Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.30278 | 1.90686 | 0.953429 | − | 0.301617i | \(-0.0975264\pi\) | ||||
0.953429 | + | 0.301617i | \(0.0975264\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.30278 | 1.02983 | 0.514916 | − | 0.857240i | \(-0.327823\pi\) | ||||
0.514916 | + | 0.857240i | \(0.327823\pi\) | |||||||
\(6\) | 3.30278 | 1.34835 | ||||||||
\(7\) | −2.60555 | −0.984806 | −0.492403 | − | 0.870367i | \(-0.663881\pi\) | ||||
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.90833 | 2.63611 | ||||||||
\(10\) | 2.30278 | 0.728202 | ||||||||
\(11\) | −2.30278 | −0.694313 | −0.347156 | − | 0.937807i | \(-0.612853\pi\) | ||||
−0.347156 | + | 0.937807i | \(0.612853\pi\) | |||||||
\(12\) | 3.30278 | 0.953429 | ||||||||
\(13\) | −1.30278 | −0.361325 | −0.180662 | − | 0.983545i | \(-0.557824\pi\) | ||||
−0.180662 | + | 0.983545i | \(0.557824\pi\) | |||||||
\(14\) | −2.60555 | −0.696363 | ||||||||
\(15\) | 7.60555 | 1.96374 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 7.90833 | 1.86401 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 2.30278 | 0.514916 | ||||||||
\(21\) | −8.60555 | −1.87789 | ||||||||
\(22\) | −2.30278 | −0.490953 | ||||||||
\(23\) | −3.90833 | −0.814942 | −0.407471 | − | 0.913218i | \(-0.633589\pi\) | ||||
−0.407471 | + | 0.913218i | \(0.633589\pi\) | |||||||
\(24\) | 3.30278 | 0.674176 | ||||||||
\(25\) | 0.302776 | 0.0605551 | ||||||||
\(26\) | −1.30278 | −0.255495 | ||||||||
\(27\) | 16.2111 | 3.11983 | ||||||||
\(28\) | −2.60555 | −0.492403 | ||||||||
\(29\) | 3.90833 | 0.725758 | 0.362879 | − | 0.931836i | \(-0.381794\pi\) | ||||
0.362879 | + | 0.931836i | \(0.381794\pi\) | |||||||
\(30\) | 7.60555 | 1.38858 | ||||||||
\(31\) | 0.302776 | 0.0543801 | 0.0271901 | − | 0.999630i | \(-0.491344\pi\) | ||||
0.0271901 | + | 0.999630i | \(0.491344\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −7.60555 | −1.32396 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −6.00000 | −1.01419 | ||||||||
\(36\) | 7.90833 | 1.31805 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | −4.30278 | −0.688996 | ||||||||
\(40\) | 2.30278 | 0.364101 | ||||||||
\(41\) | 9.90833 | 1.54742 | 0.773710 | − | 0.633540i | \(-0.218399\pi\) | ||||
0.773710 | + | 0.633540i | \(0.218399\pi\) | |||||||
\(42\) | −8.60555 | −1.32787 | ||||||||
\(43\) | −0.605551 | −0.0923457 | −0.0461729 | − | 0.998933i | \(-0.514703\pi\) | ||||
−0.0461729 | + | 0.998933i | \(0.514703\pi\) | |||||||
\(44\) | −2.30278 | −0.347156 | ||||||||
\(45\) | 18.2111 | 2.71475 | ||||||||
\(46\) | −3.90833 | −0.576251 | ||||||||
\(47\) | 4.60555 | 0.671789 | 0.335894 | − | 0.941900i | \(-0.390961\pi\) | ||||
0.335894 | + | 0.941900i | \(0.390961\pi\) | |||||||
\(48\) | 3.30278 | 0.476715 | ||||||||
\(49\) | −0.211103 | −0.0301575 | ||||||||
\(50\) | 0.302776 | 0.0428189 | ||||||||
\(51\) | 19.8167 | 2.77489 | ||||||||
\(52\) | −1.30278 | −0.180662 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 16.2111 | 2.20605 | ||||||||
\(55\) | −5.30278 | −0.715026 | ||||||||
\(56\) | −2.60555 | −0.348181 | ||||||||
\(57\) | −6.60555 | −0.874927 | ||||||||
\(58\) | 3.90833 | 0.513188 | ||||||||
\(59\) | −10.6056 | −1.38073 | −0.690363 | − | 0.723464i | \(-0.742549\pi\) | ||||
−0.690363 | + | 0.723464i | \(0.742549\pi\) | |||||||
\(60\) | 7.60555 | 0.981872 | ||||||||
\(61\) | −7.51388 | −0.962054 | −0.481027 | − | 0.876706i | \(-0.659736\pi\) | ||||
−0.481027 | + | 0.876706i | \(0.659736\pi\) | |||||||
\(62\) | 0.302776 | 0.0384525 | ||||||||
\(63\) | −20.6056 | −2.59606 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | −7.60555 | −0.936179 | ||||||||
\(67\) | −3.51388 | −0.429289 | −0.214644 | − | 0.976692i | \(-0.568859\pi\) | ||||
−0.214644 | + | 0.976692i | \(0.568859\pi\) | |||||||
\(68\) | 6.00000 | 0.727607 | ||||||||
\(69\) | −12.9083 | −1.55398 | ||||||||
\(70\) | −6.00000 | −0.717137 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 7.90833 | 0.932005 | ||||||||
\(73\) | −12.3028 | −1.43993 | −0.719965 | − | 0.694010i | \(-0.755842\pi\) | ||||
−0.719965 | + | 0.694010i | \(0.755842\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | −4.30278 | −0.487193 | ||||||||
\(79\) | −9.11943 | −1.02602 | −0.513008 | − | 0.858384i | \(-0.671469\pi\) | ||||
−0.513008 | + | 0.858384i | \(0.671469\pi\) | |||||||
\(80\) | 2.30278 | 0.257458 | ||||||||
\(81\) | 29.8167 | 3.31296 | ||||||||
\(82\) | 9.90833 | 1.09419 | ||||||||
\(83\) | 2.78890 | 0.306121 | 0.153061 | − | 0.988217i | \(-0.451087\pi\) | ||||
0.153061 | + | 0.988217i | \(0.451087\pi\) | |||||||
\(84\) | −8.60555 | −0.938943 | ||||||||
\(85\) | 13.8167 | 1.49863 | ||||||||
\(86\) | −0.605551 | −0.0652983 | ||||||||
\(87\) | 12.9083 | 1.38392 | ||||||||
\(88\) | −2.30278 | −0.245477 | ||||||||
\(89\) | 9.21110 | 0.976375 | 0.488187 | − | 0.872739i | \(-0.337658\pi\) | ||||
0.488187 | + | 0.872739i | \(0.337658\pi\) | |||||||
\(90\) | 18.2111 | 1.91962 | ||||||||
\(91\) | 3.39445 | 0.355835 | ||||||||
\(92\) | −3.90833 | −0.407471 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 4.60555 | 0.475026 | ||||||||
\(95\) | −4.60555 | −0.472520 | ||||||||
\(96\) | 3.30278 | 0.337088 | ||||||||
\(97\) | 16.4222 | 1.66742 | 0.833711 | − | 0.552201i | \(-0.186212\pi\) | ||||
0.833711 | + | 0.552201i | \(0.186212\pi\) | |||||||
\(98\) | −0.211103 | −0.0213246 | ||||||||
\(99\) | −18.2111 | −1.83028 | ||||||||
\(100\) | 0.302776 | 0.0302776 | ||||||||
\(101\) | −12.4222 | −1.23606 | −0.618028 | − | 0.786156i | \(-0.712068\pi\) | ||||
−0.618028 | + | 0.786156i | \(0.712068\pi\) | |||||||
\(102\) | 19.8167 | 1.96214 | ||||||||
\(103\) | 0.302776 | 0.0298334 | 0.0149167 | − | 0.999889i | \(-0.495252\pi\) | ||||
0.0149167 | + | 0.999889i | \(0.495252\pi\) | |||||||
\(104\) | −1.30278 | −0.127748 | ||||||||
\(105\) | −19.8167 | −1.93391 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 0.697224 | 0.0674032 | 0.0337016 | − | 0.999432i | \(-0.489270\pi\) | ||||
0.0337016 | + | 0.999432i | \(0.489270\pi\) | |||||||
\(108\) | 16.2111 | 1.55991 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −5.30278 | −0.505600 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.60555 | −0.246201 | ||||||||
\(113\) | 3.21110 | 0.302075 | 0.151038 | − | 0.988528i | \(-0.451739\pi\) | ||||
0.151038 | + | 0.988528i | \(0.451739\pi\) | |||||||
\(114\) | −6.60555 | −0.618667 | ||||||||
\(115\) | −9.00000 | −0.839254 | ||||||||
\(116\) | 3.90833 | 0.362879 | ||||||||
\(117\) | −10.3028 | −0.952492 | ||||||||
\(118\) | −10.6056 | −0.976320 | ||||||||
\(119\) | −15.6333 | −1.43310 | ||||||||
\(120\) | 7.60555 | 0.694289 | ||||||||
\(121\) | −5.69722 | −0.517929 | ||||||||
\(122\) | −7.51388 | −0.680275 | ||||||||
\(123\) | 32.7250 | 2.95071 | ||||||||
\(124\) | 0.302776 | 0.0271901 | ||||||||
\(125\) | −10.8167 | −0.967471 | ||||||||
\(126\) | −20.6056 | −1.83569 | ||||||||
\(127\) | −19.2111 | −1.70471 | −0.852355 | − | 0.522964i | \(-0.824826\pi\) | ||||
