Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(199,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.199 |
Dual form | 1350.2.j.c.1099.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | − | 2.00000i | 1.30931 | − | 0.755929i | 0.327327 | − | 0.944911i | \(-0.393852\pi\) |
0.981981 | + | 0.188982i | \(0.0605189\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410 | + | 2.00000i | 0.960769 | + | 0.554700i | 0.896410 | − | 0.443227i | \(-0.146166\pi\) |
0.0643593 | + | 0.997927i | \(0.479500\pi\) | |||||||
\(14\) | −2.00000 | + | 3.46410i | −0.534522 | + | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000i | 0.727607i | 0.931476 | + | 0.363803i | \(0.118522\pi\) | ||||
−0.931476 | + | 0.363803i | \(0.881478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.59808 | − | 1.50000i | −0.553912 | − | 0.319801i | ||||
\(23\) | 5.19615 | + | 3.00000i | 1.08347 | + | 0.625543i | 0.931831 | − | 0.362892i | \(-0.118211\pi\) |
0.151642 | + | 0.988436i | \(0.451544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 4.00000i | − | 0.755929i | ||||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | 4.33013 | − | 2.50000i | 0.702439 | − | 0.405554i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.52628 | − | 5.50000i | 1.45274 | − | 0.838742i | 0.454108 | − | 0.890947i | \(-0.349958\pi\) |
0.998636 | + | 0.0522047i | \(0.0166248\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.50000 | − | 7.79423i | 0.642857 | − | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.46410 | − | 2.00000i | 0.480384 | − | 0.277350i | ||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | + | 3.46410i | 0.267261 | + | 0.462910i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.19615 | + | 3.00000i | 0.682288 | + | 0.393919i | ||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | − | 2.00000i | − | 0.254000i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.33013 | + | 2.50000i | 0.529009 | + | 0.305424i | 0.740613 | − | 0.671932i | \(-0.234535\pi\) |
−0.211604 | + | 0.977356i | \(0.567869\pi\) | |||||||
\(68\) | 2.59808 | + | 1.50000i | 0.315063 | + | 0.181902i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.00000i | − | 0.819288i | −0.912245 | − | 0.409644i | \(-0.865653\pi\) | ||
0.912245 | − | 0.409644i | \(-0.134347\pi\) | |||||||
\(74\) | −2.00000 | − | 3.46410i | −0.232495 | − | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.50000 | + | 4.33013i | −0.286770 | + | 0.496700i | ||||
\(77\) | 10.3923 | + | 6.00000i | 1.18431 | + | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.00000 | + | 12.1244i | 0.787562 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.00000i | − | 0.331295i | ||||||
\(83\) | −10.3923 | + | 6.00000i | −1.14070 | + | 0.658586i | −0.946605 | − | 0.322396i | \(-0.895512\pi\) |
−0.194099 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.50000 | + | 9.52628i | −0.593080 | + | 1.02725i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.59808 | + | 1.50000i | −0.276956 | + | 0.159901i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0000 | 1.67726 | ||||||||
\(92\) | 5.19615 | − | 3.00000i | 0.541736 | − | 0.312772i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.52628 | + | 5.50000i | −0.967247 | + | 0.558440i | −0.898396 | − | 0.439187i | \(-0.855267\pi\) |
−0.0688512 | + | 0.997627i | \(0.521933\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.46410 | + | 2.00000i | 0.341328 | + | 0.197066i | 0.660859 | − | 0.750510i | \(-0.270192\pi\) |
−0.319531 | + | 0.947576i | \(0.603525\pi\) | |||||||
\(104\) | −2.00000 | + | 3.46410i | −0.196116 | + | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | − | 9.00000i | − | 0.870063i | −0.900415 | − | 0.435031i | \(-0.856737\pi\) | ||
0.900415 | − | 0.435031i | \(-0.143263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.46410 | − | 2.00000i | −0.327327 | − | 0.188982i | ||||
\(113\) | 15.5885 | + | 9.00000i | 1.46644 | + | 0.846649i | 0.999295 | − | 0.0375328i | \(-0.0119499\pi\) |
0.467143 | + | 0.884182i | \(0.345283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.00000i | 0.276172i | ||||||||
\(119\) | 6.00000 | + | 10.3923i | 0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −8.66025 | − | 5.00000i | −0.784063 | − | 0.452679i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | − | 10.3923i | 0.524222 | − | 0.907980i | −0.475380 | − | 0.879781i | \(-0.657689\pi\) |
0.999602 | − | 0.0281993i | \(-0.00897729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.3205 | + | 10.0000i | −1.50188 | + | 0.867110i | ||||
\(134\) | −5.00000 | −0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | −7.79423 | + | 4.50000i | −0.665906 | + | 0.384461i | −0.794524 | − | 0.607233i | \(-0.792279\pi\) |
0.128618 | + | 0.991694i | \(0.458946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.500000 | + | 0.866025i | −0.0424094 | + | 0.0734553i | −0.886451 | − | 0.462822i | \(-0.846837\pi\) |
0.844042 | + | 0.536278i | \(0.180170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.19615 | − | 3.00000i | 0.436051 | − | 0.251754i | ||||
\(143\) | 12.0000i | 1.00349i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.50000 | + | 6.06218i | 0.289662 | + | 0.501709i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.46410 | + | 2.00000i | 0.284747 | + | 0.164399i | ||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | − | 5.00000i | − | 0.405554i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.0000 | −0.966988 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.92820 | + | 4.00000i | 0.552931 | + | 0.319235i | 0.750303 | − | 0.661094i | \(-0.229907\pi\) |
−0.197372 | + | 0.980329i | \(0.563241\pi\) | |||||||
\(158\) | −12.1244 | − | 7.00000i | −0.964562 | − | 0.556890i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0000 | 1.89146 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.0000i | − | 1.25322i | −0.779334 | − | 0.626608i | \(-0.784443\pi\) | ||
