Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(881,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.cc (of order \(6\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2897.4 | ||
Root | \(0.604587 - 1.62311i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2897 |
Dual form | 3024.2.cc.c.881.4 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.266780 | − | 0.462077i | −0.119308 | − | 0.206647i | 0.800186 | − | 0.599752i | \(-0.204734\pi\) |
−0.919494 | + | 0.393105i | \(0.871401\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.54716 | − | 0.715531i | −0.962735 | − | 0.270445i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.39936 | − | 1.96262i | −1.02494 | − | 0.591752i | −0.109412 | − | 0.993996i | \(-0.534897\pi\) |
−0.915532 | + | 0.402245i | \(0.868230\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.116911 | + | 0.0674987i | −0.0324253 | + | 0.0187208i | −0.516125 | − | 0.856513i | \(-0.672626\pi\) |
0.483700 | + | 0.875234i | \(0.339293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.32533 | −1.04905 | −0.524523 | − | 0.851396i | \(-0.675756\pi\) | ||||
−0.524523 | + | 0.851396i | \(0.675756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.22935i | − | 0.511448i | −0.966750 | − | 0.255724i | \(-0.917686\pi\) | ||
0.966750 | − | 0.255724i | \(-0.0823138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.70375 | + | 0.983658i | −0.355255 | + | 0.205107i | −0.666998 | − | 0.745060i | \(-0.732421\pi\) |
0.311742 | + | 0.950167i | \(0.399088\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.35766 | − | 4.08358i | 0.471531 | − | 0.816716i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.16548 | + | 2.98229i | 0.959205 | + | 0.553798i | 0.895928 | − | 0.444198i | \(-0.146511\pi\) |
0.0632771 | + | 0.997996i | \(0.479845\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.800341 | − | 0.462077i | 0.143745 | − | 0.0829915i | −0.426402 | − | 0.904534i | \(-0.640219\pi\) |
0.570148 | + | 0.821542i | \(0.306886\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.348901 | + | 1.36787i | 0.0589751 | + | 0.231213i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.79871 | 1.28210 | 0.641050 | − | 0.767499i | \(-0.278499\pi\) | ||||
0.641050 | + | 0.767499i | \(0.278499\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.59027 | + | 7.95059i | 0.716880 | + | 1.24167i | 0.962230 | + | 0.272239i | \(0.0877640\pi\) |
−0.245349 | + | 0.969435i | \(0.578903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.24544 | + | 5.62127i | −0.494926 | + | 0.857236i | −0.999983 | − | 0.00584958i | \(-0.998138\pi\) |
0.505057 | + | 0.863086i | \(0.331471\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.04329 | + | 5.27114i | −0.443910 | + | 0.768874i | −0.997976 | − | 0.0635985i | \(-0.979742\pi\) |
0.554066 | + | 0.832473i | \(0.313076\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.97603 | + | 3.64514i | 0.853719 | + | 0.520734i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.0167i | 1.51326i | 0.653845 | + | 0.756628i | \(0.273155\pi\) | ||||
−0.653845 | + | 0.756628i | \(0.726845\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.09435i | 0.282402i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.89588 | − | 3.28377i | −0.246823 | − | 0.427510i | 0.715820 | − | 0.698285i | \(-0.246053\pi\) |
−0.962643 | + | 0.270775i | \(0.912720\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.35116 | − | 5.39889i | −1.19729 | − | 0.691258i | −0.237342 | − | 0.971426i | \(-0.576276\pi\) |
−0.959951 | + | 0.280168i | \(0.909610\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0623791 | + | 0.0360146i | 0.00773718 | + | 0.00446706i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.75701 | + | 9.97144i | 0.703331 | + | 1.21820i | 0.967291 | + | 0.253671i | \(0.0816381\pi\) |
−0.263960 | + | 0.964534i | \(0.585029\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.22884i | 0.383192i | 0.981474 | + | 0.191596i | \(0.0613664\pi\) | ||||
−0.981474 | + | 0.191596i | \(0.938634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.381041i | 0.0445975i | 0.999751 | + | 0.0222988i | \(0.00709850\pi\) | ||||
−0.999751 | + | 0.0222988i | \(0.992901\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.25438 | + | 7.43144i | 0.826714 | + | 0.846892i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.60310 | − | 7.97280i | 0.517889 | − | 0.897011i | −0.481895 | − | 0.876229i | \(-0.660051\pi\) |
0.999784 | − | 0.0207814i | \(-0.00661541\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.28020 | + | 2.21737i | −0.140520 | + | 0.243388i | −0.927693 | − | 0.373345i | \(-0.878211\pi\) |
0.787172 | + | 0.616733i | \(0.211544\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.15391 | + | 1.99863i | 0.125159 | + | 0.216782i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.1334 | −1.81614 | −0.908068 | − | 0.418822i | \(-0.862443\pi\) | ||||
−0.908068 | + | 0.418822i | \(0.862443\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.346088 | − | 0.0882763i | 0.0362799 | − | 0.00925387i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.03013 | + | 0.594746i | −0.105689 | + | 0.0610197i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6747 | + | 7.89507i | 1.38845 | + | 0.801622i | 0.993141 | − | 0.116925i | \(-0.0373038\pi\) |
0.395310 | + | 0.918548i | \(0.370637\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.36862 | − | 12.7628i | 0.733205 | − | 1.26995i | −0.222301 | − | 0.974978i | \(-0.571357\pi\) |
0.955506 | − | 0.294970i | \(-0.0953098\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1442 | − | 6.43410i | 1.09807 | − | 0.633970i | 0.162356 | − | 0.986732i | \(-0.448091\pi\) |
0.935713 | + | 0.352762i | \(0.114757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.7824i | 1.52574i | 0.646552 | + | 0.762870i | \(0.276210\pi\) | ||||
