Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(188,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.188");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.50917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 188.3 | ||
Root | \(1.93649 - 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.188 |
Dual form | 189.2.c.b.188.1 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23607i | 1.58114i | 0.612372 | + | 0.790569i | \(0.290215\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.00000 | −1.50000 | ||||||||
\(5\) | −3.87298 | −1.73205 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | − | 2.23607i | − | 0.790569i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 8.66025i | − | 2.73861i | ||||||
\(11\) | 2.23607i | 0.674200i | 0.941469 | + | 0.337100i | \(0.109446\pi\) | ||||
−0.941469 | + | 0.337100i | \(0.890554\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 3.87298 | − | 4.47214i | 1.03510 | − | 1.19523i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.19615i | 1.19208i | 0.802955 | + | 0.596040i | \(0.203260\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 11.6190 | 2.59808 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.00000 | −1.06600 | ||||||||
\(23\) | 2.23607i | 0.466252i | 0.972446 | + | 0.233126i | \(0.0748955\pi\) | ||||
−0.972446 | + | 0.233126i | \(0.925104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.0000 | 2.00000 | ||||||||
\(26\) | −7.74597 | −1.51911 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.00000 | + | 5.19615i | 1.13389 | + | 0.981981i | ||||
\(29\) | − | 4.47214i | − | 0.830455i | −0.909718 | − | 0.415227i | \(-0.863702\pi\) | ||
0.909718 | − | 0.415227i | \(-0.136298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.73205i | − | 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | − | 6.70820i | − | 1.18585i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.74597 | + | 6.70820i | 1.30931 | + | 1.13389i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | −11.6190 | −1.88484 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.66025i | 1.36931i | ||||||||
\(41\) | −3.87298 | −0.604858 | −0.302429 | − | 0.953172i | \(-0.597798\pi\) | ||||
−0.302429 | + | 0.953172i | \(0.597798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | − | 6.70820i | − | 1.01130i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.00000 | −0.737210 | ||||||||
\(47\) | −7.74597 | −1.12987 | −0.564933 | − | 0.825137i | \(-0.691098\pi\) | ||||
−0.564933 | + | 0.825137i | \(0.691098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 22.3607i | 3.16228i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 10.3923i | − | 1.44115i | ||||||
\(53\) | 8.94427i | 1.22859i | 0.789076 | + | 0.614295i | \(0.210560\pi\) | ||||
−0.789076 | + | 0.614295i | \(0.789440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.66025i | − | 1.16775i | ||||||
\(56\) | −3.87298 | + | 4.47214i | −0.517549 | + | 0.597614i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.0000 | 1.31306 | ||||||||
\(59\) | 7.74597 | 1.00844 | 0.504219 | − | 0.863576i | \(-0.331780\pi\) | ||||
0.504219 | + | 0.863576i | \(0.331780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.92820i | 0.887066i | 0.896258 | + | 0.443533i | \(0.146275\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 3.87298 | 0.491869 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | − | 13.4164i | − | 1.66410i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0000 | −1.22169 | −0.610847 | − | 0.791748i | \(-0.709171\pi\) | ||||
−0.610847 | + | 0.791748i | \(0.709171\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −15.0000 | + | 17.3205i | −1.79284 | + | 2.07020i | ||||
\(71\) | − | 11.1803i | − | 1.32686i | −0.748237 | − | 0.663431i | \(-0.769100\pi\) | ||
0.748237 | − | 0.663431i | \(-0.230900\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.3923i | 1.21633i | 0.793812 | + | 0.608164i | \(0.208094\pi\) | ||||
−0.793812 | + | 0.608164i | \(0.791906\pi\) | |||||||
\(74\) | − | 2.23607i | − | 0.259938i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 15.5885i | − | 1.78812i | ||||||
\(77\) | 3.87298 | − | 4.47214i | 0.441367 | − | 0.509647i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | 0.225018 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(80\) | 3.87298 | 0.433013 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 8.66025i | − | 0.956365i | ||||||
\(83\) | −7.74597 | −0.850230 | −0.425115 | − | 0.905139i | \(-0.639766\pi\) | ||||
−0.425115 | + | 0.905139i | \(0.639766\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.47214i | 0.482243i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | 11.6190 | 1.23161 | 0.615803 | − | 0.787900i | \(-0.288832\pi\) | ||||
0.615803 | + | 0.787900i | \(0.288832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | − | 6.92820i | 0.628971 | − | 0.726273i | ||||
\(92\) | − | 6.70820i | − | 0.699379i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 17.3205i | − | 1.78647i | ||||||
\(95\) | − | 20.1246i | − | 2.06474i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.8564i | − | 1.40690i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||
0.710742 | − | 0.703452i | \(-0.248359\pi\) | |||||||
\(98\) | −15.4919 | + | 2.23607i | −1.56492 | + | 0.225877i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −30.0000 | −3.00000 | ||||||||
\(101\) | 15.4919 | 1.54150 | 0.770752 | − | 0.637135i | \(-0.219880\pi\) | ||||
0.770752 | + | 0.637135i | \(0.219880\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.73205i | − | 0.170664i | −0.996353 | − | 0.0853320i | \(-0.972805\pi\) | ||
0.996353 | − | 0.0853320i | \(-0.0271951\pi\) | |||||||
\(104\) | 7.74597 | 0.759555 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.0000 | −1.94257 | ||||||||
\(107\) | 8.94427i | 0.864675i | 0.901712 | + | 0.432338i | \(0.142311\pi\) | ||||
−0.901712 | + | 0.432338i | \(0.857689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 19.3649 | 1.84637 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | 8.94427i | 0.841406i | 0.907198 | + | 0.420703i | \(0.138217\pi\) | ||||
−0.907198 | + | 0.420703i | \(0.861783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.66025i | − | 0.807573i | ||||||
\(116\) | 13.4164i | 1.24568i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.3205i | 1.59448i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.00000 | 0.545455 | ||||||||
\(122\) | −15.4919 | −1.40257 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.19615i | 0.466628i | ||||||||
\(125\) | −19.3649 | −1.73205 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | −0.887357 | −0.443678 | − | 0.896186i | \(-0.646327\pi\) | ||||
