Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, 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("384.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (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: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.2.d.c.193.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.82843i | − 1.26491i | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
0.774597 | − | 0.632456i | \(-0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000i | 1.20605i | 0.797724 | + | 0.603023i | \(0.206037\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.65685i | − 1.56893i | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
0.620174 | − | 0.784465i | \(-0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.82843 | −0.730297 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.00000i | − 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2.82843i | − 0.617213i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.65685 | −1.17954 | −0.589768 | − | 0.807573i | \(-0.700781\pi\) | ||||
−0.589768 | + | 0.807573i | \(0.700781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.82843i | − 0.525226i | −0.964901 | − | 0.262613i | \(-0.915416\pi\) | ||||
0.964901 | − | 0.262613i | \(-0.0845842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.48528 | 1.52400 | 0.762001 | − | 0.647576i | \(-0.224217\pi\) | ||||
0.762001 | + | 0.647576i | \(0.224217\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 8.00000i | − 1.35225i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.65685 | −0.905822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000 | 1.56174 | 0.780869 | − | 0.624695i | \(-0.214777\pi\) | ||||
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.0000i | 1.82998i | 0.403473 | + | 0.914991i | \(0.367803\pi\) | ||||
−0.403473 | + | 0.914991i | \(0.632197\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843i | 0.421637i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | −0.825137 | −0.412568 | − | 0.910927i | \(-0.635368\pi\) | ||||
−0.412568 | + | 0.910927i | \(0.635368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000i | 0.280056i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.82843i | 0.388514i | 0.980951 | + | 0.194257i | \(0.0622296\pi\) | ||||
−0.980951 | + | 0.194257i | \(0.937770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.3137 | 1.52554 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 4.00000i | − 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3137i | 1.44857i | 0.689500 | + | 0.724286i | \(0.257830\pi\) | ||||
−0.689500 | + | 0.724286i | \(0.742170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.82843 | −0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.0000 | −1.98456 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685i | 0.681005i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685 | 0.671345 | 0.335673 | − | 0.941979i | \(-0.391036\pi\) | ||||
0.335673 | + | 0.941979i | \(0.391036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000i | 0.346410i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.3137i | 1.28932i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.48528 | 0.954669 | 0.477334 | − | 0.878722i | \(-0.341603\pi\) | ||||
0.477334 | + | 0.878722i | \(0.341603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.65685i | 0.613572i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.82843 | −0.303239 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 16.0000i | − 1.67726i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 8.48528i | − 0.879883i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.3137 | −1.16076 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0000 | 1.42148 | 0.710742 | − | 0.703452i | \(-0.248359\pi\) | ||||
0.710742 | + | 0.703452i | \(0.248359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 4.00000i | − 0.402015i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.1421i | 1.40720i | 0.710599 | + | 0.703598i | \(0.248424\pi\) | ||||
−0.710599 | + | 0.703598i | \(0.751576\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.82843 | −0.278693 | −0.139347 | − | 0.990244i | \(-0.544500\pi\) | ||||
−0.139347 | + | 0.990244i | \(0.544500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.65685i | 0.541828i | 0.962604 | + | 0.270914i | \(0.0873260\pi\) | ||||
−0.962604 | + | 0.270914i | \(0.912674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.0000i | 1.49201i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.65685i | 0.522976i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.65685 | −0.518563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 10.0000i | − 0.901670i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 5.65685i | − 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.48528 | −0.752947 | −0.376473 | − | 0.926427i | \(-0.622863\pi\) | ||||
−0.376473 | + | 0.926427i | \(0.622863\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | 1.05654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000i | 1.04844i | 0.851581 | + | 0.524222i | \(0.175644\pi\) | ||||
−0.851581 | + | 0.524222i | \(0.824356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 11.3137i | − 0.981023i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.82843 | 0.243432 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.00000i | − 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.65685i | 0.476393i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.6274 | 1.89220 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.00000i | − 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 14.1421i | − 1.15857i | −0.815125 | − | 0.579284i | \(-0.803332\pi\) | ||||
0.815125 | − | 0.579284i | \(-0.196668\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.48528 | −0.690522 | −0.345261 | − | 0.938507i | \(-0.612210\pi\) | ||||
