Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(32,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bf (of order \(12\), degree \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.63456228123711897600000000.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 17x^{12} + 208x^{8} + 1377x^{4} + 6561 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(0.737552 + 1.56717i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.107 |
Dual form | 525.2.bf.e.368.2 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.578737 | − | 2.15988i | −0.409229 | − | 1.52726i | −0.796121 | − | 0.605138i | \(-0.793118\pi\) |
0.386892 | − | 0.922125i | \(-0.373549\pi\) | |||||||
\(3\) | 0.988431 | + | 1.42232i | 0.570671 | + | 0.821179i | ||||
\(4\) | −2.59808 | + | 1.50000i | −1.29904 | + | 0.750000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.50000 | − | 2.95804i | 1.02062 | − | 1.20761i | ||||
\(7\) | −0.684771 | + | 2.55560i | −0.258819 | + | 0.965926i | ||||
\(8\) | 1.58114 | + | 1.58114i | 0.559017 | + | 0.559017i | ||||
\(9\) | −1.04601 | + | 2.81174i | −0.348669 | + | 0.937246i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −4.70150 | − | 2.21266i | −1.35721 | − | 0.638739i | ||||
\(13\) | −3.74166 | + | 3.74166i | −1.03775 | + | 1.03775i | −0.0384901 | + | 0.999259i | \(0.512255\pi\) |
−0.999259 | + | 0.0384901i | \(0.987745\pi\) | |||||||
\(14\) | 5.91608 | 1.58114 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −4.31975 | − | 1.15747i | −1.04769 | − | 0.280729i | −0.306395 | − | 0.951904i | \(-0.599123\pi\) |
−0.741298 | + | 0.671176i | \(0.765790\pi\) | |||||||
\(18\) | 6.67837 | + | 0.631989i | 1.57411 | + | 0.148961i | ||||
\(19\) | 1.73205 | + | 1.00000i | 0.397360 | + | 0.229416i | 0.685344 | − | 0.728219i | \(-0.259652\pi\) |
−0.287984 | + | 0.957635i | \(0.592985\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.31174 | + | 1.55207i | −0.940898 | + | 0.338689i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.47963 | + | 1.73621i | −1.35110 | + | 0.362025i | −0.860539 | − | 0.509384i | \(-0.829873\pi\) |
−0.490557 | + | 0.871409i | \(0.663207\pi\) | |||||||
\(24\) | −0.686044 | + | 3.81174i | −0.140038 | + | 0.778068i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10.2470 | + | 5.91608i | 2.00959 | + | 1.16024i | ||||
\(27\) | −5.03311 | + | 1.29145i | −0.968622 | + | 0.248539i | ||||
\(28\) | −2.05431 | − | 7.66680i | −0.388229 | − | 1.44889i | ||||
\(29\) | 5.91608 | 1.09859 | 0.549294 | − | 0.835629i | \(-0.314897\pi\) | ||||
0.549294 | + | 0.835629i | \(0.314897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 6.47963 | + | 1.73621i | 1.14545 | + | 0.306922i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0000i | 1.71499i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | − | 8.87412i | −0.250000 | − | 1.47902i | ||||
\(37\) | 10.2224 | − | 2.73908i | 1.68055 | − | 0.450303i | 0.712627 | − | 0.701543i | \(-0.247505\pi\) |
0.967925 | + | 0.251240i | \(0.0808385\pi\) | |||||||
\(38\) | 1.15747 | − | 4.31975i | 0.187767 | − | 0.700756i | ||||
\(39\) | −9.02022 | − | 1.62348i | −1.44439 | − | 0.259964i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.91608i | 0.923936i | 0.886896 | + | 0.461968i | \(0.152857\pi\) | ||||
−0.886896 | + | 0.461968i | \(0.847143\pi\) | |||||||
\(42\) | 5.84764 | + | 8.41458i | 0.902310 | + | 1.29840i | ||||
\(43\) | −1.87083 | + | 1.87083i | −0.285299 | + | 0.285299i | −0.835218 | − | 0.549919i | \(-0.814659\pi\) |
0.549919 | + | 0.835218i | \(0.314659\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.50000 | + | 12.9904i | 1.10581 | + | 1.91533i | ||||
\(47\) | 2.31495 | + | 8.63950i | 0.337670 | + | 1.26020i | 0.900946 | + | 0.433932i | \(0.142874\pi\) |
−0.563276 | + | 0.826269i | \(0.690459\pi\) | |||||||
\(48\) | −1.72598 | + | 0.144845i | −0.249124 | + | 0.0209066i | ||||
\(49\) | −6.06218 | − | 3.50000i | −0.866025 | − | 0.500000i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.62348 | − | 7.28817i | −0.367360 | − | 1.02055i | ||||
\(52\) | 4.10862 | − | 15.3336i | 0.569764 | − | 2.12639i | ||||
\(53\) | 1.15747 | − | 4.31975i | 0.158991 | − | 0.593364i | −0.839739 | − | 0.542990i | \(-0.817292\pi\) |
0.998730 | − | 0.0503735i | \(-0.0160412\pi\) | |||||||
\(54\) | 5.70221 | + | 10.1235i | 0.775973 | + | 1.37763i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.12348 | + | 2.95804i | −0.684653 | + | 0.395285i | ||||
\(57\) | 0.289690 | + | 3.45197i | 0.0383704 | + | 0.457224i | ||||
\(58\) | −3.42385 | − | 12.7780i | −0.449574 | − | 1.67783i | ||||
\(59\) | 5.91608 | + | 10.2470i | 0.770208 | + | 1.33404i | 0.937449 | + | 0.348123i | \(0.113181\pi\) |
−0.167241 | + | 0.985916i | \(0.553486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50000 | − | 9.52628i | 0.704203 | − | 1.21972i | −0.262776 | − | 0.964857i | \(-0.584638\pi\) |
0.966978 | − | 0.254858i | \(-0.0820288\pi\) | |||||||
\(62\) | −3.16228 | + | 3.16228i | −0.401610 | + | 0.401610i | ||||
\(63\) | −6.46940 | − | 4.59857i | −0.815068 | − | 0.579366i | ||||
\(64\) | − | 13.0000i | − | 1.62500i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.684771 | − | 2.55560i | 0.0836581 | − | 0.312216i | −0.911399 | − | 0.411525i | \(-0.864996\pi\) |
0.995057 | + | 0.0993085i | \(0.0316631\pi\) | |||||||
\(68\) | 12.9593 | − | 3.47242i | 1.57154 | − | 0.421093i | ||||
\(69\) | −8.87412 | − | 7.50000i | −1.06832 | − | 0.902894i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.8322i | − | 1.40422i | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||
0.712069 | − | 0.702109i | \(-0.247758\pi\) | |||||||
\(72\) | −6.09963 | + | 2.79186i | −0.718848 | + | 0.329024i | ||||
\(73\) | 5.11120 | + | 1.36954i | 0.598221 | + | 0.160293i | 0.545208 | − | 0.838301i | \(-0.316451\pi\) |
0.0530130 | + | 0.998594i | \(0.483118\pi\) | |||||||
\(74\) | −11.8322 | − | 20.4939i | −1.37546 | − | 2.38237i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.00000 | −0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.71383 | + | 20.4221i | 0.194053 | + | 2.31235i | ||||
\(79\) | 1.73205 | + | 1.00000i | 0.194871 | + | 0.112509i | 0.594261 | − | 0.804272i | \(-0.297445\pi\) |
−0.399390 | + | 0.916781i | \(0.630778\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.81174 | − | 5.88220i | −0.756860 | − | 0.653577i | ||||
\(82\) | 12.7780 | − | 3.42385i | 1.41109 | − | 0.378101i | ||||
\(83\) | 1.58114 | + | 1.58114i | 0.173553 | + | 0.173553i | 0.788538 | − | 0.614986i | \(-0.210838\pi\) |
−0.614986 | + | 0.788538i | \(0.710838\pi\) | |||||||
\(84\) | 8.87412 | − | 10.5000i | 0.968246 | − | 1.14564i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.12348 | + | 2.95804i | 0.552479 | + | 0.318974i | ||||
\(87\) | 5.84764 | + | 8.41458i | 0.626933 | + | 0.902137i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.95804 | + | 5.12348i | −0.313552 | + | 0.543087i | −0.979129 | − | 0.203242i | \(-0.934852\pi\) |
0.665577 | + | 0.746329i | \(0.268186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.00000 | − | 12.1244i | −0.733799 | − | 1.27098i | ||||
\(92\) | 14.2302 | − | 14.2302i | 1.48361 | − | 1.48361i | ||||
\(93\) | 1.47510 | − | 3.13434i | 0.152961 | − | 0.325016i | ||||
\(94\) | 17.3205 | − | 10.0000i | 1.78647 | − | 1.03142i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.93521 | + | 10.9323i | 0.401636 | + | 1.11577i | ||||
\(97\) | −7.48331 | − | 7.48331i | −0.759815 | − | 0.759815i | 0.216473 | − | 0.976289i | \(-0.430545\pi\) |
−0.976289 | + | 0.216473i | \(0.930545\pi\) | |||||||
\(98\) | −4.05116 | + | 15.1191i | −0.409229 | + | 1.52726i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.12348 | + | 2.95804i | −0.509805 | + | 0.294336i | −0.732753 | − | 0.680494i | \(-0.761765\pi\) |
0.222949 | + | 0.974830i | \(0.428432\pi\) | |||||||
\(102\) | −14.2232 | + | 9.88431i | −1.40831 | + | 0.978693i | ||||
\(103\) | 2.05431 | + | 7.66680i | 0.202417 | + | 0.755432i | 0.990221 | + | 0.139506i | \(0.0445514\pi\) |
−0.787804 | + | 0.615926i | \(0.788782\pi\) | |||||||
\(104\) | −11.8322 | −1.16024 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0000 | −0.971286 | ||||||||
\(107\) | 0.578737 | + | 2.15988i | 0.0559486 | + | 0.208803i | 0.988241 | − | 0.152901i | \(-0.0488617\pi\) |
−0.932293 | + | 0.361704i | \(0.882195\pi\) | |||||||
\(108\) | 11.1392 | − | 10.9049i | 1.07187 | − | 1.04933i | ||||
\(109\) | −6.06218 | + | 3.50000i | −0.580651 | + | 0.335239i | −0.761392 | − | 0.648292i | \(-0.775484\pi\) |
0.180741 | + | 0.983531i | \(0.442150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0000 | + | 11.8322i | 1.32882 | + | 1.12306i | ||||
\(112\) | −1.87083 | − | 1.87083i | −0.176777 | − | 0.176777i | ||||
\(113\) | −3.16228 | − | 3.16228i | −0.297482 | − | 0.297482i | 0.542545 | − | 0.840027i | \(-0.317461\pi\) |
−0.840027 | + | 0.542545i | \(0.817461\pi\) | |||||||
\(114\) | 7.28817 | − | 2.62348i | 0.682599 | − | 0.245711i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15.3704 | + | 8.87412i | −1.42711 | + | 0.823941i | ||||
