Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(209,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.d (of order \(2\), degree \(1\), 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: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.10070523904.11 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 10x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.5 | ||
Root | \(0.420861 + 1.68014i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.209 |
Dual form | 210.2.d.a.209.6 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.420861 | − | 1.68014i | 0.242984 | − | 0.970030i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.95522 | − | 1.08495i | −0.874400 | − | 0.485206i | ||||
\(6\) | −0.420861 | + | 1.68014i | −0.171816 | + | 0.685915i | ||||
\(7\) | −2.37608 | − | 1.16372i | −0.898073 | − | 0.439846i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.64575 | − | 1.41421i | −0.881917 | − | 0.471405i | ||||
\(10\) | 1.95522 | + | 1.08495i | 0.618294 | + | 0.343092i | ||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0.420861 | − | 1.68014i | 0.121492 | − | 0.485015i | ||||
\(13\) | −0.841723 | −0.233452 | −0.116726 | − | 0.993164i | \(-0.537240\pi\) | ||||
−0.116726 | + | 0.993164i | \(0.537240\pi\) | |||||||
\(14\) | 2.37608 | + | 1.16372i | 0.635034 | + | 0.311018i | ||||
\(15\) | −2.64575 | + | 2.82843i | −0.683130 | + | 0.730297i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 1.19038i | − | 0.288709i | −0.989526 | − | 0.144354i | \(-0.953890\pi\) | ||
0.989526 | − | 0.144354i | \(-0.0461105\pi\) | |||||||
\(18\) | 2.64575 | + | 1.41421i | 0.623610 | + | 0.333333i | ||||
\(19\) | − | 4.55066i | − | 1.04399i | −0.852948 | − | 0.521996i | \(-0.825187\pi\) | ||
0.852948 | − | 0.521996i | \(-0.174813\pi\) | |||||||
\(20\) | −1.95522 | − | 1.08495i | −0.437200 | − | 0.242603i | ||||
\(21\) | −2.95522 | + | 3.50238i | −0.644881 | + | 0.764283i | ||||
\(22\) | − | 2.82843i | − | 0.603023i | ||||||
\(23\) | −3.29150 | −0.686326 | −0.343163 | − | 0.939276i | \(-0.611498\pi\) | ||||
−0.343163 | + | 0.939276i | \(0.611498\pi\) | |||||||
\(24\) | −0.420861 | + | 1.68014i | −0.0859080 | + | 0.342957i | ||||
\(25\) | 2.64575 | + | 4.24264i | 0.529150 | + | 0.848528i | ||||
\(26\) | 0.841723 | 0.165075 | ||||||||
\(27\) | −3.48957 | + | 3.85005i | −0.671569 | + | 0.740942i | ||||
\(28\) | −2.37608 | − | 1.16372i | −0.449037 | − | 0.219923i | ||||
\(29\) | − | 7.98430i | − | 1.48265i | −0.671148 | − | 0.741323i | \(-0.734198\pi\) | ||
0.671148 | − | 0.741323i | \(-0.265802\pi\) | |||||||
\(30\) | 2.64575 | − | 2.82843i | 0.483046 | − | 0.516398i | ||||
\(31\) | − | 5.53019i | − | 0.993252i | −0.867965 | − | 0.496626i | \(-0.834572\pi\) | ||
0.867965 | − | 0.496626i | \(-0.165428\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.75216 | + | 1.19038i | 0.827245 | + | 0.207218i | ||||
\(34\) | 1.19038i | 0.204148i | ||||||||
\(35\) | 3.38317 | + | 4.85326i | 0.571860 | + | 0.820352i | ||||
\(36\) | −2.64575 | − | 1.41421i | −0.440959 | − | 0.235702i | ||||
\(37\) | − | 10.8127i | − | 1.77760i | −0.458294 | − | 0.888801i | \(-0.651539\pi\) | ||
0.458294 | − | 0.888801i | \(-0.348461\pi\) | |||||||
\(38\) | 4.55066i | 0.738214i | ||||||||
\(39\) | −0.354249 | + | 1.41421i | −0.0567252 | + | 0.226455i | ||||
\(40\) | 1.95522 | + | 1.08495i | 0.309147 | + | 0.171546i | ||||
\(41\) | 7.82087 | 1.22141 | 0.610707 | − | 0.791856i | \(-0.290885\pi\) | ||||
0.610707 | + | 0.791856i | \(0.290885\pi\) | |||||||
\(42\) | 2.95522 | − | 3.50238i | 0.456000 | − | 0.540429i | ||||
\(43\) | 4.65489i | 0.709864i | 0.934892 | + | 0.354932i | \(0.115496\pi\) | ||||
−0.934892 | + | 0.354932i | \(0.884504\pi\) | |||||||
\(44\) | 2.82843i | 0.426401i | ||||||||
\(45\) | 3.63866 | + | 5.63561i | 0.542420 | + | 0.840108i | ||||
\(46\) | 3.29150 | 0.485306 | ||||||||
\(47\) | 4.33981i | 0.633027i | 0.948588 | + | 0.316513i | \(0.102512\pi\) | ||||
−0.948588 | + | 0.316513i | \(0.897488\pi\) | |||||||
\(48\) | 0.420861 | − | 1.68014i | 0.0607461 | − | 0.242508i | ||||
\(49\) | 4.29150 | + | 5.53019i | 0.613072 | + | 0.790027i | ||||
\(50\) | −2.64575 | − | 4.24264i | −0.374166 | − | 0.600000i | ||||
\(51\) | −2.00000 | − | 0.500983i | −0.280056 | − | 0.0701517i | ||||
\(52\) | −0.841723 | −0.116726 | ||||||||
\(53\) | 12.5830 | 1.72841 | 0.864204 | − | 0.503141i | \(-0.167822\pi\) | ||||
0.864204 | + | 0.503141i | \(0.167822\pi\) | |||||||
\(54\) | 3.48957 | − | 3.85005i | 0.474871 | − | 0.523925i | ||||
\(55\) | 3.06871 | − | 5.53019i | 0.413785 | − | 0.745691i | ||||
\(56\) | 2.37608 | + | 1.16372i | 0.317517 | + | 0.155509i | ||||
\(57\) | −7.64575 | − | 1.91520i | −1.01270 | − | 0.253674i | ||||
\(58\) | 7.98430i | 1.04839i | ||||||||
\(59\) | −3.91044 | −0.509095 | −0.254548 | − | 0.967060i | \(-0.581927\pi\) | ||||
−0.254548 | + | 0.967060i | \(0.581927\pi\) | |||||||
\(60\) | −2.64575 | + | 2.82843i | −0.341565 | + | 0.365148i | ||||
\(61\) | 10.0808i | 1.29072i | 0.763878 | + | 0.645360i | \(0.223293\pi\) | ||||
−0.763878 | + | 0.645360i | \(0.776707\pi\) | |||||||
\(62\) | 5.53019i | 0.702335i | ||||||||
\(63\) | 4.64076 | + | 6.43920i | 0.584681 | + | 0.811263i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.64575 | + | 0.913230i | 0.204130 | + | 0.113272i | ||||
\(66\) | −4.75216 | − | 1.19038i | −0.584950 | − | 0.146525i | ||||
\(67\) | − | 4.65489i | − | 0.568685i | −0.958723 | − | 0.284343i | \(-0.908225\pi\) | ||
0.958723 | − | 0.284343i | \(-0.0917753\pi\) | |||||||
\(68\) | − | 1.19038i | − | 0.144354i | ||||||
\(69\) | −1.38527 | + | 5.53019i | −0.166766 | + | 0.665757i | ||||
\(70\) | −3.38317 | − | 4.85326i | −0.404366 | − | 0.580076i | ||||
\(71\) | − | 12.6392i | − | 1.50000i | −0.661440 | − | 0.749998i | \(-0.730055\pi\) | ||
0.661440 | − | 0.749998i | \(-0.269945\pi\) | |||||||
\(72\) | 2.64575 | + | 1.41421i | 0.311805 | + | 0.166667i | ||||
\(73\) | 3.06871 | 0.359166 | 0.179583 | − | 0.983743i | \(-0.442525\pi\) | ||||
0.179583 | + | 0.983743i | \(0.442525\pi\) | |||||||
\(74\) | 10.8127i | 1.25695i | ||||||||
\(75\) | 8.24173 | − | 2.65967i | 0.951673 | − | 0.307113i | ||||
\(76\) | − | 4.55066i | − | 0.521996i | ||||||
\(77\) | 3.29150 | − | 6.72057i | 0.375102 | − | 0.765880i | ||||
\(78\) | 0.354249 | − | 1.41421i | 0.0401108 | − | 0.160128i | ||||
\(79\) | −7.29150 | −0.820358 | −0.410179 | − | 0.912005i | \(-0.634534\pi\) | ||||
−0.410179 | + | 0.912005i | \(0.634534\pi\) | |||||||
\(80\) | −1.95522 | − | 1.08495i | −0.218600 | − | 0.121302i | ||||
\(81\) | 5.00000 | + | 7.48331i | 0.555556 | + | 0.831479i | ||||
\(82\) | −7.82087 | −0.863671 | ||||||||
\(83\) | − | 7.70010i | − | 0.845196i | −0.906317 | − | 0.422598i | \(-0.861118\pi\) | ||
0.906317 | − | 0.422598i | \(-0.138882\pi\) | |||||||
\(84\) | −2.95522 | + | 3.50238i | −0.322441 | + | 0.382141i | ||||
\(85\) | −1.29150 | + | 2.32744i | −0.140083 | + | 0.252447i | ||||
\(86\) | − | 4.65489i | − | 0.501949i | ||||||
\(87\) | −13.4148 | − | 3.36028i | −1.43821 | − | 0.360260i | ||||
\(88\) | − | 2.82843i | − | 0.301511i | ||||||
\(89\) | −12.8712 | −1.36435 | −0.682173 | − | 0.731191i | \(-0.738965\pi\) | ||||
−0.682173 | + | 0.731191i | \(0.738965\pi\) | |||||||
\(90\) | −3.63866 | − | 5.63561i | −0.383549 | − | 0.594046i | ||||
\(91\) | 2.00000 | + | 0.979531i | 0.209657 | + | 0.102683i | ||||
\(92\) | −3.29150 | −0.343163 | ||||||||
\(93\) | −9.29150 | − | 2.32744i | −0.963484 | − | 0.241345i | ||||
\(94\) | − | 4.33981i | − | 0.447618i | ||||||
\(95\) | −4.93725 | + | 8.89753i | −0.506552 | + | 0.912867i | ||||
\(96\) | −0.420861 | + | 1.68014i | −0.0429540 | + | 0.171479i | ||||
\(97\) | 8.11905 | 0.824365 | 0.412182 | − | 0.911101i | \(-0.364767\pi\) | ||||
0.412182 | + | 0.911101i | \(0.364767\pi\) | |||||||
\(98\) | −4.29150 | − | 5.53019i | −0.433507 | − | 0.558634i | ||||
\(99\) | 4.00000 | − | 7.48331i | 0.402015 | − | 0.752101i | ||||
\(100\) | 2.64575 | + | 4.24264i | 0.264575 | + | 0.424264i | ||||
\(101\) | 3.91044 | 0.389103 | 0.194551 | − | 0.980892i | \(-0.437675\pi\) | ||||
0.194551 | + | 0.980892i | \(0.437675\pi\) | |||||||
\(102\) | 2.00000 | + | 0.500983i | 0.198030 | + | 0.0496047i | ||||
\(103\) | −12.5730 | −1.23886 | −0.619429 | − | 0.785053i | \(-0.712636\pi\) | ||||
−0.619429 | + | 0.785053i | \(0.712636\pi\) | |||||||
\(104\) | 0.841723 | 0.0825377 | ||||||||
\(105\) | 9.57802 | − | 3.64165i | 0.934719 | − | 0.355388i | ||||
\(106\) | −12.5830 | −1.22217 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −3.48957 | + | 3.85005i | −0.335784 | + | 0.370471i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −3.06871 | + | 5.53019i | −0.292590 | + | 0.527283i | ||||
\(111\) | −18.1669 | − | 4.55066i | −1.72433 | − | 0.431929i | ||||
\(112\) | −2.37608 | − | 1.16372i | −0.224518 | − | 0.109961i | ||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 7.64575 | + | 1.91520i | 0.716090 | + | 0.179375i | ||||
\(115\) | 6.43560 | + | 3.57113i | 0.600123 | + | 0.333009i | ||||
\(116\) | − | 7.98430i | − | 0.741323i | ||||||
\(117\) | 2.22699 | + | 1.19038i | 0.205885 | + | 0.110050i | ||||
\(118\) | 3.91044 | 0.359985 | ||||||||
\(119\) | −1.38527 | + | 2.82843i | −0.126987 | + | 0.259281i | ||||