−0.443678 | + | 0.896186i | \(0.646327\pi\) | |||||||
\(128\) | 15.6525i | 1.38350i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 30.0000 | 2.63117 | ||||||||
\(131\) | 7.74597 | 0.676768 | 0.338384 | − | 0.941008i | \(-0.390120\pi\) | ||||
0.338384 | + | 0.941008i | \(0.390120\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.00000 | − | 10.3923i | 0.780399 | − | 0.901127i | ||||
\(134\) | − | 22.3607i | − | 1.93167i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.3607i | 1.91040i | 0.295958 | + | 0.955201i | \(0.404361\pi\) | ||||
−0.295958 | + | 0.955201i | \(0.595639\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.46410i | 0.293821i | 0.989150 | + | 0.146911i | \(0.0469330\pi\) | ||||
−0.989150 | + | 0.146911i | \(0.953067\pi\) | |||||||
\(140\) | −23.2379 | − | 20.1246i | −1.96396 | − | 1.70084i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.0000 | 2.09795 | ||||||||
\(143\) | −7.74597 | −0.647750 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.3205i | 1.43839i | ||||||||
\(146\) | −23.2379 | −1.92318 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.00000 | 0.246598 | ||||||||
\(149\) | 8.94427i | 0.732743i | 0.930469 | + | 0.366372i | \(0.119400\pi\) | ||||
−0.930469 | + | 0.366372i | \(0.880600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 11.6190 | 0.942421 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.0000 | + | 8.66025i | 0.805823 | + | 0.697863i | ||||
\(155\) | 6.70820i | 0.538816i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.46410i | 0.276465i | 0.990400 | + | 0.138233i | \(0.0441422\pi\) | ||||
−0.990400 | + | 0.138233i | \(0.955858\pi\) | |||||||
\(158\) | 4.47214i | 0.355784i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 25.9808i | 2.05396i | ||||||||
\(161\) | 3.87298 | − | 4.47214i | 0.305234 | − | 0.352454i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 11.6190 | 0.907288 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 17.3205i | − | 1.34433i | ||||||
\(167\) | −15.4919 | −1.19880 | −0.599401 | − | 0.800449i | \(-0.704594\pi\) | ||||
−0.599401 | + | 0.800449i | \(0.704594\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.00000 | −0.457496 | ||||||||
\(173\) | 3.87298 | 0.294457 | 0.147229 | − | 0.989102i | \(-0.452965\pi\) | ||||
0.147229 | + | 0.989102i | \(0.452965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.0000 | − | 17.3205i | −1.51186 | − | 1.30931i | ||||
\(176\) | − | 2.23607i | − | 0.168550i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 25.9808i | 1.94734i | ||||||||
\(179\) | − | 17.8885i | − | 1.33705i | −0.743689 | − | 0.668526i | \(-0.766925\pi\) | ||
0.743689 | − | 0.668526i | \(-0.233075\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 15.4919 | + | 13.4164i | 1.14834 | + | 0.994490i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.00000 | 0.368605 | ||||||||
\(185\) | 3.87298 | 0.284747 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 23.2379 | 1.69480 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 45.0000 | 3.26464 | ||||||||
\(191\) | 2.23607i | 0.161796i | 0.996722 | + | 0.0808981i | \(0.0257788\pi\) | ||||
−0.996722 | + | 0.0808981i | \(0.974221\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 30.9839 | 2.22451 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | − | 20.7846i | −0.214286 | − | 1.48461i | ||||
\(197\) | 8.94427i | 0.637253i | 0.947880 | + | 0.318626i | \(0.103222\pi\) | ||||
−0.947880 | + | 0.318626i | \(0.896778\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 25.9808i | − | 1.84173i | −0.389885 | − | 0.920864i | \(-0.627485\pi\) | ||
0.389885 | − | 0.920864i | \(-0.372515\pi\) | |||||||
\(200\) | − | 22.3607i | − | 1.58114i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 34.6410i | 2.43733i | ||||||||
\(203\) | −7.74597 | + | 8.94427i | −0.543660 | + | 0.627765i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.0000 | 1.04765 | ||||||||
\(206\) | 3.87298 | 0.269844 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3.46410i | − | 0.240192i | ||||||
\(209\) | −11.6190 | −0.803700 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | − | 26.8328i | − | 1.84289i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.0000 | −1.36717 | ||||||||
\(215\) | −7.74597 | −0.528271 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | + | 3.46410i | −0.203653 | + | 0.235159i | ||||
\(218\) | − | 15.6525i | − | 1.06012i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 25.9808i | 1.75162i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.73205i | 0.115987i | 0.998317 | + | 0.0579934i | \(0.0184702\pi\) | ||||
−0.998317 | + | 0.0579934i | \(0.981530\pi\) | |||||||
\(224\) | −11.6190 | + | 13.4164i | −0.776324 | + | 0.896421i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.0000 | −1.33038 | ||||||||
\(227\) | 15.4919 | 1.02824 | 0.514118 | − | 0.857720i | \(-0.328119\pi\) | ||||
0.514118 | + | 0.857720i | \(0.328119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8564i | 0.915657i | 0.889041 | + | 0.457829i | \(0.151373\pi\) | ||||
−0.889041 | + | 0.457829i | \(0.848627\pi\) | |||||||
\(230\) | 19.3649 | 1.27688 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.0000 | −0.656532 | ||||||||
\(233\) | − | 17.8885i | − | 1.17192i | −0.810341 | − | 0.585959i | \(-0.800718\pi\) | ||
0.810341 | − | 0.585959i | \(-0.199282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.0000 | 1.95698 | ||||||||
\(236\) | −23.2379 | −1.51266 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.94427i | 0.578557i | 0.957245 | + | 0.289278i | \(0.0934153\pi\) | ||||
−0.957245 | + | 0.289278i | \(0.906585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.3205i | 1.11571i | 0.829938 | + | 0.557856i | \(0.188376\pi\) | ||||
−0.829938 | + | 0.557856i | \(0.811624\pi\) | |||||||
\(242\) | 13.4164i | 0.862439i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 20.7846i | − | 1.33060i | ||||||
\(245\) | −3.87298 | − | 26.8328i | −0.247436 | − | 1.71429i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.0000 | −1.14531 | ||||||||
\(248\) | −3.87298 | −0.245935 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 43.3013i | − | 2.73861i | ||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.00000 | −0.314347 | ||||||||
\(254\) | − | 22.3607i | − | 1.40303i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | −27.1109 | −1.69113 | −0.845565 | − | 0.533872i | \(-0.820736\pi\) | ||||
−0.845565 | + | 0.533872i | \(0.820736\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | + | 1.73205i | 0.124274 | + | 0.107624i | ||||
\(260\) | 40.2492i | 2.49615i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.3205i | 1.07006i | ||||||||