−0.646552 | + | 0.762870i | \(0.723790\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.08340 | −0.295336 | −0.147668 | − | 0.989037i | \(-0.547177\pi\) | ||||
−0.147668 | + | 0.989037i | \(0.547177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.96173 | + | 4.59671i | −0.748977 | + | 0.432422i | −0.825324 | − | 0.564659i | \(-0.809008\pi\) |
0.0763472 | + | 0.997081i | \(0.475674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.909051 | + | 0.524841i | 0.0847694 | + | 0.0489417i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.0173 | + | 3.09490i | 1.00995 | + | 0.283709i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.20375 | + | 3.81700i | 0.200340 | + | 0.347000i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.18371 | −0.463645 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.1065 | 0.896810 | 0.448405 | − | 0.893831i | \(-0.351992\pi\) | ||||
0.448405 | + | 0.893831i | \(0.351992\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.81823 | + | 13.5416i | 0.683082 | + | 1.18313i | 0.974036 | + | 0.226395i | \(0.0726940\pi\) |
−0.290954 | + | 0.956737i | \(0.593973\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.59517 | + | 5.67850i | −0.138319 | + | 0.492389i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.13891 | − | 1.23490i | −0.182739 | − | 0.105505i | 0.405840 | − | 0.913944i | \(-0.366979\pi\) |
−0.588579 | + | 0.808440i | \(0.700312\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8526 | + | 9.72984i | −1.42942 | + | 0.825274i | −0.997074 | − | 0.0764359i | \(-0.975646\pi\) |
−0.432342 | + | 0.901710i | \(0.642313\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.529897 | 0.0443122 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.18247i | − | 0.264289i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.7303 | + | 7.92720i | −1.12483 | + | 0.649422i | −0.942630 | − | 0.333840i | \(-0.891656\pi\) |
−0.182201 | + | 0.983261i | \(0.558322\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.16548 | − | 7.21482i | 0.338982 | − | 0.587134i | −0.645260 | − | 0.763963i | \(-0.723251\pi\) |
0.984242 | + | 0.176829i | \(0.0565841\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.427030 | − | 0.246546i | −0.0342999 | − | 0.0198031i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.73794 | + | 4.46750i | −0.617555 | + | 0.356545i | −0.775916 | − | 0.630836i | \(-0.782712\pi\) |
0.158362 | + | 0.987381i | \(0.449379\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.04355 | − | 1.28645i | 0.397487 | − | 0.101386i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.2062 | 1.11272 | 0.556358 | − | 0.830943i | \(-0.312198\pi\) | ||||
0.556358 | + | 0.830943i | \(0.312198\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.27308 | − | 10.8653i | −0.485425 | − | 0.840781i | 0.514434 | − | 0.857530i | \(-0.328002\pi\) |
−0.999860 | + | 0.0167485i | \(0.994669\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.49089 | + | 11.2425i | −0.499299 | + | 0.864811i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6787 | − | 18.4960i | 0.811886 | − | 1.40623i | −0.0996566 | − | 0.995022i | \(-0.531774\pi\) |
0.911543 | − | 0.411206i | \(-0.134892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.92725 | + | 8.71455i | −0.674837 | + | 0.658758i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.81113i | 0.434344i | 0.976133 | + | 0.217172i | \(0.0696833\pi\) | ||||
−0.976133 | + | 0.217172i | \(0.930317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.38877i | 0.549203i | 0.961558 | + | 0.274602i | \(0.0885460\pi\) | ||||
−0.961558 | + | 0.274602i | \(0.911454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.08054 | − | 3.60360i | −0.152964 | − | 0.264942i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7033 | + | 8.48897i | 1.07521 | + | 0.620775i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.86109 | + | 3.96125i | 0.496451 | + | 0.286626i | 0.727247 | − | 0.686376i | \(-0.240800\pi\) |
−0.230796 | + | 0.973002i | \(0.574133\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.16548 | + | 5.48277i | 0.227856 | + | 0.394659i | 0.957173 | − | 0.289518i | \(-0.0934951\pi\) |
−0.729316 | + | 0.684177i | \(0.760162\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.1580i | − | 1.07996i | −0.841677 | − | 0.539981i | \(-0.818431\pi\) | ||
0.841677 | − | 0.539981i | \(-0.181569\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.55084i | 0.606153i | 0.952966 | + | 0.303076i | \(0.0980137\pi\) | ||||
−0.952966 | + | 0.303076i | \(0.901986\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.0234 | − | 11.2924i | −0.773689 | − | 0.792573i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.44919 | − | 4.24212i | 0.171059 | − | 0.296282i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.37536 | + | 7.57835i | −0.302650 | + | 0.524205i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.80782 | + | 4.86329i | 0.193299 | + | 0.334803i | 0.946341 | − | 0.323169i | \(-0.104748\pi\) |
−0.753043 | + | 0.657971i | \(0.771415\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.46328 | 0.236194 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.36922 | + | 0.604315i | −0.160833 | + | 0.0410236i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.505679 | − | 0.291954i | 0.0340156 | − | 0.0196389i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.00510 | + | 3.46705i | 0.402131 | + | 0.232171i | 0.687403 | − | 0.726276i | \(-0.258751\pi\) |
−0.285272 | + | 0.958447i | \(0.592084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.28833 | − | 12.6238i | 0.483743 | − | 0.837868i | −0.516082 | − | 0.856539i | \(-0.672610\pi\) |
