Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [828,2,Mod(73,828)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(828, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("828.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 828.q (of order \(11\), degree \(10\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.61161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{11})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + 15500 x^{12} - 28190 x^{11} + 41920 x^{10} - 33520 x^{9} - 13837 x^{8} + \cdots + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 276) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(-1.54238 - 1.78001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 828.577 |
Dual form | 828.2.q.c.541.2 |
$q$-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 \(\left(\mathbb{Z}/828\mathbb{Z}\right)^\times\).
\(n\) | \(415\) | \(461\) | \(649\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.38954 | + | 0.701632i | 1.06863 | + | 0.313779i | 0.768323 | − | 0.640062i | \(-0.221091\pi\) |
0.300311 | + | 0.953841i | \(0.402910\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64891 | − | 3.05701i | 1.00119 | − | 1.15544i | 0.0133629 | − | 0.999911i | \(-0.495746\pi\) |
0.987831 | − | 0.155529i | \(-0.0497082\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.05943 | − | 2.60884i | 1.22396 | − | 0.786594i | 0.241024 | − | 0.970519i | \(-0.422517\pi\) |
0.982940 | + | 0.183925i | \(0.0588804\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.81278 | − | 3.24612i | −0.780123 | − | 0.900310i | 0.216995 | − | 0.976173i | \(-0.430375\pi\) |
−0.997118 | + | 0.0758623i | \(0.975829\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.87409 | + | 4.10368i | −0.454533 | + | 0.995288i | 0.534167 | + | 0.845379i | \(0.320625\pi\) |
−0.988700 | + | 0.149909i | \(0.952102\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.84032 | − | 4.02974i | −0.422198 | − | 0.924485i | −0.994529 | − | 0.104462i | \(-0.966688\pi\) |
0.572331 | − | 0.820023i | \(-0.306039\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.75085 | + | 0.655317i | −0.990620 | + | 0.136643i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.01134 | + | 0.649950i | 0.202268 | + | 0.129990i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.207351 | − | 0.454036i | 0.0385042 | − | 0.0843124i | −0.889403 | − | 0.457125i | \(-0.848879\pi\) |
0.927907 | + | 0.372812i | \(0.121607\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.727870 | + | 5.06245i | −0.130729 | + | 0.909243i | 0.813877 | + | 0.581037i | \(0.197353\pi\) |
−0.944606 | + | 0.328206i | \(0.893556\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.47457 | − | 5.44627i | 1.43246 | − | 0.920588i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.2392 | − | 3.00650i | 1.68331 | − | 0.494265i | 0.706384 | − | 0.707829i | \(-0.250325\pi\) |
0.976929 | + | 0.213564i | \(0.0685071\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.29593 | − | 2.14228i | −1.13943 | − | 0.334568i | −0.343024 | − | 0.939327i | \(-0.611451\pi\) |
−0.796409 | + | 0.604759i | \(0.793269\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.07935 | + | 7.50707i | 0.164600 | + | 1.14482i | 0.889824 | + | 0.456305i | \(0.150827\pi\) |
−0.725224 | + | 0.688513i | \(0.758264\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.67725 | 1.11984 | 0.559921 | − | 0.828546i | \(-0.310831\pi\) | ||||
0.559921 | + | 0.828546i | \(0.310831\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.33235 | − | 9.26672i | −0.190336 | − | 1.32382i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.00164 | + | 5.77220i | −0.687028 | + | 0.792873i | −0.986939 | − | 0.161095i | \(-0.948498\pi\) |
0.299911 | + | 0.953967i | \(0.403043\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.5306 | − | 3.38569i | 1.55479 | − | 0.456527i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.85219 | + | 2.13754i | 0.241134 | + | 0.278284i | 0.863397 | − | 0.504524i | \(-0.168332\pi\) |
−0.622263 | + | 0.782808i | \(0.713787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.225996 | + | 1.57184i | −0.0289358 | + | 0.201253i | −0.999161 | − | 0.0409511i | \(-0.986961\pi\) |
0.970225 | + | 0.242204i | \(0.0778703\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.44366 | − | 9.73025i | −0.551168 | − | 1.20689i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1121 | + | 6.49867i | 1.23539 | + | 0.793939i | 0.984722 | − | 0.174134i | \(-0.0557124\pi\) |
0.250671 | + | 0.968072i | \(0.419349\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.18977 | − | 2.04994i | −0.378556 | − | 0.243283i | 0.337501 | − | 0.941325i | \(-0.390418\pi\) |
−0.716057 | + | 0.698042i | \(0.754055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.09627 | − | 6.77988i | −0.362391 | − | 0.793525i | −0.999737 | − | 0.0229473i | \(-0.992695\pi\) |
0.637346 | − | 0.770578i | \(-0.280032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.77784 | − | 19.3203i | 0.316564 | − | 2.20175i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.62471 | + | 8.79938i | 0.857847 | + | 0.990008i | 1.00000 | 0.000163051i | \(5.19009e-5\pi\) | |
−0.142153 | + | 0.989845i | \(0.545403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.09163 | − | 1.49504i | 0.558879 | − | 0.164102i | 0.00991953 | − | 0.999951i | \(-0.496842\pi\) |
0.548959 | + | 0.835849i | \(0.315024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.35747 | + | 8.49098i | −0.798030 | + | 0.920976i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.58627 | + | 11.0327i | 0.168144 | + | 1.16947i | 0.882717 | + | 0.469905i | \(0.155712\pi\) |
−0.714573 | + | 0.699561i | \(0.753379\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.3742 | −1.82131 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.57012 | − | 10.9204i | −0.161091 | − | 1.12041i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.84457 | − | 2.00975i | −0.694961 | − | 0.204059i | −0.0848721 | − | 0.996392i | \(-0.527048\pi\) |
−0.610089 | + | 0.792333i | \(0.708866\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.07150 | + | 1.48913i | −0.504633 | + | 0.148174i | −0.524133 | − | 0.851636i | \(-0.675611\pi\) |