−0.852355 | + | 0.522964i | \(0.824826\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.00000 | −0.176090 | ||||||||
\(130\) | −3.00000 | −0.263117 | ||||||||
\(131\) | −10.6056 | −0.926611 | −0.463306 | − | 0.886199i | \(-0.653337\pi\) | ||||
−0.463306 | + | 0.886199i | \(0.653337\pi\) | |||||||
\(132\) | −7.60555 | −0.661978 | ||||||||
\(133\) | 5.21110 | 0.451860 | ||||||||
\(134\) | −3.51388 | −0.303553 | ||||||||
\(135\) | 37.3305 | 3.21290 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | 0.908327 | 0.0776036 | 0.0388018 | − | 0.999247i | \(-0.487646\pi\) | ||||
0.0388018 | + | 0.999247i | \(0.487646\pi\) | |||||||
\(138\) | −12.9083 | −1.09883 | ||||||||
\(139\) | −1.90833 | −0.161862 | −0.0809311 | − | 0.996720i | \(-0.525789\pi\) | ||||
−0.0809311 | + | 0.996720i | \(0.525789\pi\) | |||||||
\(140\) | −6.00000 | −0.507093 | ||||||||
\(141\) | 15.2111 | 1.28101 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 3.00000 | 0.250873 | ||||||||
\(144\) | 7.90833 | 0.659027 | ||||||||
\(145\) | 9.00000 | 0.747409 | ||||||||
\(146\) | −12.3028 | −1.01818 | ||||||||
\(147\) | −0.697224 | −0.0575061 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.8167 | 1.62344 | 0.811722 | − | 0.584044i | \(-0.198531\pi\) | ||||
0.811722 | + | 0.584044i | \(0.198531\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −20.6056 | −1.67686 | −0.838428 | − | 0.545012i | \(-0.816525\pi\) | ||||
−0.838428 | + | 0.545012i | \(0.816525\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | 47.4500 | 3.83610 | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 0.697224 | 0.0560024 | ||||||||
\(156\) | −4.30278 | −0.344498 | ||||||||
\(157\) | −7.21110 | −0.575509 | −0.287754 | − | 0.957704i | \(-0.592909\pi\) | ||||
−0.287754 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(158\) | −9.11943 | −0.725503 | ||||||||
\(159\) | −19.8167 | −1.57156 | ||||||||
\(160\) | 2.30278 | 0.182050 | ||||||||
\(161\) | 10.1833 | 0.802560 | ||||||||
\(162\) | 29.8167 | 2.34262 | ||||||||
\(163\) | −8.42221 | −0.659678 | −0.329839 | − | 0.944037i | \(-0.606994\pi\) | ||||
−0.329839 | + | 0.944037i | \(0.606994\pi\) | |||||||
\(164\) | 9.90833 | 0.773710 | ||||||||
\(165\) | −17.5139 | −1.36345 | ||||||||
\(166\) | 2.78890 | 0.216460 | ||||||||
\(167\) | 5.51388 | 0.426677 | 0.213338 | − | 0.976978i | \(-0.431566\pi\) | ||||
0.213338 | + | 0.976978i | \(0.431566\pi\) | |||||||
\(168\) | −8.60555 | −0.663933 | ||||||||
\(169\) | −11.3028 | −0.869444 | ||||||||
\(170\) | 13.8167 | 1.05969 | ||||||||
\(171\) | −15.8167 | −1.20953 | ||||||||
\(172\) | −0.605551 | −0.0461729 | ||||||||
\(173\) | −8.78890 | −0.668207 | −0.334104 | − | 0.942536i | \(-0.608434\pi\) | ||||
−0.334104 | + | 0.942536i | \(0.608434\pi\) | |||||||
\(174\) | 12.9083 | 0.978578 | ||||||||
\(175\) | −0.788897 | −0.0596350 | ||||||||
\(176\) | −2.30278 | −0.173578 | ||||||||
\(177\) | −35.0278 | −2.63285 | ||||||||
\(178\) | 9.21110 | 0.690401 | ||||||||
\(179\) | 13.8167 | 1.03271 | 0.516353 | − | 0.856376i | \(-0.327289\pi\) | ||||
0.516353 | + | 0.856376i | \(0.327289\pi\) | |||||||
\(180\) | 18.2111 | 1.35738 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 3.39445 | 0.251613 | ||||||||
\(183\) | −24.8167 | −1.83450 | ||||||||
\(184\) | −3.90833 | −0.288126 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | −13.8167 | −1.01037 | ||||||||
\(188\) | 4.60555 | 0.335894 | ||||||||
\(189\) | −42.2389 | −3.07242 | ||||||||
\(190\) | −4.60555 | −0.334122 | ||||||||
\(191\) | 5.51388 | 0.398970 | 0.199485 | − | 0.979901i | \(-0.436073\pi\) | ||||
0.199485 | + | 0.979901i | \(0.436073\pi\) | |||||||
\(192\) | 3.30278 | 0.238357 | ||||||||
\(193\) | 4.00000 | 0.287926 | 0.143963 | − | 0.989583i | \(-0.454015\pi\) | ||||
0.143963 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(194\) | 16.4222 | 1.17905 | ||||||||
\(195\) | −9.90833 | −0.709550 | ||||||||
\(196\) | −0.211103 | −0.0150788 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | −18.2111 | −1.29421 | ||||||||
\(199\) | −26.4222 | −1.87302 | −0.936510 | − | 0.350640i | \(-0.885964\pi\) | ||||
−0.936510 | + | 0.350640i | \(0.885964\pi\) | |||||||
\(200\) | 0.302776 | 0.0214095 | ||||||||
\(201\) | −11.6056 | −0.818592 | ||||||||
\(202\) | −12.4222 | −0.874023 | ||||||||
\(203\) | −10.1833 | −0.714731 | ||||||||
\(204\) | 19.8167 | 1.38744 | ||||||||
\(205\) | 22.8167 | 1.59358 | ||||||||
\(206\) | 0.302776 | 0.0210954 | ||||||||
\(207\) | −30.9083 | −2.14828 | ||||||||
\(208\) | −1.30278 | −0.0903312 | ||||||||
\(209\) | 4.60555 | 0.318573 | ||||||||
\(210\) | −19.8167 | −1.36748 | ||||||||
\(211\) | 10.3028 | 0.709272 | 0.354636 | − | 0.935004i | \(-0.384605\pi\) | ||||
0.354636 | + | 0.935004i | \(0.384605\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 19.8167 | 1.35781 | ||||||||
\(214\) | 0.697224 | 0.0476613 | ||||||||
\(215\) | −1.39445 | −0.0951006 | ||||||||
\(216\) | 16.2111 | 1.10303 | ||||||||
\(217\) | −0.788897 | −0.0535538 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | −40.6333 | −2.74574 | ||||||||
\(220\) | −5.30278 | −0.357513 | ||||||||
\(221\) | −7.81665 | −0.525805 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.81665 | −0.389512 | −0.194756 | − | 0.980852i | \(-0.562391\pi\) | ||||
−0.194756 | + | 0.980852i | \(0.562391\pi\) | |||||||
\(224\) | −2.60555 | −0.174091 | ||||||||
\(225\) | 2.39445 | 0.159630 | ||||||||
\(226\) | 3.21110 | 0.213599 | ||||||||
\(227\) | −13.8167 | −0.917044 | −0.458522 | − | 0.888683i | \(-0.651621\pi\) | ||||
−0.458522 | + | 0.888683i | \(0.651621\pi\) | |||||||
\(228\) | −6.60555 | −0.437463 | ||||||||
\(229\) | 24.6056 | 1.62598 | 0.812990 | − | 0.582277i | \(-0.197838\pi\) | ||||
0.812990 | + | 0.582277i | \(0.197838\pi\) | |||||||
\(230\) | −9.00000 | −0.593442 | ||||||||
\(231\) | 19.8167 | 1.30384 | ||||||||
\(232\) | 3.90833 | 0.256594 | ||||||||
\(233\) | 8.51388 | 0.557763 | 0.278881 | − | 0.960326i | \(-0.410036\pi\) | ||||
0.278881 | + | 0.960326i | \(0.410036\pi\) | |||||||
\(234\) | −10.3028 | −0.673514 | ||||||||
\(235\) | 10.6056 | 0.691830 | ||||||||
\(236\) | −10.6056 | −0.690363 | ||||||||
\(237\) | −30.1194 | −1.95647 | ||||||||
\(238\) | −15.6333 | −1.01336 | ||||||||
\(239\) | 17.5139 | 1.13288 | 0.566439 | − | 0.824103i | \(-0.308321\pi\) | ||||
0.566439 | + | 0.824103i | \(0.308321\pi\) | |||||||
\(240\) | 7.60555 | 0.490936 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | −5.69722 | −0.366231 | ||||||||
\(243\) | 49.8444 | 3.19752 | ||||||||
\(244\) | −7.51388 | −0.481027 | ||||||||
\(245\) | −0.486122 | −0.0310572 | ||||||||
\(246\) | 32.7250 | 2.08647 | ||||||||
\(247\) | 2.60555 | 0.165787 | ||||||||
\(248\) | 0.302776 | 0.0192263 | ||||||||
\(249\) | 9.21110 | 0.583730 | ||||||||
\(250\) | −10.8167 | −0.684105 | ||||||||
\(251\) | 21.2111 | 1.33883 | 0.669416 | − | 0.742887i | \(-0.266544\pi\) | ||||
0.669416 | + | 0.742887i | \(0.266544\pi\) | |||||||
