Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(251,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.b (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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.101415451701035401216.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 18x^{12} + 145x^{8} - 72x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.8 | ||
Root | \(-1.81768 - 0.332046i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.251 |
Dual form | 1050.2.b.f.251.15 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.68014 | + | 0.420861i | 0.970030 | + | 0.242984i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.420861 | − | 1.68014i | 0.171816 | − | 0.685915i | ||||
\(7\) | 1.16372 | + | 2.37608i | 0.439846 | + | 0.898073i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.64575 | + | 1.41421i | 0.881917 | + | 0.471405i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | −1.68014 | − | 0.420861i | −0.485015 | − | 0.121492i | ||||
\(13\) | − | 0.841723i | − | 0.233452i | −0.993164 | − | 0.116726i | \(-0.962760\pi\) | ||
0.993164 | − | 0.116726i | \(-0.0372399\pi\) | |||||||
\(14\) | 2.37608 | − | 1.16372i | 0.635034 | − | 0.311018i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.19038 | −0.288709 | −0.144354 | − | 0.989526i | \(-0.546110\pi\) | ||||
−0.144354 | + | 0.989526i | \(0.546110\pi\) | |||||||
\(18\) | 1.41421 | − | 2.64575i | 0.333333 | − | 0.623610i | ||||
\(19\) | − | 4.55066i | − | 1.04399i | −0.852948 | − | 0.521996i | \(-0.825187\pi\) | ||
0.852948 | − | 0.521996i | \(-0.174813\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.955218 | + | 4.48191i | 0.208446 | + | 0.978034i | ||||
\(22\) | 2.82843 | 0.603023 | ||||||||
\(23\) | 3.29150i | 0.686326i | 0.939276 | + | 0.343163i | \(0.111498\pi\) | ||||
−0.939276 | + | 0.343163i | \(0.888502\pi\) | |||||||
\(24\) | −0.420861 | + | 1.68014i | −0.0859080 | + | 0.342957i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.841723 | −0.165075 | ||||||||
\(27\) | 3.85005 | + | 3.48957i | 0.740942 | + | 0.671569i | ||||
\(28\) | −1.16372 | − | 2.37608i | −0.219923 | − | 0.449037i | ||||
\(29\) | 7.98430i | 1.48265i | 0.671148 | + | 0.741323i | \(0.265802\pi\) | ||||
−0.671148 | + | 0.741323i | \(0.734198\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.53019i | 0.993252i | 0.867965 | + | 0.496626i | \(0.165428\pi\) | ||||
−0.867965 | + | 0.496626i | \(0.834572\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −1.19038 | + | 4.75216i | −0.207218 | + | 0.827245i | ||||
\(34\) | 1.19038i | 0.204148i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.64575 | − | 1.41421i | −0.440959 | − | 0.235702i | ||||
\(37\) | 10.8127 | 1.77760 | 0.888801 | − | 0.458294i | \(-0.151539\pi\) | ||||
0.888801 | + | 0.458294i | \(0.151539\pi\) | |||||||
\(38\) | −4.55066 | −0.738214 | ||||||||
\(39\) | 0.354249 | − | 1.41421i | 0.0567252 | − | 0.226455i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.82087 | −1.22141 | −0.610707 | − | 0.791856i | \(-0.709115\pi\) | ||||
−0.610707 | + | 0.791856i | \(0.709115\pi\) | |||||||
\(42\) | 4.48191 | − | 0.955218i | 0.691574 | − | 0.147393i | ||||
\(43\) | 4.65489 | 0.709864 | 0.354932 | − | 0.934892i | \(-0.384504\pi\) | ||||
0.354932 | + | 0.934892i | \(0.384504\pi\) | |||||||
\(44\) | − | 2.82843i | − | 0.426401i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.29150 | 0.485306 | ||||||||
\(47\) | 4.33981 | 0.633027 | 0.316513 | − | 0.948588i | \(-0.397488\pi\) | ||||
0.316513 | + | 0.948588i | \(0.397488\pi\) | |||||||
\(48\) | 1.68014 | + | 0.420861i | 0.242508 | + | 0.0607461i | ||||
\(49\) | −4.29150 | + | 5.53019i | −0.613072 | + | 0.790027i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | − | 0.500983i | −0.280056 | − | 0.0701517i | ||||
\(52\) | 0.841723i | 0.116726i | ||||||||
\(53\) | − | 12.5830i | − | 1.72841i | −0.503141 | − | 0.864204i | \(-0.667822\pi\) | ||
0.503141 | − | 0.864204i | \(-0.332178\pi\) | |||||||
\(54\) | 3.48957 | − | 3.85005i | 0.474871 | − | 0.523925i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.37608 | + | 1.16372i | −0.317517 | + | 0.155509i | ||||
\(57\) | 1.91520 | − | 7.64575i | 0.253674 | − | 1.01270i | ||||
\(58\) | 7.98430 | 1.04839 | ||||||||
\(59\) | −3.91044 | −0.509095 | −0.254548 | − | 0.967060i | \(-0.581927\pi\) | ||||
−0.254548 | + | 0.967060i | \(0.581927\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.0808i | − | 1.29072i | −0.763878 | − | 0.645360i | \(-0.776707\pi\) | ||
0.763878 | − | 0.645360i | \(-0.223293\pi\) | |||||||
\(62\) | 5.53019 | 0.702335 | ||||||||
\(63\) | −0.281364 | + | 7.93227i | −0.0354486 | + | 0.999372i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.75216 | + | 1.19038i | 0.584950 | + | 0.146525i | ||||
\(67\) | 4.65489 | 0.568685 | 0.284343 | − | 0.958723i | \(-0.408225\pi\) | ||||
0.284343 | + | 0.958723i | \(0.408225\pi\) | |||||||
\(68\) | 1.19038 | 0.144354 | ||||||||
\(69\) | −1.38527 | + | 5.53019i | −0.166766 | + | 0.665757i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.6392i | − | 1.50000i | −0.661440 | − | 0.749998i | \(-0.730055\pi\) | ||
0.661440 | − | 0.749998i | \(-0.269945\pi\) | |||||||
\(72\) | −1.41421 | + | 2.64575i | −0.166667 | + | 0.311805i | ||||
\(73\) | 3.06871i | 0.359166i | 0.983743 | + | 0.179583i | \(0.0574748\pi\) | ||||
−0.983743 | + | 0.179583i | \(0.942525\pi\) | |||||||
\(74\) | − | 10.8127i | − | 1.25695i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.55066i | 0.521996i | ||||||||
\(77\) | −6.72057 | + | 3.29150i | −0.765880 | + | 0.375102i | ||||
\(78\) | −1.41421 | − | 0.354249i | −0.160128 | − | 0.0401108i | ||||
\(79\) | 7.29150 | 0.820358 | 0.410179 | − | 0.912005i | \(-0.365466\pi\) | ||||
0.410179 | + | 0.912005i | \(0.365466\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | + | 7.48331i | 0.555556 | + | 0.831479i | ||||
\(82\) | 7.82087i | 0.863671i | ||||||||
\(83\) | 7.70010 | 0.845196 | 0.422598 | − | 0.906317i | \(-0.361118\pi\) | ||||
0.422598 | + | 0.906317i | \(0.361118\pi\) | |||||||
\(84\) | −0.955218 | − | 4.48191i | −0.104223 | − | 0.489017i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 4.65489i | − | 0.501949i | ||||||
\(87\) | −3.36028 | + | 13.4148i | −0.360260 | + | 1.43821i | ||||
\(88\) | −2.82843 | −0.301511 | ||||||||
\(89\) | −12.8712 | −1.36435 | −0.682173 | − | 0.731191i | \(-0.738965\pi\) | ||||
−0.682173 | + | 0.731191i | \(0.738965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | − | 0.979531i | 0.209657 | − | 0.102683i | ||||
\(92\) | − | 3.29150i | − | 0.343163i | ||||||
\(93\) | −2.32744 | + | 9.29150i | −0.241345 | + | 0.963484i | ||||
\(94\) | − | 4.33981i | − | 0.447618i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.420861 | − | 1.68014i | 0.0429540 | − | 0.171479i | ||||
\(97\) | − | 8.11905i | − | 0.824365i | −0.911101 | − | 0.412182i | \(-0.864767\pi\) | ||
0.911101 | − | 0.412182i | \(-0.135233\pi\) | |||||||
\(98\) | 5.53019 | + | 4.29150i | 0.558634 | + | 0.433507i | ||||
\(99\) | −4.00000 | + | 7.48331i | −0.402015 | + | 0.752101i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.91044 | −0.389103 | −0.194551 | − | 0.980892i | \(-0.562325\pi\) | ||||
−0.194551 | + | 0.980892i | \(0.562325\pi\) | |||||||
\(102\) | −0.500983 | + | 2.00000i | −0.0496047 | + | 0.198030i | ||||
\(103\) | − | 12.5730i | − | 1.23886i | −0.785053 | − | 0.619429i | \(-0.787364\pi\) | ||
0.785053 | − | 0.619429i | \(-0.212636\pi\) | |||||||
\(104\) | 0.841723 | 0.0825377 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.5830 | −1.22217 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | −3.85005 | − | 3.48957i | −0.370471 | − | 0.335784i | ||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.1669 | + | 4.55066i | 1.72433 | + | 0.431929i | ||||
\(112\) | 1.16372 | + | 2.37608i | 0.109961 | + | 0.224518i | ||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −7.64575 | − | 1.91520i | −0.716090 | − | 0.179375i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 7.98430i | − | 0.741323i | ||||||
\(117\) | 1.19038 | − | 2.22699i | 0.110050 | − | 0.205885i | ||||
\(118\) | 3.91044i | 0.359985i | ||||||||
\(119\) | −1.38527 | − | 2.82843i | −0.126987 | − | 0.259281i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | −10.0808 | −0.912677 | ||||||||