−0.345261 | + | 0.938507i | \(0.612210\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 24.0000i | − 1.92773i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.82843 | 0.224309 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.00000i | − 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 11.3137i | − 0.880771i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3137 | −0.875481 | −0.437741 | − | 0.899101i | \(-0.644221\pi\) | ||||
−0.437741 | + | 0.899101i | \(0.644221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.0000 | −1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000i | 0.305888i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 19.7990i | − 1.50529i | −0.658427 | − | 0.752645i | \(-0.728778\pi\) | ||||
0.658427 | − | 0.752645i | \(-0.271222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.48528 | −0.641427 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000i | 0.896922i | 0.893802 | + | 0.448461i | \(0.148028\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 5.65685i | − 0.420471i | −0.977651 | − | 0.210235i | \(-0.932577\pi\) | ||||
0.977651 | − | 0.210235i | \(-0.0674230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.3137 | 0.836333 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.00000i | − 0.585018i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843i | 0.205738i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3137 | 0.818631 | 0.409316 | − | 0.912393i | \(-0.365768\pi\) | ||||
0.409316 | + | 0.912393i | \(0.365768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.0000i | 1.14578i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 8.48528i | − 0.604551i | −0.953221 | − | 0.302276i | \(-0.902254\pi\) | ||||
0.953221 | − | 0.302276i | \(-0.0977463\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.82843 | −0.200502 | −0.100251 | − | 0.994962i | \(-0.531965\pi\) | ||||
−0.100251 | + | 0.994962i | \(0.531965\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.00000i | − 0.561490i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 28.2843i | − 1.97546i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.65685 | 0.393179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000i | 0.826114i | 0.910705 | + | 0.413057i | \(0.135539\pi\) | ||||
−0.910705 | + | 0.413057i | \(0.864461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 5.65685i | − 0.387601i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 33.9411 | 2.31477 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.0000 | 1.62923 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000i | 0.135147i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.3137i | 0.761042i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.7990 | −1.32584 | −0.662919 | − | 0.748691i | \(-0.730683\pi\) | ||||
−0.662919 | + | 0.748691i | \(0.730683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 12.0000i | − 0.796468i | −0.917284 | − | 0.398234i | \(-0.869623\pi\) | ||||
0.917284 | − | 0.398234i | \(-0.130377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.65685i | 0.373815i | 0.982377 | + | 0.186908i | \(0.0598465\pi\) | ||||
−0.982377 | + | 0.186908i | \(0.940153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3137 | 0.744387 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000i | 1.04372i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8.48528i | − 0.551178i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.6274 | −1.46365 | −0.731823 | − | 0.681495i | \(-0.761330\pi\) | ||||
−0.731823 | + | 0.681495i | \(0.761330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.82843i | − 0.180702i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.6274 | −1.43975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 12.0000i | − 0.757433i | −0.925513 | − | 0.378717i | \(-0.876365\pi\) | ||||
0.925513 | − | 0.378717i | \(-0.123635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 22.6274i | − 1.42257i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.65685 | 0.354246 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.0000 | −1.87135 | −0.935674 | − | 0.352865i | \(-0.885208\pi\) | ||||
−0.935674 | + | 0.352865i | \(0.885208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.82843i | 0.175075i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6.00000i | − 0.367194i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.48528i | 0.517357i | 0.965964 | + | 0.258678i | \(0.0832870\pi\) | ||||
−0.965964 | + | 0.258678i | \(0.916713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.7990 | −1.20270 | −0.601351 | − | 0.798985i | \(-0.705371\pi\) | ||||
−0.601351 | + | 0.798985i | \(0.705371\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.0000 | −0.968364 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 12.0000i | − 0.723627i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.9706i | 1.01966i | 0.860274 | + | 0.509831i | \(0.170292\pi\) | ||||
−0.860274 | + | 0.509831i | \(0.829708\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.48528 | −0.508001 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.00000i | − 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.3137i | 0.670166i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.2843 | 1.66957 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 14.0000i | − 0.820695i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 19.7990i | − 1.15667i | −0.815800 | − | 0.578335i | \(-0.803703\pi\) | ||||
0.815800 | − | 0.578335i | \(-0.196297\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.3137 | −0.658710 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.00000 | −0.232104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32.0000i | 1.85061i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.9411i | 1.95633i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.1421 | 0.812444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.0000 | 1.83231 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 4.00000i | − 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.82843i | 0.160904i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3137 | −0.641542 | −0.320771 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320771 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.00000i | 0.450749i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.48528i | 0.476581i | 0.971194 | + | 0.238290i | \(0.0765870\pi\) | ||||
