939 | 0.481469 | − | 0.876463i | \(-0.340103\pi\) | ||||
0.481469 | + | 0.876463i | \(0.340103\pi\) | |||||||
\(30\) | −0.914214 | − | 1.58346i | −0.166912 | − | 0.289100i | ||||
\(31\) | −5.25955 | + | 9.10981i | −0.944643 | + | 1.63617i | −0.188180 | + | 0.982135i | \(0.560259\pi\) |
−0.756463 | + | 0.654036i | \(0.773074\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.07397 | − | 3.59222i | −0.361032 | − | 0.625325i | ||||
\(34\) | −3.35716 | −0.575747 | ||||||||
\(35\) | −1.53633 | + | 4.58713i | −0.259686 | + | 0.775366i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.518822 | + | 0.898626i | 0.0852938 | + | 0.147733i | 0.905516 | − | 0.424311i | \(-0.139484\pi\) |
−0.820223 | + | 0.572045i | \(0.806150\pi\) | |||||||
\(38\) | 3.66676 | − | 6.35102i | 0.594827 | − | 1.03027i | ||||
\(39\) | 1.09279 | − | 1.89277i | 0.174987 | − | 0.303086i | ||||
\(40\) | −0.914214 | − | 1.58346i | −0.144550 | − | 0.250368i | ||||
\(41\) | 7.33352 | 1.14530 | 0.572652 | − | 0.819799i | \(-0.305915\pi\) | ||||
0.572652 | + | 0.819799i | \(0.305915\pi\) | |||||||
\(42\) | −1.75255 | − | 1.98206i | −0.270424 | − | 0.305839i | ||||
\(43\) | 5.36098 | 0.817541 | 0.408771 | − | 0.912637i | \(-0.365958\pi\) | ||||
0.408771 | + | 0.912637i | \(0.365958\pi\) | |||||||
\(44\) | −2.07397 | − | 3.59222i | −0.312663 | − | 0.541548i | ||||
\(45\) | −0.914214 | + | 1.58346i | −0.136283 | + | 0.236049i | ||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | −3.61161 | − | 6.25550i | −0.526808 | − | 0.912458i | −0.999512 | − | 0.0312369i | \(-0.990055\pi\) |
0.472704 | − | 0.881221i | \(-0.343278\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −0.857156 | + | 6.94732i | −0.122451 | + | 0.992475i | ||||
\(50\) | −1.65685 | −0.234315 | ||||||||
\(51\) | 1.67858 | + | 2.90738i | 0.235048 | + | 0.407115i | ||||
\(52\) | 1.09279 | − | 1.89277i | 0.151543 | − | 0.262480i | ||||
\(53\) | −2.27137 | + | 3.93413i | −0.311997 | + | 0.540394i | −0.978794 | − | 0.204845i | \(-0.934331\pi\) |
0.666798 | + | 0.745239i | \(0.267664\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 7.58420 | 1.02265 | ||||||||
\(56\) | −1.75255 | − | 1.98206i | −0.234194 | − | 0.264864i | ||||
\(57\) | −7.33352 | −0.971349 | ||||||||
\(58\) | −2.59279 | − | 4.49085i | −0.340450 | − | 0.589677i | ||||
\(59\) | 0.235636 | − | 0.408133i | 0.0306771 | − | 0.0531344i | −0.850279 | − | 0.526332i | \(-0.823567\pi\) |
0.880956 | + | 0.473197i | \(0.156900\pi\) | |||||||
\(60\) | −0.914214 | + | 1.58346i | −0.118024 | + | 0.204424i | ||||
\(61\) | 7.37117 | + | 12.7672i | 0.943781 | + | 1.63468i | 0.758174 | + | 0.652053i | \(0.226092\pi\) |
0.185608 | + | 0.982624i | \(0.440575\pi\) | |||||||
\(62\) | 10.5191 | 1.33593 | ||||||||
\(63\) | −0.840244 | + | 2.50878i | −0.105861 | + | 0.316077i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.99809 | + | 3.46079i | 0.247833 | + | 0.429259i | ||||
\(66\) | −2.07397 | + | 3.59222i | −0.255288 | + | 0.442172i | ||||
\(67\) | −6.70249 | + | 11.6091i | −0.818840 | + | 1.41827i | 0.0876974 | + | 0.996147i | \(0.472049\pi\) |
−0.906537 | + | 0.422125i | \(0.861284\pi\) | |||||||
\(68\) | 1.67858 | + | 2.90738i | 0.203557 | + | 0.352572i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 4.74073 | − | 0.963066i | 0.566626 | − | 0.115108i | ||||
\(71\) | 14.1856 | 1.68352 | 0.841759 | − | 0.539853i | \(-0.181520\pi\) | ||||
0.841759 | + | 0.539853i | \(0.181520\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −5.75955 | + | 9.97584i | −0.674105 | + | 1.16758i | 0.302625 | + | 0.953110i | \(0.402137\pi\) |
−0.976730 | + | 0.214474i | \(0.931196\pi\) | |||||||
\(74\) | 0.518822 | − | 0.898626i | 0.0603118 | − | 0.104463i | ||||
\(75\) | 0.828427 | + | 1.43488i | 0.0956585 | + | 0.165685i | ||||
\(76\) | −7.33352 | −0.841213 | ||||||||
\(77\) | 10.7547 | − | 2.18480i | 1.22562 | − | 0.248981i | ||||
\(78\) | −2.18558 | −0.247469 | ||||||||
\(79\) | 2.59279 | + | 4.49085i | 0.291712 | + | 0.505260i | 0.974215 | − | 0.225623i | \(-0.0724418\pi\) |
−0.682503 | + | 0.730883i | \(0.739109\pi\) | |||||||
\(80\) | −0.914214 | + | 1.58346i | −0.102212 | + | 0.177037i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −3.66676 | − | 6.35102i | −0.404926 | − | 0.701352i | ||||
\(83\) | 5.80479 | 0.637159 | 0.318579 | − | 0.947896i | \(-0.396794\pi\) | ||||
0.318579 | + | 0.947896i | \(0.396794\pi\) | |||||||
\(84\) | −0.840244 | + | 2.50878i | −0.0916782 | + | 0.273731i | ||||
\(85\) | −6.13831 | −0.665794 | ||||||||
\(86\) | −2.68049 | − | 4.64274i | −0.289044 | − | 0.500640i | ||||
\(87\) | −2.59279 | + | 4.49085i | −0.277976 | + | 0.481469i | ||||
\(88\) | −2.07397 | + | 3.59222i | −0.221086 | + | 0.382932i | ||||
\(89\) | −3.34725 | − | 5.79761i | −0.354808 | − | 0.614545i | 0.632277 | − | 0.774742i | \(-0.282120\pi\) |
−0.987085 | + | 0.160197i | \(0.948787\pi\) | |||||||
\(90\) | 1.82843 | 0.192733 | ||||||||
\(91\) | 3.83034 | + | 4.33197i | 0.401528 | + | 0.454113i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −5.25955 | − | 9.10981i | −0.545390 | − | 0.944643i | ||||
\(94\) | −3.61161 | + | 6.25550i | −0.372509 | + | 0.645205i | ||||
\(95\) | 6.70441 | − | 11.6124i | 0.687857 | − | 1.19140i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −4.47127 | −0.453989 | −0.226994 | − | 0.973896i | \(-0.572890\pi\) | ||||
−0.226994 | + | 0.973896i | \(0.572890\pi\) | |||||||
\(98\) | 6.44514 | − | 2.73134i | 0.651057 | − | 0.275907i | ||||
\(99\) | 4.14794 | 0.416884 | ||||||||
\(100\) | 0.828427 | + | 1.43488i | 0.0828427 | + | 0.143488i | ||||
\(101\) | −7.65303 | + | 13.2554i | −0.761505 | + | 1.31897i | 0.180569 | + | 0.983562i | \(0.442206\pi\) |
−0.942075 | + | 0.335404i | \(0.891127\pi\) | |||||||
\(102\) | 1.67858 | − | 2.90738i | 0.166204 | − | 0.287874i | ||||
\(103\) | −3.70249 | − | 6.41291i | −0.364818 | − | 0.631883i | 0.623929 | − | 0.781481i | \(-0.285535\pi\) |
−0.988747 | + | 0.149598i | \(0.952202\pi\) | |||||||
\(104\) | −2.18558 | −0.214314 | ||||||||
\(105\) | −3.20441 | − | 3.62406i | −0.312718 | − | 0.353672i | ||||
\(106\) | 4.54274 | 0.441230 | ||||||||
\(107\) | 2.75064 | + | 4.76424i | 0.265914 | + | 0.460577i | 0.967803 | − | 0.251710i | \(-0.0809929\pi\) |
−0.701889 | + | 0.712287i | \(0.747660\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 9.34753 | − | 16.1904i | 0.895331 | − | 1.55076i | 0.0619370 | − | 0.998080i | \(-0.480272\pi\) |
0.833394 | − | 0.552679i | \(-0.186394\pi\) | |||||||
\(110\) | −3.79210 | − | 6.56811i | −0.361563 | − | 0.626245i | ||||
\(111\) | −1.03764 | −0.0984888 | ||||||||
\(112\) | −0.840244 | + | 2.50878i | −0.0793956 | + | 0.237058i | ||||
\(113\) | 5.28187 | 0.496876 | 0.248438 | − | 0.968648i | \(-0.420083\pi\) | ||||
0.248438 | + | 0.968648i | \(0.420083\pi\) | |||||||
\(114\) | 3.66676 | + | 6.35102i | 0.343424 | + | 0.594827i | ||||
\(115\) | −0.914214 | + | 1.58346i | −0.0852509 | + | 0.147659i | ||||
\(116\) | −2.59279 | + | 4.49085i | −0.240735 | + | 0.416965i | ||||
\(117\) | 1.09279 | + | 1.89277i | 0.101029 | + | 0.174987i | ||||
\(118\) | −0.471271 | −0.0433840 | ||||||||
\(119\) | −8.70441 | + | 1.76828i | −0.797932 | + | 0.162098i | ||||
\(120\) | 1.82843 | 0.166912 | ||||||||
\(121\) | −3.10270 | − | 5.37403i | −0.282063 | − | 0.488548i | ||||
\(122\) | 7.37117 | − | 12.7672i | 0.667354 | − | 1.15589i | ||||
\(123\) | −3.66676 | + | 6.35102i | −0.330621 | + | 0.572652i | ||||
\(124\) | −5.25955 | − | 9.10981i | −0.472322 | − | 0.818085i | ||||
\(125\) | −12.1716 | −1.08866 | ||||||||
\(126\) | 2.59279 | − | 0.526718i | 0.230984 | − | 0.0469238i | ||||
\(127\) | 6.49108 | 0.575991 | 0.287995 | − | 0.957632i | \(-0.407011\pi\) | ||||
0.287995 | + | 0.957632i | \(0.407011\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −2.68049 | + | 4.64274i | −0.236004 | + | 0.408771i | ||||
\(130\) | 1.99809 | − | 3.46079i | 0.175244 | − | 0.303532i | ||||
\(131\) | 2.20441 | + | 3.81814i | 0.192600 | + | 0.333593i | 0.946111 | − | 0.323842i | \(-0.104975\pi\) |
−0.753511 | + | 0.657435i | \(0.771641\pi\) | |||||||
\(132\) | 4.14794 | 0.361032 | ||||||||
\(133\) | 6.16195 | − | 18.3982i | 0.534309 | − | 1.59533i | ||||
\(134\) | 13.4050 | 1.15801 | ||||||||
\(135\) | −0.914214 | − | 1.58346i | −0.0786830 | − | 0.136283i | ||||
\(136\) | 1.67858 | − | 2.90738i | 0.143937 | − | 0.249306i | ||||
\(137\) | −0.840244 | + | 1.45535i | −0.0717869 | + | 0.124339i | −0.899685 | − | 0.436541i | \(-0.856203\pi\) |
0.827898 | + | 0.560879i | \(0.189537\pi\) | |||||||
\(138\) | −0.500000 | − | 0.866025i | −0.0425628 | − | 0.0737210i | ||||
\(139\) | −13.3137 | −1.12925 | −0.564627 | − | 0.825346i | \(-0.690980\pi\) | ||||
−0.564627 | + | 0.825346i | \(0.690980\pi\) | |||||||
\(140\) | −3.20441 | − | 3.62406i | −0.270822 | − | 0.306289i | ||||
\(141\) | 7.22323 | 0.608305 | ||||||||
\(142\) | −7.09279 | − | 12.2851i | −0.595214 | − | 1.03094i | ||||
\(143\) | 4.53283 | − | 7.85110i | 0.379054 | − | 0.656542i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −4.74073 | − | 8.21119i | −0.393696 | − | 0.681902i | ||||
\(146\) | 11.5191 | 0.953328 | ||||||||
\(147\) | −5.58798 | − | 4.21598i | −0.460889 | − | 0.347728i | ||||
\(148\) | −1.03764 | −0.0852938 | ||||||||