0.779334 | − | 0.626608i | \(-0.215557\pi\) | |||||||
\(164\) | 1.50000 | + | 2.59808i | 0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | − | 10.3923i | 0.465690 | − | 0.806599i | ||||
\(167\) | 15.5885 | + | 9.00000i | 1.20627 | + | 0.696441i | 0.961943 | − | 0.273252i | \(-0.0880992\pi\) |
0.244328 | + | 0.969693i | \(0.421432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.50000 | + | 2.59808i | 0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 11.0000i | − | 0.838742i | ||||||
\(173\) | 15.5885 | − | 9.00000i | 1.18517 | − | 0.684257i | 0.227964 | − | 0.973670i | \(-0.426793\pi\) |
0.957205 | + | 0.289412i | \(0.0934598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.50000 | − | 2.59808i | 0.113067 | − | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.19615 | + | 3.00000i | −0.389468 | + | 0.224860i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | −13.8564 | + | 8.00000i | −1.02711 | + | 0.592999i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | + | 5.19615i | −0.221163 | + | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.79423 | + | 4.50000i | −0.569970 | + | 0.329073i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.2583 | + | 6.50000i | 0.810392 | + | 0.467880i | 0.847092 | − | 0.531446i | \(-0.178351\pi\) |
−0.0366998 | + | 0.999326i | \(0.511685\pi\) | |||||||
\(194\) | 5.50000 | − | 9.52628i | 0.394877 | − | 0.683947i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.50000 | − | 7.79423i | −0.321429 | − | 0.556731i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.3923 | + | 6.00000i | 0.731200 | + | 0.422159i | ||||
\(203\) | −20.7846 | − | 12.0000i | −1.45879 | − | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.00000 | −0.278693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.00000i | − | 0.277350i | ||||||
\(209\) | −7.50000 | − | 12.9904i | −0.518786 | − | 0.898563i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | − | 3.46410i | 0.137686 | − | 0.238479i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) |
0.926620 | + | 0.375999i | \(0.122700\pi\) | |||||||
\(212\) | −5.19615 | − | 3.00000i | −0.356873 | − | 0.206041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.50000 | + | 7.79423i | 0.307614 | + | 0.532803i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000i | 0.543075i | ||||||||
\(218\) | −3.46410 | + | 2.00000i | −0.234619 | + | 0.135457i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.0526 | + | 11.0000i | −1.27585 | + | 0.736614i | −0.976083 | − | 0.217397i | \(-0.930243\pi\) |
−0.299770 | + | 0.954011i | \(0.596910\pi\) | |||||||
\(224\) | 4.00000 | 0.267261 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | −2.59808 | + | 1.50000i | −0.172440 | + | 0.0995585i | −0.583736 | − | 0.811943i | \(-0.698410\pi\) |
0.411296 | + | 0.911502i | \(0.365076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | − | 17.3205i | 0.660819 | − | 1.14457i | −0.319582 | − | 0.947559i | \(-0.603543\pi\) |
0.980401 | − | 0.197013i | \(-0.0631241\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.19615 | − | 3.00000i | 0.341144 | − | 0.196960i | ||||
\(233\) | − | 21.0000i | − | 1.37576i | −0.725826 | − | 0.687878i | \(-0.758542\pi\) | ||
0.725826 | − | 0.687878i | \(-0.241458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.50000 | − | 2.59808i | −0.0976417 | − | 0.169120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.3923 | − | 6.00000i | −0.673633 | − | 0.388922i | ||||
\(239\) | −3.00000 | + | 5.19615i | −0.194054 | + | 0.336111i | −0.946590 | − | 0.322440i | \(-0.895497\pi\) |
0.752536 | + | 0.658551i | \(0.228830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | − | 14.7224i | −0.547533 | − | 0.948355i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
0.450910 | − | 0.892570i | \(-0.351100\pi\) | |||||||
\(242\) | 2.00000i | 0.128565i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.3205 | − | 10.0000i | −1.10208 | − | 0.636285i | ||||
\(248\) | −1.73205 | − | 1.00000i | −0.109985 | − | 0.0635001i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.0000 | 1.32551 | 0.662754 | − | 0.748837i | \(-0.269387\pi\) | ||||
0.662754 | + | 0.748837i | \(0.269387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000i | 1.13165i | ||||||||
\(254\) | 1.00000 | + | 1.73205i | 0.0627456 | + | 0.108679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.79423 | − | 4.50000i | −0.486191 | − | 0.280702i | 0.236802 | − | 0.971558i | \(-0.423901\pi\) |
−0.722993 | + | 0.690856i | \(0.757234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | + | 13.8564i | 0.497096 | + | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.0000i | 0.741362i | ||||||||
\(263\) | −20.7846 | + | 12.0000i | −1.28163 | + | 0.739952i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
−0.304487 | + | 0.952517i | \(0.598485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.0000 | − | 17.3205i | 0.613139 | − | 1.06199i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.33013 | − | 2.50000i | 0.264505 | − | 0.152712i | ||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 2.59808 | − | 1.50000i | 0.157532 | − | 0.0909509i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.50000 | − | 7.79423i | 0.271855 | − | 0.470867i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.0526 | − | 11.0000i | 1.14476 | − | 0.660926i | 0.197153 | − | 0.980373i | \(-0.436830\pi\) |
0.947604 | + | 0.319447i | \(0.103497\pi\) | |||||||
\(278\) | − | 1.00000i | − | 0.0599760i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | − | 5.19615i | −0.178965 | − | 0.309976i | 0.762561 | − | 0.646916i | \(-0.223942\pi\) |
−0.941526 | + | 0.336939i | \(0.890608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.3205 | − | 10.0000i | −1.02960 | − | 0.594438i | −0.112728 | − | 0.993626i | \(-0.535959\pi\) |
−0.916869 | + | 0.399188i | \(0.869292\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | − | 10.3923i | −0.354787 | − | 0.614510i | ||||