\(117\) | −6.60676 | − | 14.4344i | −0.610795 | − | 1.33446i | ||||
\(118\) | 18.7083 | − | 18.7083i | 1.72224 | − | 1.72224i | ||||
\(119\) | 5.91608 | − | 10.2470i | 0.542326 | − | 0.939336i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | + | 9.52628i | −0.500000 | + | 0.866025i | ||||
\(122\) | −23.7586 | − | 6.36611i | −2.15101 | − | 0.576360i | ||||
\(123\) | −8.41458 | + | 5.84764i | −0.758717 | + | 0.527264i | ||||
\(124\) | 5.19615 | + | 3.00000i | 0.466628 | + | 0.269408i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.18826 | + | 16.6345i | −0.551294 | + | 1.48192i | ||||
\(127\) | 11.2250 | + | 11.2250i | 0.996055 | + | 0.996055i | 0.999992 | − | 0.00393704i | \(-0.00125320\pi\) |
−0.00393704 | + | 0.999992i | \(0.501253\pi\) | |||||||
\(128\) | −15.1191 | + | 4.05116i | −1.33635 | + | 0.358075i | ||||
\(129\) | −4.51011 | − | 0.811738i | −0.397093 | − | 0.0714695i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.74166 | + | 3.74166i | −0.324443 | + | 0.324443i | ||||
\(134\) | −5.91608 | −0.511071 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.00000 | − | 8.66025i | −0.428746 | − | 0.742611i | ||||
\(137\) | −8.63950 | − | 2.31495i | −0.738123 | − | 0.197779i | −0.129879 | − | 0.991530i | \(-0.541459\pi\) |
−0.608243 | + | 0.793750i | \(0.708126\pi\) | |||||||
\(138\) | −11.0633 | + | 23.5075i | −0.941770 | + | 2.00109i | ||||
\(139\) | 8.00000i | 0.678551i | 0.940687 | + | 0.339276i | \(0.110182\pi\) | ||||
−0.940687 | + | 0.339276i | \(0.889818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0000 | + | 11.8322i | −0.842152 | + | 0.996448i | ||||
\(142\) | −25.5560 | + | 6.84771i | −2.14461 | + | 0.574647i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.91203 | − | 2.31174i | −0.159336 | − | 0.192645i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 11.8322i | − | 0.979236i | ||||||
\(147\) | −1.01391 | − | 12.0819i | −0.0836263 | − | 0.996497i | ||||
\(148\) | −22.4499 | + | 22.4499i | −1.84537 | + | 1.84537i | ||||
\(149\) | −8.87412 | + | 15.3704i | −0.726996 | + | 1.25919i | 0.231151 | + | 0.972918i | \(0.425751\pi\) |
−0.958147 | + | 0.286276i | \(0.907582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00000 | + | 5.19615i | 0.244137 | + | 0.422857i | 0.961888 | − | 0.273442i | \(-0.0881622\pi\) |
−0.717752 | + | 0.696299i | \(0.754829\pi\) | |||||||
\(152\) | 1.15747 | + | 4.31975i | 0.0938835 | + | 0.350378i | ||||
\(153\) | 7.77300 | − | 10.9353i | 0.628410 | − | 0.884065i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 25.8704 | − | 9.31241i | 2.07129 | − | 0.745590i | ||||
\(157\) | −2.73908 | + | 10.2224i | −0.218603 | + | 0.815836i | 0.766265 | + | 0.642525i | \(0.222113\pi\) |
−0.984867 | + | 0.173311i | \(0.944553\pi\) | |||||||
\(158\) | 1.15747 | − | 4.31975i | 0.0920837 | − | 0.343661i | ||||
\(159\) | 7.28817 | − | 2.62348i | 0.577989 | − | 0.208055i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 17.7482i | − | 1.39876i | ||||||
\(162\) | −8.76261 | + | 18.1168i | −0.688456 | + | 1.42339i | ||||
\(163\) | −1.36954 | − | 5.11120i | −0.107271 | − | 0.400340i | 0.891322 | − | 0.453371i | \(-0.149779\pi\) |
−0.998593 | + | 0.0530306i | \(0.983112\pi\) | |||||||
\(164\) | −8.87412 | − | 15.3704i | −0.692952 | − | 1.20023i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.50000 | − | 4.33013i | 0.194038 | − | 0.336083i | ||||
\(167\) | 11.0680 | − | 11.0680i | 0.856465 | − | 0.856465i | −0.134454 | − | 0.990920i | \(-0.542928\pi\) |
0.990920 | + | 0.134454i | \(0.0429282\pi\) | |||||||
\(168\) | −9.27149 | − | 4.36342i | −0.715311 | − | 0.336645i | ||||
\(169\) | − | 15.0000i | − | 1.15385i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.62348 | + | 3.82407i | −0.353566 | + | 0.292434i | ||||
\(172\) | 2.05431 | − | 7.66680i | 0.156640 | − | 0.584588i | ||||
\(173\) | 8.63950 | − | 2.31495i | 0.656849 | − | 0.176002i | 0.0850256 | − | 0.996379i | \(-0.472903\pi\) |
0.571824 | + | 0.820377i | \(0.306236\pi\) | |||||||
\(174\) | 14.7902 | − | 17.5000i | 1.12124 | − | 1.32667i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.72684 | + | 18.5430i | −0.655949 | + | 1.39378i | ||||
\(178\) | 12.7780 | + | 3.42385i | 0.957751 | + | 0.256629i | ||||
\(179\) | 5.91608 | + | 10.2470i | 0.442189 | + | 0.765893i | 0.997852 | − | 0.0655145i | \(-0.0208689\pi\) |
−0.555663 | + | 0.831408i | \(0.687536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.00000 | −0.222988 | −0.111494 | − | 0.993765i | \(-0.535564\pi\) | ||||
−0.111494 | + | 0.993765i | \(0.535564\pi\) | |||||||
\(182\) | −22.1359 | + | 22.1359i | −1.64083 | + | 1.64083i | ||||
\(183\) | 18.9858 | − | 1.59329i | 1.40347 | − | 0.117780i | ||||
\(184\) | −12.9904 | − | 7.50000i | −0.957664 | − | 0.552907i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.62348 | − | 1.37209i | −0.558980 | − | 0.100606i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −18.9737 | − | 18.9737i | −1.38380 | − | 1.38380i | ||||
\(189\) | 0.146098 | − | 13.7470i | 0.0106271 | − | 0.999944i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.4939 | − | 11.8322i | −1.48289 | − | 0.856145i | −0.483076 | − | 0.875579i | \(-0.660480\pi\) |
−0.999811 | + | 0.0194337i | \(0.993814\pi\) | |||||||
\(192\) | 18.4902 | − | 12.8496i | 1.33442 | − | 0.927340i | ||||
\(193\) | −10.2224 | − | 2.73908i | −0.735824 | − | 0.197164i | −0.128603 | − | 0.991696i | \(-0.541049\pi\) |
−0.607221 | + | 0.794533i | \(0.707716\pi\) | |||||||
\(194\) | −11.8322 | + | 20.4939i | −0.849500 | + | 1.47138i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 21.0000 | 1.50000 | ||||||||
\(197\) | 18.9737 | − | 18.9737i | 1.35182 | − | 1.35182i | 0.468190 | − | 0.883628i | \(-0.344906\pi\) |
0.883628 | − | 0.468190i | \(-0.155094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.92820 | − | 4.00000i | 0.491127 | − | 0.283552i | −0.233915 | − | 0.972257i | \(-0.575154\pi\) |
0.725042 | + | 0.688705i | \(0.241820\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.31174 | − | 1.55207i | 0.304127 | − | 0.109475i | ||||
\(202\) | 9.35414 | + | 9.35414i | 0.658155 | + | 0.658155i | ||||
\(203\) | −4.05116 | + | 15.1191i | −0.284336 | + | 1.06115i | ||||
\(204\) | 17.7482 | + | 15.0000i | 1.24263 | + | 1.05021i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.3704 | − | 8.87412i | 1.07091 | − | 0.618289i | ||||
\(207\) | 1.89597 | − | 20.0351i | 0.131779 | − | 1.39254i | ||||
\(208\) | −1.36954 | − | 5.11120i | −0.0949606 | − | 0.354398i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | 3.47242 | + | 12.9593i | 0.238487 | + | 0.890045i | ||||
\(213\) | 16.8292 | − | 11.6953i | 1.15311 | − | 0.801347i | ||||
\(214\) | 4.33013 | − | 2.50000i | 0.296001 | − | 0.170896i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.0000 | − | 5.91608i | −0.680414 | − | 0.402538i | ||||
\(217\) | 5.11120 | − | 1.36954i | 0.346971 | − | 0.0929705i | ||||
\(218\) | 11.0680 | + | 11.0680i | 0.749618 | + | 0.749618i | ||||
\(219\) | 3.10414 | + | 8.62348i | 0.209758 | + | 0.582720i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.4939 | − | 11.8322i | 1.37857 | − | 0.795917i | ||||
\(222\) | 17.4537 | − | 37.0860i | 1.17141 | − | 2.48905i | ||||
\(223\) | −3.74166 | + | 3.74166i | −0.250560 | + | 0.250560i | −0.821200 | − | 0.570640i | \(-0.806695\pi\) |
0.570640 | + | 0.821200i | \(0.306695\pi\) | |||||||
\(224\) | −8.87412 | + | 15.3704i | −0.592927 | + | 1.02698i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.00000 | + | 8.66025i | −0.332595 | + | 0.576072i | ||||
\(227\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(228\) | −5.93059 | − | 8.53394i | −0.392763 | − | 0.565174i | ||||
\(229\) | −15.5885 | − | 9.00000i | −1.03011 | − | 0.594737i | −0.113097 | − | 0.993584i | \(-0.536077\pi\) |
−0.917017 | + | 0.398847i | \(0.869410\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.35414 | + | 9.35414i | 0.614130 | + | 0.614130i | ||||
\(233\) | 21.5988 | − | 5.78737i | 1.41498 | − | 0.379143i | 0.531281 | − | 0.847196i | \(-0.321711\pi\) |
0.883701 | + | 0.468052i | \(0.155044\pi\) | |||||||
\(234\) | −27.3528 | + | 22.6235i | −1.78811 | + | 1.47894i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −30.7409 | − | 17.7482i | −2.00106 | − | 1.15531i | ||||
\(237\) | 0.289690 | + | 3.45197i | 0.0188174 | + | 0.224229i | ||||
\(238\) | −25.5560 | − | 6.84771i | −1.65655 | − | 0.443871i | ||||
\(239\) | 11.8322 | 0.765359 | 0.382679 | − | 0.923881i | \(-0.375001\pi\) | ||||
0.382679 | + | 0.923881i | \(0.375001\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.00000 | + | 5.19615i | 0.193247 | + | 0.334714i | 0.946324 | − | 0.323218i | \(-0.104765\pi\) |
−0.753077 | + | 0.657932i | \(0.771431\pi\) | |||||||
\(242\) | 23.7586 | + | 6.36611i | 1.52726 | + | 0.409229i | ||||
\(243\) | 1.63345 | − | 15.5026i | 0.104786 | − | 0.994495i | ||||
\(244\) | 33.0000i | 2.11261i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.5000 | + | 14.7902i | 1.11576 | + | 0.942989i | ||||