\(149\) | −9.67886 | − | 16.7643i | −0.792923 | − | 1.37338i | −0.924150 | − | 0.382031i | \(-0.875225\pi\) |
0.131226 | − | 0.991352i | \(-0.458108\pi\) | |||||||
\(150\) | 0.828427 | − | 1.43488i | 0.0676408 | − | 0.117157i | ||||
\(151\) | −2.79210 | + | 4.83606i | −0.227218 | + | 0.393553i | −0.956983 | − | 0.290145i | \(-0.906296\pi\) |
0.729765 | + | 0.683699i | \(0.239630\pi\) | |||||||
\(152\) | 3.66676 | + | 6.35102i | 0.297414 | + | 0.515135i | ||||
\(153\) | −3.35716 | −0.271410 | ||||||||
\(154\) | −7.26946 | − | 8.22148i | −0.585790 | − | 0.662506i | ||||
\(155\) | 19.2334 | 1.54487 | ||||||||
\(156\) | 1.09279 | + | 1.89277i | 0.0874933 | + | 0.151543i | ||||
\(157\) | 11.3951 | − | 19.7369i | 0.909427 | − | 1.57517i | 0.0945641 | − | 0.995519i | \(-0.469854\pi\) |
0.814862 | − | 0.579654i | \(-0.196812\pi\) | |||||||
\(158\) | 2.59279 | − | 4.49085i | 0.206271 | − | 0.357273i | ||||
\(159\) | −2.27137 | − | 3.93413i | −0.180131 | − | 0.311997i | ||||
\(160\) | 1.82843 | 0.144550 | ||||||||
\(161\) | −0.840244 | + | 2.50878i | −0.0662205 | + | 0.197720i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 12.7184 | + | 22.0289i | 0.996183 | + | 1.72544i | 0.573685 | + | 0.819076i | \(0.305513\pi\) |
0.422498 | + | 0.906364i | \(0.361153\pi\) | |||||||
\(164\) | −3.66676 | + | 6.35102i | −0.286326 | + | 0.495931i | ||||
\(165\) | −3.79210 | + | 6.56811i | −0.295215 | + | 0.511327i | ||||
\(166\) | −2.90240 | − | 5.02710i | −0.225270 | − | 0.390178i | ||||
\(167\) | −22.1185 | −1.71158 | −0.855791 | − | 0.517323i | \(-0.826929\pi\) | ||||
−0.855791 | + | 0.517323i | \(0.826929\pi\) | |||||||
\(168\) | 2.59279 | − | 0.526718i | 0.200038 | − | 0.0406372i | ||||
\(169\) | −8.22323 | −0.632556 | ||||||||
\(170\) | 3.06916 | + | 5.31594i | 0.235394 | + | 0.407714i | ||||
\(171\) | 3.66676 | − | 6.35102i | 0.280404 | − | 0.485674i | ||||
\(172\) | −2.68049 | + | 4.64274i | −0.204385 | + | 0.354006i | ||||
\(173\) | 6.84244 | + | 11.8514i | 0.520221 | + | 0.901049i | 0.999724 | + | 0.0235086i | \(0.00748371\pi\) |
−0.479503 | + | 0.877540i | \(0.659183\pi\) | |||||||
\(174\) | 5.18558 | 0.393118 | ||||||||
\(175\) | −4.29588 | + | 0.872696i | −0.324738 | + | 0.0659696i | ||||
\(176\) | 4.14794 | 0.312663 | ||||||||
\(177\) | 0.235636 | + | 0.408133i | 0.0177115 | + | 0.0306771i | ||||
\(178\) | −3.34725 | + | 5.79761i | −0.250887 | + | 0.434549i | ||||
\(179\) | 1.38839 | − | 2.40476i | 0.103773 | − | 0.179740i | −0.809463 | − | 0.587170i | \(-0.800242\pi\) |
0.913236 | + | 0.407431i | \(0.133575\pi\) | |||||||
\(180\) | −0.914214 | − | 1.58346i | −0.0681415 | − | 0.118024i | ||||
\(181\) | −20.9629 | −1.55816 | −0.779081 | − | 0.626923i | \(-0.784314\pi\) | ||||
−0.779081 | + | 0.626923i | \(0.784314\pi\) | |||||||
\(182\) | 1.83642 | − | 5.48315i | 0.136125 | − | 0.406438i | ||||
\(183\) | −14.7423 | −1.08978 | ||||||||
\(184\) | −0.500000 | − | 0.866025i | −0.0368605 | − | 0.0638442i | ||||
\(185\) | 0.948628 | − | 1.64307i | 0.0697445 | − | 0.120801i | ||||
\(186\) | −5.25955 | + | 9.10981i | −0.385649 | + | 0.667964i | ||||
\(187\) | 6.96264 | + | 12.0596i | 0.509159 | + | 0.881888i | ||||
\(188\) | 7.22323 | 0.526808 | ||||||||
\(189\) | −1.75255 | − | 1.98206i | −0.127479 | − | 0.144174i | ||||
\(190\) | −13.4088 | −0.972777 | ||||||||
\(191\) | 4.48118 | + | 7.76163i | 0.324247 | + | 0.561612i | 0.981360 | − | 0.192180i | \(-0.0615559\pi\) |
−0.657113 | + | 0.753792i | \(0.728223\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −5.81951 | + | 10.0797i | −0.418898 | + | 0.725552i | −0.995829 | − | 0.0912408i | \(-0.970917\pi\) |
0.576931 | + | 0.816793i | \(0.304250\pi\) | |||||||
\(194\) | 2.23564 | + | 3.87223i | 0.160509 | + | 0.278010i | ||||
\(195\) | −3.99618 | −0.286172 | ||||||||
\(196\) | −5.58798 | − | 4.21598i | −0.399141 | − | 0.301141i | ||||
\(197\) | 9.58157 | 0.682658 | 0.341329 | − | 0.939944i | \(-0.389123\pi\) | ||||
0.341329 | + | 0.939944i | \(0.389123\pi\) | |||||||
\(198\) | −2.07397 | − | 3.59222i | −0.147391 | − | 0.255288i | ||||
\(199\) | 4.97637 | − | 8.61932i | 0.352765 | − | 0.611007i | −0.633968 | − | 0.773360i | \(-0.718575\pi\) |
0.986733 | + | 0.162352i | \(0.0519081\pi\) | |||||||
\(200\) | 0.828427 | − | 1.43488i | 0.0585786 | − | 0.101461i | ||||
\(201\) | −6.70249 | − | 11.6091i | −0.472758 | − | 0.818840i | ||||
\(202\) | 15.3061 | 1.07693 | ||||||||
\(203\) | −9.08798 | − | 10.2782i | −0.637851 | − | 0.721385i | ||||
\(204\) | −3.35716 | −0.235048 | ||||||||
\(205\) | −6.70441 | − | 11.6124i | −0.468256 | − | 0.811043i | ||||
\(206\) | −3.70249 | + | 6.41291i | −0.257965 | + | 0.446809i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | 1.09279 | + | 1.89277i | 0.0757715 | + | 0.131240i | ||||
\(209\) | −30.4190 | −2.10413 | ||||||||
\(210\) | −1.53633 | + | 4.58713i | −0.106017 | + | 0.316542i | ||||
\(211\) | 0.303519 | 0.0208951 | 0.0104476 | − | 0.999945i | \(-0.496674\pi\) | ||||
0.0104476 | + | 0.999945i | \(0.496674\pi\) | |||||||
\(212\) | −2.27137 | − | 3.93413i | −0.155998 | − | 0.270197i | ||||
\(213\) | −7.09279 | + | 12.2851i | −0.485990 | + | 0.841759i | ||||
\(214\) | 2.75064 | − | 4.76424i | 0.188030 | − | 0.325677i | ||||
\(215\) | −4.90108 | − | 8.48892i | −0.334251 | − | 0.578939i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 27.2738 | − | 5.54061i | 1.85147 | − | 0.376121i | ||||
\(218\) | −18.6951 | −1.26619 | ||||||||
\(219\) | −5.75955 | − | 9.97584i | −0.389194 | − | 0.674105i | ||||
\(220\) | −3.79210 | + | 6.56811i | −0.255663 | + | 0.442822i | ||||
\(221\) | −3.66867 | + | 6.35433i | −0.246782 | + | 0.427438i | ||||
\(222\) | 0.518822 | + | 0.898626i | 0.0348211 | + | 0.0603118i | ||||
\(223\) | −16.9375 | −1.13422 | −0.567111 | − | 0.823642i | \(-0.691939\pi\) | ||||
−0.567111 | + | 0.823642i | \(0.691939\pi\) | |||||||
\(224\) | 2.59279 | − | 0.526718i | 0.173238 | − | 0.0351929i | ||||
\(225\) | −1.65685 | −0.110457 | ||||||||
\(226\) | −2.64093 | − | 4.57423i | −0.175672 | − | 0.304273i | ||||
\(227\) | 10.7685 | − | 18.6515i | 0.714728 | − | 1.23795i | −0.248336 | − | 0.968674i | \(-0.579884\pi\) |
0.963064 | − | 0.269272i | \(-0.0867830\pi\) | |||||||
\(228\) | 3.66676 | − | 6.35102i | 0.242837 | − | 0.420606i | ||||
\(229\) | 0.333239 | + | 0.577187i | 0.0220211 | + | 0.0381416i | 0.876826 | − | 0.480808i | \(-0.159657\pi\) |
−0.854805 | + | 0.518950i | \(0.826323\pi\) | |||||||
\(230\) | 1.82843 | 0.120563 | ||||||||
\(231\) | −3.48528 | + | 10.4063i | −0.229315 | + | 0.684683i | ||||
\(232\) | 5.18558 | 0.340450 | ||||||||
\(233\) | 0.838334 | + | 1.45204i | 0.0549211 | + | 0.0951261i | 0.892179 | − | 0.451682i | \(-0.149176\pi\) |
−0.837258 | + | 0.546808i | \(0.815843\pi\) | |||||||
\(234\) | 1.09279 | − | 1.89277i | 0.0714380 | − | 0.123734i | ||||
\(235\) | −6.60357 | + | 11.4377i | −0.430770 | + | 0.746115i | ||||
\(236\) | 0.235636 | + | 0.408133i | 0.0153386 | + | 0.0265672i | ||||
\(237\) | −5.18558 | −0.336840 | ||||||||
\(238\) | 5.88357 | + | 6.65410i | 0.381375 | + | 0.431321i | ||||
\(239\) | 10.7220 | 0.693546 | 0.346773 | − | 0.937949i | \(-0.387278\pi\) | ||||
0.346773 | + | 0.937949i | \(0.387278\pi\) | |||||||
\(240\) | −0.914214 | − | 1.58346i | −0.0590122 | − | 0.102212i | ||||
\(241\) | −9.10171 | + | 15.7646i | −0.586292 | + | 1.01549i | 0.408420 | + | 0.912794i | \(0.366080\pi\) |
−0.994713 | + | 0.102694i | \(0.967254\pi\) | |||||||
\(242\) | −3.10270 | + | 5.37403i | −0.199449 | + | 0.345456i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −14.7423 | −0.943781 | ||||||||
\(245\) | 11.7845 | − | 4.99406i | 0.752882 | − | 0.319059i | ||||
\(246\) | 7.33352 | 0.467568 | ||||||||
\(247\) | −8.01401 | − | 13.8807i | −0.509919 | − | 0.883206i | ||||
\(248\) | −5.25955 | + | 9.10981i | −0.333982 | + | 0.578474i | ||||
\(249\) | −2.90240 | + | 5.02710i | −0.183932 | + | 0.318579i | ||||
\(250\) | 6.08579 | + | 10.5409i | 0.384899 | + | 0.666665i | ||||
\(251\) | −0.794604 | −0.0501549 | −0.0250775 | − | 0.999686i | \(-0.507983\pi\) | ||||
−0.0250775 | + | 0.999686i | \(0.507983\pi\) | |||||||
\(252\) | −1.75255 | − | 1.98206i | −0.110400 | − | 0.124858i | ||||
\(253\) | 4.14794 | 0.260779 | ||||||||
\(254\) | −3.24554 | − | 5.62144i | −0.203643 | − | 0.352721i | ||||
\(255\) | 3.06916 | − | 5.31594i | 0.192198 | − | 0.332897i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0.295595 | + | 0.511985i | 0.0184387 | + | 0.0319368i | 0.875098 | − | 0.483947i | \(-0.160797\pi\) |
−0.856659 | + | 0.515883i | \(0.827464\pi\) | |||||||
\(258\) | 5.36098 | 0.333760 | ||||||||
\(259\) | 0.871874 | − | 2.60322i | 0.0541756 | − | 0.161756i | ||||
\(260\) | −3.99618 | −0.247833 | ||||||||
\(261\) | −2.59279 | − | 4.49085i | −0.160490 | − | 0.277976i | ||||
\(262\) | 2.20441 | − | 3.81814i | 0.136189 | − | 0.235886i | ||||
\(263\) | −1.43363 | + | 2.48312i | −0.0884012 | + | 0.153115i | −0.906835 | − | 0.421485i | \(-0.861509\pi\) |
0.818434 | + | 0.574600i | \(0.194842\pi\) | |||||||
\(264\) | −2.07397 | − | 3.59222i | −0.127644 | − | 0.221086i | ||||
\(265\) | 8.30607 | 0.510238 | ||||||||
\(266\) | −19.0143 | + | 3.86270i | −1.16584 | + | 0.236837i | ||||
\(267\) | 6.69450 | 0.409697 | ||||||||