\(120\) | 2.64575 | − | 2.82843i | 0.241523 | − | 0.258199i | ||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | − | 10.0808i | − | 0.912677i | ||||||
\(123\) | 3.29150 | − | 13.1402i | 0.296785 | − | 1.18481i | ||||
\(124\) | − | 5.53019i | − | 0.496626i | ||||||
\(125\) | −0.569951 | − | 11.1658i | −0.0509780 | − | 0.998700i | ||||
\(126\) | −4.64076 | − | 6.43920i | −0.413432 | − | 0.573650i | ||||
\(127\) | 10.8127i | 0.959474i | 0.877412 | + | 0.479737i | \(0.159268\pi\) | ||||
−0.877412 | + | 0.479737i | \(0.840732\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.82087 | + | 1.95906i | 0.688589 | + | 0.172486i | ||||
\(130\) | −1.64575 | − | 0.913230i | −0.144342 | − | 0.0800956i | ||||
\(131\) | 8.96077 | 0.782906 | 0.391453 | − | 0.920198i | \(-0.371973\pi\) | ||||
0.391453 | + | 0.920198i | \(0.371973\pi\) | |||||||
\(132\) | 4.75216 | + | 1.19038i | 0.413622 | + | 0.103609i | ||||
\(133\) | −5.29570 | + | 10.8127i | −0.459196 | + | 0.937582i | ||||
\(134\) | 4.65489i | 0.402121i | ||||||||
\(135\) | 11.0000 | − | 3.74166i | 0.946729 | − | 0.322031i | ||||
\(136\) | 1.19038i | 0.102074i | ||||||||
\(137\) | −9.29150 | −0.793827 | −0.396913 | − | 0.917856i | \(-0.629919\pi\) | ||||
−0.396913 | + | 0.917856i | \(0.629919\pi\) | |||||||
\(138\) | 1.38527 | − | 5.53019i | 0.117922 | − | 0.470761i | ||||
\(139\) | 15.6110i | 1.32411i | 0.749455 | + | 0.662056i | \(0.230316\pi\) | ||||
−0.749455 | + | 0.662056i | \(0.769684\pi\) | |||||||
\(140\) | 3.38317 | + | 4.85326i | 0.285930 | + | 0.410176i | ||||
\(141\) | 7.29150 | + | 1.82646i | 0.614055 | + | 0.153816i | ||||
\(142\) | 12.6392i | 1.06066i | ||||||||
\(143\) | − | 2.38075i | − | 0.199088i | ||||||
\(144\) | −2.64575 | − | 1.41421i | −0.220479 | − | 0.117851i | ||||
\(145\) | −8.66259 | + | 15.6110i | −0.719389 | + | 1.29643i | ||||
\(146\) | −3.06871 | −0.253968 | ||||||||
\(147\) | 11.0976 | − | 4.88289i | 0.915317 | − | 0.402734i | ||||
\(148\) | − | 10.8127i | − | 0.888801i | ||||||
\(149\) | − | 3.32941i | − | 0.272756i | −0.990657 | − | 0.136378i | \(-0.956454\pi\) | ||
0.990657 | − | 0.136378i | \(-0.0435462\pi\) | |||||||
\(150\) | −8.24173 | + | 2.65967i | −0.672935 | + | 0.217161i | ||||
\(151\) | −22.5830 | −1.83778 | −0.918889 | − | 0.394515i | \(-0.870913\pi\) | ||||
−0.918889 | + | 0.394515i | \(0.870913\pi\) | |||||||
\(152\) | 4.55066i | 0.369107i | ||||||||
\(153\) | −1.68345 | + | 3.14944i | −0.136099 | + | 0.254617i | ||||
\(154\) | −3.29150 | + | 6.72057i | −0.265237 | + | 0.541559i | ||||
\(155\) | −6.00000 | + | 10.8127i | −0.481932 | + | 0.868499i | ||||
\(156\) | −0.354249 | + | 1.41421i | −0.0283626 | + | 0.113228i | ||||
\(157\) | 22.6209 | 1.80534 | 0.902672 | − | 0.430330i | \(-0.141603\pi\) | ||||
0.902672 | + | 0.430330i | \(0.141603\pi\) | |||||||
\(158\) | 7.29150 | 0.580081 | ||||||||
\(159\) | 5.29570 | − | 21.1412i | 0.419976 | − | 1.67661i | ||||
\(160\) | 1.95522 | + | 1.08495i | 0.154574 | + | 0.0857731i | ||||
\(161\) | 7.82087 | + | 3.83039i | 0.616371 | + | 0.301877i | ||||
\(162\) | −5.00000 | − | 7.48331i | −0.392837 | − | 0.587945i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 7.82087 | 0.610707 | ||||||||
\(165\) | −8.00000 | − | 7.48331i | −0.622799 | − | 0.582575i | ||||
\(166\) | 7.70010i | 0.597643i | ||||||||
\(167\) | 11.4821i | 0.888509i | 0.895901 | + | 0.444255i | \(0.146531\pi\) | ||||
−0.895901 | + | 0.444255i | \(0.853469\pi\) | |||||||
\(168\) | 2.95522 | − | 3.50238i | 0.228000 | − | 0.270215i | ||||
\(169\) | −12.2915 | −0.945500 | ||||||||
\(170\) | 1.29150 | − | 2.32744i | 0.0990537 | − | 0.178507i | ||||
\(171\) | −6.43560 | + | 12.0399i | −0.492143 | + | 0.920715i | ||||
\(172\) | 4.65489i | 0.354932i | ||||||||
\(173\) | 8.89047i | 0.675930i | 0.941159 | + | 0.337965i | \(0.109739\pi\) | ||||
−0.941159 | + | 0.337965i | \(0.890261\pi\) | |||||||
\(174\) | 13.4148 | + | 3.36028i | 1.01697 | + | 0.254742i | ||||
\(175\) | −1.34926 | − | 13.1598i | −0.101994 | − | 0.994785i | ||||
\(176\) | 2.82843i | 0.213201i | ||||||||
\(177\) | −1.64575 | + | 6.57008i | −0.123702 | + | 0.493838i | ||||
\(178\) | 12.8712 | 0.964738 | ||||||||
\(179\) | − | 9.48725i | − | 0.709110i | −0.935035 | − | 0.354555i | \(-0.884632\pi\) | ||
0.935035 | − | 0.354555i | \(-0.115368\pi\) | |||||||
\(180\) | 3.63866 | + | 5.63561i | 0.271210 | + | 0.420054i | ||||
\(181\) | − | 12.0399i | − | 0.894920i | −0.894304 | − | 0.447460i | \(-0.852329\pi\) | ||
0.894304 | − | 0.447460i | \(-0.147671\pi\) | |||||||
\(182\) | −2.00000 | − | 0.979531i | −0.148250 | − | 0.0726077i | ||||
\(183\) | 16.9373 | + | 4.24264i | 1.25204 | + | 0.313625i | ||||
\(184\) | 3.29150 | 0.242653 | ||||||||
\(185\) | −11.7313 | + | 21.1412i | −0.862503 | + | 1.55433i | ||||
\(186\) | 9.29150 | + | 2.32744i | 0.681286 | + | 0.170656i | ||||
\(187\) | 3.36689 | 0.246211 | ||||||||
\(188\) | 4.33981i | 0.316513i | ||||||||
\(189\) | 12.7719 | − | 5.08713i | 0.929018 | − | 0.370034i | ||||
\(190\) | 4.93725 | − | 8.89753i | 0.358186 | − | 0.645495i | ||||
\(191\) | − | 7.98430i | − | 0.577724i | −0.957371 | − | 0.288862i | \(-0.906723\pi\) | ||
0.957371 | − | 0.288862i | \(-0.0932768\pi\) | |||||||
\(192\) | 0.420861 | − | 1.68014i | 0.0303731 | − | 0.121254i | ||||
\(193\) | − | 8.48528i | − | 0.610784i | −0.952227 | − | 0.305392i | \(-0.901213\pi\) | ||
0.952227 | − | 0.305392i | \(-0.0987875\pi\) | |||||||
\(194\) | −8.11905 | −0.582914 | ||||||||
\(195\) | 2.22699 | − | 2.38075i | 0.159478 | − | 0.170489i | ||||
\(196\) | 4.29150 | + | 5.53019i | 0.306536 | + | 0.395014i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | −4.00000 | + | 7.48331i | −0.284268 | + | 0.531816i | ||||
\(199\) | − | 16.5906i | − | 1.17607i | −0.808834 | − | 0.588037i | \(-0.799901\pi\) | ||
0.808834 | − | 0.588037i | \(-0.200099\pi\) | |||||||
\(200\) | −2.64575 | − | 4.24264i | −0.187083 | − | 0.300000i | ||||
\(201\) | −7.82087 | − | 1.95906i | −0.551642 | − | 0.138182i | ||||
\(202\) | −3.91044 | −0.275137 | ||||||||
\(203\) | −9.29150 | + | 18.9713i | −0.652136 | + | 1.33153i | ||||
\(204\) | −2.00000 | − | 0.500983i | −0.140028 | − | 0.0350758i | ||||
\(205\) | −15.2915 | − | 8.48528i | −1.06800 | − | 0.592638i | ||||
\(206\) | 12.5730 | 0.876004 | ||||||||
\(207\) | 8.70850 | + | 4.65489i | 0.605282 | + | 0.323537i | ||||
\(208\) | −0.841723 | −0.0583630 | ||||||||
\(209\) | 12.8712 | 0.890320 | ||||||||
\(210\) | −9.57802 | + | 3.64165i | −0.660946 | + | 0.251298i | ||||
\(211\) | 21.1660 | 1.45713 | 0.728564 | − | 0.684978i | \(-0.240188\pi\) | ||||
0.728564 | + | 0.684978i | \(0.240188\pi\) | |||||||
\(212\) | 12.5830 | 0.864204 | ||||||||
\(213\) | −21.2356 | − | 5.31935i | −1.45504 | − | 0.364476i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.05034 | − | 9.10132i | 0.344430 | − | 0.620705i | ||||
\(216\) | 3.48957 | − | 3.85005i | 0.237435 | − | 0.261963i | ||||
\(217\) | −6.43560 | + | 13.1402i | −0.436877 | + | 0.892013i | ||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 1.29150 | − | 5.15587i | 0.0872717 | − | 0.348401i | ||||
\(220\) | 3.06871 | − | 5.53019i | 0.206893 | − | 0.372845i | ||||
\(221\) | 1.00197i | 0.0673996i | ||||||||
\(222\) | 18.1669 | + | 4.55066i | 1.21928 | + | 0.305420i | ||||
\(223\) | −4.75216 | −0.318228 | −0.159114 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159114 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(224\) | 2.37608 | + | 1.16372i | 0.158758 | + | 0.0777544i | ||||
\(225\) | −1.00000 | − | 14.9666i | −0.0666667 | − | 0.997775i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 1.40122i | 0.0930023i | 0.998918 | + | 0.0465011i | \(0.0148071\pi\) | ||||
−0.998918 | + | 0.0465011i | \(0.985193\pi\) | |||||||
\(228\) | −7.64575 | − | 1.91520i | −0.506352 | − | 0.126837i | ||||
\(229\) | − | 28.2835i | − | 1.86903i | −0.355930 | − | 0.934513i | \(-0.615836\pi\) | ||
0.355930 | − | 0.934513i | \(-0.384164\pi\) | |||||||
\(230\) | −6.43560 | − | 3.57113i | −0.424351 | − | 0.235473i | ||||
\(231\) | −9.90624 | − | 8.35862i | −0.651782 | − | 0.549957i | ||||
\(232\) | 7.98430i | 0.524195i | ||||||||
\(233\) | 2.70850 | 0.177440 | 0.0887198 | − | 0.996057i | \(-0.471722\pi\) | ||||
0.0887198 | + | 0.996057i | \(0.471722\pi\) | |||||||
\(234\) | −2.22699 | − | 1.19038i | −0.145583 | − | 0.0778173i | ||||
\(235\) | 4.70850 | − | 8.48528i | 0.307149 | − | 0.553519i | ||||
\(236\) | −3.91044 | −0.254548 | ||||||||
\(237\) | −3.06871 | + | 12.2508i | −0.199334 | + | 0.795772i | ||||
\(238\) | 1.38527 | − | 2.82843i | 0.0897935 | − | 0.183340i | ||||
\(239\) | 22.1264i | 1.43124i | 0.698490 | + | 0.715620i | \(0.253856\pi\) | ||||
−0.698490 | + | 0.715620i | \(0.746144\pi\) | |||||||
\(240\) | −2.64575 | + | 2.82843i | −0.170783 | + | 0.182574i | ||||
\(241\) | − | 1.95906i | − | 0.126194i | −0.998007 | − | 0.0630972i | \(-0.979902\pi\) | ||
0.998007 | − | 0.0630972i | \(-0.0200978\pi\) | |||||||
\(242\) | −3.00000 | −0.192847 | ||||||||
\(243\) | 14.6773 | − | 5.25127i | 0.941551 | − | 0.336869i | ||||
\(244\) | 10.0808i | 0.645360i | ||||||||
\(245\) | −2.39082 | − | 15.4688i | −0.152744 | − | 0.988266i | ||||
\(246\) | −3.29150 | + | 13.1402i | −0.209859 | + | 0.837787i | ||||