\(247\) | −10.2224 | + | 2.73908i | −0.650436 | + | 0.174284i | ||||
\(248\) | 1.15747 | − | 4.31975i | 0.0734997 | − | 0.274305i | ||||
\(249\) | −0.686044 | + | 3.81174i | −0.0434762 | + | 0.241559i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8322i | 0.746839i | 0.927663 | + | 0.373420i | \(0.121815\pi\) | ||||
−0.927663 | + | 0.373420i | \(0.878185\pi\) | |||||||
\(252\) | 23.7059 | + | 2.24334i | 1.49333 | + | 0.141317i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 17.7482 | − | 30.7409i | 1.11362 | − | 1.92885i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.50000 | + | 7.79423i | 0.281250 | + | 0.487139i | ||||
\(257\) | 6.94484 | + | 25.9185i | 0.433207 | + | 1.61675i | 0.745320 | + | 0.666707i | \(0.232297\pi\) |
−0.312112 | + | 0.950045i | \(0.601037\pi\) | |||||||
\(258\) | 0.856914 | + | 10.2111i | 0.0533491 | + | 0.635713i | ||||
\(259\) | 28.0000i | 1.73984i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.18826 | + | 16.6345i | −0.383044 | + | 1.02965i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.73621 | − | 6.47963i | 0.107059 | − | 0.399551i | −0.891511 | − | 0.452998i | \(-0.850354\pi\) |
0.998571 | + | 0.0534475i | \(0.0170210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.2470 | + | 5.91608i | 0.628281 | + | 0.362738i | ||||
\(267\) | −10.2111 | + | 0.856914i | −0.624907 | + | 0.0524423i | ||||
\(268\) | 2.05431 | + | 7.66680i | 0.125487 | + | 0.468324i | ||||
\(269\) | 2.95804 | + | 5.12348i | 0.180355 | + | 0.312384i | 0.942001 | − | 0.335609i | \(-0.108942\pi\) |
−0.761647 | + | 0.647993i | \(0.775609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | + | 1.73205i | −0.0607457 | + | 0.105215i | −0.894799 | − | 0.446469i | \(-0.852681\pi\) |
0.834053 | + | 0.551684i | \(0.186015\pi\) | |||||||
\(272\) | 3.16228 | − | 3.16228i | 0.191741 | − | 0.191741i | ||||
\(273\) | 10.3257 | − | 21.9404i | 0.624942 | − | 1.32789i | ||||
\(274\) | 20.0000i | 1.20824i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 34.3056 | + | 6.17439i | 2.06496 | + | 0.371655i | ||||
\(277\) | 4.10862 | − | 15.3336i | 0.246863 | − | 0.921307i | −0.725574 | − | 0.688144i | \(-0.758426\pi\) |
0.972438 | − | 0.233163i | \(-0.0749075\pi\) | |||||||
\(278\) | 17.2790 | − | 4.62990i | 1.03633 | − | 0.277683i | ||||
\(279\) | 5.91608 | − | 1.00000i | 0.354186 | − | 0.0598684i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.6643i | 1.41169i | 0.708364 | + | 0.705847i | \(0.249434\pi\) | ||||
−0.708364 | + | 0.705847i | \(0.750566\pi\) | |||||||
\(282\) | 31.3434 | + | 14.7510i | 1.86647 | + | 0.878412i | ||||
\(283\) | 5.11120 | + | 1.36954i | 0.303829 | + | 0.0814108i | 0.407513 | − | 0.913200i | \(-0.366396\pi\) |
−0.103683 | + | 0.994610i | \(0.533063\pi\) | |||||||
\(284\) | 17.7482 | + | 30.7409i | 1.05316 | + | 1.82413i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.1191 | − | 4.05116i | −0.892454 | − | 0.239132i | ||||
\(288\) | −11.6595 | + | 16.4029i | −0.687043 | + | 0.966552i | ||||
\(289\) | 2.59808 | + | 1.50000i | 0.152828 | + | 0.0882353i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.24695 | − | 18.0404i | 0.190340 | − | 1.05755i | ||||
\(292\) | −15.3336 | + | 4.10862i | −0.897331 | + | 0.240439i | ||||
\(293\) | 6.32456 | + | 6.32456i | 0.369484 | + | 0.369484i | 0.867289 | − | 0.497805i | \(-0.165860\pi\) |
−0.497805 | + | 0.867289i | \(0.665860\pi\) | |||||||
\(294\) | −25.5086 | + | 9.18216i | −1.48769 | + | 0.535515i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 20.4939 | + | 11.8322i | 1.19118 | + | 0.687730i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 38.3340 | + | 10.2716i | 2.22063 | + | 0.595016i | ||||
\(299\) | 17.7482 | − | 30.7409i | 1.02641 | − | 1.77779i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.50000 | − | 6.06218i | −0.201737 | − | 0.349418i | ||||
\(302\) | 9.48683 | − | 9.48683i | 0.545906 | − | 0.545906i | ||||
\(303\) | −9.27149 | − | 4.36342i | −0.532633 | − | 0.250672i | ||||
\(304\) | −1.73205 | + | 1.00000i | −0.0993399 | + | 0.0573539i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −28.1174 | − | 10.4601i | −1.60736 | − | 0.597963i | ||||
\(307\) | 5.61249 | + | 5.61249i | 0.320321 | + | 0.320321i | 0.848890 | − | 0.528569i | \(-0.177271\pi\) |
−0.528569 | + | 0.848890i | \(0.677271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.87412 | + | 10.5000i | −0.504831 | + | 0.597324i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.2470 | − | 5.91608i | 0.581051 | − | 0.335470i | −0.180500 | − | 0.983575i | \(-0.557772\pi\) |
0.761551 | + | 0.648105i | \(0.224438\pi\) | |||||||
\(312\) | −11.6953 | − | 16.8292i | −0.662115 | − | 0.952763i | ||||
\(313\) | 2.73908 | + | 10.2224i | 0.154822 | + | 0.577804i | 0.999121 | + | 0.0419307i | \(0.0133509\pi\) |
−0.844298 | + | 0.535873i | \(0.819982\pi\) | |||||||
\(314\) | 23.6643 | 1.33545 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | −5.78737 | − | 21.5988i | −0.325051 | − | 1.21311i | −0.914261 | − | 0.405127i | \(-0.867227\pi\) |
0.589209 | − | 0.807980i | \(-0.299439\pi\) | |||||||
\(318\) | −9.88431 | − | 14.2232i | −0.554285 | − | 0.797599i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.50000 | + | 2.95804i | −0.139536 | + | 0.165102i | ||||
\(322\) | −38.3340 | + | 10.2716i | −2.13627 | + | 0.572412i | ||||
\(323\) | −6.32456 | − | 6.32456i | −0.351908 | − | 0.351908i | ||||
\(324\) | 26.5207 | + | 5.06479i | 1.47337 | + | 0.281377i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.2470 | + | 5.91608i | −0.567526 | + | 0.327661i | ||||
\(327\) | −10.9702 | − | 5.16287i | −0.606652 | − | 0.285507i | ||||
\(328\) | −9.35414 | + | 9.35414i | −0.516496 | + | 0.516496i | ||||
\(329\) | −23.6643 | −1.30466 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00000 | + | 12.1244i | −0.384755 | + | 0.666415i | −0.991735 | − | 0.128302i | \(-0.959047\pi\) |
0.606980 | + | 0.794717i | \(0.292381\pi\) | |||||||
\(332\) | −6.47963 | − | 1.73621i | −0.355616 | − | 0.0952870i | ||||
\(333\) | −2.99112 | + | 31.6078i | −0.163912 | + | 1.73210i | ||||
\(334\) | −30.3109 | − | 17.5000i | −1.65854 | − | 0.957557i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.811738 | − | 4.51011i | 0.0442839 | − | 0.246047i | ||||
\(337\) | −3.74166 | − | 3.74166i | −0.203821 | − | 0.203821i | 0.597814 | − | 0.801635i | \(-0.296036\pi\) |
−0.801635 | + | 0.597814i | \(0.796036\pi\) | |||||||
\(338\) | −32.3981 | + | 8.68105i | −1.76223 | + | 0.472187i | ||||
\(339\) | 1.37209 | − | 7.62348i | 0.0745215 | − | 0.414050i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 10.9353 | + | 7.77300i | 0.591312 | + | 0.420316i | ||||
\(343\) | 13.0958 | − | 13.0958i | 0.707107 | − | 0.707107i | ||||
\(344\) | −5.91608 | −0.318974 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.0000 | − | 17.3205i | −0.537603 | − | 0.931156i | ||||
\(347\) | −10.7994 | − | 2.89368i | −0.579741 | − | 0.155341i | −0.0429807 | − | 0.999076i | \(-0.513685\pi\) |
−0.536760 | + | 0.843735i | \(0.680352\pi\) | |||||||
\(348\) | −27.8145 | − | 13.0903i | −1.49101 | − | 0.701711i | ||||
\(349\) | − | 31.0000i | − | 1.65939i | −0.558216 | − | 0.829696i | \(-0.688514\pi\) | ||
0.558216 | − | 0.829696i | \(-0.311486\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.0000 | − | 23.6643i | 0.747265 | − | 1.26311i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.47242 | + | 12.9593i | −0.184818 | + | 0.689752i | 0.809851 | + | 0.586636i | \(0.199548\pi\) |
−0.994669 | + | 0.103116i | \(0.967119\pi\) | |||||||
\(354\) | 45.1011 | + | 8.11738i | 2.39710 | + | 0.431434i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 17.7482i | − | 0.940655i | ||||||
\(357\) | 20.4221 | − | 1.71383i | 1.08085 | − | 0.0907054i | ||||
\(358\) | 18.7083 | − | 18.7083i | 0.988764 | − | 0.988764i | ||||
\(359\) | −5.91608 | + | 10.2470i | −0.312239 | + | 0.540813i | −0.978847 | − | 0.204595i | \(-0.934412\pi\) |
0.666608 | + | 0.745409i | \(0.267746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.50000 | − | 12.9904i | −0.394737 | − | 0.683704i | ||||
\(362\) | 1.73621 | + | 6.47963i | 0.0912532 | + | 0.340562i | ||||
\(363\) | −18.9858 | + | 1.59329i | −0.996497 | + | 0.0836263i | ||||
\(364\) | 36.3731 | + | 21.0000i | 1.90647 | + | 1.10070i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −14.4291 | − | 40.0849i | −0.754222 | − | 2.09527i | ||||
\(367\) | 2.05431 | − | 7.66680i | 0.107234 | − | 0.400204i | −0.891355 | − | 0.453306i | \(-0.850244\pi\) |
0.998589 | + | 0.0531027i | \(0.0169111\pi\) | |||||||
\(368\) | 1.73621 | − | 6.47963i | 0.0905063 | − | 0.337774i | ||||
\(369\) | −16.6345 | − | 6.18826i | −0.865956 | − | 0.322148i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.2470 | + | 5.91608i | 0.531995 | + | 0.307148i | ||||
\(372\) | 0.869070 | + | 10.3559i | 0.0450592 | + | 0.536929i | ||||
\(373\) | 5.47817 | + | 20.4448i | 0.283649 | + | 1.05859i | 0.949821 | + | 0.312794i | \(0.101265\pi\) |