\(268\) | −6.70249 | − | 11.6091i | −0.409420 | − | 0.709136i | ||||
\(269\) | 3.58897 | − | 6.21628i | 0.218823 | − | 0.379013i | −0.735625 | − | 0.677389i | \(-0.763111\pi\) |
0.954449 | + | 0.298376i | \(0.0964448\pi\) | |||||||
\(270\) | −0.914214 | + | 1.58346i | −0.0556373 | + | 0.0963666i | ||||
\(271\) | 5.25955 | + | 9.10981i | 0.319495 | + | 0.553382i | 0.980383 | − | 0.197103i | \(-0.0631534\pi\) |
−0.660888 | + | 0.750485i | \(0.729820\pi\) | |||||||
\(272\) | −3.35716 | −0.203557 | ||||||||
\(273\) | −5.66676 | + | 1.15119i | −0.342968 | + | 0.0696730i | ||||
\(274\) | 1.68049 | 0.101522 | ||||||||
\(275\) | 3.43627 | + | 5.95179i | 0.207215 | + | 0.358906i | ||||
\(276\) | −0.500000 | + | 0.866025i | −0.0300965 | + | 0.0521286i | ||||
\(277\) | 15.4642 | − | 26.7848i | 0.929156 | − | 1.60935i | 0.144419 | − | 0.989517i | \(-0.453869\pi\) |
0.784737 | − | 0.619829i | \(-0.212798\pi\) | |||||||
\(278\) | 6.65685 | + | 11.5300i | 0.399252 | + | 0.691524i | ||||
\(279\) | 10.5191 | 0.629762 | ||||||||
\(280\) | −1.53633 | + | 4.58713i | −0.0918130 | + | 0.274133i | ||||
\(281\) | −2.09949 | −0.125245 | −0.0626225 | − | 0.998037i | \(-0.519946\pi\) | ||||
−0.0626225 | + | 0.998037i | \(0.519946\pi\) | |||||||
\(282\) | −3.61161 | − | 6.25550i | −0.215068 | − | 0.372509i | ||||
\(283\) | −10.1738 | + | 17.6215i | −0.604768 | + | 1.04749i | 0.387321 | + | 0.921945i | \(0.373401\pi\) |
−0.992088 | + | 0.125543i | \(0.959933\pi\) | |||||||
\(284\) | −7.09279 | + | 12.2851i | −0.420880 | + | 0.728985i | ||||
\(285\) | 6.70441 | + | 11.6124i | 0.397135 | + | 0.687857i | ||||
\(286\) | −9.06566 | −0.536064 | ||||||||
\(287\) | −12.8523 | − | 14.5355i | −0.758650 | − | 0.858004i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 2.86475 | + | 4.96190i | 0.168515 | + | 0.291876i | ||||
\(290\) | −4.74073 | + | 8.21119i | −0.278385 | + | 0.482177i | ||||
\(291\) | 2.23564 | − | 3.87223i | 0.131055 | − | 0.226994i | ||||
\(292\) | −5.75955 | − | 9.97584i | −0.337052 | − | 0.583792i | ||||
\(293\) | −31.4853 | −1.83939 | −0.919695 | − | 0.392634i | \(-0.871564\pi\) | ||||
−0.919695 | + | 0.392634i | \(0.871564\pi\) | |||||||
\(294\) | −0.857156 | + | 6.94732i | −0.0499903 | + | 0.405176i | ||||
\(295\) | −0.861685 | −0.0501693 | ||||||||
\(296\) | 0.518822 | + | 0.898626i | 0.0301559 | + | 0.0522316i | ||||
\(297\) | −2.07397 | + | 3.59222i | −0.120344 | + | 0.208442i | ||||
\(298\) | −9.67886 | + | 16.7643i | −0.560681 | + | 0.971129i | ||||
\(299\) | 1.09279 | + | 1.89277i | 0.0631978 | + | 0.109462i | ||||
\(300\) | −1.65685 | −0.0956585 | ||||||||
\(301\) | −9.39537 | − | 10.6258i | −0.541540 | − | 0.612461i | ||||
\(302\) | 5.58420 | 0.321335 | ||||||||
\(303\) | −7.65303 | − | 13.2554i | −0.439655 | − | 0.761505i | ||||
\(304\) | 3.66676 | − | 6.35102i | 0.210303 | − | 0.364256i | ||||
\(305\) | 13.4776 | − | 23.3440i | 0.771727 | − | 1.33667i | ||||
\(306\) | 1.67858 | + | 2.90738i | 0.0959579 | + | 0.166204i | ||||
\(307\) | 1.64865 | 0.0940933 | 0.0470466 | − | 0.998893i | \(-0.485019\pi\) | ||||
0.0470466 | + | 0.998893i | \(0.485019\pi\) | |||||||
\(308\) | −3.48528 | + | 10.4063i | −0.198592 | + | 0.592953i | ||||
\(309\) | 7.40499 | 0.421255 | ||||||||
\(310\) | −9.61671 | − | 16.6566i | −0.546192 | − | 0.946033i | ||||
\(311\) | −6.08897 | + | 10.5464i | −0.345274 | + | 0.598032i | −0.985403 | − | 0.170235i | \(-0.945547\pi\) |
0.640130 | + | 0.768267i | \(0.278881\pi\) | |||||||
\(312\) | 1.09279 | − | 1.89277i | 0.0618671 | − | 0.107157i | ||||
\(313\) | −6.28347 | − | 10.8833i | −0.355163 | − | 0.615160i | 0.631983 | − | 0.774982i | \(-0.282241\pi\) |
−0.987146 | + | 0.159822i | \(0.948908\pi\) | |||||||
\(314\) | −22.7902 | −1.28612 | ||||||||
\(315\) | 4.74073 | − | 0.963066i | 0.267110 | − | 0.0542626i | ||||
\(316\) | −5.18558 | −0.291712 | ||||||||
\(317\) | 4.58897 | + | 7.94833i | 0.257742 | + | 0.446423i | 0.965637 | − | 0.259895i | \(-0.0836881\pi\) |
−0.707894 | + | 0.706318i | \(0.750355\pi\) | |||||||
\(318\) | −2.27137 | + | 3.93413i | −0.127372 | + | 0.220615i | ||||
\(319\) | −10.7547 | + | 18.6278i | −0.602150 | + | 1.04295i | ||||
\(320\) | −0.914214 | − | 1.58346i | −0.0511061 | − | 0.0885183i | ||||
\(321\) | −5.50127 | −0.307051 | ||||||||
\(322\) | 2.59279 | − | 0.526718i | 0.144491 | − | 0.0293529i | ||||
\(323\) | 24.6198 | 1.36988 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −1.81060 | + | 3.13604i | −0.100434 | + | 0.173956i | ||||
\(326\) | 12.7184 | − | 22.0289i | 0.704408 | − | 1.22007i | ||||
\(327\) | 9.34753 | + | 16.1904i | 0.516920 | + | 0.895331i | ||||
\(328\) | 7.33352 | 0.404926 | ||||||||
\(329\) | −6.06927 | + | 18.1215i | −0.334610 | + | 0.999071i | ||||
\(330\) | 7.58420 | 0.417497 | ||||||||
\(331\) | 14.6948 | + | 25.4521i | 0.807698 | + | 1.39897i | 0.914454 | + | 0.404689i | \(0.132620\pi\) |
−0.106756 | + | 0.994285i | \(0.534046\pi\) | |||||||
\(332\) | −2.90240 | + | 5.02710i | −0.159290 | + | 0.275898i | ||||
\(333\) | 0.518822 | − | 0.898626i | 0.0284313 | − | 0.0492444i | ||||
\(334\) | 11.0593 | + | 19.1552i | 0.605135 | + | 1.04813i | ||||
\(335\) | 24.5100 | 1.33913 | ||||||||
\(336\) | −1.75255 | − | 1.98206i | −0.0956093 | − | 0.108130i | ||||
\(337\) | 8.12048 | 0.442351 | 0.221175 | − | 0.975234i | \(-0.429011\pi\) | ||||
0.221175 | + | 0.975234i | \(0.429011\pi\) | |||||||
\(338\) | 4.11161 | + | 7.12152i | 0.223642 | + | 0.387360i | ||||
\(339\) | −2.64093 | + | 4.57423i | −0.143436 | + | 0.248438i | ||||
\(340\) | 3.06916 | − | 5.31594i | 0.166448 | − | 0.288297i | ||||
\(341\) | −21.8163 | − | 37.7869i | −1.18142 | − | 2.04628i | ||||
\(342\) | −7.33352 | −0.396551 | ||||||||
\(343\) | 15.2722 | − | 10.4766i | 0.824624 | − | 0.565682i | ||||
\(344\) | 5.36098 | 0.289044 | ||||||||
\(345\) | −0.914214 | − | 1.58346i | −0.0492196 | − | 0.0852509i | ||||
\(346\) | 6.84244 | − | 11.8514i | 0.367852 | − | 0.637138i | ||||
\(347\) | −14.1307 | + | 24.4751i | −0.758577 | + | 1.31389i | 0.185000 | + | 0.982739i | \(0.440772\pi\) |
−0.943576 | + | 0.331155i | \(0.892562\pi\) | |||||||
\(348\) | −2.59279 | − | 4.49085i | −0.138988 | − | 0.240735i | ||||
\(349\) | 24.1307 | 1.29169 | 0.645843 | − | 0.763471i | \(-0.276506\pi\) | ||||
0.645843 | + | 0.763471i | \(0.276506\pi\) | |||||||
\(350\) | 2.90372 | + | 3.28399i | 0.155210 | + | 0.175537i | ||||
\(351\) | −2.18558 | −0.116658 | ||||||||
\(352\) | −2.07397 | − | 3.59222i | −0.110543 | − | 0.191466i | ||||
\(353\) | −6.70441 | + | 11.6124i | −0.356839 | + | 0.618064i | −0.987431 | − | 0.158051i | \(-0.949479\pi\) |
0.630592 | + | 0.776115i | \(0.282812\pi\) | |||||||
\(354\) | 0.235636 | − | 0.408133i | 0.0125239 | − | 0.0216920i | ||||
\(355\) | −12.9687 | − | 22.4624i | −0.688305 | − | 1.19218i | ||||
\(356\) | 6.69450 | 0.354808 | ||||||||
\(357\) | 2.82083 | − | 8.42237i | 0.149294 | − | 0.445759i | ||||
\(358\) | −2.77677 | −0.146757 | ||||||||
\(359\) | 1.94254 | + | 3.36458i | 0.102523 | + | 0.177576i | 0.912724 | − | 0.408577i | \(-0.133975\pi\) |
−0.810200 | + | 0.586153i | \(0.800642\pi\) | |||||||
\(360\) | −0.914214 | + | 1.58346i | −0.0481833 | + | 0.0834559i | ||||
\(361\) | −17.3903 | + | 30.1208i | −0.915277 | + | 1.58531i | ||||
\(362\) | 10.4815 | + | 18.1544i | 0.550893 | + | 0.954175i | ||||
\(363\) | 6.20540 | 0.325699 | ||||||||
\(364\) | −5.66676 | + | 1.15119i | −0.297019 | + | 0.0603386i | ||||
\(365\) | 21.0618 | 1.10243 | ||||||||
\(366\) | 7.37117 | + | 12.7672i | 0.385297 | + | 0.667354i | ||||
\(367\) | 0.718724 | − | 1.24487i | 0.0375171 | − | 0.0649815i | −0.846657 | − | 0.532139i | \(-0.821388\pi\) |
0.884174 | + | 0.467157i | \(0.154722\pi\) | |||||||
\(368\) | −0.500000 | + | 0.866025i | −0.0260643 | + | 0.0451447i | ||||
\(369\) | −3.66676 | − | 6.35102i | −0.190884 | − | 0.330621i | ||||
\(370\) | −1.89726 | −0.0986337 | ||||||||
\(371\) | 11.7784 | − | 2.39274i | 0.611503 | − | 0.124225i | ||||
\(372\) | 10.5191 | 0.545390 | ||||||||
\(373\) | −9.14794 | − | 15.8447i | −0.473662 | − | 0.820407i | 0.525883 | − | 0.850557i | \(-0.323735\pi\) |
−0.999545 | + | 0.0301497i | \(0.990402\pi\) | |||||||
\(374\) | 6.96264 | − | 12.0596i | 0.360029 | − | 0.623589i | ||||
\(375\) | 6.08579 | − | 10.5409i | 0.314269 | − | 0.544329i | ||||
\(376\) | −3.61161 | − | 6.25550i | −0.186255 | − | 0.322603i | ||||
\(377\) | −11.3335 | −0.583706 | ||||||||
\(378\) | −0.840244 | + | 2.50878i | −0.0432175 | + | 0.129038i | ||||
\(379\) | −5.97637 | −0.306985 | −0.153493 | − | 0.988150i | \(-0.549052\pi\) | ||||
−0.153493 | + | 0.988150i | \(0.549052\pi\) | |||||||
\(380\) | 6.70441 | + | 11.6124i | 0.343929 | + | 0.595702i | ||||
\(381\) | −3.24554 | + | 5.62144i | −0.166274 | + | 0.287995i | ||||
\(382\) | 4.48118 | − | 7.76163i | 0.229277 | − | 0.397119i | ||||
\(383\) | 2.94863 | + | 5.10717i | 0.150668 | + | 0.260964i | 0.931473 | − | 0.363810i | \(-0.118524\pi\) |
−0.780805 | + | 0.624774i | \(0.785191\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −13.2917 | − | 15.0324i | −0.677407 | − | 0.766121i | ||||
\(386\) | 11.6390 | 0.592411 | ||||||||
\(387\) | −2.68049 | − | 4.64274i | −0.136257 | − | 0.236004i | ||||
\(388\) | 2.23564 | − | 3.87223i | 0.113497 | − | 0.196583i | ||||