\(263\) | 2.23607i | 0.137882i | 0.997621 | + | 0.0689409i | \(0.0219620\pi\) | ||||
−0.997621 | + | 0.0689409i | \(0.978038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 34.6410i | − | 2.12798i | ||||||
\(266\) | 23.2379 | + | 20.1246i | 1.42481 | + | 1.23392i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 30.0000 | 1.83254 | ||||||||
\(269\) | −11.6190 | −0.708420 | −0.354210 | − | 0.935166i | \(-0.615250\pi\) | ||||
−0.354210 | + | 0.935166i | \(0.615250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.3923i | − | 0.631288i | −0.948878 | − | 0.315644i | \(-0.897780\pi\) | ||
0.948878 | − | 0.315644i | \(-0.102220\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −50.0000 | −3.02061 | ||||||||
\(275\) | 22.3607i | 1.34840i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | 0.660926 | 0.330463 | − | 0.943819i | \(-0.392795\pi\) | ||||
0.330463 | + | 0.943819i | \(0.392795\pi\) | |||||||
\(278\) | −7.74597 | −0.464572 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 15.0000 | − | 17.3205i | 0.896421 | − | 1.03510i | ||||
\(281\) | 22.3607i | 1.33393i | 0.745091 | + | 0.666963i | \(0.232406\pi\) | ||||
−0.745091 | + | 0.666963i | \(0.767594\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2487i | 1.44144i | 0.693228 | + | 0.720718i | \(0.256188\pi\) | ||||
−0.693228 | + | 0.720718i | \(0.743812\pi\) | |||||||
\(284\) | 33.5410i | 1.99029i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 17.3205i | − | 1.02418i | ||||||
\(287\) | 7.74597 | + | 6.70820i | 0.457230 | + | 0.395973i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −38.7298 | −2.27429 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 31.1769i | − | 1.82449i | ||||||
\(293\) | 30.9839 | 1.81010 | 0.905048 | − | 0.425309i | \(-0.139834\pi\) | ||||
0.905048 | + | 0.425309i | \(0.139834\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.0000 | −1.74667 | ||||||||
\(296\) | 2.23607i | 0.129969i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.0000 | −1.15857 | ||||||||
\(299\) | −7.74597 | −0.447961 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | − | 3.46410i | −0.230556 | − | 0.199667i | ||||
\(302\) | − | 35.7771i | − | 2.05874i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 5.19615i | − | 0.298020i | ||||||
\(305\) | − | 26.8328i | − | 1.53644i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.19615i | 0.296560i | 0.988945 | + | 0.148280i | \(0.0473737\pi\) | ||||
−0.988945 | + | 0.148280i | \(0.952626\pi\) | |||||||
\(308\) | −11.6190 | + | 13.4164i | −0.662051 | + | 0.764471i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.0000 | −0.851943 | ||||||||
\(311\) | 7.74597 | 0.439233 | 0.219617 | − | 0.975586i | \(-0.429519\pi\) | ||||
0.219617 | + | 0.975586i | \(0.429519\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.46410i | − | 0.195803i | −0.995196 | − | 0.0979013i | \(-0.968787\pi\) | ||
0.995196 | − | 0.0979013i | \(-0.0312129\pi\) | |||||||
\(314\) | −7.74597 | −0.437130 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | − | 4.47214i | − | 0.251180i | −0.992082 | − | 0.125590i | \(-0.959918\pi\) | ||
0.992082 | − | 0.125590i | \(-0.0400824\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0000 | 0.559893 | ||||||||
\(320\) | −50.3488 | −2.81458 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.0000 | + | 8.66025i | 0.557278 | + | 0.482617i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.6410i | 1.92154i | ||||||||
\(326\) | − | 22.3607i | − | 1.23844i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.66025i | 0.478183i | ||||||||
\(329\) | 15.4919 | + | 13.4164i | 0.854098 | + | 0.739671i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 23.2379 | 1.27535 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 34.6410i | − | 1.89547i | ||||||
\(335\) | 38.7298 | 2.11604 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.0000 | 1.90657 | 0.953286 | − | 0.302070i | \(-0.0976776\pi\) | ||||
0.953286 | + | 0.302070i | \(0.0976776\pi\) | |||||||
\(338\) | 2.23607i | 0.121626i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.87298 | 0.209734 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | − | 4.47214i | − | 0.241121i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.66025i | 0.465578i | ||||||||
\(347\) | − | 11.1803i | − | 0.600192i | −0.953909 | − | 0.300096i | \(-0.902981\pi\) | ||
0.953909 | − | 0.300096i | \(-0.0970187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.8564i | − | 0.741716i | −0.928689 | − | 0.370858i | \(-0.879064\pi\) | ||
0.928689 | − | 0.370858i | \(-0.120936\pi\) | |||||||
\(350\) | 38.7298 | − | 44.7214i | 2.07020 | − | 2.39046i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.0000 | 0.799503 | ||||||||
\(353\) | −19.3649 | −1.03069 | −0.515345 | − | 0.856983i | \(-0.672336\pi\) | ||||
−0.515345 | + | 0.856983i | \(0.672336\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 43.3013i | 2.29819i | ||||||||
\(356\) | −34.8569 | −1.84741 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 40.0000 | 2.11407 | ||||||||
\(359\) | 8.94427i | 0.472061i | 0.971746 | + | 0.236030i | \(0.0758465\pi\) | ||||
−0.971746 | + | 0.236030i | \(0.924154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | −0.421053 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −18.0000 | + | 20.7846i | −0.943456 | + | 1.08941i | ||||
\(365\) | − | 40.2492i | − | 2.10674i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.73205i | 0.0904123i | 0.998978 | + | 0.0452062i | \(0.0143945\pi\) | ||||
−0.998978 | + | 0.0452062i | \(0.985606\pi\) | |||||||
\(368\) | − | 2.23607i | − | 0.116563i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.66025i | 0.450225i | ||||||||
\(371\) | 15.4919 | − | 17.8885i | 0.804301 | − | 0.928727i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0000 | 0.880227 | 0.440113 | − | 0.897942i | \(-0.354938\pi\) | ||||
0.440113 | + | 0.897942i | \(0.354938\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.3205i | 0.893237i | ||||||||
\(377\) | 15.4919 | 0.797875 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0000 | 1.33553 | 0.667765 | − | 0.744372i | \(-0.267251\pi\) | ||||
0.667765 | + | 0.744372i | \(0.267251\pi\) | |||||||
\(380\) | 60.3738i | 3.09711i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.00000 | −0.255822 | ||||||||
\(383\) | 30.9839 | 1.58320 | 0.791601 | − | 0.611039i | \(-0.209248\pi\) | ||||
0.791601 | + | 0.611039i | \(0.209248\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.0000 | + | 17.3205i | −0.764471 | + | 0.882735i | ||||
\(386\) | 4.47214i | 0.227626i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 41.5692i | 2.11036i | ||||||||
