Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2432,2,Mod(1217,2432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2432.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2432 = 2^{7} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2432.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.4196177716\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2432.1217 |
Dual form | 2432.2.c.c.1217.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2432\mathbb{Z}\right)^\times\).
\(n\) | \(1407\) | \(1921\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | −0.957427 | − | 0.288675i | \(-0.906785\pi\) | ||||
0.957427 | − | 0.288675i | \(-0.0932147\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000i | 0.894427i | 0.894427 | + | 0.447214i | \(0.147584\pi\) | ||||
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.46410 | −1.68727 | −0.843636 | − | 0.536916i | \(-0.819589\pi\) | ||||
−0.843636 | + | 0.536916i | \(0.819589\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 4.00000i | − 1.20605i | −0.797724 | − | 0.603023i | \(-0.793963\pi\) | ||||
0.797724 | − | 0.603023i | \(-0.206037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.46410i | 1.23812i | 0.785344 | + | 0.619060i | \(0.212486\pi\) | ||||
−0.785344 | + | 0.619060i | \(0.787514\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.46410i | 0.974147i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.46410 | 1.34786 | 0.673929 | − | 0.738796i | \(-0.264605\pi\) | ||||
0.673929 | + | 0.738796i | \(0.264605\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.00000i | − 0.962250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.46410i | − 0.457572i | −0.973477 | − | 0.228786i | \(-0.926524\pi\) | ||||
0.973477 | − | 0.228786i | \(-0.0734756\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | − 8.92820i | − 1.50914i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.46410 | 0.714828 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.92820i | 0.751544i | 0.926712 | + | 0.375772i | \(0.122622\pi\) | ||||
−0.926712 | + | 0.375772i | \(0.877378\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.00000i | 0.596285i | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 7.92820i | 1.11017i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 12.4641i | − 1.71208i | −0.516913 | − | 0.856038i | \(-0.672919\pi\) | ||||
0.516913 | − | 0.856038i | \(-0.327081\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000 | 1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9.92820i | − 1.29254i | −0.763108 | − | 0.646271i | \(-0.776328\pi\) | ||||
0.763108 | − | 0.646271i | \(-0.223672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 8.92820i | − 1.14314i | −0.820554 | − | 0.571570i | \(-0.806335\pi\) | ||||
0.820554 | − | 0.571570i | \(-0.193665\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.92820 | −1.12485 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.92820 | −1.10741 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.92820i | 0.724245i | 0.932130 | + | 0.362123i | \(0.117948\pi\) | ||||
−0.932130 | + | 0.362123i | \(0.882052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 6.46410i | − 0.778186i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0000 | 1.66149 | 0.830747 | − | 0.556650i | \(-0.187914\pi\) | ||||
0.830747 | + | 0.556650i | \(0.187914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | 0.819288 | 0.409644 | − | 0.912245i | \(-0.365653\pi\) | ||||
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.00000i | − 0.115470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.8564i | 2.03493i | ||||||||
\(78\) | 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 | ||||||||
\(83\) | − 2.92820i | − 0.321412i | −0.987002 | − | 0.160706i | \(-0.948623\pi\) | ||||
0.987002 | − | 0.160706i | \(-0.0513771\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 15.8564i | − 1.71987i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.46410 | −0.264179 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.928203 | 0.0983893 | 0.0491947 | − | 0.998789i | \(-0.484335\pi\) | ||||
0.0491947 | + | 0.998789i | \(0.484335\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 19.9282i | − 2.08904i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.92820i | − 0.511031i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 8.00000i | − 0.804030i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.85641i | 0.980749i | 0.871512 | + | 0.490375i | \(0.163140\pi\) | ||||
−0.871512 | + | 0.490375i | \(0.836860\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.92820 | −0.288524 | −0.144262 | − | 0.989539i | \(-0.546081\pi\) | ||||
−0.144262 | + | 0.989539i | \(0.546081\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.92820 | −0.871303 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9282i | 1.34649i | 0.739419 | + | 0.673245i | \(0.235100\pi\) | ||||
−0.739419 | + | 0.673245i | \(0.764900\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 7.39230i | − 0.708054i | −0.935235 | − | 0.354027i | \(-0.884812\pi\) | ||||
0.935235 | − | 0.354027i | \(-0.115188\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 12.9282i | 1.20556i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.92820i | 0.825413i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 35.3923 | 3.24441 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 6.92820i | − 0.624695i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000i | 1.07331i | ||||||||