0.0195002 | + | 0.999810i | \(0.493792\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.1144 | − | 10.3561i | 1.58780 | − | 1.02042i | 0.615074 | − | 0.788470i | \(-0.289126\pi\) |
0.972728 | − | 0.231949i | \(-0.0745102\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.56999 | + | 10.9195i | −0.151777 | + | 1.05563i | 0.761463 | + | 0.648209i | \(0.224482\pi\) |
−0.913240 | + | 0.407423i | \(0.866428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.724276 | + | 1.58594i | −0.0693731 | + | 0.151906i | −0.941142 | − | 0.338011i | \(-0.890246\pi\) |
0.871769 | + | 0.489917i | \(0.162973\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.5328 | + | 9.33966i | 1.36713 | + | 0.878601i | 0.998696 | − | 0.0510528i | \(-0.0162577\pi\) |
0.368434 | + | 0.929654i | \(0.379894\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.8121 | − | 1.76744i | −1.10149 | − | 0.164815i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.58068 | + | 16.5994i | 0.694920 | + | 1.52166i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.10337 | − | 11.1748i | 0.463943 | − | 1.01589i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.19377 | − | 7.14799i | −0.553988 | − | 0.639336i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0209 | + | 7.72538i | −1.06668 | + | 0.685516i | −0.951444 | − | 0.307821i | \(-0.900400\pi\) |
−0.115240 | + | 0.993338i | \(0.536764\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.51189 | + | 7.51512i | −0.568946 | + | 0.656599i | −0.965191 | − | 0.261546i | \(-0.915768\pi\) |
0.396245 | + | 0.918145i | \(0.370313\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.1938 | − | 5.04854i | −1.49089 | − | 0.437764i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.14309 | 0.695711 | 0.347855 | − | 0.937548i | \(-0.386910\pi\) | ||||
0.347855 | + | 0.937548i | \(0.386910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1303 | −0.859242 | −0.429621 | − | 0.903009i | \(-0.641353\pi\) | ||||
−0.429621 | + | 0.903009i | \(0.641353\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.8869 | − | 5.83931i | −1.66302 | − | 0.488307i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.814041 | − | 0.939453i | 0.0676024 | − | 0.0780173i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.58068 | + | 3.58648i | −0.457187 | + | 0.293816i | −0.748892 | − | 0.662692i | \(-0.769414\pi\) |
0.291705 | + | 0.956508i | \(0.405777\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.56561 | + | 6.42306i | 0.452923 | + | 0.522701i | 0.935583 | − | 0.353107i | \(-0.114875\pi\) |
−0.482660 | + | 0.875808i | \(0.660329\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.29125 | + | 11.5862i | −0.425004 | + | 0.930628i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.89510 | + | 8.52909i | 0.310863 | + | 0.680695i | 0.998992 | − | 0.0448934i | \(-0.0142948\pi\) |
−0.688129 | + | 0.725589i | \(0.741568\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.5813 | + | 16.2592i | −0.833921 | + | 1.28141i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.07886 | − | 2.62132i | −0.319481 | − | 0.205318i | 0.371064 | − | 0.928607i | \(-0.378993\pi\) |
−0.690545 | + | 0.723289i | \(0.742629\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.54815 | − | 12.1488i | 0.429329 | − | 0.940099i | −0.564107 | − | 0.825702i | \(-0.690779\pi\) |
0.993435 | − | 0.114397i | \(-0.0364934\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.775469 | + | 5.39351i | −0.0596515 | + | 0.414885i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.57692 | + | 5.51205i | −0.652091 | + | 0.419073i | −0.824430 | − | 0.565964i | \(-0.808504\pi\) |
0.172339 | + | 0.985038i | \(0.444868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.66585 | − | 1.37002i | 0.352705 | − | 0.103564i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.83694 | + | 1.71388i | 0.436274 | + | 0.128102i | 0.492492 | − | 0.870317i | \(-0.336086\pi\) |
−0.0562183 | + | 0.998419i | \(0.517904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.660855 | + | 4.59635i | 0.0491209 | + | 0.341644i | 0.999530 | + | 0.0306423i | \(0.00975529\pi\) |
−0.950409 | + | 0.311001i | \(0.899336\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 26.5764 | 1.95394 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.09810 | + | 21.5478i | 0.226556 | + | 1.57573i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.73126 | + | 8.92235i | −0.559414 | + | 0.645599i | −0.963050 | − | 0.269321i | \(-0.913201\pi\) |
0.403636 | + | 0.914920i | \(0.367746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.4550 | + | 6.29975i | −1.54436 | + | 0.453466i | −0.939410 | − | 0.342795i | \(-0.888626\pi\) |
−0.604953 | + | 0.796261i | \(0.706808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.93139 | + | 6.84519i | 0.422594 | + | 0.487699i | 0.926625 | − | 0.375986i | \(-0.122696\pi\) |
−0.504031 | + | 0.863685i | \(0.668150\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.513726 | − | 3.57304i | 0.0364171 | − | 0.253286i | −0.963478 | − | 0.267788i | \(-0.913707\pi\) |
0.999895 | + | 0.0145021i | \(0.00461632\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.838736 | − | 1.83658i | −0.0588677 | − | 0.128902i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.9308 | − | 10.2381i | −1.11266 | − | 0.715061i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.9836 | − | 11.5573i | −1.24395 | − | 0.799438i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.02026 | − | 2.23405i | −0.0702374 | − | 0.153798i | 0.871257 | − | 0.490827i | \(-0.163305\pi\) |
−0.941494 | + | 0.337029i | \(0.890578\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.68804 | + | 18.6958i | −0.183323 | + | 1.27504i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.5479 | + | 15.6351i | 0.919690 | + | 1.06138i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.5924 | − | 5.45922i | 1.25066 | − | 0.367227i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9606 | − | 12.6492i | 0.733976 | − | 0.847053i | −0.258938 | − | 0.965894i | \(-0.583372\pi\) |
