Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,2,Mod(2,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([33, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.2");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.p (of order \(66\), degree \(20\), 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: | \(1.60499308063\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{66}]$ |
Embedding invariants
Embedding label | 80.1 | ||
Root | \(-0.327068 - 0.945001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.80 |
Dual form | 201.2.p.a.98.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{19}{66}\right)\) |
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 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(3\) | −1.30900 | − | 1.13425i | −0.755750 | − | 0.654861i | ||||
\(4\) | −0.471518 | + | 1.94362i | −0.235759 | + | 0.971812i | ||||
\(5\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.816487 | + | 2.03949i | −0.308603 | + | 0.770853i | 0.690277 | + | 0.723545i | \(0.257489\pi\) |
−0.998880 | + | 0.0473083i | \(0.984936\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.426945 | + | 2.96946i | 0.142315 | + | 0.989821i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(12\) | 2.82177 | − | 2.00938i | 0.814576 | − | 0.580057i | ||||
\(13\) | 0.682051 | + | 7.14276i | 0.189167 | + | 1.98104i | 0.193731 | + | 0.981055i | \(0.437941\pi\) |
−0.00456441 | + | 0.999990i | \(0.501453\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.55534 | − | 1.83291i | −0.888835 | − | 0.458227i | ||||
\(17\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.43315 | − | 0.974087i | 0.558203 | − | 0.223471i | −0.0753671 | − | 0.997156i | \(-0.524013\pi\) |
0.633571 | + | 0.773685i | \(0.281589\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.38207 | − | 1.74358i | 0.738028 | − | 0.380480i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.07708 | + | 4.54816i | −0.415415 | + | 0.909632i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.80925 | − | 4.37128i | 0.540641 | − | 0.841254i | ||||
\(28\) | −3.57900 | − | 2.54860i | −0.676368 | − | 0.481640i | ||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.332790 | − | 3.48513i | 0.0597708 | − | 0.625948i | −0.915108 | − | 0.403210i | \(-0.867894\pi\) |
0.974878 | − | 0.222738i | \(-0.0714995\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.97283 | − | 0.570336i | −0.995472 | − | 0.0950560i | ||||
\(37\) | −5.22813 | − | 9.05539i | −0.859500 | − | 1.48870i | −0.872407 | − | 0.488780i | \(-0.837442\pi\) |
0.0129071 | − | 0.999917i | \(-0.495891\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.20888 | − | 10.1235i | 1.15435 | − | 1.62105i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.690079 | − | 0.723734i | \(-0.742424\pi\) | ||||
0.690079 | + | 0.723734i | \(0.257576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.137621 | + | 0.468693i | −0.0209869 | + | 0.0714749i | −0.969321 | − | 0.245800i | \(-0.920949\pi\) |
0.948334 | + | 0.317275i | \(0.102768\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(48\) | 2.57495 | + | 6.43192i | 0.371662 | + | 0.928368i | ||||
\(49\) | 1.57329 | + | 1.50013i | 0.224755 | + | 0.214304i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14.2044 | − | 2.04229i | −1.96980 | − | 0.283214i | ||||
\(53\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.28985 | − | 1.48473i | −0.568204 | − | 0.196657i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.4785 | + | 0.737330i | 1.98181 | + | 0.0944054i | 0.996902 | − | 0.0786561i | \(-0.0250629\pi\) |
0.984911 | + | 0.173061i | \(0.0553659\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.40478 | − | 1.55378i | −0.806926 | − | 0.195758i | ||||
\(64\) | 5.23889 | − | 6.04600i | 0.654861 | − | 0.755750i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.05134 | + | 5.51192i | 0.739289 | + | 0.673388i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.725040 | + | 15.2205i | −0.0848595 | + | 1.78142i | 0.409644 | + | 0.912245i | \(0.365653\pi\) |
−0.494504 | + | 0.869176i | \(0.664650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.87764 | − | 3.59760i | 0.909632 | − | 0.415415i | ||||
\(76\) | 0.745984 | + | 5.18843i | 0.0855702 | + | 0.595154i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.3547 | − | 10.2219i | 1.61503 | − | 1.15006i | 0.731307 | − | 0.682048i | \(-0.238911\pi\) |