\(287\) | 12.0000i | 0.708338i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.06218 | − | 3.50000i | −0.354762 | − | 0.204822i | ||||
\(293\) | −15.5885 | − | 9.00000i | −0.910687 | − | 0.525786i | −0.0300351 | − | 0.999549i | \(-0.509562\pi\) |
−0.880652 | + | 0.473763i | \(0.842895\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.00000 | −0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0000 | + | 20.7846i | 0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.0000 | − | 38.1051i | 1.26806 | − | 2.19634i | ||||
\(302\) | −8.66025 | − | 5.00000i | −0.498342 | − | 0.287718i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.50000 | + | 4.33013i | 0.143385 | + | 0.248350i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000i | 0.399511i | 0.979846 | + | 0.199756i | \(0.0640148\pi\) | ||||
−0.979846 | + | 0.199756i | \(0.935985\pi\) | |||||||
\(308\) | 10.3923 | − | 6.00000i | 0.592157 | − | 0.341882i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | + | 5.19615i | −0.170114 | + | 0.294647i | −0.938460 | − | 0.345389i | \(-0.887747\pi\) |
0.768345 | + | 0.640036i | \(0.221080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.866025 | + | 0.500000i | −0.0489506 | + | 0.0282617i | −0.524276 | − | 0.851549i | \(-0.675664\pi\) |
0.475325 | + | 0.879810i | \(0.342331\pi\) | |||||||
\(314\) | −8.00000 | −0.451466 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | 20.7846 | − | 12.0000i | 1.16738 | − | 0.673987i | 0.214318 | − | 0.976764i | \(-0.431247\pi\) |
0.953062 | + | 0.302777i | \(0.0979136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20.7846 | + | 12.0000i | −1.15828 | + | 0.668734i | ||||
\(323\) | − | 15.0000i | − | 0.834622i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.00000 | + | 13.8564i | 0.443079 | + | 0.767435i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.59808 | − | 1.50000i | −0.143455 | − | 0.0828236i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 12.0000i | 0.658586i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.8468 | − | 15.5000i | −1.46244 | − | 0.844339i | −0.463314 | − | 0.886194i | \(-0.653340\pi\) |
−0.999124 | + | 0.0418554i | \(0.986673\pi\) | |||||||
\(338\) | −2.59808 | − | 1.50000i | −0.141317 | − | 0.0815892i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | 5.50000 | + | 9.52628i | 0.296540 | + | 0.513623i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | + | 15.5885i | −0.483843 | + | 0.838041i | ||||
\(347\) | −18.1865 | − | 10.5000i | −0.976304 | − | 0.563670i | −0.0751519 | − | 0.997172i | \(-0.523944\pi\) |
−0.901152 | + | 0.433503i | \(0.857278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.00000 | − | 13.8564i | −0.428230 | − | 0.741716i | 0.568486 | − | 0.822693i | \(-0.307529\pi\) |
−0.996716 | + | 0.0809766i | \(0.974196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000i | 0.159901i | ||||||||
\(353\) | −7.79423 | + | 4.50000i | −0.414845 | + | 0.239511i | −0.692869 | − | 0.721063i | \(-0.743654\pi\) |
0.278024 | + | 0.960574i | \(0.410320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.00000 | − | 5.19615i | 0.159000 | − | 0.275396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 13.8564 | − | 8.00000i | 0.728277 | − | 0.420471i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | − | 13.8564i | 0.419314 | − | 0.726273i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.92820 | + | 4.00000i | −0.361649 | + | 0.208798i | −0.669804 | − | 0.742538i | \(-0.733622\pi\) |
0.308155 | + | 0.951336i | \(0.400289\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | − | 20.7846i | −0.623009 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.66025 | + | 5.00000i | 0.448411 | + | 0.258890i | 0.707159 | − | 0.707055i | \(-0.249977\pi\) |
−0.258748 | + | 0.965945i | \(0.583310\pi\) | |||||||
\(374\) | 4.50000 | − | 7.79423i | 0.232689 | − | 0.403030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 24.0000i | − | 1.23606i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.0000 | −1.48963 | −0.744815 | − | 0.667271i | \(-0.767462\pi\) | ||||
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3923 | + | 6.00000i | 0.531022 | + | 0.306586i | 0.741433 | − | 0.671027i | \(-0.234147\pi\) |
−0.210411 | + | 0.977613i | \(0.567480\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0000 | −0.661683 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.0000i | 0.558440i | ||||||||
\(389\) | −18.0000 | − | 31.1769i | −0.912636 | − | 1.58073i | −0.810326 | − | 0.585980i | \(-0.800710\pi\) |
−0.102311 | − | 0.994753i | \(-0.532624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | 7.79423 | + | 4.50000i | 0.393668 | + | 0.227284i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8.00000i | − | 0.401508i | −0.979642 | − | 0.200754i | \(-0.935661\pi\) | ||
0.979642 | − | 0.200754i | \(-0.0643393\pi\) | |||||||
\(398\) | 17.3205 | − | 10.0000i | 0.868199 | − | 0.501255i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5000 | − | 28.5788i | 0.823971 | − | 1.42716i | −0.0787327 | − | 0.996896i | \(-0.525087\pi\) |
0.902703 | − | 0.430263i | \(-0.141579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.92820 | + | 4.00000i | −0.345118 | + | 0.199254i | ||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.0000 | 1.19110 | ||||||||
\(407\) | −10.3923 | + | 6.00000i | −0.515127 | + | 0.297409i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.5000 | + | 26.8468i | −0.766426 | + | 1.32749i | 0.173064 | + | 0.984911i | \(0.444633\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.46410 | − | 2.00000i | 0.170664 | − | 0.0985329i | ||||
\(413\) | − | 12.0000i | − | 0.590481i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | + | 3.46410i | 0.0980581 | + | 0.169842i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.9904 | + | 7.50000i | 0.635380 | + | 0.366837i | ||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | − | 1.73205i | −0.0487370 | − | 0.0844150i | 0.840628 | − | 0.541613i | \(-0.182186\pi\) |