\(123\) | −13.1402 | − | 3.29150i | −1.18481 | − | 0.296785i | ||||
\(124\) | − | 5.53019i | − | 0.496626i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.93227 | + | 0.281364i | 0.706662 | + | 0.0250659i | ||||
\(127\) | −10.8127 | −0.959474 | −0.479737 | − | 0.877412i | \(-0.659268\pi\) | ||||
−0.479737 | + | 0.877412i | \(0.659268\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 7.82087 | + | 1.95906i | 0.688589 | + | 0.172486i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.96077 | −0.782906 | −0.391453 | − | 0.920198i | \(-0.628027\pi\) | ||||
−0.391453 | + | 0.920198i | \(0.628027\pi\) | |||||||
\(132\) | 1.19038 | − | 4.75216i | 0.103609 | − | 0.413622i | ||||
\(133\) | 10.8127 | − | 5.29570i | 0.937582 | − | 0.459196i | ||||
\(134\) | − | 4.65489i | − | 0.402121i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 1.19038i | − | 0.102074i | ||||||
\(137\) | − | 9.29150i | − | 0.793827i | −0.917856 | − | 0.396913i | \(-0.870081\pi\) | ||
0.917856 | − | 0.396913i | \(-0.129919\pi\) | |||||||
\(138\) | 5.53019 | + | 1.38527i | 0.470761 | + | 0.117922i | ||||
\(139\) | 15.6110i | 1.32411i | 0.749455 | + | 0.662056i | \(0.230316\pi\) | ||||
−0.749455 | + | 0.662056i | \(0.769684\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.29150 | + | 1.82646i | 0.614055 | + | 0.153816i | ||||
\(142\) | −12.6392 | −1.06066 | ||||||||
\(143\) | 2.38075 | 0.199088 | ||||||||
\(144\) | 2.64575 | + | 1.41421i | 0.220479 | + | 0.117851i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.06871 | 0.253968 | ||||||||
\(147\) | −9.53778 | + | 7.48537i | −0.786662 | + | 0.617383i | ||||
\(148\) | −10.8127 | −0.888801 | ||||||||
\(149\) | 3.32941i | 0.272756i | 0.990657 | + | 0.136378i | \(0.0435462\pi\) | ||||
−0.990657 | + | 0.136378i | \(0.956454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.5830 | −1.83778 | −0.918889 | − | 0.394515i | \(-0.870913\pi\) | ||||
−0.918889 | + | 0.394515i | \(0.870913\pi\) | |||||||
\(152\) | 4.55066 | 0.369107 | ||||||||
\(153\) | −3.14944 | − | 1.68345i | −0.254617 | − | 0.136099i | ||||
\(154\) | 3.29150 | + | 6.72057i | 0.265237 | + | 0.541559i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.354249 | + | 1.41421i | −0.0283626 | + | 0.113228i | ||||
\(157\) | − | 22.6209i | − | 1.80534i | −0.430330 | − | 0.902672i | \(-0.641603\pi\) | ||
0.430330 | − | 0.902672i | \(-0.358397\pi\) | |||||||
\(158\) | − | 7.29150i | − | 0.580081i | ||||||
\(159\) | 5.29570 | − | 21.1412i | 0.419976 | − | 1.67661i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.82087 | + | 3.83039i | −0.616371 | + | 0.301877i | ||||
\(162\) | 7.48331 | − | 5.00000i | 0.587945 | − | 0.392837i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 7.82087 | 0.610707 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 7.70010i | − | 0.597643i | ||||||
\(167\) | 11.4821 | 0.888509 | 0.444255 | − | 0.895901i | \(-0.353469\pi\) | ||||
0.444255 | + | 0.895901i | \(0.353469\pi\) | |||||||
\(168\) | −4.48191 | + | 0.955218i | −0.345787 | + | 0.0736966i | ||||
\(169\) | 12.2915 | 0.945500 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.43560 | − | 12.0399i | 0.492143 | − | 0.920715i | ||||
\(172\) | −4.65489 | −0.354932 | ||||||||
\(173\) | −8.89047 | −0.675930 | −0.337965 | − | 0.941159i | \(-0.609739\pi\) | ||||
−0.337965 | + | 0.941159i | \(0.609739\pi\) | |||||||
\(174\) | 13.4148 | + | 3.36028i | 1.01697 | + | 0.254742i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.82843i | 0.213201i | ||||||||
\(177\) | −6.57008 | − | 1.64575i | −0.493838 | − | 0.123702i | ||||
\(178\) | 12.8712i | 0.964738i | ||||||||
\(179\) | 9.48725i | 0.709110i | 0.935035 | + | 0.354555i | \(0.115368\pi\) | ||||
−0.935035 | + | 0.354555i | \(0.884632\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0399i | 0.894920i | 0.894304 | + | 0.447460i | \(0.147671\pi\) | ||||
−0.894304 | + | 0.447460i | \(0.852329\pi\) | |||||||
\(182\) | −0.979531 | − | 2.00000i | −0.0726077 | − | 0.148250i | ||||
\(183\) | 4.24264 | − | 16.9373i | 0.313625 | − | 1.25204i | ||||
\(184\) | −3.29150 | −0.242653 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.29150 | + | 2.32744i | 0.681286 | + | 0.170656i | ||||
\(187\) | − | 3.36689i | − | 0.246211i | ||||||
\(188\) | −4.33981 | −0.316513 | ||||||||
\(189\) | −3.81112 | + | 13.2089i | −0.277218 | + | 0.960807i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.98430i | − | 0.577724i | −0.957371 | − | 0.288862i | \(-0.906723\pi\) | ||
0.957371 | − | 0.288862i | \(-0.0932768\pi\) | |||||||
\(192\) | −1.68014 | − | 0.420861i | −0.121254 | − | 0.0303731i | ||||
\(193\) | −8.48528 | −0.610784 | −0.305392 | − | 0.952227i | \(-0.598787\pi\) | ||||
−0.305392 | + | 0.952227i | \(0.598787\pi\) | |||||||
\(194\) | −8.11905 | −0.582914 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.29150 | − | 5.53019i | 0.306536 | − | 0.395014i | ||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 7.48331 | + | 4.00000i | 0.531816 | + | 0.284268i | ||||
\(199\) | − | 16.5906i | − | 1.17607i | −0.808834 | − | 0.588037i | \(-0.799901\pi\) | ||
0.808834 | − | 0.588037i | \(-0.200099\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.82087 | + | 1.95906i | 0.551642 | + | 0.138182i | ||||
\(202\) | 3.91044i | 0.275137i | ||||||||
\(203\) | −18.9713 | + | 9.29150i | −1.33153 | + | 0.652136i | ||||
\(204\) | 2.00000 | + | 0.500983i | 0.140028 | + | 0.0350758i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.5730 | −0.876004 | ||||||||
\(207\) | −4.65489 | + | 8.70850i | −0.323537 | + | 0.605282i | ||||
\(208\) | − | 0.841723i | − | 0.0583630i | ||||||
\(209\) | 12.8712 | 0.890320 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.1660 | 1.45713 | 0.728564 | − | 0.684978i | \(-0.240188\pi\) | ||||
0.728564 | + | 0.684978i | \(0.240188\pi\) | |||||||
\(212\) | 12.5830i | 0.864204i | ||||||||
\(213\) | 5.31935 | − | 21.2356i | 0.364476 | − | 1.45504i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.48957 | + | 3.85005i | −0.237435 | + | 0.261963i | ||||
\(217\) | −13.1402 | + | 6.43560i | −0.892013 | + | 0.436877i | ||||
\(218\) | 2.00000i | 0.135457i | ||||||||
\(219\) | −1.29150 | + | 5.15587i | −0.0872717 | + | 0.348401i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00197i | 0.0673996i | ||||||||
\(222\) | 4.55066 | − | 18.1669i | 0.305420 | − | 1.21928i | ||||
\(223\) | − | 4.75216i | − | 0.318228i | −0.987260 | − | 0.159114i | \(-0.949136\pi\) | ||
0.987260 | − | 0.159114i | \(-0.0508637\pi\) | |||||||
\(224\) | 2.37608 | − | 1.16372i | 0.158758 | − | 0.0777544i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 1.40122 | 0.0930023 | 0.0465011 | − | 0.998918i | \(-0.485193\pi\) | ||||
0.0465011 | + | 0.998918i | \(0.485193\pi\) | |||||||
\(228\) | −1.91520 | + | 7.64575i | −0.126837 | + | 0.506352i | ||||
\(229\) | − | 28.2835i | − | 1.86903i | −0.355930 | − | 0.934513i | \(-0.615836\pi\) | ||
0.355930 | − | 0.934513i | \(-0.384164\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.6768 | + | 2.70176i | −0.834070 | + | 0.177763i | ||||
\(232\) | −7.98430 | −0.524195 | ||||||||
\(233\) | − | 2.70850i | − | 0.177440i | −0.996057 | − | 0.0887198i | \(-0.971722\pi\) | ||
0.996057 | − | 0.0887198i | \(-0.0282776\pi\) | |||||||
\(234\) | −2.22699 | − | 1.19038i | −0.145583 | − | 0.0778173i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.91044 | 0.254548 | ||||||||
\(237\) | 12.2508 | + | 3.06871i | 0.795772 | + | 0.199334i | ||||
\(238\) | −2.82843 | + | 1.38527i | −0.183340 | + | 0.0897935i | ||||
\(239\) | − | 22.1264i | − | 1.43124i | −0.698490 | − | 0.715620i | \(-0.746144\pi\) | ||
0.698490 | − | 0.715620i | \(-0.253856\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.95906i | 0.126194i | 0.998007 | + | 0.0630972i | \(0.0200978\pi\) | ||||
−0.998007 | + | 0.0630972i | \(0.979902\pi\) | |||||||
\(242\) | − | 3.00000i | − | 0.192847i | ||||||
\(243\) | 5.25127 | + | 14.6773i | 0.336869 | + | 0.941551i | ||||
\(244\) | 10.0808i | 0.645360i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.29150 | + | 13.1402i | −0.209859 | + | 0.837787i | ||||
\(247\) | −3.83039 | −0.243722 | ||||||||
\(248\) | −5.53019 | −0.351167 | ||||||||