−0.666172 | + | 0.745798i | \(0.732069\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.0000 | + | 17.3205i | −0.515711 | + | 0.893237i | ||||
\(377\) | −22.1359 | + | 22.1359i | −1.14006 | + | 1.14006i | ||||
\(378\) | −29.7763 | + | 7.64032i | −1.53153 | + | 0.392975i | ||||
\(379\) | 18.0000i | 0.924598i | 0.886724 | + | 0.462299i | \(0.152975\pi\) | ||||
−0.886724 | + | 0.462299i | \(0.847025\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.87043 | + | 27.0607i | −0.249519 | + | 1.38636i | ||||
\(382\) | −13.6954 | + | 51.1120i | −0.700718 | + | 2.61512i | ||||
\(383\) | 6.47963 | − | 1.73621i | 0.331093 | − | 0.0887162i | −0.0894428 | − | 0.995992i | \(-0.528509\pi\) |
0.420536 | + | 0.907276i | \(0.361842\pi\) | |||||||
\(384\) | −20.7063 | − | 17.5000i | −1.05666 | − | 0.893043i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.6643i | 1.20448i | ||||||||
\(387\) | −3.30338 | − | 7.21718i | −0.167920 | − | 0.366870i | ||||
\(388\) | 30.6672 | + | 8.21725i | 1.55689 | + | 0.417168i | ||||
\(389\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.0000 | 1.51717 | ||||||||
\(392\) | −4.05116 | − | 15.1191i | −0.204614 | − | 0.763631i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −51.9615 | − | 30.0000i | −2.61778 | − | 1.51138i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.4448 | + | 5.47817i | −1.02609 | + | 0.274941i | −0.732340 | − | 0.680939i | \(-0.761572\pi\) |
−0.293755 | + | 0.955881i | \(0.594905\pi\) | |||||||
\(398\) | −12.6491 | − | 12.6491i | −0.634043 | − | 0.634043i | ||||
\(399\) | −9.02022 | − | 1.62348i | −0.451576 | − | 0.0812754i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.3704 | + | 8.87412i | 0.767562 | + | 0.443152i | 0.832004 | − | 0.554769i | \(-0.187193\pi\) |
−0.0644419 | + | 0.997921i | \(0.520527\pi\) | |||||||
\(402\) | −5.84764 | − | 8.41458i | −0.291654 | − | 0.419681i | ||||
\(403\) | 10.2224 | + | 2.73908i | 0.509214 | + | 0.136443i | ||||
\(404\) | 8.87412 | − | 15.3704i | 0.441504 | − | 0.764707i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 35.0000 | 1.73702 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 7.37552 | − | 15.6717i | 0.365143 | − | 0.775864i | ||||
\(409\) | 11.2583 | − | 6.50000i | 0.556689 | − | 0.321404i | −0.195127 | − | 0.980778i | \(-0.562512\pi\) |
0.751815 | + | 0.659374i | \(0.229178\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.24695 | − | 14.5763i | −0.258813 | − | 0.718998i | ||||
\(412\) | −16.8375 | − | 16.8375i | −0.829522 | − | 0.829522i | ||||
\(413\) | −30.2383 | + | 8.10232i | −1.48793 | + | 0.398689i | ||||
\(414\) | −44.3706 | + | 7.50000i | −2.18070 | + | 0.368605i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −30.7409 | + | 17.7482i | −1.50719 | + | 0.870179i | ||||
\(417\) | −11.3786 | + | 7.90745i | −0.557212 | + | 0.387230i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.6643 | 1.15608 | 0.578039 | − | 0.816009i | \(-0.303818\pi\) | ||||
0.578039 | + | 0.816009i | \(0.303818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | −0.536107 | −0.268054 | − | 0.963404i | \(-0.586380\pi\) | ||||
−0.268054 | + | 0.963404i | \(0.586380\pi\) | |||||||
\(422\) | −8.10232 | − | 30.2383i | −0.394415 | − | 1.47198i | ||||
\(423\) | −26.7135 | − | 2.52796i | −1.29885 | − | 0.122913i | ||||
\(424\) | 8.66025 | − | 5.00000i | 0.420579 | − | 0.242821i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −35.0000 | − | 29.5804i | −1.69576 | − | 1.43318i | ||||
\(427\) | 20.5791 | + | 20.5791i | 0.995893 | + | 0.995893i | ||||
\(428\) | −4.74342 | − | 4.74342i | −0.229282 | − | 0.229282i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.4939 | − | 11.8322i | 0.987157 | − | 0.569935i | 0.0827334 | − | 0.996572i | \(-0.473635\pi\) |
0.904423 | + | 0.426637i | \(0.140302\pi\) | |||||||
\(432\) | 1.39813 | − | 5.00452i | 0.0672673 | − | 0.240780i | ||||
\(433\) | −11.2250 | + | 11.2250i | −0.539438 | + | 0.539438i | −0.923364 | − | 0.383926i | \(-0.874572\pi\) |
0.383926 | + | 0.923364i | \(0.374572\pi\) | |||||||
\(434\) | −5.91608 | − | 10.2470i | −0.283981 | − | 0.491869i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.5000 | − | 18.1865i | 0.502859 | − | 0.870977i | ||||
\(437\) | −12.9593 | − | 3.47242i | −0.619925 | − | 0.166108i | ||||
\(438\) | 16.8292 | − | 11.6953i | 0.804128 | − | 0.558822i | ||||
\(439\) | 27.7128 | + | 16.0000i | 1.32266 | + | 0.763638i | 0.984152 | − | 0.177325i | \(-0.0567444\pi\) |
0.338508 | + | 0.940963i | \(0.390078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.1822 | − | 13.3842i | 0.770579 | − | 0.637344i | ||||
\(442\) | −37.4166 | − | 37.4166i | −1.77972 | − | 1.77972i | ||||
\(443\) | −2.15988 | + | 0.578737i | −0.102619 | + | 0.0274966i | −0.309763 | − | 0.950814i | \(-0.600250\pi\) |
0.207144 | + | 0.978310i | \(0.433583\pi\) | |||||||
\(444\) | −54.1213 | − | 9.74085i | −2.56848 | − | 0.462280i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.2470 | + | 5.91608i | 0.485207 | + | 0.280134i | ||||
\(447\) | −30.6332 | + | 2.57074i | −1.44890 | + | 0.121592i | ||||
\(448\) | 33.2228 | + | 8.90202i | 1.56963 | + | 0.420581i | ||||
\(449\) | −17.7482 | −0.837591 | −0.418796 | − | 0.908081i | \(-0.637548\pi\) | ||||
−0.418796 | + | 0.908081i | \(0.637548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.9593 | + | 3.47242i | 0.609552 | + | 0.163329i | ||||
\(453\) | −4.42531 | + | 9.40301i | −0.207919 | + | 0.441792i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.00000 | + | 5.91608i | −0.234146 | + | 0.277046i | ||||
\(457\) | 10.2224 | − | 2.73908i | 0.478184 | − | 0.128129i | −0.0116731 | − | 0.999932i | \(-0.503716\pi\) |
0.489857 | + | 0.871803i | \(0.337049\pi\) | |||||||
\(458\) | −10.4173 | + | 38.8778i | −0.486767 | + | 1.81664i | ||||
\(459\) | 23.2366 | + | 0.246951i | 1.08459 | + | 0.0115267i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.6643i | 1.10216i | 0.834453 | + | 0.551079i | \(0.185784\pi\) | ||||
−0.834453 | + | 0.551079i | \(0.814216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.0958 | + | 13.0958i | −0.608613 | + | 0.608613i | −0.942584 | − | 0.333970i | \(-0.891612\pi\) |
0.333970 | + | 0.942584i | \(0.391612\pi\) | |||||||
\(464\) | −2.95804 | + | 5.12348i | −0.137324 | + | 0.237851i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.0000 | − | 43.3013i | −1.15810 | − | 2.00589i | ||||
\(467\) | 4.05116 | + | 15.1191i | 0.187465 | + | 0.699630i | 0.994089 | + | 0.108565i | \(0.0346256\pi\) |
−0.806624 | + | 0.591065i | \(0.798708\pi\) | |||||||
\(468\) | 38.8164 | + | 27.5914i | 1.79429 | + | 1.27541i | ||||
\(469\) | 6.06218 | + | 3.50000i | 0.279925 | + | 0.161615i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.2470 | + | 6.20828i | −0.794698 | + | 0.286062i | ||||
\(472\) | −6.84771 | + | 25.5560i | −0.315191 | + | 1.17631i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 7.28817 | − | 2.62348i | 0.334757 | − | 0.120500i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 35.4965i | 1.62698i | ||||||||
\(477\) | 10.9353 | + | 7.77300i | 0.500692 | + | 0.355901i | ||||
\(478\) | −6.84771 | − | 25.5560i | −0.313207 | − | 1.16890i | ||||
\(479\) | −17.7482 | − | 30.7409i | −0.810938 | − | 1.40459i | −0.912208 | − | 0.409726i | \(-0.865624\pi\) |
0.101271 | − | 0.994859i | \(-0.467709\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.0000 | + | 48.4974i | −1.27669 | + | 2.21129i | ||||
\(482\) | 9.48683 | − | 9.48683i | 0.432113 | − | 0.432113i | ||||
\(483\) | 25.2437 | − | 17.5429i | 1.14863 | − | 0.798230i | ||||
\(484\) | − | 33.0000i | − | 1.50000i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −34.4291 | + | 5.44390i | −1.56174 | + | 0.246940i | ||||
\(487\) | −1.36954 | + | 5.11120i | −0.0620599 | + | 0.231611i | −0.989989 | − | 0.141147i | \(-0.954921\pi\) |
0.927929 | + | 0.372757i | \(0.121588\pi\) | |||||||
\(488\) | 23.7586 | − | 6.36611i | 1.07550 | − | 0.288180i | ||||
\(489\) | 5.91608 | − | 7.00000i | 0.267534 | − | 0.316551i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.8322i | 0.533978i | 0.963700 | + | 0.266989i | \(0.0860287\pi\) | ||||
−0.963700 | + | 0.266989i | \(0.913971\pi\) | |||||||
\(492\) | 13.0903 | − | 27.8145i | 0.590154 | − | 1.25397i | ||||
\(493\) | −25.5560 | − | 6.84771i | −1.15098 | − | 0.308405i | ||||
\(494\) | 11.8322 | + | 20.4939i | 0.532354 | + | 0.922064i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 30.2383 | + | 8.10232i | 1.35637 | + | 0.363439i | ||||
\(498\) | 8.62992 | − | 0.724225i | 0.386716 | − | 0.0324533i | ||||
\(499\) | 10.3923 | + | 6.00000i | 0.465223 | + | 0.268597i | 0.714238 | − | 0.699903i | \(-0.246773\pi\) |
−0.249015 | + | 0.968500i | \(0.580107\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.6822 | + | 4.80230i | 1.19207 | + | 0.214551i | ||||
\(502\) | 25.5560 | − | 6.84771i | 1.14062 | − | 0.305628i | ||||
\(503\) | 23.7171 | + | 23.7171i | 1.05749 | + | 1.05749i | 0.998243 | + | 0.0592492i | \(0.0188707\pi\) |
