Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1450,2,Mod(349,1450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1450.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1450 = 2 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1450.b (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: | \(11.5783082931\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
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 | 349.2 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1450.349 |
Dual form | 1450.2.b.i.349.3 |
$q$-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 \(\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 2.44949i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949 | 1.00000 | ||||||||
\(7\) | 0.449490i | 0.169891i | 0.996386 | + | 0.0849456i | \(0.0270716\pi\) | ||||
−0.996386 | + | 0.0849456i | \(0.972928\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | − 2.44949i | − 0.707107i | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | 0.449490 | 0.120131 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 3.00000i | 0.707107i | ||||||||
\(19\) | −1.55051 | −0.355711 | −0.177856 | − | 0.984057i | \(-0.556916\pi\) | ||||
−0.177856 | + | 0.984057i | \(0.556916\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.10102 | −0.240262 | ||||||||
\(22\) | − 2.00000i | − 0.426401i | ||||||||
\(23\) | 2.44949i | 0.510754i | 0.966842 | + | 0.255377i | \(0.0821996\pi\) | ||||
−0.966842 | + | 0.255377i | \(0.917800\pi\) | |||||||
\(24\) | −2.44949 | −0.500000 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.44949 | 0.480384 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 0.449490i | − 0.0849456i | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 4.89898i | 0.852803i | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | − 1.44949i | − 0.238295i | −0.992877 | − | 0.119147i | \(-0.961984\pi\) | ||||
0.992877 | − | 0.119147i | \(-0.0380161\pi\) | |||||||
\(38\) | 1.55051i | 0.251526i | ||||||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.34847 | −0.522943 | −0.261472 | − | 0.965211i | \(-0.584208\pi\) | ||||
−0.261472 | + | 0.965211i | \(0.584208\pi\) | |||||||
\(42\) | 1.10102i | 0.169891i | ||||||||
\(43\) | 0.898979i | 0.137093i | 0.997648 | + | 0.0685465i | \(0.0218362\pi\) | ||||
−0.997648 | + | 0.0685465i | \(0.978164\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.44949 | 0.361158 | ||||||||
\(47\) | 3.89898i | 0.568725i | 0.958717 | + | 0.284362i | \(0.0917819\pi\) | ||||
−0.958717 | + | 0.284362i | \(0.908218\pi\) | |||||||
\(48\) | 2.44949i | 0.353553i | ||||||||
\(49\) | 6.79796 | 0.971137 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.89898 | −0.685994 | ||||||||
\(52\) | − 2.44949i | − 0.339683i | ||||||||
\(53\) | 5.55051i | 0.762421i | 0.924488 | + | 0.381211i | \(0.124493\pi\) | ||||
−0.924488 | + | 0.381211i | \(0.875507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.449490 | −0.0600656 | ||||||||
\(57\) | − 3.79796i | − 0.503052i | ||||||||
\(58\) | − 1.00000i | − 0.131306i | ||||||||
\(59\) | −13.4495 | −1.75097 | −0.875487 | − | 0.483241i | \(-0.839459\pi\) | ||||
−0.875487 | + | 0.483241i | \(0.839459\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.44949 | −0.185588 | −0.0927941 | − | 0.995685i | \(-0.529580\pi\) | ||||
−0.0927941 | + | 0.995685i | \(0.529580\pi\) | |||||||
\(62\) | 3.00000i | 0.381000i | ||||||||
\(63\) | − 1.34847i | − 0.169891i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.89898 | 0.603023 | ||||||||
\(67\) | 8.55051i | 1.04461i | 0.852758 | + | 0.522306i | \(0.174928\pi\) | ||||
−0.852758 | + | 0.522306i | \(0.825072\pi\) | |||||||
\(68\) | − 2.00000i | − 0.242536i | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.34847 | −0.397390 | −0.198695 | − | 0.980061i | \(-0.563670\pi\) | ||||
−0.198695 | + | 0.980061i | \(0.563670\pi\) | |||||||
\(72\) | − 3.00000i | − 0.353553i | ||||||||
\(73\) | − 1.34847i | − 0.157826i | −0.996881 | − | 0.0789132i | \(-0.974855\pi\) | ||||
0.996881 | − | 0.0789132i | \(-0.0251450\pi\) | |||||||
\(74\) | −1.44949 | −0.168500 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.55051 | 0.177856 | ||||||||
\(77\) | 0.898979i | 0.102448i | ||||||||
\(78\) | 6.00000i | 0.679366i | ||||||||
\(79\) | −6.89898 | −0.776196 | −0.388098 | − | 0.921618i | \(-0.626868\pi\) | ||||
−0.388098 | + | 0.921618i | \(0.626868\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 3.34847i | 0.369777i | ||||||||
\(83\) | − 6.00000i | − 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 1.10102 | 0.120131 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.898979 | 0.0969395 | ||||||||
\(87\) | 2.44949i | 0.262613i | ||||||||
\(88\) | 2.00000i | 0.213201i | ||||||||
\(89\) | −8.44949 | −0.895644 | −0.447822 | − | 0.894123i | \(-0.647800\pi\) | ||||
−0.447822 | + | 0.894123i | \(0.647800\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10102 | −0.115418 | ||||||||
\(92\) | − 2.44949i | − 0.255377i | ||||||||
\(93\) | − 7.34847i | − 0.762001i | ||||||||
\(94\) | 3.89898 | 0.402149 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.44949 | 0.250000 | ||||||||
\(97\) | 7.34847i | 0.746124i | 0.927806 | + | 0.373062i | \(0.121692\pi\) | ||||
−0.927806 | + | 0.373062i | \(0.878308\pi\) | |||||||
\(98\) | − 6.79796i | − 0.686698i | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.55051 | 0.850808 | 0.425404 | − | 0.905004i | \(-0.360132\pi\) | ||||
0.425404 | + | 0.905004i | \(0.360132\pi\) | |||||||
\(102\) | 4.89898i | 0.485071i | ||||||||
\(103\) | 2.44949i | 0.241355i | 0.992692 | + | 0.120678i | \(0.0385068\pi\) | ||||
−0.992692 | + | 0.120678i | \(0.961493\pi\) | |||||||
\(104\) | −2.44949 | −0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.55051 | 0.539113 | ||||||||
\(107\) | 19.2474i | 1.86072i | 0.366646 | + | 0.930361i | \(0.380506\pi\) | ||||
−0.366646 | + | 0.930361i | \(0.619494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.34847 | −0.512290 | −0.256145 | − | 0.966638i | \(-0.582453\pi\) | ||||
−0.256145 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.55051 | 0.337000 | ||||||||
\(112\) | 0.449490i | 0.0424728i | ||||||||
\(113\) | − 18.2474i | − 1.71658i | −0.513169 | − | 0.858288i | \(-0.671528\pi\) | ||||
0.513169 | − | 0.858288i | \(-0.328472\pi\) | |||||||
\(114\) | −3.79796 | −0.355711 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | − 7.34847i | − 0.679366i | ||||||||
\(118\) | 13.4495i | 1.23813i | ||||||||
\(119\) | −0.898979 | −0.0824093 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 1.44949i | 0.131231i | ||||||||
\(123\) | − 8.20204i | − 0.739553i | ||||||||
\(124\) | 3.00000 | 0.269408 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.34847 | −0.120131 | ||||||||
