Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(149,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.q (of order \(4\), degree \(2\), 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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-0.507829 + 1.31989i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.149 |
Dual form | 400.2.q.e.349.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31989 | + | 0.507829i | −0.933303 | + | 0.359089i | ||||
\(3\) | 0.0623209 | + | 0.0623209i | 0.0359810 | + | 0.0359810i | 0.724868 | − | 0.688887i | \(-0.241901\pi\) |
−0.688887 | + | 0.724868i | \(0.741901\pi\) | |||||||
\(4\) | 1.48422 | − | 1.34056i | 0.742110 | − | 0.670278i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.113905 | − | 0.0506084i | −0.0465015 | − | 0.0206608i | ||||
\(7\) | −0.375877 | −0.142068 | −0.0710340 | − | 0.997474i | \(-0.522630\pi\) | ||||
−0.0710340 | + | 0.997474i | \(0.522630\pi\) | |||||||
\(8\) | −1.27824 | + | 2.52312i | −0.451924 | + | 0.892056i | ||||
\(9\) | − | 2.99223i | − | 0.997411i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.36756 | + | 2.36756i | 0.713845 | + | 0.713845i | 0.967337 | − | 0.253492i | \(-0.0815793\pi\) |
−0.253492 | + | 0.967337i | \(0.581579\pi\) | |||||||
\(12\) | 0.176043 | + | 0.00895328i | 0.0508191 | + | 0.00258459i | ||||
\(13\) | 1.76442 | + | 1.76442i | 0.489363 | + | 0.489363i | 0.908105 | − | 0.418742i | \(-0.137529\pi\) |
−0.418742 | + | 0.908105i | \(0.637529\pi\) | |||||||
\(14\) | 0.496116 | − | 0.190881i | 0.132593 | − | 0.0510151i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.405819 | − | 3.97936i | 0.101455 | − | 0.994840i | ||||
\(17\) | − | 4.64955i | − | 1.12768i | −0.825883 | − | 0.563841i | \(-0.809323\pi\) | ||
0.825883 | − | 0.563841i | \(-0.190677\pi\) | |||||||
\(18\) | 1.51954 | + | 3.94942i | 0.358159 | + | 0.930887i | ||||
\(19\) | 2.34965 | − | 2.34965i | 0.539047 | − | 0.539047i | −0.384202 | − | 0.923249i | \(-0.625524\pi\) |
0.923249 | + | 0.384202i | \(0.125524\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0234250 | − | 0.0234250i | −0.00511175 | − | 0.00511175i | ||||
\(22\) | −4.32723 | − | 1.92260i | −0.922568 | − | 0.409900i | ||||
\(23\) | 2.07779 | 0.433250 | 0.216625 | − | 0.976255i | \(-0.430495\pi\) | ||||
0.216625 | + | 0.976255i | \(0.430495\pi\) | |||||||
\(24\) | −0.236904 | + | 0.0775821i | −0.0483577 | + | 0.0158364i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.22487 | − | 1.43282i | −0.632449 | − | 0.280999i | ||||
\(27\) | 0.373441 | − | 0.373441i | 0.0718688 | − | 0.0718688i | ||||
\(28\) | −0.557884 | + | 0.503884i | −0.105430 | + | 0.0952251i | ||||
\(29\) | −2.55422 | + | 2.55422i | −0.474307 | + | 0.474307i | −0.903305 | − | 0.428998i | \(-0.858867\pi\) |
0.428998 | + | 0.903305i | \(0.358867\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.51714 | 1.52972 | 0.764862 | − | 0.644194i | \(-0.222807\pi\) | ||||
0.764862 | + | 0.644194i | \(0.222807\pi\) | |||||||
\(32\) | 1.48520 | + | 5.45841i | 0.262548 | + | 0.964919i | ||||
\(33\) | 0.295096i | 0.0513697i | ||||||||
\(34\) | 2.36118 | + | 6.13690i | 0.404938 | + | 1.05247i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.01125 | − | 4.44113i | −0.668542 | − | 0.740189i | ||||
\(37\) | 7.62613 | − | 7.62613i | 1.25373 | − | 1.25373i | 0.299691 | − | 0.954036i | \(-0.403116\pi\) |
0.954036 | − | 0.299691i | \(-0.0968837\pi\) | |||||||
\(38\) | −1.90806 | + | 4.29450i | −0.309528 | + | 0.696660i | ||||
\(39\) | 0.219921i | 0.0352155i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.77709i | 0.589882i | 0.955515 | + | 0.294941i | \(0.0953001\pi\) | ||||
−0.955515 | + | 0.294941i | \(0.904700\pi\) | |||||||
\(42\) | 0.0428143 | + | 0.0190225i | 0.00660638 | + | 0.00293524i | ||||
\(43\) | 6.21191 | − | 6.21191i | 0.947307 | − | 0.947307i | −0.0513725 | − | 0.998680i | \(-0.516360\pi\) |
0.998680 | + | 0.0513725i | \(0.0163596\pi\) | |||||||
\(44\) | 6.68782 | + | 0.340133i | 1.00823 | + | 0.0512770i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.74246 | + | 1.05516i | −0.404353 | + | 0.155575i | ||||
\(47\) | 9.71696i | 1.41736i | 0.705528 | + | 0.708682i | \(0.250710\pi\) | ||||
−0.705528 | + | 0.708682i | \(0.749290\pi\) | |||||||
\(48\) | 0.273288 | − | 0.222706i | 0.0394458 | − | 0.0321449i | ||||
\(49\) | −6.85872 | −0.979817 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.289764 | − | 0.289764i | 0.0405751 | − | 0.0405751i | ||||
\(52\) | 4.98410 | + | 0.253484i | 0.691170 | + | 0.0351520i | ||||
\(53\) | 3.03609 | − | 3.03609i | 0.417040 | − | 0.417040i | −0.467143 | − | 0.884182i | \(-0.654717\pi\) |
0.884182 | + | 0.467143i | \(0.154717\pi\) | |||||||
\(54\) | −0.303257 | + | 0.682545i | −0.0412681 | + | 0.0928827i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.480459 | − | 0.948381i | 0.0642040 | − | 0.126733i | ||||
\(57\) | 0.292864 | 0.0387908 | ||||||||
\(58\) | 2.07418 | − | 4.66840i | 0.272354 | − | 0.612991i | ||||
\(59\) | 8.11663 | + | 8.11663i | 1.05670 | + | 1.05670i | 0.998293 | + | 0.0584019i | \(0.0186005\pi\) |
0.0584019 | + | 0.998293i | \(0.481400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.728329 | − | 0.728329i | 0.0932529 | − | 0.0932529i | −0.658941 | − | 0.752194i | \(-0.728995\pi\) |
0.752194 | + | 0.658941i | \(0.228995\pi\) | |||||||
\(62\) | −11.2417 | + | 4.32525i | −1.42770 | + | 0.549307i | ||||
\(63\) | 1.12471i | 0.141700i | ||||||||
\(64\) | −4.73223 | − | 6.45027i | −0.591529 | − | 0.806284i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.149858 | − | 0.389495i | −0.0184463 | − | 0.0479435i | ||||
\(67\) | −0.969239 | − | 0.969239i | −0.118411 | − | 0.118411i | 0.645418 | − | 0.763829i | \(-0.276683\pi\) |
−0.763829 | + | 0.645418i | \(0.776683\pi\) | |||||||
\(68\) | −6.23299 | − | 6.90096i | −0.755860 | − | 0.836864i | ||||
\(69\) | 0.129490 | + | 0.129490i | 0.0155887 | + | 0.0155887i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.14230i | 1.08499i | 0.840058 | + | 0.542496i | \(0.182521\pi\) | ||||
−0.840058 | + | 0.542496i | \(0.817479\pi\) | |||||||
\(72\) | 7.54975 | + | 3.82478i | 0.889747 | + | 0.450754i | ||||
\(73\) | −7.56793 | −0.885759 | −0.442879 | − | 0.896581i | \(-0.646043\pi\) | ||||
−0.442879 | + | 0.896581i | \(0.646043\pi\) | |||||||
\(74\) | −6.19289 | + | 13.9384i | −0.719908 | + | 1.62031i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.337561 | − | 6.63723i | 0.0387209 | − | 0.761343i | ||||
\(77\) | −0.889909 | − | 0.889909i | −0.101415 | − | 0.101415i | ||||
\(78\) | −0.111682 | − | 0.290271i | −0.0126455 | − | 0.0328667i | ||||
\(79\) | −11.8065 | −1.32834 | −0.664169 | − | 0.747583i | \(-0.731214\pi\) | ||||
−0.664169 | + | 0.747583i | \(0.731214\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.93015 | −0.992239 | ||||||||
\(82\) | −1.91811 | − | 4.98534i | −0.211820 | − | 0.550539i | ||||
\(83\) | −10.6393 | − | 10.6393i | −1.16782 | − | 1.16782i | −0.982720 | − | 0.185101i | \(-0.940739\pi\) |
−0.185101 | − | 0.982720i | \(-0.559261\pi\) | |||||||
\(84\) | −0.0661703 | − | 0.00336533i | −0.00721977 | − | 0.000367188i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.04445 | + | 11.3536i | −0.543957 | + | 1.22429i | ||||
\(87\) | −0.318363 | −0.0341320 | ||||||||
\(88\) | −8.99991 | + | 2.94733i | −0.959394 | + | 0.314186i | ||||
\(89\) | − | 15.7111i | − | 1.66538i | −0.553741 | − | 0.832689i | \(-0.686800\pi\) | ||
0.553741 | − | 0.832689i | \(-0.313200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.663205 | − | 0.663205i | −0.0695228 | − | 0.0695228i | ||||
\(92\) | 3.08390 | − | 2.78540i | 0.321519 | − | 0.290398i | ||||
\(93\) | 0.530796 | + | 0.530796i | 0.0550410 | + | 0.0550410i | ||||
\(94\) | −4.93455 | − | 12.8253i | −0.508960 | − | 1.32283i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.247614 | + | 0.432731i | −0.0252720 | + | 0.0441655i | ||||
\(97\) | − | 3.86020i | − | 0.391943i | −0.980610 | − | 0.195972i | \(-0.937214\pi\) | ||
0.980610 | − | 0.195972i | \(-0.0627861\pi\) | |||||||
\(98\) | 9.05275 | − | 3.48305i | 0.914466 | − | 0.351841i | ||||
\(99\) | 7.08428 | − | 7.08428i | 0.711997 | − | 0.711997i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.87437 | − | 6.87437i | −0.684026 | − | 0.684026i | 0.276879 | − | 0.960905i | \(-0.410700\pi\) |
−0.960905 | + | 0.276879i | \(0.910700\pi\) | |||||||
\(102\) | −0.235306 | + | 0.529607i | −0.0232988 | + | 0.0524390i | ||||
\(103\) | −1.15407 | −0.113714 | −0.0568571 | − | 0.998382i | \(-0.518108\pi\) | ||||
−0.0568571 | + | 0.998382i | \(0.518108\pi\) | |||||||
\(104\) | −6.70719 | + | 2.19650i | −0.657694 | + | 0.215384i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.46549 | + | 5.54913i | −0.239470 | + | 0.538979i | ||||
\(107\) | −5.70435 | + | 5.70435i | −0.551460 | + | 0.551460i | −0.926862 | − | 0.375402i | \(-0.877505\pi\) |
0.375402 | + | 0.926862i | \(0.377505\pi\) | |||||||
\(108\) | 0.0536502 | − | 1.05489i | 0.00516249 | − | 0.101507i | ||||
\(109\) | −11.1863 | + | 11.1863i | −1.07145 | + | 1.07145i | −0.0742092 | + | 0.997243i | \(0.523643\pi\) |
−0.997243 | + | 0.0742092i | \(0.976357\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.950534 | 0.0902207 | ||||||||
\(112\) | −0.152538 | + | 1.49575i | −0.0144135 | + | 0.141335i | ||||