0.0592492 | + | 0.998243i | \(0.481129\pi\) | |||||||
\(504\) | −2.95804 | − | 17.5000i | −0.131762 | − | 0.779512i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.3348 | − | 14.8265i | 0.947514 | − | 0.658467i | ||||
\(508\) | −46.0008 | − | 12.3259i | −2.04096 | − | 0.546872i | ||||
\(509\) | 8.87412 | − | 15.3704i | 0.393338 | − | 0.681282i | −0.599549 | − | 0.800338i | \(-0.704653\pi\) |
0.992888 | + | 0.119056i | \(0.0379867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.00000 | + | 12.1244i | −0.309662 | + | 0.536350i | ||||
\(512\) | −7.90569 | + | 7.90569i | −0.349386 | + | 0.349386i | ||||
\(513\) | −10.0090 | − | 2.79625i | −0.441910 | − | 0.123458i | ||||
\(514\) | 51.9615 | − | 30.0000i | 2.29192 | − | 1.32324i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.9352 | − | 4.65621i | 0.569441 | − | 0.204978i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 60.4765 | − | 16.2046i | 2.65719 | − | 0.711991i | ||||
\(519\) | 11.8322 | + | 10.0000i | 0.519374 | + | 0.438951i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.4939 | + | 11.8322i | −0.897854 | + | 0.518376i | −0.876503 | − | 0.481396i | \(-0.840130\pi\) |
−0.0213508 | + | 0.999772i | \(0.506797\pi\) | |||||||
\(522\) | 39.5098 | + | 3.73890i | 1.72929 | + | 0.163647i | ||||
\(523\) | 9.58679 | + | 35.7784i | 0.419201 | + | 1.56448i | 0.776269 | + | 0.630402i | \(0.217110\pi\) |
−0.357068 | + | 0.934078i | \(0.616224\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.0000 | −0.654031 | ||||||||
\(527\) | 2.31495 | + | 8.63950i | 0.100841 | + | 0.376343i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0526 | − | 11.0000i | 0.828372 | − | 0.478261i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.0000 | + | 5.91608i | −1.51887 | + | 0.256736i | ||||
\(532\) | 4.10862 | − | 15.3336i | 0.178131 | − | 0.664796i | ||||
\(533\) | −22.1359 | − | 22.1359i | −0.958814 | − | 0.958814i | ||||
\(534\) | 7.76034 | + | 21.5587i | 0.335823 | + | 0.932936i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.12348 | − | 2.95804i | 0.221300 | − | 0.127768i | ||||
\(537\) | −8.72684 | + | 18.5430i | −0.376591 | + | 0.800189i | ||||
\(538\) | 9.35414 | − | 9.35414i | 0.403286 | − | 0.403286i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.50000 | + | 16.4545i | −0.408437 | + | 0.707433i | −0.994715 | − | 0.102677i | \(-0.967259\pi\) |
0.586278 | + | 0.810110i | \(0.300593\pi\) | |||||||
\(542\) | 4.31975 | + | 1.15747i | 0.185549 | + | 0.0497178i | ||||
\(543\) | −2.96529 | − | 4.26697i | −0.127253 | − | 0.183113i | ||||
\(544\) | −25.9808 | − | 15.0000i | −1.11392 | − | 0.643120i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −53.3643 | − | 9.60461i | −2.28378 | − | 0.411039i | ||||
\(547\) | 24.3208 | + | 24.3208i | 1.03988 | + | 1.03988i | 0.999171 | + | 0.0407102i | \(0.0129620\pi\) |
0.0407102 | + | 0.999171i | \(0.487038\pi\) | |||||||
\(548\) | 25.9185 | − | 6.94484i | 1.10718 | − | 0.296669i | ||||
\(549\) | 21.0324 | + | 25.4291i | 0.897639 | + | 1.08529i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2470 | + | 5.91608i | 0.436535 | + | 0.252033i | ||||
\(552\) | −2.17267 | − | 25.8898i | −0.0924751 | − | 1.10194i | ||||
\(553\) | −3.74166 | + | 3.74166i | −0.159111 | + | 0.159111i | ||||
\(554\) | −35.4965 | −1.50810 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0000 | − | 20.7846i | −0.508913 | − | 0.881464i | ||||
\(557\) | 8.63950 | + | 2.31495i | 0.366068 | + | 0.0980875i | 0.437164 | − | 0.899382i | \(-0.355983\pi\) |
−0.0710962 | + | 0.997469i | \(0.522650\pi\) | |||||||
\(558\) | −5.58373 | − | 12.1993i | −0.236378 | − | 0.516436i | ||||
\(559\) | − | 14.0000i | − | 0.592137i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 51.1120 | − | 13.6954i | 2.15603 | − | 0.577706i | ||||
\(563\) | 10.9960 | − | 41.0376i | 0.463426 | − | 1.72953i | −0.198628 | − | 0.980075i | \(-0.563649\pi\) |
0.662055 | − | 0.749455i | \(-0.269685\pi\) | |||||||
\(564\) | 8.23252 | − | 45.7409i | 0.346652 | − | 1.92604i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 11.8322i | − | 0.497343i | ||||||
\(567\) | 19.6970 | − | 13.3801i | 0.827197 | − | 0.561912i | ||||
\(568\) | 18.7083 | − | 18.7083i | 0.784982 | − | 0.784982i | ||||
\(569\) | 11.8322 | − | 20.4939i | 0.496030 | − | 0.859149i | −0.503960 | − | 0.863727i | \(-0.668124\pi\) |
0.999990 | + | 0.00457819i | \(0.00145729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.00000 | − | 12.1244i | −0.292941 | − | 0.507388i | 0.681563 | − | 0.731760i | \(-0.261301\pi\) |
−0.974504 | + | 0.224371i | \(0.927967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.42766 | − | 40.8442i | −0.143192 | − | 1.70629i | ||||
\(574\) | 35.0000i | 1.46087i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 36.5526 | + | 13.5981i | 1.52302 | + | 0.566587i | ||||
\(577\) | 5.47817 | − | 20.4448i | 0.228059 | − | 0.851128i | −0.753097 | − | 0.657910i | \(-0.771441\pi\) |
0.981156 | − | 0.193218i | \(-0.0618925\pi\) | |||||||
\(578\) | 1.73621 | − | 6.47963i | 0.0722169 | − | 0.269517i | ||||
\(579\) | −6.20828 | − | 17.2470i | −0.258007 | − | 0.716759i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.12348 | + | 2.95804i | −0.212558 | + | 0.122720i | ||||
\(582\) | −40.8442 | + | 3.42766i | −1.69305 | + | 0.142081i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 5.91608 | + | 10.2470i | 0.244809 | + | 0.424022i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.0000 | − | 17.3205i | 0.413096 | − | 0.715504i | ||||
\(587\) | 12.6491 | − | 12.6491i | 0.522085 | − | 0.522085i | −0.396116 | − | 0.918201i | \(-0.629642\pi\) |
0.918201 | + | 0.396116i | \(0.129642\pi\) | |||||||
\(588\) | 20.7571 | + | 29.8688i | 0.856007 | + | 1.23177i | ||||
\(589\) | − | 4.00000i | − | 0.164817i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 45.7409 | + | 8.23252i | 1.88153 | + | 0.338641i | ||||
\(592\) | −2.73908 | + | 10.2224i | −0.112576 | + | 0.420138i | ||||
\(593\) | −30.2383 | + | 8.10232i | −1.24174 | + | 0.332722i | −0.819139 | − | 0.573595i | \(-0.805548\pi\) |
−0.422598 | + | 0.906317i | \(0.638882\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 53.2447i | − | 2.18099i | ||||||
\(597\) | 12.5373 | + | 5.90042i | 0.513119 | + | 0.241488i | ||||
\(598\) | −76.6680 | − | 20.5431i | −3.13519 | − | 0.840071i | ||||
\(599\) | −11.8322 | − | 20.4939i | −0.483449 | − | 0.837358i | 0.516370 | − | 0.856365i | \(-0.327283\pi\) |
−0.999819 | + | 0.0190072i | \(0.993949\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.0000 | 1.38689 | 0.693444 | − | 0.720510i | \(-0.256092\pi\) | ||||
0.693444 | + | 0.720510i | \(0.256092\pi\) | |||||||
\(602\) | −11.0680 | + | 11.0680i | −0.451097 | + | 0.451097i | ||||
\(603\) | 6.46940 | + | 4.59857i | 0.263454 | + | 0.187268i | ||||
\(604\) | −15.5885 | − | 9.00000i | −0.634285 | − | 0.366205i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.05869 | + | 22.5505i | −0.164873 | + | 0.916053i | ||||
\(607\) | −2.55560 | + | 0.684771i | −0.103729 | + | 0.0277940i | −0.310310 | − | 0.950635i | \(-0.600433\pi\) |
0.206581 | + | 0.978429i | \(0.433766\pi\) | |||||||
\(608\) | 9.48683 | + | 9.48683i | 0.384742 | + | 0.384742i | ||||
\(609\) | −25.5086 | + | 9.18216i | −1.03366 | + | 0.372080i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.9878 | − | 23.6643i | −1.65819 | − | 0.957356i | ||||
\(612\) | −3.79193 | + | 40.0702i | −0.153280 | + | 1.61974i | ||||
\(613\) | −35.7784 | − | 9.58679i | −1.44508 | − | 0.387207i | −0.550768 | − | 0.834659i | \(-0.685665\pi\) |
−0.894308 | + | 0.447452i | \(0.852332\pi\) | |||||||
\(614\) | 8.87412 | − | 15.3704i | 0.358130 | − | 0.620300i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6491 | + | 12.6491i | −0.509234 | + | 0.509234i | −0.914291 | − | 0.405057i | \(-0.867252\pi\) |
0.405057 | + | 0.914291i | \(0.367252\pi\) | |||||||
\(618\) | 27.8145 | + | 13.0903i | 1.11886 | + | 0.526567i | ||||
\(619\) | −31.1769 | + | 18.0000i | −1.25311 | + | 0.723481i | −0.971725 | − | 0.236115i | \(-0.924126\pi\) |
−0.281381 | + | 0.959596i | \(0.590792\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.3704 | − | 17.1066i | 1.21872 | − | 0.686466i | ||||
\(622\) | −18.7083 | − | 18.7083i | −0.750134 | − | 0.750134i | ||||
\(623\) | −11.0680 | − | 11.0680i | −0.443429 | − | 0.443429i | ||||
\(624\) | 5.91608 | − | 7.00000i | 0.236833 | − | 0.280224i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20.4939 | − | 11.8322i | 0.819101 | − | 0.472908i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.21725 | − | 30.6672i | −0.327904 | − | 1.22375i | ||||
\(629\) | −47.3286 | −1.88712 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(632\) | 1.15747 | + | 4.31975i | 0.0460418 | + | 0.171830i | ||||
\(633\) | 13.8380 | + | 19.9125i | 0.550013 | + | 0.791452i | ||||
\(634\) | −43.3013 | + | 25.0000i | −1.71971 | + | 0.992877i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −15.0000 | + | 17.7482i | −0.594789 | + | 0.703763i | ||||