\(126\) | 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 | ||||||||
\(131\) | − 7.07180i | − 0.617866i | −0.951084 | − | 0.308933i | \(-0.900028\pi\) | ||||
0.951084 | − | 0.308933i | \(-0.0999718\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.46410i | 0.387087i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.0000 | 0.860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.85641 | −0.756654 | −0.378327 | − | 0.925672i | \(-0.623500\pi\) | ||||
−0.378327 | + | 0.925672i | \(0.623500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 15.8564i | − 1.34492i | −0.740132 | − | 0.672461i | \(-0.765237\pi\) | ||||
0.740132 | − | 0.672461i | \(-0.234763\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92820i | 0.583460i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.8564 | 1.49323 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.92820 | 0.409265 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 12.9282i | − 1.06630i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 10.9282i | − 0.895273i | −0.894216 | − | 0.447637i | \(-0.852266\pi\) | ||||
0.894216 | − | 0.447637i | \(-0.147734\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.8564 | −1.28191 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.85641i | 0.791686i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.0000i | − 0.798087i | −0.916932 | − | 0.399043i | \(-0.869342\pi\) | ||||
0.916932 | − | 0.399043i | \(-0.130658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4641 | −0.988468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.8564 | −2.27420 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 23.8564i | − 1.86858i | −0.356517 | − | 0.934289i | \(-0.616036\pi\) | ||||
0.356517 | − | 0.934289i | \(-0.383964\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 8.00000i | − 0.622799i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.07180 | 0.392467 | 0.196234 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196234 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.92820 | −0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.00000i | − 0.152944i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 10.0000i | − 0.760286i | −0.924928 | − | 0.380143i | \(-0.875875\pi\) | ||||
0.924928 | − | 0.380143i | \(-0.124125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.46410 | −0.337454 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.92820 | −0.746249 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 25.8564i | − 1.93260i | −0.257421 | − | 0.966299i | \(-0.582873\pi\) | ||||
0.257421 | − | 0.966299i | \(-0.417127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000i | 0.743294i | 0.928374 | + | 0.371647i | \(0.121207\pi\) | ||||
−0.928374 | + | 0.371647i | \(0.878793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.92820 | −0.659992 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.7128i | 2.31907i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 22.3205i | 1.62358i | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 8.92820i | 0.639362i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.92820i | 0.493614i | 0.969065 | + | 0.246807i | \(0.0793814\pi\) | ||||
−0.969065 | + | 0.246807i | \(0.920619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.5359 | −0.959534 | −0.479767 | − | 0.877396i | \(-0.659279\pi\) | ||||
−0.479767 | + | 0.877396i | \(0.659279\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.92820 | 0.418143 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.0000i | 0.772049i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.8564i | 0.967773i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.9282 | 0.898572 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.8564i | 1.71119i | 0.517649 | + | 0.855593i | \(0.326807\pi\) | ||||
−0.517649 | + | 0.855593i | \(0.673193\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 14.0000i | − 0.959264i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.85641 | −0.672201 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.0000 | −1.49346 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 7.00000i | − 0.473016i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 35.3923i | − 2.38074i | ||||||||
\(222\) | 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 | ||||||||
\(227\) | 1.92820i | 0.127979i | 0.997951 | + | 0.0639897i | \(0.0203825\pi\) | ||||
−0.997951 | + | 0.0639897i | \(0.979618\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.07180i | 0.202990i | 0.994836 | + | 0.101495i | \(0.0323626\pi\) | ||||
−0.994836 | + | 0.101495i | \(0.967637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.8564 | 1.17487 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.8564 | 1.03879 | 0.519394 | − | 0.854535i | \(-0.326158\pi\) | ||||
0.519394 | + | 0.854535i | \(0.326158\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 13.8564i | − 0.903892i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2.00000i | − 0.129914i | ||||||||
\(238\) | 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 | ||||||||