−0.971194 | + | 0.238290i | \(0.923413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.3137 | 0.633446 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000i | 0.445132i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.9706i | 0.941357i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.65685 | 0.312825 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0000 | −0.882109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 20.0000i | − 1.09930i | −0.835395 | − | 0.549650i | \(-0.814761\pi\) | ||||
0.835395 | − | 0.549650i | \(-0.185239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3137 | −0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 2.00000i | − 0.108625i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.9411i | 1.83801i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.0000 | 0.861411 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 36.0000i | 1.93258i | 0.257454 | + | 0.966291i | \(0.417117\pi\) | ||||
−0.257454 | + | 0.966291i | \(0.582883\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.3137i | 0.605609i | 0.953053 | + | 0.302804i | \(0.0979229\pi\) | ||||
−0.953053 | + | 0.302804i | \(0.902077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.65685 | 0.301941 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 16.0000i | − 0.849192i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.65685i | 0.299392i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.2843 | 1.49279 | 0.746393 | − | 0.665505i | \(-0.231784\pi\) | ||||
0.746393 | + | 0.665505i | \(0.231784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000i | 0.262432i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.65685i | 0.296093i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.48528 | 0.442928 | 0.221464 | − | 0.975169i | \(-0.428916\pi\) | ||||
0.221464 | + | 0.975169i | \(0.428916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.0000 | −0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.00000i | 0.415339i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 33.9411i | − 1.75740i | −0.477370 | − | 0.878702i | \(-0.658410\pi\) | ||||
0.477370 | − | 0.878702i | \(-0.341590\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.0000 | −0.824042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000i | 1.43826i | 0.694874 | + | 0.719132i | \(0.255460\pi\) | ||||
−0.694874 | + | 0.719132i | \(0.744540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.48528i | 0.434714i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.3137 | −0.578103 | −0.289052 | − | 0.957313i | \(-0.593340\pi\) | ||||
−0.289052 | + | 0.957313i | \(0.593340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.0000 | 1.63087 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 12.0000i | − 0.609994i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.1127i | 1.57748i | 0.614729 | + | 0.788738i | \(0.289265\pi\) | ||||
−0.614729 | + | 0.788738i | \(0.710735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3137 | 0.572159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 24.0000i | − 1.20757i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.9411i | 1.70346i | 0.523984 | + | 0.851728i | \(0.324445\pi\) | ||||
−0.523984 | + | 0.851728i | \(0.675555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.3137 | −0.566394 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 48.0000i | − 2.39105i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 2.82843i | − 0.140546i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 10.0000i | − 0.493264i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11.3137i | − 0.556711i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.3137 | 0.555368 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 28.0000i | − 1.36789i | −0.729534 | − | 0.683945i | \(-0.760263\pi\) | ||||
0.729534 | − | 0.683945i | \(-0.239737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.9706i | 0.827095i | 0.910483 | + | 0.413547i | \(0.135710\pi\) | ||||
−0.910483 | + | 0.413547i | \(0.864290\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.65685 | 0.275046 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | 0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.0000i | 1.54859i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 22.6274i | − 1.09246i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.2843 | 1.36241 | 0.681203 | − | 0.732095i | \(-0.261457\pi\) | ||||
0.681203 | + | 0.732095i | \(0.261457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.0000 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.00000i | 0.383571i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.6274i | 1.08242i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.1127 | 1.48493 | 0.742464 | − | 0.669886i | \(-0.233657\pi\) | ||||
0.742464 | + | 0.669886i | \(0.233657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0000i | 0.950229i | 0.879924 | + | 0.475114i | \(0.157593\pi\) | ||||
−0.879924 | + | 0.475114i | \(0.842407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 16.9706i | − 0.804482i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1421 | −0.668900 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.0000i | 1.88353i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.48528i | 0.398673i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −45.2548 | −2.12158 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.00000 | −0.280668 | −0.140334 | − | 0.990104i | \(-0.544818\pi\) | ||||