\(249\) | 12.9373 | + | 3.24067i | 0.819865 | + | 0.205369i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.7313 | −0.740473 | −0.370237 | − | 0.928937i | \(-0.620723\pi\) | ||||
−0.370237 | + | 0.928937i | \(0.620723\pi\) | |||||||
\(252\) | 0.281364 | − | 7.93227i | 0.0177243 | − | 0.499686i | ||||
\(253\) | −9.30978 | −0.585301 | ||||||||
\(254\) | 10.8127i | 0.678451i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.2098 | −0.886384 | −0.443192 | − | 0.896427i | \(-0.646154\pi\) | ||||
−0.443192 | + | 0.896427i | \(0.646154\pi\) | |||||||
\(258\) | 1.95906 | − | 7.82087i | 0.121966 | − | 0.486906i | ||||
\(259\) | 12.5830 | + | 25.6919i | 0.781870 | + | 1.59642i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.2915 | + | 21.1245i | −0.698926 | + | 1.30757i | ||||
\(262\) | 8.96077i | 0.553598i | ||||||||
\(263\) | 6.58301i | 0.405925i | 0.979186 | + | 0.202963i | \(0.0650570\pi\) | ||||
−0.979186 | + | 0.202963i | \(0.934943\pi\) | |||||||
\(264\) | −4.75216 | − | 1.19038i | −0.292475 | − | 0.0732626i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.29570 | − | 10.8127i | −0.324700 | − | 0.662971i | ||||
\(267\) | −21.6255 | − | 5.41699i | −1.32346 | − | 0.331515i | ||||
\(268\) | −4.65489 | −0.284343 | ||||||||
\(269\) | −24.6025 | −1.50004 | −0.750021 | − | 0.661414i | \(-0.769957\pi\) | ||||
−0.750021 | + | 0.661414i | \(0.769957\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.48925i | − | 0.454940i | −0.973785 | − | 0.227470i | \(-0.926955\pi\) | ||
0.973785 | − | 0.227470i | \(-0.0730453\pi\) | |||||||
\(272\) | −1.19038 | −0.0721771 | ||||||||
\(273\) | 3.77253 | − | 0.804028i | 0.228324 | − | 0.0486620i | ||||
\(274\) | −9.29150 | −0.561320 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.38527 | − | 5.53019i | 0.0833832 | − | 0.332878i | ||||
\(277\) | −15.4676 | −0.929359 | −0.464679 | − | 0.885479i | \(-0.653830\pi\) | ||||
−0.464679 | + | 0.885479i | \(0.653830\pi\) | |||||||
\(278\) | 15.6110 | 0.936288 | ||||||||
\(279\) | −7.82087 | + | 14.6315i | −0.468223 | + | 0.875965i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.6235i | 1.23029i | 0.788412 | + | 0.615147i | \(0.210903\pi\) | ||||
−0.788412 | + | 0.615147i | \(0.789097\pi\) | |||||||
\(282\) | 1.82646 | − | 7.29150i | 0.108764 | − | 0.434203i | ||||
\(283\) | 9.74968i | 0.579558i | 0.957094 | + | 0.289779i | \(0.0935819\pi\) | ||||
−0.957094 | + | 0.289779i | \(0.906418\pi\) | |||||||
\(284\) | 12.6392i | 0.749998i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.38075i | − | 0.140777i | ||||||
\(287\) | −9.10132 | − | 18.5830i | −0.537234 | − | 1.09692i | ||||
\(288\) | 1.41421 | − | 2.64575i | 0.0833333 | − | 0.155902i | ||||
\(289\) | −15.5830 | −0.916647 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.41699 | − | 13.6412i | 0.200308 | − | 0.799659i | ||||
\(292\) | − | 3.06871i | − | 0.179583i | ||||||
\(293\) | 11.2712 | 0.658472 | 0.329236 | − | 0.944248i | \(-0.393209\pi\) | ||||
0.329236 | + | 0.944248i | \(0.393209\pi\) | |||||||
\(294\) | 7.48537 | + | 9.53778i | 0.436556 | + | 0.556254i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.8127i | 0.628477i | ||||||||
\(297\) | −9.87000 | + | 10.8896i | −0.572716 | + | 0.631878i | ||||
\(298\) | 3.32941 | 0.192868 | ||||||||
\(299\) | 2.77053 | 0.160224 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.41699 | + | 11.0604i | 0.312230 | + | 0.637510i | ||||
\(302\) | 22.5830i | 1.29951i | ||||||||
\(303\) | −6.57008 | − | 1.64575i | −0.377441 | − | 0.0945459i | ||||
\(304\) | − | 4.55066i | − | 0.260998i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.68345 | + | 3.14944i | −0.0962362 | + | 0.180041i | ||||
\(307\) | − | 14.8000i | − | 0.844682i | −0.906437 | − | 0.422341i | \(-0.861209\pi\) | ||
0.906437 | − | 0.422341i | \(-0.138791\pi\) | |||||||
\(308\) | 6.72057 | − | 3.29150i | 0.382940 | − | 0.187551i | ||||
\(309\) | 5.29150 | − | 21.1245i | 0.301023 | − | 1.20173i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.77053 | 0.157103 | 0.0785513 | − | 0.996910i | \(-0.474971\pi\) | ||||
0.0785513 | + | 0.996910i | \(0.474971\pi\) | |||||||
\(312\) | 1.41421 | + | 0.354249i | 0.0800641 | + | 0.0200554i | ||||
\(313\) | 8.11905i | 0.458916i | 0.973319 | + | 0.229458i | \(0.0736953\pi\) | ||||
−0.973319 | + | 0.229458i | \(0.926305\pi\) | |||||||
\(314\) | −22.6209 | −1.27657 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.29150 | −0.410179 | ||||||||
\(317\) | 6.00000i | 0.336994i | 0.985702 | + | 0.168497i | \(0.0538913\pi\) | ||||
−0.985702 | + | 0.168497i | \(0.946109\pi\) | |||||||
\(318\) | −21.1412 | − | 5.29570i | −1.18554 | − | 0.296968i | ||||
\(319\) | −22.5830 | −1.26441 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.83039 | + | 7.82087i | 0.213459 | + | 0.435840i | ||||
\(323\) | 5.41699i | 0.301410i | ||||||||
\(324\) | −5.00000 | − | 7.48331i | −0.277778 | − | 0.415740i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.36028 | − | 0.841723i | −0.185824 | − | 0.0465474i | ||||
\(328\) | − | 7.82087i | − | 0.431835i | ||||||
\(329\) | 5.05034 | + | 10.3117i | 0.278434 | + | 0.568505i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | −7.70010 | −0.422598 | ||||||||
\(333\) | 28.6078 | + | 15.2915i | 1.56770 | + | 0.837969i | ||||
\(334\) | − | 11.4821i | − | 0.628271i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.955218 | + | 4.48191i | 0.0521114 | + | 0.244508i | ||||
\(337\) | 22.4499 | 1.22293 | 0.611463 | − | 0.791273i | \(-0.290581\pi\) | ||||
0.611463 | + | 0.791273i | \(0.290581\pi\) | |||||||
\(338\) | − | 12.2915i | − | 0.668570i | ||||||
\(339\) | −2.52517 | + | 10.0808i | −0.137148 | + | 0.547517i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.6417 | −0.847048 | ||||||||
\(342\) | −12.0399 | − | 6.43560i | −0.651044 | − | 0.347998i | ||||
\(343\) | −18.1343 | − | 3.76135i | −0.979159 | − | 0.203094i | ||||
\(344\) | 4.65489i | 0.250975i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.89047i | 0.477955i | ||||||||
\(347\) | − | 24.0000i | − | 1.28839i | −0.764862 | − | 0.644194i | \(-0.777193\pi\) | ||
0.764862 | − | 0.644194i | \(-0.222807\pi\) | |||||||
\(348\) | 3.36028 | − | 13.4148i | 0.180130 | − | 0.719106i | ||||
\(349\) | 19.1822i | 1.02680i | 0.858150 | + | 0.513399i | \(0.171614\pi\) | ||||
−0.858150 | + | 0.513399i | \(0.828386\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.93725 | − | 3.24067i | 0.156779 | − | 0.172974i | ||||
\(352\) | 2.82843 | 0.150756 | ||||||||
\(353\) | 21.3521 | 1.13646 | 0.568228 | − | 0.822871i | \(-0.307629\pi\) | ||||
0.568228 | + | 0.822871i | \(0.307629\pi\) | |||||||
\(354\) | −1.64575 | + | 6.57008i | −0.0874707 | + | 0.349196i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.8712 | 0.682173 | ||||||||
\(357\) | −1.13707 | − | 5.33516i | −0.0601800 | − | 0.282367i | ||||
\(358\) | 9.48725 | 0.501417 | ||||||||
\(359\) | − | 26.7813i | − | 1.41346i | −0.707481 | − | 0.706732i | \(-0.750169\pi\) | ||
0.707481 | − | 0.706732i | \(-0.249831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.70850 | −0.0899209 | ||||||||
\(362\) | 12.0399 | 0.632804 | ||||||||
\(363\) | 5.04042 | + | 1.26258i | 0.264554 | + | 0.0662685i | ||||
\(364\) | −2.00000 | + | 0.979531i | −0.104828 | + | 0.0513414i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −16.9373 | − | 4.24264i | −0.885324 | − | 0.221766i | ||||
\(367\) | − | 8.11905i | − | 0.423811i | −0.977290 | − | 0.211905i | \(-0.932033\pi\) | ||
0.977290 | − | 0.211905i | \(-0.0679669\pi\) | |||||||
\(368\) | 3.29150i | 0.171581i | ||||||||
\(369\) | −20.6921 | − | 11.0604i | −1.07719 | − | 0.575780i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.8982 | − | 14.6431i | 1.55224 | − | 0.760233i | ||||
\(372\) | 2.32744 | − | 9.29150i | 0.120672 | − | 0.481742i | ||||
\(373\) | −15.4676 | −0.800883 | −0.400441 | − | 0.916322i | \(-0.631143\pi\) | ||||
−0.400441 | + | 0.916322i | \(0.631143\pi\) | |||||||
\(374\) | −3.36689 | −0.174098 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.33981i | 0.223809i | ||||||||
\(377\) | 6.72057 | 0.346127 | ||||||||
\(378\) | 13.2089 | + | 3.81112i | 0.679393 | + | 0.196023i | ||||
\(379\) | −14.5830 | −0.749079 | −0.374539 | − | 0.927211i | \(-0.622199\pi\) | ||||
