Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.46410 | 1.68727 | 0.843636 | − | 0.536916i | \(-0.180411\pi\) | ||||
0.843636 | + | 0.536916i | \(0.180411\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.46410 | −1.23812 | −0.619060 | − | 0.785344i | \(-0.712486\pi\) | ||||
−0.619060 | + | 0.785344i | \(0.712486\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.92820 | −1.92287 | −0.961436 | − | 0.275029i | \(-0.911312\pi\) | ||||
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.46410 | 0.974147 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.46410 | −1.34786 | −0.673929 | − | 0.738796i | \(-0.735395\pi\) | ||||
−0.673929 | + | 0.738796i | \(0.735395\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.46410 | 0.457572 | 0.228786 | − | 0.973477i | \(-0.426524\pi\) | ||||
0.228786 | + | 0.973477i | \(0.426524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.92820 | 0.885131 | 0.442566 | − | 0.896736i | \(-0.354068\pi\) | ||||
0.442566 | + | 0.896736i | \(0.354068\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.92820 | 1.50914 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.46410 | −0.714828 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.92820 | −1.08200 | −0.541002 | − | 0.841021i | \(-0.681955\pi\) | ||||
−0.541002 | + | 0.841021i | \(0.681955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.92820 | 0.751544 | 0.375772 | − | 0.926712i | \(-0.377378\pi\) | ||||
0.375772 | + | 0.926712i | \(0.377378\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.00000 | −0.596285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.92820 | −1.01058 | −0.505291 | − | 0.862949i | \(-0.668615\pi\) | ||||
−0.505291 | + | 0.862949i | \(0.668615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.9282 | 1.84689 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.92820 | −1.11017 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.4641 | −1.71208 | −0.856038 | − | 0.516913i | \(-0.827081\pi\) | ||||
−0.856038 | + | 0.516913i | \(0.827081\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.92820 | −1.29254 | −0.646271 | − | 0.763108i | \(-0.723672\pi\) | ||||
−0.646271 | + | 0.763108i | \(0.723672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92820 | 1.14314 | 0.571570 | − | 0.820554i | \(-0.306335\pi\) | ||||
0.571570 | + | 0.820554i | \(0.306335\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.92820 | −1.12485 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.92820 | −1.10741 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.92820 | −0.724245 | −0.362123 | − | 0.932130i | \(-0.617948\pi\) | ||||
−0.362123 | + | 0.932130i | \(0.617948\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.46410 | −0.778186 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0000 | −1.66149 | −0.830747 | − | 0.556650i | \(-0.812086\pi\) | ||||
−0.830747 | + | 0.556650i | \(0.812086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.8564 | −2.03493 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | 0.225018 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.92820 | 0.321412 | 0.160706 | − | 0.987002i | \(-0.448623\pi\) | ||||
0.160706 | + | 0.987002i | \(0.448623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.8564 | −1.71987 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.46410 | 0.264179 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.928203 | −0.0983893 | −0.0491947 | − | 0.998789i | \(-0.515665\pi\) | ||||
−0.0491947 | + | 0.998789i | \(0.515665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.9282 | −2.08904 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.92820 | 0.511031 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9282 | 1.31266 | 0.656330 | − | 0.754474i | \(-0.272108\pi\) | ||||
0.656330 | + | 0.754474i | \(0.272108\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.00000 | 0.804030 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.85641 | 0.980749 | 0.490375 | − | 0.871512i | \(-0.336860\pi\) | ||||
0.490375 | + | 0.871512i | \(0.336860\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.92820 | 0.288524 | 0.144262 | − | 0.989539i | \(-0.453919\pi\) | ||||
0.144262 | + | 0.989539i | \(0.453919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.92820 | 0.871303 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9282 | 1.34649 | 0.673245 | − | 0.739419i | \(-0.264900\pi\) | ||||
0.673245 | + | 0.739419i | \(0.264900\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.39230 | 0.708054 | 0.354027 | − | 0.935235i | \(-0.384812\pi\) | ||||
0.354027 | + | 0.935235i | \(0.384812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9282 | 1.21618 | 0.608092 | − | 0.793867i | \(-0.291935\pi\) | ||||
0.608092 | + | 0.793867i | \(0.291935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.9282 | −1.20556 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.92820 | 0.825413 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −35.3923 | −3.24441 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.92820 | −0.624695 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.928203 | 0.0823647 | 0.0411824 | − | 0.999152i | \(-0.486888\pi\) | ||||
0.0411824 | + | 0.999152i | \(0.486888\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.92820 | 0.433904 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.07180 | 0.617866 | 0.308933 | − | 0.951084i | \(-0.400028\pi\) | ||||
0.308933 | + | 0.951084i | \(0.400028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.46410 | 0.387087 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.0000 | −0.860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.85641 | 0.756654 | 0.378327 | − | 0.925672i | \(-0.376500\pi\) | ||||
0.378327 | + | 0.925672i | \(0.376500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.8564 | −1.34492 | −0.672461 | − | 0.740132i | \(-0.734763\pi\) | ||||
