Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 13x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 589.1 | ||
Root | \(3.12250 - 1.80278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.589 |
Dual form | 637.2.q.d.491.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | − | 0.866025i | −1.06066 | − | 0.612372i | −0.135045 | − | 0.990839i | \(-0.543118\pi\) |
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 3.60555i | − | 1.61245i | −0.591608 | − | 0.806226i | \(-0.701507\pi\) | ||
0.591608 | − | 0.806226i | \(-0.298493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | −3.12250 | + | 5.40833i | −0.987421 | + | 1.71026i | ||||
\(11\) | 3.00000 | + | 1.73205i | 0.904534 | + | 0.522233i | 0.878668 | − | 0.477432i | \(-0.158432\pi\) |
0.0258656 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.12250 | + | 1.80278i | 0.866025 | + | 0.500000i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | ||||
\(17\) | 3.12250 | + | 5.40833i | 0.757317 | + | 1.31171i | 0.944214 | + | 0.329332i | \(0.106824\pi\) |
−0.186897 | + | 0.982380i | \(0.559843\pi\) | |||||||
\(18\) | − | 5.19615i | − | 1.22474i | ||||||
\(19\) | 6.24500 | − | 3.60555i | 1.43270 | − | 0.827170i | 0.435375 | − | 0.900249i | \(-0.356616\pi\) |
0.997326 | + | 0.0730792i | \(0.0232826\pi\) | |||||||
\(20\) | 3.12250 | − | 1.80278i | 0.698212 | − | 0.403113i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | − | 5.19615i | −0.639602 | − | 1.10782i | ||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.00000 | −1.60000 | ||||||||
\(26\) | −3.12250 | − | 5.40833i | −0.612372 | − | 1.06066i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.500000 | + | 0.866025i | −0.0928477 | + | 0.160817i | −0.908708 | − | 0.417432i | \(-0.862930\pi\) |
0.815861 | + | 0.578249i | \(0.196264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −4.50000 | + | 2.59808i | −0.795495 | + | 0.459279i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 10.8167i | − | 1.85504i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | + | 2.59808i | −0.250000 | + | 0.433013i | ||||
\(37\) | −1.50000 | − | 0.866025i | −0.246598 | − | 0.142374i | 0.371607 | − | 0.928390i | \(-0.378807\pi\) |
−0.618206 | + | 0.786016i | \(0.712140\pi\) | |||||||
\(38\) | −12.4900 | −2.02614 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.24500 | 0.987421 | ||||||||
\(41\) | −3.12250 | − | 1.80278i | −0.487652 | − | 0.281546i | 0.235948 | − | 0.971766i | \(-0.424181\pi\) |
−0.723600 | + | 0.690220i | \(0.757514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | − | 5.19615i | −0.457496 | − | 0.792406i | 0.541332 | − | 0.840809i | \(-0.317920\pi\) |
−0.998828 | + | 0.0484030i | \(0.984587\pi\) | |||||||
\(44\) | 3.46410i | 0.522233i | ||||||||
\(45\) | 9.36750 | − | 5.40833i | 1.39642 | − | 0.806226i | ||||
\(46\) | 6.00000 | − | 3.46410i | 0.884652 | − | 0.510754i | ||||
\(47\) | 7.21110i | 1.05185i | 0.850532 | + | 0.525924i | \(0.176280\pi\) | ||||
−0.850532 | + | 0.525924i | \(0.823720\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 12.0000 | + | 6.92820i | 1.69706 | + | 0.979796i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.60555i | 0.500000i | ||||||||
\(53\) | 5.00000 | 0.686803 | 0.343401 | − | 0.939189i | \(-0.388421\pi\) | ||||
0.343401 | + | 0.939189i | \(0.388421\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.24500 | − | 10.8167i | 0.842075 | − | 1.45852i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.50000 | − | 0.866025i | 0.196960 | − | 0.113715i | ||||
\(59\) | 6.24500 | − | 3.60555i | 0.813029 | − | 0.469403i | −0.0349773 | − | 0.999388i | \(-0.511136\pi\) |
0.848007 | + | 0.529985i | \(0.177803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.12250 | − | 5.40833i | −0.399795 | − | 0.692465i | 0.593905 | − | 0.804535i | \(-0.297585\pi\) |
−0.993700 | + | 0.112070i | \(0.964252\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.50000 | − | 11.2583i | 0.806226 | − | 1.39642i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | + | 6.92820i | 1.46603 | + | 0.846415i | 0.999279 | − | 0.0379722i | \(-0.0120898\pi\) |
0.466755 | + | 0.884387i | \(0.345423\pi\) | |||||||
\(68\) | −3.12250 | + | 5.40833i | −0.378659 | + | 0.655856i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | + | 5.19615i | −1.06810 | + | 0.616670i | −0.927663 | − | 0.373419i | \(-0.878185\pi\) |
−0.140441 | + | 0.990089i | \(0.544852\pi\) | |||||||
\(72\) | −4.50000 | + | 2.59808i | −0.530330 | + | 0.306186i | ||||
\(73\) | − | 10.8167i | − | 1.26599i | −0.774154 | − | 0.632997i | \(-0.781825\pi\) | ||
0.774154 | − | 0.632997i | \(-0.218175\pi\) | |||||||
\(74\) | 1.50000 | + | 2.59808i | 0.174371 | + | 0.302020i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.24500 | + | 3.60555i | 0.716350 | + | 0.413585i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | −15.6125 | − | 9.01388i | −1.74553 | − | 1.00778i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 3.12250 | + | 5.40833i | 0.344822 | + | 0.597250i | ||||
\(83\) | 7.21110i | 0.791521i | 0.918354 | + | 0.395761i | \(0.129519\pi\) | ||||
−0.918354 | + | 0.395761i | \(0.870481\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.5000 | − | 11.2583i | 2.11507 | − | 1.22114i | ||||
\(86\) | 10.3923i | 1.12063i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00000 | + | 5.19615i | −0.319801 | + | 0.553912i | ||||
\(89\) | −6.24500 | − | 3.60555i | −0.661968 | − | 0.382188i | 0.131058 | − | 0.991375i | \(-0.458163\pi\) |
−0.793027 | + | 0.609187i | \(0.791496\pi\) | |||||||
\(90\) | −18.7350 | −1.97484 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.24500 | − | 10.8167i | 0.644122 | − | 1.11565i | ||||
\(95\) | −13.0000 | − | 22.5167i | −1.33377 | − | 2.31016i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.24500 | − | 3.60555i | 0.634083 | − | 0.366088i | −0.148248 | − | 0.988950i | \(-0.547363\pi\) |
0.782332 | + | 0.622862i | \(0.214030\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.3923i | 1.04447i | ||||||||
\(100\) | −4.00000 | − | 6.92820i | −0.400000 | − | 0.692820i | ||||
\(101\) | 3.12250 | − | 5.40833i | 0.310700 | − | 0.538149i | −0.667814 | − | 0.744328i | \(-0.732770\pi\) |
0.978514 | + | 0.206180i | \(0.0661031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4900 | 1.23068 | 0.615338 | − | 0.788263i | \(-0.289020\pi\) | ||||
0.615338 | + | 0.788263i | \(0.289020\pi\) | |||||||
\(104\) | −3.12250 | + | 5.40833i | −0.306186 | + | 0.530330i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.50000 | − | 4.33013i | −0.728464 | − | 0.420579i | ||||
\(107\) | −1.00000 | + | 1.73205i | −0.0966736 | + | 0.167444i | −0.910306 | − | 0.413936i | \(-0.864154\pi\) |
0.813632 | + | 0.581380i | \(0.197487\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.92820i | − | 0.663602i | −0.943349 | − | 0.331801i | \(-0.892344\pi\) | ||
0.943349 | − | 0.331801i | \(-0.107656\pi\) | |||||||
\(110\) | −18.7350 | + | 10.8167i | −1.78631 | + | 1.03133i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.50000 | − | 4.33013i | −0.235180 | − | 0.407344i | 0.724145 | − | 0.689648i | \(-0.242235\pi\) |
−0.959325 | + | 0.282304i | \(0.908901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.4900 | + | 7.21110i | 1.16470 | + | 0.672439i | ||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 10.8167i | 1.00000i | ||||||||
\(118\) | −12.4900 | −1.14980 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 10.8167i | 0.979294i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8167i | 0.967471i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.00000 | + | 15.5885i | −0.798621 | + | 1.38325i | 0.121894 | + | 0.992543i | \(0.461103\pi\) |
