Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 793.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.793 |
Dual form | 1386.2.k.t.991.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.292893 | + | 0.507306i | −0.130986 | + | 0.226874i | −0.924057 | − | 0.382255i | \(-0.875148\pi\) |
0.793071 | + | 0.609129i | \(0.208481\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62132 | + | 2.09077i | 0.612801 | + | 0.790237i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.292893 | + | 0.507306i | 0.0926210 | + | 0.160424i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.82843 | −1.06181 | −0.530907 | − | 0.847430i | \(-0.678149\pi\) | ||||
−0.530907 | + | 0.847430i | \(0.678149\pi\) | |||||||
\(14\) | 2.62132 | − | 0.358719i | 0.700577 | − | 0.0958718i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.82843 | + | 3.16693i | 0.443459 | + | 0.768093i | 0.997943 | − | 0.0641009i | \(-0.0204179\pi\) |
−0.554485 | + | 0.832194i | \(0.687085\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.292893 | − | 0.507306i | 0.0671943 | − | 0.116384i | −0.830471 | − | 0.557062i | \(-0.811929\pi\) |
0.897665 | + | 0.440678i | \(0.145262\pi\) | |||||||
\(20\) | 0.585786 | 0.130986 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −3.12132 | + | 5.40629i | −0.650840 | + | 1.12729i | 0.332079 | + | 0.943252i | \(0.392250\pi\) |
−0.982919 | + | 0.184037i | \(0.941083\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.32843 | + | 4.03295i | 0.465685 | + | 0.806591i | ||||
\(26\) | −1.91421 | + | 3.31552i | −0.375408 | + | 0.650226i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | − | 2.44949i | 0.188982 | − | 0.462910i | ||||
\(29\) | −2.65685 | −0.493365 | −0.246683 | − | 0.969096i | \(-0.579341\pi\) | ||||
−0.246683 | + | 0.969096i | \(0.579341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.65685 | 0.627145 | ||||||||
\(35\) | −1.53553 | + | 0.210133i | −0.259553 | + | 0.0355190i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.70711 | − | 8.15295i | 0.773844 | − | 1.34034i | −0.161599 | − | 0.986857i | \(-0.551665\pi\) |
0.935442 | − | 0.353480i | \(-0.115002\pi\) | |||||||
\(38\) | −0.292893 | − | 0.507306i | −0.0475136 | − | 0.0822959i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.292893 | − | 0.507306i | 0.0463105 | − | 0.0802121i | ||||
\(41\) | 5.41421 | 0.845558 | 0.422779 | − | 0.906233i | \(-0.361055\pi\) | ||||
0.422779 | + | 0.906233i | \(0.361055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.65685 | −0.862662 | −0.431331 | − | 0.902194i | \(-0.641956\pi\) | ||||
−0.431331 | + | 0.902194i | \(0.641956\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.12132 | + | 5.40629i | 0.460214 | + | 0.797113i | ||||
\(47\) | −5.24264 | + | 9.08052i | −0.764718 | + | 1.32453i | 0.175678 | + | 0.984448i | \(0.443788\pi\) |
−0.940396 | + | 0.340082i | \(0.889545\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | 4.65685 | 0.658579 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.91421 | + | 3.31552i | 0.265454 | + | 0.459779i | ||||
\(53\) | 3.94975 | + | 6.84116i | 0.542540 | + | 0.939706i | 0.998757 | + | 0.0498379i | \(0.0158705\pi\) |
−0.456218 | + | 0.889868i | \(0.650796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.585786 | −0.0789874 | ||||||||
\(56\) | −1.62132 | − | 2.09077i | −0.216658 | − | 0.279391i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.32843 | + | 2.30090i | −0.174431 | + | 0.302123i | ||||
\(59\) | −2.79289 | − | 4.83743i | −0.363604 | − | 0.629780i | 0.624947 | − | 0.780667i | \(-0.285120\pi\) |
−0.988551 | + | 0.150887i | \(0.951787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.91421 | + | 10.2437i | −0.757237 | + | 1.31157i | 0.187017 | + | 0.982357i | \(0.440118\pi\) |
−0.944254 | + | 0.329217i | \(0.893215\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.12132 | − | 1.94218i | 0.139083 | − | 0.240898i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.37868 | − | 2.38794i | −0.168433 | − | 0.291734i | 0.769436 | − | 0.638723i | \(-0.220537\pi\) |
−0.937869 | + | 0.346990i | \(0.887204\pi\) | |||||||
\(68\) | 1.82843 | − | 3.16693i | 0.221729 | − | 0.384047i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.585786 | + | 1.43488i | −0.0700149 | + | 0.171501i | ||||
\(71\) | 11.0711 | 1.31389 | 0.656947 | − | 0.753937i | \(-0.271848\pi\) | ||||
0.656947 | + | 0.753937i | \(0.271848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.70711 | + | 8.15295i | 0.550925 | + | 0.954230i | 0.998208 | + | 0.0598379i | \(0.0190584\pi\) |
−0.447283 | + | 0.894393i | \(0.647608\pi\) | |||||||
\(74\) | −4.70711 | − | 8.15295i | −0.547190 | − | 0.947761i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.585786 | −0.0671943 | ||||||||
\(77\) | −1.00000 | + | 2.44949i | −0.113961 | + | 0.279145i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.62132 | − | 11.4685i | 0.744957 | − | 1.29030i | −0.205258 | − | 0.978708i | \(-0.565803\pi\) |
0.950215 | − | 0.311595i | \(-0.100863\pi\) | |||||||
\(80\) | −0.292893 | − | 0.507306i | −0.0327465 | − | 0.0567185i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.70711 | − | 4.68885i | 0.298950 | − | 0.517796i | ||||
\(83\) | 12.1421 | 1.33277 | 0.666386 | − | 0.745607i | \(-0.267840\pi\) | ||||
0.666386 | + | 0.745607i | \(0.267840\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.14214 | −0.232347 | ||||||||
\(86\) | −2.82843 | + | 4.89898i | −0.304997 | + | 0.528271i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 6.24264 | − | 10.8126i | 0.661719 | − | 1.14613i | −0.318445 | − | 0.947941i | \(-0.603161\pi\) |
0.980164 | − | 0.198189i | \(-0.0635060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.20711 | − | 8.00436i | −0.650682 | − | 0.839085i | ||||
\(92\) | 6.24264 | 0.650840 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.24264 | + | 9.08052i | 0.540737 | + | 0.936584i | ||||
\(95\) | 0.171573 | + | 0.297173i | 0.0176030 | + | 0.0304893i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.82843 | −0.388718 | −0.194359 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194359 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(98\) | 5.00000 | + | 4.89898i | 0.505076 | + | 0.494872i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.32843 | − | 4.03295i | 0.232843 | − | 0.403295i | ||||
\(101\) | 3.08579 | + | 5.34474i | 0.307047 | + | 0.531821i | 0.977715 | − | 0.209936i | \(-0.0673257\pi\) |
−0.670668 | + | 0.741758i | \(0.733992\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.70711 | + | 11.6170i | −0.660871 | + | 1.14466i | 0.319516 | + | 0.947581i | \(0.396480\pi\) |
−0.980387 | + | 0.197081i | \(0.936854\pi\) | |||||||
\(104\) | 3.82843 | 0.375408 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.89949 | 0.767267 | ||||||||
\(107\) | −1.53553 | + | 2.65962i | −0.148446 | + | 0.257115i | −0.930653 | − | 0.365903i | \(-0.880760\pi\) |
0.782207 | + | 0.623018i | \(0.214094\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.24264 | − | 14.2767i | −0.789502 | − | 1.36746i | −0.926272 | − | 0.376854i | \(-0.877006\pi\) |
0.136771 | − | 0.990603i | \(-0.456328\pi\) | |||||||
\(110\) | −0.292893 | + | 0.507306i | −0.0279263 | + | 0.0483697i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.62132 | + | 0.358719i | −0.247691 | + | 0.0338958i | ||||
\(113\) | 8.17157 | 0.768717 | 0.384358 | − | 0.923184i | \(-0.374423\pi\) | ||||
0.384358 | + | 0.923184i | \(0.374423\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.82843 | − | 3.16693i | −0.170502 | − | 0.295318i | ||||
\(116\) | 1.32843 | + | 2.30090i | 0.123341 | + | 0.213634i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.58579 | −0.514213 | ||||||||
\(119\) | −3.65685 | + | 8.95743i | −0.335223 | + | 0.821126i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 5.91421 | + | 10.2437i | 0.535448 | + | 0.927423i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.7279 | 1.39563 | 0.697814 | − | 0.716279i | \(-0.254156\pi\) | ||||
0.697814 | + | 0.716279i | \(0.254156\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.12132 | − | 1.94218i | −0.0983463 | − | 0.170341i | ||||
\(131\) | −0.292893 | + | 0.507306i | −0.0255902 | + | 0.0443235i | −0.878537 | − | 0.477674i | \(-0.841480\pi\) |