−0.374539 | + | 0.927211i | \(0.622199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.1669 | − | 4.55066i | −0.930719 | − | 0.233137i | ||||
\(382\) | −7.98430 | −0.408512 | ||||||||
\(383\) | −11.4821 | −0.586706 | −0.293353 | − | 0.956004i | \(-0.594771\pi\) | ||||
−0.293353 | + | 0.956004i | \(0.594771\pi\) | |||||||
\(384\) | −0.420861 | + | 1.68014i | −0.0214770 | + | 0.0857394i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | 12.3157 | + | 6.58301i | 0.626041 | + | 0.334633i | ||||
\(388\) | 8.11905i | 0.412182i | ||||||||
\(389\) | 0.323511i | 0.0164026i | 0.999966 | + | 0.00820132i | \(0.00261059\pi\) | ||||
−0.999966 | + | 0.00820132i | \(0.997389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.91813i | − | 0.198148i | ||||||
\(392\) | −5.53019 | − | 4.29150i | −0.279317 | − | 0.216754i | ||||
\(393\) | −15.0554 | − | 3.77124i | −0.759443 | − | 0.190234i | ||||
\(394\) | 18.0000 | 0.906827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.00000 | − | 7.48331i | 0.201008 | − | 0.376051i | ||||
\(397\) | 21.5338i | 1.08075i | 0.841424 | + | 0.540375i | \(0.181718\pi\) | ||||
−0.841424 | + | 0.540375i | \(0.818282\pi\) | |||||||
\(398\) | −16.5906 | −0.831610 | ||||||||
\(399\) | 20.3957 | − | 4.34687i | 1.02106 | − | 0.217616i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.48331i | 0.373699i | 0.982389 | + | 0.186849i | \(0.0598277\pi\) | ||||
−0.982389 | + | 0.186849i | \(0.940172\pi\) | |||||||
\(402\) | 1.95906 | − | 7.82087i | 0.0977092 | − | 0.390070i | ||||
\(403\) | 4.65489 | 0.231876 | ||||||||
\(404\) | 3.91044 | 0.194551 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.29150 | + | 18.9713i | 0.461130 | + | 0.941531i | ||||
\(407\) | 30.5830i | 1.51594i | ||||||||
\(408\) | 0.500983 | − | 2.00000i | 0.0248024 | − | 0.0990148i | ||||
\(409\) | − | 13.0194i | − | 0.643770i | −0.946779 | − | 0.321885i | \(-0.895684\pi\) | ||
0.946779 | − | 0.321885i | \(-0.104316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.91044 | − | 15.6110i | 0.192888 | − | 0.770036i | ||||
\(412\) | 12.5730i | 0.619429i | ||||||||
\(413\) | −4.55066 | − | 9.29150i | −0.223923 | − | 0.457205i | ||||
\(414\) | 8.70850 | + | 4.65489i | 0.427999 | + | 0.228775i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.841723 | −0.0412689 | ||||||||
\(417\) | −6.57008 | + | 26.2288i | −0.321738 | + | 1.28443i | ||||
\(418\) | − | 12.8712i | − | 0.629551i | ||||||
\(419\) | 21.8320 | 1.06656 | 0.533281 | − | 0.845938i | \(-0.320959\pi\) | ||||
0.533281 | + | 0.845938i | \(0.320959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | − | 21.1660i | − | 1.03035i | ||||||
\(423\) | 11.4821 | + | 6.13742i | 0.558277 | + | 0.298412i | ||||
\(424\) | 12.5830 | 0.611085 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −21.2356 | − | 5.31935i | −1.02887 | − | 0.257723i | ||||
\(427\) | 23.9529 | − | 11.7313i | 1.15916 | − | 0.567718i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | + | 1.00197i | 0.193122 | + | 0.0483754i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16.4696i | − | 0.793312i | −0.917967 | − | 0.396656i | \(-0.870171\pi\) | ||
0.917967 | − | 0.396656i | \(-0.129829\pi\) | |||||||
\(432\) | 3.85005 | + | 3.48957i | 0.185236 | + | 0.167892i | ||||
\(433\) | 26.5313i | 1.27501i | 0.770445 | + | 0.637507i | \(0.220034\pi\) | ||||
−0.770445 | + | 0.637507i | \(0.779966\pi\) | |||||||
\(434\) | 6.43560 | + | 13.1402i | 0.308919 | + | 0.630748i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 14.9785 | 0.716519 | ||||||||
\(438\) | 5.15587 | + | 1.29150i | 0.246357 | + | 0.0617104i | ||||
\(439\) | − | 18.5496i | − | 0.885326i | −0.896688 | − | 0.442663i | \(-0.854034\pi\) | ||
0.896688 | − | 0.442663i | \(-0.145966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.1751 | + | 8.56241i | −0.913101 | + | 0.407734i | ||||
\(442\) | 1.00197 | 0.0476587 | ||||||||
\(443\) | − | 13.1660i | − | 0.625536i | −0.949830 | − | 0.312768i | \(-0.898744\pi\) | ||
0.949830 | − | 0.312768i | \(-0.101256\pi\) | |||||||
\(444\) | −18.1669 | − | 4.55066i | −0.862163 | − | 0.215965i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.75216 | −0.225021 | ||||||||
\(447\) | −1.40122 | + | 5.59388i | −0.0662755 | + | 0.264581i | ||||
\(448\) | −1.16372 | − | 2.37608i | −0.0549807 | − | 0.112259i | ||||
\(449\) | − | 8.30781i | − | 0.392070i | −0.980597 | − | 0.196035i | \(-0.937193\pi\) | ||
0.980597 | − | 0.196035i | \(-0.0628066\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 22.1208i | − | 1.04163i | ||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | −37.9426 | − | 9.50432i | −1.78270 | − | 0.446552i | ||||
\(454\) | − | 1.40122i | − | 0.0657625i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.64575 | + | 1.91520i | 0.358045 | + | 0.0896873i | ||||
\(457\) | −8.48528 | −0.396925 | −0.198462 | − | 0.980109i | \(-0.563595\pi\) | ||||
−0.198462 | + | 0.980109i | \(0.563595\pi\) | |||||||
\(458\) | −28.2835 | −1.32160 | ||||||||
\(459\) | −4.58301 | − | 4.15390i | −0.213916 | − | 0.193888i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.96077 | 0.417345 | 0.208672 | − | 0.977986i | \(-0.433086\pi\) | ||||
0.208672 | + | 0.977986i | \(0.433086\pi\) | |||||||
\(462\) | 2.70176 | + | 12.6768i | 0.125697 | + | 0.589777i | ||||
\(463\) | 23.9529 | 1.11319 | 0.556593 | − | 0.830786i | \(-0.312108\pi\) | ||||
0.556593 | + | 0.830786i | \(0.312108\pi\) | |||||||
\(464\) | 7.98430i | 0.370662i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.70850 | −0.125469 | ||||||||
\(467\) | 3.36028 | 0.155495 | 0.0777477 | − | 0.996973i | \(-0.475227\pi\) | ||||
0.0777477 | + | 0.996973i | \(0.475227\pi\) | |||||||
\(468\) | −1.19038 | + | 2.22699i | −0.0550251 | + | 0.102943i | ||||
\(469\) | 5.41699 | + | 11.0604i | 0.250134 | + | 0.510721i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.52026 | − | 38.0063i | 0.438670 | − | 1.75124i | ||||
\(472\) | − | 3.91044i | − | 0.179992i | ||||||
\(473\) | 13.1660i | 0.605374i | ||||||||
\(474\) | 3.06871 | − | 12.2508i | 0.140951 | − | 0.562696i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.38527 | + | 2.82843i | 0.0634936 | + | 0.129641i | ||||
\(477\) | 17.7951 | − | 33.2915i | 0.814780 | − | 1.52431i | ||||
\(478\) | −22.1264 | −1.01204 | ||||||||
\(479\) | 39.1044 | 1.78672 | 0.893362 | − | 0.449338i | \(-0.148340\pi\) | ||||
0.893362 | + | 0.449338i | \(0.148340\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 9.10132i | − | 0.414984i | ||||||
\(482\) | 1.95906 | 0.0892329 | ||||||||
\(483\) | −14.7522 | + | 3.14410i | −0.671250 | + | 0.143062i | ||||
\(484\) | −3.00000 | −0.136364 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.6773 | − | 5.25127i | 0.665777 | − | 0.238202i | ||||
\(487\) | 32.4382 | 1.46991 | 0.734957 | − | 0.678114i | \(-0.237202\pi\) | ||||
0.734957 | + | 0.678114i | \(0.237202\pi\) | |||||||
\(488\) | 10.0808 | 0.456339 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.1421i | − | 0.638226i | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(492\) | 13.1402 | + | 3.29150i | 0.592405 | + | 0.148392i | ||||
\(493\) | − | 9.50432i | − | 0.428053i | ||||||
\(494\) | 3.83039i | 0.172338i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.53019i | 0.248313i | ||||||||
\(497\) | 30.0317 | − | 14.7085i | 1.34711 | − | 0.659766i | ||||
\(498\) | 3.24067 | − | 12.9373i | 0.145218 | − | 0.579732i | ||||
\(499\) | −1.41699 | −0.0634334 | −0.0317167 | − | 0.999497i | \(-0.510097\pi\) | ||||
−0.0317167 | + | 0.999497i | \(0.510097\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.2915 | + | 4.83236i | 0.861881 | + | 0.215894i | ||||
\(502\) | 11.7313i | 0.523594i | ||||||||
\(503\) | 8.67963 | 0.387006 | 0.193503 | − | 0.981100i | \(-0.438015\pi\) | ||||
0.193503 | + | 0.981100i | \(0.438015\pi\) | |||||||
\(504\) | −7.93227 | − | 0.281364i | −0.353331 | − | 0.0125330i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.30978i | 0.413870i | ||||||||
\(507\) | 20.6515 | + | 5.17302i | 0.917164 | + | 0.229742i | ||||
\(508\) | 10.8127 | 0.479737 | ||||||||
\(509\) | 30.1436 | 1.33609 | 0.668045 | − | 0.744121i | \(-0.267131\pi\) | ||||
