Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(89,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.r (of order \(6\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.4 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.89 |
Dual form | 1386.2.r.b.1277.4 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.22474 | − | 2.12132i | 0.547723 | − | 0.948683i | −0.450708 | − | 0.892672i | \(-0.648828\pi\) |
0.998430 | − | 0.0560116i | \(-0.0178384\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 2.44949i | −0.377964 | − | 0.925820i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.12132 | − | 1.22474i | 0.670820 | − | 0.387298i | ||||
\(11\) | 0.866025 | − | 0.500000i | 0.261116 | − | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.44949i | − | 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | 0.358719 | − | 2.62132i | 0.0958718 | − | 0.700577i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.866025 | − | 1.50000i | −0.210042 | − | 0.363803i | 0.741685 | − | 0.670748i | \(-0.234027\pi\) |
−0.951727 | + | 0.306944i | \(0.900693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50000 | − | 0.866025i | −0.344124 | − | 0.198680i | 0.317970 | − | 0.948101i | \(-0.396999\pi\) |
−0.662094 | + | 0.749421i | \(0.730332\pi\) | |||||||
\(20\) | 2.44949 | 0.547723 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −6.27231 | − | 3.62132i | −1.30787 | − | 0.755097i | −0.326127 | − | 0.945326i | \(-0.605744\pi\) |
−0.981740 | + | 0.190228i | \(0.939077\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.22474 | − | 2.12132i | 0.240192 | − | 0.416025i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.62132 | − | 2.09077i | 0.306401 | − | 0.395118i | ||||
\(29\) | 1.24264i | 0.230753i | 0.993322 | + | 0.115376i | \(0.0368074\pi\) | ||||
−0.993322 | + | 0.115376i | \(0.963193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.24264 | − | 0.717439i | 0.223185 | − | 0.128856i | −0.384239 | − | 0.923234i | \(-0.625536\pi\) |
0.607424 | + | 0.794378i | \(0.292203\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.73205i | − | 0.297044i | ||||||
\(35\) | −6.42090 | − | 0.878680i | −1.08533 | − | 0.148524i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.62132 | − | 2.80821i | 0.266543 | − | 0.461667i | −0.701423 | − | 0.712745i | \(-0.747452\pi\) |
0.967967 | + | 0.251078i | \(0.0807851\pi\) | |||||||
\(38\) | −0.866025 | − | 1.50000i | −0.140488 | − | 0.243332i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.12132 | + | 1.22474i | 0.335410 | + | 0.193649i | ||||
\(41\) | 1.43488 | 0.224090 | 0.112045 | − | 0.993703i | \(-0.464260\pi\) | ||||
0.112045 | + | 0.993703i | \(0.464260\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0.866025 | + | 0.500000i | 0.130558 | + | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.62132 | − | 6.27231i | −0.533935 | − | 0.924802i | ||||
\(47\) | 3.82282 | − | 6.62132i | 0.557616 | − | 0.965819i | −0.440079 | − | 0.897959i | \(-0.645050\pi\) |
0.997695 | − | 0.0678598i | \(-0.0216171\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | + | 4.89898i | −0.714286 | + | 0.699854i | ||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.12132 | − | 1.22474i | 0.294174 | − | 0.169842i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.44949i | − | 0.330289i | ||||||
\(56\) | 2.44949 | − | 1.00000i | 0.327327 | − | 0.133631i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.621320 | + | 1.07616i | −0.0815834 | + | 0.141307i | ||||
\(59\) | −7.49706 | − | 12.9853i | −0.976034 | − | 1.69054i | −0.676481 | − | 0.736460i | \(-0.736496\pi\) |
−0.299552 | − | 0.954080i | \(-0.596837\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.00000 | + | 5.19615i | 1.15233 | + | 0.665299i | 0.949454 | − | 0.313905i | \(-0.101637\pi\) |
0.202878 | + | 0.979204i | \(0.434971\pi\) | |||||||
\(62\) | 1.43488 | 0.182230 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.19615 | − | 3.00000i | −0.644503 | − | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.24264 | + | 10.8126i | 0.762660 | + | 1.32097i | 0.941475 | + | 0.337083i | \(0.109440\pi\) |
−0.178815 | + | 0.983883i | \(0.557226\pi\) | |||||||
\(68\) | 0.866025 | − | 1.50000i | 0.105021 | − | 0.181902i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.12132 | − | 3.97141i | −0.612115 | − | 0.474674i | ||||
\(71\) | − | 7.24264i | − | 0.859543i | −0.902938 | − | 0.429772i | \(-0.858594\pi\) | ||
0.902938 | − | 0.429772i | \(-0.141406\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24264 | − | 2.44949i | 0.496564 | − | 0.286691i | −0.230730 | − | 0.973018i | \(-0.574111\pi\) |
0.727293 | + | 0.686327i | \(0.240778\pi\) | |||||||
\(74\) | 2.80821 | − | 1.62132i | 0.326448 | − | 0.188475i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.73205i | − | 0.198680i | ||||||
\(77\) | −2.09077 | − | 1.62132i | −0.238265 | − | 0.184767i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 1.22474 | + | 2.12132i | 0.136931 | + | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.24264 | + | 0.717439i | 0.137227 | + | 0.0792279i | ||||
\(83\) | 12.8418 | 1.40957 | 0.704785 | − | 0.709421i | \(-0.251043\pi\) | ||||
0.704785 | + | 0.709421i | \(0.251043\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.24264 | −0.460179 | ||||||||
\(86\) | 0.866025 | + | 0.500000i | 0.0933859 | + | 0.0539164i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | −0.507306 | + | 0.878680i | −0.0537743 | + | 0.0931399i | −0.891660 | − | 0.452707i | \(-0.850458\pi\) |
0.837885 | + | 0.545846i | \(0.183792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | + | 2.44949i | −0.628971 | + | 0.256776i | ||||
\(92\) | − | 7.24264i | − | 0.755097i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.62132 | − | 3.82282i | 0.682937 | − | 0.394294i | ||||
\(95\) | −3.67423 | + | 2.12132i | −0.376969 | + | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.16693i | − | 0.321553i | −0.986991 | − | 0.160776i | \(-0.948600\pi\) | ||
0.986991 | − | 0.160776i | \(-0.0513998\pi\) | |||||||
\(98\) | −6.77962 | + | 1.74264i | −0.684845 | + | 0.176033i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 5.25770 | + | 9.10660i | 0.523161 | + | 0.906141i | 0.999637 | + | 0.0269533i | \(0.00858054\pi\) |
−0.476476 | + | 0.879187i | \(0.658086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1213 | + | 8.15295i | 1.39142 | + | 0.803334i | 0.993472 | − | 0.114076i | \(-0.0363908\pi\) |
0.397943 | + | 0.917410i | \(0.369724\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.5446 | − | 7.24264i | −1.21273 | − | 0.700173i | −0.249380 | − | 0.968406i | \(-0.580227\pi\) |
−0.963354 | + | 0.268233i | \(0.913560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.87868 | + | 8.45012i | 0.467293 | + | 0.809375i | 0.999302 | − | 0.0373639i | \(-0.0118961\pi\) |
−0.532009 | + | 0.846739i | \(0.678563\pi\) | |||||||
\(110\) | 1.22474 | − | 2.12132i | 0.116775 | − | 0.202260i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.62132 | + | 0.358719i | 0.247691 | + | 0.0338958i | ||||
\(113\) | − | 1.75736i | − | 0.165318i | −0.996578 | − | 0.0826592i | \(-0.973659\pi\) | ||
0.996578 | − | 0.0826592i | \(-0.0263413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.3640 | + | 8.87039i | −1.43270 | + | 0.827168i | ||||
\(116\) | −1.07616 | + | 0.621320i | −0.0999188 | + | 0.0576881i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 14.9941i | − | 1.38032i | ||||||
\(119\) | −2.80821 | + | 3.62132i | −0.257428 | + | 0.331966i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 5.19615 | + | 9.00000i | 0.470438 | + | 0.814822i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.24264 | + | 0.717439i | 0.111592 | + | 0.0644279i | ||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7574 | 1.13203 | 0.566016 | − | 0.824394i | \(-0.308484\pi\) | ||||
0.566016 | + | 0.824394i | \(0.308484\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | − | 5.19615i | −0.263117 | − | 0.455733i | ||||
\(131\) | −5.70346 | + | 9.87868i | −0.498313 | + | 0.863104i | −0.999998 | − | 0.00194634i | \(-0.999380\pi\) |