0.852947 | + | 0.521998i | \(0.174813\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.53553 | − | 0.210133i | 0.133148 | − | 0.0182208i | ||||
\(134\) | −2.75736 | −0.238200 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.82843 | − | 3.16693i | −0.156786 | − | 0.271562i | ||||
\(137\) | −8.32843 | − | 14.4253i | −0.711546 | − | 1.23243i | −0.964277 | − | 0.264897i | \(-0.914662\pi\) |
0.252731 | − | 0.967537i | \(-0.418671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0.949747 | + | 1.22474i | 0.0802683 | + | 0.103510i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.53553 | − | 9.58783i | 0.464532 | − | 0.804592i | ||||
\(143\) | −1.91421 | − | 3.31552i | −0.160075 | − | 0.277257i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.778175 | − | 1.34784i | 0.0646239 | − | 0.111932i | ||||
\(146\) | 9.41421 | 0.779126 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.41421 | −0.773844 | ||||||||
\(149\) | 8.82843 | − | 15.2913i | 0.723253 | − | 1.25271i | −0.236436 | − | 0.971647i | \(-0.575979\pi\) |
0.959689 | − | 0.281064i | \(-0.0906873\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.86396 | + | 13.6208i | 0.639960 | + | 1.10844i | 0.985441 | + | 0.170018i | \(0.0543825\pi\) |
−0.345481 | + | 0.938426i | \(0.612284\pi\) | |||||||
\(152\) | −0.292893 | + | 0.507306i | −0.0237568 | + | 0.0411479i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.62132 | + | 2.09077i | 0.130650 | + | 0.168479i | ||||
\(155\) | −2.34315 | −0.188206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.82843 | − | 15.2913i | −0.704585 | − | 1.22038i | −0.966841 | − | 0.255379i | \(-0.917800\pi\) |
0.262256 | − | 0.964998i | \(-0.415534\pi\) | |||||||
\(158\) | −6.62132 | − | 11.4685i | −0.526764 | − | 0.912382i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.585786 | −0.0463105 | ||||||||
\(161\) | −16.3640 | + | 2.23936i | −1.28966 | + | 0.176486i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.86396 | + | 8.42463i | −0.380975 | + | 0.659868i | −0.991202 | − | 0.132359i | \(-0.957745\pi\) |
0.610227 | + | 0.792227i | \(0.291078\pi\) | |||||||
\(164\) | −2.70711 | − | 4.68885i | −0.211390 | − | 0.366137i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.07107 | − | 10.5154i | 0.471206 | − | 0.816153i | ||||
\(167\) | −13.7279 | −1.06230 | −0.531149 | − | 0.847278i | \(-0.678240\pi\) | ||||
−0.531149 | + | 0.847278i | \(0.678240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.65685 | 0.127450 | ||||||||
\(170\) | −1.07107 | + | 1.85514i | −0.0821472 | + | 0.142283i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.82843 | + | 4.89898i | 0.215666 | + | 0.373544i | ||||
\(173\) | −4.91421 | + | 8.51167i | −0.373621 | + | 0.647130i | −0.990120 | − | 0.140226i | \(-0.955217\pi\) |
0.616499 | + | 0.787356i | \(0.288551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.65685 | + | 11.4069i | −0.352025 | + | 0.862282i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.24264 | − | 10.8126i | −0.467906 | − | 0.810436i | ||||
\(179\) | 0.449747 | + | 0.778985i | 0.0336157 | + | 0.0582241i | 0.882344 | − | 0.470605i | \(-0.155964\pi\) |
−0.848728 | + | 0.528829i | \(0.822631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.65685 | −0.569129 | −0.284565 | − | 0.958657i | \(-0.591849\pi\) | ||||
−0.284565 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(182\) | −10.0355 | + | 1.37333i | −0.743883 | + | 0.101798i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.12132 | − | 5.40629i | 0.230107 | − | 0.398557i | ||||
\(185\) | 2.75736 | + | 4.77589i | 0.202725 | + | 0.351130i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.82843 | + | 3.16693i | −0.133708 | + | 0.231589i | ||||
\(188\) | 10.4853 | 0.764718 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.343146 | 0.0248944 | ||||||||
\(191\) | −3.58579 | + | 6.21076i | −0.259458 | + | 0.449395i | −0.966097 | − | 0.258180i | \(-0.916877\pi\) |
0.706639 | + | 0.707575i | \(0.250211\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9497 | − | 18.9655i | −0.788180 | − | 1.36517i | −0.927081 | − | 0.374862i | \(-0.877690\pi\) |
0.138901 | − | 0.990306i | \(-0.455643\pi\) | |||||||
\(194\) | −1.91421 | + | 3.31552i | −0.137433 | + | 0.238040i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.74264 | − | 1.88064i | 0.481617 | − | 0.134331i | ||||
\(197\) | 0.514719 | 0.0366722 | 0.0183361 | − | 0.999832i | \(-0.494163\pi\) | ||||
0.0183361 | + | 0.999832i | \(0.494163\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.0502525 | − | 0.0870399i | −0.00356231 | − | 0.00617010i | 0.864239 | − | 0.503082i | \(-0.167801\pi\) |
−0.867801 | + | 0.496912i | \(0.834467\pi\) | |||||||
\(200\) | −2.32843 | − | 4.03295i | −0.164645 | − | 0.285173i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.17157 | 0.434230 | ||||||||
\(203\) | −4.30761 | − | 5.55487i | −0.302335 | − | 0.389876i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.58579 | + | 2.74666i | −0.110756 | + | 0.191835i | ||||
\(206\) | 6.70711 | + | 11.6170i | 0.467306 | + | 0.809398i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.91421 | − | 3.31552i | 0.132727 | − | 0.229890i | ||||
\(209\) | 0.585786 | 0.0405197 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.41421 | 0.510416 | 0.255208 | − | 0.966886i | \(-0.417856\pi\) | ||||
0.255208 | + | 0.966886i | \(0.417856\pi\) | |||||||
\(212\) | 3.94975 | − | 6.84116i | 0.271270 | − | 0.469853i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.53553 | + | 2.65962i | 0.104967 | + | 0.181808i | ||||
\(215\) | 1.65685 | − | 2.86976i | 0.112997 | − | 0.195716i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | + | 9.79796i | −0.271538 | + | 0.665129i | ||||
\(218\) | −16.4853 | −1.11652 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.292893 | + | 0.507306i | 0.0197469 | + | 0.0342026i | ||||
\(221\) | −7.00000 | − | 12.1244i | −0.470871 | − | 0.815572i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.58579 | 0.574947 | 0.287473 | − | 0.957789i | \(-0.407185\pi\) | ||||
0.287473 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(224\) | −1.00000 | + | 2.44949i | −0.0668153 | + | 0.163663i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.08579 | − | 7.07679i | 0.271782 | − | 0.470741i | ||||
\(227\) | −14.4142 | − | 24.9662i | −0.956705 | − | 1.65706i | −0.730417 | − | 0.683001i | \(-0.760674\pi\) |
−0.226288 | − | 0.974061i | \(-0.572659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6569 | + | 20.1903i | −0.770307 | + | 1.33421i | 0.167088 | + | 0.985942i | \(0.446564\pi\) |
−0.937395 | + | 0.348268i | \(0.886770\pi\) | |||||||
\(230\) | −3.65685 | −0.241126 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.65685 | 0.174431 | ||||||||
\(233\) | 0.707107 | − | 1.22474i | 0.0463241 | − | 0.0802357i | −0.841934 | − | 0.539581i | \(-0.818583\pi\) |
0.888258 | + | 0.459345i | \(0.151916\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.07107 | − | 5.31925i | −0.200334 | − | 0.346989i | ||||
\(236\) | −2.79289 | + | 4.83743i | −0.181802 | + | 0.314890i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.92893 | + | 7.64564i | 0.384316 | + | 0.495593i | ||||
\(239\) | −20.2132 | −1.30748 | −0.653742 | − | 0.756718i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756718i | \(0.726802\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.12132 | − | 10.6024i | −0.394309 | − | 0.682963i | 0.598704 | − | 0.800971i | \(-0.295683\pi\) |
−0.993013 | + | 0.118007i | \(0.962349\pi\) | |||||||
\(242\) | 0.500000 | + | 0.866025i | 0.0321412 | + | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.8284 | 0.757237 | ||||||||
\(245\) | −2.92893 | − | 2.86976i | −0.187123 | − | 0.183342i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.12132 | + | 1.94218i | −0.0713479 | + | 0.123578i | ||||
\(248\) | −2.00000 | − | 3.46410i | −0.127000 | − | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.82843 | + | 4.89898i | −0.178885 | + | 0.309839i | ||||
\(251\) | 26.1421 | 1.65008 | 0.825038 | − | 0.565077i | \(-0.191153\pi\) | ||||
0.825038 | + | 0.565077i | \(0.191153\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.24264 | −0.392471 | ||||||||