0.992913 | + | 0.118841i | \(0.0379179\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.94100 | − | 13.5000i | −0.128829 | − | 0.896024i | −0.947042 | − | 0.321109i | \(-0.895944\pi\) |
0.818213 | − | 0.574915i | \(-0.194965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.76866 | −0.447286 | −0.223643 | − | 0.974671i | \(-0.571795\pi\) | ||||
−0.223643 | + | 0.974671i | \(0.571795\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.54002 | − | 10.7111i | −0.100890 | − | 0.701705i | −0.975998 | − | 0.217778i | \(-0.930119\pi\) |
0.875108 | − | 0.483927i | \(-0.160790\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.3451 | + | 5.38661i | 1.19670 | + | 0.351383i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3881 | − | 5.39923i | 1.18943 | − | 0.349247i | 0.373625 | − | 0.927580i | \(-0.378115\pi\) |
0.815801 | + | 0.578333i | \(0.196296\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.37372 | + | 5.38147i | −0.539399 | + | 0.346651i | −0.781804 | − | 0.623525i | \(-0.785700\pi\) |
0.242405 | + | 0.970175i | \(0.422064\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.31812 | − | 23.0780i | 0.211987 | − | 1.47440i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.90458 | + | 17.3086i | −0.502957 | + | 1.10132i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.59137 | − | 6.16400i | −0.605402 | − | 0.389068i | 0.201728 | − | 0.979442i | \(-0.435344\pi\) |
−0.807130 | + | 0.590373i | \(0.798981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.5761 | + | 15.0544i | −1.10500 | + | 0.946462i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.8691 | − | 23.8000i | −0.677995 | − | 1.48460i | −0.864754 | − | 0.502196i | \(-0.832526\pi\) |
0.186759 | − | 0.982406i | \(-0.440202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.9318 | − | 39.2652i | 1.11423 | − | 2.43982i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.2160 | − | 22.1764i | −1.18491 | − | 1.36746i | −0.914438 | − | 0.404727i | \(-0.867367\pi\) |
−0.270469 | − | 0.962729i | \(-0.587179\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0016 | + | 10.2836i | −0.982969 | + | 0.631716i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.5100 | + | 21.3616i | −1.12857 | + | 1.30244i | −0.180790 | + | 0.983522i | \(0.557866\pi\) |
−0.947782 | + | 0.318920i | \(0.896680\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.108543 | + | 0.0318710i | 0.00659349 | + | 0.00193602i | 0.285028 | − | 0.958519i | \(-0.407997\pi\) |
−0.278434 | + | 0.960455i | \(0.589815\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.80108 | 0.349818 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.96519 | −0.238245 | −0.119123 | − | 0.992880i | \(-0.538008\pi\) | ||||
−0.119123 | + | 0.992880i | \(0.538008\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.9629 | − | 4.68713i | −0.952267 | − | 0.279611i | −0.231536 | − | 0.972826i | \(-0.574375\pi\) |
−0.720730 | + | 0.693215i | \(0.756193\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0836 | − | 12.7911i | 0.658851 | − | 0.760354i | −0.323738 | − | 0.946147i | \(-0.604940\pi\) |
0.982589 | + | 0.185792i | \(0.0594852\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.8752 | + | 16.6290i | −1.52737 | + | 0.981579i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.19534 | − | 2.53355i | −0.129137 | − | 0.149032i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.50419 | + | 18.6216i | −0.496820 | + | 1.08788i | 0.480670 | + | 0.876902i | \(0.340393\pi\) |
−0.977490 | + | 0.210982i | \(0.932334\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.92611 | + | 6.40728i | 0.170365 | + | 0.373046i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.4903 | + | 13.5785i | 0.895827 | + | 0.785267i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.8083 | + | 16.5860i | 1.48756 | + | 0.956000i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.64288 | + | 3.59740i | −0.0940708 | + | 0.205986i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.39426 | + | 16.6525i | −0.136648 | + | 0.950407i | 0.799967 | + | 0.600045i | \(0.204851\pi\) |
−0.936614 | + | 0.350362i | \(0.886059\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.0518 | − | 16.0998i | 1.42055 | − | 0.912935i | 0.420571 | − | 0.907260i | \(-0.361830\pi\) |
0.999984 | − | 0.00567544i | \(-0.00180656\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.9943 | − | 8.51351i | 1.63886 | − | 0.481212i | 0.672861 | − | 0.739769i | \(-0.265065\pi\) |
0.965996 | + | 0.258557i | \(0.0832470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.02982 | − | 1.47689i | −0.282503 | − | 0.0829504i | 0.137411 | − | 0.990514i | \(-0.456122\pi\) |
−0.419914 | + | 0.907564i | \(0.637940\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.342778 | − | 2.38407i | −0.0191919 | − | 0.133483i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.9856 | 1.11203 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.734864 | − | 5.11109i | −0.0407629 | − | 0.283512i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.3364 | − | 23.4694i | 1.12118 | − | 1.29391i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1389 | + | 5.32606i | −0.997003 | + | 0.292747i | −0.739226 | − | 0.673458i | \(-0.764808\pi\) |
−0.257778 | + | 0.966204i | \(0.582990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.6036 | + | 22.6238i | 1.07106 | + | 1.23607i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.73565 | − | 12.0717i | 0.0945470 | − | 0.657589i | −0.886344 | − | 0.463028i | \(-0.846763\pi\) |
0.980891 | − | 0.194560i | \(-0.0623280\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2524 | + | 22.4496i | 0.555197 | + | 1.21571i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.03763 | − | 5.16547i | −0.433991 | − | 0.278909i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.06027 | − | 4.53736i | −0.379015 | − | 0.243578i | 0.337237 | − | 0.941420i | \(-0.390508\pi\) |
−0.716252 | + | 0.697842i | \(0.754144\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.08565 | + | 19.8948i | 0.486344 | + | 1.06494i | 0.980670 | + | 0.195668i | \(0.0626875\pi\) |