\(243\) | − 16.0000i | − 1.02640i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.8564i | 1.65191i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.46410 | 0.284044 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.92820 | −0.185567 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.9282i | 0.816021i | 0.912977 | + | 0.408010i | \(0.133777\pi\) | ||||
−0.912977 | + | 0.408010i | \(0.866223\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 25.8564i | − 1.62558i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | − 8.92820i | − 0.554772i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 4.92820i | − 0.305048i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.92820 | 0.180561 | 0.0902804 | − | 0.995916i | \(-0.471224\pi\) | ||||
0.0902804 | + | 0.995916i | \(0.471224\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.9282 | 1.53133 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 0.928203i | − 0.0568051i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 7.85641i | − 0.479014i | −0.970895 | − | 0.239507i | \(-0.923014\pi\) | ||||
0.970895 | − | 0.239507i | \(-0.0769857\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | − 4.00000i | − 0.241209i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9282i | 1.49779i | 0.662688 | + | 0.748895i | \(0.269415\pi\) | ||||
−0.662688 | + | 0.748895i | \(0.730585\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.85641 | 0.590088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.00000 | 0.238620 | 0.119310 | − | 0.992857i | \(-0.461932\pi\) | ||||
0.119310 | + | 0.992857i | \(0.461932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 18.9282i | − 1.12516i | −0.826741 | − | 0.562582i | \(-0.809808\pi\) | ||||
0.826741 | − | 0.562582i | \(-0.190192\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 2.00000i | − 0.118470i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.9282 | −1.82563 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.8564 | 2.69744 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 12.9282i | − 0.757865i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.32051i | − 0.486089i | −0.970015 | − | 0.243045i | \(-0.921854\pi\) | ||||
0.970015 | − | 0.243045i | \(-0.0781462\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.8564 | 1.15608 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −20.0000 | −1.16052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.8564i | 1.66881i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 22.0000i | − 1.26806i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.85641 | 0.566236 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.8564 | 1.02245 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.85641i | − 0.105951i | −0.998596 | − | 0.0529754i | \(-0.983130\pi\) | ||||
0.998596 | − | 0.0529754i | \(-0.0168705\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.92820i | 0.166580i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.39230 | −0.419179 | −0.209590 | − | 0.977789i | \(-0.567213\pi\) | ||||
−0.209590 | + | 0.977789i | \(0.567213\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.8564 | 0.952780 | 0.476390 | − | 0.879234i | \(-0.341945\pi\) | ||||
0.476390 | + | 0.879234i | \(0.341945\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 17.8564i | − 1.00609i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.4641i | 0.812385i | 0.913788 | + | 0.406192i | \(0.133144\pi\) | ||||
−0.913788 | + | 0.406192i | \(0.866856\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.85641 | −0.551853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.9282 | 0.777396 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.92820i | 0.441137i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.46410i | 0.247624i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.39230 | −0.408795 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.9282 | 1.70513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 9.78461i | − 0.537811i | −0.963167 | − | 0.268905i | \(-0.913338\pi\) | ||||
0.963167 | − | 0.268905i | \(-0.0866619\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000i | 0.219199i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 12.9282i | − 0.702164i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 19.7128i | − 1.06751i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −26.4641 | −1.42893 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.9282 | 0.696031 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 27.8564i | − 1.49541i | −0.664031 | − | 0.747705i | \(-0.731156\pi\) | ||||
0.664031 | − | 0.747705i | \(-0.268844\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000i | 0.749403i | 0.927146 | + | 0.374701i | \(0.122255\pi\) | ||||
−0.927146 | + | 0.374701i | \(0.877745\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 28.0000i | 1.48609i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 35.3923i | − 1.87316i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.4641 | 1.29117 | 0.645583 | − | 0.763690i | \(-0.276614\pi\) | ||||
0.645583 | + | 0.763690i | \(0.276614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000i | 0.262432i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000i | 0.732793i | ||||||||
\(366\) | 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 | ||||||||
\(371\) | 55.6410i | 2.88874i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3923i | 0.589871i | 0.955517 | + | 0.294936i | \(0.0952982\pi\) | ||||