\(254\) | 7.86396 | − | 13.6208i | 0.493429 | − | 0.854644i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.5711 | + | 21.7737i | −0.784162 | + | 1.35821i | 0.145337 | + | 0.989382i | \(0.453573\pi\) |
−0.929499 | + | 0.368826i | \(0.879760\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.6777 | − | 3.37706i | 1.53340 | − | 0.209840i | ||||
\(260\) | −2.24264 | −0.139083 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.292893 | + | 0.507306i | 0.0180950 | + | 0.0313415i | ||||
\(263\) | −8.52082 | − | 14.7585i | −0.525416 | − | 0.910047i | −0.999562 | − | 0.0296008i | \(-0.990576\pi\) |
0.474146 | − | 0.880446i | \(-0.342757\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.62742 | −0.284260 | ||||||||
\(266\) | 0.585786 | − | 1.43488i | 0.0359169 | − | 0.0879780i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.37868 | + | 2.38794i | −0.0842163 | + | 0.145867i | ||||
\(269\) | 1.17157 | + | 2.02922i | 0.0714321 | + | 0.123724i | 0.899529 | − | 0.436861i | \(-0.143910\pi\) |
−0.828097 | + | 0.560585i | \(0.810576\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.27817 | + | 3.94591i | −0.138389 | + | 0.239697i | −0.926887 | − | 0.375340i | \(-0.877526\pi\) |
0.788498 | + | 0.615038i | \(0.210859\pi\) | |||||||
\(272\) | −3.65685 | −0.221729 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.6569 | −1.00628 | ||||||||
\(275\) | −2.32843 | + | 4.03295i | −0.140409 | + | 0.243196i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.914214 | − | 1.58346i | −0.0549298 | − | 0.0951412i | 0.837253 | − | 0.546816i | \(-0.184160\pi\) |
−0.892183 | + | 0.451675i | \(0.850827\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.53553 | − | 0.210133i | 0.0917657 | − | 0.0125578i | ||||
\(281\) | −8.72792 | −0.520664 | −0.260332 | − | 0.965519i | \(-0.583832\pi\) | ||||
−0.260332 | + | 0.965519i | \(0.583832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.7071 | + | 20.2773i | 0.695915 | + | 1.20536i | 0.969871 | + | 0.243618i | \(0.0783344\pi\) |
−0.273956 | + | 0.961742i | \(0.588332\pi\) | |||||||
\(284\) | −5.53553 | − | 9.58783i | −0.328474 | − | 0.568933i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.82843 | −0.226380 | ||||||||
\(287\) | 8.77817 | + | 11.3199i | 0.518159 | + | 0.668191i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.81371 | − | 3.14144i | 0.106689 | − | 0.184790i | ||||
\(290\) | −0.778175 | − | 1.34784i | −0.0456960 | − | 0.0791478i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.70711 | − | 8.15295i | 0.275463 | − | 0.477115i | ||||
\(293\) | 10.8284 | 0.632603 | 0.316302 | − | 0.948659i | \(-0.397559\pi\) | ||||
0.316302 | + | 0.948659i | \(0.397559\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.27208 | 0.190508 | ||||||||
\(296\) | −4.70711 | + | 8.15295i | −0.273595 | + | 0.473880i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.82843 | − | 15.2913i | −0.511417 | − | 0.885800i | ||||
\(299\) | 11.9497 | − | 20.6976i | 0.691072 | − | 1.19697i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.17157 | − | 11.8272i | −0.528641 | − | 0.681707i | ||||
\(302\) | 15.7279 | 0.905040 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.292893 | + | 0.507306i | 0.0167986 | + | 0.0290960i | ||||
\(305\) | −3.46447 | − | 6.00063i | −0.198375 | − | 0.343595i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.89949 | 0.564994 | 0.282497 | − | 0.959268i | \(-0.408837\pi\) | ||||
0.282497 | + | 0.959268i | \(0.408837\pi\) | |||||||
\(308\) | 2.62132 | − | 0.358719i | 0.149364 | − | 0.0204399i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.17157 | + | 2.02922i | −0.0665409 | + | 0.115252i | ||||
\(311\) | 8.36396 | + | 14.4868i | 0.474277 | + | 0.821471i | 0.999566 | − | 0.0294522i | \(-0.00937629\pi\) |
−0.525289 | + | 0.850924i | \(0.676043\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3284 | − | 17.8894i | 0.583797 | − | 1.01117i | −0.411227 | − | 0.911533i | \(-0.634900\pi\) |
0.995024 | − | 0.0996335i | \(-0.0317670\pi\) | |||||||
\(314\) | −17.6569 | −0.996434 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.2426 | −0.744957 | ||||||||
\(317\) | 4.34315 | − | 7.52255i | 0.243935 | − | 0.422508i | −0.717896 | − | 0.696150i | \(-0.754895\pi\) |
0.961832 | + | 0.273642i | \(0.0882282\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.32843 | − | 2.30090i | −0.0743776 | − | 0.128826i | ||||
\(320\) | −0.292893 | + | 0.507306i | −0.0163732 | + | 0.0283593i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.24264 | + | 15.2913i | −0.347889 | + | 0.852150i | ||||
\(323\) | 2.14214 | 0.119192 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.91421 | − | 15.4399i | −0.494472 | − | 0.856450i | ||||
\(326\) | 4.86396 | + | 8.42463i | 0.269390 | + | 0.466597i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.41421 | −0.298950 | ||||||||
\(329\) | −27.4853 | + | 3.76127i | −1.51531 | + | 0.207366i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0355 | − | 20.8462i | 0.661533 | − | 1.14581i | −0.318680 | − | 0.947862i | \(-0.603240\pi\) |
0.980213 | − | 0.197946i | \(-0.0634271\pi\) | |||||||
\(332\) | −6.07107 | − | 10.5154i | −0.333193 | − | 0.577107i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.86396 | + | 11.8887i | −0.375579 | + | 0.650522i | ||||
\(335\) | 1.61522 | 0.0882491 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.2426 | −1.53847 | −0.769237 | − | 0.638963i | \(-0.779364\pi\) | ||||
−0.769237 | + | 0.638963i | \(0.779364\pi\) | |||||||
\(338\) | 0.828427 | − | 1.43488i | 0.0450605 | − | 0.0780471i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.07107 | + | 1.85514i | 0.0580868 | + | 0.100609i | ||||
\(341\) | −2.00000 | + | 3.46410i | −0.108306 | + | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 5.65685 | 0.304997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.91421 | + | 8.51167i | 0.264190 | + | 0.457590i | ||||
\(347\) | 8.70711 | + | 15.0812i | 0.467422 | + | 0.809599i | 0.999307 | − | 0.0372179i | \(-0.0118495\pi\) |
−0.531885 | + | 0.846816i | \(0.678516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 7.55025 | + | 9.73641i | 0.403578 | + | 0.520433i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | −1.34315 | − | 2.32640i | −0.0714884 | − | 0.123822i | 0.828065 | − | 0.560632i | \(-0.189442\pi\) |
−0.899554 | + | 0.436810i | \(0.856108\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.24264 | + | 5.61642i | −0.172101 | + | 0.298089i | ||||
\(356\) | −12.4853 | −0.661719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.899495 | 0.0475398 | ||||||||
\(359\) | 9.62132 | − | 16.6646i | 0.507794 | − | 0.879525i | −0.492165 | − | 0.870502i | \(-0.663794\pi\) |
0.999959 | − | 0.00902308i | \(-0.00287218\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.32843 | + | 16.1573i | 0.490970 | + | 0.850385i | ||||
\(362\) | −3.82843 | + | 6.63103i | −0.201218 | + | 0.348519i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.82843 | + | 9.37769i | −0.200664 | + | 0.491525i | ||||
\(365\) | −5.51472 | −0.288654 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.36396 | + | 9.29065i | 0.279996 | + | 0.484968i | 0.971384 | − | 0.237516i | \(-0.0763334\pi\) |
−0.691387 | + | 0.722485i | \(0.743000\pi\) | |||||||
\(368\) | −3.12132 | − | 5.40629i | −0.162710 | − | 0.281822i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.51472 | 0.286697 | ||||||||
\(371\) | −7.89949 | + | 19.3497i | −0.410121 | + | 1.00459i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.98528 | − | 17.2950i | 0.517018 | − | 0.895502i | −0.482786 | − | 0.875738i | \(-0.660375\pi\) |
0.999805 | − | 0.0197638i | \(-0.00629142\pi\) | |||||||
\(374\) | 1.82843 | + | 3.16693i | 0.0945457 | + | 0.163758i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.24264 | − | 9.08052i | 0.270369 | − | 0.468292i | ||||
\(377\) | 10.1716 | 0.523863 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.8701 | 1.43159 | 0.715794 | − | 0.698311i | \(-0.246065\pi\) | ||||
0.715794 | + | 0.698311i | \(0.246065\pi\) | |||||||
\(380\) | 0.171573 | − | 0.297173i | 0.00880150 | − | 0.0152447i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.58579 | + | 6.21076i | 0.183465 | + | 0.317770i | ||||
