Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5376,2,Mod(2689,5376)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5376, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("5376.2689");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5376 = 2^{8} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5376.c (of order \(2\), degree \(1\), not 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: | \(42.9275761266\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2689.4 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5376.2689 |
Dual form | 5376.2.c.bh.2689.1 |
$q$-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 \(\left(\mathbb{Z}/5376\mathbb{Z}\right)^\times\).
\(n\) | \(1793\) | \(2815\) | \(4609\) | \(5125\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.46410i | 1.54919i | 0.632456 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.46410i | 0.441443i | 0.975337 | + | 0.220722i | \(0.0708412\pi\) | ||||
−0.975337 | + | 0.220722i | \(0.929159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.00000i | − 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.46410 | −0.894427 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.535898 | 0.129974 | 0.0649872 | − | 0.997886i | \(-0.479299\pi\) | ||||
0.0649872 | + | 0.997886i | \(0.479299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820i | 1.58944i | 0.606977 | + | 0.794719i | \(0.292382\pi\) | ||||
−0.606977 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1.00000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.46410 | −0.305286 | −0.152643 | − | 0.988281i | \(-0.548779\pi\) | ||||
−0.152643 | + | 0.988281i | \(0.548779\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.92820i | 0.915144i | 0.889172 | + | 0.457572i | \(0.151281\pi\) | ||||
−0.889172 | + | 0.457572i | \(0.848719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.9282 | 1.96276 | 0.981382 | − | 0.192068i | \(-0.0615194\pi\) | ||||
0.981382 | + | 0.192068i | \(0.0615194\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.46410 | −0.254867 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.46410i | − 0.585540i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.00000i | − 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4641 | −1.79039 | −0.895196 | − | 0.445673i | \(-0.852964\pi\) | ||||
−0.895196 | + | 0.445673i | \(0.852964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 3.46410i | − 0.516398i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.9282 | −1.59404 | −0.797021 | − | 0.603951i | \(-0.793592\pi\) | ||||
−0.797021 | + | 0.603951i | \(0.793592\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.535898i | 0.0750408i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.00000i | − 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.07180 | −0.683881 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.92820 | −0.917663 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.07180i | 0.139536i | 0.997563 | + | 0.0697680i | \(0.0222259\pi\) | ||||
−0.997563 | + | 0.0697680i | \(0.977774\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92820i | 1.14314i | 0.820554 | + | 0.571570i | \(0.193665\pi\) | ||||
−0.820554 | + | 0.571570i | \(0.806335\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.92820 | 0.859338 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.92820i | − 0.357737i | −0.983873 | − | 0.178868i | \(-0.942756\pi\) | ||||
0.983873 | − | 0.178868i | \(-0.0572437\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 1.46410i | − 0.176257i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.46410 | 1.12318 | 0.561591 | − | 0.827415i | \(-0.310189\pi\) | ||||
0.561591 | + | 0.827415i | \(0.310189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.9282 | −1.51313 | −0.756566 | − | 0.653917i | \(-0.773124\pi\) | ||||
−0.756566 | + | 0.653917i | \(0.773124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 7.00000i | − 0.808290i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.46410i | − 0.166850i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9282 | 1.22952 | 0.614759 | − | 0.788715i | \(-0.289253\pi\) | ||||
0.614759 | + | 0.788715i | \(0.289253\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.00000i | − 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.85641i | 0.201356i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.92820 | −0.528359 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.46410 | −0.367194 | −0.183597 | − | 0.983002i | \(-0.558774\pi\) | ||||
−0.183597 | + | 0.983002i | \(0.558774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000i | 0.209657i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9282i | 1.13320i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.0000 | −2.46235 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.92820 | −0.906522 | −0.453261 | − | 0.891378i | \(-0.649739\pi\) | ||||
−0.453261 | + | 0.891378i | \(0.649739\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 1.46410i | − 0.147148i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 15.4641i | − 1.53874i | −0.638806 | − | 0.769368i | \(-0.720571\pi\) | ||||
0.638806 | − | 0.769368i | \(-0.279429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9282 | −1.07679 | −0.538394 | − | 0.842693i | \(-0.680969\pi\) | ||||
−0.538394 | + | 0.842693i | \(0.680969\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.46410 | 0.338062 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.3923i | − 1.19801i | −0.800746 | − | 0.599005i | \(-0.795563\pi\) | ||||
0.800746 | − | 0.599005i | \(-0.204437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.8564 | −1.86793 | −0.933967 | − | 0.357360i | \(-0.883677\pi\) | ||||
−0.933967 | + | 0.357360i | \(0.883677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 5.07180i | − 0.472947i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.535898 | −0.0491257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.85641 | 0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 11.4641i | − 1.03368i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.92820i | − 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.92820 | −0.259836 | −0.129918 | − | 0.991525i | \(-0.541471\pi\) | ||||