\(247\) | 3.83039i | 0.243722i | ||||||||
\(248\) | 5.53019i | 0.351167i | ||||||||
\(249\) | −12.9373 | − | 3.24067i | −0.819865 | − | 0.205369i | ||||
\(250\) | 0.569951 | + | 11.1658i | 0.0360469 | + | 0.706187i | ||||
\(251\) | 11.7313 | 0.740473 | 0.370237 | − | 0.928937i | \(-0.379277\pi\) | ||||
0.370237 | + | 0.928937i | \(0.379277\pi\) | |||||||
\(252\) | 4.64076 | + | 6.43920i | 0.292341 | + | 0.405632i | ||||
\(253\) | − | 9.30978i | − | 0.585301i | ||||||
\(254\) | − | 10.8127i | − | 0.678451i | ||||||
\(255\) | 3.36689 | + | 3.14944i | 0.210843 | + | 0.197225i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 14.2098i | − | 0.886384i | −0.896427 | − | 0.443192i | \(-0.853846\pi\) | ||
0.896427 | − | 0.443192i | \(-0.146154\pi\) | |||||||
\(258\) | −7.82087 | − | 1.95906i | −0.486906 | − | 0.121966i | ||||
\(259\) | −12.5830 | + | 25.6919i | −0.781870 | + | 1.59642i | ||||
\(260\) | 1.64575 | + | 0.913230i | 0.102065 | + | 0.0566361i | ||||
\(261\) | −11.2915 | + | 21.1245i | −0.698926 | + | 1.30757i | ||||
\(262\) | −8.96077 | −0.553598 | ||||||||
\(263\) | −6.58301 | −0.405925 | −0.202963 | − | 0.979186i | \(-0.565057\pi\) | ||||
−0.202963 | + | 0.979186i | \(0.565057\pi\) | |||||||
\(264\) | −4.75216 | − | 1.19038i | −0.292475 | − | 0.0732626i | ||||
\(265\) | −24.6025 | − | 13.6520i | −1.51132 | − | 0.838634i | ||||
\(266\) | 5.29570 | − | 10.8127i | 0.324700 | − | 0.662971i | ||||
\(267\) | −5.41699 | + | 21.6255i | −0.331515 | + | 1.32346i | ||||
\(268\) | − | 4.65489i | − | 0.284343i | ||||||
\(269\) | −24.6025 | −1.50004 | −0.750021 | − | 0.661414i | \(-0.769957\pi\) | ||||
−0.750021 | + | 0.661414i | \(0.769957\pi\) | |||||||
\(270\) | −11.0000 | + | 3.74166i | −0.669439 | + | 0.227710i | ||||
\(271\) | 7.48925i | 0.454940i | 0.973785 | + | 0.227470i | \(0.0730453\pi\) | ||||
−0.973785 | + | 0.227470i | \(0.926955\pi\) | |||||||
\(272\) | − | 1.19038i | − | 0.0721771i | ||||||
\(273\) | 2.48747 | − | 2.94804i | 0.150549 | − | 0.178423i | ||||
\(274\) | 9.29150 | 0.561320 | ||||||||
\(275\) | −12.0000 | + | 7.48331i | −0.723627 | + | 0.451261i | ||||
\(276\) | −1.38527 | + | 5.53019i | −0.0833832 | + | 0.332878i | ||||
\(277\) | 15.4676i | 0.929359i | 0.885479 | + | 0.464679i | \(0.153830\pi\) | ||||
−0.885479 | + | 0.464679i | \(0.846170\pi\) | |||||||
\(278\) | − | 15.6110i | − | 0.936288i | ||||||
\(279\) | −7.82087 | + | 14.6315i | −0.468223 | + | 0.875965i | ||||
\(280\) | −3.38317 | − | 4.85326i | −0.202183 | − | 0.290038i | ||||
\(281\) | 20.6235i | 1.23029i | 0.788412 | + | 0.615147i | \(0.210903\pi\) | ||||
−0.788412 | + | 0.615147i | \(0.789097\pi\) | |||||||
\(282\) | −7.29150 | − | 1.82646i | −0.434203 | − | 0.108764i | ||||
\(283\) | 9.74968 | 0.579558 | 0.289779 | − | 0.957094i | \(-0.406418\pi\) | ||||
0.289779 | + | 0.957094i | \(0.406418\pi\) | |||||||
\(284\) | − | 12.6392i | − | 0.749998i | ||||||
\(285\) | 12.8712 | + | 12.0399i | 0.762425 | + | 0.713183i | ||||
\(286\) | 2.38075i | 0.140777i | ||||||||
\(287\) | −18.5830 | − | 9.10132i | −1.09692 | − | 0.537234i | ||||
\(288\) | 2.64575 | + | 1.41421i | 0.155902 | + | 0.0833333i | ||||
\(289\) | 15.5830 | 0.916647 | ||||||||
\(290\) | 8.66259 | − | 15.6110i | 0.508685 | − | 0.916712i | ||||
\(291\) | 3.41699 | − | 13.6412i | 0.200308 | − | 0.799659i | ||||
\(292\) | 3.06871 | 0.179583 | ||||||||
\(293\) | − | 11.2712i | − | 0.658472i | −0.944248 | − | 0.329236i | \(-0.893209\pi\) | ||
0.944248 | − | 0.329236i | \(-0.106791\pi\) | |||||||
\(294\) | −11.0976 | + | 4.88289i | −0.647227 | + | 0.284776i | ||||
\(295\) | 7.64575 | + | 4.24264i | 0.445153 | + | 0.247016i | ||||
\(296\) | 10.8127i | 0.628477i | ||||||||
\(297\) | −10.8896 | − | 9.87000i | −0.631878 | − | 0.572716i | ||||
\(298\) | 3.32941i | 0.192868i | ||||||||
\(299\) | 2.77053 | 0.160224 | ||||||||
\(300\) | 8.24173 | − | 2.65967i | 0.475837 | − | 0.153556i | ||||
\(301\) | 5.41699 | − | 11.0604i | 0.312230 | − | 0.637510i | ||||
\(302\) | 22.5830 | 1.29951 | ||||||||
\(303\) | 1.64575 | − | 6.57008i | 0.0945459 | − | 0.377441i | ||||
\(304\) | − | 4.55066i | − | 0.260998i | ||||||
\(305\) | 10.9373 | − | 19.7103i | 0.626265 | − | 1.12861i | ||||
\(306\) | 1.68345 | − | 3.14944i | 0.0962362 | − | 0.180041i | ||||
\(307\) | 14.8000 | 0.844682 | 0.422341 | − | 0.906437i | \(-0.361209\pi\) | ||||
0.422341 | + | 0.906437i | \(0.361209\pi\) | |||||||
\(308\) | 3.29150 | − | 6.72057i | 0.187551 | − | 0.382940i | ||||
\(309\) | −5.29150 | + | 21.1245i | −0.301023 | + | 1.20173i | ||||
\(310\) | 6.00000 | − | 10.8127i | 0.340777 | − | 0.614122i | ||||
\(311\) | −2.77053 | −0.157103 | −0.0785513 | − | 0.996910i | \(-0.525029\pi\) | ||||
−0.0785513 | + | 0.996910i | \(0.525029\pi\) | |||||||
\(312\) | 0.354249 | − | 1.41421i | 0.0200554 | − | 0.0800641i | ||||
\(313\) | 8.11905 | 0.458916 | 0.229458 | − | 0.973319i | \(-0.426305\pi\) | ||||
0.229458 | + | 0.973319i | \(0.426305\pi\) | |||||||
\(314\) | −22.6209 | −1.27657 | ||||||||
\(315\) | −2.08747 | − | 17.6251i | −0.117615 | − | 0.993059i | ||||
\(316\) | −7.29150 | −0.410179 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | −5.29570 | + | 21.1412i | −0.296968 | + | 1.18554i | ||||
\(319\) | 22.5830 | 1.26441 | ||||||||
\(320\) | −1.95522 | − | 1.08495i | −0.109300 | − | 0.0606508i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.82087 | − | 3.83039i | −0.435840 | − | 0.213459i | ||||
\(323\) | −5.41699 | −0.301410 | ||||||||
\(324\) | 5.00000 | + | 7.48331i | 0.277778 | + | 0.415740i | ||||
\(325\) | −2.22699 | − | 3.57113i | −0.123531 | − | 0.198091i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.841723 | − | 3.36028i | 0.0465474 | − | 0.185824i | ||||
\(328\) | −7.82087 | −0.431835 | ||||||||
\(329\) | 5.05034 | − | 10.3117i | 0.278434 | − | 0.568505i | ||||
\(330\) | 8.00000 | + | 7.48331i | 0.440386 | + | 0.411943i | ||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | − | 7.70010i | − | 0.422598i | ||||||
\(333\) | −15.2915 | + | 28.6078i | −0.837969 | + | 1.56770i | ||||
\(334\) | − | 11.4821i | − | 0.628271i | ||||||
\(335\) | −5.05034 | + | 9.10132i | −0.275929 | + | 0.497258i | ||||
\(336\) | −2.95522 | + | 3.50238i | −0.161220 | + | 0.191071i | ||||
\(337\) | − | 22.4499i | − | 1.22293i | −0.791273 | − | 0.611463i | \(-0.790581\pi\) | ||
0.791273 | − | 0.611463i | \(-0.209419\pi\) | |||||||
\(338\) | 12.2915 | 0.668570 | ||||||||
\(339\) | −2.52517 | + | 10.0808i | −0.137148 | + | 0.547517i | ||||
\(340\) | −1.29150 | + | 2.32744i | −0.0700416 | + | 0.126223i | ||||
\(341\) | 15.6417 | 0.847048 | ||||||||
\(342\) | 6.43560 | − | 12.0399i | 0.347998 | − | 0.651044i | ||||
\(343\) | −3.76135 | − | 18.1343i | −0.203094 | − | 0.979159i | ||||
\(344\) | − | 4.65489i | − | 0.250975i | ||||||
\(345\) | 8.70850 | − | 9.30978i | 0.468850 | − | 0.501221i | ||||
\(346\) | − | 8.89047i | − | 0.477955i | ||||||
\(347\) | −24.0000 | −1.28839 | −0.644194 | − | 0.764862i | \(-0.722807\pi\) | ||||
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(348\) | −13.4148 | − | 3.36028i | −0.719106 | − | 0.180130i | ||||
\(349\) | 19.1822i | 1.02680i | 0.858150 | + | 0.513399i | \(0.171614\pi\) | ||||
−0.858150 | + | 0.513399i | \(0.828386\pi\) | |||||||
\(350\) | 1.34926 | + | 13.1598i | 0.0721210 | + | 0.703419i | ||||
\(351\) | 2.93725 | − | 3.24067i | 0.156779 | − | 0.172974i | ||||
\(352\) | − | 2.82843i | − | 0.150756i | ||||||
\(353\) | − | 21.3521i | − | 1.13646i | −0.822871 | − | 0.568228i | \(-0.807629\pi\) | ||
0.822871 | − | 0.568228i | \(-0.192371\pi\) | |||||||
\(354\) | 1.64575 | − | 6.57008i | 0.0874707 | − | 0.349196i | ||||
\(355\) | −13.7129 | + | 24.7124i | −0.727807 | + | 1.31160i | ||||
\(356\) | −12.8712 | −0.682173 | ||||||||
\(357\) | 4.16915 | + | 3.51782i | 0.220655 | + | 0.186183i | ||||
\(358\) | 9.48725i | 0.501417i | ||||||||
\(359\) | 26.7813i | 1.41346i | 0.707481 | + | 0.706732i | \(0.249831\pi\) | ||||
−0.707481 | + | 0.706732i | \(0.750169\pi\) | |||||||
\(360\) | −3.63866 | − | 5.63561i | −0.191774 | − | 0.297023i | ||||
\(361\) | −1.70850 | −0.0899209 | ||||||||
\(362\) | 12.0399i | 0.632804i | ||||||||
\(363\) | 1.26258 | − | 5.04042i | 0.0662685 | − | 0.264554i | ||||
\(364\) | 2.00000 | + | 0.979531i | 0.104828 | + | 0.0513414i | ||||
\(365\) | −6.00000 | − | 3.32941i | −0.314054 | − | 0.174269i | ||||
\(366\) | −16.9373 | − | 4.24264i | −0.885324 | − | 0.221766i | ||||
\(367\) | 8.11905 | 0.423811 | 0.211905 | − | 0.977290i | \(-0.432033\pi\) | ||||
0.211905 | + | 0.977290i | \(0.432033\pi\) | |||||||
\(368\) | −3.29150 | −0.171581 | ||||||||
\(369\) | −20.6921 | − | 11.0604i | −1.07719 | − | 0.575780i | ||||
\(370\) | 11.7313 | − | 21.1412i | 0.609882 | − | 1.09908i | ||||
\(371\) | −29.8982 | − | 14.6431i | −1.55224 | − | 0.760233i | ||||
\(372\) | −9.29150 | − | 2.32744i | −0.481742 | − | 0.120672i | ||||
\(373\) | − | 15.4676i | − | 0.800883i | −0.916322 | − | 0.400441i | \(-0.868857\pi\) | ||
0.916322 | − | 0.400441i | \(-0.131143\pi\) | |||||||
\(374\) | −3.36689 | −0.174098 | ||||||||
\(375\) | −19.0000 | − | 3.74166i | −0.981156 | − | 0.193218i | ||||
\(376\) | − | 4.33981i | − | 0.223809i | ||||||
\(377\) | 6.72057i | 0.346127i | ||||||||
