Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(424,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.424");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.499 |
Dual form | 525.2.r.b.424.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | + | 2.50000i | 0.327327 | + | 0.944911i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 1.73205 | + | 1.00000i | 0.500000 | + | 0.288675i | ||||
\(13\) | 1.00000i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 5.19615 | − | 3.00000i | 1.26025 | − | 0.727607i | 0.287129 | − | 0.957892i | \(-0.407299\pi\) |
0.973123 | + | 0.230285i | \(0.0739659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | − | 1.73205i | −0.436436 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.19615 | + | 3.00000i | 1.08347 | + | 0.625543i | 0.931831 | − | 0.362892i | \(-0.118211\pi\) |
0.151642 | + | 0.988436i | \(0.451544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 3.46410 | − | 4.00000i | 0.654654 | − | 0.755929i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 6.06218 | + | 3.50000i | 0.996616 | + | 0.575396i | 0.907245 | − | 0.420602i | \(-0.138181\pi\) |
0.0893706 | + | 0.995998i | \(0.471514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.500000 | − | 0.866025i | −0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.0000 | 1.87409 | 0.937043 | − | 0.349215i | \(-0.113552\pi\) | ||||
0.937043 | + | 0.349215i | \(0.113552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000i | 0.152499i | 0.997089 | + | 0.0762493i | \(0.0242945\pi\) | ||||
−0.997089 | + | 0.0762493i | \(0.975706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.19615 | − | 3.00000i | −0.757937 | − | 0.437595i | 0.0706177 | − | 0.997503i | \(-0.477503\pi\) |
−0.828554 | + | 0.559908i | \(0.810836\pi\) | |||||||
\(48\) | − | 4.00000i | − | 0.577350i | ||||||
\(49\) | −5.50000 | + | 4.33013i | −0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | + | 5.19615i | −0.420084 | + | 0.727607i | ||||
\(52\) | 1.73205 | − | 1.00000i | 0.240192 | − | 0.138675i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.00000i | 0.662266i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.59808 | + | 0.500000i | 0.327327 | + | 0.0629941i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.06218 | + | 3.50000i | −0.740613 | + | 0.427593i | −0.822292 | − | 0.569066i | \(-0.807305\pi\) |
0.0816792 | + | 0.996659i | \(0.473972\pi\) | |||||||
\(68\) | −10.3923 | − | 6.00000i | −1.26025 | − | 0.727607i | ||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.52628 | + | 5.50000i | −1.11497 | + | 0.643726i | −0.940111 | − | 0.340868i | \(-0.889279\pi\) |
−0.174855 | + | 0.984594i | \(0.555946\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.0000 | −1.14708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.50000 | + | 11.2583i | −0.731307 | + | 1.26666i | 0.225018 | + | 0.974355i | \(0.427756\pi\) |
−0.956325 | + | 0.292306i | \(0.905577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | −1.00000 | + | 5.19615i | −0.109109 | + | 0.566947i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.19615 | + | 3.00000i | −0.557086 | + | 0.321634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | + | 0.866025i | −0.262071 | + | 0.0907841i | ||||
\(92\) | − | 12.0000i | − | 1.25109i | ||||||
\(93\) | 4.33013 | + | 2.50000i | 0.449013 | + | 0.259238i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.0000i | − | 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.866025 | − | 0.500000i | −0.0853320 | − | 0.0492665i | 0.456727 | − | 0.889607i | \(-0.349022\pi\) |
−0.542059 | + | 0.840341i | \(0.682355\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.5885 | − | 9.00000i | −1.50699 | − | 0.870063i | −0.999967 | − | 0.00813215i | \(-0.997411\pi\) |
−0.507026 | − | 0.861931i | \(-0.669255\pi\) | |||||||
\(108\) | 1.73205 | − | 1.00000i | 0.166667 | − | 0.0962250i | ||||
\(109\) | −3.50000 | − | 6.06218i | −0.335239 | − | 0.580651i | 0.648292 | − | 0.761392i | \(-0.275484\pi\) |
−0.983531 | + | 0.180741i | \(0.942150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.00000 | −0.664411 | ||||||||
\(112\) | −10.3923 | − | 2.00000i | −0.981981 | − | 0.188982i | ||||
\(113\) | − | 18.0000i | − | 1.69330i | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||
0.532152 | − | 0.846649i | \(-0.321383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | − | 10.3923i | −0.557086 | − | 0.964901i | ||||
\(117\) | 0.866025 | + | 0.500000i | 0.0800641 | + | 0.0462250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0000 | + | 10.3923i | 1.10004 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.3923 | + | 6.00000i | −0.937043 | + | 0.541002i | ||||
\(124\) | −5.00000 | + | 8.66025i | −0.449013 | + | 0.777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0000i | 0.976092i | 0.872818 | + | 0.488046i | \(0.162290\pi\) | ||||
−0.872818 | + | 0.488046i | \(0.837710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.500000 | − | 0.866025i | −0.0440225 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | − | 5.19615i | 0.262111 | − | 0.453990i | −0.704692 | − | 0.709514i | \(-0.748915\pi\) |
0.966803 | + | 0.255524i | \(0.0822479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.9904 | + | 2.50000i | 1.12641 | + | 0.216777i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.19615 | − | 3.00000i | 0.443937 | − | 0.256307i | −0.261329 | − | 0.965250i | \(-0.584161\pi\) |
0.705266 | + | 0.708942i | \(0.250827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.00000 | + | 3.46410i | 0.166667 | + | 0.288675i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.59808 | − | 6.50000i | 0.214286 | − | 0.536111i | ||||
\(148\) | − | 14.0000i | − | 1.15079i | ||||||
\(149\) | −12.0000 | + | 20.7846i | −0.983078 | + | 1.70274i | −0.332896 | + | 0.942964i | \(0.608026\pi\) |
