Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(8,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.n (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.8 |
Dual form | 273.2.n.a.239.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | −0.292893 | − | 1.70711i | −0.169102 | − | 0.985599i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.29289 | + | 1.29289i | −0.578199 | + | 0.578199i | −0.934407 | − | 0.356207i | \(-0.884070\pi\) |
0.356207 | + | 0.934407i | \(0.384070\pi\) | |||||||
\(6\) | 2.00000 | + | 1.41421i | 0.816497 | + | 0.577350i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | −2.82843 | + | 1.00000i | −0.942809 | + | 0.333333i | ||||
\(10\) | − | 2.58579i | − | 0.817697i | ||||||
\(11\) | −1.41421 | − | 1.41421i | −0.426401 | − | 0.426401i | 0.460999 | − | 0.887401i | \(-0.347491\pi\) |
−0.887401 | + | 0.460999i | \(0.847491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.707107 | + | 3.53553i | −0.196116 | + | 0.980581i | ||||
\(14\) | 1.41421i | 0.377964i | ||||||||
\(15\) | 2.58579 | + | 1.82843i | 0.667647 | + | 0.472098i | ||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 1.82843 | − | 3.82843i | 0.430964 | − | 0.902369i | ||||
\(19\) | −6.12132 | − | 6.12132i | −1.40433 | − | 1.40433i | −0.785628 | − | 0.618699i | \(-0.787660\pi\) |
−0.618699 | − | 0.785628i | \(-0.712340\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41421 | − | 1.00000i | −0.308607 | − | 0.218218i | ||||
\(22\) | 2.82843 | 0.603023 | ||||||||
\(23\) | −3.82843 | −0.798282 | −0.399141 | − | 0.916890i | \(-0.630692\pi\) | ||||
−0.399141 | + | 0.916890i | \(0.630692\pi\) | |||||||
\(24\) | −2.82843 | + | 4.00000i | −0.577350 | + | 0.816497i | ||||
\(25\) | 1.65685i | 0.331371i | ||||||||
\(26\) | −2.82843 | − | 4.24264i | −0.554700 | − | 0.832050i | ||||
\(27\) | 2.53553 | + | 4.53553i | 0.487964 | + | 0.872864i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.65685i | 0.864756i | 0.901692 | + | 0.432378i | \(0.142325\pi\) | ||||
−0.901692 | + | 0.432378i | \(0.857675\pi\) | |||||||
\(30\) | −4.41421 | + | 0.757359i | −0.805921 | + | 0.138274i | ||||
\(31\) | −6.94975 | − | 6.94975i | −1.24821 | − | 1.24821i | −0.956509 | − | 0.291702i | \(-0.905778\pi\) |
−0.291702 | − | 0.956509i | \(-0.594222\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | + | 2.82843i | −0.348155 | + | 0.492366i | ||||
\(34\) | 4.00000 | − | 4.00000i | 0.685994 | − | 0.685994i | ||||
\(35\) | 1.82843i | 0.309061i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.58579 | + | 3.58579i | −0.589500 | + | 0.589500i | −0.937496 | − | 0.347996i | \(-0.886862\pi\) |
0.347996 | + | 0.937496i | \(0.386862\pi\) | |||||||
\(38\) | 12.2426 | 1.98602 | ||||||||
\(39\) | 6.24264 | + | 0.171573i | 0.999623 | + | 0.0274736i | ||||
\(40\) | 5.17157 | 0.817697 | ||||||||
\(41\) | 8.24264 | − | 8.24264i | 1.28728 | − | 1.28728i | 0.350854 | − | 0.936430i | \(-0.385891\pi\) |
0.936430 | − | 0.350854i | \(-0.114109\pi\) | |||||||
\(42\) | 2.41421 | − | 0.414214i | 0.372521 | − | 0.0639145i | ||||
\(43\) | − | 4.65685i | − | 0.710164i | −0.934835 | − | 0.355082i | \(-0.884453\pi\) | ||
0.934835 | − | 0.355082i | \(-0.115547\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.36396 | − | 4.94975i | 0.352399 | − | 0.737865i | ||||
\(46\) | 3.82843 | − | 3.82843i | 0.564471 | − | 0.564471i | ||||
\(47\) | 6.12132 | + | 6.12132i | 0.892886 | + | 0.892886i | 0.994794 | − | 0.101908i | \(-0.0324946\pi\) |
−0.101908 | + | 0.994794i | \(0.532495\pi\) | |||||||
\(48\) | −1.17157 | − | 6.82843i | −0.169102 | − | 0.985599i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −1.65685 | − | 1.65685i | −0.234315 | − | 0.234315i | ||||
\(51\) | 1.17157 | + | 6.82843i | 0.164053 | + | 0.956171i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3137i | 1.41670i | 0.705863 | + | 0.708348i | \(0.250559\pi\) | ||||
−0.705863 | + | 0.708348i | \(0.749441\pi\) | |||||||
\(54\) | −7.07107 | − | 2.00000i | −0.962250 | − | 0.272166i | ||||
\(55\) | 3.65685 | 0.493090 | ||||||||
\(56\) | −2.82843 | −0.377964 | ||||||||
\(57\) | −8.65685 | + | 12.2426i | −1.14663 | + | 1.62158i | ||||
\(58\) | −4.65685 | − | 4.65685i | −0.611475 | − | 0.611475i | ||||
\(59\) | 1.41421 | + | 1.41421i | 0.184115 | + | 0.184115i | 0.793146 | − | 0.609031i | \(-0.208442\pi\) |
−0.609031 | + | 0.793146i | \(0.708442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.89949 | 0.755353 | 0.377676 | − | 0.925938i | \(-0.376723\pi\) | ||||
0.377676 | + | 0.925938i | \(0.376723\pi\) | |||||||
\(62\) | 13.8995 | 1.76524 | ||||||||
\(63\) | −1.29289 | + | 2.70711i | −0.162889 | + | 0.341063i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −3.65685 | − | 5.48528i | −0.453577 | − | 0.680365i | ||||
\(66\) | −0.828427 | − | 4.82843i | −0.101972 | − | 0.594338i | ||||
\(67\) | 5.07107 | + | 5.07107i | 0.619530 | + | 0.619530i | 0.945411 | − | 0.325881i | \(-0.105661\pi\) |
−0.325881 | + | 0.945411i | \(0.605661\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.12132 | + | 6.53553i | 0.134991 | + | 0.786786i | ||||
\(70\) | −1.82843 | − | 1.82843i | −0.218539 | − | 0.218539i | ||||
\(71\) | −2.75736 | + | 2.75736i | −0.327238 | + | 0.327238i | −0.851535 | − | 0.524297i | \(-0.824328\pi\) |
0.524297 | + | 0.851535i | \(0.324328\pi\) | |||||||
\(72\) | 7.65685 | + | 3.65685i | 0.902369 | + | 0.430964i | ||||
\(73\) | −4.12132 | + | 4.12132i | −0.482364 | + | 0.482364i | −0.905886 | − | 0.423522i | \(-0.860794\pi\) |
0.423522 | + | 0.905886i | \(0.360794\pi\) | |||||||
\(74\) | − | 7.17157i | − | 0.833678i | ||||||
\(75\) | 2.82843 | − | 0.485281i | 0.326599 | − | 0.0560355i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | −6.41421 | + | 6.07107i | −0.726267 | + | 0.687413i | ||||
\(79\) | 0.171573 | 0.0193035 | 0.00965173 | − | 0.999953i | \(-0.496928\pi\) | ||||
0.00965173 | + | 0.999953i | \(0.496928\pi\) | |||||||
\(80\) | −5.17157 | + | 5.17157i | −0.578199 | + | 0.578199i | ||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 16.4853i | 1.82049i | ||||||||
\(83\) | 0.707107 | − | 0.707107i | 0.0776151 | − | 0.0776151i | −0.667234 | − | 0.744849i | \(-0.732522\pi\) |
0.744849 | + | 0.667234i | \(0.232522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.17157 | − | 5.17157i | 0.560936 | − | 0.560936i | ||||
\(86\) | 4.65685 | + | 4.65685i | 0.502162 | + | 0.502162i | ||||
\(87\) | 7.94975 | − | 1.36396i | 0.852302 | − | 0.146232i | ||||
\(88\) | 5.65685i | 0.603023i | ||||||||
\(89\) | −10.1213 | − | 10.1213i | −1.07286 | − | 1.07286i | −0.997128 | − | 0.0757294i | \(-0.975871\pi\) |
−0.0757294 | − | 0.997128i | \(-0.524129\pi\) | |||||||
\(90\) | 2.58579 | + | 7.31371i | 0.272566 | + | 0.770933i | ||||
\(91\) | 2.00000 | + | 3.00000i | 0.209657 | + | 0.314485i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.82843 | + | 13.8995i | −1.01916 | + | 1.44131i | ||||
\(94\) | −12.2426 | −1.26273 | ||||||||
\(95\) | 15.8284 | 1.62396 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.70711 | − | 8.70711i | −0.884073 | − | 0.884073i | 0.109873 | − | 0.993946i | \(-0.464956\pi\) |
−0.993946 | + | 0.109873i | \(0.964956\pi\) | |||||||
\(98\) | 1.00000 | + | 1.00000i | 0.101015 | + | 0.101015i | ||||
\(99\) | 5.41421 | + | 2.58579i | 0.544149 | + | 0.259881i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.65685 | −0.363871 | −0.181935 | − | 0.983311i | \(-0.558236\pi\) | ||||
−0.181935 | + | 0.983311i | \(0.558236\pi\) | |||||||
\(102\) | −8.00000 | − | 5.65685i | −0.792118 | − | 0.560112i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 8.48528 | − | 5.65685i | 0.832050 | − | 0.554700i | ||||
\(105\) | 3.12132 | − | 0.535534i | 0.304610 | − | 0.0522628i | ||||
\(106\) | −10.3137 | − | 10.3137i | −1.00176 | − | 1.00176i | ||||
\(107\) | − | 4.82843i | − | 0.466782i | −0.972383 | − | 0.233391i | \(-0.925018\pi\) | ||
0.972383 | − | 0.233391i | \(-0.0749821\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.82843 | + | 9.82843i | 0.941393 | + | 0.941393i | 0.998375 | − | 0.0569826i | \(-0.0181480\pi\) |
−0.0569826 | + | 0.998375i | \(0.518148\pi\) | |||||||
\(110\) | −3.65685 | + | 3.65685i | −0.348667 | + | 0.348667i | ||||
\(111\) | 7.17157 | + | 5.07107i | 0.680696 | + | 0.481324i | ||||
\(112\) | 2.82843 | − | 2.82843i | 0.267261 | − | 0.267261i | ||||
\(113\) | − | 4.17157i | − | 0.392429i | −0.980561 | − | 0.196214i | \(-0.937135\pi\) | ||
0.980561 | − | 0.196214i | \(-0.0628648\pi\) | |||||||
\(114\) | −3.58579 | − | 20.8995i | −0.335840 | − | 1.95742i | ||||
\(115\) | 4.94975 | − | 4.94975i | 0.461566 | − | 0.461566i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.53553 | − | 10.7071i | −0.141960 | − | 0.989872i | ||||
\(118\) | −2.82843 | −0.260378 | ||||||||
\(119\) | −2.82843 | + | 2.82843i | −0.259281 | + | 0.259281i | ||||
\(120\) | −1.51472 | − | 8.82843i | −0.138274 | − | 0.805921i | ||||
\(121\) | − | 7.00000i | − | 0.636364i | ||||||
