Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(1,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("483.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.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: | \(3.85677441763\) |
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 | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.1 |
$q$-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 | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | −0.381966 | −0.170820 | −0.0854102 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854102 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.236068 | 0.0746512 | ||||||||
\(11\) | 2.23607 | 0.674200 | 0.337100 | − | 0.941469i | \(-0.390554\pi\) | ||||
0.337100 | + | 0.941469i | \(0.390554\pi\) | |||||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | −0.145898 | −0.0404648 | −0.0202324 | − | 0.999795i | \(-0.506441\pi\) | ||||
−0.0202324 | + | 0.999795i | \(0.506441\pi\) | |||||||
\(14\) | −0.618034 | −0.165177 | ||||||||
\(15\) | 0.381966 | 0.0986232 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −5.47214 | −1.32719 | −0.663594 | − | 0.748093i | \(-0.730970\pi\) | ||||
−0.663594 | + | 0.748093i | \(0.730970\pi\) | |||||||
\(18\) | −0.618034 | −0.145672 | ||||||||
\(19\) | −8.23607 | −1.88948 | −0.944742 | − | 0.327815i | \(-0.893688\pi\) | ||||
−0.944742 | + | 0.327815i | \(0.893688\pi\) | |||||||
\(20\) | 0.618034 | 0.138197 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −1.38197 | −0.294636 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | 0.0901699 | 0.0176838 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.61803 | −0.305780 | ||||||||
\(29\) | −2.70820 | −0.502901 | −0.251450 | − | 0.967870i | \(-0.580908\pi\) | ||||
−0.251450 | + | 0.967870i | \(0.580908\pi\) | |||||||
\(30\) | −0.236068 | −0.0430999 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | −2.23607 | −0.389249 | ||||||||
\(34\) | 3.38197 | 0.580002 | ||||||||
\(35\) | −0.381966 | −0.0645640 | ||||||||
\(36\) | −1.61803 | −0.269672 | ||||||||
\(37\) | −0.527864 | −0.0867803 | −0.0433902 | − | 0.999058i | \(-0.513816\pi\) | ||||
−0.0433902 | + | 0.999058i | \(0.513816\pi\) | |||||||
\(38\) | 5.09017 | 0.825735 | ||||||||
\(39\) | 0.145898 | 0.0233624 | ||||||||
\(40\) | −0.854102 | −0.135045 | ||||||||
\(41\) | 8.70820 | 1.35999 | 0.679996 | − | 0.733215i | \(-0.261981\pi\) | ||||
0.679996 | + | 0.733215i | \(0.261981\pi\) | |||||||
\(42\) | 0.618034 | 0.0953647 | ||||||||
\(43\) | −8.32624 | −1.26974 | −0.634870 | − | 0.772619i | \(-0.718946\pi\) | ||||
−0.634870 | + | 0.772619i | \(0.718946\pi\) | |||||||
\(44\) | −3.61803 | −0.545439 | ||||||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | −0.618034 | −0.0911241 | ||||||||
\(47\) | 5.23607 | 0.763759 | 0.381880 | − | 0.924212i | \(-0.375277\pi\) | ||||
0.381880 | + | 0.924212i | \(0.375277\pi\) | |||||||
\(48\) | −1.85410 | −0.267617 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | 5.47214 | 0.766252 | ||||||||
\(52\) | 0.236068 | 0.0327367 | ||||||||
\(53\) | −3.61803 | −0.496975 | −0.248488 | − | 0.968635i | \(-0.579934\pi\) | ||||
−0.248488 | + | 0.968635i | \(0.579934\pi\) | |||||||
\(54\) | 0.618034 | 0.0841038 | ||||||||
\(55\) | −0.854102 | −0.115167 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | 8.23607 | 1.09089 | ||||||||
\(58\) | 1.67376 | 0.219776 | ||||||||
\(59\) | −4.85410 | −0.631950 | −0.315975 | − | 0.948767i | \(-0.602332\pi\) | ||||
−0.315975 | + | 0.948767i | \(0.602332\pi\) | |||||||
\(60\) | −0.618034 | −0.0797878 | ||||||||
\(61\) | −9.09017 | −1.16388 | −0.581938 | − | 0.813233i | \(-0.697706\pi\) | ||||
−0.581938 | + | 0.813233i | \(0.697706\pi\) | |||||||
\(62\) | 3.09017 | 0.392452 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 0.0557281 | 0.00691222 | ||||||||
\(66\) | 1.38197 | 0.170108 | ||||||||
\(67\) | −6.85410 | −0.837362 | −0.418681 | − | 0.908133i | \(-0.637507\pi\) | ||||
−0.418681 | + | 0.908133i | \(0.637507\pi\) | |||||||
\(68\) | 8.85410 | 1.07372 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0.236068 | 0.0282155 | ||||||||
\(71\) | 9.38197 | 1.11343 | 0.556717 | − | 0.830702i | \(-0.312061\pi\) | ||||
0.556717 | + | 0.830702i | \(0.312061\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | −3.47214 | −0.406383 | −0.203191 | − | 0.979139i | \(-0.565131\pi\) | ||||
−0.203191 | + | 0.979139i | \(0.565131\pi\) | |||||||
\(74\) | 0.326238 | 0.0379244 | ||||||||
\(75\) | 4.85410 | 0.560503 | ||||||||
\(76\) | 13.3262 | 1.52862 | ||||||||
\(77\) | 2.23607 | 0.254824 | ||||||||
\(78\) | −0.0901699 | −0.0102097 | ||||||||
\(79\) | 5.94427 | 0.668783 | 0.334391 | − | 0.942434i | \(-0.391469\pi\) | ||||
0.334391 | + | 0.942434i | \(0.391469\pi\) | |||||||
\(80\) | −0.708204 | −0.0791796 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.38197 | −0.594339 | ||||||||
\(83\) | 7.94427 | 0.871997 | 0.435999 | − | 0.899947i | \(-0.356395\pi\) | ||||
0.435999 | + | 0.899947i | \(0.356395\pi\) | |||||||
\(84\) | 1.61803 | 0.176542 | ||||||||
\(85\) | 2.09017 | 0.226711 | ||||||||
\(86\) | 5.14590 | 0.554896 | ||||||||
\(87\) | 2.70820 | 0.290350 | ||||||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | −16.3262 | −1.73058 | −0.865289 | − | 0.501274i | \(-0.832865\pi\) | ||||
−0.865289 | + | 0.501274i | \(0.832865\pi\) | |||||||
\(90\) | 0.236068 | 0.0248837 | ||||||||
\(91\) | −0.145898 | −0.0152943 | ||||||||
\(92\) | −1.61803 | −0.168692 | ||||||||
\(93\) | 5.00000 | 0.518476 | ||||||||
\(94\) | −3.23607 | −0.333775 | ||||||||
\(95\) | 3.14590 | 0.322762 | ||||||||
\(96\) | 5.61803 | 0.573388 | ||||||||
\(97\) | −17.1803 | −1.74440 | −0.872200 | − | 0.489150i | \(-0.837307\pi\) | ||||
−0.872200 | + | 0.489150i | \(0.837307\pi\) | |||||||
\(98\) | −0.618034 | −0.0624309 | ||||||||
\(99\) | 2.23607 | 0.224733 | ||||||||
\(100\) | 7.85410 | 0.785410 | ||||||||
\(101\) | −16.0902 | −1.60103 | −0.800516 | − | 0.599312i | \(-0.795441\pi\) | ||||
−0.800516 | + | 0.599312i | \(0.795441\pi\) | |||||||
\(102\) | −3.38197 | −0.334865 | ||||||||
\(103\) | 2.47214 | 0.243587 | 0.121793 | − | 0.992555i | \(-0.461135\pi\) | ||||
0.121793 | + | 0.992555i | \(0.461135\pi\) | |||||||
\(104\) | −0.326238 | −0.0319903 | ||||||||
\(105\) | 0.381966 | 0.0372761 | ||||||||
\(106\) | 2.23607 | 0.217186 | ||||||||
\(107\) | 5.85410 | 0.565937 | 0.282969 | − | 0.959129i | \(-0.408681\pi\) | ||||
0.282969 | + | 0.959129i | \(0.408681\pi\) | |||||||
\(108\) | 1.61803 | 0.155695 | ||||||||
\(109\) | 15.0344 | 1.44004 | 0.720019 | − | 0.693954i | \(-0.244133\pi\) | ||||
0.720019 | + | 0.693954i | \(0.244133\pi\) | |||||||
\(110\) | 0.527864 | 0.0503299 | ||||||||
\(111\) | 0.527864 | 0.0501026 | ||||||||
\(112\) | 1.85410 | 0.175196 | ||||||||
\(113\) | 4.09017 | 0.384771 | 0.192385 | − | 0.981319i | \(-0.438378\pi\) | ||||
0.192385 | + | 0.981319i | \(0.438378\pi\) | |||||||
\(114\) | −5.09017 | −0.476738 | ||||||||
\(115\) | −0.381966 | −0.0356185 | ||||||||
\(116\) | 4.38197 | 0.406855 | ||||||||
\(117\) | −0.145898 | −0.0134883 | ||||||||
\(118\) | 3.00000 | 0.276172 | ||||||||
\(119\) | −5.47214 | −0.501630 | ||||||||