0.999826 | + | 0.0186708i | \(0.00594345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.2722 | + | 12.2815i | −1.40571 | + | 0.811586i | −0.994971 | − | 0.100167i | \(-0.968062\pi\) |
−0.410738 | + | 0.911753i | \(0.634729\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5142i | 0.688808i | 0.938822 | + | 0.344404i | \(0.111919\pi\) | ||||
−0.938822 | + | 0.344404i | \(0.888081\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.24756 | 0.211848 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9075 | − | 9.76154i | 1.09365 | − | 0.631422i | 0.159108 | − | 0.987261i | \(-0.449138\pi\) |
0.934547 | + | 0.355839i | \(0.115805\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3780 | − | 6.56909i | −0.732922 | − | 0.423152i | 0.0865685 | − | 0.996246i | \(-0.472410\pi\) |
−0.819490 | + | 0.573093i | \(0.805743\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0900476 | − | 3.73384i | 0.00575293 | − | 0.238546i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.150478 | + | 0.260636i | 0.00957469 | + | 0.0165838i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.6864 | −1.43195 | −0.715977 | − | 0.698124i | \(-0.754019\pi\) | ||||
−0.715977 | + | 0.698124i | \(0.754019\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.72218 | 0.485489 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.80481 | − | 11.7863i | −0.424472 | − | 0.735207i | 0.571899 | − | 0.820324i | \(-0.306207\pi\) |
−0.996371 | + | 0.0851169i | \(0.972874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.8646 | − | 5.58022i | −1.23432 | − | 0.346738i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.7930 | + | 11.4275i | 1.22049 | + | 0.704651i | 0.965023 | − | 0.262167i | \(-0.0844371\pi\) |
0.255468 | + | 0.966817i | \(0.417770\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.09055 | − | 2.93903i | 0.312710 | − | 0.180543i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.6775 | −0.651018 | −0.325509 | − | 0.945539i | \(-0.605536\pi\) | ||||
−0.325509 | + | 0.945539i | \(0.605536\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.51473i | 0.274251i | 0.990554 | + | 0.137125i | \(0.0437863\pi\) | ||||
−0.990554 | + | 0.137125i | \(0.956214\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.0290 | + | 9.25436i | −0.966587 | + | 0.558059i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.34952 | − | 5.80154i | 0.201253 | − | 0.348581i | −0.747679 | − | 0.664060i | \(-0.768832\pi\) |
0.948932 | + | 0.315479i | \(0.102165\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1414 | + | 8.74187i | 0.903258 | + | 0.521496i | 0.878256 | − | 0.478191i | \(-0.158707\pi\) |
0.0250023 | + | 0.999687i | \(0.492041\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.42049 | − | 4.28422i | 0.441102 | − | 0.254670i | −0.262963 | − | 0.964806i | \(-0.584700\pi\) |
0.704065 | + | 0.710135i | \(0.251366\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00327 | − | 23.5359i | −0.354362 | − | 1.38928i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.70845 | 0.100497 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1436 | + | 21.0333i | 0.709434 | + | 1.22878i | 0.965067 | + | 0.262002i | \(0.0843826\pi\) |
−0.255633 | + | 0.966774i | \(0.582284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.01157 | + | 1.75209i | −0.0588958 | + | 0.102010i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.132791 | − | 0.230001i | 0.00767951 | − | 0.0133013i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2889 | − | 11.9961i | 0.708318 | − | 0.691441i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.76127i | 0.329890i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4777i | 0.712139i | 0.934460 | + | 0.356069i | \(0.115883\pi\) | ||||
−0.934460 | + | 0.356069i | \(0.884117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.07984 | + | 15.7267i | 0.514871 | + | 0.891782i | 0.999851 | + | 0.0172571i | \(0.00549339\pi\) |
−0.484980 | + | 0.874525i | \(0.661173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.76700 | − | 1.59753i | −0.156400 | − | 0.0902977i | 0.419757 | − | 0.907636i | \(-0.362115\pi\) |
−0.576157 | + | 0.817339i | \(0.695449\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.5893 | + | 13.0419i | 1.26874 | + | 0.732508i | 0.974750 | − | 0.223300i | \(-0.0716831\pi\) |
0.293991 | + | 0.955808i | \(0.405016\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7062 | − | 20.2757i | −0.655421 | − | 1.13522i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.64266i | 0.536532i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.636555i | 0.0353097i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.5234 | − | 11.2489i | 0.635306 | − | 0.620169i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.06484 | + | 13.9687i | −0.443283 | + | 0.767789i | −0.997931 | − | 0.0642960i | \(-0.979520\pi\) |
0.554647 | + | 0.832085i | \(0.312853\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.07171 | − | 5.32036i | 0.167826 | − | 0.290683i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.16548 | − | 7.21482i | −0.226908 | − | 0.393016i | 0.729982 | − | 0.683466i | \(-0.239528\pi\) |
−0.956890 | + | 0.290450i | \(0.906195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.62752 | −0.196441 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6137 | − | 13.5608i | −0.681075 | − | 0.732213i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.1403 | + | 17.4015i | −1.61801 | + | 0.934161i | −0.630581 | + | 0.776124i | \(0.717183\pi\) |
−0.987433 | + | 0.158037i | \(0.949483\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.6825 | + | 11.3637i | 1.05358 | + | 0.608283i | 0.923649 | − | 0.383240i | \(-0.125192\pi\) |
0.129929 | + | 0.991523i | \(0.458525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.02829 | − | 6.97721i | 0.214404 | − | 0.371359i | −0.738684 | − | 0.674052i | \(-0.764552\pi\) |