−0.494326 | + | 0.869276i | \(0.664585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.92984 | − | 20.3775i | 0.155940 | − | 1.08459i | −0.750079 | − | 0.661348i | \(-0.769985\pi\) |
0.906019 | − | 0.423237i | \(-0.139106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.18378 | − | 7.13646i | −0.328201 | − | 0.378764i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5158 | + | 6.02397i | −1.08278 | + | 0.317933i | −0.773991 | − | 0.633197i | \(-0.781742\pi\) |
−0.308790 | + | 0.951130i | \(0.599924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.409640 | + | 0.472749i | −0.0215600 | + | 0.0248815i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.64167 | − | 18.3732i | −0.138271 | − | 0.961699i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1339 | 0.581182 | 0.290591 | − | 0.956847i | \(-0.406148\pi\) | ||||
0.290591 | + | 0.956847i | \(0.406148\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.39675 | + | 30.5801i | 0.228268 | + | 1.58764i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8571 | − | 3.77518i | −0.665714 | − | 0.195471i | −0.0686206 | − | 0.997643i | \(-0.521860\pi\) |
−0.597094 | + | 0.802171i | \(0.703678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.05709 | + | 0.604015i | −0.105945 | + | 0.0311084i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.457570 | + | 0.294062i | −0.0235038 | + | 0.0151050i | −0.552340 | − | 0.833619i | \(-0.686265\pi\) |
0.528836 | + | 0.848724i | \(0.322629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.358061 | + | 2.49037i | −0.0182961 | + | 0.127252i | −0.996922 | − | 0.0783945i | \(-0.975021\pi\) |
0.978626 | + | 0.205646i | \(0.0659297\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.1935 | − | 44.2175i | 1.02915 | − | 2.25353i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5193 | + | 6.76037i | 0.533352 | + | 0.342764i | 0.779434 | − | 0.626485i | \(-0.215507\pi\) |
−0.246082 | + | 0.969249i | \(0.579143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.21429 | − | 20.7241i | 0.314270 | − | 1.04806i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0456 | + | 26.3762i | 0.606080 | + | 1.32713i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.36806 | − | 20.5132i | 0.470169 | − | 1.02953i | −0.514881 | − | 0.857262i | \(-0.672164\pi\) |
0.985051 | − | 0.172266i | \(-0.0551087\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.939019 | − | 1.08369i | −0.0468924 | − | 0.0541167i | 0.731819 | − | 0.681499i | \(-0.238672\pi\) |
−0.778711 | + | 0.627383i | \(0.784126\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.4806 | − | 11.8768i | 0.920586 | − | 0.591625i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.7218 | − | 38.9171i | 1.67153 | − | 1.92905i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.01920 | − | 0.592891i | −0.0998430 | − | 0.0293166i | 0.231429 | − | 0.972852i | \(-0.425660\pi\) |
−0.331272 | + | 0.943535i | \(0.607478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.4407 | 0.562962 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.2156 | 0.648729 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1544 | − | 4.15610i | −0.691486 | − | 0.203039i | −0.0829368 | − | 0.996555i | \(-0.526430\pi\) |
−0.608549 | + | 0.793516i | \(0.708248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.55784 | − | 1.79785i | 0.0759246 | − | 0.0876216i | −0.716516 | − | 0.697570i | \(-0.754264\pi\) |
0.792441 | + | 0.609949i | \(0.208810\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.56252 | + | 2.93216i | −0.221315 | + | 0.142230i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.20647 | + | 4.85452i | 0.203565 | + | 0.234927i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.23072 | + | 15.8331i | −0.348291 | + | 0.762652i | 0.651700 | + | 0.758477i | \(0.274056\pi\) |
−0.999991 | + | 0.00417490i | \(0.998671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.20769 | − | 17.9723i | −0.394436 | − | 0.863695i | −0.997804 | − | 0.0662322i | \(-0.978902\pi\) |
0.603368 | − | 0.797463i | \(-0.293825\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.3838 | + | 17.9387i | 0.544562 | + | 0.858123i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.4395 | − | 9.92238i | −0.736888 | − | 0.473569i | 0.117586 | − | 0.993063i | \(-0.462484\pi\) |
−0.854474 | + | 0.519493i | \(0.826121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.532229 | − | 1.16542i | 0.0252869 | − | 0.0553707i | −0.896567 | − | 0.442908i | \(-0.853947\pi\) |
0.921854 | + | 0.387537i | \(0.126674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.95047 | + | 27.4761i | −0.187270 | + | 1.30249i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.96730 | + | 5.12027i | −0.376000 | + | 0.241641i | −0.714968 | − | 0.699157i | \(-0.753559\pi\) |
0.338968 | + | 0.940798i | \(0.389922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.2062 | + | 10.3375i | −1.65779 | + | 0.486772i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −41.5163 | − | 12.1903i | −1.94631 | − | 0.571489i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.98099 | − | 20.7333i | −0.139445 | − | 0.969861i | −0.932618 | − | 0.360865i | \(-0.882482\pi\) |
0.793173 | − | 0.608996i | \(-0.208428\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.43095 | −0.346094 | −0.173047 | − | 0.984914i | \(-0.555361\pi\) | ||||
−0.173047 | + | 0.984914i | \(0.555361\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.90134 | + | 27.1344i | 0.181310 | + | 1.26104i | 0.853669 | + | 0.520816i | \(0.174372\pi\) |
−0.672358 | + | 0.740226i | \(0.734719\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.5015 | − | 28.2762i | 1.13379 | − | 1.30847i | 0.188563 | − | 0.982061i | \(-0.439617\pi\) |
0.945230 | − | 0.326405i | \(-0.105837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 46.6526 | − | 13.6984i | 2.15422 | − | 0.632535i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.9663 | + | 27.6586i | 1.10197 | + | 1.27174i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.757935 | − | 5.27155i | 0.0347764 | − | 0.241875i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.62333 | − | 14.5031i | −0.302628 | − | 0.662662i | 0.695829 | − | 0.718208i | \(-0.255037\pi\) |