0.668045 | + | 0.744121i | \(0.267131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.29150 | + | 3.57113i | −0.322557 | + | 0.157977i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 15.8799 | − | 17.5203i | 0.701113 | − | 0.773538i | ||||
\(514\) | 14.2098i | 0.626768i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.82087 | − | 1.95906i | −0.344295 | − | 0.0862429i | ||||
\(517\) | 12.2748i | 0.539847i | ||||||||
\(518\) | 25.6919 | − | 12.5830i | 1.12884 | − | 0.552866i | ||||
\(519\) | −14.9373 | − | 3.74166i | −0.655673 | − | 0.164241i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.4626 | 1.02792 | 0.513958 | − | 0.857815i | \(-0.328179\pi\) | ||||
0.513958 | + | 0.857815i | \(0.328179\pi\) | |||||||
\(522\) | 21.1245 | + | 11.2915i | 0.924593 | + | 0.494216i | ||||
\(523\) | 4.20861i | 0.184030i | 0.995758 | + | 0.0920149i | \(0.0293308\pi\) | ||||
−0.995758 | + | 0.0920149i | \(0.970669\pi\) | |||||||
\(524\) | 8.96077 | 0.391453 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.58301 | 0.287033 | ||||||||
\(527\) | − | 6.58301i | − | 0.286760i | ||||||
\(528\) | −1.19038 | + | 4.75216i | −0.0518045 | + | 0.206811i | ||||
\(529\) | 12.1660 | 0.528957 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.3460 | − | 5.53019i | −0.448980 | − | 0.239990i | ||||
\(532\) | −10.8127 | + | 5.29570i | −0.468791 | + | 0.229598i | ||||
\(533\) | 6.58301i | 0.285142i | ||||||||
\(534\) | −5.41699 | + | 21.6255i | −0.234416 | + | 0.935825i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.65489i | 0.201061i | ||||||||
\(537\) | −3.99282 | + | 15.9399i | −0.172303 | + | 0.687858i | ||||
\(538\) | 24.6025i | 1.06069i | ||||||||
\(539\) | −15.6417 | − | 12.1382i | −0.673737 | − | 0.522829i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | −7.48925 | −0.321691 | ||||||||
\(543\) | −5.06713 | + | 20.2288i | −0.217452 | + | 0.868099i | ||||
\(544\) | 1.19038i | 0.0510369i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.804028 | − | 3.77253i | −0.0344092 | − | 0.161449i | ||||
\(547\) | 16.9706 | 0.725609 | 0.362804 | − | 0.931865i | \(-0.381819\pi\) | ||||
0.362804 | + | 0.931865i | \(0.381819\pi\) | |||||||
\(548\) | 9.29150i | 0.396913i | ||||||||
\(549\) | 14.2565 | − | 26.6714i | 0.608451 | − | 1.13831i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.3338 | 1.54787 | ||||||||
\(552\) | −5.53019 | − | 1.38527i | −0.235381 | − | 0.0589609i | ||||
\(553\) | 8.48528 | + | 17.3252i | 0.360831 | + | 0.736742i | ||||
\(554\) | 15.4676i | 0.657156i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 15.6110i | − | 0.662056i | ||||||
\(557\) | 7.16601i | 0.303634i | 0.988409 | + | 0.151817i | \(0.0485124\pi\) | ||||
−0.988409 | + | 0.151817i | \(0.951488\pi\) | |||||||
\(558\) | 14.6315 | + | 7.82087i | 0.619401 | + | 0.331084i | ||||
\(559\) | − | 3.91813i | − | 0.165719i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.41699 | − | 5.65685i | 0.0598256 | − | 0.238833i | ||||
\(562\) | 20.6235 | 0.869949 | ||||||||
\(563\) | 18.7605 | 0.790660 | 0.395330 | − | 0.918539i | \(-0.370630\pi\) | ||||
0.395330 | + | 0.918539i | \(0.370630\pi\) | |||||||
\(564\) | −7.29150 | − | 1.82646i | −0.307028 | − | 0.0769079i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.74968 | 0.409810 | ||||||||
\(567\) | −11.9623 | + | 20.5889i | −0.502371 | + | 0.864652i | ||||
\(568\) | 12.6392 | 0.530328 | ||||||||
\(569\) | 11.1362i | 0.466855i | 0.972374 | + | 0.233428i | \(0.0749942\pi\) | ||||
−0.972374 | + | 0.233428i | \(0.925006\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.5830 | −1.44725 | −0.723627 | − | 0.690191i | \(-0.757526\pi\) | ||||
−0.723627 | + | 0.690191i | \(0.757526\pi\) | |||||||
\(572\) | −2.38075 | −0.0995442 | ||||||||
\(573\) | 3.36028 | − | 13.4148i | 0.140378 | − | 0.560409i | ||||
\(574\) | −18.5830 | + | 9.10132i | −0.775640 | + | 0.379882i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.64575 | − | 1.41421i | −0.110240 | − | 0.0589256i | ||||
\(577\) | 30.9853i | 1.28993i | 0.764210 | + | 0.644967i | \(0.223129\pi\) | ||||
−0.764210 | + | 0.644967i | \(0.776871\pi\) | |||||||
\(578\) | 15.5830i | 0.648168i | ||||||||
\(579\) | −14.2565 | − | 3.57113i | −0.592479 | − | 0.148411i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.96077 | + | 18.2960i | 0.371755 | + | 0.759048i | ||||
\(582\) | −13.6412 | − | 3.41699i | −0.565444 | − | 0.141639i | ||||
\(583\) | 35.5901 | 1.47399 | ||||||||
\(584\) | −3.06871 | −0.126984 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 11.2712i | − | 0.465610i | ||||||
\(587\) | −44.1054 | −1.82042 | −0.910212 | − | 0.414143i | \(-0.864081\pi\) | ||||
−0.910212 | + | 0.414143i | \(0.864081\pi\) | |||||||
\(588\) | 9.53778 | − | 7.48537i | 0.393331 | − | 0.308692i | ||||
\(589\) | 25.1660 | 1.03695 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.57551 | + | 30.2425i | −0.311615 | + | 1.24401i | ||||
\(592\) | 10.8127 | 0.444400 | ||||||||
\(593\) | −7.91094 | −0.324863 | −0.162432 | − | 0.986720i | \(-0.551934\pi\) | ||||
−0.162432 | + | 0.986720i | \(0.551934\pi\) | |||||||
\(594\) | 10.8896 | + | 9.87000i | 0.446805 | + | 0.404971i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 3.32941i | − | 0.136378i | ||||||
\(597\) | 6.98233 | − | 27.8745i | 0.285768 | − | 1.14083i | ||||
\(598\) | − | 2.77053i | − | 0.113296i | ||||||
\(599\) | − | 18.2960i | − | 0.747556i | −0.927518 | − | 0.373778i | \(-0.878062\pi\) | ||
0.927518 | − | 0.373778i | \(-0.121938\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0604i | 0.451162i | 0.974224 | + | 0.225581i | \(0.0724281\pi\) | ||||
−0.974224 | + | 0.225581i | \(0.927572\pi\) | |||||||
\(602\) | 11.0604 | − | 5.41699i | 0.450787 | − | 0.220780i | ||||
\(603\) | 12.3157 | + | 6.58301i | 0.501533 | + | 0.268081i | ||||
\(604\) | 22.5830 | 0.918889 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.64575 | + | 6.57008i | −0.0668541 | + | 0.266891i | ||||
\(607\) | − | 23.7608i | − | 0.964421i | −0.876055 | − | 0.482210i | \(-0.839834\pi\) | ||
0.876055 | − | 0.482210i | \(-0.160166\pi\) | |||||||
\(608\) | −4.55066 | −0.184554 | ||||||||
\(609\) | −35.7849 | + | 7.62674i | −1.45008 | + | 0.309051i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.65292i | − | 0.147781i | ||||||
\(612\) | 3.14944 | + | 1.68345i | 0.127309 | + | 0.0680493i | ||||
\(613\) | 40.0990 | 1.61958 | 0.809791 | − | 0.586719i | \(-0.199581\pi\) | ||||
0.809791 | + | 0.586719i | \(0.199581\pi\) | |||||||
\(614\) | −14.8000 | −0.597280 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.29150 | − | 6.72057i | −0.132618 | − | 0.270779i | ||||
\(617\) | 4.83399i | 0.194609i | 0.995255 | + | 0.0973045i | \(0.0310221\pi\) | ||||
−0.995255 | + | 0.0973045i | \(0.968978\pi\) | |||||||
\(618\) | −21.1245 | − | 5.29150i | −0.849751 | − | 0.212855i | ||||
\(619\) | − | 0.632534i | − | 0.0254237i | −0.999919 | − | 0.0127118i | \(-0.995954\pi\) | ||
0.999919 | − | 0.0127118i | \(-0.00404641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.4859 | + | 12.6724i | −0.460915 | + | 0.508528i | ||||
\(622\) | − | 2.77053i | − | 0.111088i | ||||||
\(623\) | −14.9785 | − | 30.5830i | −0.600101 | − | 1.22528i | ||||
\(624\) | 0.354249 | − | 1.41421i | 0.0141813 | − | 0.0566139i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.11905 | 0.324502 | ||||||||
\(627\) | 21.6255 | + | 5.41699i | 0.863637 | + | 0.216334i | ||||
\(628\) | 22.6209i | 0.902672i | ||||||||
\(629\) | −12.8712 | −0.513209 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.4575 | −0.814401 | −0.407200 | − | 0.913339i | \(-0.633495\pi\) | ||||
−0.407200 | + | 0.913339i | \(0.633495\pi\) | |||||||
\(632\) | 7.29150i | 0.290040i | ||||||||
\(633\) | 35.5619 | + | 8.90796i | 1.41346 | + | 0.354060i | ||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.29570 | + | 21.1412i | −0.209988 | + | 0.838304i | ||||
\(637\) | 4.65489 | + | 3.61226i | 0.184433 | + | 0.143123i | ||||
\(638\) | 22.5830i | 0.894070i | ||||||||
\(639\) | 17.8745 | − | 33.4401i | 0.707105 | − | 1.32287i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.7931i | 0.663287i | 0.943405 | + | 0.331644i | \(0.107603\pi\) | ||||
−0.943405 | + | 0.331644i | \(0.892397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 47.7669i | − | 1.88374i | −0.335971 | − | 0.941872i | \(-0.609065\pi\) | ||