0.501685 | + | 0.865051i | \(0.332714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.621320 | + | 4.54026i | −0.0538753 | + | 0.393690i | ||||
\(134\) | 12.4853i | 1.07856i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | − | 0.866025i | 0.128624 | − | 0.0742611i | ||||
\(137\) | 1.52192 | − | 0.878680i | 0.130026 | − | 0.0750707i | −0.433576 | − | 0.901117i | \(-0.642748\pi\) |
0.563602 | + | 0.826046i | \(0.309415\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.297173i | 0.0252059i | 0.999921 | + | 0.0126029i | \(0.00401175\pi\) | ||||
−0.999921 | + | 0.0126029i | \(0.995988\pi\) | |||||||
\(140\) | −2.44949 | − | 6.00000i | −0.207020 | − | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.62132 | − | 6.27231i | 0.303894 | − | 0.526361i | ||||
\(143\) | −1.22474 | − | 2.12132i | −0.102418 | − | 0.177394i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.63604 | + | 1.52192i | 0.218911 | + | 0.126388i | ||||
\(146\) | 4.89898 | 0.405442 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.24264 | 0.266543 | ||||||||
\(149\) | 4.11999 | + | 2.37868i | 0.337523 | + | 0.194869i | 0.659176 | − | 0.751989i | \(-0.270905\pi\) |
−0.321653 | + | 0.946858i | \(0.604238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.37868 | − | 2.38794i | −0.112195 | − | 0.194328i | 0.804460 | − | 0.594007i | \(-0.202455\pi\) |
−0.916655 | + | 0.399679i | \(0.869122\pi\) | |||||||
\(152\) | 0.866025 | − | 1.50000i | 0.0702439 | − | 0.121666i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | − | 2.44949i | −0.0805823 | − | 0.197386i | ||||
\(155\) | − | 3.51472i | − | 0.282309i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.62132 | − | 2.09077i | 0.289013 | − | 0.166862i | −0.348484 | − | 0.937315i | \(-0.613303\pi\) |
0.637497 | + | 0.770453i | \(0.279970\pi\) | |||||||
\(158\) | −6.92820 | + | 4.00000i | −0.551178 | + | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.44949i | 0.193649i | ||||||||
\(161\) | −2.59808 | + | 18.9853i | −0.204757 | + | 1.49625i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.48528 | − | 12.9649i | 0.586292 | − | 1.01549i | −0.408420 | − | 0.912794i | \(-0.633920\pi\) |
0.994713 | − | 0.102694i | \(-0.0327464\pi\) | |||||||
\(164\) | 0.717439 | + | 1.24264i | 0.0560226 | + | 0.0970339i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.1213 | + | 6.42090i | 0.863182 | + | 0.498358i | ||||
\(167\) | −0.420266 | −0.0325212 | −0.0162606 | − | 0.999868i | \(-0.505176\pi\) | ||||
−0.0162606 | + | 0.999868i | \(0.505176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | −3.67423 | − | 2.12132i | −0.281801 | − | 0.162698i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | + | 0.866025i | 0.0381246 | + | 0.0660338i | ||||
\(173\) | −1.01461 | + | 1.75736i | −0.0771395 | + | 0.133610i | −0.902015 | − | 0.431705i | \(-0.857912\pi\) |
0.824875 | + | 0.565315i | \(0.191245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.62132 | + | 2.09077i | −0.122560 | + | 0.158047i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.878680 | + | 0.507306i | −0.0658598 | + | 0.0380242i | ||||
\(179\) | −7.79423 | + | 4.50000i | −0.582568 | + | 0.336346i | −0.762153 | − | 0.647397i | \(-0.775858\pi\) |
0.179585 | + | 0.983742i | \(0.442524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.89898i | − | 0.364138i | −0.983286 | − | 0.182069i | \(-0.941721\pi\) | ||
0.983286 | − | 0.182069i | \(-0.0582795\pi\) | |||||||
\(182\) | −6.42090 | − | 0.878680i | −0.475949 | − | 0.0651321i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.62132 | − | 6.27231i | 0.266967 | − | 0.462401i | ||||
\(185\) | −3.97141 | − | 6.87868i | −0.291984 | − | 0.505731i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.50000 | − | 0.866025i | −0.109691 | − | 0.0633300i | ||||
\(188\) | 7.64564 | 0.557616 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.24264 | −0.307794 | ||||||||
\(191\) | −14.6969 | − | 8.48528i | −1.06343 | − | 0.613973i | −0.137053 | − | 0.990564i | \(-0.543763\pi\) |
−0.926380 | + | 0.376590i | \(0.877096\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.3640 | + | 17.9509i | 0.746014 | + | 1.29213i | 0.949719 | + | 0.313102i | \(0.101368\pi\) |
−0.203705 | + | 0.979032i | \(0.565298\pi\) | |||||||
\(194\) | 1.58346 | − | 2.74264i | 0.113686 | − | 0.196910i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.74264 | − | 1.88064i | −0.481617 | − | 0.134331i | ||||
\(197\) | 3.72792i | 0.265603i | 0.991143 | + | 0.132802i | \(0.0423974\pi\) | ||||
−0.991143 | + | 0.132802i | \(0.957603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.36396 | + | 3.67423i | −0.451129 | + | 0.260460i | −0.708307 | − | 0.705905i | \(-0.750541\pi\) |
0.257178 | + | 0.966364i | \(0.417207\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.5154i | 0.739861i | ||||||||
\(203\) | 3.04384 | − | 1.24264i | 0.213635 | − | 0.0872163i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.75736 | − | 3.04384i | 0.122739 | − | 0.212591i | ||||
\(206\) | 8.15295 | + | 14.1213i | 0.568043 | + | 0.983879i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.12132 | + | 1.22474i | 0.147087 | + | 0.0849208i | ||||
\(209\) | −1.73205 | −0.119808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.4853 | −1.54795 | −0.773975 | − | 0.633216i | \(-0.781735\pi\) | ||||
−0.773975 | + | 0.633216i | \(0.781735\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.24264 | − | 12.5446i | −0.495097 | − | 0.857533i | ||||
\(215\) | 1.22474 | − | 2.12132i | 0.0835269 | − | 0.144673i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | − | 2.32640i | −0.203653 | − | 0.157926i | ||||
\(218\) | 9.75736i | 0.660852i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.12132 | − | 1.22474i | 0.143019 | − | 0.0825723i | ||||
\(221\) | −3.67423 | + | 2.12132i | −0.247156 | + | 0.142695i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.37769i | 0.627977i | 0.949427 | + | 0.313988i | \(0.101665\pi\) | ||||
−0.949427 | + | 0.313988i | \(0.898335\pi\) | |||||||
\(224\) | 2.09077 | + | 1.62132i | 0.139695 | + | 0.108329i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.878680 | − | 1.52192i | 0.0584489 | − | 0.101236i | ||||
\(227\) | 3.16693 | + | 5.48528i | 0.210196 | + | 0.364071i | 0.951776 | − | 0.306794i | \(-0.0992563\pi\) |
−0.741579 | + | 0.670865i | \(0.765923\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | − | 6.92820i | −0.792982 | − | 0.457829i | 0.0480291 | − | 0.998846i | \(-0.484706\pi\) |
−0.841011 | + | 0.541017i | \(0.818039\pi\) | |||||||
\(230\) | −17.7408 | −1.16979 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.24264 | −0.0815834 | ||||||||
\(233\) | −15.1427 | − | 8.74264i | −0.992031 | − | 0.572749i | −0.0861503 | − | 0.996282i | \(-0.527457\pi\) |
−0.905881 | + | 0.423533i | \(0.860790\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.36396 | − | 16.2189i | −0.610837 | − | 1.05800i | ||||
\(236\) | 7.49706 | − | 12.9853i | 0.488017 | − | 0.845270i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.24264 | + | 1.73205i | −0.275010 | + | 0.112272i | ||||
\(239\) | − | 12.7279i | − | 0.823301i | −0.911342 | − | 0.411650i | \(-0.864952\pi\) | ||
0.911342 | − | 0.411650i | \(-0.135048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.9706 | + | 6.33386i | −0.706676 | + | 0.408000i | −0.809829 | − | 0.586666i | \(-0.800440\pi\) |
0.103153 | + | 0.994665i | \(0.467107\pi\) | |||||||
\(242\) | 0.866025 | − | 0.500000i | 0.0556702 | − | 0.0321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.3923i | 0.665299i | ||||||||
\(245\) | 4.26858 | + | 16.6066i | 0.272710 | + | 1.06096i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.12132 | + | 3.67423i | −0.134976 | + | 0.233786i | ||||
\(248\) | 0.717439 | + | 1.24264i | 0.0455574 | + | 0.0789078i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.48528 | + | 4.89898i | 0.536656 | + | 0.309839i | ||||
\(251\) | 18.4582 | 1.16507 | 0.582536 | − | 0.812805i | \(-0.302060\pi\) | ||||
0.582536 | + | 0.812805i | \(0.302060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.24264 | −0.455341 | ||||||||