−0.140334 | + | 0.990104i | \(0.544818\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.00000i | − 0.0933520i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 8.48528i | − 0.395199i | −0.980283 | − | 0.197599i | \(-0.936685\pi\) | ||||
0.980283 | − | 0.197599i | \(-0.0633145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.7990 | −0.920137 | −0.460069 | − | 0.887883i | \(-0.652175\pi\) | ||||
−0.460069 | + | 0.887883i | \(0.652175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.0000 | −1.11297 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 28.0000i | − 1.29569i | −0.761774 | − | 0.647843i | \(-0.775671\pi\) | ||||
0.761774 | − | 0.647843i | \(-0.224329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 11.3137i | − 0.522419i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −48.0000 | −2.20704 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000i | 0.550598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.82843i | − 0.129505i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.2843 | −1.29234 | −0.646171 | − | 0.763193i | \(-0.723631\pi\) | ||||
−0.646171 | + | 0.763193i | \(0.723631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.0000i | 0.728025i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 39.5980i | − 1.79805i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.1421 | 0.640841 | 0.320421 | − | 0.947275i | \(-0.396176\pi\) | ||||
0.320421 | + | 0.947275i | \(0.396176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 20.0000i | − 0.902587i | −0.892375 | − | 0.451294i | \(-0.850963\pi\) | ||||
0.892375 | − | 0.451294i | \(-0.149037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.65685i | 0.254772i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.3137 | −0.508513 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.00000i | − 0.179065i | −0.995984 | − | 0.0895323i | \(-0.971463\pi\) | ||||
0.995984 | − | 0.0895323i | \(-0.0285372\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.3137i | 0.505459i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.65685 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.0000 | 1.77998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.0000i | 0.843820i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 2.82843i | − 0.125368i | −0.998033 | − | 0.0626839i | \(-0.980034\pi\) | ||||
0.998033 | − | 0.0626839i | \(-0.0199660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.65685 | −0.250244 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000 | 0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000i | 0.352522i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 22.6274i | − 0.995153i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.7990 | −0.869079 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 20.0000i | − 0.874539i | −0.899331 | − | 0.437269i | \(-0.855946\pi\) | ||||
0.899331 | − | 0.437269i | \(-0.144054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.48528i | 0.370328i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.9706 | −0.739249 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000i | 0.173585i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 56.5685i | − 2.45026i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.9411 | 1.46740 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.00000i | 0.172292i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 16.9706i | − 0.729621i | −0.931082 | − | 0.364811i | \(-0.881134\pi\) | ||||
0.931082 | − | 0.364811i | \(-0.118866\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.65685 | −0.242759 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.0000 | 0.685365 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20.0000i | − 0.855138i | −0.903983 | − | 0.427569i | \(-0.859370\pi\) | ||||
0.903983 | − | 0.427569i | \(-0.140630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 11.3137i | − 0.482857i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3137 | −0.481980 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.0000 | 1.02058 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 8.48528i | − 0.359533i | −0.983709 | − | 0.179766i | \(-0.942466\pi\) | ||||
0.983709 | − | 0.179766i | \(-0.0575342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 67.8823 | 2.87111 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.00000i | 0.168580i | 0.996441 | + | 0.0842900i | \(0.0268622\pi\) | ||||
−0.996441 | + | 0.0842900i | \(0.973138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 5.65685i | − 0.237986i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.82843 | 0.118783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 4.00000i | − 0.167395i | −0.996491 | − | 0.0836974i | \(-0.973327\pi\) | ||||
0.996491 | − | 0.0836974i | \(-0.0266729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 11.3137i | − 0.472637i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.9706 | 0.707721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.0000 | −0.915872 | −0.457936 | − | 0.888985i | \(-0.651411\pi\) | ||||
−0.457936 | + | 0.888985i | \(0.651411\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 6.00000i | − 0.249351i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.3137i | 0.469372i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3137 | −0.468566 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.0000 | 0.661519 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 36.0000i | − 1.48588i | −0.669359 | − | 0.742940i | \(-0.733431\pi\) | ||||
0.669359 | − | 0.742940i | \(-0.266569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 33.9411i | − 1.39852i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.48528 | −0.349038 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.0000 | 1.39621 | 0.698106 | − | 0.715994i | \(-0.254026\pi\) | ||||