\(252\) | −20.6056 | −1.29803 | ||||||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | −19.2111 | −1.20541 | ||||||||
\(255\) | 45.6333 | 2.85767 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.21110 | −0.200303 | −0.100152 | − | 0.994972i | \(-0.531933\pi\) | ||||
−0.100152 | + | 0.994972i | \(0.531933\pi\) | |||||||
\(258\) | −2.00000 | −0.124515 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.00000 | −0.186052 | ||||||||
\(261\) | 30.9083 | 1.91318 | ||||||||
\(262\) | −10.6056 | −0.655213 | ||||||||
\(263\) | 13.8167 | 0.851971 | 0.425986 | − | 0.904730i | \(-0.359927\pi\) | ||||
0.425986 | + | 0.904730i | \(0.359927\pi\) | |||||||
\(264\) | −7.60555 | −0.468089 | ||||||||
\(265\) | −13.8167 | −0.848750 | ||||||||
\(266\) | 5.21110 | 0.319513 | ||||||||
\(267\) | 30.4222 | 1.86181 | ||||||||
\(268\) | −3.51388 | −0.214644 | ||||||||
\(269\) | −21.2111 | −1.29326 | −0.646632 | − | 0.762802i | \(-0.723823\pi\) | ||||
−0.646632 | + | 0.762802i | \(0.723823\pi\) | |||||||
\(270\) | 37.3305 | 2.27186 | ||||||||
\(271\) | −22.4222 | −1.36205 | −0.681026 | − | 0.732259i | \(-0.738466\pi\) | ||||
−0.681026 | + | 0.732259i | \(0.738466\pi\) | |||||||
\(272\) | 6.00000 | 0.363803 | ||||||||
\(273\) | 11.2111 | 0.678527 | ||||||||
\(274\) | 0.908327 | 0.0548740 | ||||||||
\(275\) | −0.697224 | −0.0420442 | ||||||||
\(276\) | −12.9083 | −0.776990 | ||||||||
\(277\) | −0.119429 | −0.00717582 | −0.00358791 | − | 0.999994i | \(-0.501142\pi\) | ||||
−0.00358791 | + | 0.999994i | \(0.501142\pi\) | |||||||
\(278\) | −1.90833 | −0.114454 | ||||||||
\(279\) | 2.39445 | 0.143352 | ||||||||
\(280\) | −6.00000 | −0.358569 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 15.2111 | 0.905808 | ||||||||
\(283\) | −24.6056 | −1.46265 | −0.731324 | − | 0.682030i | \(-0.761097\pi\) | ||||
−0.731324 | + | 0.682030i | \(0.761097\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | −15.2111 | −0.901028 | ||||||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | −25.8167 | −1.52391 | ||||||||
\(288\) | 7.90833 | 0.466003 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 9.00000 | 0.528498 | ||||||||
\(291\) | 54.2389 | 3.17954 | ||||||||
\(292\) | −12.3028 | −0.719965 | ||||||||
\(293\) | 11.0278 | 0.644248 | 0.322124 | − | 0.946697i | \(-0.395603\pi\) | ||||
0.322124 | + | 0.946697i | \(0.395603\pi\) | |||||||
\(294\) | −0.697224 | −0.0406630 | ||||||||
\(295\) | −24.4222 | −1.42192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −37.3305 | −2.16614 | ||||||||
\(298\) | 19.8167 | 1.14795 | ||||||||
\(299\) | 5.09167 | 0.294459 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 1.57779 | 0.0909426 | ||||||||
\(302\) | −20.6056 | −1.18572 | ||||||||
\(303\) | −41.0278 | −2.35698 | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | −17.3028 | −0.990754 | ||||||||
\(306\) | 47.4500 | 2.71253 | ||||||||
\(307\) | 17.9083 | 1.02208 | 0.511041 | − | 0.859556i | \(-0.329260\pi\) | ||||
0.511041 | + | 0.859556i | \(0.329260\pi\) | |||||||
\(308\) | 6.00000 | 0.341882 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0.697224 | 0.0395997 | ||||||||
\(311\) | −15.9083 | −0.902078 | −0.451039 | − | 0.892504i | \(-0.648947\pi\) | ||||
−0.451039 | + | 0.892504i | \(0.648947\pi\) | |||||||
\(312\) | −4.30278 | −0.243597 | ||||||||
\(313\) | 9.02776 | 0.510279 | 0.255139 | − | 0.966904i | \(-0.417879\pi\) | ||||
0.255139 | + | 0.966904i | \(0.417879\pi\) | |||||||
\(314\) | −7.21110 | −0.406946 | ||||||||
\(315\) | −47.4500 | −2.67350 | ||||||||
\(316\) | −9.11943 | −0.513008 | ||||||||
\(317\) | 9.21110 | 0.517347 | 0.258674 | − | 0.965965i | \(-0.416715\pi\) | ||||
0.258674 | + | 0.965965i | \(0.416715\pi\) | |||||||
\(318\) | −19.8167 | −1.11126 | ||||||||
\(319\) | −9.00000 | −0.503903 | ||||||||
\(320\) | 2.30278 | 0.128729 | ||||||||
\(321\) | 2.30278 | 0.128528 | ||||||||
\(322\) | 10.1833 | 0.567496 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 29.8167 | 1.65648 | ||||||||
\(325\) | −0.394449 | −0.0218801 | ||||||||
\(326\) | −8.42221 | −0.466463 | ||||||||
\(327\) | −6.60555 | −0.365288 | ||||||||
\(328\) | 9.90833 | 0.547096 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | −17.5139 | −0.964107 | ||||||||
\(331\) | 13.2111 | 0.726148 | 0.363074 | − | 0.931760i | \(-0.381727\pi\) | ||||
0.363074 | + | 0.931760i | \(0.381727\pi\) | |||||||
\(332\) | 2.78890 | 0.153061 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.51388 | 0.301706 | ||||||||
\(335\) | −8.09167 | −0.442095 | ||||||||
\(336\) | −8.60555 | −0.469471 | ||||||||
\(337\) | 6.11943 | 0.333347 | 0.166673 | − | 0.986012i | \(-0.446697\pi\) | ||||
0.166673 | + | 0.986012i | \(0.446697\pi\) | |||||||
\(338\) | −11.3028 | −0.614790 | ||||||||
\(339\) | 10.6056 | 0.576014 | ||||||||
\(340\) | 13.8167 | 0.749313 | ||||||||
\(341\) | −0.697224 | −0.0377568 | ||||||||
\(342\) | −15.8167 | −0.855267 | ||||||||
\(343\) | 18.7889 | 1.01451 | ||||||||
\(344\) | −0.605551 | −0.0326491 | ||||||||
\(345\) | −29.7250 | −1.60034 | ||||||||
\(346\) | −8.78890 | −0.472494 | ||||||||
\(347\) | −10.1833 | −0.546671 | −0.273335 | − | 0.961919i | \(-0.588127\pi\) | ||||
−0.273335 | + | 0.961919i | \(0.588127\pi\) | |||||||
\(348\) | 12.9083 | 0.691959 | ||||||||
\(349\) | 28.2389 | 1.51159 | 0.755796 | − | 0.654807i | \(-0.227250\pi\) | ||||
0.755796 | + | 0.654807i | \(0.227250\pi\) | |||||||
\(350\) | −0.788897 | −0.0421683 | ||||||||
\(351\) | −21.1194 | −1.12727 | ||||||||
\(352\) | −2.30278 | −0.122738 | ||||||||
\(353\) | −10.1833 | −0.542005 | −0.271002 | − | 0.962579i | \(-0.587355\pi\) | ||||
−0.271002 | + | 0.962579i | \(0.587355\pi\) | |||||||
\(354\) | −35.0278 | −1.86170 | ||||||||
\(355\) | 13.8167 | 0.733312 | ||||||||
\(356\) | 9.21110 | 0.488187 | ||||||||
\(357\) | −51.6333 | −2.73272 | ||||||||
\(358\) | 13.8167 | 0.730233 | ||||||||
\(359\) | 3.21110 | 0.169476 | 0.0847378 | − | 0.996403i | \(-0.472995\pi\) | ||||
0.0847378 | + | 0.996403i | \(0.472995\pi\) | |||||||
\(360\) | 18.2111 | 0.959809 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 20.0000 | 1.05118 | ||||||||
\(363\) | −18.8167 | −0.987618 | ||||||||
\(364\) | 3.39445 | 0.177917 | ||||||||
\(365\) | −28.3305 | −1.48289 | ||||||||
\(366\) | −24.8167 | −1.29719 | ||||||||
\(367\) | 3.81665 | 0.199228 | 0.0996139 | − | 0.995026i | \(-0.468239\pi\) | ||||
0.0996139 | + | 0.995026i | \(0.468239\pi\) | |||||||
\(368\) | −3.90833 | −0.203736 | ||||||||
\(369\) | 78.3583 | 4.07917 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.6333 | 0.811641 | ||||||||
\(372\) | 1.00000 | 0.0518476 | ||||||||
\(373\) | −17.8167 | −0.922511 | −0.461256 | − | 0.887267i | \(-0.652601\pi\) | ||||
−0.461256 | + | 0.887267i | \(0.652601\pi\) | |||||||
\(374\) | −13.8167 | −0.714442 | ||||||||
\(375\) | −35.7250 | −1.84483 | ||||||||
\(376\) | 4.60555 | 0.237513 | ||||||||
\(377\) | −5.09167 | −0.262235 | ||||||||
\(378\) | −42.2389 | −2.17253 | ||||||||
\(379\) | 24.3305 | 1.24978 | 0.624888 | − | 0.780715i | \(-0.285145\pi\) | ||||