\(378\) | −12.7719 | + | 5.08713i | −0.656915 | + | 0.261654i | ||||
\(379\) | 14.5830 | 0.749079 | 0.374539 | − | 0.927211i | \(-0.377801\pi\) | ||||
0.374539 | + | 0.927211i | \(0.377801\pi\) | |||||||
\(380\) | −4.93725 | + | 8.89753i | −0.253276 | + | 0.456434i | ||||
\(381\) | 18.1669 | + | 4.55066i | 0.930719 | + | 0.233137i | ||||
\(382\) | 7.98430i | 0.408512i | ||||||||
\(383\) | 11.4821i | 0.586706i | 0.956004 | + | 0.293353i | \(0.0947712\pi\) | ||||
−0.956004 | + | 0.293353i | \(0.905229\pi\) | |||||||
\(384\) | −0.420861 | + | 1.68014i | −0.0214770 | + | 0.0857394i | ||||
\(385\) | −13.7271 | + | 9.56904i | −0.699598 | + | 0.487684i | ||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | 6.58301 | − | 12.3157i | 0.334633 | − | 0.626041i | ||||
\(388\) | 8.11905 | 0.412182 | ||||||||
\(389\) | − | 0.323511i | − | 0.0164026i | −0.999966 | − | 0.00820132i | \(-0.997389\pi\) | ||
0.999966 | − | 0.00820132i | \(-0.00261059\pi\) | |||||||
\(390\) | −2.22699 | + | 2.38075i | −0.112768 | + | 0.120554i | ||||
\(391\) | 3.91813i | 0.198148i | ||||||||
\(392\) | −4.29150 | − | 5.53019i | −0.216754 | − | 0.279317i | ||||
\(393\) | 3.77124 | − | 15.0554i | 0.190234 | − | 0.759443i | ||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | 14.2565 | + | 7.91094i | 0.717321 | + | 0.398043i | ||||
\(396\) | 4.00000 | − | 7.48331i | 0.201008 | − | 0.376051i | ||||
\(397\) | −21.5338 | −1.08075 | −0.540375 | − | 0.841424i | \(-0.681718\pi\) | ||||
−0.540375 | + | 0.841424i | \(0.681718\pi\) | |||||||
\(398\) | 16.5906i | 0.831610i | ||||||||
\(399\) | 15.9382 | + | 13.4482i | 0.797906 | + | 0.673251i | ||||
\(400\) | 2.64575 | + | 4.24264i | 0.132288 | + | 0.212132i | ||||
\(401\) | 7.48331i | 0.373699i | 0.982389 | + | 0.186849i | \(0.0598277\pi\) | ||||
−0.982389 | + | 0.186849i | \(0.940172\pi\) | |||||||
\(402\) | 7.82087 | + | 1.95906i | 0.390070 | + | 0.0977092i | ||||
\(403\) | 4.65489i | 0.231876i | ||||||||
\(404\) | 3.91044 | 0.194551 | ||||||||
\(405\) | −1.65704 | − | 20.0563i | −0.0823389 | − | 0.996604i | ||||
\(406\) | 9.29150 | − | 18.9713i | 0.461130 | − | 0.941531i | ||||
\(407\) | 30.5830 | 1.51594 | ||||||||
\(408\) | 2.00000 | + | 0.500983i | 0.0990148 | + | 0.0248024i | ||||
\(409\) | − | 13.0194i | − | 0.643770i | −0.946779 | − | 0.321885i | \(-0.895684\pi\) | ||
0.946779 | − | 0.321885i | \(-0.104316\pi\) | |||||||
\(410\) | 15.2915 | + | 8.48528i | 0.755193 | + | 0.419058i | ||||
\(411\) | −3.91044 | + | 15.6110i | −0.192888 | + | 0.770036i | ||||
\(412\) | −12.5730 | −0.619429 | ||||||||
\(413\) | 9.29150 | + | 4.55066i | 0.457205 | + | 0.223923i | ||||
\(414\) | −8.70850 | − | 4.65489i | −0.427999 | − | 0.228775i | ||||
\(415\) | −8.35425 | + | 15.0554i | −0.410094 | + | 0.739039i | ||||
\(416\) | 0.841723 | 0.0412689 | ||||||||
\(417\) | 26.2288 | + | 6.57008i | 1.28443 | + | 0.321738i | ||||
\(418\) | −12.8712 | −0.629551 | ||||||||
\(419\) | 21.8320 | 1.06656 | 0.533281 | − | 0.845938i | \(-0.320959\pi\) | ||||
0.533281 | + | 0.845938i | \(0.320959\pi\) | |||||||
\(420\) | 9.57802 | − | 3.64165i | 0.467359 | − | 0.177694i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | −21.1660 | −1.03035 | ||||||||
\(423\) | 6.13742 | − | 11.4821i | 0.298412 | − | 0.558277i | ||||
\(424\) | −12.5830 | −0.611085 | ||||||||
\(425\) | 5.05034 | − | 3.14944i | 0.244977 | − | 0.152770i | ||||
\(426\) | 21.2356 | + | 5.31935i | 1.02887 | + | 0.257723i | ||||
\(427\) | 11.7313 | − | 23.9529i | 0.567718 | − | 1.15916i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | − | 1.00197i | −0.193122 | − | 0.0483754i | ||||
\(430\) | −5.05034 | + | 9.10132i | −0.243549 | + | 0.438905i | ||||
\(431\) | − | 16.4696i | − | 0.793312i | −0.917967 | − | 0.396656i | \(-0.870171\pi\) | ||
0.917967 | − | 0.396656i | \(-0.129829\pi\) | |||||||
\(432\) | −3.48957 | + | 3.85005i | −0.167892 | + | 0.185236i | ||||
\(433\) | 26.5313 | 1.27501 | 0.637507 | − | 0.770445i | \(-0.279966\pi\) | ||||
0.637507 | + | 0.770445i | \(0.279966\pi\) | |||||||
\(434\) | 6.43560 | − | 13.1402i | 0.308919 | − | 0.630748i | ||||
\(435\) | 22.5830 | + | 21.1245i | 1.08277 | + | 1.01284i | ||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 14.9785i | 0.716519i | ||||||||
\(438\) | −1.29150 | + | 5.15587i | −0.0617104 | + | 0.246357i | ||||
\(439\) | − | 18.5496i | − | 0.885326i | −0.896688 | − | 0.442663i | \(-0.854034\pi\) | ||
0.896688 | − | 0.442663i | \(-0.145966\pi\) | |||||||
\(440\) | −3.06871 | + | 5.53019i | −0.146295 | + | 0.263641i | ||||
\(441\) | −3.53338 | − | 20.7006i | −0.168256 | − | 0.985743i | ||||
\(442\) | − | 1.00197i | − | 0.0476587i | ||||||
\(443\) | 13.1660 | 0.625536 | 0.312768 | − | 0.949830i | \(-0.398744\pi\) | ||||
0.312768 | + | 0.949830i | \(0.398744\pi\) | |||||||
\(444\) | −18.1669 | − | 4.55066i | −0.862163 | − | 0.215965i | ||||
\(445\) | 25.1660 | + | 13.9647i | 1.19298 | + | 0.661989i | ||||
\(446\) | 4.75216 | 0.225021 | ||||||||
\(447\) | −5.59388 | − | 1.40122i | −0.264581 | − | 0.0662755i | ||||
\(448\) | −2.37608 | − | 1.16372i | −0.112259 | − | 0.0549807i | ||||
\(449\) | 8.30781i | 0.392070i | 0.980597 | + | 0.196035i | \(0.0628066\pi\) | ||||
−0.980597 | + | 0.196035i | \(0.937193\pi\) | |||||||
\(450\) | 1.00000 | + | 14.9666i | 0.0471405 | + | 0.705534i | ||||
\(451\) | 22.1208i | 1.04163i | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | −9.50432 | + | 37.9426i | −0.446552 | + | 1.78270i | ||||
\(454\) | − | 1.40122i | − | 0.0657625i | ||||||
\(455\) | −2.84769 | − | 4.08510i | −0.133502 | − | 0.191513i | ||||
\(456\) | 7.64575 | + | 1.91520i | 0.358045 | + | 0.0896873i | ||||
\(457\) | 8.48528i | 0.396925i | 0.980109 | + | 0.198462i | \(0.0635948\pi\) | ||||
−0.980109 | + | 0.198462i | \(0.936405\pi\) | |||||||
\(458\) | 28.2835i | 1.32160i | ||||||||
\(459\) | 4.58301 | + | 4.15390i | 0.213916 | + | 0.193888i | ||||
\(460\) | 6.43560 | + | 3.57113i | 0.300062 | + | 0.166505i | ||||
\(461\) | −8.96077 | −0.417345 | −0.208672 | − | 0.977986i | \(-0.566914\pi\) | ||||
−0.208672 | + | 0.977986i | \(0.566914\pi\) | |||||||
\(462\) | 9.90624 | + | 8.35862i | 0.460880 | + | 0.388878i | ||||
\(463\) | 23.9529i | 1.11319i | 0.830786 | + | 0.556593i | \(0.187892\pi\) | ||||
−0.830786 | + | 0.556593i | \(0.812108\pi\) | |||||||
\(464\) | − | 7.98430i | − | 0.370662i | ||||||
\(465\) | 15.6417 | + | 14.6315i | 0.725368 | + | 0.678520i | ||||
\(466\) | −2.70850 | −0.125469 | ||||||||
\(467\) | 3.36028i | 0.155495i | 0.996973 | + | 0.0777477i | \(0.0247729\pi\) | ||||
−0.996973 | + | 0.0777477i | \(0.975227\pi\) | |||||||
\(468\) | 2.22699 | + | 1.19038i | 0.102943 | + | 0.0550251i | ||||
\(469\) | −5.41699 | + | 11.0604i | −0.250134 | + | 0.510721i | ||||
\(470\) | −4.70850 | + | 8.48528i | −0.217187 | + | 0.391397i | ||||
\(471\) | 9.52026 | − | 38.0063i | 0.438670 | − | 1.75124i | ||||
\(472\) | 3.91044 | 0.179992 | ||||||||
\(473\) | −13.1660 | −0.605374 | ||||||||
\(474\) | 3.06871 | − | 12.2508i | 0.140951 | − | 0.562696i | ||||
\(475\) | 19.3068 | − | 12.0399i | 0.885857 | − | 0.552429i | ||||
\(476\) | −1.38527 | + | 2.82843i | −0.0634936 | + | 0.129641i | ||||
\(477\) | −33.2915 | − | 17.7951i | −1.52431 | − | 0.814780i | ||||
\(478\) | − | 22.1264i | − | 1.01204i | ||||||
\(479\) | 39.1044 | 1.78672 | 0.893362 | − | 0.449338i | \(-0.148340\pi\) | ||||
0.893362 | + | 0.449338i | \(0.148340\pi\) | |||||||
\(480\) | 2.64575 | − | 2.82843i | 0.120761 | − | 0.129099i | ||||
\(481\) | 9.10132i | 0.414984i | ||||||||
\(482\) | 1.95906i | 0.0892329i | ||||||||
\(483\) | 9.72711 | − | 11.5281i | 0.442599 | − | 0.524547i | ||||
\(484\) | 3.00000 | 0.136364 | ||||||||
\(485\) | −15.8745 | − | 8.80879i | −0.720824 | − | 0.399987i | ||||
\(486\) | −14.6773 | + | 5.25127i | −0.665777 | + | 0.238202i | ||||
\(487\) | − | 32.4382i | − | 1.46991i | −0.678114 | − | 0.734957i | \(-0.737202\pi\) | ||
0.678114 | − | 0.734957i | \(-0.262798\pi\) | |||||||
\(488\) | − | 10.0808i | − | 0.456339i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.39082 | + | 15.4688i | 0.108006 | + | 0.698809i | ||||
\(491\) | − | 14.1421i | − | 0.638226i | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(492\) | 3.29150 | − | 13.1402i | 0.148392 | − | 0.592405i | ||||
\(493\) | −9.50432 | −0.428053 | ||||||||
\(494\) | − | 3.83039i | − | 0.172338i | ||||||
\(495\) | −15.9399 | + | 10.2917i | −0.716446 | + | 0.462577i | ||||
\(496\) | − | 5.53019i | − | 0.248313i | ||||||
\(497\) | −14.7085 | + | 30.0317i | −0.659766 | + | 1.34711i | ||||
\(498\) | 12.9373 | + | 3.24067i | 0.579732 | + | 0.145218i | ||||
\(499\) | 1.41699 | 0.0634334 | 0.0317167 | − | 0.999497i | \(-0.489903\pi\) | ||||
0.0317167 | + | 0.999497i | \(0.489903\pi\) | |||||||
\(500\) | −0.569951 | − | 11.1658i | −0.0254890 | − | 0.499350i | ||||
\(501\) | 19.2915 | + | 4.83236i | 0.861881 | + | 0.215894i | ||||
\(502\) | −11.7313 | −0.523594 | ||||||||
\(503\) | − | 8.67963i | − | 0.387006i | −0.981100 | − | 0.193503i | \(-0.938015\pi\) | ||
0.981100 | − | 0.193503i | \(-0.0619848\pi\) | |||||||
\(504\) | −4.64076 | − | 6.43920i | −0.206716 | − | 0.286825i | ||||
\(505\) | −7.64575 | − | 4.24264i | −0.340231 | − | 0.188795i | ||||