−0.920514 | + | 0.390709i | \(0.872230\pi\) | |||||||
\(128\) | 10.5000 | + | 6.06218i | 0.928078 | + | 0.535826i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19.5000 | + | 11.2583i | −1.71026 | + | 0.987421i | ||||
\(131\) | −12.4900 | −1.09126 | −0.545628 | − | 0.838027i | \(-0.683709\pi\) | ||||
−0.545628 | + | 0.838027i | \(0.683709\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.0000 | − | 20.7846i | −1.03664 | − | 1.79552i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.36750 | + | 5.40833i | −0.803256 | + | 0.463760i | ||||
\(137\) | 7.50000 | − | 4.33013i | 0.640768 | − | 0.369948i | −0.144142 | − | 0.989557i | \(-0.546042\pi\) |
0.784910 | + | 0.619609i | \(0.212709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.24500 | + | 10.8167i | 0.529694 | + | 0.917457i | 0.999400 | + | 0.0346338i | \(0.0110265\pi\) |
−0.469706 | + | 0.882823i | \(0.655640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.0000 | 1.51053 | ||||||||
\(143\) | 6.24500 | + | 10.8167i | 0.522233 | + | 0.904534i | ||||
\(144\) | 15.0000 | 1.25000 | ||||||||
\(145\) | 3.12250 | + | 1.80278i | 0.259309 | + | 0.149712i | ||||
\(146\) | −9.36750 | + | 16.2250i | −0.775260 | + | 1.34279i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.73205i | − | 0.142374i | ||||||
\(149\) | 13.5000 | − | 7.79423i | 1.10596 | − | 0.638528i | 0.168182 | − | 0.985756i | \(-0.446210\pi\) |
0.937781 | + | 0.347228i | \(0.112877\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) | ||
0.990016 | − | 0.140952i | \(-0.0450164\pi\) | |||||||
\(152\) | 6.24500 | + | 10.8167i | 0.506536 | + | 0.877346i | ||||
\(153\) | −9.36750 | + | 16.2250i | −0.757317 | + | 1.31171i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.24500 | −0.498405 | −0.249203 | − | 0.968451i | \(-0.580168\pi\) | ||||
−0.249203 | + | 0.968451i | \(0.580168\pi\) | |||||||
\(158\) | 9.00000 | + | 5.19615i | 0.716002 | + | 0.413384i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.36750 | + | 16.2250i | 0.740566 | + | 1.28270i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 13.5000 | − | 7.79423i | 1.06066 | − | 0.612372i | ||||
\(163\) | −9.00000 | + | 5.19615i | −0.704934 | + | 0.406994i | −0.809183 | − | 0.587557i | \(-0.800090\pi\) |
0.104248 | + | 0.994551i | \(0.466756\pi\) | |||||||
\(164\) | − | 3.60555i | − | 0.281546i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.24500 | − | 10.8167i | 0.484706 | − | 0.839535i | ||||
\(167\) | −6.24500 | − | 3.60555i | −0.483252 | − | 0.279006i | 0.238518 | − | 0.971138i | \(-0.423338\pi\) |
−0.721771 | + | 0.692132i | \(0.756672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.50000 | + | 11.2583i | 0.500000 | + | 0.866025i | ||||
\(170\) | −39.0000 | −2.99116 | ||||||||
\(171\) | 18.7350 | + | 10.8167i | 1.43270 | + | 0.827170i | ||||
\(172\) | 3.00000 | − | 5.19615i | 0.228748 | − | 0.396203i | ||||
\(173\) | −12.4900 | − | 21.6333i | −0.949597 | − | 1.64475i | −0.746275 | − | 0.665638i | \(-0.768160\pi\) |
−0.203322 | − | 0.979112i | \(-0.565174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.0000 | − | 8.66025i | 1.13067 | − | 0.652791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.24500 | + | 10.8167i | 0.468082 | + | 0.810742i | ||||
\(179\) | −8.00000 | + | 13.8564i | −0.597948 | + | 1.03568i | 0.395175 | + | 0.918606i | \(0.370684\pi\) |
−0.993124 | + | 0.117071i | \(0.962650\pi\) | |||||||
\(180\) | 9.36750 | + | 5.40833i | 0.698212 | + | 0.403113i | ||||
\(181\) | 6.24500 | 0.464187 | 0.232094 | − | 0.972693i | \(-0.425442\pi\) | ||||
0.232094 | + | 0.972693i | \(0.425442\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00000 | − | 3.46410i | −0.442326 | − | 0.255377i | ||||
\(185\) | −3.12250 | + | 5.40833i | −0.229571 | + | 0.397628i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.6333i | 1.58198i | ||||||||
\(188\) | −6.24500 | + | 3.60555i | −0.455463 | + | 0.262962i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 45.0333i | 3.26706i | ||||||||
\(191\) | −2.00000 | − | 3.46410i | −0.144715 | − | 0.250654i | 0.784552 | − | 0.620063i | \(-0.212893\pi\) |
−0.929267 | + | 0.369410i | \(0.879560\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50000 | + | 4.33013i | 0.539862 | + | 0.311689i | 0.745023 | − | 0.667039i | \(-0.232439\pi\) |
−0.205161 | + | 0.978728i | \(0.565772\pi\) | |||||||
\(194\) | −12.4900 | −0.896729 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(198\) | 9.00000 | − | 15.5885i | 0.639602 | − | 1.10782i | ||||
\(199\) | −6.24500 | − | 10.8167i | −0.442696 | − | 0.766772i | 0.555192 | − | 0.831722i | \(-0.312645\pi\) |
−0.997889 | + | 0.0649497i | \(0.979311\pi\) | |||||||
\(200\) | − | 13.8564i | − | 0.979796i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.36750 | + | 5.40833i | −0.659095 | + | 0.380529i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.50000 | + | 11.2583i | −0.453980 | + | 0.786316i | ||||
\(206\) | −18.7350 | − | 10.8167i | −1.30533 | − | 0.753632i | ||||
\(207\) | −12.0000 | −0.834058 | ||||||||
\(208\) | 15.6125 | − | 9.01388i | 1.08253 | − | 0.625000i | ||||
\(209\) | 24.9800 | 1.72790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | − | 17.3205i | 0.688428 | − | 1.19239i | −0.283918 | − | 0.958849i | \(-0.591634\pi\) |
0.972346 | − | 0.233544i | \(-0.0750324\pi\) | |||||||
\(212\) | 2.50000 | + | 4.33013i | 0.171701 | + | 0.297394i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.00000 | − | 1.73205i | 0.205076 | − | 0.118401i | ||||
\(215\) | −18.7350 | + | 10.8167i | −1.27772 | + | 0.737690i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | + | 10.3923i | −0.406371 | + | 0.703856i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.4900 | 0.842075 | ||||||||
\(221\) | 22.5167i | 1.51463i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.24500 | − | 3.60555i | −0.418196 | − | 0.241446i | 0.276109 | − | 0.961126i | \(-0.410955\pi\) |
−0.694305 | + | 0.719681i | \(0.744288\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0000 | − | 20.7846i | −0.800000 | − | 1.38564i | ||||
\(226\) | 8.66025i | 0.576072i | ||||||||
\(227\) | −12.4900 | + | 7.21110i | −0.828990 | + | 0.478618i | −0.853507 | − | 0.521082i | \(-0.825529\pi\) |
0.0245166 | + | 0.999699i | \(0.492195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.6333i | − | 1.42957i | −0.699345 | − | 0.714785i | \(-0.746525\pi\) | ||
0.699345 | − | 0.714785i | \(-0.253475\pi\) | |||||||
\(230\) | −12.4900 | − | 21.6333i | −0.823566 | − | 1.42646i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.50000 | − | 0.866025i | −0.0984798 | − | 0.0568574i | ||||
\(233\) | 2.00000 | 0.131024 | 0.0655122 | − | 0.997852i | \(-0.479132\pi\) | ||||
0.0655122 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(234\) | 9.36750 | − | 16.2250i | 0.612372 | − | 1.06066i | ||||
\(235\) | 26.0000 | 1.69605 | ||||||||
\(236\) | 6.24500 | + | 3.60555i | 0.406515 | + | 0.234701i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 17.3205i | − | 1.12037i | −0.828367 | − | 0.560185i | \(-0.810730\pi\) | ||
0.828367 | − | 0.560185i | \(-0.189270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.36750 | + | 5.40833i | −0.603414 | + | 0.348381i | −0.770383 | − | 0.637581i | \(-0.779935\pi\) |
0.166970 | + | 0.985962i | \(0.446602\pi\) | |||||||