0.698106 | + | 0.715994i | \(0.254026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.0000i | 0.655936i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.82843i | 0.115760i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.5980 | −1.61793 | −0.808965 | − | 0.587857i | \(-0.799972\pi\) | ||||
−0.808965 | + | 0.587857i | \(0.799972\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.1421i | 0.574960i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1421 | 0.574012 | 0.287006 | − | 0.957929i | \(-0.407340\pi\) | ||||
0.287006 | + | 0.957929i | \(0.407340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.00000 | −0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.0000i | 1.29458i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 11.3137i | − 0.456956i | −0.973549 | − | 0.228478i | \(-0.926625\pi\) | ||||
0.973549 | − | 0.228478i | \(-0.0733750\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28.2843 | −1.14053 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.0000 | 1.52982 | 0.764911 | − | 0.644136i | \(-0.222783\pi\) | ||||
0.764911 | + | 0.644136i | \(0.222783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 36.0000i | − 1.44696i | −0.690344 | − | 0.723481i | \(-0.742541\pi\) | ||||
0.690344 | − | 0.723481i | \(-0.257459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 5.65685i | − 0.227002i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9706 | 0.679911 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 16.0000i | − 0.638978i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.48528 | −0.337794 | −0.168897 | − | 0.985634i | \(-0.554020\pi\) | ||||
−0.168897 | + | 0.985634i | \(0.554020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0000 | 0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.0000i | 0.952411i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 5.65685i | − 0.224133i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.65685 | −0.223782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.0000 | −1.34292 | −0.671460 | − | 0.741041i | \(-0.734332\pi\) | ||||
−0.671460 | + | 0.741041i | \(0.734332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.0000i | 1.73519i | 0.497271 | + | 0.867595i | \(0.334335\pi\) | ||||
−0.497271 | + | 0.867595i | \(0.665665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 33.9411i | − 1.33643i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.5980 | 1.55676 | 0.778379 | − | 0.627795i | \(-0.216042\pi\) | ||||
0.778379 | + | 0.627795i | \(0.216042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 24.0000i | − 0.940634i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 42.4264i | − 1.66027i | −0.557560 | − | 0.830137i | \(-0.688262\pi\) | ||||
0.557560 | − | 0.830137i | \(-0.311738\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.9411 | 1.32619 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 4.00000i | − 0.155818i | −0.996960 | − | 0.0779089i | \(-0.975176\pi\) | ||||
0.996960 | − | 0.0779089i | \(-0.0248243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.2548i | 1.76021i | 0.474780 | + | 0.880105i | \(0.342528\pi\) | ||||
−0.474780 | + | 0.880105i | \(0.657472\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.3137 | 0.439388 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −32.0000 | −1.24091 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000i | 0.619522i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.7990i | 0.765473i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −45.2548 | −1.74704 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3.00000i | − 0.115470i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.7990i | 0.760937i | 0.924794 | + | 0.380468i | \(0.124237\pi\) | ||||
−0.924794 | + | 0.380468i | \(0.875763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.5980 | 1.51963 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.0000i | 0.765279i | 0.923898 | + | 0.382639i | \(0.124985\pi\) | ||||
−0.923898 | + | 0.382639i | \(0.875015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 28.2843i | − 1.08069i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.65685 | 0.215822 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.0000 | 0.609551 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000i | 1.06517i | 0.846376 | + | 0.532585i | \(0.178779\pi\) | ||||
−0.846376 | + | 0.532585i | \(0.821221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 11.3137i | − 0.429772i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.3137 | −0.429153 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.0000 | −0.757554 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 6.00000i | − 0.226941i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.7990i | 0.747798i | 0.927470 | + | 0.373899i | \(0.121979\pi\) | ||||
−0.927470 | + | 0.373899i | \(0.878021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.0000 | 0.602595 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.0000i | 1.50435i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 16.9706i | − 0.637343i | −0.947865 | − | 0.318671i | \(-0.896763\pi\) | ||||
0.947865 | − | 0.318671i | \(-0.103237\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.48528 | −0.318223 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48.0000 | −1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 64.0000i | − 2.39346i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.6274i | 0.845036i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.9706 | −0.632895 | −0.316448 | − | 0.948610i | \(-0.602490\pi\) | ||||
−0.316448 | + | 0.948610i | \(0.602490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.00000i | − 0.223142i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.48528i | 0.315135i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.4558 | 0.944105 | 0.472052 | − | 0.881570i | \(-0.343513\pi\) | ||||
0.472052 | + | 0.881570i | \(0.343513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 24.0000i | − 0.887672i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.9706i | 0.626822i | 0.949618 | + | 0.313411i | \(0.101472\pi\) | ||||