\(506\) | 9.30978i | 0.413870i | ||||||||
\(507\) | −5.17302 | + | 20.6515i | −0.229742 | + | 0.917164i | ||||
\(508\) | 10.8127i | 0.479737i | ||||||||
\(509\) | 30.1436 | 1.33609 | 0.668045 | − | 0.744121i | \(-0.267131\pi\) | ||||
0.668045 | + | 0.744121i | \(0.267131\pi\) | |||||||
\(510\) | −3.36689 | − | 3.14944i | −0.149088 | − | 0.139459i | ||||
\(511\) | −7.29150 | − | 3.57113i | −0.322557 | − | 0.157977i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 17.5203 | + | 15.8799i | 0.773538 | + | 0.701113i | ||||
\(514\) | 14.2098i | 0.626768i | ||||||||
\(515\) | 24.5830 | + | 13.6412i | 1.08326 | + | 0.601101i | ||||
\(516\) | 7.82087 | + | 1.95906i | 0.344295 | + | 0.0862429i | ||||
\(517\) | −12.2748 | −0.539847 | ||||||||
\(518\) | 12.5830 | − | 25.6919i | 0.552866 | − | 1.12884i | ||||
\(519\) | 14.9373 | + | 3.74166i | 0.655673 | + | 0.164241i | ||||
\(520\) | −1.64575 | − | 0.913230i | −0.0721710 | − | 0.0400478i | ||||
\(521\) | −23.4626 | −1.02792 | −0.513958 | − | 0.857815i | \(-0.671821\pi\) | ||||
−0.513958 | + | 0.857815i | \(0.671821\pi\) | |||||||
\(522\) | 11.2915 | − | 21.1245i | 0.494216 | − | 0.924593i | ||||
\(523\) | 4.20861 | 0.184030 | 0.0920149 | − | 0.995758i | \(-0.470669\pi\) | ||||
0.0920149 | + | 0.995758i | \(0.470669\pi\) | |||||||
\(524\) | 8.96077 | 0.391453 | ||||||||
\(525\) | −22.6781 | − | 3.27149i | −0.989755 | − | 0.142780i | ||||
\(526\) | 6.58301 | 0.287033 | ||||||||
\(527\) | −6.58301 | −0.286760 | ||||||||
\(528\) | 4.75216 | + | 1.19038i | 0.206811 | + | 0.0518045i | ||||
\(529\) | −12.1660 | −0.528957 | ||||||||
\(530\) | 24.6025 | + | 13.6520i | 1.06866 | + | 0.593004i | ||||
\(531\) | 10.3460 | + | 5.53019i | 0.448980 | + | 0.239990i | ||||
\(532\) | −5.29570 | + | 10.8127i | −0.229598 | + | 0.468791i | ||||
\(533\) | −6.58301 | −0.285142 | ||||||||
\(534\) | 5.41699 | − | 21.6255i | 0.234416 | − | 0.935825i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.65489i | 0.201061i | ||||||||
\(537\) | −15.9399 | − | 3.99282i | −0.687858 | − | 0.172303i | ||||
\(538\) | 24.6025 | 1.06069 | ||||||||
\(539\) | −15.6417 | + | 12.1382i | −0.673737 | + | 0.522829i | ||||
\(540\) | 11.0000 | − | 3.74166i | 0.473365 | − | 0.161015i | ||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | − | 7.48925i | − | 0.321691i | ||||||
\(543\) | −20.2288 | − | 5.06713i | −0.868099 | − | 0.217452i | ||||
\(544\) | 1.19038i | 0.0510369i | ||||||||
\(545\) | −3.91044 | − | 2.16991i | −0.167505 | − | 0.0929486i | ||||
\(546\) | −2.48747 | + | 2.94804i | −0.106454 | + | 0.126164i | ||||
\(547\) | − | 16.9706i | − | 0.725609i | −0.931865 | − | 0.362804i | \(-0.881819\pi\) | ||
0.931865 | − | 0.362804i | \(-0.118181\pi\) | |||||||
\(548\) | −9.29150 | −0.396913 | ||||||||
\(549\) | 14.2565 | − | 26.6714i | 0.608451 | − | 1.13831i | ||||
\(550\) | 12.0000 | − | 7.48331i | 0.511682 | − | 0.319090i | ||||
\(551\) | −36.3338 | −1.54787 | ||||||||
\(552\) | 1.38527 | − | 5.53019i | 0.0589609 | − | 0.235381i | ||||
\(553\) | 17.3252 | + | 8.48528i | 0.736742 | + | 0.360831i | ||||
\(554\) | − | 15.4676i | − | 0.657156i | ||||||
\(555\) | 30.5830 | + | 28.6078i | 1.29818 | + | 1.21433i | ||||
\(556\) | 15.6110i | 0.662056i | ||||||||
\(557\) | 7.16601 | 0.303634 | 0.151817 | − | 0.988409i | \(-0.451488\pi\) | ||||
0.151817 | + | 0.988409i | \(0.451488\pi\) | |||||||
\(558\) | 7.82087 | − | 14.6315i | 0.331084 | − | 0.619401i | ||||
\(559\) | − | 3.91813i | − | 0.165719i | ||||||
\(560\) | 3.38317 | + | 4.85326i | 0.142965 | + | 0.205088i | ||||
\(561\) | 1.41699 | − | 5.65685i | 0.0598256 | − | 0.238833i | ||||
\(562\) | − | 20.6235i | − | 0.869949i | ||||||
\(563\) | − | 18.7605i | − | 0.790660i | −0.918539 | − | 0.395330i | \(-0.870630\pi\) | ||
0.918539 | − | 0.395330i | \(-0.129370\pi\) | |||||||
\(564\) | 7.29150 | + | 1.82646i | 0.307028 | + | 0.0769079i | ||||
\(565\) | 11.7313 | + | 6.50972i | 0.493540 | + | 0.273866i | ||||
\(566\) | −9.74968 | −0.409810 | ||||||||
\(567\) | −3.17190 | − | 23.5996i | −0.133207 | − | 0.991088i | ||||
\(568\) | 12.6392i | 0.530328i | ||||||||
\(569\) | − | 11.1362i | − | 0.466855i | −0.972374 | − | 0.233428i | \(-0.925006\pi\) | ||
0.972374 | − | 0.233428i | \(-0.0749942\pi\) | |||||||
\(570\) | −12.8712 | − | 12.0399i | −0.539116 | − | 0.504296i | ||||
\(571\) | −34.5830 | −1.44725 | −0.723627 | − | 0.690191i | \(-0.757526\pi\) | ||||
−0.723627 | + | 0.690191i | \(0.757526\pi\) | |||||||
\(572\) | − | 2.38075i | − | 0.0995442i | ||||||
\(573\) | −13.4148 | − | 3.36028i | −0.560409 | − | 0.140378i | ||||
\(574\) | 18.5830 | + | 9.10132i | 0.775640 | + | 0.379882i | ||||
\(575\) | −8.70850 | − | 13.9647i | −0.363169 | − | 0.582367i | ||||
\(576\) | −2.64575 | − | 1.41421i | −0.110240 | − | 0.0589256i | ||||
\(577\) | −30.9853 | −1.28993 | −0.644967 | − | 0.764210i | \(-0.723129\pi\) | ||||
−0.644967 | + | 0.764210i | \(0.723129\pi\) | |||||||
\(578\) | −15.5830 | −0.648168 | ||||||||
\(579\) | −14.2565 | − | 3.57113i | −0.592479 | − | 0.148411i | ||||
\(580\) | −8.66259 | + | 15.6110i | −0.359695 | + | 0.648213i | ||||
\(581\) | −8.96077 | + | 18.2960i | −0.371755 | + | 0.759048i | ||||
\(582\) | −3.41699 | + | 13.6412i | −0.141639 | + | 0.565444i | ||||
\(583\) | 35.5901i | 1.47399i | ||||||||
\(584\) | −3.06871 | −0.126984 | ||||||||
\(585\) | −3.06275 | − | 4.74362i | −0.126629 | − | 0.196125i | ||||
\(586\) | 11.2712i | 0.465610i | ||||||||
\(587\) | − | 44.1054i | − | 1.82042i | −0.414143 | − | 0.910212i | \(-0.635919\pi\) | ||
0.414143 | − | 0.910212i | \(-0.364081\pi\) | |||||||
\(588\) | 11.0976 | − | 4.88289i | 0.457659 | − | 0.201367i | ||||
\(589\) | −25.1660 | −1.03695 | ||||||||
\(590\) | −7.64575 | − | 4.24264i | −0.314771 | − | 0.174667i | ||||
\(591\) | 7.57551 | − | 30.2425i | 0.311615 | − | 1.24401i | ||||
\(592\) | − | 10.8127i | − | 0.444400i | ||||||
\(593\) | 7.91094i | 0.324863i | 0.986720 | + | 0.162432i | \(0.0519337\pi\) | ||||
−0.986720 | + | 0.162432i | \(0.948066\pi\) | |||||||
\(594\) | 10.8896 | + | 9.87000i | 0.446805 | + | 0.404971i | ||||
\(595\) | 5.77721 | − | 4.02724i | 0.236843 | − | 0.165101i | ||||
\(596\) | − | 3.32941i | − | 0.136378i | ||||||
\(597\) | −27.8745 | − | 6.98233i | −1.14083 | − | 0.285768i | ||||
\(598\) | −2.77053 | −0.113296 | ||||||||
\(599\) | 18.2960i | 0.747556i | 0.927518 | + | 0.373778i | \(0.121938\pi\) | ||||
−0.927518 | + | 0.373778i | \(0.878062\pi\) | |||||||
\(600\) | −8.24173 | + | 2.65967i | −0.336467 | + | 0.108581i | ||||
\(601\) | − | 11.0604i | − | 0.451162i | −0.974224 | − | 0.225581i | \(-0.927572\pi\) | ||
0.974224 | − | 0.225581i | \(-0.0724281\pi\) | |||||||
\(602\) | −5.41699 | + | 11.0604i | −0.220780 | + | 0.450787i | ||||
\(603\) | −6.58301 | + | 12.3157i | −0.268081 | + | 0.501533i | ||||
\(604\) | −22.5830 | −0.918889 | ||||||||
\(605\) | −5.86565 | − | 3.25486i | −0.238473 | − | 0.132329i | ||||
\(606\) | −1.64575 | + | 6.57008i | −0.0668541 | + | 0.266891i | ||||
\(607\) | 23.7608 | 0.964421 | 0.482210 | − | 0.876055i | \(-0.339834\pi\) | ||||
0.482210 | + | 0.876055i | \(0.339834\pi\) | |||||||
\(608\) | 4.55066i | 0.184554i | ||||||||
\(609\) | 27.9641 | + | 23.5953i | 1.13316 | + | 0.956131i | ||||
\(610\) | −10.9373 | + | 19.7103i | −0.442836 | + | 0.798045i | ||||
\(611\) | − | 3.65292i | − | 0.147781i | ||||||
\(612\) | −1.68345 | + | 3.14944i | −0.0680493 | + | 0.127309i | ||||
\(613\) | 40.0990i | 1.61958i | 0.586719 | + | 0.809791i | \(0.300419\pi\) | ||||
−0.586719 | + | 0.809791i | \(0.699581\pi\) | |||||||
\(614\) | −14.8000 | −0.597280 | ||||||||
\(615\) | −20.6921 | + | 22.1208i | −0.834385 | + | 0.891995i | ||||
\(616\) | −3.29150 | + | 6.72057i | −0.132618 | + | 0.270779i | ||||
\(617\) | 4.83399 | 0.194609 | 0.0973045 | − | 0.995255i | \(-0.468978\pi\) | ||||
0.0973045 | + | 0.995255i | \(0.468978\pi\) | |||||||
\(618\) | 5.29150 | − | 21.1245i | 0.212855 | − | 0.849751i | ||||
\(619\) | − | 0.632534i | − | 0.0254237i | −0.999919 | − | 0.0127118i | \(-0.995954\pi\) | ||
0.999919 | − | 0.0127118i | \(-0.00404641\pi\) | |||||||
\(620\) | −6.00000 | + | 10.8127i | −0.240966 | + | 0.434249i | ||||
\(621\) | 11.4859 | − | 12.6724i | 0.460915 | − | 0.508528i | ||||
\(622\) | 2.77053 | 0.111088 | ||||||||
\(623\) | 30.5830 | + | 14.9785i | 1.22528 | + | 0.600101i | ||||
\(624\) | −0.354249 | + | 1.41421i | −0.0141813 | + | 0.0566139i | ||||
\(625\) | −11.0000 | + | 22.4499i | −0.440000 | + | 0.897998i | ||||
\(626\) | −8.11905 | −0.324502 | ||||||||
\(627\) | 5.41699 | − | 21.6255i | 0.216334 | − | 0.863637i | ||||
\(628\) | 22.6209 | 0.902672 | ||||||||
\(629\) | −12.8712 | −0.513209 | ||||||||
\(630\) | 2.08747 | + | 17.6251i | 0.0831666 | + | 0.702199i | ||||
\(631\) | −20.4575 | −0.814401 | −0.407200 | − | 0.913339i | \(-0.633495\pi\) | ||||
−0.407200 | + | 0.913339i | \(0.633495\pi\) | |||||||
\(632\) | 7.29150 | 0.290040 | ||||||||
\(633\) | 8.90796 | − | 35.5619i | 0.354060 | − | 1.41346i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | 11.7313 | − | 21.1412i | 0.465543 | − | 0.838964i | ||||
\(636\) | 5.29570 | − | 21.1412i | 0.209988 | − | 0.838304i | ||||
\(637\) | −3.61226 | − | 4.65489i | −0.143123 | − | 0.184433i | ||||
