Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.d.199.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421i | 1.70711i | 0.521005 | + | 0.853553i | \(0.325557\pi\) | ||||
−0.521005 | + | 0.853553i | \(0.674443\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.41421 | 0.985599 | ||||||||
\(7\) | 0.414214i | 0.156558i | 0.996931 | + | 0.0782790i | \(0.0249425\pi\) | ||||
−0.996931 | + | 0.0782790i | \(0.975058\pi\) | |||||||
\(8\) | − 4.41421i | − 1.56066i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 3.82843i | 1.10517i | ||||||||
\(13\) | 2.82843i | 0.784465i | 0.919866 | + | 0.392232i | \(0.128297\pi\) | ||||
−0.919866 | + | 0.392232i | \(0.871703\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 2.41421i | 0.585533i | 0.956184 | + | 0.292766i | \(0.0945758\pi\) | ||||
−0.956184 | + | 0.292766i | \(0.905424\pi\) | |||||||
\(18\) | − 2.41421i | − 0.569036i | ||||||||
\(19\) | −6.41421 | −1.47152 | −0.735761 | − | 0.677242i | \(-0.763175\pi\) | ||||
−0.735761 | + | 0.677242i | \(0.763175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.414214 | 0.0903888 | ||||||||
\(22\) | − 2.41421i | − 0.514712i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | −0.994550 | − | 0.104257i | \(-0.966753\pi\) | ||||
0.994550 | − | 0.104257i | \(-0.0332465\pi\) | |||||||
\(24\) | −4.41421 | −0.901048 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.82843 | −1.33916 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 1.58579i | − 0.299685i | ||||||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.48528 | −1.52400 | −0.762001 | − | 0.647576i | \(-0.775783\pi\) | ||||
−0.762001 | + | 0.647576i | \(0.775783\pi\) | |||||||
\(32\) | − 1.58579i | − 0.280330i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | −5.82843 | −0.999567 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | − 0.171573i | − 0.0282064i | −0.999901 | − | 0.0141032i | \(-0.995511\pi\) | ||||
0.999901 | − | 0.0141032i | \(-0.00448934\pi\) | |||||||
\(38\) | − 15.4853i | − 2.51204i | ||||||||
\(39\) | 2.82843 | 0.452911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8995 | −1.70222 | −0.851108 | − | 0.524991i | \(-0.824069\pi\) | ||||
−0.851108 | + | 0.524991i | \(0.824069\pi\) | |||||||
\(42\) | 1.00000i | 0.154303i | ||||||||
\(43\) | 11.6569i | 1.77765i | 0.458243 | + | 0.888827i | \(0.348479\pi\) | ||||
−0.458243 | + | 0.888827i | \(0.651521\pi\) | |||||||
\(44\) | 3.82843 | 0.577157 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.41421 | 0.355956 | ||||||||
\(47\) | − 7.48528i | − 1.09184i | −0.837837 | − | 0.545920i | \(-0.816180\pi\) | ||||
0.837837 | − | 0.545920i | \(-0.183820\pi\) | |||||||
\(48\) | − 3.00000i | − 0.433013i | ||||||||
\(49\) | 6.82843 | 0.975490 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.41421 | 0.338058 | ||||||||
\(52\) | − 10.8284i | − 1.50163i | ||||||||
\(53\) | − 7.65685i | − 1.05175i | −0.850562 | − | 0.525875i | \(-0.823738\pi\) | ||||
0.850562 | − | 0.525875i | \(-0.176262\pi\) | |||||||
\(54\) | −2.41421 | −0.328533 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.82843 | 0.244334 | ||||||||
\(57\) | 6.41421i | 0.849583i | ||||||||
\(58\) | − 2.82843i | − 0.371391i | ||||||||
\(59\) | −11.0000 | −1.43208 | −0.716039 | − | 0.698060i | \(-0.754047\pi\) | ||||
−0.716039 | + | 0.698060i | \(0.754047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82843 | 1.13036 | 0.565182 | − | 0.824966i | \(-0.308806\pi\) | ||||
0.565182 | + | 0.824966i | \(0.308806\pi\) | |||||||
\(62\) | − 20.4853i | − 2.60163i | ||||||||
\(63\) | − 0.414214i | − 0.0521860i | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.41421 | −0.297169 | ||||||||
\(67\) | − 0.343146i | − 0.0419219i | −0.999780 | − | 0.0209610i | \(-0.993327\pi\) | ||||
0.999780 | − | 0.0209610i | \(-0.00667257\pi\) | |||||||
\(68\) | − 9.24264i | − 1.12083i | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.82843 | 0.929063 | 0.464532 | − | 0.885556i | \(-0.346223\pi\) | ||||
0.464532 | + | 0.885556i | \(0.346223\pi\) | |||||||
\(72\) | 4.41421i | 0.520220i | ||||||||
\(73\) | 8.82843i | 1.03329i | 0.856200 | + | 0.516645i | \(0.172819\pi\) | ||||
−0.856200 | + | 0.516645i | \(0.827181\pi\) | |||||||
\(74\) | 0.414214 | 0.0481513 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 24.5563 | 2.81681 | ||||||||
\(77\) | − 0.414214i | − 0.0472040i | ||||||||
\(78\) | 6.82843i | 0.773167i | ||||||||
\(79\) | −13.2426 | −1.48991 | −0.744957 | − | 0.667113i | \(-0.767530\pi\) | ||||
−0.744957 | + | 0.667113i | \(0.767530\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 26.3137i | − 2.90586i | ||||||||
\(83\) | 4.48528i | 0.492324i | 0.969229 | + | 0.246162i | \(0.0791695\pi\) | ||||
−0.969229 | + | 0.246162i | \(0.920831\pi\) | |||||||
\(84\) | −1.58579 | −0.173023 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −28.1421 | −3.03464 | ||||||||
\(87\) | 1.17157i | 0.125606i | ||||||||
\(88\) | 4.41421i | 0.470557i | ||||||||
\(89\) | −3.65685 | −0.387626 | −0.193813 | − | 0.981039i | \(-0.562085\pi\) | ||||
−0.193813 | + | 0.981039i | \(0.562085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.17157 | −0.122814 | ||||||||
\(92\) | 3.82843i | 0.399141i | ||||||||
\(93\) | 8.48528i | 0.879883i | ||||||||
\(94\) | 18.0711 | 1.86389 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.58579 | −0.161849 | ||||||||
\(97\) | 5.82843i | 0.591787i | 0.955221 | + | 0.295894i | \(0.0956174\pi\) | ||||
−0.955221 | + | 0.295894i | \(0.904383\pi\) | |||||||
\(98\) | 16.4853i | 1.66526i | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.8995 | 1.48256 | 0.741278 | − | 0.671199i | \(-0.234220\pi\) | ||||
0.741278 | + | 0.671199i | \(0.234220\pi\) | |||||||
\(102\) | 5.82843i | 0.577100i | ||||||||
\(103\) | 13.6569i | 1.34565i | 0.739802 | + | 0.672825i | \(0.234919\pi\) | ||||
−0.739802 | + | 0.672825i | \(0.765081\pi\) | |||||||
\(104\) | 12.4853 | 1.22428 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.4853 | 1.79545 | ||||||||
\(107\) | − 5.31371i | − 0.513696i | −0.966452 | − | 0.256848i | \(-0.917316\pi\) | ||||
0.966452 | − | 0.256848i | \(-0.0826839\pi\) | |||||||
\(108\) | − 3.82843i | − 0.368391i | ||||||||
\(109\) | −5.31371 | −0.508961 | −0.254480 | − | 0.967078i | \(-0.581904\pi\) | ||||
−0.254480 | + | 0.967078i | \(0.581904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.171573 | −0.0162850 | ||||||||
\(112\) | 1.24264i | 0.117419i | ||||||||
\(113\) | 10.0000i | 0.940721i | 0.882474 | + | 0.470360i | \(0.155876\pi\) | ||||
−0.882474 | + | 0.470360i | \(0.844124\pi\) | |||||||
\(114\) | −15.4853 | −1.45033 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.48528 | 0.416448 | ||||||||
\(117\) | − 2.82843i | − 0.261488i | ||||||||
\(118\) | − 26.5563i | − 2.44471i | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 21.3137i | 1.92965i | ||||||||
\(123\) | 10.8995i | 0.982774i | ||||||||