−0.889365 | + | 0.457198i | \(0.848853\pi\) | |||||||
\(422\) | 4.00000i | 0.194717i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.6410 | + | 20.0000i | 1.67640 | + | 0.967868i | ||||
\(428\) | −7.79423 | − | 4.50000i | −0.376748 | − | 0.217516i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.0000i | − | 0.624740i | −0.949960 | − | 0.312370i | \(-0.898877\pi\) | ||
0.949960 | − | 0.312370i | \(-0.101123\pi\) | |||||||
\(434\) | −4.00000 | − | 6.92820i | −0.192006 | − | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | − | 3.46410i | 0.0957826 | − | 0.165900i | ||||
\(437\) | −25.9808 | − | 15.0000i | −1.24283 | − | 0.717547i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | \(-0.243367\pi\) |
−0.960323 | + | 0.278889i | \(0.910034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 12.0000i | − | 0.570782i | ||||||
\(443\) | −2.59808 | + | 1.50000i | −0.123438 | + | 0.0712672i | −0.560448 | − | 0.828190i | \(-0.689371\pi\) |
0.437009 | + | 0.899457i | \(0.356038\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.0000 | − | 19.0526i | 0.520865 | − | 0.902165i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.46410 | + | 2.00000i | −0.163663 | + | 0.0944911i | ||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | −0.423793 | ||||||||
\(452\) | 15.5885 | − | 9.00000i | 0.733219 | − | 0.423324i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.50000 | − | 2.59808i | 0.0703985 | − | 0.121934i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.866025 | − | 0.500000i | 0.0405110 | − | 0.0233890i | −0.479608 | − | 0.877483i | \(-0.659221\pi\) |
0.520119 | + | 0.854094i | \(0.325888\pi\) | |||||||
\(458\) | 20.0000i | 0.934539i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3205 | − | 10.0000i | −0.804952 | − | 0.464739i | 0.0402476 | − | 0.999190i | \(-0.487185\pi\) |
−0.845200 | + | 0.534450i | \(0.820519\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5000 | + | 18.1865i | 0.486403 | + | 0.842475i | ||||
\(467\) | 21.0000i | 0.971764i | 0.874024 | + | 0.485882i | \(0.161502\pi\) | ||||
−0.874024 | + | 0.485882i | \(0.838498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0000 | 0.923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.59808 | + | 1.50000i | 0.119586 | + | 0.0690431i | ||||
\(473\) | 28.5788 | + | 16.5000i | 1.31406 | + | 0.758671i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | 0.550019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 6.00000i | − | 0.274434i | ||||||
\(479\) | 3.00000 | + | 5.19615i | 0.137073 | + | 0.237418i | 0.926388 | − | 0.376571i | \(-0.122897\pi\) |
−0.789314 | + | 0.613990i | \(0.789564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | 14.7224 | + | 8.50000i | 0.670588 | + | 0.387164i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.00000 | − | 1.73205i | −0.0454545 | − | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.00000i | − | 0.0906287i | −0.998973 | − | 0.0453143i | \(-0.985571\pi\) | ||
0.998973 | − | 0.0453143i | \(-0.0144289\pi\) | |||||||
\(488\) | −8.66025 | + | 5.00000i | −0.392031 | + | 0.226339i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.5000 | + | 28.5788i | −0.744635 | + | 1.28974i | 0.205731 | + | 0.978609i | \(0.434043\pi\) |
−0.950365 | + | 0.311136i | \(0.899290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5885 | − | 9.00000i | 0.702069 | − | 0.405340i | ||||
\(494\) | 20.0000 | 0.899843 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −20.7846 | + | 12.0000i | −0.932317 | + | 0.538274i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.5000 | + | 26.8468i | −0.693875 | + | 1.20183i | 0.276683 | + | 0.960961i | \(0.410765\pi\) |
−0.970558 | + | 0.240866i | \(0.922569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.1865 | + | 10.5000i | −0.811705 | + | 0.468638i | ||||
\(503\) | − | 6.00000i | − | 0.267527i | −0.991013 | − | 0.133763i | \(-0.957294\pi\) | ||
0.991013 | − | 0.133763i | \(-0.0427062\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00000 | − | 15.5885i | −0.400099 | − | 0.692991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.73205 | − | 1.00000i | −0.0768473 | − | 0.0443678i | ||||
\(509\) | 6.00000 | − | 10.3923i | 0.265945 | − | 0.460631i | −0.701866 | − | 0.712309i | \(-0.747649\pi\) |
0.967811 | + | 0.251679i | \(0.0809826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | − | 24.2487i | −0.619324 | − | 1.07270i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.00000 | 0.396973 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.8564 | − | 8.00000i | −0.608816 | − | 0.351500i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | 0.131432 | 0.0657162 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657162 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000i | 0.874539i | 0.899331 | + | 0.437269i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(524\) | −6.00000 | − | 10.3923i | −0.262111 | − | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | − | 20.7846i | 0.523225 | − | 0.906252i | ||||
\(527\) | −5.19615 | − | 3.00000i | −0.226348 | − | 0.130682i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 20.0000i | 0.867110i | ||||||||
\(533\) | −10.3923 | + | 6.00000i | −0.450141 | + | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.50000 | + | 4.33013i | −0.107984 | + | 0.187033i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.19615 | + | 3.00000i | −0.224022 | + | 0.129339i | ||||
\(539\) | 27.0000 | 1.16297 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | 13.8564 | − | 8.00000i | 0.595184 | − | 0.343629i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.866025 | − | 0.500000i | 0.0370286 | − | 0.0213785i | −0.481371 | − | 0.876517i | \(-0.659861\pi\) |
0.518400 | + | 0.855138i | \(0.326528\pi\) | |||||||