\(383\) | −3.19239 | + | 5.52938i | −0.163123 | + | 0.282538i | −0.935987 | − | 0.352034i | \(-0.885490\pi\) |
0.772864 | + | 0.634572i | \(0.218824\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.949747 | − | 1.22474i | −0.0484036 | − | 0.0624188i | ||||
\(386\) | −21.8995 | −1.11465 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.91421 | + | 3.31552i | 0.0971795 | + | 0.168320i | ||||
\(389\) | −11.3640 | − | 19.6830i | −0.576176 | − | 0.997966i | −0.995913 | − | 0.0903199i | \(-0.971211\pi\) |
0.419737 | − | 0.907646i | \(-0.362122\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.8284 | −1.15448 | ||||||||
\(392\) | 1.74264 | − | 6.77962i | 0.0880166 | − | 0.342422i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.257359 | − | 0.445759i | 0.0129656 | − | 0.0224570i | ||||
\(395\) | 3.87868 | + | 6.71807i | 0.195158 | + | 0.338023i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0000 | + | 19.0526i | −0.552074 | + | 0.956221i | 0.446051 | + | 0.895008i | \(0.352830\pi\) |
−0.998125 | + | 0.0612128i | \(0.980503\pi\) | |||||||
\(398\) | −0.100505 | −0.00503786 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.65685 | −0.232843 | ||||||||
\(401\) | 9.15685 | − | 15.8601i | 0.457271 | − | 0.792017i | −0.541544 | − | 0.840672i | \(-0.682160\pi\) |
0.998816 | + | 0.0486549i | \(0.0154934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.65685 | − | 13.2621i | −0.381415 | − | 0.660630i | ||||
\(404\) | 3.08579 | − | 5.34474i | 0.153524 | − | 0.265911i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.96447 | + | 0.953065i | −0.345641 | + | 0.0472998i | ||||
\(407\) | 9.41421 | 0.466645 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.36396 | − | 2.36245i | −0.0674435 | − | 0.116816i | 0.830332 | − | 0.557269i | \(-0.188151\pi\) |
−0.897775 | + | 0.440454i | \(0.854818\pi\) | |||||||
\(410\) | 1.58579 | + | 2.74666i | 0.0783164 | + | 0.135648i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.4142 | 0.660871 | ||||||||
\(413\) | 5.58579 | − | 13.6823i | 0.274859 | − | 0.673263i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.55635 | + | 6.15978i | −0.174574 | + | 0.302372i | ||||
\(416\) | −1.91421 | − | 3.31552i | −0.0938520 | − | 0.162557i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.292893 | − | 0.507306i | 0.0143259 | − | 0.0248131i | ||||
\(419\) | 26.1421 | 1.27713 | 0.638563 | − | 0.769569i | \(-0.279529\pi\) | ||||
0.638563 | + | 0.769569i | \(0.279529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.686292 | 0.0334478 | 0.0167239 | − | 0.999860i | \(-0.494676\pi\) | ||||
0.0167239 | + | 0.999860i | \(0.494676\pi\) | |||||||
\(422\) | 3.70711 | − | 6.42090i | 0.180459 | − | 0.312564i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.94975 | − | 6.84116i | −0.191817 | − | 0.332236i | ||||
\(425\) | −8.51472 | + | 14.7479i | −0.413025 | + | 0.715379i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.0061 | + | 4.24309i | −1.50049 | + | 0.205337i | ||||
\(428\) | 3.07107 | 0.148446 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.65685 | − | 2.86976i | −0.0799006 | − | 0.138392i | ||||
\(431\) | −8.79289 | − | 15.2297i | −0.423539 | − | 0.733591i | 0.572744 | − | 0.819734i | \(-0.305879\pi\) |
−0.996283 | + | 0.0861437i | \(0.972546\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.1421 | 1.25631 | 0.628155 | − | 0.778088i | \(-0.283810\pi\) | ||||
0.628155 | + | 0.778088i | \(0.283810\pi\) | |||||||
\(434\) | 6.48528 | + | 8.36308i | 0.311303 | + | 0.401441i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.24264 | + | 14.2767i | −0.394751 | + | 0.683729i | ||||
\(437\) | 1.82843 | + | 3.16693i | 0.0874655 | + | 0.151495i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.6924 | − | 23.7159i | 0.653502 | − | 1.13190i | −0.328765 | − | 0.944412i | \(-0.606632\pi\) |
0.982267 | − | 0.187487i | \(-0.0600342\pi\) | |||||||
\(440\) | 0.585786 | 0.0279263 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.0000 | −0.665912 | ||||||||
\(443\) | 6.31371 | − | 10.9357i | 0.299973 | − | 0.519569i | −0.676156 | − | 0.736758i | \(-0.736356\pi\) |
0.976130 | + | 0.217189i | \(0.0696889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.65685 | + | 6.33386i | 0.173352 | + | 0.300254i | ||||
\(446\) | 4.29289 | − | 7.43551i | 0.203274 | − | 0.352082i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.62132 | + | 2.09077i | 0.0766002 | + | 0.0987796i | ||||
\(449\) | −22.3431 | −1.05444 | −0.527219 | − | 0.849729i | \(-0.676765\pi\) | ||||
−0.527219 | + | 0.849729i | \(0.676765\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.70711 | + | 4.68885i | 0.127473 | + | 0.220789i | ||||
\(452\) | −4.08579 | − | 7.07679i | −0.192179 | − | 0.332864i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28.8284 | −1.35299 | ||||||||
\(455\) | 5.87868 | − | 0.804479i | 0.275597 | − | 0.0377146i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.82843 | − | 10.0951i | 0.272642 | − | 0.472230i | −0.696895 | − | 0.717173i | \(-0.745436\pi\) |
0.969538 | + | 0.244943i | \(0.0787691\pi\) | |||||||
\(458\) | 11.6569 | + | 20.1903i | 0.544689 | + | 0.943429i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.82843 | + | 3.16693i | −0.0852509 | + | 0.147659i | ||||
\(461\) | 8.31371 | 0.387208 | 0.193604 | − | 0.981080i | \(-0.437982\pi\) | ||||
0.193604 | + | 0.981080i | \(0.437982\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.8284 | 0.596188 | 0.298094 | − | 0.954537i | \(-0.403649\pi\) | ||||
0.298094 | + | 0.954537i | \(0.403649\pi\) | |||||||
\(464\) | 1.32843 | − | 2.30090i | 0.0616707 | − | 0.106817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.707107 | − | 1.22474i | −0.0327561 | − | 0.0567352i | ||||
\(467\) | −17.0000 | + | 29.4449i | −0.786666 | + | 1.36255i | 0.141332 | + | 0.989962i | \(0.454861\pi\) |
−0.927999 | + | 0.372584i | \(0.878472\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.75736 | − | 6.75412i | 0.127323 | − | 0.311876i | ||||
\(470\) | −6.14214 | −0.283316 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.79289 | + | 4.83743i | 0.128553 | + | 0.222661i | ||||
\(473\) | −2.82843 | − | 4.89898i | −0.130051 | − | 0.225255i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.72792 | 0.125166 | ||||||||
\(476\) | 9.58579 | − | 1.31178i | 0.439364 | − | 0.0601256i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.1066 | + | 17.5051i | −0.462265 | + | 0.800667i | ||||
\(479\) | −5.96447 | − | 10.3308i | −0.272523 | − | 0.472024i | 0.696984 | − | 0.717087i | \(-0.254525\pi\) |
−0.969507 | + | 0.245062i | \(0.921192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0208 | + | 31.2130i | −0.821678 | + | 1.42319i | ||||
\(482\) | −12.2426 | −0.557637 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 1.12132 | − | 1.94218i | 0.0509165 | − | 0.0881900i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.82843 | + | 8.36308i | 0.218797 | + | 0.378967i | 0.954440 | − | 0.298402i | \(-0.0964534\pi\) |
−0.735644 | + | 0.677369i | \(0.763120\pi\) | |||||||
\(488\) | 5.91421 | − | 10.2437i | 0.267724 | − | 0.463711i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.94975 | + | 1.10165i | −0.178431 | + | 0.0497676i | ||||
\(491\) | −19.1716 | −0.865201 | −0.432600 | − | 0.901586i | \(-0.642404\pi\) | ||||
−0.432600 | + | 0.901586i | \(0.642404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.85786 | − | 8.41407i | −0.218787 | − | 0.378951i | ||||
\(494\) | 1.12132 | + | 1.94218i | 0.0504506 | + | 0.0873830i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 17.9497 | + | 23.1471i | 0.805156 | + | 1.03829i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.0711 | + | 19.1757i | −0.495609 | + | 0.858420i | −0.999987 | − | 0.00506282i | \(-0.998388\pi\) |
0.504378 | + | 0.863483i | \(0.331722\pi\) | |||||||
\(500\) | 2.82843 | + | 4.89898i | 0.126491 | + | 0.219089i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.0711 | − | 22.6398i | 0.583390 | − | 1.01046i | ||||
\(503\) | −4.21320 | −0.187857 | −0.0939287 | − | 0.995579i | \(-0.529943\pi\) | ||||