−0.955517 | + | 0.294936i | \(0.904702\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0000 | 0.619677 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.0000 | 0.566529 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.85641i | 0.352190i | 0.984373 | + | 0.176095i | \(0.0563466\pi\) | ||||
−0.984373 | + | 0.176095i | \(0.943653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 0.928203i | − 0.0475533i | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 9.85641i | 0.501029i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.8564i | 1.31097i | 0.755207 | + | 0.655486i | \(0.227536\pi\) | ||||
−0.755207 | + | 0.655486i | \(0.772464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.2487 | −2.59176 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.07180 | −0.356725 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000i | 0.201262i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8.92820i | − 0.448094i | −0.974578 | − | 0.224047i | \(-0.928073\pi\) | ||||
0.974578 | − | 0.224047i | \(-0.0719269\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 22.0000i | 1.09590i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000i | 0.0993808i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.85641i | 0.436854i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 44.3205i | 2.18087i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.85641 | 0.287480 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.8564 | −0.776492 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.7846i | 1.50393i | 0.659205 | + | 0.751963i | \(0.270893\pi\) | ||||
−0.659205 | + | 0.751963i | \(0.729107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5359i | 0.562225i | 0.959675 | + | 0.281113i | \(0.0907035\pi\) | ||||
−0.959675 | + | 0.281113i | \(0.909297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.8564 | −0.673722 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.92820 | −0.384574 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.8564i | 1.92879i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 17.8564i | − 0.862115i | ||||||||
\(430\) | 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 | ||||||||
\(435\) | − 4.92820i | − 0.236289i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6.46410i | − 0.309220i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | −0.190910 | −0.0954548 | − | 0.995434i | \(-0.530431\pi\) | ||||
−0.0954548 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25.8564 | 1.23126 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 17.8564i | − 0.848383i | −0.905572 | − | 0.424192i | \(-0.860558\pi\) | ||||
0.905572 | − | 0.424192i | \(-0.139442\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.85641i | 0.0880021i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | − 27.7128i | − 1.30495i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 16.0000i | − 0.751746i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 39.8564 | 1.86850 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.0000 | 1.45012 | 0.725059 | − | 0.688686i | \(-0.241812\pi\) | ||||
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 39.6410i | 1.85028i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8564i | 0.645357i | 0.946509 | + | 0.322679i | \(0.104583\pi\) | ||||
−0.946509 | + | 0.322679i | \(0.895417\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | − 2.78461i | − 0.128856i | −0.997922 | − | 0.0644282i | \(-0.979478\pi\) | ||||
0.997922 | − | 0.0644282i | \(-0.0205223\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 26.4641i | − 1.22200i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.7128 | 0.906396 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.00000i | − 0.0458831i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 24.9282i | − 1.14138i | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 28.8564i | 1.31301i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.8564i | 1.17408i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.6410 | 1.56973 | 0.784867 | − | 0.619664i | \(-0.212731\pi\) | ||||
0.784867 | + | 0.619664i | \(0.212731\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.8564 | −1.07882 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1436i | 0.638291i | 0.947706 | + | 0.319146i | \(0.103396\pi\) | ||||
−0.947706 | + | 0.319146i | \(0.896604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.5359i | 0.879853i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.0000 | 0.719147 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −62.4974 | −2.80339 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.7846i | 1.01998i | 0.860181 | + | 0.509990i | \(0.170351\pi\) | ||||
−0.860181 | + | 0.509990i | \(0.829649\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 5.07180i | − 0.226591i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.3205 | −0.995222 | −0.497611 | − | 0.867400i | \(-0.665789\pi\) | ||||
−0.497611 | + | 0.867400i | \(0.665789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.7128 | −0.877209 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.92820i | 0.307692i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 18.0000i | − 0.797836i | −0.916987 | − | 0.398918i | \(-0.869386\pi\) | ||||