0.883723 | − | 0.468010i | \(-0.155029\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.63544 | + | 2.53559i | −0.959493 | + | 0.281733i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(84\) | 1.79415 | + | 7.39560i | 0.195758 | + | 0.806926i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.1244 | − | 4.44094i | −1.58547 | − | 0.465537i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.38864 | + | 4.18456i | −0.455080 | + | 0.433918i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.48859 | + | 5.47824i | −0.963421 | + | 0.556231i | −0.897224 | − | 0.441575i | \(-0.854420\pi\) |
−0.0661967 | + | 0.997807i | \(0.521086\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.86053 | − | 6.18159i | −0.786053 | − | 0.618159i | ||||
\(101\) | 0 | 0 | 0.618159 | − | 0.786053i | \(-0.287879\pi\) | ||||
−0.618159 | + | 0.786053i | \(0.712121\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.24672 | − | 0.596490i | −0.615508 | − | 0.0587739i | −0.217355 | − | 0.976093i | \(-0.569743\pi\) |
−0.398153 | + | 0.917319i | \(0.630349\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(108\) | 7.17151 | + | 7.52126i | 0.690079 | + | 0.723734i | ||||
\(109\) | 17.6383 | + | 8.05513i | 1.68944 | + | 0.771541i | 0.998832 | + | 0.0483110i | \(0.0153839\pi\) |
0.690607 | + | 0.723230i | \(0.257343\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.42749 | + | 17.7835i | −0.325323 | + | 1.68793i | ||||
\(112\) | 6.64108 | − | 5.75453i | 0.627523 | − | 0.543752i | ||||
\(113\) | 0 | 0 | −0.458227 | − | 0.888835i | \(-0.651515\pi\) | ||||
0.458227 | + | 0.888835i | \(0.348485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.9190 | + | 5.07489i | −1.93396 | + | 0.469173i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9502 | − | 1.04562i | 0.995472 | − | 0.0950560i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.61686 | + | 2.29012i | 0.594212 | + | 0.205659i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.6291 | − | 7.45795i | −1.65306 | − | 0.661786i | −0.657289 | − | 0.753639i | \(-0.728297\pi\) |
−0.995773 | + | 0.0918526i | \(0.970721\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.711760 | − | 0.457421i | 0.0626670 | − | 0.0402736i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.75771i | 0.499257i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8320 | + | 16.8550i | 0.918760 | + | 1.42962i | 0.902951 | + | 0.429744i | \(0.141396\pi\) |
0.0158092 | + | 0.999875i | \(0.494968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.92482 | − | 11.3400i | 0.327068 | − | 0.945001i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.357906 | − | 3.74816i | −0.0295196 | − | 0.309143i | ||||
\(148\) | 20.0654 | − | 5.89174i | 1.64937 | − | 0.484298i | ||||
\(149\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.75525 | − | 23.7234i | −0.468355 | − | 1.93059i | −0.346544 | − | 0.938034i | \(-0.612645\pi\) |
−0.121811 | − | 0.992553i | \(-0.538870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 16.2771 | + | 18.7847i | 1.30321 | + | 1.50398i | ||||
\(157\) | 18.2449 | + | 3.51641i | 1.45610 | + | 0.280640i | 0.855039 | − | 0.518564i | \(-0.173533\pi\) |
0.601060 | + | 0.799204i | \(0.294745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8396 | − | 18.7747i | 0.849019 | − | 1.47054i | −0.0330650 | − | 0.999453i | \(-0.510527\pi\) |
0.882084 | − | 0.471091i | \(-0.156140\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37.7887 | + | 7.28318i | −2.90682 | + | 0.560244i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.93134 | + | 6.80928i | 0.300637 | + | 0.520719i | ||||
\(172\) | −0.846071 | − | 0.488479i | −0.0645123 | − | 0.0372462i | ||||
\(173\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.58000 | − | 7.94968i | −0.572994 | − | 0.600939i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.92125 | − | 22.8870i | −0.588782 | − | 1.70117i | −0.706129 | − | 0.708083i | \(-0.749560\pi\) |
0.117348 | − | 0.993091i | \(-0.462561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.4249 | − | 18.5216i | −1.43593 | − | 1.36916i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.62145 | + | 9.29852i | 0.481640 | + | 0.676368i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.945001 | − | 0.327068i | \(-0.893939\pi\) | ||||
0.945001 | + | 0.327068i | \(0.106061\pi\) | |||||||
\(192\) | −13.7154 | + | 1.97197i | −0.989821 | + | 0.142315i | ||||
\(193\) | −7.76952 | − | 17.0129i | −0.559262 | − | 1.22461i | −0.952320 | − | 0.305100i | \(-0.901310\pi\) |
0.393058 | − | 0.919514i | \(-0.371417\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.65751 | + | 2.35054i | −0.261251 | + | 0.167896i | ||||
\(197\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0500 | + | 11.0490i | −0.995975 | + | 0.783243i | −0.976269 | − | 0.216563i | \(-0.930515\pi\) |