\(254\) | 11.0482 | + | 6.37868i | 0.693226 | + | 0.400234i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.85578 | − | 13.6066i | 0.490030 | − | 0.848756i | −0.509904 | − | 0.860231i | \(-0.670319\pi\) |
0.999934 | + | 0.0114746i | \(0.00365256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.50000 | − | 1.16320i | −0.528164 | − | 0.0722776i | ||||
\(260\) | − | 6.00000i | − | 0.372104i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.87868 | + | 5.70346i | −0.610307 | + | 0.352361i | ||||
\(263\) | −22.9369 | + | 13.2426i | −1.41435 | + | 0.816576i | −0.995795 | − | 0.0916144i | \(-0.970797\pi\) |
−0.418557 | + | 0.908191i | \(0.637464\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.80821 | + | 3.62132i | −0.172182 | + | 0.222037i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.24264 | + | 10.8126i | −0.381330 | + | 0.660483i | ||||
\(269\) | 13.3491 | + | 23.1213i | 0.813909 | + | 1.40973i | 0.910109 | + | 0.414370i | \(0.135998\pi\) |
−0.0961996 | + | 0.995362i | \(0.530669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.75736 | + | 1.01461i | 0.106752 | + | 0.0616333i | 0.552425 | − | 0.833562i | \(-0.313702\pi\) |
−0.445673 | + | 0.895196i | \(0.647036\pi\) | |||||||
\(272\) | 1.73205 | 0.105021 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.75736 | 0.106166 | ||||||||
\(275\) | −0.866025 | − | 0.500000i | −0.0522233 | − | 0.0301511i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7279 | + | 25.5095i | 0.884915 | + | 1.53272i | 0.845811 | + | 0.533483i | \(0.179117\pi\) |
0.0391041 | + | 0.999235i | \(0.487550\pi\) | |||||||
\(278\) | −0.148586 | + | 0.257359i | −0.00891162 | + | 0.0154354i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.878680 | − | 6.42090i | 0.0525112 | − | 0.383722i | ||||
\(281\) | 23.4853i | 1.40101i | 0.713645 | + | 0.700507i | \(0.247043\pi\) | ||||
−0.713645 | + | 0.700507i | \(0.752957\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.4853 | + | 15.2913i | −1.57439 | + | 0.908973i | −0.578765 | + | 0.815494i | \(0.696465\pi\) |
−0.995621 | + | 0.0934783i | \(0.970201\pi\) | |||||||
\(284\) | 6.27231 | − | 3.62132i | 0.372193 | − | 0.214886i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.44949i | − | 0.144841i | ||||||
\(287\) | −1.43488 | − | 3.51472i | −0.0846982 | − | 0.207467i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | − | 12.1244i | 0.411765 | − | 0.713197i | ||||
\(290\) | 1.52192 | + | 2.63604i | 0.0893701 | + | 0.154794i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.24264 | + | 2.44949i | 0.248282 | + | 0.143346i | ||||
\(293\) | −7.05130 | −0.411941 | −0.205971 | − | 0.978558i | \(-0.566035\pi\) | ||||
−0.205971 | + | 0.978558i | \(0.566035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.7279 | −2.13838 | ||||||||
\(296\) | 2.80821 | + | 1.62132i | 0.163224 | + | 0.0942373i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.37868 | + | 4.11999i | 0.137793 | + | 0.238665i | ||||
\(299\) | −8.87039 | + | 15.3640i | −0.512988 | + | 0.888521i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | − | 2.44949i | −0.0576390 | − | 0.141186i | ||||
\(302\) | − | 2.75736i | − | 0.158668i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.50000 | − | 0.866025i | 0.0860309 | − | 0.0496700i | ||||
\(305\) | 22.0454 | − | 12.7279i | 1.26232 | − | 0.728799i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.52255i | 0.429335i | 0.976687 | + | 0.214667i | \(0.0688667\pi\) | ||||
−0.976687 | + | 0.214667i | \(0.931133\pi\) | |||||||
\(308\) | 0.358719 | − | 2.62132i | 0.0204399 | − | 0.149364i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.75736 | − | 3.04384i | 0.0998113 | − | 0.172878i | ||||
\(311\) | 13.2005 | + | 22.8640i | 0.748532 | + | 1.29650i | 0.948526 | + | 0.316699i | \(0.102575\pi\) |
−0.199994 | + | 0.979797i | \(0.564092\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.98528 | + | 4.03295i | 0.394831 | + | 0.227956i | 0.684251 | − | 0.729246i | \(-0.260129\pi\) |
−0.289420 | + | 0.957202i | \(0.593462\pi\) | |||||||
\(314\) | 4.18154 | 0.235978 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 6.71807 | + | 3.87868i | 0.377324 | + | 0.217848i | 0.676654 | − | 0.736302i | \(-0.263430\pi\) |
−0.299329 | + | 0.954150i | \(0.596763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.621320 | + | 1.07616i | 0.0347873 | + | 0.0602533i | ||||
\(320\) | −1.22474 | + | 2.12132i | −0.0684653 | + | 0.118585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.7426 | + | 15.1427i | −0.654392 | + | 0.843870i | ||||
\(323\) | 3.00000i | 0.166924i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.12132 | + | 1.22474i | −0.117670 | + | 0.0679366i | ||||
\(326\) | 12.9649 | − | 7.48528i | 0.718059 | − | 0.414571i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.43488i | 0.0792279i | ||||||||
\(329\) | −20.0417 | − | 2.74264i | −1.10493 | − | 0.151207i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.00000 | − | 12.1244i | 0.384755 | − | 0.666415i | −0.606980 | − | 0.794717i | \(-0.707619\pi\) |
0.991735 | + | 0.128302i | \(0.0409527\pi\) | |||||||
\(332\) | 6.42090 | + | 11.1213i | 0.352393 | + | 0.610362i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.363961 | − | 0.210133i | −0.0199151 | − | 0.0114980i | ||||
\(335\) | 30.5826 | 1.67090 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2426 | −1.32058 | −0.660290 | − | 0.751010i | \(-0.729567\pi\) | ||||
−0.660290 | + | 0.751010i | \(0.729567\pi\) | |||||||
\(338\) | 6.06218 | + | 3.50000i | 0.329739 | + | 0.190375i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.12132 | − | 3.67423i | −0.115045 | − | 0.199263i | ||||
\(341\) | 0.717439 | − | 1.24264i | 0.0388515 | − | 0.0672928i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | 1.00000i | 0.0539164i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.75736 | + | 1.01461i | −0.0944762 | + | 0.0545459i | ||||
\(347\) | 13.4361 | − | 7.75736i | 0.721290 | − | 0.416437i | −0.0939374 | − | 0.995578i | \(-0.529945\pi\) |
0.815227 | + | 0.579141i | \(0.196612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.6969i | − | 0.786709i | −0.919387 | − | 0.393355i | \(-0.871314\pi\) | ||
0.919387 | − | 0.393355i | \(-0.128686\pi\) | |||||||
\(350\) | −2.44949 | + | 1.00000i | −0.130931 | + | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 4.39167 | + | 7.60660i | 0.233745 | + | 0.404859i | 0.958907 | − | 0.283720i | \(-0.0915685\pi\) |
−0.725162 | + | 0.688578i | \(0.758235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.3640 | − | 8.87039i | −0.815434 | − | 0.470791i | ||||
\(356\) | −1.01461 | −0.0537743 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.00000 | −0.475665 | ||||||||
\(359\) | 0.891519 | + | 0.514719i | 0.0470526 | + | 0.0271658i | 0.523342 | − | 0.852123i | \(-0.324685\pi\) |
−0.476289 | + | 0.879289i | \(0.658018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | − | 13.8564i | −0.421053 | − | 0.729285i | ||||
\(362\) | 2.44949 | − | 4.24264i | 0.128742 | − | 0.222988i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.12132 | − | 3.97141i | −0.268430 | − | 0.208158i | ||||
\(365\) | − | 12.0000i | − | 0.628109i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2426 | − | 5.91359i | 0.534661 | − | 0.308687i | −0.208251 | − | 0.978075i | \(-0.566777\pi\) |
0.742913 | + | 0.669388i | \(0.233444\pi\) | |||||||
\(368\) | 6.27231 | − | 3.62132i | 0.326967 | − | 0.188774i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 7.94282i | − | 0.412927i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0000 | − | 29.4449i | 0.880227 | − | 1.52460i | 0.0291379 | − | 0.999575i | \(-0.490724\pi\) |
0.851089 | − | 0.525022i | \(-0.175943\pi\) | |||||||
\(374\) | −0.866025 | − | 1.50000i | −0.0447811 | − | 0.0775632i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.62132 | + | 3.82282i | 0.341469 | + | 0.197147i | ||||
\(377\) | 3.04384 | 0.156766 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.7279 | −1.68112 | −0.840560 | − | 0.541718i | \(-0.817774\pi\) | ||||
−0.840560 | + | 0.541718i | \(0.817774\pi\) | |||||||