\(389\) | 35.7771i | 1.81397i | 0.421163 | + | 0.906985i | \(0.361622\pi\) | ||||
−0.421163 | + | 0.906985i | \(0.638378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 15.4919 | − | 2.23607i | 0.782461 | − | 0.112938i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.0000 | −1.00759 | ||||||||
\(395\) | −7.74597 | −0.389742 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.7846i | − | 1.04315i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||
0.853206 | − | 0.521575i | \(-0.174655\pi\) | |||||||
\(398\) | 58.0948 | 2.91203 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.0000 | −0.500000 | ||||||||
\(401\) | − | 31.3050i | − | 1.56329i | −0.623721 | − | 0.781647i | \(-0.714380\pi\) | ||
0.623721 | − | 0.781647i | \(-0.285620\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000 | 0.298881 | ||||||||
\(404\) | −46.4758 | −2.31226 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.0000 | − | 17.3205i | −0.992583 | − | 0.859602i | ||||
\(407\) | − | 2.23607i | − | 0.110838i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.3205i | − | 0.856444i | −0.903674 | − | 0.428222i | \(-0.859140\pi\) | ||
0.903674 | − | 0.428222i | \(-0.140860\pi\) | |||||||
\(410\) | 33.5410i | 1.65647i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.19615i | 0.255996i | ||||||||
\(413\) | −15.4919 | − | 13.4164i | −0.762308 | − | 0.660178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.0000 | 1.47264 | ||||||||
\(416\) | 23.2379 | 1.13933 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 25.9808i | − | 1.27076i | ||||||
\(419\) | −15.4919 | −0.756830 | −0.378415 | − | 0.925636i | \(-0.623531\pi\) | ||||
−0.378415 | + | 0.925636i | \(0.623531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | 0.536107 | 0.268054 | − | 0.963404i | \(-0.413620\pi\) | ||||
0.268054 | + | 0.963404i | \(0.413620\pi\) | |||||||
\(422\) | 17.8885i | 0.870801i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 20.0000 | 0.971286 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | − | 13.8564i | 0.580721 | − | 0.670559i | ||||
\(428\) | − | 26.8328i | − | 1.29701i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 17.3205i | − | 0.835269i | ||||||
\(431\) | 2.23607i | 0.107708i | 0.998549 | + | 0.0538538i | \(0.0171505\pi\) | ||||
−0.998549 | + | 0.0538538i | \(0.982850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.3923i | 0.499422i | 0.968320 | + | 0.249711i | \(0.0803357\pi\) | ||||
−0.968320 | + | 0.249711i | \(0.919664\pi\) | |||||||
\(434\) | −7.74597 | − | 6.70820i | −0.371818 | − | 0.322004i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.0000 | 1.00572 | ||||||||
\(437\) | −11.6190 | −0.555810 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.1051i | 1.81866i | 0.416078 | + | 0.909329i | \(0.363404\pi\) | ||||
−0.416078 | + | 0.909329i | \(0.636596\pi\) | |||||||
\(440\) | −19.3649 | −0.923186 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 24.5967i | − | 1.16863i | −0.811528 | − | 0.584313i | \(-0.801364\pi\) | ||
0.811528 | − | 0.584313i | \(-0.198636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −45.0000 | −2.13320 | ||||||||
\(446\) | −3.87298 | −0.183391 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −26.0000 | − | 22.5167i | −1.22838 | − | 1.06381i | ||||
\(449\) | 8.94427i | 0.422106i | 0.977475 | + | 0.211053i | \(0.0676893\pi\) | ||||
−0.977475 | + | 0.211053i | \(0.932311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8.66025i | − | 0.407795i | ||||||
\(452\) | − | 26.8328i | − | 1.26211i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 34.6410i | 1.62578i | ||||||||
\(455\) | −23.2379 | + | 26.8328i | −1.08941 | + | 1.25794i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.0000 | −1.16945 | −0.584725 | − | 0.811231i | \(-0.698798\pi\) | ||||
−0.584725 | + | 0.811231i | \(0.698798\pi\) | |||||||
\(458\) | −30.9839 | −1.44778 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 25.9808i | 1.21136i | ||||||||
\(461\) | 3.87298 | 0.180383 | 0.0901914 | − | 0.995924i | \(-0.471252\pi\) | ||||
0.0901914 | + | 0.995924i | \(0.471252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 4.47214i | 0.207614i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 40.0000 | 1.85296 | ||||||||
\(467\) | −23.2379 | −1.07532 | −0.537661 | − | 0.843161i | \(-0.680692\pi\) | ||||
−0.537661 | + | 0.843161i | \(0.680692\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0000 | + | 17.3205i | 0.923514 | + | 0.799787i | ||||
\(470\) | 67.0820i | 3.09426i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 17.3205i | − | 0.797241i | ||||||
\(473\) | 4.47214i | 0.205629i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 51.9615i | 2.38416i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.0000 | −0.914779 | ||||||||
\(479\) | −30.9839 | −1.41569 | −0.707845 | − | 0.706368i | \(-0.750332\pi\) | ||||
−0.707845 | + | 0.706368i | \(0.750332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3.46410i | − | 0.157949i | ||||||
\(482\) | −38.7298 | −1.76410 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.0000 | −0.818182 | ||||||||
\(485\) | 53.6656i | 2.43683i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0000 | −0.453143 | −0.226572 | − | 0.973995i | \(-0.572752\pi\) | ||||
−0.226572 | + | 0.973995i | \(0.572752\pi\) | |||||||
\(488\) | 15.4919 | 0.701287 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 60.0000 | − | 8.66025i | 2.71052 | − | 0.391230i | ||||
\(491\) | − | 38.0132i | − | 1.71551i | −0.514059 | − | 0.857755i | \(-0.671859\pi\) | ||
0.514059 | − | 0.857755i | \(-0.328141\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | − | 40.2492i | − | 1.81090i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73205i | 0.0777714i | ||||||||
\(497\) | −19.3649 | + | 22.3607i | −0.868635 | + | 1.00301i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.0000 | 1.70111 | 0.850557 | − | 0.525883i | \(-0.176265\pi\) | ||||
0.850557 | + | 0.525883i | \(0.176265\pi\) | |||||||
\(500\) | 58.0948 | 2.59808 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.2379 | 1.03613 | 0.518063 | − | 0.855342i | \(-0.326653\pi\) | ||||
0.518063 | + | 0.855342i | \(0.326653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −60.0000 | −2.66996 | ||||||||
\(506\) | − | 11.1803i | − | 0.497027i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.0000 | 1.33103 | ||||||||
\(509\) | −15.4919 | −0.686668 | −0.343334 | − | 0.939213i | \(-0.611556\pi\) | ||||
−0.343334 | + | 0.939213i | \(0.611556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0000 | − | 20.7846i | 0.796273 | − | 0.919457i | ||||
