Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(1,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.a (trivial) |
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: | yes |
Analytic conductor: | \(2.29170653801\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.618034 | 0.437016 | 0.218508 | − | 0.975835i | \(-0.429881\pi\) | ||||
0.218508 | + | 0.975835i | \(0.429881\pi\) | |||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 1.61803 | 0.723607 | 0.361803 | − | 0.932254i | \(-0.382161\pi\) | ||||
0.361803 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 2.61803 | 0.755761 | ||||||||
\(13\) | −6.23607 | −1.72957 | −0.864787 | − | 0.502139i | \(-0.832547\pi\) | ||||
−0.864787 | + | 0.502139i | \(0.832547\pi\) | |||||||
\(14\) | −0.618034 | −0.165177 | ||||||||
\(15\) | −2.61803 | −0.675973 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −4.23607 | −1.02740 | −0.513699 | − | 0.857971i | \(-0.671725\pi\) | ||||
−0.513699 | + | 0.857971i | \(0.671725\pi\) | |||||||
\(18\) | −0.236068 | −0.0556418 | ||||||||
\(19\) | 2.85410 | 0.654776 | 0.327388 | − | 0.944890i | \(-0.393832\pi\) | ||||
0.327388 | + | 0.944890i | \(0.393832\pi\) | |||||||
\(20\) | −2.61803 | −0.585410 | ||||||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | −0.618034 | −0.131765 | ||||||||
\(23\) | −3.61803 | −0.754412 | −0.377206 | − | 0.926129i | \(-0.623115\pi\) | ||||
−0.377206 | + | 0.926129i | \(0.623115\pi\) | |||||||
\(24\) | 3.61803 | 0.738528 | ||||||||
\(25\) | −2.38197 | −0.476393 | ||||||||
\(26\) | −3.85410 | −0.755852 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | 1.61803 | 0.305780 | ||||||||
\(29\) | −5.85410 | −1.08708 | −0.543540 | − | 0.839383i | \(-0.682916\pi\) | ||||
−0.543540 | + | 0.839383i | \(0.682916\pi\) | |||||||
\(30\) | −1.61803 | −0.295411 | ||||||||
\(31\) | 8.09017 | 1.45304 | 0.726519 | − | 0.687147i | \(-0.241137\pi\) | ||||
0.726519 | + | 0.687147i | \(0.241137\pi\) | |||||||
\(32\) | 5.61803 | 0.993137 | ||||||||
\(33\) | 1.61803 | 0.281664 | ||||||||
\(34\) | −2.61803 | −0.448989 | ||||||||
\(35\) | −1.61803 | −0.273498 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | −2.76393 | −0.454388 | −0.227194 | − | 0.973850i | \(-0.572955\pi\) | ||||
−0.227194 | + | 0.973850i | \(0.572955\pi\) | |||||||
\(38\) | 1.76393 | 0.286148 | ||||||||
\(39\) | 10.0902 | 1.61572 | ||||||||
\(40\) | −3.61803 | −0.572061 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 1.61803 | 0.243928 | ||||||||
\(45\) | −0.618034 | −0.0921311 | ||||||||
\(46\) | −2.23607 | −0.329690 | ||||||||
\(47\) | 9.70820 | 1.41609 | 0.708044 | − | 0.706169i | \(-0.249578\pi\) | ||||
0.708044 | + | 0.706169i | \(0.249578\pi\) | |||||||
\(48\) | −3.00000 | −0.433013 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.47214 | −0.208191 | ||||||||
\(51\) | 6.85410 | 0.959766 | ||||||||
\(52\) | 10.0902 | 1.39925 | ||||||||
\(53\) | 2.38197 | 0.327188 | 0.163594 | − | 0.986528i | \(-0.447691\pi\) | ||||
0.163594 | + | 0.986528i | \(0.447691\pi\) | |||||||
\(54\) | 3.38197 | 0.460227 | ||||||||
\(55\) | −1.61803 | −0.218176 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | −4.61803 | −0.611674 | ||||||||
\(58\) | −3.61803 | −0.475071 | ||||||||
\(59\) | 8.38197 | 1.09124 | 0.545620 | − | 0.838033i | \(-0.316294\pi\) | ||||
0.545620 | + | 0.838033i | \(0.316294\pi\) | |||||||
\(60\) | 4.23607 | 0.546874 | ||||||||
\(61\) | 9.47214 | 1.21278 | 0.606391 | − | 0.795166i | \(-0.292616\pi\) | ||||
0.606391 | + | 0.795166i | \(0.292616\pi\) | |||||||
\(62\) | 5.00000 | 0.635001 | ||||||||
\(63\) | 0.381966 | 0.0481232 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | −10.0902 | −1.25153 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −12.0902 | −1.47705 | −0.738525 | − | 0.674226i | \(-0.764477\pi\) | ||||
−0.738525 | + | 0.674226i | \(0.764477\pi\) | |||||||
\(68\) | 6.85410 | 0.831182 | ||||||||
\(69\) | 5.85410 | 0.704751 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −5.94427 | −0.705455 | −0.352728 | − | 0.935726i | \(-0.614746\pi\) | ||||
−0.352728 | + | 0.935726i | \(0.614746\pi\) | |||||||
\(72\) | 0.854102 | 0.100657 | ||||||||
\(73\) | −9.94427 | −1.16389 | −0.581944 | − | 0.813229i | \(-0.697708\pi\) | ||||
−0.581944 | + | 0.813229i | \(0.697708\pi\) | |||||||
\(74\) | −1.70820 | −0.198575 | ||||||||
\(75\) | 3.85410 | 0.445033 | ||||||||
\(76\) | −4.61803 | −0.529725 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 6.23607 | 0.706096 | ||||||||
\(79\) | −11.7082 | −1.31728 | −0.658638 | − | 0.752460i | \(-0.728867\pi\) | ||||
−0.658638 | + | 0.752460i | \(0.728867\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | −0.618034 | −0.0682504 | ||||||||
\(83\) | −5.47214 | −0.600645 | −0.300322 | − | 0.953838i | \(-0.597094\pi\) | ||||
−0.300322 | + | 0.953838i | \(0.597094\pi\) | |||||||
\(84\) | −2.61803 | −0.285651 | ||||||||
\(85\) | −6.85410 | −0.743432 | ||||||||
\(86\) | −0.618034 | −0.0666443 | ||||||||
\(87\) | 9.47214 | 1.01552 | ||||||||
\(88\) | 2.23607 | 0.238366 | ||||||||
\(89\) | −9.32624 | −0.988579 | −0.494290 | − | 0.869297i | \(-0.664572\pi\) | ||||
−0.494290 | + | 0.869297i | \(0.664572\pi\) | |||||||
\(90\) | −0.381966 | −0.0402628 | ||||||||
\(91\) | 6.23607 | 0.653718 | ||||||||
\(92\) | 5.85410 | 0.610332 | ||||||||
\(93\) | −13.0902 | −1.35739 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 4.61803 | 0.473800 | ||||||||
\(96\) | −9.09017 | −0.927762 | ||||||||
\(97\) | 2.56231 | 0.260163 | 0.130081 | − | 0.991503i | \(-0.458476\pi\) | ||||
0.130081 | + | 0.991503i | \(0.458476\pi\) | |||||||
\(98\) | 0.618034 | 0.0624309 | ||||||||
\(99\) | 0.381966 | 0.0383890 | ||||||||
\(100\) | 3.85410 | 0.385410 | ||||||||
\(101\) | −17.4721 | −1.73854 | −0.869271 | − | 0.494335i | \(-0.835411\pi\) | ||||
−0.869271 | + | 0.494335i | \(0.835411\pi\) | |||||||
\(102\) | 4.23607 | 0.419433 | ||||||||
\(103\) | −1.09017 | −0.107418 | −0.0537088 | − | 0.998557i | \(-0.517104\pi\) | ||||
−0.0537088 | + | 0.998557i | \(0.517104\pi\) | |||||||
\(104\) | 13.9443 | 1.36735 | ||||||||
\(105\) | 2.61803 | 0.255494 | ||||||||
\(106\) | 1.47214 | 0.142986 | ||||||||
\(107\) | −0.763932 | −0.0738521 | −0.0369260 | − | 0.999318i | \(-0.511757\pi\) | ||||
−0.0369260 | + | 0.999318i | \(0.511757\pi\) | |||||||
\(108\) | −8.85410 | −0.851986 | ||||||||
\(109\) | 8.47214 | 0.811483 | 0.405742 | − | 0.913988i | \(-0.367013\pi\) | ||||
0.405742 | + | 0.913988i | \(0.367013\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 4.47214 | 0.424476 | ||||||||
\(112\) | −1.85410 | −0.175196 | ||||||||
\(113\) | 14.4164 | 1.35618 | 0.678091 | − | 0.734978i | \(-0.262808\pi\) | ||||
0.678091 | + | 0.734978i | \(0.262808\pi\) | |||||||
\(114\) | −2.85410 | −0.267311 | ||||||||
\(115\) | −5.85410 | −0.545898 | ||||||||
\(116\) | 9.47214 | 0.879466 | ||||||||
\(117\) | 2.38197 | 0.220213 | ||||||||
\(118\) | 5.18034 | 0.476889 | ||||||||
\(119\) | 4.23607 | 0.388320 | ||||||||
\(120\) | 5.85410 | 0.534404 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 5.85410 | 0.530005 | ||||||||