\(120\) | 0.854102 | 0.0779685 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | 5.61803 | 0.508633 | ||||||||
\(123\) | −8.70820 | −0.785192 | ||||||||
\(124\) | 8.09017 | 0.726519 | ||||||||
\(125\) | 3.76393 | 0.336656 | ||||||||
\(126\) | −0.618034 | −0.0550588 | ||||||||
\(127\) | −18.3262 | −1.62619 | −0.813095 | − | 0.582131i | \(-0.802219\pi\) | ||||
−0.813095 | + | 0.582131i | \(0.802219\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 8.32624 | 0.733084 | ||||||||
\(130\) | −0.0344419 | −0.00302075 | ||||||||
\(131\) | 14.4164 | 1.25957 | 0.629784 | − | 0.776771i | \(-0.283144\pi\) | ||||
0.629784 | + | 0.776771i | \(0.283144\pi\) | |||||||
\(132\) | 3.61803 | 0.314909 | ||||||||
\(133\) | −8.23607 | −0.714158 | ||||||||
\(134\) | 4.23607 | 0.365941 | ||||||||
\(135\) | 0.381966 | 0.0328744 | ||||||||
\(136\) | −12.2361 | −1.04923 | ||||||||
\(137\) | −2.05573 | −0.175633 | −0.0878164 | − | 0.996137i | \(-0.527989\pi\) | ||||
−0.0878164 | + | 0.996137i | \(0.527989\pi\) | |||||||
\(138\) | 0.618034 | 0.0526105 | ||||||||
\(139\) | 13.1459 | 1.11502 | 0.557510 | − | 0.830170i | \(-0.311757\pi\) | ||||
0.557510 | + | 0.830170i | \(0.311757\pi\) | |||||||
\(140\) | 0.618034 | 0.0522334 | ||||||||
\(141\) | −5.23607 | −0.440956 | ||||||||
\(142\) | −5.79837 | −0.486589 | ||||||||
\(143\) | −0.326238 | −0.0272814 | ||||||||
\(144\) | 1.85410 | 0.154508 | ||||||||
\(145\) | 1.03444 | 0.0859057 | ||||||||
\(146\) | 2.14590 | 0.177596 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0.854102 | 0.0702067 | ||||||||
\(149\) | 16.6525 | 1.36422 | 0.682112 | − | 0.731248i | \(-0.261062\pi\) | ||||
0.682112 | + | 0.731248i | \(0.261062\pi\) | |||||||
\(150\) | −3.00000 | −0.244949 | ||||||||
\(151\) | 11.7082 | 0.952800 | 0.476400 | − | 0.879229i | \(-0.341941\pi\) | ||||
0.476400 | + | 0.879229i | \(0.341941\pi\) | |||||||
\(152\) | −18.4164 | −1.49377 | ||||||||
\(153\) | −5.47214 | −0.442396 | ||||||||
\(154\) | −1.38197 | −0.111362 | ||||||||
\(155\) | 1.90983 | 0.153401 | ||||||||
\(156\) | −0.236068 | −0.0189006 | ||||||||
\(157\) | 8.18034 | 0.652862 | 0.326431 | − | 0.945221i | \(-0.394154\pi\) | ||||
0.326431 | + | 0.945221i | \(0.394154\pi\) | |||||||
\(158\) | −3.67376 | −0.292269 | ||||||||
\(159\) | 3.61803 | 0.286929 | ||||||||
\(160\) | 2.14590 | 0.169648 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −0.618034 | −0.0485573 | ||||||||
\(163\) | 15.5066 | 1.21457 | 0.607284 | − | 0.794484i | \(-0.292259\pi\) | ||||
0.607284 | + | 0.794484i | \(0.292259\pi\) | |||||||
\(164\) | −14.0902 | −1.10026 | ||||||||
\(165\) | 0.854102 | 0.0664917 | ||||||||
\(166\) | −4.90983 | −0.381077 | ||||||||
\(167\) | 2.52786 | 0.195612 | 0.0978060 | − | 0.995205i | \(-0.468818\pi\) | ||||
0.0978060 | + | 0.995205i | \(0.468818\pi\) | |||||||
\(168\) | −2.23607 | −0.172516 | ||||||||
\(169\) | −12.9787 | −0.998363 | ||||||||
\(170\) | −1.29180 | −0.0990762 | ||||||||
\(171\) | −8.23607 | −0.629828 | ||||||||
\(172\) | 13.4721 | 1.02724 | ||||||||
\(173\) | −24.7082 | −1.87853 | −0.939265 | − | 0.343193i | \(-0.888492\pi\) | ||||
−0.939265 | + | 0.343193i | \(0.888492\pi\) | |||||||
\(174\) | −1.67376 | −0.126888 | ||||||||
\(175\) | −4.85410 | −0.366936 | ||||||||
\(176\) | 4.14590 | 0.312509 | ||||||||
\(177\) | 4.85410 | 0.364857 | ||||||||
\(178\) | 10.0902 | 0.756290 | ||||||||
\(179\) | −9.03444 | −0.675266 | −0.337633 | − | 0.941278i | \(-0.609626\pi\) | ||||
−0.337633 | + | 0.941278i | \(0.609626\pi\) | |||||||
\(180\) | 0.618034 | 0.0460655 | ||||||||
\(181\) | 7.18034 | 0.533710 | 0.266855 | − | 0.963737i | \(-0.414015\pi\) | ||||
0.266855 | + | 0.963737i | \(0.414015\pi\) | |||||||
\(182\) | 0.0901699 | 0.00668384 | ||||||||
\(183\) | 9.09017 | 0.671965 | ||||||||
\(184\) | 2.23607 | 0.164845 | ||||||||
\(185\) | 0.201626 | 0.0148238 | ||||||||
\(186\) | −3.09017 | −0.226582 | ||||||||
\(187\) | −12.2361 | −0.894790 | ||||||||
\(188\) | −8.47214 | −0.617894 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −1.94427 | −0.141052 | ||||||||
\(191\) | 8.29180 | 0.599973 | 0.299987 | − | 0.953943i | \(-0.403018\pi\) | ||||
0.299987 | + | 0.953943i | \(0.403018\pi\) | |||||||
\(192\) | 0.236068 | 0.0170367 | ||||||||
\(193\) | 4.18034 | 0.300907 | 0.150454 | − | 0.988617i | \(-0.451927\pi\) | ||||
0.150454 | + | 0.988617i | \(0.451927\pi\) | |||||||
\(194\) | 10.6180 | 0.762330 | ||||||||
\(195\) | −0.0557281 | −0.00399077 | ||||||||
\(196\) | −1.61803 | −0.115574 | ||||||||
\(197\) | −9.67376 | −0.689227 | −0.344614 | − | 0.938745i | \(-0.611990\pi\) | ||||
−0.344614 | + | 0.938745i | \(0.611990\pi\) | |||||||
\(198\) | −1.38197 | −0.0982120 | ||||||||
\(199\) | 10.5623 | 0.748742 | 0.374371 | − | 0.927279i | \(-0.377859\pi\) | ||||
0.374371 | + | 0.927279i | \(0.377859\pi\) | |||||||
\(200\) | −10.8541 | −0.767501 | ||||||||
\(201\) | 6.85410 | 0.483451 | ||||||||
\(202\) | 9.94427 | 0.699677 | ||||||||
\(203\) | −2.70820 | −0.190079 | ||||||||
\(204\) | −8.85410 | −0.619911 | ||||||||
\(205\) | −3.32624 | −0.232315 | ||||||||
\(206\) | −1.52786 | −0.106451 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −0.270510 | −0.0187565 | ||||||||
\(209\) | −18.4164 | −1.27389 | ||||||||
\(210\) | −0.236068 | −0.0162902 | ||||||||
\(211\) | 15.0000 | 1.03264 | 0.516321 | − | 0.856395i | \(-0.327301\pi\) | ||||
0.516321 | + | 0.856395i | \(0.327301\pi\) | |||||||
\(212\) | 5.85410 | 0.402061 | ||||||||
\(213\) | −9.38197 | −0.642842 | ||||||||
\(214\) | −3.61803 | −0.247324 | ||||||||
\(215\) | 3.18034 | 0.216897 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | −5.00000 | −0.339422 | ||||||||
\(218\) | −9.29180 | −0.629320 | ||||||||
\(219\) | 3.47214 | 0.234625 | ||||||||
\(220\) | 1.38197 | 0.0931721 | ||||||||
\(221\) | 0.798374 | 0.0537044 | ||||||||
\(222\) | −0.326238 | −0.0218957 | ||||||||
\(223\) | 2.67376 | 0.179048 | 0.0895242 | − | 0.995985i | \(-0.471465\pi\) | ||||
0.0895242 | + | 0.995985i | \(0.471465\pi\) | |||||||
\(224\) | −5.61803 | −0.375371 | ||||||||
\(225\) | −4.85410 | −0.323607 | ||||||||
\(226\) | −2.52786 | −0.168151 | ||||||||
\(227\) | −18.2705 | −1.21266 | −0.606328 | − | 0.795215i | \(-0.707358\pi\) | ||||
−0.606328 | + | 0.795215i | \(0.707358\pi\) | |||||||
\(228\) | −13.3262 | −0.882552 | ||||||||
\(229\) | −21.3262 | −1.40928 | −0.704639 | − | 0.709566i | \(-0.748891\pi\) | ||||
−0.704639 | + | 0.709566i | \(0.748891\pi\) | |||||||
\(230\) | 0.236068 | 0.0155659 | ||||||||
\(231\) | −2.23607 | −0.147122 | ||||||||
\(232\) | −6.05573 | −0.397578 | ||||||||
\(233\) | −4.09017 | −0.267956 | −0.133978 | − | 0.990984i | \(-0.542775\pi\) | ||||
−0.133978 | + | 0.990984i | \(0.542775\pi\) | |||||||
\(234\) | 0.0901699 | 0.00589459 | ||||||||
\(235\) | −2.00000 | −0.130466 | ||||||||
\(236\) | 7.85410 | 0.511258 | ||||||||
\(237\) | −5.94427 | −0.386122 | ||||||||
\(238\) | 3.38197 | 0.219220 | ||||||||
\(239\) | −4.38197 | −0.283446 | −0.141723 | − | 0.989906i | \(-0.545264\pi\) | ||||
−0.141723 | + | 0.989906i | \(0.545264\pi\) | |||||||
\(240\) | 0.708204 | 0.0457144 | ||||||||
\(241\) | 15.2918 | 0.985031 | 0.492516 | − | 0.870304i | \(-0.336077\pi\) | ||||