\(122\) | −5.89949 | + | 5.89949i | −0.534115 | + | 0.534115i | ||||
\(123\) | −16.4853 | − | 11.6569i | −1.48643 | − | 1.05106i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.60660 | − | 8.60660i | −0.769798 | − | 0.769798i | ||||
\(126\) | −1.41421 | − | 4.00000i | −0.125988 | − | 0.356348i | ||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(129\) | −7.94975 | + | 1.36396i | −0.699936 | + | 0.120090i | ||||
\(130\) | 9.14214 | + | 1.82843i | 0.801818 | + | 0.160364i | ||||
\(131\) | 5.07107i | 0.443061i | 0.975153 | + | 0.221531i | \(0.0711053\pi\) | ||||
−0.975153 | + | 0.221531i | \(0.928895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.65685 | −0.750644 | ||||||||
\(134\) | −10.1421 | −0.876147 | ||||||||
\(135\) | −9.14214 | − | 2.58579i | −0.786830 | − | 0.222549i | ||||
\(136\) | 8.00000 | + | 8.00000i | 0.685994 | + | 0.685994i | ||||
\(137\) | 3.58579 | + | 3.58579i | 0.306354 | + | 0.306354i | 0.843494 | − | 0.537139i | \(-0.180495\pi\) |
−0.537139 | + | 0.843494i | \(0.680495\pi\) | |||||||
\(138\) | −7.65685 | − | 5.41421i | −0.651795 | − | 0.460888i | ||||
\(139\) | −3.17157 | −0.269009 | −0.134505 | − | 0.990913i | \(-0.542944\pi\) | ||||
−0.134505 | + | 0.990913i | \(0.542944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.65685 | − | 12.2426i | 0.729039 | − | 1.03102i | ||||
\(142\) | − | 5.51472i | − | 0.462785i | ||||||
\(143\) | 6.00000 | − | 4.00000i | 0.501745 | − | 0.334497i | ||||
\(144\) | −11.3137 | + | 4.00000i | −0.942809 | + | 0.333333i | ||||
\(145\) | −6.02082 | − | 6.02082i | −0.500001 | − | 0.500001i | ||||
\(146\) | − | 8.24264i | − | 0.682166i | ||||||
\(147\) | −1.70711 | + | 0.292893i | −0.140800 | + | 0.0241574i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.24264 | − | 4.24264i | 0.347571 | − | 0.347571i | −0.511633 | − | 0.859204i | \(-0.670959\pi\) |
0.859204 | + | 0.511633i | \(0.170959\pi\) | |||||||
\(150\) | −2.34315 | + | 3.31371i | −0.191317 | + | 0.270563i | ||||
\(151\) | −8.89949 | + | 8.89949i | −0.724231 | + | 0.724231i | −0.969464 | − | 0.245233i | \(-0.921135\pi\) |
0.245233 | + | 0.969464i | \(0.421135\pi\) | |||||||
\(152\) | 24.4853i | 1.98602i | ||||||||
\(153\) | 11.3137 | − | 4.00000i | 0.914659 | − | 0.323381i | ||||
\(154\) | 2.00000 | − | 2.00000i | 0.161165 | − | 0.161165i | ||||
\(155\) | 17.9706 | 1.44343 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.48528 | 0.677199 | 0.338600 | − | 0.940931i | \(-0.390047\pi\) | ||||
0.338600 | + | 0.940931i | \(0.390047\pi\) | |||||||
\(158\) | −0.171573 | + | 0.171573i | −0.0136496 | + | 0.0136496i | ||||
\(159\) | 17.6066 | − | 3.02082i | 1.39629 | − | 0.239566i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.70711 | + | 2.70711i | −0.213350 | + | 0.213350i | ||||
\(162\) | −1.34315 | + | 12.6569i | −0.105527 | + | 0.994416i | ||||
\(163\) | −6.75736 | + | 6.75736i | −0.529277 | + | 0.529277i | −0.920357 | − | 0.391080i | \(-0.872102\pi\) |
0.391080 | + | 0.920357i | \(0.372102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.07107 | − | 6.24264i | −0.0833825 | − | 0.485989i | ||||
\(166\) | 1.41421i | 0.109764i | ||||||||
\(167\) | −6.94975 | − | 6.94975i | −0.537788 | − | 0.537788i | 0.385091 | − | 0.922879i | \(-0.374170\pi\) |
−0.922879 | + | 0.385091i | \(0.874170\pi\) | |||||||
\(168\) | 0.828427 | + | 4.82843i | 0.0639145 | + | 0.372521i | ||||
\(169\) | −12.0000 | − | 5.00000i | −0.923077 | − | 0.384615i | ||||
\(170\) | 10.3431i | 0.793283i | ||||||||
\(171\) | 23.4350 | + | 11.1924i | 1.79212 | + | 0.855903i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.2426 | −1.38696 | −0.693481 | − | 0.720475i | \(-0.743924\pi\) | ||||
−0.693481 | + | 0.720475i | \(0.743924\pi\) | |||||||
\(174\) | −6.58579 | + | 9.31371i | −0.499267 | + | 0.706070i | ||||
\(175\) | 1.17157 | + | 1.17157i | 0.0885626 | + | 0.0885626i | ||||
\(176\) | −5.65685 | − | 5.65685i | −0.426401 | − | 0.426401i | ||||
\(177\) | 2.00000 | − | 2.82843i | 0.150329 | − | 0.212598i | ||||
\(178\) | 20.2426 | 1.51725 | ||||||||
\(179\) | −18.1716 | −1.35821 | −0.679104 | − | 0.734042i | \(-0.737631\pi\) | ||||
−0.679104 | + | 0.734042i | \(0.737631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.00000i | − | 0.148659i | −0.997234 | − | 0.0743294i | \(-0.976318\pi\) | ||
0.997234 | − | 0.0743294i | \(-0.0236816\pi\) | |||||||
\(182\) | −5.00000 | − | 1.00000i | −0.370625 | − | 0.0741249i | ||||
\(183\) | −1.72792 | − | 10.0711i | −0.127732 | − | 0.744475i | ||||
\(184\) | 7.65685 | + | 7.65685i | 0.564471 | + | 0.564471i | ||||
\(185\) | − | 9.27208i | − | 0.681697i | ||||||
\(186\) | −4.07107 | − | 23.7279i | −0.298505 | − | 1.73982i | ||||
\(187\) | 5.65685 | + | 5.65685i | 0.413670 | + | 0.413670i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.00000 | + | 1.41421i | 0.363696 | + | 0.102869i | ||||
\(190\) | −15.8284 | + | 15.8284i | −1.14831 | + | 1.14831i | ||||
\(191\) | − | 13.3137i | − | 0.963346i | −0.876351 | − | 0.481673i | \(-0.840029\pi\) | ||
0.876351 | − | 0.481673i | \(-0.159971\pi\) | |||||||
\(192\) | 13.6569 | − | 2.34315i | 0.985599 | − | 0.169102i | ||||
\(193\) | −12.2426 | + | 12.2426i | −0.881245 | + | 0.881245i | −0.993661 | − | 0.112417i | \(-0.964141\pi\) |
0.112417 | + | 0.993661i | \(0.464141\pi\) | |||||||
\(194\) | 17.4142 | 1.25027 | ||||||||
\(195\) | −8.29289 | + | 7.84924i | −0.593866 | + | 0.562096i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.65685 | + | 2.65685i | −0.189293 | + | 0.189293i | −0.795390 | − | 0.606097i | \(-0.792734\pi\) |
0.606097 | + | 0.795390i | \(0.292734\pi\) | |||||||
\(198\) | −8.00000 | + | 2.82843i | −0.568535 | + | 0.201008i | ||||
\(199\) | 6.34315i | 0.449654i | 0.974399 | + | 0.224827i | \(0.0721816\pi\) | ||||
−0.974399 | + | 0.224827i | \(0.927818\pi\) | |||||||
\(200\) | 3.31371 | − | 3.31371i | 0.234315 | − | 0.234315i | ||||
\(201\) | 7.17157 | − | 10.1421i | 0.505844 | − | 0.715371i | ||||
\(202\) | 3.65685 | − | 3.65685i | 0.257295 | − | 0.257295i | ||||
\(203\) | 3.29289 | + | 3.29289i | 0.231116 | + | 0.231116i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.3137i | 1.48861i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.8284 | − | 3.82843i | 0.752628 | − | 0.266094i | ||||
\(208\) | −2.82843 | + | 14.1421i | −0.196116 | + | 0.980581i | ||||
\(209\) | 17.3137i | 1.19761i | ||||||||
\(210\) | −2.58579 | + | 3.65685i | −0.178436 | + | 0.252347i | ||||
\(211\) | 0.514719 | 0.0354347 | 0.0177173 | − | 0.999843i | \(-0.494360\pi\) | ||||
0.0177173 | + | 0.999843i | \(0.494360\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.51472 | + | 3.89949i | 0.377862 | + | 0.267189i | ||||
\(214\) | 4.82843 | + | 4.82843i | 0.330064 | + | 0.330064i | ||||
\(215\) | 6.02082 | + | 6.02082i | 0.410616 | + | 0.410616i | ||||
\(216\) | 4.00000 | − | 14.1421i | 0.272166 | − | 0.962250i | ||||
\(217\) | −9.82843 | −0.667197 | ||||||||
\(218\) | −19.6569 | −1.33133 | ||||||||
\(219\) | 8.24264 | + | 5.82843i | 0.556986 | + | 0.393849i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.82843 | − | 14.1421i | 0.190261 | − | 0.951303i | ||||
\(222\) | −12.2426 | + | 2.10051i | −0.821672 | + | 0.140977i | ||||
\(223\) | −3.77817 | − | 3.77817i | −0.253005 | − | 0.253005i | 0.569196 | − | 0.822202i | \(-0.307254\pi\) |
−0.822202 | + | 0.569196i | \(0.807254\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.65685 | − | 4.68629i | −0.110457 | − | 0.312419i | ||||
\(226\) | 4.17157 | + | 4.17157i | 0.277489 | + | 0.277489i | ||||
\(227\) | −15.0711 | + | 15.0711i | −1.00030 | + | 1.00030i | −0.000301949 | 1.00000i | \(0.500096\pi\) | |
−1.00000 | 0.000301949i | \(0.999904\pi\) | ||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.4853 | + | 10.4853i | −0.692887 | + | 0.692887i | −0.962866 | − | 0.269979i | \(-0.912983\pi\) |
0.269979 | + | 0.962866i | \(0.412983\pi\) | |||||||
\(230\) | 9.89949i | 0.652753i | ||||||||
\(231\) | 0.585786 | + | 3.41421i | 0.0385419 | + | 0.224639i | ||||
\(232\) | 9.31371 | − | 9.31371i | 0.611475 | − | 0.611475i | ||||
\(233\) | 6.31371 | 0.413625 | 0.206812 | − | 0.978381i | \(-0.433691\pi\) | ||||
0.206812 | + | 0.978381i | \(0.433691\pi\) | |||||||
\(234\) | 12.2426 | + | 9.17157i | 0.800326 | + | 0.599564i | ||||
\(235\) | −15.8284 | −1.03253 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0502525 | − | 0.292893i | −0.00326425 | − | 0.0190255i | ||||
\(238\) | − | 5.65685i | − | 0.366679i | ||||||
\(239\) | 4.07107 | − | 4.07107i | 0.263335 | − | 0.263335i | −0.563072 | − | 0.826408i | \(-0.690381\pi\) |
0.826408 | + | 0.563072i | \(0.190381\pi\) | |||||||
\(240\) | 10.3431 | + | 7.31371i | 0.667647 | + | 0.472098i | ||||
\(241\) | 5.29289 | − | 5.29289i | 0.340945 | − | 0.340945i | −0.515777 | − | 0.856723i | \(-0.672497\pi\) |
0.856723 | + | 0.515777i | \(0.172497\pi\) | |||||||
\(242\) | 7.00000 | + | 7.00000i | 0.449977 | + | 0.449977i | ||||