−0.650183 | + | 0.759778i | \(0.725308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | + | 1.73205i | −0.0800641 | + | 0.138675i | ||||
\(157\) | −8.66025 | + | 5.00000i | −0.691164 | + | 0.399043i | −0.804048 | − | 0.594565i | \(-0.797324\pi\) |
0.112884 | + | 0.993608i | \(0.463991\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | + | 15.5885i | −0.236433 | + | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.46410 | − | 2.00000i | −0.271329 | − | 0.156652i | 0.358162 | − | 0.933659i | \(-0.383403\pi\) |
−0.629492 | + | 0.777007i | \(0.716737\pi\) | |||||||
\(164\) | −12.0000 | − | 20.7846i | −0.937043 | − | 1.62301i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000i | 0.928588i | 0.885681 | + | 0.464294i | \(0.153692\pi\) | ||||
−0.885681 | + | 0.464294i | \(0.846308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.50000 | − | 4.33013i | −0.191180 | − | 0.331133i | ||||
\(172\) | 1.73205 | − | 1.00000i | 0.132068 | − | 0.0762493i | ||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.19615 | + | 3.00000i | 0.390567 | + | 0.225494i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.00000 | + | 15.5885i | 0.672692 | + | 1.16514i | 0.977138 | + | 0.212607i | \(0.0681952\pi\) |
−0.304446 | + | 0.952529i | \(0.598471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.00000i | − | 0.147844i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.0000i | 0.875190i | ||||||||
\(189\) | −2.50000 | + | 0.866025i | −0.181848 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | − | 5.19615i | 0.217072 | − | 0.375980i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.953912 | + | 0.300088i | \(0.0970159\pi\) | |||||||
\(192\) | −6.92820 | + | 4.00000i | −0.500000 | + | 0.288675i | ||||
\(193\) | −4.33013 | + | 2.50000i | −0.311689 | + | 0.179954i | −0.647682 | − | 0.761911i | \(-0.724262\pi\) |
0.335993 | + | 0.941865i | \(0.390928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.0000 | + | 5.19615i | 0.928571 | + | 0.371154i | ||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | − | 13.8564i | −0.567105 | − | 0.982255i | −0.996850 | − | 0.0793045i | \(-0.974730\pi\) |
0.429745 | − | 0.902950i | \(-0.358603\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | − | 6.06218i | 0.246871 | − | 0.427593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.19615 | + | 15.0000i | 0.364698 | + | 1.05279i | ||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.19615 | − | 3.00000i | 0.361158 | − | 0.208514i | ||||
\(208\) | −3.46410 | − | 2.00000i | −0.240192 | − | 0.138675i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.3923 | + | 6.00000i | −0.712069 | + | 0.411113i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.66025 | − | 10.0000i | 0.587896 | − | 0.678844i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.50000 | − | 9.52628i | 0.371656 | − | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.3923 | − | 6.00000i | 0.689761 | − | 0.398234i | −0.113761 | − | 0.993508i | \(-0.536290\pi\) |
0.803523 | + | 0.595274i | \(0.202957\pi\) | |||||||
\(228\) | 8.66025 | − | 5.00000i | 0.573539 | − | 0.331133i | ||||
\(229\) | 14.5000 | − | 25.1147i | 0.958187 | − | 1.65963i | 0.231287 | − | 0.972886i | \(-0.425707\pi\) |
0.726900 | − | 0.686743i | \(-0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.19615 | + | 3.00000i | 0.340411 | + | 0.196537i | 0.660454 | − | 0.750867i | \(-0.270364\pi\) |
−0.320043 | + | 0.947403i | \(0.603697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | − | 13.0000i | − | 0.844441i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | − | 1.73205i | −0.0644157 | − | 0.111571i | 0.832019 | − | 0.554747i | \(-0.187185\pi\) |
−0.896435 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 4.00000 | 0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.33013 | + | 2.50000i | 0.275519 | + | 0.159071i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | −1.73205 | − | 5.00000i | −0.109109 | − | 0.314970i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 10.3923 | + | 6.00000i | 0.648254 | + | 0.374270i | 0.787787 | − | 0.615948i | \(-0.211227\pi\) |
−0.139533 | + | 0.990217i | \(0.544560\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.50000 | + | 18.1865i | −0.217479 | + | 1.13006i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.3923 | − | 6.00000i | 0.640817 | − | 0.369976i | −0.144112 | − | 0.989561i | \(-0.546033\pi\) |
0.784929 | + | 0.619586i | \(0.212699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000i | 0.367194i | ||||||||
\(268\) | 12.1244 | + | 7.00000i | 0.740613 | + | 0.427593i | ||||
\(269\) | −9.00000 | − | 15.5885i | −0.548740 | − | 0.950445i | −0.998361 | − | 0.0572259i | \(-0.981774\pi\) |
0.449622 | − | 0.893219i | \(-0.351559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 24.0000i | 1.45521i | ||||||||
\(273\) | 1.73205 | − | 2.00000i | 0.104828 | − | 0.121046i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | + | 10.3923i | 0.361158 | + | 0.625543i | ||||
\(277\) | 19.9186 | − | 11.5000i | 1.19679 | − | 0.690968i | 0.236953 | − | 0.971521i | \(-0.423851\pi\) |
0.959839 | + | 0.280553i | \(0.0905179\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.00000 | −0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0000 | −1.43172 | −0.715860 | − | 0.698244i | \(-0.753965\pi\) | ||||
−0.715860 | + | 0.698244i | \(0.753965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.52628 | + | 5.50000i | −0.566279 | + | 0.326941i | −0.755662 | − | 0.654962i | \(-0.772685\pi\) |
0.189383 | + | 0.981903i | \(0.439351\pi\) | |||||||
\(284\) | −12.0000 | − | 20.7846i | −0.712069 | − | 1.23334i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3923 | + | 30.0000i | 0.613438 | + | 1.77084i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.50000 | − | 16.4545i | 0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | + | 8.66025i | 0.293105 | + | 0.507673i | ||||