−0.129918 | + | 0.991525i | \(0.541471\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000i | 1.04844i | 0.851581 | + | 0.524222i | \(0.175644\pi\) | ||||
−0.851581 | + | 0.524222i | \(0.824356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 6.92820i | − 0.600751i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.46410 | 0.298142 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.92820 | 0.762788 | 0.381394 | − | 0.924413i | \(-0.375444\pi\) | ||||
0.381394 | + | 0.924413i | \(0.375444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8564i | 1.51456i | 0.653090 | + | 0.757280i | \(0.273472\pi\) | ||||
−0.653090 | + | 0.757280i | \(0.726528\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 10.9282i | − 0.920321i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.92820 | 0.244869 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.0718 | −1.41774 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 18.0000i | − 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.8564 | 1.77865 | 0.889325 | − | 0.457277i | \(-0.151175\pi\) | ||||
0.889325 | + | 0.457277i | \(0.151175\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.535898 | −0.0433248 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 37.8564i | 3.04070i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.928203i | 0.0740787i | 0.999314 | + | 0.0370393i | \(0.0117927\pi\) | ||||
−0.999314 | + | 0.0370393i | \(0.988207\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.46410 | 0.115387 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.9282i | 0.855963i | 0.903788 | + | 0.427981i | \(0.140775\pi\) | ||||
−0.903788 | + | 0.427981i | \(0.859225\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 5.07180i | − 0.394839i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.9282 | −0.845650 | −0.422825 | − | 0.906211i | \(-0.638961\pi\) | ||||
−0.422825 | + | 0.906211i | \(0.638961\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 6.92820i | − 0.529813i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 22.3923i | − 1.70246i | −0.524797 | − | 0.851228i | \(-0.675859\pi\) | ||||
0.524797 | − | 0.851228i | \(-0.324141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.00000 | 0.529150 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.07180 | −0.0805612 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.46410i | 0.707380i | 0.935363 | + | 0.353690i | \(0.115073\pi\) | ||||
−0.935363 | + | 0.353690i | \(0.884927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.00000i | − 0.445976i | −0.974821 | − | 0.222988i | \(-0.928419\pi\) | ||||
0.974821 | − | 0.222988i | \(-0.0715812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.92820 | −0.659992 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.92820 | 0.509372 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.784610i | 0.0573763i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.46410 | −0.684798 | −0.342399 | − | 0.939555i | \(-0.611240\pi\) | ||||
−0.342399 | + | 0.939555i | \(0.611240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.8564 | 1.14137 | 0.570685 | − | 0.821169i | \(-0.306678\pi\) | ||||
0.570685 | + | 0.821169i | \(0.306678\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.92820i | 0.496139i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 7.85641i | − 0.559746i | −0.960037 | − | 0.279873i | \(-0.909708\pi\) | ||||
0.960037 | − | 0.279873i | \(-0.0902923\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.85641 | 0.415150 | 0.207575 | − | 0.978219i | \(-0.433443\pi\) | ||||
0.207575 | + | 0.978219i | \(0.433443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.92820 | 0.206540 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.92820i | − 0.345892i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 39.7128i | − 2.77366i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.46410 | 0.101762 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.1436 | −0.701647 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 16.0000i | − 1.10149i | −0.834675 | − | 0.550743i | \(-0.814345\pi\) | ||||
0.834675 | − | 0.550743i | \(-0.185655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.46410i | 0.648470i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.7128 | −1.89000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.9282 | −0.741855 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 12.9282i | − 0.873607i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.07180i | − 0.0720969i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 22.9282i | − 1.52180i | −0.648870 | − | 0.760899i | \(-0.724758\pi\) | ||||
0.648870 | − | 0.760899i | \(-0.275242\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 27.8564i | − 1.84080i | −0.390974 | − | 0.920402i | \(-0.627862\pi\) | ||||
0.390974 | − | 0.920402i | \(-0.372138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.46410 | 0.0963308 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.9282 | −0.846955 | −0.423477 | − | 0.905907i | \(-0.639191\pi\) | ||||
−0.423477 | + | 0.905907i | \(0.639191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 37.8564i | − 2.46948i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.9282i | 0.709863i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.5359 | −0.940249 | −0.470125 | − | 0.882600i | \(-0.655791\pi\) | ||||
−0.470125 | + | 0.882600i | \(0.655791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.07180 | −0.197872 | −0.0989359 | − | 0.995094i | \(-0.531544\pi\) | ||||
−0.0989359 | + | 0.995094i | \(0.531544\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.46410i | 0.221313i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8564 | 0.881662 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.07180i | 0.572607i | 0.958139 | + | 0.286303i | \(0.0924265\pi\) | ||||
−0.958139 | + | 0.286303i | \(0.907573\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.14359i | − 0.134767i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.85641 | −0.116253 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4641 | 0.715111 | 0.357556 | − | 0.933892i | \(-0.383610\pi\) | ||||