\(242\) | − | 1.73205i | − | 0.111340i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.12250 | − | 5.40833i | 0.199898 | − | 0.346233i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.0000 | 1.65434 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.36750 | − | 16.2250i | 0.592453 | − | 1.02616i | ||||
\(251\) | −6.24500 | − | 10.8167i | −0.394181 | − | 0.682741i | 0.598815 | − | 0.800887i | \(-0.295638\pi\) |
−0.992996 | + | 0.118146i | \(0.962305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | + | 6.92820i | −0.754434 | + | 0.435572i | ||||
\(254\) | 27.0000 | − | 15.5885i | 1.69413 | − | 0.978107i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | −9.36750 | + | 16.2250i | −0.584328 | + | 1.01209i | 0.410630 | + | 0.911802i | \(0.365309\pi\) |
−0.994959 | + | 0.100285i | \(0.968025\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.0000 | 0.806226 | ||||||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | 18.7350 | + | 10.8167i | 1.15745 | + | 0.668255i | ||||
\(263\) | −1.00000 | + | 1.73205i | −0.0616626 | + | 0.106803i | −0.895209 | − | 0.445647i | \(-0.852974\pi\) |
0.833546 | + | 0.552450i | \(0.186307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 18.0278i | − | 1.10744i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.8564i | 0.846415i | ||||||||
\(269\) | −12.4900 | − | 21.6333i | −0.761528 | − | 1.31901i | −0.942063 | − | 0.335437i | \(-0.891116\pi\) |
0.180534 | − | 0.983569i | \(-0.442217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.24500 | + | 3.60555i | 0.379357 | + | 0.219022i | 0.677538 | − | 0.735487i | \(-0.263047\pi\) |
−0.298182 | + | 0.954509i | \(0.596380\pi\) | |||||||
\(272\) | 31.2250 | 1.89329 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.0000 | −0.906183 | ||||||||
\(275\) | −24.0000 | − | 13.8564i | −1.44725 | − | 0.835573i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.5000 | − | 21.6506i | −0.751052 | − | 1.30086i | −0.947313 | − | 0.320309i | \(-0.896213\pi\) |
0.196261 | − | 0.980552i | \(-0.437120\pi\) | |||||||
\(278\) | − | 21.6333i | − | 1.29748i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5167i | 1.34323i | 0.740900 | + | 0.671616i | \(0.234399\pi\) | ||||
−0.740900 | + | 0.671616i | \(0.765601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.24500 | + | 10.8167i | −0.371227 | + | 0.642983i | −0.989755 | − | 0.142779i | \(-0.954396\pi\) |
0.618528 | + | 0.785763i | \(0.287729\pi\) | |||||||
\(284\) | −9.00000 | − | 5.19615i | −0.534052 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 21.6333i | − | 1.27920i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −13.5000 | − | 7.79423i | −0.795495 | − | 0.459279i | ||||
\(289\) | −11.0000 | + | 19.0526i | −0.647059 | + | 1.12074i | ||||
\(290\) | −3.12250 | − | 5.40833i | −0.183359 | − | 0.317588i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.36750 | − | 5.40833i | 0.548191 | − | 0.316498i | ||||
\(293\) | 15.6125 | − | 9.01388i | 0.912092 | − | 0.526596i | 0.0309881 | − | 0.999520i | \(-0.490135\pi\) |
0.881104 | + | 0.472923i | \(0.156801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.0000 | − | 22.5167i | −0.756889 | − | 1.31097i | ||||
\(296\) | 1.50000 | − | 2.59808i | 0.0871857 | − | 0.151010i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −27.0000 | −1.56407 | ||||||||
\(299\) | −12.4900 | + | 7.21110i | −0.722315 | + | 0.417029i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.00000 | + | 5.19615i | −0.172631 | + | 0.299005i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 36.0555i | − | 2.06793i | ||||||
\(305\) | −19.5000 | + | 11.2583i | −1.11657 | + | 0.644650i | ||||
\(306\) | 28.1025 | − | 16.2250i | 1.60651 | − | 0.927520i | ||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.9800 | 1.41649 | 0.708243 | − | 0.705969i | \(-0.249488\pi\) | ||||
0.708243 | + | 0.705969i | \(0.249488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | 9.36750 | + | 5.40833i | 0.528638 | + | 0.305210i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.00000 | − | 5.19615i | −0.168763 | − | 0.292306i | ||||
\(317\) | 15.5885i | 0.875535i | 0.899088 | + | 0.437767i | \(0.144231\pi\) | ||||
−0.899088 | + | 0.437767i | \(0.855769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | + | 1.73205i | −0.167968 | + | 0.0969762i | ||||
\(320\) | 3.60555i | 0.201556i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.0000 | + | 22.5167i | 2.17002 | + | 1.25286i | ||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | −24.9800 | − | 14.4222i | −1.38564 | − | 0.800000i | ||||
\(326\) | 18.0000 | 0.996928 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.12250 | − | 5.40833i | 0.172411 | − | 0.298625i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.00000 | − | 5.19615i | 0.494685 | − | 0.285606i | −0.231831 | − | 0.972756i | \(-0.574472\pi\) |
0.726516 | + | 0.687150i | \(0.241138\pi\) | |||||||
\(332\) | −6.24500 | + | 3.60555i | −0.342739 | + | 0.197880i | ||||
\(333\) | − | 5.19615i | − | 0.284747i | ||||||
\(334\) | 6.24500 | + | 10.8167i | 0.341711 | + | 0.591861i | ||||
\(335\) | 24.9800 | − | 43.2666i | 1.36480 | − | 2.36391i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | 0.599208 | 0.299604 | − | 0.954064i | \(-0.403145\pi\) | ||||
0.299604 | + | 0.954064i | \(0.403145\pi\) | |||||||
\(338\) | − | 22.5167i | − | 1.22474i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.5000 | + | 11.2583i | 1.05754 | + | 0.610569i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −18.7350 | − | 32.4500i | −1.01307 | − | 1.75469i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.00000 | − | 5.19615i | 0.485247 | − | 0.280158i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 43.2666i | 2.32603i | ||||||||
\(347\) | 14.0000 | + | 24.2487i | 0.751559 | + | 1.30174i | 0.947067 | + | 0.321037i | \(0.104031\pi\) |
−0.195507 | + | 0.980702i | \(0.562635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.7350 | − | 10.8167i | −1.00286 | − | 0.579002i | −0.0937676 | − | 0.995594i | \(-0.529891\pi\) |
−0.909094 | + | 0.416592i | \(0.863224\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.0000 | −0.959403 | ||||||||
\(353\) | −21.8575 | − | 12.6194i | −1.16336 | − | 0.671664i | −0.211251 | − | 0.977432i | \(-0.567754\pi\) |
−0.952106 | + | 0.305767i | \(0.901087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.7350 | + | 32.4500i | 0.994350 | + | 1.72227i | ||||
\(356\) | − | 7.21110i | − | 0.382188i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.0000 | − | 13.8564i | 1.26844 | − | 0.732334i | ||||
\(359\) | 27.7128i | 1.46263i | 0.682042 | + | 0.731313i | \(0.261092\pi\) | ||||
−0.682042 | + | 0.731313i | \(0.738908\pi\) | |||||||
\(360\) | 9.36750 | + | 16.2250i | 0.493710 | + | 0.855132i | ||||
\(361\) | 16.5000 | − | 28.5788i | 0.868421 | − | 1.50415i | ||||
\(362\) | −9.36750 | − | 5.40833i | −0.492345 | − | 0.284255i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.0000 | −2.04135 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.4900 | + | 21.6333i | −0.651972 | + | 1.12925i | 0.330671 | + | 0.943746i | \(0.392725\pi\) |
−0.982644 | + | 0.185503i | \(0.940608\pi\) | |||||||
\(368\) | 10.0000 | + | 17.3205i | 0.521286 | + | 0.902894i | ||||
\(369\) | − | 10.8167i | − | 0.563093i | ||||||
\(370\) | 9.36750 | − | 5.40833i | 0.486993 | − | 0.281166i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.50000 | − | 12.9904i | −0.388335 | − | 0.672616i | 0.603890 | − | 0.797067i | \(-0.293616\pi\) |
−0.992226 | + | 0.124451i | \(0.960283\pi\) | |||||||