0.335971 | − | 0.941872i | \(-0.390935\pi\) | |||||||
\(644\) | 7.82087 | − | 3.83039i | 0.308185 | − | 0.150939i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.41699 | 0.213129 | ||||||||
\(647\) | 15.4002 | 0.605444 | 0.302722 | − | 0.953079i | \(-0.402105\pi\) | ||||
0.302722 | + | 0.953079i | \(0.402105\pi\) | |||||||
\(648\) | −7.48331 | + | 5.00000i | −0.293972 | + | 0.196419i | ||||
\(649\) | − | 11.0604i | − | 0.434158i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.7858 | + | 5.28253i | −0.971434 | + | 0.207039i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 19.1660i | − | 0.750024i | −0.927020 | − | 0.375012i | \(-0.877639\pi\) | ||
0.927020 | − | 0.375012i | \(-0.122361\pi\) | |||||||
\(654\) | −0.841723 | + | 3.36028i | −0.0329140 | + | 0.131397i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.82087 | −0.305354 | ||||||||
\(657\) | −4.33981 | + | 8.11905i | −0.169312 | + | 0.316754i | ||||
\(658\) | 10.3117 | − | 5.05034i | 0.401994 | − | 0.196883i | ||||
\(659\) | 32.7617i | 1.27621i | 0.769948 | + | 0.638107i | \(0.220282\pi\) | ||||
−0.769948 | + | 0.638107i | \(0.779718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.979531i | 0.0380994i | 0.999819 | + | 0.0190497i | \(0.00606407\pi\) | ||||
−0.999819 | + | 0.0190497i | \(0.993936\pi\) | |||||||
\(662\) | − | 8.00000i | − | 0.310929i | ||||||
\(663\) | −0.421689 | + | 1.68345i | −0.0163770 | + | 0.0653796i | ||||
\(664\) | 7.70010i | 0.298822i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.2915 | − | 28.6078i | 0.592534 | − | 1.10853i | ||||
\(667\) | −26.2803 | −1.01758 | ||||||||
\(668\) | −11.4821 | −0.444255 | ||||||||
\(669\) | 2.00000 | − | 7.98430i | 0.0773245 | − | 0.308691i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.5129 | 1.10073 | ||||||||
\(672\) | 4.48191 | − | 0.955218i | 0.172894 | − | 0.0368483i | ||||
\(673\) | −38.5960 | −1.48777 | −0.743883 | − | 0.668309i | \(-0.767018\pi\) | ||||
−0.743883 | + | 0.668309i | \(0.767018\pi\) | |||||||
\(674\) | − | 22.4499i | − | 0.864740i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.2915 | −0.472750 | ||||||||
\(677\) | −42.4933 | −1.63315 | −0.816575 | − | 0.577239i | \(-0.804130\pi\) | ||||
−0.816575 | + | 0.577239i | \(0.804130\pi\) | |||||||
\(678\) | 10.0808 | + | 2.52517i | 0.387153 | + | 0.0969785i | ||||
\(679\) | 19.2915 | − | 9.44832i | 0.740340 | − | 0.362593i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.35425 | + | 0.589720i | 0.0902150 | + | 0.0225981i | ||||
\(682\) | 15.6417i | 0.598953i | ||||||||
\(683\) | − | 5.41699i | − | 0.207276i | −0.994615 | − | 0.103638i | \(-0.966952\pi\) | ||
0.994615 | − | 0.103638i | \(-0.0330483\pi\) | |||||||
\(684\) | −6.43560 | + | 12.0399i | −0.246071 | + | 0.460358i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.76135 | + | 18.1343i | −0.143609 | + | 0.692370i | ||||
\(687\) | 11.9034 | − | 47.5203i | 0.454144 | − | 1.81301i | ||||
\(688\) | 4.65489 | 0.177466 | ||||||||
\(689\) | −10.5914 | −0.403500 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.50972i | 0.247641i | 0.992305 | + | 0.123821i | \(0.0395148\pi\) | ||||
−0.992305 | + | 0.123821i | \(0.960485\pi\) | |||||||
\(692\) | 8.89047 | 0.337965 | ||||||||
\(693\) | −22.4358 | − | 0.795819i | −0.852267 | − | 0.0302306i | ||||
\(694\) | −24.0000 | −0.911028 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.4148 | − | 3.36028i | −0.508485 | − | 0.127371i | ||||
\(697\) | 9.30978 | 0.352633 | ||||||||
\(698\) | 19.1822 | 0.726056 | ||||||||
\(699\) | 1.13990 | − | 4.55066i | 0.0431151 | − | 0.172122i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.32548i | 0.0500626i | 0.999687 | + | 0.0250313i | \(0.00796854\pi\) | ||||
−0.999687 | + | 0.0250313i | \(0.992031\pi\) | |||||||
\(702\) | −3.24067 | − | 2.93725i | −0.122311 | − | 0.110860i | ||||
\(703\) | − | 49.2050i | − | 1.85580i | ||||||
\(704\) | − | 2.82843i | − | 0.106600i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 21.3521i | − | 0.803596i | ||||||
\(707\) | −4.55066 | − | 9.29150i | −0.171145 | − | 0.349443i | ||||
\(708\) | 6.57008 | + | 1.64575i | 0.246919 | + | 0.0618511i | ||||
\(709\) | −20.5830 | −0.773011 | −0.386505 | − | 0.922287i | \(-0.626318\pi\) | ||||
−0.386505 | + | 0.922287i | \(0.626318\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.2915 | + | 10.3117i | 0.723488 | + | 0.386721i | ||||
\(712\) | − | 12.8712i | − | 0.482369i | ||||||
\(713\) | −18.2026 | −0.681694 | ||||||||
\(714\) | −5.33516 | + | 1.13707i | −0.199663 | + | 0.0425537i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 9.48725i | − | 0.354555i | ||||||
\(717\) | 9.31216 | − | 37.1755i | 0.347769 | − | 1.38835i | ||||
\(718\) | −26.7813 | −0.999470 | ||||||||
\(719\) | −36.3338 | −1.35502 | −0.677511 | − | 0.735512i | \(-0.736942\pi\) | ||||
−0.677511 | + | 0.735512i | \(0.736942\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.8745 | − | 14.6315i | 1.11258 | − | 0.544906i | ||||
\(722\) | 1.70850i | 0.0635837i | ||||||||
\(723\) | −0.824494 | + | 3.29150i | −0.0306633 | + | 0.122412i | ||||
\(724\) | − | 12.0399i | − | 0.447460i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.26258 | − | 5.04042i | 0.0468589 | − | 0.187068i | ||||
\(727\) | 7.03196i | 0.260801i | 0.991461 | + | 0.130401i | \(0.0416263\pi\) | ||||
−0.991461 | + | 0.130401i | \(0.958374\pi\) | |||||||
\(728\) | 0.979531 | + | 2.00000i | 0.0363038 | + | 0.0741249i | ||||
\(729\) | 2.64575 | + | 26.8701i | 0.0979908 | + | 0.995187i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.54107 | −0.204944 | ||||||||
\(732\) | −4.24264 | + | 16.9373i | −0.156813 | + | 0.626019i | ||||
\(733\) | 24.9007i | 0.919728i | 0.887989 | + | 0.459864i | \(0.152102\pi\) | ||||
−0.887989 | + | 0.459864i | \(0.847898\pi\) | |||||||
\(734\) | −8.11905 | −0.299680 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.29150 | 0.121326 | ||||||||
\(737\) | 13.1660i | 0.484976i | ||||||||
\(738\) | −11.0604 | + | 20.6921i | −0.407138 | + | 0.761686i | ||||
\(739\) | −9.16601 | −0.337177 | −0.168589 | − | 0.985687i | \(-0.553921\pi\) | ||||
−0.168589 | + | 0.985687i | \(0.553921\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.43560 | − | 1.61206i | −0.236418 | − | 0.0592207i | ||||
\(742\) | −14.6431 | − | 29.8982i | −0.537566 | − | 1.09760i | ||||
\(743\) | 33.8745i | 1.24274i | 0.783519 | + | 0.621368i | \(0.213423\pi\) | ||||
−0.783519 | + | 0.621368i | \(0.786577\pi\) | |||||||
\(744\) | −9.29150 | − | 2.32744i | −0.340643 | − | 0.0853282i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.4676i | 0.566310i | ||||||||
\(747\) | 20.3725 | + | 10.8896i | 0.745392 | + | 0.398429i | ||||
\(748\) | 3.36689i | 0.123106i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.1660 | 0.772359 | 0.386179 | − | 0.922424i | \(-0.373795\pi\) | ||||
0.386179 | + | 0.922424i | \(0.373795\pi\) | |||||||
\(752\) | 4.33981 | 0.158257 | ||||||||
\(753\) | −19.7103 | − | 4.93725i | −0.718282 | − | 0.179924i | ||||
\(754\) | − | 6.72057i | − | 0.244749i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.81112 | − | 13.2089i | 0.138609 | − | 0.480404i | ||||
\(757\) | −3.15194 | −0.114559 | −0.0572796 | − | 0.998358i | \(-0.518243\pi\) | ||||
−0.0572796 | + | 0.998358i | \(0.518243\pi\) | |||||||
\(758\) | 14.5830i | 0.529679i | ||||||||
\(759\) | −15.6417 | − | 3.91813i | −0.567759 | − | 0.142219i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.6921 | −0.750087 | −0.375044 | − | 0.927007i | \(-0.622372\pi\) | ||||
−0.375044 | + | 0.927007i | \(0.622372\pi\) | |||||||
\(762\) | −4.55066 | + | 18.1669i | −0.164853 | + | 0.658118i | ||||
\(763\) | −2.32744 | − | 4.75216i | −0.0842591 | − | 0.172040i | ||||
\(764\) | 7.98430i | 0.288862i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.4821i | 0.414864i | ||||||||
\(767\) | 3.29150i | 0.118849i | ||||||||
\(768\) | 1.68014 | + | 0.420861i | 0.0606269 | + | 0.0151865i | ||||
\(769\) | 35.1402i | 1.26719i | 0.773666 | + | 0.633594i | \(0.218421\pi\) | ||||
−0.773666 | + | 0.633594i | \(0.781579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.8745 | − | 5.98036i | −0.859819 | − | 0.215378i | ||||