\(637\) | 35.7784 | − | 9.58679i | 1.41759 | − | 0.379843i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.2689 | + | 12.3765i | 1.31610 | + | 0.489608i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.12348 | + | 2.95804i | −0.202365 | + | 0.116836i | −0.597758 | − | 0.801676i | \(-0.703942\pi\) |
0.395393 | + | 0.918512i | \(0.370608\pi\) | |||||||
\(642\) | 7.83584 | + | 3.68776i | 0.309256 | + | 0.145544i | ||||
\(643\) | −3.74166 | + | 3.74166i | −0.147557 | + | 0.147557i | −0.777026 | − | 0.629469i | \(-0.783272\pi\) |
0.629469 | + | 0.777026i | \(0.283272\pi\) | |||||||
\(644\) | 26.6224 | + | 46.1113i | 1.04907 | + | 1.81704i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.0000 | + | 17.3205i | −0.393445 | + | 0.681466i | ||||
\(647\) | 15.1191 | + | 4.05116i | 0.594394 | + | 0.159267i | 0.543461 | − | 0.839435i | \(-0.317114\pi\) |
0.0509336 | + | 0.998702i | \(0.483780\pi\) | |||||||
\(648\) | −1.46973 | − | 20.0709i | −0.0577366 | − | 0.788458i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.00000 | + | 5.91608i | 0.274352 | + | 0.231869i | ||||
\(652\) | 11.2250 | + | 11.2250i | 0.439604 | + | 0.439604i | ||||
\(653\) | −12.9593 | + | 3.47242i | −0.507135 | + | 0.135886i | −0.503309 | − | 0.864106i | \(-0.667884\pi\) |
−0.00382551 | + | 0.999993i | \(0.501218\pi\) | |||||||
\(654\) | −4.80230 | + | 26.6822i | −0.187785 | + | 1.04336i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.12348 | − | 2.95804i | −0.200038 | − | 0.115492i | ||||
\(657\) | −9.19714 | + | 12.9388i | −0.358815 | + | 0.504791i | ||||
\(658\) | 13.6954 | + | 51.1120i | 0.533903 | + | 1.99255i | ||||
\(659\) | −11.8322 | −0.460915 | −0.230458 | − | 0.973082i | \(-0.574022\pi\) | ||||
−0.230458 | + | 0.973082i | \(0.574022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.50000 | − | 16.4545i | −0.369507 | − | 0.640005i | 0.619981 | − | 0.784617i | \(-0.287140\pi\) |
−0.989489 | + | 0.144611i | \(0.953807\pi\) | |||||||
\(662\) | 30.2383 | + | 8.10232i | 1.17524 | + | 0.314906i | ||||
\(663\) | 37.0860 | + | 17.4537i | 1.44030 | + | 0.677845i | ||||
\(664\) | 5.00000i | 0.194038i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 70.0000 | − | 11.8322i | 2.71244 | − | 0.458487i | ||||
\(667\) | −38.3340 | + | 10.2716i | −1.48430 | + | 0.397716i | ||||
\(668\) | −12.1535 | + | 45.3574i | −0.470232 | + | 1.75493i | ||||
\(669\) | −9.02022 | − | 1.62348i | −0.348742 | − | 0.0627672i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −30.6332 | + | 2.57074i | −1.18170 | + | 0.0991685i | ||||
\(673\) | 14.9666 | − | 14.9666i | 0.576921 | − | 0.576921i | −0.357133 | − | 0.934054i | \(-0.616246\pi\) |
0.934054 | + | 0.357133i | \(0.116246\pi\) | |||||||
\(674\) | −5.91608 | + | 10.2470i | −0.227879 | + | 0.394698i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.5000 | + | 38.9711i | 0.865385 | + | 1.49889i | ||||
\(677\) | 1.15747 | + | 4.31975i | 0.0444853 | + | 0.166022i | 0.984595 | − | 0.174851i | \(-0.0559443\pi\) |
−0.940110 | + | 0.340872i | \(0.889278\pi\) | |||||||
\(678\) | −17.2598 | + | 1.44845i | −0.662860 | + | 0.0556274i | ||||
\(679\) | 24.2487 | − | 14.0000i | 0.930580 | − | 0.537271i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.89368 | − | 10.7994i | 0.110724 | − | 0.413227i | −0.888208 | − | 0.459442i | \(-0.848049\pi\) |
0.998932 | + | 0.0462153i | \(0.0147160\pi\) | |||||||
\(684\) | 6.27604 | − | 16.8704i | 0.239971 | − | 0.645057i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −35.8643 | − | 20.7063i | −1.36931 | − | 0.790569i | ||||
\(687\) | −2.60721 | − | 31.0677i | −0.0994712 | − | 1.18531i | ||||
\(688\) | −0.684771 | − | 2.55560i | −0.0261066 | − | 0.0974313i | ||||
\(689\) | 11.8322 | + | 20.4939i | 0.450769 | + | 0.780755i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | − | 13.8564i | 0.304334 | − | 0.527123i | −0.672779 | − | 0.739844i | \(-0.734899\pi\) |
0.977113 | + | 0.212721i | \(0.0682327\pi\) | |||||||
\(692\) | −18.9737 | + | 18.9737i | −0.721271 | + | 0.721271i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.0000i | 0.948987i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.05869 | + | 22.5505i | −0.153844 | + | 0.854776i | ||||
\(697\) | 6.84771 | − | 25.5560i | 0.259375 | − | 0.968002i | ||||
\(698\) | −66.9562 | + | 17.9408i | −2.53433 | + | 0.679071i | ||||
\(699\) | 29.5804 | + | 25.0000i | 1.11883 | + | 0.945587i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 17.7482i | − | 0.670342i | −0.942157 | − | 0.335171i | \(-0.891206\pi\) | ||
0.942157 | − | 0.335171i | \(-0.108794\pi\) | |||||||
\(702\) | −59.2143 | − | 16.5428i | −2.23490 | − | 0.624369i | ||||
\(703\) | 20.4448 | + | 5.47817i | 0.771090 | + | 0.206613i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.0000 | 1.12906 | ||||||||
\(707\) | −4.05116 | − | 15.1191i | −0.152360 | − | 0.568613i | ||||
\(708\) | −5.14149 | − | 61.2663i | −0.193229 | − | 2.30253i | ||||
\(709\) | −19.9186 | − | 11.5000i | −0.748058 | − | 0.431892i | 0.0769337 | − | 0.997036i | \(-0.475487\pi\) |
−0.824992 | + | 0.565145i | \(0.808820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.62348 | + | 3.82407i | −0.173394 | + | 0.143414i | ||||
\(712\) | −12.7780 | + | 3.42385i | −0.478876 | + | 0.128314i | ||||
\(713\) | 9.48683 | + | 9.48683i | 0.355285 | + | 0.355285i | ||||
\(714\) | −15.5207 | − | 43.1174i | −0.580847 | − | 1.61363i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −30.7409 | − | 17.7482i | −1.14884 | − | 0.663283i | ||||
\(717\) | 11.6953 | + | 16.8292i | 0.436768 | + | 0.628496i | ||||
\(718\) | 25.5560 | + | 6.84771i | 0.953741 | + | 0.255554i | ||||
\(719\) | −23.6643 | + | 40.9878i | −0.882530 | + | 1.52859i | −0.0340117 | + | 0.999421i | \(0.510828\pi\) |
−0.848519 | + | 0.529166i | \(0.822505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.0000 | −0.782081 | ||||||||
\(722\) | −23.7171 | + | 23.7171i | −0.882658 | + | 0.882658i | ||||
\(723\) | −4.42531 | + | 9.40301i | −0.164579 | + | 0.349702i | ||||
\(724\) | 7.79423 | − | 4.50000i | 0.289670 | − | 0.167241i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14.4291 | + | 40.0849i | 0.535515 | + | 1.48769i | ||||
\(727\) | 20.5791 | + | 20.5791i | 0.763237 | + | 0.763237i | 0.976906 | − | 0.213669i | \(-0.0685414\pi\) |
−0.213669 | + | 0.976906i | \(0.568541\pi\) | |||||||
\(728\) | 8.10232 | − | 30.2383i | 0.300292 | − | 1.12070i | ||||
\(729\) | 23.6643 | − | 13.0000i | 0.876456 | − | 0.481481i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.2470 | − | 5.91608i | 0.378997 | − | 0.218814i | ||||
\(732\) | −46.9367 | + | 32.6182i | −1.73483 | + | 1.20560i | ||||
\(733\) | −8.21725 | − | 30.6672i | −0.303511 | − | 1.13272i | −0.934219 | − | 0.356699i | \(-0.883902\pi\) |
0.630708 | − | 0.776020i | \(-0.282764\pi\) | |||||||
\(734\) | −17.7482 | −0.655099 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −45.0000 | −1.65872 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.73890 | + | 39.5098i | −0.137631 | + | 1.45437i | ||||
\(739\) | −27.7128 | + | 16.0000i | −1.01943 | + | 0.588570i | −0.913939 | − | 0.405851i | \(-0.866975\pi\) |
−0.105493 | + | 0.994420i | \(0.533642\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.0000 | − | 11.8322i | −0.514303 | − | 0.434665i | ||||
\(742\) | 6.84771 | − | 25.5560i | 0.251387 | − | 0.938190i | ||||
\(743\) | −20.5548 | − | 20.5548i | −0.754083 | − | 0.754083i | 0.221156 | − | 0.975238i | \(-0.429017\pi\) |
−0.975238 | + | 0.221156i | \(0.929017\pi\) | |||||||
\(744\) | 7.28817 | − | 2.62348i | 0.267197 | − | 0.0961813i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 40.9878 | − | 23.6643i | 1.50067 | − | 0.866412i | ||||
\(747\) | −6.09963 | + | 2.79186i | −0.223174 | + | 0.102149i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.91608 | −0.216169 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.0000 | − | 31.1769i | 0.656829 | − | 1.13766i | −0.324603 | − | 0.945851i | \(-0.605231\pi\) |
0.981432 | − | 0.191811i | \(-0.0614361\pi\) | |||||||
\(752\) | −8.63950 | − | 2.31495i | −0.315050 | − | 0.0844175i | ||||
\(753\) | −16.8292 | + | 11.6953i | −0.613289 | + | 0.426200i | ||||
\(754\) | 60.6218 | + | 35.0000i | 2.20771 | + | 1.27462i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 20.2409 | + | 35.9348i | 0.736153 | + | 1.30694i | ||||
\(757\) | −26.1916 | − | 26.1916i | −0.951950 | − | 0.951950i | 0.0469474 | − | 0.998897i | \(-0.485051\pi\) |
−0.998897 | + | 0.0469474i | \(0.985051\pi\) | |||||||
\(758\) | 38.8778 | − | 10.4173i | 1.41210 | − | 0.378372i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.4939 | + | 11.8322i | 0.742903 | + | 0.428915i | 0.823124 | − | 0.567862i | \(-0.192229\pi\) |
−0.0802206 | + | 0.996777i | \(0.525562\pi\) | |||||||
\(762\) | 61.2663 | − | 5.14149i | 2.21945 | − | 0.186256i | ||||
\(763\) | −4.79340 | − | 17.8892i | −0.173533 | − | 0.647632i | ||||
