Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(125,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("756.125");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.x (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: | \(6.03669039281\) |
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 | 125.5 | ||
Root | \(-0.604587 - 1.62311i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.125 |
Dual form | 756.2.x.a.629.5 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 | \(-0.795266\pi\) |
0.919494 | + | 0.393105i | \(0.128599\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.89325 | + | 1.84814i | −0.715580 | + | 0.698531i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.39936 | − | 1.96262i | 1.02494 | − | 0.591752i | 0.109412 | − | 0.993996i | \(-0.465103\pi\) |
0.915532 | + | 0.402245i | \(0.131770\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.116911 | + | 0.0674987i | 0.0324253 | + | 0.0187208i | 0.516125 | − | 0.856513i | \(-0.327374\pi\) |
−0.483700 | + | 0.875234i | \(0.660707\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.32533 | 1.04905 | 0.524523 | − | 0.851396i | \(-0.324244\pi\) | ||||
0.524523 | + | 0.851396i | \(0.324244\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.22935i | 0.511448i | 0.966750 | + | 0.255724i | \(0.0823138\pi\) | ||||
−0.966750 | + | 0.255724i | \(0.917686\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.70375 | + | 0.983658i | 0.355255 | + | 0.205107i | 0.666998 | − | 0.745060i | \(-0.267579\pi\) |
−0.311742 | + | 0.950167i | \(0.600912\pi\) | |||||||
\(24\) | 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 | 0.0632771 | − | 0.997996i | \(-0.479845\pi\) |
0.895928 | + | 0.444198i | \(0.146511\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.800341 | + | 0.462077i | 0.143745 | + | 0.0829915i | 0.570148 | − | 0.821542i | \(-0.306886\pi\) |
−0.426402 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(32\) | 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 | 0.245349 | + | 0.969435i | \(0.421097\pi\) |
−0.962230 | + | 0.272239i | \(0.912236\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24544 | + | 5.62127i | 0.494926 | + | 0.857236i | 0.999983 | − | 0.00584958i | \(-0.00186199\pi\) |
−0.505057 | + | 0.863086i | \(0.668529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.04329 | − | 5.27114i | −0.443910 | − | 0.768874i | 0.554066 | − | 0.832473i | \(-0.313076\pi\) |
−0.997976 | + | 0.0635985i | \(0.979742\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.168767 | − | 6.99797i | 0.0241096 | − | 0.999709i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.0167i | − | 1.51326i | −0.653845 | − | 0.756628i | \(-0.726845\pi\) | ||
0.653845 | − | 0.756628i | \(-0.273155\pi\) | |||||||
\(54\) | 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 | −0.962643 | − | 0.270775i | \(-0.912720\pi\) |
0.715820 | + | 0.698285i | \(0.246053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.35116 | − | 5.39889i | 1.19729 | − | 0.691258i | 0.237342 | − | 0.971426i | \(-0.423724\pi\) |
0.959951 | + | 0.280168i | \(0.0903903\pi\) | |||||||
\(62\) | 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 | 0.263960 | + | 0.964534i | \(0.414971\pi\) |
−0.967291 | + | 0.253671i | \(0.918362\pi\) | |||||||
\(68\) | 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 | ||||||||
\(77\) | −2.80863 | + | 9.99820i | −0.320073 | + | 1.13940i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.60310 | − | 7.97280i | −0.517889 | − | 0.897011i | −0.999784 | − | 0.0207814i | \(-0.993385\pi\) |
0.481895 | − | 0.876229i | \(-0.339949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.28020 | − | 2.21737i | −0.140520 | − | 0.243388i | 0.787172 | − | 0.616733i | \(-0.211544\pi\) |
−0.927693 | + | 0.373345i | \(0.878211\pi\) | |||||||
\(84\) | 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 | \(-0.137557\pi\) | ||||
0.908068 | + | 0.418822i | \(0.137557\pi\) | |||||||
\(90\) | 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 | \(-0.962696\pi\) |