\(123\) | 1.61803 | 0.145893 | ||||||||
\(124\) | −13.0902 | −1.17553 | ||||||||
\(125\) | −11.9443 | −1.06833 | ||||||||
\(126\) | 0.236068 | 0.0210306 | ||||||||
\(127\) | −3.29180 | −0.292100 | −0.146050 | − | 0.989277i | \(-0.546656\pi\) | ||||
−0.146050 | + | 0.989277i | \(0.546656\pi\) | |||||||
\(128\) | −11.3820 | −1.00603 | ||||||||
\(129\) | 1.61803 | 0.142460 | ||||||||
\(130\) | −6.23607 | −0.546939 | ||||||||
\(131\) | 10.8541 | 0.948327 | 0.474164 | − | 0.880437i | \(-0.342751\pi\) | ||||
0.474164 | + | 0.880437i | \(0.342751\pi\) | |||||||
\(132\) | −2.61803 | −0.227871 | ||||||||
\(133\) | −2.85410 | −0.247482 | ||||||||
\(134\) | −7.47214 | −0.645494 | ||||||||
\(135\) | 8.85410 | 0.762040 | ||||||||
\(136\) | 9.47214 | 0.812229 | ||||||||
\(137\) | 15.7984 | 1.34975 | 0.674873 | − | 0.737934i | \(-0.264198\pi\) | ||||
0.674873 | + | 0.737934i | \(0.264198\pi\) | |||||||
\(138\) | 3.61803 | 0.307988 | ||||||||
\(139\) | −5.94427 | −0.504187 | −0.252093 | − | 0.967703i | \(-0.581119\pi\) | ||||
−0.252093 | + | 0.967703i | \(0.581119\pi\) | |||||||
\(140\) | 2.61803 | 0.221264 | ||||||||
\(141\) | −15.7082 | −1.32287 | ||||||||
\(142\) | −3.67376 | −0.308295 | ||||||||
\(143\) | 6.23607 | 0.521486 | ||||||||
\(144\) | −0.708204 | −0.0590170 | ||||||||
\(145\) | −9.47214 | −0.786618 | ||||||||
\(146\) | −6.14590 | −0.508638 | ||||||||
\(147\) | −1.61803 | −0.133453 | ||||||||
\(148\) | 4.47214 | 0.367607 | ||||||||
\(149\) | 18.9443 | 1.55198 | 0.775988 | − | 0.630748i | \(-0.217252\pi\) | ||||
0.775988 | + | 0.630748i | \(0.217252\pi\) | |||||||
\(150\) | 2.38197 | 0.194487 | ||||||||
\(151\) | −19.9443 | −1.62304 | −0.811521 | − | 0.584323i | \(-0.801360\pi\) | ||||
−0.811521 | + | 0.584323i | \(0.801360\pi\) | |||||||
\(152\) | −6.38197 | −0.517646 | ||||||||
\(153\) | 1.61803 | 0.130810 | ||||||||
\(154\) | 0.618034 | 0.0498026 | ||||||||
\(155\) | 13.0902 | 1.05143 | ||||||||
\(156\) | −16.3262 | −1.30715 | ||||||||
\(157\) | −8.00000 | −0.638470 | −0.319235 | − | 0.947676i | \(-0.603426\pi\) | ||||
−0.319235 | + | 0.947676i | \(0.603426\pi\) | |||||||
\(158\) | −7.23607 | −0.575671 | ||||||||
\(159\) | −3.85410 | −0.305650 | ||||||||
\(160\) | 9.09017 | 0.718641 | ||||||||
\(161\) | 3.61803 | 0.285141 | ||||||||
\(162\) | −4.76393 | −0.374290 | ||||||||
\(163\) | −16.9443 | −1.32718 | −0.663589 | − | 0.748097i | \(-0.730968\pi\) | ||||
−0.663589 | + | 0.748097i | \(0.730968\pi\) | |||||||
\(164\) | 1.61803 | 0.126347 | ||||||||
\(165\) | 2.61803 | 0.203814 | ||||||||
\(166\) | −3.38197 | −0.262491 | ||||||||
\(167\) | −10.4164 | −0.806046 | −0.403023 | − | 0.915190i | \(-0.632041\pi\) | ||||
−0.403023 | + | 0.915190i | \(0.632041\pi\) | |||||||
\(168\) | −3.61803 | −0.279137 | ||||||||
\(169\) | 25.8885 | 1.99143 | ||||||||
\(170\) | −4.23607 | −0.324892 | ||||||||
\(171\) | −1.09017 | −0.0833674 | ||||||||
\(172\) | 1.61803 | 0.123374 | ||||||||
\(173\) | 4.70820 | 0.357958 | 0.178979 | − | 0.983853i | \(-0.442721\pi\) | ||||
0.178979 | + | 0.983853i | \(0.442721\pi\) | |||||||
\(174\) | 5.85410 | 0.443798 | ||||||||
\(175\) | 2.38197 | 0.180060 | ||||||||
\(176\) | −1.85410 | −0.139758 | ||||||||
\(177\) | −13.5623 | −1.01941 | ||||||||
\(178\) | −5.76393 | −0.432025 | ||||||||
\(179\) | 3.03444 | 0.226805 | 0.113402 | − | 0.993549i | \(-0.463825\pi\) | ||||
0.113402 | + | 0.993549i | \(0.463825\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −2.94427 | −0.218846 | −0.109423 | − | 0.993995i | \(-0.534900\pi\) | ||||
−0.109423 | + | 0.993995i | \(0.534900\pi\) | |||||||
\(182\) | 3.85410 | 0.285685 | ||||||||
\(183\) | −15.3262 | −1.13295 | ||||||||
\(184\) | 8.09017 | 0.596415 | ||||||||
\(185\) | −4.47214 | −0.328798 | ||||||||
\(186\) | −8.09017 | −0.593200 | ||||||||
\(187\) | 4.23607 | 0.309772 | ||||||||
\(188\) | −15.7082 | −1.14564 | ||||||||
\(189\) | −5.47214 | −0.398039 | ||||||||
\(190\) | 2.85410 | 0.207058 | ||||||||
\(191\) | 22.4721 | 1.62603 | 0.813013 | − | 0.582245i | \(-0.197826\pi\) | ||||
0.813013 | + | 0.582245i | \(0.197826\pi\) | |||||||
\(192\) | 0.381966 | 0.0275660 | ||||||||
\(193\) | −22.7082 | −1.63457 | −0.817286 | − | 0.576232i | \(-0.804522\pi\) | ||||
−0.817286 | + | 0.576232i | \(0.804522\pi\) | |||||||
\(194\) | 1.58359 | 0.113695 | ||||||||
\(195\) | 16.3262 | 1.16915 | ||||||||
\(196\) | −1.61803 | −0.115574 | ||||||||
\(197\) | −9.61803 | −0.685257 | −0.342628 | − | 0.939471i | \(-0.611317\pi\) | ||||
−0.342628 | + | 0.939471i | \(0.611317\pi\) | |||||||
\(198\) | 0.236068 | 0.0167766 | ||||||||
\(199\) | −21.3607 | −1.51422 | −0.757109 | − | 0.653288i | \(-0.773389\pi\) | ||||
−0.757109 | + | 0.653288i | \(0.773389\pi\) | |||||||
\(200\) | 5.32624 | 0.376622 | ||||||||
\(201\) | 19.5623 | 1.37982 | ||||||||
\(202\) | −10.7984 | −0.759771 | ||||||||
\(203\) | 5.85410 | 0.410877 | ||||||||
\(204\) | −11.0902 | −0.776467 | ||||||||
\(205\) | −1.61803 | −0.113008 | ||||||||
\(206\) | −0.673762 | −0.0469432 | ||||||||
\(207\) | 1.38197 | 0.0960533 | ||||||||
\(208\) | −11.5623 | −0.801702 | ||||||||
\(209\) | −2.85410 | −0.197422 | ||||||||
\(210\) | 1.61803 | 0.111655 | ||||||||
\(211\) | 14.0344 | 0.966171 | 0.483085 | − | 0.875573i | \(-0.339516\pi\) | ||||
0.483085 | + | 0.875573i | \(0.339516\pi\) | |||||||
\(212\) | −3.85410 | −0.264701 | ||||||||
\(213\) | 9.61803 | 0.659017 | ||||||||
\(214\) | −0.472136 | −0.0322745 | ||||||||
\(215\) | −1.61803 | −0.110349 | ||||||||
\(216\) | −12.2361 | −0.832559 | ||||||||
\(217\) | −8.09017 | −0.549197 | ||||||||
\(218\) | 5.23607 | 0.354631 | ||||||||
\(219\) | 16.0902 | 1.08727 | ||||||||
\(220\) | 2.61803 | 0.176508 | ||||||||
\(221\) | 26.4164 | 1.77696 | ||||||||
\(222\) | 2.76393 | 0.185503 | ||||||||
\(223\) | −1.32624 | −0.0888115 | −0.0444057 | − | 0.999014i | \(-0.514139\pi\) | ||||
−0.0444057 | + | 0.999014i | \(0.514139\pi\) | |||||||
\(224\) | −5.61803 | −0.375371 | ||||||||
\(225\) | 0.909830 | 0.0606553 | ||||||||
\(226\) | 8.90983 | 0.592673 | ||||||||
\(227\) | 5.65248 | 0.375168 | 0.187584 | − | 0.982249i | \(-0.439934\pi\) | ||||
0.187584 | + | 0.982249i | \(0.439934\pi\) | |||||||
\(228\) | 7.47214 | 0.494854 | ||||||||
\(229\) | 21.2361 | 1.40332 | 0.701659 | − | 0.712512i | \(-0.252443\pi\) | ||||
0.701659 | + | 0.712512i | \(0.252443\pi\) | |||||||
\(230\) | −3.61803 | −0.238566 | ||||||||
\(231\) | −1.61803 | −0.106459 | ||||||||
\(232\) | 13.0902 | 0.859412 | ||||||||
\(233\) | −6.32624 | −0.414446 | −0.207223 | − | 0.978294i | \(-0.566443\pi\) | ||||
−0.207223 | + | 0.978294i | \(0.566443\pi\) | |||||||
\(234\) | 1.47214 | 0.0962365 | ||||||||
\(235\) | 15.7082 | 1.02469 | ||||||||
\(236\) | −13.5623 | −0.882831 | ||||||||
\(237\) | 18.9443 | 1.23056 | ||||||||
\(238\) | 2.61803 | 0.169702 | ||||||||
\(239\) | −6.14590 | −0.397545 | −0.198773 | − | 0.980046i | \(-0.563696\pi\) | ||||
−0.198773 | + | 0.980046i | \(0.563696\pi\) | |||||||
\(240\) | −4.85410 | −0.313331 | ||||||||
\(241\) | −4.76393 | −0.306872 | −0.153436 | − | 0.988159i | \(-0.549034\pi\) | ||||
−0.153436 | + | 0.988159i | \(0.549034\pi\) | |||||||