\(113\) | 4.08163i | 0.383967i | 0.981398 | + | 0.191984i | \(0.0614920\pi\) | ||||
−0.981398 | + | 0.191984i | \(0.938508\pi\) | |||||||
\(114\) | −0.386549 | + | 0.148725i | −0.0362036 | + | 0.0139294i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.366950 | + | 7.21510i | −0.0340705 | + | 0.669905i | ||||
\(117\) | 5.27956 | − | 5.27956i | 0.488096 | − | 0.488096i | ||||
\(118\) | −14.8349 | − | 6.59120i | −1.36566 | − | 0.606769i | ||||
\(119\) | 1.74766i | 0.160208i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.210643i | 0.0191493i | ||||||||
\(122\) | −0.591448 | + | 1.33118i | −0.0535472 | + | 0.120519i | ||||
\(123\) | −0.235392 | + | 0.235392i | −0.0212245 | + | 0.0212245i | ||||
\(124\) | 12.6413 | − | 11.4177i | 1.13522 | − | 1.02534i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.571160 | − | 1.48449i | −0.0508830 | − | 0.132249i | ||||
\(127\) | 17.0918i | 1.51665i | 0.651876 | + | 0.758326i | \(0.273982\pi\) | ||||
−0.651876 | + | 0.758326i | \(0.726018\pi\) | |||||||
\(128\) | 9.52166 | + | 6.11049i | 0.841603 | + | 0.540096i | ||||
\(129\) | 0.774263 | 0.0681701 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.56424 | + | 3.56424i | −0.311409 | + | 0.311409i | −0.845455 | − | 0.534046i | \(-0.820671\pi\) |
0.534046 | + | 0.845455i | \(0.320671\pi\) | |||||||
\(132\) | 0.395593 | + | 0.437988i | 0.0344320 | + | 0.0381220i | ||||
\(133\) | −0.883179 | + | 0.883179i | −0.0765813 | + | 0.0765813i | ||||
\(134\) | 1.77150 | + | 0.787081i | 0.153034 | + | 0.0679935i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.7314 | + | 5.94322i | 1.00596 | + | 0.509627i | ||||
\(137\) | −16.6995 | −1.42673 | −0.713366 | − | 0.700792i | \(-0.752830\pi\) | ||||
−0.713366 | + | 0.700792i | \(0.752830\pi\) | |||||||
\(138\) | −0.236671 | − | 0.105154i | −0.0201468 | − | 0.00895128i | ||||
\(139\) | 7.56455 | + | 7.56455i | 0.641616 | + | 0.641616i | 0.950953 | − | 0.309336i | \(-0.100107\pi\) |
−0.309336 | + | 0.950953i | \(0.600107\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.605569 | + | 0.605569i | −0.0509982 | + | 0.0509982i | ||||
\(142\) | −4.64272 | − | 12.0668i | −0.389609 | − | 1.01263i | ||||
\(143\) | 8.35474i | 0.698658i | ||||||||
\(144\) | −11.9072 | − | 1.21431i | −0.992264 | − | 0.101192i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.98883 | − | 3.84321i | 0.826682 | − | 0.318066i | ||||
\(147\) | −0.427441 | − | 0.427441i | −0.0352548 | − | 0.0352548i | ||||
\(148\) | 1.09560 | − | 21.5421i | 0.0900579 | − | 1.77075i | ||||
\(149\) | 10.2542 | + | 10.2542i | 0.840056 | + | 0.840056i | 0.988866 | − | 0.148810i | \(-0.0475444\pi\) |
−0.148810 | + | 0.988866i | \(0.547544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.0430i | − | 1.54970i | −0.632147 | − | 0.774849i | \(-0.717826\pi\) | ||
0.632147 | − | 0.774849i | \(-0.282174\pi\) | |||||||
\(152\) | 2.92503 | + | 8.93184i | 0.237252 | + | 0.724468i | ||||
\(153\) | −13.9125 | −1.12476 | ||||||||
\(154\) | 1.62650 | + | 0.722661i | 0.131067 | + | 0.0582337i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.294816 | + | 0.326411i | 0.0236042 | + | 0.0261338i | ||||
\(157\) | 10.1335 | + | 10.1335i | 0.808741 | + | 0.808741i | 0.984443 | − | 0.175702i | \(-0.0562196\pi\) |
−0.175702 | + | 0.984443i | \(0.556220\pi\) | |||||||
\(158\) | 15.5833 | − | 5.99569i | 1.23974 | − | 0.476991i | ||||
\(159\) | 0.378424 | 0.0300110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.780994 | −0.0615509 | ||||||||
\(162\) | 11.7868 | − | 4.53499i | 0.926060 | − | 0.356302i | ||||
\(163\) | 7.35501 | + | 7.35501i | 0.576089 | + | 0.576089i | 0.933823 | − | 0.357735i | \(-0.116451\pi\) |
−0.357735 | + | 0.933823i | \(0.616451\pi\) | |||||||
\(164\) | 5.06340 | + | 5.60603i | 0.395385 | + | 0.437758i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.4457 | + | 8.63981i | 1.50928 | + | 0.670579i | ||||
\(167\) | −8.02936 | −0.621331 | −0.310665 | − | 0.950519i | \(-0.600552\pi\) | ||||
−0.310665 | + | 0.950519i | \(0.600552\pi\) | |||||||
\(168\) | 0.0890465 | − | 0.0291613i | 0.00687009 | − | 0.00224984i | ||||
\(169\) | − | 6.77363i | − | 0.521048i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.03070 | − | 7.03070i | −0.537651 | − | 0.537651i | ||||
\(172\) | 0.892429 | − | 17.5472i | 0.0680471 | − | 1.33797i | ||||
\(173\) | 10.4326 | + | 10.4326i | 0.793177 | + | 0.793177i | 0.982009 | − | 0.188832i | \(-0.0604702\pi\) |
−0.188832 | + | 0.982009i | \(0.560470\pi\) | |||||||
\(174\) | 0.420204 | − | 0.161674i | 0.0318556 | − | 0.0122564i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.3822 | − | 8.46056i | 0.782585 | − | 0.637739i | ||||
\(177\) | 1.01167i | 0.0760418i | ||||||||
\(178\) | 7.97857 | + | 20.7370i | 0.598019 | + | 1.55430i | ||||
\(179\) | 8.30280 | − | 8.30280i | 0.620580 | − | 0.620580i | −0.325099 | − | 0.945680i | \(-0.605398\pi\) |
0.945680 | + | 0.325099i | \(0.105398\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4772 | − | 10.4772i | −0.778765 | − | 0.778765i | 0.200856 | − | 0.979621i | \(-0.435628\pi\) |
−0.979621 | + | 0.200856i | \(0.935628\pi\) | |||||||
\(182\) | 1.21215 | + | 0.538564i | 0.0898508 | + | 0.0399210i | ||||
\(183\) | 0.0907802 | 0.00671066 | ||||||||
\(184\) | −2.65591 | + | 5.24251i | −0.195796 | + | 0.386483i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.970145 | − | 0.431039i | −0.0711345 | − | 0.0316053i | ||||
\(187\) | 11.0081 | − | 11.0081i | 0.804990 | − | 0.804990i | ||||
\(188\) | 13.0261 | + | 14.4221i | 0.950028 | + | 1.05184i | ||||
\(189\) | −0.140368 | + | 0.140368i | −0.0102103 | + | 0.0102103i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.68079 | 0.121618 | 0.0608089 | − | 0.998149i | \(-0.480632\pi\) | ||||
0.0608089 | + | 0.998149i | \(0.480632\pi\) | |||||||
\(192\) | 0.107070 | − | 0.696903i | 0.00772710 | − | 0.0502947i | ||||
\(193\) | 1.61403i | 0.116181i | 0.998311 | + | 0.0580903i | \(0.0185011\pi\) | ||||
−0.998311 | + | 0.0580903i | \(0.981499\pi\) | |||||||
\(194\) | 1.96032 | + | 5.09503i | 0.140743 | + | 0.365802i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.1798 | + | 9.19449i | −0.727132 | + | 0.656750i | ||||
\(197\) | −5.10322 | + | 5.10322i | −0.363589 | + | 0.363589i | −0.865133 | − | 0.501543i | \(-0.832766\pi\) |
0.501543 | + | 0.865133i | \(0.332766\pi\) | |||||||
\(198\) | −5.75287 | + | 12.9481i | −0.408839 | + | 0.920179i | ||||
\(199\) | 11.1545i | 0.790725i | 0.918525 | + | 0.395362i | \(0.129381\pi\) | ||||
−0.918525 | + | 0.395362i | \(0.870619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 0.120808i | − | 0.00852111i | ||||||
\(202\) | 12.5644 | + | 5.58241i | 0.884030 | + | 0.392777i | ||||
\(203\) | 0.960072 | − | 0.960072i | 0.0673839 | − | 0.0673839i | ||||
\(204\) | 0.0416288 | − | 0.818519i | 0.00291460 | − | 0.0573078i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.52325 | − | 0.586072i | 0.106130 | − | 0.0408335i | ||||
\(207\) | − | 6.21724i | − | 0.432128i | ||||||
\(208\) | 7.73731 | − | 6.30524i | 0.536486 | − | 0.437189i | ||||
\(209\) | 11.1259 | 0.769591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.48377 | + | 2.48377i | −0.170989 | + | 0.170989i | −0.787414 | − | 0.616425i | \(-0.788581\pi\) |
0.616425 | + | 0.787414i | \(0.288581\pi\) | |||||||
\(212\) | 0.436178 | − | 8.57628i | 0.0299568 | − | 0.589022i | ||||
\(213\) | −0.569756 | + | 0.569756i | −0.0390391 | + | 0.0390391i | ||||
\(214\) | 4.63228 | − | 10.4259i | 0.316656 | − | 0.712703i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.464890 | + | 1.41958i | 0.0316317 | + | 0.0965903i | ||||
\(217\) | −3.20140 | −0.217325 | ||||||||
\(218\) | 9.08395 | − | 20.4454i | 0.615243 | − | 1.38474i | ||||
\(219\) | −0.471640 | − | 0.471640i | −0.0318705 | − | 0.0318705i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.20377 | − | 8.20377i | 0.551846 | − | 0.551846i | ||||
\(222\) | −1.25460 | + | 0.482708i | −0.0842033 | + | 0.0323973i | ||||
\(223\) | 21.1384i | 1.41553i | 0.706448 | + | 0.707765i | \(0.250297\pi\) | ||||
−0.706448 | + | 0.707765i | \(0.749703\pi\) | |||||||
\(224\) | −0.558251 | − | 2.05169i | −0.0372997 | − | 0.137084i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.07277 | − | 5.38730i | −0.137878 | − | 0.358358i | ||||
\(227\) | −14.4885 | − | 14.4885i | −0.961634 | − | 0.961634i | 0.0376566 | − | 0.999291i | \(-0.488011\pi\) |
−0.999291 | + | 0.0376566i | \(0.988011\pi\) | |||||||
\(228\) | 0.434675 | − | 0.392601i | 0.0287871 | − | 0.0260006i | ||||
\(229\) | 10.0956 | + | 10.0956i | 0.667138 | + | 0.667138i | 0.957053 | − | 0.289914i | \(-0.0936268\pi\) |
−0.289914 | + | 0.957053i | \(0.593627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.110920i | − | 0.00729799i | ||||||
\(232\) | −3.17970 | − | 9.70949i | −0.208758 | − | 0.637459i | ||||
\(233\) | 3.44995 | 0.226014 | 0.113007 | − | 0.993594i | \(-0.463952\pi\) | ||||
0.113007 | + | 0.993594i | \(0.463952\pi\) | |||||||
\(234\) | −4.28733 | + | 9.64955i | −0.280271 | + | 0.630811i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.9277 | + | 1.16607i | 1.49246 | + | 0.0759047i | ||||
\(237\) | −0.735793 | − | 0.735793i | −0.0477949 | − | 0.0477949i | ||||
\(238\) | −0.887511 | − | 2.30672i | −0.0575288 | − | 0.149522i | ||||
\(239\) | −18.0060 | −1.16471 | −0.582354 | − | 0.812935i | \(-0.697868\pi\) | ||||