0.492516 | + | 0.870304i | \(0.336077\pi\) | |||||||
\(242\) | 3.70820 | 0.238372 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 14.7082 | 0.941596 | ||||||||
\(245\) | −0.381966 | −0.0244029 | ||||||||
\(246\) | 5.38197 | 0.343142 | ||||||||
\(247\) | 1.20163 | 0.0764576 | ||||||||
\(248\) | −11.1803 | −0.709952 | ||||||||
\(249\) | −7.94427 | −0.503448 | ||||||||
\(250\) | −2.32624 | −0.147124 | ||||||||
\(251\) | −25.7082 | −1.62269 | −0.811344 | − | 0.584569i | \(-0.801263\pi\) | ||||
−0.811344 | + | 0.584569i | \(0.801263\pi\) | |||||||
\(252\) | −1.61803 | −0.101927 | ||||||||
\(253\) | 2.23607 | 0.140580 | ||||||||
\(254\) | 11.3262 | 0.710671 | ||||||||
\(255\) | −2.09017 | −0.130892 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 16.2918 | 1.01625 | 0.508127 | − | 0.861282i | \(-0.330338\pi\) | ||||
0.508127 | + | 0.861282i | \(0.330338\pi\) | |||||||
\(258\) | −5.14590 | −0.320370 | ||||||||
\(259\) | −0.527864 | −0.0327999 | ||||||||
\(260\) | −0.0901699 | −0.00559210 | ||||||||
\(261\) | −2.70820 | −0.167634 | ||||||||
\(262\) | −8.90983 | −0.550451 | ||||||||
\(263\) | 5.00000 | 0.308313 | 0.154157 | − | 0.988046i | \(-0.450734\pi\) | ||||
0.154157 | + | 0.988046i | \(0.450734\pi\) | |||||||
\(264\) | −5.00000 | −0.307729 | ||||||||
\(265\) | 1.38197 | 0.0848935 | ||||||||
\(266\) | 5.09017 | 0.312098 | ||||||||
\(267\) | 16.3262 | 0.999150 | ||||||||
\(268\) | 11.0902 | 0.677440 | ||||||||
\(269\) | 3.85410 | 0.234989 | 0.117494 | − | 0.993074i | \(-0.462514\pi\) | ||||
0.117494 | + | 0.993074i | \(0.462514\pi\) | |||||||
\(270\) | −0.236068 | −0.0143666 | ||||||||
\(271\) | 5.18034 | 0.314683 | 0.157342 | − | 0.987544i | \(-0.449708\pi\) | ||||
0.157342 | + | 0.987544i | \(0.449708\pi\) | |||||||
\(272\) | −10.1459 | −0.615185 | ||||||||
\(273\) | 0.145898 | 0.00883015 | ||||||||
\(274\) | 1.27051 | 0.0767543 | ||||||||
\(275\) | −10.8541 | −0.654527 | ||||||||
\(276\) | 1.61803 | 0.0973942 | ||||||||
\(277\) | −30.2148 | −1.81543 | −0.907715 | − | 0.419587i | \(-0.862175\pi\) | ||||
−0.907715 | + | 0.419587i | \(0.862175\pi\) | |||||||
\(278\) | −8.12461 | −0.487282 | ||||||||
\(279\) | −5.00000 | −0.299342 | ||||||||
\(280\) | −0.854102 | −0.0510424 | ||||||||
\(281\) | 27.5967 | 1.64628 | 0.823142 | − | 0.567836i | \(-0.192219\pi\) | ||||
0.823142 | + | 0.567836i | \(0.192219\pi\) | |||||||
\(282\) | 3.23607 | 0.192705 | ||||||||
\(283\) | −1.32624 | −0.0788367 | −0.0394183 | − | 0.999223i | \(-0.512550\pi\) | ||||
−0.0394183 | + | 0.999223i | \(0.512550\pi\) | |||||||
\(284\) | −15.1803 | −0.900787 | ||||||||
\(285\) | −3.14590 | −0.186347 | ||||||||
\(286\) | 0.201626 | 0.0119224 | ||||||||
\(287\) | 8.70820 | 0.514029 | ||||||||
\(288\) | −5.61803 | −0.331046 | ||||||||
\(289\) | 12.9443 | 0.761428 | ||||||||
\(290\) | −0.639320 | −0.0375422 | ||||||||
\(291\) | 17.1803 | 1.00713 | ||||||||
\(292\) | 5.61803 | 0.328771 | ||||||||
\(293\) | −18.4721 | −1.07915 | −0.539577 | − | 0.841936i | \(-0.681416\pi\) | ||||
−0.539577 | + | 0.841936i | \(0.681416\pi\) | |||||||
\(294\) | 0.618034 | 0.0360445 | ||||||||
\(295\) | 1.85410 | 0.107950 | ||||||||
\(296\) | −1.18034 | −0.0686059 | ||||||||
\(297\) | −2.23607 | −0.129750 | ||||||||
\(298\) | −10.2918 | −0.596188 | ||||||||
\(299\) | −0.145898 | −0.00843750 | ||||||||
\(300\) | −7.85410 | −0.453457 | ||||||||
\(301\) | −8.32624 | −0.479916 | ||||||||
\(302\) | −7.23607 | −0.416389 | ||||||||
\(303\) | 16.0902 | 0.924356 | ||||||||
\(304\) | −15.2705 | −0.875824 | ||||||||
\(305\) | 3.47214 | 0.198814 | ||||||||
\(306\) | 3.38197 | 0.193334 | ||||||||
\(307\) | 8.05573 | 0.459765 | 0.229882 | − | 0.973218i | \(-0.426166\pi\) | ||||
0.229882 | + | 0.973218i | \(0.426166\pi\) | |||||||
\(308\) | −3.61803 | −0.206157 | ||||||||
\(309\) | −2.47214 | −0.140635 | ||||||||
\(310\) | −1.18034 | −0.0670388 | ||||||||
\(311\) | 5.38197 | 0.305183 | 0.152592 | − | 0.988289i | \(-0.451238\pi\) | ||||
0.152592 | + | 0.988289i | \(0.451238\pi\) | |||||||
\(312\) | 0.326238 | 0.0184696 | ||||||||
\(313\) | −10.4721 | −0.591920 | −0.295960 | − | 0.955200i | \(-0.595640\pi\) | ||||
−0.295960 | + | 0.955200i | \(0.595640\pi\) | |||||||
\(314\) | −5.05573 | −0.285311 | ||||||||
\(315\) | −0.381966 | −0.0215213 | ||||||||
\(316\) | −9.61803 | −0.541057 | ||||||||
\(317\) | −28.8541 | −1.62061 | −0.810304 | − | 0.586010i | \(-0.800698\pi\) | ||||
−0.810304 | + | 0.586010i | \(0.800698\pi\) | |||||||
\(318\) | −2.23607 | −0.125392 | ||||||||
\(319\) | −6.05573 | −0.339056 | ||||||||
\(320\) | 0.0901699 | 0.00504065 | ||||||||
\(321\) | −5.85410 | −0.326744 | ||||||||
\(322\) | −0.618034 | −0.0344417 | ||||||||
\(323\) | 45.0689 | 2.50770 | ||||||||
\(324\) | −1.61803 | −0.0898908 | ||||||||
\(325\) | 0.708204 | 0.0392841 | ||||||||
\(326\) | −9.58359 | −0.530786 | ||||||||
\(327\) | −15.0344 | −0.831407 | ||||||||
\(328\) | 19.4721 | 1.07517 | ||||||||
\(329\) | 5.23607 | 0.288674 | ||||||||
\(330\) | −0.527864 | −0.0290580 | ||||||||
\(331\) | −6.94427 | −0.381692 | −0.190846 | − | 0.981620i | \(-0.561123\pi\) | ||||
−0.190846 | + | 0.981620i | \(0.561123\pi\) | |||||||
\(332\) | −12.8541 | −0.705460 | ||||||||
\(333\) | −0.527864 | −0.0289268 | ||||||||
\(334\) | −1.56231 | −0.0854856 | ||||||||
\(335\) | 2.61803 | 0.143038 | ||||||||
\(336\) | −1.85410 | −0.101150 | ||||||||
\(337\) | 1.56231 | 0.0851042 | 0.0425521 | − | 0.999094i | \(-0.486451\pi\) | ||||
0.0425521 | + | 0.999094i | \(0.486451\pi\) | |||||||
\(338\) | 8.02129 | 0.436300 | ||||||||
\(339\) | −4.09017 | −0.222148 | ||||||||
\(340\) | −3.38197 | −0.183413 | ||||||||
\(341\) | −11.1803 | −0.605449 | ||||||||
\(342\) | 5.09017 | 0.275245 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −18.6180 | −1.00382 | ||||||||
\(345\) | 0.381966 | 0.0205644 | ||||||||
\(346\) | 15.2705 | 0.820948 | ||||||||
\(347\) | 27.6525 | 1.48446 | 0.742231 | − | 0.670144i | \(-0.233768\pi\) | ||||
0.742231 | + | 0.670144i | \(0.233768\pi\) | |||||||
\(348\) | −4.38197 | −0.234898 | ||||||||
\(349\) | 31.5066 | 1.68651 | 0.843254 | − | 0.537515i | \(-0.180637\pi\) | ||||
0.843254 | + | 0.537515i | \(0.180637\pi\) | |||||||
\(350\) | 3.00000 | 0.160357 | ||||||||
\(351\) | 0.145898 | 0.00778746 | ||||||||
\(352\) | −12.5623 | −0.669573 | ||||||||
\(353\) | 22.5967 | 1.20270 | 0.601352 | − | 0.798984i | \(-0.294629\pi\) | ||||
0.601352 | + | 0.798984i | \(0.294629\pi\) | |||||||
\(354\) | −3.00000 | −0.159448 | ||||||||
\(355\) | −3.58359 | −0.190197 | ||||||||
\(356\) | 26.4164 | 1.40007 | ||||||||
\(357\) | 5.47214 | 0.289616 | ||||||||
\(358\) | 5.58359 | 0.295102 | ||||||||
\(359\) | −1.79837 | −0.0949145 | −0.0474573 | − | 0.998873i | \(-0.515112\pi\) | ||||
−0.0474573 | + | 0.998873i | \(0.515112\pi\) | |||||||
\(360\) | −0.854102 | −0.0450151 | ||||||||
\(361\) | 48.8328 | 2.57015 | ||||||||
\(362\) | −4.43769 | −0.233240 | ||||||||
\(363\) | 6.00000 | 0.314918 | ||||||||
\(364\) | 0.236068 | 0.0123733 | ||||||||
\(365\) | 1.32624 | 0.0694185 | ||||||||
\(366\) | −5.61803 | −0.293659 | ||||||||
\(367\) | 23.4508 | 1.22412 | 0.612062 | − | 0.790810i | \(-0.290340\pi\) | ||||