\(242\) | −6.18034 | −0.397287 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | −15.3262 | −0.981162 | ||||||||
\(245\) | 1.61803 | 0.103372 | ||||||||
\(246\) | 1.00000 | 0.0637577 | ||||||||
\(247\) | −17.7984 | −1.13248 | ||||||||
\(248\) | −18.0902 | −1.14873 | ||||||||
\(249\) | 8.85410 | 0.561106 | ||||||||
\(250\) | −7.38197 | −0.466877 | ||||||||
\(251\) | 2.05573 | 0.129756 | 0.0648782 | − | 0.997893i | \(-0.479334\pi\) | ||||
0.0648782 | + | 0.997893i | \(0.479334\pi\) | |||||||
\(252\) | −0.618034 | −0.0389325 | ||||||||
\(253\) | 3.61803 | 0.227464 | ||||||||
\(254\) | −2.03444 | −0.127652 | ||||||||
\(255\) | 11.0902 | 0.694493 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 24.1246 | 1.50485 | 0.752426 | − | 0.658677i | \(-0.228884\pi\) | ||||
0.752426 | + | 0.658677i | \(0.228884\pi\) | |||||||
\(258\) | 1.00000 | 0.0622573 | ||||||||
\(259\) | 2.76393 | 0.171742 | ||||||||
\(260\) | 16.3262 | 1.01251 | ||||||||
\(261\) | 2.23607 | 0.138409 | ||||||||
\(262\) | 6.70820 | 0.414434 | ||||||||
\(263\) | −12.7082 | −0.783621 | −0.391811 | − | 0.920046i | \(-0.628151\pi\) | ||||
−0.391811 | + | 0.920046i | \(0.628151\pi\) | |||||||
\(264\) | −3.61803 | −0.222675 | ||||||||
\(265\) | 3.85410 | 0.236756 | ||||||||
\(266\) | −1.76393 | −0.108154 | ||||||||
\(267\) | 15.0902 | 0.923503 | ||||||||
\(268\) | 19.5623 | 1.19496 | ||||||||
\(269\) | 23.2705 | 1.41883 | 0.709414 | − | 0.704792i | \(-0.248960\pi\) | ||||
0.709414 | + | 0.704792i | \(0.248960\pi\) | |||||||
\(270\) | 5.47214 | 0.333024 | ||||||||
\(271\) | 4.23607 | 0.257323 | 0.128661 | − | 0.991689i | \(-0.458932\pi\) | ||||
0.128661 | + | 0.991689i | \(0.458932\pi\) | |||||||
\(272\) | −7.85410 | −0.476225 | ||||||||
\(273\) | −10.0902 | −0.610685 | ||||||||
\(274\) | 9.76393 | 0.589861 | ||||||||
\(275\) | 2.38197 | 0.143638 | ||||||||
\(276\) | −9.47214 | −0.570156 | ||||||||
\(277\) | −0.819660 | −0.0492486 | −0.0246243 | − | 0.999697i | \(-0.507839\pi\) | ||||
−0.0246243 | + | 0.999697i | \(0.507839\pi\) | |||||||
\(278\) | −3.67376 | −0.220338 | ||||||||
\(279\) | −3.09017 | −0.185004 | ||||||||
\(280\) | 3.61803 | 0.216219 | ||||||||
\(281\) | −24.7082 | −1.47397 | −0.736984 | − | 0.675910i | \(-0.763751\pi\) | ||||
−0.736984 | + | 0.675910i | \(0.763751\pi\) | |||||||
\(282\) | −9.70820 | −0.578115 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 9.61803 | 0.570725 | ||||||||
\(285\) | −7.47214 | −0.442611 | ||||||||
\(286\) | 3.85410 | 0.227898 | ||||||||
\(287\) | 1.00000 | 0.0590281 | ||||||||
\(288\) | −2.14590 | −0.126448 | ||||||||
\(289\) | 0.944272 | 0.0555454 | ||||||||
\(290\) | −5.85410 | −0.343765 | ||||||||
\(291\) | −4.14590 | −0.243037 | ||||||||
\(292\) | 16.0902 | 0.941606 | ||||||||
\(293\) | −12.2361 | −0.714839 | −0.357419 | − | 0.933944i | \(-0.616343\pi\) | ||||
−0.357419 | + | 0.933944i | \(0.616343\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 13.5623 | 0.789628 | ||||||||
\(296\) | 6.18034 | 0.359225 | ||||||||
\(297\) | −5.47214 | −0.317526 | ||||||||
\(298\) | 11.7082 | 0.678238 | ||||||||
\(299\) | 22.5623 | 1.30481 | ||||||||
\(300\) | −6.23607 | −0.360040 | ||||||||
\(301\) | 1.00000 | 0.0576390 | ||||||||
\(302\) | −12.3262 | −0.709295 | ||||||||
\(303\) | 28.2705 | 1.62410 | ||||||||
\(304\) | 5.29180 | 0.303505 | ||||||||
\(305\) | 15.3262 | 0.877578 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 23.5279 | 1.34281 | 0.671403 | − | 0.741092i | \(-0.265692\pi\) | ||||
0.671403 | + | 0.741092i | \(0.265692\pi\) | |||||||
\(308\) | −1.61803 | −0.0921960 | ||||||||
\(309\) | 1.76393 | 0.100347 | ||||||||
\(310\) | 8.09017 | 0.459491 | ||||||||
\(311\) | 0.618034 | 0.0350455 | 0.0175227 | − | 0.999846i | \(-0.494422\pi\) | ||||
0.0175227 | + | 0.999846i | \(0.494422\pi\) | |||||||
\(312\) | −22.5623 | −1.27734 | ||||||||
\(313\) | −29.4721 | −1.66586 | −0.832932 | − | 0.553376i | \(-0.813339\pi\) | ||||
−0.832932 | + | 0.553376i | \(0.813339\pi\) | |||||||
\(314\) | −4.94427 | −0.279021 | ||||||||
\(315\) | 0.618034 | 0.0348223 | ||||||||
\(316\) | 18.9443 | 1.06570 | ||||||||
\(317\) | −8.12461 | −0.456324 | −0.228162 | − | 0.973623i | \(-0.573272\pi\) | ||||
−0.228162 | + | 0.973623i | \(0.573272\pi\) | |||||||
\(318\) | −2.38197 | −0.133574 | ||||||||
\(319\) | 5.85410 | 0.327767 | ||||||||
\(320\) | −0.381966 | −0.0213525 | ||||||||
\(321\) | 1.23607 | 0.0689906 | ||||||||
\(322\) | 2.23607 | 0.124611 | ||||||||
\(323\) | −12.0902 | −0.672715 | ||||||||
\(324\) | 12.4721 | 0.692896 | ||||||||
\(325\) | 14.8541 | 0.823957 | ||||||||
\(326\) | −10.4721 | −0.579998 | ||||||||
\(327\) | −13.7082 | −0.758065 | ||||||||
\(328\) | 2.23607 | 0.123466 | ||||||||
\(329\) | −9.70820 | −0.535231 | ||||||||
\(330\) | 1.61803 | 0.0890698 | ||||||||
\(331\) | 33.8885 | 1.86268 | 0.931341 | − | 0.364147i | \(-0.118639\pi\) | ||||
0.931341 | + | 0.364147i | \(0.118639\pi\) | |||||||
\(332\) | 8.85410 | 0.485932 | ||||||||
\(333\) | 1.05573 | 0.0578535 | ||||||||
\(334\) | −6.43769 | −0.352255 | ||||||||
\(335\) | −19.5623 | −1.06880 | ||||||||
\(336\) | 3.00000 | 0.163663 | ||||||||
\(337\) | −20.4721 | −1.11519 | −0.557594 | − | 0.830114i | \(-0.688275\pi\) | ||||
−0.557594 | + | 0.830114i | \(0.688275\pi\) | |||||||
\(338\) | 16.0000 | 0.870285 | ||||||||
\(339\) | −23.3262 | −1.26691 | ||||||||
\(340\) | 11.0902 | 0.601449 | ||||||||
\(341\) | −8.09017 | −0.438107 | ||||||||
\(342\) | −0.673762 | −0.0364329 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.23607 | 0.120561 | ||||||||
\(345\) | 9.47214 | 0.509963 | ||||||||
\(346\) | 2.90983 | 0.156433 | ||||||||
\(347\) | −4.29180 | −0.230396 | −0.115198 | − | 0.993343i | \(-0.536750\pi\) | ||||
−0.115198 | + | 0.993343i | \(0.536750\pi\) | |||||||
\(348\) | −15.3262 | −0.821573 | ||||||||
\(349\) | 16.7082 | 0.894370 | 0.447185 | − | 0.894442i | \(-0.352427\pi\) | ||||
0.447185 | + | 0.894442i | \(0.352427\pi\) | |||||||
\(350\) | 1.47214 | 0.0786890 | ||||||||
\(351\) | −34.1246 | −1.82144 | ||||||||
\(352\) | −5.61803 | −0.299442 | ||||||||
\(353\) | 10.3607 | 0.551443 | 0.275722 | − | 0.961238i | \(-0.411083\pi\) | ||||
0.275722 | + | 0.961238i | \(0.411083\pi\) | |||||||
\(354\) | −8.38197 | −0.445496 | ||||||||
\(355\) | −9.61803 | −0.510472 | ||||||||
\(356\) | 15.0902 | 0.799777 | ||||||||
\(357\) | −6.85410 | −0.362758 | ||||||||
\(358\) | 1.87539 | 0.0991173 | ||||||||
\(359\) | 22.1803 | 1.17063 | 0.585317 | − | 0.810805i | \(-0.300970\pi\) | ||||
0.585317 | + | 0.810805i | \(0.300970\pi\) | |||||||
\(360\) | 1.38197 | 0.0728360 | ||||||||
\(361\) | −10.8541 | −0.571269 | ||||||||
\(362\) | −1.81966 | −0.0956392 | ||||||||
\(363\) | 16.1803 | 0.849248 | ||||||||
\(364\) | −10.0902 | −0.528869 | ||||||||
\(365\) | −16.0902 | −0.842198 | ||||||||
\(366\) | −9.47214 | −0.495116 | ||||||||
\(367\) | 27.2705 | 1.42351 | 0.711755 | − | 0.702428i | \(-0.247901\pi\) | ||||
0.711755 | + | 0.702428i | \(0.247901\pi\) | |||||||
\(368\) | −6.70820 | −0.349689 | ||||||||
\(369\) | 0.381966 | 0.0198844 | ||||||||