\(764\) | 70.9930 | 2.56844 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.50000 | − | 12.9904i | −0.270986 | − | 0.469362i | ||||
\(767\) | −60.4765 | − | 16.2046i | −2.18368 | − | 0.585115i | ||||
\(768\) | −6.63797 | + | 14.1045i | −0.239527 | + | 0.508953i | ||||
\(769\) | 34.0000i | 1.22607i | 0.790055 | + | 0.613036i | \(0.210052\pi\) | ||||
−0.790055 | + | 0.613036i | \(0.789948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.0000 | + | 35.4965i | −1.08042 | + | 1.27837i | ||||
\(772\) | 30.6672 | − | 8.21725i | 1.10374 | − | 0.295745i | ||||
\(773\) | 1.15747 | − | 4.31975i | 0.0416314 | − | 0.155371i | −0.941981 | − | 0.335666i | \(-0.891039\pi\) |
0.983613 | + | 0.180295i | \(0.0577053\pi\) | |||||||
\(774\) | −13.6764 | + | 11.3117i | −0.491589 | + | 0.406592i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 23.6643i | − | 0.849500i | ||||||
\(777\) | −39.8251 | + | 27.6761i | −1.42872 | + | 0.992874i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.91608 | + | 10.2470i | −0.211966 | + | 0.367135i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −17.3621 | − | 64.7963i | −0.620868 | − | 2.31711i | ||||
\(783\) | −29.7763 | + | 7.64032i | −1.06412 | + | 0.273043i | ||||
\(784\) | 6.06218 | − | 3.50000i | 0.216506 | − | 0.125000i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.0106 | + | 48.5564i | −0.463779 | + | 1.73085i | 0.197125 | + | 0.980378i | \(0.436840\pi\) |
−0.660904 | + | 0.750470i | \(0.729827\pi\) | |||||||
\(788\) | −20.8345 | + | 77.7555i | −0.742199 | + | 2.76993i | ||||
\(789\) | 10.9323 | − | 3.93521i | 0.389198 | − | 0.140097i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.2470 | − | 5.91608i | 0.364340 | − | 0.210352i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.0650 | + | 56.2232i | 0.534972 | + | 1.99654i | ||||
\(794\) | 23.6643 | + | 40.9878i | 0.839815 | + | 1.45460i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.0000 | + | 20.7846i | −0.425329 | + | 0.736691i | ||||
\(797\) | 31.6228 | − | 31.6228i | 1.12014 | − | 1.12014i | 0.128416 | − | 0.991720i | \(-0.459011\pi\) |
0.991720 | − | 0.128416i | \(-0.0409892\pi\) | |||||||
\(798\) | 1.71383 | + | 20.4221i | 0.0606689 | + | 0.722935i | ||||
\(799\) | − | 40.0000i | − | 1.41510i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.3117 | − | 13.6764i | −0.399681 | − | 0.483233i | ||||
\(802\) | 10.2716 | − | 38.3340i | 0.362701 | − | 1.35362i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −8.87412 | + | 10.5000i | −0.312966 | + | 0.370306i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 23.6643i | − | 0.833540i | ||||||
\(807\) | −4.36342 | + | 9.27149i | −0.153600 | + | 0.326372i | ||||
\(808\) | −12.7780 | − | 3.42385i | −0.449528 | − | 0.120451i | ||||
\(809\) | −20.7063 | − | 35.8643i | −0.727994 | − | 1.26092i | −0.957730 | − | 0.287670i | \(-0.907120\pi\) |
0.229736 | − | 0.973253i | \(-0.426214\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.00000 | −0.210688 | −0.105344 | − | 0.994436i | \(-0.533594\pi\) | ||||
−0.105344 | + | 0.994436i | \(0.533594\pi\) | |||||||
\(812\) | −12.1535 | − | 45.3574i | −0.426503 | − | 1.59173i | ||||
\(813\) | −3.45197 | + | 0.289690i | −0.121066 | + | 0.0101599i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.62348 | + | 1.37209i | 0.266875 | + | 0.0480327i | ||||
\(817\) | −5.11120 | + | 1.36954i | −0.178818 | + | 0.0479142i | ||||
\(818\) | −20.5548 | − | 20.5548i | −0.718682 | − | 0.718682i | ||||
\(819\) | 41.4126 | − | 7.00000i | 1.44707 | − | 0.244600i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.4939 | + | 11.8322i | 0.715242 | + | 0.412945i | 0.812999 | − | 0.582265i | \(-0.197833\pi\) |
−0.0977569 | + | 0.995210i | \(0.531167\pi\) | |||||||
\(822\) | −28.4465 | + | 19.7686i | −0.992184 | + | 0.689510i | ||||
\(823\) | 17.8892 | + | 4.79340i | 0.623578 | + | 0.167087i | 0.556754 | − | 0.830677i | \(-0.312047\pi\) |
0.0668243 | + | 0.997765i | \(0.478713\pi\) | |||||||
\(824\) | −8.87412 | + | 15.3704i | −0.309145 | + | 0.535454i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 35.0000 | + | 60.6218i | 1.21781 | + | 2.10930i | ||||
\(827\) | 14.2302 | − | 14.2302i | 0.494834 | − | 0.494834i | −0.414991 | − | 0.909825i | \(-0.636215\pi\) |
0.909825 | + | 0.414991i | \(0.136215\pi\) | |||||||
\(828\) | 25.1268 | + | 54.8967i | 0.873216 | + | 1.90779i | ||||
\(829\) | −1.73205 | + | 1.00000i | −0.0601566 | + | 0.0347314i | −0.529777 | − | 0.848137i | \(-0.677724\pi\) |
0.469620 | + | 0.882869i | \(0.344391\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.8704 | − | 9.31241i | 0.897435 | − | 0.323044i | ||||
\(832\) | 48.6415 | + | 48.6415i | 1.68634 | + | 1.68634i | ||||
\(833\) | 22.1359 | + | 22.1359i | 0.766965 | + | 0.766965i | ||||
\(834\) | 23.6643 | + | 20.0000i | 0.819428 | + | 0.692543i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.26996 | + | 7.42615i | 0.251287 | + | 0.256685i | ||||
\(838\) | −13.6954 | − | 51.1120i | −0.473100 | − | 1.76563i | ||||
\(839\) | 23.6643 | 0.816983 | 0.408492 | − | 0.912762i | \(-0.366055\pi\) | ||||
0.408492 | + | 0.912762i | \(0.366055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.00000 | 0.206897 | ||||||||
\(842\) | 6.36611 | + | 23.7586i | 0.219391 | + | 0.818777i | ||||
\(843\) | −33.6583 | + | 23.3906i | −1.15925 | + | 0.805613i | ||||
\(844\) | −36.3731 | + | 21.0000i | −1.25201 | + | 0.722850i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.0000 | + | 59.1608i | 0.343807 | + | 2.03399i | ||||
\(847\) | −20.5791 | − | 20.5791i | −0.707107 | − | 0.707107i | ||||
\(848\) | 3.16228 | + | 3.16228i | 0.108593 | + | 0.108593i | ||||
\(849\) | 3.10414 | + | 8.62348i | 0.106534 | + | 0.295957i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −61.4817 | + | 35.4965i | −2.10757 | + | 1.21680i | ||||
\(852\) | −26.1805 | + | 55.6290i | −0.896930 | + | 1.90582i | ||||
\(853\) | 26.1916 | − | 26.1916i | 0.896783 | − | 0.896783i | −0.0983669 | − | 0.995150i | \(-0.531362\pi\) |
0.995150 | + | 0.0983669i | \(0.0313619\pi\) | |||||||
\(854\) | 32.5384 | − | 56.3582i | 1.11344 | − | 1.92854i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.50000 | + | 4.33013i | −0.0854482 | + | 0.148001i | ||||
\(857\) | 25.9185 | + | 6.94484i | 0.885359 | + | 0.237231i | 0.672718 | − | 0.739899i | \(-0.265127\pi\) |
0.212641 | + | 0.977130i | \(0.431793\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.46410 | − | 2.00000i | −0.118194 | − | 0.0682391i | 0.439738 | − | 0.898126i | \(-0.355071\pi\) |
−0.557931 | + | 0.829887i | \(0.688405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.18216 | − | 25.5086i | −0.312927 | − | 0.869330i | ||||
\(862\) | −37.4166 | − | 37.4166i | −1.27441 | − | 1.27441i | ||||
\(863\) | 28.0784 | − | 7.52358i | 0.955799 | − | 0.256106i | 0.252978 | − | 0.967472i | \(-0.418590\pi\) |
0.702821 | + | 0.711366i | \(0.251923\pi\) | |||||||
\(864\) | −34.8549 | − | 0.370426i | −1.18579 | − | 0.0126022i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.7409 | + | 17.7482i | 1.04462 | + | 0.603110i | ||||
\(867\) | 0.434535 | + | 5.17795i | 0.0147576 | + | 0.175852i | ||||
\(868\) | −11.2250 | + | 11.2250i | −0.381000 | + | 0.381000i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | + | 12.1244i | 0.237186 | + | 0.410818i | ||||
\(872\) | −15.1191 | − | 4.05116i | −0.511998 | − | 0.137190i | ||||
\(873\) | 28.8687 | − | 13.2135i | 0.977058 | − | 0.447210i | ||||
\(874\) | 30.0000i | 1.01477i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.0000 | − | 17.7482i | −0.709524 | − | 0.599657i | ||||
\(877\) | −15.3336 | + | 4.10862i | −0.517779 | + | 0.138738i | −0.508239 | − | 0.861216i | \(-0.669703\pi\) |
−0.00953982 | + | 0.999954i | \(0.503037\pi\) | |||||||
\(878\) | 18.5196 | − | 69.1160i | 0.625006 | − | 2.33255i | ||||
\(879\) | −2.74417 | + | 15.2470i | −0.0925587 | + | 0.514267i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 53.2447i | − | 1.79386i | −0.442172 | − | 0.896930i | \(-0.645792\pi\) | ||
0.442172 | − | 0.896930i | \(-0.354208\pi\) | |||||||
\(882\) | −38.2735 | − | 27.2055i | −1.28874 | − | 0.916057i | ||||
\(883\) | 33.6749 | − | 33.6749i | 1.13325 | − | 1.13325i | 0.143618 | − | 0.989633i | \(-0.454126\pi\) |
0.989633 | − | 0.143618i | \(-0.0458736\pi\) | |||||||
\(884\) | −35.4965 | + | 61.4817i | −1.19388 | + | 2.06785i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.50000 | + | 4.33013i | 0.0839891 | + | 0.145473i | ||||
\(887\) | 1.73621 | + | 6.47963i | 0.0582963 | + | 0.217565i | 0.988929 | − | 0.148390i | \(-0.0474091\pi\) |
−0.930633 | + | 0.365955i | \(0.880742\pi\) | |||||||
\(888\) | 3.42766 | + | 40.8442i | 0.115025 | + | 1.37064i | ||||
\(889\) | −36.3731 | + | 21.0000i | −1.21991 | + | 0.704317i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.10862 | − | 15.3336i | 0.137567 | − | 0.513407i | ||||
\(893\) | −4.62990 | + | 17.2790i | −0.154934 | + | 0.578220i | ||||
\(894\) | 23.2810 | + | 64.6761i | 0.778634 | + | 2.16309i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 41.4126i | − | 1.38350i | ||||||