\(292\) | 19.0526 | + | 11.0000i | 1.11497 | + | 0.643726i | ||||
\(293\) | − | 12.0000i | − | 0.701047i | −0.936554 | − | 0.350524i | \(-0.886004\pi\) | ||
0.936554 | − | 0.350524i | \(-0.113996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | + | 5.19615i | −0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.50000 | + | 0.866025i | −0.144098 | + | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.0000 | + | 17.3205i | 0.573539 | + | 0.993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.00000i | − | 0.399511i | −0.979846 | − | 0.199756i | \(-0.935985\pi\) | ||
0.979846 | − | 0.199756i | \(-0.0640148\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | − | 10.3923i | −0.340229 | − | 0.589294i | 0.644246 | − | 0.764818i | \(-0.277171\pi\) |
−0.984475 | + | 0.175525i | \(0.943838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.7224 | + | 8.50000i | 0.832161 | + | 0.480448i | 0.854592 | − | 0.519300i | \(-0.173807\pi\) |
−0.0224310 | + | 0.999748i | \(0.507141\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.0000 | 1.46261 | ||||||||
\(317\) | −5.19615 | − | 3.00000i | −0.291845 | − | 0.168497i | 0.346929 | − | 0.937892i | \(-0.387225\pi\) |
−0.638774 | + | 0.769395i | \(0.720558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 30.0000i | − | 1.66924i | ||||||
\(324\) | −1.00000 | + | 1.73205i | −0.0555556 | + | 0.0962250i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.06218 | + | 3.50000i | 0.335239 | + | 0.193550i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.00000 | − | 15.5885i | 0.165395 | − | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.5000 | + | 19.9186i | −0.632097 | + | 1.09482i | 0.355025 | + | 0.934857i | \(0.384472\pi\) |
−0.987122 | + | 0.159968i | \(0.948861\pi\) | |||||||
\(332\) | 20.7846 | − | 12.0000i | 1.14070 | − | 0.658586i | ||||
\(333\) | 6.06218 | − | 3.50000i | 0.332205 | − | 0.191799i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.0000 | − | 3.46410i | 0.545545 | − | 0.188982i | ||||
\(337\) | − | 13.0000i | − | 0.708155i | −0.935216 | − | 0.354078i | \(-0.884795\pi\) | ||
0.935216 | − | 0.354078i | \(-0.115205\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.00000 | + | 15.5885i | 0.488813 | + | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.7846 | + | 12.0000i | −1.11578 | + | 0.644194i | −0.940319 | − | 0.340293i | \(-0.889474\pi\) |
−0.175457 | + | 0.984487i | \(0.556140\pi\) | |||||||
\(348\) | 10.3923 | + | 6.00000i | 0.557086 | + | 0.321634i | ||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.0000 | −0.635999 | ||||||||
\(357\) | −15.5885 | − | 3.00000i | −0.825029 | − | 0.158777i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.00000 | + | 5.19615i | −0.158334 | + | 0.274242i | −0.934268 | − | 0.356572i | \(-0.883946\pi\) |
0.775934 | + | 0.630814i | \(0.217279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.0000i | 0.577350i | ||||||||
\(364\) | 4.00000 | + | 3.46410i | 0.209657 | + | 0.181568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4545 | + | 9.50000i | −0.858917 | + | 0.495896i | −0.863649 | − | 0.504093i | \(-0.831827\pi\) |
0.00473247 | + | 0.999989i | \(0.498494\pi\) | |||||||
\(368\) | −20.7846 | + | 12.0000i | −1.08347 | + | 0.625543i | ||||
\(369\) | 6.00000 | − | 10.3923i | 0.312348 | − | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 10.0000i | − | 0.518476i | ||||||
\(373\) | 14.7224 | + | 8.50000i | 0.762299 | + | 0.440113i | 0.830120 | − | 0.557584i | \(-0.188272\pi\) |
−0.0678218 | + | 0.997697i | \(0.521605\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.0000 | 1.28416 | 0.642082 | − | 0.766636i | \(-0.278071\pi\) | ||||
0.642082 | + | 0.766636i | \(0.278071\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.50000 | − | 9.52628i | −0.281774 | − | 0.488046i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.866025 | + | 0.500000i | 0.0440225 | + | 0.0254164i | ||||
\(388\) | −17.3205 | + | 10.0000i | −0.879316 | + | 0.507673i | ||||
\(389\) | 6.00000 | + | 10.3923i | 0.304212 | + | 0.526911i | 0.977086 | − | 0.212847i | \(-0.0682735\pi\) |
−0.672874 | + | 0.739758i | \(0.734940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0000 | 1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.00000i | 0.302660i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.1147 | − | 14.5000i | −1.26047 | − | 0.727734i | −0.287307 | − | 0.957839i | \(-0.592760\pi\) |
−0.973166 | + | 0.230105i | \(0.926093\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.5000 | + | 4.33013i | −0.625783 | + | 0.216777i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | + | 20.7846i | −0.599251 | + | 1.03793i | 0.393680 | + | 0.919247i | \(0.371202\pi\) |
−0.992932 | + | 0.118686i | \(0.962132\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.33013 | − | 2.50000i | 0.215699 | − | 0.124534i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.50000 | + | 4.33013i | 0.123617 | + | 0.214111i | 0.921192 | − | 0.389109i | \(-0.127217\pi\) |
−0.797574 | + | 0.603220i | \(0.793884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00000 | + | 5.19615i | −0.147979 | + | 0.256307i | ||||
\(412\) | 2.00000i | 0.0985329i | ||||||||
\(413\) | 10.3923 | − | 12.0000i | 0.511372 | − | 0.590481i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.33013 | − | 2.50000i | 0.212047 | − | 0.122426i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0000 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.00000 | −0.341159 | −0.170580 | − | 0.985344i | \(-0.554564\pi\) | ||||