0.357556 | + | 0.933892i | \(0.383610\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000i | 0.124274i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 4.92820i | − 0.305048i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3923 | 0.764142 | 0.382071 | − | 0.924133i | \(-0.375211\pi\) | ||||
0.382071 | + | 0.924133i | \(0.375211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.92820 | 0.425596 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3.46410i | − 0.212000i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3.46410i | − 0.211210i | −0.994408 | − | 0.105605i | \(-0.966322\pi\) | ||||
0.994408 | − | 0.105605i | \(-0.0336779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.92820 | −0.177876 | −0.0889378 | − | 0.996037i | \(-0.528347\pi\) | ||||
−0.0889378 | + | 0.996037i | \(0.528347\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 10.2487i | − 0.618021i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.143594i | 0.00862770i | 0.999991 | + | 0.00431385i | \(0.00137315\pi\) | ||||
−0.999991 | + | 0.00431385i | \(0.998627\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.9282 | −0.654254 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.9282 | −0.771232 | −0.385616 | − | 0.922659i | \(-0.626011\pi\) | ||||
−0.385616 | + | 0.922659i | \(0.626011\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9282i | 0.887390i | 0.896178 | + | 0.443695i | \(0.146333\pi\) | ||||
−0.896178 | + | 0.443695i | \(0.853667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 24.0000i | − 1.42164i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.4641 | 0.676705 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7128 | −0.983107 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 8.92820i | − 0.523381i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.5359i | 0.966037i | 0.875610 | + | 0.483019i | \(0.160460\pi\) | ||||
−0.875610 | + | 0.483019i | \(0.839540\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.71281 | −0.216168 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.46410 | 0.0849558 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.92820i | 0.169342i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 8.00000i | − 0.461112i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.4641 | 0.888389 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.9282 | −1.77094 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.9282i | 1.30858i | 0.756243 | + | 0.654291i | \(0.227033\pi\) | ||||
−0.756243 | + | 0.654291i | \(0.772967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 10.9282i | − 0.621684i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9282 | 1.07332 | 0.536660 | − | 0.843799i | \(-0.319686\pi\) | ||||
0.536660 | + | 0.843799i | \(0.319686\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.46410i | 0.195180i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 0.143594i | − 0.00806502i | −0.999992 | − | 0.00403251i | \(-0.998716\pi\) | ||||
0.999992 | − | 0.00403251i | \(-0.00128359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.21539 | −0.403984 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.3923 | 0.691671 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.71281i | 0.206586i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0000i | 0.776580i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.00000 | −0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.9282 | 0.602491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 24.0000i | − 1.31916i | −0.751635 | − | 0.659580i | \(-0.770734\pi\) | ||||
0.751635 | − | 0.659580i | \(-0.229266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000i | 0.109599i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.1436 | 0.554204 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.85641 | 0.427966 | 0.213983 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213983 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 19.8564i | − 1.07845i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.07180 | 0.273056 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 23.3205i | − 1.25191i | −0.779859 | − | 0.625955i | \(-0.784709\pi\) | ||||
0.779859 | − | 0.625955i | \(-0.215291\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 10.7846i | − 0.577287i | −0.957437 | − | 0.288643i | \(-0.906796\pi\) | ||||
0.957437 | − | 0.288643i | \(-0.0932042\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.53590 | 0.454320 | 0.227160 | − | 0.973857i | \(-0.427056\pi\) | ||||
0.227160 | + | 0.973857i | \(0.427056\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32.7846i | 1.74003i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 0.535898i | − 0.0283628i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.32051 | 0.386362 | 0.193181 | − | 0.981163i | \(-0.438120\pi\) | ||||
0.193181 | + | 0.981163i | \(0.438120\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.0000 | −1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.85641i | 0.464841i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 44.7846i | − 2.34413i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.4641 | 0.596797 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000i | 0.103835i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.0000i | 1.55334i | 0.629907 | + | 0.776671i | \(0.283093\pi\) | ||||
−0.629907 | + | 0.776671i | \(0.716907\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.92820 | 0.357771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.85641 | 0.507631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2.92820i | − 0.150016i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.7128 | −1.82484 | −0.912420 | − | 0.409256i | \(-0.865788\pi\) | ||||
−0.912420 | + | 0.409256i | \(0.865788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.07180 | 0.258483 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 8.00000i | − 0.406663i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.7846i | 0.749609i | 0.927104 | + | 0.374805i | \(0.122290\pi\) | ||||