\(370\) | −2.76393 | −0.143690 | ||||||||
\(371\) | −2.38197 | −0.123666 | ||||||||
\(372\) | 21.1803 | 1.09815 | ||||||||
\(373\) | 12.7426 | 0.659789 | 0.329895 | − | 0.944018i | \(-0.392987\pi\) | ||||
0.329895 | + | 0.944018i | \(0.392987\pi\) | |||||||
\(374\) | 2.61803 | 0.135375 | ||||||||
\(375\) | 19.3262 | 0.998003 | ||||||||
\(376\) | −21.7082 | −1.11952 | ||||||||
\(377\) | 36.5066 | 1.88018 | ||||||||
\(378\) | −3.38197 | −0.173950 | ||||||||
\(379\) | −10.6525 | −0.547181 | −0.273590 | − | 0.961846i | \(-0.588211\pi\) | ||||
−0.273590 | + | 0.961846i | \(0.588211\pi\) | |||||||
\(380\) | −7.47214 | −0.383312 | ||||||||
\(381\) | 5.32624 | 0.272871 | ||||||||
\(382\) | 13.8885 | 0.710600 | ||||||||
\(383\) | −23.1803 | −1.18446 | −0.592230 | − | 0.805769i | \(-0.701752\pi\) | ||||
−0.592230 | + | 0.805769i | \(0.701752\pi\) | |||||||
\(384\) | 18.4164 | 0.939808 | ||||||||
\(385\) | 1.61803 | 0.0824626 | ||||||||
\(386\) | −14.0344 | −0.714334 | ||||||||
\(387\) | 0.381966 | 0.0194164 | ||||||||
\(388\) | −4.14590 | −0.210476 | ||||||||
\(389\) | −30.6869 | −1.55589 | −0.777944 | − | 0.628333i | \(-0.783737\pi\) | ||||
−0.777944 | + | 0.628333i | \(0.783737\pi\) | |||||||
\(390\) | 10.0902 | 0.510936 | ||||||||
\(391\) | 15.3262 | 0.775081 | ||||||||
\(392\) | −2.23607 | −0.112938 | ||||||||
\(393\) | −17.5623 | −0.885901 | ||||||||
\(394\) | −5.94427 | −0.299468 | ||||||||
\(395\) | −18.9443 | −0.953190 | ||||||||
\(396\) | −0.618034 | −0.0310574 | ||||||||
\(397\) | −34.4508 | −1.72904 | −0.864519 | − | 0.502600i | \(-0.832377\pi\) | ||||
−0.864519 | + | 0.502600i | \(0.832377\pi\) | |||||||
\(398\) | −13.2016 | −0.661738 | ||||||||
\(399\) | 4.61803 | 0.231191 | ||||||||
\(400\) | −4.41641 | −0.220820 | ||||||||
\(401\) | 21.2361 | 1.06048 | 0.530239 | − | 0.847848i | \(-0.322102\pi\) | ||||
0.530239 | + | 0.847848i | \(0.322102\pi\) | |||||||
\(402\) | 12.0902 | 0.603003 | ||||||||
\(403\) | −50.4508 | −2.51314 | ||||||||
\(404\) | 28.2705 | 1.40651 | ||||||||
\(405\) | −12.4721 | −0.619745 | ||||||||
\(406\) | 3.61803 | 0.179560 | ||||||||
\(407\) | 2.76393 | 0.137003 | ||||||||
\(408\) | −15.3262 | −0.758762 | ||||||||
\(409\) | −25.6525 | −1.26843 | −0.634217 | − | 0.773155i | \(-0.718677\pi\) | ||||
−0.634217 | + | 0.773155i | \(0.718677\pi\) | |||||||
\(410\) | −1.00000 | −0.0493865 | ||||||||
\(411\) | −25.5623 | −1.26090 | ||||||||
\(412\) | 1.76393 | 0.0869027 | ||||||||
\(413\) | −8.38197 | −0.412450 | ||||||||
\(414\) | 0.854102 | 0.0419768 | ||||||||
\(415\) | −8.85410 | −0.434631 | ||||||||
\(416\) | −35.0344 | −1.71770 | ||||||||
\(417\) | 9.61803 | 0.470997 | ||||||||
\(418\) | −1.76393 | −0.0862767 | ||||||||
\(419\) | −9.27051 | −0.452894 | −0.226447 | − | 0.974023i | \(-0.572711\pi\) | ||||
−0.226447 | + | 0.974023i | \(0.572711\pi\) | |||||||
\(420\) | −4.23607 | −0.206699 | ||||||||
\(421\) | −20.4721 | −0.997751 | −0.498875 | − | 0.866674i | \(-0.666253\pi\) | ||||
−0.498875 | + | 0.866674i | \(0.666253\pi\) | |||||||
\(422\) | 8.67376 | 0.422232 | ||||||||
\(423\) | −3.70820 | −0.180299 | ||||||||
\(424\) | −5.32624 | −0.258665 | ||||||||
\(425\) | 10.0902 | 0.489445 | ||||||||
\(426\) | 5.94427 | 0.288001 | ||||||||
\(427\) | −9.47214 | −0.458389 | ||||||||
\(428\) | 1.23607 | 0.0597476 | ||||||||
\(429\) | −10.0902 | −0.487158 | ||||||||
\(430\) | −1.00000 | −0.0482243 | ||||||||
\(431\) | −9.47214 | −0.456257 | −0.228128 | − | 0.973631i | \(-0.573261\pi\) | ||||
−0.228128 | + | 0.973631i | \(0.573261\pi\) | |||||||
\(432\) | 10.1459 | 0.488145 | ||||||||
\(433\) | −0.965558 | −0.0464018 | −0.0232009 | − | 0.999731i | \(-0.507386\pi\) | ||||
−0.0232009 | + | 0.999731i | \(0.507386\pi\) | |||||||
\(434\) | −5.00000 | −0.240008 | ||||||||
\(435\) | 15.3262 | 0.734837 | ||||||||
\(436\) | −13.7082 | −0.656504 | ||||||||
\(437\) | −10.3262 | −0.493971 | ||||||||
\(438\) | 9.94427 | 0.475156 | ||||||||
\(439\) | −13.9443 | −0.665524 | −0.332762 | − | 0.943011i | \(-0.607981\pi\) | ||||
−0.332762 | + | 0.943011i | \(0.607981\pi\) | |||||||
\(440\) | 3.61803 | 0.172483 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | 16.3262 | 0.776560 | ||||||||
\(443\) | 16.8541 | 0.800763 | 0.400381 | − | 0.916349i | \(-0.368878\pi\) | ||||
0.400381 | + | 0.916349i | \(0.368878\pi\) | |||||||
\(444\) | −7.23607 | −0.343409 | ||||||||
\(445\) | −15.0902 | −0.715343 | ||||||||
\(446\) | −0.819660 | −0.0388120 | ||||||||
\(447\) | −30.6525 | −1.44981 | ||||||||
\(448\) | 0.236068 | 0.0111532 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0.562306 | 0.0265074 | ||||||||
\(451\) | 1.00000 | 0.0470882 | ||||||||
\(452\) | −23.3262 | −1.09717 | ||||||||
\(453\) | 32.2705 | 1.51620 | ||||||||
\(454\) | 3.49342 | 0.163954 | ||||||||
\(455\) | 10.0902 | 0.473034 | ||||||||
\(456\) | 10.3262 | 0.483570 | ||||||||
\(457\) | −16.4164 | −0.767927 | −0.383964 | − | 0.923348i | \(-0.625441\pi\) | ||||
−0.383964 | + | 0.923348i | \(0.625441\pi\) | |||||||
\(458\) | 13.1246 | 0.613273 | ||||||||
\(459\) | −23.1803 | −1.08197 | ||||||||
\(460\) | 9.47214 | 0.441641 | ||||||||
\(461\) | 23.6525 | 1.10161 | 0.550803 | − | 0.834635i | \(-0.314322\pi\) | ||||
0.550803 | + | 0.834635i | \(0.314322\pi\) | |||||||
\(462\) | −1.00000 | −0.0465242 | ||||||||
\(463\) | 31.3820 | 1.45844 | 0.729222 | − | 0.684277i | \(-0.239882\pi\) | ||||
0.729222 | + | 0.684277i | \(0.239882\pi\) | |||||||
\(464\) | −10.8541 | −0.503889 | ||||||||
\(465\) | −21.1803 | −0.982215 | ||||||||
\(466\) | −3.90983 | −0.181119 | ||||||||
\(467\) | −4.23607 | −0.196022 | −0.0980109 | − | 0.995185i | \(-0.531248\pi\) | ||||
−0.0980109 | + | 0.995185i | \(0.531248\pi\) | |||||||
\(468\) | −3.85410 | −0.178156 | ||||||||
\(469\) | 12.0902 | 0.558272 | ||||||||
\(470\) | 9.70820 | 0.447806 | ||||||||
\(471\) | 12.9443 | 0.596441 | ||||||||
\(472\) | −18.7426 | −0.862700 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 11.7082 | 0.537776 | ||||||||
\(475\) | −6.79837 | −0.311931 | ||||||||
\(476\) | −6.85410 | −0.314157 | ||||||||
\(477\) | −0.909830 | −0.0416583 | ||||||||
\(478\) | −3.79837 | −0.173734 | ||||||||
\(479\) | 0.562306 | 0.0256924 | 0.0128462 | − | 0.999917i | \(-0.495911\pi\) | ||||
0.0128462 | + | 0.999917i | \(0.495911\pi\) | |||||||
\(480\) | −14.7082 | −0.671335 | ||||||||
\(481\) | 17.2361 | 0.785897 | ||||||||
\(482\) | −2.94427 | −0.134108 | ||||||||
\(483\) | −5.85410 | −0.266371 | ||||||||
\(484\) | 16.1803 | 0.735470 | ||||||||
\(485\) | 4.14590 | 0.188256 | ||||||||
\(486\) | −2.43769 | −0.110576 | ||||||||
\(487\) | −10.7639 | −0.487760 | −0.243880 | − | 0.969805i | \(-0.578420\pi\) | ||||
−0.243880 | + | 0.969805i | \(0.578420\pi\) | |||||||
\(488\) | −21.1803 | −0.958789 | ||||||||
\(489\) | 27.4164 | 1.23981 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 21.2705 | 0.959925 | 0.479962 | − | 0.877289i | \(-0.340650\pi\) | ||||
0.479962 | + | 0.877289i | \(0.340650\pi\) | |||||||
\(492\) | −2.61803 | −0.118030 | ||||||||
\(493\) | 24.7984 | 1.11686 | ||||||||
\(494\) | −11.0000 | −0.494913 | ||||||||
\(495\) | 0.618034 | 0.0277786 | ||||||||