\(243\) | −11.7071 | − | 10.2929i | −0.751011 | − | 0.660289i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.29289 | + | 1.29289i | 0.0825999 | + | 0.0825999i | ||||
\(246\) | 28.1421 | − | 4.82843i | 1.79428 | − | 0.307849i | ||||
\(247\) | 25.9706 | − | 17.3137i | 1.65247 | − | 1.10164i | ||||
\(248\) | 27.7990i | 1.76524i | ||||||||
\(249\) | −1.41421 | − | 1.00000i | −0.0896221 | − | 0.0633724i | ||||
\(250\) | 17.2132 | 1.08866 | ||||||||
\(251\) | 14.9706 | 0.944934 | 0.472467 | − | 0.881348i | \(-0.343364\pi\) | ||||
0.472467 | + | 0.881348i | \(0.343364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.41421 | + | 5.41421i | 0.340389 | + | 0.340389i | ||||
\(254\) | 2.00000 | + | 2.00000i | 0.125491 | + | 0.125491i | ||||
\(255\) | −10.3431 | − | 7.31371i | −0.647713 | − | 0.458002i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.142136 | −0.00886618 | −0.00443309 | − | 0.999990i | \(-0.501411\pi\) | ||||
−0.00443309 | + | 0.999990i | \(0.501411\pi\) | |||||||
\(258\) | 6.58579 | − | 9.31371i | 0.410013 | − | 0.579846i | ||||
\(259\) | 5.07107i | 0.315101i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.65685 | − | 13.1716i | −0.288252 | − | 0.815300i | ||||
\(262\) | −5.07107 | − | 5.07107i | −0.313292 | − | 0.313292i | ||||
\(263\) | 10.5147i | 0.648365i | 0.945995 | + | 0.324183i | \(0.105089\pi\) | ||||
−0.945995 | + | 0.324183i | \(0.894911\pi\) | |||||||
\(264\) | 9.65685 | − | 1.65685i | 0.594338 | − | 0.101972i | ||||
\(265\) | −13.3345 | − | 13.3345i | −0.819133 | − | 0.819133i | ||||
\(266\) | 8.65685 | − | 8.65685i | 0.530786 | − | 0.530786i | ||||
\(267\) | −14.3137 | + | 20.2426i | −0.875985 | + | 1.23883i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 27.6985i | − | 1.68881i | −0.535708 | − | 0.844403i | \(-0.679955\pi\) | ||
0.535708 | − | 0.844403i | \(-0.320045\pi\) | |||||||
\(270\) | 11.7279 | − | 6.55635i | 0.713739 | − | 0.399007i | ||||
\(271\) | 7.89949 | − | 7.89949i | 0.479860 | − | 0.479860i | −0.425227 | − | 0.905087i | \(-0.639806\pi\) |
0.905087 | + | 0.425227i | \(0.139806\pi\) | |||||||
\(272\) | −16.0000 | −0.970143 | ||||||||
\(273\) | 4.53553 | − | 4.29289i | 0.274503 | − | 0.259818i | ||||
\(274\) | −7.17157 | −0.433251 | ||||||||
\(275\) | 2.34315 | − | 2.34315i | 0.141297 | − | 0.141297i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 19.4853i | − | 1.17076i | −0.810760 | − | 0.585379i | \(-0.800946\pi\) | ||
0.810760 | − | 0.585379i | \(-0.199054\pi\) | |||||||
\(278\) | 3.17157 | − | 3.17157i | 0.190218 | − | 0.190218i | ||||
\(279\) | 26.6066 | + | 12.7071i | 1.59290 | + | 0.760755i | ||||
\(280\) | 3.65685 | − | 3.65685i | 0.218539 | − | 0.218539i | ||||
\(281\) | 17.1421 | + | 17.1421i | 1.02261 | + | 1.02261i | 0.999738 | + | 0.0228758i | \(0.00728222\pi\) |
0.0228758 | + | 0.999738i | \(0.492718\pi\) | |||||||
\(282\) | 3.58579 | + | 20.8995i | 0.213530 | + | 1.24455i | ||||
\(283\) | 1.17157i | 0.0696428i | 0.999394 | + | 0.0348214i | \(0.0110862\pi\) | ||||
−0.999394 | + | 0.0348214i | \(0.988914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.63604 | − | 27.0208i | −0.274615 | − | 1.60057i | ||||
\(286\) | −2.00000 | + | 10.0000i | −0.118262 | + | 0.591312i | ||||
\(287\) | − | 11.6569i | − | 0.688082i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 12.0416 | 0.707109 | ||||||||
\(291\) | −12.3137 | + | 17.4142i | −0.721842 | + | 1.02084i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.05025 | + | 3.05025i | 0.178198 | + | 0.178198i | 0.790570 | − | 0.612372i | \(-0.209785\pi\) |
−0.612372 | + | 0.790570i | \(0.709785\pi\) | |||||||
\(294\) | 1.41421 | − | 2.00000i | 0.0824786 | − | 0.116642i | ||||
\(295\) | −3.65685 | −0.212910 | ||||||||
\(296\) | 14.3431 | 0.833678 | ||||||||
\(297\) | 2.82843 | − | 10.0000i | 0.164122 | − | 0.580259i | ||||
\(298\) | 8.48528i | 0.491539i | ||||||||
\(299\) | 2.70711 | − | 13.5355i | 0.156556 | − | 0.782780i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.29289 | − | 3.29289i | −0.189799 | − | 0.189799i | ||||
\(302\) | − | 17.7990i | − | 1.02422i | ||||||
\(303\) | 1.07107 | + | 6.24264i | 0.0615312 | + | 0.358630i | ||||
\(304\) | −24.4853 | − | 24.4853i | −1.40433 | − | 1.40433i | ||||
\(305\) | −7.62742 | + | 7.62742i | −0.436745 | + | 0.436745i | ||||
\(306\) | −7.31371 | + | 15.3137i | −0.418097 | + | 0.875426i | ||||
\(307\) | −8.36396 | + | 8.36396i | −0.477356 | + | 0.477356i | −0.904285 | − | 0.426929i | \(-0.859595\pi\) |
0.426929 | + | 0.904285i | \(0.359595\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.9706 | + | 17.9706i | −1.02066 | + | 1.02066i | ||||
\(311\) | 0.443651 | 0.0251571 | 0.0125786 | − | 0.999921i | \(-0.495996\pi\) | ||||
0.0125786 | + | 0.999921i | \(0.495996\pi\) | |||||||
\(312\) | −12.1421 | − | 12.8284i | −0.687413 | − | 0.726267i | ||||
\(313\) | 16.1421 | 0.912407 | 0.456204 | − | 0.889875i | \(-0.349209\pi\) | ||||
0.456204 | + | 0.889875i | \(0.349209\pi\) | |||||||
\(314\) | −8.48528 | + | 8.48528i | −0.478852 | + | 0.478852i | ||||
\(315\) | −1.82843 | − | 5.17157i | −0.103020 | − | 0.291385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.75736 | + | 2.75736i | −0.154869 | + | 0.154869i | −0.780288 | − | 0.625420i | \(-0.784928\pi\) |
0.625420 | + | 0.780288i | \(0.284928\pi\) | |||||||
\(318\) | −14.5858 | + | 20.6274i | −0.817930 | + | 1.15673i | ||||
\(319\) | 6.58579 | − | 6.58579i | 0.368733 | − | 0.368733i | ||||
\(320\) | −10.3431 | − | 10.3431i | −0.578199 | − | 0.578199i | ||||
\(321\) | −8.24264 | + | 1.41421i | −0.460059 | + | 0.0789337i | ||||
\(322\) | − | 5.41421i | − | 0.301722i | ||||||
\(323\) | 24.4853 | + | 24.4853i | 1.36240 | + | 1.36240i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.85786 | − | 1.17157i | −0.324936 | − | 0.0649872i | ||||
\(326\) | − | 13.5147i | − | 0.748511i | ||||||
\(327\) | 13.8995 | − | 19.6569i | 0.768644 | − | 1.08703i | ||||
\(328\) | −32.9706 | −1.82049 | ||||||||
\(329\) | 8.65685 | 0.477268 | ||||||||
\(330\) | 7.31371 | + | 5.17157i | 0.402606 | + | 0.284686i | ||||
\(331\) | 2.65685 | + | 2.65685i | 0.146034 | + | 0.146034i | 0.776344 | − | 0.630310i | \(-0.217072\pi\) |
−0.630310 | + | 0.776344i | \(0.717072\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.55635 | − | 13.7279i | 0.359286 | − | 0.752285i | ||||
\(334\) | 13.8995 | 0.760547 | ||||||||
\(335\) | −13.1127 | −0.716423 | ||||||||
\(336\) | −5.65685 | − | 4.00000i | −0.308607 | − | 0.218218i | ||||
\(337\) | − | 7.14214i | − | 0.389057i | −0.980897 | − | 0.194528i | \(-0.937682\pi\) | ||
0.980897 | − | 0.194528i | \(-0.0623177\pi\) | |||||||
\(338\) | 17.0000 | − | 7.00000i | 0.924678 | − | 0.380750i | ||||
\(339\) | −7.12132 | + | 1.22183i | −0.386777 | + | 0.0663604i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.6569i | 1.06448i | ||||||||
\(342\) | −34.6274 | + | 12.2426i | −1.87244 | + | 0.662006i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | −9.31371 | + | 9.31371i | −0.502162 | + | 0.502162i | ||||
\(345\) | −9.89949 | − | 7.00000i | −0.532971 | − | 0.376867i | ||||
\(346\) | 18.2426 | − | 18.2426i | 0.980730 | − | 0.980730i | ||||
\(347\) | 6.00000i | 0.322097i | 0.986947 | + | 0.161048i | \(0.0514875\pi\) | ||||
−0.986947 | + | 0.161048i | \(0.948512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.9497 | − | 22.9497i | 1.22847 | − | 1.22847i | 0.263930 | − | 0.964542i | \(-0.414981\pi\) |
0.964542 | − | 0.263930i | \(-0.0850188\pi\) | |||||||
\(350\) | −2.34315 | −0.125246 | ||||||||
\(351\) | −17.8284 | + | 5.75736i | −0.951611 | + | 0.307305i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.31371 | − | 5.31371i | 0.282820 | − | 0.282820i | −0.551413 | − | 0.834233i | \(-0.685911\pi\) |
0.834233 | + | 0.551413i | \(0.185911\pi\) | |||||||
\(354\) | 0.828427 | + | 4.82843i | 0.0440304 | + | 0.256628i | ||||
\(355\) | − | 7.12994i | − | 0.378418i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.65685 | + | 4.00000i | 0.299392 | + | 0.211702i | ||||
\(358\) | 18.1716 | − | 18.1716i | 0.960397 | − | 0.960397i | ||||
\(359\) | −11.1716 | − | 11.1716i | −0.589613 | − | 0.589613i | 0.347914 | − | 0.937527i | \(-0.386890\pi\) |
−0.937527 | + | 0.347914i | \(0.886890\pi\) | |||||||
\(360\) | −14.6274 | + | 5.17157i | −0.770933 | + | 0.272566i | ||||
\(361\) | 55.9411i | 2.94427i | ||||||||
\(362\) | 2.00000 | + | 2.00000i | 0.105118 | + | 0.105118i | ||||
\(363\) | −11.9497 | + | 2.05025i | −0.627199 | + | 0.107610i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 10.6569i | − | 0.557805i | ||||||
\(366\) | 11.7990 | + | 8.34315i | 0.616743 | + | 0.436103i | ||||
\(367\) | −33.6985 | −1.75905 | −0.879523 | − | 0.475856i | \(-0.842138\pi\) | ||||
−0.879523 | + | 0.475856i | \(0.842138\pi\) | |||||||
\(368\) | −15.3137 | −0.798282 | ||||||||
\(369\) | −15.0711 | + | 31.5563i | −0.784568 | + | 1.64276i | ||||
\(370\) | 9.27208 | + | 9.27208i | 0.482032 | + | 0.482032i | ||||