−0.927104 | + | 0.374805i | \(0.877710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.784610 | −0.0396794 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.8564i | 1.90476i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 10.7846i | − 0.541264i | −0.962683 | − | 0.270632i | \(-0.912767\pi\) | ||||
0.962683 | − | 0.270632i | \(-0.0872327\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.92820 | 0.346844 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.92820 | 0.246103 | 0.123051 | − | 0.992400i | \(-0.460732\pi\) | ||||
0.123051 | + | 0.992400i | \(0.460732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 21.8564i | − 1.08875i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.46410i | 0.172133i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.92820 | 0.145146 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.92820 | −0.243684 | −0.121842 | − | 0.992550i | \(-0.538880\pi\) | ||||
−0.121842 | + | 0.992550i | \(0.538880\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.92820i | 0.440396i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.07180i | − 0.0527397i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.8564 | 0.680184 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.8564 | −0.874432 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.0718i | 0.834012i | 0.908904 | + | 0.417006i | \(0.136921\pi\) | ||||
−0.908904 | + | 0.417006i | \(0.863079\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4.14359i | − 0.201946i | −0.994889 | − | 0.100973i | \(-0.967804\pi\) | ||||
0.994889 | − | 0.100973i | \(-0.0321956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.9282 | 0.531347 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.75129 | −0.181964 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 8.92820i | − 0.432066i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.92820i | 0.141375i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2487 | 0.493663 | 0.246832 | − | 0.969058i | \(-0.420611\pi\) | ||||
0.246832 | + | 0.969058i | \(0.420611\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.8564 | −1.33869 | −0.669347 | − | 0.742950i | \(-0.733426\pi\) | ||||
−0.669347 | + | 0.742950i | \(0.733426\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 17.0718i | − 0.818530i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 10.1436i | − 0.485234i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8564 | 0.661330 | 0.330665 | − | 0.943748i | \(-0.392727\pi\) | ||||
0.330665 | + | 0.943748i | \(0.392727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.3923i | 1.34896i | 0.738294 | + | 0.674480i | \(0.235632\pi\) | ||||
−0.738294 | + | 0.674480i | \(0.764368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 12.0000i | − 0.568855i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0000 | 0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.85641 | 0.370767 | 0.185383 | − | 0.982666i | \(-0.440647\pi\) | ||||
0.185383 | + | 0.982666i | \(0.440647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 16.7846i | − 0.790356i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.8564i | 1.02690i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.92820 | −0.324799 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.7128 | −1.76413 | −0.882065 | − | 0.471127i | \(-0.843847\pi\) | ||||
−0.882065 | + | 0.471127i | \(0.843847\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 0.535898i | − 0.0250136i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.1769i | 1.26576i | 0.774252 | + | 0.632878i | \(0.218126\pi\) | ||||
−0.774252 | + | 0.632878i | \(0.781874\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.7846 | −1.52363 | −0.761815 | − | 0.647795i | \(-0.775691\pi\) | ||||
−0.761815 | + | 0.647795i | \(0.775691\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −37.8564 | −1.75555 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.7846i | 0.961797i | 0.876776 | + | 0.480899i | \(0.159689\pi\) | ||||
−0.876776 | + | 0.480899i | \(0.840311\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.92820i | 0.135212i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.928203 | −0.0427693 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.7128 | −0.538556 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 48.4974i | − 2.22521i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.07180 | 0.231736 | 0.115868 | − | 0.993265i | \(-0.463035\pi\) | ||||
0.115868 | + | 0.993265i | \(0.463035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.46410i | 0.0666189i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 30.9282i | − 1.40438i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7128 | −1.25579 | −0.627894 | − | 0.778299i | \(-0.716083\pi\) | ||||
−0.627894 | + | 0.778299i | \(0.716083\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.9282 | −0.494190 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.53590i | 0.294961i | 0.989065 | + | 0.147480i | \(0.0471164\pi\) | ||||
−0.989065 | + | 0.147480i | \(0.952884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.64102i | 0.118945i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.07180 | 0.227960 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.46410 | −0.424523 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 21.8564i | − 0.978427i | −0.872164 | − | 0.489214i | \(-0.837284\pi\) | ||||
0.872164 | − | 0.489214i | \(-0.162716\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 10.9282i | − 0.488236i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.5692 | 2.38380 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000i | 0.399704i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.2487i | 1.78399i | 0.452043 | + | 0.891996i | \(0.350696\pi\) | ||||
−0.452043 | + | 0.891996i | \(0.649304\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.9282 | 0.571910 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.92820 | 0.305888 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 37.8564i | − 1.66815i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16.0000i | − 0.703679i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.3923 | 0.982913 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.3923 | −1.33151 | −0.665756 | − | 0.746170i | \(-0.731891\pi\) | ||||