−0.0939287 | + | 0.995579i | \(0.529943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.61522 | −0.160875 | ||||||||
\(506\) | −3.12132 | + | 5.40629i | −0.138760 | + | 0.240339i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.86396 | − | 13.6208i | −0.348907 | − | 0.604324i | ||||
\(509\) | 4.65685 | − | 8.06591i | 0.206411 | − | 0.357515i | −0.744170 | − | 0.667990i | \(-0.767155\pi\) |
0.950582 | + | 0.310475i | \(0.100488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.41421 | + | 23.0600i | −0.416460 | + | 1.02012i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.5711 | + | 21.7737i | 0.554486 | + | 0.960398i | ||||
\(515\) | −3.92893 | − | 6.80511i | −0.173129 | − | 0.299869i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.4853 | −0.461142 | ||||||||
\(518\) | 9.41421 | − | 23.0600i | 0.413637 | − | 1.01320i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.12132 | + | 1.94218i | −0.0491731 | + | 0.0851704i | ||||
\(521\) | −14.1421 | − | 24.4949i | −0.619578 | − | 1.07314i | −0.989563 | − | 0.144103i | \(-0.953970\pi\) |
0.369984 | − | 0.929038i | \(-0.379363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.36396 | − | 11.0227i | 0.278277 | − | 0.481989i | −0.692680 | − | 0.721245i | \(-0.743570\pi\) |
0.970957 | + | 0.239256i | \(0.0769035\pi\) | |||||||
\(524\) | 0.585786 | 0.0255902 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.0416 | −0.743050 | ||||||||
\(527\) | −7.31371 | + | 12.6677i | −0.318590 | + | 0.551814i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.98528 | − | 13.8309i | −0.347186 | − | 0.601344i | ||||
\(530\) | −2.31371 | + | 4.00746i | −0.100501 | + | 0.174073i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.949747 | − | 1.22474i | −0.0411768 | − | 0.0530994i | ||||
\(533\) | −20.7279 | −0.897826 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.899495 | − | 1.55797i | −0.0388886 | − | 0.0673570i | ||||
\(536\) | 1.37868 | + | 2.38794i | 0.0595499 | + | 0.103143i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.34315 | 0.101020 | ||||||||
\(539\) | −6.74264 | + | 1.88064i | −0.290426 | + | 0.0810048i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.42893 | − | 11.1352i | 0.276401 | − | 0.478741i | −0.694086 | − | 0.719892i | \(-0.744191\pi\) |
0.970488 | + | 0.241151i | \(0.0775248\pi\) | |||||||
\(542\) | 2.27817 | + | 3.94591i | 0.0978560 | + | 0.169492i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.82843 | + | 3.16693i | −0.0783932 | + | 0.135781i | ||||
\(545\) | 9.65685 | 0.413654 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.8701 | 1.49094 | 0.745468 | − | 0.666541i | \(-0.232226\pi\) | ||||
0.745468 | + | 0.666541i | \(0.232226\pi\) | |||||||
\(548\) | −8.32843 | + | 14.4253i | −0.355773 | + | 0.616217i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.32843 | + | 4.03295i | 0.0992845 | + | 0.171966i | ||||
\(551\) | −0.778175 | + | 1.34784i | −0.0331514 | + | 0.0574198i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.7132 | − | 4.75039i | 1.47616 | − | 0.202007i | ||||
\(554\) | −1.82843 | −0.0776824 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.75736 | + | 6.50794i | 0.159204 | + | 0.275750i | 0.934582 | − | 0.355748i | \(-0.115774\pi\) |
−0.775378 | + | 0.631498i | \(0.782440\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.6569 | 0.915987 | ||||||||
\(560\) | 0.585786 | − | 1.43488i | 0.0247540 | − | 0.0606347i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.36396 | + | 7.55860i | −0.184083 | + | 0.318840i | ||||
\(563\) | 4.53553 | + | 7.85578i | 0.191150 | + | 0.331081i | 0.945632 | − | 0.325240i | \(-0.105445\pi\) |
−0.754482 | + | 0.656321i | \(0.772112\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.39340 | + | 4.14549i | −0.100691 | + | 0.174402i | ||||
\(566\) | 23.4142 | 0.984173 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.0711 | −0.464532 | ||||||||
\(569\) | −2.00000 | + | 3.46410i | −0.0838444 | + | 0.145223i | −0.904898 | − | 0.425628i | \(-0.860053\pi\) |
0.821054 | + | 0.570851i | \(0.193387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.1924 | − | 22.8499i | −0.552084 | − | 0.956238i | −0.998124 | − | 0.0612248i | \(-0.980499\pi\) |
0.446040 | − | 0.895013i | \(-0.352834\pi\) | |||||||
\(572\) | −1.91421 | + | 3.31552i | −0.0800373 | + | 0.138629i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.1924 | − | 1.94218i | 0.592379 | − | 0.0810652i | ||||
\(575\) | −29.0711 | −1.21235 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.84315 | + | 8.38857i | 0.201623 | + | 0.349221i | 0.949051 | − | 0.315121i | \(-0.102045\pi\) |
−0.747429 | + | 0.664342i | \(0.768712\pi\) | |||||||
\(578\) | −1.81371 | − | 3.14144i | −0.0754403 | − | 0.130666i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.55635 | −0.0646239 | ||||||||
\(581\) | 19.6863 | + | 25.3864i | 0.816725 | + | 1.05321i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.94975 | + | 6.84116i | −0.163582 | + | 0.283332i | ||||
\(584\) | −4.70711 | − | 8.15295i | −0.194781 | − | 0.337371i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.41421 | − | 9.37769i | 0.223659 | − | 0.387389i | ||||
\(587\) | 25.1005 | 1.03601 | 0.518004 | − | 0.855378i | \(-0.326675\pi\) | ||||
0.518004 | + | 0.855378i | \(0.326675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.34315 | 0.0965476 | ||||||||
\(590\) | 1.63604 | − | 2.83370i | 0.0673547 | − | 0.116662i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.70711 | + | 8.15295i | 0.193461 | + | 0.335084i | ||||
\(593\) | 11.8492 | − | 20.5235i | 0.486590 | − | 0.842799i | −0.513291 | − | 0.858215i | \(-0.671574\pi\) |
0.999881 | + | 0.0154159i | \(0.00490721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.47309 | − | 4.47871i | −0.142383 | − | 0.183609i | ||||
\(596\) | −17.6569 | −0.723253 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.9497 | − | 20.6976i | −0.488662 | − | 0.846387i | ||||
\(599\) | 21.3137 | + | 36.9164i | 0.870855 | + | 1.50836i | 0.861114 | + | 0.508412i | \(0.169767\pi\) |
0.00974040 | + | 0.999953i | \(0.496899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.9411 | 1.30291 | 0.651453 | − | 0.758689i | \(-0.274160\pi\) | ||||
0.651453 | + | 0.758689i | \(0.274160\pi\) | |||||||
\(602\) | −14.8284 | + | 2.02922i | −0.604362 | + | 0.0827050i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.86396 | − | 13.6208i | 0.319980 | − | 0.554222i | ||||
\(605\) | −0.292893 | − | 0.507306i | −0.0119078 | − | 0.0206249i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.4853 | − | 37.2136i | 0.872061 | − | 1.51045i | 0.0121994 | − | 0.999926i | \(-0.496117\pi\) |
0.859861 | − | 0.510528i | \(-0.170550\pi\) | |||||||
\(608\) | 0.585786 | 0.0237568 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.92893 | −0.280544 | ||||||||
\(611\) | 20.0711 | − | 34.7641i | 0.811988 | − | 1.40641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.3137 | − | 24.7921i | −0.578125 | − | 1.00134i | −0.995694 | − | 0.0926971i | \(-0.970451\pi\) |
0.417569 | − | 0.908645i | \(-0.362882\pi\) | |||||||
\(614\) | 4.94975 | − | 8.57321i | 0.199756 | − | 0.345987i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | − | 2.44949i | 0.0402911 | − | 0.0986928i | ||||
\(617\) | 41.9706 | 1.68967 | 0.844836 | − | 0.535026i | \(-0.179698\pi\) | ||||
0.844836 | + | 0.535026i | \(0.179698\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9706 | + | 19.0016i | 0.440944 | + | 0.763738i | 0.997760 | − | 0.0668984i | \(-0.0213104\pi\) |
−0.556816 | + | 0.830636i | \(0.687977\pi\) | |||||||
\(620\) | 1.17157 | + | 2.02922i | 0.0470515 | + | 0.0814956i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.7279 | 0.670729 | ||||||||
\(623\) | 32.7279 | − | 4.47871i | 1.31122 | − | 0.179436i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.98528 | + | 17.2950i | −0.399411 | + | 0.691801i | ||||
\(626\) | −10.3284 | − | 17.8894i | −0.412807 | − | 0.715003i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.82843 | + | 15.2913i | −0.352293 | + | 0.610189i | ||||
\(629\) | 34.4264 | 1.37267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2721 | 0.926447 | 0.463223 | − | 0.886242i | \(-0.346693\pi\) | ||||
0.463223 | + | 0.886242i | \(0.346693\pi\) | |||||||