\(371\) | 7.29289 | + | 7.29289i | 0.378628 | + | 0.378628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6274 | 1.17160 | 0.585802 | − | 0.810454i | \(-0.300780\pi\) | ||||
0.585802 | + | 0.810454i | \(0.300780\pi\) | |||||||
\(374\) | −11.3137 | −0.585018 | ||||||||
\(375\) | −12.1716 | + | 17.2132i | −0.628537 | + | 0.888886i | ||||
\(376\) | − | 24.4853i | − | 1.26273i | ||||||
\(377\) | −16.4645 | − | 3.29289i | −0.847963 | − | 0.169593i | ||||
\(378\) | −6.41421 | + | 3.58579i | −0.329912 | + | 0.184433i | ||||
\(379\) | −7.41421 | − | 7.41421i | −0.380843 | − | 0.380843i | 0.490563 | − | 0.871406i | \(-0.336791\pi\) |
−0.871406 | + | 0.490563i | \(0.836791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.41421 | + | 0.585786i | −0.174915 | + | 0.0300107i | ||||
\(382\) | 13.3137 | + | 13.3137i | 0.681189 | + | 0.681189i | ||||
\(383\) | 25.8995 | − | 25.8995i | 1.32340 | − | 1.32340i | 0.412399 | − | 0.911003i | \(-0.364691\pi\) |
0.911003 | − | 0.412399i | \(-0.135309\pi\) | |||||||
\(384\) | −11.3137 | + | 16.0000i | −0.577350 | + | 0.816497i | ||||
\(385\) | 2.58579 | − | 2.58579i | 0.131784 | − | 0.131784i | ||||
\(386\) | − | 24.4853i | − | 1.24627i | ||||||
\(387\) | 4.65685 | + | 13.1716i | 0.236721 | + | 0.669549i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.17157 | −0.0594011 | −0.0297006 | − | 0.999559i | \(-0.509455\pi\) | ||||
−0.0297006 | + | 0.999559i | \(0.509455\pi\) | |||||||
\(390\) | 0.443651 | − | 16.1421i | 0.0224651 | − | 0.817389i | ||||
\(391\) | 15.3137 | 0.774448 | ||||||||
\(392\) | −2.00000 | + | 2.00000i | −0.101015 | + | 0.101015i | ||||
\(393\) | 8.65685 | − | 1.48528i | 0.436681 | − | 0.0749225i | ||||
\(394\) | − | 5.31371i | − | 0.267701i | ||||||
\(395\) | −0.221825 | + | 0.221825i | −0.0111612 | + | 0.0111612i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.6066 | + | 24.6066i | −1.23497 | + | 1.23497i | −0.272938 | + | 0.962032i | \(0.587996\pi\) |
−0.962032 | + | 0.272938i | \(0.912004\pi\) | |||||||
\(398\) | −6.34315 | − | 6.34315i | −0.317953 | − | 0.317953i | ||||
\(399\) | 2.53553 | + | 14.7782i | 0.126935 | + | 0.739834i | ||||
\(400\) | 6.62742i | 0.331371i | ||||||||
\(401\) | −18.0711 | − | 18.0711i | −0.902426 | − | 0.902426i | 0.0932195 | − | 0.995646i | \(-0.470284\pi\) |
−0.995646 | + | 0.0932195i | \(0.970284\pi\) | |||||||
\(402\) | 2.97056 | + | 17.3137i | 0.148158 | + | 0.863529i | ||||
\(403\) | 29.4853 | − | 19.6569i | 1.46877 | − | 0.979178i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.73654 | + | 16.3640i | −0.0862896 | + | 0.813132i | ||||
\(406\) | −6.58579 | −0.326847 | ||||||||
\(407\) | 10.1421 | 0.502727 | ||||||||
\(408\) | 11.3137 | − | 16.0000i | 0.560112 | − | 0.792118i | ||||
\(409\) | 10.3640 | + | 10.3640i | 0.512465 | + | 0.512465i | 0.915281 | − | 0.402816i | \(-0.131969\pi\) |
−0.402816 | + | 0.915281i | \(0.631969\pi\) | |||||||
\(410\) | −21.3137 | − | 21.3137i | −1.05261 | − | 1.05261i | ||||
\(411\) | 5.07107 | − | 7.17157i | 0.250137 | − | 0.353748i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.00000 | 0.0984136 | ||||||||
\(414\) | −7.00000 | + | 14.6569i | −0.344031 | + | 0.720345i | ||||
\(415\) | 1.82843i | 0.0897540i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.928932 | + | 5.41421i | 0.0454900 | + | 0.265135i | ||||
\(418\) | −17.3137 | − | 17.3137i | −0.846841 | − | 0.846841i | ||||
\(419\) | 28.6274i | 1.39854i | 0.714857 | + | 0.699270i | \(0.246492\pi\) | ||||
−0.714857 | + | 0.699270i | \(0.753508\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(422\) | −0.514719 | + | 0.514719i | −0.0250561 | + | 0.0250561i | ||||
\(423\) | −23.4350 | − | 11.1924i | −1.13945 | − | 0.544193i | ||||
\(424\) | 20.6274 | − | 20.6274i | 1.00176 | − | 1.00176i | ||||
\(425\) | − | 6.62742i | − | 0.321477i | ||||||
\(426\) | −9.41421 | + | 1.61522i | −0.456120 | + | 0.0782578i | ||||
\(427\) | 4.17157 | − | 4.17157i | 0.201877 | − | 0.201877i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.58579 | − | 9.07107i | −0.414526 | − | 0.437955i | ||||
\(430\) | −12.0416 | −0.580699 | ||||||||
\(431\) | −1.48528 | + | 1.48528i | −0.0715435 | + | 0.0715435i | −0.741973 | − | 0.670430i | \(-0.766110\pi\) |
0.670430 | + | 0.741973i | \(0.266110\pi\) | |||||||
\(432\) | 10.1421 | + | 18.1421i | 0.487964 | + | 0.872864i | ||||
\(433\) | 8.58579i | 0.412607i | 0.978488 | + | 0.206303i | \(0.0661433\pi\) | ||||
−0.978488 | + | 0.206303i | \(0.933857\pi\) | |||||||
\(434\) | 9.82843 | − | 9.82843i | 0.471780 | − | 0.471780i | ||||
\(435\) | −8.51472 | + | 12.0416i | −0.408250 | + | 0.577352i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.4350 | + | 23.4350i | 1.12105 | + | 1.12105i | ||||
\(438\) | −14.0711 | + | 2.41421i | −0.672342 | + | 0.115356i | ||||
\(439\) | 21.2132i | 1.01245i | 0.862401 | + | 0.506225i | \(0.168960\pi\) | ||||
−0.862401 | + | 0.506225i | \(0.831040\pi\) | |||||||
\(440\) | −7.31371 | − | 7.31371i | −0.348667 | − | 0.348667i | ||||
\(441\) | 1.00000 | + | 2.82843i | 0.0476190 | + | 0.134687i | ||||
\(442\) | 11.3137 | + | 16.9706i | 0.538138 | + | 0.807207i | ||||
\(443\) | 18.6569i | 0.886414i | 0.896419 | + | 0.443207i | \(0.146159\pi\) | ||||
−0.896419 | + | 0.443207i | \(0.853841\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.1716 | 1.24065 | ||||||||
\(446\) | 7.55635 | 0.357804 | ||||||||
\(447\) | −8.48528 | − | 6.00000i | −0.401340 | − | 0.283790i | ||||
\(448\) | 5.65685 | + | 5.65685i | 0.267261 | + | 0.267261i | ||||
\(449\) | −15.5858 | − | 15.5858i | −0.735539 | − | 0.735539i | 0.236172 | − | 0.971711i | \(-0.424107\pi\) |
−0.971711 | + | 0.236172i | \(0.924107\pi\) | |||||||
\(450\) | 6.34315 | + | 3.02944i | 0.299019 | + | 0.142809i | ||||
\(451\) | −23.3137 | −1.09780 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.7990 | + | 12.5858i | 0.836269 | + | 0.591332i | ||||
\(454\) | − | 30.1421i | − | 1.41464i | ||||||
\(455\) | −6.46447 | − | 1.29289i | −0.303059 | − | 0.0606118i | ||||
\(456\) | 41.7990 | − | 7.17157i | 1.95742 | − | 0.335840i | ||||
\(457\) | −10.8284 | − | 10.8284i | −0.506532 | − | 0.506532i | 0.406928 | − | 0.913460i | \(-0.366600\pi\) |
−0.913460 | + | 0.406928i | \(0.866600\pi\) | |||||||
\(458\) | − | 20.9706i | − | 0.979890i | ||||||
\(459\) | −10.1421 | − | 18.1421i | −0.473394 | − | 0.846802i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.4853 | + | 18.4853i | −0.860945 | + | 0.860945i | −0.991448 | − | 0.130503i | \(-0.958341\pi\) |
0.130503 | + | 0.991448i | \(0.458341\pi\) | |||||||
\(462\) | −4.00000 | − | 2.82843i | −0.186097 | − | 0.131590i | ||||
\(463\) | 14.6569 | − | 14.6569i | 0.681162 | − | 0.681162i | −0.279100 | − | 0.960262i | \(-0.590036\pi\) |
0.960262 | + | 0.279100i | \(0.0900362\pi\) | |||||||
\(464\) | 18.6274i | 0.864756i | ||||||||
\(465\) | −5.26346 | − | 30.6777i | −0.244087 | − | 1.42264i | ||||
\(466\) | −6.31371 | + | 6.31371i | −0.292477 | + | 0.292477i | ||||
\(467\) | −9.21320 | −0.426336 | −0.213168 | − | 0.977016i | \(-0.568378\pi\) | ||||
−0.213168 | + | 0.977016i | \(0.568378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.17157 | 0.331152 | ||||||||
\(470\) | 15.8284 | − | 15.8284i | 0.730111 | − | 0.730111i | ||||
\(471\) | −2.48528 | − | 14.4853i | −0.114516 | − | 0.667447i | ||||
\(472\) | − | 5.65685i | − | 0.260378i | ||||||
\(473\) | −6.58579 | + | 6.58579i | −0.302815 | + | 0.302815i | ||||
\(474\) | 0.343146 | + | 0.242641i | 0.0157612 | + | 0.0111449i | ||||
\(475\) | 10.1421 | − | 10.1421i | 0.465353 | − | 0.465353i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.3137 | − | 29.1716i | −0.472232 | − | 1.33567i | ||||
\(478\) | 8.14214i | 0.372413i | ||||||||
\(479\) | −16.0208 | − | 16.0208i | −0.732010 | − | 0.732010i | 0.239008 | − | 0.971018i | \(-0.423178\pi\) |
−0.971018 | + | 0.239008i | \(0.923178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1421 | − | 15.2132i | −0.462442 | − | 0.693662i | ||||
\(482\) | 10.5858i | 0.482169i | ||||||||
\(483\) | 5.41421 | + | 3.82843i | 0.246355 | + | 0.174199i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.5147 | 1.02234 | ||||||||
\(486\) | 22.0000 | − | 1.41421i | 0.997940 | − | 0.0641500i | ||||
\(487\) | −25.8284 | − | 25.8284i | −1.17040 | − | 1.17040i | −0.982115 | − | 0.188283i | \(-0.939708\pi\) |
−0.188283 | − | 0.982115i | \(-0.560292\pi\) | |||||||
\(488\) | −11.7990 | − | 11.7990i | −0.534115 | − | 0.534115i | ||||
\(489\) | 13.5147 | + | 9.55635i | 0.611157 | + | 0.432153i | ||||
\(490\) | −2.58579 | −0.116814 | ||||||||
\(491\) | −4.97056 | −0.224318 | −0.112159 | − | 0.993690i | \(-0.535777\pi\) | ||||
−0.112159 | + | 0.993690i | \(0.535777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 18.6274i | − | 0.838937i | ||||||
\(494\) | −8.65685 | + | 43.2843i | −0.389490 | + | 1.94745i | ||||
\(495\) | −10.3431 | + | 3.65685i | −0.464890 | + | 0.164363i | ||||