−0.395310 | + | 0.918548i | \(0.629363\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.36862 | − | 12.7628i | −0.733205 | − | 1.26995i | −0.955506 | − | 0.294970i | \(-0.904690\pi\) |
0.222301 | − | 0.974978i | \(-0.428643\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1442 | + | 6.43410i | 1.09807 | + | 0.633970i | 0.935713 | − | 0.352762i | \(-0.114757\pi\) |
0.162356 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(104\) | 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 | 0.0763472 | − | 0.997081i | \(-0.475674\pi\) |
−0.825324 | + | 0.564659i | \(0.809008\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.909051 | − | 0.524841i | 0.0847694 | − | 0.0489417i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.18891 | + | 7.99380i | −0.750676 | + | 0.732791i | ||||
\(120\) | 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 | \(-0.648008\pi\) | ||||
−0.448405 | + | 0.893831i | \(0.648008\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.81823 | − | 13.5416i | 0.683082 | − | 1.18313i | −0.290954 | − | 0.956737i | \(-0.593973\pi\) |
0.974036 | − | 0.226395i | \(-0.0726940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.12015 | − | 4.22071i | −0.357262 | − | 0.365982i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.13891 | + | 1.23490i | −0.182739 | + | 0.105505i | −0.588579 | − | 0.808440i | \(-0.700312\pi\) |
0.405840 | + | 0.913944i | \(0.366979\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8526 | − | 9.72984i | −1.42942 | − | 0.825274i | −0.432342 | − | 0.901710i | \(-0.642313\pi\) |
−0.997074 | + | 0.0764359i | \(0.975646\pi\) | |||||||
\(140\) | 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 | −0.182201 | − | 0.983261i | \(-0.558322\pi\) |
−0.942630 | + | 0.333840i | \(0.891656\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.16548 | − | 7.21482i | −0.338982 | − | 0.587134i | 0.645260 | − | 0.763963i | \(-0.276749\pi\) |
−0.984242 | + | 0.176829i | \(0.943416\pi\) | |||||||
\(152\) | 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 | \(-0.217288\pi\) |
−0.158362 | + | 0.987381i | \(0.550621\pi\) | |||||||
\(158\) | 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 | \(-0.687802\pi\) | ||||
−0.556358 | + | 0.830943i | \(0.687802\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.27308 | + | 10.8653i | −0.485425 | + | 0.840781i | −0.999860 | − | 0.0167485i | \(-0.994669\pi\) |
0.514434 | + | 0.857530i | \(0.328002\pi\) | |||||||
\(168\) | 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 | −0.911543 | − | 0.411206i | \(-0.865108\pi\) |
0.0996566 | − | 0.995022i | \(-0.468226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.0106 | − | 3.37395i | −0.907920 | − | 0.255047i | ||||
\(176\) | 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 | \(-0.759200\pi\) |
0.230796 | + | 0.973002i | \(0.425867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.16548 | − | 5.48277i | 0.227856 | − | 0.394659i | −0.729316 | − | 0.684177i | \(-0.760162\pi\) |
0.957173 | + | 0.289518i | \(0.0934951\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1580i | 1.07996i | 0.841677 | + | 0.539981i | \(0.181569\pi\) | ||||
−0.841677 | + | 0.539981i | \(0.818431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.55084i | − | 0.606153i | −0.952966 | − | 0.303076i | \(-0.901986\pi\) | ||
0.952966 | − | 0.303076i | \(-0.0980137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.26784 | + | 15.1927i | −0.299544 | + | 1.06632i | ||||
\(204\) | 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 | \(-0.895252\pi\) |
0.753043 | + | 0.657971i | \(0.228585\pi\) | |||||||
\(212\) | 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 | −0.285272 | − | 0.958447i | \(-0.592084\pi\) |
0.687403 | + | 0.726276i | \(0.258751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.28833 | + | 12.6238i | 0.483743 | + | 0.837868i | 0.999826 | − | 0.0186708i | \(-0.00594345\pi\) |