\(124\) | 32.4853 | 2.91726 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 7.24264i | 0.642680i | 0.946964 | + | 0.321340i | \(0.104133\pi\) | ||||
−0.946964 | + | 0.321340i | \(0.895867\pi\) | |||||||
\(128\) | 20.5563i | 1.81694i | ||||||||
\(129\) | 11.6569 | 1.02633 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.82843 | 0.596602 | 0.298301 | − | 0.954472i | \(-0.403580\pi\) | ||||
0.298301 | + | 0.954472i | \(0.403580\pi\) | |||||||
\(132\) | − 3.82843i | − 0.333222i | ||||||||
\(133\) | − 2.65685i | − 0.230378i | ||||||||
\(134\) | 0.828427 | 0.0715652 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.6569 | 0.913818 | ||||||||
\(137\) | − 12.1421i | − 1.03737i | −0.854965 | − | 0.518686i | \(-0.826421\pi\) | ||||
0.854965 | − | 0.518686i | \(-0.173579\pi\) | |||||||
\(138\) | − 2.41421i | − 0.205512i | ||||||||
\(139\) | 18.9706 | 1.60906 | 0.804531 | − | 0.593911i | \(-0.202417\pi\) | ||||
0.804531 | + | 0.593911i | \(0.202417\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.48528 | −0.630374 | ||||||||
\(142\) | 18.8995i | 1.58601i | ||||||||
\(143\) | − 2.82843i | − 0.236525i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −21.3137 | −1.76394 | ||||||||
\(147\) | − 6.82843i | − 0.563199i | ||||||||
\(148\) | 0.656854i | 0.0539931i | ||||||||
\(149\) | −7.72792 | −0.633096 | −0.316548 | − | 0.948576i | \(-0.602524\pi\) | ||||
−0.316548 | + | 0.948576i | \(0.602524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | 28.3137i | 2.29655i | ||||||||
\(153\) | − 2.41421i | − 0.195178i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.8284 | −0.866968 | ||||||||
\(157\) | 6.00000i | 0.478852i | 0.970915 | + | 0.239426i | \(0.0769593\pi\) | ||||
−0.970915 | + | 0.239426i | \(0.923041\pi\) | |||||||
\(158\) | − 31.9706i | − 2.54344i | ||||||||
\(159\) | −7.65685 | −0.607228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.414214 | 0.0326446 | ||||||||
\(162\) | 2.41421i | 0.189679i | ||||||||
\(163\) | − 15.7990i | − 1.23747i | −0.785599 | − | 0.618736i | \(-0.787645\pi\) | ||||
0.785599 | − | 0.618736i | \(-0.212355\pi\) | |||||||
\(164\) | 41.7279 | 3.25840 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.8284 | −0.840449 | ||||||||
\(167\) | 21.7990i | 1.68686i | 0.537242 | + | 0.843428i | \(0.319466\pi\) | ||||
−0.537242 | + | 0.843428i | \(0.680534\pi\) | |||||||
\(168\) | − 1.82843i | − 0.141066i | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.41421 | 0.490507 | ||||||||
\(172\) | − 44.6274i | − 3.40281i | ||||||||
\(173\) | 12.5563i | 0.954642i | 0.878729 | + | 0.477321i | \(0.158392\pi\) | ||||
−0.878729 | + | 0.477321i | \(0.841608\pi\) | |||||||
\(174\) | −2.82843 | −0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 11.0000i | 0.826811i | ||||||||
\(178\) | − 8.82843i | − 0.661719i | ||||||||
\(179\) | −16.7990 | −1.25562 | −0.627808 | − | 0.778368i | \(-0.716048\pi\) | ||||
−0.627808 | + | 0.778368i | \(0.716048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.9706 | −1.63306 | −0.816530 | − | 0.577304i | \(-0.804105\pi\) | ||||
−0.816530 | + | 0.577304i | \(0.804105\pi\) | |||||||
\(182\) | − 2.82843i | − 0.209657i | ||||||||
\(183\) | − 8.82843i | − 0.652616i | ||||||||
\(184\) | −4.41421 | −0.325420 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −20.4853 | −1.50205 | ||||||||
\(187\) | − 2.41421i | − 0.176545i | ||||||||
\(188\) | 28.6569i | 2.09002i | ||||||||
\(189\) | −0.414214 | −0.0301296 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.17157 | 0.446559 | 0.223280 | − | 0.974754i | \(-0.428324\pi\) | ||||
0.223280 | + | 0.974754i | \(0.428324\pi\) | |||||||
\(192\) | − 9.82843i | − 0.709306i | ||||||||
\(193\) | − 3.31371i | − 0.238526i | −0.992863 | − | 0.119263i | \(-0.961947\pi\) | ||||
0.992863 | − | 0.119263i | \(-0.0380532\pi\) | |||||||
\(194\) | −14.0711 | −1.01024 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −26.1421 | −1.86730 | ||||||||
\(197\) | 4.75736i | 0.338948i | 0.985535 | + | 0.169474i | \(0.0542068\pi\) | ||||
−0.985535 | + | 0.169474i | \(0.945793\pi\) | |||||||
\(198\) | 2.41421i | 0.171571i | ||||||||
\(199\) | −10.8284 | −0.767607 | −0.383803 | − | 0.923415i | \(-0.625386\pi\) | ||||
−0.383803 | + | 0.923415i | \(0.625386\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.343146 | −0.0242036 | ||||||||
\(202\) | 35.9706i | 2.53088i | ||||||||
\(203\) | − 0.485281i | − 0.0340601i | ||||||||
\(204\) | −9.24264 | −0.647114 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −32.9706 | −2.29717 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | 8.48528i | 0.588348i | ||||||||
\(209\) | 6.41421 | 0.443680 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.3137 | −0.916553 | −0.458277 | − | 0.888810i | \(-0.651533\pi\) | ||||
−0.458277 | + | 0.888810i | \(0.651533\pi\) | |||||||
\(212\) | 29.3137i | 2.01327i | ||||||||
\(213\) | − 7.82843i | − 0.536395i | ||||||||
\(214\) | 12.8284 | 0.876933 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.41421 | 0.300349 | ||||||||
\(217\) | − 3.51472i | − 0.238595i | ||||||||
\(218\) | − 12.8284i | − 0.868851i | ||||||||
\(219\) | 8.82843 | 0.596570 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.82843 | −0.459330 | ||||||||
\(222\) | − 0.414214i | − 0.0278002i | ||||||||
\(223\) | 21.1716i | 1.41775i | 0.705332 | + | 0.708877i | \(0.250798\pi\) | ||||
−0.705332 | + | 0.708877i | \(0.749202\pi\) | |||||||
\(224\) | 0.656854 | 0.0438879 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.1421 | −1.60591 | ||||||||
\(227\) | − 18.4853i | − 1.22691i | −0.789729 | − | 0.613456i | \(-0.789779\pi\) | ||||
0.789729 | − | 0.613456i | \(-0.210221\pi\) | |||||||
\(228\) | − 24.5563i | − 1.62628i | ||||||||
\(229\) | 2.51472 | 0.166177 | 0.0830886 | − | 0.996542i | \(-0.473522\pi\) | ||||
0.0830886 | + | 0.996542i | \(0.473522\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.414214 | −0.0272533 | ||||||||
\(232\) | 5.17157i | 0.339530i | ||||||||
\(233\) | − 16.5563i | − 1.08464i | −0.840171 | − | 0.542321i | \(-0.817546\pi\) | ||||
0.840171 | − | 0.542321i | \(-0.182454\pi\) | |||||||
\(234\) | 6.82843 | 0.446388 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 42.1127 | 2.74130 | ||||||||
\(237\) | 13.2426i | 0.860202i | ||||||||
\(238\) | − 2.41421i | − 0.156490i | ||||||||
\(239\) | −23.6569 | −1.53023 | −0.765117 | − | 0.643891i | \(-0.777319\pi\) | ||||
−0.765117 | + | 0.643891i | \(0.777319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1421 | 0.910975 | 0.455488 | − | 0.890242i | \(-0.349465\pi\) | ||||
0.455488 | + | 0.890242i | \(0.349465\pi\) | |||||||
\(242\) | 2.41421i | 0.155192i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −33.7990 | −2.16376 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.3137 | −1.67770 | ||||||||
\(247\) | − 18.1421i | − 1.15436i | ||||||||
\(248\) | 37.4558i | 2.37845i | ||||||||
\(249\) | 4.48528 | 0.284243 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.97056 | 0.566217 | 0.283108 | − | 0.959088i | \(-0.408634\pi\) | ||||