0.953088 | + | 0.302693i | \(0.0978856\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.49197 | − | 0.861390i | 0.0791856 | − | 0.0457178i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.8217i | − | 0.940594i | −0.882508 | − | 0.470297i | \(-0.844147\pi\) | ||
0.882508 | − | 0.470297i | \(-0.155853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.0300 | 0.738421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.176070 | − | 0.101654i | 0.00921594 | − | 0.00532083i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.5888 | − | 11.8870i | −1.07473 | − | 0.620494i | −0.145258 | − | 0.989394i | \(-0.546401\pi\) |
−0.929469 | + | 0.368900i | \(0.879734\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.88277 | − | 28.0612i | 0.409253 | − | 1.45687i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.26858 | − | 9.12545i | −0.272797 | − | 0.472498i | 0.696780 | − | 0.717285i | \(-0.254615\pi\) |
−0.969577 | + | 0.244787i | \(0.921282\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.805203 | −0.0414700 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0049 | −1.23305 | −0.616525 | − | 0.787336i | \(-0.711460\pi\) | ||||
−0.616525 | + | 0.787336i | \(0.711460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0980 | + | 31.3466i | 0.924764 | + | 1.60174i | 0.791941 | + | 0.610598i | \(0.209071\pi\) |
0.132823 | + | 0.991140i | \(0.457596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.49857 | − | 5.33465i | 0.0763743 | − | 0.271879i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6031 | − | 10.7405i | −0.943215 | − | 0.544565i | −0.0522481 | − | 0.998634i | \(-0.516639\pi\) |
−0.890967 | + | 0.454069i | \(0.849972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.36925 | − | 4.25464i | 0.372679 | − | 0.215166i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.91207 | −0.247153 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.3049i | 1.06926i | 0.845086 | + | 0.534630i | \(0.179549\pi\) | ||||
−0.845086 | + | 0.534630i | \(0.820451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.6821 | + | 9.05406i | −0.783126 | + | 0.452138i | −0.837537 | − | 0.546381i | \(-0.816005\pi\) |
0.0544110 | + | 0.998519i | \(0.482672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0623791 | + | 0.108044i | −0.00310733 | + | 0.00538205i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.5106 | − | 15.3059i | −1.31408 | − | 0.758685i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.6807 | − | 10.2080i | 0.874254 | − | 0.504751i | 0.00549461 | − | 0.999985i | \(-0.498251\pi\) |
0.868760 | + | 0.495234i | \(0.164918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.47948 | + | 9.72083i | 0.122007 | + | 0.478331i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.36613 | 0.0670607 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6789 | + | 21.9606i | 0.619407 | + | 1.07284i | 0.989594 | + | 0.143887i | \(0.0459602\pi\) |
−0.370187 | + | 0.928957i | \(0.620706\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.21875 | + | 5.57503i | −0.156872 | + | 0.271710i | −0.933739 | − | 0.357954i | \(-0.883474\pi\) |
0.776867 | + | 0.629665i | \(0.216808\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.1976 | + | 17.6628i | −0.494658 | + | 0.856773i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.9558 | + | 20.4429i | 0.965729 | + | 0.989300i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.1392i | − | 0.729230i | −0.931158 | − | 0.364615i | \(-0.881201\pi\) | ||
0.931158 | − | 0.364615i | \(-0.118799\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.44792i | 0.405981i | 0.979181 | + | 0.202991i | \(0.0650661\pi\) | ||||
−0.979181 | + | 0.202991i | \(0.934934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.19292 | + | 3.79824i | 0.104901 | + | 0.181695i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.6831 | + | 13.6734i | 1.13033 | + | 0.652598i | 0.944018 | − | 0.329893i | \(-0.107013\pi\) |
0.186314 | + | 0.982490i | \(0.440346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.6520 | − | 8.45931i | −0.696135 | − | 0.401914i | 0.109771 | − | 0.993957i | \(-0.464988\pi\) |
−0.805906 | + | 0.592043i | \(0.798322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.57085 | + | 7.91695i | 0.216679 | + | 0.375299i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.5985i | − | 1.06649i | −0.845962 | − | 0.533244i | \(-0.820973\pi\) | ||
0.845962 | − | 0.533244i | \(-0.179027\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 36.0358i | − | 1.69686i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.133120 | − | 0.136369i | −0.00624076 | − | 0.00639308i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4018 | − | 30.1408i | 0.814022 | − | 1.40993i | −0.0960053 | − | 0.995381i | \(-0.530607\pi\) |
0.910028 | − | 0.414547i | \(-0.136060\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.8264 | + | 23.9479i | −0.643958 | + | 1.11537i | 0.340584 | + | 0.940214i | \(0.389375\pi\) |
−0.984541 | + | 0.175153i | \(0.943958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.6272 | − | 18.4069i | −0.493889 | − | 0.855440i | 0.506087 | − | 0.862483i | \(-0.331092\pi\) |
−0.999975 | + | 0.00704260i | \(0.997758\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.80757 | −0.407566 | −0.203783 | − | 0.979016i | \(-0.565324\pi\) | ||||
−0.203783 | + | 0.979016i | \(0.565324\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.52915 | − | 29.5181i | −0.347664 | − | 1.36302i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.0648 | − | 12.7391i | 1.01454 | − | 0.585746i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.10373 | − | 5.25604i | −0.417708 | − | 0.241164i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.83139 | − | 11.8323i | 0.312134 | − | 0.540633i | −0.666690 | − | 0.745335i | \(-0.732289\pi\) |