\(632\) | −6.62132 | + | 11.4685i | −0.263382 | + | 0.456191i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.34315 | − | 7.52255i | −0.172488 | − | 0.298759i | ||||
\(635\) | −4.60660 | + | 7.97887i | −0.182807 | + | 0.316632i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.67157 | − | 25.9553i | 0.264337 | − | 1.02839i | ||||
\(638\) | −2.65685 | −0.105186 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.292893 | + | 0.507306i | 0.0115776 | + | 0.0200530i | ||||
\(641\) | 7.64214 | + | 13.2366i | 0.301846 | + | 0.522813i | 0.976554 | − | 0.215272i | \(-0.0690638\pi\) |
−0.674708 | + | 0.738085i | \(0.735730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.58579 | 0.0625373 | 0.0312687 | − | 0.999511i | \(-0.490045\pi\) | ||||
0.0312687 | + | 0.999511i | \(0.490045\pi\) | |||||||
\(644\) | 10.1213 | + | 13.0519i | 0.398836 | + | 0.514318i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.07107 | − | 1.85514i | 0.0421406 | − | 0.0729897i | ||||
\(647\) | 15.0919 | + | 26.1399i | 0.593323 | + | 1.02767i | 0.993781 | + | 0.111351i | \(0.0355177\pi\) |
−0.400458 | + | 0.916315i | \(0.631149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.79289 | − | 4.83743i | 0.109631 | − | 0.189886i | ||||
\(650\) | −17.8284 | −0.699288 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.72792 | 0.380975 | ||||||||
\(653\) | −9.19239 | + | 15.9217i | −0.359726 | + | 0.623064i | −0.987915 | − | 0.154997i | \(-0.950463\pi\) |
0.628189 | + | 0.778061i | \(0.283796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.171573 | − | 0.297173i | −0.00670391 | − | 0.0116115i | ||||
\(656\) | −2.70711 | + | 4.68885i | −0.105695 | + | 0.183069i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.4853 | + | 25.6836i | −0.408759 | + | 1.00125i | ||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.48528 | − | 16.4290i | −0.368935 | − | 0.639014i | 0.620465 | − | 0.784234i | \(-0.286944\pi\) |
−0.989399 | + | 0.145221i | \(0.953611\pi\) | |||||||
\(662\) | −12.0355 | − | 20.8462i | −0.467774 | − | 0.810209i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.1421 | −0.471206 | ||||||||
\(665\) | −0.343146 | + | 0.840532i | −0.0133066 | + | 0.0325944i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.29289 | − | 14.3637i | 0.321102 | − | 0.556165i | ||||
\(668\) | 6.86396 | + | 11.8887i | 0.265575 | + | 0.459989i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.807612 | − | 1.39882i | 0.0312008 | − | 0.0540413i | ||||
\(671\) | −11.8284 | −0.456631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.55635 | 0.214182 | 0.107091 | − | 0.994249i | \(-0.465846\pi\) | ||||
0.107091 | + | 0.994249i | \(0.465846\pi\) | |||||||
\(674\) | −14.1213 | + | 24.4588i | −0.543933 | + | 0.942119i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.828427 | − | 1.43488i | −0.0318626 | − | 0.0551876i | ||||
\(677\) | −17.6569 | + | 30.5826i | −0.678608 | + | 1.17538i | 0.296792 | + | 0.954942i | \(0.404083\pi\) |
−0.975400 | + | 0.220441i | \(0.929250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.20711 | − | 8.00436i | −0.238207 | − | 0.307179i | ||||
\(680\) | 2.14214 | 0.0821472 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.00000 | + | 3.46410i | 0.0765840 | + | 0.132647i | ||||
\(683\) | 6.79289 | + | 11.7656i | 0.259923 | + | 0.450200i | 0.966221 | − | 0.257715i | \(-0.0829695\pi\) |
−0.706298 | + | 0.707914i | \(0.749636\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.75736 | 0.372810 | ||||||||
\(686\) | −2.13604 | + | 18.3967i | −0.0815543 | + | 0.702388i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.82843 | − | 4.89898i | 0.107833 | − | 0.186772i | ||||
\(689\) | −15.1213 | − | 26.1909i | −0.576076 | − | 0.997794i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.0355 | + | 24.3103i | −0.533937 | + | 0.924806i | 0.465277 | + | 0.885165i | \(0.345955\pi\) |
−0.999214 | + | 0.0396407i | \(0.987379\pi\) | |||||||
\(692\) | 9.82843 | 0.373621 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.4142 | 0.661035 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.89949 | + | 17.1464i | 0.374970 | + | 0.649467i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.2071 | − | 1.67050i | 0.461385 | − | 0.0631391i | ||||
\(701\) | 26.1127 | 0.986263 | 0.493132 | − | 0.869955i | \(-0.335852\pi\) | ||||
0.493132 | + | 0.869955i | \(0.335852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.75736 | − | 4.77589i | −0.103996 | − | 0.180126i | ||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.68629 | −0.101100 | ||||||||
\(707\) | −6.17157 | + | 15.1172i | −0.232106 | + | 0.568541i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.02082 | − | 10.4284i | 0.226116 | − | 0.391645i | −0.730537 | − | 0.682873i | \(-0.760730\pi\) |
0.956654 | + | 0.291228i | \(0.0940637\pi\) | |||||||
\(710\) | 3.24264 | + | 5.61642i | 0.121694 | + | 0.210780i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.24264 | + | 10.8126i | −0.233953 | + | 0.405218i | ||||
\(713\) | −24.9706 | −0.935155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.24264 | 0.0838700 | ||||||||
\(716\) | 0.449747 | − | 0.778985i | 0.0168079 | − | 0.0291121i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.62132 | − | 16.6646i | −0.359064 | − | 0.621918i | ||||
\(719\) | −0.757359 | + | 1.31178i | −0.0282447 | + | 0.0489213i | −0.879802 | − | 0.475340i | \(-0.842325\pi\) |
0.851558 | + | 0.524261i | \(0.175658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.1630 | + | 4.81194i | −1.30954 | + | 0.179206i | ||||
\(722\) | 18.6569 | 0.694336 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.82843 | + | 6.63103i | 0.142282 | + | 0.246440i | ||||
\(725\) | −6.18629 | − | 10.7150i | −0.229753 | − | 0.397944i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.4264 | 1.35098 | 0.675490 | − | 0.737369i | \(-0.263932\pi\) | ||||
0.675490 | + | 0.737369i | \(0.263932\pi\) | |||||||
\(728\) | 6.20711 | + | 8.00436i | 0.230051 | + | 0.296661i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.75736 | + | 4.77589i | −0.102054 | + | 0.176763i | ||||
\(731\) | −10.3431 | − | 17.9149i | −0.382555 | − | 0.662605i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.50000 | − | 11.2583i | 0.240083 | − | 0.415836i | −0.720655 | − | 0.693294i | \(-0.756159\pi\) |
0.960738 | + | 0.277458i | \(0.0894920\pi\) | |||||||
\(734\) | 10.7279 | 0.395975 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.24264 | −0.230107 | ||||||||
\(737\) | 1.37868 | − | 2.38794i | 0.0507843 | − | 0.0879610i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.2132 | + | 45.4026i | 0.964268 | + | 1.67016i | 0.711568 | + | 0.702617i | \(0.247985\pi\) |
0.252700 | + | 0.967545i | \(0.418681\pi\) | |||||||
\(740\) | 2.75736 | − | 4.77589i | 0.101363 | − | 0.175565i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.8076 | + | 16.5160i | 0.470182 | + | 0.606323i | ||||
\(743\) | 13.3137 | 0.488433 | 0.244216 | − | 0.969721i | \(-0.421469\pi\) | ||||
0.244216 | + | 0.969721i | \(0.421469\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.17157 | + | 8.95743i | 0.189472 | + | 0.328175i | ||||
\(746\) | −9.98528 | − | 17.2950i | −0.365587 | − | 0.633215i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.65685 | 0.133708 | ||||||||
\(749\) | −8.05025 | + | 1.10165i | −0.294150 | + | 0.0402535i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.8284 | + | 39.5400i | −0.833021 | + | 1.44283i | 0.0626103 | + | 0.998038i | \(0.480057\pi\) |
−0.895631 | + | 0.444797i | \(0.853276\pi\) | |||||||
\(752\) | −5.24264 | − | 9.08052i | −0.191179 | − | 0.331132i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.08579 | − | 8.80884i | 0.185213 | − | 0.320799i | ||||
\(755\) | −9.21320 | −0.335303 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.34315 | 0.303237 | 0.151618 | − | 0.988439i | \(-0.451552\pi\) | ||||
0.151618 | + | 0.988439i | \(0.451552\pi\) | |||||||
\(758\) | 13.9350 | − | 24.1362i | 0.506143 | − | 0.876665i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.171573 | − | 0.297173i | −0.00622360 | − | 0.0107796i | ||||
\(761\) | 15.4853 | − | 26.8213i | 0.561341 | − | 0.972271i | −0.436039 | − | 0.899928i | \(-0.643619\pi\) |