−0.582354 | + | 0.812935i | \(0.697868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6235 | 0.813154 | 0.406577 | − | 0.913617i | \(-0.366722\pi\) | ||||
0.406577 | + | 0.913617i | \(0.366722\pi\) | |||||||
\(242\) | −0.106970 | − | 0.278025i | −0.00687632 | − | 0.0178721i | ||||
\(243\) | −1.67686 | − | 1.67686i | −0.107571 | − | 0.107571i | ||||
\(244\) | 0.104635 | − | 2.05737i | 0.00669856 | − | 0.131709i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.191152 | − | 0.430230i | 0.0121874 | − | 0.0274304i | ||||
\(247\) | 8.29155 | 0.527578 | ||||||||
\(248\) | −10.8869 | + | 21.4897i | −0.691320 | + | 1.36460i | ||||
\(249\) | − | 1.32611i | − | 0.0840386i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.17919 | − | 9.17919i | −0.579386 | − | 0.579386i | 0.355348 | − | 0.934734i | \(-0.384362\pi\) |
−0.934734 | + | 0.355348i | \(0.884362\pi\) | |||||||
\(252\) | 1.50774 | + | 1.66932i | 0.0949785 | + | 0.105157i | ||||
\(253\) | 4.91929 | + | 4.91929i | 0.309273 | + | 0.309273i | ||||
\(254\) | −8.67970 | − | 22.5593i | −0.544613 | − | 1.41550i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6706 | − | 3.22980i | −0.979414 | − | 0.201863i | ||||
\(257\) | 16.2897i | 1.01612i | 0.861321 | + | 0.508061i | \(0.169637\pi\) | ||||
−0.861321 | + | 0.508061i | \(0.830363\pi\) | |||||||
\(258\) | −1.02194 | + | 0.393193i | −0.0636233 | + | 0.0244791i | ||||
\(259\) | −2.86648 | + | 2.86648i | −0.178115 | + | 0.178115i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.64282 | + | 7.64282i | 0.473079 | + | 0.473079i | ||||
\(262\) | 2.89438 | − | 6.51442i | 0.178815 | − | 0.402462i | ||||
\(263\) | −10.4898 | −0.646831 | −0.323416 | − | 0.946257i | \(-0.604831\pi\) | ||||
−0.323416 | + | 0.946257i | \(0.604831\pi\) | |||||||
\(264\) | −0.744562 | − | 0.377202i | −0.0458246 | − | 0.0232152i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.717196 | − | 1.61420i | 0.0439741 | − | 0.0989731i | ||||
\(267\) | 0.979132 | − | 0.979132i | 0.0599219 | − | 0.0599219i | ||||
\(268\) | −2.73788 | − | 0.139245i | −0.167243 | − | 0.00850574i | ||||
\(269\) | 8.46636 | − | 8.46636i | 0.516203 | − | 0.516203i | −0.400217 | − | 0.916420i | \(-0.631065\pi\) |
0.916420 | + | 0.400217i | \(0.131065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.92117 | −0.541923 | −0.270961 | − | 0.962590i | \(-0.587342\pi\) | ||||
−0.270961 | + | 0.962590i | \(0.587342\pi\) | |||||||
\(272\) | −18.5022 | − | 1.88688i | −1.12186 | − | 0.114409i | ||||
\(273\) | − | 0.0826631i | − | 0.00500300i | ||||||
\(274\) | 22.0415 | − | 8.48047i | 1.33157 | − | 0.512324i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.365780 | + | 0.0186031i | 0.0220174 | + | 0.00111977i | ||||
\(277\) | −9.36430 | + | 9.36430i | −0.562646 | + | 0.562646i | −0.930058 | − | 0.367412i | \(-0.880244\pi\) |
0.367412 | + | 0.930058i | \(0.380244\pi\) | |||||||
\(278\) | −13.8259 | − | 6.14288i | −0.829220 | − | 0.368425i | ||||
\(279\) | − | 25.4853i | − | 1.52576i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.12921i | 0.186673i | 0.995635 | + | 0.0933365i | \(0.0297532\pi\) | ||||
−0.995635 | + | 0.0933365i | \(0.970247\pi\) | |||||||
\(282\) | 0.491760 | − | 1.10681i | 0.0292839 | − | 0.0659096i | ||||
\(283\) | −2.07308 | + | 2.07308i | −0.123232 | + | 0.123232i | −0.766033 | − | 0.642801i | \(-0.777772\pi\) |
0.642801 | + | 0.766033i | \(0.277772\pi\) | |||||||
\(284\) | 12.2558 | + | 13.5692i | 0.727246 | + | 0.805183i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.24277 | − | 11.0273i | −0.250880 | − | 0.652060i | ||||
\(287\) | − | 1.41972i | − | 0.0838035i | ||||||
\(288\) | 16.3328 | − | 4.44405i | 0.962420 | − | 0.261868i | ||||
\(289\) | −4.61834 | −0.271667 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.240571 | − | 0.240571i | 0.0141025 | − | 0.0141025i | ||||
\(292\) | −11.2325 | + | 10.1452i | −0.657331 | + | 0.593705i | ||||
\(293\) | 12.3528 | − | 12.3528i | 0.721659 | − | 0.721659i | −0.247284 | − | 0.968943i | \(-0.579538\pi\) |
0.968943 | + | 0.247284i | \(0.0795382\pi\) | |||||||
\(294\) | 0.781242 | + | 0.347109i | 0.0455630 | + | 0.0202438i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.49362 | + | 28.9896i | 0.551806 | + | 1.68499i | ||||
\(297\) | 1.76829 | 0.102606 | ||||||||
\(298\) | −18.7418 | − | 8.32703i | −1.08568 | − | 0.482372i | ||||
\(299\) | 3.66610 | + | 3.66610i | 0.212016 | + | 0.212016i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.33491 | + | 2.33491i | −0.134582 | + | 0.134582i | ||||
\(302\) | 9.67058 | + | 25.1347i | 0.556479 | + | 1.44634i | ||||
\(303\) | − | 0.856834i | − | 0.0492238i | ||||||
\(304\) | −8.39657 | − | 10.3036i | −0.481576 | − | 0.590954i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 18.3630 | − | 7.06519i | 1.04974 | − | 0.403890i | ||||
\(307\) | 10.5938 | + | 10.5938i | 0.604619 | + | 0.604619i | 0.941535 | − | 0.336916i | \(-0.109384\pi\) |
−0.336916 | + | 0.941535i | \(0.609384\pi\) | |||||||
\(308\) | −2.51379 | − | 0.127848i | −0.143237 | − | 0.00728483i | ||||
\(309\) | −0.0719229 | − | 0.0719229i | −0.00409155 | − | 0.00409155i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.4153i | 1.10094i | 0.834854 | + | 0.550471i | \(0.185552\pi\) | ||||
−0.834854 | + | 0.550471i | \(0.814448\pi\) | |||||||
\(312\) | −0.554885 | − | 0.281110i | −0.0314142 | − | 0.0159147i | ||||
\(313\) | 2.56569 | 0.145022 | 0.0725108 | − | 0.997368i | \(-0.476899\pi\) | ||||
0.0725108 | + | 0.997368i | \(0.476899\pi\) | |||||||
\(314\) | −18.5212 | − | 8.22902i | −1.04521 | − | 0.464391i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.5235 | + | 15.8273i | −0.985773 | + | 0.890355i | ||||
\(317\) | −7.32418 | − | 7.32418i | −0.411367 | − | 0.411367i | 0.470848 | − | 0.882215i | \(-0.343948\pi\) |
−0.882215 | + | 0.470848i | \(0.843948\pi\) | |||||||
\(318\) | −0.499478 | + | 0.192175i | −0.0280093 | + | 0.0107766i | ||||
\(319\) | −12.0945 | −0.677163 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.711000 | −0.0396842 | ||||||||
\(322\) | 1.03083 | − | 0.396611i | 0.0574457 | − | 0.0221023i | ||||
\(323\) | −10.9248 | − | 10.9248i | −0.607873 | − | 0.607873i | ||||
\(324\) | −13.2543 | + | 11.9714i | −0.736351 | + | 0.665076i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.4429 | − | 5.97272i | −0.744533 | − | 0.330798i | ||||
\(327\) | −1.39428 | −0.0771038 | ||||||||
\(328\) | −9.53004 | − | 4.82801i | −0.526208 | − | 0.266582i | ||||
\(329\) | − | 3.65238i | − | 0.201362i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.17652 | + | 4.17652i | 0.229562 | + | 0.229562i | 0.812510 | − | 0.582948i | \(-0.198101\pi\) |
−0.582948 | + | 0.812510i | \(0.698101\pi\) | |||||||
\(332\) | −30.0538 | − | 1.52849i | −1.64942 | − | 0.0838870i | ||||
\(333\) | −22.8191 | − | 22.8191i | −1.25048 | − | 1.25048i | ||||
\(334\) | 10.5979 | − | 4.07754i | 0.579890 | − | 0.223113i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.102723 | + | 0.0837101i | −0.00560398 | + | 0.00456676i | ||||
\(337\) | 12.4540i | 0.678410i | 0.940712 | + | 0.339205i | \(0.110158\pi\) | ||||
−0.940712 | + | 0.339205i | \(0.889842\pi\) | |||||||
\(338\) | 3.43984 | + | 8.94045i | 0.187103 | + | 0.486296i | ||||
\(339\) | −0.254371 | + | 0.254371i | −0.0138155 | + | 0.0138155i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.1648 | + | 20.1648i | 1.09199 | + | 1.09199i | ||||
\(342\) | 12.8501 | + | 5.70936i | 0.694856 | + | 0.308727i | ||||
\(343\) | 5.20917 | 0.281269 | ||||||||
\(344\) | 7.73309 | + | 23.6136i | 0.416940 | + | 1.27316i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.0679 | − | 8.47193i | −1.02510 | − | 0.455454i | ||||
\(347\) | 17.5107 | − | 17.5107i | 0.940024 | − | 0.940024i | −0.0582766 | − | 0.998300i | \(-0.518561\pi\) |
0.998300 | + | 0.0582766i | \(0.0185605\pi\) | |||||||
\(348\) | −0.472520 | + | 0.426783i | −0.0253297 | + | 0.0228780i | ||||
\(349\) | −8.42042 | + | 8.42042i | −0.450735 | + | 0.450735i | −0.895598 | − | 0.444863i | \(-0.853252\pi\) |
0.444863 | + | 0.895598i | \(0.353252\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.31782 | 0.0703398 | ||||||||
\(352\) | −9.40680 | + | 16.4394i | −0.501384 | + | 0.876221i | ||||
\(353\) | − | 9.71293i | − | 0.516967i | −0.966016 | − | 0.258484i | \(-0.916777\pi\) | ||
0.966016 | − | 0.258484i | \(-0.0832228\pi\) | |||||||
\(354\) | −0.513755 | − | 1.33529i | −0.0273058 | − | 0.0709701i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −21.0617 | − | 23.3188i | −1.11627 | − | 1.23589i | ||||
\(357\) | −0.108916 | + | 0.108916i | −0.00576443 | + | 0.00576443i | ||||
\(358\) | −6.74238 | + | 15.1752i | −0.356346 | + | 0.802033i | ||||
\(359\) | 6.77551i | 0.357598i | 0.983886 | + | 0.178799i | \(0.0572212\pi\) | ||||
−0.983886 | + | 0.178799i | \(0.942779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.95830i | 0.418858i | ||||||||
\(362\) | 19.1494 | + | 8.50814i | 1.00647 | + | 0.447178i | ||||
\(363\) | −0.0131274 | + | 0.0131274i | −0.000689012 | + | 0.000689012i | ||||
\(364\) | −1.87341 | − | 0.0952789i | −0.0981932 | − | 0.00499397i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.119820 | + | 0.0461008i | −0.00626308 | + | 0.00240973i | ||||
\(367\) | − | 34.4591i | − | 1.79875i | −0.437176 | − | 0.899376i | \(-0.644021\pi\) | ||