−0.0197060 | + | 0.999806i | \(0.506273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.66928 | − | 14.0788i | −0.117742 | − | 0.993044i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.6671 | − | 26.6451i | 0.739629 | − | 1.84750i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.01717 | − | 2.93892i | 0.0700249 | − | 0.202324i | −0.904558 | − | 0.426350i | \(-0.859799\pi\) |
0.974583 | + | 0.224027i | \(0.0719203\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.83616 | + | 3.52428i | 0.464069 | + | 0.239244i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.2129 | − | 19.1012i | 1.23072 | − | 1.29074i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.2927 | + | 22.2650i | 1.29193 | + | 1.49097i | 0.770097 | + | 0.637927i | \(0.220208\pi\) |
0.521837 | + | 0.853045i | \(0.325247\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.3924 | − | 4.22599i | −0.959493 | − | 0.281733i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(228\) | 4.90850 | − | 7.63777i | 0.325073 | − | 0.505824i | ||||
\(229\) | 15.1505 | + | 10.7886i | 1.00117 | + | 0.712933i | 0.958187 | − | 0.286143i | \(-0.0923732\pi\) |
0.0429870 | + | 0.999076i | \(0.486313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.189251 | − | 0.981929i | \(-0.560606\pi\) | ||||
0.189251 | + | 0.981929i | \(0.439394\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30.3845 | − | 2.90137i | −1.97369 | − | 0.188464i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.50813 | − | 6.11050i | −0.612473 | − | 0.393612i | 0.197311 | − | 0.980341i | \(-0.436779\pi\) |
−0.809784 | + | 0.586729i | \(0.800415\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.1798 | + | 6.47568i | 0.909632 | + | 0.415415i | ||||
\(244\) | −8.73146 | + | 29.7366i | −0.558974 | + | 1.90369i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.61720 | + | 16.7150i | 0.548299 | + | 1.06355i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.971812 | − | 0.235759i | \(-0.0757576\pi\) | ||||
−0.971812 | + | 0.235759i | \(0.924242\pi\) | |||||||
\(252\) | 6.03993 | − | 11.7158i | 0.380480 | − | 0.738028i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.28091 | + | 13.0332i | 0.580057 | + | 0.814576i | ||||
\(257\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.7370 | − | 3.26909i | 1.41281 | − | 0.203132i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.5664 | + | 9.16256i | −0.828700 | + | 0.559692i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.79145 | + | 2.41880i | 0.169568 | + | 0.146932i | 0.735511 | − | 0.677513i | \(-0.236942\pi\) |
−0.565943 | + | 0.824445i | \(0.691488\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.7607 | + | 22.9681i | 0.893358 | + | 1.39009i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00223 | − | 13.9258i | −0.120302 | − | 0.836720i | −0.957214 | − | 0.289382i | \(-0.906550\pi\) |
0.836912 | − | 0.547338i | \(-0.184359\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.4911 | − | 0.499751i | 0.628083 | − | 0.0299193i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.0950560 | − | 0.995472i | \(-0.530303\pi\) | ||||
0.0950560 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.03154 | + | 21.0848i | −0.180206 | + | 1.25336i | 0.676068 | + | 0.736839i | \(0.263682\pi\) |
−0.856274 | + | 0.516522i | \(0.827227\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1102 | + | 7.78985i | −0.888835 | + | 0.458227i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.6342 | + | 3.59146i | 1.09236 | + | 0.210535i | ||||
\(292\) | −29.2410 | − | 8.58593i | −1.71120 | − | 0.502453i | ||||
\(293\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.27793 | + | 17.0075i | 0.189251 | + | 0.981929i | ||||
\(301\) | −0.843526 | − | 0.663357i | −0.0486201 | − | 0.0382352i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.4361 | − | 0.996527i | −0.598551 | − | 0.0571547i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.1966 | + | 26.9578i | −1.09561 | + | 1.53856i | −0.279960 | + | 0.960012i | \(0.590321\pi\) |
−0.815646 | + | 0.578551i | \(0.803618\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.50037 | + | 7.86616i | 0.426681 | + | 0.447490i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4766 | − | 11.6776i | 0.761744 | − | 0.660055i | −0.184747 | − | 0.982786i | \(-0.559147\pi\) |
0.946491 | + | 0.322731i | \(0.104601\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0991 | + | 32.7200i | 0.736882 | + | 1.84064i | ||||
\(317\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.856474 | − | 17.9796i | −0.0475819 | − | 0.998867i | ||||