−0.516082 | + | 0.856539i | \(0.672610\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2722 | + | 12.2815i | 1.40571 | + | 0.811586i | 0.994971 | − | 0.100167i | \(-0.0319377\pi\) |
0.410738 | + | 0.911753i | \(0.365271\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 10.5142i | − | 0.688808i | −0.938822 | − | 0.344404i | \(-0.888081\pi\) | ||
0.938822 | − | 0.344404i | \(-0.111919\pi\) | |||||||
\(234\) | 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 | \(-0.550862\pi\) |
−0.934547 | + | 0.355839i | \(0.884195\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3780 | − | 6.56909i | 0.732922 | − | 0.423152i | −0.0865685 | − | 0.996246i | \(-0.527590\pi\) |
0.819490 | + | 0.573093i | \(0.194257\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.18857 | − | 1.94490i | −0.203711 | − | 0.124255i | ||||
\(246\) | 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 | \(-0.693793\pi\) |
0.996371 | + | 0.0851169i | \(0.0271264\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.7649 | + | 14.4131i | −0.917445 | + | 0.895586i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.7930 | + | 11.4275i | −1.22049 | + | 0.704651i | −0.965023 | − | 0.262167i | \(-0.915563\pi\) |
−0.255468 | + | 0.966817i | \(0.582230\pi\) | |||||||
\(264\) | 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 | \(-0.394464\pi\) | ||||
0.325509 | + | 0.945539i | \(0.394464\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.51473i | − | 0.274251i | −0.990554 | − | 0.137125i | \(-0.956214\pi\) | ||
0.990554 | − | 0.137125i | \(-0.0437863\pi\) | |||||||
\(272\) | 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 | 0.948932 | − | 0.315479i | \(-0.102165\pi\) |
−0.747679 | + | 0.664060i | \(0.768832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1414 | − | 8.74187i | 0.903258 | − | 0.521496i | 0.0250023 | − | 0.999687i | \(-0.492041\pi\) |
0.878256 | + | 0.478191i | \(0.158707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.42049 | + | 4.28422i | 0.441102 | + | 0.254670i | 0.704065 | − | 0.710135i | \(-0.251366\pi\) |
−0.262963 | + | 0.964806i | \(0.584700\pi\) | |||||||
\(284\) | 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 | 0.255633 | + | 0.966774i | \(0.417716\pi\) |
−0.965067 | + | 0.262002i | \(0.915617\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | −16.5333 | − | 4.64443i | −0.952965 | − | 0.267700i | ||||
\(302\) | 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 | \(-0.884117\pi\) | ||
0.934460 | − | 0.356069i | \(-0.115883\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.07984 | − | 15.7267i | 0.514871 | − | 0.891782i | −0.484980 | − | 0.874525i | \(-0.661173\pi\) |
0.999851 | − | 0.0172571i | \(-0.00549339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.76700 | − | 1.59753i | 0.156400 | − | 0.0902977i | −0.419757 | − | 0.907636i | \(-0.637885\pi\) |
0.576157 | + | 0.817339i | \(0.304551\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.5893 | − | 13.0419i | 1.26874 | − | 0.732508i | 0.293991 | − | 0.955808i | \(-0.405016\pi\) |
0.974750 | + | 0.223300i | \(0.0716831\pi\) | |||||||
\(318\) | 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 | ||||||||
\(329\) | 15.5035 | + | 4.35514i | 0.854736 | + | 0.240107i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.06484 | + | 13.9687i | 0.443283 | + | 0.767789i | 0.997931 | − | 0.0642960i | \(-0.0204802\pi\) |
−0.554647 | + | 0.832085i | \(0.687147\pi\) | |||||||
\(332\) | 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 | −0.956890 | − | 0.290450i | \(-0.906195\pi\) |
0.729982 | + | 0.683466i | \(0.239528\pi\) | |||||||
\(338\) | 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 | 0.987433 | + | 0.158037i | \(0.0505166\pi\) |
0.630581 | + | 0.776124i | \(0.282817\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.6825 | + | 11.3637i | −1.05358 | + | 0.608283i | −0.923649 | − | 0.383240i | \(-0.874808\pi\) |
−0.129929 | + | 0.991523i | \(0.541475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.02829 | − | 6.97721i | −0.214404 | − | 0.371359i | 0.738684 | − | 0.674052i | \(-0.235448\pi\) |