\(127\) | 10.7980i | 0.958164i | 0.877770 | + | 0.479082i | \(0.159030\pi\) | ||||
−0.877770 | + | 0.479082i | \(0.840970\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −2.20204 | −0.193879 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.34847 | 0.642039 | 0.321019 | − | 0.947073i | \(-0.395975\pi\) | ||||
0.321019 | + | 0.947073i | \(0.395975\pi\) | |||||||
\(132\) | − 4.89898i | − 0.426401i | ||||||||
\(133\) | − 0.696938i | − 0.0604322i | ||||||||
\(134\) | 8.55051 | 0.738652 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | 8.89898i | 0.760291i | 0.924927 | + | 0.380146i | \(0.124126\pi\) | ||||
−0.924927 | + | 0.380146i | \(0.875874\pi\) | |||||||
\(138\) | 6.00000i | 0.510754i | ||||||||
\(139\) | 6.55051 | 0.555607 | 0.277804 | − | 0.960638i | \(-0.410394\pi\) | ||||
0.277804 | + | 0.960638i | \(0.410394\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.55051 | −0.804298 | ||||||||
\(142\) | 3.34847i | 0.280997i | ||||||||
\(143\) | 4.89898i | 0.409673i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.34847 | −0.111600 | ||||||||
\(147\) | 16.6515i | 1.37340i | ||||||||
\(148\) | 1.44949i | 0.119147i | ||||||||
\(149\) | 3.79796 | 0.311141 | 0.155570 | − | 0.987825i | \(-0.450278\pi\) | ||||
0.155570 | + | 0.987825i | \(0.450278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.34847 | −0.272495 | −0.136247 | − | 0.990675i | \(-0.543504\pi\) | ||||
−0.136247 | + | 0.990675i | \(0.543504\pi\) | |||||||
\(152\) | − 1.55051i | − 0.125763i | ||||||||
\(153\) | − 6.00000i | − 0.485071i | ||||||||
\(154\) | 0.898979 | 0.0724418 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | 2.34847i | 0.187428i | 0.995599 | + | 0.0937141i | \(0.0298740\pi\) | ||||
−0.995599 | + | 0.0937141i | \(0.970126\pi\) | |||||||
\(158\) | 6.89898i | 0.548853i | ||||||||
\(159\) | −13.5959 | −1.07823 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.10102 | −0.0867726 | ||||||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | − 7.55051i | − 0.591402i | −0.955281 | − | 0.295701i | \(-0.904447\pi\) | ||||
0.955281 | − | 0.295701i | \(-0.0955531\pi\) | |||||||
\(164\) | 3.34847 | 0.261472 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | − 1.79796i | − 0.139130i | −0.997577 | − | 0.0695651i | \(-0.977839\pi\) | ||||
0.997577 | − | 0.0695651i | \(-0.0221612\pi\) | |||||||
\(168\) | − 1.10102i | − 0.0849456i | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.65153 | 0.355711 | ||||||||
\(172\) | − 0.898979i | − 0.0685465i | ||||||||
\(173\) | − 16.0000i | − 1.21646i | −0.793762 | − | 0.608229i | \(-0.791880\pi\) | ||||
0.793762 | − | 0.608229i | \(-0.208120\pi\) | |||||||
\(174\) | 2.44949 | 0.185695 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | − 32.9444i | − 2.47625i | ||||||||
\(178\) | 8.44949i | 0.633316i | ||||||||
\(179\) | −7.24745 | −0.541700 | −0.270850 | − | 0.962622i | \(-0.587305\pi\) | ||||
−0.270850 | + | 0.962622i | \(0.587305\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0454 | 1.34130 | 0.670652 | − | 0.741772i | \(-0.266014\pi\) | ||||
0.670652 | + | 0.741772i | \(0.266014\pi\) | |||||||
\(182\) | 1.10102i | 0.0816131i | ||||||||
\(183\) | − 3.55051i | − 0.262461i | ||||||||
\(184\) | −2.44949 | −0.180579 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.34847 | −0.538816 | ||||||||
\(187\) | 4.00000i | 0.292509i | ||||||||
\(188\) | − 3.89898i | − 0.284362i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.6969 | 1.28051 | 0.640253 | − | 0.768164i | \(-0.278830\pi\) | ||||
0.640253 | + | 0.768164i | \(0.278830\pi\) | |||||||
\(192\) | − 2.44949i | − 0.176777i | ||||||||
\(193\) | 9.34847i | 0.672918i | 0.941698 | + | 0.336459i | \(0.109229\pi\) | ||||
−0.941698 | + | 0.336459i | \(0.890771\pi\) | |||||||
\(194\) | 7.34847 | 0.527589 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.79796 | −0.485568 | ||||||||
\(197\) | − 14.8990i | − 1.06151i | −0.847526 | − | 0.530754i | \(-0.821909\pi\) | ||||
0.847526 | − | 0.530754i | \(-0.178091\pi\) | |||||||
\(198\) | 6.00000i | 0.426401i | ||||||||
\(199\) | 15.3485 | 1.08802 | 0.544012 | − | 0.839077i | \(-0.316905\pi\) | ||||
0.544012 | + | 0.839077i | \(0.316905\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.9444 | −1.47730 | ||||||||
\(202\) | − 8.55051i | − 0.601612i | ||||||||
\(203\) | 0.449490i | 0.0315480i | ||||||||
\(204\) | 4.89898 | 0.342997 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.44949 | 0.170664 | ||||||||
\(207\) | − 7.34847i | − 0.510754i | ||||||||
\(208\) | 2.44949i | 0.169842i | ||||||||
\(209\) | −3.10102 | −0.214502 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.4949 | 1.82398 | 0.911992 | − | 0.410208i | \(-0.134544\pi\) | ||||
0.911992 | + | 0.410208i | \(0.134544\pi\) | |||||||
\(212\) | − 5.55051i | − 0.381211i | ||||||||
\(213\) | − 8.20204i | − 0.561995i | ||||||||
\(214\) | 19.2474 | 1.31573 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1.34847i | − 0.0915401i | ||||||||
\(218\) | 5.34847i | 0.362244i | ||||||||
\(219\) | 3.30306 | 0.223200 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.89898 | −0.329541 | ||||||||
\(222\) | − 3.55051i | − 0.238295i | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | 0.449490 | 0.0300328 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.2474 | −1.21380 | ||||||||
\(227\) | 9.24745i | 0.613775i | 0.951746 | + | 0.306887i | \(0.0992875\pi\) | ||||
−0.951746 | + | 0.306887i | \(0.900713\pi\) | |||||||
\(228\) | 3.79796i | 0.251526i | ||||||||
\(229\) | 26.8990 | 1.77753 | 0.888767 | − | 0.458359i | \(-0.151562\pi\) | ||||
0.888767 | + | 0.458359i | \(0.151562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.20204 | −0.144884 | ||||||||
\(232\) | 1.00000i | 0.0656532i | ||||||||
\(233\) | − 11.0000i | − 0.720634i | −0.932830 | − | 0.360317i | \(-0.882669\pi\) | ||||
0.932830 | − | 0.360317i | \(-0.117331\pi\) | |||||||
\(234\) | −7.34847 | −0.480384 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.4495 | 0.875487 | ||||||||
\(237\) | − 16.8990i | − 1.09771i | ||||||||
\(238\) | 0.898979i | 0.0582722i | ||||||||
\(239\) | 17.5959 | 1.13819 | 0.569093 | − | 0.822273i | \(-0.307295\pi\) | ||||
0.569093 | + | 0.822273i | \(0.307295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0000 | 1.09507 | 0.547533 | − | 0.836784i | \(-0.315567\pi\) | ||||
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | − 22.0454i | − 1.41421i | ||||||||
\(244\) | 1.44949 | 0.0927941 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.20204 | −0.522943 | ||||||||
\(247\) | − 3.79796i | − 0.241658i | ||||||||
\(248\) | − 3.00000i | − 0.190500i | ||||||||