−0.665756 | + | 0.746170i | \(0.731891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 28.0000i | − 1.22435i | −0.790721 | − | 0.612177i | \(-0.790294\pi\) | ||||
0.790721 | − | 0.612177i | \(-0.209706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.00000i | 0.305505i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.85641 | 0.255109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8564 | −0.906800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.07180i | − 0.0465120i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.9282i | 0.993131i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 42.9282 | 1.85595 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.46410 | −0.408406 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.46410i | 0.0630633i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.85641i | 0.337773i | 0.985635 | + | 0.168887i | \(0.0540172\pi\) | ||||
−0.985635 | + | 0.168887i | \(0.945983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.00000 | 0.257485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.92820 | −0.296772 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9282i | 0.467256i | 0.972326 | + | 0.233628i | \(0.0750598\pi\) | ||||
−0.972326 | + | 0.233628i | \(0.924940\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 8.92820i | − 0.381046i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.1436 | −1.45457 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9282 | −0.464714 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.92820i | 0.294086i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.14359i | 0.175570i | 0.996139 | + | 0.0877848i | \(0.0279788\pi\) | ||||
−0.996139 | + | 0.0877848i | \(0.972021\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.784610 | −0.0331262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.0718i | 1.39381i | 0.717163 | + | 0.696905i | \(0.245440\pi\) | ||||
−0.717163 | + | 0.696905i | \(0.754560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 68.7846i | − 2.89379i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.9282 | 1.04504 | 0.522522 | − | 0.852626i | \(-0.324991\pi\) | ||||
0.522522 | + | 0.852626i | \(0.324991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 16.7846i | − 0.702414i | −0.936298 | − | 0.351207i | \(-0.885771\pi\) | ||||
0.936298 | − | 0.351207i | \(-0.114229\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 9.46410i | − 0.395369i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2487 | 0.427401 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.8564 | 0.993155 | 0.496578 | − | 0.867992i | \(-0.334590\pi\) | ||||
0.496578 | + | 0.867992i | \(0.334590\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.8564i | 0.658970i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.00000i | 0.165948i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.92820 | 0.121274 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.92820 | −0.286446 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.7846i | 0.857873i | 0.903335 | + | 0.428936i | \(0.141112\pi\) | ||||
−0.903335 | + | 0.428936i | \(0.858888\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 75.7128i | 3.11969i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.85641 | 0.323169 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.53590 | 0.350527 | 0.175264 | − | 0.984522i | \(-0.443922\pi\) | ||||
0.175264 | + | 0.984522i | \(0.443922\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.85641i | − 0.0761052i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.85641i | 0.239687i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.3923 | −1.16008 | −0.580039 | − | 0.814589i | \(-0.696963\pi\) | ||||
−0.580039 | + | 0.814589i | \(0.696963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.5692 | −1.77723 | −0.888613 | − | 0.458658i | \(-0.848330\pi\) | ||||
−0.888613 | + | 0.458658i | \(0.848330\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.92820i | 0.119246i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.6795i | 1.24730i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.8564 | −0.562414 | −0.281207 | − | 0.959647i | \(-0.590735\pi\) | ||||
−0.281207 | + | 0.959647i | \(0.590735\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.92820 | 0.199701 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.8564i | 0.884216i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.8564i | 1.12511i | 0.826760 | + | 0.562555i | \(0.190181\pi\) | ||||
−0.826760 | + | 0.562555i | \(0.809819\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 39.7128 | 1.60138 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.7846 | −0.756240 | −0.378120 | − | 0.925757i | \(-0.623429\pi\) | ||||
−0.378120 | + | 0.925757i | \(0.623429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.46410i | 0.0587524i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.46410 | 0.138786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 10.1436i | − 0.405096i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.07180i | − 0.0427353i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.9282 | 1.07199 | 0.535997 | − | 0.844220i | \(-0.319936\pi\) | ||||
0.535997 | + | 0.844220i | \(0.319936\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.0000 | 0.635943 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 10.1436i | − 0.402536i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.00000i | − 0.0792429i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.46410 | −0.374394 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.78461 | −0.267976 | −0.133988 | − | 0.990983i | \(-0.542778\pi\) | ||||
−0.133988 | + | 0.990983i | \(0.542778\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 12.7846i | − 0.504176i | −0.967704 | − | 0.252088i | \(-0.918883\pi\) | ||||
0.967704 | − | 0.252088i | \(-0.0811172\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 27.7128i | − 1.09119i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.07180 | −0.199393 | −0.0996965 | − | 0.995018i | \(-0.531787\pi\) | ||||