\(380\) | −3.67423 | − | 2.12132i | −0.188484 | − | 0.108821i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.48528 | − | 14.6969i | −0.434145 | − | 0.751961i | ||||
\(383\) | 19.2372 | − | 33.3198i | 0.982975 | − | 1.70256i | 0.332364 | − | 0.943151i | \(-0.392154\pi\) |
0.650611 | − | 0.759411i | \(-0.274513\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | + | 2.44949i | −0.305788 | + | 0.124838i | ||||
\(386\) | 20.7279i | 1.05502i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.74264 | − | 1.58346i | 0.139236 | − | 0.0803882i | ||||
\(389\) | −31.8073 | + | 18.3640i | −1.61269 | + | 0.931090i | −0.623952 | + | 0.781462i | \(0.714474\pi\) |
−0.988742 | + | 0.149627i | \(0.952193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.5446i | 0.634409i | ||||||||
\(392\) | −4.89898 | − | 5.00000i | −0.247436 | − | 0.252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.86396 | + | 3.22848i | −0.0939050 | + | 0.162648i | ||||
\(395\) | 9.79796 | + | 16.9706i | 0.492989 | + | 0.853882i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.3492 | + | 16.3674i | 1.42281 | + | 0.821458i | 0.996538 | − | 0.0831378i | \(-0.0264941\pi\) |
0.426270 | + | 0.904596i | \(0.359827\pi\) | |||||||
\(398\) | −7.34847 | −0.368345 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 24.4588 | + | 14.1213i | 1.22142 | + | 0.705185i | 0.965220 | − | 0.261440i | \(-0.0841972\pi\) |
0.256197 | + | 0.966625i | \(0.417531\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.75736 | − | 3.04384i | −0.0875403 | − | 0.151624i | ||||
\(404\) | −5.25770 | + | 9.10660i | −0.261580 | + | 0.453070i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.25736 | + | 0.445759i | 0.161660 | + | 0.0221227i | ||||
\(407\) | − | 3.24264i | − | 0.160732i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.363961 | − | 0.210133i | 0.0179967 | − | 0.0103904i | −0.490975 | − | 0.871174i | \(-0.663359\pi\) |
0.508971 | + | 0.860783i | \(0.330026\pi\) | |||||||
\(410\) | 3.04384 | − | 1.75736i | 0.150324 | − | 0.0867898i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.3059i | 0.803334i | ||||||||
\(413\) | −24.3103 | + | 31.3492i | −1.19623 | + | 1.54260i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.7279 | − | 27.2416i | 0.772053 | − | 1.33724i | ||||
\(416\) | 1.22474 | + | 2.12132i | 0.0600481 | + | 0.104006i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.50000 | − | 0.866025i | −0.0733674 | − | 0.0423587i | ||||
\(419\) | −4.60181 | −0.224813 | −0.112406 | − | 0.993662i | \(-0.535856\pi\) | ||||
−0.112406 | + | 0.993662i | \(0.535856\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.6985 | 1.39868 | 0.699339 | − | 0.714790i | \(-0.253478\pi\) | ||||
0.699339 | + | 0.714790i | \(0.253478\pi\) | |||||||
\(422\) | −19.4728 | − | 11.2426i | −0.947922 | − | 0.547283i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.866025 | + | 1.50000i | −0.0420084 | + | 0.0727607i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.72792 | − | 27.2416i | 0.180407 | − | 1.31831i | ||||
\(428\) | − | 14.4853i | − | 0.700173i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.12132 | − | 1.22474i | 0.102299 | − | 0.0590624i | ||||
\(431\) | 14.6969 | − | 8.48528i | 0.707927 | − | 0.408722i | −0.102366 | − | 0.994747i | \(-0.532641\pi\) |
0.810293 | + | 0.586025i | \(0.199308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.3280i | − | 1.02496i | −0.858700 | − | 0.512478i | \(-0.828727\pi\) | ||
0.858700 | − | 0.512478i | \(-0.171273\pi\) | |||||||
\(434\) | −1.43488 | − | 3.51472i | −0.0688763 | − | 0.168712i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.87868 | + | 8.45012i | −0.233646 | + | 0.404687i | ||||
\(437\) | 6.27231 | + | 10.8640i | 0.300045 | + | 0.519694i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.6213 | + | 12.4831i | 1.03193 | + | 0.595785i | 0.917537 | − | 0.397651i | \(-0.130175\pi\) |
0.114393 | + | 0.993436i | \(0.463508\pi\) | |||||||
\(440\) | 2.44949 | 0.116775 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.24264 | −0.201802 | ||||||||
\(443\) | −2.59808 | − | 1.50000i | −0.123438 | − | 0.0712672i | 0.437009 | − | 0.899457i | \(-0.356038\pi\) |
−0.560448 | + | 0.828190i | \(0.689371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.24264 | + | 2.15232i | 0.0589068 | + | 0.102030i | ||||
\(446\) | −4.68885 | + | 8.12132i | −0.222023 | + | 0.384556i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | + | 2.44949i | 0.0472456 | + | 0.115728i | ||||
\(449\) | − | 13.4558i | − | 0.635021i | −0.948255 | − | 0.317510i | \(-0.897153\pi\) | ||
0.948255 | − | 0.317510i | \(-0.102847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.24264 | − | 0.717439i | 0.0585137 | − | 0.0337829i | ||||
\(452\) | 1.52192 | − | 0.878680i | 0.0715850 | − | 0.0413296i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.33386i | 0.297263i | ||||||||
\(455\) | −2.15232 | + | 15.7279i | −0.100902 | + | 0.737336i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.8492 | + | 29.1837i | −0.788174 | + | 1.36516i | 0.138910 | + | 0.990305i | \(0.455640\pi\) |
−0.927084 | + | 0.374853i | \(0.877693\pi\) | |||||||
\(458\) | −6.92820 | − | 12.0000i | −0.323734 | − | 0.560723i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.3640 | − | 8.87039i | −0.716348 | − | 0.413584i | ||||
\(461\) | −19.4728 | −0.906940 | −0.453470 | − | 0.891272i | \(-0.649814\pi\) | ||||
−0.453470 | + | 0.891272i | \(0.649814\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4558 | −1.36893 | −0.684465 | − | 0.729046i | \(-0.739964\pi\) | ||||
−0.684465 | + | 0.729046i | \(0.739964\pi\) | |||||||
\(464\) | −1.07616 | − | 0.621320i | −0.0499594 | − | 0.0288441i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.74264 | − | 15.1427i | −0.404995 | − | 0.701472i | ||||
\(467\) | 2.59808 | − | 4.50000i | 0.120225 | − | 0.208235i | −0.799632 | − | 0.600491i | \(-0.794972\pi\) |
0.919856 | + | 0.392256i | \(0.128305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.2426 | − | 26.1039i | 0.934718 | − | 1.20536i | ||||
\(470\) | − | 18.7279i | − | 0.863855i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.9853 | − | 7.49706i | 0.597696 | − | 0.345080i | ||||
\(473\) | 0.866025 | − | 0.500000i | 0.0398199 | − | 0.0229900i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.73205i | 0.0794719i | ||||||||
\(476\) | −4.54026 | − | 0.621320i | −0.208102 | − | 0.0284782i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.36396 | − | 11.0227i | 0.291081 | − | 0.504167i | ||||
\(479\) | −13.1390 | − | 22.7574i | −0.600335 | − | 1.03981i | −0.992770 | − | 0.120031i | \(-0.961701\pi\) |
0.392435 | − | 0.919780i | \(-0.371633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.87868 | − | 3.97141i | −0.313641 | − | 0.181081i | ||||
\(482\) | −12.6677 | −0.576999 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −6.71807 | − | 3.87868i | −0.305052 | − | 0.176122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.606602 | − | 1.05066i | −0.0274877 | − | 0.0476102i | 0.851954 | − | 0.523616i | \(-0.175417\pi\) |
−0.879442 | + | 0.476006i | \(0.842084\pi\) | |||||||
\(488\) | −5.19615 | + | 9.00000i | −0.235219 | + | 0.407411i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.60660 | + | 16.5160i | −0.208105 | + | 0.746118i | ||||
\(491\) | 17.2721i | 0.779478i | 0.920925 | + | 0.389739i | \(0.127435\pi\) | ||||
−0.920925 | + | 0.389739i | \(0.872565\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.86396 | − | 1.07616i | 0.0839486 | − | 0.0484677i | ||||
\(494\) | −3.67423 | + | 2.12132i | −0.165312 | + | 0.0954427i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.43488i | 0.0644279i | ||||||||
\(497\) | −17.7408 | + | 7.24264i | −0.795782 | + | 0.324877i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.60660 | − | 4.51477i | 0.116688 | − | 0.202109i | −0.801766 | − | 0.597639i | \(-0.796106\pi\) |
0.918453 | + | 0.395530i | \(0.129439\pi\) | |||||||
\(500\) | 4.89898 | + | 8.48528i | 0.219089 | + | 0.379473i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.9853 | + | 9.22911i | 0.713458 | + | 0.411915i | ||||