\(496\) | −27.7990 | − | 27.7990i | −1.24821 | − | 1.24821i | ||||
\(497\) | 3.89949i | 0.174916i | ||||||||
\(498\) | 2.41421 | − | 0.414214i | 0.108183 | − | 0.0185614i | ||||
\(499\) | −14.0000 | − | 14.0000i | −0.626726 | − | 0.626726i | 0.320517 | − | 0.947243i | \(-0.396143\pi\) |
−0.947243 | + | 0.320517i | \(0.896143\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.82843 | + | 13.8995i | −0.439102 | + | 0.620984i | ||||
\(502\) | −14.9706 | + | 14.9706i | −0.668169 | + | 0.668169i | ||||
\(503\) | 11.0711i | 0.493635i | 0.969062 | + | 0.246817i | \(0.0793847\pi\) | ||||
−0.969062 | + | 0.246817i | \(0.920615\pi\) | |||||||
\(504\) | 8.00000 | − | 2.82843i | 0.356348 | − | 0.125988i | ||||
\(505\) | 4.72792 | − | 4.72792i | 0.210390 | − | 0.210390i | ||||
\(506\) | −10.8284 | −0.481382 | ||||||||
\(507\) | −5.02082 | + | 21.9497i | −0.222982 | + | 0.974823i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.8787 | + | 21.8787i | −0.969755 | + | 0.969755i | −0.999556 | − | 0.0298004i | \(-0.990513\pi\) |
0.0298004 | + | 0.999556i | \(0.490513\pi\) | |||||||
\(510\) | 17.6569 | − | 3.02944i | 0.781859 | − | 0.134146i | ||||
\(511\) | 5.82843i | 0.257834i | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 12.2426 | − | 43.2843i | 0.540526 | − | 1.91105i | ||||
\(514\) | 0.142136 | − | 0.142136i | 0.00626933 | − | 0.00626933i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 17.3137i | − | 0.761456i | ||||||
\(518\) | −5.07107 | − | 5.07107i | −0.222810 | − | 0.222810i | ||||
\(519\) | 5.34315 | + | 31.1421i | 0.234538 | + | 1.36699i | ||||
\(520\) | −3.65685 | + | 18.2843i | −0.160364 | + | 0.801818i | ||||
\(521\) | − | 40.2843i | − | 1.76489i | −0.470419 | − | 0.882443i | \(-0.655897\pi\) | ||
0.470419 | − | 0.882443i | \(-0.344103\pi\) | |||||||
\(522\) | 17.8284 | + | 8.51472i | 0.780329 | + | 0.372679i | ||||
\(523\) | 20.7279 | 0.906369 | 0.453184 | − | 0.891417i | \(-0.350288\pi\) | ||||
0.453184 | + | 0.891417i | \(0.350288\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.65685 | − | 2.34315i | 0.0723110 | − | 0.102263i | ||||
\(526\) | −10.5147 | − | 10.5147i | −0.458464 | − | 0.458464i | ||||
\(527\) | 27.7990 | + | 27.7990i | 1.21094 | + | 1.21094i | ||||
\(528\) | −8.00000 | + | 11.3137i | −0.348155 | + | 0.492366i | ||||
\(529\) | −8.34315 | −0.362745 | ||||||||
\(530\) | 26.6690 | 1.15843 | ||||||||
\(531\) | −5.41421 | − | 2.58579i | −0.234957 | − | 0.112214i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.3137 | + | 34.9706i | 1.00983 | + | 1.51474i | ||||
\(534\) | −5.92893 | − | 34.5563i | −0.256570 | − | 1.49540i | ||||
\(535\) | 6.24264 | + | 6.24264i | 0.269893 | + | 0.269893i | ||||
\(536\) | − | 20.2843i | − | 0.876147i | ||||||
\(537\) | 5.32233 | + | 31.0208i | 0.229676 | + | 1.33865i | ||||
\(538\) | 27.6985 | + | 27.6985i | 1.19417 | + | 1.19417i | ||||
\(539\) | −1.41421 | + | 1.41421i | −0.0609145 | + | 0.0609145i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0710678 | + | 0.0710678i | −0.00305544 | + | 0.00305544i | −0.708633 | − | 0.705577i | \(-0.750688\pi\) |
0.705577 | + | 0.708633i | \(0.250688\pi\) | |||||||
\(542\) | 15.7990i | 0.678625i | ||||||||
\(543\) | −3.41421 | + | 0.585786i | −0.146518 | + | 0.0251385i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.4142 | −1.08863 | ||||||||
\(546\) | −0.242641 | + | 8.82843i | −0.0103841 | + | 0.377822i | ||||
\(547\) | −3.34315 | −0.142943 | −0.0714713 | − | 0.997443i | \(-0.522769\pi\) | ||||
−0.0714713 | + | 0.997443i | \(0.522769\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.6863 | + | 5.89949i | −0.712154 | + | 0.251784i | ||||
\(550\) | 4.68629i | 0.199824i | ||||||||
\(551\) | 28.5061 | − | 28.5061i | 1.21440 | − | 1.21440i | ||||
\(552\) | 10.8284 | − | 15.3137i | 0.460888 | − | 0.651795i | ||||
\(553\) | 0.121320 | − | 0.121320i | 0.00515907 | − | 0.00515907i | ||||
\(554\) | 19.4853 | + | 19.4853i | 0.827850 | + | 0.827850i | ||||
\(555\) | −15.8284 | + | 2.71573i | −0.671879 | + | 0.115276i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.7990 | + | 11.7990i | 0.499939 | + | 0.499939i | 0.911419 | − | 0.411480i | \(-0.134988\pi\) |
−0.411480 | + | 0.911419i | \(0.634988\pi\) | |||||||
\(558\) | −39.3137 | + | 13.8995i | −1.66428 | + | 0.588413i | ||||
\(559\) | 16.4645 | + | 3.29289i | 0.696373 | + | 0.139275i | ||||
\(560\) | 7.31371i | 0.309061i | ||||||||
\(561\) | 8.00000 | − | 11.3137i | 0.337760 | − | 0.477665i | ||||
\(562\) | −34.2843 | −1.44619 | ||||||||
\(563\) | −13.0711 | −0.550880 | −0.275440 | − | 0.961318i | \(-0.588824\pi\) | ||||
−0.275440 | + | 0.961318i | \(0.588824\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.39340 | + | 5.39340i | 0.226902 | + | 0.226902i | ||||
\(566\) | −1.17157 | − | 1.17157i | −0.0492449 | − | 0.0492449i | ||||
\(567\) | 0.949747 | − | 8.94975i | 0.0398856 | − | 0.375854i | ||||
\(568\) | 11.0294 | 0.462785 | ||||||||
\(569\) | 9.48528 | 0.397644 | 0.198822 | − | 0.980036i | \(-0.436288\pi\) | ||||
0.198822 | + | 0.980036i | \(0.436288\pi\) | |||||||
\(570\) | 31.6569 | + | 22.3848i | 1.32596 | + | 0.937595i | ||||
\(571\) | − | 14.4558i | − | 0.604958i | −0.953156 | − | 0.302479i | \(-0.902186\pi\) | ||
0.953156 | − | 0.302479i | \(-0.0978143\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.7279 | + | 3.89949i | −0.949473 | + | 0.162904i | ||||
\(574\) | 11.6569 | + | 11.6569i | 0.486548 | + | 0.486548i | ||||
\(575\) | − | 6.34315i | − | 0.264527i | ||||||
\(576\) | −8.00000 | − | 22.6274i | −0.333333 | − | 0.942809i | ||||
\(577\) | −9.17157 | − | 9.17157i | −0.381818 | − | 0.381818i | 0.489939 | − | 0.871757i | \(-0.337019\pi\) |
−0.871757 | + | 0.489939i | \(0.837019\pi\) | |||||||
\(578\) | 1.00000 | − | 1.00000i | 0.0415945 | − | 0.0415945i | ||||
\(579\) | 24.4853 | + | 17.3137i | 1.01757 | + | 0.719533i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.00000i | − | 0.0414870i | ||||||
\(582\) | −5.10051 | − | 29.7279i | −0.211423 | − | 1.23226i | ||||
\(583\) | 14.5858 | − | 14.5858i | 0.604082 | − | 0.604082i | ||||
\(584\) | 16.4853 | 0.682166 | ||||||||
\(585\) | 15.8284 | + | 11.8579i | 0.654425 | + | 0.490262i | ||||
\(586\) | −6.10051 | −0.252010 | ||||||||
\(587\) | −7.19239 | + | 7.19239i | −0.296862 | + | 0.296862i | −0.839783 | − | 0.542922i | \(-0.817318\pi\) |
0.542922 | + | 0.839783i | \(0.317318\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 85.0833i | 3.50579i | ||||||||
\(590\) | 3.65685 | − | 3.65685i | 0.150550 | − | 0.150550i | ||||
\(591\) | 5.31371 | + | 3.75736i | 0.218577 | + | 0.154557i | ||||
\(592\) | −14.3431 | + | 14.3431i | −0.589500 | + | 0.589500i | ||||
\(593\) | −17.0919 | − | 17.0919i | −0.701880 | − | 0.701880i | 0.262934 | − | 0.964814i | \(-0.415310\pi\) |
−0.964814 | + | 0.262934i | \(0.915310\pi\) | |||||||
\(594\) | 7.17157 | + | 12.8284i | 0.294253 | + | 0.526357i | ||||
\(595\) | − | 7.31371i | − | 0.299833i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.8284 | − | 1.85786i | 0.443178 | − | 0.0760373i | ||||
\(598\) | 10.8284 | + | 16.2426i | 0.442807 | + | 0.664211i | ||||
\(599\) | − | 34.4558i | − | 1.40783i | −0.710285 | − | 0.703914i | \(-0.751434\pi\) | ||
0.710285 | − | 0.703914i | \(-0.248566\pi\) | |||||||
\(600\) | −6.62742 | − | 4.68629i | −0.270563 | − | 0.191317i | ||||
\(601\) | −14.4853 | −0.590867 | −0.295433 | − | 0.955363i | \(-0.595464\pi\) | ||||
−0.295433 | + | 0.955363i | \(0.595464\pi\) | |||||||
\(602\) | 6.58579 | 0.268417 | ||||||||
\(603\) | −19.4142 | − | 9.27208i | −0.790608 | − | 0.377588i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.05025 | + | 9.05025i | 0.367945 | + | 0.367945i | ||||
\(606\) | −7.31371 | − | 5.17157i | −0.297099 | − | 0.210081i | ||||
\(607\) | 3.17157 | 0.128730 | 0.0643651 | − | 0.997926i | \(-0.479498\pi\) | ||||
0.0643651 | + | 0.997926i | \(0.479498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.65685 | − | 6.58579i | 0.188705 | − | 0.266870i | ||||
\(610\) | − | 15.2548i | − | 0.617650i | ||||||
\(611\) | −25.9706 | + | 17.3137i | −1.05066 | + | 0.700438i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2426 | + | 19.2426i | 0.777203 | + | 0.777203i | 0.979354 | − | 0.202151i | \(-0.0647933\pi\) |
−0.202151 | + | 0.979354i | \(0.564793\pi\) | |||||||
\(614\) | − | 16.7279i | − | 0.675084i | ||||||
\(615\) | 36.3848 | − | 6.24264i | 1.46718 | − | 0.251728i | ||||
\(616\) | 4.00000 | + | 4.00000i | 0.161165 | + | 0.161165i | ||||
\(617\) | −32.3137 | + | 32.3137i | −1.30090 | + | 1.30090i | −0.373116 | + | 0.927785i | \(0.621711\pi\) |
−0.927785 | + | 0.373116i | \(0.878289\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.89949 | − | 3.89949i | 0.156734 | − | 0.156734i | −0.624384 | − | 0.781118i | \(-0.714650\pi\) |
0.781118 | + | 0.624384i | \(0.214650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.70711 | − | 17.3640i | −0.389533 | − | 0.696792i | ||||