\(249\) | 14.6969 | 0.931381 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 31.1464 | 1.96595 | 0.982973 | − | 0.183752i | \(-0.0588245\pi\) | ||||
0.982973 | + | 0.183752i | \(0.0588245\pi\) | |||||||
\(252\) | 1.34847i | 0.0849456i | ||||||||
\(253\) | 4.89898i | 0.307996i | ||||||||
\(254\) | 10.7980 | 0.677524 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.69694i | 0.168230i | 0.996456 | + | 0.0841152i | \(0.0268064\pi\) | ||||
−0.996456 | + | 0.0841152i | \(0.973194\pi\) | |||||||
\(258\) | 2.20204i | 0.137093i | ||||||||
\(259\) | 0.651531 | 0.0404842 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | − 7.34847i | − 0.453990i | ||||||||
\(263\) | 2.79796i | 0.172530i | 0.996272 | + | 0.0862648i | \(0.0274931\pi\) | ||||
−0.996272 | + | 0.0862648i | \(0.972507\pi\) | |||||||
\(264\) | −4.89898 | −0.301511 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.696938 | −0.0427320 | ||||||||
\(267\) | − 20.6969i | − 1.26663i | ||||||||
\(268\) | − 8.55051i | − 0.522306i | ||||||||
\(269\) | −9.65153 | −0.588464 | −0.294232 | − | 0.955734i | \(-0.595064\pi\) | ||||
−0.294232 | + | 0.955734i | \(0.595064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6969 | −0.832030 | −0.416015 | − | 0.909358i | \(-0.636574\pi\) | ||||
−0.416015 | + | 0.909358i | \(0.636574\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | − 2.69694i | − 0.163226i | ||||||||
\(274\) | 8.89898 | 0.537607 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | − 30.9444i | − 1.85927i | −0.368484 | − | 0.929634i | \(-0.620123\pi\) | ||||
0.368484 | − | 0.929634i | \(-0.379877\pi\) | |||||||
\(278\) | − 6.55051i | − 0.392873i | ||||||||
\(279\) | 9.00000 | 0.538816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.20204 | −0.548948 | −0.274474 | − | 0.961595i | \(-0.588504\pi\) | ||||
−0.274474 | + | 0.961595i | \(0.588504\pi\) | |||||||
\(282\) | 9.55051i | 0.568725i | ||||||||
\(283\) | 24.0000i | 1.42665i | 0.700832 | + | 0.713326i | \(0.252812\pi\) | ||||
−0.700832 | + | 0.713326i | \(0.747188\pi\) | |||||||
\(284\) | 3.34847 | 0.198695 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.89898 | 0.289683 | ||||||||
\(287\) | − 1.50510i | − 0.0888434i | ||||||||
\(288\) | 3.00000i | 0.176777i | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.0000 | −1.05518 | ||||||||
\(292\) | 1.34847i | 0.0789132i | ||||||||
\(293\) | − 2.55051i | − 0.149002i | −0.997221 | − | 0.0745012i | \(-0.976264\pi\) | ||||
0.997221 | − | 0.0745012i | \(-0.0237365\pi\) | |||||||
\(294\) | 16.6515 | 0.971137 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.44949 | 0.0842499 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 3.79796i | − 0.220010i | ||||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.404082 | −0.0232909 | ||||||||
\(302\) | 3.34847i | 0.192683i | ||||||||
\(303\) | 20.9444i | 1.20322i | ||||||||
\(304\) | −1.55051 | −0.0889279 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.00000 | −0.342997 | ||||||||
\(307\) | 33.3939i | 1.90589i | 0.303144 | + | 0.952945i | \(0.401964\pi\) | ||||
−0.303144 | + | 0.952945i | \(0.598036\pi\) | |||||||
\(308\) | − 0.898979i | − 0.0512241i | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5959 | 1.11118 | 0.555591 | − | 0.831456i | \(-0.312492\pi\) | ||||
0.555591 | + | 0.831456i | \(0.312492\pi\) | |||||||
\(312\) | − 6.00000i | − 0.339683i | ||||||||
\(313\) | 6.59592i | 0.372823i | 0.982472 | + | 0.186412i | \(0.0596858\pi\) | ||||
−0.982472 | + | 0.186412i | \(0.940314\pi\) | |||||||
\(314\) | 2.34847 | 0.132532 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.89898 | 0.388098 | ||||||||
\(317\) | − 28.3485i | − 1.59221i | −0.605159 | − | 0.796104i | \(-0.706891\pi\) | ||||
0.605159 | − | 0.796104i | \(-0.293109\pi\) | |||||||
\(318\) | 13.5959i | 0.762421i | ||||||||
\(319\) | 2.00000 | 0.111979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −47.1464 | −2.63146 | ||||||||
\(322\) | 1.10102i | 0.0613575i | ||||||||
\(323\) | − 3.10102i | − 0.172545i | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.55051 | −0.418184 | ||||||||
\(327\) | − 13.1010i | − 0.724488i | ||||||||
\(328\) | − 3.34847i | − 0.184888i | ||||||||
\(329\) | −1.75255 | −0.0966213 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.75255 | −0.316189 | −0.158094 | − | 0.987424i | \(-0.550535\pi\) | ||||
−0.158094 | + | 0.987424i | \(0.550535\pi\) | |||||||
\(332\) | 6.00000i | 0.329293i | ||||||||
\(333\) | 4.34847i | 0.238295i | ||||||||
\(334\) | −1.79796 | −0.0983799 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.10102 | −0.0600656 | ||||||||
\(337\) | − 4.20204i | − 0.228900i | −0.993429 | − | 0.114450i | \(-0.963489\pi\) | ||||
0.993429 | − | 0.114450i | \(-0.0365105\pi\) | |||||||
\(338\) | − 7.00000i | − 0.380750i | ||||||||
\(339\) | 44.6969 | 2.42760 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | − 4.65153i | − 0.251526i | ||||||||
\(343\) | 6.20204i | 0.334879i | ||||||||
\(344\) | −0.898979 | −0.0484697 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.0000 | −0.860165 | ||||||||
\(347\) | − 19.0454i | − 1.02241i | −0.859458 | − | 0.511206i | \(-0.829199\pi\) | ||||
0.859458 | − | 0.511206i | \(-0.170801\pi\) | |||||||
\(348\) | − 2.44949i | − 0.131306i | ||||||||
\(349\) | −22.9444 | −1.22818 | −0.614092 | − | 0.789234i | \(-0.710478\pi\) | ||||
−0.614092 | + | 0.789234i | \(0.710478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 2.00000i | − 0.106600i | ||||||||
\(353\) | 2.79796i | 0.148920i | 0.997224 | + | 0.0744602i | \(0.0237234\pi\) | ||||
−0.997224 | + | 0.0744602i | \(0.976277\pi\) | |||||||
\(354\) | −32.9444 | −1.75097 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.44949 | 0.447822 | ||||||||
\(357\) | − 2.20204i | − 0.116544i | ||||||||
\(358\) | 7.24745i | 0.383040i | ||||||||
\(359\) | −22.5959 | −1.19257 | −0.596283 | − | 0.802774i | \(-0.703357\pi\) | ||||
−0.596283 | + | 0.802774i | \(0.703357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5959 | −0.873469 | ||||||||
\(362\) | − 18.0454i | − 0.948446i | ||||||||
\(363\) | − 17.1464i | − 0.899954i | ||||||||
\(364\) | 1.10102 | 0.0577092 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.55051 | −0.185588 | ||||||||
\(367\) | 20.7980i | 1.08564i | 0.839848 | + | 0.542822i | \(0.182644\pi\) | ||||
−0.839848 | + | 0.542822i | \(0.817356\pi\) | |||||||
\(368\) | 2.44949i | 0.127688i | ||||||||
\(369\) | 10.0454 | 0.522943 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.49490 | −0.129529 | ||||||||
\(372\) | 7.34847i | 0.381000i | ||||||||
\(373\) | − 20.4949i | − 1.06119i | −0.847627 | − | 0.530593i | \(-0.821969\pi\) | ||||
0.847627 | − | 0.530593i | \(-0.178031\pi\) | |||||||
\(374\) | 4.00000 | 0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.89898 | −0.201075 | ||||||||