\(548\) | 9.00000i | 0.384461i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0000 | + | 25.9808i | 0.639021 | + | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 48.4974 | + | 28.0000i | 2.06232 | + | 1.19068i | ||||
\(554\) | −11.0000 | + | 19.0526i | −0.467345 | + | 0.809466i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.500000 | + | 0.866025i | 0.0212047 | + | 0.0367277i | ||||
\(557\) | − | 12.0000i | − | 0.508456i | −0.967144 | − | 0.254228i | \(-0.918179\pi\) | ||
0.967144 | − | 0.254228i | \(-0.0818214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.0000 | 1.86100 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.19615 | + | 3.00000i | 0.219186 | + | 0.126547i | ||||
\(563\) | −2.59808 | − | 1.50000i | −0.109496 | − | 0.0632175i | 0.444252 | − | 0.895902i | \(-0.353470\pi\) |
−0.553748 | + | 0.832684i | \(0.686803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20.0000 | 0.840663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | 19.5000 | + | 33.7750i | 0.817483 | + | 1.41592i | 0.907532 | + | 0.419984i | \(0.137964\pi\) |
−0.0900490 | + | 0.995937i | \(0.528702\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5000 | + | 25.1147i | −0.606806 | + | 1.05102i | 0.384957 | + | 0.922934i | \(0.374216\pi\) |
−0.991763 | + | 0.128085i | \(0.959117\pi\) | |||||||
\(572\) | 10.3923 | + | 6.00000i | 0.434524 | + | 0.250873i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | − | 10.3923i | −0.250435 | − | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000i | 0.291414i | 0.989328 | + | 0.145707i | \(0.0465456\pi\) | ||||
−0.989328 | + | 0.145707i | \(0.953454\pi\) | |||||||
\(578\) | −6.92820 | + | 4.00000i | −0.288175 | + | 0.166378i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | + | 41.5692i | −0.995688 | + | 1.72458i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.5885 | − | 9.00000i | 0.645608 | − | 0.372742i | ||||
\(584\) | 7.00000 | 0.289662 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.0000 | 0.743573 | ||||||||
\(587\) | 33.7750 | − | 19.5000i | 1.39404 | − | 0.804851i | 0.400283 | − | 0.916392i | \(-0.368912\pi\) |
0.993760 | + | 0.111540i | \(0.0355784\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00000 | − | 8.66025i | 0.206021 | − | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.46410 | − | 2.00000i | 0.142374 | − | 0.0821995i | ||||
\(593\) | 18.0000i | 0.739171i | 0.929197 | + | 0.369586i | \(0.120500\pi\) | ||||
−0.929197 | + | 0.369586i | \(0.879500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −20.7846 | − | 12.0000i | −0.849946 | − | 0.490716i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5000 | + | 21.6506i | 0.509886 | + | 0.883148i | 0.999934 | + | 0.0114528i | \(0.00364562\pi\) |
−0.490049 | + | 0.871695i | \(0.663021\pi\) | |||||||
\(602\) | 44.0000i | 1.79331i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.92820 | + | 4.00000i | 0.281207 | + | 0.162355i | 0.633970 | − | 0.773358i | \(-0.281424\pi\) |
−0.352763 | + | 0.935713i | \(0.614758\pi\) | |||||||
\(608\) | −4.33013 | − | 2.50000i | −0.175610 | − | 0.101388i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000i | 0.0807792i | 0.999184 | + | 0.0403896i | \(0.0128599\pi\) | ||||
−0.999184 | + | 0.0403896i | \(0.987140\pi\) | |||||||
\(614\) | −3.50000 | − | 6.06218i | −0.141249 | − | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | + | 10.3923i | −0.241747 | + | 0.418718i | ||||
\(617\) | 33.7750 | + | 19.5000i | 1.35973 | + | 0.785040i | 0.989587 | − | 0.143934i | \(-0.0459755\pi\) |
0.370143 | + | 0.928975i | \(0.379309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.50000 | − | 16.4545i | −0.381837 | − | 0.661361i | 0.609488 | − | 0.792796i | \(-0.291375\pi\) |
−0.991325 | + | 0.131434i | \(0.958042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 6.00000i | − | 0.240578i | ||||||
\(623\) | 20.7846 | − | 12.0000i | 0.832718 | − | 0.480770i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.500000 | − | 0.866025i | 0.0199840 | − | 0.0346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.92820 | − | 4.00000i | 0.276465 | − | 0.159617i | ||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | −12.1244 | + | 7.00000i | −0.482281 | + | 0.278445i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.0000 | + | 20.7846i | −0.476581 | + | 0.825462i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.1769 | − | 18.0000i | 1.23527 | − | 0.713186i | ||||
\(638\) | 18.0000i | 0.712627i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.50000 | + | 7.79423i | 0.177739 | + | 0.307854i | 0.941106 | − | 0.338112i | \(-0.109788\pi\) |
−0.763367 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.9186 | − | 11.5000i | −0.785512 | − | 0.453516i | 0.0528680 | − | 0.998602i | \(-0.483164\pi\) |
−0.838380 | + | 0.545086i | \(0.816497\pi\) | |||||||
\(644\) | 12.0000 | − | 20.7846i | 0.472866 | − | 0.819028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.50000 | + | 12.9904i | 0.295084 | + | 0.511100i | ||||
\(647\) | 6.00000i | 0.235884i | 0.993020 | + | 0.117942i | \(0.0376297\pi\) | ||||
−0.993020 | + | 0.117942i | \(0.962370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.00000 | 0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.8564 | − | 8.00000i | −0.542659 | − | 0.313304i | ||||
\(653\) | 36.3731 | + | 21.0000i | 1.42339 | + | 0.821794i | 0.996587 | − | 0.0825519i | \(-0.0263070\pi\) |
0.426801 | + | 0.904345i | \(0.359640\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.00000 | 0.117130 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0000 | + | 31.1769i | 0.701180 | + | 1.21448i | 0.968052 | + | 0.250748i | \(0.0806766\pi\) |
−0.266872 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | −3.46410 | − | 2.00000i | −0.134636 | − | 0.0777322i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | − | 10.3923i | −0.232845 | − | 0.403300i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 36.0000i | − | 1.39393i | ||||||