\(325\) | −33.9031 | − | 11.7340i | −1.88060 | − | 0.650883i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.9519 | − | 30.5504i | −0.771541 | − | 1.68944i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.8823 | − | 5.79379i | −1.31269 | − | 0.318455i | −0.482481 | − | 0.875907i | \(-0.660264\pi\) |
−0.830210 | + | 0.557451i | \(0.811779\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.6575 | − | 19.3909i | 1.35122 | − | 1.06261i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −15.2202 | −0.830332 | ||||||||
\(337\) | 22.0887 | + | 28.0881i | 1.20325 | + | 1.53006i | 0.782211 | + | 0.623014i | \(0.214092\pi\) |
0.421039 | + | 0.907043i | \(0.361666\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.3323 | + | 8.37210i | −0.989853 | + | 0.452051i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.814576 | − | 0.580057i | \(-0.196970\pi\) | ||||
−0.814576 | + | 0.580057i | \(0.803030\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.117428 | − | 0.0344801i | 0.00628580 | − | 0.00184568i | −0.278588 | − | 0.960411i | \(-0.589866\pi\) |
0.284874 | + | 0.958565i | \(0.408048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.1391 | + | 17.0844i | 1.76883 | + | 0.911896i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.690079 | − | 0.723734i | \(-0.257576\pi\) | ||||
−0.690079 | + | 0.723734i | \(0.742424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.77956 | + | 8.37129i | −0.462082 | + | 0.440594i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.5198 | − | 11.0516i | −0.814576 | − | 0.580057i | ||||
\(364\) | 15.7629 | − | 27.3022i | 0.826203 | − | 1.43103i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.65738 | − | 29.3533i | −0.295313 | − | 1.53223i | −0.761865 | − | 0.647736i | \(-0.775716\pi\) |
0.466552 | − | 0.884494i | \(-0.345496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.06388 | − | 10.5030i | −0.314398 | − | 0.544553i | ||||
\(373\) | 15.6267 | + | 9.02205i | 0.809117 | + | 0.467144i | 0.846649 | − | 0.532151i | \(-0.178616\pi\) |
−0.0375318 | + | 0.999295i | \(0.511950\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.73268 | + | 24.5555i | −0.243101 | + | 1.26133i | 0.631076 | + | 0.775721i | \(0.282614\pi\) |
−0.874177 | + | 0.485608i | \(0.838598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.9262 | + | 30.8925i | 0.815923 | + | 1.58267i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.371662 | − | 0.928368i | \(-0.621212\pi\) | ||||
0.371662 | + | 0.928368i | \(0.378788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.45052 | − | 0.208554i | −0.0737342 | − | 0.0106014i | ||||
\(388\) | −6.17360 | − | 21.0253i | −0.313417 | − | 1.06740i | ||||
\(389\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.63457 | − | 5.54910i | 0.433357 | − | 0.278501i | −0.305722 | − | 0.952121i | \(-0.598898\pi\) |
0.739078 | + | 0.673620i | \(0.235261\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.53069 | − | 7.53682i | 0.326944 | − | 0.377313i | ||||
\(400\) | 15.7211 | − | 12.3632i | 0.786053 | − | 0.618159i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.1204 | 1.25134 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.30319 | − | 8.25096i | 0.163332 | − | 0.407984i | −0.824013 | − | 0.566571i | \(-0.808270\pi\) |
0.987345 | + | 0.158587i | \(0.0506939\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.10479 | − | 11.8600i | 0.202229 | − | 0.584301i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.93869 | − | 34.3493i | 0.241849 | − | 1.68209i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.0436 | − | 15.2304i | 1.85413 | − | 0.742282i | 0.907384 | − | 0.420303i | \(-0.138076\pi\) |
0.946747 | − | 0.321979i | \(-0.104348\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.1417 | + | 30.9661i | −0.684366 | + | 1.49855i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | −18.0000 | + | 10.3923i | −0.866025 | + | 0.500000i | ||||
\(433\) | 1.81441 | − | 19.0013i | 0.0871947 | − | 0.913145i | −0.840996 | − | 0.541041i | \(-0.818030\pi\) |
0.928191 | − | 0.372104i | \(-0.121363\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.9729 | + | 30.4840i | −1.14809 | + | 1.45992i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.4497 | − | 31.9558i | −0.880555 | − | 1.52517i | −0.850725 | − | 0.525610i | \(-0.823837\pi\) |
−0.0298292 | − | 0.999555i | \(-0.509496\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.78286 | + | 5.31229i | −0.180136 | + | 0.252966i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.690079 | − | 0.723734i | \(-0.742424\pi\) | ||||
0.690079 | + | 0.723734i | \(0.257576\pi\) | |||||||
\(444\) | −32.9483 | − | 15.0470i | −1.56366 | − | 0.714098i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.05324 | + | 15.6211i | 0.380480 | + | 0.738028i | ||||