−0.672461 | + | 0.740132i | \(0.734763\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.92820 | −0.583460 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.8564 | 1.49323 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.92820 | 0.409265 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.9282 | 1.06630 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.9282 | −0.895273 | −0.447637 | − | 0.894216i | \(-0.647734\pi\) | ||||
−0.447637 | + | 0.894216i | \(0.647734\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.8564 | 1.28191 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.85641 | 0.791686 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4641 | −0.988468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.8564 | −2.27420 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.8564 | 1.86858 | 0.934289 | − | 0.356517i | \(-0.116036\pi\) | ||||
0.934289 | + | 0.356517i | \(0.116036\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00000 | −0.622799 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.07180 | −0.392467 | −0.196234 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196234 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.92820 | 0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0000 | 0.760286 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.46410 | −0.337454 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.92820 | −0.746249 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.8564 | 1.93260 | 0.966299 | − | 0.257421i | \(-0.0828728\pi\) | ||||
0.966299 | + | 0.257421i | \(0.0828728\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.92820 | 0.659992 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | 0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.7128 | 2.31907 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.3205 | −1.62358 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.53590 | −0.255849 | −0.127924 | − | 0.991784i | \(-0.540831\pi\) | ||||
−0.127924 | + | 0.991784i | \(0.540831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.85641 | 0.709480 | 0.354740 | − | 0.934965i | \(-0.384569\pi\) | ||||
0.354740 | + | 0.934965i | \(0.384569\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.92820 | −0.639362 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.92820 | 0.493614 | 0.246807 | − | 0.969065i | \(-0.420619\pi\) | ||||
0.246807 | + | 0.969065i | \(0.420619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.5359 | 0.959534 | 0.479767 | − | 0.877396i | \(-0.340721\pi\) | ||||
0.479767 | + | 0.877396i | \(0.340721\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.92820 | −0.418143 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.0000 | 0.772049 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.8564 | −0.967773 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.9282 | 0.898572 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.8564 | −1.71119 | −0.855593 | − | 0.517649i | \(-0.826807\pi\) | ||||
−0.855593 | + | 0.517649i | \(0.826807\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.0000 | −0.959264 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.85641 | 0.672201 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.0000 | 1.49346 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.00000 | −0.473016 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.3923 | 2.38074 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.9282 | −1.80325 | −0.901623 | − | 0.432523i | \(-0.857623\pi\) | ||||
−0.901623 | + | 0.432523i | \(0.857623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.92820 | −0.127979 | −0.0639897 | − | 0.997951i | \(-0.520382\pi\) | ||||
−0.0639897 | + | 0.997951i | \(0.520382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.07180 | 0.202990 | 0.101495 | − | 0.994836i | \(-0.467637\pi\) | ||||
0.101495 | + | 0.994836i | \(0.467637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.8564 | −1.17487 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.8564 | −1.03879 | −0.519394 | − | 0.854535i | \(-0.673842\pi\) | ||||
−0.519394 | + | 0.854535i | \(0.673842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.8564 | −0.903892 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000 | 0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.3205 | −1.05569 | −0.527843 | − | 0.849342i | \(-0.676999\pi\) | ||||
−0.527843 | + | 0.849342i | \(0.676999\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.7846 | −1.59652 | −0.798259 | − | 0.602315i | \(-0.794245\pi\) | ||||
−0.798259 | + | 0.602315i | \(0.794245\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.8564 | 1.65191 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.46410 | −0.284044 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.92820 | 0.185567 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.9282 | 0.816021 | 0.408010 | − | 0.912977i | \(-0.366223\pi\) | ||||
0.408010 | + | 0.912977i | \(0.366223\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.8564 | 1.62558 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.8564 | −0.992967 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.928203 | −0.0578997 | −0.0289499 | − | 0.999581i | \(-0.509216\pi\) | ||||
−0.0289499 | + | 0.999581i | \(0.509216\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.92820 | 0.554772 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.92820 | −0.305048 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.92820 | −0.180561 | −0.0902804 | − | 0.995916i | \(-0.528776\pi\) | ||||
−0.0902804 | + | 0.995916i | \(0.528776\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.9282 | −1.53133 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.928203 | −0.0568051 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.85641 | 0.479014 | 0.239507 | − | 0.970895i | \(-0.423014\pi\) | ||||