0.283108 | + | 0.959088i | \(0.408634\pi\) | |||||||
\(252\) | 1.58579i | 0.0998952i | ||||||||
\(253\) | 1.00000i | 0.0628695i | ||||||||
\(254\) | −17.4853 | −1.09712 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 9.31371i | 0.580973i | 0.956879 | + | 0.290487i | \(0.0938172\pi\) | ||||
−0.956879 | + | 0.290487i | \(0.906183\pi\) | |||||||
\(258\) | 28.1421i | 1.75205i | ||||||||
\(259\) | 0.0710678 | 0.00441594 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.17157 | 0.0725185 | ||||||||
\(262\) | 16.4853i | 1.01846i | ||||||||
\(263\) | − 22.9706i | − 1.41643i | −0.705999 | − | 0.708213i | \(-0.749502\pi\) | ||||
0.705999 | − | 0.708213i | \(-0.250498\pi\) | |||||||
\(264\) | 4.41421 | 0.271676 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.41421 | 0.393281 | ||||||||
\(267\) | 3.65685i | 0.223796i | ||||||||
\(268\) | 1.31371i | 0.0802475i | ||||||||
\(269\) | 15.7990 | 0.963281 | 0.481641 | − | 0.876369i | \(-0.340041\pi\) | ||||
0.481641 | + | 0.876369i | \(0.340041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.89949 | 0.540606 | 0.270303 | − | 0.962775i | \(-0.412876\pi\) | ||||
0.270303 | + | 0.962775i | \(0.412876\pi\) | |||||||
\(272\) | 7.24264i | 0.439150i | ||||||||
\(273\) | 1.17157i | 0.0709068i | ||||||||
\(274\) | 29.3137 | 1.77091 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.82843 | 0.230444 | ||||||||
\(277\) | 4.82843i | 0.290112i | 0.989423 | + | 0.145056i | \(0.0463362\pi\) | ||||
−0.989423 | + | 0.145056i | \(0.953664\pi\) | |||||||
\(278\) | 45.7990i | 2.74684i | ||||||||
\(279\) | 8.48528 | 0.508001 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.0711 | 1.91320 | 0.956600 | − | 0.291405i | \(-0.0941227\pi\) | ||||
0.956600 | + | 0.291405i | \(0.0941227\pi\) | |||||||
\(282\) | − 18.0711i | − 1.07612i | ||||||||
\(283\) | 0.899495i | 0.0534694i | 0.999643 | + | 0.0267347i | \(0.00851094\pi\) | ||||
−0.999643 | + | 0.0267347i | \(0.991489\pi\) | |||||||
\(284\) | −29.9706 | −1.77843 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.82843 | 0.403773 | ||||||||
\(287\) | − 4.51472i | − 0.266495i | ||||||||
\(288\) | 1.58579i | 0.0934434i | ||||||||
\(289\) | 11.1716 | 0.657151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.82843 | 0.341668 | ||||||||
\(292\) | − 33.7990i | − 1.97794i | ||||||||
\(293\) | − 17.5858i | − 1.02737i | −0.857978 | − | 0.513686i | \(-0.828280\pi\) | ||||
0.857978 | − | 0.513686i | \(-0.171720\pi\) | |||||||
\(294\) | 16.4853 | 0.961441 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.757359 | −0.0440206 | ||||||||
\(297\) | − 1.00000i | − 0.0580259i | ||||||||
\(298\) | − 18.6569i | − 1.08076i | ||||||||
\(299\) | 2.82843 | 0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.82843 | −0.278306 | ||||||||
\(302\) | 33.7990i | 1.94491i | ||||||||
\(303\) | − 14.8995i | − 0.855954i | ||||||||
\(304\) | −19.2426 | −1.10364 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.82843 | 0.333189 | ||||||||
\(307\) | 6.68629i | 0.381607i | 0.981628 | + | 0.190803i | \(0.0611093\pi\) | ||||
−0.981628 | + | 0.190803i | \(0.938891\pi\) | |||||||
\(308\) | 1.58579i | 0.0903586i | ||||||||
\(309\) | 13.6569 | 0.776911 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.6569 | 0.774409 | 0.387205 | − | 0.921994i | \(-0.373441\pi\) | ||||
0.387205 | + | 0.921994i | \(0.373441\pi\) | |||||||
\(312\) | − 12.4853i | − 0.706840i | ||||||||
\(313\) | 27.1421i | 1.53416i | 0.641549 | + | 0.767082i | \(0.278292\pi\) | ||||
−0.641549 | + | 0.767082i | \(0.721708\pi\) | |||||||
\(314\) | −14.4853 | −0.817452 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 50.6985 | 2.85201 | ||||||||
\(317\) | 30.8284i | 1.73150i | 0.500479 | + | 0.865748i | \(0.333157\pi\) | ||||
−0.500479 | + | 0.865748i | \(0.666843\pi\) | |||||||
\(318\) | − 18.4853i | − 1.03660i | ||||||||
\(319\) | 1.17157 | 0.0655955 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.31371 | −0.296582 | ||||||||
\(322\) | 1.00000i | 0.0557278i | ||||||||
\(323\) | − 15.4853i | − 0.861624i | ||||||||
\(324\) | −3.82843 | −0.212690 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 38.1421 | 2.11250 | ||||||||
\(327\) | 5.31371i | 0.293849i | ||||||||
\(328\) | 48.1127i | 2.65658i | ||||||||
\(329\) | 3.10051 | 0.170936 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.1421 | −1.76669 | −0.883346 | − | 0.468722i | \(-0.844715\pi\) | ||||
−0.883346 | + | 0.468722i | \(0.844715\pi\) | |||||||
\(332\) | − 17.1716i | − 0.942412i | ||||||||
\(333\) | 0.171573i | 0.00940214i | ||||||||
\(334\) | −52.6274 | −2.87964 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.24264 | 0.0677916 | ||||||||
\(337\) | 4.14214i | 0.225637i | 0.993616 | + | 0.112818i | \(0.0359878\pi\) | ||||
−0.993616 | + | 0.112818i | \(0.964012\pi\) | |||||||
\(338\) | 12.0711i | 0.656580i | ||||||||
\(339\) | 10.0000 | 0.543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.48528 | 0.459504 | ||||||||
\(342\) | 15.4853i | 0.837348i | ||||||||
\(343\) | 5.72792i | 0.309279i | ||||||||
\(344\) | 51.4558 | 2.77431 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.3137 | −1.62968 | ||||||||
\(347\) | − 21.1716i | − 1.13655i | −0.822839 | − | 0.568275i | \(-0.807611\pi\) | ||||
0.822839 | − | 0.568275i | \(-0.192389\pi\) | |||||||
\(348\) | − 4.48528i | − 0.240436i | ||||||||
\(349\) | 2.48528 | 0.133034 | 0.0665170 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665170 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.82843 | −0.150970 | ||||||||
\(352\) | 1.58579i | 0.0845227i | ||||||||
\(353\) | 4.48528i | 0.238727i | 0.992851 | + | 0.119364i | \(0.0380855\pi\) | ||||
−0.992851 | + | 0.119364i | \(0.961915\pi\) | |||||||
\(354\) | −26.5563 | −1.41145 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | 1.00000i | 0.0529256i | ||||||||
\(358\) | − 40.5563i | − 2.14347i | ||||||||
\(359\) | −15.5147 | −0.818836 | −0.409418 | − | 0.912347i | \(-0.634268\pi\) | ||||
−0.409418 | + | 0.912347i | \(0.634268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.1421 | 1.16538 | ||||||||
\(362\) | − 53.0416i | − 2.78781i | ||||||||
\(363\) | − 1.00000i | − 0.0524864i | ||||||||
\(364\) | 4.48528 | 0.235093 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 21.3137 | 1.11409 | ||||||||
\(367\) | 1.31371i | 0.0685750i | 0.999412 | + | 0.0342875i | \(0.0109162\pi\) | ||||
−0.999412 | + | 0.0342875i | \(0.989084\pi\) | |||||||
\(368\) | − 3.00000i | − 0.156386i | ||||||||
\(369\) | 10.8995 | 0.567405 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.17157 | 0.164660 | ||||||||
\(372\) | − 32.4853i | − 1.68428i | ||||||||
\(373\) | 23.6569i | 1.22491i | 0.790507 | + | 0.612453i | \(0.209817\pi\) | ||||
−0.790507 | + | 0.612453i | \(0.790183\pi\) | |||||||
\(374\) | 5.82843 | 0.301381 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33.0416 | −1.70399 | ||||||||
\(377\) | − 3.31371i | − 0.170665i | ||||||||