\(377\) | 2.44949i | 0.126155i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.14643 | 0.469820 | 0.234910 | − | 0.972017i | \(-0.424520\pi\) | ||||
0.234910 | + | 0.972017i | \(0.424520\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.4495 | −1.35505 | ||||||||
\(382\) | − 17.6969i | − 0.905454i | ||||||||
\(383\) | 7.79796i | 0.398457i | 0.979953 | + | 0.199229i | \(0.0638436\pi\) | ||||
−0.979953 | + | 0.199229i | \(0.936156\pi\) | |||||||
\(384\) | −2.44949 | −0.125000 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.34847 | 0.475825 | ||||||||
\(387\) | − 2.69694i | − 0.137093i | ||||||||
\(388\) | − 7.34847i | − 0.373062i | ||||||||
\(389\) | 9.65153 | 0.489352 | 0.244676 | − | 0.969605i | \(-0.421318\pi\) | ||||
0.244676 | + | 0.969605i | \(0.421318\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.89898 | −0.247752 | ||||||||
\(392\) | 6.79796i | 0.343349i | ||||||||
\(393\) | 18.0000i | 0.907980i | ||||||||
\(394\) | −14.8990 | −0.750600 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.00000 | 0.301511 | ||||||||
\(397\) | 21.1464i | 1.06131i | 0.847588 | + | 0.530654i | \(0.178054\pi\) | ||||
−0.847588 | + | 0.530654i | \(0.821946\pi\) | |||||||
\(398\) | − 15.3485i | − 0.769349i | ||||||||
\(399\) | 1.70714 | 0.0854641 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.595918 | −0.0297587 | −0.0148794 | − | 0.999889i | \(-0.504736\pi\) | ||||
−0.0148794 | + | 0.999889i | \(0.504736\pi\) | |||||||
\(402\) | 20.9444i | 1.04461i | ||||||||
\(403\) | − 7.34847i | − 0.366053i | ||||||||
\(404\) | −8.55051 | −0.425404 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.449490 | 0.0223078 | ||||||||
\(407\) | − 2.89898i | − 0.143697i | ||||||||
\(408\) | − 4.89898i | − 0.242536i | ||||||||
\(409\) | −13.7980 | −0.682265 | −0.341133 | − | 0.940015i | \(-0.610811\pi\) | ||||
−0.341133 | + | 0.940015i | \(0.610811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.7980 | −1.07521 | ||||||||
\(412\) | − 2.44949i | − 0.120678i | ||||||||
\(413\) | − 6.04541i | − 0.297475i | ||||||||
\(414\) | −7.34847 | −0.361158 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.44949 | 0.120096 | ||||||||
\(417\) | 16.0454i | 0.785747i | ||||||||
\(418\) | 3.10102i | 0.151676i | ||||||||
\(419\) | −24.1464 | −1.17963 | −0.589815 | − | 0.807538i | \(-0.700799\pi\) | ||||
−0.589815 | + | 0.807538i | \(0.700799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.55051 | 0.416726 | 0.208363 | − | 0.978052i | \(-0.433186\pi\) | ||||
0.208363 | + | 0.978052i | \(0.433186\pi\) | |||||||
\(422\) | − 26.4949i | − 1.28975i | ||||||||
\(423\) | − 11.6969i | − 0.568725i | ||||||||
\(424\) | −5.55051 | −0.269557 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.20204 | −0.397390 | ||||||||
\(427\) | − 0.651531i | − 0.0315298i | ||||||||
\(428\) | − 19.2474i | − 0.930361i | ||||||||
\(429\) | −12.0000 | −0.579365 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5505 | 0.652705 | 0.326353 | − | 0.945248i | \(-0.394180\pi\) | ||||
0.326353 | + | 0.945248i | \(0.394180\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.5505i | 1.22788i | 0.789353 | + | 0.613940i | \(0.210416\pi\) | ||||
−0.789353 | + | 0.613940i | \(0.789584\pi\) | |||||||
\(434\) | −1.34847 | −0.0647286 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.34847 | 0.256145 | ||||||||
\(437\) | − 3.79796i | − 0.181681i | ||||||||
\(438\) | − 3.30306i | − 0.157826i | ||||||||
\(439\) | 10.6969 | 0.510537 | 0.255269 | − | 0.966870i | \(-0.417836\pi\) | ||||
0.255269 | + | 0.966870i | \(0.417836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.3939 | −0.971137 | ||||||||
\(442\) | 4.89898i | 0.233021i | ||||||||
\(443\) | − 22.8990i | − 1.08796i | −0.839097 | − | 0.543982i | \(-0.816916\pi\) | ||||
0.839097 | − | 0.543982i | \(-0.183084\pi\) | |||||||
\(444\) | −3.55051 | −0.168500 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | 9.30306i | 0.440020i | ||||||||
\(448\) | − 0.449490i | − 0.0212364i | ||||||||
\(449\) | −6.20204 | −0.292692 | −0.146346 | − | 0.989233i | \(-0.546751\pi\) | ||||
−0.146346 | + | 0.989233i | \(0.546751\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.69694 | −0.315347 | ||||||||
\(452\) | 18.2474i | 0.858288i | ||||||||
\(453\) | − 8.20204i | − 0.385366i | ||||||||
\(454\) | 9.24745 | 0.434004 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.79796 | 0.177856 | ||||||||
\(457\) | − 1.79796i | − 0.0841050i | −0.999115 | − | 0.0420525i | \(-0.986610\pi\) | ||||
0.999115 | − | 0.0420525i | \(-0.0133897\pi\) | |||||||
\(458\) | − 26.8990i | − 1.25691i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.2929 | 1.87663 | 0.938313 | − | 0.345788i | \(-0.112388\pi\) | ||||
0.938313 | + | 0.345788i | \(0.112388\pi\) | |||||||
\(462\) | 2.20204i | 0.102448i | ||||||||
\(463\) | − 12.8990i | − 0.599466i | −0.954023 | − | 0.299733i | \(-0.903102\pi\) | ||||
0.954023 | − | 0.299733i | \(-0.0968977\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.0000 | −0.509565 | ||||||||
\(467\) | − 30.9444i | − 1.43194i | −0.698133 | − | 0.715968i | \(-0.745986\pi\) | ||||
0.698133 | − | 0.715968i | \(-0.254014\pi\) | |||||||
\(468\) | 7.34847i | 0.339683i | ||||||||
\(469\) | −3.84337 | −0.177470 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.75255 | −0.265064 | ||||||||
\(472\) | − 13.4495i | − 0.619063i | ||||||||
\(473\) | 1.79796i | 0.0826702i | ||||||||
\(474\) | −16.8990 | −0.776196 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.898979 | 0.0412047 | ||||||||
\(477\) | − 16.6515i | − 0.762421i | ||||||||
\(478\) | − 17.5959i | − 0.804819i | ||||||||
\(479\) | 23.7980 | 1.08736 | 0.543678 | − | 0.839294i | \(-0.317031\pi\) | ||||
0.543678 | + | 0.839294i | \(0.317031\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.55051 | 0.161889 | ||||||||
\(482\) | − 17.0000i | − 0.774329i | ||||||||
\(483\) | − 2.69694i | − 0.122715i | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0454 | −1.00000 | ||||||||
\(487\) | 18.8990i | 0.856395i | 0.903685 | + | 0.428197i | \(0.140851\pi\) | ||||
−0.903685 | + | 0.428197i | \(0.859149\pi\) | |||||||
\(488\) | − 1.44949i | − 0.0656153i | ||||||||
\(489\) | 18.4949 | 0.836368 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.4949 | −1.01518 | −0.507590 | − | 0.861599i | \(-0.669464\pi\) | ||||
−0.507590 | + | 0.861599i | \(0.669464\pi\) | |||||||
\(492\) | 8.20204i | 0.369777i | ||||||||
\(493\) | 2.00000i | 0.0900755i | ||||||||
\(494\) | −3.79796 | −0.170878 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | −0.134704 | ||||||||
\(497\) | − 1.50510i | − 0.0675131i | ||||||||
\(498\) | − 14.6969i | − 0.658586i | ||||||||