−0.0996965 | + | 0.995018i | \(0.531787\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.56922 | −0.0615972 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 10.9282i | − 0.428310i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.9282i | 0.818984i | 0.912314 | + | 0.409492i | \(0.134294\pi\) | ||||
−0.912314 | + | 0.409492i | \(0.865706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.5692 | −1.62424 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.9282 | 0.504377 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.5359i | 0.566238i | 0.959085 | + | 0.283119i | \(0.0913692\pi\) | ||||
−0.959085 | + | 0.283119i | \(0.908631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.7846i | 1.04180i | 0.853618 | + | 0.520900i | \(0.174404\pi\) | ||||
−0.853618 | + | 0.520900i | \(0.825596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.07180 | 0.0416251 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0000 | 0.930680 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.21539i | − 0.279381i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000i | 0.927894i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0718 | −0.504631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8564 | 1.22797 | 0.613987 | − | 0.789316i | \(-0.289565\pi\) | ||||
0.613987 | + | 0.789316i | \(0.289565\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.00000i | 0.269430i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.60770i | − 0.0617887i | −0.999523 | − | 0.0308944i | \(-0.990164\pi\) | ||||
0.999523 | − | 0.0308944i | \(-0.00983555\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.92820 | 0.342633 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.9282 | 0.878611 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.2487i | 0.698268i | 0.937073 | + | 0.349134i | \(0.113524\pi\) | ||||
−0.937073 | + | 0.349134i | \(0.886476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.9282i | 1.18171i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.8564 | 1.06279 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 41.8564i | − 1.59229i | −0.605104 | − | 0.796146i | \(-0.706869\pi\) | ||||
0.605104 | − | 0.796146i | \(-0.293131\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.46410i | 0.0556166i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −61.8564 | −2.34635 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.14359 | −0.232705 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 12.9282i | − 0.488990i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 28.6410i | − 1.08176i | −0.841101 | − | 0.540878i | \(-0.818092\pi\) | ||||
0.841101 | − | 0.540878i | \(-0.181908\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.8564 | 0.522604 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 37.8564 | 1.42575 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.4641i | 0.581587i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.7128i | 0.665219i | 0.943065 | + | 0.332609i | \(0.107929\pi\) | ||||
−0.943065 | + | 0.332609i | \(0.892071\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.9282 | −0.409840 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.1436i | 0.379349i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 14.5359i | − 0.542853i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.8564 | 0.516757 | 0.258378 | − | 0.966044i | \(-0.416812\pi\) | ||||
0.258378 | + | 0.966044i | \(0.416812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.9282 | 0.406988 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 3.07180i | − 0.114241i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 34.4974i | − 1.28120i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.0718 | 0.781510 | 0.390755 | − | 0.920495i | \(-0.372214\pi\) | ||||
0.390755 | + | 0.920495i | \(0.372214\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.28719i | 0.158567i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5.71281i | − 0.211008i | −0.994419 | − | 0.105504i | \(-0.966354\pi\) | ||||
0.994419 | − | 0.105504i | \(-0.0336455\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.46410 | −0.127775 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.28719 | 0.157921 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 37.0718i | − 1.36371i | −0.731488 | − | 0.681854i | \(-0.761174\pi\) | ||||
0.731488 | − | 0.681854i | \(-0.238826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.8564i | 0.509028i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.6077 | 0.425845 | 0.212923 | − | 0.977069i | \(-0.431702\pi\) | ||||
0.212923 | + | 0.977069i | \(0.431702\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 62.3538 | 2.28447 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000i | 0.146352i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.3923i | 0.452805i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.7128 | −1.01125 | −0.505627 | − | 0.862752i | \(-0.668739\pi\) | ||||
−0.505627 | + | 0.862752i | \(0.668739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.07180 | −0.330595 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 75.7128i | 2.75547i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 26.0000i | − 0.944986i | −0.881334 | − | 0.472493i | \(-0.843354\pi\) | ||||
0.881334 | − | 0.472493i | \(-0.156646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.14359 | 0.0778075 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.4641 | −0.995573 | −0.497786 | − | 0.867300i | \(-0.665854\pi\) | ||||
−0.497786 | + | 0.867300i | \(0.665854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.00000i | − 0.0724049i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.85641i | − 0.0671185i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.14359 | 0.0774007 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.14359 | 0.149422 | 0.0747109 | − | 0.997205i | \(-0.476197\pi\) | ||||
0.0747109 | + | 0.997205i | \(0.476197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4641i | 0.412870i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 5.32051i | − 0.191365i | −0.995412 | − | 0.0956827i | \(-0.969497\pi\) | ||||