0.239507 | + | 0.970895i | \(0.423014\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.60770 | −0.279898 | −0.139949 | − | 0.990159i | \(-0.544694\pi\) | ||||
−0.139949 | + | 0.990159i | \(0.544694\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.9282 | −1.20611 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | 0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9282 | 1.49779 | 0.748895 | − | 0.662688i | \(-0.230585\pi\) | ||||
0.748895 | + | 0.662688i | \(0.230585\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.85641 | −0.590088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.00000 | −0.238620 | −0.119310 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119310 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.9282 | −1.12516 | −0.562582 | − | 0.826741i | \(-0.690192\pi\) | ||||
−0.562582 | + | 0.826741i | \(0.690192\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.9282 | −1.82563 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.8564 | 2.69744 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.9282 | 0.757865 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.32051 | −0.486089 | −0.243045 | − | 0.970015i | \(-0.578146\pi\) | ||||
−0.243045 | + | 0.970015i | \(0.578146\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.8564 | −1.15608 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.0000 | 1.16052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.8564 | 1.66881 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.0000 | 1.26806 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.85641 | 0.566236 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.8564 | 1.02245 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.85641 | 0.105951 | 0.0529754 | − | 0.998596i | \(-0.483130\pi\) | ||||
0.0529754 | + | 0.998596i | \(0.483130\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.92820 | 0.166580 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.39230 | 0.419179 | 0.209590 | − | 0.977789i | \(-0.432787\pi\) | ||||
0.209590 | + | 0.977789i | \(0.432787\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.8564 | −0.952780 | −0.476390 | − | 0.879234i | \(-0.658055\pi\) | ||||
−0.476390 | + | 0.879234i | \(0.658055\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.8564 | −1.00609 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.4641 | −0.812385 | −0.406192 | − | 0.913788i | \(-0.633144\pi\) | ||||
−0.406192 | + | 0.913788i | \(0.633144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.85641 | −0.551853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.9282 | 0.777396 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.92820 | −0.441137 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.46410 | 0.247624 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.39230 | 0.408795 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.9282 | −1.70513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.78461 | −0.537811 | −0.268905 | − | 0.963167i | \(-0.586662\pi\) | ||||
−0.268905 | + | 0.963167i | \(0.586662\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.8564 | −0.647785 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.07180 | −0.385225 | −0.192613 | − | 0.981275i | \(-0.561696\pi\) | ||||
−0.192613 | + | 0.981275i | \(0.561696\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.9282 | 0.702164 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.7128 | −1.06751 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 26.4641 | 1.42893 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.9282 | −0.696031 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.8564 | −1.49541 | −0.747705 | − | 0.664031i | \(-0.768844\pi\) | ||||
−0.747705 | + | 0.664031i | \(0.768844\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.3205 | 1.19138 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0718 | 0.536068 | 0.268034 | − | 0.963410i | \(-0.413626\pi\) | ||||
0.268034 | + | 0.963410i | \(0.413626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.0000 | −1.48609 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −35.3923 | −1.87316 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4641 | −1.29117 | −0.645583 | − | 0.763690i | \(-0.723386\pi\) | ||||
−0.645583 | + | 0.763690i | \(0.723386\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0000 | −0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.0718 | −0.682342 | −0.341171 | − | 0.940001i | \(-0.610824\pi\) | ||||
−0.341171 | + | 0.940001i | \(0.610824\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.8564 | 0.721336 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −55.6410 | −2.88874 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3923 | 0.589871 | 0.294936 | − | 0.955517i | \(-0.404702\pi\) | ||||
0.294936 | + | 0.955517i | \(0.404702\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.0000 | −0.566529 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.85641 | 0.352190 | 0.176095 | − | 0.984373i | \(-0.443653\pi\) | ||||
0.176095 | + | 0.984373i | \(0.443653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.928203 | 0.0475533 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.7846 | 1.26643 | 0.633217 | − | 0.773974i | \(-0.281734\pi\) | ||||
0.633217 | + | 0.773974i | \(0.281734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −35.7128 | −1.82009 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.85641 | −0.501029 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.8564 | 1.31097 | 0.655486 | − | 0.755207i | \(-0.272464\pi\) | ||||
0.655486 | + | 0.755207i | \(0.272464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51.2487 | 2.59176 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.07180 | 0.356725 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.92820 | 0.448094 | 0.224047 | − | 0.974578i | \(-0.428073\pi\) | ||||