0.916987 | − | 0.398918i | \(-0.130614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.2487 | −1.38236 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.00000 | −0.220755 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 5.85641i | − 0.258064i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.7128i | 1.21881i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.0000 | −0.438951 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0718 | −0.572686 | −0.286343 | − | 0.958127i | \(-0.592440\pi\) | ||||
−0.286343 | + | 0.958127i | \(0.592440\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.0000i | 1.35554i | 0.735276 | + | 0.677768i | \(0.237052\pi\) | ||||
−0.735276 | + | 0.677768i | \(0.762948\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.46410i | 0.194829i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −39.0718 | −1.70199 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.7846 | 0.816722 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 19.8564i | − 0.861695i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.9282i | 1.33965i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.8564 | −1.20434 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.8564 | −1.11579 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 51.7128i | − 2.22743i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7846i | 0.549653i | 0.961494 | + | 0.274827i | \(0.0886205\pi\) | ||||
−0.961494 | + | 0.274827i | \(0.911380\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0000 | 0.429141 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.7846 | 0.633303 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.14359i | 0.262681i | 0.991337 | + | 0.131341i | \(0.0419281\pi\) | ||||
−0.991337 | + | 0.131341i | \(0.958072\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 17.8564i | − 0.762093i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.46410 | −0.104974 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.92820 | −0.379666 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.00000i | 0.169791i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 22.0000i | − 0.932170i | −0.884740 | − | 0.466085i | \(-0.845664\pi\) | ||||
0.884740 | − | 0.466085i | \(-0.154336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.0000 | −0.930501 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.7128 | 1.33892 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 31.7128i | − 1.33654i | −0.743921 | − | 0.668268i | \(-0.767036\pi\) | ||||
0.743921 | − | 0.668268i | \(-0.232964\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.8564i | 1.08779i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.46410 | −0.187475 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.78461 | −0.368270 | −0.184135 | − | 0.982901i | \(-0.558948\pi\) | ||||
−0.184135 | + | 0.982901i | \(0.558948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 28.7846i | − 1.20460i | −0.798270 | − | 0.602299i | \(-0.794251\pi\) | ||||
0.798270 | − | 0.602299i | \(-0.205749\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.53590i | 0.147714i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | − 9.85641i | − 0.409618i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0718i | 0.542310i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.8564 | −2.06484 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.8564 | −0.738272 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 4.92820i | − 0.203063i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 70.7846i | 2.90189i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5359i | 0.553987i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.85641 | 0.402722 | 0.201361 | − | 0.979517i | \(-0.435464\pi\) | ||||
0.201361 | + | 0.979517i | \(0.435464\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.8564 | −1.13629 | −0.568143 | − | 0.822930i | \(-0.692338\pi\) | ||||
−0.568143 | + | 0.822930i | \(0.692338\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.8564i | 0.482830i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 10.0000i | − 0.406558i | ||||||||
\(606\) | 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 | ||||||||
\(611\) | − 30.9282i | − 1.25122i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 34.6410i | − 1.39914i | −0.714565 | − | 0.699569i | \(-0.753375\pi\) | ||||
0.714565 | − | 0.699569i | \(-0.246625\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.8564 | 0.558744 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.0000 | 0.563619 | 0.281809 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281809 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.8564i | 1.11964i | 0.828613 | + | 0.559822i | \(0.189130\pi\) | ||||
−0.828613 | + | 0.559822i | \(0.810870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 32.3205i | − 1.29698i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.14359 | −0.166010 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.00000i | 0.159745i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 15.8564i | − 0.632236i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.6410 | 1.53827 | 0.769137 | − | 0.639084i | \(-0.220686\pi\) | ||||
0.769137 | + | 0.639084i | \(0.220686\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.8564 | 0.987953 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.85641i | 0.0736692i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 57.7128i | 2.28666i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 32.9282i | 1.29856i | 0.760549 | + | 0.649281i | \(0.224930\pi\) | ||||