0.995412 | − | 0.0956827i | \(-0.0305034\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −76.4974 | −2.74787 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.00000 | −0.0717496 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 79.4256i | − 2.84572i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8564i | 0.495821i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.92820 | 0.176120 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.21539 | −0.114762 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.7128i | 0.845270i | 0.906300 | + | 0.422635i | \(0.138895\pi\) | ||||
−0.906300 | + | 0.422635i | \(0.861105\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.3923i | 0.441178i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.8564 | 0.706013 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.8564 | 0.634100 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.92820i | 0.245718i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6.39230i | − 0.226427i | −0.993571 | − | 0.113214i | \(-0.963886\pi\) | ||||
0.993571 | − | 0.113214i | \(-0.0361144\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.85641 | −0.207185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.46410 | 0.122398 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 18.9282i | − 0.667962i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.07180i | 0.178757i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.46410 | 0.121942 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.0000 | 1.33601 | 0.668004 | − | 0.744157i | \(-0.267149\pi\) | ||||
0.668004 | + | 0.744157i | \(0.267149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.5692i | 1.31923i | 0.751602 | + | 0.659617i | \(0.229281\pi\) | ||||
−0.751602 | + | 0.659617i | \(0.770719\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.92820i | − 0.102697i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.8564 | −1.32605 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −55.4256 | −1.93910 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 2.00000i | − 0.0698857i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 12.1436i | − 0.423814i | −0.977290 | − | 0.211907i | \(-0.932033\pi\) | ||||
0.977290 | − | 0.211907i | \(-0.0679674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.0718 | −0.734517 | −0.367258 | − | 0.930119i | \(-0.619704\pi\) | ||||
−0.367258 | + | 0.930119i | \(0.619704\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.2487 | 0.356814 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.1769i | 1.29277i | 0.763012 | + | 0.646384i | \(0.223720\pi\) | ||||
−0.763012 | + | 0.646384i | \(0.776280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 21.7128i | − 0.754117i | −0.926189 | − | 0.377059i | \(-0.876936\pi\) | ||||
0.926189 | − | 0.377059i | \(-0.123064\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.143594 | −0.00498120 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.535898 | 0.0185678 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 37.8564i | − 1.31007i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 10.9282i | − 0.377734i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.9282 | −0.377283 | −0.188642 | − | 0.982046i | \(-0.560408\pi\) | ||||
−0.188642 | + | 0.982046i | \(0.560408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.71281 | 0.162511 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 12.9282i | − 0.445271i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.1769i | 1.07252i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.85641 | −0.304310 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.9282 | −0.512335 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.92820i | 0.100378i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0718i | 0.789963i | 0.918689 | + | 0.394982i | \(0.129249\pi\) | ||||
−0.918689 | + | 0.394982i | \(0.870751\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.0000 | 0.820783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −55.1769 | −1.88481 | −0.942404 | − | 0.334477i | \(-0.891440\pi\) | ||||
−0.942404 | + | 0.334477i | \(0.891440\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.9282i | 1.32821i | 0.747638 | + | 0.664107i | \(0.231188\pi\) | ||||
−0.747638 | + | 0.664107i | \(0.768812\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4641i | 0.390696i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.46410 | 0.322162 | 0.161081 | − | 0.986941i | \(-0.448502\pi\) | ||||
0.161081 | + | 0.986941i | \(0.448502\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 77.5692 | 2.63743 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 16.7128i | − 0.567597i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.0000i | 0.542763i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.85641 | −0.198437 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.92820 | 0.302174 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.92820i | 0.234216i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 8.14359i | − 0.274990i | −0.990502 | − | 0.137495i | \(-0.956095\pi\) | ||||
0.990502 | − | 0.137495i | \(-0.0439050\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.5359 | −0.557742 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.3205 | −0.448779 | −0.224390 | − | 0.974500i | \(-0.572039\pi\) | ||||
−0.224390 | + | 0.974500i | \(0.572039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 33.5692i | − 1.12969i | −0.825196 | − | 0.564847i | \(-0.808935\pi\) | ||||
0.825196 | − | 0.564847i | \(-0.191065\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 3.71281i | − 0.124805i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.9282 | −0.904161 | −0.452080 | − | 0.891977i | \(-0.649318\pi\) | ||||