0.437176 | − | 0.899376i | \(-0.355979\pi\) | |||||||
\(368\) | 0.843208 | − | 8.26828i | 0.0439553 | − | 0.431014i | ||||
\(369\) | 11.3019 | 0.588355 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.14120 | + | 1.14120i | −0.0592480 | + | 0.0592480i | ||||
\(372\) | 1.49938 | + | 0.0762564i | 0.0777392 | + | 0.00395371i | ||||
\(373\) | 3.55187 | − | 3.55187i | 0.183909 | − | 0.183909i | −0.609148 | − | 0.793057i | \(-0.708488\pi\) |
0.793057 | + | 0.609148i | \(0.208488\pi\) | |||||||
\(374\) | −8.93924 | + | 20.1197i | −0.462237 | + | 1.04036i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.5170 | − | 12.4206i | −1.26437 | − | 0.640541i | ||||
\(377\) | −9.01345 | −0.464216 | ||||||||
\(378\) | 0.113987 | − | 0.256553i | 0.00586288 | − | 0.0131957i | ||||
\(379\) | −26.4464 | − | 26.4464i | −1.35846 | − | 1.35846i | −0.875817 | − | 0.482644i | \(-0.839677\pi\) |
−0.482644 | − | 0.875817i | \(-0.660323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.06518 | + | 1.06518i | −0.0545706 | + | 0.0545706i | ||||
\(382\) | −2.21846 | + | 0.853554i | −0.113506 | + | 0.0436716i | ||||
\(383\) | − | 30.8614i | − | 1.57695i | −0.615069 | − | 0.788473i | \(-0.710872\pi\) | ||
0.615069 | − | 0.788473i | \(-0.289128\pi\) | |||||||
\(384\) | 0.212587 | + | 0.974209i | 0.0108485 | + | 0.0497149i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.819651 | − | 2.13034i | −0.0417192 | − | 0.108432i | ||||
\(387\) | −18.5875 | − | 18.5875i | −0.944854 | − | 0.944854i | ||||
\(388\) | −5.17481 | − | 5.72938i | −0.262711 | − | 0.290865i | ||||
\(389\) | −9.50959 | − | 9.50959i | −0.482155 | − | 0.482155i | 0.423664 | − | 0.905819i | \(-0.360744\pi\) |
−0.905819 | + | 0.423664i | \(0.860744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.66080i | − | 0.488568i | ||||||
\(392\) | 8.76705 | − | 17.3053i | 0.442803 | − | 0.874052i | ||||
\(393\) | −0.444253 | −0.0224096 | ||||||||
\(394\) | 4.14413 | − | 9.32725i | 0.208778 | − | 0.469900i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.01776 | − | 20.0115i | 0.0511442 | − | 1.00562i | ||||
\(397\) | 24.8540 | + | 24.8540i | 1.24739 | + | 1.24739i | 0.956870 | + | 0.290518i | \(0.0938276\pi\) |
0.290518 | + | 0.956870i | \(0.406172\pi\) | |||||||
\(398\) | −5.66460 | − | 14.7228i | −0.283941 | − | 0.737986i | ||||
\(399\) | −0.110081 | −0.00551094 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.69303 | 0.234359 | 0.117179 | − | 0.993111i | \(-0.462615\pi\) | ||||
0.117179 | + | 0.993111i | \(0.462615\pi\) | |||||||
\(402\) | 0.0613496 | + | 0.159453i | 0.00305984 | + | 0.00795278i | ||||
\(403\) | 15.0278 | + | 15.0278i | 0.748590 | + | 0.748590i | ||||
\(404\) | −19.4186 | − | 0.987602i | −0.966110 | − | 0.0491350i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.779638 | + | 1.75474i | −0.0386928 | + | 0.0870864i | ||||
\(407\) | 36.1106 | 1.78993 | ||||||||
\(408\) | 0.360722 | + | 1.10150i | 0.0178584 | + | 0.0545322i | ||||
\(409\) | 28.2641i | 1.39757i | 0.715331 | + | 0.698786i | \(0.246276\pi\) | ||||
−0.715331 | + | 0.698786i | \(0.753724\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.04073 | − | 1.04073i | −0.0513352 | − | 0.0513352i | ||||
\(412\) | −1.71290 | + | 1.54710i | −0.0843885 | + | 0.0762202i | ||||
\(413\) | −3.05085 | − | 3.05085i | −0.150123 | − | 0.150123i | ||||
\(414\) | 3.15729 | + | 8.20607i | 0.155172 | + | 0.403306i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.01042 | + | 12.2514i | −0.343714 | + | 0.600676i | ||||
\(417\) | 0.942858i | 0.0461720i | ||||||||
\(418\) | −14.6849 | + | 5.65003i | −0.718262 | + | 0.276352i | ||||
\(419\) | −23.0355 | + | 23.0355i | −1.12536 | + | 1.12536i | −0.134433 | + | 0.990923i | \(0.542921\pi\) |
−0.990923 | + | 0.134433i | \(0.957079\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.40760 | + | 5.40760i | 0.263550 | + | 0.263550i | 0.826495 | − | 0.562945i | \(-0.190332\pi\) |
−0.562945 | + | 0.826495i | \(0.690332\pi\) | |||||||
\(422\) | 2.01697 | − | 4.53962i | 0.0981846 | − | 0.220985i | ||||
\(423\) | 29.0754 | 1.41369 | ||||||||
\(424\) | 3.77958 | + | 11.5413i | 0.183552 | + | 0.560493i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.462677 | − | 1.04135i | 0.0224168 | − | 0.0504538i | ||||
\(427\) | −0.273762 | + | 0.273762i | −0.0132483 | + | 0.0132483i | ||||
\(428\) | −0.819511 | + | 16.1135i | −0.0396126 | + | 0.778876i | ||||
\(429\) | −0.520675 | + | 0.520675i | −0.0251384 | + | 0.0251384i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.6839 | −0.610961 | −0.305481 | − | 0.952198i | \(-0.598817\pi\) | ||||
−0.305481 | + | 0.952198i | \(0.598817\pi\) | |||||||
\(432\) | −1.33451 | − | 1.63761i | −0.0642065 | − | 0.0787894i | ||||
\(433\) | − | 23.8511i | − | 1.14621i | −0.819482 | − | 0.573104i | \(-0.805739\pi\) | ||
0.819482 | − | 0.573104i | \(-0.194261\pi\) | |||||||
\(434\) | 4.22549 | − | 1.62576i | 0.202830 | − | 0.0780390i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.60707 | + | 31.5988i | −0.0769647 | + | 1.51331i | ||||
\(437\) | 4.88208 | − | 4.88208i | 0.233542 | − | 0.233542i | ||||
\(438\) | 0.862025 | + | 0.383001i | 0.0411891 | + | 0.0183005i | ||||
\(439\) | 4.65878i | 0.222352i | 0.993801 | + | 0.111176i | \(0.0354617\pi\) | ||||
−0.993801 | + | 0.111176i | \(0.964538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5229i | 0.977280i | ||||||||
\(442\) | −6.66197 | + | 14.9942i | −0.316878 | + | 0.713201i | ||||
\(443\) | −8.74048 | + | 8.74048i | −0.415273 | + | 0.415273i | −0.883571 | − | 0.468298i | \(-0.844867\pi\) |
0.468298 | + | 0.883571i | \(0.344867\pi\) | |||||||
\(444\) | 1.41080 | − | 1.27424i | 0.0669537 | − | 0.0604729i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.7347 | − | 27.9003i | −0.508302 | − | 1.32112i | ||||
\(447\) | 1.27810i | 0.0604520i | ||||||||
\(448\) | 1.77874 | + | 2.42451i | 0.0840374 | + | 0.114547i | ||||
\(449\) | 7.28525 | 0.343812 | 0.171906 | − | 0.985113i | \(-0.445007\pi\) | ||||
0.171906 | + | 0.985113i | \(0.445007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.94247 | + | 8.94247i | −0.421085 | + | 0.421085i | ||||
\(452\) | 5.47165 | + | 6.05803i | 0.257365 | + | 0.284946i | ||||
\(453\) | 1.18678 | − | 1.18678i | 0.0557596 | − | 0.0557596i | ||||
\(454\) | 26.4809 | + | 11.7655i | 1.24281 | + | 0.552184i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.374350 | + | 0.738931i | −0.0175305 | + | 0.0346036i | ||||
\(457\) | 25.2194 | 1.17971 | 0.589857 | − | 0.807508i | \(-0.299184\pi\) | ||||
0.589857 | + | 0.807508i | \(0.299184\pi\) | |||||||
\(458\) | −18.4520 | − | 8.19828i | −0.862204 | − | 0.383080i | ||||
\(459\) | −1.73633 | − | 1.73633i | −0.0810451 | − | 0.0810451i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.6698 | − | 13.6698i | 0.636667 | − | 0.636667i | −0.313064 | − | 0.949732i | \(-0.601356\pi\) |
0.949732 | + | 0.313064i | \(0.101356\pi\) | |||||||
\(462\) | 0.0563283 | + | 0.146402i | 0.00262063 | + | 0.00681124i | ||||
\(463\) | 2.77045i | 0.128754i | 0.997926 | + | 0.0643768i | \(0.0205060\pi\) | ||||
−0.997926 | + | 0.0643768i | \(0.979494\pi\) | |||||||
\(464\) | 9.12761 | + | 11.2007i | 0.423739 | + | 0.519980i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.55355 | + | 1.75198i | −0.210939 | + | 0.0811590i | ||||
\(467\) | 17.9587 | + | 17.9587i | 0.831031 | + | 0.831031i | 0.987658 | − | 0.156627i | \(-0.0500621\pi\) |
−0.156627 | + | 0.987658i | \(0.550062\pi\) | |||||||
\(468\) | 0.758484 | − | 14.9136i | 0.0350609 | − | 0.689380i | ||||
\(469\) | 0.364314 | + | 0.364314i | 0.0168225 | + | 0.0168225i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.26306i | 0.0581986i | ||||||||
\(472\) | −30.8542 | + | 10.1042i | −1.42018 | + | 0.465085i | ||||
\(473\) | 29.4141 | 1.35246 | ||||||||
\(474\) | 1.34482 | + | 0.597509i | 0.0617697 | + | 0.0274445i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.34283 | + | 2.59391i | 0.107384 | + | 0.118892i | ||||
\(477\) | −9.08470 | − | 9.08470i | −0.415960 | − | 0.415960i | ||||
\(478\) | 23.7659 | − | 9.14394i | 1.08703 | − | 0.418234i | ||||
\(479\) | 22.4540 | 1.02595 | 0.512975 | − | 0.858403i | \(-0.328543\pi\) | ||||
0.512975 | + | 0.858403i | \(0.328543\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.9114 | 1.22705 | ||||||||
\(482\) | −16.6617 | + | 6.41059i | −0.758919 | + | 0.291995i | ||||
\(483\) | −0.0486722 | − | 0.0486722i | −0.00221466 | − | 0.00221466i | ||||
\(484\) | 0.282378 | + | 0.312640i | 0.0128354 | + | 0.0142109i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.06483 | + | 1.36171i | 0.139023 | + | 0.0617685i | ||||
\(487\) | −27.7615 | −1.25799 | −0.628997 | − | 0.777408i | \(-0.716534\pi\) | ||||
−0.628997 | + | 0.777408i | \(0.716534\pi\) | |||||||
\(488\) | 0.906683 | + | 2.76863i | 0.0410436 | + | 0.125330i | ||||
\(489\) | 0.916741i | 0.0414565i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.8993 | + | 16.8993i | 0.762656 | + | 0.762656i | 0.976802 | − | 0.214146i | \(-0.0686968\pi\) |
−0.214146 | + | 0.976802i | \(0.568697\pi\) | |||||||
\(492\) | −0.0338174 | + | 0.664929i | −0.00152460 | + | 0.0299773i | ||||
\(493\) | 11.8760 | + | 11.8760i | 0.534867 | + | 0.534867i | ||||
\(494\) | −10.9439 | + | 4.21068i | −0.492391 | + | 0.189448i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.45642 | − | 33.8928i | 0.155198 | − | 1.52183i | ||||