0.624888 | + | 0.780715i | \(0.285145\pi\) | |||||||
\(380\) | −4.60555 | −0.236260 | ||||||||
\(381\) | −63.4500 | −3.25064 | ||||||||
\(382\) | 5.51388 | 0.282115 | ||||||||
\(383\) | 36.8444 | 1.88266 | 0.941331 | − | 0.337486i | \(-0.109576\pi\) | ||||
0.941331 | + | 0.337486i | \(0.109576\pi\) | |||||||
\(384\) | 3.30278 | 0.168544 | ||||||||
\(385\) | 13.8167 | 0.704162 | ||||||||
\(386\) | 4.00000 | 0.203595 | ||||||||
\(387\) | −4.78890 | −0.243433 | ||||||||
\(388\) | 16.4222 | 0.833711 | ||||||||
\(389\) | 37.1194 | 1.88203 | 0.941015 | − | 0.338365i | \(-0.109874\pi\) | ||||
0.941015 | + | 0.338365i | \(0.109874\pi\) | |||||||
\(390\) | −9.90833 | −0.501728 | ||||||||
\(391\) | −23.4500 | −1.18592 | ||||||||
\(392\) | −0.211103 | −0.0106623 | ||||||||
\(393\) | −35.0278 | −1.76692 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | −21.0000 | −1.05662 | ||||||||
\(396\) | −18.2111 | −0.915142 | ||||||||
\(397\) | 6.18335 | 0.310333 | 0.155167 | − | 0.987888i | \(-0.450409\pi\) | ||||
0.155167 | + | 0.987888i | \(0.450409\pi\) | |||||||
\(398\) | −26.4222 | −1.32443 | ||||||||
\(399\) | 17.2111 | 0.861633 | ||||||||
\(400\) | 0.302776 | 0.0151388 | ||||||||
\(401\) | 7.81665 | 0.390345 | 0.195173 | − | 0.980769i | \(-0.437473\pi\) | ||||
0.195173 | + | 0.980769i | \(0.437473\pi\) | |||||||
\(402\) | −11.6056 | −0.578832 | ||||||||
\(403\) | −0.394449 | −0.0196489 | ||||||||
\(404\) | −12.4222 | −0.618028 | ||||||||
\(405\) | 68.6611 | 3.41180 | ||||||||
\(406\) | −10.1833 | −0.505391 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 19.8167 | 0.981071 | ||||||||
\(409\) | −31.0278 | −1.53422 | −0.767112 | − | 0.641513i | \(-0.778307\pi\) | ||||
−0.767112 | + | 0.641513i | \(0.778307\pi\) | |||||||
\(410\) | 22.8167 | 1.12683 | ||||||||
\(411\) | 3.00000 | 0.147979 | ||||||||
\(412\) | 0.302776 | 0.0149167 | ||||||||
\(413\) | 27.6333 | 1.35975 | ||||||||
\(414\) | −30.9083 | −1.51906 | ||||||||
\(415\) | 6.42221 | 0.315254 | ||||||||
\(416\) | −1.30278 | −0.0638738 | ||||||||
\(417\) | −6.30278 | −0.308648 | ||||||||
\(418\) | 4.60555 | 0.225265 | ||||||||
\(419\) | 36.1472 | 1.76591 | 0.882953 | − | 0.469462i | \(-0.155552\pi\) | ||||
0.882953 | + | 0.469462i | \(0.155552\pi\) | |||||||
\(420\) | −19.8167 | −0.966954 | ||||||||
\(421\) | 3.72498 | 0.181544 | 0.0907722 | − | 0.995872i | \(-0.471066\pi\) | ||||
0.0907722 | + | 0.995872i | \(0.471066\pi\) | |||||||
\(422\) | 10.3028 | 0.501531 | ||||||||
\(423\) | 36.4222 | 1.77091 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 1.81665 | 0.0881207 | ||||||||
\(426\) | 19.8167 | 0.960120 | ||||||||
\(427\) | 19.5778 | 0.947436 | ||||||||
\(428\) | 0.697224 | 0.0337016 | ||||||||
\(429\) | 9.90833 | 0.478379 | ||||||||
\(430\) | −1.39445 | −0.0672463 | ||||||||
\(431\) | −9.21110 | −0.443683 | −0.221842 | − | 0.975083i | \(-0.571207\pi\) | ||||
−0.221842 | + | 0.975083i | \(0.571207\pi\) | |||||||
\(432\) | 16.2111 | 0.779957 | ||||||||
\(433\) | 34.9361 | 1.67892 | 0.839461 | − | 0.543421i | \(-0.182871\pi\) | ||||
0.839461 | + | 0.543421i | \(0.182871\pi\) | |||||||
\(434\) | −0.788897 | −0.0378683 | ||||||||
\(435\) | 29.7250 | 1.42520 | ||||||||
\(436\) | −2.00000 | −0.0957826 | ||||||||
\(437\) | 7.81665 | 0.373921 | ||||||||
\(438\) | −40.6333 | −1.94153 | ||||||||
\(439\) | −30.3305 | −1.44760 | −0.723799 | − | 0.690011i | \(-0.757606\pi\) | ||||
−0.723799 | + | 0.690011i | \(0.757606\pi\) | |||||||
\(440\) | −5.30278 | −0.252800 | ||||||||
\(441\) | −1.66947 | −0.0794985 | ||||||||
\(442\) | −7.81665 | −0.371800 | ||||||||
\(443\) | 32.7250 | 1.55481 | 0.777405 | − | 0.629000i | \(-0.216535\pi\) | ||||
0.777405 | + | 0.629000i | \(0.216535\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.2111 | 1.00550 | ||||||||
\(446\) | −5.81665 | −0.275427 | ||||||||
\(447\) | 65.4500 | 3.09568 | ||||||||
\(448\) | −2.60555 | −0.123101 | ||||||||
\(449\) | 15.2111 | 0.717856 | 0.358928 | − | 0.933365i | \(-0.383142\pi\) | ||||
0.358928 | + | 0.933365i | \(0.383142\pi\) | |||||||
\(450\) | 2.39445 | 0.112875 | ||||||||
\(451\) | −22.8167 | −1.07439 | ||||||||
\(452\) | 3.21110 | 0.151038 | ||||||||
\(453\) | −68.0555 | −3.19753 | ||||||||
\(454\) | −13.8167 | −0.648448 | ||||||||
\(455\) | 7.81665 | 0.366450 | ||||||||
\(456\) | −6.60555 | −0.309333 | ||||||||
\(457\) | 2.60555 | 0.121883 | 0.0609413 | − | 0.998141i | \(-0.480590\pi\) | ||||
0.0609413 | + | 0.998141i | \(0.480590\pi\) | |||||||
\(458\) | 24.6056 | 1.14974 | ||||||||
\(459\) | 97.2666 | 4.54002 | ||||||||
\(460\) | −9.00000 | −0.419627 | ||||||||
\(461\) | −12.4222 | −0.578560 | −0.289280 | − | 0.957245i | \(-0.593416\pi\) | ||||
−0.289280 | + | 0.957245i | \(0.593416\pi\) | |||||||
\(462\) | 19.8167 | 0.921954 | ||||||||
\(463\) | −26.6972 | −1.24073 | −0.620363 | − | 0.784315i | \(-0.713015\pi\) | ||||
−0.620363 | + | 0.784315i | \(0.713015\pi\) | |||||||
\(464\) | 3.90833 | 0.181440 | ||||||||
\(465\) | 2.30278 | 0.106789 | ||||||||
\(466\) | 8.51388 | 0.394398 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | −10.3028 | −0.476246 | ||||||||
\(469\) | 9.15559 | 0.422766 | ||||||||
\(470\) | 10.6056 | 0.489198 | ||||||||
\(471\) | −23.8167 | −1.09741 | ||||||||
\(472\) | −10.6056 | −0.488160 | ||||||||
\(473\) | 1.39445 | 0.0641168 | ||||||||
\(474\) | −30.1194 | −1.38343 | ||||||||
\(475\) | −0.605551 | −0.0277846 | ||||||||
\(476\) | −15.6333 | −0.716551 | ||||||||
\(477\) | −47.4500 | −2.17258 | ||||||||
\(478\) | 17.5139 | 0.801066 | ||||||||
\(479\) | 13.1194 | 0.599442 | 0.299721 | − | 0.954027i | \(-0.403106\pi\) | ||||
0.299721 | + | 0.954027i | \(0.403106\pi\) | |||||||
\(480\) | 7.60555 | 0.347144 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −8.00000 | −0.364390 | ||||||||
\(483\) | 33.6333 | 1.53037 | ||||||||
\(484\) | −5.69722 | −0.258965 | ||||||||
\(485\) | 37.8167 | 1.71717 | ||||||||
\(486\) | 49.8444 | 2.26099 | ||||||||
\(487\) | 37.2111 | 1.68620 | 0.843098 | − | 0.537760i | \(-0.180729\pi\) | ||||
0.843098 | + | 0.537760i | \(0.180729\pi\) | |||||||
\(488\) | −7.51388 | −0.340137 | ||||||||
\(489\) | −27.8167 | −1.25791 | ||||||||
\(490\) | −0.486122 | −0.0219607 | ||||||||
\(491\) | 17.7250 | 0.799917 | 0.399959 | − | 0.916533i | \(-0.369025\pi\) | ||||
0.399959 | + | 0.916533i | \(0.369025\pi\) | |||||||
\(492\) | 32.7250 | 1.47536 | ||||||||
\(493\) | 23.4500 | 1.05613 | ||||||||
\(494\) | 2.60555 | 0.117229 | ||||||||
\(495\) | −41.9361 | −1.88489 | ||||||||
\(496\) | 0.302776 | 0.0135950 | ||||||||
\(497\) | −15.6333 | −0.701250 | ||||||||
\(498\) | 9.21110 | 0.412759 | ||||||||
\(499\) | 42.2389 | 1.89087 | 0.945436 | − | 0.325809i | \(-0.105637\pi\) | ||||
0.945436 | + | 0.325809i | \(0.105637\pi\) | |||||||
\(500\) | −10.8167 | −0.483735 | ||||||||
\(501\) | 18.2111 | 0.813612 | ||||||||
\(502\) | 21.2111 | 0.946698 | ||||||||
\(503\) | 6.48612 | 0.289202 | 0.144601 | − | 0.989490i | \(-0.453810\pi\) | ||||