\(378\) | − 1.00000i | − 0.0514344i | ||||||||
\(379\) | −9.17157 | −0.471112 | −0.235556 | − | 0.971861i | \(-0.575691\pi\) | ||||
−0.235556 | + | 0.971861i | \(0.575691\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.24264 | 0.371052 | ||||||||
\(382\) | 14.8995i | 0.762324i | ||||||||
\(383\) | − 20.0000i | − 1.02195i | −0.859595 | − | 0.510976i | \(-0.829284\pi\) | ||||
0.859595 | − | 0.510976i | \(-0.170716\pi\) | |||||||
\(384\) | 20.5563 | 1.04901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | − 11.6569i | − 0.592551i | ||||||||
\(388\) | − 22.3137i | − 1.13281i | ||||||||
\(389\) | 17.6569 | 0.895238 | 0.447619 | − | 0.894224i | \(-0.352272\pi\) | ||||
0.447619 | + | 0.894224i | \(0.352272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.41421 | 0.122092 | ||||||||
\(392\) | − 30.1421i | − 1.52241i | ||||||||
\(393\) | − 6.82843i | − 0.344449i | ||||||||
\(394\) | −11.4853 | −0.578620 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.82843 | −0.192386 | ||||||||
\(397\) | − 35.9411i | − 1.80383i | −0.431910 | − | 0.901917i | \(-0.642160\pi\) | ||||
0.431910 | − | 0.901917i | \(-0.357840\pi\) | |||||||
\(398\) | − 26.1421i | − 1.31039i | ||||||||
\(399\) | −2.65685 | −0.133009 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.7990 | 1.58797 | 0.793983 | − | 0.607940i | \(-0.208004\pi\) | ||||
0.793983 | + | 0.607940i | \(0.208004\pi\) | |||||||
\(402\) | − 0.828427i | − 0.0413182i | ||||||||
\(403\) | − 24.0000i | − 1.19553i | ||||||||
\(404\) | −57.0416 | −2.83793 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.17157 | 0.0581442 | ||||||||
\(407\) | 0.171573i | 0.00850455i | ||||||||
\(408\) | − 10.6569i | − 0.527593i | ||||||||
\(409\) | 4.14214 | 0.204815 | 0.102408 | − | 0.994743i | \(-0.467345\pi\) | ||||
0.102408 | + | 0.994743i | \(0.467345\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.1421 | −0.598927 | ||||||||
\(412\) | − 52.2843i | − 2.57586i | ||||||||
\(413\) | − 4.55635i | − 0.224203i | ||||||||
\(414\) | −2.41421 | −0.118652 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.48528 | 0.219909 | ||||||||
\(417\) | − 18.9706i | − 0.928992i | ||||||||
\(418\) | 15.4853i | 0.757410i | ||||||||
\(419\) | 25.4853 | 1.24504 | 0.622519 | − | 0.782605i | \(-0.286109\pi\) | ||||
0.622519 | + | 0.782605i | \(0.286109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0000 | −1.31590 | −0.657950 | − | 0.753062i | \(-0.728576\pi\) | ||||
−0.657950 | + | 0.753062i | \(0.728576\pi\) | |||||||
\(422\) | − 32.1421i | − 1.56465i | ||||||||
\(423\) | 7.48528i | 0.363947i | ||||||||
\(424\) | −33.7990 | −1.64142 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 18.8995 | 0.915684 | ||||||||
\(427\) | 3.65685i | 0.176968i | ||||||||
\(428\) | 20.3431i | 0.983323i | ||||||||
\(429\) | −2.82843 | −0.136558 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.17157 | 0.0564327 | 0.0282163 | − | 0.999602i | \(-0.491017\pi\) | ||||
0.0282163 | + | 0.999602i | \(0.491017\pi\) | |||||||
\(432\) | 3.00000i | 0.144338i | ||||||||
\(433\) | 13.3137i | 0.639816i | 0.947449 | + | 0.319908i | \(0.103652\pi\) | ||||
−0.947449 | + | 0.319908i | \(0.896348\pi\) | |||||||
\(434\) | 8.48528 | 0.407307 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.3431 | 0.974260 | ||||||||
\(437\) | 6.41421i | 0.306833i | ||||||||
\(438\) | 21.3137i | 1.01841i | ||||||||
\(439\) | −2.27208 | −0.108440 | −0.0542202 | − | 0.998529i | \(-0.517267\pi\) | ||||
−0.0542202 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.82843 | −0.325163 | ||||||||
\(442\) | − 16.4853i | − 0.784125i | ||||||||
\(443\) | 7.97056i | 0.378693i | 0.981910 | + | 0.189346i | \(0.0606369\pi\) | ||||
−0.981910 | + | 0.189346i | \(0.939363\pi\) | |||||||
\(444\) | 0.656854 | 0.0311729 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −51.1127 | −2.42026 | ||||||||
\(447\) | 7.72792i | 0.365518i | ||||||||
\(448\) | 4.07107i | 0.192340i | ||||||||
\(449\) | 6.48528 | 0.306059 | 0.153030 | − | 0.988222i | \(-0.451097\pi\) | ||||
0.153030 | + | 0.988222i | \(0.451097\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8995 | 0.513237 | ||||||||
\(452\) | − 38.2843i | − 1.80074i | ||||||||
\(453\) | − 14.0000i | − 0.657777i | ||||||||
\(454\) | 44.6274 | 2.09447 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 28.3137 | 1.32591 | ||||||||
\(457\) | 3.85786i | 0.180463i | 0.995921 | + | 0.0902316i | \(0.0287607\pi\) | ||||
−0.995921 | + | 0.0902316i | \(0.971239\pi\) | |||||||
\(458\) | 6.07107i | 0.283682i | ||||||||
\(459\) | −2.41421 | −0.112686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.7696 | −1.52623 | −0.763115 | − | 0.646263i | \(-0.776331\pi\) | ||||
−0.763115 | + | 0.646263i | \(0.776331\pi\) | |||||||
\(462\) | − 1.00000i | − 0.0465242i | ||||||||
\(463\) | − 34.9706i | − 1.62522i | −0.582808 | − | 0.812610i | \(-0.698046\pi\) | ||||
0.582808 | − | 0.812610i | \(-0.301954\pi\) | |||||||
\(464\) | −3.51472 | −0.163167 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 39.9706 | 1.85160 | ||||||||
\(467\) | 10.6274i | 0.491778i | 0.969298 | + | 0.245889i | \(0.0790799\pi\) | ||||
−0.969298 | + | 0.245889i | \(0.920920\pi\) | |||||||
\(468\) | 10.8284i | 0.500544i | ||||||||
\(469\) | 0.142136 | 0.00656321 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | 0.276465 | ||||||||
\(472\) | 48.5563i | 2.23499i | ||||||||
\(473\) | − 11.6569i | − 0.535983i | ||||||||
\(474\) | −31.9706 | −1.46846 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.82843 | 0.175476 | ||||||||
\(477\) | 7.65685i | 0.350583i | ||||||||
\(478\) | − 57.1127i | − 2.61227i | ||||||||
\(479\) | 24.4853 | 1.11876 | 0.559381 | − | 0.828911i | \(-0.311039\pi\) | ||||
0.559381 | + | 0.828911i | \(0.311039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.485281 | 0.0221269 | ||||||||
\(482\) | 34.1421i | 1.55513i | ||||||||
\(483\) | − 0.414214i | − 0.0188474i | ||||||||
\(484\) | −3.82843 | −0.174019 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.41421 | 0.109511 | ||||||||
\(487\) | − 6.48528i | − 0.293876i | −0.989146 | − | 0.146938i | \(-0.953058\pi\) | ||||
0.989146 | − | 0.146938i | \(-0.0469418\pi\) | |||||||
\(488\) | − 38.9706i | − 1.76411i | ||||||||
\(489\) | −15.7990 | −0.714455 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.1421 | −1.08952 | −0.544760 | − | 0.838592i | \(-0.683379\pi\) | ||||
−0.544760 | + | 0.838592i | \(0.683379\pi\) | |||||||
\(492\) | − 41.7279i | − 1.88124i | ||||||||
\(493\) | − 2.82843i | − 0.127386i | ||||||||
\(494\) | 43.7990 | 1.97061 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.4558 | −1.14300 | ||||||||
\(497\) | 3.24264i | 0.145452i | ||||||||
\(498\) | 10.8284i | 0.485233i | ||||||||
\(499\) | −35.1716 | −1.57450 | −0.787248 | − | 0.616637i | \(-0.788495\pi\) | ||||
−0.787248 | + | 0.616637i | \(0.788495\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.7990 | 0.973907 | ||||||||
\(502\) | 21.6569i | 0.966593i | ||||||||