\(668\) | 15.5885 | − | 9.00000i | 0.603136 | − | 0.348220i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0000 | + | 25.9808i | −0.579069 | + | 1.00298i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.1244 | − | 7.00000i | 0.467360 | − | 0.269830i | −0.247774 | − | 0.968818i | \(-0.579699\pi\) |
0.715134 | + | 0.698988i | \(0.246366\pi\) | |||||||
\(674\) | 31.0000 | 1.19408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −31.1769 | + | 18.0000i | −1.19823 | + | 0.691796i | −0.960159 | − | 0.279453i | \(-0.909847\pi\) |
−0.238067 | + | 0.971249i | \(0.576514\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.0000 | + | 38.1051i | −0.844283 | + | 1.46234i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.19615 | − | 3.00000i | 0.198971 | − | 0.114876i | ||||
\(683\) | 21.0000i | 0.803543i | 0.915740 | + | 0.401771i | \(0.131605\pi\) | ||||
−0.915740 | + | 0.401771i | \(0.868395\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.00000 | + | 6.92820i | 0.152721 | + | 0.264520i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.52628 | − | 5.50000i | −0.363186 | − | 0.209686i | ||||
\(689\) | 12.0000 | − | 20.7846i | 0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | − | 18.0000i | − | 0.684257i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.0000 | 0.797149 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.79423 | − | 4.50000i | −0.295227 | − | 0.170450i | ||||
\(698\) | 13.8564 | + | 8.00000i | 0.524473 | + | 0.302804i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 20.0000i | − | 0.754314i | ||||||
\(704\) | −1.50000 | − | 2.59808i | −0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.50000 | − | 7.79423i | 0.169360 | − | 0.293340i | ||||
\(707\) | −41.5692 | − | 24.0000i | −1.56337 | − | 0.902613i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0000 | − | 29.4449i | −0.638448 | − | 1.10583i | −0.985773 | − | 0.168080i | \(-0.946243\pi\) |
0.347325 | − | 0.937745i | \(-0.387090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000i | 0.224860i | ||||||||
\(713\) | −10.3923 | + | 6.00000i | −0.389195 | + | 0.224702i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.7846 | − | 12.0000i | 0.775675 | − | 0.447836i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | −5.19615 | + | 3.00000i | −0.193381 | + | 0.111648i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.00000 | + | 13.8564i | −0.297318 | + | 0.514969i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2487 | − | 14.0000i | 0.899335 | − | 0.519231i | 0.0223506 | − | 0.999750i | \(-0.492885\pi\) |
0.876984 | + | 0.480519i | \(0.159552\pi\) | |||||||
\(728\) | 16.0000i | 0.592999i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5000 | + | 28.5788i | 0.610275 | + | 1.05703i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.7128 | − | 16.0000i | −1.02360 | − | 0.590973i | −0.108453 | − | 0.994102i | \(-0.534590\pi\) |
−0.915144 | + | 0.403128i | \(0.867923\pi\) | |||||||
\(734\) | 4.00000 | − | 6.92820i | 0.147643 | − | 0.255725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | 15.0000i | 0.552532i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.0000 | −1.06678 | −0.533391 | − | 0.845869i | \(-0.679083\pi\) | ||||
−0.533391 | + | 0.845869i | \(0.679083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.7846 | + | 12.0000i | 0.763027 | + | 0.440534i | ||||
\(743\) | −5.19615 | − | 3.00000i | −0.190628 | − | 0.110059i | 0.401648 | − | 0.915794i | \(-0.368437\pi\) |
−0.592277 | + | 0.805735i | \(0.701771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.0000 | −0.366126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.00000i | 0.329073i | ||||||||
\(749\) | −18.0000 | − | 31.1769i | −0.657706 | − | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0000 | − | 24.2487i | 0.510867 | − | 0.884848i | −0.489053 | − | 0.872254i | \(-0.662658\pi\) |
0.999921 | − | 0.0125942i | \(-0.00400897\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0000 | + | 20.7846i | 0.437014 | + | 0.756931i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 38.0000i | − | 1.38113i | −0.723269 | − | 0.690567i | \(-0.757361\pi\) | ||
0.723269 | − | 0.690567i | \(-0.242639\pi\) | |||||||
\(758\) | 25.1147 | − | 14.5000i | 0.912208 | − | 0.526664i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.00000 | − | 15.5885i | 0.326250 | − | 0.565081i | −0.655515 | − | 0.755182i | \(-0.727548\pi\) |
0.981764 | + | 0.190101i | \(0.0608816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8564 | − | 8.00000i | 0.501636 | − | 0.289619i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.0000 | −0.433578 | ||||||||
\(767\) | 10.3923 | − | 6.00000i | 0.375244 | − | 0.216647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.0000 | − | 43.3013i | 0.901523 | − | 1.56148i | 0.0760054 | − | 0.997107i | \(-0.475783\pi\) |
0.825518 | − | 0.564376i | \(-0.190883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.2583 | − | 6.50000i | 0.405196 | − | 0.233940i | ||||
\(773\) | 30.0000i | 1.07903i | 0.841978 | + | 0.539513i | \(0.181391\pi\) | ||||
−0.841978 | + | 0.539513i | \(0.818609\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.50000 | − | 9.52628i | −0.197438 | − | 0.341974i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.1769 | + | 18.0000i | 1.11775 | + | 0.645331i | ||||
\(779\) | 7.50000 | − | 12.9904i | 0.268715 | − | 0.465429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | − | 15.5885i | −0.322045 | − | 0.557799i | ||||
\(782\) | − | 18.0000i | − | 0.643679i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.46410 | − | 2.00000i | −0.123482 | − | 0.0712923i | 0.436987 | − | 0.899468i | \(-0.356046\pi\) |
−0.560469 | + | 0.828176i | \(0.689379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 72.0000 | 2.56003 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.0000i | 1.42044i | ||||||||