−0.998456 | + | 0.0555460i | \(0.982310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.5600 | − | 24.7810i | −1.75818 | − | 1.12992i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.9453 | − | 9.60474i | −0.678630 | − | 0.436129i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.29565 | + | 13.7855i | 0.285283 | + | 0.624683i | 0.996968 | − | 0.0778164i | \(-0.0247948\pi\) |
−0.711685 | + | 0.702499i | \(0.752068\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.02270 | − | 34.9336i | 0.226671 | − | 1.57653i | −0.485315 | − | 0.874340i | \(-0.661295\pi\) |
0.711986 | − | 0.702194i | \(-0.247796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.47462 | + | 1.70181i | 0.0664137 | + | 0.0766455i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.7161 | + | 4.32104i | −0.660107 | + | 0.193825i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.9697 | − | 18.4300i | 0.714902 | − | 0.825041i | −0.275782 | − | 0.961220i | \(-0.588937\pi\) |
0.990684 | + | 0.136179i | \(0.0434824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.74046 | + | 32.9706i | 0.211367 | + | 1.47009i | 0.768599 | + | 0.639731i | \(0.220954\pi\) |
−0.557232 | + | 0.830357i | \(0.688137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.1634 | −0.585762 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.84114 | + | 19.7605i | 0.125931 | + | 0.875870i | 0.950636 | + | 0.310307i | \(0.100432\pi\) |
−0.824705 | + | 0.565563i | \(0.808659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.9279 | − | 8.49399i | −1.27969 | − | 0.375752i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 45.7722 | − | 13.4399i | 2.01697 | − | 0.592235i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.1653 | − | 20.0287i | 1.37065 | − | 0.880861i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.86877 | − | 40.8182i | 0.257116 | − | 1.78828i | −0.296014 | − | 0.955184i | \(-0.595657\pi\) |
0.553130 | − | 0.833095i | \(-0.313433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.28867 | − | 9.39088i | 0.187530 | − | 0.410634i | −0.792392 | − | 0.610012i | \(-0.791165\pi\) |
0.979923 | + | 0.199377i | \(0.0638920\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.4106 | − | 12.4744i | −0.845538 | − | 0.543394i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.1411 | − | 6.22662i | 0.962657 | − | 0.270723i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.5677 | + | 29.7092i | 0.587683 | + | 1.28685i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.4131 | + | 24.9911i | −0.493429 | + | 1.08046i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.5840 | − | 34.1417i | −1.27427 | − | 1.47059i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.0203 | + | 18.6502i | −1.24768 | + | 0.801834i | −0.986548 | − | 0.163469i | \(-0.947732\pi\) |
−0.261130 | + | 0.965304i | \(0.584095\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.84343 | + | 3.28150i | −0.121799 | + | 0.140564i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.85374 | + | 2.89332i | 0.421315 | + | 0.123709i | 0.485516 | − | 0.874228i | \(-0.338632\pi\) |
−0.0642009 | + | 0.997937i | \(0.520450\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.21124 | −0.0942019 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.0969 | 2.00277 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.0734 | + | 8.53672i | 1.23188 | + | 0.361712i | 0.831959 | − | 0.554837i | \(-0.187220\pi\) |
0.399921 | + | 0.916550i | \(0.369038\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.3329 | − | 24.6194i | 0.902283 | − | 1.04129i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.7756 | − | 17.2076i | 1.12846 | − | 0.725214i | 0.163218 | − | 0.986590i | \(-0.447813\pi\) |
0.965237 | + | 0.261376i | \(0.0841763\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.1737 | + | 32.5141i | 1.18528 | + | 1.36788i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.827716 | − | 1.81245i | 0.0346997 | − | 0.0759817i | −0.891488 | − | 0.453043i | \(-0.850338\pi\) |
0.926188 | + | 0.377062i | \(0.123066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.19617 | − | 9.18833i | −0.175604 | − | 0.384520i | 0.801280 | − | 0.598290i | \(-0.204153\pi\) |
−0.976884 | + | 0.213770i | \(0.931426\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.23065 | − | 2.42506i | −0.218133 | − | 0.101132i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.09996 | + | 5.84819i | 0.378836 | + | 0.243463i | 0.716176 | − | 0.697920i | \(-0.245891\pi\) |
−0.337340 | + | 0.941383i | \(0.609527\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.91693 | − | 19.5254i | 0.369937 | − | 0.810048i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.24508 | + | 36.4803i | −0.217229 | + | 1.51086i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.2092 | + | 12.3450i | −0.792848 | + | 0.509532i | −0.873275 | − | 0.487228i | \(-0.838008\pi\) |
0.0804270 | + | 0.996761i | \(0.474372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.7398 | − | 6.38340i | 0.895775 | − | 0.263023i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.7448 | − | 3.74220i | −0.523365 | − | 0.153674i | 0.00936967 | − | 0.999956i | \(-0.497017\pi\) |
−0.532735 | + | 0.846282i | \(0.678836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.46768 | + | 44.9837i | 0.265149 | + | 1.84415i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.3103 | −0.625563 | −0.312781 | − | 0.949825i | \(-0.601261\pi\) | ||||
−0.312781 | + | 0.949825i | \(0.601261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.13065 | + | 21.7741i | 0.127702 | + | 0.888185i | 0.948457 | + | 0.316905i | \(0.102644\pi\) |
−0.820755 | + | 0.571280i | \(0.806447\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.0353 | − | 23.1220i | 0.814552 | − | 0.940043i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.82069 | + | 0.534602i | −0.0738994 | + | 0.0216988i | −0.318473 | − | 0.947932i | \(-0.603170\pi\) |
0.244574 | + | 0.969631i | \(0.421352\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.5944 | − | 24.9212i | −0.873615 | − | 1.00821i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.90508 | + | 20.2052i | −0.117335 | + | 0.816082i | 0.843136 | + | 0.537701i | \(0.180707\pi\) |