−0.953088 | + | 0.302693i | \(0.902114\pi\) | |||||||
\(354\) | 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 | −0.929469 | − | 0.368900i | \(-0.879734\pi\) |
−0.145258 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.3603 | + | 20.8573i | 1.05706 | + | 1.08286i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.26858 | + | 9.12545i | −0.272797 | + | 0.472498i | −0.969577 | − | 0.244787i | \(-0.921282\pi\) |
0.696780 | + | 0.717285i | \(0.254615\pi\) | |||||||
\(374\) | 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 | \(-0.288540\pi\) | ||||
0.616525 | + | 0.787336i | \(0.288540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0980 | − | 31.3466i | 0.924764 | − | 1.60174i | 0.132823 | − | 0.991140i | \(-0.457596\pi\) |
0.791941 | − | 0.610598i | \(-0.209071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.87065 | + | 3.96512i | 0.197267 | + | 0.202081i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6031 | + | 10.7405i | −0.943215 | + | 0.544565i | −0.890967 | − | 0.454069i | \(-0.849972\pi\) |
−0.0522481 | + | 0.998634i | \(0.516639\pi\) | |||||||
\(390\) | 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 | 0.0544110 | − | 0.998519i | \(-0.482672\pi\) |
−0.837537 | + | 0.546381i | \(0.816005\pi\) | |||||||
\(402\) | 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 | \(-0.501749\pi\) |
−0.868760 | + | 0.495234i | \(0.835082\pi\) | |||||||
\(410\) | 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 | −0.370187 | − | 0.928957i | \(-0.620706\pi\) |
0.989594 | − | 0.143887i | \(-0.0459602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.21875 | − | 5.57503i | −0.156872 | − | 0.271710i | 0.776867 | − | 0.629665i | \(-0.216808\pi\) |
−0.933739 | + | 0.357954i | \(0.883474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.1976 | + | 17.6628i | 0.494658 | + | 0.856773i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.72615 | + | 27.5037i | −0.373895 | + | 1.33100i | ||||
\(428\) | 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 | 0.186314 | − | 0.982490i | \(-0.440346\pi\) |
0.944018 | + | 0.329893i | \(0.107013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.6520 | − | 8.45931i | 0.696135 | − | 0.401914i | −0.109771 | − | 0.993957i | \(-0.535012\pi\) |
0.805906 | + | 0.592043i | \(0.201678\pi\) | |||||||
\(444\) | 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 | \(0.179027\pi\) | ||||
−0.845962 | + | 0.533244i | \(0.820973\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.0358i | 1.69686i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0515391 | + | 0.183470i | −0.00241619 | + | 0.00860120i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4018 | + | 30.1408i | 0.814022 | + | 1.40993i | 0.910028 | + | 0.414547i | \(0.136060\pi\) |
−0.0960053 | + | 0.995381i | \(0.530607\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8264 | + | 23.9479i | 0.643958 | + | 1.11537i | 0.984541 | + | 0.175153i | \(0.0560420\pi\) |
−0.340584 | + | 0.940214i | \(0.610625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6272 | − | 18.4069i | 0.493889 | − | 0.855440i | −0.506087 | − | 0.862483i | \(-0.668908\pi\) |
0.999975 | + | 0.00704260i | \(0.00224175\pi\) | |||||||
\(464\) | 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 | 0.978824 | − | 0.204703i | \(-0.0656227\pi\) |
−0.666690 | + | 0.745335i | \(0.732289\pi\) | |||||||
\(480\) | 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 | \(-0.377102\pi\) | ||||
0.376575 | + | 0.926386i | \(0.377102\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.8129 | − | 10.2843i | −0.803883 | − | 0.464122i | 0.0409440 | − | 0.999161i | \(-0.486963\pi\) |
−0.844827 | + | 0.535039i | \(0.820297\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.3424 | − | 12.8994i | 1.00625 | − | 0.580959i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.96734 | − | 6.11299i | −0.267672 | − | 0.274205i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.34609 | − | 2.33149i | 0.0602592 | − | 0.104372i | −0.834322 | − | 0.551277i | \(-0.814141\pi\) |