0.224047 | + | 0.974578i | \(0.428073\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.46410 | 0.223485 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | −0.599251 | −0.299626 | − | 0.954057i | \(-0.596862\pi\) | ||||
−0.299626 | + | 0.954057i | \(0.596862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0000 | −1.09590 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | 0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.00000 | 0.296681 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.85641 | 0.436854 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −44.3205 | −2.18087 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.85641 | 0.287480 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.8564 | −0.776492 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.7846 | −1.50393 | −0.751963 | − | 0.659205i | \(-0.770893\pi\) | ||||
−0.751963 | + | 0.659205i | \(0.770893\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5359 | 0.562225 | 0.281113 | − | 0.959675i | \(-0.409297\pi\) | ||||
0.281113 | + | 0.959675i | \(0.409297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.8564 | 0.673722 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.92820 | 0.384574 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.8564 | 1.92879 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.8564 | 0.862115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.9282 | −0.622730 | −0.311365 | − | 0.950290i | \(-0.600786\pi\) | ||||
−0.311365 | + | 0.950290i | \(0.600786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.7846 | −1.19107 | −0.595536 | − | 0.803328i | \(-0.703060\pi\) | ||||
−0.595536 | + | 0.803328i | \(0.703060\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.92820 | 0.236289 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.46410 | −0.309220 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | 0.190910 | 0.0954548 | − | 0.995434i | \(-0.469569\pi\) | ||||
0.0954548 | + | 0.995434i | \(0.469569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.8564 | −1.23126 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.8564 | −0.848383 | −0.424192 | − | 0.905572i | \(-0.639442\pi\) | ||||
−0.424192 | + | 0.905572i | \(0.639442\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.85641 | −0.0880021 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.9282 | −0.516886 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.0000 | 0.943858 | 0.471929 | − | 0.881636i | \(-0.343558\pi\) | ||||
0.471929 | + | 0.881636i | \(0.343558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.7128 | 1.30495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.0000 | −0.751746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −39.8564 | −1.86850 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.0000 | −1.45012 | −0.725059 | − | 0.688686i | \(-0.758188\pi\) | ||||
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 39.6410 | 1.85028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.8564 | −0.645357 | −0.322679 | − | 0.946509i | \(-0.604583\pi\) | ||||
−0.322679 | + | 0.946509i | \(0.604583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.7846 | −0.780047 | −0.390023 | − | 0.920805i | \(-0.627533\pi\) | ||||
−0.390023 | + | 0.920805i | \(0.627533\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.85641 | 0.457080 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.78461 | 0.128856 | 0.0644282 | − | 0.997922i | \(-0.479478\pi\) | ||||
0.0644282 | + | 0.997922i | \(0.479478\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.4641 | −1.22200 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0000 | 0.460776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.7128 | −0.906396 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.9282 | 1.14138 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.7846 | 0.766908 | 0.383454 | − | 0.923560i | \(-0.374734\pi\) | ||||
0.383454 | + | 0.923560i | \(0.374734\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.92820 | −0.407091 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −28.8564 | −1.31301 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.8564 | 1.17408 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.6410 | −1.56973 | −0.784867 | − | 0.619664i | \(-0.787269\pi\) | ||||
−0.784867 | + | 0.619664i | \(0.787269\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.8564 | 1.07882 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1436 | 0.638291 | 0.319146 | − | 0.947706i | \(-0.396604\pi\) | ||||
0.319146 | + | 0.947706i | \(0.396604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.5359 | −0.879853 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.0000 | 0.719147 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −62.4974 | −2.80339 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.7846 | −1.01998 | −0.509990 | − | 0.860181i | \(-0.670351\pi\) | ||||
−0.509990 | + | 0.860181i | \(0.670351\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.07180 | −0.226591 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.3205 | 0.995222 | 0.497611 | − | 0.867400i | \(-0.334211\pi\) | ||||
0.497611 | + | 0.867400i | \(0.334211\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.7128 | 0.877209 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.92820 | 0.307692 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.0000 | 0.797836 | 0.398918 | − | 0.916987i | \(-0.369386\pi\) | ||||
0.398918 | + | 0.916987i | \(0.369386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.2487 | −1.38236 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.00000 | −0.220755 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.85641 | 0.258064 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.7128 | 1.21881 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.0000 | 0.438951 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0718 | 0.572686 | 0.286343 | − | 0.958127i | \(-0.407560\pi\) | ||||