\(374\) | 18.7350 | − | 32.4500i | 0.968763 | − | 1.67795i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.4900 | −0.644122 | ||||||||
\(377\) | −3.12250 | + | 1.80278i | −0.160817 | + | 0.0928477i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0000 | + | 10.3923i | 0.924598 | + | 0.533817i | 0.885099 | − | 0.465403i | \(-0.154091\pi\) |
0.0394989 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(380\) | 13.0000 | − | 22.5167i | 0.666886 | − | 1.15508i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.92820i | 0.354478i | ||||||||
\(383\) | 31.2250 | − | 18.0278i | 1.59552 | − | 0.921175i | 0.603187 | − | 0.797600i | \(-0.293897\pi\) |
0.992335 | − | 0.123576i | \(-0.0394362\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.50000 | − | 12.9904i | −0.381740 | − | 0.661193i | ||||
\(387\) | 9.00000 | − | 15.5885i | 0.457496 | − | 0.792406i | ||||
\(388\) | 6.24500 | + | 3.60555i | 0.317042 | + | 0.183044i | ||||
\(389\) | 17.0000 | 0.861934 | 0.430967 | − | 0.902368i | \(-0.358172\pi\) | ||||
0.430967 | + | 0.902368i | \(0.358172\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.9800 | −1.26329 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.6333i | 1.08849i | ||||||||
\(396\) | −9.00000 | + | 5.19615i | −0.452267 | + | 0.261116i | ||||
\(397\) | 6.24500 | − | 3.60555i | 0.313427 | − | 0.180957i | −0.335032 | − | 0.942207i | \(-0.608747\pi\) |
0.648459 | + | 0.761249i | \(0.275414\pi\) | |||||||
\(398\) | 21.6333i | 1.08438i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | + | 34.6410i | −1.00000 | + | 1.73205i | ||||
\(401\) | 7.50000 | + | 4.33013i | 0.374532 | + | 0.216236i | 0.675437 | − | 0.737418i | \(-0.263955\pi\) |
−0.300904 | + | 0.953654i | \(0.597289\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.24500 | 0.310700 | ||||||||
\(405\) | 28.1025 | + | 16.2250i | 1.39642 | + | 0.806226i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.00000 | − | 5.19615i | −0.148704 | − | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.8575 | − | 12.6194i | 1.08078 | − | 0.623991i | 0.149676 | − | 0.988735i | \(-0.452177\pi\) |
0.931108 | + | 0.364744i | \(0.118844\pi\) | |||||||
\(410\) | 19.5000 | − | 11.2583i | 0.963036 | − | 0.556009i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.24500 | + | 10.8167i | 0.307669 | + | 0.532898i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.0000 | + | 10.3923i | 0.884652 | + | 0.510754i | ||||
\(415\) | 26.0000 | 1.27629 | ||||||||
\(416\) | −18.7350 | −0.918559 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −37.4700 | − | 21.6333i | −1.83272 | − | 1.05812i | ||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.5167i | 1.09739i | 0.836021 | + | 0.548697i | \(0.184876\pi\) | ||||
−0.836021 | + | 0.548697i | \(0.815124\pi\) | |||||||
\(422\) | −30.0000 | + | 17.3205i | −1.46038 | + | 0.843149i | ||||
\(423\) | −18.7350 | + | 10.8167i | −0.910927 | + | 0.525924i | ||||
\(424\) | 8.66025i | 0.420579i | ||||||||
\(425\) | −24.9800 | − | 43.2666i | −1.21171 | − | 2.09874i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 37.4700 | 1.80696 | ||||||||
\(431\) | −24.0000 | − | 13.8564i | −1.15604 | − | 0.667440i | −0.205688 | − | 0.978618i | \(-0.565943\pi\) |
−0.950352 | + | 0.311178i | \(0.899276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.36750 | + | 16.2250i | 0.450173 | + | 0.779723i | 0.998396 | − | 0.0566092i | \(-0.0180289\pi\) |
−0.548223 | + | 0.836332i | \(0.684696\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.00000 | − | 3.46410i | 0.287348 | − | 0.165900i | ||||
\(437\) | 28.8444i | 1.37982i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.24500 | − | 10.8167i | 0.298057 | − | 0.516251i | −0.677634 | − | 0.735399i | \(-0.736995\pi\) |
0.975691 | + | 0.219149i | \(0.0703280\pi\) | |||||||
\(440\) | 18.7350 | + | 10.8167i | 0.893156 | + | 0.515664i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.5000 | − | 33.7750i | 0.927520 | − | 1.60651i | ||||
\(443\) | 16.0000 | 0.760183 | 0.380091 | − | 0.924949i | \(-0.375893\pi\) | ||||
0.380091 | + | 0.924949i | \(0.375893\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.0000 | + | 22.5167i | −0.616259 | + | 1.06739i | ||||
\(446\) | 6.24500 | + | 10.8167i | 0.295709 | + | 0.512183i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | − | 3.46410i | 0.283158 | − | 0.163481i | −0.351694 | − | 0.936115i | \(-0.614394\pi\) |
0.634852 | + | 0.772634i | \(0.281061\pi\) | |||||||
\(450\) | 41.5692i | 1.95959i | ||||||||
\(451\) | −6.24500 | − | 10.8167i | −0.294065 | − | 0.509336i | ||||
\(452\) | 2.50000 | − | 4.33013i | 0.117590 | − | 0.203672i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.9800 | 1.17237 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.5000 | − | 19.9186i | −1.61384 | − | 0.931752i | −0.988469 | − | 0.151426i | \(-0.951613\pi\) |
−0.625373 | − | 0.780326i | \(-0.715053\pi\) | |||||||
\(458\) | −18.7350 | + | 32.4500i | −0.875429 | + | 1.51629i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.4222i | 0.672439i | ||||||||
\(461\) | −34.3475 | + | 19.8305i | −1.59972 | + | 0.923600i | −0.608182 | + | 0.793797i | \(0.708101\pi\) |
−0.991540 | + | 0.129802i | \(0.958566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.3923i | − | 0.482971i | −0.970404 | − | 0.241486i | \(-0.922365\pi\) | ||
0.970404 | − | 0.241486i | \(-0.0776347\pi\) | |||||||
\(464\) | 2.50000 | + | 4.33013i | 0.116060 | + | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 1.73205i | −0.138972 | − | 0.0802357i | ||||
\(467\) | −12.4900 | −0.577968 | −0.288984 | − | 0.957334i | \(-0.593317\pi\) | ||||
−0.288984 | + | 0.957334i | \(0.593317\pi\) | |||||||
\(468\) | −9.36750 | + | 5.40833i | −0.433013 | + | 0.250000i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −39.0000 | − | 22.5167i | −1.79894 | − | 1.03862i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.24500 | + | 10.8167i | 0.287449 | + | 0.497877i | ||||
\(473\) | − | 20.7846i | − | 0.955677i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −49.9600 | + | 28.8444i | −2.29232 | + | 1.32347i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.50000 | + | 12.9904i | 0.343401 | + | 0.594789i | ||||
\(478\) | −15.0000 | + | 25.9808i | −0.686084 | + | 1.18833i | ||||
\(479\) | −12.4900 | − | 7.21110i | −0.570682 | − | 0.329484i | 0.186739 | − | 0.982409i | \(-0.440208\pi\) |
−0.757422 | + | 0.652926i | \(0.773541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.12250 | − | 5.40833i | −0.142374 | − | 0.246598i | ||||
\(482\) | 18.7350 | 0.853356 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | + | 0.866025i | −0.0227273 | + | 0.0393648i | ||||
\(485\) | −13.0000 | − | 22.5167i | −0.590300 | − | 1.02243i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.0000 | + | 10.3923i | −0.815658 | + | 0.470920i | −0.848917 | − | 0.528526i | \(-0.822745\pi\) |
0.0332590 | + | 0.999447i | \(0.489411\pi\) | |||||||
\(488\) | 9.36750 | − | 5.40833i | 0.424047 | − | 0.244823i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00000 | − | 3.46410i | 0.0902587 | − | 0.156333i | −0.817361 | − | 0.576126i | \(-0.804564\pi\) |
0.907620 | + | 0.419793i | \(0.137897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.24500 | −0.281261 | ||||||||
\(494\) | −39.0000 | − | 22.5167i | −1.75469 | − | 1.01307i | ||||
\(495\) | 37.4700 | 1.68415 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 27.7128i | − | 1.24060i | −0.784366 | − | 0.620298i | \(-0.787012\pi\) | ||
0.784366 | − | 0.620298i | \(-0.212988\pi\) | |||||||