\(897\) | 61.2663 | − | 5.14149i | 2.04562 | − | 0.171669i | ||||
\(898\) | 10.2716 | + | 38.3340i | 0.342766 | + | 1.27922i | ||||
\(899\) | −5.91608 | − | 10.2470i | −0.197312 | − | 0.341755i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0000 | + | 17.3205i | −0.333148 | + | 0.577030i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.16287 | − | 10.9702i | 0.171809 | − | 0.365065i | ||||
\(904\) | − | 10.0000i | − | 0.332595i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 22.8704 | + | 4.11626i | 0.759819 | + | 0.136754i | ||||
\(907\) | 14.3802 | − | 53.6676i | 0.477486 | − | 1.78200i | −0.134257 | − | 0.990947i | \(-0.542865\pi\) |
0.611743 | − | 0.791057i | \(-0.290469\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.95804 | − | 17.5000i | −0.0981120 | − | 0.580438i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 23.6643i | − | 0.784034i | −0.919958 | − | 0.392017i | \(-0.871777\pi\) | ||
0.919958 | − | 0.392017i | \(-0.128223\pi\) | |||||||
\(912\) | −3.13434 | − | 1.47510i | −0.103788 | − | 0.0488456i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −11.8322 | − | 20.4939i | −0.391373 | − | 0.677878i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 54.0000 | 1.78421 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −12.9145 | − | 50.3311i | −0.426242 | − | 1.66117i | ||||
\(919\) | −12.1244 | − | 7.00000i | −0.399946 | − | 0.230909i | 0.286515 | − | 0.958076i | \(-0.407503\pi\) |
−0.686461 | + | 0.727167i | \(0.740837\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.43521 | + | 13.5303i | −0.0802430 | + | 0.445839i | ||||
\(922\) | 51.1120 | − | 13.6954i | 1.68328 | − | 0.451035i | ||||
\(923\) | 44.2719 | + | 44.2719i | 1.45723 | + | 1.45723i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35.8643 | + | 20.7063i | 1.17857 | + | 0.680451i | ||||
\(927\) | −23.7059 | − | 2.24334i | −0.778602 | − | 0.0736809i | ||||
\(928\) | 38.3340 | + | 10.2716i | 1.25837 | + | 0.337181i | ||||
\(929\) | −20.7063 | + | 35.8643i | −0.679351 | + | 1.17667i | 0.295826 | + | 0.955242i | \(0.404405\pi\) |
−0.975177 | + | 0.221428i | \(0.928928\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | − | 12.1244i | −0.229416 | − | 0.397360i | ||||
\(932\) | −47.4342 | + | 47.4342i | −1.55376 | + | 1.55376i | ||||
\(933\) | 18.5430 | + | 8.72684i | 0.607070 | + | 0.285704i | ||||
\(934\) | 30.3109 | − | 17.5000i | 0.991803 | − | 0.572617i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.3765 | − | 33.2689i | 0.404539 | − | 1.08743i | ||||
\(937\) | −22.4499 | − | 22.4499i | −0.733408 | − | 0.733408i | 0.237885 | − | 0.971293i | \(-0.423546\pi\) |
−0.971293 | + | 0.237885i | \(0.923546\pi\) | |||||||
\(938\) | 4.05116 | − | 15.1191i | 0.132275 | − | 0.493657i | ||||
\(939\) | −11.8322 | + | 14.0000i | −0.386128 | + | 0.456873i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.9878 | + | 23.6643i | −1.33616 | + | 0.771435i | −0.986236 | − | 0.165342i | \(-0.947127\pi\) |
−0.349928 | + | 0.936777i | \(0.613794\pi\) | |||||||
\(942\) | 23.3906 | + | 33.6583i | 0.762105 | + | 1.09665i | ||||
\(943\) | −10.2716 | − | 38.3340i | −0.334488 | − | 1.24833i | ||||
\(944\) | −11.8322 | −0.385104 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.52358 | + | 28.0784i | 0.244484 | + | 0.912425i | 0.973642 | + | 0.228080i | \(0.0732449\pi\) |
−0.729159 | + | 0.684345i | \(0.760088\pi\) | |||||||
\(948\) | −5.93059 | − | 8.53394i | −0.192617 | − | 0.277169i | ||||
\(949\) | −24.2487 | + | 14.0000i | −0.787146 | + | 0.454459i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.0000 | − | 29.5804i | 0.810681 | − | 0.959210i | ||||
\(952\) | 25.5560 | − | 6.84771i | 0.828275 | − | 0.221936i | ||||
\(953\) | 18.9737 | + | 18.9737i | 0.614617 | + | 0.614617i | 0.944146 | − | 0.329528i | \(-0.106890\pi\) |
−0.329528 | + | 0.944146i | \(0.606890\pi\) | |||||||
\(954\) | 10.4601 | − | 28.1174i | 0.338657 | − | 0.910334i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −30.7409 | + | 17.7482i | −0.994230 | + | 0.574019i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −56.1249 | + | 56.1249i | −1.81331 | + | 1.81331i | ||||
\(959\) | 11.8322 | − | 20.4939i | 0.382080 | − | 0.661783i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 120.953 | + | 32.4093i | 3.89968 | + | 1.04492i | ||||
\(963\) | −6.67837 | − | 0.631989i | −0.215207 | − | 0.0203656i | ||||
\(964\) | −15.5885 | − | 9.00000i | −0.502070 | − | 0.289870i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −52.5000 | − | 44.3706i | −1.68916 | − | 1.42760i | ||||
\(967\) | 20.5791 | + | 20.5791i | 0.661780 | + | 0.661780i | 0.955799 | − | 0.294020i | \(-0.0949931\pi\) |
−0.294020 | + | 0.955799i | \(0.594993\pi\) | |||||||
\(968\) | −23.7586 | + | 6.36611i | −0.763631 | + | 0.204614i | ||||
\(969\) | 2.74417 | − | 15.2470i | 0.0881556 | − | 0.489803i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.9878 | − | 23.6643i | −1.31536 | − | 0.759424i | −0.332383 | − | 0.943145i | \(-0.607853\pi\) |
−0.982979 | + | 0.183720i | \(0.941186\pi\) | |||||||
\(972\) | 19.0101 | + | 42.7272i | 0.609750 | + | 1.37048i | ||||
\(973\) | −20.4448 | − | 5.47817i | −0.655430 | − | 0.175622i | ||||
\(974\) | 11.8322 | 0.379127 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.50000 | + | 9.52628i | 0.176051 | + | 0.304929i | ||||
\(977\) | −34.5580 | − | 9.25979i | −1.10561 | − | 0.296247i | −0.340562 | − | 0.940222i | \(-0.610617\pi\) |
−0.765047 | + | 0.643975i | \(0.777284\pi\) | |||||||
\(978\) | −18.5430 | − | 8.72684i | −0.592939 | − | 0.279054i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.50000 | − | 20.7063i | −0.111746 | − | 0.661101i | ||||
\(982\) | 25.5560 | − | 6.84771i | 0.815525 | − | 0.218519i | ||||
\(983\) | −8.68105 | + | 32.3981i | −0.276883 | + | 1.03334i | 0.677687 | + | 0.735351i | \(0.262983\pi\) |
−0.954569 | + | 0.297989i | \(0.903684\pi\) | |||||||
\(984\) | −22.5505 | − | 4.05869i | −0.718885 | − | 0.129386i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 59.1608i | 1.88406i | ||||||||
\(987\) | −23.3906 | − | 33.6583i | −0.744530 | − | 1.07136i | ||||
\(988\) | 22.4499 | − | 22.4499i | 0.714228 | − | 0.714228i | ||||
\(989\) | 8.87412 | − | 15.3704i | 0.282181 | − | 0.488751i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0000 | + | 32.9090i | 0.603555 | + | 1.04539i | 0.992278 | + | 0.124033i | \(0.0395829\pi\) |
−0.388723 | + | 0.921355i | \(0.627084\pi\) | |||||||
\(992\) | −3.47242 | − | 12.9593i | −0.110250 | − | 0.411457i | ||||
\(993\) | −24.1638 | + | 2.02783i | −0.766814 | + | 0.0643512i | ||||
\(994\) | − | 70.0000i | − | 2.22027i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.93521 | − | 10.9323i | −0.124692 | − | 0.346402i | ||||
\(997\) | 4.10862 | − | 15.3336i | 0.130121 | − | 0.485620i | −0.869849 | − | 0.493318i | \(-0.835784\pi\) |
0.999970 | + | 0.00769834i | \(0.00245048\pi\) | |||||||
\(998\) | 6.94484 | − | 25.9185i | 0.219835 | − | 0.820436i | ||||
\(999\) | −47.9130 | + | 26.9878i | −1.51590 | + | 0.853856i |
(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 | 525.2.bf.e.107.2 | yes | 16 | |
3.2 | odd | 2 | inner | 525.2.bf.e.107.4 | yes | 16 | |
5.2 | odd | 4 | inner | 525.2.bf.e.443.4 | yes | 16 | |
5.3 | odd | 4 | inner | 525.2.bf.e.443.1 | yes | 16 | |
5.4 | even | 2 | inner | 525.2.bf.e.107.3 | yes | 16 | |
7.4 | even | 3 | inner | 525.2.bf.e.32.3 | yes | 16 | |
15.2 | even | 4 | inner | 525.2.bf.e.443.2 | yes | 16 | |
15.8 | even | 4 | inner | 525.2.bf.e.443.3 | yes | 16 | |
15.14 | odd | 2 | inner | 525.2.bf.e.107.1 | yes | 16 | |
21.11 | odd | 6 | inner | 525.2.bf.e.32.1 | ✓ | 16 | |
35.4 | even | 6 | inner | 525.2.bf.e.32.2 | yes | 16 | |
35.18 | odd | 12 | inner | 525.2.bf.e.368.4 | yes | 16 | |
35.32 | odd | 12 | inner | 525.2.bf.e.368.1 | yes | 16 | |
105.32 | even | 12 | inner | 525.2.bf.e.368.3 | yes | 16 | |
105.53 | even | 12 | inner | 525.2.bf.e.368.2 | yes | 16 | |
105.74 | odd | 6 | inner | 525.2.bf.e.32.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bf.e.32.1 | ✓ | 16 | 21.11 | odd | 6 | inner | |
525.2.bf.e.32.2 | yes | 16 | 35.4 | even | 6 | inner | |
525.2.bf.e.32.3 | yes | 16 | 7.4 | even | 3 | inner | |
525.2.bf.e.32.4 | yes | 16 | 105.74 | odd | 6 | inner | |
525.2.bf.e.107.1 | yes | 16 | 15.14 | odd | 2 | inner | |
525.2.bf.e.107.2 | yes | 16 | 1.1 | even | 1 | trivial | |
525.2.bf.e.107.3 | yes | 16 | 5.4 | even | 2 | inner | |
525.2.bf.e.107.4 | yes | 16 | 3.2 | odd | 2 | inner | |
525.2.bf.e.368.1 | yes | 16 | 35.32 | odd | 12 | inner | |
525.2.bf.e.368.2 | yes | 16 | 105.53 | even | 12 | inner | |
525.2.bf.e.368.3 | yes | 16 | 105.32 | even | 12 | inner | |
525.2.bf.e.368.4 | yes | 16 | 35.18 | odd | 12 | inner | |
525.2.bf.e.443.1 | yes | 16 | 5.3 | odd | 4 | inner | |
525.2.bf.e.443.2 | yes | 16 | 15.2 | even | 4 | inner | |
525.2.bf.e.443.3 | yes | 16 | 15.8 | even | 4 | inner | |
525.2.bf.e.443.4 | yes | 16 | 5.2 | odd | 4 | inner |