\(449\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.3748 | + | 37.5818i | −0.910306 | + | 1.76575i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3468 | − | 20.1472i | −0.671114 | − | 0.942448i | 0.328884 | − | 0.944370i | \(-0.393327\pi\) |
−0.999998 | + | 0.00192256i | \(0.999388\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1908 | − | 1.19999i | −1.17072 | − | 0.0557680i | −0.546802 | − | 0.837262i | \(-0.684155\pi\) |
−0.623913 | + | 0.781494i | \(0.714458\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(468\) | − | 43.0515i | − | 1.99006i | ||||||
\(469\) | −16.1823 | + | 7.84122i | −0.747230 | + | 0.362074i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.8940 | − | 25.2972i | −0.916666 | − | 1.16564i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.623535 | + | 13.0896i | −0.0286098 | + | 0.600593i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 61.1146 | − | 43.5195i | 2.78659 | − | 1.98432i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.13093 | + | 21.7761i | −0.142315 | + | 0.989821i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9440 | − | 30.3556i | 1.31158 | − | 1.37554i | 0.430486 | − | 0.902597i | \(-0.358342\pi\) |
0.881092 | − | 0.472946i | \(-0.156809\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.4841 | + | 12.2812i | −1.60465 | + | 0.555374i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.57110 | + | 11.7809i | −0.339952 | + | 0.528976i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.9923 | − | 8.07843i | 0.626379 | − | 0.361640i | −0.152969 | − | 0.988231i | \(-0.548884\pi\) |
0.779349 | + | 0.626591i | \(0.215550\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.618159 | − | 0.786053i | \(-0.287879\pi\) | ||||
−0.618159 | + | 0.786053i | \(0.712121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 57.7262 | + | 33.3283i | 2.56371 | + | 1.48016i | ||||
\(508\) | 23.2794 | − | 32.6913i | 1.03286 | − | 1.45044i | ||||
\(509\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.4499 | − | 13.9060i | −1.34703 | − | 0.615166i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.57733 | − | 13.3725i | 0.113792 | − | 0.590408i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.553446 | + | 1.59908i | 0.0243641 | + | 0.0703954i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.2397 | − | 4.12889i | 1.89074 | − | 0.180544i | 0.915595 | − | 0.402102i | \(-0.131720\pi\) |
0.975147 | + | 0.221558i | \(0.0711142\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.905260 | + | 19.0037i | 0.0395088 | + | 0.829391i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.3525 | + | 8.54824i | 0.928368 | + | 0.371662i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.1908 | − | 2.71486i | −0.485184 | − | 0.117704i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.0515 | − | 38.9809i | −1.07705 | − | 1.67592i | −0.612887 | − | 0.790171i | \(-0.709992\pi\) |
−0.464162 | − | 0.885750i | \(-0.653645\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.5907 | + | 38.9436i | −0.669060 | + | 1.67123i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.1181 | + | 1.57761i | −1.41603 | + | 0.0674536i | −0.741577 | − | 0.670868i | \(-0.765922\pi\) |
−0.674449 | + | 0.738321i | \(0.735619\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.41897 | + | 46.2775i | 0.188597 | + | 1.97508i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.12707 | + | 37.6223i | 0.388123 | + | 1.59986i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37.8672 | + | 13.1060i | −1.60593 | + | 0.555816i | ||||
\(557\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.44162 | − | 0.663318i | −0.145565 | − | 0.0280554i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.87942 | − | 19.6821i | 0.0789280 | − | 0.826572i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.6490 | + | 7.06351i | −1.53371 | + | 0.295599i | −0.885056 | − | 0.465484i | \(-0.845880\pi\) |
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.1901 | + | 12.9754i | 0.841254 | + | 0.540641i | ||||
\(577\) | 23.0448 | + | 24.1687i | 0.959369 | + | 1.00616i | 0.999976 | + | 0.00698200i | \(0.00222246\pi\) |
−0.0406067 | + | 0.999175i | \(0.512929\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.12661 | + | 31.0824i | −0.379289 | + | 1.29174i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
−0.458227 | + | 0.888835i | \(0.651515\pi\) | |||||||
\(588\) | 7.45377 | + | 1.07169i | 0.307388 | + | 0.0441958i | ||||
\(589\) | −2.58509 | − | 8.80402i | −0.106517 | − | 0.362763i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.99012 | + | 41.7777i | 0.0817933 | + | 1.71705i | ||||