\(794\) | 4.00000 | + | 6.92820i | 0.141955 | + | 0.245873i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0000 | + | 17.3205i | −0.354441 | + | 0.613909i | ||||
\(797\) | 41.5692 | + | 24.0000i | 1.47246 | + | 0.850124i | 0.999520 | − | 0.0309726i | \(-0.00986046\pi\) |
0.472937 | + | 0.881096i | \(0.343194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.0000i | 1.16527i | ||||||||
\(803\) | 18.1865 | − | 10.5000i | 0.641789 | − | 0.370537i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | − | 6.92820i | 0.140894 | − | 0.244036i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.3923 | − | 6.00000i | 0.365600 | − | 0.211079i | ||||
\(809\) | −39.0000 | −1.37117 | −0.685583 | − | 0.727994i | \(-0.740453\pi\) | ||||
−0.685583 | + | 0.727994i | \(0.740453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.0000 | 1.22902 | 0.614508 | − | 0.788911i | \(-0.289355\pi\) | ||||
0.614508 | + | 0.788911i | \(0.289355\pi\) | |||||||
\(812\) | −20.7846 | + | 12.0000i | −0.729397 | + | 0.421117i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | − | 10.3923i | 0.210300 | − | 0.364250i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.6314 | + | 27.5000i | −1.66641 | + | 0.962103i | ||||
\(818\) | − | 31.0000i | − | 1.08389i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.0000 | − | 41.5692i | −0.837606 | − | 1.45078i | −0.891891 | − | 0.452250i | \(-0.850621\pi\) |
0.0542853 | − | 0.998525i | \(-0.482712\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.46410 | + | 2.00000i | 0.120751 | + | 0.0697156i | 0.559159 | − | 0.829060i | \(-0.311124\pi\) |
−0.438408 | + | 0.898776i | \(0.644457\pi\) | |||||||
\(824\) | −2.00000 | + | 3.46410i | −0.0696733 | + | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | + | 10.3923i | 0.208767 | + | 0.361595i | ||||
\(827\) | − | 36.0000i | − | 1.25184i | −0.779886 | − | 0.625921i | \(-0.784723\pi\) | ||
0.779886 | − | 0.625921i | \(-0.215277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.0000 | −1.52818 | −0.764092 | − | 0.645108i | \(-0.776812\pi\) | ||||
−0.764092 | + | 0.645108i | \(0.776812\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.46410 | − | 2.00000i | −0.120096 | − | 0.0693375i | ||||
\(833\) | 23.3827 | + | 13.5000i | 0.810162 | + | 0.467747i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.0000 | −0.518786 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.0000 | + | 25.9808i | 0.517858 | + | 0.896956i | 0.999785 | + | 0.0207443i | \(0.00660359\pi\) |
−0.481927 | + | 0.876211i | \(0.660063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 1.73205 | + | 1.00000i | 0.0596904 | + | 0.0344623i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.00000 | − | 3.46410i | −0.0688428 | − | 0.119239i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.00000i | − | 0.274883i | ||||||
\(848\) | −5.19615 | + | 3.00000i | −0.178437 | + | 0.103020i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | + | 20.7846i | −0.411355 | + | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.1051 | − | 22.0000i | 1.30469 | − | 0.753266i | 0.323489 | − | 0.946232i | \(-0.395144\pi\) |
0.981205 | + | 0.192966i | \(0.0618108\pi\) | |||||||
\(854\) | −40.0000 | −1.36877 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | 0.307614 | ||||||||
\(857\) | −15.5885 | + | 9.00000i | −0.532492 | + | 0.307434i | −0.742030 | − | 0.670366i | \(-0.766137\pi\) |
0.209539 | + | 0.977800i | \(0.432804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.50000 | + | 16.4545i | −0.324136 | + | 0.561420i | −0.981337 | − | 0.192295i | \(-0.938407\pi\) |
0.657201 | + | 0.753715i | \(0.271740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.7846 | − | 12.0000i | 0.707927 | − | 0.408722i | ||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.50000 | + | 11.2583i | 0.220879 | + | 0.382574i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.92820 | + | 4.00000i | 0.235159 | + | 0.135769i | ||||
\(869\) | −21.0000 | + | 36.3731i | −0.712376 | + | 1.23387i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0000 | + | 17.3205i | 0.338837 | + | 0.586883i | ||||
\(872\) | 4.00000i | 0.135457i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 30.0000 | 1.01477 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.73205 | + | 1.00000i | 0.0584872 | + | 0.0337676i | 0.528958 | − | 0.848648i | \(-0.322583\pi\) |
−0.470471 | + | 0.882415i | \(0.655916\pi\) | |||||||
\(878\) | 8.66025 | + | 5.00000i | 0.292269 | + | 0.168742i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.0000i | 1.37976i | 0.723924 | + | 0.689880i | \(0.242337\pi\) | ||||
−0.723924 | + | 0.689880i | \(0.757663\pi\) | |||||||
\(884\) | 6.00000 | + | 10.3923i | 0.201802 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.50000 | − | 2.59808i | 0.0503935 | − | 0.0872841i | ||||
\(887\) | 36.3731 | + | 21.0000i | 1.22129 | + | 0.705111i | 0.965193 | − | 0.261540i | \(-0.0842305\pi\) |
0.256096 | + | 0.966651i | \(0.417564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | − | 6.92820i | −0.134156 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.0000i | 0.736614i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | − | 3.46410i | 0.0668153 | − | 0.115728i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.9904 | − | 7.50000i | 0.433495 | − | 0.250278i | ||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | 0.599667 | ||||||||
\(902\) | 7.79423 | − | 4.50000i | 0.259519 | − | 0.149834i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.00000 | + | 15.5885i | −0.299336 | + | 0.518464i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.33013 | + | 2.50000i | −0.143780 | + | 0.0830111i | −0.570164 | − | 0.821531i | \(-0.693120\pi\) |
0.426385 | + | 0.904542i | \(0.359787\pi\) | |||||||
\(908\) | 3.00000i | 0.0995585i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0000 | − | 25.9808i | −0.496972 | − | 0.860781i | 0.503022 | − | 0.864274i | \(-0.332222\pi\) |