−0.960471 | + | 0.278381i | \(0.910202\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.44479 | − | 18.4915i | −0.339975 | − | 0.744440i | 0.660002 | − | 0.751264i | \(-0.270555\pi\) |
−0.999977 | + | 0.00682330i | \(0.997828\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.4504 | − | 18.9266i | −1.18371 | − | 0.760725i | −0.207647 | − | 0.978204i | \(-0.566580\pi\) |
−0.976065 | + | 0.217479i | \(0.930217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 37.9290 | + | 24.3755i | 1.51959 | + | 0.976583i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.2820 | − | 26.8939i | −0.491281 | − | 1.07576i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.85144 | + | 47.6528i | −0.273185 | + | 1.90004i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.2459 | − | 23.3650i | −0.805976 | − | 0.930146i | 0.192717 | − | 0.981254i | \(-0.438270\pi\) |
−0.998693 | + | 0.0511081i | \(0.983725\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.1448 | + | 10.0258i | −1.35500 | + | 0.397863i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.3332 | + | 30.3902i | −1.04336 | + | 1.20410i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.05443 | + | 49.0646i | 0.278633 | + | 1.93794i | 0.341422 | + | 0.939910i | \(0.389092\pi\) |
−0.0627883 | + | 0.998027i | \(0.519999\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.1135 | 1.42418 | 0.712089 | − | 0.702089i | \(-0.247749\pi\) | ||||
0.712089 | + | 0.702089i | \(0.247749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.05843 | + | 14.3167i | 0.0809251 | + | 0.562846i | 0.989434 | + | 0.144982i | \(0.0463123\pi\) |
−0.908509 | + | 0.417865i | \(0.862779\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.0953 | + | 3.84513i | 0.514036 | + | 0.150935i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.8195 | + | 11.6921i | −1.55826 | + | 0.457545i | −0.943555 | − | 0.331215i | \(-0.892542\pi\) |
−0.614701 | + | 0.788760i | \(0.710723\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.8333 | + | 13.3887i | −0.814023 | + | 0.523141i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.38046 | − | 23.5116i | 0.131684 | − | 0.915881i | −0.811675 | − | 0.584109i | \(-0.801444\pi\) |
0.943359 | − | 0.331773i | \(-0.107647\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.6367 | + | 40.8086i | −0.724882 | + | 1.58727i | 0.0820519 | + | 0.996628i | \(0.473853\pi\) |
−0.806934 | + | 0.590642i | \(0.798875\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −37.5429 | − | 24.1274i | −1.45585 | − | 0.935620i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.687558 | + | 2.29294i | −0.0266223 | + | 0.0887829i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.18325 | + | 6.97034i | 0.122888 | + | 0.269087i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.4662 | + | 40.4353i | −0.711819 | + | 1.55867i | 0.113207 | + | 0.993571i | \(0.463888\pi\) |
−0.825026 | + | 0.565095i | \(0.808840\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.0916 | − | 18.5707i | −0.618451 | − | 0.713731i | 0.356961 | − | 0.934119i | \(-0.383813\pi\) |
−0.975412 | + | 0.220389i | \(0.929267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.2745 | + | 15.6003i | −0.931569 | + | 0.598683i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.6796 | + | 27.3277i | −0.906076 | + | 1.04567i | 0.0926750 | + | 0.995696i | \(0.470458\pi\) |
−0.998751 | + | 0.0499707i | \(0.984087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.4582 | + | 5.71345i | 0.743461 | + | 0.218300i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.8057 | 1.24980 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.9939 | −1.14102 | −0.570511 | − | 0.821290i | \(-0.693255\pi\) | ||||
−0.570511 | + | 0.821290i | \(0.693255\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.2068 | − | 7.10776i | −0.918216 | − | 0.269613i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.4644 | − | 25.9253i | 0.850901 | − | 0.981992i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.9924 | + | 25.0589i | −1.47272 | + | 0.946462i | −0.474934 | + | 0.880022i | \(0.657528\pi\) |
−0.997790 | + | 0.0664406i | \(0.978836\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.9588 | − | 35.7283i | −1.16763 | − | 1.34752i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.88168 | + | 19.4482i | −0.334030 | + | 0.731424i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.678476 | − | 1.48565i | −0.0254807 | − | 0.0557949i | 0.896464 | − | 0.443117i | \(-0.146127\pi\) |
−0.921944 | + | 0.387322i | \(0.873400\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.140495 | − | 24.5279i | 0.00526157 | − | 0.918578i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43.4234 | − | 27.9065i | −1.62394 | − | 1.04364i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.86499 | + | 4.08377i | −0.0695525 | + | 0.152299i | −0.941215 | − | 0.337807i | \(-0.890315\pi\) |
0.871663 | + | 0.490106i | \(0.163042\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.0270 | − | 76.6943i | 0.410666 | − | 2.85625i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.504804 | − | 0.324418i | 0.0187479 | − | 0.0120486i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.1042 | + | 7.37125i | −0.931062 | + | 0.273384i | −0.711881 | − | 0.702300i | \(-0.752157\pi\) |
−0.219181 | + | 0.975684i | \(0.570338\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.8294 | − | 9.63959i | −1.21424 | − | 0.356533i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.67175 | + | 32.4927i | 0.172555 | + | 1.20015i | 0.873461 | + | 0.486894i | \(0.161870\pi\) |
−0.700906 | + | 0.713253i | \(0.747221\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58.0034 | 2.13658 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.53138 | + | 10.6510i | 0.0563328 | + | 0.391803i | 0.998408 | + | 0.0564017i | \(0.0179628\pi\) |
−0.942075 | + | 0.335401i | \(0.891128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.99673 | − | 10.3828i | 0.330058 | − | 0.380907i | −0.566329 | − | 0.824179i | \(-0.691637\pi\) |