0.612062 | + | 0.790810i | \(0.290340\pi\) | |||||||
\(368\) | 1.85410 | 0.0966517 | ||||||||
\(369\) | 8.70820 | 0.453331 | ||||||||
\(370\) | −0.124612 | −0.00647826 | ||||||||
\(371\) | −3.61803 | −0.187839 | ||||||||
\(372\) | −8.09017 | −0.419456 | ||||||||
\(373\) | −32.8885 | −1.70290 | −0.851452 | − | 0.524432i | \(-0.824278\pi\) | ||||
−0.851452 | + | 0.524432i | \(0.824278\pi\) | |||||||
\(374\) | 7.56231 | 0.391038 | ||||||||
\(375\) | −3.76393 | −0.194369 | ||||||||
\(376\) | 11.7082 | 0.603805 | ||||||||
\(377\) | 0.395122 | 0.0203498 | ||||||||
\(378\) | 0.618034 | 0.0317882 | ||||||||
\(379\) | −3.05573 | −0.156962 | −0.0784811 | − | 0.996916i | \(-0.525007\pi\) | ||||
−0.0784811 | + | 0.996916i | \(0.525007\pi\) | |||||||
\(380\) | −5.09017 | −0.261120 | ||||||||
\(381\) | 18.3262 | 0.938882 | ||||||||
\(382\) | −5.12461 | −0.262198 | ||||||||
\(383\) | −13.4721 | −0.688394 | −0.344197 | − | 0.938897i | \(-0.611849\pi\) | ||||
−0.344197 | + | 0.938897i | \(0.611849\pi\) | |||||||
\(384\) | −11.3820 | −0.580834 | ||||||||
\(385\) | −0.854102 | −0.0435291 | ||||||||
\(386\) | −2.58359 | −0.131501 | ||||||||
\(387\) | −8.32624 | −0.423246 | ||||||||
\(388\) | 27.7984 | 1.41125 | ||||||||
\(389\) | −18.1246 | −0.918954 | −0.459477 | − | 0.888190i | \(-0.651963\pi\) | ||||
−0.459477 | + | 0.888190i | \(0.651963\pi\) | |||||||
\(390\) | 0.0344419 | 0.00174403 | ||||||||
\(391\) | −5.47214 | −0.276738 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | −14.4164 | −0.727212 | ||||||||
\(394\) | 5.97871 | 0.301203 | ||||||||
\(395\) | −2.27051 | −0.114242 | ||||||||
\(396\) | −3.61803 | −0.181813 | ||||||||
\(397\) | 10.7639 | 0.540226 | 0.270113 | − | 0.962829i | \(-0.412939\pi\) | ||||
0.270113 | + | 0.962829i | \(0.412939\pi\) | |||||||
\(398\) | −6.52786 | −0.327212 | ||||||||
\(399\) | 8.23607 | 0.412319 | ||||||||
\(400\) | −9.00000 | −0.450000 | ||||||||
\(401\) | 29.1803 | 1.45720 | 0.728598 | − | 0.684941i | \(-0.240172\pi\) | ||||
0.728598 | + | 0.684941i | \(0.240172\pi\) | |||||||
\(402\) | −4.23607 | −0.211276 | ||||||||
\(403\) | 0.729490 | 0.0363385 | ||||||||
\(404\) | 26.0344 | 1.29526 | ||||||||
\(405\) | −0.381966 | −0.0189800 | ||||||||
\(406\) | 1.67376 | 0.0830674 | ||||||||
\(407\) | −1.18034 | −0.0585073 | ||||||||
\(408\) | 12.2361 | 0.605776 | ||||||||
\(409\) | −7.65248 | −0.378391 | −0.189195 | − | 0.981939i | \(-0.560588\pi\) | ||||
−0.189195 | + | 0.981939i | \(0.560588\pi\) | |||||||
\(410\) | 2.05573 | 0.101525 | ||||||||
\(411\) | 2.05573 | 0.101402 | ||||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | −4.85410 | −0.238855 | ||||||||
\(414\) | −0.618034 | −0.0303747 | ||||||||
\(415\) | −3.03444 | −0.148955 | ||||||||
\(416\) | 0.819660 | 0.0401871 | ||||||||
\(417\) | −13.1459 | −0.643757 | ||||||||
\(418\) | 11.3820 | 0.556710 | ||||||||
\(419\) | −0.562306 | −0.0274704 | −0.0137352 | − | 0.999906i | \(-0.504372\pi\) | ||||
−0.0137352 | + | 0.999906i | \(0.504372\pi\) | |||||||
\(420\) | −0.618034 | −0.0301570 | ||||||||
\(421\) | 26.3262 | 1.28306 | 0.641531 | − | 0.767097i | \(-0.278300\pi\) | ||||
0.641531 | + | 0.767097i | \(0.278300\pi\) | |||||||
\(422\) | −9.27051 | −0.451281 | ||||||||
\(423\) | 5.23607 | 0.254586 | ||||||||
\(424\) | −8.09017 | −0.392893 | ||||||||
\(425\) | 26.5623 | 1.28846 | ||||||||
\(426\) | 5.79837 | 0.280932 | ||||||||
\(427\) | −9.09017 | −0.439904 | ||||||||
\(428\) | −9.47214 | −0.457853 | ||||||||
\(429\) | 0.326238 | 0.0157509 | ||||||||
\(430\) | −1.96556 | −0.0947876 | ||||||||
\(431\) | 31.0902 | 1.49756 | 0.748780 | − | 0.662818i | \(-0.230640\pi\) | ||||
0.748780 | + | 0.662818i | \(0.230640\pi\) | |||||||
\(432\) | −1.85410 | −0.0892055 | ||||||||
\(433\) | −17.1246 | −0.822956 | −0.411478 | − | 0.911420i | \(-0.634987\pi\) | ||||
−0.411478 | + | 0.911420i | \(0.634987\pi\) | |||||||
\(434\) | 3.09017 | 0.148333 | ||||||||
\(435\) | −1.03444 | −0.0495977 | ||||||||
\(436\) | −24.3262 | −1.16502 | ||||||||
\(437\) | −8.23607 | −0.393985 | ||||||||
\(438\) | −2.14590 | −0.102535 | ||||||||
\(439\) | −0.0557281 | −0.00265976 | −0.00132988 | − | 0.999999i | \(-0.500423\pi\) | ||||
−0.00132988 | + | 0.999999i | \(0.500423\pi\) | |||||||
\(440\) | −1.90983 | −0.0910476 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.493422 | −0.0234697 | ||||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | −0.854102 | −0.0405339 | ||||||||
\(445\) | 6.23607 | 0.295618 | ||||||||
\(446\) | −1.65248 | −0.0782470 | ||||||||
\(447\) | −16.6525 | −0.787635 | ||||||||
\(448\) | −0.236068 | −0.0111532 | ||||||||
\(449\) | 24.0902 | 1.13689 | 0.568443 | − | 0.822723i | \(-0.307546\pi\) | ||||
0.568443 | + | 0.822723i | \(0.307546\pi\) | |||||||
\(450\) | 3.00000 | 0.141421 | ||||||||
\(451\) | 19.4721 | 0.916907 | ||||||||
\(452\) | −6.61803 | −0.311286 | ||||||||
\(453\) | −11.7082 | −0.550099 | ||||||||
\(454\) | 11.2918 | 0.529950 | ||||||||
\(455\) | 0.0557281 | 0.00261257 | ||||||||
\(456\) | 18.4164 | 0.862427 | ||||||||
\(457\) | −8.20163 | −0.383656 | −0.191828 | − | 0.981429i | \(-0.561442\pi\) | ||||
−0.191828 | + | 0.981429i | \(0.561442\pi\) | |||||||
\(458\) | 13.1803 | 0.615877 | ||||||||
\(459\) | 5.47214 | 0.255417 | ||||||||
\(460\) | 0.618034 | 0.0288160 | ||||||||
\(461\) | 12.8541 | 0.598675 | 0.299338 | − | 0.954147i | \(-0.403234\pi\) | ||||
0.299338 | + | 0.954147i | \(0.403234\pi\) | |||||||
\(462\) | 1.38197 | 0.0642949 | ||||||||
\(463\) | −34.5967 | −1.60785 | −0.803924 | − | 0.594733i | \(-0.797258\pi\) | ||||
−0.803924 | + | 0.594733i | \(0.797258\pi\) | |||||||
\(464\) | −5.02129 | −0.233107 | ||||||||
\(465\) | −1.90983 | −0.0885662 | ||||||||
\(466\) | 2.52786 | 0.117101 | ||||||||
\(467\) | −16.8885 | −0.781509 | −0.390754 | − | 0.920495i | \(-0.627786\pi\) | ||||
−0.390754 | + | 0.920495i | \(0.627786\pi\) | |||||||
\(468\) | 0.236068 | 0.0109122 | ||||||||
\(469\) | −6.85410 | −0.316493 | ||||||||
\(470\) | 1.23607 | 0.0570156 | ||||||||
\(471\) | −8.18034 | −0.376930 | ||||||||
\(472\) | −10.8541 | −0.499601 | ||||||||
\(473\) | −18.6180 | −0.856058 | ||||||||
\(474\) | 3.67376 | 0.168741 | ||||||||
\(475\) | 39.9787 | 1.83435 | ||||||||
\(476\) | 8.85410 | 0.405827 | ||||||||
\(477\) | −3.61803 | −0.165658 | ||||||||
\(478\) | 2.70820 | 0.123870 | ||||||||
\(479\) | 25.6525 | 1.17209 | 0.586046 | − | 0.810278i | \(-0.300684\pi\) | ||||
0.586046 | + | 0.810278i | \(0.300684\pi\) | |||||||
\(480\) | −2.14590 | −0.0979464 | ||||||||
\(481\) | 0.0770143 | 0.00351155 | ||||||||
\(482\) | −9.45085 | −0.430474 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 9.70820 | 0.441282 | ||||||||
\(485\) | 6.56231 | 0.297979 | ||||||||
\(486\) | 0.618034 | 0.0280346 | ||||||||
\(487\) | 22.2361 | 1.00761 | 0.503806 | − | 0.863817i | \(-0.331933\pi\) | ||||
0.503806 | + | 0.863817i | \(0.331933\pi\) | |||||||
\(488\) | −20.3262 | −0.920126 | ||||||||
\(489\) | −15.5066 | −0.701232 | ||||||||
\(490\) | 0.236068 | 0.0106645 | ||||||||
\(491\) | 16.9098 | 0.763130 | 0.381565 | − | 0.924342i | \(-0.375385\pi\) | ||||
0.381565 | + | 0.924342i | \(0.375385\pi\) | |||||||