\(500\) | −9.36750 | + | 5.40833i | −0.418927 | + | 0.241868i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.6333i | 0.965542i | ||||||||
\(503\) | 6.24500 | + | 10.8167i | 0.278451 | + | 0.482291i | 0.971000 | − | 0.239080i | \(-0.0768458\pi\) |
−0.692549 | + | 0.721371i | \(0.743512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.5000 | − | 11.2583i | −0.867739 | − | 0.500989i | ||||
\(506\) | 24.0000 | 1.06693 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.0000 | −0.798621 | ||||||||
\(509\) | 3.12250 | + | 1.80278i | 0.138402 | + | 0.0799066i | 0.567602 | − | 0.823303i | \(-0.307871\pi\) |
−0.429200 | + | 0.903209i | \(0.641204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.1025 | − | 16.2250i | 1.23955 | − | 0.715653i | ||||
\(515\) | − | 45.0333i | − | 1.98441i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.4900 | + | 21.6333i | −0.549309 | + | 0.951432i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.5000 | + | 11.2583i | 0.855132 | + | 0.493710i | ||||
\(521\) | −6.24500 | −0.273598 | −0.136799 | − | 0.990599i | \(-0.543681\pi\) | ||||
−0.136799 | + | 0.990599i | \(0.543681\pi\) | |||||||
\(522\) | 4.50000 | + | 2.59808i | 0.196960 | + | 0.113715i | ||||
\(523\) | −12.4900 | + | 21.6333i | −0.546149 | + | 0.945958i | 0.452384 | + | 0.891823i | \(0.350574\pi\) |
−0.998534 | + | 0.0541354i | \(0.982760\pi\) | |||||||
\(524\) | −6.24500 | − | 10.8167i | −0.272814 | − | 0.472528i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.00000 | − | 1.73205i | 0.130806 | − | 0.0755210i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | −15.6125 | + | 27.0416i | −0.678163 | + | 1.17461i | ||||
\(531\) | 18.7350 | + | 10.8167i | 0.813029 | + | 0.469403i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.50000 | − | 11.2583i | −0.281546 | − | 0.487652i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.24500 | + | 3.60555i | 0.269995 | + | 0.155882i | ||||
\(536\) | −12.0000 | + | 20.7846i | −0.518321 | + | 0.897758i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 43.2666i | 1.86536i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 5.19615i | − | 0.223400i | −0.993742 | − | 0.111700i | \(-0.964370\pi\) | ||
0.993742 | − | 0.111700i | \(-0.0356296\pi\) | |||||||
\(542\) | −6.24500 | − | 10.8167i | −0.268246 | − | 0.464615i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.1025 | − | 16.2250i | −1.20488 | − | 0.695640i | ||||
\(545\) | −24.9800 | −1.07003 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 7.50000 | + | 4.33013i | 0.320384 | + | 0.184974i | ||||
\(549\) | 9.36750 | − | 16.2250i | 0.399795 | − | 0.692465i | ||||
\(550\) | 24.0000 | + | 41.5692i | 1.02336 | + | 1.77252i | ||||
\(551\) | 7.21110i | 0.307203i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 43.3013i | 1.83969i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.24500 | + | 10.8167i | −0.264847 | + | 0.458728i | ||||
\(557\) | −1.50000 | − | 0.866025i | −0.0635570 | − | 0.0366947i | 0.467885 | − | 0.883789i | \(-0.345016\pi\) |
−0.531442 | + | 0.847095i | \(0.678350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 21.6333i | − | 0.914991i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.5000 | − | 33.7750i | 0.822558 | − | 1.42471i | ||||
\(563\) | 6.24500 | + | 10.8167i | 0.263195 | + | 0.455868i | 0.967089 | − | 0.254437i | \(-0.0818903\pi\) |
−0.703894 | + | 0.710305i | \(0.748557\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.6125 | + | 9.01388i | −0.656823 | + | 0.379217i | ||||
\(566\) | 18.7350 | − | 10.8167i | 0.787491 | − | 0.454658i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.00000 | − | 15.5885i | −0.377632 | − | 0.654077i | ||||
\(569\) | −5.00000 | + | 8.66025i | −0.209611 | + | 0.363057i | −0.951592 | − | 0.307364i | \(-0.900553\pi\) |
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0000 | 1.00437 | 0.502184 | − | 0.864761i | \(-0.332530\pi\) | ||||
0.502184 | + | 0.864761i | \(0.332530\pi\) | |||||||
\(572\) | −6.24500 | + | 10.8167i | −0.261116 | + | 0.452267i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.0000 | − | 27.7128i | 0.667246 | − | 1.15570i | ||||
\(576\) | −1.50000 | − | 2.59808i | −0.0625000 | − | 0.108253i | ||||
\(577\) | − | 18.0278i | − | 0.750505i | −0.926923 | − | 0.375253i | \(-0.877556\pi\) | ||
0.926923 | − | 0.375253i | \(-0.122444\pi\) | |||||||
\(578\) | 33.0000 | − | 19.0526i | 1.37262 | − | 0.792482i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.60555i | 0.149712i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0000 | + | 8.66025i | 0.621237 | + | 0.358671i | ||||
\(584\) | 18.7350 | 0.775260 | ||||||||
\(585\) | 39.0000 | 1.61245 | ||||||||
\(586\) | −31.2250 | −1.28989 | ||||||||
\(587\) | −24.9800 | − | 14.4222i | −1.03103 | − | 0.595268i | −0.113754 | − | 0.993509i | \(-0.536287\pi\) |
−0.917281 | + | 0.398241i | \(0.869621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 45.0333i | 1.85399i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.50000 | + | 4.33013i | −0.308248 | + | 0.177967i | ||||
\(593\) | − | 18.0278i | − | 0.740311i | −0.928970 | − | 0.370156i | \(-0.879304\pi\) | ||
0.928970 | − | 0.370156i | \(-0.120696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.5000 | + | 7.79423i | 0.552982 | + | 0.319264i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.9800 | 1.02151 | ||||||||
\(599\) | −10.0000 | −0.408589 | −0.204294 | − | 0.978909i | \(-0.565490\pi\) | ||||
−0.204294 | + | 0.978909i | \(0.565490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.8575 | + | 37.8583i | −0.891586 | + | 1.54427i | −0.0536116 | + | 0.998562i | \(0.517073\pi\) |
−0.837974 | + | 0.545710i | \(0.816260\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41.5692i | 1.69283i | ||||||||
\(604\) | 3.00000 | − | 1.73205i | 0.122068 | − | 0.0704761i | ||||
\(605\) | 3.12250 | − | 1.80278i | 0.126948 | − | 0.0732933i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.7350 | + | 32.4500i | 0.760430 | + | 1.31710i | 0.942629 | + | 0.333842i | \(0.108345\pi\) |
−0.182199 | + | 0.983262i | \(0.558322\pi\) | |||||||
\(608\) | −18.7350 | + | 32.4500i | −0.759804 | + | 1.31602i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39.0000 | 1.57906 | ||||||||
\(611\) | −13.0000 | + | 22.5167i | −0.525924 | + | 0.910927i | ||||
\(612\) | −18.7350 | −0.757317 | ||||||||
\(613\) | −1.50000 | − | 0.866025i | −0.0605844 | − | 0.0349784i | 0.469402 | − | 0.882985i | \(-0.344470\pi\) |
−0.529986 | + | 0.848006i | \(0.677803\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.5000 | − | 11.2583i | 0.785040 | − | 0.453243i | −0.0531732 | − | 0.998585i | \(-0.516934\pi\) |
0.838214 | + | 0.545342i | \(0.183600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 36.0555i | − | 1.44919i | −0.689173 | − | 0.724597i | \(-0.742026\pi\) | ||
0.689173 | − | 0.724597i | \(-0.257974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −37.4700 | − | 21.6333i | −1.50241 | − | 0.867417i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.12250 | − | 5.40833i | −0.124601 | − | 0.215816i | ||||
\(629\) | − | 10.8167i | − | 0.431288i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0000 | + | 6.92820i | −0.477712 | + | 0.275807i | −0.719463 | − | 0.694531i | \(-0.755612\pi\) |
0.241750 | + | 0.970339i | \(0.422279\pi\) | |||||||
\(632\) | − | 10.3923i | − | 0.413384i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.5000 | − | 23.3827i | 0.536153 | − | 0.928645i | ||||
\(635\) | 56.2050 | + | 32.4500i | 2.23043 | + | 1.28774i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.00000 | 0.237542 | ||||||||