−0.760549 | + | 0.649281i | \(0.775070\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.85641i | 0.388096i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.5359 | −0.532151 | −0.266076 | − | 0.963952i | \(-0.585727\pi\) | ||||
−0.266076 | + | 0.963952i | \(0.585727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.7128 | −1.55886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.0000i | 0.862248i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 6.78461i | − 0.265502i | −0.991149 | − | 0.132751i | \(-0.957619\pi\) | ||||
0.991149 | − | 0.132751i | \(-0.0423811\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.1436 | 0.552636 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.0000 | 0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.85641i | 0.111270i | 0.998451 | + | 0.0556349i | \(0.0177183\pi\) | ||||
−0.998451 | + | 0.0556349i | \(0.982282\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 30.4641i | − 1.18492i | −0.805601 | − | 0.592458i | \(-0.798158\pi\) | ||||
0.805601 | − | 0.592458i | \(-0.201842\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −35.3923 | −1.37452 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.92820 | −0.346221 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 15.9282i | − 0.616742i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.9282i | 1.04110i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − 5.00000i | − 0.192450i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.39230i | 0.284109i | 0.989859 | + | 0.142055i | \(0.0453709\pi\) | ||||
−0.989859 | + | 0.142055i | \(0.954629\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −57.7128 | −2.21481 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.92820 | 0.0738889 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8564i | 0.683256i | 0.939835 | + | 0.341628i | \(0.110978\pi\) | ||||
−0.939835 | + | 0.341628i | \(0.889022\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 17.7128i | − 0.676772i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.07180 | 0.117196 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 55.6410 | 2.11975 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.85641i | 0.298872i | 0.988771 | + | 0.149436i | \(0.0477458\pi\) | ||||
−0.988771 | + | 0.149436i | \(0.952254\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 35.7128i | 1.35662i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 31.7128 | 1.20294 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −54.9282 | −2.08055 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 15.8564i | − 0.599744i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.71281i | 0.291309i | 0.989336 | + | 0.145654i | \(0.0465288\pi\) | ||||
−0.989336 | + | 0.145654i | \(0.953471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.8564 | −0.521862 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 44.0000i | − 1.65479i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 10.7846i | − 0.405025i | −0.979280 | − | 0.202512i | \(-0.935089\pi\) | ||||
0.979280 | − | 0.202512i | \(-0.0649106\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.00000 | 0.150012 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.8564 | 1.19303 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.7128i | 1.33558i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.3205i | 0.609501i | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 24.7846i | 0.921750i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.46410i | − 0.0915144i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.320508 | 0.0118870 | 0.00594349 | − | 0.999982i | \(-0.498108\pi\) | ||||
0.00594349 | + | 0.999982i | \(0.498108\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 39.0718i | − 1.44512i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.8564i | 1.61987i | 0.586517 | + | 0.809937i | \(0.300499\pi\) | ||||
−0.586517 | + | 0.809937i | \(0.699501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25.8564 | 0.953728 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.7128 | 0.873473 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.85641i | 0.362574i | 0.983430 | + | 0.181287i | \(0.0580263\pi\) | ||||
−0.983430 | + | 0.181287i | \(0.941974\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 4.46410i | − 0.163993i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.9282 | −0.621036 | −0.310518 | − | 0.950568i | \(-0.600502\pi\) | ||||
−0.310518 | + | 0.950568i | \(0.600502\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.8564 | 0.800757 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 5.85641i | − 0.214275i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 62.1769i | − 2.27190i | ||||||||
\(750\) | 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 | ||||||||
\(755\) | 32.0000i | 1.16460i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.21539i | − 0.0441741i | −0.999756 | − | 0.0220871i | \(-0.992969\pi\) | ||||
0.999756 | − | 0.0220871i | \(-0.00703110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.8564 | −0.938528 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.7128 | 1.76584 | 0.882919 | − | 0.469525i | \(-0.155575\pi\) | ||||