\(503\) | 20.1903 | 0.900239 | 0.450120 | − | 0.892968i | \(-0.351381\pi\) | ||||
0.450120 | + | 0.892968i | \(0.351381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.7574 | 1.14619 | ||||||||
\(506\) | −6.27231 | − | 3.62132i | −0.278838 | − | 0.160987i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.37868 | + | 11.0482i | 0.283008 | + | 0.490184i | ||||
\(509\) | 20.1903 | − | 34.9706i | 0.894918 | − | 1.55004i | 0.0610113 | − | 0.998137i | \(-0.480567\pi\) |
0.833906 | − | 0.551906i | \(-0.186099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.2426 | − | 7.94282i | −0.453108 | − | 0.351369i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.6066 | − | 7.85578i | 0.600161 | − | 0.346503i | ||||
\(515\) | 34.5900 | − | 19.9706i | 1.52422 | − | 0.880008i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7.64564i | − | 0.336255i | ||||||
\(518\) | −6.77962 | − | 5.25736i | −0.297879 | − | 0.230995i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | − | 5.19615i | 0.131559 | − | 0.227866i | ||||
\(521\) | 12.9649 | + | 22.4558i | 0.568002 | + | 0.983808i | 0.996763 | + | 0.0803906i | \(0.0256168\pi\) |
−0.428761 | + | 0.903418i | \(0.641050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.7279 | − | 10.8126i | −0.818915 | − | 0.472801i | 0.0311273 | − | 0.999515i | \(-0.490090\pi\) |
−0.850042 | + | 0.526715i | \(0.823424\pi\) | |||||||
\(524\) | −11.4069 | −0.498313 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.4853 | −1.15481 | ||||||||
\(527\) | −2.15232 | − | 1.24264i | −0.0937564 | − | 0.0541303i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.7279 | + | 25.5095i | 0.640344 | + | 1.10911i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.24264 | + | 1.73205i | −0.183942 | + | 0.0750939i | ||||
\(533\) | − | 3.51472i | − | 0.152239i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.7279 | + | 17.7408i | −1.32848 | + | 0.767001i | ||||
\(536\) | −10.8126 | + | 6.24264i | −0.467032 | + | 0.269641i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.6982i | 1.15104i | ||||||||
\(539\) | −1.88064 | + | 6.74264i | −0.0810048 | + | 0.290426i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.75736 | − | 16.9002i | 0.419502 | − | 0.726598i | −0.576388 | − | 0.817176i | \(-0.695538\pi\) |
0.995889 | + | 0.0905782i | \(0.0288715\pi\) | |||||||
\(542\) | 1.01461 | + | 1.75736i | 0.0435813 | + | 0.0754850i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.50000 | + | 0.866025i | 0.0643120 | + | 0.0371305i | ||||
\(545\) | 23.9006 | 1.02379 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5147 | −0.449577 | −0.224788 | − | 0.974408i | \(-0.572169\pi\) | ||||
−0.224788 | + | 0.974408i | \(0.572169\pi\) | |||||||
\(548\) | 1.52192 | + | 0.878680i | 0.0650131 | + | 0.0375353i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.500000 | − | 0.866025i | −0.0213201 | − | 0.0369274i | ||||
\(551\) | 1.07616 | − | 1.86396i | 0.0458459 | − | 0.0794074i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.9706 | + | 2.86976i | 0.891759 | + | 0.122034i | ||||
\(554\) | 29.4558i | 1.25146i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.257359 | + | 0.148586i | −0.0109145 | + | 0.00630147i | ||||
\(557\) | 33.5139 | − | 19.3492i | 1.42003 | − | 0.819854i | 0.423728 | − | 0.905790i | \(-0.360721\pi\) |
0.996301 | + | 0.0859359i | \(0.0273880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.44949i | − | 0.103602i | ||||||
\(560\) | 3.97141 | − | 5.12132i | 0.167823 | − | 0.216415i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.7426 | + | 20.3389i | −0.495333 | + | 0.857943i | ||||
\(563\) | −2.53653 | − | 4.39340i | −0.106902 | − | 0.185160i | 0.807612 | − | 0.589715i | \(-0.200760\pi\) |
−0.914514 | + | 0.404555i | \(0.867426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.72792 | − | 2.15232i | −0.156835 | − | 0.0905486i | ||||
\(566\) | −30.5826 | −1.28548 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.24264 | 0.303894 | ||||||||
\(569\) | −24.6435 | − | 14.2279i | −1.03311 | − | 0.596466i | −0.115235 | − | 0.993338i | \(-0.536762\pi\) |
−0.917874 | + | 0.396873i | \(0.870095\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7426 | + | 23.8030i | 0.575112 | + | 0.996123i | 0.996030 | + | 0.0890238i | \(0.0283747\pi\) |
−0.420918 | + | 0.907099i | \(0.638292\pi\) | |||||||
\(572\) | 1.22474 | − | 2.12132i | 0.0512092 | − | 0.0886969i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.514719 | − | 3.76127i | 0.0214839 | − | 0.156993i | ||||
\(575\) | 7.24264i | 0.302039i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.00000 | − | 1.73205i | 0.124892 | − | 0.0721062i | −0.436253 | − | 0.899824i | \(-0.643695\pi\) |
0.561144 | + | 0.827718i | \(0.310361\pi\) | |||||||
\(578\) | 12.1244 | − | 7.00000i | 0.504307 | − | 0.291162i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.04384i | 0.126388i | ||||||||
\(581\) | −12.8418 | − | 31.4558i | −0.532767 | − | 1.30501i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.44949 | + | 4.24264i | 0.101361 | + | 0.175562i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.10660 | − | 3.52565i | −0.252261 | − | 0.145643i | ||||
\(587\) | −14.4508 | −0.596446 | −0.298223 | − | 0.954496i | \(-0.596394\pi\) | ||||
−0.298223 | + | 0.954496i | \(0.596394\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.48528 | −0.102404 | ||||||||
\(590\) | −31.8073 | − | 18.3640i | −1.30949 | − | 0.756032i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.62132 | + | 2.80821i | 0.0666359 | + | 0.115417i | ||||
\(593\) | 2.89525 | − | 5.01472i | 0.118894 | − | 0.205930i | −0.800436 | − | 0.599418i | \(-0.795399\pi\) |
0.919329 | + | 0.393489i | \(0.128732\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.24264 | + | 10.3923i | 0.173931 | + | 0.426043i | ||||
\(596\) | 4.75736i | 0.194869i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.3640 | + | 8.87039i | −0.628279 | + | 0.362737i | ||||
\(599\) | −15.5885 | + | 9.00000i | −0.636927 | + | 0.367730i | −0.783430 | − | 0.621480i | \(-0.786532\pi\) |
0.146503 | + | 0.989210i | \(0.453198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1464i | 0.699417i | 0.936858 | + | 0.349709i | \(0.113719\pi\) | ||||
−0.936858 | + | 0.349709i | \(0.886281\pi\) | |||||||
\(602\) | 0.358719 | − | 2.62132i | 0.0146203 | − | 0.106837i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.37868 | − | 2.38794i | 0.0560977 | − | 0.0971640i | ||||
\(605\) | −1.22474 | − | 2.12132i | −0.0497930 | − | 0.0862439i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.4853 | + | 17.0233i | 1.19677 | + | 0.690956i | 0.959834 | − | 0.280569i | \(-0.0905232\pi\) |
0.236937 | + | 0.971525i | \(0.423857\pi\) | |||||||
\(608\) | 1.73205 | 0.0702439 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.4558 | 1.03068 | ||||||||
\(611\) | −16.2189 | − | 9.36396i | −0.656145 | − | 0.378825i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.3640 | − | 28.3432i | −0.660934 | − | 1.14477i | −0.980371 | − | 0.197164i | \(-0.936827\pi\) |
0.319436 | − | 0.947608i | \(-0.396506\pi\) | |||||||
\(614\) | −3.76127 | + | 6.51472i | −0.151793 | + | 0.262913i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.62132 | − | 2.09077i | 0.0653249 | − | 0.0842395i | ||||
\(617\) | 9.21320i | 0.370910i | 0.982653 | + | 0.185455i | \(0.0593758\pi\) | ||||
−0.982653 | + | 0.185455i | \(0.940624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.2132 | + | 17.4436i | −1.21437 | + | 0.701118i | −0.963708 | − | 0.266957i | \(-0.913982\pi\) |
−0.250663 | + | 0.968074i | \(0.580649\pi\) | |||||||
\(620\) | 3.04384 | − | 1.75736i | 0.122243 | − | 0.0705772i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.4010i | 1.05858i | ||||||||
\(623\) | 2.65962 | + | 0.363961i | 0.106556 | + | 0.0145818i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 4.03295 | + | 6.98528i | 0.161189 | + | 0.279188i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.62132 | + | 2.09077i | 0.144506 | + | 0.0834308i | ||||