\(492\) | 14.0902 | 0.635234 | ||||||||
\(493\) | 14.8197 | 0.667444 | ||||||||
\(494\) | −0.742646 | −0.0334132 | ||||||||
\(495\) | −0.854102 | −0.0383890 | ||||||||
\(496\) | −9.27051 | −0.416258 | ||||||||
\(497\) | 9.38197 | 0.420839 | ||||||||
\(498\) | 4.90983 | 0.220015 | ||||||||
\(499\) | −11.7984 | −0.528168 | −0.264084 | − | 0.964500i | \(-0.585070\pi\) | ||||
−0.264084 | + | 0.964500i | \(0.585070\pi\) | |||||||
\(500\) | −6.09017 | −0.272361 | ||||||||
\(501\) | −2.52786 | −0.112937 | ||||||||
\(502\) | 15.8885 | 0.709140 | ||||||||
\(503\) | −9.90983 | −0.441857 | −0.220929 | − | 0.975290i | \(-0.570909\pi\) | ||||
−0.220929 | + | 0.975290i | \(0.570909\pi\) | |||||||
\(504\) | 2.23607 | 0.0996024 | ||||||||
\(505\) | 6.14590 | 0.273489 | ||||||||
\(506\) | −1.38197 | −0.0614359 | ||||||||
\(507\) | 12.9787 | 0.576405 | ||||||||
\(508\) | 29.6525 | 1.31562 | ||||||||
\(509\) | 12.2918 | 0.544824 | 0.272412 | − | 0.962181i | \(-0.412179\pi\) | ||||
0.272412 | + | 0.962181i | \(0.412179\pi\) | |||||||
\(510\) | 1.29180 | 0.0572017 | ||||||||
\(511\) | −3.47214 | −0.153598 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 8.23607 | 0.363631 | ||||||||
\(514\) | −10.0689 | −0.444119 | ||||||||
\(515\) | −0.944272 | −0.0416096 | ||||||||
\(516\) | −13.4721 | −0.593078 | ||||||||
\(517\) | 11.7082 | 0.514926 | ||||||||
\(518\) | 0.326238 | 0.0143341 | ||||||||
\(519\) | 24.7082 | 1.08457 | ||||||||
\(520\) | 0.124612 | 0.00546459 | ||||||||
\(521\) | −12.4721 | −0.546414 | −0.273207 | − | 0.961955i | \(-0.588084\pi\) | ||||
−0.273207 | + | 0.961955i | \(0.588084\pi\) | |||||||
\(522\) | 1.67376 | 0.0732586 | ||||||||
\(523\) | −20.8328 | −0.910955 | −0.455478 | − | 0.890247i | \(-0.650532\pi\) | ||||
−0.455478 | + | 0.890247i | \(0.650532\pi\) | |||||||
\(524\) | −23.3262 | −1.01901 | ||||||||
\(525\) | 4.85410 | 0.211850 | ||||||||
\(526\) | −3.09017 | −0.134738 | ||||||||
\(527\) | 27.3607 | 1.19185 | ||||||||
\(528\) | −4.14590 | −0.180427 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.854102 | −0.0370998 | ||||||||
\(531\) | −4.85410 | −0.210650 | ||||||||
\(532\) | 13.3262 | 0.577766 | ||||||||
\(533\) | −1.27051 | −0.0550319 | ||||||||
\(534\) | −10.0902 | −0.436644 | ||||||||
\(535\) | −2.23607 | −0.0966736 | ||||||||
\(536\) | −15.3262 | −0.661993 | ||||||||
\(537\) | 9.03444 | 0.389865 | ||||||||
\(538\) | −2.38197 | −0.102694 | ||||||||
\(539\) | 2.23607 | 0.0963143 | ||||||||
\(540\) | −0.618034 | −0.0265959 | ||||||||
\(541\) | −18.7639 | −0.806724 | −0.403362 | − | 0.915040i | \(-0.632159\pi\) | ||||
−0.403362 | + | 0.915040i | \(0.632159\pi\) | |||||||
\(542\) | −3.20163 | −0.137522 | ||||||||
\(543\) | −7.18034 | −0.308138 | ||||||||
\(544\) | 30.7426 | 1.31808 | ||||||||
\(545\) | −5.74265 | −0.245988 | ||||||||
\(546\) | −0.0901699 | −0.00385892 | ||||||||
\(547\) | −24.3820 | −1.04250 | −0.521249 | − | 0.853405i | \(-0.674534\pi\) | ||||
−0.521249 | + | 0.853405i | \(0.674534\pi\) | |||||||
\(548\) | 3.32624 | 0.142090 | ||||||||
\(549\) | −9.09017 | −0.387959 | ||||||||
\(550\) | 6.70820 | 0.286039 | ||||||||
\(551\) | 22.3050 | 0.950223 | ||||||||
\(552\) | −2.23607 | −0.0951734 | ||||||||
\(553\) | 5.94427 | 0.252776 | ||||||||
\(554\) | 18.6738 | 0.793372 | ||||||||
\(555\) | −0.201626 | −0.00855855 | ||||||||
\(556\) | −21.2705 | −0.902071 | ||||||||
\(557\) | −12.7639 | −0.540825 | −0.270413 | − | 0.962745i | \(-0.587160\pi\) | ||||
−0.270413 | + | 0.962745i | \(0.587160\pi\) | |||||||
\(558\) | 3.09017 | 0.130817 | ||||||||
\(559\) | 1.21478 | 0.0513798 | ||||||||
\(560\) | −0.708204 | −0.0299271 | ||||||||
\(561\) | 12.2361 | 0.516607 | ||||||||
\(562\) | −17.0557 | −0.719452 | ||||||||
\(563\) | −11.5623 | −0.487293 | −0.243647 | − | 0.969864i | \(-0.578344\pi\) | ||||
−0.243647 | + | 0.969864i | \(0.578344\pi\) | |||||||
\(564\) | 8.47214 | 0.356741 | ||||||||
\(565\) | −1.56231 | −0.0657267 | ||||||||
\(566\) | 0.819660 | 0.0344529 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 20.9787 | 0.880247 | ||||||||
\(569\) | −43.7771 | −1.83523 | −0.917615 | − | 0.397469i | \(-0.869889\pi\) | ||||
−0.917615 | + | 0.397469i | \(0.869889\pi\) | |||||||
\(570\) | 1.94427 | 0.0814366 | ||||||||
\(571\) | 26.7771 | 1.12059 | 0.560293 | − | 0.828294i | \(-0.310688\pi\) | ||||
0.560293 | + | 0.828294i | \(0.310688\pi\) | |||||||
\(572\) | 0.527864 | 0.0220711 | ||||||||
\(573\) | −8.29180 | −0.346395 | ||||||||
\(574\) | −5.38197 | −0.224639 | ||||||||
\(575\) | −4.85410 | −0.202430 | ||||||||
\(576\) | −0.236068 | −0.00983617 | ||||||||
\(577\) | 9.41641 | 0.392010 | 0.196005 | − | 0.980603i | \(-0.437203\pi\) | ||||
0.196005 | + | 0.980603i | \(0.437203\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | −4.18034 | −0.173729 | ||||||||
\(580\) | −1.67376 | −0.0694992 | ||||||||
\(581\) | 7.94427 | 0.329584 | ||||||||
\(582\) | −10.6180 | −0.440132 | ||||||||
\(583\) | −8.09017 | −0.335061 | ||||||||
\(584\) | −7.76393 | −0.321274 | ||||||||
\(585\) | 0.0557281 | 0.00230407 | ||||||||
\(586\) | 11.4164 | 0.471607 | ||||||||
\(587\) | −17.5623 | −0.724874 | −0.362437 | − | 0.932008i | \(-0.618055\pi\) | ||||
−0.362437 | + | 0.932008i | \(0.618055\pi\) | |||||||
\(588\) | 1.61803 | 0.0667266 | ||||||||
\(589\) | 41.1803 | 1.69681 | ||||||||
\(590\) | −1.14590 | −0.0471759 | ||||||||
\(591\) | 9.67376 | 0.397925 | ||||||||
\(592\) | −0.978714 | −0.0402249 | ||||||||
\(593\) | −37.7082 | −1.54849 | −0.774245 | − | 0.632886i | \(-0.781870\pi\) | ||||
−0.774245 | + | 0.632886i | \(0.781870\pi\) | |||||||
\(594\) | 1.38197 | 0.0567028 | ||||||||
\(595\) | 2.09017 | 0.0856886 | ||||||||
\(596\) | −26.9443 | −1.10368 | ||||||||
\(597\) | −10.5623 | −0.432286 | ||||||||
\(598\) | 0.0901699 | 0.00368732 | ||||||||
\(599\) | 41.2705 | 1.68627 | 0.843134 | − | 0.537704i | \(-0.180708\pi\) | ||||
0.843134 | + | 0.537704i | \(0.180708\pi\) | |||||||
\(600\) | 10.8541 | 0.443117 | ||||||||
\(601\) | −25.5066 | −1.04044 | −0.520218 | − | 0.854034i | \(-0.674149\pi\) | ||||
−0.520218 | + | 0.854034i | \(0.674149\pi\) | |||||||
\(602\) | 5.14590 | 0.209731 | ||||||||
\(603\) | −6.85410 | −0.279121 | ||||||||
\(604\) | −18.9443 | −0.770831 | ||||||||
\(605\) | 2.29180 | 0.0931748 | ||||||||
\(606\) | −9.94427 | −0.403958 | ||||||||
\(607\) | −10.6180 | −0.430973 | −0.215486 | − | 0.976507i | \(-0.569134\pi\) | ||||
−0.215486 | + | 0.976507i | \(0.569134\pi\) | |||||||
\(608\) | 46.2705 | 1.87652 | ||||||||
\(609\) | 2.70820 | 0.109742 | ||||||||
\(610\) | −2.14590 | −0.0868849 | ||||||||
\(611\) | −0.763932 | −0.0309054 | ||||||||
\(612\) | 8.85410 | 0.357906 | ||||||||
\(613\) | −37.6525 | −1.52077 | −0.760385 | − | 0.649473i | \(-0.774990\pi\) | ||||
−0.760385 | + | 0.649473i | \(0.774990\pi\) | |||||||
\(614\) | −4.97871 | −0.200925 | ||||||||
\(615\) | 3.32624 | 0.134127 | ||||||||
\(616\) | 5.00000 | 0.201456 | ||||||||
\(617\) | 37.7426 | 1.51946 | 0.759731 | − | 0.650238i | \(-0.225331\pi\) | ||||
0.759731 | + | 0.650238i | \(0.225331\pi\) | |||||||
\(618\) | 1.52786 | 0.0614597 | ||||||||
\(619\) | −33.2705 | −1.33725 | −0.668627 | − | 0.743598i | \(-0.733118\pi\) | ||||