\(499\) | 9.65153 | 0.432062 | 0.216031 | − | 0.976387i | \(-0.430689\pi\) | ||||
0.216031 | + | 0.976387i | \(0.430689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.40408 | 0.196760 | ||||||||
\(502\) | − 31.1464i | − 1.39013i | ||||||||
\(503\) | − 14.7980i | − 0.659808i | −0.944014 | − | 0.329904i | \(-0.892984\pi\) | ||||
0.944014 | − | 0.329904i | \(-0.107016\pi\) | |||||||
\(504\) | 1.34847 | 0.0600656 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.89898 | 0.217786 | ||||||||
\(507\) | 17.1464i | 0.761500i | ||||||||
\(508\) | − 10.7980i | − 0.479082i | ||||||||
\(509\) | −41.3939 | −1.83475 | −0.917376 | − | 0.398022i | \(-0.869697\pi\) | ||||
−0.917376 | + | 0.398022i | \(0.869697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.606123 | 0.0268133 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.69694 | 0.118957 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.20204 | 0.0969395 | ||||||||
\(517\) | 7.79796i | 0.342954i | ||||||||
\(518\) | − 0.651531i | − 0.0286266i | ||||||||
\(519\) | 39.1918 | 1.72033 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.8990 | −0.871790 | −0.435895 | − | 0.899997i | \(-0.643568\pi\) | ||||
−0.435895 | + | 0.899997i | \(0.643568\pi\) | |||||||
\(522\) | 3.00000i | 0.131306i | ||||||||
\(523\) | − 22.5505i | − 0.986065i | −0.870011 | − | 0.493032i | \(-0.835888\pi\) | ||||
0.870011 | − | 0.493032i | \(-0.164112\pi\) | |||||||
\(524\) | −7.34847 | −0.321019 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.79796 | 0.121997 | ||||||||
\(527\) | − 6.00000i | − 0.261364i | ||||||||
\(528\) | 4.89898i | 0.213201i | ||||||||
\(529\) | 17.0000 | 0.739130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.3485 | 1.75097 | ||||||||
\(532\) | 0.696938i | 0.0302161i | ||||||||
\(533\) | − 8.20204i | − 0.355270i | ||||||||
\(534\) | −20.6969 | −0.895644 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.55051 | −0.369326 | ||||||||
\(537\) | − 17.7526i | − 0.766079i | ||||||||
\(538\) | 9.65153i | 0.416107i | ||||||||
\(539\) | 13.5959 | 0.585618 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0454 | 0.990799 | 0.495400 | − | 0.868665i | \(-0.335022\pi\) | ||||
0.495400 | + | 0.868665i | \(0.335022\pi\) | |||||||
\(542\) | 13.6969i | 0.588334i | ||||||||
\(543\) | 44.2020i | 1.89689i | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.69694 | −0.115418 | ||||||||
\(547\) | 22.0000i | 0.940652i | 0.882493 | + | 0.470326i | \(0.155864\pi\) | ||||
−0.882493 | + | 0.470326i | \(0.844136\pi\) | |||||||
\(548\) | − 8.89898i | − 0.380146i | ||||||||
\(549\) | 4.34847 | 0.185588 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.55051 | −0.0660540 | ||||||||
\(552\) | − 6.00000i | − 0.255377i | ||||||||
\(553\) | − 3.10102i | − 0.131869i | ||||||||
\(554\) | −30.9444 | −1.31470 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.55051 | −0.277804 | ||||||||
\(557\) | − 42.4949i | − 1.80057i | −0.435304 | − | 0.900283i | \(-0.643359\pi\) | ||||
0.435304 | − | 0.900283i | \(-0.356641\pi\) | |||||||
\(558\) | − 9.00000i | − 0.381000i | ||||||||
\(559\) | −2.20204 | −0.0931364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.79796 | −0.413670 | ||||||||
\(562\) | 9.20204i | 0.388165i | ||||||||
\(563\) | − 2.20204i | − 0.0928050i | −0.998923 | − | 0.0464025i | \(-0.985224\pi\) | ||||
0.998923 | − | 0.0464025i | \(-0.0147757\pi\) | |||||||
\(564\) | 9.55051 | 0.402149 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | − 4.04541i | − 0.169891i | ||||||||
\(568\) | − 3.34847i | − 0.140499i | ||||||||
\(569\) | −20.6969 | −0.867661 | −0.433830 | − | 0.900995i | \(-0.642838\pi\) | ||||
−0.433830 | + | 0.900995i | \(0.642838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.0454 | −0.797026 | −0.398513 | − | 0.917163i | \(-0.630474\pi\) | ||||
−0.398513 | + | 0.917163i | \(0.630474\pi\) | |||||||
\(572\) | − 4.89898i | − 0.204837i | ||||||||
\(573\) | 43.3485i | 1.81091i | ||||||||
\(574\) | −1.50510 | −0.0628218 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | 24.9444i | 1.03845i | 0.854638 | + | 0.519224i | \(0.173779\pi\) | ||||
−0.854638 | + | 0.519224i | \(0.826221\pi\) | |||||||
\(578\) | − 13.0000i | − 0.540729i | ||||||||
\(579\) | −22.8990 | −0.951649 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.69694 | 0.111888 | ||||||||
\(582\) | 18.0000i | 0.746124i | ||||||||
\(583\) | 11.1010i | 0.459757i | ||||||||
\(584\) | 1.34847 | 0.0558001 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.55051 | −0.105361 | ||||||||
\(587\) | 39.2474i | 1.61992i | 0.586488 | + | 0.809958i | \(0.300510\pi\) | ||||
−0.586488 | + | 0.809958i | \(0.699490\pi\) | |||||||
\(588\) | − 16.6515i | − 0.686698i | ||||||||
\(589\) | 4.65153 | 0.191663 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.4949 | 1.50120 | ||||||||
\(592\) | − 1.44949i | − 0.0595737i | ||||||||
\(593\) | 40.3939i | 1.65878i | 0.558672 | + | 0.829389i | \(0.311311\pi\) | ||||
−0.558672 | + | 0.829389i | \(0.688689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.79796 | −0.155570 | ||||||||
\(597\) | 37.5959i | 1.53870i | ||||||||
\(598\) | 6.00000i | 0.245358i | ||||||||
\(599\) | 21.8990 | 0.894768 | 0.447384 | − | 0.894342i | \(-0.352356\pi\) | ||||
0.447384 | + | 0.894342i | \(0.352356\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.6969 | 0.925827 | 0.462914 | − | 0.886403i | \(-0.346804\pi\) | ||||
0.462914 | + | 0.886403i | \(0.346804\pi\) | |||||||
\(602\) | 0.404082i | 0.0164692i | ||||||||
\(603\) | − 25.6515i | − 1.04461i | ||||||||
\(604\) | 3.34847 | 0.136247 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 20.9444 | 0.850808 | ||||||||
\(607\) | − 24.3939i | − 0.990117i | −0.868860 | − | 0.495058i | \(-0.835147\pi\) | ||||
0.868860 | − | 0.495058i | \(-0.164853\pi\) | |||||||
\(608\) | 1.55051i | 0.0628815i | ||||||||
\(609\) | −1.10102 | −0.0446156 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.55051 | −0.386372 | ||||||||
\(612\) | 6.00000i | 0.242536i | ||||||||
\(613\) | 37.1010i | 1.49850i | 0.662289 | + | 0.749248i | \(0.269585\pi\) | ||||
−0.662289 | + | 0.749248i | \(0.730415\pi\) | |||||||
\(614\) | 33.3939 | 1.34767 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.898979 | −0.0362209 | ||||||||
\(617\) | − 9.55051i | − 0.384489i | −0.981347 | − | 0.192245i | \(-0.938423\pi\) | ||||
0.981347 | − | 0.192245i | \(-0.0615767\pi\) | |||||||
\(618\) | 6.00000i | 0.241355i | ||||||||
\(619\) | 6.89898 | 0.277293 | 0.138647 | − | 0.990342i | \(-0.455725\pi\) | ||||
0.138647 | + | 0.990342i | \(0.455725\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 19.5959i | − 0.785725i | ||||||||