\(629\) | −5.61642 | −0.223941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.6985 | 1.50075 | 0.750376 | − | 0.661011i | \(-0.229872\pi\) | ||||
0.750376 | + | 0.661011i | \(0.229872\pi\) | |||||||
\(632\) | −6.92820 | − | 4.00000i | −0.275589 | − | 0.159111i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.87868 | + | 6.71807i | 0.154042 | + | 0.266809i | ||||
\(635\) | 15.6245 | − | 27.0624i | 0.620040 | − | 1.07394i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0000 | + | 12.2474i | 0.475457 | + | 0.485262i | ||||
\(638\) | 1.24264i | 0.0491966i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.12132 | + | 1.22474i | −0.0838525 | + | 0.0484123i | ||||
\(641\) | 0.630399 | − | 0.363961i | 0.0248993 | − | 0.0143756i | −0.487499 | − | 0.873124i | \(-0.662091\pi\) |
0.512398 | + | 0.858748i | \(0.328757\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25.2633i | − | 0.996288i | −0.867094 | − | 0.498144i | \(-0.834015\pi\) | ||
0.867094 | − | 0.498144i | \(-0.165985\pi\) | |||||||
\(644\) | −17.7408 | + | 7.24264i | −0.699084 | + | 0.285400i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.50000 | + | 2.59808i | −0.0590167 | + | 0.102220i | ||||
\(647\) | −19.7700 | − | 34.2426i | −0.777239 | − | 1.34622i | −0.933528 | − | 0.358506i | \(-0.883286\pi\) |
0.156289 | − | 0.987711i | \(-0.450047\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.9853 | − | 7.49706i | −0.509717 | − | 0.294285i | ||||
\(650\) | −2.44949 | −0.0960769 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.9706 | 0.586292 | ||||||||
\(653\) | −2.41344 | − | 1.39340i | −0.0944451 | − | 0.0545279i | 0.452034 | − | 0.892001i | \(-0.350699\pi\) |
−0.546479 | + | 0.837473i | \(0.684032\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9706 | + | 24.1977i | 0.545875 | + | 0.945483i | ||||
\(656\) | −0.717439 | + | 1.24264i | −0.0280113 | + | 0.0485170i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.9853 | − | 12.3960i | −0.623171 | − | 0.483248i | ||||
\(659\) | 16.2426i | 0.632723i | 0.948639 | + | 0.316362i | \(0.102461\pi\) | ||||
−0.948639 | + | 0.316362i | \(0.897539\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6213 | − | 9.01897i | 0.607599 | − | 0.350797i | −0.164426 | − | 0.986389i | \(-0.552577\pi\) |
0.772025 | + | 0.635592i | \(0.219244\pi\) | |||||||
\(662\) | 12.1244 | − | 7.00000i | 0.471226 | − | 0.272063i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.8418i | 0.498358i | ||||||||
\(665\) | 8.87039 | + | 6.87868i | 0.343979 | + | 0.266744i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.50000 | − | 7.79423i | 0.174241 | − | 0.301794i | ||||
\(668\) | −0.210133 | − | 0.363961i | −0.00813029 | − | 0.0140821i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 26.4853 | + | 15.2913i | 1.02322 | + | 0.590754i | ||||
\(671\) | 10.3923 | 0.401190 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.2426 | 1.47415 | 0.737073 | − | 0.675813i | \(-0.236207\pi\) | ||||
0.737073 | + | 0.675813i | \(0.236207\pi\) | |||||||
\(674\) | −20.9947 | − | 12.1213i | −0.808687 | − | 0.466896i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.50000 | + | 6.06218i | 0.134615 | + | 0.233161i | ||||
\(677\) | −4.24309 | + | 7.34924i | −0.163075 | + | 0.282454i | −0.935970 | − | 0.352080i | \(-0.885475\pi\) |
0.772895 | + | 0.634534i | \(0.218808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.75736 | + | 3.16693i | −0.297700 | + | 0.121536i | ||||
\(680\) | − | 4.24264i | − | 0.162698i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.24264 | − | 0.717439i | 0.0475832 | − | 0.0274722i | ||||
\(683\) | −5.64191 | + | 3.25736i | −0.215882 | + | 0.124639i | −0.604042 | − | 0.796953i | \(-0.706444\pi\) |
0.388160 | + | 0.921592i | \(0.373111\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4.30463i | − | 0.164472i | ||||||
\(686\) | 11.0482 | + | 14.8640i | 0.421822 | + | 0.567509i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.500000 | + | 0.866025i | −0.0190623 | + | 0.0330169i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.5147 | − | 10.6895i | −0.704333 | − | 0.406647i | 0.104626 | − | 0.994512i | \(-0.466635\pi\) |
−0.808959 | + | 0.587865i | \(0.799969\pi\) | |||||||
\(692\) | −2.02922 | −0.0771395 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.5147 | 0.588931 | ||||||||
\(695\) | 0.630399 | + | 0.363961i | 0.0239124 | + | 0.0138058i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.24264 | − | 2.15232i | −0.0470684 | − | 0.0815248i | ||||
\(698\) | 7.34847 | − | 12.7279i | 0.278144 | − | 0.481759i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.62132 | − | 0.358719i | −0.0990766 | − | 0.0135583i | ||||
\(701\) | − | 40.7574i | − | 1.53938i | −0.638415 | − | 0.769692i | \(-0.720410\pi\) | ||
0.638415 | − | 0.769692i | \(-0.279590\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.86396 | + | 2.80821i | −0.183448 | + | 0.105914i | ||||
\(704\) | −0.866025 | + | 0.500000i | −0.0326396 | + | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.78335i | 0.330566i | ||||||||
\(707\) | 17.0488 | − | 21.9853i | 0.641187 | − | 0.826842i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.37868 | + | 2.38794i | −0.0517774 | + | 0.0896811i | −0.890752 | − | 0.454489i | \(-0.849822\pi\) |
0.838975 | + | 0.544170i | \(0.183155\pi\) | |||||||
\(710\) | −8.87039 | − | 15.3640i | −0.332900 | − | 0.576599i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.878680 | − | 0.507306i | −0.0329299 | − | 0.0190121i | ||||
\(713\) | −10.3923 | −0.389195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | −0.224387 | ||||||||
\(716\) | −7.79423 | − | 4.50000i | −0.291284 | − | 0.168173i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.514719 | + | 0.891519i | 0.0192091 | + | 0.0332712i | ||||
\(719\) | 3.40256 | − | 5.89340i | 0.126894 | − | 0.219787i | −0.795578 | − | 0.605851i | \(-0.792833\pi\) |
0.922472 | + | 0.386065i | \(0.126166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.84924 | − | 42.7430i | 0.217837 | − | 1.59183i | ||||
\(722\) | − | 16.0000i | − | 0.595458i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.24264 | − | 2.44949i | 0.157676 | − | 0.0910346i | ||||
\(725\) | 1.07616 | − | 0.621320i | 0.0399675 | − | 0.0230753i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.1051i | 1.41324i | 0.707593 | + | 0.706620i | \(0.249781\pi\) | ||||
−0.707593 | + | 0.706620i | \(0.750219\pi\) | |||||||
\(728\) | −2.44949 | − | 6.00000i | −0.0907841 | − | 0.222375i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | − | 10.3923i | 0.222070 | − | 0.384636i | ||||
\(731\) | −0.866025 | − | 1.50000i | −0.0320311 | − | 0.0554795i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.45584 | − | 2.57258i | −0.164580 | − | 0.0950205i | 0.415447 | − | 0.909617i | \(-0.363625\pi\) |
−0.580028 | + | 0.814597i | \(0.696958\pi\) | |||||||
\(734\) | 11.8272 | 0.436549 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.24264 | 0.266967 | ||||||||
\(737\) | 10.8126 | + | 6.24264i | 0.398286 | + | 0.229951i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.72792 | − | 2.99285i | −0.0635626 | − | 0.110094i | 0.832493 | − | 0.554036i | \(-0.186913\pi\) |
−0.896055 | + | 0.443942i | \(0.853580\pi\) | |||||||
\(740\) | 3.97141 | − | 6.87868i | 0.145992 | − | 0.252865i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.6985i | 1.30965i | 0.755780 | + | 0.654825i | \(0.227258\pi\) | ||||
−0.755780 | + | 0.654825i | \(0.772742\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0919 | − | 5.82655i | 0.369738 | − | 0.213468i | ||||
\(746\) | 29.4449 | − | 17.0000i | 1.07805 | − | 0.622414i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.73205i | − | 0.0633300i | ||||||
\(749\) | −5.19615 | + | 37.9706i | −0.189863 | + | 1.38741i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8787 | − | 18.8424i | 0.396969 | − | 0.687570i | −0.596382 | − | 0.802701i | \(-0.703395\pi\) |
0.993350 | + | 0.115131i | \(0.0367288\pi\) | |||||||
\(752\) | 3.82282 | + | 6.62132i | 0.139404 | + | 0.241455i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.63604 | + | 1.52192i | 0.0959989 | + | 0.0554250i | ||||