0.144601 | + | 0.989490i | \(0.453810\pi\) | |||||||
\(504\) | −20.6056 | −0.917844 | ||||||||
\(505\) | −28.6056 | −1.27293 | ||||||||
\(506\) | 9.00000 | 0.400099 | ||||||||
\(507\) | −37.3305 | −1.65791 | ||||||||
\(508\) | −19.2111 | −0.852355 | ||||||||
\(509\) | −4.18335 | −0.185424 | −0.0927118 | − | 0.995693i | \(-0.529554\pi\) | ||||
−0.0927118 | + | 0.995693i | \(0.529554\pi\) | |||||||
\(510\) | 45.6333 | 2.02068 | ||||||||
\(511\) | 32.0555 | 1.41805 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −32.4222 | −1.43148 | ||||||||
\(514\) | −3.21110 | −0.141636 | ||||||||
\(515\) | 0.697224 | 0.0307234 | ||||||||
\(516\) | −2.00000 | −0.0880451 | ||||||||
\(517\) | −10.6056 | −0.466432 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.0278 | −1.27418 | ||||||||
\(520\) | −3.00000 | −0.131559 | ||||||||
\(521\) | 33.6333 | 1.47350 | 0.736751 | − | 0.676164i | \(-0.236359\pi\) | ||||
0.736751 | + | 0.676164i | \(0.236359\pi\) | |||||||
\(522\) | 30.9083 | 1.35282 | ||||||||
\(523\) | 18.2389 | 0.797530 | 0.398765 | − | 0.917053i | \(-0.369439\pi\) | ||||
0.398765 | + | 0.917053i | \(0.369439\pi\) | |||||||
\(524\) | −10.6056 | −0.463306 | ||||||||
\(525\) | −2.60555 | −0.113716 | ||||||||
\(526\) | 13.8167 | 0.602435 | ||||||||
\(527\) | 1.81665 | 0.0791347 | ||||||||
\(528\) | −7.60555 | −0.330989 | ||||||||
\(529\) | −7.72498 | −0.335869 | ||||||||
\(530\) | −13.8167 | −0.600157 | ||||||||
\(531\) | −83.8722 | −3.63974 | ||||||||
\(532\) | 5.21110 | 0.225930 | ||||||||
\(533\) | −12.9083 | −0.559122 | ||||||||
\(534\) | 30.4222 | 1.31650 | ||||||||
\(535\) | 1.60555 | 0.0694140 | ||||||||
\(536\) | −3.51388 | −0.151776 | ||||||||
\(537\) | 45.6333 | 1.96922 | ||||||||
\(538\) | −21.2111 | −0.914476 | ||||||||
\(539\) | 0.486122 | 0.0209387 | ||||||||
\(540\) | 37.3305 | 1.60645 | ||||||||
\(541\) | −25.9361 | −1.11508 | −0.557540 | − | 0.830150i | \(-0.688255\pi\) | ||||
−0.557540 | + | 0.830150i | \(0.688255\pi\) | |||||||
\(542\) | −22.4222 | −0.963116 | ||||||||
\(543\) | 66.0555 | 2.83471 | ||||||||
\(544\) | 6.00000 | 0.257248 | ||||||||
\(545\) | −4.60555 | −0.197280 | ||||||||
\(546\) | 11.2111 | 0.479791 | ||||||||
\(547\) | 20.6056 | 0.881030 | 0.440515 | − | 0.897745i | \(-0.354796\pi\) | ||||
0.440515 | + | 0.897745i | \(0.354796\pi\) | |||||||
\(548\) | 0.908327 | 0.0388018 | ||||||||
\(549\) | −59.4222 | −2.53608 | ||||||||
\(550\) | −0.697224 | −0.0297297 | ||||||||
\(551\) | −7.81665 | −0.333001 | ||||||||
\(552\) | −12.9083 | −0.549415 | ||||||||
\(553\) | 23.7611 | 1.01043 | ||||||||
\(554\) | −0.119429 | −0.00507407 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.90833 | −0.0809311 | ||||||||
\(557\) | −11.5139 | −0.487859 | −0.243929 | − | 0.969793i | \(-0.578436\pi\) | ||||
−0.243929 | + | 0.969793i | \(0.578436\pi\) | |||||||
\(558\) | 2.39445 | 0.101365 | ||||||||
\(559\) | 0.788897 | 0.0333668 | ||||||||
\(560\) | −6.00000 | −0.253546 | ||||||||
\(561\) | −45.6333 | −1.92664 | ||||||||
\(562\) | 12.0000 | 0.506189 | ||||||||
\(563\) | 28.0555 | 1.18240 | 0.591199 | − | 0.806525i | \(-0.298655\pi\) | ||||
0.591199 | + | 0.806525i | \(0.298655\pi\) | |||||||
\(564\) | 15.2111 | 0.640503 | ||||||||
\(565\) | 7.39445 | 0.311087 | ||||||||
\(566\) | −24.6056 | −1.03425 | ||||||||
\(567\) | −77.6888 | −3.26262 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | −18.4222 | −0.772299 | −0.386150 | − | 0.922436i | \(-0.626195\pi\) | ||||
−0.386150 | + | 0.922436i | \(0.626195\pi\) | |||||||
\(570\) | −15.2111 | −0.637123 | ||||||||
\(571\) | −16.6972 | −0.698757 | −0.349379 | − | 0.936982i | \(-0.613607\pi\) | ||||
−0.349379 | + | 0.936982i | \(0.613607\pi\) | |||||||
\(572\) | 3.00000 | 0.125436 | ||||||||
\(573\) | 18.2111 | 0.760780 | ||||||||
\(574\) | −25.8167 | −1.07757 | ||||||||
\(575\) | −1.18335 | −0.0493489 | ||||||||
\(576\) | 7.90833 | 0.329514 | ||||||||
\(577\) | −22.2389 | −0.925816 | −0.462908 | − | 0.886406i | \(-0.653194\pi\) | ||||
−0.462908 | + | 0.886406i | \(0.653194\pi\) | |||||||
\(578\) | 19.0000 | 0.790296 | ||||||||
\(579\) | 13.2111 | 0.549035 | ||||||||
\(580\) | 9.00000 | 0.373705 | ||||||||
\(581\) | −7.26662 | −0.301470 | ||||||||
\(582\) | 54.2389 | 2.24827 | ||||||||
\(583\) | 13.8167 | 0.572227 | ||||||||
\(584\) | −12.3028 | −0.509092 | ||||||||
\(585\) | −23.7250 | −0.980907 | ||||||||
\(586\) | 11.0278 | 0.455552 | ||||||||
\(587\) | 45.6333 | 1.88349 | 0.941744 | − | 0.336330i | \(-0.109186\pi\) | ||||
0.941744 | + | 0.336330i | \(0.109186\pi\) | |||||||
\(588\) | −0.697224 | −0.0287530 | ||||||||
\(589\) | −0.605551 | −0.0249513 | ||||||||
\(590\) | −24.4222 | −1.00545 | ||||||||
\(591\) | −19.8167 | −0.815148 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.4861 | 0.759134 | 0.379567 | − | 0.925164i | \(-0.376073\pi\) | ||||
0.379567 | + | 0.925164i | \(0.376073\pi\) | |||||||
\(594\) | −37.3305 | −1.53169 | ||||||||
\(595\) | −36.0000 | −1.47586 | ||||||||
\(596\) | 19.8167 | 0.811722 | ||||||||
\(597\) | −87.2666 | −3.57158 | ||||||||
\(598\) | 5.09167 | 0.208214 | ||||||||
\(599\) | −20.7889 | −0.849411 | −0.424706 | − | 0.905331i | \(-0.639622\pi\) | ||||
−0.424706 | + | 0.905331i | \(0.639622\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −24.3028 | −0.991331 | −0.495665 | − | 0.868514i | \(-0.665076\pi\) | ||||
−0.495665 | + | 0.868514i | \(0.665076\pi\) | |||||||
\(602\) | 1.57779 | 0.0643061 | ||||||||
\(603\) | −27.7889 | −1.13165 | ||||||||
\(604\) | −20.6056 | −0.838428 | ||||||||
\(605\) | −13.1194 | −0.533381 | ||||||||
\(606\) | −41.0278 | −1.66664 | ||||||||
\(607\) | 13.4861 | 0.547385 | 0.273692 | − | 0.961817i | \(-0.411755\pi\) | ||||
0.273692 | + | 0.961817i | \(0.411755\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | −33.6333 | −1.36289 | ||||||||
\(610\) | −17.3028 | −0.700569 | ||||||||
\(611\) | −6.00000 | −0.242734 | ||||||||
\(612\) | 47.4500 | 1.91805 | ||||||||
\(613\) | −29.8167 | −1.20428 | −0.602142 | − | 0.798389i | \(-0.705686\pi\) | ||||
−0.602142 | + | 0.798389i | \(0.705686\pi\) | |||||||
\(614\) | 17.9083 | 0.722721 | ||||||||
\(615\) | 75.3583 | 3.03874 | ||||||||
\(616\) | 6.00000 | 0.241747 | ||||||||
\(617\) | −42.5694 | −1.71378 | −0.856890 | − | 0.515500i | \(-0.827606\pi\) | ||||
−0.856890 | + | 0.515500i | \(0.827606\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −6.30278 | −0.253330 | −0.126665 | − | 0.991946i | \(-0.540427\pi\) | ||||
−0.126665 | + | 0.991946i | \(0.540427\pi\) | |||||||
\(620\) | 0.697224 | 0.0280012 | ||||||||
\(621\) | −63.3583 | −2.54248 | ||||||||
\(622\) | −15.9083 | −0.637866 | ||||||||
\(623\) | −24.0000 | −0.961540 | ||||||||
\(624\) | −4.30278 | −0.172249 | ||||||||
\(625\) | −26.4222 | −1.05689 | ||||||||
\(626\) | 9.02776 | 0.360822 | ||||||||
\(627\) | 15.2111 | 0.607473 | ||||||||
\(628\) | −7.21110 | −0.287754 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −47.4500 | −1.89045 | ||||||||
\(631\) | −14.6972 | −0.585087 | −0.292544 | − | 0.956252i | \(-0.594502\pi\) | ||||