\(512\) | 11.1803i | 0.494106i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 60.6218i | − | 2.67391i | ||||||
\(515\) | 6.70820i | 0.295599i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 17.3205i | − | 0.761755i | ||||||
\(518\) | −3.87298 | + | 4.47214i | −0.170169 | + | 0.196494i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −30.0000 | −1.31559 | ||||||||
\(521\) | 34.8569 | 1.52711 | 0.763553 | − | 0.645745i | \(-0.223453\pi\) | ||||
0.763553 | + | 0.645745i | \(0.223453\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5885i | 0.681636i | 0.940129 | + | 0.340818i | \(0.110704\pi\) | ||||
−0.940129 | + | 0.340818i | \(0.889296\pi\) | |||||||
\(524\) | −23.2379 | −1.01515 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.00000 | −0.218010 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.0000 | 0.782609 | ||||||||
\(530\) | 77.4597 | 3.36463 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −27.0000 | + | 31.1769i | −1.17060 | + | 1.35169i | ||||
\(533\) | − | 13.4164i | − | 0.581129i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 34.6410i | − | 1.49766i | ||||||
\(536\) | 22.3607i | 0.965834i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 25.9808i | − | 1.12011i | ||||||
\(539\) | −15.4919 | + | 2.23607i | −0.667285 | + | 0.0963143i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | −0.0429934 | −0.0214967 | − | 0.999769i | \(-0.506843\pi\) | ||||
−0.0214967 | + | 0.999769i | \(0.506843\pi\) | |||||||
\(542\) | 23.2379 | 0.998153 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.1109 | 1.16130 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | −0.684111 | −0.342055 | − | 0.939680i | \(-0.611123\pi\) | ||||
−0.342055 | + | 0.939680i | \(0.611123\pi\) | |||||||
\(548\) | − | 67.0820i | − | 2.86560i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −50.0000 | −2.13201 | ||||||||
\(551\) | 23.2379 | 0.989968 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | − | 3.46410i | −0.170097 | − | 0.147309i | ||||
\(554\) | 24.5967i | 1.04502i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 10.3923i | − | 0.440732i | ||||||
\(557\) | 8.94427i | 0.378981i | 0.981883 | + | 0.189490i | \(0.0606836\pi\) | ||||
−0.981883 | + | 0.189490i | \(0.939316\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.92820i | 0.293032i | ||||||||
\(560\) | −7.74597 | − | 6.70820i | −0.327327 | − | 0.283473i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −50.0000 | −2.10912 | ||||||||
\(563\) | −38.7298 | −1.63227 | −0.816134 | − | 0.577863i | \(-0.803887\pi\) | ||||
−0.816134 | + | 0.577863i | \(0.803887\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 34.6410i | − | 1.45736i | ||||||
\(566\) | −54.2218 | −2.27911 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.0000 | −1.04898 | ||||||||
\(569\) | − | 17.8885i | − | 0.749927i | −0.927040 | − | 0.374963i | \(-0.877655\pi\) | ||
0.927040 | − | 0.374963i | \(-0.122345\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | −0.669579 | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | 23.2379 | 0.971625 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.0000 | + | 17.3205i | −0.626088 | + | 0.722944i | ||||
\(575\) | 22.3607i | 0.932505i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 20.7846i | − | 0.865275i | −0.901568 | − | 0.432637i | \(-0.857583\pi\) | ||
0.901568 | − | 0.432637i | \(-0.142417\pi\) | |||||||
\(578\) | − | 38.0132i | − | 1.58114i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 51.9615i | − | 2.15758i | ||||||
\(581\) | 15.4919 | + | 13.4164i | 0.642714 | + | 0.556606i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.0000 | −0.828315 | ||||||||
\(584\) | 23.2379 | 0.961591 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 69.2820i | 2.86201i | ||||||||
\(587\) | −30.9839 | −1.27884 | −0.639421 | − | 0.768857i | \(-0.720826\pi\) | ||||
−0.639421 | + | 0.768857i | \(0.720826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.00000 | 0.370839 | ||||||||
\(590\) | − | 67.0820i | − | 2.76172i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | 0.0410997 | ||||||||
\(593\) | 34.8569 | 1.43140 | 0.715700 | − | 0.698408i | \(-0.246108\pi\) | ||||
0.715700 | + | 0.698408i | \(0.246108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 26.8328i | − | 1.09911i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 17.3205i | − | 0.708288i | ||||||
\(599\) | 29.0689i | 1.18772i | 0.804568 | + | 0.593861i | \(0.202397\pi\) | ||||
−0.804568 | + | 0.593861i | \(0.797603\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.2487i | − | 0.989126i | −0.869142 | − | 0.494563i | \(-0.835328\pi\) | ||
0.869142 | − | 0.494563i | \(-0.164672\pi\) | |||||||
\(602\) | 7.74597 | − | 8.94427i | 0.315702 | − | 0.364541i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 48.0000 | 1.95309 | ||||||||
\(605\) | −23.2379 | −0.944755 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 38.1051i | − | 1.54664i | −0.634017 | − | 0.773320i | \(-0.718595\pi\) | ||
0.634017 | − | 0.773320i | \(-0.281405\pi\) | |||||||
\(608\) | 34.8569 | 1.41363 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 60.0000 | 2.42933 | ||||||||
\(611\) | − | 26.8328i | − | 1.08554i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0000 | 0.686624 | 0.343312 | − | 0.939222i | \(-0.388451\pi\) | ||||
0.343312 | + | 0.939222i | \(0.388451\pi\) | |||||||
\(614\) | −11.6190 | −0.468903 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.0000 | − | 8.66025i | −0.402911 | − | 0.348932i | ||||
\(617\) | 22.3607i | 0.900207i | 0.892976 | + | 0.450104i | \(0.148613\pi\) | ||||
−0.892976 | + | 0.450104i | \(0.851387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.5167i | 0.905021i | 0.891759 | + | 0.452510i | \(0.149471\pi\) | ||||
−0.891759 | + | 0.452510i | \(0.850529\pi\) | |||||||
\(620\) | − | 20.1246i | − | 0.808224i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.3205i | 0.694489i | ||||||||
\(623\) | −23.2379 | − | 20.1246i | −0.931007 | − | 0.806276i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 7.74597 | 0.309591 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 10.3923i | − | 0.414698i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | − | 4.47214i | − | 0.177892i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.0000 | 0.397151 | ||||||||
\(635\) | 38.7298 | 1.53695 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.0000 | + | 3.46410i | −0.950915 | + | 0.137253i | ||||
\(638\) | 22.3607i | 0.885268i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 60.6218i | − | 2.39629i | ||||||
\(641\) | − | 17.8885i | − | 0.706555i | −0.935519 | − | 0.353278i | \(-0.885067\pi\) | ||