0.997380 | − | 0.0723433i | \(-0.0230477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.4853 | − | 40.3805i | 0.596807 | − | 1.46187i | ||||
\(764\) | 7.17157 | 0.259458 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.19239 | + | 5.52938i | 0.115346 | + | 0.199785i | ||||
\(767\) | 10.6924 | + | 18.5198i | 0.386080 | + | 0.668710i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.9706 | 0.828340 | 0.414170 | − | 0.910200i | \(-0.364072\pi\) | ||||
0.414170 | + | 0.910200i | \(0.364072\pi\) | |||||||
\(770\) | −1.53553 | + | 0.210133i | −0.0553368 | + | 0.00757267i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.9497 | + | 18.9655i | −0.394090 | + | 0.682584i | ||||
\(773\) | −10.9706 | − | 19.0016i | −0.394584 | − | 0.683439i | 0.598464 | − | 0.801150i | \(-0.295778\pi\) |
−0.993048 | + | 0.117710i | \(0.962445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.31371 | + | 16.1318i | −0.334558 | + | 0.579472i | ||||
\(776\) | 3.82843 | 0.137433 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.7279 | −0.814835 | ||||||||
\(779\) | 1.58579 | − | 2.74666i | 0.0568167 | − | 0.0984094i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.53553 | + | 9.58783i | 0.198077 | + | 0.343079i | ||||
\(782\) | −11.4142 | + | 19.7700i | −0.408171 | + | 0.706974i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.00000 | − | 4.89898i | −0.178571 | − | 0.174964i | ||||
\(785\) | 10.3431 | 0.369163 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.77817 | − | 11.7401i | −0.241616 | − | 0.418491i | 0.719559 | − | 0.694431i | \(-0.244344\pi\) |
−0.961175 | + | 0.275941i | \(0.911011\pi\) | |||||||
\(788\) | −0.257359 | − | 0.445759i | −0.00916805 | − | 0.0158795i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.75736 | 0.275994 | ||||||||
\(791\) | 13.2487 | + | 17.0849i | 0.471071 | + | 0.607468i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.6421 | − | 39.2173i | 0.804046 | − | 1.39265i | ||||
\(794\) | 11.0000 | + | 19.0526i | 0.390375 | + | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.0502525 | + | 0.0870399i | −0.00178115 | + | 0.00308505i | ||||
\(797\) | 7.65685 | 0.271220 | 0.135610 | − | 0.990762i | \(-0.456701\pi\) | ||||
0.135610 | + | 0.990762i | \(0.456701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.3431 | −1.35648 | ||||||||
\(800\) | −2.32843 | + | 4.03295i | −0.0823223 | + | 0.142586i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.15685 | − | 15.8601i | −0.323340 | − | 0.560041i | ||||
\(803\) | −4.70711 | + | 8.15295i | −0.166110 | + | 0.287711i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.65685 | − | 8.95743i | 0.128887 | − | 0.315708i | ||||
\(806\) | −15.3137 | −0.539402 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.08579 | − | 5.34474i | −0.108558 | − | 0.188027i | ||||
\(809\) | −23.3137 | − | 40.3805i | −0.819666 | − | 1.41970i | −0.905928 | − | 0.423431i | \(-0.860826\pi\) |
0.0862619 | − | 0.996272i | \(-0.472508\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.2843 | −0.852736 | −0.426368 | − | 0.904550i | \(-0.640207\pi\) | ||||
−0.426368 | + | 0.904550i | \(0.640207\pi\) | |||||||
\(812\) | −2.65685 | + | 6.50794i | −0.0932373 | + | 0.228384i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.70711 | − | 8.15295i | 0.164984 | − | 0.285761i | ||||
\(815\) | −2.84924 | − | 4.93503i | −0.0998046 | − | 0.172867i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.65685 | + | 2.86976i | −0.0579660 | + | 0.100400i | ||||
\(818\) | −2.72792 | −0.0953796 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.17157 | 0.110756 | ||||||||
\(821\) | −14.7426 | + | 25.5350i | −0.514522 | + | 0.891178i | 0.485336 | + | 0.874328i | \(0.338697\pi\) |
−0.999858 | + | 0.0168502i | \(0.994636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.7279 | + | 37.6339i | 0.757388 | + | 1.31183i | 0.944178 | + | 0.329434i | \(0.106858\pi\) |
−0.186791 | + | 0.982400i | \(0.559809\pi\) | |||||||
\(824\) | 6.70711 | − | 11.6170i | 0.233653 | − | 0.404699i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.05635 | − | 11.6786i | −0.315111 | − | 0.406350i | ||||
\(827\) | 21.3553 | 0.742598 | 0.371299 | − | 0.928513i | \(-0.378913\pi\) | ||||
0.371299 | + | 0.928513i | \(0.378913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.8787 | − | 18.8424i | −0.377832 | − | 0.654425i | 0.612914 | − | 0.790149i | \(-0.289997\pi\) |
−0.990747 | + | 0.135725i | \(0.956664\pi\) | |||||||
\(830\) | 3.55635 | + | 6.15978i | 0.123443 | + | 0.213809i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.82843 | −0.132727 | ||||||||
\(833\) | −24.6569 | + | 6.87722i | −0.854309 | + | 0.238281i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.02082 | − | 6.96426i | 0.139146 | − | 0.241008i | ||||
\(836\) | −0.292893 | − | 0.507306i | −0.0101299 | − | 0.0175455i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.0711 | − | 22.6398i | 0.451533 | − | 0.782077i | ||||
\(839\) | 18.4853 | 0.638183 | 0.319091 | − | 0.947724i | \(-0.396622\pi\) | ||||
0.319091 | + | 0.947724i | \(0.396622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.9411 | −0.756591 | ||||||||
\(842\) | 0.343146 | − | 0.594346i | 0.0118256 | − | 0.0204825i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.70711 | − | 6.42090i | −0.127604 | − | 0.221016i | ||||
\(845\) | −0.485281 | + | 0.840532i | −0.0166942 | + | 0.0289152i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.62132 | + | 0.358719i | −0.0900696 | + | 0.0123257i | ||||
\(848\) | −7.89949 | −0.271270 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.51472 | + | 14.7479i | 0.292052 | + | 0.505850i | ||||
\(851\) | 29.3848 | + | 50.8959i | 1.00730 | + | 1.74469i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | −11.8284 | + | 28.9736i | −0.404760 | + | 0.991457i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.53553 | − | 2.65962i | 0.0524835 | − | 0.0909040i | ||||
\(857\) | −17.3137 | − | 29.9882i | −0.591425 | − | 1.02438i | −0.994041 | − | 0.109009i | \(-0.965232\pi\) |
0.402616 | − | 0.915369i | \(-0.368101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.86396 | − | 4.96053i | 0.0977171 | − | 0.169251i | −0.813022 | − | 0.582233i | \(-0.802179\pi\) |
0.910739 | + | 0.412982i | \(0.135513\pi\) | |||||||
\(860\) | −3.31371 | −0.112997 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.5858 | −0.598974 | ||||||||
\(863\) | 17.6066 | − | 30.4955i | 0.599336 | − | 1.03808i | −0.393584 | − | 0.919289i | \(-0.628765\pi\) |
0.992919 | − | 0.118791i | \(-0.0379019\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.87868 | − | 4.98602i | −0.0978780 | − | 0.169530i | ||||
\(866\) | 13.0711 | − | 22.6398i | 0.444173 | − | 0.769330i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.4853 | − | 1.43488i | 0.355894 | − | 0.0487029i | ||||
\(869\) | 13.2426 | 0.449226 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.27817 | + | 9.14207i | 0.178844 | + | 0.309767i | ||||
\(872\) | 8.24264 | + | 14.2767i | 0.279131 | + | 0.483469i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.65685 | 0.123695 | ||||||||
\(875\) | −9.17157 | − | 11.8272i | −0.310056 | − | 0.399832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.81371 | + | 16.9978i | −0.331385 | + | 0.573976i | −0.982784 | − | 0.184760i | \(-0.940849\pi\) |
0.651398 | + | 0.758736i | \(0.274183\pi\) | |||||||
\(878\) | −13.6924 | − | 23.7159i | −0.462096 | − | 0.800373i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.292893 | − | 0.507306i | 0.00987343 | − | 0.0171013i | ||||
\(881\) | −6.45584 | −0.217503 | −0.108751 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108751 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.7279 | 0.529287 | 0.264643 | − | 0.964346i | \(-0.414746\pi\) | ||||
0.264643 | + | 0.964346i | \(0.414746\pi\) | |||||||
\(884\) | −7.00000 | + | 12.1244i | −0.235435 | + | 0.407786i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.31371 | − | 10.9357i | −0.212113 | − | 0.367391i | ||||
\(887\) | −1.55025 | + | 2.68512i | −0.0520524 | + | 0.0901574i | −0.890878 | − | 0.454243i | \(-0.849910\pi\) |