\(593\) | 0 | 0 | −0.945001 | − | 0.327068i | \(-0.893939\pi\) | ||||
0.945001 | + | 0.327068i | \(0.106061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.9237 | + | 1.47308i | 1.26562 | + | 0.0602890i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.6111 | − | 26.4320i | 1.37102 | − | 1.07818i | 0.383022 | − | 0.923739i | \(-0.374883\pi\) |
0.988001 | − | 0.154446i | \(-0.0493591\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.7839 | + | 20.3225i | −0.561322 | + | 0.827597i | ||||
\(604\) | 48.8231 | 1.98659 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.2694 | + | 42.3310i | −0.416821 | + | 1.71816i | 0.245901 | + | 0.969295i | \(0.420916\pi\) |
−0.662722 | + | 0.748866i | \(0.730599\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.3131 | − | 38.4657i | 0.537711 | − | 1.55361i | −0.269287 | − | 0.963060i | \(-0.586788\pi\) |
0.806998 | − | 0.590554i | \(-0.201091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.4775 | + | 16.7433i | 1.30538 | + | 0.672970i | 0.963735 | − | 0.266860i | \(-0.0859860\pi\) |
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −44.1854 | + | 22.7792i | −1.76883 | + | 0.911896i | ||||
\(625\) | −16.3715 | − | 18.8937i | −0.654861 | − | 0.755750i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.4374 | + | 33.8031i | −0.616018 | + | 1.34889i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.1520 | + | 10.0776i | 0.563382 | + | 0.401183i | 0.825960 | − | 0.563728i | \(-0.190633\pi\) |
−0.262578 | + | 0.964911i | \(0.584573\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.66495 | + | 2.69331i | −0.185415 | + | 0.107049i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.64197 | + | 12.2608i | −0.382029 | + | 0.485789i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.6763 | − | 25.4984i | −1.56468 | − | 1.00556i | −0.981100 | − | 0.193502i | \(-0.938015\pi\) |
−0.583579 | − | 0.812056i | \(-0.698348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.95108 | − | 12.3672i | −0.194048 | − | 0.484709i | ||||
\(652\) | 31.3798 | + | 29.9206i | 1.22893 | + | 1.17178i | ||||
\(653\) | 0 | 0 | 0.971812 | − | 0.235759i | \(-0.0757576\pi\) | ||||
−0.971812 | + | 0.235759i | \(0.924242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −45.5062 | + | 4.34531i | −1.77537 | + | 0.169527i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.4692 | + | 4.09325i | −1.10732 | + | 0.159209i | −0.671630 | − | 0.740887i | \(-0.734405\pi\) |
−0.435692 | + | 0.900096i | \(0.643496\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 51.0275i | − | 1.97284i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.2464 | + | 32.2742i | 1.43574 | + | 1.24408i | 0.922590 | + | 0.385782i | \(0.126068\pi\) |
0.513153 | + | 0.858297i | \(0.328477\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.0463 | + | 21.8564i | 0.540641 | + | 0.841254i | ||||
\(676\) | 3.66230 | − | 76.8811i | 0.140858 | − | 2.95697i | ||||
\(677\) | 0 | 0 | 0.371662 | − | 0.928368i | \(-0.378788\pi\) | ||||
−0.371662 | + | 0.928368i | \(0.621212\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.42548 | − | 23.8248i | −0.131458 | − | 0.914311i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.0950560 | − | 0.995472i | \(-0.530303\pi\) | ||||
0.0950560 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(684\) | −15.0884 | + | 4.43034i | −0.576918 | + | 0.169398i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.59494 | − | 31.3068i | −0.289765 | − | 1.19443i | ||||
\(688\) | 1.34836 | − | 1.41412i | 0.0514056 | − | 0.0539127i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.9655 | − | 23.1813i | 1.71057 | − | 0.881858i | 0.730572 | − | 0.682836i | \(-0.239254\pi\) |
0.979995 | − | 0.199023i | \(-0.0637767\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 19.0253 | − | 10.9843i | 0.719088 | − | 0.415166i | ||||
\(701\) | 0 | 0 | 0.0950560 | − | 0.995472i | \(-0.469697\pi\) | ||||
−0.0950560 | + | 0.995472i | \(0.530303\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.5416 | − | 16.9405i | −0.812456 | − | 0.638923i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.6170 | + | 41.5913i | −1.11229 | + | 1.56199i | −0.324677 | + | 0.945825i | \(0.605256\pi\) |
−0.787614 | + | 0.616169i | \(0.788684\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.4823 | + | 38.2616i | 1.36819 | + | 1.43492i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.31690 | − | 12.2531i | 0.235254 | − | 0.456329i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.51526 | + | 18.7832i | 0.205115 | + | 0.698556i | ||||