0.935519 | − | 0.353278i | \(-0.114933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.8372i | 1.57102i | 0.618846 | + | 0.785512i | \(0.287600\pi\) | ||||
−0.618846 | + | 0.785512i | \(0.712400\pi\) | |||||||
\(644\) | −11.6190 | + | 13.4164i | −0.457851 | + | 0.528681i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.2379 | 0.913576 | 0.456788 | − | 0.889576i | \(-0.349000\pi\) | ||||
0.456788 | + | 0.889576i | \(0.349000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.3205i | 0.679889i | ||||||||
\(650\) | −77.4597 | −3.03822 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30.0000 | 1.17489 | ||||||||
\(653\) | 49.1935i | 1.92509i | 0.271122 | + | 0.962545i | \(0.412605\pi\) | ||||
−0.271122 | + | 0.962545i | \(0.587395\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.0000 | −1.17220 | ||||||||
\(656\) | 3.87298 | 0.151215 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −30.0000 | + | 34.6410i | −1.16952 | + | 1.35045i | ||||
\(659\) | 2.23607i | 0.0871048i | 0.999051 | + | 0.0435524i | \(0.0138676\pi\) | ||||
−0.999051 | + | 0.0435524i | \(0.986132\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.0333i | 1.75159i | 0.482680 | + | 0.875797i | \(0.339663\pi\) | ||||
−0.482680 | + | 0.875797i | \(0.660337\pi\) | |||||||
\(662\) | − | 8.94427i | − | 0.347629i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.3205i | 0.672166i | ||||||||
\(665\) | −34.8569 | + | 40.2492i | −1.35169 | + | 1.56080i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0000 | 0.387202 | ||||||||
\(668\) | 46.4758 | 1.79820 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 86.6025i | 3.34575i | ||||||||
\(671\) | −15.4919 | −0.598059 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 78.2624i | 3.01455i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.00000 | −0.115385 | ||||||||
\(677\) | 27.1109 | 1.04196 | 0.520978 | − | 0.853570i | \(-0.325567\pi\) | ||||
0.520978 | + | 0.853570i | \(0.325567\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.0000 | + | 27.7128i | −0.921035 | + | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.66025i | 0.331618i | ||||||||
\(683\) | 29.0689i | 1.11229i | 0.831085 | + | 0.556145i | \(0.187720\pi\) | ||||
−0.831085 | + | 0.556145i | \(0.812280\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 86.6025i | − | 3.30891i | ||||||
\(686\) | 34.8569 | + | 22.3607i | 1.33084 | + | 0.853735i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00000 | −0.0762493 | ||||||||
\(689\) | −30.9839 | −1.18039 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.3205i | 0.658903i | 0.944172 | + | 0.329452i | \(0.106864\pi\) | ||||
−0.944172 | + | 0.329452i | \(0.893136\pi\) | |||||||
\(692\) | −11.6190 | −0.441686 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.0000 | 0.948987 | ||||||||
\(695\) | − | 13.4164i | − | 0.508913i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 30.9839 | 1.17276 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 60.0000 | + | 51.9615i | 2.26779 | + | 1.96396i | ||||
\(701\) | − | 31.3050i | − | 1.18237i | −0.806535 | − | 0.591186i | \(-0.798660\pi\) | ||
0.806535 | − | 0.591186i | \(-0.201340\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.19615i | − | 0.195977i | ||||||
\(704\) | 29.0689i | 1.09557i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 43.3013i | − | 1.62966i | ||||||
\(707\) | −30.9839 | − | 26.8328i | −1.16527 | − | 1.00915i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.0000 | −1.61490 | −0.807449 | − | 0.589937i | \(-0.799153\pi\) | ||||
−0.807449 | + | 0.589937i | \(0.799153\pi\) | |||||||
\(710\) | −96.8246 | −3.63376 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 25.9808i | − | 0.973670i | ||||||
\(713\) | 3.87298 | 0.145044 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.0000 | 1.12194 | ||||||||
\(716\) | 53.6656i | 2.00558i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.0000 | −0.746393 | ||||||||
\(719\) | −23.2379 | −0.866627 | −0.433314 | − | 0.901243i | \(-0.642656\pi\) | ||||
−0.433314 | + | 0.901243i | \(0.642656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00000 | + | 3.46410i | −0.111726 | + | 0.129010i | ||||
\(722\) | − | 17.8885i | − | 0.665743i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 44.7214i | − | 1.66091i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.46410i | − | 0.128476i | −0.997935 | − | 0.0642382i | \(-0.979538\pi\) | ||
0.997935 | − | 0.0642382i | \(-0.0204617\pi\) | |||||||
\(728\) | −15.4919 | − | 13.4164i | −0.574169 | − | 0.497245i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 90.0000 | 3.33105 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 38.1051i | − | 1.40744i | −0.710475 | − | 0.703722i | \(-0.751520\pi\) | ||
0.710475 | − | 0.703722i | \(-0.248480\pi\) | |||||||
\(734\) | −3.87298 | −0.142954 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.0000 | 0.552907 | ||||||||
\(737\) | − | 22.3607i | − | 0.823666i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | −11.6190 | −0.427121 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 40.0000 | + | 34.6410i | 1.46845 | + | 1.27171i | ||||
\(743\) | − | 11.1803i | − | 0.410167i | −0.978744 | − | 0.205083i | \(-0.934253\pi\) | ||
0.978744 | − | 0.205083i | \(-0.0657466\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 34.6410i | − | 1.26915i | ||||||
\(746\) | 38.0132i | 1.39176i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.4919 | − | 17.8885i | 0.566063 | − | 0.653633i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.0000 | −1.67856 | −0.839282 | − | 0.543696i | \(-0.817024\pi\) | ||||
−0.839282 | + | 0.543696i | \(0.817024\pi\) | |||||||
\(752\) | 7.74597 | 0.282466 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.6410i | 1.26155i | ||||||||
\(755\) | 61.9677 | 2.25524 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.0000 | −1.23575 | −0.617876 | − | 0.786276i | \(-0.712006\pi\) | ||||
−0.617876 | + | 0.786276i | \(0.712006\pi\) | |||||||
\(758\) | 58.1378i | 2.11166i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −45.0000 | −1.63232 | ||||||||
\(761\) | −15.4919 | −0.561582 | −0.280791 | − | 0.959769i | \(-0.590597\pi\) | ||||
−0.280791 | + | 0.959769i | \(0.590597\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | + | 12.1244i | 0.506834 | + | 0.438931i | ||||
\(764\) | − | 6.70820i | − | 0.242694i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 69.2820i | 2.50326i | ||||||||
\(767\) | 26.8328i | 0.968877i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.3205i | − | 0.624593i | −0.949985 | − | 0.312297i | \(-0.898902\pi\) | ||
0.949985 | − | 0.312297i | \(-0.101098\pi\) | |||||||