0.896387 | + | 0.443272i | \(0.146182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8516 | + | 4.65446i | −0.580759 | + | 0.170526i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.2223 | + | 33.7244i | 1.06776 | + | 1.23226i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.35281 | − | 9.40898i | 0.0493646 | − | 0.343338i | −0.950139 | − | 0.311827i | \(-0.899059\pi\) |
0.999503 | − | 0.0315111i | \(-0.0100319\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.79262 | + | 19.2532i | 0.319996 | + | 0.700694i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4271 | + | 22.1249i | 1.25127 | + | 0.804144i | 0.987065 | − | 0.160322i | \(-0.0512531\pi\) |
0.264208 | + | 0.964466i | \(0.414889\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.7600 | − | 11.4136i | −0.643798 | − | 0.413744i | 0.177597 | − | 0.984103i | \(-0.443168\pi\) |
−0.821395 | + | 0.570359i | \(0.806804\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.92970 | + | 6.41514i | 0.106062 | + | 0.232244i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.72891 | − | 12.0248i | 0.0624273 | − | 0.434191i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.4272 | − | 18.9580i | −0.592380 | − | 0.683643i | 0.377839 | − | 0.925871i | \(-0.376667\pi\) |
−0.970219 | + | 0.242228i | \(0.922122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.5088 | − | 7.49005i | 0.917487 | − | 0.269399i | 0.211298 | − | 0.977422i | \(-0.432231\pi\) |
0.706189 | + | 0.708023i | \(0.250413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.02646 | + | 4.64679i | −0.144635 | + | 0.166917i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.79402 | + | 33.3431i | 0.171764 | + | 1.19464i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.2966 | −0.654704 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.32322 | + | 23.1135i | 0.118611 | + | 0.824957i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.4544 | + | 6.59320i | 0.800412 | + | 0.235022i | 0.656262 | − | 0.754534i | \(-0.272137\pi\) |
0.144151 | + | 0.989556i | \(0.453955\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 67.0475 | − | 19.6869i | 2.38393 | − | 0.699986i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.73803 | − | 3.68761i | 0.203764 | − | 0.130951i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.60649 | − | 11.1734i | 0.0569047 | − | 0.395781i | −0.941386 | − | 0.337332i | \(-0.890475\pi\) |
0.998290 | − | 0.0584489i | \(-0.0186155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.3878 | + | 31.5050i | −0.509005 | + | 1.11457i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.2567 | − | 19.4448i | −1.06774 | − | 0.686192i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.6924 | + | 31.4280i | −1.29324 | + | 1.10769i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.3175 | − | 31.3510i | −0.503377 | − | 1.10224i | −0.975357 | − | 0.220633i | \(-0.929188\pi\) |
0.471980 | − | 0.881609i | \(-0.343540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.81825 | + | 21.4990i | −0.344765 | + | 0.754931i | −1.00000 | 0.000494599i | \(-0.999843\pi\) | |
0.655234 | + | 0.755426i | \(0.272570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.90739 | − | 9.12562i | −0.276984 | − | 0.319656i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.2652 | − | 18.1649i | 0.988873 | − | 0.635510i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.23368 | + | 8.34811i | −0.252457 | + | 0.291351i | −0.867805 | − | 0.496904i | \(-0.834470\pi\) |
0.615348 | + | 0.788255i | \(0.289015\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.7025 | − | 11.6577i | −1.38394 | − | 0.406362i | −0.496802 | − | 0.867864i | \(-0.665493\pi\) |
−0.887139 | + | 0.461502i | \(0.847311\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.3095 | 1.15828 | 0.579142 | − | 0.815227i | \(-0.303388\pi\) | ||||
0.579142 | + | 0.815227i | \(0.303388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.7169 | −0.927917 | −0.463959 | − | 0.885857i | \(-0.653571\pi\) | ||||
−0.463959 | + | 0.885857i | \(0.653571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.5246 | + | 11.8991i | 1.40409 | + | 0.412279i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.7815 | − | 25.1372i | 0.753779 | − | 0.869907i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.30959 | − | 4.69759i | 0.252355 | − | 0.162179i | −0.408348 | − | 0.912827i | \(-0.633895\pi\) |
0.660703 | + | 0.750648i | \(0.270258\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.8278 | + | 21.7284i | 0.649235 | + | 0.749257i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.63727 | + | 12.3439i | −0.193928 | + | 0.424643i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.6431 | − | 45.2022i | −0.709307 | − | 1.55317i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46.6746 | + | 20.9933i | −1.59999 | + | 0.719642i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.0828 | + | 13.5491i | 0.721861 | + | 0.463912i | 0.849284 | − | 0.527937i | \(-0.177034\pi\) |
−0.127423 | + | 0.991848i | \(0.540671\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.96621 | + | 21.8230i | −0.340439 | + | 0.745458i | −0.999981 | − | 0.00621000i | \(-0.998023\pi\) |
0.659541 | + | 0.751668i | \(0.270751\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.08109 | − | 7.51915i | 0.0368863 | − | 0.256550i | −0.963031 | − | 0.269390i | \(-0.913178\pi\) |
0.999918 | + | 0.0128397i | \(0.00408711\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.12515 | + | 2.00841i | −0.106381 | + | 0.0683672i | −0.592750 | − | 0.805387i | \(-0.701958\pi\) |
0.486368 | + | 0.873754i | \(0.338321\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.3623 | + | 7.15342i | −0.828343 | + | 0.243224i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53.9081 | + | 15.8289i | 1.82871 | + | 0.536957i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.34771 | − | 51.1044i | −0.248968 | − | 1.73161i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.2582 | −1.29336 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.74616 | − | 33.0103i | −0.160266 | − | 1.11468i | −0.898131 | − | 0.439729i | \(-0.855075\pi\) |