\(622\) | −0.443651 | + | 0.443651i | −0.0177888 | + | 0.0177888i | ||||
\(623\) | −14.3137 | −0.573467 | ||||||||
\(624\) | 24.9706 | + | 0.686292i | 0.999623 | + | 0.0274736i | ||||
\(625\) | 13.9706 | 0.558823 | ||||||||
\(626\) | −16.1421 | + | 16.1421i | −0.645169 | + | 0.645169i | ||||
\(627\) | 29.5563 | − | 5.07107i | 1.18037 | − | 0.202519i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.3431 | − | 14.3431i | 0.571899 | − | 0.571899i | ||||
\(630\) | 7.00000 | + | 3.34315i | 0.278887 | + | 0.133194i | ||||
\(631\) | 9.34315 | − | 9.34315i | 0.371945 | − | 0.371945i | −0.496240 | − | 0.868185i | \(-0.665287\pi\) |
0.868185 | + | 0.496240i | \(0.165287\pi\) | |||||||
\(632\) | −0.343146 | − | 0.343146i | −0.0136496 | − | 0.0136496i | ||||
\(633\) | −0.150758 | − | 0.878680i | −0.00599208 | − | 0.0349244i | ||||
\(634\) | − | 5.51472i | − | 0.219017i | ||||||
\(635\) | 2.58579 | + | 2.58579i | 0.102614 | + | 0.102614i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.53553 | + | 0.707107i | 0.140083 | + | 0.0280166i | ||||
\(638\) | 13.1716i | 0.521468i | ||||||||
\(639\) | 5.04163 | − | 10.5563i | 0.199444 | − | 0.417603i | ||||
\(640\) | 20.6863 | 0.817697 | ||||||||
\(641\) | 31.0000 | 1.22443 | 0.612213 | − | 0.790693i | \(-0.290279\pi\) | ||||
0.612213 | + | 0.790693i | \(0.290279\pi\) | |||||||
\(642\) | 6.82843 | − | 9.65685i | 0.269497 | − | 0.381126i | ||||
\(643\) | 19.0711 | + | 19.0711i | 0.752089 | + | 0.752089i | 0.974869 | − | 0.222779i | \(-0.0715130\pi\) |
−0.222779 | + | 0.974869i | \(0.571513\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.51472 | − | 12.0416i | 0.335267 | − | 0.474139i | ||||
\(646\) | −48.9706 | −1.92672 | ||||||||
\(647\) | −14.1005 | −0.554348 | −0.277174 | − | 0.960820i | \(-0.589398\pi\) | ||||
−0.277174 | + | 0.960820i | \(0.589398\pi\) | |||||||
\(648\) | −25.3137 | − | 2.68629i | −0.994416 | − | 0.105527i | ||||
\(649\) | − | 4.00000i | − | 0.157014i | ||||||
\(650\) | 7.02944 | − | 4.68629i | 0.275717 | − | 0.183811i | ||||
\(651\) | 2.87868 | + | 16.7782i | 0.112824 | + | 0.657589i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.4853i | 1.11472i | 0.830273 | + | 0.557358i | \(0.188185\pi\) | ||||
−0.830273 | + | 0.557358i | \(0.811815\pi\) | |||||||
\(654\) | 5.75736 | + | 33.5563i | 0.225131 | + | 1.31216i | ||||
\(655\) | −6.55635 | − | 6.55635i | −0.256178 | − | 0.256178i | ||||
\(656\) | 32.9706 | − | 32.9706i | 1.28728 | − | 1.28728i | ||||
\(657\) | 7.53553 | − | 15.7782i | 0.293989 | − | 0.615565i | ||||
\(658\) | −8.65685 | + | 8.65685i | −0.337479 | + | 0.337479i | ||||
\(659\) | − | 5.97056i | − | 0.232580i | −0.993215 | − | 0.116290i | \(-0.962900\pi\) | ||
0.993215 | − | 0.116290i | \(-0.0371002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.8492 | + | 28.8492i | −1.12211 | + | 1.12211i | −0.130681 | + | 0.991424i | \(0.541716\pi\) |
−0.991424 | + | 0.130681i | \(0.958284\pi\) | |||||||
\(662\) | −5.31371 | −0.206523 | ||||||||
\(663\) | −24.9706 | − | 0.686292i | −0.969776 | − | 0.0266534i | ||||
\(664\) | −2.82843 | −0.109764 | ||||||||
\(665\) | 11.1924 | − | 11.1924i | 0.434022 | − | 0.434022i | ||||
\(666\) | 7.17157 | + | 20.2843i | 0.277893 | + | 0.786000i | ||||
\(667\) | − | 17.8284i | − | 0.690319i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.34315 | + | 7.55635i | −0.206578 | + | 0.292145i | ||||
\(670\) | 13.1127 | − | 13.1127i | 0.506588 | − | 0.506588i | ||||
\(671\) | −8.34315 | − | 8.34315i | −0.322084 | − | 0.322084i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 27.0000i | − | 1.04077i | −0.853931 | − | 0.520387i | \(-0.825788\pi\) | ||
0.853931 | − | 0.520387i | \(-0.174212\pi\) | |||||||
\(674\) | 7.14214 | + | 7.14214i | 0.275105 | + | 0.275105i | ||||
\(675\) | −7.51472 | + | 4.20101i | −0.289242 | + | 0.161697i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.58579i | − | 0.0993798i | −0.998765 | − | 0.0496899i | \(-0.984177\pi\) | ||
0.998765 | − | 0.0496899i | \(-0.0158233\pi\) | |||||||
\(678\) | 5.89949 | − | 8.34315i | 0.226569 | − | 0.320417i | ||||
\(679\) | −12.3137 | −0.472557 | ||||||||
\(680\) | −20.6863 | −0.793283 | ||||||||
\(681\) | 30.1421 | + | 21.3137i | 1.15505 | + | 0.816743i | ||||
\(682\) | −19.6569 | − | 19.6569i | −0.752700 | − | 0.752700i | ||||
\(683\) | 27.7990 | + | 27.7990i | 1.06370 | + | 1.06370i | 0.997828 | + | 0.0658706i | \(0.0209825\pi\) |
0.0658706 | + | 0.997828i | \(0.479018\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.27208 | −0.354268 | ||||||||
\(686\) | 1.41421 | 0.0539949 | ||||||||
\(687\) | 20.9706 | + | 14.8284i | 0.800077 | + | 0.565740i | ||||
\(688\) | − | 18.6274i | − | 0.710164i | ||||||
\(689\) | −36.4645 | − | 7.29289i | −1.38919 | − | 0.277837i | ||||
\(690\) | 16.8995 | − | 2.89949i | 0.643353 | − | 0.110382i | ||||
\(691\) | −5.39340 | − | 5.39340i | −0.205175 | − | 0.205175i | 0.597038 | − | 0.802213i | \(-0.296344\pi\) |
−0.802213 | + | 0.597038i | \(0.796344\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.65685 | − | 2.00000i | 0.214886 | − | 0.0759737i | ||||
\(694\) | −6.00000 | − | 6.00000i | −0.227757 | − | 0.227757i | ||||
\(695\) | 4.10051 | − | 4.10051i | 0.155541 | − | 0.155541i | ||||
\(696\) | −18.6274 | − | 13.1716i | −0.706070 | − | 0.499267i | ||||
\(697\) | −32.9706 | + | 32.9706i | −1.24885 | + | 1.24885i | ||||
\(698\) | 45.8995i | 1.73732i | ||||||||
\(699\) | −1.84924 | − | 10.7782i | −0.0699448 | − | 0.407668i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.48528 | 0.358254 | 0.179127 | − | 0.983826i | \(-0.442673\pi\) | ||||
0.179127 | + | 0.983826i | \(0.442673\pi\) | |||||||
\(702\) | 12.0711 | − | 23.5858i | 0.455593 | − | 0.890188i | ||||
\(703\) | 43.8995 | 1.65570 | ||||||||
\(704\) | 11.3137 | − | 11.3137i | 0.426401 | − | 0.426401i | ||||
\(705\) | 4.63604 | + | 27.0208i | 0.174603 | + | 1.01766i | ||||
\(706\) | 10.6274i | 0.399968i | ||||||||
\(707\) | −2.58579 | + | 2.58579i | −0.0972485 | + | 0.0972485i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.6985 | − | 27.6985i | 1.04024 | − | 1.04024i | 0.0410827 | − | 0.999156i | \(-0.486919\pi\) |
0.999156 | − | 0.0410827i | \(-0.0130807\pi\) | |||||||
\(710\) | 7.12994 | + | 7.12994i | 0.267582 | + | 0.267582i | ||||
\(711\) | −0.485281 | + | 0.171573i | −0.0181995 | + | 0.00643449i | ||||
\(712\) | 40.4853i | 1.51725i | ||||||||
\(713\) | 26.6066 | + | 26.6066i | 0.996425 | + | 0.996425i | ||||
\(714\) | −9.65685 | + | 1.65685i | −0.361399 | + | 0.0620062i | ||||
\(715\) | −2.58579 | + | 12.9289i | −0.0967029 | + | 0.483515i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.14214 | − | 5.75736i | −0.304074 | − | 0.215013i | ||||
\(718\) | 22.3431 | 0.833839 | ||||||||
\(719\) | −30.3848 | −1.13316 | −0.566580 | − | 0.824006i | \(-0.691734\pi\) | ||||
−0.566580 | + | 0.824006i | \(0.691734\pi\) | |||||||
\(720\) | 9.45584 | − | 19.7990i | 0.352399 | − | 0.737865i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −55.9411 | − | 55.9411i | −2.08191 | − | 2.08191i | ||||
\(723\) | −10.5858 | − | 7.48528i | −0.393690 | − | 0.278381i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.71573 | −0.286555 | ||||||||
\(726\) | 9.89949 | − | 14.0000i | 0.367405 | − | 0.519589i | ||||
\(727\) | 43.4558i | 1.61169i | 0.592128 | + | 0.805844i | \(0.298288\pi\) | ||||
−0.592128 | + | 0.805844i | \(0.701712\pi\) | |||||||
\(728\) | 2.00000 | − | 10.0000i | 0.0741249 | − | 0.370625i | ||||
\(729\) | −14.1421 | + | 23.0000i | −0.523783 | + | 0.851852i | ||||
\(730\) | 10.6569 | + | 10.6569i | 0.394428 | + | 0.394428i | ||||
\(731\) | 18.6274i | 0.688960i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.1213 | + | 24.1213i | 0.890941 | + | 0.890941i | 0.994612 | − | 0.103670i | \(-0.0330587\pi\) |
−0.103670 | + | 0.994612i | \(0.533059\pi\) | |||||||
\(734\) | 33.6985 | − | 33.6985i | 1.24383 | − | 1.24383i | ||||
\(735\) | 1.82843 | − | 2.58579i | 0.0674426 | − | 0.0953782i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 14.3431i | − | 0.528337i | ||||||
\(738\) | −16.4853 | − | 46.6274i | −0.606832 | − | 1.71638i | ||||
\(739\) | −32.0416 | + | 32.0416i | −1.17867 | + | 1.17867i | −0.198587 | + | 0.980083i | \(0.563635\pi\) |
−0.980083 | + | 0.198587i | \(0.936365\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.1630 | − | 39.2635i | −1.36522 | − | 1.44238i | ||||
\(742\) | −14.5858 | −0.535461 | ||||||||
\(743\) | 30.2132 | − | 30.2132i | 1.10841 | − | 1.10841i | 0.115056 | − | 0.993359i | \(-0.463295\pi\) |
0.993359 | − | 0.115056i | \(-0.0367047\pi\) | |||||||
\(744\) | 47.4558 | − | 8.14214i | 1.73982 | − | 0.298505i | ||||
\(745\) | 10.9706i | 0.401930i | ||||||||
\(746\) | −22.6274 | + | 22.6274i | −0.828449 | + | 0.828449i | ||||
\(747\) | −1.29289 | + | 2.70711i | −0.0473045 | + | 0.0990479i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.41421 | − | 3.41421i | −0.124753 | − | 0.124753i | ||||