\(772\) | 8.48528 | 0.305392 | ||||||||
\(773\) | 7.35310 | 0.264473 | 0.132236 | − | 0.991218i | \(-0.457784\pi\) | ||||
0.132236 | + | 0.991218i | \(0.457784\pi\) | |||||||
\(774\) | 6.58301 | − | 12.3157i | 0.236621 | − | 0.442678i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.11905 | 0.291457 | ||||||||
\(777\) | 10.3285 | + | 48.4617i | 0.370533 | + | 1.73855i | ||||
\(778\) | 0.323511 | 0.0115984 | ||||||||
\(779\) | 35.5901i | 1.27515i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.7490 | 1.27920 | ||||||||
\(782\) | −3.91813 | −0.140112 | ||||||||
\(783\) | −27.8618 | + | 30.7399i | −0.995699 | + | 1.09856i | ||||
\(784\) | −4.29150 | + | 5.53019i | −0.153268 | + | 0.197507i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.77124 | + | 15.0554i | −0.134516 | + | 0.537007i | ||||
\(787\) | − | 24.9007i | − | 0.887614i | −0.896122 | − | 0.443807i | \(-0.853628\pi\) | ||
0.896122 | − | 0.443807i | \(-0.146372\pi\) | |||||||
\(788\) | − | 18.0000i | − | 0.641223i | ||||||
\(789\) | −2.77053 | + | 11.0604i | −0.0986336 | + | 0.393760i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.2565 | + | 6.98233i | −0.506902 | + | 0.248263i | ||||
\(792\) | −7.48331 | − | 4.00000i | −0.265908 | − | 0.142134i | ||||
\(793\) | −8.48528 | −0.301321 | ||||||||
\(794\) | 21.5338 | 0.764206 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.5906i | 0.588037i | ||||||||
\(797\) | 6.93141 | 0.245523 | 0.122762 | − | 0.992436i | \(-0.460825\pi\) | ||||
0.122762 | + | 0.992436i | \(0.460825\pi\) | |||||||
\(798\) | −4.34687 | − | 20.3957i | −0.153878 | − | 0.721999i | ||||
\(799\) | −5.16601 | −0.182760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −34.0540 | − | 18.2026i | −1.20324 | − | 0.643159i | ||||
\(802\) | 7.48331 | 0.264245 | ||||||||
\(803\) | −8.67963 | −0.306297 | ||||||||
\(804\) | −7.82087 | − | 1.95906i | −0.275821 | − | 0.0690908i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 4.65489i | − | 0.163961i | ||||||
\(807\) | −41.3357 | − | 10.3542i | −1.45509 | − | 0.364487i | ||||
\(808\) | − | 3.91044i | − | 0.137569i | ||||||
\(809\) | − | 33.7637i | − | 1.18707i | −0.804809 | − | 0.593533i | \(-0.797732\pi\) | ||
0.804809 | − | 0.593533i | \(-0.202268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.6305i | 1.00535i | 0.864475 | + | 0.502676i | \(0.167651\pi\) | ||||
−0.864475 | + | 0.502676i | \(0.832349\pi\) | |||||||
\(812\) | 18.9713 | − | 9.29150i | 0.665763 | − | 0.326068i | ||||
\(813\) | 3.15194 | − | 12.5830i | 0.110543 | − | 0.441305i | ||||
\(814\) | 30.5830 | 1.07193 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00000 | − | 0.500983i | −0.0700140 | − | 0.0175379i | ||||
\(817\) | − | 21.1828i | − | 0.741093i | ||||||
\(818\) | −13.0194 | −0.455214 | ||||||||
\(819\) | 6.67677 | + | 0.236831i | 0.233305 | + | 0.00827554i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.98036i | 0.208716i | 0.994540 | + | 0.104358i | \(0.0332788\pi\) | ||||
−0.994540 | + | 0.104358i | \(0.966721\pi\) | |||||||
\(822\) | −15.6110 | − | 3.91044i | −0.544498 | − | 0.136392i | ||||
\(823\) | −19.2980 | −0.672686 | −0.336343 | − | 0.941740i | \(-0.609190\pi\) | ||||
−0.336343 | + | 0.941740i | \(0.609190\pi\) | |||||||
\(824\) | 12.5730 | 0.438002 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.29150 | + | 4.55066i | −0.323293 | + | 0.158338i | ||||
\(827\) | 36.0000i | 1.25184i | 0.779886 | + | 0.625921i | \(0.215277\pi\) | ||||
−0.779886 | + | 0.625921i | \(0.784723\pi\) | |||||||
\(828\) | 4.65489 | − | 8.70850i | 0.161769 | − | 0.302641i | ||||
\(829\) | 45.2211i | 1.57059i | 0.619120 | + | 0.785296i | \(0.287489\pi\) | ||||
−0.619120 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.9878 | − | 6.50972i | −0.901506 | − | 0.225820i | ||||
\(832\) | 0.841723i | 0.0291815i | ||||||||
\(833\) | 5.10850 | − | 6.58301i | 0.176999 | − | 0.228088i | ||||
\(834\) | 26.2288 | + | 6.57008i | 0.908228 | + | 0.227503i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.8712 | −0.445160 | ||||||||
\(837\) | −19.2980 | + | 21.2915i | −0.667037 | + | 0.735942i | ||||
\(838\) | − | 21.8320i | − | 0.754173i | ||||||
\(839\) | 26.2331 | 0.905669 | 0.452834 | − | 0.891595i | \(-0.350413\pi\) | ||||
0.452834 | + | 0.891595i | \(0.350413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.7490 | −1.19824 | ||||||||
\(842\) | 10.0000i | 0.344623i | ||||||||
\(843\) | −8.67963 | + | 34.6504i | −0.298942 | + | 1.19342i | ||||
\(844\) | −21.1660 | −0.728564 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.13742 | − | 11.4821i | 0.211009 | − | 0.394762i | ||||
\(847\) | 3.49117 | + | 7.12824i | 0.119958 | + | 0.244929i | ||||
\(848\) | − | 12.5830i | − | 0.432102i | ||||||
\(849\) | −4.10326 | + | 16.3808i | −0.140824 | + | 0.562189i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.5901i | 1.22001i | ||||||||
\(852\) | −5.31935 | + | 21.2356i | −0.182238 | + | 0.727520i | ||||
\(853\) | − | 5.89206i | − | 0.201740i | −0.994900 | − | 0.100870i | \(-0.967837\pi\) | ||
0.994900 | − | 0.100870i | \(-0.0321627\pi\) | |||||||
\(854\) | −11.7313 | − | 23.9529i | −0.401437 | − | 0.819651i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.1545 | 0.825103 | 0.412551 | − | 0.910934i | \(-0.364638\pi\) | ||||
0.412551 | + | 0.910934i | \(0.364638\pi\) | |||||||
\(858\) | 1.00197 | − | 4.00000i | 0.0342066 | − | 0.136558i | ||||
\(859\) | − | 2.59160i | − | 0.0884241i | −0.999022 | − | 0.0442121i | \(-0.985922\pi\) | ||
0.999022 | − | 0.0442121i | \(-0.0140777\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.47063 | − | 35.0525i | −0.254598 | − | 1.19459i | ||||
\(862\) | −16.4696 | −0.560956 | ||||||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 3.48957 | − | 3.85005i | 0.118718 | − | 0.130981i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.5313 | 0.901571 | ||||||||
\(867\) | −26.1817 | − | 6.55829i | −0.889176 | − | 0.222731i | ||||
\(868\) | 13.1402 | − | 6.43560i | 0.446006 | − | 0.218439i | ||||
\(869\) | 20.6235i | 0.699604i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.91813i | − | 0.132761i | ||||||
\(872\) | − | 2.00000i | − | 0.0677285i | ||||||
\(873\) | 11.4821 | − | 21.4810i | 0.388609 | − | 0.727021i | ||||
\(874\) | − | 14.9785i | − | 0.506656i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.29150 | − | 5.15587i | 0.0436358 | − | 0.174201i | ||||
\(877\) | 1.50295 | 0.0507510 | 0.0253755 | − | 0.999678i | \(-0.491922\pi\) | ||||
0.0253755 | + | 0.999678i | \(0.491922\pi\) | |||||||
\(878\) | −18.5496 | −0.626020 | ||||||||
\(879\) | 18.9373 | + | 4.74362i | 0.638738 | + | 0.159998i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.8712 | −0.433642 | −0.216821 | − | 0.976211i | \(-0.569569\pi\) | ||||
−0.216821 | + | 0.976211i | \(0.569569\pi\) | |||||||
\(882\) | 8.56241 | + | 19.1751i | 0.288311 | + | 0.645660i | ||||
\(883\) | 13.9647 | 0.469948 | 0.234974 | − | 0.972002i | \(-0.424499\pi\) | ||||
0.234974 | + | 0.972002i | \(0.424499\pi\) | |||||||
\(884\) | − | 1.00197i | − | 0.0336998i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.1660 | −0.442321 | ||||||||
\(887\) | 44.6632 | 1.49964 | 0.749822 | − | 0.661640i | \(-0.230139\pi\) | ||||
0.749822 | + | 0.661640i | \(0.230139\pi\) | |||||||
\(888\) | −4.55066 | + | 18.1669i | −0.152710 | + | 0.609642i | ||||
\(889\) | −12.5830 | − | 25.6919i | −0.422020 | − | 0.861678i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.1660 | + | 14.1421i | −0.709088 | + | 0.473779i | ||||
\(892\) | 4.75216i | 0.159114i | ||||||||
\(893\) | − | 19.7490i | − | 0.660876i | ||||||
\(894\) | 5.59388 | + | 1.40122i | 0.187087 | + | 0.0468638i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.37608 | + | 1.16372i | −0.0793792 | + | 0.0388772i | ||||
\(897\) | 4.65489 | + | 1.16601i | 0.155422 | + | 0.0389320i | ||||
\(898\) | −8.30781 | −0.277235 | ||||||||
\(899\) | −44.1547 | −1.47264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.9785i | 0.499006i | ||||||||
\(902\) | −22.1208 | −0.736541 | ||||||||
\(903\) | 4.44643 | + | 20.8628i | 0.147968 | + | 0.694271i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.50432 | + | 37.9426i | −0.315760 | + | 1.26056i | ||||
\(907\) | −33.9411 | −1.12700 | −0.563498 | − | 0.826117i | \(-0.690545\pi\) | ||||