\(638\) | −22.5830 | −0.894070 | ||||||||
\(639\) | −17.8745 | + | 33.4401i | −0.707105 | + | 1.32287i | ||||
\(640\) | 1.95522 | + | 1.08495i | 0.0772868 | + | 0.0428866i | ||||
\(641\) | 16.7931i | 0.663287i | 0.943405 | + | 0.331644i | \(0.107603\pi\) | ||||
−0.943405 | + | 0.331644i | \(0.892397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.7669 | −1.88374 | −0.941872 | − | 0.335971i | \(-0.890935\pi\) | ||||
−0.941872 | + | 0.335971i | \(0.890935\pi\) | |||||||
\(644\) | 7.82087 | + | 3.83039i | 0.308185 | + | 0.150939i | ||||
\(645\) | −13.1660 | − | 12.3157i | −0.518411 | − | 0.484929i | ||||
\(646\) | 5.41699 | 0.213129 | ||||||||
\(647\) | 15.4002i | 0.605444i | 0.953079 | + | 0.302722i | \(0.0978954\pi\) | ||||
−0.953079 | + | 0.302722i | \(0.902105\pi\) | |||||||
\(648\) | −5.00000 | − | 7.48331i | −0.196419 | − | 0.293972i | ||||
\(649\) | − | 11.0604i | − | 0.434158i | ||||||
\(650\) | 2.22699 | + | 3.57113i | 0.0873497 | + | 0.140071i | ||||
\(651\) | 19.3688 | + | 16.3429i | 0.759125 | + | 0.640529i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.1660 | 0.750024 | 0.375012 | − | 0.927020i | \(-0.377639\pi\) | ||||
0.375012 | + | 0.927020i | \(0.377639\pi\) | |||||||
\(654\) | −0.841723 | + | 3.36028i | −0.0329140 | + | 0.131397i | ||||
\(655\) | −17.5203 | − | 9.72202i | −0.684573 | − | 0.379871i | ||||
\(656\) | 7.82087 | 0.305354 | ||||||||
\(657\) | −8.11905 | − | 4.33981i | −0.316754 | − | 0.169312i | ||||
\(658\) | −5.05034 | + | 10.3117i | −0.196883 | + | 0.401994i | ||||
\(659\) | − | 32.7617i | − | 1.27621i | −0.769948 | − | 0.638107i | \(-0.779718\pi\) | ||
0.769948 | − | 0.638107i | \(-0.220282\pi\) | |||||||
\(660\) | −8.00000 | − | 7.48331i | −0.311400 | − | 0.291288i | ||||
\(661\) | − | 0.979531i | − | 0.0380994i | −0.999819 | − | 0.0190497i | \(-0.993936\pi\) | ||
0.999819 | − | 0.0190497i | \(-0.00606407\pi\) | |||||||
\(662\) | −8.00000 | −0.310929 | ||||||||
\(663\) | 1.68345 | + | 0.421689i | 0.0653796 | + | 0.0163770i | ||||
\(664\) | 7.70010i | 0.298822i | ||||||||
\(665\) | 22.0856 | − | 15.3956i | 0.856441 | − | 0.597017i | ||||
\(666\) | 15.2915 | − | 28.6078i | 0.592534 | − | 1.10853i | ||||
\(667\) | 26.2803i | 1.01758i | ||||||||
\(668\) | 11.4821i | 0.444255i | ||||||||
\(669\) | −2.00000 | + | 7.98430i | −0.0773245 | + | 0.308691i | ||||
\(670\) | 5.05034 | − | 9.10132i | 0.195112 | − | 0.351615i | ||||
\(671\) | −28.5129 | −1.10073 | ||||||||
\(672\) | 2.95522 | − | 3.50238i | 0.114000 | − | 0.135107i | ||||
\(673\) | − | 38.5960i | − | 1.48777i | −0.668309 | − | 0.743883i | \(-0.732982\pi\) | ||
0.668309 | − | 0.743883i | \(-0.267018\pi\) | |||||||
\(674\) | 22.4499i | 0.864740i | ||||||||
\(675\) | −25.5669 | − | 4.61874i | −0.984071 | − | 0.177775i | ||||
\(676\) | −12.2915 | −0.472750 | ||||||||
\(677\) | − | 42.4933i | − | 1.63315i | −0.577239 | − | 0.816575i | \(-0.695870\pi\) | ||
0.577239 | − | 0.816575i | \(-0.304130\pi\) | |||||||
\(678\) | 2.52517 | − | 10.0808i | 0.0969785 | − | 0.387153i | ||||
\(679\) | −19.2915 | − | 9.44832i | −0.740340 | − | 0.362593i | ||||
\(680\) | 1.29150 | − | 2.32744i | 0.0495269 | − | 0.0892534i | ||||
\(681\) | 2.35425 | + | 0.589720i | 0.0902150 | + | 0.0225981i | ||||
\(682\) | −15.6417 | −0.598953 | ||||||||
\(683\) | 5.41699 | 0.207276 | 0.103638 | − | 0.994615i | \(-0.466952\pi\) | ||||
0.103638 | + | 0.994615i | \(0.466952\pi\) | |||||||
\(684\) | −6.43560 | + | 12.0399i | −0.246071 | + | 0.460358i | ||||
\(685\) | 18.1669 | + | 10.0808i | 0.694122 | + | 0.385169i | ||||
\(686\) | 3.76135 | + | 18.1343i | 0.143609 | + | 0.692370i | ||||
\(687\) | −47.5203 | − | 11.9034i | −1.81301 | − | 0.454144i | ||||
\(688\) | 4.65489i | 0.177466i | ||||||||
\(689\) | −10.5914 | −0.403500 | ||||||||
\(690\) | −8.70850 | + | 9.30978i | −0.331527 | + | 0.354417i | ||||
\(691\) | − | 6.50972i | − | 0.247641i | −0.992305 | − | 0.123821i | \(-0.960485\pi\) | ||
0.992305 | − | 0.123821i | \(-0.0395148\pi\) | |||||||
\(692\) | 8.89047i | 0.337965i | ||||||||
\(693\) | −18.2128 | + | 13.1261i | −0.691848 | + | 0.498618i | ||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | 16.9373 | − | 30.5230i | 0.642467 | − | 1.15780i | ||||
\(696\) | 13.4148 | + | 3.36028i | 0.508485 | + | 0.127371i | ||||
\(697\) | − | 9.30978i | − | 0.352633i | ||||||
\(698\) | − | 19.1822i | − | 0.726056i | ||||||
\(699\) | 1.13990 | − | 4.55066i | 0.0431151 | − | 0.172122i | ||||
\(700\) | −1.34926 | − | 13.1598i | −0.0509972 | − | 0.497392i | ||||
\(701\) | 1.32548i | 0.0500626i | 0.999687 | + | 0.0250313i | \(0.00796854\pi\) | ||||
−0.999687 | + | 0.0250313i | \(0.992031\pi\) | |||||||
\(702\) | −2.93725 | + | 3.24067i | −0.110860 | + | 0.122311i | ||||
\(703\) | −49.2050 | −1.85580 | ||||||||
\(704\) | 2.82843i | 0.106600i | ||||||||
\(705\) | −12.2748 | − | 11.4821i | −0.462298 | − | 0.432440i | ||||
\(706\) | 21.3521i | 0.803596i | ||||||||
\(707\) | −9.29150 | − | 4.55066i | −0.349443 | − | 0.171145i | ||||
\(708\) | −1.64575 | + | 6.57008i | −0.0618511 | + | 0.246919i | ||||
\(709\) | 20.5830 | 0.773011 | 0.386505 | − | 0.922287i | \(-0.373682\pi\) | ||||
0.386505 | + | 0.922287i | \(0.373682\pi\) | |||||||
\(710\) | 13.7129 | − | 24.7124i | 0.514637 | − | 0.927438i | ||||
\(711\) | 19.2915 | + | 10.3117i | 0.723488 | + | 0.386721i | ||||
\(712\) | 12.8712 | 0.482369 | ||||||||
\(713\) | 18.2026i | 0.681694i | ||||||||
\(714\) | −4.16915 | − | 3.51782i | −0.156027 | − | 0.131651i | ||||
\(715\) | −2.58301 | + | 4.65489i | −0.0965989 | + | 0.174083i | ||||
\(716\) | − | 9.48725i | − | 0.354555i | ||||||
\(717\) | 37.1755 | + | 9.31216i | 1.38835 | + | 0.347769i | ||||
\(718\) | − | 26.7813i | − | 0.999470i | ||||||
\(719\) | −36.3338 | −1.35502 | −0.677511 | − | 0.735512i | \(-0.736942\pi\) | ||||
−0.677511 | + | 0.735512i | \(0.736942\pi\) | |||||||
\(720\) | 3.63866 | + | 5.63561i | 0.135605 | + | 0.210027i | ||||
\(721\) | 29.8745 | + | 14.6315i | 1.11258 | + | 0.544906i | ||||
\(722\) | 1.70850 | 0.0635837 | ||||||||
\(723\) | −3.29150 | − | 0.824494i | −0.122412 | − | 0.0306633i | ||||
\(724\) | − | 12.0399i | − | 0.447460i | ||||||
\(725\) | 33.8745 | − | 21.1245i | 1.25807 | − | 0.784543i | ||||
\(726\) | −1.26258 | + | 5.04042i | −0.0468589 | + | 0.187068i | ||||
\(727\) | −7.03196 | −0.260801 | −0.130401 | − | 0.991461i | \(-0.541626\pi\) | ||||
−0.130401 | + | 0.991461i | \(0.541626\pi\) | |||||||
\(728\) | −2.00000 | − | 0.979531i | −0.0741249 | − | 0.0363038i | ||||
\(729\) | −2.64575 | − | 26.8701i | −0.0979908 | − | 0.995187i | ||||
\(730\) | 6.00000 | + | 3.32941i | 0.222070 | + | 0.123227i | ||||
\(731\) | 5.54107 | 0.204944 | ||||||||
\(732\) | 16.9373 | + | 4.24264i | 0.626019 | + | 0.156813i | ||||
\(733\) | 24.9007 | 0.919728 | 0.459864 | − | 0.887989i | \(-0.347898\pi\) | ||||
0.459864 | + | 0.887989i | \(0.347898\pi\) | |||||||
\(734\) | −8.11905 | −0.299680 | ||||||||
\(735\) | −26.9960 | − | 2.49331i | −0.995762 | − | 0.0919670i | ||||
\(736\) | 3.29150 | 0.121326 | ||||||||
\(737\) | 13.1660 | 0.484976 | ||||||||
\(738\) | 20.6921 | + | 11.0604i | 0.761686 | + | 0.407138i | ||||
\(739\) | 9.16601 | 0.337177 | 0.168589 | − | 0.985687i | \(-0.446079\pi\) | ||||
0.168589 | + | 0.985687i | \(0.446079\pi\) | |||||||
\(740\) | −11.7313 | + | 21.1412i | −0.431251 | + | 0.777167i | ||||
\(741\) | 6.43560 | + | 1.61206i | 0.236418 | + | 0.0592207i | ||||
\(742\) | 29.8982 | + | 14.6431i | 1.09760 | + | 0.537566i | ||||
\(743\) | −33.8745 | −1.24274 | −0.621368 | − | 0.783519i | \(-0.713423\pi\) | ||||
−0.621368 | + | 0.783519i | \(0.713423\pi\) | |||||||
\(744\) | 9.29150 | + | 2.32744i | 0.340643 | + | 0.0853282i | ||||
\(745\) | −3.61226 | + | 6.50972i | −0.132343 | + | 0.238498i | ||||
\(746\) | 15.4676i | 0.566310i | ||||||||
\(747\) | −10.8896 | + | 20.3725i | −0.398429 | + | 0.745392i | ||||
\(748\) | 3.36689 | 0.123106 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 19.0000 | + | 3.74166i | 0.693782 | + | 0.136626i | ||||
\(751\) | 21.1660 | 0.772359 | 0.386179 | − | 0.922424i | \(-0.373795\pi\) | ||||
0.386179 | + | 0.922424i | \(0.373795\pi\) | |||||||
\(752\) | 4.33981i | 0.158257i | ||||||||
\(753\) | 4.93725 | − | 19.7103i | 0.179924 | − | 0.718282i | ||||
\(754\) | − | 6.72057i | − | 0.244749i | ||||||
\(755\) | 44.1547 | + | 24.5015i | 1.60695 | + | 0.891701i | ||||
\(756\) | 12.7719 | − | 5.08713i | 0.464509 | − | 0.185017i | ||||
\(757\) | 3.15194i | 0.114559i | 0.998358 | + | 0.0572796i | \(0.0182426\pi\) | ||||
−0.998358 | + | 0.0572796i | \(0.981757\pi\) | |||||||
\(758\) | −14.5830 | −0.529679 | ||||||||
\(759\) | −15.6417 | − | 3.91813i | −0.567759 | − | 0.142219i | ||||
\(760\) | 4.93725 | − | 8.89753i | 0.179093 | − | 0.322747i | ||||
\(761\) | 20.6921 | 0.750087 | 0.375044 | − | 0.927007i | \(-0.377628\pi\) | ||||
0.375044 | + | 0.927007i | \(0.377628\pi\) | |||||||
\(762\) | −18.1669 | − | 4.55066i | −0.658118 | − | 0.164853i | ||||
\(763\) | −4.75216 | − | 2.32744i | −0.172040 | − | 0.0842591i | ||||
\(764\) | − | 7.98430i | − | 0.288862i | ||||||
\(765\) | 6.70850 | − | 4.33138i | 0.242546 | − | 0.156601i | ||||
\(766\) | − | 11.4821i | − | 0.414864i | ||||||
\(767\) | 3.29150 | 0.118849 | ||||||||