\(503\) | 34.2843i | 1.52866i | 0.644825 | + | 0.764330i | \(0.276930\pi\) | ||||
−0.644825 | + | 0.764330i | \(0.723070\pi\) | |||||||
\(504\) | −1.82843 | −0.0814446 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.41421 | −0.107325 | ||||||||
\(507\) | − 5.00000i | − 0.222058i | ||||||||
\(508\) | − 27.7279i | − 1.23023i | ||||||||
\(509\) | −4.62742 | −0.205107 | −0.102553 | − | 0.994728i | \(-0.532701\pi\) | ||||
−0.102553 | + | 0.994728i | \(0.532701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.65685 | −0.161770 | ||||||||
\(512\) | − 31.2426i | − 1.38074i | ||||||||
\(513\) | − 6.41421i | − 0.283194i | ||||||||
\(514\) | −22.4853 | −0.991783 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −44.6274 | −1.96461 | ||||||||
\(517\) | 7.48528i | 0.329202i | ||||||||
\(518\) | 0.171573i | 0.00753848i | ||||||||
\(519\) | 12.5563 | 0.551163 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.1421 | −1.58342 | −0.791708 | − | 0.610900i | \(-0.790808\pi\) | ||||
−0.791708 | + | 0.610900i | \(0.790808\pi\) | |||||||
\(522\) | 2.82843i | 0.123797i | ||||||||
\(523\) | − 42.2132i | − 1.84585i | −0.384974 | − | 0.922927i | \(-0.625790\pi\) | ||||
0.384974 | − | 0.922927i | \(-0.374210\pi\) | |||||||
\(524\) | −26.1421 | −1.14202 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 55.4558 | 2.41799 | ||||||||
\(527\) | − 20.4853i | − 0.892353i | ||||||||
\(528\) | 3.00000i | 0.130558i | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.0000 | 0.477359 | ||||||||
\(532\) | 10.1716i | 0.440994i | ||||||||
\(533\) | − 30.8284i | − 1.33533i | ||||||||
\(534\) | −8.82843 | −0.382043 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.51472 | −0.0654259 | ||||||||
\(537\) | 16.7990i | 0.724930i | ||||||||
\(538\) | 38.1421i | 1.64442i | ||||||||
\(539\) | −6.82843 | −0.294121 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.3137 | 0.486414 | 0.243207 | − | 0.969974i | \(-0.421801\pi\) | ||||
0.243207 | + | 0.969974i | \(0.421801\pi\) | |||||||
\(542\) | 21.4853i | 0.922872i | ||||||||
\(543\) | 21.9706i | 0.942847i | ||||||||
\(544\) | 3.82843 | 0.164142 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.82843 | −0.121046 | ||||||||
\(547\) | 35.8701i | 1.53369i | 0.641831 | + | 0.766846i | \(0.278175\pi\) | ||||
−0.641831 | + | 0.766846i | \(0.721825\pi\) | |||||||
\(548\) | 46.4853i | 1.98575i | ||||||||
\(549\) | −8.82843 | −0.376788 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.51472 | 0.320138 | ||||||||
\(552\) | 4.41421i | 0.187881i | ||||||||
\(553\) | − 5.48528i | − 0.233258i | ||||||||
\(554\) | −11.6569 | −0.495252 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −72.6274 | −3.08009 | ||||||||
\(557\) | − 5.17157i | − 0.219127i | −0.993980 | − | 0.109563i | \(-0.965055\pi\) | ||||
0.993980 | − | 0.109563i | \(-0.0349452\pi\) | |||||||
\(558\) | 20.4853i | 0.867211i | ||||||||
\(559\) | −32.9706 | −1.39451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.41421 | −0.101928 | ||||||||
\(562\) | 77.4264i | 3.26604i | ||||||||
\(563\) | − 15.3137i | − 0.645396i | −0.946502 | − | 0.322698i | \(-0.895410\pi\) | ||||
0.946502 | − | 0.322698i | \(-0.104590\pi\) | |||||||
\(564\) | 28.6569 | 1.20667 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.17157 | −0.0912780 | ||||||||
\(567\) | 0.414214i | 0.0173953i | ||||||||
\(568\) | − 34.5563i | − 1.44995i | ||||||||
\(569\) | −15.2426 | −0.639005 | −0.319502 | − | 0.947585i | \(-0.603516\pi\) | ||||
−0.319502 | + | 0.947585i | \(0.603516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.02944 | −0.377870 | −0.188935 | − | 0.981990i | \(-0.560504\pi\) | ||||
−0.188935 | + | 0.981990i | \(0.560504\pi\) | |||||||
\(572\) | 10.8284i | 0.452759i | ||||||||
\(573\) | − 6.17157i | − 0.257821i | ||||||||
\(574\) | 10.8995 | 0.454936 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | 23.9706i | 0.997908i | 0.866629 | + | 0.498954i | \(0.166282\pi\) | ||||
−0.866629 | + | 0.498954i | \(0.833718\pi\) | |||||||
\(578\) | 26.9706i | 1.12183i | ||||||||
\(579\) | −3.31371 | −0.137713 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.85786 | −0.0770772 | ||||||||
\(582\) | 14.0711i | 0.583265i | ||||||||
\(583\) | 7.65685i | 0.317115i | ||||||||
\(584\) | 38.9706 | 1.61261 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.4558 | 1.75383 | ||||||||
\(587\) | − 36.6569i | − 1.51299i | −0.653999 | − | 0.756495i | \(-0.726910\pi\) | ||||
0.653999 | − | 0.756495i | \(-0.273090\pi\) | |||||||
\(588\) | 26.1421i | 1.07808i | ||||||||
\(589\) | 54.4264 | 2.24260 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.75736 | 0.195692 | ||||||||
\(592\) | − 0.514719i | − 0.0211548i | ||||||||
\(593\) | − 3.79899i | − 0.156006i | −0.996953 | − | 0.0780029i | \(-0.975146\pi\) | ||||
0.996953 | − | 0.0780029i | \(-0.0248543\pi\) | |||||||
\(594\) | 2.41421 | 0.0990564 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 29.5858 | 1.21188 | ||||||||
\(597\) | 10.8284i | 0.443178i | ||||||||
\(598\) | 6.82843i | 0.279235i | ||||||||
\(599\) | −36.3137 | −1.48374 | −0.741869 | − | 0.670545i | \(-0.766060\pi\) | ||||
−0.741869 | + | 0.670545i | \(0.766060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.8284 | −0.604864 | −0.302432 | − | 0.953171i | \(-0.597799\pi\) | ||||
−0.302432 | + | 0.953171i | \(0.597799\pi\) | |||||||
\(602\) | − 11.6569i | − 0.475098i | ||||||||
\(603\) | 0.343146i | 0.0139740i | ||||||||
\(604\) | −53.5980 | −2.18087 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 35.9706 | 1.46120 | ||||||||
\(607\) | − 2.97056i | − 0.120571i | −0.998181 | − | 0.0602857i | \(-0.980799\pi\) | ||||
0.998181 | − | 0.0602857i | \(-0.0192012\pi\) | |||||||
\(608\) | 10.1716i | 0.412512i | ||||||||
\(609\) | −0.485281 | −0.0196646 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.1716 | 0.856510 | ||||||||
\(612\) | 9.24264i | 0.373612i | ||||||||
\(613\) | 42.0000i | 1.69636i | 0.529705 | + | 0.848182i | \(0.322303\pi\) | ||||
−0.529705 | + | 0.848182i | \(0.677697\pi\) | |||||||
\(614\) | −16.1421 | −0.651444 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.82843 | −0.0736694 | ||||||||
\(617\) | − 9.85786i | − 0.396863i | −0.980115 | − | 0.198431i | \(-0.936415\pi\) | ||||
0.980115 | − | 0.198431i | \(-0.0635847\pi\) | |||||||
\(618\) | 32.9706i | 1.32627i | ||||||||
\(619\) | −38.6274 | −1.55257 | −0.776283 | − | 0.630384i | \(-0.782897\pi\) | ||||
−0.776283 | + | 0.630384i | \(0.782897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 32.9706i | 1.32200i | ||||||||
\(623\) | − 1.51472i | − 0.0606859i | ||||||||
\(624\) | 8.48528 | 0.339683 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −65.5269 | −2.61898 | ||||||||
\(627\) | − 6.41421i | − 0.256159i | ||||||||
\(628\) | − 22.9706i | − 0.916625i | ||||||||
\(629\) | 0.414214 | 0.0165158 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.6274 | 1.06002 | 0.530010 | − | 0.847991i | \(-0.322188\pi\) | ||||