0.894581 | + | 0.446905i | \(0.147474\pi\) | |||||||
\(500\) | 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 | \(-0.875233\pi\) |
0.792908 | + | 0.609342i | \(0.208566\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.704217 | − | 0.721405i | −0.0311527 | − | 0.0319131i | ||||
\(512\) | 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 | \(-0.828567\pi\) | ||||
−0.858442 | + | 0.512911i | \(0.828567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 23.0358i | − | 1.00728i | −0.863912 | − | 0.503642i | \(-0.831993\pi\) | ||
0.863912 | − | 0.503642i | \(-0.168007\pi\) | |||||||
\(524\) | 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 | 0.993680 | + | 0.112249i | \(0.0358055\pi\) |
−0.399629 | + | 0.916677i | \(0.630861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.64857 | + | 11.5157i | 0.283238 | + | 0.490583i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.4497 | + | 6.58732i | 0.997181 | + | 0.280121i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.61667i | 0.153243i | 0.997060 | + | 0.0766216i | \(0.0244133\pi\) | ||||
−0.997060 | + | 0.0766216i | \(0.975587\pi\) | |||||||
\(558\) | 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 | −0.748272 | − | 0.663393i | \(-0.769116\pi\) |
0.948651 | + | 0.316326i | \(0.102449\pi\) | |||||||
\(564\) | 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 | −0.678420 | − | 0.734674i | \(-0.737335\pi\) |
0.297036 | + | 0.954866i | \(0.404002\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.24201 | + | 3.88328i | −0.0938252 | + | 0.162510i | −0.909118 | − | 0.416539i | \(-0.863243\pi\) |
0.815292 | + | 0.579049i | \(0.196576\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | 6.52175 | + | 1.83205i | 0.270568 | + | 0.0760061i | ||||
\(582\) | 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 | 0.725439 | − | 0.688287i | \(-0.241637\pi\) |
−0.958793 | + | 0.284105i | \(0.908304\pi\) | |||||||
\(588\) | 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 | \(-0.562155\pi\) | ||||
−0.194028 | + | 0.980996i | \(0.562155\pi\) | |||||||
\(594\) | 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 | \(-0.601552\pi\) |
−0.979150 | + | 0.203140i | \(0.934885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.92247 | − | 1.10994i | 0.0784193 | − | 0.0452754i | −0.460278 | − | 0.887775i | \(-0.652250\pi\) |
0.538697 | + | 0.842500i | \(0.318917\pi\) | |||||||
\(602\) | 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 | 0.534452 | − | 0.845199i | \(-0.320518\pi\) |
−0.464737 | + | 0.885449i | \(0.653851\pi\) | |||||||
\(608\) | 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 | 0.523922 | − | 0.851766i | \(-0.324468\pi\) |
−0.475690 | + | 0.879613i | \(0.657802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.22550 | − | 3.01694i | 0.210031 | − | 0.121261i | −0.391295 | − | 0.920265i | \(-0.627973\pi\) |
0.601326 | + | 0.799004i | \(0.294639\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.4378 | + | 31.6649i | −1.29959 | + | 1.26863i | ||||
\(624\) | 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 | \(-0.633600\pi\) | ||||
−0.407502 | + | 0.913204i | \(0.633600\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.69622 | + | 4.67000i | −0.106996 | + | 0.185323i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.492084 | − | 0.806748i | 0.0194971 | − | 0.0319645i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.2246 | + | 23.2237i | −1.58878 | + | 0.917281i | −0.595269 | + | 0.803527i | \(0.702954\pi\) |
−0.993509 | + | 0.113754i | \(0.963712\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.74133 | + | 5.62416i | 0.384161 | + | 0.221795i | 0.679627 | − | 0.733558i | \(-0.262142\pi\) |
−0.295466 | + | 0.955353i | \(0.595475\pi\) | |||||||
\(644\) | 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 | 0.440157 | − | 0.897921i | \(-0.354923\pi\) |
−0.557543 | + | 0.830148i | \(0.688256\pi\) | |||||||
\(654\) | 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 | \(-0.655223\pi\) |