0.882919 | + | 0.469525i | \(0.155575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.0000i | 1.19468i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 31.7128i | − 1.14658i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0.928203i | 0.0334284i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 54.4641i | − 1.95894i | −0.201596 | − | 0.979469i | \(-0.564613\pi\) | ||||
0.201596 | − | 0.979469i | \(-0.435387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.92820 | 0.177026 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.92820 | −0.320298 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6.92820i | − 0.248229i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 56.0000i | − 2.00384i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.3205 | −0.440299 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7846i | 0.705245i | 0.935766 | + | 0.352623i | \(0.114710\pi\) | ||||
−0.935766 | + | 0.352623i | \(0.885290\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 2.92820i | − 0.104247i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −57.7128 | −2.05203 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.8564 | 1.41534 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 24.9282i | − 0.884112i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 30.1769i | − 1.06892i | −0.845193 | − | 0.534461i | \(-0.820515\pi\) | ||||
0.845193 | − | 0.534461i | \(-0.179485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.9282 | 1.94322 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.85641 | 0.0655929 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 28.0000i | − 0.988099i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 57.7128i | − 2.03411i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.85641 | −0.276559 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.0718 | −0.635371 | −0.317685 | − | 0.948196i | \(-0.602906\pi\) | ||||
−0.317685 | + | 0.948196i | \(0.602906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.14359i | 0.0401570i | 0.999798 | + | 0.0200785i | \(0.00639161\pi\) | ||||
−0.999798 | + | 0.0200785i | \(0.993608\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.60770i | 0.161599i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.7128 | 1.67131 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.92820 | 0.172416 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 39.8564i | − 1.39270i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 44.6410i | − 1.55798i | −0.627035 | − | 0.778991i | \(-0.715732\pi\) | ||||
0.627035 | − | 0.778991i | \(-0.284268\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.5359 | −0.820410 | −0.410205 | − | 0.911993i | \(-0.634543\pi\) | ||||
−0.410205 | + | 0.911993i | \(0.634543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 14.7128i | − 0.511615i | −0.966728 | − | 0.255807i | \(-0.917659\pi\) | ||||
0.966728 | − | 0.255807i | \(-0.0823413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.3205i | 0.427909i | 0.976844 | + | 0.213954i | \(0.0686344\pi\) | ||||
−0.976844 | + | 0.213954i | \(0.931366\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.9282 | 0.864750 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −102.497 | −3.55133 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.1436i | 0.351034i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 24.6410i | − 0.851718i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.0000 | 0.759524 | 0.379762 | − | 0.925084i | \(-0.376006\pi\) | ||||
0.379762 | + | 0.925084i | \(0.376006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.9282 | 0.790628 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 4.00000i | − 0.137767i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 13.8564i | − 0.476675i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.3205 | 0.766942 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.9282 | −0.649614 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.9282i | 0.443173i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 13.0718i | − 0.447570i | −0.974639 | − | 0.223785i | \(-0.928159\pi\) | ||||
0.974639 | − | 0.223785i | \(-0.0718413\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −49.8564 | −1.70306 | −0.851531 | − | 0.524304i | \(-0.824326\pi\) | ||||
−0.851531 | + | 0.524304i | \(0.824326\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 21.0718i | − 0.718960i | −0.933153 | − | 0.359480i | \(-0.882954\pi\) | ||||
0.933153 | − | 0.359480i | \(-0.117046\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30.9282i | 1.05403i | ||||||||
\(862\) | 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 | ||||||||
\(867\) | − 45.8564i | − 1.55737i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 8.00000i | − 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.4641 | −0.896702 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.8564 | 0.875107 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 53.5692i | − 1.81097i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.2487i | 1.05519i | 0.849495 | + | 0.527597i | \(0.176907\pi\) | ||||
−0.849495 | + | 0.527597i | \(0.823093\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 49.7128i | − 1.67297i | −0.547990 | − | 0.836485i | \(-0.684607\pi\) | ||||
0.547990 | − | 0.836485i | \(-0.315393\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 19.8564i | − 0.667466i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.9282 | 0.434087 | 0.217043 | − | 0.976162i | \(-0.430359\pi\) | ||||