−0.170580 | + | 0.985344i | \(0.554564\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.19615 | + | 3.00000i | −0.252646 | + | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.19615 | − | 1.00000i | −0.251459 | − | 0.0483934i | ||||
\(428\) | 36.0000i | 1.74013i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | −3.46410 | − | 2.00000i | −0.166667 | − | 0.0962250i | ||||
\(433\) | − | 29.0000i | − | 1.39365i | −0.717241 | − | 0.696826i | \(-0.754595\pi\) | ||
0.717241 | − | 0.696826i | \(-0.245405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | + | 12.1244i | −0.335239 | + | 0.580651i | ||||
\(437\) | 25.9808 | − | 15.0000i | 1.24283 | − | 0.717547i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0000 | + | 24.2487i | −0.668184 | + | 1.15733i | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1769 | − | 18.0000i | −1.48126 | − | 0.855206i | −0.481486 | − | 0.876454i | \(-0.659903\pi\) |
−0.999774 | + | 0.0212481i | \(0.993236\pi\) | |||||||
\(444\) | 7.00000 | + | 12.1244i | 0.332205 | + | 0.575396i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 24.0000i | − | 1.13516i | ||||||
\(448\) | 6.92820 | + | 20.0000i | 0.327327 | + | 0.944911i | ||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −31.1769 | + | 18.0000i | −1.46644 | + | 0.846649i | ||||
\(453\) | −13.8564 | − | 8.00000i | −0.651031 | − | 0.375873i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.52628 | − | 5.50000i | −0.445621 | − | 0.257279i | 0.260358 | − | 0.965512i | \(-0.416159\pi\) |
−0.705979 | + | 0.708233i | \(0.749493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.00000 | + | 5.19615i | 0.140028 | + | 0.242536i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.00000i | 0.325318i | 0.986682 | + | 0.162659i | \(0.0520070\pi\) | ||||
−0.986682 | + | 0.162659i | \(0.947993\pi\) | |||||||
\(464\) | −12.0000 | + | 20.7846i | −0.557086 | + | 0.964901i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.9808 | − | 15.0000i | −1.20225 | − | 0.694117i | −0.241192 | − | 0.970477i | \(-0.577538\pi\) |
−0.961054 | + | 0.276360i | \(0.910872\pi\) | |||||||
\(468\) | − | 2.00000i | − | 0.0924500i | ||||||
\(469\) | −14.0000 | − | 12.1244i | −0.646460 | − | 0.559851i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | − | 8.66025i | 0.230388 | − | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.00000 | − | 31.1769i | 0.275010 | − | 1.42899i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.50000 | + | 6.06218i | −0.159586 | + | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.19615 | − | 15.0000i | −0.236433 | − | 0.682524i | ||||
\(484\) | −22.0000 | −1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.06218 | + | 3.50000i | −0.274703 | + | 0.158600i | −0.631023 | − | 0.775764i | \(-0.717365\pi\) |
0.356320 | + | 0.934364i | \(0.384031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 20.7846 | + | 12.0000i | 0.937043 | + | 0.541002i | ||||
\(493\) | 31.1769 | − | 18.0000i | 1.40414 | − | 0.810679i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | 10.3923 | + | 30.0000i | 0.466159 | + | 1.34568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.50000 | − | 14.7224i | 0.380512 | − | 0.659067i | −0.610623 | − | 0.791921i | \(-0.709081\pi\) |
0.991136 | + | 0.132855i | \(0.0424144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000i | 0.267527i | 0.991013 | + | 0.133763i | \(0.0427062\pi\) | ||||
−0.991013 | + | 0.133763i | \(0.957294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.3923 | + | 6.00000i | −0.461538 | + | 0.266469i | ||||
\(508\) | 19.0526 | − | 11.0000i | 0.845321 | − | 0.488046i | ||||
\(509\) | −9.00000 | + | 15.5885i | −0.398918 | + | 0.690946i | −0.993593 | − | 0.113020i | \(-0.963948\pi\) |
0.594675 | + | 0.803966i | \(0.297281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.0000 | − | 19.0526i | −0.973223 | − | 0.842836i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.33013 | + | 2.50000i | 0.191180 | + | 0.110378i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | + | 20.7846i | 0.525730 | + | 0.910590i | 0.999551 | + | 0.0299693i | \(0.00954094\pi\) |
−0.473821 | + | 0.880621i | \(0.657126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.2391 | − | 21.5000i | −1.62835 | − | 0.940129i | −0.984585 | − | 0.174908i | \(-0.944037\pi\) |
−0.643767 | − | 0.765222i | \(-0.722629\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.9808 | − | 15.0000i | −1.13174 | − | 0.653410i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | −8.66025 | − | 25.0000i | −0.375470 | − | 1.08389i | ||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.5885 | − | 9.00000i | −0.672692 | − | 0.388379i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.50000 | − | 16.4545i | 0.408437 | − | 0.707433i | −0.586278 | − | 0.810110i | \(-0.699407\pi\) |
0.994715 | + | 0.102677i | \(0.0327407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.06218 | − | 3.50000i | 0.260153 | − | 0.150199i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000i | 0.342055i | 0.985266 | + | 0.171028i | \(0.0547087\pi\) | ||||
−0.985266 | + | 0.171028i | \(0.945291\pi\) | |||||||
\(548\) | −10.3923 | − | 6.00000i | −0.443937 | − | 0.256307i | ||||
\(549\) | 1.00000 | + | 1.73205i | 0.0426790 | + | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0000 | − | 25.9808i | 0.639021 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.7750 | − | 6.50000i | −1.43626 | − | 0.276408i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.00000 | + | 8.66025i | 0.212047 | + | 0.367277i | ||||
\(557\) | 15.5885 | − | 9.00000i | 0.660504 | − | 0.381342i | −0.131965 | − | 0.991254i | \(-0.542129\pi\) |
0.792469 | + | 0.609912i | \(0.208795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.00000 | −0.0422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.5885 | − | 9.00000i | 0.656975 | − | 0.379305i | −0.134148 | − | 0.990961i | \(-0.542830\pi\) |