−0.292544 | + | 0.956252i | \(0.594502\pi\) | |||||||
\(632\) | −9.11943 | −0.362751 | ||||||||
\(633\) | 34.0278 | 1.35248 | ||||||||
\(634\) | 9.21110 | 0.365820 | ||||||||
\(635\) | −44.2389 | −1.75557 | ||||||||
\(636\) | −19.8167 | −0.785781 | ||||||||
\(637\) | 0.275019 | 0.0108967 | ||||||||
\(638\) | −9.00000 | −0.356313 | ||||||||
\(639\) | 47.4500 | 1.87709 | ||||||||
\(640\) | 2.30278 | 0.0910252 | ||||||||
\(641\) | −20.5139 | −0.810249 | −0.405125 | − | 0.914261i | \(-0.632772\pi\) | ||||
−0.405125 | + | 0.914261i | \(0.632772\pi\) | |||||||
\(642\) | 2.30278 | 0.0908833 | ||||||||
\(643\) | 8.18335 | 0.322720 | 0.161360 | − | 0.986896i | \(-0.448412\pi\) | ||||
0.161360 | + | 0.986896i | \(0.448412\pi\) | |||||||
\(644\) | 10.1833 | 0.401280 | ||||||||
\(645\) | −4.60555 | −0.181343 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | −20.9361 | −0.823082 | −0.411541 | − | 0.911391i | \(-0.635009\pi\) | ||||
−0.411541 | + | 0.911391i | \(0.635009\pi\) | |||||||
\(648\) | 29.8167 | 1.17131 | ||||||||
\(649\) | 24.4222 | 0.958655 | ||||||||
\(650\) | −0.394449 | −0.0154716 | ||||||||
\(651\) | −2.60555 | −0.102120 | ||||||||
\(652\) | −8.42221 | −0.329839 | ||||||||
\(653\) | 3.90833 | 0.152945 | 0.0764723 | − | 0.997072i | \(-0.475634\pi\) | ||||
0.0764723 | + | 0.997072i | \(0.475634\pi\) | |||||||
\(654\) | −6.60555 | −0.258297 | ||||||||
\(655\) | −24.4222 | −0.954255 | ||||||||
\(656\) | 9.90833 | 0.386855 | ||||||||
\(657\) | −97.2944 | −3.79581 | ||||||||
\(658\) | −12.0000 | −0.467809 | ||||||||
\(659\) | −16.8806 | −0.657574 | −0.328787 | − | 0.944404i | \(-0.606640\pi\) | ||||
−0.328787 | + | 0.944404i | \(0.606640\pi\) | |||||||
\(660\) | −17.5139 | −0.681727 | ||||||||
\(661\) | 30.5139 | 1.18685 | 0.593426 | − | 0.804888i | \(-0.297775\pi\) | ||||
0.593426 | + | 0.804888i | \(0.297775\pi\) | |||||||
\(662\) | 13.2111 | 0.513464 | ||||||||
\(663\) | −25.8167 | −1.00264 | ||||||||
\(664\) | 2.78890 | 0.108230 | ||||||||
\(665\) | 12.0000 | 0.465340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.2750 | −0.591451 | ||||||||
\(668\) | 5.51388 | 0.213338 | ||||||||
\(669\) | −19.2111 | −0.742744 | ||||||||
\(670\) | −8.09167 | −0.312609 | ||||||||
\(671\) | 17.3028 | 0.667966 | ||||||||
\(672\) | −8.60555 | −0.331966 | ||||||||
\(673\) | 20.6972 | 0.797819 | 0.398910 | − | 0.916990i | \(-0.369389\pi\) | ||||
0.398910 | + | 0.916990i | \(0.369389\pi\) | |||||||
\(674\) | 6.11943 | 0.235712 | ||||||||
\(675\) | 4.90833 | 0.188922 | ||||||||
\(676\) | −11.3028 | −0.434722 | ||||||||
\(677\) | 14.2389 | 0.547244 | 0.273622 | − | 0.961837i | \(-0.411778\pi\) | ||||
0.273622 | + | 0.961837i | \(0.411778\pi\) | |||||||
\(678\) | 10.6056 | 0.407304 | ||||||||
\(679\) | −42.7889 | −1.64209 | ||||||||
\(680\) | 13.8167 | 0.529844 | ||||||||
\(681\) | −45.6333 | −1.74867 | ||||||||
\(682\) | −0.697224 | −0.0266981 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | −15.8167 | −0.604765 | ||||||||
\(685\) | 2.09167 | 0.0799187 | ||||||||
\(686\) | 18.7889 | 0.717363 | ||||||||
\(687\) | 81.2666 | 3.10051 | ||||||||
\(688\) | −0.605551 | −0.0230864 | ||||||||
\(689\) | 7.81665 | 0.297791 | ||||||||
\(690\) | −29.7250 | −1.13161 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | −8.78890 | −0.334104 | ||||||||
\(693\) | 47.4500 | 1.80247 | ||||||||
\(694\) | −10.1833 | −0.386555 | ||||||||
\(695\) | −4.39445 | −0.166691 | ||||||||
\(696\) | 12.9083 | 0.489289 | ||||||||
\(697\) | 59.4500 | 2.25183 | ||||||||
\(698\) | 28.2389 | 1.06886 | ||||||||
\(699\) | 28.1194 | 1.06357 | ||||||||
\(700\) | −0.788897 | −0.0298175 | ||||||||
\(701\) | −40.1194 | −1.51529 | −0.757645 | − | 0.652667i | \(-0.773650\pi\) | ||||
−0.757645 | + | 0.652667i | \(0.773650\pi\) | |||||||
\(702\) | −21.1194 | −0.797101 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.30278 | −0.0867891 | ||||||||
\(705\) | 35.0278 | 1.31922 | ||||||||
\(706\) | −10.1833 | −0.383255 | ||||||||
\(707\) | 32.3667 | 1.21727 | ||||||||
\(708\) | −35.0278 | −1.31642 | ||||||||
\(709\) | 41.3305 | 1.55220 | 0.776100 | − | 0.630609i | \(-0.217195\pi\) | ||||
0.776100 | + | 0.630609i | \(0.217195\pi\) | |||||||
\(710\) | 13.8167 | 0.518530 | ||||||||
\(711\) | −72.1194 | −2.70469 | ||||||||
\(712\) | 9.21110 | 0.345201 | ||||||||
\(713\) | −1.18335 | −0.0443167 | ||||||||
\(714\) | −51.6333 | −1.93233 | ||||||||
\(715\) | 6.90833 | 0.258357 | ||||||||
\(716\) | 13.8167 | 0.516353 | ||||||||
\(717\) | 57.8444 | 2.16024 | ||||||||
\(718\) | 3.21110 | 0.119837 | ||||||||
\(719\) | −51.6333 | −1.92560 | −0.962799 | − | 0.270220i | \(-0.912904\pi\) | ||||
−0.962799 | + | 0.270220i | \(0.912904\pi\) | |||||||
\(720\) | 18.2111 | 0.678688 | ||||||||
\(721\) | −0.788897 | −0.0293801 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | −26.4222 | −0.982652 | ||||||||
\(724\) | 20.0000 | 0.743294 | ||||||||
\(725\) | 1.18335 | 0.0439484 | ||||||||
\(726\) | −18.8167 | −0.698352 | ||||||||
\(727\) | −19.0917 | −0.708071 | −0.354035 | − | 0.935232i | \(-0.615191\pi\) | ||||
−0.354035 | + | 0.935232i | \(0.615191\pi\) | |||||||
\(728\) | 3.39445 | 0.125807 | ||||||||
\(729\) | 75.1749 | 2.78426 | ||||||||
\(730\) | −28.3305 | −1.04856 | ||||||||
\(731\) | −3.63331 | −0.134383 | ||||||||
\(732\) | −24.8167 | −0.917250 | ||||||||
\(733\) | −13.6333 | −0.503558 | −0.251779 | − | 0.967785i | \(-0.581016\pi\) | ||||
−0.251779 | + | 0.967785i | \(0.581016\pi\) | |||||||
\(734\) | 3.81665 | 0.140875 | ||||||||
\(735\) | −1.60555 | −0.0592217 | ||||||||
\(736\) | −3.90833 | −0.144063 | ||||||||
\(737\) | 8.09167 | 0.298061 | ||||||||
\(738\) | 78.3583 | 2.88441 | ||||||||
\(739\) | −2.66947 | −0.0981980 | −0.0490990 | − | 0.998794i | \(-0.515635\pi\) | ||||
−0.0490990 | + | 0.998794i | \(0.515635\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.60555 | 0.316133 | ||||||||
\(742\) | 15.6333 | 0.573917 | ||||||||
\(743\) | −29.4500 | −1.08041 | −0.540207 | − | 0.841532i | \(-0.681654\pi\) | ||||
−0.540207 | + | 0.841532i | \(0.681654\pi\) | |||||||
\(744\) | 1.00000 | 0.0366618 | ||||||||
\(745\) | 45.6333 | 1.67188 | ||||||||
\(746\) | −17.8167 | −0.652314 | ||||||||
\(747\) | 22.0555 | 0.806969 | ||||||||
\(748\) | −13.8167 | −0.505187 | ||||||||
\(749\) | −1.81665 | −0.0663791 | ||||||||
\(750\) | −35.7250 | −1.30449 | ||||||||
\(751\) | 14.0000 | 0.510867 | 0.255434 | − | 0.966827i | \(-0.417782\pi\) | ||||
0.255434 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(752\) | 4.60555 | 0.167947 | ||||||||
\(753\) | 70.0555 | 2.55296 | ||||||||
\(754\) | −5.09167 | −0.185428 | ||||||||
\(755\) | −47.4500 | −1.72688 | ||||||||
\(756\) | −42.2389 | −1.53621 | ||||||||
\(757\) | −5.69722 | −0.207069 | −0.103535 | − | 0.994626i | \(-0.533015\pi\) | ||||
−0.103535 | + | 0.994626i | \(0.533015\pi\) | |||||||
\(758\) | 24.3305 | 0.883725 | ||||||||
\(759\) | 29.7250 | 1.07895 | ||||||||
\(760\) | −4.60555 | −0.167061 | ||||||||