0.217043 | + | 0.976162i | \(0.430359\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.14359 | −0.138972 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 4.00000i | − 0.134005i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.92820i | 0.231843i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 51.7128 | 1.72857 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.8564 | 0.963487 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 12.1436i | − 0.405012i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 98.8179i | 3.29210i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.0000 | −0.732114 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0000 | −0.664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.1436i | 0.436426i | 0.975901 | + | 0.218213i | \(0.0700227\pi\) | ||||
−0.975901 | + | 0.218213i | \(0.929977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.7128i | 0.653833i | ||||||||
\(910\) | 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 | ||||||||
\(915\) | − 17.8564i | − 0.590315i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.5692i | 1.04251i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.39230 | −0.177876 | −0.0889379 | − | 0.996037i | \(-0.528347\pi\) | ||||
−0.0889379 | + | 0.996037i | \(0.528347\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.85641 | −0.0611707 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 62.4974i | 2.05713i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000i | 0.0657596i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | − 12.9282i | − 0.423705i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.39230i | 0.242013i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −63.4256 | −2.07424 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.9282 | 0.977712 | 0.488856 | − | 0.872365i | \(-0.337414\pi\) | ||||
0.488856 | + | 0.872365i | \(0.337414\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 16.8564i | − 0.550088i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 41.1051i | − 1.33999i | −0.742366 | − | 0.669994i | \(-0.766297\pi\) | ||||
0.742366 | − | 0.669994i | \(-0.233703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.7846 | 1.45839 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −44.6410 | −1.45217 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 16.9282i | − 0.550093i | −0.961431 | − | 0.275046i | \(-0.911307\pi\) | ||||
0.961431 | − | 0.275046i | \(-0.0886932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.2487i | 1.01438i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.4641 | 0.469031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.21539 | 0.233729 | 0.116865 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116865 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 7.07180i | − 0.228838i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.85641i | 0.318612i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.5359 | 1.27668 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.71281 | −0.216542 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.8564i | 0.897660i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.7128i | 0.634578i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7846 | 0.797019 | 0.398510 | − | 0.917164i | \(-0.369528\pi\) | ||||
0.398510 | + | 0.917164i | \(0.369528\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.92820 | 0.254691 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.8564i | 0.829772i | 0.909873 | + | 0.414886i | \(0.136178\pi\) | ||||
−0.909873 | + | 0.414886i | \(0.863822\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.7846i | 2.26925i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | − 3.71281i | − 0.118662i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 14.7846i | − 0.472036i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.6410 | 0.658346 | 0.329173 | − | 0.944270i | \(-0.393230\pi\) | ||||
0.329173 | + | 0.944270i | \(0.393230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.8564 | −0.441502 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 30.9282i | − 0.984456i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.8564i | 1.01297i | ||||||||
\(990\) | 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 | ||||||||
\(995\) | − 27.0718i | − 0.858234i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 42.7846i | − 1.35500i | −0.735522 | − | 0.677501i | \(-0.763063\pi\) | ||||
0.735522 | − | 0.677501i | \(-0.236937\pi\) | |||||||
\(998\) | 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 | 2432.2.c.c.1217.1 | ✓ | 4 | |
4.3 | odd | 2 | 2432.2.c.d.1217.4 | yes | 4 | ||
8.3 | odd | 2 | 2432.2.c.d.1217.2 | yes | 4 | ||
8.5 | even | 2 | inner | 2432.2.c.c.1217.3 | yes | 4 | |
16.3 | odd | 4 | 4864.2.a.u.1.1 | 2 | |||
16.5 | even | 4 | 4864.2.a.s.1.2 | 2 | |||
16.11 | odd | 4 | 4864.2.a.v.1.1 | 2 | |||
16.13 | even | 4 | 4864.2.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.c.1217.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2432.2.c.c.1217.3 | yes | 4 | 8.5 | even | 2 | inner | |
2432.2.c.d.1217.2 | yes | 4 | 8.3 | odd | 2 | ||
2432.2.c.d.1217.4 | yes | 4 | 4.3 | odd | 2 | ||
4864.2.a.s.1.2 | 2 | 16.5 | even | 4 | |||
4864.2.a.u.1.1 | 2 | 16.3 | odd | 4 | |||
4864.2.a.v.1.1 | 2 | 16.11 | odd | 4 | |||
4864.2.a.x.1.2 | 2 | 16.13 | even | 4 |