0.530010 | + | 0.847991i | \(0.322188\pi\) | |||||||
\(632\) | 58.4558i | 2.32525i | ||||||||
\(633\) | 13.3137i | 0.529172i | ||||||||
\(634\) | −74.4264 | −2.95585 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 29.3137 | 1.16236 | ||||||||
\(637\) | 19.3137i | 0.765237i | ||||||||
\(638\) | 2.82843i | 0.111979i | ||||||||
\(639\) | −7.82843 | −0.309688 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.4853 | −1.67807 | −0.839034 | − | 0.544079i | \(-0.816879\pi\) | ||||
−0.839034 | + | 0.544079i | \(0.816879\pi\) | |||||||
\(642\) | − 12.8284i | − 0.506298i | ||||||||
\(643\) | 32.9706i | 1.30023i | 0.759835 | + | 0.650116i | \(0.225280\pi\) | ||||
−0.759835 | + | 0.650116i | \(0.774720\pi\) | |||||||
\(644\) | −1.58579 | −0.0624887 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 37.3848 | 1.47088 | ||||||||
\(647\) | 17.3431i | 0.681829i | 0.940094 | + | 0.340915i | \(0.110737\pi\) | ||||
−0.940094 | + | 0.340915i | \(0.889263\pi\) | |||||||
\(648\) | − 4.41421i | − 0.173407i | ||||||||
\(649\) | 11.0000 | 0.431788 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.51472 | −0.137753 | ||||||||
\(652\) | 60.4853i | 2.36879i | ||||||||
\(653\) | 40.4853i | 1.58431i | 0.610319 | + | 0.792156i | \(0.291041\pi\) | ||||
−0.610319 | + | 0.792156i | \(0.708959\pi\) | |||||||
\(654\) | −12.8284 | −0.501631 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −32.6985 | −1.27666 | ||||||||
\(657\) | − 8.82843i | − 0.344430i | ||||||||
\(658\) | 7.48528i | 0.291807i | ||||||||
\(659\) | −15.1127 | −0.588707 | −0.294354 | − | 0.955697i | \(-0.595104\pi\) | ||||
−0.294354 | + | 0.955697i | \(0.595104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.6569 | −1.34800 | −0.673998 | − | 0.738733i | \(-0.735424\pi\) | ||||
−0.673998 | + | 0.738733i | \(0.735424\pi\) | |||||||
\(662\) | − 77.5980i | − 3.01593i | ||||||||
\(663\) | 6.82843i | 0.265194i | ||||||||
\(664\) | 19.7990 | 0.768350 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.414214 | −0.0160504 | ||||||||
\(667\) | 1.17157i | 0.0453635i | ||||||||
\(668\) | − 83.4558i | − 3.22900i | ||||||||
\(669\) | 21.1716 | 0.818540 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.82843 | −0.340818 | ||||||||
\(672\) | − 0.656854i | − 0.0253387i | ||||||||
\(673\) | − 11.6569i | − 0.449339i | −0.974435 | − | 0.224669i | \(-0.927870\pi\) | ||||
0.974435 | − | 0.224669i | \(-0.0721302\pi\) | |||||||
\(674\) | −10.0000 | −0.385186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.1421 | −0.736236 | ||||||||
\(677\) | 40.4853i | 1.55598i | 0.628279 | + | 0.777988i | \(0.283760\pi\) | ||||
−0.628279 | + | 0.777988i | \(0.716240\pi\) | |||||||
\(678\) | 24.1421i | 0.927173i | ||||||||
\(679\) | −2.41421 | −0.0926490 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.4853 | −0.708358 | ||||||||
\(682\) | 20.4853i | 0.784422i | ||||||||
\(683\) | − 29.4853i | − 1.12822i | −0.825699 | − | 0.564111i | \(-0.809219\pi\) | ||||
0.825699 | − | 0.564111i | \(-0.190781\pi\) | |||||||
\(684\) | −24.5563 | −0.938935 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.8284 | −0.527972 | ||||||||
\(687\) | − 2.51472i | − 0.0959425i | ||||||||
\(688\) | 34.9706i | 1.33324i | ||||||||
\(689\) | 21.6569 | 0.825060 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4558 | 0.587968 | 0.293984 | − | 0.955810i | \(-0.405019\pi\) | ||||
0.293984 | + | 0.955810i | \(0.405019\pi\) | |||||||
\(692\) | − 48.0711i | − 1.82739i | ||||||||
\(693\) | 0.414214i | 0.0157347i | ||||||||
\(694\) | 51.1127 | 1.94021 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.17157 | 0.196028 | ||||||||
\(697\) | − 26.3137i | − 0.996703i | ||||||||
\(698\) | 6.00000i | 0.227103i | ||||||||
\(699\) | −16.5563 | −0.626219 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.61522 | −0.174315 | −0.0871573 | − | 0.996195i | \(-0.527778\pi\) | ||||
−0.0871573 | + | 0.996195i | \(0.527778\pi\) | |||||||
\(702\) | − 6.82843i | − 0.257722i | ||||||||
\(703\) | 1.10051i | 0.0415063i | ||||||||
\(704\) | −9.82843 | −0.370423 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.8284 | −0.407533 | ||||||||
\(707\) | 6.17157i | 0.232106i | ||||||||
\(708\) | − 42.1127i | − 1.58269i | ||||||||
\(709\) | 0.857864 | 0.0322178 | 0.0161089 | − | 0.999870i | \(-0.494872\pi\) | ||||
0.0161089 | + | 0.999870i | \(0.494872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.2426 | 0.496638 | ||||||||
\(712\) | 16.1421i | 0.604952i | ||||||||
\(713\) | 8.48528i | 0.317776i | ||||||||
\(714\) | −2.41421 | −0.0903497 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 64.3137 | 2.40352 | ||||||||
\(717\) | 23.6569i | 0.883481i | ||||||||
\(718\) | − 37.4558i | − 1.39784i | ||||||||
\(719\) | 1.65685 | 0.0617902 | 0.0308951 | − | 0.999523i | \(-0.490164\pi\) | ||||
0.0308951 | + | 0.999523i | \(0.490164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.65685 | −0.210672 | ||||||||
\(722\) | 53.4558i | 1.98942i | ||||||||
\(723\) | − 14.1421i | − 0.525952i | ||||||||
\(724\) | 84.1127 | 3.12602 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.41421 | 0.0895999 | ||||||||
\(727\) | − 16.9706i | − 0.629403i | −0.949191 | − | 0.314702i | \(-0.898096\pi\) | ||||
0.949191 | − | 0.314702i | \(-0.101904\pi\) | |||||||
\(728\) | 5.17157i | 0.191671i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.1421 | −1.04087 | ||||||||
\(732\) | 33.7990i | 1.24925i | ||||||||
\(733\) | − 3.85786i | − 0.142493i | −0.997459 | − | 0.0712467i | \(-0.977302\pi\) | ||||
0.997459 | − | 0.0712467i | \(-0.0226978\pi\) | |||||||
\(734\) | −3.17157 | −0.117065 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.58579 | −0.0584529 | ||||||||
\(737\) | 0.343146i | 0.0126399i | ||||||||
\(738\) | 26.3137i | 0.968621i | ||||||||
\(739\) | −17.5858 | −0.646904 | −0.323452 | − | 0.946245i | \(-0.604843\pi\) | ||||
−0.323452 | + | 0.946245i | \(0.604843\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.1421 | −0.666468 | ||||||||
\(742\) | 7.65685i | 0.281092i | ||||||||
\(743\) | − 31.1127i | − 1.14141i | −0.821154 | − | 0.570707i | \(-0.806669\pi\) | ||||
0.821154 | − | 0.570707i | \(-0.193331\pi\) | |||||||
\(744\) | 37.4558 | 1.37320 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −57.1127 | −2.09104 | ||||||||
\(747\) | − 4.48528i | − 0.164108i | ||||||||
\(748\) | 9.24264i | 0.337944i | ||||||||
\(749\) | 2.20101 | 0.0804232 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.5980 | −1.73687 | −0.868437 | − | 0.495799i | \(-0.834875\pi\) | ||||
−0.868437 | + | 0.495799i | \(0.834875\pi\) | |||||||
\(752\) | − 22.4558i | − 0.818880i | ||||||||
\(753\) | − 8.97056i | − 0.326905i | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.58579 | 0.0576745 | ||||||||
\(757\) | − 33.3137i | − 1.21081i | −0.795919 | − | 0.605404i | \(-0.793012\pi\) | ||||
0.795919 | − | 0.605404i | \(-0.206988\pi\) | |||||||
\(758\) | − 22.1421i | − 0.804239i | ||||||||