0.978824 | + | 0.204703i | \(0.0656227\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.911756 | + | 0.526403i | −0.0415725 | + | 0.0240019i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8.42499i | − | 0.382559i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6206 | −0.753149 | −0.376575 | − | 0.926386i | \(-0.622898\pi\) | ||||
−0.376575 | + | 0.926386i | \(0.622898\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.8129 | − | 10.2843i | 0.803883 | − | 0.464122i | −0.0409440 | − | 0.999161i | \(-0.513037\pi\) |
0.844827 | + | 0.535039i | \(0.179703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.3424 | − | 12.8994i | −1.00625 | − | 0.580959i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.31033 | − | 8.22436i | 0.103633 | − | 0.368913i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.34609 | − | 2.33149i | −0.0602592 | − | 0.104372i | 0.834322 | − | 0.551277i | \(-0.185859\pi\) |
−0.894581 | + | 0.446905i | \(0.852526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.3871 | −1.22113 | −0.610566 | − | 0.791965i | \(-0.709058\pi\) | ||||
−0.610566 | + | 0.791965i | \(0.709058\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.86321 | −0.349908 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.96117 | + | 5.12890i | 0.131252 | + | 0.227334i | 0.924159 | − | 0.382007i | \(-0.124767\pi\) |
−0.792908 | + | 0.609342i | \(0.791434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.272647 | − | 0.970572i | 0.0120612 | − | 0.0429356i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.94609 | − | 3.43298i | −0.262016 | − | 0.151275i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.6905 | − | 11.9456i | 0.909966 | − | 0.525369i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.1886 | 1.71688 | 0.858442 | − | 0.512911i | \(-0.171433\pi\) | ||||
0.858442 | + | 0.512911i | \(0.171433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.0358i | 1.00728i | 0.863912 | + | 0.503642i | \(0.168007\pi\) | ||||
−0.863912 | + | 0.503642i | \(0.831993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.46173 | + | 1.99863i | −0.150796 | + | 0.0870618i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.56484 | + | 16.5668i | −0.415862 | + | 0.720295i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.07331 | − | 0.619675i | −0.0464901 | − | 0.0268411i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.29267 | − | 4.21043i | 0.315290 | − | 0.182033i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.1606 | − | 24.1198i | −0.566869 | − | 1.03891i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.32605 | −0.142998 | −0.0714990 | − | 0.997441i | \(-0.522778\pi\) | ||||
−0.0714990 | + | 0.997441i | \(0.522778\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.822590 | + | 1.42477i | 0.0352359 | + | 0.0610303i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.8937 | + | 24.0646i | −0.594051 | + | 1.02893i | 0.399629 | + | 0.916677i | \(0.369139\pi\) |
−0.993680 | + | 0.112249i | \(0.964195\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.64857 | − | 11.5157i | 0.283238 | − | 0.490583i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.4296 | + | 17.0143i | −0.741182 | + | 0.723523i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3.61667i | − | 0.153243i | −0.997060 | − | 0.0766216i | \(-0.975587\pi\) | ||
0.997060 | − | 0.0766216i | \(-0.0244133\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.876252i | − | 0.0370615i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.75452 | + | 8.23506i | 0.200379 | + | 0.347067i | 0.948651 | − | 0.316326i | \(-0.102449\pi\) |
−0.748272 | + | 0.663393i | \(0.769116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.24807 | + | 2.45262i | 0.178718 | + | 0.103183i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.09742 | − | 5.25240i | −0.381384 | − | 0.220192i | 0.297036 | − | 0.954866i | \(-0.404002\pi\) |
−0.678420 | + | 0.734674i | \(0.737335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.24201 | + | 3.88328i | 0.0938252 | + | 0.162510i | 0.909118 | − | 0.416539i | \(-0.136757\pi\) |
−0.815292 | + | 0.579049i | \(0.803424\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.27651i | 0.386857i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 47.1812i | − | 1.96418i | −0.188410 | − | 0.982090i | \(-0.560333\pi\) | ||
0.188410 | − | 0.982090i | \(-0.439667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.84747 | − | 4.73198i | 0.201107 | − | 0.196316i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.6215 | − | 37.4496i | 0.895473 | − | 1.55100i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.65373 | + | 9.79255i | −0.233354 | + | 0.404182i | −0.958793 | − | 0.284105i | \(-0.908304\pi\) |
0.725439 | + | 0.688287i | \(0.241637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03013 | − | 1.78424i | −0.0424458 | − | 0.0735183i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.44980 | 0.388057 | 0.194028 | − | 0.980996i | \(-0.437845\pi\) | ||||
0.194028 | + | 0.980996i | \(0.437845\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.50911 | − | 5.91649i | −0.0618676 | − | 0.242553i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.6406 | − | 18.2677i | 1.29280 | − | 0.746398i | 0.313650 | − | 0.949539i | \(-0.398448\pi\) |
0.979150 | + | 0.203140i | \(0.0651147\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.92247 | − | 1.10994i | −0.0784193 | − | 0.0452754i | 0.460278 | − | 0.887775i | \(-0.347750\pi\) |
−0.538697 | + | 0.842500i | \(0.681083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.17583 | − | 2.03660i | 0.0478043 | − | 0.0827995i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.71759 | − | 0.991653i | 0.0697149 | − | 0.0402499i | −0.464737 | − | 0.885449i | \(-0.653851\pi\) |