−0.563498 | + | 0.826117i | \(0.690545\pi\) | |||||||
\(908\) | −1.40122 | −0.0465011 | ||||||||
\(909\) | −10.3460 | − | 5.53019i | −0.343156 | − | 0.183425i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.15390i | − | 0.137625i | −0.997630 | − | 0.0688125i | \(-0.978079\pi\) | ||
0.997630 | − | 0.0688125i | \(-0.0219210\pi\) | |||||||
\(912\) | 1.91520 | − | 7.64575i | 0.0634185 | − | 0.253176i | ||||
\(913\) | 21.7792i | 0.720785i | ||||||||
\(914\) | 8.48528i | 0.280668i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.2835i | 0.934513i | ||||||||
\(917\) | −10.4278 | − | 21.2915i | −0.344358 | − | 0.703107i | ||||
\(918\) | −4.15390 | + | 4.58301i | −0.137099 | + | 0.151262i | ||||
\(919\) | −10.1255 | −0.334009 | −0.167005 | − | 0.985956i | \(-0.553409\pi\) | ||||
−0.167005 | + | 0.985956i | \(0.553409\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.22876 | − | 24.8661i | 0.205245 | − | 0.819367i | ||||
\(922\) | − | 8.96077i | − | 0.295107i | ||||||
\(923\) | −10.6387 | −0.350177 | ||||||||
\(924\) | 12.6768 | − | 2.70176i | 0.417035 | − | 0.0888815i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 23.9529i | − | 0.787141i | ||||||
\(927\) | 17.7809 | − | 33.2651i | 0.584003 | − | 1.09257i | ||||
\(928\) | 7.98430 | 0.262097 | ||||||||
\(929\) | 30.7928 | 1.01028 | 0.505139 | − | 0.863038i | \(-0.331441\pi\) | ||||
0.505139 | + | 0.863038i | \(0.331441\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.1660 | + | 19.5292i | 0.824783 | + | 0.640043i | ||||
\(932\) | 2.70850i | 0.0887198i | ||||||||
\(933\) | 4.65489 | + | 1.16601i | 0.152394 | + | 0.0381735i | ||||
\(934\) | − | 3.36028i | − | 0.109952i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.22699 | + | 1.19038i | 0.0727914 | + | 0.0389087i | ||||
\(937\) | − | 3.06871i | − | 0.100250i | −0.998743 | − | 0.0501252i | \(-0.984038\pi\) | ||
0.998743 | − | 0.0501252i | \(-0.0159620\pi\) | |||||||
\(938\) | 11.0604 | − | 5.41699i | 0.361134 | − | 0.176871i | ||||
\(939\) | −3.41699 | + | 13.6412i | −0.111509 | + | 0.445162i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.2443 | 1.31193 | 0.655963 | − | 0.754793i | \(-0.272263\pi\) | ||||
0.655963 | + | 0.754793i | \(0.272263\pi\) | |||||||
\(942\) | −38.0063 | − | 9.52026i | −1.23831 | − | 0.310187i | ||||
\(943\) | − | 25.7424i | − | 0.838288i | ||||||
\(944\) | −3.91044 | −0.127274 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.1660 | 0.428064 | ||||||||
\(947\) | 24.0000i | 0.779895i | 0.920837 | + | 0.389948i | \(0.127507\pi\) | ||||
−0.920837 | + | 0.389948i | \(0.872493\pi\) | |||||||
\(948\) | −12.2508 | − | 3.06871i | −0.397886 | − | 0.0996671i | ||||
\(949\) | 2.58301 | 0.0838479 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.52517 | + | 10.0808i | −0.0818842 | + | 0.326894i | ||||
\(952\) | 2.82843 | − | 1.38527i | 0.0916698 | − | 0.0448967i | ||||
\(953\) | 27.8745i | 0.902944i | 0.892285 | + | 0.451472i | \(0.149101\pi\) | ||||
−0.892285 | + | 0.451472i | \(0.850899\pi\) | |||||||
\(954\) | −33.2915 | − | 17.7951i | −1.07785 | − | 0.576136i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.1264i | 0.715620i | ||||||||
\(957\) | −37.9426 | − | 9.50432i | −1.22651 | − | 0.307231i | ||||
\(958\) | − | 39.1044i | − | 1.26340i | ||||||
\(959\) | 22.0773 | − | 10.8127i | 0.712915 | − | 0.349161i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.416995 | 0.0134514 | ||||||||
\(962\) | −9.10132 | −0.293438 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.95906i | − | 0.0630972i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.14410 | + | 14.7522i | 0.101160 | + | 0.474645i | ||||
\(967\) | −49.4087 | −1.58888 | −0.794439 | − | 0.607344i | \(-0.792235\pi\) | ||||
−0.794439 | + | 0.607344i | \(0.792235\pi\) | |||||||
\(968\) | 3.00000i | 0.0964237i | ||||||||
\(969\) | −2.27980 | + | 9.10132i | −0.0732379 | + | 0.292376i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.6025 | 0.789532 | 0.394766 | − | 0.918782i | \(-0.370826\pi\) | ||||
0.394766 | + | 0.918782i | \(0.370826\pi\) | |||||||
\(972\) | −5.25127 | − | 14.6773i | −0.168435 | − | 0.470776i | ||||
\(973\) | −37.0931 | + | 18.1669i | −1.18915 | + | 0.582404i | ||||
\(974\) | − | 32.4382i | − | 1.03939i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 10.0808i | − | 0.322680i | ||||||
\(977\) | − | 51.8745i | − | 1.65961i | −0.558052 | − | 0.829806i | \(-0.688451\pi\) | ||
0.558052 | − | 0.829806i | \(-0.311549\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 36.4053i | − | 1.16352i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.29150 | − | 2.82843i | −0.168945 | − | 0.0903047i | ||||
\(982\) | −14.1421 | −0.451294 | ||||||||
\(983\) | 62.0225 | 1.97821 | 0.989105 | − | 0.147213i | \(-0.0470304\pi\) | ||||
0.989105 | + | 0.147213i | \(0.0470304\pi\) | |||||||
\(984\) | 3.29150 | − | 13.1402i | 0.104929 | − | 0.418893i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.50432 | −0.302679 | ||||||||
\(987\) | 4.14547 | + | 19.4507i | 0.131952 | + | 0.619122i | ||||
\(988\) | 3.83039 | 0.121861 | ||||||||
\(989\) | 15.3216i | 0.487198i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.708497 | −0.0225062 | −0.0112531 | − | 0.999937i | \(-0.503582\pi\) | ||||
−0.0112531 | + | 0.999937i | \(0.503582\pi\) | |||||||
\(992\) | 5.53019 | 0.175584 | ||||||||
\(993\) | 13.4411 | + | 3.36689i | 0.426541 | + | 0.106845i | ||||
\(994\) | −14.7085 | − | 30.0317i | −0.466525 | − | 0.952548i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.9373 | − | 3.24067i | −0.409933 | − | 0.102685i | ||||
\(997\) | 42.2259i | 1.33731i | 0.743574 | + | 0.668653i | \(0.233129\pi\) | ||||
−0.743574 | + | 0.668653i | \(0.766871\pi\) | |||||||
\(998\) | 1.41699i | 0.0448542i | ||||||||
\(999\) | 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 | 1050.2.b.f.251.8 | 16 | ||
3.2 | odd | 2 | inner | 1050.2.b.f.251.10 | 16 | ||
5.2 | odd | 4 | 210.2.d.b.209.5 | yes | 8 | ||
5.3 | odd | 4 | 210.2.d.a.209.4 | yes | 8 | ||
5.4 | even | 2 | inner | 1050.2.b.f.251.9 | 16 | ||
7.6 | odd | 2 | inner | 1050.2.b.f.251.1 | 16 | ||
15.2 | even | 4 | 210.2.d.a.209.6 | yes | 8 | ||
15.8 | even | 4 | 210.2.d.b.209.3 | yes | 8 | ||
15.14 | odd | 2 | inner | 1050.2.b.f.251.7 | 16 | ||
20.3 | even | 4 | 1680.2.k.e.209.5 | 8 | |||
20.7 | even | 4 | 1680.2.k.f.209.4 | 8 | |||
21.20 | even | 2 | inner | 1050.2.b.f.251.15 | 16 | ||
35.13 | even | 4 | 210.2.d.a.209.5 | yes | 8 | ||
35.27 | even | 4 | 210.2.d.b.209.4 | yes | 8 | ||
35.34 | odd | 2 | inner | 1050.2.b.f.251.16 | 16 | ||
60.23 | odd | 4 | 1680.2.k.f.209.6 | 8 | |||
60.47 | odd | 4 | 1680.2.k.e.209.3 | 8 | |||
105.62 | odd | 4 | 210.2.d.a.209.3 | ✓ | 8 | ||
105.83 | odd | 4 | 210.2.d.b.209.6 | yes | 8 | ||
105.104 | even | 2 | inner | 1050.2.b.f.251.2 | 16 | ||
140.27 | odd | 4 | 1680.2.k.f.209.5 | 8 | |||
140.83 | odd | 4 | 1680.2.k.e.209.4 | 8 | |||
420.83 | even | 4 | 1680.2.k.f.209.3 | 8 | |||
420.167 | even | 4 | 1680.2.k.e.209.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.d.a.209.3 | ✓ | 8 | 105.62 | odd | 4 | ||
210.2.d.a.209.4 | yes | 8 | 5.3 | odd | 4 | ||
210.2.d.a.209.5 | yes | 8 | 35.13 | even | 4 | ||
210.2.d.a.209.6 | yes | 8 | 15.2 | even | 4 | ||
210.2.d.b.209.3 | yes | 8 | 15.8 | even | 4 | ||
210.2.d.b.209.4 | yes | 8 | 35.27 | even | 4 | ||
210.2.d.b.209.5 | yes | 8 | 5.2 | odd | 4 | ||
210.2.d.b.209.6 | yes | 8 | 105.83 | odd | 4 | ||
1050.2.b.f.251.1 | 16 | 7.6 | odd | 2 | inner | ||
1050.2.b.f.251.2 | 16 | 105.104 | even | 2 | inner | ||
1050.2.b.f.251.7 | 16 | 15.14 | odd | 2 | inner | ||
1050.2.b.f.251.8 | 16 | 1.1 | even | 1 | trivial | ||
1050.2.b.f.251.9 | 16 | 5.4 | even | 2 | inner | ||
1050.2.b.f.251.10 | 16 | 3.2 | odd | 2 | inner | ||
1050.2.b.f.251.15 | 16 | 21.20 | even | 2 | inner | ||
1050.2.b.f.251.16 | 16 | 35.34 | odd | 2 | inner | ||
1680.2.k.e.209.3 | 8 | 60.47 | odd | 4 | |||
1680.2.k.e.209.4 | 8 | 140.83 | odd | 4 | |||
1680.2.k.e.209.5 | 8 | 20.3 | even | 4 | |||
1680.2.k.e.209.6 | 8 | 420.167 | even | 4 | |||
1680.2.k.f.209.3 | 8 | 420.83 | even | 4 | |||
1680.2.k.f.209.4 | 8 | 20.7 | even | 4 | |||
1680.2.k.f.209.5 | 8 | 140.27 | odd | 4 | |||
1680.2.k.f.209.6 | 8 | 60.23 | odd | 4 |