\(759\) | 1.00000 | 0.0362977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.8284 | −0.392530 | −0.196265 | − | 0.980551i | \(-0.562881\pi\) | ||||
−0.196265 | + | 0.980551i | \(0.562881\pi\) | |||||||
\(762\) | 17.4853i | 0.633425i | ||||||||
\(763\) | − 2.20101i | − 0.0796819i | ||||||||
\(764\) | −23.6274 | −0.854810 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 48.2843 | 1.74458 | ||||||||
\(767\) | − 31.1127i | − 1.12341i | ||||||||
\(768\) | 29.9706i | 1.08147i | ||||||||
\(769\) | −3.65685 | −0.131870 | −0.0659348 | − | 0.997824i | \(-0.521003\pi\) | ||||
−0.0659348 | + | 0.997824i | \(0.521003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.31371 | 0.335425 | ||||||||
\(772\) | 12.6863i | 0.456590i | ||||||||
\(773\) | − 4.82843i | − 0.173666i | −0.996223 | − | 0.0868332i | \(-0.972325\pi\) | ||||
0.996223 | − | 0.0868332i | \(-0.0276747\pi\) | |||||||
\(774\) | 28.1421 | 1.01155 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 25.7279 | 0.923579 | ||||||||
\(777\) | − 0.0710678i | − 0.00254954i | ||||||||
\(778\) | 42.6274i | 1.52827i | ||||||||
\(779\) | 69.9117 | 2.50485 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.82843 | −0.280123 | ||||||||
\(782\) | 5.82843i | 0.208424i | ||||||||
\(783\) | − 1.17157i | − 0.0418686i | ||||||||
\(784\) | 20.4853 | 0.731617 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 16.4853 | 0.588011 | ||||||||
\(787\) | − 22.0711i | − 0.786749i | −0.919378 | − | 0.393374i | \(-0.871308\pi\) | ||||
0.919378 | − | 0.393374i | \(-0.128692\pi\) | |||||||
\(788\) | − 18.2132i | − 0.648819i | ||||||||
\(789\) | −22.9706 | −0.817774 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.14214 | −0.147277 | ||||||||
\(792\) | − 4.41421i | − 0.156852i | ||||||||
\(793\) | 24.9706i | 0.886731i | ||||||||
\(794\) | 86.7696 | 3.07934 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 41.4558 | 1.46936 | ||||||||
\(797\) | 7.02944i | 0.248995i | 0.992220 | + | 0.124498i | \(0.0397319\pi\) | ||||
−0.992220 | + | 0.124498i | \(0.960268\pi\) | |||||||
\(798\) | − 6.41421i | − 0.227061i | ||||||||
\(799\) | 18.0711 | 0.639308 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.65685 | 0.129209 | ||||||||
\(802\) | 76.7696i | 2.71083i | ||||||||
\(803\) | − 8.82843i | − 0.311548i | ||||||||
\(804\) | 1.31371 | 0.0463309 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 57.9411 | 2.04089 | ||||||||
\(807\) | − 15.7990i | − 0.556151i | ||||||||
\(808\) | − 65.7696i | − 2.31376i | ||||||||
\(809\) | 17.7279 | 0.623281 | 0.311640 | − | 0.950200i | \(-0.399122\pi\) | ||||
0.311640 | + | 0.950200i | \(0.399122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.2132 | −1.13116 | −0.565579 | − | 0.824694i | \(-0.691347\pi\) | ||||
−0.565579 | + | 0.824694i | \(0.691347\pi\) | |||||||
\(812\) | 1.85786i | 0.0651983i | ||||||||
\(813\) | − 8.89949i | − 0.312119i | ||||||||
\(814\) | −0.414214 | −0.0145182 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.24264 | 0.253543 | ||||||||
\(817\) | − 74.7696i | − 2.61586i | ||||||||
\(818\) | 10.0000i | 0.349642i | ||||||||
\(819\) | 1.17157 | 0.0409381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.7990 | −0.830590 | −0.415295 | − | 0.909687i | \(-0.636322\pi\) | ||||
−0.415295 | + | 0.909687i | \(0.636322\pi\) | |||||||
\(822\) | − 29.3137i | − 1.02243i | ||||||||
\(823\) | − 18.9706i | − 0.661272i | −0.943758 | − | 0.330636i | \(-0.892737\pi\) | ||||
0.943758 | − | 0.330636i | \(-0.107263\pi\) | |||||||
\(824\) | 60.2843 | 2.10010 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.0000 | 0.382739 | ||||||||
\(827\) | − 35.3137i | − 1.22798i | −0.789315 | − | 0.613989i | \(-0.789564\pi\) | ||||
0.789315 | − | 0.613989i | \(-0.210436\pi\) | |||||||
\(828\) | − 3.82843i | − 0.133047i | ||||||||
\(829\) | −19.9411 | −0.692584 | −0.346292 | − | 0.938127i | \(-0.612559\pi\) | ||||
−0.346292 | + | 0.938127i | \(0.612559\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.82843 | 0.167496 | ||||||||
\(832\) | 27.7990i | 0.963757i | ||||||||
\(833\) | 16.4853i | 0.571181i | ||||||||
\(834\) | 45.7990 | 1.58589 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −24.5563 | −0.849299 | ||||||||
\(837\) | − 8.48528i | − 0.293294i | ||||||||
\(838\) | 61.5269i | 2.12541i | ||||||||
\(839\) | 24.6863 | 0.852265 | 0.426133 | − | 0.904661i | \(-0.359876\pi\) | ||||
0.426133 | + | 0.904661i | \(0.359876\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | − 65.1838i | − 2.24638i | ||||||||
\(843\) | − 32.0711i | − 1.10459i | ||||||||
\(844\) | 50.9706 | 1.75448 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.0711 | −0.621296 | ||||||||
\(847\) | 0.414214i | 0.0142325i | ||||||||
\(848\) | − 22.9706i | − 0.788812i | ||||||||
\(849\) | 0.899495 | 0.0308706 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.171573 | −0.00588144 | ||||||||
\(852\) | 29.9706i | 1.02677i | ||||||||
\(853\) | 24.8284i | 0.850109i | 0.905168 | + | 0.425055i | \(0.139745\pi\) | ||||
−0.905168 | + | 0.425055i | \(0.860255\pi\) | |||||||
\(854\) | −8.82843 | −0.302103 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.4558 | −0.801704 | ||||||||
\(857\) | 22.6985i | 0.775365i | 0.921793 | + | 0.387683i | \(0.126724\pi\) | ||||
−0.921793 | + | 0.387683i | \(0.873276\pi\) | |||||||
\(858\) | − 6.82843i | − 0.233119i | ||||||||
\(859\) | 3.51472 | 0.119921 | 0.0599603 | − | 0.998201i | \(-0.480903\pi\) | ||||
0.0599603 | + | 0.998201i | \(0.480903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.51472 | −0.153861 | ||||||||
\(862\) | 2.82843i | 0.0963366i | ||||||||
\(863\) | 51.3137i | 1.74674i | 0.487058 | + | 0.873369i | \(0.338070\pi\) | ||||
−0.487058 | + | 0.873369i | \(0.661930\pi\) | |||||||
\(864\) | 1.58579 | 0.0539496 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −32.1421 | −1.09223 | ||||||||
\(867\) | − 11.1716i | − 0.379407i | ||||||||
\(868\) | 13.4558i | 0.456721i | ||||||||
\(869\) | 13.2426 | 0.449226 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.970563 | 0.0328863 | ||||||||
\(872\) | 23.4558i | 0.794315i | ||||||||
\(873\) | − 5.82843i | − 0.197262i | ||||||||
\(874\) | −15.4853 | −0.523797 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −33.7990 | −1.14196 | ||||||||
\(877\) | − 47.1127i | − 1.59088i | −0.606031 | − | 0.795441i | \(-0.707239\pi\) | ||||
0.606031 | − | 0.795441i | \(-0.292761\pi\) | |||||||
\(878\) | − 5.48528i | − 0.185119i | ||||||||
\(879\) | −17.5858 | −0.593154 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.0000 | −0.808581 | −0.404290 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404290 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(882\) | − 16.4853i | − 0.555088i | ||||||||
\(883\) | 6.62742i | 0.223030i | 0.993763 | + | 0.111515i | \(0.0355704\pi\) | ||||
−0.993763 | + | 0.111515i | \(0.964430\pi\) | |||||||
\(884\) | 26.1421 | 0.879255 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.2426 | −0.646469 | ||||||||