\(755\) | −6.75412 | −0.245808 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.6690 | 1.51449 | 0.757244 | − | 0.653132i | \(-0.226546\pi\) | ||||
0.757244 | + | 0.653132i | \(0.226546\pi\) | |||||||
\(758\) | −28.3432 | − | 16.3640i | −1.02947 | − | 0.594366i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.12132 | − | 3.67423i | −0.0769484 | − | 0.133278i | ||||
\(761\) | 18.0379 | − | 31.2426i | 0.653875 | − | 1.13254i | −0.328299 | − | 0.944574i | \(-0.606476\pi\) |
0.982175 | − | 0.187971i | \(-0.0601911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.8198 | − | 20.4004i | 0.572715 | − | 0.738544i | ||||
\(764\) | − | 16.9706i | − | 0.613973i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.3198 | − | 19.2372i | 1.20389 | − | 0.695068i | ||||
\(767\) | −31.8073 | + | 18.3640i | −1.14850 | + | 0.663084i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.53716i | − | 0.307858i | −0.988082 | − | 0.153929i | \(-0.950807\pi\) | ||
0.988082 | − | 0.153929i | \(-0.0491927\pi\) | |||||||
\(770\) | −6.42090 | − | 0.878680i | −0.231393 | − | 0.0316654i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.3640 | + | 17.9509i | −0.373007 | + | 0.646067i | ||||
\(773\) | 15.7986 | + | 27.3640i | 0.568236 | + | 0.984213i | 0.996741 | + | 0.0806737i | \(0.0257072\pi\) |
−0.428505 | + | 0.903540i | \(0.640959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.24264 | − | 0.717439i | −0.0446370 | − | 0.0257712i | ||||
\(776\) | 3.16693 | 0.113686 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.7279 | −1.31676 | ||||||||
\(779\) | −2.15232 | − | 1.24264i | −0.0771148 | − | 0.0445222i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.62132 | − | 6.27231i | −0.129581 | − | 0.224441i | ||||
\(782\) | −6.27231 | + | 10.8640i | −0.224297 | + | 0.388494i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.74264 | − | 6.77962i | −0.0622372 | − | 0.242129i | ||||
\(785\) | − | 10.2426i | − | 0.365576i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.47056 | − | 3.73578i | 0.230651 | − | 0.133166i | −0.380222 | − | 0.924895i | \(-0.624152\pi\) |
0.610872 | + | 0.791729i | \(0.290819\pi\) | |||||||
\(788\) | −3.22848 | + | 1.86396i | −0.115010 | + | 0.0664009i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 19.5959i | 0.697191i | ||||||||
\(791\) | −4.30463 | + | 1.75736i | −0.153055 | + | 0.0624845i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.7279 | − | 22.0454i | 0.451982 | − | 0.782855i | ||||
\(794\) | 16.3674 | + | 28.3492i | 0.580859 | + | 1.00608i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.36396 | − | 3.67423i | −0.225565 | − | 0.130230i | ||||
\(797\) | 21.0308 | 0.744949 | 0.372475 | − | 0.928042i | \(-0.378509\pi\) | ||||
0.372475 | + | 0.928042i | \(0.378509\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.2426 | −0.468491 | ||||||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.1213 | + | 24.4588i | 0.498641 | + | 0.863672i | ||||
\(803\) | 2.44949 | − | 4.24264i | 0.0864406 | − | 0.149720i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 37.0919 | + | 28.7635i | 1.30732 | + | 1.01378i | ||||
\(806\) | − | 3.51472i | − | 0.123801i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.10660 | + | 5.25770i | −0.320369 | + | 0.184965i | ||||
\(809\) | −39.7862 | + | 22.9706i | −1.39881 | + | 0.807602i | −0.994268 | − | 0.106918i | \(-0.965902\pi\) |
−0.404540 | + | 0.914520i | \(0.632568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 56.5123i | − | 1.98442i | −0.124589 | − | 0.992208i | \(-0.539761\pi\) | ||
0.124589 | − | 0.992208i | \(-0.460239\pi\) | |||||||
\(812\) | 2.59808 | + | 2.01472i | 0.0911746 | + | 0.0707028i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.62132 | − | 2.80821i | 0.0568272 | − | 0.0984277i | ||||
\(815\) | −18.3351 | − | 31.7574i | −0.642251 | − | 1.11241i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.50000 | − | 0.866025i | −0.0524784 | − | 0.0302984i | ||||
\(818\) | 0.420266 | 0.0146943 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.51472 | 0.122739 | ||||||||
\(821\) | 8.23999 | + | 4.75736i | 0.287578 | + | 0.166033i | 0.636849 | − | 0.770989i | \(-0.280238\pi\) |
−0.349271 | + | 0.937022i | \(0.613571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.6066 | + | 37.4237i | 0.753159 | + | 1.30451i | 0.946284 | + | 0.323335i | \(0.104804\pi\) |
−0.193126 | + | 0.981174i | \(0.561863\pi\) | |||||||
\(824\) | −8.15295 | + | 14.1213i | −0.284021 | + | 0.491940i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.7279 | + | 14.9941i | −1.27793 | + | 0.521712i | ||||
\(827\) | − | 14.4853i | − | 0.503703i | −0.967766 | − | 0.251851i | \(-0.918961\pi\) | ||
0.967766 | − | 0.251851i | \(-0.0810394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.3198 | + | 14.0410i | −0.844662 | + | 0.487666i | −0.858846 | − | 0.512234i | \(-0.828818\pi\) |
0.0141844 | + | 0.999899i | \(0.495485\pi\) | |||||||
\(830\) | 27.2416 | − | 15.7279i | 0.945568 | − | 0.545924i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.44949i | 0.0849208i | ||||||||
\(833\) | 11.6786 | + | 3.25736i | 0.404639 | + | 0.112861i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.514719 | + | 0.891519i | −0.0178126 | + | 0.0308523i | ||||
\(836\) | −0.866025 | − | 1.50000i | −0.0299521 | − | 0.0518786i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.98528 | − | 2.30090i | −0.137669 | − | 0.0794834i | ||||
\(839\) | −24.2487 | −0.837158 | −0.418579 | − | 0.908180i | \(-0.637472\pi\) | ||||
−0.418579 | + | 0.908180i | \(0.637472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.4558 | 0.946753 | ||||||||
\(842\) | 24.8536 | + | 14.3492i | 0.856512 | + | 0.494508i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.2426 | − | 19.4728i | −0.386988 | − | 0.670282i | ||||
\(845\) | 8.57321 | − | 14.8492i | 0.294928 | − | 0.510829i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.62132 | − | 0.358719i | −0.0900696 | − | 0.0123257i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.50000 | + | 0.866025i | −0.0514496 | + | 0.0297044i | ||||
\(851\) | −20.3389 | + | 11.7426i | −0.697207 | + | 0.402533i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12.2474i | − | 0.419345i | −0.977772 | − | 0.209672i | \(-0.932760\pi\) | ||
0.977772 | − | 0.209672i | \(-0.0672397\pi\) | |||||||
\(854\) | 16.8493 | − | 21.7279i | 0.576570 | − | 0.743514i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.24264 | − | 12.5446i | 0.247548 | − | 0.428766i | ||||
\(857\) | −8.09140 | − | 14.0147i | −0.276397 | − | 0.478734i | 0.694090 | − | 0.719889i | \(-0.255807\pi\) |
−0.970487 | + | 0.241155i | \(0.922474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.0919 | + | 16.2189i | 0.958483 | + | 0.553380i | 0.895706 | − | 0.444647i | \(-0.146671\pi\) |
0.0627770 | + | 0.998028i | \(0.480004\pi\) | |||||||
\(860\) | 2.44949 | 0.0835269 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.9706 | 0.578020 | ||||||||
\(863\) | −22.0454 | − | 12.7279i | −0.750434 | − | 0.433264i | 0.0754164 | − | 0.997152i | \(-0.475971\pi\) |
−0.825851 | + | 0.563889i | \(0.809305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.48528 | + | 4.30463i | 0.0845021 | + | 0.146362i | ||||
\(866\) | 10.6640 | − | 18.4706i | 0.362377 | − | 0.627655i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.514719 | − | 3.76127i | 0.0174707 | − | 0.127666i | ||||
\(869\) | 8.00000i | 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.4853 | − | 15.2913i | 0.897420 | − | 0.518125i | ||||
\(872\) | −8.45012 | + | 4.87868i | −0.286157 | + | 0.165213i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.5446i | 0.424328i | ||||||||
\(875\) | −9.79796 | − | 24.0000i | −0.331231 | − | 0.811348i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.1213 | + | 31.3870i | −0.611914 | + | 1.05987i | 0.379004 | + | 0.925395i | \(0.376267\pi\) |
−0.990918 | + | 0.134470i | \(0.957067\pi\) | |||||||
\(878\) | 12.4831 | + | 21.6213i | 0.421283 | + | 0.729684i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.12132 | + | 1.22474i | 0.0715097 | + | 0.0412861i | ||||