\(389\) | 8.55675 | − | 14.8207i | 0.433844 | − | 0.751441i | −0.563356 | − | 0.826214i | \(-0.690490\pi\) |
0.997201 | + | 0.0747736i | \(0.0238234\pi\) | |||||||
\(390\) | 1.99809 | + | 3.46079i | 0.101177 | + | 0.175244i | ||||
\(391\) | −3.35716 | −0.169779 | ||||||||
\(392\) | −0.857156 | + | 6.94732i | −0.0432929 | + | 0.350893i | ||||
\(393\) | −4.40881 | −0.222395 | ||||||||
\(394\) | −4.79078 | − | 8.29788i | −0.241356 | − | 0.418041i | ||||
\(395\) | 4.74073 | − | 8.21119i | 0.238532 | − | 0.413150i | ||||
\(396\) | −2.07397 | + | 3.59222i | −0.104221 | + | 0.180516i | ||||
\(397\) | 6.42249 | + | 11.1241i | 0.322336 | + | 0.558302i | 0.980970 | − | 0.194162i | \(-0.0621987\pi\) |
−0.658634 | + | 0.752464i | \(0.728865\pi\) | |||||||
\(398\) | −9.95273 | −0.498885 | ||||||||
\(399\) | 12.8523 | + | 14.5355i | 0.643422 | + | 0.727686i | ||||
\(400\) | −1.65685 | −0.0828427 | ||||||||
\(401\) | −8.71650 | − | 15.0974i | −0.435281 | − | 0.753930i | 0.562037 | − | 0.827112i | \(-0.310018\pi\) |
−0.997319 | + | 0.0731824i | \(0.976684\pi\) | |||||||
\(402\) | −6.70249 | + | 11.6091i | −0.334290 | + | 0.579007i | ||||
\(403\) | 11.4952 | − | 19.9102i | 0.572616 | − | 0.991800i | ||||
\(404\) | −7.65303 | − | 13.2554i | −0.380753 | − | 0.659483i | ||||
\(405\) | 1.82843 | 0.0908553 | ||||||||
\(406\) | −4.35716 | + | 13.0095i | −0.216242 | + | 0.645651i | ||||
\(407\) | −4.30408 | −0.213346 | ||||||||
\(408\) | 1.67858 | + | 2.90738i | 0.0831020 | + | 0.143937i | ||||
\(409\) | 4.53382 | − | 7.85281i | 0.224183 | − | 0.388297i | −0.731891 | − | 0.681422i | \(-0.761362\pi\) |
0.956074 | + | 0.293125i | \(0.0946953\pi\) | |||||||
\(410\) | −6.70441 | + | 11.6124i | −0.331107 | + | 0.573494i | ||||
\(411\) | −0.840244 | − | 1.45535i | −0.0414462 | − | 0.0717869i | ||||
\(412\) | 7.40499 | 0.364818 | ||||||||
\(413\) | −1.22191 | + | 0.248227i | −0.0601262 | + | 0.0122145i | ||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −5.30682 | − | 9.19168i | −0.260502 | − | 0.451202i | ||||
\(416\) | 1.09279 | − | 1.89277i | 0.0535785 | − | 0.0928007i | ||||
\(417\) | 6.65685 | − | 11.5300i | 0.325988 | − | 0.564627i | ||||
\(418\) | 15.2095 | + | 26.3436i | 0.743921 | + | 1.28851i | ||||
\(419\) | −6.63902 | −0.324338 | −0.162169 | − | 0.986763i | \(-0.551849\pi\) | ||||
−0.162169 | + | 0.986763i | \(0.551849\pi\) | |||||||
\(420\) | 4.74073 | − | 0.963066i | 0.231324 | − | 0.0469928i | ||||
\(421\) | −0.942543 | −0.0459367 | −0.0229684 | − | 0.999736i | \(-0.507312\pi\) | ||||
−0.0229684 | + | 0.999736i | \(0.507312\pi\) | |||||||
\(422\) | −0.151760 | − | 0.262855i | −0.00738754 | − | 0.0127956i | ||||
\(423\) | −3.61161 | + | 6.25550i | −0.175603 | + | 0.304153i | ||||
\(424\) | −2.27137 | + | 3.93413i | −0.110307 | + | 0.191058i | ||||
\(425\) | −2.78116 | − | 4.81711i | −0.134906 | − | 0.233664i | ||||
\(426\) | 14.1856 | 0.687294 | ||||||||
\(427\) | 12.3872 | − | 36.9853i | 0.599457 | − | 1.78984i | ||||
\(428\) | −5.50127 | −0.265914 | ||||||||
\(429\) | 4.53283 | + | 7.85110i | 0.218847 | + | 0.379054i | ||||
\(430\) | −4.90108 | + | 8.48892i | −0.236351 | + | 0.409372i | ||||
\(431\) | 17.6849 | − | 30.6311i | 0.851850 | − | 1.47545i | −0.0276860 | − | 0.999617i | \(-0.508814\pi\) |
0.879536 | − | 0.475832i | \(-0.157853\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 32.7627 | 1.57448 | 0.787238 | − | 0.616650i | \(-0.211510\pi\) | ||||
0.787238 | + | 0.616650i | \(0.211510\pi\) | |||||||
\(434\) | −18.4352 | − | 20.8495i | −0.884919 | − | 1.00081i | ||||
\(435\) | 9.48146 | 0.454601 | ||||||||
\(436\) | 9.34753 | + | 16.1904i | 0.447666 | + | 0.775380i | ||||
\(437\) | 3.66676 | − | 6.35102i | 0.175405 | − | 0.303810i | ||||
\(438\) | −5.75955 | + | 9.97584i | −0.275202 | + | 0.476664i | ||||
\(439\) | 9.65817 | + | 16.7284i | 0.460959 | + | 0.798405i | 0.999009 | − | 0.0445080i | \(-0.0141720\pi\) |
−0.538050 | + | 0.842913i | \(0.680839\pi\) | |||||||
\(440\) | 7.58420 | 0.361563 | ||||||||
\(441\) | 6.44514 | − | 2.73134i | 0.306911 | − | 0.130064i | ||||
\(442\) | 7.33734 | 0.349002 | ||||||||
\(443\) | −7.20441 | − | 12.4784i | −0.342292 | − | 0.592866i | 0.642566 | − | 0.766230i | \(-0.277870\pi\) |
−0.984858 | + | 0.173364i | \(0.944536\pi\) | |||||||
\(444\) | 0.518822 | − | 0.898626i | 0.0246222 | − | 0.0426469i | ||||
\(445\) | −6.12020 | + | 10.6005i | −0.290125 | + | 0.502512i | ||||
\(446\) | 8.46877 | + | 14.6683i | 0.401008 | + | 0.694566i | ||||
\(447\) | 19.3577 | 0.915589 | ||||||||
\(448\) | −1.75255 | − | 1.98206i | −0.0828001 | − | 0.0936437i | ||||
\(449\) | −11.0580 | −0.521860 | −0.260930 | − | 0.965358i | \(-0.584029\pi\) | ||||
−0.260930 | + | 0.965358i | \(0.584029\pi\) | |||||||
\(450\) | 0.828427 | + | 1.43488i | 0.0390524 | + | 0.0676408i | ||||
\(451\) | −15.2095 | + | 26.3436i | −0.716187 | + | 1.24047i | ||||
\(452\) | −2.64093 | + | 4.57423i | −0.124219 | + | 0.215154i | ||||
\(453\) | −2.79210 | − | 4.83606i | −0.131184 | − | 0.227218i | ||||
\(454\) | −21.5369 | −1.01078 | ||||||||
\(455\) | 3.35777 | − | 10.0255i | 0.157415 | − | 0.470005i | ||||
\(456\) | −7.33352 | −0.343424 | ||||||||
\(457\) | 12.9225 | + | 22.3824i | 0.604489 | + | 1.04701i | 0.992132 | + | 0.125196i | \(0.0399559\pi\) |
−0.387643 | + | 0.921809i | \(0.626711\pi\) | |||||||
\(458\) | 0.333239 | − | 0.577187i | 0.0155712 | − | 0.0269702i | ||||
\(459\) | 1.67858 | − | 2.90738i | 0.0783493 | − | 0.135705i | ||||
\(460\) | −0.914214 | − | 1.58346i | −0.0426254 | − | 0.0738294i | ||||
\(461\) | −39.3341 | −1.83197 | −0.915986 | − | 0.401211i | \(-0.868589\pi\) | ||||
−0.915986 | + | 0.401211i | \(0.868589\pi\) | |||||||
\(462\) | 10.7547 | − | 2.18480i | 0.500356 | − | 0.101646i | ||||
\(463\) | 25.0778 | 1.16547 | 0.582733 | − | 0.812664i | \(-0.301983\pi\) | ||||
0.582733 | + | 0.812664i | \(0.301983\pi\) | |||||||
\(464\) | −2.59279 | − | 4.49085i | −0.120367 | − | 0.208482i | ||||
\(465\) | −9.61671 | + | 16.6566i | −0.445964 | + | 0.772433i | ||||
\(466\) | 0.838334 | − | 1.45204i | 0.0388351 | − | 0.0672643i | ||||
\(467\) | 11.4815 | + | 19.8865i | 0.531299 | + | 0.920236i | 0.999333 | + | 0.0365258i | \(0.0116291\pi\) |
−0.468034 | + | 0.883710i | \(0.655038\pi\) | |||||||
\(468\) | −2.18558 | −0.101029 | ||||||||
\(469\) | 34.7563 | − | 7.06066i | 1.60490 | − | 0.326031i | ||||
\(470\) | 13.2071 | 0.609200 | ||||||||
\(471\) | 11.3951 | + | 19.7369i | 0.525058 | + | 0.909427i | ||||
\(472\) | 0.235636 | − | 0.408133i | 0.0108460 | − | 0.0187858i | ||||
\(473\) | −11.1185 | + | 19.2578i | −0.511229 | + | 0.885475i | ||||
\(474\) | 2.59279 | + | 4.49085i | 0.119091 | + | 0.206271i | ||||
\(475\) | 12.1506 | 0.557507 | ||||||||
\(476\) | 2.82083 | − | 8.42237i | 0.129293 | − | 0.386039i | ||||
\(477\) | 4.54274 | 0.207998 | ||||||||
\(478\) | −5.36098 | − | 9.28548i | −0.245205 | − | 0.424708i | ||||
\(479\) | 8.30578 | − | 14.3860i | 0.379501 | − | 0.657315i | −0.611489 | − | 0.791253i | \(-0.709429\pi\) |
0.990990 | + | 0.133938i | \(0.0427624\pi\) | |||||||
\(480\) | −0.914214 | + | 1.58346i | −0.0417279 | + | 0.0722749i | ||||
\(481\) | −1.13393 | − | 1.96402i | −0.0517027 | − | 0.0895517i | ||||
\(482\) | 18.2034 | 0.829143 | ||||||||
\(483\) | −1.75255 | − | 1.98206i | −0.0797437 | − | 0.0901870i | ||||
\(484\) | 6.20540 | 0.282063 | ||||||||
\(485\) | 4.08770 | + | 7.08010i | 0.185613 | + | 0.321491i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 7.41131 | − | 12.8368i | 0.335839 | − | 0.581690i | −0.647807 | − | 0.761805i | \(-0.724314\pi\) |
0.983646 | + | 0.180115i | \(0.0576470\pi\) | |||||||
\(488\) | 7.37117 | + | 12.7672i | 0.333677 | + | 0.577946i | ||||
\(489\) | −25.4368 | −1.15029 | ||||||||
\(490\) | −10.2172 | − | 7.70861i | −0.461567 | − | 0.348240i | ||||
\(491\) | 22.2466 | 1.00398 | 0.501988 | − | 0.864875i | \(-0.332602\pi\) | ||||
0.501988 | + | 0.864875i | \(0.332602\pi\) | |||||||
\(492\) | −3.66676 | − | 6.35102i | −0.165310 | − | 0.286326i | ||||
\(493\) | 8.70441 | − | 15.0765i | 0.392027 | − | 0.679010i | ||||
\(494\) | −8.01401 | + | 13.8807i | −0.360567 | + | 0.624521i | ||||
\(495\) | −3.79210 | − | 6.56811i | −0.170442 | − | 0.295215i | ||||
\(496\) | 10.5191 | 0.472322 | ||||||||
\(497\) | −24.8609 | − | 28.1167i | −1.11516 | − | 1.26121i | ||||
\(498\) | 5.80479 | 0.260119 | ||||||||
\(499\) | 5.64284 | + | 9.77369i | 0.252608 | + | 0.437531i | 0.964243 | − | 0.265019i | \(-0.0853782\pi\) |
−0.711635 | + | 0.702550i | \(0.752045\pi\) | |||||||
\(500\) | 6.08579 | − | 10.5409i | 0.272165 | − | 0.471403i | ||||
\(501\) | 11.0593 | − | 19.1552i | 0.494091 | − | 0.855791i | ||||
\(502\) | 0.397302 | + | 0.688147i | 0.0177325 | + | 0.0307135i | ||||
\(503\) | 27.1339 | 1.20984 | 0.604920 | − | 0.796286i | \(-0.293205\pi\) | ||||
0.604920 | + | 0.796286i | \(0.293205\pi\) | |||||||
\(504\) | −0.840244 | + | 2.50878i | −0.0374274 | + | 0.111750i | ||||
\(505\) | 27.9860 | 1.24536 | ||||||||
\(506\) | −2.07397 | − | 3.59222i | −0.0921992 | − | 0.159694i | ||||
\(507\) | 4.11161 | − | 7.12152i | 0.182603 | − | 0.316278i | ||||
\(508\) | −3.24554 | + | 5.62144i | −0.143998 | + | 0.249411i | ||||
\(509\) | 19.3976 | + | 33.5976i | 0.859783 | + | 1.48919i | 0.872136 | + | 0.489264i | \(0.162734\pi\) |