0.534452 | + | 0.845199i | \(0.320518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 0.821673i | − | 0.0332413i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.1365 | −0.934476 | −0.467238 | − | 0.884132i | \(-0.654751\pi\) | ||||
−0.467238 | + | 0.884132i | \(0.654751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.19807 | − | 0.691704i | 0.0482323 | − | 0.0278470i | −0.475690 | − | 0.879613i | \(-0.657802\pi\) |
0.523922 | + | 0.851766i | \(0.324468\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.22550 | + | 3.01694i | 0.210031 | + | 0.121261i | 0.601326 | − | 0.799004i | \(-0.294639\pi\) |
−0.391295 | + | 0.920265i | \(0.627973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 43.6415 | + | 12.2595i | 1.74846 | + | 0.491165i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.4054 | − | 18.0226i | −0.416215 | − | 0.720905i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.7320 | −1.34498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4727 | 0.815004 | 0.407502 | − | 0.913204i | \(-0.366400\pi\) | ||||
0.407502 | + | 0.913204i | \(0.366400\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.69622 | − | 4.67000i | −0.106996 | − | 0.185323i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.944707 | − | 0.0227832i | −0.0374306 | − | 0.000902701i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.2246 | − | 23.2237i | −1.58878 | − | 0.917281i | −0.993509 | − | 0.113754i | \(-0.963712\pi\) |
−0.595269 | − | 0.803527i | \(-0.702954\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.74133 | − | 5.62416i | 0.384161 | − | 0.221795i | −0.295466 | − | 0.955353i | \(-0.595475\pi\) |
0.679627 | + | 0.733558i | \(0.262142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.65015 | 0.182816 | 0.0914081 | − | 0.995814i | \(-0.470863\pi\) | ||||
0.0914081 | + | 0.995814i | \(0.470863\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8836i | 0.584232i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.99966 | + | 1.73186i | −0.117386 | + | 0.0677727i | −0.557543 | − | 0.830148i | \(-0.688256\pi\) |
0.440157 | + | 0.897921i | \(0.354923\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.17150 | − | 7.22524i | 0.162994 | − | 0.282314i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.59819 | − | 0.922715i | −0.0622566 | − | 0.0359439i | 0.468549 | − | 0.883438i | \(-0.344777\pi\) |
−0.530805 | + | 0.847494i | \(0.678110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5196 | + | 10.1149i | −0.681433 | + | 0.393426i | −0.800395 | − | 0.599473i | \(-0.795377\pi\) |
0.118962 | + | 0.992899i | \(0.462043\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.04947 | − | 0.777823i | 0.118253 | − | 0.0301627i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.7342 | −0.454351 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1919 | + | 36.7055i | 0.818106 | + | 1.41700i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.31596 | + | 12.6716i | −0.282009 | + | 0.488455i | −0.971880 | − | 0.235478i | \(-0.924334\pi\) |
0.689870 | + | 0.723933i | \(0.257668\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.71449 | − | 13.3619i | 0.296492 | − | 0.513539i | −0.678839 | − | 0.734287i | \(-0.737517\pi\) |
0.975331 | + | 0.220748i | \(0.0708499\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.1823 | − | 29.8946i | −1.11992 | − | 1.14725i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.7197i | − | 0.601499i | −0.953703 | − | 0.300750i | \(-0.902763\pi\) | ||
0.953703 | − | 0.300750i | \(-0.0972368\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.31779i | 0.0503501i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.743611 | − | 1.28797i | −0.0283293 | − | 0.0490678i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.5878 | − | 24.0107i | −1.58207 | − | 0.913411i | −0.994556 | − | 0.104199i | \(-0.966772\pi\) |
−0.587517 | − | 0.809212i | \(-0.699894\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.99187 | + | 5.19146i | 0.341081 | + | 0.196923i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.8544 | − | 34.3889i | −0.752040 | − | 1.30257i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.7005i | − | 0.932923i | −0.884541 | − | 0.466462i | \(-0.845529\pi\) | ||
0.884541 | − | 0.466462i | \(-0.154471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 17.3860i | − | 0.655727i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.9012 | + | 27.2365i | −1.04933 | + | 1.02433i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0432 | + | 29.5196i | −0.640070 | + | 1.10863i | 0.345347 | + | 0.938475i | \(0.387761\pi\) |
−0.985417 | + | 0.170159i | \(0.945572\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.909051 | + | 1.57452i | −0.0340442 | + | 0.0589663i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.141366 | − | 0.244853i | −0.00528679 | − | 0.00915698i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.4758 | −0.689032 | −0.344516 | − | 0.938780i | \(-0.611957\pi\) | ||||
−0.344516 | + | 0.938780i | \(0.611957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.9898 | + | 8.41466i | −1.22860 | + | 0.313378i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.3569 | − | 14.0624i | 0.904591 | − | 0.522266i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.2911 | + | 22.6847i | 1.45723 | + | 0.841330i | 0.998874 | − | 0.0474398i | \(-0.0151062\pi\) |
0.458353 | + | 0.888770i | \(0.348440\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.0376 | − | 24.3138i | 0.519200 | − | 0.899280i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.3683 | − | 25.0387i | 1.60184 | − | 0.924825i | 0.610724 | − | 0.791843i | \(-0.290878\pi\) |
0.991119 | − | 0.132981i | \(-0.0424550\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 45.1953i | − | 1.66479i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9404 | 0.623163 | 0.311582 | − | 0.950219i | \(-0.399141\pi\) | ||||