\(496\) | 15.0000 | 0.673520 | ||||||||
\(497\) | 5.94427 | 0.266637 | ||||||||
\(498\) | 5.47214 | 0.245212 | ||||||||
\(499\) | 24.6525 | 1.10360 | 0.551798 | − | 0.833978i | \(-0.313942\pi\) | ||||
0.551798 | + | 0.833978i | \(0.313942\pi\) | |||||||
\(500\) | 19.3262 | 0.864296 | ||||||||
\(501\) | 16.8541 | 0.752986 | ||||||||
\(502\) | 1.27051 | 0.0567056 | ||||||||
\(503\) | 24.6869 | 1.10074 | 0.550368 | − | 0.834922i | \(-0.314488\pi\) | ||||
0.550368 | + | 0.834922i | \(0.314488\pi\) | |||||||
\(504\) | −0.854102 | −0.0380447 | ||||||||
\(505\) | −28.2705 | −1.25802 | ||||||||
\(506\) | 2.23607 | 0.0994053 | ||||||||
\(507\) | −41.8885 | −1.86034 | ||||||||
\(508\) | 5.32624 | 0.236314 | ||||||||
\(509\) | 16.0344 | 0.710714 | 0.355357 | − | 0.934731i | \(-0.384359\pi\) | ||||
0.355357 | + | 0.934731i | \(0.384359\pi\) | |||||||
\(510\) | 6.85410 | 0.303505 | ||||||||
\(511\) | 9.94427 | 0.439909 | ||||||||
\(512\) | 18.7082 | 0.826794 | ||||||||
\(513\) | 15.6180 | 0.689553 | ||||||||
\(514\) | 14.9098 | 0.657644 | ||||||||
\(515\) | −1.76393 | −0.0777281 | ||||||||
\(516\) | −2.61803 | −0.115253 | ||||||||
\(517\) | −9.70820 | −0.426966 | ||||||||
\(518\) | 1.70820 | 0.0750542 | ||||||||
\(519\) | −7.61803 | −0.334395 | ||||||||
\(520\) | 22.5623 | 0.989423 | ||||||||
\(521\) | −23.9098 | −1.04751 | −0.523754 | − | 0.851869i | \(-0.675469\pi\) | ||||
−0.523754 | + | 0.851869i | \(0.675469\pi\) | |||||||
\(522\) | 1.38197 | 0.0604870 | ||||||||
\(523\) | 17.4721 | 0.764003 | 0.382002 | − | 0.924162i | \(-0.375235\pi\) | ||||
0.382002 | + | 0.924162i | \(0.375235\pi\) | |||||||
\(524\) | −17.5623 | −0.767213 | ||||||||
\(525\) | −3.85410 | −0.168207 | ||||||||
\(526\) | −7.85410 | −0.342455 | ||||||||
\(527\) | −34.2705 | −1.49285 | ||||||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | −9.90983 | −0.430862 | ||||||||
\(530\) | 2.38197 | 0.103466 | ||||||||
\(531\) | −3.20163 | −0.138939 | ||||||||
\(532\) | 4.61803 | 0.200217 | ||||||||
\(533\) | 6.23607 | 0.270114 | ||||||||
\(534\) | 9.32624 | 0.403586 | ||||||||
\(535\) | −1.23607 | −0.0534399 | ||||||||
\(536\) | 27.0344 | 1.16771 | ||||||||
\(537\) | −4.90983 | −0.211875 | ||||||||
\(538\) | 14.3820 | 0.620051 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | −14.3262 | −0.616503 | ||||||||
\(541\) | 40.7426 | 1.75166 | 0.875832 | − | 0.482617i | \(-0.160314\pi\) | ||||
0.875832 | + | 0.482617i | \(0.160314\pi\) | |||||||
\(542\) | 2.61803 | 0.112454 | ||||||||
\(543\) | 4.76393 | 0.204440 | ||||||||
\(544\) | −23.7984 | −1.02035 | ||||||||
\(545\) | 13.7082 | 0.587195 | ||||||||
\(546\) | −6.23607 | −0.266879 | ||||||||
\(547\) | −15.0000 | −0.641354 | −0.320677 | − | 0.947189i | \(-0.603910\pi\) | ||||
−0.320677 | + | 0.947189i | \(0.603910\pi\) | |||||||
\(548\) | −25.5623 | −1.09197 | ||||||||
\(549\) | −3.61803 | −0.154414 | ||||||||
\(550\) | 1.47214 | 0.0627721 | ||||||||
\(551\) | −16.7082 | −0.711793 | ||||||||
\(552\) | −13.0902 | −0.557155 | ||||||||
\(553\) | 11.7082 | 0.497883 | ||||||||
\(554\) | −0.506578 | −0.0215224 | ||||||||
\(555\) | 7.23607 | 0.307154 | ||||||||
\(556\) | 9.61803 | 0.407895 | ||||||||
\(557\) | −28.2148 | −1.19550 | −0.597749 | − | 0.801683i | \(-0.703938\pi\) | ||||
−0.597749 | + | 0.801683i | \(0.703938\pi\) | |||||||
\(558\) | −1.90983 | −0.0808496 | ||||||||
\(559\) | 6.23607 | 0.263758 | ||||||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | −6.85410 | −0.289380 | ||||||||
\(562\) | −15.2705 | −0.644148 | ||||||||
\(563\) | 9.47214 | 0.399203 | 0.199601 | − | 0.979877i | \(-0.436035\pi\) | ||||
0.199601 | + | 0.979877i | \(0.436035\pi\) | |||||||
\(564\) | 25.4164 | 1.07022 | ||||||||
\(565\) | 23.3262 | 0.981342 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.70820 | 0.323714 | ||||||||
\(568\) | 13.2918 | 0.557711 | ||||||||
\(569\) | 0.381966 | 0.0160128 | 0.00800642 | − | 0.999968i | \(-0.497451\pi\) | ||||
0.00800642 | + | 0.999968i | \(0.497451\pi\) | |||||||
\(570\) | −4.61803 | −0.193428 | ||||||||
\(571\) | 19.8885 | 0.832310 | 0.416155 | − | 0.909294i | \(-0.363377\pi\) | ||||
0.416155 | + | 0.909294i | \(0.363377\pi\) | |||||||
\(572\) | −10.0902 | −0.421891 | ||||||||
\(573\) | −36.3607 | −1.51899 | ||||||||
\(574\) | 0.618034 | 0.0257962 | ||||||||
\(575\) | 8.61803 | 0.359397 | ||||||||
\(576\) | 0.0901699 | 0.00375708 | ||||||||
\(577\) | −21.1803 | −0.881749 | −0.440875 | − | 0.897569i | \(-0.645332\pi\) | ||||
−0.440875 | + | 0.897569i | \(0.645332\pi\) | |||||||
\(578\) | 0.583592 | 0.0242742 | ||||||||
\(579\) | 36.7426 | 1.52697 | ||||||||
\(580\) | 15.3262 | 0.636387 | ||||||||
\(581\) | 5.47214 | 0.227022 | ||||||||
\(582\) | −2.56231 | −0.106211 | ||||||||
\(583\) | −2.38197 | −0.0986510 | ||||||||
\(584\) | 22.2361 | 0.920135 | ||||||||
\(585\) | 3.85410 | 0.159348 | ||||||||
\(586\) | −7.56231 | −0.312396 | ||||||||
\(587\) | −37.0689 | −1.53000 | −0.764998 | − | 0.644032i | \(-0.777260\pi\) | ||||
−0.764998 | + | 0.644032i | \(0.777260\pi\) | |||||||
\(588\) | 2.61803 | 0.107966 | ||||||||
\(589\) | 23.0902 | 0.951414 | ||||||||
\(590\) | 8.38197 | 0.345080 | ||||||||
\(591\) | 15.5623 | 0.640148 | ||||||||
\(592\) | −5.12461 | −0.210620 | ||||||||
\(593\) | −34.8328 | −1.43041 | −0.715206 | − | 0.698914i | \(-0.753667\pi\) | ||||
−0.715206 | + | 0.698914i | \(0.753667\pi\) | |||||||
\(594\) | −3.38197 | −0.138764 | ||||||||
\(595\) | 6.85410 | 0.280991 | ||||||||
\(596\) | −30.6525 | −1.25557 | ||||||||
\(597\) | 34.5623 | 1.41454 | ||||||||
\(598\) | 13.9443 | 0.570224 | ||||||||
\(599\) | 26.6525 | 1.08899 | 0.544495 | − | 0.838764i | \(-0.316721\pi\) | ||||
0.544495 | + | 0.838764i | \(0.316721\pi\) | |||||||
\(600\) | −8.61803 | −0.351830 | ||||||||
\(601\) | −13.5623 | −0.553218 | −0.276609 | − | 0.960983i | \(-0.589211\pi\) | ||||
−0.276609 | + | 0.960983i | \(0.589211\pi\) | |||||||
\(602\) | 0.618034 | 0.0251892 | ||||||||
\(603\) | 4.61803 | 0.188061 | ||||||||
\(604\) | 32.2705 | 1.31307 | ||||||||
\(605\) | −16.1803 | −0.657824 | ||||||||
\(606\) | 17.4721 | 0.709757 | ||||||||
\(607\) | 11.8328 | 0.480279 | 0.240140 | − | 0.970738i | \(-0.422807\pi\) | ||||
0.240140 | + | 0.970738i | \(0.422807\pi\) | |||||||
\(608\) | 16.0344 | 0.650282 | ||||||||
\(609\) | −9.47214 | −0.383830 | ||||||||
\(610\) | 9.47214 | 0.383516 | ||||||||
\(611\) | −60.5410 | −2.44923 | ||||||||
\(612\) | −2.61803 | −0.105828 | ||||||||
\(613\) | −6.27051 | −0.253264 | −0.126632 | − | 0.991950i | \(-0.540417\pi\) | ||||
−0.126632 | + | 0.991950i | \(0.540417\pi\) | |||||||
\(614\) | 14.5410 | 0.586828 | ||||||||
\(615\) | 2.61803 | 0.105569 | ||||||||
\(616\) | −2.23607 | −0.0900937 | ||||||||
\(617\) | −32.5967 | −1.31230 | −0.656148 | − | 0.754632i | \(-0.727815\pi\) | ||||
−0.656148 | + | 0.754632i | \(0.727815\pi\) | |||||||
\(618\) | 1.09017 | 0.0438531 | ||||||||
\(619\) | −5.67376 | −0.228048 | −0.114024 | − | 0.993478i | \(-0.536374\pi\) | ||||
−0.114024 | + | 0.993478i | \(0.536374\pi\) | |||||||
\(620\) | −21.1803 | −0.850623 | ||||||||
\(621\) | −19.7984 | −0.794481 | ||||||||