\(761\) | 16.8806 | 0.611920 | 0.305960 | − | 0.952044i | \(-0.401023\pi\) | ||||
0.305960 | + | 0.952044i | \(0.401023\pi\) | |||||||
\(762\) | −63.4500 | −2.29855 | ||||||||
\(763\) | 5.21110 | 0.188655 | ||||||||
\(764\) | 5.51388 | 0.199485 | ||||||||
\(765\) | 109.267 | 3.95054 | ||||||||
\(766\) | 36.8444 | 1.33124 | ||||||||
\(767\) | 13.8167 | 0.498890 | ||||||||
\(768\) | 3.30278 | 0.119179 | ||||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | 13.8167 | 0.497918 | ||||||||
\(771\) | −10.6056 | −0.381950 | ||||||||
\(772\) | 4.00000 | 0.143963 | ||||||||
\(773\) | 22.0555 | 0.793282 | 0.396641 | − | 0.917974i | \(-0.370176\pi\) | ||||
0.396641 | + | 0.917974i | \(0.370176\pi\) | |||||||
\(774\) | −4.78890 | −0.172133 | ||||||||
\(775\) | 0.0916731 | 0.00329299 | ||||||||
\(776\) | 16.4222 | 0.589523 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.1194 | 1.33080 | ||||||||
\(779\) | −19.8167 | −0.710005 | ||||||||
\(780\) | −9.90833 | −0.354775 | ||||||||
\(781\) | −13.8167 | −0.494399 | ||||||||
\(782\) | −23.4500 | −0.838569 | ||||||||
\(783\) | 63.3583 | 2.26424 | ||||||||
\(784\) | −0.211103 | −0.00753938 | ||||||||
\(785\) | −16.6056 | −0.592678 | ||||||||
\(786\) | −35.0278 | −1.24940 | ||||||||
\(787\) | 10.7889 | 0.384583 | 0.192291 | − | 0.981338i | \(-0.438408\pi\) | ||||
0.192291 | + | 0.981338i | \(0.438408\pi\) | |||||||
\(788\) | −6.00000 | −0.213741 | ||||||||
\(789\) | 45.6333 | 1.62459 | ||||||||
\(790\) | −21.0000 | −0.747146 | ||||||||
\(791\) | −8.36669 | −0.297485 | ||||||||
\(792\) | −18.2111 | −0.647103 | ||||||||
\(793\) | 9.78890 | 0.347614 | ||||||||
\(794\) | 6.18335 | 0.219439 | ||||||||
\(795\) | −45.6333 | −1.61845 | ||||||||
\(796\) | −26.4222 | −0.936510 | ||||||||
\(797\) | −22.3305 | −0.790988 | −0.395494 | − | 0.918469i | \(-0.629427\pi\) | ||||
−0.395494 | + | 0.918469i | \(0.629427\pi\) | |||||||
\(798\) | 17.2111 | 0.609266 | ||||||||
\(799\) | 27.6333 | 0.977596 | ||||||||
\(800\) | 0.302776 | 0.0107047 | ||||||||
\(801\) | 72.8444 | 2.57383 | ||||||||
\(802\) | 7.81665 | 0.276016 | ||||||||
\(803\) | 28.3305 | 0.999763 | ||||||||
\(804\) | −11.6056 | −0.409296 | ||||||||
\(805\) | 23.4500 | 0.826503 | ||||||||
\(806\) | −0.394449 | −0.0138939 | ||||||||
\(807\) | −70.0555 | −2.46607 | ||||||||
\(808\) | −12.4222 | −0.437012 | ||||||||
\(809\) | 35.4500 | 1.24635 | 0.623177 | − | 0.782081i | \(-0.285842\pi\) | ||||
0.623177 | + | 0.782081i | \(0.285842\pi\) | |||||||
\(810\) | 68.6611 | 2.41250 | ||||||||
\(811\) | −7.14719 | −0.250972 | −0.125486 | − | 0.992095i | \(-0.540049\pi\) | ||||
−0.125486 | + | 0.992095i | \(0.540049\pi\) | |||||||
\(812\) | −10.1833 | −0.357365 | ||||||||
\(813\) | −74.0555 | −2.59724 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.3944 | −0.679358 | ||||||||
\(816\) | 19.8167 | 0.693722 | ||||||||
\(817\) | 1.21110 | 0.0423711 | ||||||||
\(818\) | −31.0278 | −1.08486 | ||||||||
\(819\) | 26.8444 | 0.938020 | ||||||||
\(820\) | 22.8167 | 0.796792 | ||||||||
\(821\) | −3.21110 | −0.112068 | −0.0560341 | − | 0.998429i | \(-0.517846\pi\) | ||||
−0.0560341 | + | 0.998429i | \(0.517846\pi\) | |||||||
\(822\) | 3.00000 | 0.104637 | ||||||||
\(823\) | 44.8444 | 1.56318 | 0.781589 | − | 0.623794i | \(-0.214410\pi\) | ||||
0.781589 | + | 0.623794i | \(0.214410\pi\) | |||||||
\(824\) | 0.302776 | 0.0105477 | ||||||||
\(825\) | −2.30278 | −0.0801724 | ||||||||
\(826\) | 27.6333 | 0.961486 | ||||||||
\(827\) | −34.6056 | −1.20335 | −0.601676 | − | 0.798740i | \(-0.705500\pi\) | ||||
−0.601676 | + | 0.798740i | \(0.705500\pi\) | |||||||
\(828\) | −30.9083 | −1.07414 | ||||||||
\(829\) | 27.7250 | 0.962928 | 0.481464 | − | 0.876466i | \(-0.340105\pi\) | ||||
0.481464 | + | 0.876466i | \(0.340105\pi\) | |||||||
\(830\) | 6.42221 | 0.222918 | ||||||||
\(831\) | −0.394449 | −0.0136833 | ||||||||
\(832\) | −1.30278 | −0.0451656 | ||||||||
\(833\) | −1.26662 | −0.0438856 | ||||||||
\(834\) | −6.30278 | −0.218247 | ||||||||
\(835\) | 12.6972 | 0.439406 | ||||||||
\(836\) | 4.60555 | 0.159286 | ||||||||
\(837\) | 4.90833 | 0.169657 | ||||||||
\(838\) | 36.1472 | 1.24868 | ||||||||
\(839\) | −12.9722 | −0.447852 | −0.223926 | − | 0.974606i | \(-0.571887\pi\) | ||||
−0.223926 | + | 0.974606i | \(0.571887\pi\) | |||||||
\(840\) | −19.8167 | −0.683740 | ||||||||
\(841\) | −13.7250 | −0.473275 | ||||||||
\(842\) | 3.72498 | 0.128371 | ||||||||
\(843\) | 39.6333 | 1.36504 | ||||||||
\(844\) | 10.3028 | 0.354636 | ||||||||
\(845\) | −26.0278 | −0.895382 | ||||||||
\(846\) | 36.4222 | 1.25222 | ||||||||
\(847\) | 14.8444 | 0.510060 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | −81.2666 | −2.78906 | ||||||||
\(850\) | 1.81665 | 0.0623107 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 19.8167 | 0.678907 | ||||||||
\(853\) | −42.5416 | −1.45660 | −0.728299 | − | 0.685260i | \(-0.759689\pi\) | ||||
−0.728299 | + | 0.685260i | \(0.759689\pi\) | |||||||
\(854\) | 19.5778 | 0.669938 | ||||||||
\(855\) | −36.4222 | −1.24561 | ||||||||
\(856\) | 0.697224 | 0.0238306 | ||||||||
\(857\) | −42.8444 | −1.46354 | −0.731769 | − | 0.681553i | \(-0.761305\pi\) | ||||
−0.731769 | + | 0.681553i | \(0.761305\pi\) | |||||||
\(858\) | 9.90833 | 0.338265 | ||||||||
\(859\) | −48.0555 | −1.63963 | −0.819816 | − | 0.572626i | \(-0.805925\pi\) | ||||
−0.819816 | + | 0.572626i | \(0.805925\pi\) | |||||||
\(860\) | −1.39445 | −0.0475503 | ||||||||
\(861\) | −85.2666 | −2.90588 | ||||||||
\(862\) | −9.21110 | −0.313731 | ||||||||
\(863\) | 12.0000 | 0.408485 | 0.204242 | − | 0.978920i | \(-0.434527\pi\) | ||||
0.204242 | + | 0.978920i | \(0.434527\pi\) | |||||||
\(864\) | 16.2111 | 0.551513 | ||||||||
\(865\) | −20.2389 | −0.688142 | ||||||||
\(866\) | 34.9361 | 1.18718 | ||||||||
\(867\) | 62.7527 | 2.13119 | ||||||||
\(868\) | −0.788897 | −0.0267769 | ||||||||
\(869\) | 21.0000 | 0.712376 | ||||||||
\(870\) | 29.7250 | 1.00777 | ||||||||
\(871\) | 4.57779 | 0.155113 | ||||||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | 129.872 | 4.39551 | ||||||||
\(874\) | 7.81665 | 0.264402 | ||||||||
\(875\) | 28.1833 | 0.952771 | ||||||||
\(876\) | −40.6333 | −1.37287 | ||||||||
\(877\) | −7.21110 | −0.243502 | −0.121751 | − | 0.992561i | \(-0.538851\pi\) | ||||
−0.121751 | + | 0.992561i | \(0.538851\pi\) | |||||||
\(878\) | −30.3305 | −1.02361 | ||||||||
\(879\) | 36.4222 | 1.22849 | ||||||||
\(880\) | −5.30278 | −0.178757 | ||||||||
\(881\) | −28.5416 | −0.961592 | −0.480796 | − | 0.876832i | \(-0.659652\pi\) | ||||
−0.480796 | + | 0.876832i | \(0.659652\pi\) | |||||||
\(882\) | −1.66947 | −0.0562139 | ||||||||
\(883\) | −26.4222 | −0.889178 | −0.444589 | − | 0.895735i | \(-0.646650\pi\) | ||||
−0.444589 | + | 0.895735i | \(0.646650\pi\) | |||||||
\(884\) | −7.81665 | −0.262903 | ||||||||
\(885\) | −80.6611 | −2.71139 | ||||||||
\(886\) | 32.7250 | 1.09942 | ||||||||
\(887\) | −0.422205 | −0.0141763 | −0.00708813 | − | 0.999975i | \(-0.502256\pi\) | ||||