\(623\) | − 3.79796i | − 0.152162i | ||||||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.59592 | 0.263626 | ||||||||
\(627\) | − 7.59592i | − 0.303352i | ||||||||
\(628\) | − 2.34847i | − 0.0937141i | ||||||||
\(629\) | 2.89898 | 0.115590 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | − 6.89898i | − 0.274427i | ||||||||
\(633\) | 64.8990i | 2.57950i | ||||||||
\(634\) | −28.3485 | −1.12586 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.5959 | 0.539113 | ||||||||
\(637\) | 16.6515i | 0.659758i | ||||||||
\(638\) | − 2.00000i | − 0.0791808i | ||||||||
\(639\) | 10.0454 | 0.397390 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.247449 | −0.00977364 | −0.00488682 | − | 0.999988i | \(-0.501556\pi\) | ||||
−0.00488682 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(642\) | 47.1464i | 1.86072i | ||||||||
\(643\) | 38.8434i | 1.53183i | 0.642940 | + | 0.765916i | \(0.277714\pi\) | ||||
−0.642940 | + | 0.765916i | \(0.722286\pi\) | |||||||
\(644\) | 1.10102 | 0.0433863 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.10102 | −0.122008 | ||||||||
\(647\) | − 0.404082i | − 0.0158861i | −0.999968 | − | 0.00794305i | \(-0.997472\pi\) | ||||
0.999968 | − | 0.00794305i | \(-0.00252838\pi\) | |||||||
\(648\) | − 9.00000i | − 0.353553i | ||||||||
\(649\) | −26.8990 | −1.05588 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.30306 | 0.129457 | ||||||||
\(652\) | 7.55051i | 0.295701i | ||||||||
\(653\) | − 13.2474i | − 0.518413i | −0.965822 | − | 0.259206i | \(-0.916539\pi\) | ||||
0.965822 | − | 0.259206i | \(-0.0834610\pi\) | |||||||
\(654\) | −13.1010 | −0.512290 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.34847 | −0.130736 | ||||||||
\(657\) | 4.04541i | 0.157826i | ||||||||
\(658\) | 1.75255i | 0.0683216i | ||||||||
\(659\) | 9.30306 | 0.362396 | 0.181198 | − | 0.983447i | \(-0.442003\pi\) | ||||
0.181198 | + | 0.983447i | \(0.442003\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.2474 | 1.33207 | 0.666036 | − | 0.745920i | \(-0.267990\pi\) | ||||
0.666036 | + | 0.745920i | \(0.267990\pi\) | |||||||
\(662\) | 5.75255i | 0.223579i | ||||||||
\(663\) | − 12.0000i | − 0.466041i | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.34847 | 0.168500 | ||||||||
\(667\) | 2.44949i | 0.0948446i | ||||||||
\(668\) | 1.79796i | 0.0695651i | ||||||||
\(669\) | −9.79796 | −0.378811 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.89898 | −0.111914 | ||||||||
\(672\) | 1.10102i | 0.0424728i | ||||||||
\(673\) | 2.79796i | 0.107853i | 0.998545 | + | 0.0539267i | \(0.0171737\pi\) | ||||
−0.998545 | + | 0.0539267i | \(0.982826\pi\) | |||||||
\(674\) | −4.20204 | −0.161857 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | − 19.0454i | − 0.731974i | −0.930620 | − | 0.365987i | \(-0.880731\pi\) | ||||
0.930620 | − | 0.365987i | \(-0.119269\pi\) | |||||||
\(678\) | − 44.6969i | − 1.71658i | ||||||||
\(679\) | −3.30306 | −0.126760 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.6515 | −0.868009 | ||||||||
\(682\) | 6.00000i | 0.229752i | ||||||||
\(683\) | 20.8990i | 0.799677i | 0.916586 | + | 0.399839i | \(0.130934\pi\) | ||||
−0.916586 | + | 0.399839i | \(0.869066\pi\) | |||||||
\(684\) | −4.65153 | −0.177856 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.20204 | 0.236795 | ||||||||
\(687\) | 65.8888i | 2.51381i | ||||||||
\(688\) | 0.898979i | 0.0342733i | ||||||||
\(689\) | −13.5959 | −0.517963 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.94439 | 0.378302 | 0.189151 | − | 0.981948i | \(-0.439426\pi\) | ||||
0.189151 | + | 0.981948i | \(0.439426\pi\) | |||||||
\(692\) | 16.0000i | 0.608229i | ||||||||
\(693\) | − 2.69694i | − 0.102448i | ||||||||
\(694\) | −19.0454 | −0.722954 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.44949 | −0.0928477 | ||||||||
\(697\) | − 6.69694i | − 0.253665i | ||||||||
\(698\) | 22.9444i | 0.868458i | ||||||||
\(699\) | 26.9444 | 1.01913 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3939 | 1.26127 | 0.630635 | − | 0.776080i | \(-0.282795\pi\) | ||||
0.630635 | + | 0.776080i | \(0.282795\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.24745i | 0.0847641i | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.79796 | 0.105303 | ||||||||
\(707\) | 3.84337i | 0.144545i | ||||||||
\(708\) | 32.9444i | 1.23813i | ||||||||
\(709\) | −31.3939 | −1.17902 | −0.589511 | − | 0.807760i | \(-0.700679\pi\) | ||||
−0.589511 | + | 0.807760i | \(0.700679\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.6969 | 0.776196 | ||||||||
\(712\) | − 8.44949i | − 0.316658i | ||||||||
\(713\) | − 7.34847i | − 0.275202i | ||||||||
\(714\) | −2.20204 | −0.0824093 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.24745 | 0.270850 | ||||||||
\(717\) | 43.1010i | 1.60964i | ||||||||
\(718\) | 22.5959i | 0.843272i | ||||||||
\(719\) | −36.7423 | −1.37026 | −0.685129 | − | 0.728422i | \(-0.740254\pi\) | ||||
−0.685129 | + | 0.728422i | \(0.740254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.10102 | −0.0410041 | ||||||||
\(722\) | 16.5959i | 0.617636i | ||||||||
\(723\) | 41.6413i | 1.54866i | ||||||||
\(724\) | −18.0454 | −0.670652 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −17.1464 | −0.636364 | ||||||||
\(727\) | − 5.59592i | − 0.207541i | −0.994601 | − | 0.103771i | \(-0.966909\pi\) | ||||
0.994601 | − | 0.103771i | \(-0.0330908\pi\) | |||||||
\(728\) | − 1.10102i | − 0.0408065i | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.79796 | −0.0664999 | ||||||||
\(732\) | 3.55051i | 0.131231i | ||||||||
\(733\) | 10.8990i | 0.402563i | 0.979533 | + | 0.201281i | \(0.0645106\pi\) | ||||
−0.979533 | + | 0.201281i | \(0.935489\pi\) | |||||||
\(734\) | 20.7980 | 0.767667 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.44949 | 0.0902894 | ||||||||
\(737\) | 17.1010i | 0.629924i | ||||||||
\(738\) | − 10.0454i | − 0.369777i | ||||||||
\(739\) | −10.0000 | −0.367856 | −0.183928 | − | 0.982940i | \(-0.558881\pi\) | ||||
−0.183928 | + | 0.982940i | \(0.558881\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.30306 | 0.341757 | ||||||||
\(742\) | 2.49490i | 0.0915906i | ||||||||
\(743\) | − 16.6969i | − 0.612551i | −0.951943 | − | 0.306276i | \(-0.900917\pi\) | ||||
0.951943 | − | 0.306276i | \(-0.0990829\pi\) | |||||||
\(744\) | 7.34847 | 0.269408 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.4949 | −0.750372 | ||||||||
\(747\) | 18.0000i | 0.658586i | ||||||||
\(748\) | − 4.00000i | − 0.146254i | ||||||||
\(749\) | −8.65153 | −0.316120 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.8990 | 1.23699 | 0.618496 | − | 0.785788i | \(-0.287742\pi\) | ||||
0.618496 | + | 0.785788i | \(0.287742\pi\) | |||||||
\(752\) | 3.89898i | 0.142181i | ||||||||
\(753\) | 76.2929i | 2.78027i | ||||||||