0.791123 | + | 0.611656i | \(0.209497\pi\) | |||||||
\(564\) | −6.00000 | − | 10.3923i | −0.252646 | − | 0.437595i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.73205 | − | 2.00000i | 0.0727393 | − | 0.0839921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.0000 | + | 20.7846i | −0.503066 | + | 0.871336i | 0.496928 | + | 0.867792i | \(0.334461\pi\) |
−0.999994 | + | 0.00354413i | \(0.998872\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50000 | + | 6.06218i | 0.146470 | + | 0.253694i | 0.929921 | − | 0.367760i | \(-0.119875\pi\) |
−0.783450 | + | 0.621455i | \(0.786542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000i | 0.250654i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(577\) | −6.06218 | + | 3.50000i | −0.252372 | + | 0.145707i | −0.620850 | − | 0.783930i | \(-0.713212\pi\) |
0.368478 | + | 0.929636i | \(0.379879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.50000 | − | 4.33013i | 0.103896 | − | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.0000 | + | 10.3923i | −1.24461 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18.0000i | − | 0.742940i | −0.928445 | − | 0.371470i | \(-0.878854\pi\) | ||
0.928445 | − | 0.371470i | \(-0.121146\pi\) | |||||||
\(588\) | −13.8564 | + | 2.00000i | −0.571429 | + | 0.0824786i | ||||
\(589\) | −25.0000 | −1.03011 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | − | 5.19615i | −0.123404 | − | 0.213741i | ||||
\(592\) | −24.2487 | + | 14.0000i | −0.996616 | + | 0.575396i | ||||
\(593\) | 31.1769 | + | 18.0000i | 1.28028 | + | 0.739171i | 0.976900 | − | 0.213697i | \(-0.0685507\pi\) |
0.303383 | + | 0.952869i | \(0.401884\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 48.0000 | 1.96616 | ||||||||
\(597\) | 13.8564 | + | 8.00000i | 0.567105 | + | 0.327418i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | + | 10.3923i | 0.245153 | + | 0.424618i | 0.962175 | − | 0.272433i | \(-0.0878284\pi\) |
−0.717021 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | −0.0407909 | −0.0203954 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203954 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.00000i | 0.285062i | ||||||||
\(604\) | 16.0000 | − | 27.7128i | 0.651031 | − | 1.12762i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.4545 | + | 9.50000i | 0.667867 | + | 0.385593i | 0.795268 | − | 0.606258i | \(-0.207330\pi\) |
−0.127401 | + | 0.991851i | \(0.540664\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.0000 | − | 10.3923i | −0.486265 | − | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | − | 5.19615i | 0.121367 | − | 0.210214i | ||||
\(612\) | −10.3923 | + | 6.00000i | −0.420084 | + | 0.242536i | ||||
\(613\) | −32.9090 | + | 19.0000i | −1.32918 | + | 0.767403i | −0.985173 | − | 0.171564i | \(-0.945118\pi\) |
−0.344008 | + | 0.938967i | \(0.611785\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 42.0000i | − | 1.69086i | −0.534089 | − | 0.845428i | \(-0.679345\pi\) | ||
0.534089 | − | 0.845428i | \(-0.320655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.5000 | + | 30.3109i | 0.703384 | + | 1.21830i | 0.967271 | + | 0.253744i | \(0.0816620\pi\) |
−0.263887 | + | 0.964554i | \(0.585005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.00000 | + | 5.19615i | −0.120386 | + | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.5885 | + | 3.00000i | 0.624538 | + | 0.120192i | ||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.3205 | + | 10.0000i | 0.691164 | + | 0.399043i | ||||
\(629\) | 42.0000 | 1.67465 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.46410 | − | 2.00000i | 0.137686 | − | 0.0794929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.33013 | − | 5.50000i | −0.171566 | − | 0.217918i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | − | 10.3923i | 0.237356 | − | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | + | 25.9808i | 0.592464 | + | 1.02618i | 0.993899 | + | 0.110291i | \(0.0351782\pi\) |
−0.401435 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.0000i | 0.985904i | 0.870057 | + | 0.492952i | \(0.164082\pi\) | ||||
−0.870057 | + | 0.492952i | \(0.835918\pi\) | |||||||
\(644\) | 30.0000 | − | 10.3923i | 1.18217 | − | 0.409514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7846 | + | 12.0000i | −0.817127 | + | 0.471769i | −0.849425 | − | 0.527710i | \(-0.823051\pi\) |
0.0322975 | + | 0.999478i | \(0.489718\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.50000 | + | 12.9904i | −0.0979827 | + | 0.509133i | ||||
\(652\) | 8.00000i | 0.313304i | ||||||||
\(653\) | −20.7846 | − | 12.0000i | −0.813365 | − | 0.469596i | 0.0347583 | − | 0.999396i | \(-0.488934\pi\) |
−0.848123 | + | 0.529799i | \(0.822267\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.0000 | + | 41.5692i | −0.937043 | + | 1.62301i | ||||
\(657\) | 11.0000i | 0.429151i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.50000 | + | 11.2583i | 0.252821 | + | 0.437898i | 0.964301 | − | 0.264807i | \(-0.0853084\pi\) |
−0.711481 | + | 0.702706i | \(0.751975\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.19615 | − | 3.00000i | −0.201802 | − | 0.116510i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.1769 | + | 18.0000i | 1.20717 | + | 0.696963i | ||||
\(668\) | 20.7846 | − | 12.0000i | 0.804181 | − | 0.464294i | ||||
\(669\) | −2.00000 | − | 3.46410i | −0.0773245 | − | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.0000i | 1.19496i | 0.801883 | + | 0.597481i | \(0.203832\pi\) | ||||
−0.801883 | + | 0.597481i | \(0.796168\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | − | 20.7846i | −0.461538 | − | 0.799408i | ||||
\(677\) | 15.5885 | + | 9.00000i | 0.599113 | + | 0.345898i | 0.768693 | − | 0.639618i | \(-0.220908\pi\) |