\(497\) | − | 3.43638i | − | 0.154143i | ||||||
\(498\) | 0.673435 | + | 1.75032i | 0.0301773 | + | 0.0784335i | ||||
\(499\) | 1.81950 | − | 1.81950i | 0.0814520 | − | 0.0814520i | −0.665207 | − | 0.746659i | \(-0.731657\pi\) |
0.746659 | + | 0.665207i | \(0.231657\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.500397 | − | 0.500397i | −0.0223561 | − | 0.0223561i | ||||
\(502\) | 16.7770 | + | 7.45407i | 0.748794 | + | 0.332691i | ||||
\(503\) | −42.2076 | −1.88195 | −0.940973 | − | 0.338482i | \(-0.890087\pi\) | ||||
−0.940973 | + | 0.338482i | \(0.890087\pi\) | |||||||
\(504\) | −2.83778 | − | 1.43764i | −0.126405 | − | 0.0640378i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.99108 | − | 3.99477i | −0.399702 | − | 0.177589i | ||||
\(507\) | 0.422139 | − | 0.422139i | 0.0187478 | − | 0.0187478i | ||||
\(508\) | 22.9125 | + | 25.3680i | 1.01658 | + | 1.12552i | ||||
\(509\) | 21.9831 | − | 21.9831i | 0.974382 | − | 0.974382i | −0.0252980 | − | 0.999680i | \(-0.508053\pi\) |
0.999680 | + | 0.0252980i | \(0.00805345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.84461 | 0.125838 | ||||||||
\(512\) | 22.3237 | − | 3.69500i | 0.986577 | − | 0.163298i | ||||
\(513\) | − | 1.75491i | − | 0.0774812i | ||||||
\(514\) | −8.27236 | − | 21.5006i | −0.364878 | − | 0.948349i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.14918 | − | 1.03794i | 0.0505897 | − | 0.0456929i | ||||
\(517\) | −23.0054 | + | 23.0054i | −1.01178 | + | 1.01178i | ||||
\(518\) | 2.32776 | − | 5.23913i | 0.102276 | − | 0.230194i | ||||
\(519\) | 1.30034i | 0.0570786i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.1418i | − | 1.23291i | −0.787388 | − | 0.616457i | \(-0.788567\pi\) | ||
0.787388 | − | 0.616457i | \(-0.211433\pi\) | |||||||
\(522\) | −13.9689 | − | 6.20644i | −0.611403 | − | 0.271649i | ||||
\(523\) | 9.58093 | − | 9.58093i | 0.418945 | − | 0.418945i | −0.465895 | − | 0.884840i | \(-0.654268\pi\) |
0.884840 | + | 0.465895i | \(0.154268\pi\) | |||||||
\(524\) | −0.512054 | + | 10.0682i | −0.0223692 | + | 0.439830i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.8454 | − | 5.32704i | 0.603690 | − | 0.232270i | ||||
\(527\) | − | 39.6009i | − | 1.72504i | ||||||
\(528\) | 1.17429 | + | 0.119756i | 0.0511046 | + | 0.00521170i | ||||
\(529\) | −18.6828 | −0.812295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.2868 | − | 24.2868i | 1.05396 | − | 1.05396i | ||||
\(532\) | −0.126881 | + | 2.49478i | −0.00550100 | + | 0.108163i | ||||
\(533\) | −6.66438 | + | 6.66438i | −0.288666 | + | 0.288666i | ||||
\(534\) | −0.795116 | + | 1.78958i | −0.0344080 | + | 0.0774426i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.68442 | − | 1.20659i | 0.159143 | − | 0.0521166i | ||||
\(537\) | 1.03488 | 0.0446582 | ||||||||
\(538\) | −6.87521 | + | 15.4741i | −0.296411 | + | 0.667137i | ||||
\(539\) | −16.2384 | − | 16.2384i | −0.699437 | − | 0.699437i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.9128 | + | 26.9128i | −1.15707 | + | 1.15707i | −0.171972 | + | 0.985102i | \(0.555014\pi\) |
−0.985102 | + | 0.171972i | \(0.944986\pi\) | |||||||
\(542\) | 11.7750 | − | 4.53043i | 0.505778 | − | 0.194598i | ||||
\(543\) | − | 1.30590i | − | 0.0560415i | ||||||
\(544\) | 25.3791 | − | 6.90550i | 1.08812 | − | 0.296071i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.0419787 | + | 0.109106i | 0.00179652 | + | 0.00466931i | ||||
\(547\) | 10.6627 | + | 10.6627i | 0.455902 | + | 0.455902i | 0.897308 | − | 0.441406i | \(-0.145520\pi\) |
−0.441406 | + | 0.897308i | \(0.645520\pi\) | |||||||
\(548\) | −24.7857 | + | 22.3866i | −1.05879 | + | 0.956307i | ||||
\(549\) | −2.17933 | − | 2.17933i | −0.0930115 | − | 0.0930115i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0030i | 0.511347i | ||||||||
\(552\) | −0.492236 | + | 0.161199i | −0.0209510 | + | 0.00686110i | ||||
\(553\) | 4.43780 | 0.188714 | ||||||||
\(554\) | 7.60439 | − | 17.1153i | 0.323079 | − | 0.727159i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.3681 | + | 1.08675i | 0.906211 | + | 0.0460887i | ||||
\(557\) | −22.8060 | − | 22.8060i | −0.966320 | − | 0.966320i | 0.0331307 | − | 0.999451i | \(-0.489452\pi\) |
−0.999451 | + | 0.0331307i | \(0.989452\pi\) | |||||||
\(558\) | 12.9421 | + | 33.6378i | 0.547885 | + | 1.42400i | ||||
\(559\) | 21.9209 | 0.927153 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.37207 | 0.0579287 | ||||||||
\(562\) | −1.58910 | − | 4.13021i | −0.0670322 | − | 0.174223i | ||||
\(563\) | −0.472513 | − | 0.472513i | −0.0199140 | − | 0.0199140i | 0.697080 | − | 0.716994i | \(-0.254482\pi\) |
−0.716994 | + | 0.697080i | \(0.754482\pi\) | |||||||
\(564\) | −0.0869987 | + | 1.71060i | −0.00366331 | + | 0.0720292i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.68347 | − | 3.78900i | 0.0707614 | − | 0.159264i | ||||
\(567\) | 3.35664 | 0.140965 | ||||||||
\(568\) | −23.0671 | − | 11.6860i | −0.967874 | − | 0.490334i | ||||
\(569\) | 3.14792i | 0.131967i | 0.997821 | + | 0.0659837i | \(0.0210185\pi\) | ||||
−0.997821 | + | 0.0659837i | \(0.978981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.78162 | + | 5.78162i | 0.241953 | + | 0.241953i | 0.817658 | − | 0.575704i | \(-0.195272\pi\) |
−0.575704 | + | 0.817658i | \(0.695272\pi\) | |||||||
\(572\) | 11.2000 | + | 12.4003i | 0.468295 | + | 0.518481i | ||||
\(573\) | 0.104748 | + | 0.104748i | 0.00437593 | + | 0.00437593i | ||||
\(574\) | 0.720975 | + | 1.87388i | 0.0300929 | + | 0.0782141i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −19.3007 | + | 14.1599i | −0.804196 | + | 0.589997i | ||||
\(577\) | − | 29.0110i | − | 1.20774i | −0.797081 | − | 0.603872i | \(-0.793624\pi\) | ||
0.797081 | − | 0.603872i | \(-0.206376\pi\) | |||||||
\(578\) | 6.09570 | − | 2.34532i | 0.253548 | − | 0.0975526i | ||||
\(579\) | −0.100588 | + | 0.100588i | −0.00418029 | + | 0.00418029i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.99908 | + | 3.99908i | 0.165910 | + | 0.165910i | ||||
\(582\) | −0.195358 | + | 0.439696i | −0.00809786 | + | 0.0182260i | ||||
\(583\) | 14.3762 | 0.595403 | ||||||||
\(584\) | 9.67359 | − | 19.0948i | 0.400296 | − | 0.790147i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.0312 | + | 22.5775i | −0.414387 | + | 0.932666i | ||||
\(587\) | −20.4099 | + | 20.4099i | −0.842408 | + | 0.842408i | −0.989172 | − | 0.146764i | \(-0.953114\pi\) |
0.146764 | + | 0.989172i | \(0.453114\pi\) | |||||||
\(588\) | −1.20743 | − | 0.0614080i | −0.0497934 | − | 0.00253242i | ||||
\(589\) | 20.0123 | − | 20.0123i | 0.824592 | − | 0.824592i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.636074 | −0.0261646 | ||||||||
\(592\) | −27.2523 | − | 33.4419i | −1.12006 | − | 1.37446i | ||||
\(593\) | 28.9098i | 1.18718i | 0.804766 | + | 0.593592i | \(0.202291\pi\) | ||||
−0.804766 | + | 0.593592i | \(0.797709\pi\) | |||||||
\(594\) | −2.33394 | + | 0.897986i | −0.0957628 | + | 0.0368448i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 28.9658 | + | 1.47316i | 1.18648 | + | 0.0603430i | ||||
\(597\) | −0.695161 | + | 0.695161i | −0.0284511 | + | 0.0284511i | ||||
\(598\) | −6.70060 | − | 2.97710i | −0.274008 | − | 0.121743i | ||||
\(599\) | − | 11.7893i | − | 0.481696i | −0.970563 | − | 0.240848i | \(-0.922574\pi\) | ||
0.970563 | − | 0.240848i | \(-0.0774256\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.7398i | − | 0.723621i | −0.932252 | − | 0.361810i | \(-0.882159\pi\) | ||
0.932252 | − | 0.361810i | \(-0.117841\pi\) | |||||||
\(602\) | 1.89609 | − | 4.26756i | 0.0772790 | − | 0.173933i | ||||
\(603\) | −2.90019 | + | 2.90019i | −0.118105 | + | 0.118105i | ||||
\(604\) | −25.5282 | − | 28.2640i | −1.03873 | − | 1.15005i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.435125 | + | 1.13093i | 0.0176757 | + | 0.0459408i | ||||
\(607\) | 25.8393i | 1.04878i | 0.851477 | + | 0.524392i | \(0.175707\pi\) | ||||
−0.851477 | + | 0.524392i | \(0.824293\pi\) | |||||||
\(608\) | 16.3150 | + | 9.33565i | 0.661662 | + | 0.378611i | ||||
\(609\) | 0.119665 | 0.00484907 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.1448 | + | 17.1448i | −0.693605 | + | 0.693605i | ||||
\(612\) | −20.6493 | + | 18.6505i | −0.834697 | + | 0.753903i | ||||
\(613\) | −31.5411 | + | 31.5411i | −1.27393 | + | 1.27393i | −0.329929 | + | 0.944006i | \(0.607025\pi\) |
−0.944006 | + | 0.329929i | \(0.892975\pi\) | |||||||
\(614\) | −19.3625 | − | 8.60280i | −0.781405 | − | 0.347181i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.38286 | − | 1.10783i | 0.136299 | − | 0.0446358i | ||||
\(617\) | 15.0637 | 0.606440 | 0.303220 | − | 0.952921i | \(-0.401938\pi\) | ||||
0.303220 | + | 0.952921i | \(0.401938\pi\) | |||||||
\(618\) | 0.131455 | + | 0.0584058i | 0.00528789 | + | 0.00234943i | ||||
\(619\) | 10.4975 | + | 10.4975i | 0.421929 | + | 0.421929i | 0.885868 | − | 0.463938i | \(-0.153564\pi\) |
−0.463938 | + | 0.885868i | \(0.653564\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.775933 | − | 0.775933i | 0.0311371 | − | 0.0311371i | ||||
\(622\) | −9.85966 | − | 25.6261i | −0.395336 | − | 1.02751i | ||||
\(623\) | 5.90545i | 0.236597i | ||||||||
\(624\) | 0.875144 | + | 0.0892481i | 0.0350338 | + | 0.00357278i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.38644 | + | 1.30293i | −0.135349 | + | 0.0520757i | ||||