\(639\) | −27.0000 | − | 15.5885i | −1.06810 | − | 0.616670i | ||||
\(640\) | 21.8575 | − | 37.8583i | 0.863993 | − | 1.49648i | ||||
\(641\) | 14.5000 | + | 25.1147i | 0.572716 | + | 0.991972i | 0.996286 | + | 0.0861092i | \(0.0274434\pi\) |
−0.423570 | + | 0.905863i | \(0.639223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −39.0000 | − | 67.5500i | −1.53443 | − | 2.65772i | ||||
\(647\) | −6.24500 | + | 10.8167i | −0.245516 | + | 0.425247i | −0.962277 | − | 0.272073i | \(-0.912291\pi\) |
0.716760 | + | 0.697320i | \(0.245624\pi\) | |||||||
\(648\) | −13.5000 | − | 7.79423i | −0.530330 | − | 0.306186i | ||||
\(649\) | 24.9800 | 0.980550 | ||||||||
\(650\) | 24.9800 | + | 43.2666i | 0.979796 | + | 1.69706i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.00000 | − | 5.19615i | −0.352467 | − | 0.203497i | ||||
\(653\) | −19.0000 | + | 32.9090i | −0.743527 | + | 1.28783i | 0.207352 | + | 0.978266i | \(0.433515\pi\) |
−0.950880 | + | 0.309561i | \(0.899818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.0333i | 1.75960i | ||||||||
\(656\) | −15.6125 | + | 9.01388i | −0.609566 | + | 0.351933i | ||||
\(657\) | 28.1025 | − | 16.2250i | 1.09638 | − | 0.632997i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.00000 | + | 3.46410i | 0.0779089 | + | 0.134942i | 0.902348 | − | 0.431009i | \(-0.141842\pi\) |
−0.824439 | + | 0.565951i | \(0.808509\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.36750 | − | 5.40833i | −0.364353 | − | 0.210360i | 0.306635 | − | 0.951827i | \(-0.400797\pi\) |
−0.670989 | + | 0.741468i | \(0.734130\pi\) | |||||||
\(662\) | −18.0000 | −0.699590 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.4900 | −0.484706 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.50000 | + | 7.79423i | −0.174371 | + | 0.302020i | ||||
\(667\) | −2.00000 | − | 3.46410i | −0.0774403 | − | 0.134131i | ||||
\(668\) | − | 7.21110i | − | 0.279006i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −74.9400 | + | 43.2666i | −2.89518 | + | 1.67154i | ||||
\(671\) | − | 21.6333i | − | 0.835145i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.50000 | + | 2.59808i | −0.0578208 | + | 0.100148i | −0.893487 | − | 0.449089i | \(-0.851749\pi\) |
0.835666 | + | 0.549238i | \(0.185082\pi\) | |||||||
\(674\) | −16.5000 | − | 9.52628i | −0.635556 | − | 0.366939i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.50000 | + | 11.2583i | −0.250000 | + | 0.433013i | ||||
\(677\) | −24.9800 | −0.960059 | −0.480030 | − | 0.877252i | \(-0.659374\pi\) | ||||
−0.480030 | + | 0.877252i | \(0.659374\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 19.5000 | + | 33.7750i | 0.747791 | + | 1.29521i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.0000 | + | 22.5167i | −1.49229 | + | 0.861576i | −0.999961 | − | 0.00883113i | \(-0.997189\pi\) |
−0.492333 | + | 0.870407i | \(0.663856\pi\) | |||||||
\(684\) | 21.6333i | 0.827170i | ||||||||
\(685\) | −15.6125 | − | 27.0416i | −0.596523 | − | 1.03321i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −30.0000 | −1.14374 | ||||||||
\(689\) | 15.6125 | + | 9.01388i | 0.594789 | + | 0.343401i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9800 | + | 14.4222i | 0.950284 | + | 0.548647i | 0.893169 | − | 0.449721i | \(-0.148477\pi\) |
0.0571146 | + | 0.998368i | \(0.481810\pi\) | |||||||
\(692\) | 12.4900 | − | 21.6333i | 0.474798 | − | 0.822375i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 48.4974i | − | 1.84094i | ||||||
\(695\) | 39.0000 | − | 22.5167i | 1.47935 | − | 0.854106i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 22.5167i | − | 0.852879i | ||||||
\(698\) | 18.7350 | + | 32.4500i | 0.709130 | + | 1.22825i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.0000 | 0.528773 | 0.264386 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264386 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.4900 | −0.471069 | ||||||||
\(704\) | −3.00000 | − | 1.73205i | −0.113067 | − | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.8575 | + | 37.8583i | 0.822618 | + | 1.42482i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.5000 | − | 16.4545i | 1.07034 | − | 0.617961i | 0.142066 | − | 0.989857i | \(-0.454626\pi\) |
0.928274 | + | 0.371896i | \(0.121292\pi\) | |||||||
\(710\) | − | 64.8999i | − | 2.43565i | ||||||
\(711\) | −9.00000 | − | 15.5885i | −0.337526 | − | 0.584613i | ||||
\(712\) | 6.24500 | − | 10.8167i | 0.234041 | − | 0.405371i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39.0000 | − | 22.5167i | 1.45852 | − | 0.842075i | ||||
\(716\) | −16.0000 | −0.597948 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.0000 | − | 41.5692i | 0.895672 | − | 1.55135i | ||||
\(719\) | −18.7350 | − | 32.4500i | −0.698697 | − | 1.21018i | −0.968918 | − | 0.247381i | \(-0.920430\pi\) |
0.270221 | − | 0.962798i | \(-0.412903\pi\) | |||||||
\(720\) | − | 54.0833i | − | 2.01556i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −49.5000 | + | 28.5788i | −1.84220 | + | 1.06359i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.12250 | + | 5.40833i | 0.116047 | + | 0.200999i | ||||
\(725\) | 4.00000 | − | 6.92820i | 0.148556 | − | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.9800 | −0.926457 | −0.463228 | − | 0.886239i | \(-0.653309\pi\) | ||||
−0.463228 | + | 0.886239i | \(0.653309\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 58.5000 | + | 33.7750i | 2.16518 | + | 1.25007i | ||||
\(731\) | 18.7350 | − | 32.4500i | 0.692939 | − | 1.20021i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 10.8167i | − | 0.399522i | −0.979845 | − | 0.199761i | \(-0.935983\pi\) | ||
0.979845 | − | 0.199761i | \(-0.0640166\pi\) | |||||||
\(734\) | 37.4700 | − | 21.6333i | 1.38304 | − | 0.798500i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 20.7846i | − | 0.766131i | ||||||
\(737\) | 24.0000 | + | 41.5692i | 0.884051 | + | 1.53122i | ||||
\(738\) | −9.36750 | + | 16.2250i | −0.344822 | + | 0.597250i | ||||
\(739\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | −6.24500 | −0.229571 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0000 | − | 10.3923i | −0.660356 | − | 0.381257i | 0.132057 | − | 0.991242i | \(-0.457842\pi\) |
−0.792413 | + | 0.609985i | \(0.791175\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.1025 | − | 48.6749i | −1.02960 | − | 1.78331i | ||||
\(746\) | 25.9808i | 0.951223i | ||||||||
\(747\) | −18.7350 | + | 10.8167i | −0.685478 | + | 0.395761i | ||||
\(748\) | −18.7350 | + | 10.8167i | −0.685019 | + | 0.395496i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.0000 | + | 36.3731i | −0.766301 | + | 1.32727i | 0.173255 | + | 0.984877i | \(0.444571\pi\) |
−0.939556 | + | 0.342395i | \(0.888762\pi\) | |||||||
\(752\) | 31.2250 | + | 18.0278i | 1.13866 | + | 0.657405i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.24500 | 0.227429 | ||||||||
\(755\) | −12.4900 | −0.454557 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.00000 | − | 12.1244i | 0.254419 | − | 0.440667i | −0.710318 | − | 0.703881i | \(-0.751449\pi\) |
0.964738 | + | 0.263213i | \(0.0847823\pi\) | |||||||
\(758\) | −18.0000 | − | 31.1769i | −0.653789 | − | 1.13240i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 39.0000 | − | 22.5167i | 1.41468 | − | 0.816765i | ||||
\(761\) | 31.2250 | − | 18.0278i | 1.13191 | − | 0.653506i | 0.187492 | − | 0.982266i | \(-0.439964\pi\) |
0.944413 | + | 0.328761i | \(0.106631\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.00000 | − | 3.46410i | 0.0723575 | − | 0.125327i | ||||