0.311582 | + | 0.950219i | \(0.399141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.4723 | − | 19.9026i | 1.26467 | − | 0.730156i | 0.290693 | − | 0.956816i | \(-0.406114\pi\) |
0.973974 | + | 0.226661i | \(0.0727808\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.32595 | + | 4.22964i | 0.268402 | + | 0.154962i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.2928 | − | 40.2002i | 0.412629 | − | 1.46888i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.7028 | − | 25.4659i | −0.536512 | − | 0.929265i | −0.999089 | − | 0.0426862i | \(-0.986408\pi\) |
0.462577 | − | 0.886579i | \(-0.346925\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.44507 | −0.161773 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4010 | −0.995908 | −0.497954 | − | 0.867203i | \(-0.665915\pi\) | ||||
−0.497954 | + | 0.867203i | \(0.665915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.11067 | + | 10.5840i | 0.221511 | + | 0.383669i | 0.955267 | − | 0.295744i | \(-0.0955676\pi\) |
−0.733756 | + | 0.679413i | \(0.762234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.85390 | + | 2.20627i | 0.284330 | + | 0.0798722i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.443300 | + | 0.255939i | 0.0160066 | + | 0.00924143i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.4039 | + | 16.9764i | −1.06033 | + | 0.612184i | −0.925524 | − | 0.378688i | \(-0.876375\pi\) |
−0.134809 | + | 0.990872i | \(0.543042\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.2094 | −1.08656 | −0.543279 | − | 0.839552i | \(-0.682817\pi\) | ||||
−0.543279 | + | 0.839552i | \(0.682817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.35767i | − | 0.156532i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.7246 | − | 10.2333i | 0.635051 | − | 0.366647i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.33698 | − | 10.9760i | 0.226755 | − | 0.392751i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.12866 | + | 2.38368i | 0.147358 | + | 0.0850772i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.3310 | + | 19.2436i | −1.18812 | + | 0.685962i | −0.957879 | − | 0.287172i | \(-0.907285\pi\) |
−0.230241 | + | 0.973134i | \(0.573952\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.5689 | − | 6.01168i | 0.838013 | − | 0.213751i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.45767 | 0.0517635 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.72949 | + | 11.6558i | 0.238371 | + | 0.412870i | 0.960247 | − | 0.279152i | \(-0.0900533\pi\) |
−0.721876 | + | 0.692022i | \(0.756720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.1632 | − | 22.7994i | 0.465682 | − | 0.806584i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.747839 | − | 1.29529i | 0.0263907 | − | 0.0457100i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.93996 | − | 1.98731i | −0.0683745 | − | 0.0700434i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 51.7842i | 1.82064i | 0.413909 | + | 0.910318i | \(0.364163\pi\) | ||||
−0.413909 | + | 0.910318i | \(0.635837\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.2471i | 0.956775i | 0.878149 | + | 0.478387i | \(0.158779\pi\) | ||||
−0.878149 | + | 0.478387i | \(0.841221\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.78993 | − | 6.56436i | −0.132756 | − | 0.229939i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.5318 | + | 7.23523i | 0.438432 | + | 0.253129i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3465 | − | 12.9017i | −0.779897 | − | 0.450274i | 0.0564968 | − | 0.998403i | \(-0.482007\pi\) |
−0.836394 | + | 0.548129i | \(0.815340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.570514 | − | 0.988159i | −0.0198869 | − | 0.0344451i | 0.855911 | − | 0.517124i | \(-0.172997\pi\) |
−0.875798 | + | 0.482679i | \(0.839664\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.1713i | 0.805746i | 0.915256 | + | 0.402873i | \(0.131988\pi\) | ||||
−0.915256 | + | 0.402873i | \(0.868012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.60364i | 0.333548i | 0.985995 | + | 0.166774i | \(0.0533351\pi\) | ||||
−0.985995 | + | 0.166774i | \(0.946665\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.8483 | − | 15.7664i | −0.895590 | − | 0.546274i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.34707 | + | 5.79729i | −0.115830 | + | 0.200623i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.7821 | + | 27.3354i | −0.544859 | + | 0.943723i | 0.453757 | + | 0.891126i | \(0.350083\pi\) |
−0.998616 | + | 0.0525978i | \(0.983250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.28812 | + | 5.69519i | 0.113383 | + | 0.196386i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.92656 | 0.238281 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.88211 | − | 11.2993i | −0.0990304 | − | 0.388250i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.2870 | + | 7.67126i | −0.455473 | + | 0.262967i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.50412 | + | 4.33250i | 0.256936 | + | 0.148342i | 0.622936 | − | 0.782273i | \(-0.285940\pi\) |
−0.366000 | + | 0.930615i | \(0.619273\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.4439 | − | 19.8214i | 0.390917 | − | 0.677088i | −0.601654 | − | 0.798757i | \(-0.705491\pi\) |
0.992571 | + | 0.121669i | \(0.0388247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.4922 | − | 6.63503i | 0.392109 | − | 0.226384i | −0.290964 | − | 0.956734i | \(-0.593976\pi\) |
0.683074 | + | 0.730350i | \(0.260643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 0.746752i | − | 0.0254197i | −0.999919 | − | 0.0127099i | \(-0.995954\pi\) | ||