−0.668627 | + | 0.743598i | \(0.733118\pi\) | |||||||
\(620\) | −3.09017 | −0.124104 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −3.32624 | −0.133370 | ||||||||
\(623\) | −16.3262 | −0.654097 | ||||||||
\(624\) | 0.270510 | 0.0108291 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 6.47214 | 0.258679 | ||||||||
\(627\) | 18.4164 | 0.735480 | ||||||||
\(628\) | −13.2361 | −0.528177 | ||||||||
\(629\) | 2.88854 | 0.115174 | ||||||||
\(630\) | 0.236068 | 0.00940517 | ||||||||
\(631\) | −38.2361 | −1.52215 | −0.761077 | − | 0.648662i | \(-0.775329\pi\) | ||||
−0.761077 | + | 0.648662i | \(0.775329\pi\) | |||||||
\(632\) | 13.2918 | 0.528719 | ||||||||
\(633\) | −15.0000 | −0.596196 | ||||||||
\(634\) | 17.8328 | 0.708232 | ||||||||
\(635\) | 7.00000 | 0.277787 | ||||||||
\(636\) | −5.85410 | −0.232130 | ||||||||
\(637\) | −0.145898 | −0.00578069 | ||||||||
\(638\) | 3.74265 | 0.148173 | ||||||||
\(639\) | 9.38197 | 0.371145 | ||||||||
\(640\) | −4.34752 | −0.171851 | ||||||||
\(641\) | −28.6180 | −1.13034 | −0.565172 | − | 0.824973i | \(-0.691190\pi\) | ||||
−0.565172 | + | 0.824973i | \(0.691190\pi\) | |||||||
\(642\) | 3.61803 | 0.142792 | ||||||||
\(643\) | 2.50658 | 0.0988498 | 0.0494249 | − | 0.998778i | \(-0.484261\pi\) | ||||
0.0494249 | + | 0.998778i | \(0.484261\pi\) | |||||||
\(644\) | −1.61803 | −0.0637595 | ||||||||
\(645\) | −3.18034 | −0.125226 | ||||||||
\(646\) | −27.8541 | −1.09590 | ||||||||
\(647\) | 2.09017 | 0.0821731 | 0.0410865 | − | 0.999156i | \(-0.486918\pi\) | ||||
0.0410865 | + | 0.999156i | \(0.486918\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | −10.8541 | −0.426061 | ||||||||
\(650\) | −0.437694 | −0.0171678 | ||||||||
\(651\) | 5.00000 | 0.195965 | ||||||||
\(652\) | −25.0902 | −0.982607 | ||||||||
\(653\) | −32.0902 | −1.25579 | −0.627893 | − | 0.778300i | \(-0.716082\pi\) | ||||
−0.627893 | + | 0.778300i | \(0.716082\pi\) | |||||||
\(654\) | 9.29180 | 0.363338 | ||||||||
\(655\) | −5.50658 | −0.215160 | ||||||||
\(656\) | 16.1459 | 0.630391 | ||||||||
\(657\) | −3.47214 | −0.135461 | ||||||||
\(658\) | −3.23607 | −0.126155 | ||||||||
\(659\) | −28.5967 | −1.11397 | −0.556986 | − | 0.830522i | \(-0.688042\pi\) | ||||
−0.556986 | + | 0.830522i | \(0.688042\pi\) | |||||||
\(660\) | −1.38197 | −0.0537930 | ||||||||
\(661\) | 6.81966 | 0.265254 | 0.132627 | − | 0.991166i | \(-0.457659\pi\) | ||||
0.132627 | + | 0.991166i | \(0.457659\pi\) | |||||||
\(662\) | 4.29180 | 0.166805 | ||||||||
\(663\) | −0.798374 | −0.0310063 | ||||||||
\(664\) | 17.7639 | 0.689374 | ||||||||
\(665\) | 3.14590 | 0.121993 | ||||||||
\(666\) | 0.326238 | 0.0126415 | ||||||||
\(667\) | −2.70820 | −0.104862 | ||||||||
\(668\) | −4.09017 | −0.158253 | ||||||||
\(669\) | −2.67376 | −0.103374 | ||||||||
\(670\) | −1.61803 | −0.0625101 | ||||||||
\(671\) | −20.3262 | −0.784686 | ||||||||
\(672\) | 5.61803 | 0.216720 | ||||||||
\(673\) | 21.9443 | 0.845890 | 0.422945 | − | 0.906155i | \(-0.360996\pi\) | ||||
0.422945 | + | 0.906155i | \(0.360996\pi\) | |||||||
\(674\) | −0.965558 | −0.0371919 | ||||||||
\(675\) | 4.85410 | 0.186834 | ||||||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | 0.798374 | 0.0306840 | 0.0153420 | − | 0.999882i | \(-0.495116\pi\) | ||||
0.0153420 | + | 0.999882i | \(0.495116\pi\) | |||||||
\(678\) | 2.52786 | 0.0970820 | ||||||||
\(679\) | −17.1803 | −0.659321 | ||||||||
\(680\) | 4.67376 | 0.179231 | ||||||||
\(681\) | 18.2705 | 0.700127 | ||||||||
\(682\) | 6.90983 | 0.264591 | ||||||||
\(683\) | 40.7082 | 1.55766 | 0.778828 | − | 0.627237i | \(-0.215814\pi\) | ||||
0.778828 | + | 0.627237i | \(0.215814\pi\) | |||||||
\(684\) | 13.3262 | 0.509541 | ||||||||
\(685\) | 0.785218 | 0.0300016 | ||||||||
\(686\) | −0.618034 | −0.0235966 | ||||||||
\(687\) | 21.3262 | 0.813647 | ||||||||
\(688\) | −15.4377 | −0.588557 | ||||||||
\(689\) | 0.527864 | 0.0201100 | ||||||||
\(690\) | −0.236068 | −0.00898695 | ||||||||
\(691\) | −20.7984 | −0.791207 | −0.395604 | − | 0.918421i | \(-0.629465\pi\) | ||||
−0.395604 | + | 0.918421i | \(0.629465\pi\) | |||||||
\(692\) | 39.9787 | 1.51976 | ||||||||
\(693\) | 2.23607 | 0.0849412 | ||||||||
\(694\) | −17.0902 | −0.648734 | ||||||||
\(695\) | −5.02129 | −0.190468 | ||||||||
\(696\) | 6.05573 | 0.229542 | ||||||||
\(697\) | −47.6525 | −1.80497 | ||||||||
\(698\) | −19.4721 | −0.737031 | ||||||||
\(699\) | 4.09017 | 0.154704 | ||||||||
\(700\) | 7.85410 | 0.296857 | ||||||||
\(701\) | −31.7984 | −1.20101 | −0.600504 | − | 0.799622i | \(-0.705033\pi\) | ||||
−0.600504 | + | 0.799622i | \(0.705033\pi\) | |||||||
\(702\) | −0.0901699 | −0.00340325 | ||||||||
\(703\) | 4.34752 | 0.163970 | ||||||||
\(704\) | −0.527864 | −0.0198946 | ||||||||
\(705\) | 2.00000 | 0.0753244 | ||||||||
\(706\) | −13.9656 | −0.525601 | ||||||||
\(707\) | −16.0902 | −0.605133 | ||||||||
\(708\) | −7.85410 | −0.295175 | ||||||||
\(709\) | −12.3262 | −0.462922 | −0.231461 | − | 0.972844i | \(-0.574350\pi\) | ||||
−0.231461 | + | 0.972844i | \(0.574350\pi\) | |||||||
\(710\) | 2.21478 | 0.0831193 | ||||||||
\(711\) | 5.94427 | 0.222928 | ||||||||
\(712\) | −36.5066 | −1.36814 | ||||||||
\(713\) | −5.00000 | −0.187251 | ||||||||
\(714\) | −3.38197 | −0.126567 | ||||||||
\(715\) | 0.124612 | 0.00466022 | ||||||||
\(716\) | 14.6180 | 0.546302 | ||||||||
\(717\) | 4.38197 | 0.163648 | ||||||||
\(718\) | 1.11146 | 0.0414792 | ||||||||
\(719\) | 9.29180 | 0.346526 | 0.173263 | − | 0.984876i | \(-0.444569\pi\) | ||||
0.173263 | + | 0.984876i | \(0.444569\pi\) | |||||||
\(720\) | −0.708204 | −0.0263932 | ||||||||
\(721\) | 2.47214 | 0.0920672 | ||||||||
\(722\) | −30.1803 | −1.12320 | ||||||||
\(723\) | −15.2918 | −0.568708 | ||||||||
\(724\) | −11.6180 | −0.431781 | ||||||||
\(725\) | 13.1459 | 0.488226 | ||||||||
\(726\) | −3.70820 | −0.137624 | ||||||||
\(727\) | −30.2361 | −1.12139 | −0.560697 | − | 0.828021i | \(-0.689467\pi\) | ||||
−0.560697 | + | 0.828021i | \(0.689467\pi\) | |||||||
\(728\) | −0.326238 | −0.0120912 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.819660 | −0.0303370 | ||||||||
\(731\) | 45.5623 | 1.68518 | ||||||||
\(732\) | −14.7082 | −0.543631 | ||||||||
\(733\) | 28.5410 | 1.05419 | 0.527093 | − | 0.849807i | \(-0.323282\pi\) | ||||
0.527093 | + | 0.849807i | \(0.323282\pi\) | |||||||
\(734\) | −14.4934 | −0.534962 | ||||||||
\(735\) | 0.381966 | 0.0140890 | ||||||||
\(736\) | −5.61803 | −0.207083 | ||||||||
\(737\) | −15.3262 | −0.564549 | ||||||||
\(738\) | −5.38197 | −0.198113 | ||||||||
\(739\) | −40.4164 | −1.48674 | −0.743371 | − | 0.668880i | \(-0.766774\pi\) | ||||
−0.743371 | + | 0.668880i | \(0.766774\pi\) | |||||||
\(740\) | −0.326238 | −0.0119927 | ||||||||
\(741\) | −1.20163 | −0.0441428 | ||||||||
\(742\) | 2.23607 | 0.0820886 | ||||||||
\(743\) | 25.3951 | 0.931657 | 0.465828 | − | 0.884875i | \(-0.345756\pi\) | ||||
0.465828 | + | 0.884875i | \(0.345756\pi\) | |||||||
\(744\) | 11.1803 | 0.409891 | ||||||||
\(745\) | −6.36068 | −0.233037 | ||||||||
\(746\) | 20.3262 | 0.744196 | ||||||||
\(747\) | 7.94427 | 0.290666 | ||||||||
\(748\) | 19.7984 | 0.723900 | ||||||||
\(749\) | 5.85410 | 0.213904 | ||||||||