0.530805 | + | 0.847494i | \(0.321890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.5196 | + | 10.1149i | 0.681433 | + | 0.393426i | 0.800395 | − | 0.599473i | \(-0.204623\pi\) |
−0.118962 | + | 0.992899i | \(0.537957\pi\) | |||||||
\(662\) | 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 | 0.689870 | − | 0.723933i | \(-0.257668\pi\) |
−0.971880 | + | 0.235478i | \(0.924334\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.71449 | − | 13.3619i | −0.296492 | − | 0.513539i | 0.678839 | − | 0.734287i | \(-0.262483\pi\) |
−0.975331 | + | 0.220748i | \(0.929150\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.2983 | − | 40.2200i | 0.433590 | − | 1.54350i | ||||
\(680\) | 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 | −0.587517 | + | 0.809212i | \(0.699894\pi\) |
−0.994556 | + | 0.104199i | \(0.966772\pi\) | |||||||
\(692\) | 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 | \(0.154471\pi\) | ||||
−0.884541 | + | 0.466462i | \(0.845529\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.3860i | 0.655727i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37.5381 | + | 10.5449i | 1.41176 | + | 0.396583i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0432 | − | 29.5196i | −0.640070 | − | 1.10863i | −0.985417 | − | 0.170159i | \(-0.945572\pi\) |
0.345347 | − | 0.938475i | \(-0.387761\pi\) | |||||||
\(710\) | 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 | 0.458353 | − | 0.888770i | \(-0.348440\pi\) |
0.998874 | + | 0.0474398i | \(0.0151062\pi\) | |||||||
\(728\) | 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 | −0.991119 | − | 0.132981i | \(-0.957545\pi\) |
−0.610724 | − | 0.791843i | \(-0.709122\pi\) | |||||||
\(734\) | 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 | \(-0.600859\pi\) | ||||
−0.311582 | + | 0.950219i | \(0.600859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.4723 | − | 19.9026i | −1.26467 | − | 0.730156i | −0.290693 | − | 0.956816i | \(-0.593886\pi\) |
−0.973974 | + | 0.226661i | \(0.927219\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.32595 | + | 4.22964i | −0.268402 | + | 0.154962i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.1680 | − | 29.8799i | −1.06578 | − | 1.09179i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.7028 | − | 25.4659i | 0.536512 | − | 0.929265i | −0.462577 | − | 0.886579i | \(-0.653075\pi\) |
0.999089 | − | 0.0426862i | \(-0.0135916\pi\) | |||||||
\(752\) | 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 | \(-0.904432\pi\) |
0.733756 | + | 0.679413i | \(0.237766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.83763 | − | 5.69855i | 0.211337 | − | 0.206301i | ||||
\(764\) | 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 | \(-0.123625\pi\) |
0.134809 | + | 0.990872i | \(0.456958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.2094 | 1.08656 | 0.543279 | − | 0.839552i | \(-0.317183\pi\) | ||||
0.543279 | + | 0.839552i | \(0.317183\pi\) | |||||||
\(774\) | 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 | −0.230241 | − | 0.973134i | \(-0.573952\pi\) |
−0.957879 | + | 0.287172i | \(0.907285\pi\) | |||||||
\(788\) | 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 | \(-0.909947\pi\) |
0.721876 | + | 0.692022i | \(0.243280\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | −0.751079 | + | 2.67371i | −0.0264721 | + | 0.0942357i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 51.7842i | − | 1.82064i | −0.413909 | − | 0.910318i | \(-0.635837\pi\) | ||
0.413909 | − | 0.910318i | \(-0.364163\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.2471i | − | 0.956775i | −0.878149 | − | 0.478387i | \(-0.841221\pi\) | ||
0.878149 | − | 0.478387i | \(-0.158779\pi\) | |||||||
\(812\) | 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 | −0.836394 | − | 0.548129i | \(-0.815340\pi\) |
0.0564968 | + | 0.998403i | \(0.482007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.570514 | − | 0.988159i | 0.0198869 | − | 0.0344451i | −0.855911 | − | 0.517124i | \(-0.827003\pi\) |