\(622\) | 0.381966 | 0.0153154 | ||||||||
\(623\) | 9.32624 | 0.373648 | ||||||||
\(624\) | 18.7082 | 0.748928 | ||||||||
\(625\) | −7.41641 | −0.296656 | ||||||||
\(626\) | −18.2148 | −0.728009 | ||||||||
\(627\) | 4.61803 | 0.184427 | ||||||||
\(628\) | 12.9443 | 0.516533 | ||||||||
\(629\) | 11.7082 | 0.466837 | ||||||||
\(630\) | 0.381966 | 0.0152179 | ||||||||
\(631\) | −40.4853 | −1.61169 | −0.805847 | − | 0.592124i | \(-0.798290\pi\) | ||||
−0.805847 | + | 0.592124i | \(0.798290\pi\) | |||||||
\(632\) | 26.1803 | 1.04140 | ||||||||
\(633\) | −22.7082 | −0.902570 | ||||||||
\(634\) | −5.02129 | −0.199421 | ||||||||
\(635\) | −5.32624 | −0.211365 | ||||||||
\(636\) | 6.23607 | 0.247276 | ||||||||
\(637\) | −6.23607 | −0.247082 | ||||||||
\(638\) | 3.61803 | 0.143239 | ||||||||
\(639\) | 2.27051 | 0.0898200 | ||||||||
\(640\) | −18.4164 | −0.727972 | ||||||||
\(641\) | 17.1803 | 0.678583 | 0.339291 | − | 0.940681i | \(-0.389813\pi\) | ||||
0.339291 | + | 0.940681i | \(0.389813\pi\) | |||||||
\(642\) | 0.763932 | 0.0301500 | ||||||||
\(643\) | 27.9230 | 1.10118 | 0.550588 | − | 0.834777i | \(-0.314404\pi\) | ||||
0.550588 | + | 0.834777i | \(0.314404\pi\) | |||||||
\(644\) | −5.85410 | −0.230684 | ||||||||
\(645\) | 2.61803 | 0.103085 | ||||||||
\(646\) | −7.47214 | −0.293987 | ||||||||
\(647\) | −21.3607 | −0.839775 | −0.419887 | − | 0.907576i | \(-0.637930\pi\) | ||||
−0.419887 | + | 0.907576i | \(0.637930\pi\) | |||||||
\(648\) | 17.2361 | 0.677097 | ||||||||
\(649\) | −8.38197 | −0.329021 | ||||||||
\(650\) | 9.18034 | 0.360083 | ||||||||
\(651\) | 13.0902 | 0.513044 | ||||||||
\(652\) | 27.4164 | 1.07371 | ||||||||
\(653\) | 27.6180 | 1.08078 | 0.540389 | − | 0.841416i | \(-0.318277\pi\) | ||||
0.540389 | + | 0.841416i | \(0.318277\pi\) | |||||||
\(654\) | −8.47214 | −0.331287 | ||||||||
\(655\) | 17.5623 | 0.686216 | ||||||||
\(656\) | −1.85410 | −0.0723905 | ||||||||
\(657\) | 3.79837 | 0.148189 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | 39.0689 | 1.52191 | 0.760954 | − | 0.648806i | \(-0.224731\pi\) | ||||
0.760954 | + | 0.648806i | \(0.224731\pi\) | |||||||
\(660\) | −4.23607 | −0.164889 | ||||||||
\(661\) | 30.7639 | 1.19658 | 0.598289 | − | 0.801280i | \(-0.295847\pi\) | ||||
0.598289 | + | 0.801280i | \(0.295847\pi\) | |||||||
\(662\) | 20.9443 | 0.814022 | ||||||||
\(663\) | −42.7426 | −1.65999 | ||||||||
\(664\) | 12.2361 | 0.474852 | ||||||||
\(665\) | −4.61803 | −0.179080 | ||||||||
\(666\) | 0.652476 | 0.0252829 | ||||||||
\(667\) | 21.1803 | 0.820106 | ||||||||
\(668\) | 16.8541 | 0.652105 | ||||||||
\(669\) | 2.14590 | 0.0829652 | ||||||||
\(670\) | −12.0902 | −0.467084 | ||||||||
\(671\) | −9.47214 | −0.365668 | ||||||||
\(672\) | 9.09017 | 0.350661 | ||||||||
\(673\) | 19.8328 | 0.764499 | 0.382249 | − | 0.924059i | \(-0.375150\pi\) | ||||
0.382249 | + | 0.924059i | \(0.375150\pi\) | |||||||
\(674\) | −12.6525 | −0.487355 | ||||||||
\(675\) | −13.0344 | −0.501696 | ||||||||
\(676\) | −41.8885 | −1.61110 | ||||||||
\(677\) | 31.9098 | 1.22639 | 0.613197 | − | 0.789930i | \(-0.289883\pi\) | ||||
0.613197 | + | 0.789930i | \(0.289883\pi\) | |||||||
\(678\) | −14.4164 | −0.553659 | ||||||||
\(679\) | −2.56231 | −0.0983323 | ||||||||
\(680\) | 15.3262 | 0.587734 | ||||||||
\(681\) | −9.14590 | −0.350472 | ||||||||
\(682\) | −5.00000 | −0.191460 | ||||||||
\(683\) | 18.0557 | 0.690883 | 0.345442 | − | 0.938440i | \(-0.387729\pi\) | ||||
0.345442 | + | 0.938440i | \(0.387729\pi\) | |||||||
\(684\) | 1.76393 | 0.0674456 | ||||||||
\(685\) | 25.5623 | 0.976686 | ||||||||
\(686\) | −0.618034 | −0.0235966 | ||||||||
\(687\) | −34.3607 | −1.31094 | ||||||||
\(688\) | −1.85410 | −0.0706870 | ||||||||
\(689\) | −14.8541 | −0.565896 | ||||||||
\(690\) | 5.85410 | 0.222862 | ||||||||
\(691\) | 5.67376 | 0.215840 | 0.107920 | − | 0.994160i | \(-0.465581\pi\) | ||||
0.107920 | + | 0.994160i | \(0.465581\pi\) | |||||||
\(692\) | −7.61803 | −0.289594 | ||||||||
\(693\) | −0.381966 | −0.0145097 | ||||||||
\(694\) | −2.65248 | −0.100687 | ||||||||
\(695\) | −9.61803 | −0.364833 | ||||||||
\(696\) | −21.1803 | −0.802839 | ||||||||
\(697\) | 4.23607 | 0.160453 | ||||||||
\(698\) | 10.3262 | 0.390854 | ||||||||
\(699\) | 10.2361 | 0.387164 | ||||||||
\(700\) | −3.85410 | −0.145671 | ||||||||
\(701\) | 7.61803 | 0.287729 | 0.143865 | − | 0.989597i | \(-0.454047\pi\) | ||||
0.143865 | + | 0.989597i | \(0.454047\pi\) | |||||||
\(702\) | −21.0902 | −0.795997 | ||||||||
\(703\) | −7.88854 | −0.297522 | ||||||||
\(704\) | 0.236068 | 0.00889715 | ||||||||
\(705\) | −25.4164 | −0.957237 | ||||||||
\(706\) | 6.40325 | 0.240990 | ||||||||
\(707\) | 17.4721 | 0.657107 | ||||||||
\(708\) | 21.9443 | 0.824716 | ||||||||
\(709\) | −31.1246 | −1.16891 | −0.584455 | − | 0.811426i | \(-0.698692\pi\) | ||||
−0.584455 | + | 0.811426i | \(0.698692\pi\) | |||||||
\(710\) | −5.94427 | −0.223085 | ||||||||
\(711\) | 4.47214 | 0.167718 | ||||||||
\(712\) | 20.8541 | 0.781541 | ||||||||
\(713\) | −29.2705 | −1.09619 | ||||||||
\(714\) | −4.23607 | −0.158531 | ||||||||
\(715\) | 10.0902 | 0.377351 | ||||||||
\(716\) | −4.90983 | −0.183489 | ||||||||
\(717\) | 9.94427 | 0.371376 | ||||||||
\(718\) | 13.7082 | 0.511586 | ||||||||
\(719\) | −0.819660 | −0.0305682 | −0.0152841 | − | 0.999883i | \(-0.504865\pi\) | ||||
−0.0152841 | + | 0.999883i | \(0.504865\pi\) | |||||||
\(720\) | −1.14590 | −0.0427051 | ||||||||
\(721\) | 1.09017 | 0.0406001 | ||||||||
\(722\) | −6.70820 | −0.249653 | ||||||||
\(723\) | 7.70820 | 0.286671 | ||||||||
\(724\) | 4.76393 | 0.177050 | ||||||||
\(725\) | 13.9443 | 0.517877 | ||||||||
\(726\) | 10.0000 | 0.371135 | ||||||||
\(727\) | 41.1591 | 1.52650 | 0.763252 | − | 0.646100i | \(-0.223601\pi\) | ||||
0.763252 | + | 0.646100i | \(0.223601\pi\) | |||||||
\(728\) | −13.9443 | −0.516809 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | −9.94427 | −0.368054 | ||||||||
\(731\) | 4.23607 | 0.156677 | ||||||||
\(732\) | 24.7984 | 0.916574 | ||||||||
\(733\) | −2.05573 | −0.0759300 | −0.0379650 | − | 0.999279i | \(-0.512088\pi\) | ||||
−0.0379650 | + | 0.999279i | \(0.512088\pi\) | |||||||
\(734\) | 16.8541 | 0.622096 | ||||||||
\(735\) | −2.61803 | −0.0965676 | ||||||||
\(736\) | −20.3262 | −0.749235 | ||||||||
\(737\) | 12.0902 | 0.445347 | ||||||||
\(738\) | 0.236068 | 0.00868978 | ||||||||
\(739\) | −48.3262 | −1.77771 | −0.888855 | − | 0.458189i | \(-0.848498\pi\) | ||||
−0.888855 | + | 0.458189i | \(0.848498\pi\) | |||||||
\(740\) | 7.23607 | 0.266003 | ||||||||
\(741\) | 28.7984 | 1.05793 | ||||||||
\(742\) | −1.47214 | −0.0540438 | ||||||||
\(743\) | 50.6869 | 1.85952 | 0.929761 | − | 0.368163i | \(-0.120013\pi\) | ||||
0.929761 | + | 0.368163i | \(0.120013\pi\) | |||||||
\(744\) | 29.2705 | 1.07311 | ||||||||
\(745\) | 30.6525 | 1.12302 | ||||||||
\(746\) | 7.87539 | 0.288338 | ||||||||
\(747\) | 2.09017 | 0.0764753 | ||||||||
\(748\) | −6.85410 | −0.250611 | ||||||||
\(749\) | 0.763932 | 0.0279135 | ||||||||
\(750\) | 11.9443 | 0.436143 | ||||||||