\(750\) | 2.32624 | 0.0849422 | ||||||||
\(751\) | −32.0902 | −1.17099 | −0.585493 | − | 0.810677i | \(-0.699099\pi\) | ||||
−0.585493 | + | 0.810677i | \(0.699099\pi\) | |||||||
\(752\) | 9.70820 | 0.354022 | ||||||||
\(753\) | 25.7082 | 0.936859 | ||||||||
\(754\) | −0.244199 | −0.00889319 | ||||||||
\(755\) | −4.47214 | −0.162758 | ||||||||
\(756\) | 1.61803 | 0.0588473 | ||||||||
\(757\) | −32.4164 | −1.17819 | −0.589097 | − | 0.808062i | \(-0.700516\pi\) | ||||
−0.589097 | + | 0.808062i | \(0.700516\pi\) | |||||||
\(758\) | 1.88854 | 0.0685950 | ||||||||
\(759\) | −2.23607 | −0.0811641 | ||||||||
\(760\) | 7.03444 | 0.255166 | ||||||||
\(761\) | 53.8885 | 1.95346 | 0.976729 | − | 0.214477i | \(-0.0688046\pi\) | ||||
0.976729 | + | 0.214477i | \(0.0688046\pi\) | |||||||
\(762\) | −11.3262 | −0.410306 | ||||||||
\(763\) | 15.0344 | 0.544283 | ||||||||
\(764\) | −13.4164 | −0.485389 | ||||||||
\(765\) | 2.09017 | 0.0755703 | ||||||||
\(766\) | 8.32624 | 0.300839 | ||||||||
\(767\) | 0.708204 | 0.0255718 | ||||||||
\(768\) | 6.56231 | 0.236797 | ||||||||
\(769\) | 47.9574 | 1.72939 | 0.864695 | − | 0.502298i | \(-0.167512\pi\) | ||||
0.864695 | + | 0.502298i | \(0.167512\pi\) | |||||||
\(770\) | 0.527864 | 0.0190229 | ||||||||
\(771\) | −16.2918 | −0.586735 | ||||||||
\(772\) | −6.76393 | −0.243439 | ||||||||
\(773\) | −36.0132 | −1.29530 | −0.647652 | − | 0.761937i | \(-0.724249\pi\) | ||||
−0.647652 | + | 0.761937i | \(0.724249\pi\) | |||||||
\(774\) | 5.14590 | 0.184965 | ||||||||
\(775\) | 24.2705 | 0.871822 | ||||||||
\(776\) | −38.4164 | −1.37907 | ||||||||
\(777\) | 0.527864 | 0.0189370 | ||||||||
\(778\) | 11.2016 | 0.401598 | ||||||||
\(779\) | −71.7214 | −2.56968 | ||||||||
\(780\) | 0.0901699 | 0.00322860 | ||||||||
\(781\) | 20.9787 | 0.750677 | ||||||||
\(782\) | 3.38197 | 0.120939 | ||||||||
\(783\) | 2.70820 | 0.0967833 | ||||||||
\(784\) | 1.85410 | 0.0662179 | ||||||||
\(785\) | −3.12461 | −0.111522 | ||||||||
\(786\) | 8.90983 | 0.317803 | ||||||||
\(787\) | −1.79837 | −0.0641051 | −0.0320526 | − | 0.999486i | \(-0.510204\pi\) | ||||
−0.0320526 | + | 0.999486i | \(0.510204\pi\) | |||||||
\(788\) | 15.6525 | 0.557596 | ||||||||
\(789\) | −5.00000 | −0.178005 | ||||||||
\(790\) | 1.40325 | 0.0499255 | ||||||||
\(791\) | 4.09017 | 0.145430 | ||||||||
\(792\) | 5.00000 | 0.177667 | ||||||||
\(793\) | 1.32624 | 0.0470961 | ||||||||
\(794\) | −6.65248 | −0.236088 | ||||||||
\(795\) | −1.38197 | −0.0490133 | ||||||||
\(796\) | −17.0902 | −0.605745 | ||||||||
\(797\) | −3.70820 | −0.131351 | −0.0656757 | − | 0.997841i | \(-0.520920\pi\) | ||||
−0.0656757 | + | 0.997841i | \(0.520920\pi\) | |||||||
\(798\) | −5.09017 | −0.180190 | ||||||||
\(799\) | −28.6525 | −1.01365 | ||||||||
\(800\) | 27.2705 | 0.964158 | ||||||||
\(801\) | −16.3262 | −0.576859 | ||||||||
\(802\) | −18.0344 | −0.636818 | ||||||||
\(803\) | −7.76393 | −0.273983 | ||||||||
\(804\) | −11.0902 | −0.391120 | ||||||||
\(805\) | −0.381966 | −0.0134625 | ||||||||
\(806\) | −0.450850 | −0.0158805 | ||||||||
\(807\) | −3.85410 | −0.135671 | ||||||||
\(808\) | −35.9787 | −1.26573 | ||||||||
\(809\) | −2.43769 | −0.0857048 | −0.0428524 | − | 0.999081i | \(-0.513645\pi\) | ||||
−0.0428524 | + | 0.999081i | \(0.513645\pi\) | |||||||
\(810\) | 0.236068 | 0.00829458 | ||||||||
\(811\) | −25.5410 | −0.896867 | −0.448433 | − | 0.893816i | \(-0.648018\pi\) | ||||
−0.448433 | + | 0.893816i | \(0.648018\pi\) | |||||||
\(812\) | 4.38197 | 0.153777 | ||||||||
\(813\) | −5.18034 | −0.181682 | ||||||||
\(814\) | 0.729490 | 0.0255686 | ||||||||
\(815\) | −5.92299 | −0.207473 | ||||||||
\(816\) | 10.1459 | 0.355177 | ||||||||
\(817\) | 68.5755 | 2.39915 | ||||||||
\(818\) | 4.72949 | 0.165363 | ||||||||
\(819\) | −0.145898 | −0.00509809 | ||||||||
\(820\) | 5.38197 | 0.187946 | ||||||||
\(821\) | 12.2918 | 0.428987 | 0.214493 | − | 0.976725i | \(-0.431190\pi\) | ||||
0.214493 | + | 0.976725i | \(0.431190\pi\) | |||||||
\(822\) | −1.27051 | −0.0443141 | ||||||||
\(823\) | 8.02129 | 0.279604 | 0.139802 | − | 0.990179i | \(-0.455353\pi\) | ||||
0.139802 | + | 0.990179i | \(0.455353\pi\) | |||||||
\(824\) | 5.52786 | 0.192572 | ||||||||
\(825\) | 10.8541 | 0.377891 | ||||||||
\(826\) | 3.00000 | 0.104383 | ||||||||
\(827\) | −22.8541 | −0.794715 | −0.397357 | − | 0.917664i | \(-0.630073\pi\) | ||||
−0.397357 | + | 0.917664i | \(0.630073\pi\) | |||||||
\(828\) | −1.61803 | −0.0562306 | ||||||||
\(829\) | 35.0689 | 1.21799 | 0.608996 | − | 0.793173i | \(-0.291572\pi\) | ||||
0.608996 | + | 0.793173i | \(0.291572\pi\) | |||||||
\(830\) | 1.87539 | 0.0650957 | ||||||||
\(831\) | 30.2148 | 1.04814 | ||||||||
\(832\) | 0.0344419 | 0.00119406 | ||||||||
\(833\) | −5.47214 | −0.189598 | ||||||||
\(834\) | 8.12461 | 0.281332 | ||||||||
\(835\) | −0.965558 | −0.0334145 | ||||||||
\(836\) | 29.7984 | 1.03060 | ||||||||
\(837\) | 5.00000 | 0.172825 | ||||||||
\(838\) | 0.347524 | 0.0120050 | ||||||||
\(839\) | −2.72949 | −0.0942325 | −0.0471162 | − | 0.998889i | \(-0.515003\pi\) | ||||
−0.0471162 | + | 0.998889i | \(0.515003\pi\) | |||||||
\(840\) | 0.854102 | 0.0294693 | ||||||||
\(841\) | −21.6656 | −0.747091 | ||||||||
\(842\) | −16.2705 | −0.560719 | ||||||||
\(843\) | −27.5967 | −0.950482 | ||||||||
\(844\) | −24.2705 | −0.835425 | ||||||||
\(845\) | 4.95743 | 0.170541 | ||||||||
\(846\) | −3.23607 | −0.111258 | ||||||||
\(847\) | −6.00000 | −0.206162 | ||||||||
\(848\) | −6.70820 | −0.230361 | ||||||||
\(849\) | 1.32624 | 0.0455164 | ||||||||
\(850\) | −16.4164 | −0.563078 | ||||||||
\(851\) | −0.527864 | −0.0180949 | ||||||||
\(852\) | 15.1803 | 0.520070 | ||||||||
\(853\) | −42.6525 | −1.46039 | −0.730196 | − | 0.683237i | \(-0.760571\pi\) | ||||
−0.730196 | + | 0.683237i | \(0.760571\pi\) | |||||||
\(854\) | 5.61803 | 0.192245 | ||||||||
\(855\) | 3.14590 | 0.107587 | ||||||||
\(856\) | 13.0902 | 0.447413 | ||||||||
\(857\) | 43.9574 | 1.50156 | 0.750779 | − | 0.660554i | \(-0.229679\pi\) | ||||
0.750779 | + | 0.660554i | \(0.229679\pi\) | |||||||
\(858\) | −0.201626 | −0.00688340 | ||||||||
\(859\) | 1.41641 | 0.0483272 | 0.0241636 | − | 0.999708i | \(-0.492308\pi\) | ||||
0.0241636 | + | 0.999708i | \(0.492308\pi\) | |||||||
\(860\) | −5.14590 | −0.175474 | ||||||||
\(861\) | −8.70820 | −0.296775 | ||||||||
\(862\) | −19.2148 | −0.654458 | ||||||||
\(863\) | 31.5967 | 1.07557 | 0.537783 | − | 0.843083i | \(-0.319262\pi\) | ||||
0.537783 | + | 0.843083i | \(0.319262\pi\) | |||||||
\(864\) | 5.61803 | 0.191129 | ||||||||
\(865\) | 9.43769 | 0.320891 | ||||||||
\(866\) | 10.5836 | 0.359645 | ||||||||
\(867\) | −12.9443 | −0.439611 | ||||||||
\(868\) | 8.09017 | 0.274598 | ||||||||
\(869\) | 13.2918 | 0.450893 | ||||||||
\(870\) | 0.639320 | 0.0216750 | ||||||||
\(871\) | 1.00000 | 0.0338837 | ||||||||
\(872\) | 33.6180 | 1.13845 | ||||||||
\(873\) | −17.1803 | −0.581466 | ||||||||
\(874\) | 5.09017 | 0.172178 | ||||||||
\(875\) | 3.76393 | 0.127244 | ||||||||
\(876\) | −5.61803 | −0.189816 | ||||||||
\(877\) | −26.4721 | −0.893901 | −0.446950 | − | 0.894559i | \(-0.647490\pi\) | ||||
−0.446950 | + | 0.894559i | \(0.647490\pi\) | |||||||