\(881\) | 14.6969 | 0.495152 | 0.247576 | − | 0.968868i | \(-0.420366\pi\) | ||||
0.247576 | + | 0.968868i | \(0.420366\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.7279 | −1.10138 | −0.550691 | − | 0.834709i | \(-0.685636\pi\) | ||||
−0.550691 | + | 0.834709i | \(0.685636\pi\) | |||||||
\(884\) | −3.67423 | − | 2.12132i | −0.123578 | − | 0.0713477i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.50000 | − | 2.59808i | −0.0503935 | − | 0.0872841i | ||||
\(887\) | 6.92820 | − | 12.0000i | 0.232626 | − | 0.402921i | −0.725954 | − | 0.687743i | \(-0.758601\pi\) |
0.958580 | + | 0.284823i | \(0.0919348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.7574 | − | 31.2490i | −0.427868 | − | 1.04806i | ||||
\(890\) | 2.48528i | 0.0833068i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.12132 | + | 4.68885i | −0.271922 | + | 0.156994i | ||||
\(893\) | −11.4685 | + | 6.62132i | −0.383777 | + | 0.221574i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.0454i | 0.736897i | ||||||||
\(896\) | −0.358719 | + | 2.62132i | −0.0119840 | + | 0.0875722i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.72792 | − | 11.6531i | 0.224514 | − | 0.388869i | ||||
\(899\) | 0.891519 | + | 1.54416i | 0.0297338 | + | 0.0515005i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.43488 | 0.0477762 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.75736 | 0.0584489 | ||||||||
\(905\) | −10.3923 | − | 6.00000i | −0.345452 | − | 0.199447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.2426 | − | 41.9895i | −0.804964 | − | 1.39424i | −0.916316 | − | 0.400457i | \(-0.868851\pi\) |
0.111352 | − | 0.993781i | \(-0.464482\pi\) | |||||||
\(908\) | −3.16693 | + | 5.48528i | −0.105098 | + | 0.182035i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.72792 | + | 12.5446i | −0.322477 | + | 0.415850i | ||||
\(911\) | 9.72792i | 0.322300i | 0.986930 | + | 0.161150i | \(0.0515204\pi\) | ||||
−0.986930 | + | 0.161150i | \(0.948480\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1213 | − | 6.42090i | 0.368062 | − | 0.212501i | ||||
\(914\) | −29.1837 | + | 16.8492i | −0.965312 | + | 0.557323i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.8564i | − | 0.457829i | ||||||
\(917\) | 29.9012 | + | 4.09188i | 0.987424 | + | 0.135126i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.37868 | + | 7.58410i | −0.144439 | + | 0.250176i | −0.929164 | − | 0.369669i | \(-0.879471\pi\) |
0.784724 | + | 0.619845i | \(0.212805\pi\) | |||||||
\(920\) | −8.87039 | − | 15.3640i | −0.292448 | − | 0.506535i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.8640 | − | 9.73641i | −0.555385 | − | 0.320652i | ||||
\(923\) | −17.7408 | −0.583945 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.24264 | −0.106617 | ||||||||
\(926\) | −25.5095 | − | 14.7279i | −0.838294 | − | 0.483990i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.621320 | − | 1.07616i | −0.0203958 | − | 0.0353266i | ||||
\(929\) | −14.4868 | + | 25.0919i | −0.475297 | + | 0.823238i | −0.999600 | − | 0.0282938i | \(-0.990993\pi\) |
0.524303 | + | 0.851532i | \(0.324326\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.7426 | − | 3.01834i | 0.384850 | − | 0.0989222i | ||||
\(932\) | − | 17.4853i | − | 0.572749i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.50000 | − | 2.59808i | 0.147244 | − | 0.0850117i | ||||
\(935\) | −3.67423 | + | 2.12132i | −0.120160 | + | 0.0693746i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 56.0921i | − | 1.83245i | −0.400666 | − | 0.916224i | \(-0.631221\pi\) | ||
0.400666 | − | 0.916224i | \(-0.368779\pi\) | |||||||
\(938\) | 30.5826 | − | 12.4853i | 0.998556 | − | 0.407659i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.36396 | − | 16.2189i | 0.305419 | − | 0.529001i | ||||
\(941\) | 7.70719 | + | 13.3492i | 0.251247 | + | 0.435173i | 0.963869 | − | 0.266375i | \(-0.0858260\pi\) |
−0.712622 | + | 0.701548i | \(0.752493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.00000 | − | 5.19615i | −0.293080 | − | 0.169210i | ||||
\(944\) | 14.9941 | 0.488017 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | 18.1865 | + | 10.5000i | 0.590983 | + | 0.341204i | 0.765486 | − | 0.643452i | \(-0.222499\pi\) |
−0.174503 | + | 0.984657i | \(0.555832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | − | 10.3923i | −0.194768 | − | 0.337348i | ||||
\(950\) | −0.866025 | + | 1.50000i | −0.0280976 | + | 0.0486664i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.62132 | − | 2.80821i | −0.117368 | − | 0.0910146i | ||||
\(953\) | 48.0000i | 1.55487i | 0.628962 | + | 0.777436i | \(0.283480\pi\) | ||||
−0.628962 | + | 0.777436i | \(0.716520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.0000 | + | 20.7846i | −1.16493 | + | 0.672574i | ||||
\(956\) | 11.0227 | − | 6.36396i | 0.356500 | − | 0.205825i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 26.2779i | − | 0.849002i | ||||||
\(959\) | −3.67423 | − | 2.84924i | −0.118647 | − | 0.0920068i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.4706 | + | 25.0637i | −0.466792 | + | 0.808508i | ||||
\(962\) | −3.97141 | − | 6.87868i | −0.128043 | − | 0.221778i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.9706 | − | 6.33386i | −0.353338 | − | 0.204000i | ||||
\(965\) | 50.7728 | 1.63444 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7574 | 0.796143 | 0.398072 | − | 0.917354i | \(-0.369680\pi\) | ||||
0.398072 | + | 0.917354i | \(0.369680\pi\) | |||||||
\(968\) | 0.866025 | + | 0.500000i | 0.0278351 | + | 0.0160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.87868 | − | 6.71807i | −0.124537 | − | 0.215704i | ||||
\(971\) | 28.5533 | − | 49.4558i | 0.916320 | − | 1.58711i | 0.111364 | − | 0.993780i | \(-0.464478\pi\) |
0.804956 | − | 0.593334i | \(-0.202189\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.727922 | − | 0.297173i | 0.0233361 | − | 0.00952693i | ||||
\(974\) | − | 1.21320i | − | 0.0388735i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.00000 | + | 5.19615i | −0.288083 | + | 0.166325i | ||||
\(977\) | 53.2223 | − | 30.7279i | 1.70273 | − | 0.983073i | 0.759760 | − | 0.650203i | \(-0.225316\pi\) |
0.942973 | − | 0.332870i | \(-0.108017\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.01461i | 0.0324271i | ||||||||
\(980\) | −12.2474 | + | 12.0000i | −0.391230 | + | 0.383326i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.63604 | + | 14.9581i | −0.275587 | + | 0.477331i | ||||
\(983\) | −29.0352 | − | 50.2904i | −0.926078 | − | 1.60401i | −0.789819 | − | 0.613340i | \(-0.789825\pi\) |
−0.136259 | − | 0.990673i | \(-0.543508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.90812 | + | 4.56575i | 0.251974 | + | 0.145477i | ||||
\(986\) | 2.15232 | 0.0685437 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.24264 | −0.134976 | ||||||||
\(989\) | −6.27231 | − | 3.62132i | −0.199448 | − | 0.115151i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.24264 | − | 10.8126i | −0.198304 | − | 0.343473i | 0.749675 | − | 0.661807i | \(-0.230210\pi\) |
−0.947979 | + | 0.318334i | \(0.896877\pi\) | |||||||
\(992\) | −0.717439 | + | 1.24264i | −0.0227787 | + | 0.0394539i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.9853 | − | 2.59808i | −0.602177 | − | 0.0824060i | ||||
\(995\) | 18.0000i | 0.570638i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.5772 | + | 15.9217i | −0.873378 | + | 0.504245i | −0.868469 | − | 0.495743i | \(-0.834896\pi\) |
−0.00490839 | + | 0.999988i | \(0.501562\pi\) | |||||||
\(998\) | 4.51477 | − | 2.60660i | 0.142912 | − | 0.0825105i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.r.b.89.4 | yes | 8 | |
3.2 | odd | 2 | inner | 1386.2.r.b.89.1 | ✓ | 8 | |
7.3 | odd | 6 | inner | 1386.2.r.b.1277.1 | yes | 8 | |
21.17 | even | 6 | inner | 1386.2.r.b.1277.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.b.89.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
1386.2.r.b.89.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1386.2.r.b.1277.1 | yes | 8 | 7.3 | odd | 6 | inner | |
1386.2.r.b.1277.4 | yes | 8 | 21.17 | even | 6 | inner |