\(768\) | 0.420861 | − | 1.68014i | 0.0151865 | − | 0.0606269i | ||||
\(769\) | 35.1402i | 1.26719i | 0.773666 | + | 0.633594i | \(0.218421\pi\) | ||||
−0.773666 | + | 0.633594i | \(0.781579\pi\) | |||||||
\(770\) | 13.7271 | − | 9.56904i | 0.494691 | − | 0.344844i | ||||
\(771\) | −23.8745 | − | 5.98036i | −0.859819 | − | 0.215378i | ||||
\(772\) | − | 8.48528i | − | 0.305392i | ||||||
\(773\) | − | 7.35310i | − | 0.264473i | −0.991218 | − | 0.132236i | \(-0.957784\pi\) | ||
0.991218 | − | 0.132236i | \(-0.0422158\pi\) | |||||||
\(774\) | −6.58301 | + | 12.3157i | −0.236621 | + | 0.442678i | ||||
\(775\) | 23.4626 | − | 14.6315i | 0.842802 | − | 0.525579i | ||||
\(776\) | −8.11905 | −0.291457 | ||||||||
\(777\) | 37.8703 | + | 31.9540i | 1.35859 | + | 1.14634i | ||||
\(778\) | 0.323511i | 0.0115984i | ||||||||
\(779\) | − | 35.5901i | − | 1.27515i | ||||||
\(780\) | 2.22699 | − | 2.38075i | 0.0797390 | − | 0.0852446i | ||||
\(781\) | 35.7490 | 1.27920 | ||||||||
\(782\) | − | 3.91813i | − | 0.140112i | ||||||
\(783\) | 30.7399 | + | 27.8618i | 1.09856 | + | 0.995699i | ||||
\(784\) | 4.29150 | + | 5.53019i | 0.153268 | + | 0.197507i | ||||
\(785\) | −44.2288 | − | 24.5426i | −1.57859 | − | 0.875963i | ||||
\(786\) | −3.77124 | + | 15.0554i | −0.134516 | + | 0.537007i | ||||
\(787\) | 24.9007 | 0.887614 | 0.443807 | − | 0.896122i | \(-0.353628\pi\) | ||||
0.443807 | + | 0.896122i | \(0.353628\pi\) | |||||||
\(788\) | 18.0000 | 0.641223 | ||||||||
\(789\) | −2.77053 | + | 11.0604i | −0.0986336 | + | 0.393760i | ||||
\(790\) | −14.2565 | − | 7.91094i | −0.507223 | − | 0.281459i | ||||
\(791\) | 14.2565 | + | 6.98233i | 0.506902 | + | 0.248263i | ||||
\(792\) | −4.00000 | + | 7.48331i | −0.142134 | + | 0.265908i | ||||
\(793\) | − | 8.48528i | − | 0.301321i | ||||||
\(794\) | 21.5338 | 0.764206 | ||||||||
\(795\) | −33.2915 | + | 35.5901i | −1.18073 | + | 1.26225i | ||||
\(796\) | − | 16.5906i | − | 0.588037i | ||||||
\(797\) | 6.93141i | 0.245523i | 0.992436 | + | 0.122762i | \(0.0391750\pi\) | ||||
−0.992436 | + | 0.122762i | \(0.960825\pi\) | |||||||
\(798\) | −15.9382 | − | 13.4482i | −0.564204 | − | 0.476061i | ||||
\(799\) | 5.16601 | 0.182760 | ||||||||
\(800\) | −2.64575 | − | 4.24264i | −0.0935414 | − | 0.150000i | ||||
\(801\) | 34.0540 | + | 18.2026i | 1.20324 | + | 0.643159i | ||||
\(802\) | − | 7.48331i | − | 0.264245i | ||||||
\(803\) | 8.67963i | 0.306297i | ||||||||
\(804\) | −7.82087 | − | 1.95906i | −0.275821 | − | 0.0690908i | ||||
\(805\) | −11.1357 | − | 15.9745i | −0.392482 | − | 0.563028i | ||||
\(806\) | − | 4.65489i | − | 0.163961i | ||||||
\(807\) | −10.3542 | + | 41.3357i | −0.364487 | + | 1.45509i | ||||
\(808\) | −3.91044 | −0.137569 | ||||||||
\(809\) | 33.7637i | 1.18707i | 0.804809 | + | 0.593533i | \(0.202268\pi\) | ||||
−0.804809 | + | 0.593533i | \(0.797732\pi\) | |||||||
\(810\) | 1.65704 | + | 20.0563i | 0.0582224 | + | 0.704706i | ||||
\(811\) | − | 28.6305i | − | 1.00535i | −0.864475 | − | 0.502676i | \(-0.832349\pi\) | ||
0.864475 | − | 0.502676i | \(-0.167651\pi\) | |||||||
\(812\) | −9.29150 | + | 18.9713i | −0.326068 | + | 0.665763i | ||||
\(813\) | 12.5830 | + | 3.15194i | 0.441305 | + | 0.110543i | ||||
\(814\) | −30.5830 | −1.07193 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00000 | − | 0.500983i | −0.0700140 | − | 0.0175379i | ||||
\(817\) | 21.1828 | 0.741093 | ||||||||
\(818\) | 13.0194i | 0.455214i | ||||||||
\(819\) | −3.90624 | − | 5.42002i | −0.136495 | − | 0.189391i | ||||
\(820\) | −15.2915 | − | 8.48528i | −0.534002 | − | 0.296319i | ||||
\(821\) | 5.98036i | 0.208716i | 0.994540 | + | 0.104358i | \(0.0332788\pi\) | ||||
−0.994540 | + | 0.104358i | \(0.966721\pi\) | |||||||
\(822\) | 3.91044 | − | 15.6110i | 0.136392 | − | 0.544498i | ||||
\(823\) | − | 19.2980i | − | 0.672686i | −0.941740 | − | 0.336343i | \(-0.890810\pi\) | ||
0.941740 | − | 0.336343i | \(-0.109190\pi\) | |||||||
\(824\) | 12.5730 | 0.438002 | ||||||||
\(825\) | 7.52269 | + | 23.3111i | 0.261906 | + | 0.811590i | ||||
\(826\) | −9.29150 | − | 4.55066i | −0.323293 | − | 0.158338i | ||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 8.70850 | + | 4.65489i | 0.302641 | + | 0.161769i | ||||
\(829\) | 45.2211i | 1.57059i | 0.619120 | + | 0.785296i | \(0.287489\pi\) | ||||
−0.619120 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(830\) | 8.35425 | − | 15.0554i | 0.289980 | − | 0.522579i | ||||
\(831\) | 25.9878 | + | 6.50972i | 0.901506 | + | 0.225820i | ||||
\(832\) | −0.841723 | −0.0291815 | ||||||||
\(833\) | 6.58301 | − | 5.10850i | 0.228088 | − | 0.176999i | ||||
\(834\) | −26.2288 | − | 6.57008i | −0.908228 | − | 0.227503i | ||||
\(835\) | 12.4575 | − | 22.4499i | 0.431110 | − | 0.776912i | ||||
\(836\) | 12.8712 | 0.445160 | ||||||||
\(837\) | 21.2915 | + | 19.2980i | 0.735942 | + | 0.667037i | ||||
\(838\) | −21.8320 | −0.754173 | ||||||||
\(839\) | 26.2331 | 0.905669 | 0.452834 | − | 0.891595i | \(-0.350413\pi\) | ||||
0.452834 | + | 0.891595i | \(0.350413\pi\) | |||||||
\(840\) | −9.57802 | + | 3.64165i | −0.330473 | + | 0.125649i | ||||
\(841\) | −34.7490 | −1.19824 | ||||||||
\(842\) | 10.0000 | 0.344623 | ||||||||
\(843\) | 34.6504 | + | 8.67963i | 1.19342 | + | 0.298942i | ||||
\(844\) | 21.1660 | 0.728564 | ||||||||
\(845\) | 24.0326 | + | 13.3357i | 0.826745 | + | 0.458762i | ||||
\(846\) | −6.13742 | + | 11.4821i | −0.211009 | + | 0.394762i | ||||
\(847\) | −7.12824 | − | 3.49117i | −0.244929 | − | 0.119958i | ||||
\(848\) | 12.5830 | 0.432102 | ||||||||
\(849\) | 4.10326 | − | 16.3808i | 0.140824 | − | 0.562189i | ||||
\(850\) | −5.05034 | + | 3.14944i | −0.173225 | + | 0.108025i | ||||
\(851\) | 35.5901i | 1.22001i | ||||||||
\(852\) | −21.2356 | − | 5.31935i | −0.727520 | − | 0.182238i | ||||
\(853\) | −5.89206 | −0.201740 | −0.100870 | − | 0.994900i | \(-0.532163\pi\) | ||||
−0.100870 | + | 0.994900i | \(0.532163\pi\) | |||||||
\(854\) | −11.7313 | + | 23.9529i | −0.401437 | + | 0.819651i | ||||
\(855\) | 25.6458 | − | 16.5583i | 0.877066 | − | 0.566282i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.1545i | 0.825103i | 0.910934 | + | 0.412551i | \(0.135362\pi\) | ||||
−0.910934 | + | 0.412551i | \(0.864638\pi\) | |||||||
\(858\) | 4.00000 | + | 1.00197i | 0.136558 | + | 0.0342066i | ||||
\(859\) | − | 2.59160i | − | 0.0884241i | −0.999022 | − | 0.0442121i | \(-0.985922\pi\) | ||
0.999022 | − | 0.0442121i | \(-0.0140777\pi\) | |||||||
\(860\) | 5.05034 | − | 9.10132i | 0.172215 | − | 0.310352i | ||||
\(861\) | −23.1124 | + | 27.3917i | −0.787668 | + | 0.933506i | ||||
\(862\) | 16.4696i | 0.560956i | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 3.48957 | − | 3.85005i | 0.118718 | − | 0.130981i | ||||
\(865\) | 9.64575 | − | 17.3828i | 0.327965 | − | 0.591033i | ||||
\(866\) | −26.5313 | −0.901571 | ||||||||
\(867\) | 6.55829 | − | 26.1817i | 0.222731 | − | 0.889176i | ||||
\(868\) | −6.43560 | + | 13.1402i | −0.218439 | + | 0.446006i | ||||
\(869\) | − | 20.6235i | − | 0.699604i | ||||||
\(870\) | −22.5830 | − | 21.1245i | −0.765636 | − | 0.716187i | ||||
\(871\) | 3.91813i | 0.132761i | ||||||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | −21.4810 | − | 11.4821i | −0.727021 | − | 0.388609i | ||||
\(874\) | − | 14.9785i | − | 0.506656i | ||||||
\(875\) | −11.6396 | + | 27.1941i | −0.393492 | + | 0.919328i | ||||
\(876\) | 1.29150 | − | 5.15587i | 0.0436358 | − | 0.174201i | ||||
\(877\) | − | 1.50295i | − | 0.0507510i | −0.999678 | − | 0.0253755i | \(-0.991922\pi\) | ||
0.999678 | − | 0.0253755i | \(-0.00807814\pi\) | |||||||
\(878\) | 18.5496i | 0.626020i | ||||||||
\(879\) | −18.9373 | − | 4.74362i | −0.638738 | − | 0.159998i | ||||
\(880\) | 3.06871 | − | 5.53019i | 0.103446 | − | 0.186423i | ||||
\(881\) | 12.8712 | 0.433642 | 0.216821 | − | 0.976211i | \(-0.430431\pi\) | ||||
0.216821 | + | 0.976211i | \(0.430431\pi\) | |||||||
\(882\) | 3.53338 | + | 20.7006i | 0.118975 | + | 0.697026i | ||||
\(883\) | 13.9647i | 0.469948i | 0.972002 | + | 0.234974i | \(0.0755006\pi\) | ||||
−0.972002 | + | 0.234974i | \(0.924499\pi\) | |||||||
\(884\) | 1.00197i | 0.0336998i | ||||||||
\(885\) | 10.3460 | − | 11.0604i | 0.347778 | − | 0.371791i | ||||
\(886\) | −13.1660 | −0.442321 | ||||||||
\(887\) | 44.6632i | 1.49964i | 0.661640 | + | 0.749822i | \(0.269861\pi\) | ||||
−0.661640 | + | 0.749822i | \(0.730139\pi\) | |||||||
\(888\) | 18.1669 | + | 4.55066i | 0.609642 | + | 0.152710i | ||||
\(889\) | 12.5830 | − | 25.6919i | 0.422020 | − | 0.861678i | ||||
\(890\) | −25.1660 | − | 13.9647i | −0.843567 | − | 0.468097i | ||||
\(891\) | −21.1660 | + | 14.1421i | −0.709088 | + | 0.473779i | ||||
\(892\) | −4.75216 | −0.159114 | ||||||||
\(893\) | 19.7490 | 0.660876 | ||||||||
\(894\) | 5.59388 | + | 1.40122i | 0.187087 | + | 0.0468638i | ||||
\(895\) | −10.2932 | + | 18.5496i | −0.344065 | + | 0.620046i | ||||
\(896\) | 2.37608 | + | 1.16372i | 0.0793792 | + | 0.0388772i | ||||
\(897\) | 1.16601 | − | 4.65489i | 0.0389320 | − | 0.155422i | ||||
\(898\) | − | 8.30781i | − | 0.277235i | ||||||
\(899\) | −44.1547 | −1.47264 | ||||||||
\(900\) | −1.00000 | − | 14.9666i | −0.0333333 | − | 0.498888i | ||||
\(901\) | − | 14.9785i | − | 0.499006i | ||||||