\(627\) | 0.693373 | + | 0.693373i | 0.0276906 | + | 0.0276906i | ||||
\(628\) | 28.6249 | + | 1.45582i | 1.14226 | + | 0.0580936i | ||||
\(629\) | −35.4581 | − | 35.4581i | −1.41381 | − | 1.41381i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 43.6349i | − | 1.73708i | −0.495621 | − | 0.868539i | \(-0.665060\pi\) | ||
0.495621 | − | 0.868539i | \(-0.334940\pi\) | |||||||
\(632\) | 15.0915 | − | 29.7892i | 0.600308 | − | 1.18495i | ||||
\(633\) | −0.309581 | −0.0123047 | ||||||||
\(634\) | 13.3865 | + | 5.94768i | 0.531647 | + | 0.236213i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.561665 | − | 0.507299i | 0.0222714 | − | 0.0201157i | ||||
\(637\) | −12.1017 | − | 12.1017i | −0.479486 | − | 0.479486i | ||||
\(638\) | 15.9634 | − | 6.14194i | 0.631999 | − | 0.243162i | ||||
\(639\) | 27.3559 | 1.08218 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.2710 | −1.35362 | −0.676812 | − | 0.736156i | \(-0.736639\pi\) | ||||
−0.676812 | + | 0.736156i | \(0.736639\pi\) | |||||||
\(642\) | 0.938442 | − | 0.361066i | 0.0370374 | − | 0.0142501i | ||||
\(643\) | 30.1937 | + | 30.1937i | 1.19072 | + | 1.19072i | 0.976865 | + | 0.213857i | \(0.0686027\pi\) |
0.213857 | + | 0.976865i | \(0.431397\pi\) | |||||||
\(644\) | −1.15917 | + | 1.04697i | −0.0456776 | + | 0.0412562i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.9675 | + | 8.87163i | 0.785611 | + | 0.349049i | ||||
\(647\) | −15.7474 | −0.619096 | −0.309548 | − | 0.950884i | \(-0.600178\pi\) | ||||
−0.309548 | + | 0.950884i | \(0.600178\pi\) | |||||||
\(648\) | 11.4148 | − | 22.5318i | 0.448417 | − | 0.885133i | ||||
\(649\) | 38.4331i | 1.50863i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.199514 | − | 0.199514i | −0.00781956 | − | 0.00781956i | ||||
\(652\) | 20.7763 | + | 1.05665i | 0.813661 | + | 0.0413817i | ||||
\(653\) | −5.80619 | − | 5.80619i | −0.227214 | − | 0.227214i | 0.584314 | − | 0.811528i | \(-0.301364\pi\) |
−0.811528 | + | 0.584314i | \(0.801364\pi\) | |||||||
\(654\) | 1.84029 | − | 0.708054i | 0.0719612 | − | 0.0276871i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.0304 | + | 1.53282i | 0.586839 | + | 0.0598464i | ||||
\(657\) | 22.6450i | 0.883465i | ||||||||
\(658\) | 1.85478 | + | 4.82074i | 0.0723070 | + | 0.187932i | ||||
\(659\) | −1.76782 | + | 1.76782i | −0.0688647 | + | 0.0688647i | −0.740700 | − | 0.671836i | \(-0.765506\pi\) |
0.671836 | + | 0.740700i | \(0.265506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4824 | − | 12.4824i | −0.485509 | − | 0.485509i | 0.421377 | − | 0.906886i | \(-0.361547\pi\) |
−0.906886 | + | 0.421377i | \(0.861547\pi\) | |||||||
\(662\) | −7.63350 | − | 3.39159i | −0.296685 | − | 0.131818i | ||||
\(663\) | 1.02253 | 0.0397119 | ||||||||
\(664\) | 40.4439 | − | 13.2447i | 1.56953 | − | 0.513995i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 41.7070 | + | 18.5306i | 1.61611 | + | 0.718044i | ||||
\(667\) | −5.30714 | + | 5.30714i | −0.205493 | + | 0.205493i | ||||
\(668\) | −11.9173 | + | 10.7638i | −0.461096 | + | 0.416464i | ||||
\(669\) | −1.31736 | + | 1.31736i | −0.0509322 | + | 0.0509322i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.44872 | 0.133136 | ||||||||
\(672\) | 0.0930723 | − | 0.162654i | 0.00359034 | − | 0.00627450i | ||||
\(673\) | 14.1113i | 0.543950i | 0.962304 | + | 0.271975i | \(0.0876768\pi\) | ||||
−0.962304 | + | 0.271975i | \(0.912323\pi\) | |||||||
\(674\) | −6.32447 | − | 16.4379i | −0.243610 | − | 0.633162i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.08043 | − | 10.0536i | −0.349247 | − | 0.386675i | ||||
\(677\) | 8.31191 | − | 8.31191i | 0.319453 | − | 0.319453i | −0.529104 | − | 0.848557i | \(-0.677472\pi\) |
0.848557 | + | 0.529104i | \(0.177472\pi\) | |||||||
\(678\) | 0.206565 | − | 0.464918i | 0.00793306 | − | 0.0178551i | ||||
\(679\) | 1.45096i | 0.0556827i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.80587i | − | 0.0692011i | ||||||
\(682\) | −36.8556 | − | 16.3751i | −1.41127 | − | 0.627034i | ||||
\(683\) | −30.0811 | + | 30.0811i | −1.15102 | + | 1.15102i | −0.164673 | + | 0.986348i | \(0.552657\pi\) |
−0.986348 | + | 0.164673i | \(0.947343\pi\) | |||||||
\(684\) | −19.8601 | − | 1.01006i | −0.759372 | − | 0.0386206i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.87553 | + | 2.64537i | −0.262509 | + | 0.101001i | ||||
\(687\) | 1.25834i | 0.0480086i | ||||||||
\(688\) | −22.1985 | − | 27.2403i | −0.846310 | − | 1.03853i | ||||
\(689\) | 10.7139 | 0.408167 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0212 | − | 24.0212i | 0.913810 | − | 0.913810i | −0.0827600 | − | 0.996570i | \(-0.526373\pi\) |
0.996570 | + | 0.0827600i | \(0.0263735\pi\) | |||||||
\(692\) | 29.4698 | + | 1.49879i | 1.12027 | + | 0.0569756i | ||||
\(693\) | −2.66282 | + | 2.66282i | −0.101152 | + | 0.101152i | ||||
\(694\) | −14.2198 | + | 32.0046i | −0.539775 | + | 1.21488i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.406942 | − | 0.803266i | 0.0154251 | − | 0.0304477i | ||||
\(697\) | 17.5618 | 0.665200 | ||||||||
\(698\) | 6.83790 | − | 15.3902i | 0.258818 | − | 0.582526i | ||||
\(699\) | 0.215004 | + | 0.215004i | 0.00813219 | + | 0.00813219i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0971 | − | 10.0971i | 0.381363 | − | 0.381363i | −0.490230 | − | 0.871593i | \(-0.663087\pi\) |
0.871593 | + | 0.490230i | \(0.163087\pi\) | |||||||
\(702\) | −1.73937 | + | 0.669225i | −0.0656484 | + | 0.0252583i | ||||
\(703\) | − | 35.8375i | − | 1.35164i | ||||||
\(704\) | 4.06756 | − | 26.4752i | 0.153302 | − | 0.997822i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.93251 | + | 12.8200i | 0.185637 | + | 0.482487i | ||||
\(707\) | 2.58392 | + | 2.58392i | 0.0971782 | + | 0.0971782i | ||||
\(708\) | 1.35620 | + | 1.50154i | 0.0509692 | + | 0.0564314i | ||||
\(709\) | 4.67310 | + | 4.67310i | 0.175502 | + | 0.175502i | 0.789392 | − | 0.613890i | \(-0.210396\pi\) |
−0.613890 | + | 0.789392i | \(0.710396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 35.3279i | 1.32490i | ||||||||
\(712\) | 39.6410 | + | 20.0825i | 1.48561 | + | 0.752625i | ||||
\(713\) | 17.6968 | 0.662752 | ||||||||
\(714\) | 0.0884462 | − | 0.199067i | 0.00331002 | − | 0.00744990i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.19282 | − | 23.4536i | 0.0445776 | − | 0.876500i | ||||
\(717\) | −1.12215 | − | 1.12215i | −0.0419074 | − | 0.0419074i | ||||
\(718\) | −3.44080 | − | 8.94293i | −0.128409 | − | 0.333747i | ||||
\(719\) | 23.5339 | 0.877667 | 0.438833 | − | 0.898568i | \(-0.355392\pi\) | ||||
0.438833 | + | 0.898568i | \(0.355392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.433789 | 0.0161552 | ||||||||
\(722\) | −4.04145 | − | 10.5041i | −0.150407 | − | 0.390921i | ||||
\(723\) | 0.786710 | + | 0.786710i | 0.0292581 | + | 0.0292581i | ||||
\(724\) | −29.5958 | − | 1.50520i | −1.09992 | − | 0.0559404i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.0106603 | − | 0.0239933i | 0.000395641 | − | 0.000890474i | ||||
\(727\) | −16.6692 | −0.618226 | −0.309113 | − | 0.951025i | \(-0.600032\pi\) | ||||
−0.309113 | + | 0.951025i | \(0.600032\pi\) | |||||||
\(728\) | 2.52108 | − | 0.825612i | 0.0934373 | − | 0.0305992i | ||||
\(729\) | 26.5814i | 0.984498i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.8826 | − | 28.8826i | −1.06826 | − | 1.06826i | ||||
\(732\) | 0.134738 | − | 0.121696i | 0.00498005 | − | 0.00449801i | ||||
\(733\) | −27.4684 | − | 27.4684i | −1.01457 | − | 1.01457i | −0.999892 | − | 0.0146760i | \(-0.995328\pi\) |
−0.0146760 | − | 0.999892i | \(-0.504672\pi\) | |||||||
\(734\) | 17.4993 | + | 45.4823i | 0.645912 | + | 1.67878i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.08593 | + | 11.3414i | 0.113749 | + | 0.418051i | ||||
\(737\) | − | 4.58945i | − | 0.169055i | ||||||
\(738\) | −14.9173 | + | 5.73944i | −0.549114 | + | 0.211272i | ||||
\(739\) | −22.7939 | + | 22.7939i | −0.838486 | + | 0.838486i | −0.988660 | − | 0.150174i | \(-0.952017\pi\) |
0.150174 | + | 0.988660i | \(0.452017\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.516736 | + | 0.516736i | 0.0189828 | + | 0.0189828i | ||||
\(742\) | 0.926722 | − | 2.08579i | 0.0340210 | − | 0.0765717i | ||||
\(743\) | 16.4964 | 0.605196 | 0.302598 | − | 0.953118i | \(-0.402146\pi\) | ||||
0.302598 | + | 0.953118i | \(0.402146\pi\) | |||||||
\(744\) | −2.01774 | + | 0.660778i | −0.0739740 | + | 0.0242253i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.88434 | + | 6.49181i | −0.105603 | + | 0.237682i | ||||
\(747\) | −31.8354 | + | 31.8354i | −1.16480 | + | 1.16480i | ||||
\(748\) | 1.58147 | − | 31.0954i | 0.0578242 | − | 1.13696i | ||||
\(749\) | 2.14413 | − | 2.14413i | 0.0783449 | − | 0.0783449i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6997 | −0.791833 | −0.395917 | − | 0.918286i | \(-0.629573\pi\) | ||||
−0.395917 | + | 0.918286i | \(0.629573\pi\) | |||||||
\(752\) | 38.6673 | + | 3.94333i | 1.41005 | + | 0.143798i | ||||
\(753\) | − | 1.14411i | − | 0.0416937i | ||||||
\(754\) | 11.8968 | − | 4.57729i | 0.433254 | − | 0.166695i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.0201658 | + | 0.396508i | −0.000733425 | + | 0.0144209i | ||||
\(757\) | 1.73819 | − | 1.73819i | 0.0631757 | − | 0.0631757i | −0.674813 | − | 0.737989i | \(-0.735776\pi\) |