\(751\) | 35.5410 | 1.29691 | 0.648455 | − | 0.761253i | \(-0.275415\pi\) | ||||
0.648455 | + | 0.761253i | \(0.275415\pi\) | |||||||
\(752\) | 18.0000 | 0.656392 | ||||||||
\(753\) | −3.32624 | −0.121215 | ||||||||
\(754\) | 22.5623 | 0.821671 | ||||||||
\(755\) | −32.2705 | −1.17444 | ||||||||
\(756\) | 8.85410 | 0.322021 | ||||||||
\(757\) | 4.65248 | 0.169097 | 0.0845486 | − | 0.996419i | \(-0.473055\pi\) | ||||
0.0845486 | + | 0.996419i | \(0.473055\pi\) | |||||||
\(758\) | −6.58359 | −0.239127 | ||||||||
\(759\) | −5.85410 | −0.212490 | ||||||||
\(760\) | −10.3262 | −0.374572 | ||||||||
\(761\) | −31.7771 | −1.15192 | −0.575959 | − | 0.817478i | \(-0.695371\pi\) | ||||
−0.575959 | + | 0.817478i | \(0.695371\pi\) | |||||||
\(762\) | 3.29180 | 0.119249 | ||||||||
\(763\) | −8.47214 | −0.306712 | ||||||||
\(764\) | −36.3607 | −1.31548 | ||||||||
\(765\) | 2.61803 | 0.0946552 | ||||||||
\(766\) | −14.3262 | −0.517628 | ||||||||
\(767\) | −52.2705 | −1.88738 | ||||||||
\(768\) | 10.6180 | 0.383145 | ||||||||
\(769\) | −46.1803 | −1.66531 | −0.832653 | − | 0.553795i | \(-0.813179\pi\) | ||||
−0.832653 | + | 0.553795i | \(0.813179\pi\) | |||||||
\(770\) | 1.00000 | 0.0360375 | ||||||||
\(771\) | −39.0344 | −1.40579 | ||||||||
\(772\) | 36.7426 | 1.32240 | ||||||||
\(773\) | −10.8197 | −0.389156 | −0.194578 | − | 0.980887i | \(-0.562334\pi\) | ||||
−0.194578 | + | 0.980887i | \(0.562334\pi\) | |||||||
\(774\) | 0.236068 | 0.00848529 | ||||||||
\(775\) | −19.2705 | −0.692217 | ||||||||
\(776\) | −5.72949 | −0.205677 | ||||||||
\(777\) | −4.47214 | −0.160437 | ||||||||
\(778\) | −18.9656 | −0.679948 | ||||||||
\(779\) | −2.85410 | −0.102259 | ||||||||
\(780\) | −26.4164 | −0.945859 | ||||||||
\(781\) | 5.94427 | 0.212703 | ||||||||
\(782\) | 9.47214 | 0.338723 | ||||||||
\(783\) | −32.0344 | −1.14482 | ||||||||
\(784\) | 1.85410 | 0.0662179 | ||||||||
\(785\) | −12.9443 | −0.462001 | ||||||||
\(786\) | −10.8541 | −0.387153 | ||||||||
\(787\) | 18.1803 | 0.648059 | 0.324030 | − | 0.946047i | \(-0.394962\pi\) | ||||
0.324030 | + | 0.946047i | \(0.394962\pi\) | |||||||
\(788\) | 15.5623 | 0.554384 | ||||||||
\(789\) | 20.5623 | 0.732037 | ||||||||
\(790\) | −11.7082 | −0.416559 | ||||||||
\(791\) | −14.4164 | −0.512588 | ||||||||
\(792\) | −0.854102 | −0.0303492 | ||||||||
\(793\) | −59.0689 | −2.09760 | ||||||||
\(794\) | −21.2918 | −0.755618 | ||||||||
\(795\) | −6.23607 | −0.221171 | ||||||||
\(796\) | 34.5623 | 1.22503 | ||||||||
\(797\) | −23.8328 | −0.844202 | −0.422101 | − | 0.906549i | \(-0.638707\pi\) | ||||
−0.422101 | + | 0.906549i | \(0.638707\pi\) | |||||||
\(798\) | 2.85410 | 0.101034 | ||||||||
\(799\) | −41.1246 | −1.45488 | ||||||||
\(800\) | −13.3820 | −0.473124 | ||||||||
\(801\) | 3.56231 | 0.125868 | ||||||||
\(802\) | 13.1246 | 0.463446 | ||||||||
\(803\) | 9.94427 | 0.350926 | ||||||||
\(804\) | −31.6525 | −1.11630 | ||||||||
\(805\) | 5.85410 | 0.206330 | ||||||||
\(806\) | −31.1803 | −1.09828 | ||||||||
\(807\) | −37.6525 | −1.32543 | ||||||||
\(808\) | 39.0689 | 1.37444 | ||||||||
\(809\) | 52.8115 | 1.85675 | 0.928377 | − | 0.371639i | \(-0.121204\pi\) | ||||
0.928377 | + | 0.371639i | \(0.121204\pi\) | |||||||
\(810\) | −7.70820 | −0.270839 | ||||||||
\(811\) | −9.06888 | −0.318452 | −0.159226 | − | 0.987242i | \(-0.550900\pi\) | ||||
−0.159226 | + | 0.987242i | \(0.550900\pi\) | |||||||
\(812\) | −9.47214 | −0.332407 | ||||||||
\(813\) | −6.85410 | −0.240384 | ||||||||
\(814\) | 1.70820 | 0.0598725 | ||||||||
\(815\) | −27.4164 | −0.960355 | ||||||||
\(816\) | 12.7082 | 0.444876 | ||||||||
\(817\) | −2.85410 | −0.0998524 | ||||||||
\(818\) | −15.8541 | −0.554326 | ||||||||
\(819\) | −2.38197 | −0.0832326 | ||||||||
\(820\) | 2.61803 | 0.0914257 | ||||||||
\(821\) | −20.7771 | −0.725125 | −0.362563 | − | 0.931959i | \(-0.618098\pi\) | ||||
−0.362563 | + | 0.931959i | \(0.618098\pi\) | |||||||
\(822\) | −15.7984 | −0.551032 | ||||||||
\(823\) | −36.0344 | −1.25608 | −0.628041 | − | 0.778180i | \(-0.716143\pi\) | ||||
−0.628041 | + | 0.778180i | \(0.716143\pi\) | |||||||
\(824\) | 2.43769 | 0.0849211 | ||||||||
\(825\) | −3.85410 | −0.134183 | ||||||||
\(826\) | −5.18034 | −0.180247 | ||||||||
\(827\) | 35.2492 | 1.22574 | 0.612868 | − | 0.790185i | \(-0.290016\pi\) | ||||
0.612868 | + | 0.790185i | \(0.290016\pi\) | |||||||
\(828\) | −2.23607 | −0.0777087 | ||||||||
\(829\) | −7.36068 | −0.255647 | −0.127823 | − | 0.991797i | \(-0.540799\pi\) | ||||
−0.127823 | + | 0.991797i | \(0.540799\pi\) | |||||||
\(830\) | −5.47214 | −0.189941 | ||||||||
\(831\) | 1.32624 | 0.0460067 | ||||||||
\(832\) | 1.47214 | 0.0510371 | ||||||||
\(833\) | −4.23607 | −0.146771 | ||||||||
\(834\) | 5.94427 | 0.205833 | ||||||||
\(835\) | −16.8541 | −0.583260 | ||||||||
\(836\) | 4.61803 | 0.159718 | ||||||||
\(837\) | 44.2705 | 1.53021 | ||||||||
\(838\) | −5.72949 | −0.197922 | ||||||||
\(839\) | −3.23607 | −0.111721 | −0.0558607 | − | 0.998439i | \(-0.517790\pi\) | ||||
−0.0558607 | + | 0.998439i | \(0.517790\pi\) | |||||||
\(840\) | −5.85410 | −0.201986 | ||||||||
\(841\) | 5.27051 | 0.181742 | ||||||||
\(842\) | −12.6525 | −0.436033 | ||||||||
\(843\) | 39.9787 | 1.37694 | ||||||||
\(844\) | −22.7082 | −0.781649 | ||||||||
\(845\) | 41.8885 | 1.44101 | ||||||||
\(846\) | −2.29180 | −0.0787936 | ||||||||
\(847\) | 10.0000 | 0.343604 | ||||||||
\(848\) | 4.41641 | 0.151660 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.23607 | 0.213895 | ||||||||
\(851\) | 10.0000 | 0.342796 | ||||||||
\(852\) | −15.5623 | −0.533156 | ||||||||
\(853\) | 28.2492 | 0.967235 | 0.483617 | − | 0.875279i | \(-0.339323\pi\) | ||||
0.483617 | + | 0.875279i | \(0.339323\pi\) | |||||||
\(854\) | −5.85410 | −0.200323 | ||||||||
\(855\) | −1.76393 | −0.0603252 | ||||||||
\(856\) | 1.70820 | 0.0583852 | ||||||||
\(857\) | 4.61803 | 0.157749 | 0.0788745 | − | 0.996885i | \(-0.474867\pi\) | ||||
0.0788745 | + | 0.996885i | \(0.474867\pi\) | |||||||
\(858\) | −6.23607 | −0.212896 | ||||||||
\(859\) | −49.0344 | −1.67303 | −0.836517 | − | 0.547941i | \(-0.815412\pi\) | ||||
−0.836517 | + | 0.547941i | \(0.815412\pi\) | |||||||
\(860\) | 2.61803 | 0.0892742 | ||||||||
\(861\) | −1.61803 | −0.0551425 | ||||||||
\(862\) | −5.85410 | −0.199392 | ||||||||
\(863\) | −34.2361 | −1.16541 | −0.582705 | − | 0.812684i | \(-0.698006\pi\) | ||||
−0.582705 | + | 0.812684i | \(0.698006\pi\) | |||||||
\(864\) | 30.7426 | 1.04589 | ||||||||
\(865\) | 7.61803 | 0.259021 | ||||||||
\(866\) | −0.596748 | −0.0202783 | ||||||||
\(867\) | −1.52786 | −0.0518890 | ||||||||
\(868\) | 13.0902 | 0.444309 | ||||||||
\(869\) | 11.7082 | 0.397174 | ||||||||
\(870\) | 9.47214 | 0.321135 | ||||||||
\(871\) | 75.3951 | 2.55467 | ||||||||
\(872\) | −18.9443 | −0.641534 | ||||||||
\(873\) | −0.978714 | −0.0331244 | ||||||||
\(874\) | −6.38197 | −0.215873 | ||||||||
\(875\) | 11.9443 | 0.403790 | ||||||||
\(876\) | −26.0344 | −0.879622 | ||||||||
\(877\) | 2.14590 | 0.0724618 | 0.0362309 | − | 0.999343i | \(-0.488465\pi\) | ||||
0.0362309 | + | 0.999343i | \(0.488465\pi\) | |||||||
\(878\) | −8.61803 | −0.290845 | ||||||||