\(724\) | 48.2186 | − | 4.60432i | 1.79203 | − | 0.171118i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.0163 | − | 17.3108i | −1.85500 | − | 0.642023i | −0.990153 | − | 0.139992i | \(-0.955292\pi\) |
−0.864850 | − | 0.502031i | \(-0.832586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.2162 | − | 24.5601i | −0.415415 | − | 0.909632i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 45.1583 | − | 29.0215i | 1.66910 | − | 1.07266i | ||||
\(733\) | −45.2214 | − | 10.9706i | −1.67029 | − | 0.405208i | −0.714589 | − | 0.699544i | \(-0.753386\pi\) |
−0.955702 | + | 0.294336i | \(0.904902\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.4214 | − | 20.8815i | −0.604072 | − | 0.768140i | 0.383799 | − | 0.923417i | \(-0.374616\pi\) |
−0.987871 | + | 0.155277i | \(0.950373\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.67918 | − | 31.6540i | 0.282102 | − | 1.16284i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.5547 | + | 15.4314i | −1.91775 | + | 0.563101i | −0.948753 | + | 0.316017i | \(0.897654\pi\) |
−0.968994 | + | 0.247084i | \(0.920528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −21.1950 | + | 8.48518i | −0.770853 | + | 0.308603i | ||||
\(757\) | 26.7229 | − | 9.24888i | 0.971259 | − | 0.336156i | 0.205053 | − | 0.978751i | \(-0.434263\pi\) |
0.766206 | + | 0.642595i | \(0.222142\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.8297 | + | 29.3961i | −1.11611 | + | 1.06421i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.63427 | − | 27.5873i | 0.0950560 | − | 0.995472i | ||||
\(769\) | −6.39275 | − | 33.1687i | −0.230528 | − | 1.19610i | −0.894060 | − | 0.447947i | \(-0.852155\pi\) |
0.663532 | − | 0.748148i | \(-0.269057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 36.7301 | − | 7.07914i | 1.32194 | − | 0.254784i | ||||
\(773\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.1597 | + | 8.75246i | 0.544553 | + | 0.314398i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −33.4707 | − | 21.5103i | −1.20075 | − | 0.771678i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.84398 | − | 8.21714i | −0.101571 | − | 0.293469i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.9020 | − | 12.3487i | 1.81446 | − | 0.440183i | 0.822719 | − | 0.568448i | \(-0.192456\pi\) |
0.991740 | + | 0.128265i | \(0.0409408\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.29052 | + | 111.062i | 0.187872 | + | 3.94392i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.8503 | − | 32.5176i | −0.526355 | − | 1.15256i | ||||
\(797\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 28.1510 | + | 3.39397i | 0.992811 | + | 0.119696i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.82335 | − | 14.5460i | 0.204486 | − | 0.510780i | −0.790306 | − | 0.612713i | \(-0.790078\pi\) |
0.994791 | + | 0.101932i | \(0.0325026\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.910463 | − | 6.33241i | −0.0319313 | − | 0.222087i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.121696 | + | 1.27445i | 0.00425759 | + | 0.0445875i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.72990 | − | 46.8075i | 0.235162 | − | 1.63559i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −51.8626 | + | 20.7627i | −1.80782 | + | 0.723741i | −0.819159 | + | 0.573567i | \(0.805559\pi\) |
−0.988660 | + | 0.150174i | \(0.952017\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.4899 | − | 40.4872i | 0.642181 | − | 1.40618i | −0.256054 | − | 0.966663i | \(-0.582422\pi\) |
0.898234 | − | 0.439517i | \(-0.144850\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.1744 | + | 20.4998i | −0.457017 | + | 0.711132i | ||||
\(832\) | 46.7583 | + | 33.2964i | 1.62105 | + | 1.15435i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.2996 | − | 11.2453i | −0.494266 | − | 0.388695i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | − | 25.1147i | −0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.23254 | + | 3.36275i | 0.180111 | + | 0.115751i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.80817 | + | 23.1865i | −0.233931 | + | 0.796697i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.8837 | − | 24.1614i | 0.956967 | − | 0.829217i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.4332 | − | 27.1110i | −0.973535 | − | 0.928264i | 0.0239089 | − | 0.999714i | \(-0.492389\pi\) |
−0.997444 | + | 0.0714502i | \(0.977237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.6581 | + | 14.9673i | 0.363651 | + | 0.510677i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
−0.591696 | + | 0.806161i | \(0.701542\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.6149 | + | 6.94189i | 0.971812 | + | 0.235759i | ||||