−0.00708813 | + | 0.999975i | \(0.502256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.0555 | 1.67881 | ||||||||
\(890\) | 21.2111 | 0.710998 | ||||||||
\(891\) | −68.6611 | −2.30023 | ||||||||
\(892\) | −5.81665 | −0.194756 | ||||||||
\(893\) | −9.21110 | −0.308238 | ||||||||
\(894\) | 65.4500 | 2.18897 | ||||||||
\(895\) | 31.8167 | 1.06351 | ||||||||
\(896\) | −2.60555 | −0.0870454 | ||||||||
\(897\) | 16.8167 | 0.561492 | ||||||||
\(898\) | 15.2111 | 0.507601 | ||||||||
\(899\) | 1.18335 | 0.0394668 | ||||||||
\(900\) | 2.39445 | 0.0798150 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | −22.8167 | −0.759711 | ||||||||
\(903\) | 5.21110 | 0.173415 | ||||||||
\(904\) | 3.21110 | 0.106800 | ||||||||
\(905\) | 46.0555 | 1.53094 | ||||||||
\(906\) | −68.0555 | −2.26099 | ||||||||
\(907\) | −26.0000 | −0.863316 | −0.431658 | − | 0.902037i | \(-0.642071\pi\) | ||||
−0.431658 | + | 0.902037i | \(0.642071\pi\) | |||||||
\(908\) | −13.8167 | −0.458522 | ||||||||
\(909\) | −98.2389 | −3.25838 | ||||||||
\(910\) | 7.81665 | 0.259120 | ||||||||
\(911\) | 17.5778 | 0.582378 | 0.291189 | − | 0.956665i | \(-0.405949\pi\) | ||||
0.291189 | + | 0.956665i | \(0.405949\pi\) | |||||||
\(912\) | −6.60555 | −0.218732 | ||||||||
\(913\) | −6.42221 | −0.212544 | ||||||||
\(914\) | 2.60555 | 0.0861840 | ||||||||
\(915\) | −57.1472 | −1.88923 | ||||||||
\(916\) | 24.6056 | 0.812990 | ||||||||
\(917\) | 27.6333 | 0.912532 | ||||||||
\(918\) | 97.2666 | 3.21028 | ||||||||
\(919\) | 9.57779 | 0.315942 | 0.157971 | − | 0.987444i | \(-0.449505\pi\) | ||||
0.157971 | + | 0.987444i | \(0.449505\pi\) | |||||||
\(920\) | −9.00000 | −0.296721 | ||||||||
\(921\) | 59.1472 | 1.94897 | ||||||||
\(922\) | −12.4222 | −0.409104 | ||||||||
\(923\) | −7.81665 | −0.257288 | ||||||||
\(924\) | 19.8167 | 0.651920 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −26.6972 | −0.877325 | ||||||||
\(927\) | 2.39445 | 0.0786440 | ||||||||
\(928\) | 3.90833 | 0.128297 | ||||||||
\(929\) | −18.4861 | −0.606510 | −0.303255 | − | 0.952909i | \(-0.598073\pi\) | ||||
−0.303255 | + | 0.952909i | \(0.598073\pi\) | |||||||
\(930\) | 2.30278 | 0.0755110 | ||||||||
\(931\) | 0.422205 | 0.0138372 | ||||||||
\(932\) | 8.51388 | 0.278881 | ||||||||
\(933\) | −52.5416 | −1.72014 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.8167 | −1.04052 | ||||||||
\(936\) | −10.3028 | −0.336757 | ||||||||
\(937\) | −18.0917 | −0.591029 | −0.295515 | − | 0.955338i | \(-0.595491\pi\) | ||||
−0.295515 | + | 0.955338i | \(0.595491\pi\) | |||||||
\(938\) | 9.15559 | 0.298941 | ||||||||
\(939\) | 29.8167 | 0.973030 | ||||||||
\(940\) | 10.6056 | 0.345915 | ||||||||
\(941\) | 13.8167 | 0.450410 | 0.225205 | − | 0.974311i | \(-0.427695\pi\) | ||||
0.225205 | + | 0.974311i | \(0.427695\pi\) | |||||||
\(942\) | −23.8167 | −0.775989 | ||||||||
\(943\) | −38.7250 | −1.26106 | ||||||||
\(944\) | −10.6056 | −0.345181 | ||||||||
\(945\) | −97.2666 | −3.16408 | ||||||||
\(946\) | 1.39445 | 0.0453374 | ||||||||
\(947\) | 3.63331 | 0.118067 | 0.0590333 | − | 0.998256i | \(-0.481198\pi\) | ||||
0.0590333 | + | 0.998256i | \(0.481198\pi\) | |||||||
\(948\) | −30.1194 | −0.978234 | ||||||||
\(949\) | 16.0278 | 0.520283 | ||||||||
\(950\) | −0.605551 | −0.0196467 | ||||||||
\(951\) | 30.4222 | 0.986508 | ||||||||
\(952\) | −15.6333 | −0.506678 | ||||||||
\(953\) | 49.7527 | 1.61165 | 0.805825 | − | 0.592154i | \(-0.201722\pi\) | ||||
0.805825 | + | 0.592154i | \(0.201722\pi\) | |||||||
\(954\) | −47.4500 | −1.53625 | ||||||||
\(955\) | 12.6972 | 0.410873 | ||||||||
\(956\) | 17.5139 | 0.566439 | ||||||||
\(957\) | −29.7250 | −0.960872 | ||||||||
\(958\) | 13.1194 | 0.423870 | ||||||||
\(959\) | −2.36669 | −0.0764245 | ||||||||
\(960\) | 7.60555 | 0.245468 | ||||||||
\(961\) | −30.9083 | −0.997043 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.51388 | 0.177682 | ||||||||
\(964\) | −8.00000 | −0.257663 | ||||||||
\(965\) | 9.21110 | 0.296516 | ||||||||
\(966\) | 33.6333 | 1.08213 | ||||||||
\(967\) | 6.72498 | 0.216261 | 0.108130 | − | 0.994137i | \(-0.465514\pi\) | ||||
0.108130 | + | 0.994137i | \(0.465514\pi\) | |||||||
\(968\) | −5.69722 | −0.183116 | ||||||||
\(969\) | −39.6333 | −1.27321 | ||||||||
\(970\) | 37.8167 | 1.21422 | ||||||||
\(971\) | −22.5416 | −0.723395 | −0.361698 | − | 0.932295i | \(-0.617803\pi\) | ||||
−0.361698 | + | 0.932295i | \(0.617803\pi\) | |||||||
\(972\) | 49.8444 | 1.59876 | ||||||||
\(973\) | 4.97224 | 0.159403 | ||||||||
\(974\) | 37.2111 | 1.19232 | ||||||||
\(975\) | −1.30278 | −0.0417222 | ||||||||
\(976\) | −7.51388 | −0.240513 | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | −27.8167 | −0.889479 | ||||||||
\(979\) | −21.2111 | −0.677910 | ||||||||
\(980\) | −0.486122 | −0.0155286 | ||||||||
\(981\) | −15.8167 | −0.504987 | ||||||||
\(982\) | 17.7250 | 0.565627 | ||||||||
\(983\) | −12.0000 | −0.382741 | −0.191370 | − | 0.981518i | \(-0.561293\pi\) | ||||
−0.191370 | + | 0.981518i | \(0.561293\pi\) | |||||||
\(984\) | 32.7250 | 1.04323 | ||||||||
\(985\) | −13.8167 | −0.440235 | ||||||||
\(986\) | 23.4500 | 0.746799 | ||||||||
\(987\) | −39.6333 | −1.26154 | ||||||||
\(988\) | 2.60555 | 0.0828936 | ||||||||
\(989\) | 2.36669 | 0.0752564 | ||||||||
\(990\) | −41.9361 | −1.33282 | ||||||||
\(991\) | −50.6972 | −1.61045 | −0.805225 | − | 0.592969i | \(-0.797956\pi\) | ||||
−0.805225 | + | 0.592969i | \(0.797956\pi\) | |||||||
\(992\) | 0.302776 | 0.00961314 | ||||||||
\(993\) | 43.6333 | 1.38466 | ||||||||
\(994\) | −15.6333 | −0.495858 | ||||||||
\(995\) | −60.8444 | −1.92890 | ||||||||
\(996\) | 9.21110 | 0.291865 | ||||||||
\(997\) | 52.4222 | 1.66023 | 0.830114 | − | 0.557594i | \(-0.188275\pi\) | ||||
0.830114 | + | 0.557594i | \(0.188275\pi\) | |||||||
\(998\) | 42.2389 | 1.33705 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2738.2.a.l.1.2 | 2 | ||
37.36 | even | 2 | 74.2.a.a.1.2 | ✓ | 2 | ||
111.110 | odd | 2 | 666.2.a.j.1.2 | 2 | |||
148.147 | odd | 2 | 592.2.a.f.1.1 | 2 | |||
185.73 | odd | 4 | 1850.2.b.i.149.4 | 4 | |||
185.147 | odd | 4 | 1850.2.b.i.149.1 | 4 | |||
185.184 | even | 2 | 1850.2.a.u.1.1 | 2 | |||
259.258 | odd | 2 | 3626.2.a.a.1.1 | 2 | |||
296.147 | odd | 2 | 2368.2.a.ba.1.2 | 2 | |||
296.221 | even | 2 | 2368.2.a.s.1.1 | 2 | |||
407.406 | odd | 2 | 8954.2.a.p.1.2 | 2 | |||
444.443 | even | 2 | 5328.2.a.bf.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.a.a.1.2 | ✓ | 2 | 37.36 | even | 2 | ||
592.2.a.f.1.1 | 2 | 148.147 | odd | 2 | |||
666.2.a.j.1.2 | 2 | 111.110 | odd | 2 | |||
1850.2.a.u.1.1 | 2 | 185.184 | even | 2 | |||
1850.2.b.i.149.1 | 4 | 185.147 | odd | 4 | |||
1850.2.b.i.149.4 | 4 | 185.73 | odd | 4 | |||
2368.2.a.s.1.1 | 2 | 296.221 | even | 2 | |||
2368.2.a.ba.1.2 | 2 | 296.147 | odd | 2 | |||
2738.2.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3626.2.a.a.1.1 | 2 | 259.258 | odd | 2 | |||
5328.2.a.bf.1.2 | 2 | 444.443 | even | 2 | |||
8954.2.a.p.1.2 | 2 | 407.406 | odd | 2 |