−0.169580 | + | 0.985517i | \(0.554241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.0000 | − | 8.66025i | 0.959412 | − | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | + | 10.3923i | −0.229920 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.5885 | + | 9.00000i | −0.596476 | + | 0.344375i | −0.767654 | − | 0.640865i | \(-0.778576\pi\) |
0.171178 | + | 0.985240i | \(0.445243\pi\) | |||||||
\(684\) | −5.00000 | + | 8.66025i | −0.191180 | + | 0.331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.0000i | 1.10642i | ||||||||
\(688\) | −3.46410 | − | 2.00000i | −0.132068 | − | 0.0762493i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.50000 | + | 9.52628i | −0.209230 | + | 0.362397i | −0.951472 | − | 0.307735i | \(-0.900429\pi\) |
0.742242 | + | 0.670132i | \(0.233762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 62.3538 | − | 36.0000i | 2.36182 | − | 1.36360i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.3109 | − | 17.5000i | 1.14320 | − | 0.660025i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 12.0000i | − | 0.450988i | ||||||
\(709\) | −5.00000 | + | 8.66025i | −0.187779 | + | 0.325243i | −0.944509 | − | 0.328484i | \(-0.893462\pi\) |
0.756730 | + | 0.653727i | \(0.226796\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.50000 | + | 11.2583i | 0.243769 | + | 0.422220i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 30.0000i | − | 1.12351i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.0000 | − | 31.1769i | 0.672692 | − | 1.16514i | ||||
\(717\) | −5.19615 | + | 3.00000i | −0.194054 | + | 0.112037i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.00000 | − | 5.19615i | 0.111881 | − | 0.193784i | −0.804648 | − | 0.593753i | \(-0.797646\pi\) |
0.916529 | + | 0.399969i | \(0.130979\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.500000 | − | 2.59808i | 0.0186210 | − | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.73205 | + | 1.00000i | 0.0644157 | + | 0.0371904i | ||||
\(724\) | 7.00000 | + | 12.1244i | 0.260153 | + | 0.450598i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.00000i | − | 0.259616i | −0.991539 | − | 0.129808i | \(-0.958564\pi\) | ||
0.991539 | − | 0.129808i | \(-0.0414360\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | + | 5.19615i | 0.110959 | + | 0.192187i | ||||
\(732\) | −3.46410 | + | 2.00000i | −0.128037 | + | 0.0739221i | ||||
\(733\) | −11.2583 | − | 6.50000i | −0.415836 | − | 0.240083i | 0.277458 | − | 0.960738i | \(-0.410508\pi\) |
−0.693294 | + | 0.720655i | \(0.743841\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.50000 | − | 6.06218i | −0.128750 | − | 0.223001i | 0.794443 | − | 0.607339i | \(-0.207763\pi\) |
−0.923192 | + | 0.384338i | \(0.874430\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.00000 | −0.183680 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000i | 0.880475i | 0.897881 | + | 0.440237i | \(0.145106\pi\) | ||||
−0.897881 | + | 0.440237i | \(0.854894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.3923 | + | 6.00000i | 0.380235 | + | 0.219529i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.00000 | − | 46.7654i | 0.328853 | − | 1.70877i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.50000 | − | 16.4545i | 0.346660 | − | 0.600433i | −0.638994 | − | 0.769212i | \(-0.720649\pi\) |
0.985654 | + | 0.168779i | \(0.0539825\pi\) | |||||||
\(752\) | 20.7846 | − | 12.0000i | 0.757937 | − | 0.437595i | ||||
\(753\) | 15.5885 | − | 9.00000i | 0.568075 | − | 0.327978i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.00000 | + | 3.46410i | 0.145479 | + | 0.125988i | ||||
\(757\) | 50.0000i | 1.81728i | 0.417579 | + | 0.908640i | \(0.362879\pi\) | ||||
−0.417579 | + | 0.908640i | \(0.637121\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | − | 36.3731i | 0.761249 | − | 1.31852i | −0.180957 | − | 0.983491i | \(-0.557920\pi\) |
0.942207 | − | 0.335032i | \(-0.108747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1244 | − | 14.0000i | 0.438931 | − | 0.506834i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.19615 | − | 3.00000i | 0.187622 | − | 0.108324i | ||||
\(768\) | 13.8564 | + | 8.00000i | 0.500000 | + | 0.288675i | ||||
\(769\) | 13.0000 | 0.468792 | 0.234396 | − | 0.972141i | \(-0.424689\pi\) | ||||
0.234396 | + | 0.972141i | \(0.424689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 8.66025 | + | 5.00000i | 0.311689 | + | 0.179954i | ||||
\(773\) | 20.7846 | − | 12.0000i | 0.747570 | − | 0.431610i | −0.0772449 | − | 0.997012i | \(-0.524612\pi\) |
0.824815 | + | 0.565402i | \(0.191279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.06218 | − | 17.5000i | −0.217479 | − | 0.627809i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.0000 | − | 51.9615i | 1.07486 | − | 1.86171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.00000i | 0.214423i | ||||||||
\(784\) | −4.00000 | − | 27.7128i | −0.142857 | − | 0.989743i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.2487 | + | 14.0000i | −0.864373 | + | 0.499046i | −0.865474 | − | 0.500953i | \(-0.832983\pi\) |
0.00110111 | + | 0.999999i | \(0.499650\pi\) | |||||||
\(788\) | 10.3923 | − | 6.00000i | 0.370211 | − | 0.213741i | ||||
\(789\) | −6.00000 | + | 10.3923i | −0.213606 | + | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.0000 | − | 15.5885i | 1.60002 | − | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.73205 | − | 1.00000i | −0.0615069 | − | 0.0355110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.0000 | + | 27.7128i | −0.567105 | + | 0.982255i | ||||
\(797\) | 18.0000i | 0.637593i | 0.947823 | + | 0.318796i | \(0.103279\pi\) | ||||