\(754\) | 2.44949 | 0.0892052 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 39.3939i | − 1.43179i | −0.698205 | − | 0.715897i | \(-0.746018\pi\) | ||||
0.698205 | − | 0.715897i | \(-0.253982\pi\) | |||||||
\(758\) | − 9.14643i | − 0.332213i | ||||||||
\(759\) | −12.0000 | −0.435572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.8990 | 0.866337 | 0.433169 | − | 0.901313i | \(-0.357395\pi\) | ||||
0.433169 | + | 0.901313i | \(0.357395\pi\) | |||||||
\(762\) | 26.4495i | 0.958164i | ||||||||
\(763\) | − 2.40408i | − 0.0870336i | ||||||||
\(764\) | −17.6969 | −0.640253 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.79796 | 0.281752 | ||||||||
\(767\) | − 32.9444i | − 1.18955i | ||||||||
\(768\) | 2.44949i | 0.0883883i | ||||||||
\(769\) | 8.44949 | 0.304696 | 0.152348 | − | 0.988327i | \(-0.451316\pi\) | ||||
0.152348 | + | 0.988327i | \(0.451316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.60612 | −0.237914 | ||||||||
\(772\) | − 9.34847i | − 0.336459i | ||||||||
\(773\) | − 12.5505i | − 0.451410i | −0.974196 | − | 0.225705i | \(-0.927531\pi\) | ||||
0.974196 | − | 0.225705i | \(-0.0724686\pi\) | |||||||
\(774\) | −2.69694 | −0.0969395 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.34847 | −0.263795 | ||||||||
\(777\) | 1.59592i | 0.0572532i | ||||||||
\(778\) | − 9.65153i | − 0.346024i | ||||||||
\(779\) | 5.19184 | 0.186017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.69694 | −0.239635 | ||||||||
\(782\) | 4.89898i | 0.175187i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.79796 | 0.242784 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.0000 | 0.642039 | ||||||||
\(787\) | 45.4495i | 1.62010i | 0.586361 | + | 0.810050i | \(0.300560\pi\) | ||||
−0.586361 | + | 0.810050i | \(0.699440\pi\) | |||||||
\(788\) | 14.8990i | 0.530754i | ||||||||
\(789\) | −6.85357 | −0.243994 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.20204 | 0.291631 | ||||||||
\(792\) | − 6.00000i | − 0.213201i | ||||||||
\(793\) | − 3.55051i | − 0.126082i | ||||||||
\(794\) | 21.1464 | 0.750459 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.3485 | −0.544012 | ||||||||
\(797\) | − 18.0000i | − 0.637593i | −0.947823 | − | 0.318796i | \(-0.896721\pi\) | ||||
0.947823 | − | 0.318796i | \(-0.103279\pi\) | |||||||
\(798\) | − 1.70714i | − 0.0604322i | ||||||||
\(799\) | −7.79796 | −0.275872 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.3485 | 0.895644 | ||||||||
\(802\) | 0.595918i | 0.0210426i | ||||||||
\(803\) | − 2.69694i | − 0.0951729i | ||||||||
\(804\) | 20.9444 | 0.738652 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.34847 | −0.258839 | ||||||||
\(807\) | − 23.6413i | − 0.832214i | ||||||||
\(808\) | 8.55051i | 0.300806i | ||||||||
\(809\) | 7.59592 | 0.267058 | 0.133529 | − | 0.991045i | \(-0.457369\pi\) | ||||
0.133529 | + | 0.991045i | \(0.457369\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.5505 | −0.862085 | −0.431043 | − | 0.902332i | \(-0.641854\pi\) | ||||
−0.431043 | + | 0.902332i | \(0.641854\pi\) | |||||||
\(812\) | − 0.449490i | − 0.0157740i | ||||||||
\(813\) | − 33.5505i | − 1.17667i | ||||||||
\(814\) | −2.89898 | −0.101609 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.89898 | −0.171499 | ||||||||
\(817\) | − 1.39388i | − 0.0487656i | ||||||||
\(818\) | 13.7980i | 0.482434i | ||||||||
\(819\) | 3.30306 | 0.115418 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.2474 | 1.54425 | 0.772123 | − | 0.635473i | \(-0.219195\pi\) | ||||
0.772123 | + | 0.635473i | \(0.219195\pi\) | |||||||
\(822\) | 21.7980i | 0.760291i | ||||||||
\(823\) | 7.79796i | 0.271820i | 0.990721 | + | 0.135910i | \(0.0433958\pi\) | ||||
−0.990721 | + | 0.135910i | \(0.956604\pi\) | |||||||
\(824\) | −2.44949 | −0.0853320 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.04541 | −0.210347 | ||||||||
\(827\) | − 48.6969i | − 1.69336i | −0.532104 | − | 0.846679i | \(-0.678598\pi\) | ||||
0.532104 | − | 0.846679i | \(-0.321402\pi\) | |||||||
\(828\) | 7.34847i | 0.255377i | ||||||||
\(829\) | 34.4949 | 1.19806 | 0.599029 | − | 0.800728i | \(-0.295554\pi\) | ||||
0.599029 | + | 0.800728i | \(0.295554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 75.7980 | 2.62940 | ||||||||
\(832\) | − 2.44949i | − 0.0849208i | ||||||||
\(833\) | 13.5959i | 0.471071i | ||||||||
\(834\) | 16.0454 | 0.555607 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.10102 | 0.107251 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.1464i | 0.834125i | ||||||||
\(839\) | 11.2020 | 0.386737 | 0.193369 | − | 0.981126i | \(-0.438059\pi\) | ||||
0.193369 | + | 0.981126i | \(0.438059\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | − 8.55051i | − 0.294670i | ||||||||
\(843\) | − 22.5403i | − 0.776329i | ||||||||
\(844\) | −26.4949 | −0.911992 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.6969 | −0.402149 | ||||||||
\(847\) | − 3.14643i | − 0.108113i | ||||||||
\(848\) | 5.55051i | 0.190605i | ||||||||
\(849\) | −58.7878 | −2.01759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.55051 | 0.121710 | ||||||||
\(852\) | 8.20204i | 0.280997i | ||||||||
\(853\) | 27.7980i | 0.951784i | 0.879504 | + | 0.475892i | \(0.157875\pi\) | ||||
−0.879504 | + | 0.475892i | \(0.842125\pi\) | |||||||
\(854\) | −0.651531 | −0.0222949 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.2474 | −0.657864 | ||||||||
\(857\) | − 19.3939i | − 0.662482i | −0.943546 | − | 0.331241i | \(-0.892533\pi\) | ||||
0.943546 | − | 0.331241i | \(-0.107467\pi\) | |||||||
\(858\) | 12.0000i | 0.409673i | ||||||||
\(859\) | −13.1010 | −0.447001 | −0.223501 | − | 0.974704i | \(-0.571748\pi\) | ||||
−0.223501 | + | 0.974704i | \(0.571748\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.68673 | 0.125644 | ||||||||
\(862\) | − 13.5505i | − 0.461532i | ||||||||
\(863\) | 36.2474i | 1.23388i | 0.787011 | + | 0.616939i | \(0.211627\pi\) | ||||
−0.787011 | + | 0.616939i | \(0.788373\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25.5505 | 0.868242 | ||||||||
\(867\) | 31.8434i | 1.08146i | ||||||||
\(868\) | 1.34847i | 0.0457700i | ||||||||
\(869\) | −13.7980 | −0.468064 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.9444 | −0.709673 | ||||||||
\(872\) | − 5.34847i | − 0.181122i | ||||||||
\(873\) | − 22.0454i | − 0.746124i | ||||||||
\(874\) | −3.79796 | −0.128468 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.30306 | −0.111600 | ||||||||
\(877\) | − 8.00000i | − 0.270141i | −0.990836 | − | 0.135070i | \(-0.956874\pi\) | ||||
0.990836 | − | 0.135070i | \(-0.0431261\pi\) | |||||||
\(878\) | − 10.6969i | − 0.361004i | ||||||||
\(879\) | 6.24745 | 0.210721 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | 20.3939i | 0.686698i | ||||||||