\(902\) | − | 22.1208i | − | 0.736541i | ||||||
\(903\) | −16.3032 | − | 13.7562i | −0.542537 | − | 0.457778i | ||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | −13.0627 | + | 23.5406i | −0.434220 | + | 0.782518i | ||||
\(906\) | 9.50432 | − | 37.9426i | 0.315760 | − | 1.26056i | ||||
\(907\) | 33.9411i | 1.12700i | 0.826117 | + | 0.563498i | \(0.190545\pi\) | ||||
−0.826117 | + | 0.563498i | \(0.809455\pi\) | |||||||
\(908\) | 1.40122i | 0.0465011i | ||||||||
\(909\) | −10.3460 | − | 5.53019i | −0.343156 | − | 0.183425i | ||||
\(910\) | 2.84769 | + | 4.08510i | 0.0944000 | + | 0.135420i | ||||
\(911\) | − | 4.15390i | − | 0.137625i | −0.997630 | − | 0.0688125i | \(-0.978079\pi\) | ||
0.997630 | − | 0.0688125i | \(-0.0219210\pi\) | |||||||
\(912\) | −7.64575 | − | 1.91520i | −0.253176 | − | 0.0634185i | ||||
\(913\) | 21.7792 | 0.720785 | ||||||||
\(914\) | − | 8.48528i | − | 0.280668i | ||||||
\(915\) | −28.5129 | − | 26.6714i | −0.942609 | − | 0.881730i | ||||
\(916\) | − | 28.2835i | − | 0.934513i | ||||||
\(917\) | −21.2915 | − | 10.4278i | −0.703107 | − | 0.344358i | ||||
\(918\) | −4.58301 | − | 4.15390i | −0.151262 | − | 0.137099i | ||||
\(919\) | 10.1255 | 0.334009 | 0.167005 | − | 0.985956i | \(-0.446591\pi\) | ||||
0.167005 | + | 0.985956i | \(0.446591\pi\) | |||||||
\(920\) | −6.43560 | − | 3.57113i | −0.212176 | − | 0.117737i | ||||
\(921\) | 6.22876 | − | 24.8661i | 0.205245 | − | 0.819367i | ||||
\(922\) | 8.96077 | 0.295107 | ||||||||
\(923\) | 10.6387i | 0.350177i | ||||||||
\(924\) | −9.90624 | − | 8.35862i | −0.325891 | − | 0.274978i | ||||
\(925\) | 45.8745 | − | 28.6078i | 1.50834 | − | 0.940618i | ||||
\(926\) | − | 23.9529i | − | 0.787141i | ||||||
\(927\) | 33.2651 | + | 17.7809i | 1.09257 | + | 0.584003i | ||||
\(928\) | 7.98430i | 0.262097i | ||||||||
\(929\) | 30.7928 | 1.01028 | 0.505139 | − | 0.863038i | \(-0.331441\pi\) | ||||
0.505139 | + | 0.863038i | \(0.331441\pi\) | |||||||
\(930\) | −15.6417 | − | 14.6315i | −0.512913 | − | 0.479786i | ||||
\(931\) | 25.1660 | − | 19.5292i | 0.824783 | − | 0.640043i | ||||
\(932\) | 2.70850 | 0.0887198 | ||||||||
\(933\) | −1.16601 | + | 4.65489i | −0.0381735 | + | 0.152394i | ||||
\(934\) | − | 3.36028i | − | 0.109952i | ||||||
\(935\) | −6.58301 | − | 3.65292i | −0.215287 | − | 0.119463i | ||||
\(936\) | −2.22699 | − | 1.19038i | −0.0727914 | − | 0.0389087i | ||||
\(937\) | 3.06871 | 0.100250 | 0.0501252 | − | 0.998743i | \(-0.484038\pi\) | ||||
0.0501252 | + | 0.998743i | \(0.484038\pi\) | |||||||
\(938\) | 5.41699 | − | 11.0604i | 0.176871 | − | 0.361134i | ||||
\(939\) | 3.41699 | − | 13.6412i | 0.111509 | − | 0.445162i | ||||
\(940\) | 4.70850 | − | 8.48528i | 0.153574 | − | 0.276759i | ||||
\(941\) | −40.2443 | −1.31193 | −0.655963 | − | 0.754793i | \(-0.727737\pi\) | ||||
−0.655963 | + | 0.754793i | \(0.727737\pi\) | |||||||
\(942\) | −9.52026 | + | 38.0063i | −0.310187 | + | 1.23831i | ||||
\(943\) | −25.7424 | −0.838288 | ||||||||
\(944\) | −3.91044 | −0.127274 | ||||||||
\(945\) | −30.4911 | − | 3.91047i | −0.991876 | − | 0.127208i | ||||
\(946\) | 13.1660 | 0.428064 | ||||||||
\(947\) | 24.0000 | 0.779895 | 0.389948 | − | 0.920837i | \(-0.372493\pi\) | ||||
0.389948 | + | 0.920837i | \(0.372493\pi\) | |||||||
\(948\) | −3.06871 | + | 12.2508i | −0.0996671 | + | 0.397886i | ||||
\(949\) | −2.58301 | −0.0838479 | ||||||||
\(950\) | −19.3068 | + | 12.0399i | −0.626396 | + | 0.390626i | ||||
\(951\) | 2.52517 | − | 10.0808i | 0.0818842 | − | 0.326894i | ||||
\(952\) | 1.38527 | − | 2.82843i | 0.0448967 | − | 0.0916698i | ||||
\(953\) | −27.8745 | −0.902944 | −0.451472 | − | 0.892285i | \(-0.649101\pi\) | ||||
−0.451472 | + | 0.892285i | \(0.649101\pi\) | |||||||
\(954\) | 33.2915 | + | 17.7951i | 1.07785 | + | 0.576136i | ||||
\(955\) | −8.66259 | + | 15.6110i | −0.280315 | + | 0.505161i | ||||
\(956\) | 22.1264i | 0.715620i | ||||||||
\(957\) | 9.50432 | − | 37.9426i | 0.307231 | − | 1.22651i | ||||
\(958\) | −39.1044 | −1.26340 | ||||||||
\(959\) | 22.0773 | + | 10.8127i | 0.712915 | + | 0.349161i | ||||
\(960\) | −2.64575 | + | 2.82843i | −0.0853913 | + | 0.0912871i | ||||
\(961\) | 0.416995 | 0.0134514 | ||||||||
\(962\) | − | 9.10132i | − | 0.293438i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.95906i | − | 0.0630972i | ||||||
\(965\) | −9.20614 | + | 16.5906i | −0.296356 | + | 0.534069i | ||||
\(966\) | −9.72711 | + | 11.5281i | −0.312965 | + | 0.370911i | ||||
\(967\) | 49.4087i | 1.58888i | 0.607344 | + | 0.794439i | \(0.292235\pi\) | ||||
−0.607344 | + | 0.794439i | \(0.707765\pi\) | |||||||
\(968\) | −3.00000 | −0.0964237 | ||||||||
\(969\) | −2.27980 | + | 9.10132i | −0.0732379 | + | 0.292376i | ||||
\(970\) | 15.8745 | + | 8.80879i | 0.509700 | + | 0.282833i | ||||
\(971\) | −24.6025 | −0.789532 | −0.394766 | − | 0.918782i | \(-0.629174\pi\) | ||||
−0.394766 | + | 0.918782i | \(0.629174\pi\) | |||||||
\(972\) | 14.6773 | − | 5.25127i | 0.470776 | − | 0.168435i | ||||
\(973\) | 18.1669 | − | 37.0931i | 0.582404 | − | 1.18915i | ||||
\(974\) | 32.4382i | 1.03939i | ||||||||
\(975\) | −6.93725 | + | 2.23871i | −0.222170 | + | 0.0716960i | ||||
\(976\) | 10.0808i | 0.322680i | ||||||||
\(977\) | −51.8745 | −1.65961 | −0.829806 | − | 0.558052i | \(-0.811549\pi\) | ||||
−0.829806 | + | 0.558052i | \(0.811549\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 36.4053i | − | 1.16352i | ||||||
\(980\) | −2.39082 | − | 15.4688i | −0.0763720 | − | 0.494133i | ||||
\(981\) | −5.29150 | − | 2.82843i | −0.168945 | − | 0.0903047i | ||||
\(982\) | 14.1421i | 0.451294i | ||||||||
\(983\) | − | 62.0225i | − | 1.97821i | −0.147213 | − | 0.989105i | \(-0.547030\pi\) | ||
0.147213 | − | 0.989105i | \(-0.452970\pi\) | |||||||
\(984\) | −3.29150 | + | 13.1402i | −0.104929 | + | 0.418893i | ||||
\(985\) | −35.1939 | − | 19.5292i | −1.12137 | − | 0.622251i | ||||
\(986\) | 9.50432 | 0.302679 | ||||||||
\(987\) | −15.1997 | − | 12.8251i | −0.483812 | − | 0.408227i | ||||
\(988\) | 3.83039i | 0.121861i | ||||||||
\(989\) | − | 15.3216i | − | 0.487198i | ||||||
\(990\) | 15.9399 | − | 10.2917i | 0.506604 | − | 0.327092i | ||||
\(991\) | −0.708497 | −0.0225062 | −0.0112531 | − | 0.999937i | \(-0.503582\pi\) | ||||
−0.0112531 | + | 0.999937i | \(0.503582\pi\) | |||||||
\(992\) | 5.53019i | 0.175584i | ||||||||
\(993\) | 3.36689 | − | 13.4411i | 0.106845 | − | 0.426541i | ||||
\(994\) | 14.7085 | − | 30.0317i | 0.466525 | − | 0.952548i | ||||
\(995\) | −18.0000 | + | 32.4382i | −0.570638 | + | 1.02836i | ||||
\(996\) | −12.9373 | − | 3.24067i | −0.409933 | − | 0.102685i | ||||
\(997\) | −42.2259 | −1.33731 | −0.668653 | − | 0.743574i | \(-0.733129\pi\) | ||||
−0.668653 | + | 0.743574i | \(0.733129\pi\) | |||||||
\(998\) | −1.41699 | −0.0448542 | ||||||||
\(999\) | 41.6295 | + | 37.7318i | 1.31710 | + | 1.19378i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 210.2.d.a.209.5 | yes | 8 | |
3.2 | odd | 2 | 210.2.d.b.209.6 | yes | 8 | ||
4.3 | odd | 2 | 1680.2.k.e.209.4 | 8 | |||
5.2 | odd | 4 | 1050.2.b.f.251.1 | 16 | |||
5.3 | odd | 4 | 1050.2.b.f.251.16 | 16 | |||
5.4 | even | 2 | 210.2.d.b.209.4 | yes | 8 | ||
7.6 | odd | 2 | inner | 210.2.d.a.209.4 | yes | 8 | |
12.11 | even | 2 | 1680.2.k.f.209.3 | 8 | |||
15.2 | even | 4 | 1050.2.b.f.251.15 | 16 | |||
15.8 | even | 4 | 1050.2.b.f.251.2 | 16 | |||
15.14 | odd | 2 | inner | 210.2.d.a.209.3 | ✓ | 8 | |
20.19 | odd | 2 | 1680.2.k.f.209.5 | 8 | |||
21.20 | even | 2 | 210.2.d.b.209.3 | yes | 8 | ||
28.27 | even | 2 | 1680.2.k.e.209.5 | 8 | |||
35.13 | even | 4 | 1050.2.b.f.251.9 | 16 | |||
35.27 | even | 4 | 1050.2.b.f.251.8 | 16 | |||
35.34 | odd | 2 | 210.2.d.b.209.5 | yes | 8 | ||
60.59 | even | 2 | 1680.2.k.e.209.6 | 8 | |||
84.83 | odd | 2 | 1680.2.k.f.209.6 | 8 | |||
105.62 | odd | 4 | 1050.2.b.f.251.10 | 16 | |||
105.83 | odd | 4 | 1050.2.b.f.251.7 | 16 | |||
105.104 | even | 2 | inner | 210.2.d.a.209.6 | yes | 8 | |
140.139 | even | 2 | 1680.2.k.f.209.4 | 8 | |||
420.419 | odd | 2 | 1680.2.k.e.209.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.d.a.209.3 | ✓ | 8 | 15.14 | odd | 2 | inner | |
210.2.d.a.209.4 | yes | 8 | 7.6 | odd | 2 | inner | |
210.2.d.a.209.5 | yes | 8 | 1.1 | even | 1 | trivial | |
210.2.d.a.209.6 | yes | 8 | 105.104 | even | 2 | inner | |
210.2.d.b.209.3 | yes | 8 | 21.20 | even | 2 | ||
210.2.d.b.209.4 | yes | 8 | 5.4 | even | 2 | ||
210.2.d.b.209.5 | yes | 8 | 35.34 | odd | 2 | ||
210.2.d.b.209.6 | yes | 8 | 3.2 | odd | 2 | ||
1050.2.b.f.251.1 | 16 | 5.2 | odd | 4 | |||
1050.2.b.f.251.2 | 16 | 15.8 | even | 4 | |||
1050.2.b.f.251.7 | 16 | 105.83 | odd | 4 | |||
1050.2.b.f.251.8 | 16 | 35.27 | even | 4 | |||
1050.2.b.f.251.9 | 16 | 35.13 | even | 4 | |||
1050.2.b.f.251.10 | 16 | 105.62 | odd | 4 | |||
1050.2.b.f.251.15 | 16 | 15.2 | even | 4 | |||
1050.2.b.f.251.16 | 16 | 5.3 | odd | 4 | |||
1680.2.k.e.209.3 | 8 | 420.419 | odd | 2 | |||
1680.2.k.e.209.4 | 8 | 4.3 | odd | 2 | |||
1680.2.k.e.209.5 | 8 | 28.27 | even | 2 | |||
1680.2.k.e.209.6 | 8 | 60.59 | even | 2 | |||
1680.2.k.f.209.3 | 8 | 12.11 | even | 2 | |||
1680.2.k.f.209.4 | 8 | 140.139 | even | 2 | |||
1680.2.k.f.209.5 | 8 | 20.19 | odd | 2 | |||
1680.2.k.f.209.6 | 8 | 84.83 | odd | 2 |