−0.947823 | + | 0.318796i | \(0.896721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.0000 | −1.27359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −14.0000 | −0.493742 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.5885 | + | 9.00000i | 0.548740 | + | 0.316815i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.00000 | + | 15.5885i | 0.316423 | + | 0.548061i | 0.979739 | − | 0.200279i | \(-0.0641847\pi\) |
−0.663316 | + | 0.748340i | \(0.730851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | 20.7846 | − | 24.0000i | 0.729397 | − | 0.842235i | ||||
\(813\) | 16.0000i | 0.561144i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12.0000 | − | 20.7846i | −0.420084 | − | 0.727607i | ||||
\(817\) | 4.33013 | + | 2.50000i | 0.151492 | + | 0.0874639i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.500000 | + | 2.59808i | −0.0174714 | + | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0000 | − | 20.7846i | 0.418803 | − | 0.725388i | −0.577016 | − | 0.816733i | \(-0.695783\pi\) |
0.995819 | + | 0.0913446i | \(0.0291165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.6410 | − | 20.0000i | 1.20751 | − | 0.697156i | 0.245295 | − | 0.969448i | \(-0.421115\pi\) |
0.962215 | + | 0.272292i | \(0.0877817\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.00000i | − | 0.208640i | −0.994544 | − | 0.104320i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104320i | \(-0.0332667\pi\) | |||||||
\(828\) | −10.3923 | − | 6.00000i | −0.361158 | − | 0.208514i | ||||
\(829\) | −9.50000 | − | 16.4545i | −0.329949 | − | 0.571488i | 0.652553 | − | 0.757743i | \(-0.273698\pi\) |
−0.982501 | + | 0.186256i | \(0.940365\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.5000 | + | 19.9186i | −0.398931 | + | 0.690968i | ||||
\(832\) | 8.00000i | 0.277350i | ||||||||
\(833\) | −15.5885 | + | 39.0000i | −0.540108 | + | 1.35127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.33013 | − | 2.50000i | 0.149671 | − | 0.0864126i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.0000 | 1.03572 | 0.517858 | − | 0.855467i | \(-0.326730\pi\) | ||||
0.517858 | + | 0.855467i | \(0.326730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.7846 | − | 12.0000i | 0.715860 | − | 0.413302i | ||||
\(844\) | 4.00000 | + | 6.92820i | 0.137686 | + | 0.238479i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.5788 | + | 5.50000i | 0.981981 | + | 0.188982i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.50000 | − | 9.52628i | 0.188760 | − | 0.326941i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.0000 | + | 36.3731i | 0.719871 | + | 1.24685i | ||||
\(852\) | 20.7846 | + | 12.0000i | 0.712069 | + | 0.411113i | ||||
\(853\) | − | 17.0000i | − | 0.582069i | −0.956713 | − | 0.291034i | \(-0.906001\pi\) | ||
0.956713 | − | 0.291034i | \(-0.0939994\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.3731 | − | 21.0000i | 1.24248 | − | 0.717346i | 0.272882 | − | 0.962048i | \(-0.412023\pi\) |
0.969599 | + | 0.244701i | \(0.0786899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.00000 | + | 3.46410i | −0.0682391 | + | 0.118194i | −0.898126 | − | 0.439738i | \(-0.855071\pi\) |
0.829887 | + | 0.557931i | \(0.188405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24.0000 | − | 20.7846i | −0.817918 | − | 0.708338i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.19615 | − | 3.00000i | −0.176879 | − | 0.102121i | 0.408946 | − | 0.912558i | \(-0.365896\pi\) |
−0.585826 | + | 0.810437i | \(0.699230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.0000i | 0.645274i | ||||||||
\(868\) | −25.9808 | − | 5.00000i | −0.881845 | − | 0.169711i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.50000 | − | 6.06218i | −0.118593 | − | 0.205409i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.66025 | − | 5.00000i | −0.293105 | − | 0.169224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.0000 | −0.743311 | ||||||||
\(877\) | −1.73205 | − | 1.00000i | −0.0584872 | − | 0.0337676i | 0.470471 | − | 0.882415i | \(-0.344084\pi\) |
−0.528958 | + | 0.848648i | \(0.677417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.00000 | + | 10.3923i | 0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.0000i | 1.04323i | 0.853180 | + | 0.521617i | \(0.174671\pi\) | ||||
−0.853180 | + | 0.521617i | \(0.825329\pi\) | |||||||
\(884\) | 6.00000 | − | 10.3923i | 0.201802 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.3923 | − | 6.00000i | −0.348939 | − | 0.201460i | 0.315279 | − | 0.948999i | \(-0.397902\pi\) |
−0.664218 | + | 0.747539i | \(0.731235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.5000 | + | 9.52628i | −0.922320 | + | 0.319501i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.92820 | − | 4.00000i | 0.231973 | − | 0.133930i | ||||
\(893\) | −25.9808 | + | 15.0000i | −0.869413 | + | 0.501956i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.00000i | − | 0.200334i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.0000 | − | 25.9808i | −0.500278 | − | 0.866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.73205 | − | 2.00000i | 0.0576390 | − | 0.0665558i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.8468 | + | 15.5000i | −0.891433 | + | 0.514669i | −0.874411 | − | 0.485186i | \(-0.838752\pi\) |
−0.0170220 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(908\) | −20.7846 | − | 12.0000i | −0.689761 | − | 0.398234i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.0000 | −0.596367 | −0.298183 | − | 0.954509i | \(-0.596381\pi\) | ||||
−0.298183 | + | 0.954509i | \(0.596381\pi\) | |||||||
\(912\) | −17.3205 | − | 10.0000i | −0.573539 | − | 0.331133i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −58.0000 | −1.91637 | ||||||||
\(917\) | 15.5885 | + | 3.00000i | 0.514776 | + | 0.0990687i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.5000 | − | 40.7032i | 0.775193 | − | 1.34267i | −0.159492 | − | 0.987199i | \(-0.550986\pi\) |