0.999919 | − | 0.0127099i | \(-0.00404579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3955 | −0.387457 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.2951 | + | 18.0683i | −1.06162 | + | 0.612924i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.34612 | − | 0.777181i | −0.0456114 | − | 0.0263338i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.2037 | + | 3.70910i | 0.446367 | + | 0.125391i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.18959 | − | 3.79249i | −0.0739373 | − | 0.128063i | 0.826686 | − | 0.562663i | \(-0.190223\pi\) |
−0.900624 | + | 0.434600i | \(0.856890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1505 | 0.476742 | 0.238371 | − | 0.971174i | \(-0.423387\pi\) | ||||
0.238371 | + | 0.971174i | \(0.423387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.0261 | −0.774890 | −0.387445 | − | 0.921893i | \(-0.626642\pi\) | ||||
−0.387445 | + | 0.921893i | \(0.626642\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.1812 | − | 45.3471i | −0.879077 | − | 1.52261i | −0.852355 | − | 0.522963i | \(-0.824826\pi\) |
−0.0267221 | − | 0.999643i | \(-0.508507\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.7429 | − | 7.23153i | −0.863391 | − | 0.242538i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7512 | + | 6.78456i | 0.393239 | + | 0.227037i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.68519 | − | 1.55029i | 0.0897560 | − | 0.0518206i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.51219 | 0.183842 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 47.6507i | − | 1.58748i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.41418 | − | 1.97118i | 0.113491 | − | 0.0655242i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.1902 | + | 21.1141i | −0.404770 | + | 0.701082i | −0.994295 | − | 0.106669i | \(-0.965982\pi\) |
0.589525 | + | 0.807750i | \(0.299315\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8606 | − | 27.0550i | −1.55256 | − | 0.896372i | −0.997932 | − | 0.0642741i | \(-0.979527\pi\) |
−0.554629 | − | 0.832098i | \(-0.687140\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.70372 | − | 5.02509i | 0.288051 | − | 0.166306i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.2249 | − | 40.0867i | −0.337655 | − | 1.32378i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.51894 | −0.215040 | −0.107520 | − | 0.994203i | \(-0.534291\pi\) | ||||
−0.107520 | + | 0.994203i | \(0.534291\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.217942 | − | 0.377487i | −0.00717365 | − | 0.0124251i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.3867 | − | 31.8467i | 0.604550 | − | 1.04711i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.9048 | + | 24.0838i | −0.456202 | + | 0.790165i | −0.998756 | − | 0.0498555i | \(-0.984124\pi\) |
0.542554 | + | 0.840021i | \(0.317457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.12629 | − | 13.3227i | 0.266328 | − | 0.436633i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9.05875i | − | 0.296253i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.8174i | 1.79081i | 0.445256 | + | 0.895403i | \(0.353113\pi\) | ||||
−0.445256 | + | 0.895403i | \(0.646887\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.56526 | − | 4.44317i | −0.0836252 | − | 0.144843i | 0.821179 | − | 0.570670i | \(-0.193317\pi\) |
−0.904805 | + | 0.425827i | \(0.859983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.6413 | − | 9.03052i | −0.509351 | − | 0.294074i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.606033 | − | 0.349893i | −0.0196934 | − | 0.0113700i | 0.490121 | − | 0.871654i | \(-0.336953\pi\) |
−0.509814 | + | 0.860284i | \(0.670286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0257198 | − | 0.0445480i | −0.000834899 | − | 0.00144609i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 0.162845i | − | 0.00527506i | −0.999997 | − | 0.00263753i | \(-0.999160\pi\) | ||
0.999997 | − | 0.00263753i | \(-0.000839552\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.22714i | − | 0.136787i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.56453 | + | 4.67594i | 0.147396 | + | 0.150994i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0730 | + | 26.1071i | −0.486225 | + | 0.842166i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.68897 | − | 2.92539i | 0.0543700 | − | 0.0941716i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.6968 | + | 27.1876i | 0.504773 | + | 0.874293i | 0.999985 | + | 0.00552073i | \(0.00175731\pi\) |
−0.495211 | + | 0.868773i | \(0.664909\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.92239 | −0.0937841 | −0.0468920 | − | 0.998900i | \(-0.514932\pi\) | ||||
−0.0468920 | + | 0.998900i | \(0.514932\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.8882 | − | 12.7249i | 1.59934 | − | 0.407942i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.7013 | − | 14.2613i | 0.790264 | − | 0.456259i | −0.0497913 | − | 0.998760i | \(-0.515856\pi\) |
0.840056 | + | 0.542500i | \(0.182522\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.2425 | + | 33.6263i | 1.86144 | + | 1.07470i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.62897 | − | 9.74967i | 0.179536 | − | 0.310966i | −0.762185 | − | 0.647359i | \(-0.775874\pi\) |
0.941722 | + | 0.336393i | \(0.109207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.00416 | + | 4.04386i | −0.223171 | + | 0.128848i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 12.7696i | − | 0.406050i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.1622 | −0.672240 | −0.336120 | − | 0.941819i | \(-0.609115\pi\) | ||||
−0.336120 | + | 0.941819i | \(0.609115\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.95114 | − | 2.28119i | 0.125260 | − | 0.0723187i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.6576 | + | 8.46256i | 0.464210 | + | 0.268012i | 0.713813 | − | 0.700336i | \(-0.246967\pi\) |
−0.249603 | + | 0.968348i | \(0.580300\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))