\(883\) | − 23.9444i | − 0.805793i | −0.915246 | − | 0.402896i | \(-0.868003\pi\) | ||||
0.915246 | − | 0.402896i | \(-0.131997\pi\) | |||||||
\(884\) | 4.89898 | 0.164771 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.8990 | −0.769306 | ||||||||
\(887\) | 28.2020i | 0.946932i | 0.880812 | + | 0.473466i | \(0.156997\pi\) | ||||
−0.880812 | + | 0.473466i | \(0.843003\pi\) | |||||||
\(888\) | 3.55051i | 0.119147i | ||||||||
\(889\) | −4.85357 | −0.162784 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0000 | −0.603023 | ||||||||
\(892\) | − 4.00000i | − 0.133930i | ||||||||
\(893\) | − 6.04541i | − 0.202302i | ||||||||
\(894\) | 9.30306 | 0.311141 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.449490 | −0.0150164 | ||||||||
\(897\) | − 14.6969i | − 0.490716i | ||||||||
\(898\) | 6.20204i | 0.206965i | ||||||||
\(899\) | −3.00000 | −0.100056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.1010 | −0.369829 | ||||||||
\(902\) | 6.69694i | 0.222984i | ||||||||
\(903\) | − 0.989795i | − 0.0329383i | ||||||||
\(904\) | 18.2474 | 0.606901 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.20204 | −0.272495 | ||||||||
\(907\) | 6.65153i | 0.220860i | 0.993884 | + | 0.110430i | \(0.0352229\pi\) | ||||
−0.993884 | + | 0.110430i | \(0.964777\pi\) | |||||||
\(908\) | − 9.24745i | − 0.306887i | ||||||||
\(909\) | −25.6515 | −0.850808 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.50510 | 0.0829978 | 0.0414989 | − | 0.999139i | \(-0.486787\pi\) | ||||
0.0414989 | + | 0.999139i | \(0.486787\pi\) | |||||||
\(912\) | − 3.79796i | − 0.125763i | ||||||||
\(913\) | − 12.0000i | − 0.397142i | ||||||||
\(914\) | −1.79796 | −0.0594712 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −26.8990 | −0.888767 | ||||||||
\(917\) | 3.30306i | 0.109077i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.1464 | 1.95106 | 0.975530 | − | 0.219865i | \(-0.0705617\pi\) | ||||
0.975530 | + | 0.219865i | \(0.0705617\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −81.7980 | −2.69533 | ||||||||
\(922\) | − 40.2929i | − 1.32697i | ||||||||
\(923\) | − 8.20204i | − 0.269973i | ||||||||
\(924\) | 2.20204 | 0.0724418 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.8990 | −0.423887 | ||||||||
\(927\) | − 7.34847i | − 0.241355i | ||||||||
\(928\) | − 1.00000i | − 0.0328266i | ||||||||
\(929\) | −9.49490 | −0.311517 | −0.155759 | − | 0.987795i | \(-0.549782\pi\) | ||||
−0.155759 | + | 0.987795i | \(0.549782\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.5403 | −0.345445 | ||||||||
\(932\) | 11.0000i | 0.360317i | ||||||||
\(933\) | 48.0000i | 1.57145i | ||||||||
\(934\) | −30.9444 | −1.01253 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.34847 | 0.240192 | ||||||||
\(937\) | 15.2929i | 0.499596i | 0.968298 | + | 0.249798i | \(0.0803642\pi\) | ||||
−0.968298 | + | 0.249798i | \(0.919636\pi\) | |||||||
\(938\) | 3.84337i | 0.125490i | ||||||||
\(939\) | −16.1566 | −0.527252 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.55051 | 0.115743 | 0.0578717 | − | 0.998324i | \(-0.481569\pi\) | ||||
0.0578717 | + | 0.998324i | \(0.481569\pi\) | |||||||
\(942\) | 5.75255i | 0.187428i | ||||||||
\(943\) | − 8.20204i | − 0.267095i | ||||||||
\(944\) | −13.4495 | −0.437744 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.79796 | 0.0584567 | ||||||||
\(947\) | − 22.6515i | − 0.736076i | −0.929811 | − | 0.368038i | \(-0.880030\pi\) | ||||
0.929811 | − | 0.368038i | \(-0.119970\pi\) | |||||||
\(948\) | 16.8990i | 0.548853i | ||||||||
\(949\) | 3.30306 | 0.107222 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 69.4393 | 2.25172 | ||||||||
\(952\) | − 0.898979i | − 0.0291361i | ||||||||
\(953\) | − 34.2929i | − 1.11085i | −0.831565 | − | 0.555427i | \(-0.812555\pi\) | ||||
0.831565 | − | 0.555427i | \(-0.187445\pi\) | |||||||
\(954\) | −16.6515 | −0.539113 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17.5959 | −0.569093 | ||||||||
\(957\) | 4.89898i | 0.158362i | ||||||||
\(958\) | − 23.7980i | − 0.768877i | ||||||||
\(959\) | −4.00000 | −0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | − 3.55051i | − 0.114473i | ||||||||
\(963\) | − 57.7423i | − 1.86072i | ||||||||
\(964\) | −17.0000 | −0.547533 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.69694 | −0.0867726 | ||||||||
\(967\) | − 28.0000i | − 0.900419i | −0.892923 | − | 0.450210i | \(-0.851349\pi\) | ||||
0.892923 | − | 0.450210i | \(-0.148651\pi\) | |||||||
\(968\) | − 7.00000i | − 0.224989i | ||||||||
\(969\) | 7.59592 | 0.244016 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.9444 | −0.993053 | −0.496526 | − | 0.868022i | \(-0.665391\pi\) | ||||
−0.496526 | + | 0.868022i | \(0.665391\pi\) | |||||||
\(972\) | 22.0454i | 0.707107i | ||||||||
\(973\) | 2.94439i | 0.0943927i | ||||||||
\(974\) | 18.8990 | 0.605562 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.44949 | −0.0463970 | ||||||||
\(977\) | − 9.89898i | − 0.316696i | −0.987383 | − | 0.158348i | \(-0.949383\pi\) | ||||
0.987383 | − | 0.158348i | \(-0.0506169\pi\) | |||||||
\(978\) | − 18.4949i | − 0.591402i | ||||||||
\(979\) | −16.8990 | −0.540094 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.0454 | 0.512290 | ||||||||
\(982\) | 22.4949i | 0.717841i | ||||||||
\(983\) | 39.0000i | 1.24391i | 0.783054 | + | 0.621953i | \(0.213661\pi\) | ||||
−0.783054 | + | 0.621953i | \(0.786339\pi\) | |||||||
\(984\) | 8.20204 | 0.261472 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.00000 | 0.0636930 | ||||||||
\(987\) | − 4.29286i | − 0.136643i | ||||||||
\(988\) | 3.79796i | 0.120829i | ||||||||
\(989\) | −2.20204 | −0.0700208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.4949 | −1.66756 | −0.833778 | − | 0.552100i | \(-0.813827\pi\) | ||||
−0.833778 | + | 0.552100i | \(0.813827\pi\) | |||||||
\(992\) | 3.00000i | 0.0952501i | ||||||||
\(993\) | − 14.0908i | − 0.447159i | ||||||||
\(994\) | −1.50510 | −0.0477390 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −14.6969 | −0.465690 | ||||||||
\(997\) | 43.7423i | 1.38533i | 0.721258 | + | 0.692667i | \(0.243564\pi\) | ||||
−0.721258 | + | 0.692667i | \(0.756436\pi\) | |||||||
\(998\) | − 9.65153i | − 0.305514i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1450.2.b.i.349.2 | 4 | ||
5.2 | odd | 4 | 1450.2.a.o.1.2 | yes | 2 | ||
5.3 | odd | 4 | 1450.2.a.j.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1450.2.b.i.349.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1450.2.a.j.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
1450.2.a.o.1.2 | yes | 2 | 5.2 | odd | 4 | ||
1450.2.b.i.349.2 | 4 | 1.1 | even | 1 | trivial | ||
1450.2.b.i.349.3 | 4 | 5.4 | even | 2 | inner |