\(868\) | −10.0732 | + | 11.6252i | −0.341908 | + | 0.394583i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.2430 | + | 46.9827i | −1.19416 | + | 1.59195i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.3186 | − | 25.8371i | −0.687679 | − | 0.874455i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 28.5377 | + | 44.4056i | 0.964201 | + | 1.50033i | ||||
\(877\) | 2.35955 | − | 49.5330i | 0.0796763 | − | 1.67261i | −0.506357 | − | 0.862324i | \(-0.669008\pi\) |
0.586033 | − | 0.810287i | \(-0.300689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.3387 | + | 25.8767i | −1.22289 | + | 0.870819i | −0.994702 | − | 0.102797i | \(-0.967221\pi\) |
−0.228192 | + | 0.973616i | \(0.573281\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.4208 | − | 31.9044i | 1.02028 | − | 1.07004i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −52.3715 | + | 26.9994i | −1.75353 | + | 0.904007i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 15.0000 | − | 25.9808i | 0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.351760 | + | 1.82510i | 0.0117058 | + | 0.0607356i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 57.7344 | + | 5.51296i | 1.91704 | + | 0.183055i | 0.984178 | − | 0.177183i | \(-0.0566983\pi\) |
0.932861 | + | 0.360238i | \(0.117304\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(912\) | 12.5305 | + | 13.1416i | 0.414927 | + | 0.435162i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.1128 | + | 24.3599i | −0.928872 | + | 0.804872i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.700819 | − | 1.75056i | −0.0231179 | − | 0.0577457i | 0.916360 | − | 0.400356i | \(-0.131113\pi\) |
−0.939478 | + | 0.342610i | \(0.888689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 55.7052 | − | 13.5139i | 1.83555 | − | 0.445299i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 52.0446 | − | 4.96966i | 1.71122 | − | 0.163401i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.895749 | − | 18.8041i | −0.0294203 | − | 0.617607i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.28930 | + | 2.11752i | 0.173350 | + | 0.0693988i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.1714i | 0.724307i | 0.932119 | + | 0.362153i | \(0.117958\pi\) | ||||
−0.932119 | + | 0.362153i | \(0.882042\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.8862 | −1.00793 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(948\) | 19.9660 | − | 57.6880i | 0.648466 | − | 1.87362i | ||||
\(949\) | −109.211 | + | 5.20234i | −3.54513 | + | 0.168875i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.4044 | + | 3.54716i | 0.593690 | + | 0.114424i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.3598 | − | 15.5990i | 0.526913 | − | 0.502410i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.24681 | − | 7.35569i | 0.136568 | − | 0.236543i | −0.789627 | − | 0.613587i | \(-0.789726\pi\) |
0.926195 | + | 0.377044i | \(0.123059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(972\) | −19.2723 | + | 24.5067i | −0.618159 | + | 0.786053i | ||||
\(973\) | −43.2196 | + | 8.32990i | −1.38556 | + | 0.267044i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 31.0697 | + | 53.8143i | 0.995028 | + | 1.72344i | ||||
\(976\) | −53.6797 | − | 30.9920i | −1.71825 | − | 0.992030i | ||||
\(977\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.3888 | + | 55.8153i | −0.523256 | + | 1.78205i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36.5509 | + | 8.86715i | −1.16284 | + | 0.282102i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.3752 | + | 59.1745i | 0.551941 | + | 1.87974i | 0.469031 | + | 0.883182i | \(0.344603\pi\) |
0.0829100 | + | 0.996557i | \(0.473579\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.6903 | + | 34.6726i | 0.783521 | + | 1.10030i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.8556 | + | 36.9086i | 0.533821 | + | 1.16891i | 0.963937 | + | 0.266132i | \(0.0857457\pi\) |
−0.430115 | + | 0.902774i | \(0.641527\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −54.2708 | − | 2.58524i | −1.71705 | − | 0.0817933i |
(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 | 201.2.p.a.80.1 | ✓ | 20 | |
3.2 | odd | 2 | CM | 201.2.p.a.80.1 | ✓ | 20 | |
67.31 | odd | 66 | inner | 201.2.p.a.98.1 | yes | 20 | |
201.98 | even | 66 | inner | 201.2.p.a.98.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.2.p.a.80.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
201.2.p.a.80.1 | ✓ | 20 | 3.2 | odd | 2 | CM | |
201.2.p.a.98.1 | yes | 20 | 67.31 | odd | 66 | inner | |
201.2.p.a.98.1 | yes | 20 | 201.98 | even | 66 | inner |