\(887\) | 6.14214i | 0.206233i | 0.994669 | + | 0.103116i | \(0.0328814\pi\) | ||||
−0.994669 | + | 0.103116i | \(0.967119\pi\) | |||||||
\(888\) | 0.757359i | 0.0254153i | ||||||||
\(889\) | −3.00000 | −0.100617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | − 81.0538i | − 2.71388i | ||||||||
\(893\) | 48.0122i | 1.60667i | ||||||||
\(894\) | −18.6569 | −0.623979 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.51472 | −0.284457 | ||||||||
\(897\) | − 2.82843i | − 0.0944384i | ||||||||
\(898\) | 15.6569i | 0.522476i | ||||||||
\(899\) | 9.94113 | 0.331555 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.4853 | 0.615834 | ||||||||
\(902\) | 26.3137i | 0.876151i | ||||||||
\(903\) | 4.82843i | 0.160680i | ||||||||
\(904\) | 44.1421 | 1.46815 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 33.7990 | 1.12290 | ||||||||
\(907\) | 14.4853i | 0.480976i | 0.970652 | + | 0.240488i | \(0.0773074\pi\) | ||||
−0.970652 | + | 0.240488i | \(0.922693\pi\) | |||||||
\(908\) | 70.7696i | 2.34857i | ||||||||
\(909\) | −14.8995 | −0.494185 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.4853 | 1.50699 | 0.753497 | − | 0.657451i | \(-0.228365\pi\) | ||||
0.753497 | + | 0.657451i | \(0.228365\pi\) | |||||||
\(912\) | 19.2426i | 0.637188i | ||||||||
\(913\) | − 4.48528i | − 0.148441i | ||||||||
\(914\) | −9.31371 | −0.308070 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.62742 | −0.318099 | ||||||||
\(917\) | 2.82843i | 0.0934029i | ||||||||
\(918\) | − 5.82843i | − 0.192367i | ||||||||
\(919\) | −44.2132 | −1.45846 | −0.729230 | − | 0.684269i | \(-0.760121\pi\) | ||||
−0.729230 | + | 0.684269i | \(0.760121\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.68629 | 0.220321 | ||||||||
\(922\) | − 79.1127i | − 2.60544i | ||||||||
\(923\) | 22.1421i | 0.728817i | ||||||||
\(924\) | 1.58579 | 0.0521685 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 84.4264 | 2.77442 | ||||||||
\(927\) | − 13.6569i | − 0.448550i | ||||||||
\(928\) | 1.85786i | 0.0609874i | ||||||||
\(929\) | −25.7990 | −0.846437 | −0.423219 | − | 0.906028i | \(-0.639100\pi\) | ||||
−0.423219 | + | 0.906028i | \(0.639100\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.7990 | −1.43545 | ||||||||
\(932\) | 63.3848i | 2.07624i | ||||||||
\(933\) | − 13.6569i | − 0.447105i | ||||||||
\(934\) | −25.6569 | −0.839518 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.4853 | −0.408094 | ||||||||
\(937\) | − 16.0000i | − 0.522697i | −0.965244 | − | 0.261349i | \(-0.915833\pi\) | ||||
0.965244 | − | 0.261349i | \(-0.0841672\pi\) | |||||||
\(938\) | 0.343146i | 0.0112041i | ||||||||
\(939\) | 27.1421 | 0.885750 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.10051 | −0.101074 | −0.0505368 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505368 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(942\) | 14.4853i | 0.471956i | ||||||||
\(943\) | 10.8995i | 0.354936i | ||||||||
\(944\) | −33.0000 | −1.07406 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.1421 | 0.914980 | ||||||||
\(947\) | 2.79899i | 0.0909549i | 0.998965 | + | 0.0454775i | \(0.0144809\pi\) | ||||
−0.998965 | + | 0.0454775i | \(0.985519\pi\) | |||||||
\(948\) | − 50.6985i | − 1.64661i | ||||||||
\(949\) | −24.9706 | −0.810579 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.8284 | 0.999680 | ||||||||
\(952\) | 4.41421i | 0.143065i | ||||||||
\(953\) | − 19.0416i | − 0.616819i | −0.951254 | − | 0.308409i | \(-0.900203\pi\) | ||||
0.951254 | − | 0.308409i | \(-0.0997967\pi\) | |||||||
\(954\) | −18.4853 | −0.598483 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 90.5685 | 2.92920 | ||||||||
\(957\) | − 1.17157i | − 0.0378716i | ||||||||
\(958\) | 59.1127i | 1.90984i | ||||||||
\(959\) | 5.02944 | 0.162409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0000 | 1.32258 | ||||||||
\(962\) | 1.17157i | 0.0377730i | ||||||||
\(963\) | 5.31371i | 0.171232i | ||||||||
\(964\) | −54.1421 | −1.74380 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.00000 | 0.0321745 | ||||||||
\(967\) | 38.0000i | 1.22200i | 0.791632 | + | 0.610999i | \(0.209232\pi\) | ||||
−0.791632 | + | 0.610999i | \(0.790768\pi\) | |||||||
\(968\) | − 4.41421i | − 0.141878i | ||||||||
\(969\) | −15.4853 | −0.497459 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.6863 | −0.888495 | −0.444248 | − | 0.895904i | \(-0.646529\pi\) | ||||
−0.444248 | + | 0.895904i | \(0.646529\pi\) | |||||||
\(972\) | 3.82843i | 0.122797i | ||||||||
\(973\) | 7.85786i | 0.251912i | ||||||||
\(974\) | 15.6569 | 0.501678 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.4853 | 0.847773 | ||||||||
\(977\) | − 52.5685i | − 1.68182i | −0.541178 | − | 0.840908i | \(-0.682021\pi\) | ||||
0.541178 | − | 0.840908i | \(-0.317979\pi\) | |||||||
\(978\) | − 38.1421i | − 1.21965i | ||||||||
\(979\) | 3.65685 | 0.116874 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.31371 | 0.169654 | ||||||||
\(982\) | − 58.2843i | − 1.85993i | ||||||||
\(983\) | 5.28427i | 0.168542i | 0.996443 | + | 0.0842710i | \(0.0268562\pi\) | ||||
−0.996443 | + | 0.0842710i | \(0.973144\pi\) | |||||||
\(984\) | 48.1127 | 1.53378 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.82843 | 0.217461 | ||||||||
\(987\) | − 3.10051i | − 0.0986902i | ||||||||
\(988\) | 69.4558i | 2.20968i | ||||||||
\(989\) | 11.6569 | 0.370666 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.2843 | 0.453755 | 0.226877 | − | 0.973923i | \(-0.427148\pi\) | ||||
0.226877 | + | 0.973923i | \(0.427148\pi\) | |||||||
\(992\) | 13.4558i | 0.427223i | ||||||||
\(993\) | 32.1421i | 1.02000i | ||||||||
\(994\) | −7.82843 | −0.248303 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −17.1716 | −0.544102 | ||||||||
\(997\) | 43.2548i | 1.36989i | 0.728593 | + | 0.684947i | \(0.240175\pi\) | ||||
−0.728593 | + | 0.684947i | \(0.759825\pi\) | |||||||
\(998\) | − 84.9117i | − 2.68783i | ||||||||
\(999\) | 0.171573 | 0.00542833 |
(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 | 825.2.c.d.199.4 | 4 | ||
3.2 | odd | 2 | 2475.2.c.o.199.1 | 4 | |||
5.2 | odd | 4 | 825.2.a.d.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 825.2.a.f.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 825.2.c.d.199.1 | 4 | ||
15.2 | even | 4 | 2475.2.a.w.1.2 | 2 | |||
15.8 | even | 4 | 2475.2.a.l.1.1 | 2 | |||
15.14 | odd | 2 | 2475.2.c.o.199.4 | 4 | |||
55.32 | even | 4 | 9075.2.a.ca.1.2 | 2 | |||
55.43 | even | 4 | 9075.2.a.w.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.a.d.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
825.2.a.f.1.2 | yes | 2 | 5.3 | odd | 4 | ||
825.2.c.d.199.1 | 4 | 5.4 | even | 2 | inner | ||
825.2.c.d.199.4 | 4 | 1.1 | even | 1 | trivial | ||
2475.2.a.l.1.1 | 2 | 15.8 | even | 4 | |||
2475.2.a.w.1.2 | 2 | 15.2 | even | 4 | |||
2475.2.c.o.199.1 | 4 | 3.2 | odd | 2 | |||
2475.2.c.o.199.4 | 4 | 15.14 | odd | 2 | |||
9075.2.a.w.1.1 | 2 | 55.43 | even | 4 | |||
9075.2.a.ca.1.2 | 2 | 55.32 | even | 4 |