−0.0123530 | + | 0.999924i | \(0.503932\pi\) | |||||||
\(510\) | −6.13831 | −0.271809 | ||||||||
\(511\) | 29.8666 | − | 6.06733i | 1.32122 | − | 0.268403i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.66676 | + | 6.35102i | 0.161891 | + | 0.280404i | ||||
\(514\) | 0.295595 | − | 0.511985i | 0.0130381 | − | 0.0225827i | ||||
\(515\) | −6.76974 | + | 11.7255i | −0.298310 | + | 0.516689i | ||||
\(516\) | −2.68049 | − | 4.64274i | −0.118002 | − | 0.204385i | ||||
\(517\) | 29.9615 | 1.31771 | ||||||||
\(518\) | −2.69039 | + | 0.546546i | −0.118209 | + | 0.0240139i | ||||
\(519\) | −13.6849 | −0.600699 | ||||||||
\(520\) | 1.99809 | + | 3.46079i | 0.0876220 | + | 0.151766i | ||||
\(521\) | −0.764956 | + | 1.32494i | −0.0335133 | + | 0.0580468i | −0.882296 | − | 0.470696i | \(-0.844003\pi\) |
0.848782 | + | 0.528743i | \(0.177336\pi\) | |||||||
\(522\) | −2.59279 | + | 4.49085i | −0.113483 | + | 0.196559i | ||||
\(523\) | −4.21141 | − | 7.29438i | −0.184152 | − | 0.318961i | 0.759138 | − | 0.650929i | \(-0.225621\pi\) |
−0.943290 | + | 0.331968i | \(0.892287\pi\) | |||||||
\(524\) | −4.40881 | −0.192600 | ||||||||
\(525\) | 1.39216 | − | 4.15669i | 0.0607589 | − | 0.181413i | ||||
\(526\) | 2.86725 | 0.125018 | ||||||||
\(527\) | 17.6571 | + | 30.5831i | 0.769157 | + | 1.33222i | ||||
\(528\) | −2.07397 | + | 3.59222i | −0.0902579 | + | 0.156331i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −4.15303 | − | 7.19326i | −0.180396 | − | 0.312455i | ||||
\(531\) | −0.471271 | −0.0204514 | ||||||||
\(532\) | 12.8523 | + | 14.5355i | 0.557220 | + | 0.630194i | ||||
\(533\) | −16.0280 | −0.694251 | ||||||||
\(534\) | −3.34725 | − | 5.79761i | −0.144850 | − | 0.250887i | ||||
\(535\) | 5.02934 | − | 8.71107i | 0.217437 | − | 0.376612i | ||||
\(536\) | −6.70249 | + | 11.6091i | −0.289504 | + | 0.501435i | ||||
\(537\) | 1.38839 | + | 2.40476i | 0.0599133 | + | 0.103773i | ||||
\(538\) | −7.17794 | −0.309463 | ||||||||
\(539\) | −23.1786 | − | 17.4876i | −0.998373 | − | 0.753245i | ||||
\(540\) | 1.82843 | 0.0786830 | ||||||||
\(541\) | 2.82692 | + | 4.89636i | 0.121539 | + | 0.210511i | 0.920375 | − | 0.391038i | \(-0.127884\pi\) |
−0.798836 | + | 0.601549i | \(0.794551\pi\) | |||||||
\(542\) | 5.25955 | − | 9.10981i | 0.225917 | − | 0.391300i | ||||
\(543\) | 10.4815 | − | 18.1544i | 0.449803 | − | 0.779081i | ||||
\(544\) | 1.67858 | + | 2.90738i | 0.0719684 | + | 0.124653i | ||||
\(545\) | −34.1826 | −1.46422 | ||||||||
\(546\) | 3.83034 | + | 4.33197i | 0.163923 | + | 0.185391i | ||||
\(547\) | −26.2480 | −1.12229 | −0.561143 | − | 0.827719i | \(-0.689638\pi\) | ||||
−0.561143 | + | 0.827719i | \(0.689638\pi\) | |||||||
\(548\) | −0.840244 | − | 1.45535i | −0.0358935 | − | 0.0621693i | ||||
\(549\) | 7.37117 | − | 12.7672i | 0.314594 | − | 0.544892i | ||||
\(550\) | 3.43627 | − | 5.95179i | 0.146523 | − | 0.253785i | ||||
\(551\) | 19.0143 | + | 32.9337i | 0.810036 | + | 1.40302i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 4.35716 | − | 13.0095i | 0.185285 | − | 0.553220i | ||||
\(554\) | −30.9285 | −1.31403 | ||||||||
\(555\) | 0.948628 | + | 1.64307i | 0.0402670 | + | 0.0697445i | ||||
\(556\) | 6.65685 | − | 11.5300i | 0.282314 | − | 0.488981i | ||||
\(557\) | −18.6211 | + | 32.2527i | −0.789001 | + | 1.36659i | 0.137578 | + | 0.990491i | \(0.456068\pi\) |
−0.926579 | + | 0.376099i | \(0.877265\pi\) | |||||||
\(558\) | −5.25955 | − | 9.10981i | −0.222655 | − | 0.385649i | ||||
\(559\) | −11.7169 | −0.495570 | ||||||||
\(560\) | 4.74073 | − | 0.963066i | 0.200332 | − | 0.0406970i | ||||
\(561\) | −13.9253 | −0.587926 | ||||||||
\(562\) | 1.04974 | + | 1.81821i | 0.0442808 | + | 0.0766965i | ||||
\(563\) | −6.74483 | + | 11.6824i | −0.284261 | + | 0.492354i | −0.972430 | − | 0.233196i | \(-0.925082\pi\) |
0.688169 | + | 0.725551i | \(0.258415\pi\) | |||||||
\(564\) | −3.61161 | + | 6.25550i | −0.152076 | + | 0.263404i | ||||
\(565\) | −4.82875 | − | 8.36365i | −0.203147 | − | 0.351861i | ||||
\(566\) | 20.3475 | 0.855271 | ||||||||
\(567\) | 2.59279 | − | 0.526718i | 0.108887 | − | 0.0221201i | ||||
\(568\) | 14.1856 | 0.595214 | ||||||||
\(569\) | 8.36897 | + | 14.4955i | 0.350846 | + | 0.607682i | 0.986398 | − | 0.164375i | \(-0.0525609\pi\) |
−0.635552 | + | 0.772058i | \(0.719228\pi\) | |||||||
\(570\) | 6.70441 | − | 11.6124i | 0.280817 | − | 0.486389i | ||||
\(571\) | 13.0836 | − | 22.6614i | 0.547530 | − | 0.948350i | −0.450913 | − | 0.892568i | \(-0.648901\pi\) |
0.998443 | − | 0.0557822i | \(-0.0177652\pi\) | |||||||
\(572\) | 4.53283 | + | 7.85110i | 0.189527 | + | 0.328271i | ||||
\(573\) | −8.96236 | −0.374408 | ||||||||
\(574\) | −6.16195 | + | 18.3982i | −0.257195 | + | 0.767926i | ||||
\(575\) | −1.65685 | −0.0690956 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −9.89858 | + | 17.1448i | −0.412083 | + | 0.713749i | −0.995117 | − | 0.0986987i | \(-0.968532\pi\) |
0.583034 | + | 0.812448i | \(0.301865\pi\) | |||||||
\(578\) | 2.86475 | − | 4.96190i | 0.119158 | − | 0.206388i | ||||
\(579\) | −5.81951 | − | 10.0797i | −0.241851 | − | 0.418898i | ||||
\(580\) | 9.48146 | 0.393696 | ||||||||
\(581\) | −10.1732 | − | 11.5055i | −0.422054 | − | 0.477327i | ||||
\(582\) | −4.47127 | −0.185340 | ||||||||
\(583\) | −9.42150 | − | 16.3185i | −0.390199 | − | 0.675844i | ||||
\(584\) | −5.75955 | + | 9.97584i | −0.238332 | + | 0.412803i | ||||
\(585\) | 1.99809 | − | 3.46079i | 0.0826108 | − | 0.143086i | ||||
\(586\) | 15.7426 | + | 27.2671i | 0.650322 | + | 1.12639i | ||||
\(587\) | −3.20078 | −0.132110 | −0.0660551 | − | 0.997816i | \(-0.521041\pi\) | ||||
−0.0660551 | + | 0.997816i | \(0.521041\pi\) | |||||||
\(588\) | 6.44514 | − | 2.73134i | 0.265793 | − | 0.112639i | ||||
\(589\) | −77.1421 | −3.17858 | ||||||||
\(590\) | 0.430843 | + | 0.746241i | 0.0177375 | + | 0.0307223i | ||||
\(591\) | −4.79078 | + | 8.29788i | −0.197066 | + | 0.341329i | ||||
\(592\) | 0.518822 | − | 0.898626i | 0.0213235 | − | 0.0369333i | ||||
\(593\) | 16.0517 | + | 27.8023i | 0.659162 | + | 1.14170i | 0.980833 | + | 0.194851i | \(0.0624224\pi\) |
−0.321670 | + | 0.946852i | \(0.604244\pi\) | |||||||
\(594\) | 4.14794 | 0.170192 | ||||||||
\(595\) | 10.7577 | + | 12.1665i | 0.441022 | + | 0.498779i | ||||
\(596\) | 19.3577 | 0.792923 | ||||||||
\(597\) | 4.97637 | + | 8.61932i | 0.203669 | + | 0.352765i | ||||
\(598\) | 1.09279 | − | 1.89277i | 0.0446876 | − | 0.0774011i | ||||
\(599\) | −22.5921 | + | 39.1306i | −0.923087 | + | 1.59883i | −0.128479 | + | 0.991712i | \(0.541009\pi\) |
−0.794608 | + | 0.607122i | \(0.792324\pi\) | |||||||
\(600\) | 0.828427 | + | 1.43488i | 0.0338204 | + | 0.0585786i | ||||
\(601\) | 15.5166 | 0.632934 | 0.316467 | − | 0.948604i | \(-0.397503\pi\) | ||||
0.316467 | + | 0.948604i | \(0.397503\pi\) | |||||||
\(602\) | −4.50453 | + | 13.4495i | −0.183591 | + | 0.548162i | ||||
\(603\) | 13.4050 | 0.545893 | ||||||||
\(604\) | −2.79210 | − | 4.83606i | −0.113609 | − | 0.196777i | ||||
\(605\) | −5.67306 | + | 9.82602i | −0.230643 | + | 0.399485i | ||||
\(606\) | −7.65303 | + | 13.2554i | −0.310883 | + | 0.538466i | ||||
\(607\) | −2.43113 | − | 4.21083i | −0.0986763 | − | 0.170912i | 0.812461 | − | 0.583016i | \(-0.198128\pi\) |
−0.911137 | + | 0.412104i | \(0.864794\pi\) | |||||||
\(608\) | −7.33352 | −0.297414 | ||||||||
\(609\) | 13.4451 | − | 2.73134i | 0.544824 | − | 0.110680i | ||||
\(610\) | −26.9553 | −1.09139 | ||||||||
\(611\) | 7.89348 | + | 13.6719i | 0.319336 | + | 0.553106i | ||||
\(612\) | 1.67858 | − | 2.90738i | 0.0678525 | − | 0.117524i | ||||
\(613\) | −3.40499 | + | 5.89761i | −0.137526 | + | 0.238202i | −0.926560 | − | 0.376148i | \(-0.877248\pi\) |
0.789033 | + | 0.614350i | \(0.210582\pi\) | |||||||
\(614\) | −0.824324 | − | 1.42777i | −0.0332670 | − | 0.0576201i | ||||
\(615\) | 13.4088 | 0.540695 | ||||||||
\(616\) | 10.7547 | − | 2.18480i | 0.433321 | − | 0.0880279i | ||||
\(617\) | 7.70087 | 0.310025 | 0.155013 | − | 0.987912i | \(-0.450458\pi\) | ||||
0.155013 | + | 0.987912i | \(0.450458\pi\) | |||||||
\(618\) | −3.70249 | − | 6.41291i | −0.148936 | − | 0.257965i | ||||
\(619\) | −1.56828 | + | 2.71635i | −0.0630346 | + | 0.109179i | −0.895820 | − | 0.444416i | \(-0.853411\pi\) |
0.832786 | + | 0.553595i | \(0.186745\pi\) | |||||||
\(620\) | −9.61671 | + | 16.6566i | −0.386216 | + | 0.668946i | ||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | 12.1779 | 0.488291 | ||||||||
\(623\) | −5.62501 | + | 16.7950i | −0.225361 | + | 0.672879i | ||||
\(624\) | −2.18558 | −0.0874933 | ||||||||
\(625\) | 6.98528 | + | 12.0989i | 0.279411 | + | 0.483954i | ||||
\(626\) | −6.28347 | + | 10.8833i | −0.251138 | + | 0.434984i | ||||
\(627\) | 15.2095 | − | 26.3436i | 0.607409 | − | 1.05206i | ||||
\(628\) | 11.3951 | + | 19.7369i | 0.454713 | + | 0.787587i | ||||
\(629\) | 3.48353 | 0.138898 | ||||||||
\(630\) | −3.20441 | − | 3.62406i | −0.127667 | − | 0.144386i | ||||
\(631\) | −22.1045 | −0.879966 | −0.439983 | − | 0.898006i | \(-0.645016\pi\) | ||||
−0.439983 | + | 0.898006i | \(0.645016\pi\) | |||||||
\(632\) | 2.59279 | + | 4.49085i | 0.103136 | + | 0.178636i | ||||
\(633\) | −0.151760 | + | 0.262855i | −0.00603190 | + | 0.0104476i | ||||