\(765\) | 58.5000 | + | 33.7750i | 2.11507 | + | 1.22114i | ||||
\(766\) | −62.4500 | −2.25641 | ||||||||
\(767\) | 26.0000 | 0.938806 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.7350 | − | 10.8167i | −0.675601 | − | 0.390059i | 0.122594 | − | 0.992457i | \(-0.460879\pi\) |
−0.798196 | + | 0.602398i | \(0.794212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.66025i | 0.311689i | ||||||||
\(773\) | −6.24500 | + | 3.60555i | −0.224617 | + | 0.129683i | −0.608086 | − | 0.793871i | \(-0.708063\pi\) |
0.383469 | + | 0.923554i | \(0.374729\pi\) | |||||||
\(774\) | −27.0000 | + | 15.5885i | −0.970495 | + | 0.560316i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.24500 | + | 10.8167i | 0.224182 | + | 0.388295i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.5000 | − | 14.7224i | −0.914219 | − | 0.527825i | ||||
\(779\) | −26.0000 | −0.931547 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | 37.4700 | + | 21.6333i | 1.33992 | + | 0.773606i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.5167i | 0.803654i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.4900 | − | 7.21110i | 0.445220 | − | 0.257048i | −0.260589 | − | 0.965450i | \(-0.583917\pi\) |
0.705809 | + | 0.708402i | \(0.250583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.7350 | − | 32.4500i | 0.666561 | − | 1.15452i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −18.0000 | −0.639602 | ||||||||
\(793\) | − | 22.5167i | − | 0.799590i | ||||||
\(794\) | −12.4900 | −0.443253 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.24500 | − | 10.8167i | 0.221348 | − | 0.383386i | ||||
\(797\) | 12.4900 | + | 21.6333i | 0.442418 | + | 0.766291i | 0.997868 | − | 0.0652589i | \(-0.0207873\pi\) |
−0.555450 | + | 0.831550i | \(0.687454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.0000 | + | 22.5167i | −1.37972 | + | 0.796582i | ||||
\(800\) | 36.0000 | − | 20.7846i | 1.27279 | − | 0.734847i | ||||
\(801\) | − | 21.6333i | − | 0.764375i | ||||||
\(802\) | −7.50000 | − | 12.9904i | −0.264834 | − | 0.458706i | ||||
\(803\) | 18.7350 | − | 32.4500i | 0.661144 | − | 1.14513i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.36750 | + | 5.40833i | 0.329547 | + | 0.190264i | ||||
\(809\) | 3.50000 | − | 6.06218i | 0.123053 | − | 0.213135i | −0.797917 | − | 0.602767i | \(-0.794065\pi\) |
0.920970 | + | 0.389633i | \(0.127398\pi\) | |||||||
\(810\) | −28.1025 | − | 48.6749i | −0.987421 | − | 1.71026i | ||||
\(811\) | 43.2666i | 1.51930i | 0.650334 | + | 0.759648i | \(0.274629\pi\) | ||||
−0.650334 | + | 0.759648i | \(0.725371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.3923i | 0.364250i | ||||||||
\(815\) | 18.7350 | + | 32.4500i | 0.656258 | + | 1.13667i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.4700 | − | 21.6333i | −1.31091 | − | 0.756854i | ||||
\(818\) | −43.7150 | −1.52846 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.0000 | −0.453980 | ||||||||
\(821\) | −12.0000 | − | 6.92820i | −0.418803 | − | 0.241796i | 0.275762 | − | 0.961226i | \(-0.411070\pi\) |
−0.694565 | + | 0.719430i | \(0.744403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | − | 13.8564i | −0.278862 | − | 0.483004i | 0.692240 | − | 0.721668i | \(-0.256624\pi\) |
−0.971102 | + | 0.238664i | \(0.923291\pi\) | |||||||
\(824\) | 21.6333i | 0.753632i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.3205i | 0.602293i | 0.953578 | + | 0.301147i | \(0.0973693\pi\) | ||||
−0.953578 | + | 0.301147i | \(0.902631\pi\) | |||||||
\(828\) | −6.00000 | − | 10.3923i | −0.208514 | − | 0.361158i | ||||
\(829\) | 9.36750 | − | 16.2250i | 0.325347 | − | 0.563517i | −0.656236 | − | 0.754556i | \(-0.727852\pi\) |
0.981582 | + | 0.191039i | \(0.0611857\pi\) | |||||||
\(830\) | −39.0000 | − | 22.5167i | −1.35371 | − | 0.781565i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.12250 | − | 1.80278i | −0.108253 | − | 0.0625000i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.0000 | + | 22.5167i | −0.449884 | + | 0.779221i | ||||
\(836\) | 12.4900 | + | 21.6333i | 0.431976 | + | 0.748204i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.7150 | − | 25.2389i | 1.50921 | − | 0.871342i | 0.509267 | − | 0.860609i | \(-0.329917\pi\) |
0.999942 | − | 0.0107333i | \(-0.00341659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 19.5000 | − | 33.7750i | 0.672014 | − | 1.16396i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.0000 | 0.688428 | ||||||||
\(845\) | 40.5925 | − | 23.4361i | 1.39642 | − | 0.806226i | ||||
\(846\) | 37.4700 | 1.28824 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.5000 | − | 21.6506i | 0.429252 | − | 0.743486i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 86.5332i | 2.96807i | ||||||||
\(851\) | 6.00000 | − | 3.46410i | 0.205677 | − | 0.118748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.2389i | − | 0.864162i | −0.901835 | − | 0.432081i | \(-0.857779\pi\) | ||
0.901835 | − | 0.432081i | \(-0.142221\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 39.0000 | − | 67.5500i | 1.33377 | − | 2.31016i | ||||
\(856\) | −3.00000 | − | 1.73205i | −0.102538 | − | 0.0592003i | ||||
\(857\) | −31.2250 | −1.06663 | −0.533313 | − | 0.845918i | \(-0.679053\pi\) | ||||
−0.533313 | + | 0.845918i | \(0.679053\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.9600 | −1.70461 | −0.852306 | − | 0.523043i | \(-0.824797\pi\) | ||||
−0.852306 | + | 0.523043i | \(0.824797\pi\) | |||||||
\(860\) | −18.7350 | − | 10.8167i | −0.638858 | − | 0.368845i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.0000 | + | 41.5692i | 0.817443 | + | 1.41585i | ||||
\(863\) | − | 38.1051i | − | 1.29711i | −0.761166 | − | 0.648557i | \(-0.775373\pi\) | ||
0.761166 | − | 0.648557i | \(-0.224627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −78.0000 | + | 45.0333i | −2.65208 | + | 1.53118i | ||||
\(866\) | − | 32.4500i | − | 1.10269i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.0000 | − | 10.3923i | −0.610608 | − | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.9800 | + | 43.2666i | 0.846415 | + | 1.46603i | ||||
\(872\) | 12.0000 | 0.406371 | ||||||||
\(873\) | 18.7350 | + | 10.8167i | 0.634083 | + | 0.366088i | ||||
\(874\) | 24.9800 | − | 43.2666i | 0.844961 | − | 1.46352i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.5000 | + | 23.3827i | −1.36759 | + | 0.789577i | −0.990620 | − | 0.136649i | \(-0.956367\pi\) |
−0.376968 | + | 0.926226i | \(0.623033\pi\) | |||||||
\(878\) | −18.7350 | + | 10.8167i | −0.632275 | + | 0.365044i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −31.2250 | − | 54.0833i | −1.05259 | − | 1.82315i | ||||
\(881\) | −21.8575 | + | 37.8583i | −0.736398 | + | 1.27548i | 0.217710 | + | 0.976014i | \(0.430141\pi\) |
−0.954107 | + | 0.299465i | \(0.903192\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | −19.5000 | + | 11.2583i | −0.655856 | + | 0.378659i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0000 | − | 13.8564i | −0.806296 | − | 0.465515i | ||||
\(887\) | 12.4900 | − | 21.6333i | 0.419373 | − | 0.726375i | −0.576503 | − | 0.817095i | \(-0.695583\pi\) |
0.995877 | + | 0.0907193i | \(0.0289166\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 39.0000 | − | 22.5167i | 1.30728 | − | 0.754760i | ||||
\(891\) | −27.0000 | + | 15.5885i | −0.904534 | + | 0.522233i | ||||
\(892\) | − | 7.21110i | − | 0.241446i | ||||||