\(750\) | −5.04163 | − | 29.3848i | −0.184094 | − | 1.07298i | ||||
\(751\) | 4.37258i | 0.159558i | 0.996813 | + | 0.0797789i | \(0.0254214\pi\) | ||||
−0.996813 | + | 0.0797789i | \(0.974579\pi\) | |||||||
\(752\) | 24.4853 | + | 24.4853i | 0.892886 | + | 0.892886i | ||||
\(753\) | −4.38478 | − | 25.5563i | −0.159790 | − | 0.931325i | ||||
\(754\) | 19.7574 | − | 13.1716i | 0.719521 | − | 0.479680i | ||||
\(755\) | − | 23.0122i | − | 0.837499i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.3137 | −1.10177 | −0.550885 | − | 0.834581i | \(-0.685710\pi\) | ||||
−0.550885 | + | 0.834581i | \(0.685710\pi\) | |||||||
\(758\) | 14.8284 | 0.538593 | ||||||||
\(759\) | 7.65685 | − | 10.8284i | 0.277926 | − | 0.393047i | ||||
\(760\) | −31.6569 | − | 31.6569i | −1.14831 | − | 1.14831i | ||||
\(761\) | −7.15076 | − | 7.15076i | −0.259215 | − | 0.259215i | 0.565520 | − | 0.824735i | \(-0.308676\pi\) |
−0.824735 | + | 0.565520i | \(0.808676\pi\) | |||||||
\(762\) | 2.82843 | − | 4.00000i | 0.102463 | − | 0.144905i | ||||
\(763\) | 13.8995 | 0.503196 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.45584 | + | 19.7990i | −0.341877 | + | 0.715834i | ||||
\(766\) | 51.7990i | 1.87157i | ||||||||
\(767\) | −6.00000 | + | 4.00000i | −0.216647 | + | 0.144432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.36396 | + | 6.36396i | 0.229490 | + | 0.229490i | 0.812480 | − | 0.582989i | \(-0.198117\pi\) |
−0.582989 | + | 0.812480i | \(0.698117\pi\) | |||||||
\(770\) | 5.17157i | 0.186371i | ||||||||
\(771\) | 0.0416306 | + | 0.242641i | 0.00149929 | + | 0.00873849i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.14214 | − | 6.14214i | 0.220917 | − | 0.220917i | −0.587967 | − | 0.808885i | \(-0.700072\pi\) |
0.808885 | + | 0.587967i | \(0.200072\pi\) | |||||||
\(774\) | −17.8284 | − | 8.51472i | −0.640830 | − | 0.306055i | ||||
\(775\) | 11.5147 | − | 11.5147i | 0.413621 | − | 0.413621i | ||||
\(776\) | 34.8284i | 1.25027i | ||||||||
\(777\) | 8.65685 | − | 1.48528i | 0.310563 | − | 0.0532842i | ||||
\(778\) | 1.17157 | − | 1.17157i | 0.0420029 | − | 0.0420029i | ||||
\(779\) | −100.912 | −3.61554 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.79899 | 0.279070 | ||||||||
\(782\) | −15.3137 | + | 15.3137i | −0.547617 | + | 0.547617i | ||||
\(783\) | −21.1213 | + | 11.8076i | −0.754814 | + | 0.421970i | ||||
\(784\) | − | 4.00000i | − | 0.142857i | ||||||
\(785\) | −10.9706 | + | 10.9706i | −0.391556 | + | 0.391556i | ||||
\(786\) | −7.17157 | + | 10.1421i | −0.255802 | + | 0.361758i | ||||
\(787\) | 26.4645 | − | 26.4645i | 0.943356 | − | 0.943356i | −0.0551232 | − | 0.998480i | \(-0.517555\pi\) |
0.998480 | + | 0.0551232i | \(0.0175552\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.9497 | − | 3.07969i | 0.639028 | − | 0.109640i | ||||
\(790\) | − | 0.443651i | − | 0.0157844i | ||||||
\(791\) | −2.94975 | − | 2.94975i | −0.104881 | − | 0.104881i | ||||
\(792\) | −5.65685 | − | 16.0000i | −0.201008 | − | 0.568535i | ||||
\(793\) | −4.17157 | + | 20.8579i | −0.148137 | + | 0.740684i | ||||
\(794\) | − | 49.2132i | − | 1.74651i | ||||||
\(795\) | −18.8579 | + | 26.6690i | −0.668820 | + | 0.945854i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.7990 | −0.772160 | −0.386080 | − | 0.922465i | \(-0.626171\pi\) | ||||
−0.386080 | + | 0.922465i | \(0.626171\pi\) | |||||||
\(798\) | −17.3137 | − | 12.2426i | −0.612899 | − | 0.433385i | ||||
\(799\) | −24.4853 | − | 24.4853i | −0.866227 | − | 0.866227i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.7487 | + | 18.5061i | 1.36912 | + | 0.653881i | ||||
\(802\) | 36.1421 | 1.27622 | ||||||||
\(803\) | 11.6569 | 0.411361 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 7.00000i | − | 0.246718i | ||||||
\(806\) | −9.82843 | + | 49.1421i | −0.346192 | + | 1.73096i | ||||
\(807\) | −47.2843 | + | 8.11270i | −1.66449 | + | 0.285581i | ||||
\(808\) | 7.31371 | + | 7.31371i | 0.257295 | + | 0.257295i | ||||
\(809\) | 29.9706i | 1.05371i | 0.849956 | + | 0.526854i | \(0.176629\pi\) | ||||
−0.849956 | + | 0.526854i | \(0.823371\pi\) | |||||||
\(810\) | −14.6274 | − | 18.1005i | −0.513955 | − | 0.635987i | ||||
\(811\) | −20.2426 | − | 20.2426i | −0.710815 | − | 0.710815i | 0.255891 | − | 0.966706i | \(-0.417631\pi\) |
−0.966706 | + | 0.255891i | \(0.917631\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.7990 | − | 11.1716i | −0.554095 | − | 0.391804i | ||||
\(814\) | −10.1421 | + | 10.1421i | −0.355482 | + | 0.355482i | ||||
\(815\) | − | 17.4731i | − | 0.612056i | ||||||
\(816\) | 4.68629 | + | 27.3137i | 0.164053 | + | 0.956171i | ||||
\(817\) | −28.5061 | + | 28.5061i | −0.997302 | + | 0.997302i | ||||
\(818\) | −20.7279 | −0.724735 | ||||||||
\(819\) | −8.65685 | − | 6.48528i | −0.302495 | − | 0.226614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.7574 | − | 21.7574i | 0.759337 | − | 0.759337i | −0.216865 | − | 0.976202i | \(-0.569583\pi\) |
0.976202 | + | 0.216865i | \(0.0695830\pi\) | |||||||
\(822\) | 2.10051 | + | 12.2426i | 0.0732635 | + | 0.427011i | ||||
\(823\) | − | 11.3137i | − | 0.394371i | −0.980366 | − | 0.197186i | \(-0.936820\pi\) | ||
0.980366 | − | 0.197186i | \(-0.0631801\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.68629 | − | 3.31371i | −0.163156 | − | 0.115369i | ||||
\(826\) | −2.00000 | + | 2.00000i | −0.0695889 | + | 0.0695889i | ||||
\(827\) | −25.8701 | − | 25.8701i | −0.899590 | − | 0.899590i | 0.0958096 | − | 0.995400i | \(-0.469456\pi\) |
−0.995400 | + | 0.0958096i | \(0.969456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.8995i | 0.482749i | 0.970432 | + | 0.241375i | \(0.0775983\pi\) | ||||
−0.970432 | + | 0.241375i | \(0.922402\pi\) | |||||||
\(830\) | −1.82843 | − | 1.82843i | −0.0634656 | − | 0.0634656i | ||||
\(831\) | −33.2635 | + | 5.70711i | −1.15390 | + | 0.197977i | ||||
\(832\) | −28.2843 | − | 5.65685i | −0.980581 | − | 0.196116i | ||||
\(833\) | 4.00000i | 0.138592i | ||||||||
\(834\) | −6.34315 | − | 4.48528i | −0.219645 | − | 0.155313i | ||||
\(835\) | 17.9706 | 0.621897 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.8995 | − | 49.1421i | 0.480437 | − | 1.69860i | ||||
\(838\) | −28.6274 | − | 28.6274i | −0.988918 | − | 0.988918i | ||||
\(839\) | 5.21320 | + | 5.21320i | 0.179980 | + | 0.179980i | 0.791347 | − | 0.611367i | \(-0.209380\pi\) |
−0.611367 | + | 0.791347i | \(0.709380\pi\) | |||||||
\(840\) | −7.31371 | − | 5.17157i | −0.252347 | − | 0.178436i | ||||
\(841\) | 7.31371 | 0.252197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.2426 | − | 34.2843i | 0.834961 | − | 1.18081i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.9792 | − | 9.05025i | 0.756107 | − | 0.311338i | ||||
\(846\) | 34.6274 | − | 12.2426i | 1.19052 | − | 0.420911i | ||||
\(847\) | −4.94975 | − | 4.94975i | −0.170075 | − | 0.170075i | ||||
\(848\) | 41.2548i | 1.41670i | ||||||||
\(849\) | 2.00000 | − | 0.343146i | 0.0686398 | − | 0.0117767i | ||||
\(850\) | 6.62742 | + | 6.62742i | 0.227319 | + | 0.227319i | ||||
\(851\) | 13.7279 | − | 13.7279i | 0.470587 | − | 0.470587i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.0208 | + | 18.0208i | −0.617021 | + | 0.617021i | −0.944766 | − | 0.327745i | \(-0.893711\pi\) |
0.327745 | + | 0.944766i | \(0.393711\pi\) | |||||||
\(854\) | 8.34315i | 0.285497i | ||||||||
\(855\) | −44.7696 | + | 15.8284i | −1.53109 | + | 0.541321i | ||||
\(856\) | −9.65685 | + | 9.65685i | −0.330064 | + | 0.330064i | ||||
\(857\) | 41.2132 | 1.40782 | 0.703908 | − | 0.710291i | \(-0.251437\pi\) | ||||
0.703908 | + | 0.710291i | \(0.251437\pi\) | |||||||
\(858\) | 17.6569 | + | 0.485281i | 0.602795 | + | 0.0165672i | ||||
\(859\) | −12.3431 | −0.421143 | −0.210571 | − | 0.977578i | \(-0.567532\pi\) | ||||
−0.210571 | + | 0.977578i | \(0.567532\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.8995 | + | 3.41421i | −0.678173 | + | 0.116356i | ||||
\(862\) | − | 2.97056i | − | 0.101178i | ||||||
\(863\) | −25.7990 | + | 25.7990i | −0.878208 | + | 0.878208i | −0.993349 | − | 0.115141i | \(-0.963268\pi\) |
0.115141 | + | 0.993349i | \(0.463268\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.5858 | − | 23.5858i | 0.801941 | − | 0.801941i | ||||
\(866\) | −8.58579 | − | 8.58579i | −0.291757 | − | 0.291757i | ||||
\(867\) | 0.292893 | + | 1.70711i | 0.00994718 | + | 0.0579764i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.242641 | − | 0.242641i | −0.00823102 | − | 0.00823102i | ||||
\(870\) | −3.52691 | − | 20.5563i | −0.119574 | − | 0.696926i | ||||
\(871\) | −21.5147 | + | 14.3431i | −0.728998 | + | 0.485999i | ||||
\(872\) | − | 39.3137i | − | 1.33133i | ||||||
\(873\) | 33.3345 | + | 15.9203i | 1.12820 | + | 0.538821i | ||||
\(874\) | −46.8701 | −1.58540 | ||||||||
\(875\) | −12.1716 | −0.411474 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.51472 | + | 9.51472i | 0.321289 | + | 0.321289i | 0.849262 | − | 0.527972i | \(-0.177048\pi\) |