\(770\) | −38.7298 | − | 33.5410i | −1.39573 | − | 1.20873i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.00000 | −0.215945 | ||||||||
\(773\) | 11.6190 | 0.417905 | 0.208952 | − | 0.977926i | \(-0.432995\pi\) | ||||
0.208952 | + | 0.977926i | \(0.432995\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 17.3205i | − | 0.622171i | ||||||
\(776\) | −30.9839 | −1.11226 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −80.0000 | −2.86814 | ||||||||
\(779\) | − | 20.1246i | − | 0.721039i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.0000 | 0.894570 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | − | 6.92820i | −0.0357143 | − | 0.247436i | ||||
\(785\) | − | 13.4164i | − | 0.478852i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38.1051i | − | 1.35830i | −0.733999 | − | 0.679150i | \(-0.762348\pi\) | ||
0.733999 | − | 0.679150i | \(-0.237652\pi\) | |||||||
\(788\) | − | 26.8328i | − | 0.955879i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 17.3205i | − | 0.616236i | ||||||
\(791\) | 15.4919 | − | 17.8885i | 0.550830 | − | 0.636043i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | −0.852265 | ||||||||
\(794\) | 46.4758 | 1.64936 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 77.9423i | 2.76259i | ||||||||
\(797\) | −3.87298 | −0.137188 | −0.0685941 | − | 0.997645i | \(-0.521851\pi\) | ||||
−0.0685941 | + | 0.997645i | \(0.521851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | − | 67.0820i | − | 2.37171i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 70.0000 | 2.47179 | ||||||||
\(803\) | −23.2379 | −0.820048 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.0000 | + | 17.3205i | −0.528681 | + | 0.610468i | ||||
\(806\) | 13.4164i | 0.472573i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 34.6410i | − | 1.21867i | ||||||
\(809\) | − | 31.3050i | − | 1.10062i | −0.834959 | − | 0.550312i | \(-0.814509\pi\) | ||
0.834959 | − | 0.550312i | \(-0.185491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.3731i | 1.27723i | 0.769526 | + | 0.638616i | \(0.220493\pi\) | ||||
−0.769526 | + | 0.638616i | \(0.779507\pi\) | |||||||
\(812\) | 23.2379 | − | 26.8328i | 0.815490 | − | 0.941647i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.00000 | 0.175250 | ||||||||
\(815\) | 38.7298 | 1.35665 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3923i | 0.363581i | ||||||||
\(818\) | 38.7298 | 1.35416 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −45.0000 | −1.57147 | ||||||||
\(821\) | 22.3607i | 0.780393i | 0.920732 | + | 0.390197i | \(0.127593\pi\) | ||||
−0.920732 | + | 0.390197i | \(0.872407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | 0.697156 | 0.348578 | − | 0.937280i | \(-0.386665\pi\) | ||||
0.348578 | + | 0.937280i | \(0.386665\pi\) | |||||||
\(824\) | −3.87298 | −0.134922 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.0000 | − | 34.6410i | 1.04383 | − | 1.20532i | ||||
\(827\) | − | 11.1803i | − | 0.388779i | −0.980924 | − | 0.194389i | \(-0.937728\pi\) | ||
0.980924 | − | 0.194389i | \(-0.0622725\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.1769i | 1.08282i | 0.840759 | + | 0.541409i | \(0.182109\pi\) | ||||
−0.840759 | + | 0.541409i | \(0.817891\pi\) | |||||||
\(830\) | 67.0820i | 2.32845i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 45.0333i | 1.56125i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 60.0000 | 2.07639 | ||||||||
\(836\) | 34.8569 | 1.20555 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 34.6410i | − | 1.19665i | ||||||
\(839\) | 38.7298 | 1.33710 | 0.668551 | − | 0.743666i | \(-0.266915\pi\) | ||||
0.668551 | + | 0.743666i | \(0.266915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.00000 | 0.310345 | ||||||||
\(842\) | 24.5967i | 0.847660i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.0000 | −0.826114 | ||||||||
\(845\) | −3.87298 | −0.133235 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.0000 | − | 10.3923i | −0.412325 | − | 0.357084i | ||||
\(848\) | − | 8.94427i | − | 0.307148i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.23607i | − | 0.0766514i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13.8564i | − | 0.474434i | −0.971457 | − | 0.237217i | \(-0.923765\pi\) | ||
0.971457 | − | 0.237217i | \(-0.0762353\pi\) | |||||||
\(854\) | 30.9839 | + | 26.8328i | 1.06025 | + | 0.918200i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.0000 | 0.683586 | ||||||||
\(857\) | 27.1109 | 0.926090 | 0.463045 | − | 0.886335i | \(-0.346757\pi\) | ||||
0.463045 | + | 0.886335i | \(0.346757\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 22.5167i | − | 0.768259i | −0.923279 | − | 0.384129i | \(-0.874502\pi\) | ||
0.923279 | − | 0.384129i | \(-0.125498\pi\) | |||||||
\(860\) | 23.2379 | 0.792406 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.00000 | −0.170301 | ||||||||
\(863\) | 8.94427i | 0.304467i | 0.988345 | + | 0.152233i | \(0.0486465\pi\) | ||||
−0.988345 | + | 0.152233i | \(0.951353\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0000 | −0.510015 | ||||||||
\(866\) | −23.2379 | −0.789656 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.00000 | − | 10.3923i | 0.305480 | − | 0.352738i | ||||
\(869\) | 4.47214i | 0.151707i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 34.6410i | − | 1.17377i | ||||||
\(872\) | 15.6525i | 0.530060i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 25.9808i | − | 0.878812i | ||||||
\(875\) | 38.7298 | + | 33.5410i | 1.30931 | + | 1.13389i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.0000 | −1.55331 | −0.776655 | − | 0.629926i | \(-0.783085\pi\) | ||||
−0.776655 | + | 0.629926i | \(0.783085\pi\) | |||||||
\(878\) | −85.2056 | −2.87555 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.66025i | 0.291937i | ||||||||
\(881\) | −34.8569 | −1.17436 | −0.587179 | − | 0.809457i | \(-0.699761\pi\) | ||||
−0.587179 | + | 0.809457i | \(0.699761\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 55.0000 | 1.84776 | ||||||||
\(887\) | 7.74597 | 0.260084 | 0.130042 | − | 0.991508i | \(-0.458489\pi\) | ||||
0.130042 | + | 0.991508i | \(0.458489\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | + | 17.3205i | 0.670778 | + | 0.580911i | ||||
\(890\) | − | 100.623i | − | 3.37289i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 5.19615i | − | 0.173980i | ||||||
\(893\) | − | 40.2492i | − | 1.34689i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 69.2820i | 2.31584i | ||||||||
\(896\) | 27.1109 | − | 31.3050i | 0.905711 | − | 1.04583i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.0000 | −0.667409 | ||||||||