0.838825 | + | 0.544401i | \(0.183243\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.5000 | + | 32.8835i | 0.855243 | + | 1.10288i | ||||
\(890\) | 7.31371 | 0.245156 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.29289 | − | 7.43551i | −0.143737 | − | 0.248959i | ||||
\(893\) | 3.07107 | + | 5.31925i | 0.102769 | + | 0.178002i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.526912 | −0.0176127 | ||||||||
\(896\) | 2.62132 | − | 0.358719i | 0.0875722 | − | 0.0119840i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.1716 | + | 19.3497i | −0.372800 | + | 0.645709i | ||||
\(899\) | −5.31371 | − | 9.20361i | −0.177222 | − | 0.306958i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4437 | + | 25.0171i | −0.481188 | + | 0.833442i | ||||
\(902\) | 5.41421 | 0.180274 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.17157 | −0.271782 | ||||||||
\(905\) | 2.24264 | − | 3.88437i | 0.0745479 | − | 0.129121i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.34315 | − | 9.25460i | −0.177416 | − | 0.307294i | 0.763579 | − | 0.645715i | \(-0.223441\pi\) |
−0.940995 | + | 0.338421i | \(0.890107\pi\) | |||||||
\(908\) | −14.4142 | + | 24.9662i | −0.478352 | + | 0.828531i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.24264 | − | 5.49333i | 0.0743428 | − | 0.182102i | ||||
\(911\) | 30.4853 | 1.01002 | 0.505011 | − | 0.863113i | \(-0.331488\pi\) | ||||
0.505011 | + | 0.863113i | \(0.331488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.07107 | + | 10.5154i | 0.200923 | + | 0.348009i | ||||
\(914\) | −5.82843 | − | 10.0951i | −0.192787 | − | 0.333917i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.3137 | 0.770307 | ||||||||
\(917\) | −1.53553 | + | 0.210133i | −0.0507078 | + | 0.00693920i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.0711 | + | 19.1757i | −0.365201 | + | 0.632546i | −0.988808 | − | 0.149191i | \(-0.952333\pi\) |
0.623608 | + | 0.781738i | \(0.285666\pi\) | |||||||
\(920\) | 1.82843 | + | 3.16693i | 0.0602815 | + | 0.104411i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.15685 | − | 7.19988i | 0.136899 | − | 0.237116i | ||||
\(923\) | −42.3848 | −1.39511 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.8406 | 1.44147 | ||||||||
\(926\) | 6.41421 | − | 11.1097i | 0.210784 | − | 0.365089i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.32843 | − | 2.30090i | −0.0436078 | − | 0.0755309i | ||||
\(929\) | −20.2279 | + | 35.0358i | −0.663657 | + | 1.14949i | 0.315991 | + | 0.948762i | \(0.397663\pi\) |
−0.979648 | + | 0.200725i | \(0.935670\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.92893 | + | 2.86976i | 0.0959919 | + | 0.0940524i | ||||
\(932\) | −1.41421 | −0.0463241 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.0000 | + | 29.4449i | 0.556257 | + | 0.963465i | ||||
\(935\) | −1.07107 | − | 1.85514i | −0.0350277 | − | 0.0606697i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.4142 | −0.634235 | −0.317117 | − | 0.948386i | \(-0.602715\pi\) | ||||
−0.317117 | + | 0.948386i | \(0.602715\pi\) | |||||||
\(938\) | −4.47056 | − | 5.76500i | −0.145969 | − | 0.188234i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.07107 | + | 5.31925i | −0.100167 | + | 0.173495i | ||||
\(941\) | 12.3284 | + | 21.3535i | 0.401895 | + | 0.696103i | 0.993955 | − | 0.109791i | \(-0.0350183\pi\) |
−0.592059 | + | 0.805894i | \(0.701685\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.8995 | + | 29.2708i | −0.550323 | + | 0.953188i | ||||
\(944\) | 5.58579 | 0.181802 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.65685 | −0.183920 | ||||||||
\(947\) | 17.4142 | − | 30.1623i | 0.565886 | − | 0.980143i | −0.431081 | − | 0.902313i | \(-0.641868\pi\) |
0.996967 | − | 0.0778298i | \(-0.0247991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0208 | − | 31.2130i | −0.584980 | − | 1.01322i | ||||
\(950\) | 1.36396 | − | 2.36245i | 0.0442527 | − | 0.0766480i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.65685 | − | 8.95743i | 0.118519 | − | 0.290312i | ||||
\(953\) | −5.55635 | −0.179988 | −0.0899939 | − | 0.995942i | \(-0.528685\pi\) | ||||
−0.0899939 | + | 0.995942i | \(0.528685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.10051 | − | 3.63818i | −0.0679707 | − | 0.117729i | ||||
\(956\) | 10.1066 | + | 17.5051i | 0.326871 | + | 0.566157i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.9289 | −0.385406 | ||||||||
\(959\) | 16.6569 | − | 40.8008i | 0.537878 | − | 1.31753i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 18.0208 | + | 31.2130i | 0.581014 | + | 1.00635i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.12132 | + | 10.6024i | −0.197154 | + | 0.341482i | ||||
\(965\) | 12.8284 | 0.412962 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.2843 | −1.16682 | −0.583412 | − | 0.812177i | \(-0.698283\pi\) | ||||
−0.583412 | + | 0.812177i | \(0.698283\pi\) | |||||||
\(968\) | 0.500000 | − | 0.866025i | 0.0160706 | − | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.12132 | − | 1.94218i | −0.0360034 | − | 0.0623598i | ||||
\(971\) | 11.1360 | − | 19.2882i | 0.357372 | − | 0.618987i | −0.630149 | − | 0.776475i | \(-0.717006\pi\) |
0.987521 | + | 0.157487i | \(0.0503393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.65685 | 0.309426 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.91421 | − | 10.2437i | −0.189309 | − | 0.327893i | ||||
\(977\) | 20.0000 | + | 34.6410i | 0.639857 | + | 1.10826i | 0.985464 | + | 0.169885i | \(0.0543396\pi\) |
−0.345607 | + | 0.938379i | \(0.612327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4853 | 0.399031 | ||||||||
\(980\) | −1.02082 | + | 3.97141i | −0.0326087 | + | 0.126862i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.58579 | + | 16.6031i | −0.305895 | + | 0.529825i | ||||
\(983\) | 16.2132 | + | 28.0821i | 0.517121 | + | 0.895680i | 0.999802 | + | 0.0198836i | \(0.00632957\pi\) |
−0.482681 | + | 0.875796i | \(0.660337\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.150758 | + | 0.261120i | −0.00480354 | + | 0.00831997i | ||||
\(986\) | −9.71573 | −0.309412 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.24264 | 0.0713479 | ||||||||
\(989\) | 17.6569 | − | 30.5826i | 0.561455 | − | 0.972469i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.807612 | + | 1.39882i | 0.0256546 | + | 0.0444351i | 0.878568 | − | 0.477618i | \(-0.158500\pi\) |
−0.852913 | + | 0.522053i | \(0.825166\pi\) | |||||||
\(992\) | −2.00000 | + | 3.46410i | −0.0635001 | + | 0.109985i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 29.0208 | − | 3.97141i | 0.920484 | − | 0.125965i | ||||
\(995\) | 0.0588745 | 0.00186645 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.58579 | − | 11.4069i | −0.208574 | − | 0.361261i | 0.742692 | − | 0.669634i | \(-0.233549\pi\) |
−0.951266 | + | 0.308373i | \(0.900216\pi\) | |||||||
\(998\) | 11.0711 | + | 19.1757i | 0.350449 | + | 0.606995i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1386.2.k.t.793.2 | 4 | ||
3.2 | odd | 2 | 154.2.e.e.23.2 | ✓ | 4 | ||
7.2 | even | 3 | 9702.2.a.cx.1.1 | 2 | |||
7.4 | even | 3 | inner | 1386.2.k.t.991.2 | 4 | ||
7.5 | odd | 6 | 9702.2.a.ch.1.2 | 2 | |||
12.11 | even | 2 | 1232.2.q.f.177.1 | 4 | |||
21.2 | odd | 6 | 1078.2.a.t.1.1 | 2 | |||
21.5 | even | 6 | 1078.2.a.x.1.2 | 2 | |||
21.11 | odd | 6 | 154.2.e.e.67.2 | yes | 4 | ||
21.17 | even | 6 | 1078.2.e.m.67.1 | 4 | |||
21.20 | even | 2 | 1078.2.e.m.177.1 | 4 | |||
84.11 | even | 6 | 1232.2.q.f.529.1 | 4 | |||
84.23 | even | 6 | 8624.2.a.cc.1.2 | 2 | |||
84.47 | odd | 6 | 8624.2.a.bh.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.e.23.2 | ✓ | 4 | 3.2 | odd | 2 | ||
154.2.e.e.67.2 | yes | 4 | 21.11 | odd | 6 | ||
1078.2.a.t.1.1 | 2 | 21.2 | odd | 6 | |||
1078.2.a.x.1.2 | 2 | 21.5 | even | 6 | |||
1078.2.e.m.67.1 | 4 | 21.17 | even | 6 | |||
1078.2.e.m.177.1 | 4 | 21.20 | even | 2 | |||
1232.2.q.f.177.1 | 4 | 12.11 | even | 2 | |||
1232.2.q.f.529.1 | 4 | 84.11 | even | 6 | |||
1386.2.k.t.793.2 | 4 | 1.1 | even | 1 | trivial | ||
1386.2.k.t.991.2 | 4 | 7.4 | even | 3 | inner | ||
8624.2.a.bh.1.1 | 2 | 84.47 | odd | 6 | |||
8624.2.a.cc.1.2 | 2 | 84.23 | even | 6 | |||
9702.2.a.ch.1.2 | 2 | 7.5 | odd | 6 | |||
9702.2.a.cx.1.1 | 2 | 7.2 | even | 3 |