\(634\) | 4.58897 | − | 7.94833i | 0.182251 | − | 0.315669i | ||||
\(635\) | −5.93424 | − | 10.2784i | −0.235493 | − | 0.407886i | ||||
\(636\) | 4.54274 | 0.180131 | ||||||||
\(637\) | 1.87339 | − | 15.1839i | 0.0742262 | − | 0.601610i | ||||
\(638\) | 21.5095 | 0.851568 | ||||||||
\(639\) | −7.09279 | − | 12.2851i | −0.280586 | − | 0.485990i | ||||
\(640\) | −0.914214 | + | 1.58346i | −0.0361375 | + | 0.0625919i | ||||
\(641\) | 9.27415 | − | 16.0633i | 0.366307 | − | 0.634462i | −0.622678 | − | 0.782478i | \(-0.713955\pi\) |
0.988985 | + | 0.148016i | \(0.0472886\pi\) | |||||||
\(642\) | 2.75064 | + | 4.76424i | 0.108559 | + | 0.188030i | ||||
\(643\) | −12.4114 | −0.489456 | −0.244728 | − | 0.969592i | \(-0.578699\pi\) | ||||
−0.244728 | + | 0.969592i | \(0.578699\pi\) | |||||||
\(644\) | −1.75255 | − | 1.98206i | −0.0690600 | − | 0.0781043i | ||||
\(645\) | 9.80216 | 0.385959 | ||||||||
\(646\) | −12.3099 | − | 21.3214i | −0.484326 | − | 0.838877i | ||||
\(647\) | −18.9101 | + | 32.7532i | −0.743432 | + | 1.28766i | 0.207492 | + | 0.978237i | \(0.433470\pi\) |
−0.950924 | + | 0.309425i | \(0.899863\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 0.977402 | + | 1.69291i | 0.0383664 | + | 0.0664525i | ||||
\(650\) | 3.62119 | 0.142035 | ||||||||
\(651\) | −8.83862 | + | 26.3901i | −0.346413 | + | 1.03431i | ||||
\(652\) | −25.4368 | −0.996183 | ||||||||
\(653\) | −9.75474 | − | 16.8957i | −0.381732 | − | 0.661180i | 0.609578 | − | 0.792726i | \(-0.291339\pi\) |
−0.991310 | + | 0.131546i | \(0.958006\pi\) | |||||||
\(654\) | 9.34753 | − | 16.1904i | 0.365517 | − | 0.633095i | ||||
\(655\) | 4.03059 | − | 6.98119i | 0.157488 | − | 0.272778i | ||||
\(656\) | −3.66676 | − | 6.35102i | −0.143163 | − | 0.247966i | ||||
\(657\) | 11.5191 | 0.449403 | ||||||||
\(658\) | 18.7283 | − | 3.80461i | 0.730106 | − | 0.148319i | ||||
\(659\) | −33.6772 | −1.31188 | −0.655939 | − | 0.754814i | \(-0.727727\pi\) | ||||
−0.655939 | + | 0.754814i | \(0.727727\pi\) | |||||||
\(660\) | −3.79210 | − | 6.56811i | −0.147607 | − | 0.255663i | ||||
\(661\) | −13.6983 | + | 23.7262i | −0.532803 | + | 0.922842i | 0.466463 | + | 0.884541i | \(0.345528\pi\) |
−0.999266 | + | 0.0383011i | \(0.987805\pi\) | |||||||
\(662\) | 14.6948 | − | 25.4521i | 0.571129 | − | 0.989224i | ||||
\(663\) | −3.66867 | − | 6.35433i | −0.142479 | − | 0.246782i | ||||
\(664\) | 5.80479 | 0.225270 | ||||||||
\(665\) | −34.7662 | + | 7.06267i | −1.34818 | + | 0.273879i | ||||
\(666\) | −1.03764 | −0.0402079 | ||||||||
\(667\) | −2.59279 | − | 4.49085i | −0.100393 | − | 0.173886i | ||||
\(668\) | 11.0593 | − | 19.1552i | 0.427895 | − | 0.741136i | ||||
\(669\) | 8.46877 | − | 14.6683i | 0.327422 | − | 0.567111i | ||||
\(670\) | −12.2550 | − | 21.2263i | −0.473453 | − | 0.820044i | ||||
\(671\) | −61.1503 | −2.36068 | ||||||||
\(672\) | −0.840244 | + | 2.50878i | −0.0324131 | + | 0.0967784i | ||||
\(673\) | 7.79715 | 0.300558 | 0.150279 | − | 0.988644i | \(-0.451983\pi\) | ||||
0.150279 | + | 0.988644i | \(0.451983\pi\) | |||||||
\(674\) | −4.06024 | − | 7.03255i | −0.156395 | − | 0.270884i | ||||
\(675\) | 0.828427 | − | 1.43488i | 0.0318862 | − | 0.0552285i | ||||
\(676\) | 4.11161 | − | 7.12152i | 0.158139 | − | 0.273905i | ||||
\(677\) | 0.0283290 | + | 0.0490673i | 0.00108877 | + | 0.00188581i | 0.866569 | − | 0.499057i | \(-0.166320\pi\) |
−0.865481 | + | 0.500943i | \(0.832987\pi\) | |||||||
\(678\) | 5.28187 | 0.202849 | ||||||||
\(679\) | 7.83611 | + | 8.86235i | 0.300722 | + | 0.340106i | ||||
\(680\) | −6.13831 | −0.235394 | ||||||||
\(681\) | 10.7685 | + | 18.6515i | 0.412649 | + | 0.714728i | ||||
\(682\) | −21.8163 | + | 37.7869i | −0.835389 | + | 1.44694i | ||||
\(683\) | 17.9817 | − | 31.1453i | 0.688052 | − | 1.19174i | −0.284415 | − | 0.958701i | \(-0.591799\pi\) |
0.972467 | − | 0.233040i | \(-0.0748674\pi\) | |||||||
\(684\) | 3.66676 | + | 6.35102i | 0.140202 | + | 0.242837i | ||||
\(685\) | 3.07265 | 0.117400 | ||||||||
\(686\) | −16.7091 | − | 7.98786i | −0.637956 | − | 0.304978i | ||||
\(687\) | −0.666478 | −0.0254277 | ||||||||
\(688\) | −2.68049 | − | 4.64274i | −0.102193 | − | 0.177003i | ||||
\(689\) | 4.96427 | − | 8.59836i | 0.189123 | − | 0.327571i | ||||
\(690\) | −0.914214 | + | 1.58346i | −0.0348035 | + | 0.0602815i | ||||
\(691\) | 11.0181 | + | 19.0839i | 0.419149 | + | 0.725987i | 0.995854 | − | 0.0909653i | \(-0.0289952\pi\) |
−0.576705 | + | 0.816952i | \(0.695662\pi\) | |||||||
\(692\) | −13.6849 | −0.520221 | ||||||||
\(693\) | −7.26946 | − | 8.22148i | −0.276144 | − | 0.312308i | ||||
\(694\) | 28.2614 | 1.07279 | ||||||||
\(695\) | 12.1716 | + | 21.0818i | 0.461694 | + | 0.799678i | ||||
\(696\) | −2.59279 | + | 4.49085i | −0.0982795 | + | 0.170225i | ||||
\(697\) | 12.3099 | − | 21.3214i | 0.466270 | − | 0.807604i | ||||
\(698\) | −12.0653 | − | 20.8978i | −0.456680 | − | 0.790992i | ||||
\(699\) | −1.67667 | −0.0634174 | ||||||||
\(700\) | 1.39216 | − | 4.15669i | 0.0526188 | − | 0.157108i | ||||
\(701\) | 37.5337 | 1.41763 | 0.708814 | − | 0.705396i | \(-0.249231\pi\) | ||||
0.708814 | + | 0.705396i | \(0.249231\pi\) | |||||||
\(702\) | 1.09279 | + | 1.89277i | 0.0412448 | + | 0.0714380i | ||||
\(703\) | −3.80479 | + | 6.59009i | −0.143500 | + | 0.248550i | ||||
\(704\) | −2.07397 | + | 3.59222i | −0.0781657 | + | 0.135387i | ||||
\(705\) | −6.60357 | − | 11.4377i | −0.248705 | − | 0.430770i | ||||
\(706\) | 13.4088 | 0.504647 | ||||||||
\(707\) | 39.6854 | − | 8.06199i | 1.49252 | − | 0.303202i | ||||
\(708\) | −0.471271 | −0.0177115 | ||||||||
\(709\) | −20.4894 | − | 35.4887i | −0.769495 | − | 1.33280i | −0.937837 | − | 0.347076i | \(-0.887175\pi\) |
0.168342 | − | 0.985729i | \(-0.446159\pi\) | |||||||
\(710\) | −12.9687 | + | 22.4624i | −0.486705 | + | 0.842998i | ||||
\(711\) | 2.59279 | − | 4.49085i | 0.0972373 | − | 0.168420i | ||||
\(712\) | −3.34725 | − | 5.79761i | −0.125443 | − | 0.217274i | ||||
\(713\) | 10.5191 | 0.393944 | ||||||||
\(714\) | −8.70441 | + | 1.76828i | −0.325754 | + | 0.0661761i | ||||
\(715\) | −16.5759 | −0.619904 | ||||||||
\(716\) | 1.38839 | + | 2.40476i | 0.0518864 | + | 0.0898699i | ||||
\(717\) | −5.36098 | + | 9.28548i | −0.200209 | + | 0.346773i | ||||
\(718\) | 1.94254 | − | 3.36458i | 0.0724950 | − | 0.125565i | ||||
\(719\) | −8.86985 | − | 15.3630i | −0.330789 | − | 0.572944i | 0.651877 | − | 0.758324i | \(-0.273982\pi\) |
−0.982667 | + | 0.185380i | \(0.940648\pi\) | |||||||
\(720\) | 1.82843 | 0.0681415 | ||||||||
\(721\) | −6.22200 | + | 18.5775i | −0.231719 | + | 0.691863i | ||||
\(722\) | 34.7805 | 1.29440 | ||||||||
\(723\) | −9.10171 | − | 15.7646i | −0.338496 | − | 0.586292i | ||||
\(724\) | 10.4815 | − | 18.1544i | 0.389540 | − | 0.674704i | ||||
\(725\) | 4.29588 | − | 7.44068i | 0.159545 | − | 0.276340i | ||||
\(726\) | −3.10270 | − | 5.37403i | −0.115152 | − | 0.199449i | ||||
\(727\) | 14.4240 | 0.534957 | 0.267478 | − | 0.963564i | \(-0.413810\pi\) | ||||
0.267478 | + | 0.963564i | \(0.413810\pi\) | |||||||
\(728\) | 3.83034 | + | 4.33197i | 0.141962 | + | 0.160553i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.5309 | − | 18.2401i | −0.389767 | − | 0.675096i | ||||
\(731\) | 8.99882 | − | 15.5864i | 0.332833 | − | 0.576484i | ||||
\(732\) | 7.37117 | − | 12.7672i | 0.272446 | − | 0.471891i | ||||
\(733\) | 15.8427 | + | 27.4404i | 0.585164 | + | 1.01353i | 0.994855 | + | 0.101310i | \(0.0323033\pi\) |
−0.409691 | + | 0.912224i | \(0.634363\pi\) | |||||||
\(734\) | −1.43745 | −0.0530572 | ||||||||
\(735\) | −1.56725 | + | 12.7027i | −0.0578088 | + | 0.468545i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −27.8015 | − | 48.1537i | −1.02408 | − | 1.77376i | ||||
\(738\) | −3.66676 | + | 6.35102i | −0.134975 | + | 0.233784i | ||||
\(739\) | 2.10011 | − | 3.63749i | 0.0772536 | − | 0.133807i | −0.824810 | − | 0.565409i | \(-0.808718\pi\) |
0.902064 | + | 0.431602i | \(0.142052\pi\) | |||||||
\(740\) | 0.948628 | + | 1.64307i | 0.0348723 | + | 0.0604005i | ||||
\(741\) | 16.0280 | 0.588804 | ||||||||
\(742\) | −7.96136 | − | 9.00400i | −0.292271 | − | 0.330547i | ||||
\(743\) | −42.3168 | −1.55245 | −0.776227 | − | 0.630454i | \(-0.782869\pi\) | ||||
−0.776227 | + | 0.630454i | \(0.782869\pi\) | |||||||
\(744\) | −5.25955 | − | 9.10981i | −0.192825 | − | 0.333982i | ||||
\(745\) | −17.6971 | + | 30.6523i | −0.648371 | + | 1.12301i | ||||
\(746\) | −9.14794 | + | 15.8447i | −0.334930 | + | 0.580115i | ||||
\(747\) | −2.90240 | − | 5.02710i | −0.106193 | − | 0.183932i | ||||
\(748\) | −13.9253 | −0.509159 | ||||||||
\(749\) | 4.62241 | − | 13.8015i | 0.168899 | − | 0.504296i | ||||
\(750\) | −12.1716 | −0.444443 | ||||||||
\(751\) | −8.22219 | − | 14.2413i | −0.300032 | − | 0.519671i | 0.676111 | − | 0.736800i | \(-0.263664\pi\) |
−0.976143 | + | 0.217129i | \(0.930331\pi\) | |||||||
\(752\) | −3.61161 | + | 6.25550i | −0.131702 | + | 0.228115i | ||||
\(753\) | 0.397302 | − | 0.688147i | 0.0144785 | − | 0.0250775i | ||||
\(754\) | 5.66676 | + | 9.81512i | 0.206371 | + | 0.357446i | ||||
\(755\) | 10.2103 | 0.371591 | ||||||||
\(756\) | 2.59279 | − | 0.526718i | 0.0942989 | − | 0.0191566i | ||||
\(757\) | 45.4215 | 1.65087 | 0.825437 | − | 0.564494i | \(-0.190929\pi\) | ||||