\(893\) | 26.0000 | + | 45.0333i | 0.870057 | + | 1.50698i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 49.9600 | + | 28.8444i | 1.66998 | + | 0.964162i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.0000 | −0.400445 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 12.0000 | − | 20.7846i | 0.400000 | − | 0.692820i | ||||
\(901\) | 15.6125 | + | 27.0416i | 0.520128 | + | 0.900887i | ||||
\(902\) | 21.6333i | 0.720310i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.50000 | − | 4.33013i | 0.249446 | − | 0.144018i | ||||
\(905\) | − | 22.5167i | − | 0.748479i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.0000 | − | 19.0526i | 0.365249 | − | 0.632630i | −0.623567 | − | 0.781770i | \(-0.714317\pi\) |
0.988816 | + | 0.149140i | \(0.0476505\pi\) | |||||||
\(908\) | −12.4900 | − | 7.21110i | −0.414495 | − | 0.239309i | ||||
\(909\) | 18.7350 | 0.621401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.00000 | −0.265052 | −0.132526 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132526 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4900 | + | 21.6333i | −0.413359 | + | 0.715958i | ||||
\(914\) | 34.5000 | + | 59.7558i | 1.14116 | + | 1.97654i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.7350 | − | 10.8167i | 0.619022 | − | 0.357392i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00000 | + | 1.73205i | 0.0329870 | + | 0.0571351i | 0.882048 | − | 0.471160i | \(-0.156165\pi\) |
−0.849061 | + | 0.528295i | \(0.822831\pi\) | |||||||
\(920\) | −12.4900 | + | 21.6333i | −0.411783 | + | 0.713229i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 68.6950 | 2.26235 | ||||||||
\(923\) | −37.4700 | −1.23334 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0000 | + | 6.92820i | 0.394558 | + | 0.227798i | ||||
\(926\) | −9.00000 | + | 15.5885i | −0.295758 | + | 0.512268i | ||||
\(927\) | 18.7350 | + | 32.4500i | 0.615338 | + | 1.06580i | ||||
\(928\) | − | 5.19615i | − | 0.170572i | ||||||
\(929\) | −21.8575 | + | 12.6194i | −0.717121 | + | 0.414030i | −0.813692 | − | 0.581296i | \(-0.802546\pi\) |
0.0965711 | + | 0.995326i | \(0.469212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.00000 | + | 1.73205i | 0.0327561 | + | 0.0567352i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.7350 | + | 10.8167i | 0.613028 | + | 0.353932i | ||||
\(935\) | 78.0000 | 2.55087 | ||||||||
\(936\) | −18.7350 | −0.612372 | ||||||||
\(937\) | −6.24500 | −0.204015 | −0.102008 | − | 0.994784i | \(-0.532527\pi\) | ||||
−0.102008 | + | 0.994784i | \(0.532527\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.0000 | + | 22.5167i | 0.424013 | + | 0.734412i | ||||
\(941\) | 7.21110i | 0.235075i | 0.993068 | + | 0.117538i | \(0.0375001\pi\) | ||||
−0.993068 | + | 0.117538i | \(0.962500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.4900 | − | 7.21110i | 0.406730 | − | 0.234826i | ||||
\(944\) | − | 36.0555i | − | 1.17351i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.0000 | + | 31.1769i | −0.585230 | + | 1.01365i | ||||
\(947\) | −18.0000 | − | 10.3923i | −0.584921 | − | 0.337705i | 0.178165 | − | 0.984001i | \(-0.442984\pi\) |
−0.763087 | + | 0.646296i | \(0.776317\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.5000 | − | 33.7750i | 0.632997 | − | 1.09638i | ||||
\(950\) | 99.9200 | 3.24183 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.00000 | + | 8.66025i | 0.161966 | + | 0.280533i | 0.935574 | − | 0.353132i | \(-0.114883\pi\) |
−0.773608 | + | 0.633665i | \(0.781550\pi\) | |||||||
\(954\) | − | 25.9808i | − | 0.841158i | ||||||
\(955\) | −12.4900 | + | 7.21110i | −0.404167 | + | 0.233346i | ||||
\(956\) | 15.0000 | − | 8.66025i | 0.485135 | − | 0.280093i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.4900 | + | 21.6333i | 0.403533 | + | 0.698940i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 10.8167i | 0.348743i | ||||||||
\(963\) | −6.00000 | −0.193347 | ||||||||
\(964\) | −9.36750 | − | 5.40833i | −0.301707 | − | 0.174190i | ||||
\(965\) | 15.6125 | − | 27.0416i | 0.502584 | − | 0.870501i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.4974i | 1.55957i | 0.626046 | + | 0.779786i | \(0.284672\pi\) | ||||
−0.626046 | + | 0.779786i | \(0.715328\pi\) | |||||||
\(968\) | −1.50000 | + | 0.866025i | −0.0482118 | + | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 45.0333i | 1.44593i | ||||||||
\(971\) | 6.24500 | + | 10.8167i | 0.200412 | + | 0.347123i | 0.948661 | − | 0.316294i | \(-0.102439\pi\) |
−0.748250 | + | 0.663417i | \(0.769105\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 36.0000 | 1.15351 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.2250 | −0.999488 | ||||||||
\(977\) | 4.50000 | + | 2.59808i | 0.143968 | + | 0.0831198i | 0.570254 | − | 0.821469i | \(-0.306845\pi\) |
−0.426286 | + | 0.904588i | \(0.640178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.4900 | − | 21.6333i | −0.399182 | − | 0.691404i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0000 | − | 10.3923i | 0.574696 | − | 0.331801i | ||||
\(982\) | −6.00000 | + | 3.46410i | −0.191468 | + | 0.110544i | ||||
\(983\) | 50.4777i | 1.60999i | 0.593282 | + | 0.804995i | \(0.297832\pi\) | ||||
−0.593282 | + | 0.804995i | \(0.702168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.36750 | + | 5.40833i | 0.298322 | + | 0.172236i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.0000 | + | 22.5167i | 0.413585 | + | 0.716350i | ||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | −56.2050 | − | 32.4500i | −1.78631 | − | 1.03133i | ||||
\(991\) | 6.00000 | − | 10.3923i | 0.190596 | − | 0.330122i | −0.754852 | − | 0.655895i | \(-0.772291\pi\) |
0.945448 | + | 0.325773i | \(0.105625\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.0000 | + | 22.5167i | −1.23638 | + | 0.713826i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.6125 | + | 27.0416i | 0.494453 | + | 0.856417i | 0.999980 | − | 0.00639370i | \(-0.00203519\pi\) |
−0.505527 | + | 0.862811i | \(0.668702\pi\) | |||||||
\(998\) | −24.0000 | + | 41.5692i | −0.759707 | + | 1.31585i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.q.d.589.1 | yes | 4 | |
7.2 | even | 3 | 637.2.k.e.459.1 | 4 | |||
7.3 | odd | 6 | 637.2.u.f.30.1 | 4 | |||
7.4 | even | 3 | 637.2.u.f.30.2 | 4 | |||
7.5 | odd | 6 | 637.2.k.e.459.2 | 4 | |||
7.6 | odd | 2 | inner | 637.2.q.d.589.2 | yes | 4 | |
13.6 | odd | 12 | 8281.2.a.br.1.3 | 4 | |||
13.7 | odd | 12 | 8281.2.a.br.1.2 | 4 | |||
13.10 | even | 6 | inner | 637.2.q.d.491.2 | yes | 4 | |
91.6 | even | 12 | 8281.2.a.br.1.4 | 4 | |||
91.10 | odd | 6 | 637.2.k.e.569.2 | 4 | |||
91.20 | even | 12 | 8281.2.a.br.1.1 | 4 | |||
91.23 | even | 6 | 637.2.u.f.361.2 | 4 | |||
91.62 | odd | 6 | inner | 637.2.q.d.491.1 | ✓ | 4 | |
91.75 | odd | 6 | 637.2.u.f.361.1 | 4 | |||
91.88 | even | 6 | 637.2.k.e.569.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.k.e.459.1 | 4 | 7.2 | even | 3 | |||
637.2.k.e.459.2 | 4 | 7.5 | odd | 6 | |||
637.2.k.e.569.1 | 4 | 91.88 | even | 6 | |||
637.2.k.e.569.2 | 4 | 91.10 | odd | 6 | |||
637.2.q.d.491.1 | ✓ | 4 | 91.62 | odd | 6 | inner | |
637.2.q.d.491.2 | yes | 4 | 13.10 | even | 6 | inner | |
637.2.q.d.589.1 | yes | 4 | 1.1 | even | 1 | trivial | |
637.2.q.d.589.2 | yes | 4 | 7.6 | odd | 2 | inner | |
637.2.u.f.30.1 | 4 | 7.3 | odd | 6 | |||
637.2.u.f.30.2 | 4 | 7.4 | even | 3 | |||
637.2.u.f.361.1 | 4 | 91.75 | odd | 6 | |||
637.2.u.f.361.2 | 4 | 91.23 | even | 6 | |||
8281.2.a.br.1.1 | 4 | 91.20 | even | 12 | |||
8281.2.a.br.1.2 | 4 | 13.7 | odd | 12 | |||
8281.2.a.br.1.3 | 4 | 13.6 | odd | 12 | |||
8281.2.a.br.1.4 | 4 | 91.6 | even | 12 |