0.737989 | + | 0.674813i | \(0.235776\pi\) | |||||||
\(758\) | 48.3366 | + | 21.4761i | 1.75566 | + | 0.780047i | ||||
\(759\) | 0.613149i | 0.0222559i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 46.5311i | − | 1.68675i | −0.537323 | − | 0.843376i | \(-0.680565\pi\) | ||
0.537323 | − | 0.843376i | \(-0.319435\pi\) | |||||||
\(762\) | 0.864989 | − | 1.94684i | 0.0313352 | − | 0.0705266i | ||||
\(763\) | 4.20467 | − | 4.20467i | 0.152219 | − | 0.152219i | ||||
\(764\) | 2.49467 | − | 2.25320i | 0.0902538 | − | 0.0815178i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.6723 | + | 40.7337i | 0.566264 | + | 1.47177i | ||||
\(767\) | 28.6423i | 1.03421i | ||||||||
\(768\) | −0.775323 | − | 1.17789i | −0.0279770 | − | 0.0425035i | ||||
\(769\) | −15.4731 | −0.557976 | −0.278988 | − | 0.960295i | \(-0.589999\pi\) | ||||
−0.278988 | + | 0.960295i | \(0.589999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.01519 | + | 1.01519i | −0.0365610 | + | 0.0365610i | ||||
\(772\) | 2.16370 | + | 2.39558i | 0.0778732 | + | 0.0862187i | ||||
\(773\) | 5.69848 | − | 5.69848i | 0.204960 | − | 0.204960i | −0.597161 | − | 0.802121i | \(-0.703705\pi\) |
0.802121 | + | 0.597161i | \(0.203705\pi\) | |||||||
\(774\) | 33.9727 | + | 15.0942i | 1.22112 | + | 0.542549i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.73972 | + | 4.93424i | 0.349636 | + | 0.177129i | ||||
\(777\) | −0.357284 | −0.0128175 | ||||||||
\(778\) | 17.3808 | + | 7.72237i | 0.623134 | + | 0.276860i | ||||
\(779\) | 8.87484 | + | 8.87484i | 0.317974 | + | 0.317974i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.6449 | + | 21.6449i | −0.774516 | + | 0.774516i | ||||
\(782\) | 4.90603 | + | 12.7512i | 0.175439 | + | 0.455982i | ||||
\(783\) | 1.90770i | 0.0681757i | ||||||||
\(784\) | −2.78340 | + | 27.2933i | −0.0994072 | + | 0.974761i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.586365 | − | 0.225604i | 0.0209149 | − | 0.00804704i | ||||
\(787\) | 18.1351 | + | 18.1351i | 0.646448 | + | 0.646448i | 0.952133 | − | 0.305685i | \(-0.0988855\pi\) |
−0.305685 | + | 0.952133i | \(0.598885\pi\) | |||||||
\(788\) | −0.733151 | + | 14.4155i | −0.0261174 | + | 0.513529i | ||||
\(789\) | −0.653736 | − | 0.653736i | −0.0232736 | − | 0.0232736i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.53419i | − | 0.0545495i | ||||||
\(792\) | 8.81908 | + | 26.9298i | 0.313372 | + | 0.956910i | ||||
\(793\) | 2.57016 | 0.0912690 | ||||||||
\(794\) | −45.4262 | − | 20.1830i | −1.61211 | − | 0.716268i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.9533 | + | 16.5558i | 0.530005 | + | 0.586805i | ||||
\(797\) | 4.51575 | + | 4.51575i | 0.159956 | + | 0.159956i | 0.782547 | − | 0.622591i | \(-0.213920\pi\) |
−0.622591 | + | 0.782547i | \(0.713920\pi\) | |||||||
\(798\) | 0.145295 | − | 0.0559023i | 0.00514338 | − | 0.00197892i | ||||
\(799\) | 45.1795 | 1.59834 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.0114 | −1.66107 | ||||||||
\(802\) | −6.19429 | + | 2.38326i | −0.218728 | + | 0.0841557i | ||||
\(803\) | −17.9175 | − | 17.9175i | −0.632294 | − | 0.632294i | ||||
\(804\) | −0.161949 | − | 0.179305i | −0.00571151 | − | 0.00632360i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.4667 | − | 12.2035i | −0.967472 | − | 0.429851i | ||||
\(807\) | 1.05526 | 0.0371470 | ||||||||
\(808\) | 26.1319 | − | 8.55778i | 0.919317 | − | 0.301062i | ||||
\(809\) | 3.33368i | 0.117206i | 0.998281 | + | 0.0586030i | \(0.0186646\pi\) | ||||
−0.998281 | + | 0.0586030i | \(0.981335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.1948 | + | 37.1948i | 1.30609 | + | 1.30609i | 0.924215 | + | 0.381873i | \(0.124721\pi\) |
0.381873 | + | 0.924215i | \(0.375279\pi\) | |||||||
\(812\) | 0.137928 | − | 2.71199i | 0.00484033 | − | 0.0951722i | ||||
\(813\) | −0.555975 | − | 0.555975i | −0.0194989 | − | 0.0194989i | ||||
\(814\) | −47.6620 | + | 18.3380i | −1.67055 | + | 0.642746i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.03548 | − | 1.27067i | −0.0362492 | − | 0.0444823i | ||||
\(817\) | − | 29.1916i | − | 1.02129i | ||||||
\(818\) | −14.3533 | − | 37.3055i | −0.501853 | − | 1.30436i | ||||
\(819\) | −1.98446 | + | 1.98446i | −0.0693428 | + | 0.0693428i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.5278 | − | 25.5278i | −0.890926 | − | 0.890926i | 0.103684 | − | 0.994610i | \(-0.466937\pi\) |
−0.994610 | + | 0.103684i | \(0.966937\pi\) | |||||||
\(822\) | 1.90215 | + | 0.845133i | 0.0663452 | + | 0.0294774i | ||||
\(823\) | −16.8858 | −0.588603 | −0.294301 | − | 0.955713i | \(-0.595087\pi\) | ||||
−0.294301 | + | 0.955713i | \(0.595087\pi\) | |||||||
\(824\) | 1.47518 | − | 2.91186i | 0.0513902 | − | 0.101440i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.57610 | + | 2.47748i | 0.194017 | + | 0.0862026i | ||||
\(827\) | −11.5765 | + | 11.5765i | −0.402556 | + | 0.402556i | −0.879133 | − | 0.476577i | \(-0.841877\pi\) |
0.476577 | + | 0.879133i | \(0.341877\pi\) | |||||||
\(828\) | −8.33455 | − | 9.22775i | −0.289646 | − | 0.320686i | ||||
\(829\) | −5.97296 | + | 5.97296i | −0.207449 | + | 0.207449i | −0.803182 | − | 0.595733i | \(-0.796862\pi\) |
0.595733 | + | 0.803182i | \(0.296862\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.16718 | −0.0404891 | ||||||||
\(832\) | 3.03135 | − | 19.7307i | 0.105093 | − | 0.684037i | ||||
\(833\) | 31.8900i | 1.10492i | ||||||||
\(834\) | −0.478810 | − | 1.24447i | −0.0165798 | − | 0.0430925i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.5132 | − | 14.9148i | 0.571122 | − | 0.515840i | ||||
\(837\) | 3.18065 | − | 3.18065i | 0.109939 | − | 0.109939i | ||||
\(838\) | 18.7062 | − | 42.1023i | 0.646195 | − | 1.45440i | ||||
\(839\) | 27.2960i | 0.942362i | 0.882037 | + | 0.471181i | \(0.156172\pi\) | ||||
−0.882037 | + | 0.471181i | \(0.843828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.9519i | 0.550066i | ||||||||
\(842\) | −9.88356 | − | 4.39130i | −0.340610 | − | 0.151334i | ||||
\(843\) | −0.195015 | + | 0.195015i | −0.00671668 | + | 0.00671668i | ||||
\(844\) | −0.356828 | + | 7.01608i | −0.0122825 | + | 0.241503i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −38.3763 | + | 14.7653i | −1.31941 | + | 0.507642i | ||||
\(847\) | − | 0.0791757i | − | 0.00272051i | ||||||
\(848\) | −10.8496 | − | 13.3138i | −0.372577 | − | 0.457198i | ||||
\(849\) | −0.258392 | −0.00886799 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.8455 | − | 15.8455i | 0.543177 | − | 0.543177i | ||||
\(852\) | −0.0818536 | + | 1.60943i | −0.00280426 | + | 0.0551383i | ||||
\(853\) | −29.1167 | + | 29.1167i | −0.996938 | + | 0.996938i | −0.999995 | − | 0.00305738i | \(-0.999027\pi\) |
0.00305738 | + | 0.999995i | \(0.499027\pi\) | |||||||
\(854\) | 0.222311 | − | 0.500360i | 0.00760734 | − | 0.0171220i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.10124 | − | 21.6842i | −0.242715 | − | 0.741152i | ||||
\(857\) | 22.0170 | 0.752087 | 0.376044 | − | 0.926602i | \(-0.377284\pi\) | ||||
0.376044 | + | 0.926602i | \(0.377284\pi\) | |||||||
\(858\) | 0.422820 | − | 0.951647i | 0.0144348 | − | 0.0324887i | ||||
\(859\) | −16.8910 | − | 16.8910i | −0.576312 | − | 0.576312i | 0.357573 | − | 0.933885i | \(-0.383604\pi\) |
−0.933885 | + | 0.357573i | \(0.883604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0884782 | − | 0.0884782i | 0.00301533 | − | 0.00301533i | ||||
\(862\) | 16.7413 | − | 6.44124i | 0.570212 | − | 0.219390i | ||||
\(863\) | − | 46.2073i | − | 1.57292i | −0.617644 | − | 0.786458i | \(-0.711913\pi\) | ||
0.617644 | − | 0.786458i | \(-0.288087\pi\) | |||||||
\(864\) | 2.59303 | + | 1.48376i | 0.0882166 | + | 0.0504785i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.1122 | + | 31.4808i | 0.411591 | + | 1.06976i | ||||
\(867\) | −0.287819 | − | 0.287819i | −0.00977484 | − | 0.00977484i | ||||
\(868\) | −4.75158 | + | 4.29165i | −0.161279 | + | 0.145668i | ||||
\(869\) | −27.9526 | − | 27.9526i | −0.948227 | − | 0.948227i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.42029i | − | 0.115892i | ||||||
\(872\) | −13.9256 | − | 42.5230i | −0.471580 | − | 1.44001i | ||||
\(873\) | −11.5506 | −0.390929 | ||||||||
\(874\) | −3.96455 | + | 8.92307i | −0.134103 | + | 0.301827i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.33228 | − | 0.0677578i | −0.0450135 | − | 0.00228932i | ||||
\(877\) | −21.6380 | − | 21.6380i | −0.730664 | − | 0.730664i | 0.240087 | − | 0.970751i | \(-0.422824\pi\) |
−0.970751 | + | 0.240087i | \(0.922824\pi\) | |||||||
\(878\) | −2.36586 | − | 6.14908i | −0.0798440 | − | 0.207521i | ||||
\(879\) | 1.53968 | 0.0519320 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.6649 | −1.20158 | −0.600790 | − | 0.799407i | \(-0.705147\pi\) | ||||
−0.600790 | + | 0.799407i | \(0.705147\pi\) | |||||||
\(882\) | −10.4221 | − | 27.0879i | −0.350930 | − | 0.912098i | ||||
\(883\) | −17.5681 | − | 17.5681i | −0.591213 | − | 0.591213i | 0.346746 | − | 0.937959i | \(-0.387287\pi\) |
−0.937959 | + | 0.346746i | \(0.887287\pi\) | |||||||
\(884\) | 1.17859 | − | 23.1738i | 0.0396402 | − | 0.779420i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.09781 | − | 15.9751i | 0.238456 | − | 0.536695i | ||||
\(887\) | 51.2454 | 1.72065 | 0.860326 | − | 0.509744i | \(-0.170260\pi\) | ||||
0.860326 | + | 0.509744i | \(0.170260\pi\) | |||||||