0.825437 | + | 0.564494i | \(0.190929\pi\) | |||||||
\(758\) | 2.98818 | + | 5.17568i | 0.108536 | + | 0.187989i | ||||
\(759\) | −2.07397 | + | 3.59222i | −0.0752803 | + | 0.130389i | ||||
\(760\) | 6.70441 | − | 11.6124i | 0.243194 | − | 0.421225i | ||||
\(761\) | −7.82107 | − | 13.5465i | −0.283513 | − | 0.491060i | 0.688734 | − | 0.725014i | \(-0.258167\pi\) |
−0.972248 | + | 0.233954i | \(0.924833\pi\) | |||||||
\(762\) | 6.49108 | 0.235147 | ||||||||
\(763\) | −48.4724 | + | 9.84704i | −1.75482 | + | 0.356487i | ||||
\(764\) | −8.96236 | −0.324247 | ||||||||
\(765\) | 3.06916 | + | 5.31594i | 0.110966 | + | 0.192198i | ||||
\(766\) | 2.94863 | − | 5.10717i | 0.106538 | − | 0.184530i | ||||
\(767\) | −0.515001 | + | 0.892008i | −0.0185956 | + | 0.0322086i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | −14.1205 | −0.509198 | −0.254599 | − | 0.967047i | \(-0.581943\pi\) | ||||
−0.254599 | + | 0.967047i | \(0.581943\pi\) | |||||||
\(770\) | −6.37258 | + | 19.0271i | −0.229652 | + | 0.685690i | ||||
\(771\) | −0.591190 | −0.0212912 | ||||||||
\(772\) | −5.81951 | − | 10.0797i | −0.209449 | − | 0.362776i | ||||
\(773\) | −8.80260 | + | 15.2466i | −0.316608 | + | 0.548380i | −0.979778 | − | 0.200088i | \(-0.935877\pi\) |
0.663170 | + | 0.748468i | \(0.269210\pi\) | |||||||
\(774\) | −2.68049 | + | 4.64274i | −0.0963482 | + | 0.166880i | ||||
\(775\) | 8.71431 | + | 15.0936i | 0.313027 | + | 0.542179i | ||||
\(776\) | −4.47127 | −0.160509 | ||||||||
\(777\) | 1.81852 | + | 2.05668i | 0.0652391 | + | 0.0737829i | ||||
\(778\) | −17.1135 | −0.613549 | ||||||||
\(779\) | 26.8903 | + | 46.5753i | 0.963444 | + | 1.66873i | ||||
\(780\) | 1.99809 | − | 3.46079i | 0.0715431 | − | 0.123916i | ||||
\(781\) | −29.4205 | + | 50.9577i | −1.05275 | + | 1.82341i | ||||
\(782\) | 1.67858 | + | 2.90738i | 0.0600258 | + | 0.103968i | ||||
\(783\) | 5.18558 | 0.185318 | ||||||||
\(784\) | 6.44514 | − | 2.73134i | 0.230183 | − | 0.0975479i | ||||
\(785\) | −41.6702 | −1.48727 | ||||||||
\(786\) | 2.20441 | + | 3.81814i | 0.0786285 | + | 0.136189i | ||||
\(787\) | 4.37916 | − | 7.58493i | 0.156100 | − | 0.270374i | −0.777359 | − | 0.629057i | \(-0.783441\pi\) |
0.933459 | + | 0.358684i | \(0.116774\pi\) | |||||||
\(788\) | −4.79078 | + | 8.29788i | −0.170665 | + | 0.295600i | ||||
\(789\) | −1.43363 | − | 2.48312i | −0.0510385 | − | 0.0884012i | ||||
\(790\) | −9.48146 | −0.337335 | ||||||||
\(791\) | −9.25672 | − | 10.4690i | −0.329131 | − | 0.372235i | ||||
\(792\) | 4.14794 | 0.147391 | ||||||||
\(793\) | −16.1103 | − | 27.9038i | −0.572093 | − | 0.990895i | ||||
\(794\) | 6.42249 | − | 11.1241i | 0.227926 | − | 0.394779i | ||||
\(795\) | −4.15303 | + | 7.19326i | −0.147293 | + | 0.255119i | ||||
\(796\) | 4.97637 | + | 8.61932i | 0.176383 | + | 0.305504i | ||||
\(797\) | 16.5708 | 0.586966 | 0.293483 | − | 0.955964i | \(-0.405186\pi\) | ||||
0.293483 | + | 0.955964i | \(0.405186\pi\) | |||||||
\(798\) | 6.16195 | − | 18.3982i | 0.218131 | − | 0.651290i | ||||
\(799\) | −24.2495 | −0.857886 | ||||||||
\(800\) | 0.828427 | + | 1.43488i | 0.0292893 | + | 0.0507306i | ||||
\(801\) | −3.34725 | + | 5.79761i | −0.118269 | + | 0.204848i | ||||
\(802\) | −8.71650 | + | 15.0974i | −0.307790 | + | 0.533109i | ||||
\(803\) | −23.8903 | − | 41.3792i | −0.843069 | − | 1.46024i | ||||
\(804\) | 13.4050 | 0.472758 | ||||||||
\(805\) | 4.74073 | − | 0.963066i | 0.167089 | − | 0.0339436i | ||||
\(806\) | −22.9904 | −0.809801 | ||||||||
\(807\) | 3.58897 | + | 6.21628i | 0.126338 | + | 0.218823i | ||||
\(808\) | −7.65303 | + | 13.2554i | −0.269233 | + | 0.466325i | ||||
\(809\) | −13.9276 | + | 24.1234i | −0.489669 | + | 0.848132i | −0.999929 | − | 0.0118879i | \(-0.996216\pi\) |
0.510260 | + | 0.860020i | \(0.329549\pi\) | |||||||
\(810\) | −0.914214 | − | 1.58346i | −0.0321222 | − | 0.0556373i | ||||
\(811\) | 31.5623 | 1.10830 | 0.554151 | − | 0.832416i | \(-0.313043\pi\) | ||||
0.554151 | + | 0.832416i | \(0.313043\pi\) | |||||||
\(812\) | 13.4451 | − | 2.73134i | 0.471832 | − | 0.0958513i | ||||
\(813\) | −10.5191 | −0.368921 | ||||||||
\(814\) | 2.15204 | + | 3.72745i | 0.0754290 | + | 0.130647i | ||||
\(815\) | 23.2547 | − | 40.2783i | 0.814576 | − | 1.41089i | ||||
\(816\) | 1.67858 | − | 2.90738i | 0.0587620 | − | 0.101779i | ||||
\(817\) | 19.6574 | + | 34.0476i | 0.687726 | + | 1.19118i | ||||
\(818\) | −9.06765 | −0.317043 | ||||||||
\(819\) | 1.83642 | − | 5.48315i | 0.0641698 | − | 0.191597i | ||||
\(820\) | 13.4088 | 0.468256 | ||||||||
\(821\) | 12.4965 | + | 21.6446i | 0.436131 | + | 0.755401i | 0.997387 | − | 0.0722410i | \(-0.0230151\pi\) |
−0.561256 | + | 0.827642i | \(0.689682\pi\) | |||||||
\(822\) | −0.840244 | + | 1.45535i | −0.0293069 | + | 0.0507610i | ||||
\(823\) | 4.04401 | − | 7.00444i | 0.140965 | − | 0.244159i | −0.786895 | − | 0.617087i | \(-0.788313\pi\) |
0.927860 | + | 0.372928i | \(0.121646\pi\) | |||||||
\(824\) | −3.70249 | − | 6.41291i | −0.128983 | − | 0.223404i | ||||
\(825\) | −6.87253 | −0.239271 | ||||||||
\(826\) | 0.825925 | + | 0.934090i | 0.0287376 | + | 0.0325011i | ||||
\(827\) | −19.3864 | −0.674130 | −0.337065 | − | 0.941481i | \(-0.609434\pi\) | ||||
−0.337065 | + | 0.941481i | \(0.609434\pi\) | |||||||
\(828\) | −0.500000 | − | 0.866025i | −0.0173762 | − | 0.0300965i | ||||
\(829\) | −13.4126 | + | 23.2313i | −0.465838 | + | 0.806856i | −0.999239 | − | 0.0390071i | \(-0.987581\pi\) |
0.533401 | + | 0.845863i | \(0.320914\pi\) | |||||||
\(830\) | −5.30682 | + | 9.19168i | −0.184202 | + | 0.319048i | ||||
\(831\) | 15.4642 | + | 26.7848i | 0.536449 | + | 0.929156i | ||||
\(832\) | −2.18558 | −0.0757715 | ||||||||
\(833\) | 18.7597 | + | 14.1537i | 0.649986 | + | 0.490397i | ||||
\(834\) | −13.3137 | −0.461016 | ||||||||
\(835\) | 20.2210 | + | 35.0239i | 0.699778 | + | 1.21205i | ||||
\(836\) | 15.2095 | − | 26.3436i | 0.526032 | − | 0.911113i | ||||
\(837\) | −5.25955 | + | 9.10981i | −0.181797 | + | 0.314881i | ||||
\(838\) | 3.31951 | + | 5.74956i | 0.114671 | + | 0.198615i | ||||
\(839\) | −4.82979 | −0.166743 | −0.0833715 | − | 0.996519i | \(-0.526569\pi\) | ||||
−0.0833715 | + | 0.996519i | \(0.526569\pi\) | |||||||
\(840\) | −3.20441 | − | 3.62406i | −0.110562 | − | 0.125042i | ||||
\(841\) | −2.10973 | −0.0727493 | ||||||||
\(842\) | 0.471271 | + | 0.816266i | 0.0162411 | + | 0.0281304i | ||||
\(843\) | 1.04974 | − | 1.81821i | 0.0361551 | − | 0.0626225i | ||||
\(844\) | −0.151760 | + | 0.262855i | −0.00522378 | + | 0.00904786i | ||||
\(845\) | 7.51779 | + | 13.0212i | 0.258620 | + | 0.447942i | ||||
\(846\) | 7.22323 | 0.248340 | ||||||||
\(847\) | −5.21405 | + | 15.5680i | −0.179157 | + | 0.534922i | ||||
\(848\) | 4.54274 | 0.155998 | ||||||||
\(849\) | −10.1738 | − | 17.6215i | −0.349163 | − | 0.604768i | ||||
\(850\) | −2.78116 | + | 4.81711i | −0.0953930 | + | 0.165225i | ||||
\(851\) | 0.518822 | − | 0.898626i | 0.0177850 | − | 0.0308045i | ||||
\(852\) | −7.09279 | − | 12.2851i | −0.242995 | − | 0.420880i | ||||
\(853\) | 15.3330 | 0.524990 | 0.262495 | − | 0.964933i | \(-0.415455\pi\) | ||||
0.262495 | + | 0.964933i | \(0.415455\pi\) | |||||||
\(854\) | −38.2238 | + | 7.76506i | −1.30799 | + | 0.265715i | ||||
\(855\) | −13.4088 | −0.458572 | ||||||||
\(856\) | 2.75064 | + | 4.76424i | 0.0940148 | + | 0.162838i | ||||
\(857\) | 18.8013 | − | 32.5647i | 0.642239 | − | 1.11239i | −0.342693 | − | 0.939447i | \(-0.611339\pi\) |
0.984932 | − | 0.172943i | \(-0.0553275\pi\) | |||||||
\(858\) | 4.53283 | − | 7.85110i | 0.154748 | − | 0.268032i | ||||
\(859\) | −18.5628 | − | 32.1518i | −0.633356 | − | 1.09700i | −0.986861 | − | 0.161572i | \(-0.948344\pi\) |
0.353505 | − | 0.935433i | \(-0.384990\pi\) | |||||||
\(860\) | 9.80216 | 0.334251 | ||||||||
\(861\) | 19.0143 | − | 3.86270i | 0.648005 | − | 0.131641i | ||||
\(862\) | −35.3697 | −1.20470 | ||||||||
\(863\) | −16.5731 | − | 28.7054i | −0.564154 | − | 0.977143i | −0.997128 | − | 0.0757367i | \(-0.975869\pi\) |
0.432974 | − | 0.901406i | \(-0.357464\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 12.5109 | − | 21.6695i | 0.425383 | − | 0.736785i | ||||
\(866\) | −16.3814 | − | 28.3733i | −0.556661 | − | 0.964165i | ||||
\(867\) | −5.72950 | −0.194584 | ||||||||
\(868\) | −8.83862 | + | 26.3901i | −0.300002 | + | 0.895740i | ||||
\(869\) | −21.5095 | −0.729659 | ||||||||
\(870\) | −4.74073 | − | 8.21119i | −0.160726 | − | 0.278385i | ||||
\(871\) | 14.6489 | − | 25.3726i | 0.496358 | − | 0.859717i | ||||
\(872\) | 9.34753 | − | 16.1904i | 0.316547 | − | 0.548276i | ||||
\(873\) | 2.23564 | + | 3.87223i | 0.0756648 | + | 0.131055i | ||||
\(874\) | −7.33352 | −0.248060 | ||||||||
\(875\) | 21.3313 | + | 24.1248i | 0.721128 | + | 0.815568i | ||||
\(876\) | 11.5191 | 0.389194 | ||||||||
\(877\) | −16.4301 | − | 28.4578i | −0.554806 | − | 0.960953i | −0.997919 | − | 0.0644865i | \(-0.979459\pi\) |
0.443112 | − | 0.896466i | \(-0.353874\pi\) | |||||||
\(878\) | 9.65817 | − | 16.7284i | 0.325948 | − | 0.564558i | ||||
\(879\) | 15.7426 | − | 27.2671i | 0.530986 | − | 0.919695i | ||||
\(880\) | −3.79210 | − | 6.56811i | −0.127832 | − | 0.221411i | ||||
\(881\) | 10.6907 | 0.360178 | 0.180089 | − | 0.983650i | \(-0.442361\pi\) | ||||