\(878\) | 0.0344419 | 0.00116236 | ||||||||
\(879\) | 18.4721 | 0.623050 | ||||||||
\(880\) | −1.58359 | −0.0533829 | ||||||||
\(881\) | −40.5410 | −1.36586 | −0.682931 | − | 0.730483i | \(-0.739295\pi\) | ||||
−0.682931 | + | 0.730483i | \(0.739295\pi\) | |||||||
\(882\) | −0.618034 | −0.0208103 | ||||||||
\(883\) | 7.74265 | 0.260561 | 0.130280 | − | 0.991477i | \(-0.458412\pi\) | ||||
0.130280 | + | 0.991477i | \(0.458412\pi\) | |||||||
\(884\) | −1.29180 | −0.0434478 | ||||||||
\(885\) | −1.85410 | −0.0623250 | ||||||||
\(886\) | 2.47214 | 0.0830530 | ||||||||
\(887\) | 22.3262 | 0.749642 | 0.374821 | − | 0.927097i | \(-0.377704\pi\) | ||||
0.374821 | + | 0.927097i | \(0.377704\pi\) | |||||||
\(888\) | 1.18034 | 0.0396096 | ||||||||
\(889\) | −18.3262 | −0.614642 | ||||||||
\(890\) | −3.85410 | −0.129190 | ||||||||
\(891\) | 2.23607 | 0.0749111 | ||||||||
\(892\) | −4.32624 | −0.144853 | ||||||||
\(893\) | −43.1246 | −1.44311 | ||||||||
\(894\) | 10.2918 | 0.344209 | ||||||||
\(895\) | 3.45085 | 0.115349 | ||||||||
\(896\) | 11.3820 | 0.380245 | ||||||||
\(897\) | 0.145898 | 0.00487139 | ||||||||
\(898\) | −14.8885 | −0.496837 | ||||||||
\(899\) | 13.5410 | 0.451618 | ||||||||
\(900\) | 7.85410 | 0.261803 | ||||||||
\(901\) | 19.7984 | 0.659579 | ||||||||
\(902\) | −12.0344 | −0.400703 | ||||||||
\(903\) | 8.32624 | 0.277080 | ||||||||
\(904\) | 9.14590 | 0.304188 | ||||||||
\(905\) | −2.74265 | −0.0911686 | ||||||||
\(906\) | 7.23607 | 0.240402 | ||||||||
\(907\) | −0.673762 | −0.0223719 | −0.0111860 | − | 0.999937i | \(-0.503561\pi\) | ||||
−0.0111860 | + | 0.999937i | \(0.503561\pi\) | |||||||
\(908\) | 29.5623 | 0.981060 | ||||||||
\(909\) | −16.0902 | −0.533677 | ||||||||
\(910\) | −0.0344419 | −0.00114174 | ||||||||
\(911\) | −31.7082 | −1.05054 | −0.525270 | − | 0.850936i | \(-0.676036\pi\) | ||||
−0.525270 | + | 0.850936i | \(0.676036\pi\) | |||||||
\(912\) | 15.2705 | 0.505657 | ||||||||
\(913\) | 17.7639 | 0.587900 | ||||||||
\(914\) | 5.06888 | 0.167664 | ||||||||
\(915\) | −3.47214 | −0.114785 | ||||||||
\(916\) | 34.5066 | 1.14013 | ||||||||
\(917\) | 14.4164 | 0.476072 | ||||||||
\(918\) | −3.38197 | −0.111622 | ||||||||
\(919\) | −48.4853 | −1.59938 | −0.799691 | − | 0.600412i | \(-0.795003\pi\) | ||||
−0.799691 | + | 0.600412i | \(0.795003\pi\) | |||||||
\(920\) | −0.854102 | −0.0281589 | ||||||||
\(921\) | −8.05573 | −0.265445 | ||||||||
\(922\) | −7.94427 | −0.261631 | ||||||||
\(923\) | −1.36881 | −0.0450549 | ||||||||
\(924\) | 3.61803 | 0.119025 | ||||||||
\(925\) | 2.56231 | 0.0842481 | ||||||||
\(926\) | 21.3820 | 0.702655 | ||||||||
\(927\) | 2.47214 | 0.0811956 | ||||||||
\(928\) | 15.2148 | 0.499450 | ||||||||
\(929\) | −8.74265 | −0.286837 | −0.143418 | − | 0.989662i | \(-0.545809\pi\) | ||||
−0.143418 | + | 0.989662i | \(0.545809\pi\) | |||||||
\(930\) | 1.18034 | 0.0387049 | ||||||||
\(931\) | −8.23607 | −0.269926 | ||||||||
\(932\) | 6.61803 | 0.216781 | ||||||||
\(933\) | −5.38197 | −0.176198 | ||||||||
\(934\) | 10.4377 | 0.341532 | ||||||||
\(935\) | 4.67376 | 0.152848 | ||||||||
\(936\) | −0.326238 | −0.0106634 | ||||||||
\(937\) | 11.3607 | 0.371137 | 0.185569 | − | 0.982631i | \(-0.440587\pi\) | ||||
0.185569 | + | 0.982631i | \(0.440587\pi\) | |||||||
\(938\) | 4.23607 | 0.138313 | ||||||||
\(939\) | 10.4721 | 0.341745 | ||||||||
\(940\) | 3.23607 | 0.105549 | ||||||||
\(941\) | 18.8328 | 0.613932 | 0.306966 | − | 0.951720i | \(-0.400686\pi\) | ||||
0.306966 | + | 0.951720i | \(0.400686\pi\) | |||||||
\(942\) | 5.05573 | 0.164725 | ||||||||
\(943\) | 8.70820 | 0.283578 | ||||||||
\(944\) | −9.00000 | −0.292925 | ||||||||
\(945\) | 0.381966 | 0.0124254 | ||||||||
\(946\) | 11.5066 | 0.374111 | ||||||||
\(947\) | 42.7214 | 1.38826 | 0.694129 | − | 0.719851i | \(-0.255790\pi\) | ||||
0.694129 | + | 0.719851i | \(0.255790\pi\) | |||||||
\(948\) | 9.61803 | 0.312379 | ||||||||
\(949\) | 0.506578 | 0.0164442 | ||||||||
\(950\) | −24.7082 | −0.801640 | ||||||||
\(951\) | 28.8541 | 0.935658 | ||||||||
\(952\) | −12.2361 | −0.396573 | ||||||||
\(953\) | −15.9230 | −0.515796 | −0.257898 | − | 0.966172i | \(-0.583030\pi\) | ||||
−0.257898 | + | 0.966172i | \(0.583030\pi\) | |||||||
\(954\) | 2.23607 | 0.0723954 | ||||||||
\(955\) | −3.16718 | −0.102488 | ||||||||
\(956\) | 7.09017 | 0.229312 | ||||||||
\(957\) | 6.05573 | 0.195754 | ||||||||
\(958\) | −15.8541 | −0.512223 | ||||||||
\(959\) | −2.05573 | −0.0663829 | ||||||||
\(960\) | −0.0901699 | −0.00291022 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | −0.0475975 | −0.00153460 | ||||||||
\(963\) | 5.85410 | 0.188646 | ||||||||
\(964\) | −24.7426 | −0.796907 | ||||||||
\(965\) | −1.59675 | −0.0514011 | ||||||||
\(966\) | 0.618034 | 0.0198849 | ||||||||
\(967\) | −7.52786 | −0.242080 | −0.121040 | − | 0.992648i | \(-0.538623\pi\) | ||||
−0.121040 | + | 0.992648i | \(0.538623\pi\) | |||||||
\(968\) | −13.4164 | −0.431220 | ||||||||
\(969\) | −45.0689 | −1.44782 | ||||||||
\(970\) | −4.05573 | −0.130222 | ||||||||
\(971\) | −2.90983 | −0.0933809 | −0.0466904 | − | 0.998909i | \(-0.514867\pi\) | ||||
−0.0466904 | + | 0.998909i | \(0.514867\pi\) | |||||||
\(972\) | 1.61803 | 0.0518985 | ||||||||
\(973\) | 13.1459 | 0.421438 | ||||||||
\(974\) | −13.7426 | −0.440343 | ||||||||
\(975\) | −0.708204 | −0.0226807 | ||||||||
\(976\) | −16.8541 | −0.539487 | ||||||||
\(977\) | 7.02129 | 0.224631 | 0.112315 | − | 0.993673i | \(-0.464173\pi\) | ||||
0.112315 | + | 0.993673i | \(0.464173\pi\) | |||||||
\(978\) | 9.58359 | 0.306449 | ||||||||
\(979\) | −36.5066 | −1.16676 | ||||||||
\(980\) | 0.618034 | 0.0197424 | ||||||||
\(981\) | 15.0344 | 0.480013 | ||||||||
\(982\) | −10.4508 | −0.333500 | ||||||||
\(983\) | −14.6393 | −0.466922 | −0.233461 | − | 0.972366i | \(-0.575005\pi\) | ||||
−0.233461 | + | 0.972366i | \(0.575005\pi\) | |||||||
\(984\) | −19.4721 | −0.620749 | ||||||||
\(985\) | 3.69505 | 0.117734 | ||||||||
\(986\) | −9.15905 | −0.291684 | ||||||||
\(987\) | −5.23607 | −0.166666 | ||||||||
\(988\) | −1.94427 | −0.0618555 | ||||||||
\(989\) | −8.32624 | −0.264759 | ||||||||
\(990\) | 0.527864 | 0.0167766 | ||||||||
\(991\) | 18.3262 | 0.582152 | 0.291076 | − | 0.956700i | \(-0.405987\pi\) | ||||
0.291076 | + | 0.956700i | \(0.405987\pi\) | |||||||
\(992\) | 28.0902 | 0.891864 | ||||||||
\(993\) | 6.94427 | 0.220370 | ||||||||
\(994\) | −5.79837 | −0.183913 | ||||||||
\(995\) | −4.03444 | −0.127900 | ||||||||
\(996\) | 12.8541 | 0.407298 | ||||||||
\(997\) | 41.5410 | 1.31562 | 0.657809 | − | 0.753185i | \(-0.271484\pi\) | ||||
0.657809 | + | 0.753185i | \(0.271484\pi\) | |||||||
\(998\) | 7.29180 | 0.230818 | ||||||||
\(999\) | 0.527864 | 0.0167009 |
(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 | 483.2.a.g.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1449.2.a.f.1.2 | 2 | |||
4.3 | odd | 2 | 7728.2.a.bg.1.2 | 2 | |||
7.6 | odd | 2 | 3381.2.a.u.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.g.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1449.2.a.f.1.2 | 2 | 3.2 | odd | 2 | |||
3381.2.a.u.1.1 | 2 | 7.6 | odd | 2 | |||
7728.2.a.bg.1.2 | 2 | 4.3 | odd | 2 |