\(899\) | −7.74597 | −0.258342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 19.3649 | 0.644781 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.0000 | 0.665190 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0000 | −0.531271 | −0.265636 | − | 0.964073i | \(-0.585582\pi\) | ||||
−0.265636 | + | 0.964073i | \(0.585582\pi\) | |||||||
\(908\) | −46.4758 | −1.54235 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −60.0000 | − | 51.9615i | −1.98898 | − | 1.72251i | ||||
\(911\) | 35.7771i | 1.18535i | 0.805443 | + | 0.592674i | \(0.201928\pi\) | ||||
−0.805443 | + | 0.592674i | \(0.798072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 17.3205i | − | 0.573225i | ||||||
\(914\) | − | 55.9017i | − | 1.84906i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 41.5692i | − | 1.37349i | ||||||
\(917\) | −15.4919 | − | 13.4164i | −0.511589 | − | 0.443049i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0000 | −0.923635 | −0.461817 | − | 0.886975i | \(-0.652802\pi\) | ||||
−0.461817 | + | 0.886975i | \(0.652802\pi\) | |||||||
\(920\) | −19.3649 | −0.638442 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.66025i | 0.285210i | ||||||||
\(923\) | 38.7298 | 1.27481 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 17.8885i | 0.587854i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −30.0000 | −0.984798 | ||||||||
\(929\) | 15.4919 | 0.508274 | 0.254137 | − | 0.967168i | \(-0.418209\pi\) | ||||
0.254137 | + | 0.967168i | \(0.418209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.0000 | + | 5.19615i | −1.17985 | + | 0.170297i | ||||
\(932\) | 53.6656i | 1.75788i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 51.9615i | − | 1.70023i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.7846i | 0.679004i | 0.940605 | + | 0.339502i | \(0.110258\pi\) | ||||
−0.940605 | + | 0.339502i | \(0.889742\pi\) | |||||||
\(938\) | −38.7298 | + | 44.7214i | −1.26457 | + | 1.46020i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −90.0000 | −2.93548 | ||||||||
\(941\) | −3.87298 | −0.126256 | −0.0631278 | − | 0.998005i | \(-0.520108\pi\) | ||||
−0.0631278 | + | 0.998005i | \(0.520108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.66025i | − | 0.282017i | ||||||
\(944\) | −7.74597 | −0.252110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0000 | −0.325128 | ||||||||
\(947\) | 15.6525i | 0.508637i | 0.967121 | + | 0.254319i | \(0.0818512\pi\) | ||||
−0.967121 | + | 0.254319i | \(0.918149\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.0000 | −1.16861 | ||||||||
\(950\) | −116.190 | −3.76969 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.3607i | 0.724333i | 0.932113 | + | 0.362167i | \(0.117963\pi\) | ||||
−0.932113 | + | 0.362167i | \(0.882037\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.66025i | − | 0.280239i | ||||||
\(956\) | − | 26.8328i | − | 0.867835i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 69.2820i | − | 2.23840i | ||||||
\(959\) | 38.7298 | − | 44.7214i | 1.25065 | − | 1.44413i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 7.74597 | 0.249740 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 51.9615i | − | 1.67357i | ||||||
\(965\) | −7.74597 | −0.249351 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.0000 | 1.80084 | 0.900419 | − | 0.435023i | \(-0.143260\pi\) | ||||
0.900419 | + | 0.435023i | \(0.143260\pi\) | |||||||
\(968\) | − | 13.4164i | − | 0.431220i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −120.000 | −3.85297 | ||||||||
\(971\) | −23.2379 | −0.745740 | −0.372870 | − | 0.927884i | \(-0.621626\pi\) | ||||
−0.372870 | + | 0.927884i | \(0.621626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | − | 6.92820i | 0.192351 | − | 0.222108i | ||||
\(974\) | − | 22.3607i | − | 0.716482i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 6.92820i | − | 0.221766i | ||||||
\(977\) | − | 17.8885i | − | 0.572305i | −0.958184 | − | 0.286153i | \(-0.907624\pi\) | ||
0.958184 | − | 0.286153i | \(-0.0923764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.9808i | 0.830349i | ||||||||
\(980\) | 11.6190 | + | 80.4984i | 0.371154 | + | 2.57143i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 85.0000 | 2.71246 | ||||||||
\(983\) | −54.2218 | −1.72941 | −0.864703 | − | 0.502284i | \(-0.832493\pi\) | ||||
−0.864703 | + | 0.502284i | \(0.832493\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 34.6410i | − | 1.10375i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 54.0000 | 1.71797 | ||||||||
\(989\) | 4.47214i | 0.142206i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.0000 | 0.825917 | 0.412959 | − | 0.910750i | \(-0.364495\pi\) | ||||
0.412959 | + | 0.910750i | \(0.364495\pi\) | |||||||
\(992\) | −11.6190 | −0.368902 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −50.0000 | − | 43.3013i | −1.58590 | − | 1.37343i | ||||
\(995\) | 100.623i | 3.18997i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.7128i | 0.877674i | 0.898567 | + | 0.438837i | \(0.144609\pi\) | ||||
−0.898567 | + | 0.438837i | \(0.855391\pi\) | |||||||
\(998\) | 84.9706i | 2.68970i | ||||||||
\(999\) | 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 | 189.2.c.b.188.3 | yes | 4 | |
3.2 | odd | 2 | inner | 189.2.c.b.188.2 | yes | 4 | |
4.3 | odd | 2 | 3024.2.k.i.1889.2 | 4 | |||
7.6 | odd | 2 | inner | 189.2.c.b.188.4 | yes | 4 | |
9.2 | odd | 6 | 567.2.o.c.377.1 | 4 | |||
9.4 | even | 3 | 567.2.o.d.188.1 | 4 | |||
9.5 | odd | 6 | 567.2.o.d.188.2 | 4 | |||
9.7 | even | 3 | 567.2.o.c.377.2 | 4 | |||
12.11 | even | 2 | 3024.2.k.i.1889.4 | 4 | |||
21.20 | even | 2 | inner | 189.2.c.b.188.1 | ✓ | 4 | |
28.27 | even | 2 | 3024.2.k.i.1889.3 | 4 | |||
63.13 | odd | 6 | 567.2.o.c.188.1 | 4 | |||
63.20 | even | 6 | 567.2.o.d.377.1 | 4 | |||
63.34 | odd | 6 | 567.2.o.d.377.2 | 4 | |||
63.41 | even | 6 | 567.2.o.c.188.2 | 4 | |||
84.83 | odd | 2 | 3024.2.k.i.1889.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.c.b.188.1 | ✓ | 4 | 21.20 | even | 2 | inner | |
189.2.c.b.188.2 | yes | 4 | 3.2 | odd | 2 | inner | |
189.2.c.b.188.3 | yes | 4 | 1.1 | even | 1 | trivial | |
189.2.c.b.188.4 | yes | 4 | 7.6 | odd | 2 | inner | |
567.2.o.c.188.1 | 4 | 63.13 | odd | 6 | |||
567.2.o.c.188.2 | 4 | 63.41 | even | 6 | |||
567.2.o.c.377.1 | 4 | 9.2 | odd | 6 | |||
567.2.o.c.377.2 | 4 | 9.7 | even | 3 | |||
567.2.o.d.188.1 | 4 | 9.4 | even | 3 | |||
567.2.o.d.188.2 | 4 | 9.5 | odd | 6 | |||
567.2.o.d.377.1 | 4 | 63.20 | even | 6 | |||
567.2.o.d.377.2 | 4 | 63.34 | odd | 6 | |||
3024.2.k.i.1889.1 | 4 | 84.83 | odd | 2 | |||
3024.2.k.i.1889.2 | 4 | 4.3 | odd | 2 | |||
3024.2.k.i.1889.3 | 4 | 28.27 | even | 2 | |||
3024.2.k.i.1889.4 | 4 | 12.11 | even | 2 |