−0.527972 | + | 0.849262i | \(0.677048\pi\) | |||||||
\(878\) | −21.2132 | − | 21.2132i | −0.715911 | − | 0.715911i | ||||
\(879\) | 4.31371 | − | 6.10051i | 0.145498 | − | 0.205765i | ||||
\(880\) | 14.6274 | 0.493090 | ||||||||
\(881\) | 46.2843 | 1.55936 | 0.779678 | − | 0.626180i | \(-0.215383\pi\) | ||||
0.779678 | + | 0.626180i | \(0.215383\pi\) | |||||||
\(882\) | −3.82843 | − | 1.82843i | −0.128910 | − | 0.0615663i | ||||
\(883\) | 31.3137i | 1.05379i | 0.849930 | + | 0.526895i | \(0.176644\pi\) | ||||
−0.849930 | + | 0.526895i | \(0.823356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.07107 | + | 6.24264i | 0.0360036 | + | 0.209844i | ||||
\(886\) | −18.6569 | − | 18.6569i | −0.626789 | − | 0.626789i | ||||
\(887\) | − | 28.8701i | − | 0.969362i | −0.874691 | − | 0.484681i | \(-0.838936\pi\) | ||
0.874691 | − | 0.484681i | \(-0.161064\pi\) | |||||||
\(888\) | −4.20101 | − | 24.4853i | −0.140977 | − | 0.821672i | ||||
\(889\) | −1.41421 | − | 1.41421i | −0.0474312 | − | 0.0474312i | ||||
\(890\) | −26.1716 | + | 26.1716i | −0.877273 | + | 0.877273i | ||||
\(891\) | −17.8995 | − | 1.89949i | −0.599656 | − | 0.0636355i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 74.9411i | − | 2.50781i | ||||||
\(894\) | 14.4853 | − | 2.48528i | 0.484460 | − | 0.0831202i | ||||
\(895\) | 23.4939 | − | 23.4939i | 0.785315 | − | 0.785315i | ||||
\(896\) | −11.3137 | −0.377964 | ||||||||
\(897\) | −23.8995 | − | 0.656854i | −0.797981 | − | 0.0219317i | ||||
\(898\) | 31.1716 | 1.04021 | ||||||||
\(899\) | 32.3640 | − | 32.3640i | 1.07940 | − | 1.07940i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 41.2548i | − | 1.37440i | ||||||
\(902\) | 23.3137 | − | 23.3137i | 0.776262 | − | 0.776262i | ||||
\(903\) | −4.65685 | + | 6.58579i | −0.154970 | + | 0.219161i | ||||
\(904\) | −8.34315 | + | 8.34315i | −0.277489 | + | 0.277489i | ||||
\(905\) | 2.58579 | + | 2.58579i | 0.0859544 | + | 0.0859544i | ||||
\(906\) | −30.3848 | + | 5.21320i | −1.00947 | + | 0.173197i | ||||
\(907\) | − | 45.6274i | − | 1.51503i | −0.652816 | − | 0.757517i | \(-0.726412\pi\) | ||
0.652816 | − | 0.757517i | \(-0.273588\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3431 | − | 3.65685i | 0.343060 | − | 0.121290i | ||||
\(910\) | 7.75736 | − | 5.17157i | 0.257154 | − | 0.171436i | ||||
\(911\) | − | 23.8284i | − | 0.789471i | −0.918795 | − | 0.394736i | \(-0.870836\pi\) | ||
0.918795 | − | 0.394736i | \(-0.129164\pi\) | |||||||
\(912\) | −34.6274 | + | 48.9706i | −1.14663 | + | 1.62158i | ||||
\(913\) | −2.00000 | −0.0661903 | ||||||||
\(914\) | 21.6569 | 0.716345 | ||||||||
\(915\) | 15.2548 | + | 10.7868i | 0.504309 | + | 0.356600i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.58579 | + | 3.58579i | 0.118413 | + | 0.118413i | ||||
\(918\) | 28.2843 | + | 8.00000i | 0.933520 | + | 0.264039i | ||||
\(919\) | 52.8284 | 1.74265 | 0.871325 | − | 0.490707i | \(-0.163262\pi\) | ||||
0.871325 | + | 0.490707i | \(0.163262\pi\) | |||||||
\(920\) | −19.7990 | −0.652753 | ||||||||
\(921\) | 16.7279 | + | 11.8284i | 0.551204 | + | 0.389760i | ||||
\(922\) | − | 36.9706i | − | 1.21756i | ||||||
\(923\) | −7.79899 | − | 11.6985i | −0.256707 | − | 0.385060i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.94113 | − | 5.94113i | −0.195343 | − | 0.195343i | ||||
\(926\) | 29.3137i | 0.963308i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.92031 | + | 7.92031i | −0.259857 | + | 0.259857i | −0.824996 | − | 0.565139i | \(-0.808823\pi\) |
0.565139 | + | 0.824996i | \(0.308823\pi\) | |||||||
\(930\) | 35.9411 | + | 25.4142i | 1.17856 | + | 0.833365i | ||||
\(931\) | −6.12132 | + | 6.12132i | −0.200618 | + | 0.200618i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.129942 | − | 0.757359i | −0.00425412 | − | 0.0247948i | ||||
\(934\) | 9.21320 | − | 9.21320i | 0.301465 | − | 0.301465i | ||||
\(935\) | −14.6274 | −0.478368 | ||||||||
\(936\) | −18.3431 | + | 24.4853i | −0.599564 | + | 0.800326i | ||||
\(937\) | 20.8701 | 0.681795 | 0.340898 | − | 0.940100i | \(-0.389269\pi\) | ||||
0.340898 | + | 0.940100i | \(0.389269\pi\) | |||||||
\(938\) | −7.17157 | + | 7.17157i | −0.234160 | + | 0.234160i | ||||
\(939\) | −4.72792 | − | 27.5563i | −0.154290 | − | 0.899267i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.39340 | + | 5.39340i | −0.175820 | + | 0.175820i | −0.789531 | − | 0.613711i | \(-0.789676\pi\) |
0.613711 | + | 0.789531i | \(0.289676\pi\) | |||||||
\(942\) | 16.9706 | + | 12.0000i | 0.552931 | + | 0.390981i | ||||
\(943\) | −31.5563 | + | 31.5563i | −1.02762 | + | 1.02762i | ||||
\(944\) | 5.65685 | + | 5.65685i | 0.184115 | + | 0.184115i | ||||
\(945\) | −8.29289 | + | 4.63604i | −0.269768 | + | 0.150810i | ||||
\(946\) | − | 13.1716i | − | 0.428245i | ||||||
\(947\) | 19.4142 | + | 19.4142i | 0.630877 | + | 0.630877i | 0.948288 | − | 0.317411i | \(-0.102813\pi\) |
−0.317411 | + | 0.948288i | \(0.602813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.6569 | − | 17.4853i | −0.378398 | − | 0.567596i | ||||
\(950\) | 20.2843i | 0.658109i | ||||||||
\(951\) | 5.51472 | + | 3.89949i | 0.178827 | + | 0.126450i | ||||
\(952\) | 11.3137 | 0.366679 | ||||||||
\(953\) | 29.9706 | 0.970842 | 0.485421 | − | 0.874281i | \(-0.338666\pi\) | ||||
0.485421 | + | 0.874281i | \(0.338666\pi\) | |||||||
\(954\) | 39.4853 | + | 18.8579i | 1.27838 | + | 0.610546i | ||||
\(955\) | 17.2132 | + | 17.2132i | 0.557006 | + | 0.557006i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.1716 | − | 9.31371i | −0.425776 | − | 0.301069i | ||||
\(958\) | 32.0416 | 1.03522 | ||||||||
\(959\) | 5.07107 | 0.163753 | ||||||||
\(960\) | −14.6274 | + | 20.6863i | −0.472098 | + | 0.667647i | ||||
\(961\) | 65.5980i | 2.11606i | ||||||||
\(962\) | 25.3553 | + | 5.07107i | 0.817489 | + | 0.163498i | ||||
\(963\) | 4.82843 | + | 13.6569i | 0.155594 | + | 0.440086i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 31.6569i | − | 1.01907i | ||||||
\(966\) | −9.24264 | + | 1.58579i | −0.297377 | + | 0.0510218i | ||||
\(967\) | 20.3848 | + | 20.3848i | 0.655530 | + | 0.655530i | 0.954319 | − | 0.298789i | \(-0.0965827\pi\) |
−0.298789 | + | 0.954319i | \(0.596583\pi\) | |||||||
\(968\) | −14.0000 | + | 14.0000i | −0.449977 | + | 0.449977i | ||||
\(969\) | 34.6274 | − | 48.9706i | 1.11239 | − | 1.57316i | ||||
\(970\) | −22.5147 | + | 22.5147i | −0.722904 | + | 0.722904i | ||||
\(971\) | 56.5269i | 1.81403i | 0.421093 | + | 0.907017i | \(0.361647\pi\) | ||||
−0.421093 | + | 0.907017i | \(0.638353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.24264 | + | 2.24264i | −0.0718958 | + | 0.0718958i | ||||
\(974\) | 51.6569 | 1.65519 | ||||||||
\(975\) | −0.284271 | + | 10.3431i | −0.00910397 | + | 0.331246i | ||||
\(976\) | 23.5980 | 0.755353 | ||||||||
\(977\) | 7.55635 | − | 7.55635i | 0.241749 | − | 0.241749i | −0.575824 | − | 0.817573i | \(-0.695319\pi\) |
0.817573 | + | 0.575824i | \(0.195319\pi\) | |||||||
\(978\) | −23.0711 | + | 3.95837i | −0.737731 | + | 0.126575i | ||||
\(979\) | 28.6274i | 0.914936i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.6274 | − | 17.9706i | −1.20135 | − | 0.573756i | ||||
\(982\) | 4.97056 | − | 4.97056i | 0.158617 | − | 0.158617i | ||||
\(983\) | 7.19239 | + | 7.19239i | 0.229402 | + | 0.229402i | 0.812443 | − | 0.583041i | \(-0.198137\pi\) |
−0.583041 | + | 0.812443i | \(0.698137\pi\) | |||||||
\(984\) | 9.65685 | + | 56.2843i | 0.307849 | + | 1.79428i | ||||
\(985\) | − | 6.87006i | − | 0.218898i | ||||||
\(986\) | 18.6274 | + | 18.6274i | 0.593218 | + | 0.593218i | ||||
\(987\) | −2.53553 | − | 14.7782i | −0.0807069 | − | 0.470394i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.8284i | 0.566911i | ||||||||
\(990\) | 6.68629 | − | 14.0000i | 0.212504 | − | 0.444949i | ||||
\(991\) | −9.02944 | −0.286830 | −0.143415 | − | 0.989663i | \(-0.545808\pi\) | ||||
−0.143415 | + | 0.989663i | \(0.545808\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.75736 | − | 5.31371i | 0.119236 | − | 0.168625i | ||||
\(994\) | −3.89949 | − | 3.89949i | −0.123684 | − | 0.123684i | ||||
\(995\) | −8.20101 | − | 8.20101i | −0.259989 | − | 0.259989i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6863 | 0.908504 | 0.454252 | − | 0.890873i | \(-0.349907\pi\) | ||||
0.454252 | + | 0.890873i | \(0.349907\pi\) | |||||||
\(998\) | 28.0000 | 0.886325 | ||||||||
\(999\) | −25.3553 | − | 7.17157i | −0.802207 | − | 0.226899i |
(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 | 273.2.n.a.8.2 | ✓ | 4 | |
3.2 | odd | 2 | 273.2.n.b.8.2 | yes | 4 | ||
13.5 | odd | 4 | 273.2.n.b.239.2 | yes | 4 | ||
39.5 | even | 4 | inner | 273.2.n.a.239.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.n.a.8.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
273.2.n.a.239.2 | yes | 4 | 39.5 | even | 4 | inner | |
273.2.n.b.8.2 | yes | 4 | 3.2 | odd | 2 | ||
273.2.n.b.239.2 | yes | 4 | 13.5 | odd | 4 |