\(888\) | −1.21501 | + | 2.39831i | −0.0407729 | + | 0.0804819i | ||||
\(889\) | − | 6.42441i | − | 0.215468i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.1426 | − | 21.1426i | −0.708305 | − | 0.708305i | ||||
\(892\) | 28.3372 | + | 31.3740i | 0.948799 | + | 1.05048i | ||||
\(893\) | 22.8315 | + | 22.8315i | 0.764025 | + | 0.764025i | ||||
\(894\) | −0.649055 | − | 1.68695i | −0.0217077 | − | 0.0564201i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.57897 | − | 2.29679i | −0.119565 | − | 0.0767304i | ||||
\(897\) | 0.456949i | 0.0152571i | ||||||||
\(898\) | −9.61574 | + | 3.69966i | −0.320881 | + | 0.123459i | ||||
\(899\) | −21.7547 | + | 21.7547i | −0.725559 | + | 0.725559i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.1165 | − | 14.1165i | −0.470288 | − | 0.470288i | ||||
\(902\) | 7.26184 | − | 16.3443i | 0.241793 | − | 0.544207i | ||||
\(903\) | −0.291028 | −0.00968479 | ||||||||
\(904\) | −10.2984 | − | 5.21728i | −0.342520 | − | 0.173524i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.963736 | + | 2.16909i | −0.0320180 | + | 0.0720633i | ||||
\(907\) | −29.6745 | + | 29.6745i | −0.985324 | + | 0.985324i | −0.999894 | − | 0.0145695i | \(-0.995362\pi\) |
0.0145695 | + | 0.999894i | \(0.495362\pi\) | |||||||
\(908\) | −40.9267 | − | 2.08148i | −1.35820 | − | 0.0690762i | ||||
\(909\) | −20.5697 | + | 20.5697i | −0.682255 | + | 0.682255i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9064 | −0.825187 | −0.412593 | − | 0.910915i | \(-0.635377\pi\) | ||||
−0.412593 | + | 0.910915i | \(0.635377\pi\) | |||||||
\(912\) | 0.118850 | − | 1.16541i | 0.00393552 | − | 0.0385907i | ||||
\(913\) | − | 50.3785i | − | 1.66729i | ||||||
\(914\) | −33.2869 | + | 12.8071i | −1.10103 | + | 0.423623i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.5179 | + | 1.45038i | 0.942258 | + | 0.0479220i | ||||
\(917\) | 1.33971 | − | 1.33971i | 0.0442413 | − | 0.0442413i | ||||
\(918\) | 3.17353 | + | 1.41001i | 0.104742 | + | 0.0465373i | ||||
\(919\) | 15.6940i | 0.517696i | 0.965918 | + | 0.258848i | \(0.0833429\pi\) | ||||
−0.965918 | + | 0.258848i | \(0.916657\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.32043i | 0.0435096i | ||||||||
\(922\) | −11.1007 | + | 24.9846i | −0.365584 | + | 0.822824i | ||||
\(923\) | −16.1309 | + | 16.1309i | −0.530954 | + | 0.530954i | ||||
\(924\) | −0.148694 | − | 0.164630i | −0.00489168 | − | 0.00541591i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.40691 | − | 3.65669i | −0.0462340 | − | 0.120166i | ||||
\(927\) | 3.45326i | 0.113420i | ||||||||
\(928\) | −17.7355 | − | 10.1485i | −0.582196 | − | 0.333139i | ||||
\(929\) | −6.00598 | −0.197050 | −0.0985249 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985249 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.1156 | + | 16.1156i | −0.528167 | + | 0.528167i | ||||
\(932\) | 5.12048 | − | 4.62485i | 0.167727 | − | 0.151492i | ||||
\(933\) | −1.20998 | + | 1.20998i | −0.0396130 | + | 0.0396130i | ||||
\(934\) | −32.8235 | − | 14.5836i | −1.07402 | − | 0.477190i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.57243 | + | 20.0695i | 0.214826 | + | 0.655991i | ||||
\(937\) | −4.83037 | −0.157801 | −0.0789006 | − | 0.996882i | \(-0.525141\pi\) | ||||
−0.0789006 | + | 0.996882i | \(0.525141\pi\) | |||||||
\(938\) | −0.665864 | − | 0.295846i | −0.0217412 | − | 0.00965970i | ||||
\(939\) | 0.159896 | + | 0.159896i | 0.00521802 | + | 0.00521802i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.63878 | + | 3.63878i | −0.118621 | + | 0.118621i | −0.763925 | − | 0.645305i | \(-0.776730\pi\) |
0.645305 | + | 0.763925i | \(0.276730\pi\) | |||||||
\(942\) | −0.641416 | − | 1.66710i | −0.0208985 | − | 0.0543169i | ||||
\(943\) | 7.84801i | 0.255566i | ||||||||
\(944\) | 35.5929 | − | 29.0051i | 1.15845 | − | 0.944036i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.8234 | + | 14.9373i | −1.26226 | + | 0.485654i | ||||
\(947\) | 34.7720 | + | 34.7720i | 1.12994 | + | 1.12994i | 0.990187 | + | 0.139751i | \(0.0446302\pi\) |
0.139751 | + | 0.990187i | \(0.455370\pi\) | |||||||
\(948\) | −2.07845 | − | 0.105707i | −0.0675049 | − | 0.00343321i | ||||
\(949\) | −13.3530 | − | 13.3530i | −0.433457 | − | 0.433457i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 0.912899i | − | 0.0296028i | ||||||
\(952\) | −4.40955 | − | 2.23392i | −0.142914 | − | 0.0724017i | ||||
\(953\) | −1.89827 | −0.0614910 | −0.0307455 | − | 0.999527i | \(-0.509788\pi\) | ||||
−0.0307455 | + | 0.999527i | \(0.509788\pi\) | |||||||
\(954\) | 16.6043 | + | 7.37733i | 0.537583 | + | 0.238850i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −26.7248 | + | 24.1380i | −0.864342 | + | 0.780679i | ||||
\(957\) | −0.753741 | − | 0.753741i | −0.0243650 | − | 0.0243650i | ||||
\(958\) | −29.6368 | + | 11.4028i | −0.957523 | + | 0.368408i | ||||
\(959\) | 6.27694 | 0.202693 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.5417 | 1.34006 | ||||||||
\(962\) | −35.5201 | + | 13.6664i | −1.14521 | + | 0.440622i | ||||
\(963\) | 17.0687 | + | 17.0687i | 0.550033 | + | 0.550033i | ||||
\(964\) | 18.7361 | − | 16.9226i | 0.603450 | − | 0.545039i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.0889591 | + | 0.0395248i | 0.00286221 | + | 0.00127169i | ||||
\(967\) | −61.5753 | −1.98013 | −0.990064 | − | 0.140616i | \(-0.955092\pi\) | ||||
−0.990064 | + | 0.140616i | \(0.955092\pi\) | |||||||
\(968\) | −0.531476 | − | 0.269251i | −0.0170823 | − | 0.00865406i | ||||
\(969\) | − | 1.36169i | − | 0.0437437i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.6595 | + | 22.6595i | 0.727179 | + | 0.727179i | 0.970057 | − | 0.242878i | \(-0.0780913\pi\) |
−0.242878 | + | 0.970057i | \(0.578091\pi\) | |||||||
\(972\) | −4.73675 | − | 0.240905i | −0.151931 | − | 0.00772702i | ||||
\(973\) | −2.84334 | − | 2.84334i | −0.0911532 | − | 0.0911532i | ||||
\(974\) | 36.6421 | − | 14.0981i | 1.17409 | − | 0.451732i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.60271 | − | 3.19385i | −0.0833108 | − | 0.102233i | ||||
\(977\) | − | 25.3240i | − | 0.810186i | −0.914276 | − | 0.405093i | \(-0.867239\pi\) | ||
0.914276 | − | 0.405093i | \(-0.132761\pi\) | |||||||
\(978\) | −0.465547 | − | 1.21000i | −0.0148866 | − | 0.0386915i | ||||
\(979\) | 37.1970 | − | 37.1970i | 1.18882 | − | 1.18882i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.4720 | + | 33.4720i | 1.06868 | + | 1.06868i | ||||
\(982\) | −30.8872 | − | 13.7233i | −0.985651 | − | 0.437928i | ||||
\(983\) | −5.01686 | −0.160013 | −0.0800065 | − | 0.996794i | \(-0.525494\pi\) | ||||
−0.0800065 | + | 0.996794i | \(0.525494\pi\) | |||||||
\(984\) | −0.293035 | − | 0.894806i | −0.00934160 | − | 0.0285254i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −21.7060 | − | 9.64403i | −0.691259 | − | 0.307128i | ||||
\(987\) | 0.227620 | − | 0.227620i | 0.00724521 | − | 0.00724521i | ||||
\(988\) | 12.3065 | − | 11.1153i | 0.391521 | − | 0.353624i | ||||
\(989\) | 12.9071 | − | 12.9071i | 0.410420 | − | 0.410420i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.2998 | 1.31193 | 0.655965 | − | 0.754791i | \(-0.272262\pi\) | ||||
0.655965 | + | 0.754791i | \(0.272262\pi\) | |||||||
\(992\) | 12.6496 | + | 46.4900i | 0.401626 | + | 1.47606i | ||||
\(993\) | 0.520569i | 0.0165198i | ||||||||
\(994\) | 1.74509 | + | 4.53564i | 0.0553510 | + | 0.143862i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.77772 | − | 1.96824i | −0.0563292 | − | 0.0623659i | ||||
\(997\) | −1.23850 | + | 1.23850i | −0.0392235 | + | 0.0392235i | −0.726447 | − | 0.687223i | \(-0.758830\pi\) |
0.687223 | + | 0.726447i | \(0.258830\pi\) | |||||||
\(998\) | −1.47755 | + | 3.32553i | −0.0467709 | + | 0.105268i | ||||
\(999\) | − | 5.69582i | − | 0.180208i |
(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 | 400.2.q.e.149.1 | 12 | ||
4.3 | odd | 2 | 1600.2.q.e.49.4 | 12 | |||
5.2 | odd | 4 | 400.2.l.g.101.2 | yes | 12 | ||
5.3 | odd | 4 | 400.2.l.f.101.5 | ✓ | 12 | ||
5.4 | even | 2 | 400.2.q.f.149.6 | 12 | |||
16.3 | odd | 4 | 1600.2.q.f.849.3 | 12 | |||
16.13 | even | 4 | 400.2.q.f.349.6 | 12 | |||
20.3 | even | 4 | 1600.2.l.g.1201.3 | 12 | |||
20.7 | even | 4 | 1600.2.l.f.1201.4 | 12 | |||
20.19 | odd | 2 | 1600.2.q.f.49.3 | 12 | |||
80.3 | even | 4 | 1600.2.l.g.401.3 | 12 | |||
80.13 | odd | 4 | 400.2.l.f.301.5 | yes | 12 | ||
80.19 | odd | 4 | 1600.2.q.e.849.4 | 12 | |||
80.29 | even | 4 | inner | 400.2.q.e.349.1 | 12 | ||
80.67 | even | 4 | 1600.2.l.f.401.4 | 12 | |||
80.77 | odd | 4 | 400.2.l.g.301.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.5 | ✓ | 12 | 5.3 | odd | 4 | ||
400.2.l.f.301.5 | yes | 12 | 80.13 | odd | 4 | ||
400.2.l.g.101.2 | yes | 12 | 5.2 | odd | 4 | ||
400.2.l.g.301.2 | yes | 12 | 80.77 | odd | 4 | ||
400.2.q.e.149.1 | 12 | 1.1 | even | 1 | trivial | ||
400.2.q.e.349.1 | 12 | 80.29 | even | 4 | inner | ||
400.2.q.f.149.6 | 12 | 5.4 | even | 2 | |||
400.2.q.f.349.6 | 12 | 16.13 | even | 4 | |||
1600.2.l.f.401.4 | 12 | 80.67 | even | 4 | |||
1600.2.l.f.1201.4 | 12 | 20.7 | even | 4 | |||
1600.2.l.g.401.3 | 12 | 80.3 | even | 4 | |||
1600.2.l.g.1201.3 | 12 | 20.3 | even | 4 | |||
1600.2.q.e.49.4 | 12 | 4.3 | odd | 2 | |||
1600.2.q.e.849.4 | 12 | 80.19 | odd | 4 | |||
1600.2.q.f.49.3 | 12 | 20.19 | odd | 2 | |||
1600.2.q.f.849.3 | 12 | 16.3 | odd | 4 |