0.180089 | + | 0.983650i | \(0.442361\pi\) | |||||||
\(882\) | −5.58798 | − | 4.21598i | −0.188157 | − | 0.141959i | ||||
\(883\) | 5.83725 | 0.196439 | 0.0982196 | − | 0.995165i | \(-0.468685\pi\) | ||||
0.0982196 | + | 0.995165i | \(0.468685\pi\) | |||||||
\(884\) | −3.66867 | − | 6.35433i | −0.123391 | − | 0.213719i | ||||
\(885\) | 0.430843 | − | 0.746241i | 0.0144826 | − | 0.0250846i | ||||
\(886\) | −7.20441 | + | 12.4784i | −0.242037 | + | 0.419220i | ||||
\(887\) | −27.0459 | − | 46.8448i | −0.908111 | − | 1.57289i | −0.816686 | − | 0.577082i | \(-0.804191\pi\) |
−0.0914246 | − | 0.995812i | \(-0.529142\pi\) | |||||||
\(888\) | −1.03764 | −0.0348211 | ||||||||
\(889\) | −11.3759 | − | 12.8657i | −0.381537 | − | 0.431503i | ||||
\(890\) | 12.2404 | 0.410299 | ||||||||
\(891\) | −2.07397 | − | 3.59222i | −0.0694806 | − | 0.120344i | ||||
\(892\) | 8.46877 | − | 14.6683i | 0.283555 | − | 0.491132i | ||||
\(893\) | 26.4858 | − | 45.8748i | 0.886315 | − | 1.53514i | ||||
\(894\) | −9.67886 | − | 16.7643i | −0.323710 | − | 0.560681i | ||||
\(895\) | −5.07713 | −0.169710 | ||||||||
\(896\) | −0.840244 | + | 2.50878i | −0.0280706 | + | 0.0838125i | ||||
\(897\) | −2.18558 | −0.0729745 | ||||||||
\(898\) | 5.52901 | + | 9.57653i | 0.184505 | + | 0.319573i | ||||
\(899\) | −27.2738 | + | 47.2397i | −0.909634 | + | 1.57553i | ||||
\(900\) | 0.828427 | − | 1.43488i | 0.0276142 | − | 0.0478293i | ||||
\(901\) | 7.62534 | + | 13.2075i | 0.254037 | + | 0.440005i | ||||
\(902\) | 30.4190 | 1.01284 | ||||||||
\(903\) | 13.8999 | − | 2.82373i | 0.462560 | − | 0.0939677i | ||||
\(904\) | 5.28187 | 0.175672 | ||||||||
\(905\) | 19.1646 | + | 33.1940i | 0.637052 | + | 1.10341i | ||||
\(906\) | −2.79210 | + | 4.83606i | −0.0927614 | + | 0.160667i | ||||
\(907\) | 6.56446 | − | 11.3700i | 0.217969 | − | 0.377534i | −0.736218 | − | 0.676745i | \(-0.763390\pi\) |
0.954187 | + | 0.299211i | \(0.0967234\pi\) | |||||||
\(908\) | 10.7685 | + | 18.6515i | 0.357364 | + | 0.618973i | ||||
\(909\) | 15.3061 | 0.507670 | ||||||||
\(910\) | −10.3613 | + | 2.10486i | −0.343472 | + | 0.0697755i | ||||
\(911\) | 2.77432 | 0.0919172 | 0.0459586 | − | 0.998943i | \(-0.485366\pi\) | ||||
0.0459586 | + | 0.998943i | \(0.485366\pi\) | |||||||
\(912\) | 3.66676 | + | 6.35102i | 0.121419 | + | 0.210303i | ||||
\(913\) | −12.0390 | + | 20.8521i | −0.398432 | + | 0.690104i | ||||
\(914\) | 12.9225 | − | 22.3824i | 0.427438 | − | 0.740344i | ||||
\(915\) | 13.4776 | + | 23.3440i | 0.445557 | + | 0.771727i | ||||
\(916\) | −0.666478 | −0.0220211 | ||||||||
\(917\) | 3.70448 | − | 11.0607i | 0.122333 | − | 0.365258i | ||||
\(918\) | −3.35716 | −0.110803 | ||||||||
\(919\) | 10.5934 | + | 18.3483i | 0.349443 | + | 0.605254i | 0.986151 | − | 0.165852i | \(-0.0530373\pi\) |
−0.636707 | + | 0.771106i | \(0.719704\pi\) | |||||||
\(920\) | −0.914214 | + | 1.58346i | −0.0301407 | + | 0.0522053i | ||||
\(921\) | −0.824324 | + | 1.42777i | −0.0271624 | + | 0.0470466i | ||||
\(922\) | 19.6670 | + | 34.0643i | 0.647700 | + | 1.12185i | ||||
\(923\) | −31.0038 | −1.02050 | ||||||||
\(924\) | −7.26946 | − | 8.22148i | −0.239148 | − | 0.270467i | ||||
\(925\) | 1.71923 | 0.0565278 | ||||||||
\(926\) | −12.5389 | − | 21.7180i | −0.412054 | − | 0.713699i | ||||
\(927\) | −3.70249 | + | 6.41291i | −0.121606 | + | 0.210628i | ||||
\(928\) | −2.59279 | + | 4.49085i | −0.0851126 | + | 0.147419i | ||||
\(929\) | 18.0239 | + | 31.2183i | 0.591346 | + | 1.02424i | 0.994051 | + | 0.108911i | \(0.0347364\pi\) |
−0.402706 | + | 0.915329i | \(0.631930\pi\) | |||||||
\(930\) | 19.2334 | 0.630689 | ||||||||
\(931\) | −47.2655 | + | 20.0304i | −1.54907 | + | 0.656468i | ||||
\(932\) | −1.67667 | −0.0549211 | ||||||||
\(933\) | −6.08897 | − | 10.5464i | −0.199344 | − | 0.345274i | ||||
\(934\) | 11.4815 | − | 19.8865i | 0.375685 | − | 0.650705i | ||||
\(935\) | 12.7307 | − | 22.0502i | 0.416338 | − | 0.721118i | ||||
\(936\) | 1.09279 | + | 1.89277i | 0.0357190 | + | 0.0618671i | ||||
\(937\) | −14.4789 | −0.473005 | −0.236503 | − | 0.971631i | \(-0.576001\pi\) | ||||
−0.236503 | + | 0.971631i | \(0.576001\pi\) | |||||||
\(938\) | −23.4929 | − | 26.5695i | −0.767070 | − | 0.867526i | ||||
\(939\) | 12.5669 | 0.410107 | ||||||||
\(940\) | −6.60357 | − | 11.4377i | −0.215385 | − | 0.373057i | ||||
\(941\) | 20.1498 | − | 34.9005i | 0.656865 | − | 1.13772i | −0.324557 | − | 0.945866i | \(-0.605215\pi\) |
0.981423 | − | 0.191858i | \(-0.0614514\pi\) | |||||||
\(942\) | 11.3951 | − | 19.7369i | 0.371272 | − | 0.643062i | ||||
\(943\) | −3.66676 | − | 6.35102i | −0.119406 | − | 0.206818i | ||||
\(944\) | −0.471271 | −0.0153386 | ||||||||
\(945\) | −1.53633 | + | 4.58713i | −0.0499767 | + | 0.149219i | ||||
\(946\) | 22.2370 | 0.722987 | ||||||||
\(947\) | 27.7301 | + | 48.0300i | 0.901108 | + | 1.56076i | 0.826058 | + | 0.563584i | \(0.190578\pi\) |
0.0750492 | + | 0.997180i | \(0.476089\pi\) | |||||||
\(948\) | 2.59279 | − | 4.49085i | 0.0842100 | − | 0.145856i | ||||
\(949\) | 12.5880 | − | 21.8030i | 0.408623 | − | 0.707756i | ||||
\(950\) | −6.07529 | − | 10.5227i | −0.197108 | − | 0.341402i | ||||
\(951\) | −9.17794 | −0.297615 | ||||||||
\(952\) | −8.70441 | + | 1.76828i | −0.282111 | + | 0.0573102i | ||||
\(953\) | −42.0164 | −1.36105 | −0.680523 | − | 0.732727i | \(-0.738247\pi\) | ||||
−0.680523 | + | 0.732727i | \(0.738247\pi\) | |||||||
\(954\) | −2.27137 | − | 3.93413i | −0.0735383 | − | 0.127372i | ||||
\(955\) | 8.19351 | − | 14.1916i | 0.265136 | − | 0.459228i | ||||
\(956\) | −5.36098 | + | 9.28548i | −0.173386 | + | 0.300314i | ||||
\(957\) | −10.7547 | − | 18.6278i | −0.347651 | − | 0.602150i | ||||
\(958\) | −16.6116 | −0.536695 | ||||||||
\(959\) | 4.35716 | − | 0.885144i | 0.140700 | − | 0.0285828i | ||||
\(960\) | 1.82843 | 0.0590122 | ||||||||
\(961\) | −39.8258 | − | 68.9803i | −1.28470 | − | 2.22517i | ||||
\(962\) | −1.13393 | + | 1.96402i | −0.0365593 | + | 0.0633226i | ||||
\(963\) | 2.75064 | − | 4.76424i | 0.0886380 | − | 0.153526i | ||||
\(964\) | −9.10171 | − | 15.7646i | −0.293146 | − | 0.507744i | ||||
\(965\) | 21.2811 | 0.685063 | ||||||||
\(966\) | −0.840244 | + | 2.50878i | −0.0270344 | + | 0.0807188i | ||||
\(967\) | 6.71167 | 0.215833 | 0.107916 | − | 0.994160i | \(-0.465582\pi\) | ||||
0.107916 | + | 0.994160i | \(0.465582\pi\) | |||||||
\(968\) | −3.10270 | − | 5.37403i | −0.0997245 | − | 0.172728i | ||||
\(969\) | −12.3099 | + | 21.3214i | −0.395451 | + | 0.684940i | ||||
\(970\) | 4.08770 | − | 7.08010i | 0.131248 | − | 0.227328i | ||||
\(971\) | −18.7308 | − | 32.4427i | −0.601101 | − | 1.04114i | −0.992655 | − | 0.120982i | \(-0.961396\pi\) |
0.391554 | − | 0.920155i | \(-0.371938\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 23.3329 | + | 26.3886i | 0.748019 | + | 0.845980i | ||||
\(974\) | −14.8226 | −0.474948 | ||||||||
\(975\) | −1.81060 | − | 3.13604i | −0.0579855 | − | 0.100434i | ||||
\(976\) | 7.37117 | − | 12.7672i | 0.235945 | − | 0.408669i | ||||
\(977\) | −26.6316 | + | 46.1273i | −0.852020 | + | 1.47574i | 0.0273621 | + | 0.999626i | \(0.491289\pi\) |
−0.879382 | + | 0.476117i | \(0.842044\pi\) | |||||||
\(978\) | 12.7184 | + | 22.0289i | 0.406690 | + | 0.704408i | ||||
\(979\) | 27.7684 | 0.887481 | ||||||||
\(980\) | −1.56725 | + | 12.7027i | −0.0500639 | + | 0.405772i | ||||
\(981\) | −18.6951 | −0.596887 | ||||||||
\(982\) | −11.1233 | − | 19.2661i | −0.354959 | − | 0.614807i | ||||
\(983\) | 7.95245 | − | 13.7740i | 0.253644 | − | 0.439324i | −0.710883 | − | 0.703311i | \(-0.751704\pi\) |
0.964526 | + | 0.263987i | \(0.0850376\pi\) | |||||||
\(984\) | −3.66676 | + | 6.35102i | −0.116892 | + | 0.202463i | ||||
\(985\) | −8.75960 | − | 15.1721i | −0.279104 | − | 0.483422i | ||||
\(986\) | −17.4088 | −0.554409 | ||||||||
\(987\) | −12.6590 | − | 14.3169i | −0.402942 | − | 0.455712i | ||||
\(988\) | 16.0280 | 0.509919 | ||||||||
\(989\) | −2.68049 | − | 4.64274i | −0.0852346 | − | 0.147631i | ||||
\(990\) | −3.79210 | + | 6.56811i | −0.120521 | + | 0.208748i | ||||
\(991\) | −7.79847 | + | 13.5073i | −0.247727 | + | 0.429075i | −0.962895 | − | 0.269877i | \(-0.913017\pi\) |
0.715168 | + | 0.698952i | \(0.246350\pi\) | |||||||
\(992\) | −5.25955 | − | 9.10981i | −0.166991 | − | 0.289237i | ||||
\(993\) | −29.3896 | −0.932650 | ||||||||
\(994\) | −11.9194 | + | 35.5885i | −0.378059 | + | 1.12880i | ||||
\(995\) | −18.1978 | −0.576910 | ||||||||
\(996\) | −2.90240 | − | 5.02710i | −0.0919660 | − | 0.159290i | ||||
\(997\) | 4.37725 | − | 7.58162i | 0.138629 | − | 0.240112i | −0.788349 | − | 0.615228i | \(-0.789064\pi\) |
0.926978 | + | 0.375116i | \(0.122397\pi\) | |||||||
\(998\) | 5.64284 | − | 9.77369i | 0.178621 | − | 0.309381i | ||||
\(999\) | 0.518822 | + | 0.898626i | 0.0164148 | + | 0.0284313i |
(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 | 966.2.i.l.277.1 | ✓ | 8 | |
7.2 | even | 3 | inner | 966.2.i.l.415.1 | yes | 8 | |
7.3 | odd | 6 | 6762.2.a.cm.1.2 | 4 | |||
7.4 | even | 3 | 6762.2.a.cp.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.l.277.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
966.2.i.l.415.1 | yes | 8 | 7.2 | even | 3 | inner | |
6762.2.a.cm.1.2 | 4 | 7.3 | odd | 6 | |||
6762.2.a.cp.1.4 | 4 | 7.4 | even | 3 |