−0.452080 | + | 0.891977i | \(0.649318\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.92820 | 0.0982088 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.46410i | 0.0490492i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 75.7128i | − 2.53363i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.7846 | −1.09587 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.92820 | −0.0977699 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 53.8564i | 1.79621i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.07180i | − 0.0357067i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7846 | 0.690904 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.7128i | 1.45146i | 0.687980 | + | 0.725730i | \(0.258498\pi\) | ||||
−0.687980 | + | 0.725730i | \(0.741502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.4641i | 0.512912i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.1769 | −0.966674 | −0.483337 | − | 0.875434i | \(-0.660575\pi\) | ||||
−0.483337 | + | 0.875434i | \(0.660575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.85641 | 0.193819 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 30.9282i | − 1.02245i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 12.0000i | − 0.396275i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.9282 | −0.755510 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 18.9282i | − 0.623029i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000i | 0.460317i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.9282 | 0.358929 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.6077 | 0.446454 | 0.223227 | − | 0.974766i | \(-0.428341\pi\) | ||||
0.223227 | + | 0.974766i | \(0.428341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.92820i | 0.227063i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.9282i | 0.619682i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.71797 | −0.0888870 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000i | 0.456873i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.5359i | 1.19104i | 0.803342 | + | 0.595518i | \(0.203053\pi\) | ||||
−0.803342 | + | 0.595518i | \(0.796947\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.7846 | 0.546582 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.46410 | −0.112687 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.2487i | 0.852969i | 0.904495 | + | 0.426484i | \(0.140248\pi\) | ||||
−0.904495 | + | 0.426484i | \(0.859752\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.8564i | 0.839334i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.143594 | 0.00465634 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.0000 | 0.712650 | 0.356325 | − | 0.934362i | \(-0.384030\pi\) | ||||
0.356325 | + | 0.934362i | \(0.384030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 32.7846i | − 1.06089i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 7.21539i | − 0.233240i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.92820 | −0.288307 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 88.4256 | 2.85244 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.3923i | 0.399336i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.9282i | 1.76820i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.9282 | 1.12322 | 0.561608 | − | 0.827404i | \(-0.310183\pi\) | ||||
0.561608 | + | 0.827404i | \(0.310183\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.71281 | −0.119273 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.85641i | − 0.0595749i | −0.999556 | − | 0.0297875i | \(-0.990517\pi\) | ||||
0.999556 | − | 0.0297875i | \(-0.00948305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 17.8564i | − 0.572450i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.0000 | −0.448359 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.4974 | 1.23164 | 0.615821 | − | 0.787886i | \(-0.288825\pi\) | ||||
0.615821 | + | 0.787886i | \(0.288825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 5.07180i | − 0.162095i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 2.00000i | − 0.0638551i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.71281 | −0.118420 | −0.0592102 | − | 0.998246i | \(-0.518858\pi\) | ||||
−0.0592102 | + | 0.998246i | \(0.518858\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.2154 | 0.867154 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.9282i | 0.347849i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 11.7128i | − 0.372446i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000 | 1.27064 | 0.635321 | − | 0.772248i | \(-0.280868\pi\) | ||||
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.0000 | 0.761617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.2872i | 0.643147i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.0718i | 0.984054i | 0.870580 | + | 0.492027i | \(0.163744\pi\) | ||||
−0.870580 | + | 0.492027i | \(0.836256\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 5376.2.c.bh.2689.4 | 4 | ||
4.3 | odd | 2 | 5376.2.c.bn.2689.2 | 4 | |||
8.3 | odd | 2 | 5376.2.c.bn.2689.3 | 4 | |||
8.5 | even | 2 | inner | 5376.2.c.bh.2689.1 | 4 | ||
16.3 | odd | 4 | 672.2.a.j.1.2 | yes | 2 | ||
16.5 | even | 4 | 1344.2.a.v.1.1 | 2 | |||
16.11 | odd | 4 | 1344.2.a.u.1.1 | 2 | |||
16.13 | even | 4 | 672.2.a.i.1.2 | ✓ | 2 | ||
48.5 | odd | 4 | 4032.2.a.bs.1.2 | 2 | |||
48.11 | even | 4 | 4032.2.a.br.1.2 | 2 | |||
48.29 | odd | 4 | 2016.2.a.t.1.1 | 2 | |||
48.35 | even | 4 | 2016.2.a.s.1.1 | 2 | |||
112.13 | odd | 4 | 4704.2.a.bn.1.1 | 2 | |||
112.27 | even | 4 | 9408.2.a.dx.1.2 | 2 | |||
112.69 | odd | 4 | 9408.2.a.do.1.2 | 2 | |||
112.83 | even | 4 | 4704.2.a.bm.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.a.i.1.2 | ✓ | 2 | 16.13 | even | 4 | ||
672.2.a.j.1.2 | yes | 2 | 16.3 | odd | 4 | ||
1344.2.a.u.1.1 | 2 | 16.11 | odd | 4 | |||
1344.2.a.v.1.1 | 2 | 16.5 | even | 4 | |||
2016.2.a.s.1.1 | 2 | 48.35 | even | 4 | |||
2016.2.a.t.1.1 | 2 | 48.29 | odd | 4 | |||
4032.2.a.br.1.2 | 2 | 48.11 | even | 4 | |||
4032.2.a.bs.1.2 | 2 | 48.5 | odd | 4 | |||
4704.2.a.bm.1.1 | 2 | 112.83 | even | 4 | |||
4704.2.a.bn.1.1 | 2 | 112.13 | odd | 4 | |||
5376.2.c.bh.2689.1 | 4 | 8.5 | even | 2 | inner | ||
5376.2.c.bh.2689.4 | 4 | 1.1 | even | 1 | trivial | ||
5376.2.c.bn.2689.2 | 4 | 4.3 | odd | 2 | |||
5376.2.c.bn.2689.3 | 4 | 8.3 | odd | 2 | |||
9408.2.a.do.1.2 | 2 | 112.69 | odd | 4 | |||
9408.2.a.dx.1.2 | 2 | 112.27 | even | 4 |