0.286343 | + | 0.958127i | \(0.407560\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.0000 | 1.35554 | 0.677768 | − | 0.735276i | \(-0.262948\pi\) | ||||
0.677768 | + | 0.735276i | \(0.262948\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.46410 | −0.194829 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −39.0718 | −1.70199 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.7846 | 0.816722 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.8564 | 0.861695 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.9282 | 1.33965 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.8564 | 1.20434 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.8564 | 1.11579 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −51.7128 | −2.22743 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.7846 | −0.549653 | −0.274827 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274827 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0000 | 0.429141 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.7846 | 0.633303 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.14359 | −0.262681 | −0.131341 | − | 0.991337i | \(-0.541928\pi\) | ||||
−0.131341 | + | 0.991337i | \(0.541928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.8564 | −0.762093 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.46410 | 0.104974 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.92820 | 0.379666 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.00000 | 0.169791 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.0000 | 0.932170 | 0.466085 | − | 0.884740i | \(-0.345664\pi\) | ||||
0.466085 | + | 0.884740i | \(0.345664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.0000 | −0.930501 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.7128 | 1.33892 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.7128 | 1.33654 | 0.668268 | − | 0.743921i | \(-0.267036\pi\) | ||||
0.668268 | + | 0.743921i | \(0.267036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.8564 | 1.08779 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.46410 | 0.187475 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.78461 | 0.368270 | 0.184135 | − | 0.982901i | \(-0.441052\pi\) | ||||
0.184135 | + | 0.982901i | \(0.441052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.7846 | −1.20460 | −0.602299 | − | 0.798270i | \(-0.705749\pi\) | ||||
−0.602299 | + | 0.798270i | \(0.705749\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.53590 | −0.147714 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.46410 | 0.269572 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7846 | 0.490600 | 0.245300 | − | 0.969447i | \(-0.421114\pi\) | ||||
0.245300 | + | 0.969447i | \(0.421114\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.85641 | 0.409618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0718 | 0.542310 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 49.8564 | 2.06484 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.8564 | 0.738272 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.92820 | 0.203063 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.92820 | 0.284988 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.1436 | 0.662938 | 0.331469 | − | 0.943466i | \(-0.392456\pi\) | ||||
0.331469 | + | 0.943466i | \(0.392456\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −70.7846 | −2.90189 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5359 | 0.553987 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.85641 | −0.402722 | −0.201361 | − | 0.979517i | \(-0.564536\pi\) | ||||
−0.201361 | + | 0.979517i | \(0.564536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.8564 | 1.13629 | 0.568143 | − | 0.822930i | \(-0.307662\pi\) | ||||
0.568143 | + | 0.822930i | \(0.307662\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.8564 | 0.482830 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0000 | 0.406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.8564 | −1.61772 | −0.808861 | − | 0.588000i | \(-0.799915\pi\) | ||||
−0.808861 | + | 0.588000i | \(0.799915\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.0000 | 0.445742 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.9282 | 1.25122 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.6410 | −1.39914 | −0.699569 | − | 0.714565i | \(-0.746625\pi\) | ||||
−0.699569 | + | 0.714565i | \(0.746625\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.8564 | −0.558744 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.0000 | −0.563619 | −0.281809 | − | 0.959470i | \(-0.590935\pi\) | ||||
−0.281809 | + | 0.959470i | \(0.590935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.8564 | 1.11964 | 0.559822 | − | 0.828613i | \(-0.310870\pi\) | ||||
0.559822 | + | 0.828613i | \(0.310870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.3205 | 1.29698 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.14359 | −0.166010 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.00000 | −0.159745 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.8564 | −0.632236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.6410 | −1.53827 | −0.769137 | − | 0.639084i | \(-0.779314\pi\) | ||||
−0.769137 | + | 0.639084i | \(0.779314\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.8564 | −0.987953 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.85641 | 0.0736692 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −57.7128 | −2.28666 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.0000 | 1.10766 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.78461 | 0.346971 | 0.173486 | − | 0.984836i | \(-0.444497\pi\) | ||||
0.173486 | + | 0.984836i | \(0.444497\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.9282 | −1.29856 | −0.649281 | − | 0.760549i | \(-0.724930\pi\) | ||||