−0.999994 | + | 0.00349271i | \(0.998888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.1769 | − | 18.0000i | −1.03181 | − | 0.595713i | ||||
\(914\) | −0.500000 | + | 0.866025i | −0.0165385 | + | 0.0286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | − | 17.3205i | −0.330409 | − | 0.572286i | ||||
\(917\) | − | 48.0000i | − | 1.58510i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0000 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.7846 | − | 12.0000i | −0.684134 | − | 0.394985i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.0000 | 0.657241 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 6.00000i | − | 0.196960i | ||||||
\(929\) | −15.0000 | − | 25.9808i | −0.492134 | − | 0.852401i | 0.507825 | − | 0.861460i | \(-0.330450\pi\) |
−0.999959 | + | 0.00905914i | \(0.997116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.5000 | + | 38.9711i | −0.737408 | + | 1.27723i | ||||
\(932\) | −18.1865 | − | 10.5000i | −0.595720 | − | 0.343939i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.5000 | − | 18.1865i | −0.343570 | − | 0.595082i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.0000i | 0.326686i | 0.986569 | + | 0.163343i | \(0.0522277\pi\) | ||||
−0.986569 | + | 0.163343i | \(0.947772\pi\) | |||||||
\(938\) | −17.3205 | + | 10.0000i | −0.565535 | + | 0.326512i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0000 | − | 20.7846i | 0.391189 | − | 0.677559i | −0.601418 | − | 0.798935i | \(-0.705397\pi\) |
0.992607 | + | 0.121376i | \(0.0387306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.5885 | + | 9.00000i | −0.507630 | + | 0.293080i | ||||
\(944\) | −3.00000 | −0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.0000 | −1.07292 | ||||||||
\(947\) | 23.3827 | − | 13.5000i | 0.759835 | − | 0.438691i | −0.0694014 | − | 0.997589i | \(-0.522109\pi\) |
0.829237 | + | 0.558898i | \(0.188776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0000 | − | 24.2487i | 0.454459 | − | 0.787146i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.3923 | + | 6.00000i | −0.336817 | + | 0.194461i | ||||
\(953\) | − | 51.0000i | − | 1.65205i | −0.563632 | − | 0.826026i | \(-0.690596\pi\) | ||
0.563632 | − | 0.826026i | \(-0.309404\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | + | 5.19615i | 0.0970269 | + | 0.168056i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.19615 | − | 3.00000i | −0.167880 | − | 0.0969256i | ||||
\(959\) | −18.0000 | + | 31.1769i | −0.581250 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | − | 16.0000i | − | 0.515861i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.0000 | −0.547533 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.0526 | − | 11.0000i | −0.612689 | − | 0.353736i | 0.161328 | − | 0.986901i | \(-0.448422\pi\) |
−0.774017 | + | 0.633165i | \(0.781756\pi\) | |||||||
\(968\) | 1.73205 | + | 1.00000i | 0.0556702 | + | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −60.0000 | −1.92549 | −0.962746 | − | 0.270408i | \(-0.912841\pi\) | ||||
−0.962746 | + | 0.270408i | \(0.912841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.00000i | 0.128234i | ||||||||
\(974\) | 1.00000 | + | 1.73205i | 0.0320421 | + | 0.0554985i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.00000 | − | 8.66025i | 0.160046 | − | 0.277208i | ||||
\(977\) | 7.79423 | + | 4.50000i | 0.249359 | + | 0.143968i | 0.619471 | − | 0.785020i | \(-0.287347\pi\) |
−0.370111 | + | 0.928987i | \(0.620681\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.00000 | + | 15.5885i | 0.287641 | + | 0.498209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 33.0000i | − | 1.05307i | ||||||
\(983\) | −31.1769 | + | 18.0000i | −0.994389 | + | 0.574111i | −0.906583 | − | 0.422027i | \(-0.861319\pi\) |
−0.0878058 | + | 0.996138i | \(0.527985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.00000 | + | 15.5885i | −0.286618 | + | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.3205 | + | 10.0000i | −0.551039 | + | 0.318142i | ||||
\(989\) | 66.0000 | 2.09868 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | −1.73205 | + | 1.00000i | −0.0549927 | + | 0.0317500i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0000 | − | 20.7846i | 0.380617 | − | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.5167 | + | 13.0000i | −0.713110 | + | 0.411714i | −0.812211 | − | 0.583363i | \(-0.801736\pi\) |
0.0991016 | + | 0.995077i | \(0.468403\pi\) | |||||||
\(998\) | − | 31.0000i | − | 0.981288i | ||||||
\(999\) | 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 twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.2.e.b.31.1 | ✓ | 2 | 15.2 | even | 4 | ||
90.2.e.b.61.1 | yes | 2 | 45.2 | even | 12 | ||
270.2.e.a.91.1 | 2 | 5.2 | odd | 4 | |||
270.2.e.a.181.1 | 2 | 45.7 | odd | 12 | |||
450.2.e.d.151.1 | 2 | 45.38 | even | 12 | |||
450.2.e.d.301.1 | 2 | 15.8 | even | 4 | |||
450.2.j.a.49.1 | 4 | 15.14 | odd | 2 | |||
450.2.j.a.49.2 | 4 | 3.2 | odd | 2 | |||
450.2.j.a.349.1 | 4 | 9.2 | odd | 6 | |||
450.2.j.a.349.2 | 4 | 45.29 | odd | 6 | |||
720.2.q.c.241.1 | 2 | 180.47 | odd | 12 | |||
720.2.q.c.481.1 | 2 | 60.47 | odd | 4 | |||
810.2.a.a.1.1 | 1 | 45.32 | even | 12 | |||
810.2.a.e.1.1 | 1 | 45.22 | odd | 12 | |||
1350.2.e.g.451.1 | 2 | 45.43 | odd | 12 | |||
1350.2.e.g.901.1 | 2 | 5.3 | odd | 4 | |||
1350.2.j.c.199.1 | 4 | 1.1 | even | 1 | trivial | ||
1350.2.j.c.199.2 | 4 | 5.4 | even | 2 | inner | ||
1350.2.j.c.1099.1 | 4 | 45.34 | even | 6 | inner | ||
1350.2.j.c.1099.2 | 4 | 9.7 | even | 3 | inner | ||
2160.2.q.d.721.1 | 2 | 180.7 | even | 12 | |||
2160.2.q.d.1441.1 | 2 | 20.7 | even | 4 | |||
4050.2.a.q.1.1 | 1 | 45.13 | odd | 12 | |||
4050.2.a.bi.1.1 | 1 | 45.23 | even | 12 | |||
4050.2.c.d.649.1 | 2 | 9.4 | even | 3 | |||
4050.2.c.d.649.2 | 2 | 45.4 | even | 6 | |||
4050.2.c.p.649.1 | 2 | 45.14 | odd | 6 | |||
4050.2.c.p.649.2 | 2 | 9.5 | odd | 6 | |||
6480.2.a.l.1.1 | 1 | 180.67 | even | 12 | |||
6480.2.a.z.1.1 | 1 | 180.167 | odd | 12 |