0.934686 | − | 0.355475i | \(-0.115681\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.50000 | + | 6.06218i | 0.115329 | + | 0.199756i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000i | 0.394985i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.866025 | + | 0.500000i | −0.0284440 | + | 0.0164222i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00000 | + | 10.3923i | −0.196854 | + | 0.340960i | −0.947507 | − | 0.319736i | \(-0.896406\pi\) |
0.750653 | + | 0.660697i | \(0.229739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | + | 34.6410i | 0.163868 | + | 1.13531i | ||||
\(932\) | − | 12.0000i | − | 0.393073i | ||||||
\(933\) | 10.3923 | + | 6.00000i | 0.340229 | + | 0.196431i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.0000i | 0.947389i | 0.880689 | + | 0.473694i | \(0.157080\pi\) | ||||
−0.880689 | + | 0.473694i | \(0.842920\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0000 | −0.554774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0000 | + | 25.9808i | 0.488986 | + | 0.846949i | 0.999920 | − | 0.0126715i | \(-0.00403357\pi\) |
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 62.3538 | + | 36.0000i | 2.03052 | + | 1.17232i | ||||
\(944\) | 24.0000 | 0.781133 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.5692 | − | 24.0000i | −1.35082 | − | 0.779895i | −0.362454 | − | 0.932002i | \(-0.618061\pi\) |
−0.988364 | + | 0.152106i | \(0.951394\pi\) | |||||||
\(948\) | −22.5167 | + | 13.0000i | −0.731307 | + | 0.422220i | ||||
\(949\) | −5.50000 | − | 9.52628i | −0.178538 | − | 0.309236i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000 | 0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.00000 | − | 10.3923i | −0.194054 | − | 0.336111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.0000 | + | 10.3923i | 0.387500 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.5885 | + | 9.00000i | −0.502331 | + | 0.290021i | ||||
\(964\) | −2.00000 | + | 3.46410i | −0.0644157 | + | 0.111571i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 55.0000i | − | 1.76868i | −0.466843 | − | 0.884340i | \(-0.654609\pi\) | ||
0.466843 | − | 0.884340i | \(-0.345391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.0000 | + | 25.9808i | 0.481869 | + | 0.834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | − | 20.7846i | 0.385098 | − | 0.667010i | −0.606685 | − | 0.794943i | \(-0.707501\pi\) |
0.991783 | + | 0.127933i | \(0.0408342\pi\) | |||||||
\(972\) | − | 2.00000i | − | 0.0641500i | ||||||
\(973\) | −4.33013 | − | 12.5000i | −0.138817 | − | 0.400732i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | − | 6.92820i | −0.128037 | − | 0.221766i | ||||
\(977\) | −10.3923 | + | 6.00000i | −0.332479 | + | 0.191957i | −0.656941 | − | 0.753942i | \(-0.728150\pi\) |
0.324462 | + | 0.945899i | \(0.394817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.00000 | −0.223493 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.5885 | + | 9.00000i | −0.497195 | + | 0.287055i | −0.727554 | − | 0.686050i | \(-0.759343\pi\) |
0.230360 | + | 0.973106i | \(0.426010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.19615 | + | 15.0000i | 0.165395 | + | 0.477455i | ||||
\(988\) | − | 10.0000i | − | 0.318142i | ||||||
\(989\) | −3.00000 | + | 5.19615i | −0.0953945 | + | 0.165228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5000 | + | 37.2391i | 0.682970 | + | 1.18294i | 0.974070 | + | 0.226246i | \(0.0726454\pi\) |
−0.291100 | + | 0.956693i | \(0.594021\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 23.0000i | − | 0.729883i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.0000 | + | 20.7846i | −0.380235 | + | 0.658586i | ||||
\(997\) | −26.8468 | + | 15.5000i | −0.850246 | + | 0.490890i | −0.860734 | − | 0.509055i | \(-0.829995\pi\) |
0.0104877 | + | 0.999945i | \(0.496662\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.50000 | + | 6.06218i | −0.110735 | + | 0.191799i |
(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.r.b.499.1 | 4 | ||
5.2 | odd | 4 | 525.2.i.c.226.1 | 2 | |||
5.3 | odd | 4 | 105.2.i.a.16.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 525.2.r.b.499.2 | 4 | ||
7.4 | even | 3 | inner | 525.2.r.b.424.2 | 4 | ||
15.8 | even | 4 | 315.2.j.b.226.1 | 2 | |||
20.3 | even | 4 | 1680.2.bg.m.961.1 | 2 | |||
35.2 | odd | 12 | 3675.2.a.h.1.1 | 1 | |||
35.3 | even | 12 | 735.2.i.c.361.1 | 2 | |||
35.4 | even | 6 | inner | 525.2.r.b.424.1 | 4 | ||
35.12 | even | 12 | 3675.2.a.i.1.1 | 1 | |||
35.13 | even | 4 | 735.2.i.c.226.1 | 2 | |||
35.18 | odd | 12 | 105.2.i.a.46.1 | yes | 2 | ||
35.23 | odd | 12 | 735.2.a.e.1.1 | 1 | |||
35.32 | odd | 12 | 525.2.i.c.151.1 | 2 | |||
35.33 | even | 12 | 735.2.a.d.1.1 | 1 | |||
105.23 | even | 12 | 2205.2.a.f.1.1 | 1 | |||
105.53 | even | 12 | 315.2.j.b.46.1 | 2 | |||
105.68 | odd | 12 | 2205.2.a.d.1.1 | 1 | |||
140.123 | even | 12 | 1680.2.bg.m.1201.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.a.16.1 | ✓ | 2 | 5.3 | odd | 4 | ||
105.2.i.a.46.1 | yes | 2 | 35.18 | odd | 12 | ||
315.2.j.b.46.1 | 2 | 105.53 | even | 12 | |||
315.2.j.b.226.1 | 2 | 15.8 | even | 4 | |||
525.2.i.c.151.1 | 2 | 35.32 | odd | 12 | |||
525.2.i.c.226.1 | 2 | 5.2 | odd | 4 | |||
525.2.r.b.424.1 | 4 | 35.4 | even | 6 | inner | ||
525.2.r.b.424.2 | 4 | 7.4 | even | 3 | inner | ||
525.2.r.b.499.1 | 4 | 1.1 | even | 1 | trivial | ||
525.2.r.b.499.2 | 4 | 5.4 | even | 2 | inner | ||
735.2.a.d.1.1 | 1 | 35.33 | even | 12 | |||
735.2.a.e.1.1 | 1 | 35.23 | odd | 12 | |||
735.2.i.c.226.1 | 2 | 35.13 | even | 4 | |||
735.2.i.c.361.1 | 2 | 35.3 | even | 12 | |||
1680.2.bg.m.961.1 | 2 | 20.3 | even | 4 | |||
1680.2.bg.m.1201.1 | 2 | 140.123 | even | 12 | |||
2205.2.a.d.1.1 | 1 | 105.68 | odd | 12 | |||
2205.2.a.f.1.1 | 1 | 105.23 | even | 12 | |||
3675.2.a.h.1.1 | 1 | 35.2 | odd | 12 | |||
3675.2.a.i.1.1 | 1 | 35.12 | even | 12 |