−0.649281 | + | 0.760549i | \(0.724930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.85641 | 0.388096 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.5359 | 0.532151 | 0.266076 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266076 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39.7128 | 1.55886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.0000 | 0.862248 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.78461 | 0.265502 | 0.132751 | − | 0.991149i | \(-0.457619\pi\) | ||||
0.132751 | + | 0.991149i | \(0.457619\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.1436 | 0.552636 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.0000 | 0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.85641 | −0.111270 | −0.0556349 | − | 0.998451i | \(-0.517718\pi\) | ||||
−0.0556349 | + | 0.998451i | \(0.517718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.4641 | −1.18492 | −0.592458 | − | 0.805601i | \(-0.701842\pi\) | ||||
−0.592458 | + | 0.805601i | \(0.701842\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.3923 | 1.37452 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.92820 | 0.346221 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.9282 | −0.616742 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.9282 | −1.04110 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.7128 | −1.37868 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.07180 | 0.349692 | 0.174846 | − | 0.984596i | \(-0.444057\pi\) | ||||
0.174846 | + | 0.984596i | \(0.444057\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.39230 | 0.284109 | 0.142055 | − | 0.989859i | \(-0.454629\pi\) | ||||
0.142055 | + | 0.989859i | \(0.454629\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 57.7128 | 2.21481 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.92820 | −0.0738889 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8564 | 0.683256 | 0.341628 | − | 0.939835i | \(-0.389022\pi\) | ||||
0.341628 | + | 0.939835i | \(0.389022\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.7128 | 0.676772 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.07180 | 0.117196 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 55.6410 | 2.11975 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.85641 | −0.298872 | −0.149436 | − | 0.988771i | \(-0.547746\pi\) | ||||
−0.149436 | + | 0.988771i | \(0.547746\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 35.7128 | 1.35662 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.7128 | −1.20294 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.9282 | 2.08055 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.8564 | −0.599744 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.71281 | −0.291309 | −0.145654 | − | 0.989336i | \(-0.546529\pi\) | ||||
−0.145654 | + | 0.989336i | \(0.546529\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.8564 | −0.521862 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 44.0000 | 1.65479 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.7846 | −0.405025 | −0.202512 | − | 0.979280i | \(-0.564911\pi\) | ||||
−0.202512 | + | 0.979280i | \(0.564911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | −0.150012 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.8564 | −1.19303 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.7128 | 1.33558 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.3205 | −0.609501 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.3923 | −0.499449 | −0.249724 | − | 0.968317i | \(-0.580340\pi\) | ||||
−0.249724 | + | 0.968317i | \(0.580340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.0718 | 0.486819 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.7846 | −0.921750 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.46410 | −0.0915144 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.320508 | −0.0118870 | −0.00594349 | − | 0.999982i | \(-0.501892\pi\) | ||||
−0.00594349 | + | 0.999982i | \(0.501892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.0718 | −1.44512 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.8564 | −1.61987 | −0.809937 | − | 0.586517i | \(-0.800499\pi\) | ||||
−0.809937 | + | 0.586517i | \(0.800499\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25.8564 | 0.953728 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.7128 | 0.873473 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.85641 | −0.362574 | −0.181287 | − | 0.983430i | \(-0.558026\pi\) | ||||
−0.181287 | + | 0.983430i | \(0.558026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.46410 | −0.163993 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.9282 | 0.621036 | 0.310518 | − | 0.950568i | \(-0.399498\pi\) | ||||
0.310518 | + | 0.950568i | \(0.399498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.8564 | −0.800757 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.85641 | −0.214275 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 62.1769 | 2.27190 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.0718 | −1.20681 | −0.603404 | − | 0.797436i | \(-0.706189\pi\) | ||||
−0.603404 | + | 0.797436i | \(0.706189\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.9282 | 0.471130 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.0000 | −1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.21539 | −0.0441741 | −0.0220871 | − | 0.999756i | \(-0.507031\pi\) | ||||
−0.0220871 | + | 0.999756i | \(0.507031\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.8564 | 0.938528 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.7128 | −1.76584 | −0.882919 | − | 0.469525i | \(-0.844425\pi\) | ||||
−0.882919 | + | 0.469525i | \(0.844425\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.0000 | 1.19468 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 31.7128 | 1.14658 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44.3205 | 1.60032 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.0000 | −1.69486 | −0.847432 | − | 0.530904i | \(-0.821852\pi\) | ||||