\(879\) | 19.7984 | 0.667783 | ||||||||
\(880\) | −3.00000 | −0.101130 | ||||||||
\(881\) | 2.58359 | 0.0870434 | 0.0435217 | − | 0.999052i | \(-0.486142\pi\) | ||||
0.0435217 | + | 0.999052i | \(0.486142\pi\) | |||||||
\(882\) | −0.236068 | −0.00794882 | ||||||||
\(883\) | 5.61803 | 0.189062 | 0.0945309 | − | 0.995522i | \(-0.469865\pi\) | ||||
0.0945309 | + | 0.995522i | \(0.469865\pi\) | |||||||
\(884\) | −42.7426 | −1.43759 | ||||||||
\(885\) | −21.9443 | −0.737649 | ||||||||
\(886\) | 10.4164 | 0.349946 | ||||||||
\(887\) | 45.8885 | 1.54079 | 0.770393 | − | 0.637569i | \(-0.220060\pi\) | ||||
0.770393 | + | 0.637569i | \(0.220060\pi\) | |||||||
\(888\) | −10.0000 | −0.335578 | ||||||||
\(889\) | 3.29180 | 0.110403 | ||||||||
\(890\) | −9.32624 | −0.312616 | ||||||||
\(891\) | 7.70820 | 0.258235 | ||||||||
\(892\) | 2.14590 | 0.0718500 | ||||||||
\(893\) | 27.7082 | 0.927220 | ||||||||
\(894\) | −18.9443 | −0.633591 | ||||||||
\(895\) | 4.90983 | 0.164118 | ||||||||
\(896\) | 11.3820 | 0.380245 | ||||||||
\(897\) | −36.5066 | −1.21892 | ||||||||
\(898\) | −3.70820 | −0.123744 | ||||||||
\(899\) | −47.3607 | −1.57957 | ||||||||
\(900\) | −1.47214 | −0.0490712 | ||||||||
\(901\) | −10.0902 | −0.336152 | ||||||||
\(902\) | 0.618034 | 0.0205783 | ||||||||
\(903\) | −1.61803 | −0.0538448 | ||||||||
\(904\) | −32.2361 | −1.07216 | ||||||||
\(905\) | −4.76393 | −0.158358 | ||||||||
\(906\) | 19.9443 | 0.662604 | ||||||||
\(907\) | −57.1591 | −1.89794 | −0.948968 | − | 0.315374i | \(-0.897870\pi\) | ||||
−0.948968 | + | 0.315374i | \(0.897870\pi\) | |||||||
\(908\) | −9.14590 | −0.303517 | ||||||||
\(909\) | 6.67376 | 0.221355 | ||||||||
\(910\) | 6.23607 | 0.206724 | ||||||||
\(911\) | −11.6393 | −0.385628 | −0.192814 | − | 0.981235i | \(-0.561761\pi\) | ||||
−0.192814 | + | 0.981235i | \(0.561761\pi\) | |||||||
\(912\) | −8.56231 | −0.283526 | ||||||||
\(913\) | 5.47214 | 0.181101 | ||||||||
\(914\) | −10.1459 | −0.335596 | ||||||||
\(915\) | −24.7984 | −0.819809 | ||||||||
\(916\) | −34.3607 | −1.13531 | ||||||||
\(917\) | −10.8541 | −0.358434 | ||||||||
\(918\) | −14.3262 | −0.472836 | ||||||||
\(919\) | −0.549150 | −0.0181148 | −0.00905740 | − | 0.999959i | \(-0.502883\pi\) | ||||
−0.00905740 | + | 0.999959i | \(0.502883\pi\) | |||||||
\(920\) | 13.0902 | 0.431570 | ||||||||
\(921\) | −38.0689 | −1.25441 | ||||||||
\(922\) | 14.6180 | 0.481419 | ||||||||
\(923\) | 37.0689 | 1.22014 | ||||||||
\(924\) | 2.61803 | 0.0861270 | ||||||||
\(925\) | 6.58359 | 0.216467 | ||||||||
\(926\) | 19.3951 | 0.637363 | ||||||||
\(927\) | 0.416408 | 0.0136766 | ||||||||
\(928\) | −32.8885 | −1.07962 | ||||||||
\(929\) | −4.43769 | −0.145596 | −0.0727980 | − | 0.997347i | \(-0.523193\pi\) | ||||
−0.0727980 | + | 0.997347i | \(0.523193\pi\) | |||||||
\(930\) | −13.0902 | −0.429244 | ||||||||
\(931\) | 2.85410 | 0.0935394 | ||||||||
\(932\) | 10.2361 | 0.335294 | ||||||||
\(933\) | −1.00000 | −0.0327385 | ||||||||
\(934\) | −2.61803 | −0.0856647 | ||||||||
\(935\) | 6.85410 | 0.224153 | ||||||||
\(936\) | −5.32624 | −0.174094 | ||||||||
\(937\) | −23.5836 | −0.770442 | −0.385221 | − | 0.922824i | \(-0.625875\pi\) | ||||
−0.385221 | + | 0.922824i | \(0.625875\pi\) | |||||||
\(938\) | 7.47214 | 0.243974 | ||||||||
\(939\) | 47.6869 | 1.55620 | ||||||||
\(940\) | −25.4164 | −0.828992 | ||||||||
\(941\) | 45.8673 | 1.49523 | 0.747615 | − | 0.664132i | \(-0.231199\pi\) | ||||
0.747615 | + | 0.664132i | \(0.231199\pi\) | |||||||
\(942\) | 8.00000 | 0.260654 | ||||||||
\(943\) | 3.61803 | 0.117819 | ||||||||
\(944\) | 15.5410 | 0.505817 | ||||||||
\(945\) | −8.85410 | −0.288024 | ||||||||
\(946\) | 0.618034 | 0.0200940 | ||||||||
\(947\) | −21.2705 | −0.691199 | −0.345599 | − | 0.938382i | \(-0.612324\pi\) | ||||
−0.345599 | + | 0.938382i | \(0.612324\pi\) | |||||||
\(948\) | −30.6525 | −0.995546 | ||||||||
\(949\) | 62.0132 | 2.01303 | ||||||||
\(950\) | −4.20163 | −0.136319 | ||||||||
\(951\) | 13.1459 | 0.426285 | ||||||||
\(952\) | −9.47214 | −0.306994 | ||||||||
\(953\) | −1.09017 | −0.0353141 | −0.0176570 | − | 0.999844i | \(-0.505621\pi\) | ||||
−0.0176570 | + | 0.999844i | \(0.505621\pi\) | |||||||
\(954\) | −0.562306 | −0.0182053 | ||||||||
\(955\) | 36.3607 | 1.17660 | ||||||||
\(956\) | 9.94427 | 0.321621 | ||||||||
\(957\) | −9.47214 | −0.306191 | ||||||||
\(958\) | 0.347524 | 0.0112280 | ||||||||
\(959\) | −15.7984 | −0.510156 | ||||||||
\(960\) | 0.618034 | 0.0199470 | ||||||||
\(961\) | 34.4508 | 1.11132 | ||||||||
\(962\) | 10.6525 | 0.343450 | ||||||||
\(963\) | 0.291796 | 0.00940300 | ||||||||
\(964\) | 7.70820 | 0.248265 | ||||||||
\(965\) | −36.7426 | −1.18279 | ||||||||
\(966\) | −3.61803 | −0.116408 | ||||||||
\(967\) | 29.8885 | 0.961151 | 0.480575 | − | 0.876953i | \(-0.340428\pi\) | ||||
0.480575 | + | 0.876953i | \(0.340428\pi\) | |||||||
\(968\) | 22.3607 | 0.718699 | ||||||||
\(969\) | 19.5623 | 0.628432 | ||||||||
\(970\) | 2.56231 | 0.0822707 | ||||||||
\(971\) | −44.5967 | −1.43118 | −0.715589 | − | 0.698522i | \(-0.753842\pi\) | ||||
−0.715589 | + | 0.698522i | \(0.753842\pi\) | |||||||
\(972\) | 6.38197 | 0.204702 | ||||||||
\(973\) | 5.94427 | 0.190565 | ||||||||
\(974\) | −6.65248 | −0.213159 | ||||||||
\(975\) | −24.0344 | −0.769718 | ||||||||
\(976\) | 17.5623 | 0.562156 | ||||||||
\(977\) | 27.2016 | 0.870257 | 0.435129 | − | 0.900368i | \(-0.356703\pi\) | ||||
0.435129 | + | 0.900368i | \(0.356703\pi\) | |||||||
\(978\) | 16.9443 | 0.541818 | ||||||||
\(979\) | 9.32624 | 0.298068 | ||||||||
\(980\) | −2.61803 | −0.0836300 | ||||||||
\(981\) | −3.23607 | −0.103320 | ||||||||
\(982\) | 13.1459 | 0.419502 | ||||||||
\(983\) | 43.4721 | 1.38655 | 0.693273 | − | 0.720675i | \(-0.256168\pi\) | ||||
0.693273 | + | 0.720675i | \(0.256168\pi\) | |||||||
\(984\) | −3.61803 | −0.115339 | ||||||||
\(985\) | −15.5623 | −0.495856 | ||||||||
\(986\) | 15.3262 | 0.488087 | ||||||||
\(987\) | 15.7082 | 0.499998 | ||||||||
\(988\) | 28.7984 | 0.916198 | ||||||||
\(989\) | 3.61803 | 0.115047 | ||||||||
\(990\) | 0.381966 | 0.0121397 | ||||||||
\(991\) | 39.1803 | 1.24460 | 0.622302 | − | 0.782777i | \(-0.286197\pi\) | ||||
0.622302 | + | 0.782777i | \(0.286197\pi\) | |||||||
\(992\) | 45.4508 | 1.44307 | ||||||||
\(993\) | −54.8328 | −1.74007 | ||||||||
\(994\) | 3.67376 | 0.116525 | ||||||||
\(995\) | −34.5623 | −1.09570 | ||||||||
\(996\) | −14.3262 | −0.453944 | ||||||||
\(997\) | 18.3951 | 0.582579 | 0.291290 | − | 0.956635i | \(-0.405916\pi\) | ||||
0.291290 | + | 0.956635i | \(0.405916\pi\) | |||||||
\(998\) | 15.2361 | 0.482289 | ||||||||
\(999\) | −15.1246 | −0.478522 |
(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 | 287.2.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2583.2.a.g.1.1 | 2 | |||
4.3 | odd | 2 | 4592.2.a.n.1.2 | 2 | |||
5.4 | even | 2 | 7175.2.a.g.1.1 | 2 | |||
7.6 | odd | 2 | 2009.2.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2009.2.a.a.1.2 | 2 | 7.6 | odd | 2 | |||
2583.2.a.g.1.1 | 2 | 3.2 | odd | 2 | |||
4592.2.a.n.1.2 | 2 | 4.3 | odd | 2 | |||
7175.2.a.g.1.1 | 2 | 5.4 | even | 2 |