0.875798 | + | 0.482679i | \(0.160336\pi\) | |||||||
\(824\) | 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 | ||||||||
\(833\) | 0.729974 | − | 30.2685i | 0.0252921 | − | 1.04874i | ||||
\(834\) | 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 | −0.998616 | − | 0.0525978i | \(-0.983250\pi\) |
0.453757 | − | 0.891126i | \(-0.350083\pi\) | |||||||
\(840\) | 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 | \(-0.714060\pi\) |
0.366000 | + | 0.930615i | \(0.380727\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.4439 | − | 19.8214i | −0.390917 | − | 0.677088i | 0.601654 | − | 0.798757i | \(-0.294509\pi\) |
−0.992571 | + | 0.121669i | \(0.961175\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.4922 | + | 6.63503i | 0.392109 | + | 0.226384i | 0.683074 | − | 0.730350i | \(-0.260643\pi\) |
−0.290964 | + | 0.956734i | \(0.593976\pi\) | |||||||
\(860\) | 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 | ||||||||
\(875\) | −9.81404 | + | 9.58021i | −0.331775 | + | 0.323870i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.18959 | + | 3.79249i | −0.0739373 | + | 0.128063i | −0.900624 | − | 0.434600i | \(-0.856890\pi\) |
0.826686 | + | 0.562663i | \(0.190223\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.1505 | −0.476742 | −0.238371 | − | 0.971174i | \(-0.576613\pi\) | ||||
−0.238371 | + | 0.971174i | \(0.576613\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0261 | 0.774890 | 0.387445 | − | 0.921893i | \(-0.373358\pi\) | ||||
0.387445 | + | 0.921893i | \(0.373358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.1812 | + | 45.3471i | −0.879077 | + | 1.52261i | −0.0267221 | + | 0.999643i | \(0.508507\pi\) |
−0.852355 | + | 0.522963i | \(0.824826\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.1342 | − | 18.6783i | 0.641739 | − | 0.626449i | ||||
\(890\) | 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 | \(-0.0340184\pi\) |
−0.589525 | + | 0.807750i | \(0.700685\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.8606 | − | 27.0550i | 1.55256 | − | 0.896372i | 0.554629 | − | 0.832098i | \(-0.312860\pi\) |
0.997932 | − | 0.0642741i | \(-0.0204732\pi\) | |||||||
\(912\) | 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 | \(-0.465709\pi\) | ||||
0.107520 | + | 0.994203i | \(0.465709\pi\) | |||||||
\(920\) | 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 | \(-0.0158761\pi\) |
−0.542554 | + | 0.840021i | \(0.682543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.6009 | + | 0.376242i | 0.511299 | + | 0.0123308i | ||||
\(932\) | 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 | \(-0.806683\pi\) |
0.904805 | + | 0.425827i | \(0.140017\pi\) | |||||||
\(942\) | 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 | \(-0.663047\pi\) |
0.509814 | + | 0.860284i | \(0.329714\pi\) | |||||||
\(948\) | 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 | \(0.000839552\pi\) | ||||
−0.999997 | + | 0.00263753i | \(0.999160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.22714i | 0.136787i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.76722 | − | 6.29097i | 0.0570664 | − | 0.203146i | ||||
\(960\) | 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 | 0.495211 | + | 0.868773i | \(0.335091\pi\) |
−0.999985 | + | 0.00552073i | \(0.998243\pi\) | |||||||
\(968\) | 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 | 0.840056 | − | 0.542500i | \(-0.182522\pi\) |
−0.0497913 | + | 0.998760i | \(0.515856\pi\) | |||||||
\(978\) | 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 | 0.941722 | − | 0.336393i | \(-0.109207\pi\) |
−0.762185 | + | 0.647359i | \(0.775874\pi\) | |||||||
\(984\) | 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 | \(-0.390885\pi\) | ||||
0.336120 | + | 0.941819i | \(0.390885\pi\) | |||||||
\(992\) | 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 | \(-0.753033\pi\) |
0.249603 | + | 0.968348i | \(0.419700\pi\) | |||||||
\(998\) | 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 \(a_p\))