−0.847432 | + | 0.530904i | \(0.821852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.928203 | −0.0334284 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −54.4641 | −1.95894 | −0.979469 | − | 0.201596i | \(-0.935387\pi\) | ||||
−0.979469 | + | 0.201596i | \(0.935387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.92820 | −0.177026 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.92820 | 0.320298 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.92820 | −0.248229 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.0000 | 2.00384 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.3205 | −0.440299 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.7846 | −0.705245 | −0.352623 | − | 0.935766i | \(-0.614710\pi\) | ||||
−0.352623 | + | 0.935766i | \(0.614710\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.92820 | −0.104247 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.7128 | 2.05203 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.8564 | −1.41534 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.9282 | −0.884112 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.1769 | 1.06892 | 0.534461 | − | 0.845193i | \(-0.320515\pi\) | ||||
0.534461 | + | 0.845193i | \(0.320515\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.9282 | 1.94322 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.85641 | 0.0655929 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.0000 | 0.988099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −57.7128 | −2.03411 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.85641 | 0.276559 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0718 | 0.635371 | 0.317685 | − | 0.948196i | \(-0.397094\pi\) | ||||
0.317685 | + | 0.948196i | \(0.397094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.14359 | 0.0401570 | 0.0200785 | − | 0.999798i | \(-0.493608\pi\) | ||||
0.0200785 | + | 0.999798i | \(0.493608\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.60770 | −0.161599 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.7128 | 1.67131 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.92820 | 0.172416 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 39.8564 | 1.39270 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.6410 | −1.55798 | −0.778991 | − | 0.627035i | \(-0.784268\pi\) | ||||
−0.778991 | + | 0.627035i | \(0.784268\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.5359 | 0.820410 | 0.410205 | − | 0.911993i | \(-0.365457\pi\) | ||||
0.410205 | + | 0.911993i | \(0.365457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00000 | 0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.7128 | −0.511615 | −0.255807 | − | 0.966728i | \(-0.582341\pi\) | ||||
−0.255807 | + | 0.966728i | \(0.582341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3205 | −0.427909 | −0.213954 | − | 0.976844i | \(-0.568634\pi\) | ||||
−0.213954 | + | 0.976844i | \(0.568634\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.9282 | 0.864750 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −102.497 | −3.55133 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.1436 | −0.351034 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.6410 | −0.851718 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.0000 | −0.759524 | −0.379762 | − | 0.925084i | \(-0.623994\pi\) | ||||
−0.379762 | + | 0.925084i | \(0.623994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.9282 | −0.790628 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.00000 | −0.137767 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.8564 | 0.476675 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.3205 | 0.766942 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.9282 | −0.649614 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.9282 | −0.443173 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.0718 | −0.447570 | −0.223785 | − | 0.974639i | \(-0.571841\pi\) | ||||
−0.223785 | + | 0.974639i | \(0.571841\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.8564 | 1.70306 | 0.851531 | − | 0.524304i | \(-0.175674\pi\) | ||||
0.851531 | + | 0.524304i | \(0.175674\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.0718 | −0.718960 | −0.359480 | − | 0.933153i | \(-0.617046\pi\) | ||||
−0.359480 | + | 0.933153i | \(0.617046\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.9282 | −1.05403 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.7846 | 0.503274 | 0.251637 | − | 0.967822i | \(-0.419031\pi\) | ||||
0.251637 | + | 0.967822i | \(0.419031\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.0000 | 0.680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45.8564 | 1.55737 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.00000 | −0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.4641 | 0.896702 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.8564 | −0.875107 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −53.5692 | −1.81097 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.2487 | −1.05519 | −0.527597 | − | 0.849495i | \(-0.676907\pi\) | ||||
−0.527597 | + | 0.849495i | \(0.676907\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.32051 | −0.280644 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0000 | −0.741199 | −0.370599 | − | 0.928793i | \(-0.620848\pi\) | ||||
−0.370599 | + | 0.928793i | \(0.620848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.7128 | 1.67297 | 0.836485 | − | 0.547990i | \(-0.184607\pi\) | ||||
0.836485 | + | 0.547990i | \(0.184607\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.8564 | −0.667466 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.9282 | −0.434087 | −0.217043 | − | 0.976162i | \(-0.569641\pi\) | ||||