0.737864 | − | 0.674949i | \(-0.235834\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.9310 | + | 18.3853i | −0.536728 | + | 0.619417i | −0.957739 | − | 0.287638i | \(-0.907130\pi\) |
0.421011 | + | 0.907056i | \(0.361675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.9814 | − | 7.92247i | 0.907998 | − | 0.266612i | 0.205800 | − | 0.978594i | \(-0.434020\pi\) |
0.702198 | + | 0.711982i | \(0.252202\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.0130 | + | 18.4800i | 0.537665 | + | 0.620498i | 0.957964 | − | 0.286887i | \(-0.0926204\pi\) |
−0.420299 | + | 0.907385i | \(0.638075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.22583 | + | 57.2119i | −0.275885 | + | 1.91882i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.1286 | − | 30.9373i | −0.472795 | − | 1.03528i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.7451 | + | 8.19077i | 0.426021 | + | 0.273787i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.14761 | + | 1.38019i | 0.0716268 | + | 0.0460318i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.3137 | − | 31.3427i | −0.476860 | − | 1.04418i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.64580 | + | 11.4468i | −0.0547084 | + | 0.380505i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.09587 | − | 5.88095i | −0.169206 | − | 0.195274i | 0.664813 | − | 0.747010i | \(-0.268511\pi\) |
−0.834019 | + | 0.551736i | \(0.813966\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.4926 | − | 9.83430i | 1.10966 | − | 0.325825i | 0.324975 | − | 0.945723i | \(-0.394644\pi\) |
0.784683 | + | 0.619897i | \(0.212826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.7688 | − | 19.3522i | 0.554966 | − | 0.640465i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.72435 | + | 39.8138i | 0.189035 | + | 1.31477i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.9522 | 0.592187 | 0.296093 | − | 0.955159i | \(-0.404316\pi\) | ||||
0.296093 | + | 0.955159i | \(0.404316\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.31776 | + | 16.1204i | 0.0762900 | + | 0.530609i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.3094 | + | 3.61436i | 0.404730 | + | 0.118840i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.1532 | − | 5.91751i | 0.661205 | − | 0.194147i | 0.0661220 | − | 0.997812i | \(-0.478937\pi\) |
0.595083 | + | 0.803664i | \(0.297119\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.8905 | + | 22.4228i | −1.14349 | + | 0.734876i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.71557 | + | 53.6630i | −0.252326 | + | 1.75497i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.2393 | + | 22.4210i | −0.334504 | + | 0.732462i | −0.999902 | − | 0.0140270i | \(-0.995535\pi\) |
0.665397 | + | 0.746489i | \(0.268262\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.2493 | − | 25.2240i | −1.27949 | − | 0.822279i | −0.288666 | − | 0.957430i | \(-0.593212\pi\) |
−0.990825 | + | 0.135151i | \(0.956848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.0657 | + | 5.39649i | 1.17446 | + | 0.175734i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.3997 | − | 22.7721i | −0.337944 | − | 0.739995i | 0.662010 | − | 0.749495i | \(-0.269703\pi\) |
−0.999955 | + | 0.00949957i | \(0.996976\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.2992 | + | 29.1211i | −0.431709 | + | 0.945312i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.6866 | − | 25.0277i | −0.702499 | − | 0.810727i | 0.286589 | − | 0.958054i | \(-0.407479\pi\) |
−0.989088 | + | 0.147326i | \(0.952933\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.7344 | + | 15.8958i | −0.800385 | + | 0.514376i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.5703 | − | 24.8935i | 0.696542 | − | 0.803852i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.64567 | + | 1.36409i | 0.149860 | + | 0.0440030i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −55.6876 | −1.79265 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0764 | 0.388352 | 0.194176 | − | 0.980967i | \(-0.437797\pi\) | ||||
0.194176 | + | 0.980967i | \(0.437797\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.4911 | − | 13.9446i | −1.52406 | − | 0.447505i | −0.590834 | − | 0.806793i | \(-0.701201\pi\) |
−0.933227 | + | 0.359288i | \(0.883020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.8343 | + | 30.9684i | −0.860269 | + | 0.992803i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.3854 | − | 11.8156i | 0.588200 | − | 0.378013i | −0.212427 | − | 0.977177i | \(-0.568137\pi\) |
0.800626 | + | 0.599164i | \(0.204500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.2219 | + | 40.6483i | 1.12570 | + | 1.29912i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.00858 | + | 6.58788i | −0.0959589 | + | 0.210121i | −0.951524 | − | 0.307575i | \(-0.900483\pi\) |
0.855565 | + | 0.517695i | \(0.173210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.37048 | + | 20.5185i | 0.298568 | + | 0.653774i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.0474 | − | 34.9577i | −0.319487 | − | 1.11159i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.3042 | + | 30.4005i | 1.50267 | + | 0.965705i | 0.994533 | + | 0.104427i | \(0.0333008\pi\) |
0.508134 | + | 0.861278i | \(0.330336\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.73453 | − | 8.17747i | 0.118392 | − | 0.259243i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.91121 | − | 61.9788i | 0.282221 | − | 1.96289i | 0.0126093 | − | 0.999920i | \(-0.495986\pi\) |
0.269612 | − | 0.962969i | \(-0.413105\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 828.2.q.c.577.2 | 20 | ||
3.2 | odd | 2 | 276.2.i.a.25.1 | ✓ | 20 | ||
23.12 | even | 11 | inner | 828.2.q.c.541.2 | 20 | ||
69.14 | even | 22 | 6348.2.a.t.1.3 | 10 | |||
69.32 | odd | 22 | 6348.2.a.s.1.8 | 10 | |||
69.35 | odd | 22 | 276.2.i.a.265.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.25.1 | ✓ | 20 | 3.2 | odd | 2 | ||
276.2.i.a.265.1 | yes | 20 | 69.35 | odd | 22 | ||
828.2.q.c.541.2 | 20 | 23.12 | even | 11 | inner | ||
828.2.q.c.577.2 | 20 | 1.1 | even | 1 | trivial | ||
6348.2.a.s.1.8 | 10 | 69.32 | odd | 22 | |||
6348.2.a.t.1.3 | 10 | 69.14 | even | 22 |