−0.217043 | + | 0.976162i | \(0.569641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.14359 | 0.138972 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.92820 | −0.231843 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 51.7128 | 1.72857 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.8564 | 0.963487 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.1436 | 0.405012 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 98.8179 | 3.29210 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.0000 | 0.732114 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.0000 | 0.664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.1436 | 0.436426 | 0.218213 | − | 0.975901i | \(-0.429977\pi\) | ||||
0.218213 | + | 0.975901i | \(0.429977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.7128 | −0.653833 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.85641 | −0.260294 | −0.130147 | − | 0.991495i | \(-0.541545\pi\) | ||||
−0.130147 | + | 0.991495i | \(0.541545\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.7128 | −0.387638 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.8564 | 0.590315 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.5692 | 1.04251 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.39230 | 0.177876 | 0.0889379 | − | 0.996037i | \(-0.471653\pi\) | ||||
0.0889379 | + | 0.996037i | \(0.471653\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.85641 | 0.0611707 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 62.4974 | 2.05713 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.85641 | −0.192350 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.71281 | 0.285858 | 0.142929 | − | 0.989733i | \(-0.454348\pi\) | ||||
0.142929 | + | 0.989733i | \(0.454348\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.9282 | 0.423705 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.39230 | 0.242013 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 63.4256 | 2.07424 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.9282 | −0.977712 | −0.488856 | − | 0.872365i | \(-0.662586\pi\) | ||||
−0.488856 | + | 0.872365i | \(0.662586\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.8564 | −0.550088 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.1051 | 1.33999 | 0.669994 | − | 0.742366i | \(-0.266297\pi\) | ||||
0.669994 | + | 0.742366i | \(0.266297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.7846 | 1.45839 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −44.6410 | −1.45217 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.9282 | 0.550093 | 0.275046 | − | 0.961431i | \(-0.411307\pi\) | ||||
0.275046 | + | 0.961431i | \(0.411307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.2487 | 1.01438 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.4641 | −0.469031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.21539 | −0.233729 | −0.116865 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116865 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.07180 | −0.228838 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.85641 | −0.318612 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.5359 | 1.27668 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.71281 | −0.216542 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.8564 | −0.897660 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.7128 | 0.634578 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.7846 | −0.797019 | −0.398510 | − | 0.917164i | \(-0.630472\pi\) | ||||
−0.398510 | + | 0.917164i | \(0.630472\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.92820 | −0.254691 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.8564 | 0.829772 | 0.414886 | − | 0.909873i | \(-0.363822\pi\) | ||||
0.414886 | + | 0.909873i | \(0.363822\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −70.7846 | −2.26925 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.46410 | 0.142966 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.00000 | 0.191957 | 0.0959785 | − | 0.995383i | \(-0.469402\pi\) | ||||
0.0959785 | + | 0.995383i | \(0.469402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.71281 | 0.118662 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.7846 | −0.472036 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.6410 | −0.658346 | −0.329173 | − | 0.944270i | \(-0.606770\pi\) | ||||
−0.329173 | + | 0.944270i | \(0.606770\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.8564 | 0.441502 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30.9282 | −0.984456 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31.8564 | −1.01297 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.5692 | −1.38402 | −0.692011 | − | 0.721887i | \(-0.743275\pi\) | ||||
−0.692011 | + | 0.721887i | \(0.743275\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.78461 | −0.310505 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.0718 | 0.858234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.7846 | −1.35500 | −0.677501 | − | 0.735522i | \(-0.736937\pi\) | ||||
−0.677501 | + | 0.735522i | \(0.736937\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.0000 | −0.316386 |
(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 | 4864.2.a.x.1.2 | 2 | ||
4.3 | odd | 2 | 4864.2.a.u.1.1 | 2 | |||
8.3 | odd | 2 | 4864.2.a.v.1.1 | 2 | |||
8.5 | even | 2 | 4864.2.a.s.1.2 | 2 | |||
16.3 | odd | 4 | 2432.2.c.d.1217.2 | yes | 4 | ||
16.5 | even | 4 | 2432.2.c.c.1217.1 | ✓ | 4 | ||
16.11 | odd | 4 | 2432.2.c.d.1217.4 | yes | 4 | ||
16.13 | even | 4 | 2432.2.c.c.1217.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.c.1217.1 | ✓ | 4 | 16.5 | even | 4 | ||
2432.2.c.c.1217.3 | yes | 4 | 16.13 | even | 4 | ||
2432.2.c.d.1217.2 | yes | 4 | 16.3 | odd | 4 | ||
2432.2.c.d.1217.4 | yes | 4 | 16.11 | odd | 4 | ||
4864.2.a.s.1.2 | 2 | 8.5 | even | 2 | |||
4864.2.a.u.1.1 | 2 | 4.3 | odd | 2 | |||
4864.2.a.v.1.1 | 2 | 8.3 | odd | 2 | |||
4864.2.a.x.1.2 | 2 | 1.1 | even | 1 | trivial |