−0.949618 | + | 0.313411i | \(0.898528\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.82843 | −0.104328 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | 0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 36.0000i | − 1.32428i | −0.749380 | − | 0.662141i | \(-0.769648\pi\) | ||||
0.749380 | − | 0.662141i | \(-0.230352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.6274i | 0.831239i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.6274 | 0.830119 | 0.415060 | − | 0.909794i | \(-0.363761\pi\) | ||||
0.415060 | + | 0.909794i | \(0.363761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.0000 | −1.46549 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.00000i | − 0.146352i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.9411i | 1.24018i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.0833 | −1.75458 | −0.877292 | − | 0.479958i | \(-0.840652\pi\) | ||||
−0.877292 | + | 0.479958i | \(0.840652\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.0000i | 0.873449i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.2843i | 1.02801i | 0.857787 | + | 0.514005i | \(0.171839\pi\) | ||||
−0.857787 | + | 0.514005i | \(0.828161\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.6274 | −0.821323 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000 | 1.52250 | 0.761249 | − | 0.648459i | \(-0.224586\pi\) | ||||
0.761249 | + | 0.648459i | \(0.224586\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0000i | 0.579239i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 5.65685i | − 0.204524i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.6274 | −0.817029 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.0000 | 1.37032 | 0.685158 | − | 0.728395i | \(-0.259733\pi\) | ||||
0.685158 | + | 0.728395i | \(0.259733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.0000i | 1.08042i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.82843i | 0.101731i | 0.998706 | + | 0.0508657i | \(0.0161981\pi\) | ||||
−0.998706 | + | 0.0508657i | \(0.983802\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.4558 | −0.914401 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 40.0000i | − 1.43315i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.6274i | 0.809673i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.82843 | 0.101080 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 20.0000i | − 0.712923i | −0.934310 | − | 0.356462i | \(-0.883983\pi\) | ||||
0.934310 | − | 0.356462i | \(-0.116017\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.65685 | 0.201135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 64.0000 | 2.27271 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 8.00000i | − 0.283731i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 19.7990i | − 0.701316i | −0.936504 | − | 0.350658i | \(-0.885958\pi\) | ||||
0.936504 | − | 0.350658i | \(-0.114042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.3137 | 0.400250 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 8.00000i | − 0.282314i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 45.2548i | 1.59502i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.48528 | 0.298696 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.0000 | 0.351581 | 0.175791 | − | 0.984428i | \(-0.443752\pi\) | ||||
0.175791 | + | 0.984428i | \(0.443752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 20.0000i | − 0.702295i | −0.936320 | − | 0.351147i | \(-0.885792\pi\) | ||||
0.936320 | − | 0.351147i | \(-0.114208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.7990i | 0.694381i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.3137 | −0.396302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.0000 | 1.67931 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.0000i | 0.559085i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 31.1127i | − 1.08584i | −0.839784 | − | 0.542920i | \(-0.817319\pi\) | ||||
0.839784 | − | 0.542920i | \(-0.182681\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.7990 | −0.690149 | −0.345075 | − | 0.938575i | \(-0.612146\pi\) | ||||
−0.345075 | + | 0.938575i | \(0.612146\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0000 | −0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.9117i | 1.76824i | 0.467264 | + | 0.884118i | \(0.345240\pi\) | ||||
−0.467264 | + | 0.884118i | \(0.654760\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.9706 | 0.588702 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0000i | 1.10741i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.48528i | 0.293294i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.65685 | −0.195296 | −0.0976481 | − | 0.995221i | \(-0.531132\pi\) | ||||
−0.0976481 | + | 0.995221i | \(0.531132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.0000i | 0.344418i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 53.7401i | 1.84872i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.1421 | −0.485930 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 22.6274i | − 0.774748i | −0.921923 | − | 0.387374i | \(-0.873382\pi\) | ||||
0.921923 | − | 0.387374i | \(-0.126618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.3137 | 0.386921 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.00000 | −0.204956 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000i | 1.50126i | 0.660722 | + | 0.750630i | \(0.270250\pi\) | ||||
−0.660722 | + | 0.750630i | \(0.729750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 28.2843i | − 0.963925i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.5685 | 1.92562 | 0.962808 | − | 0.270187i | \(-0.0870856\pi\) | ||||
0.962808 | + | 0.270187i | \(0.0870856\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −56.0000 | −1.90406 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000i | 0.441503i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.9411i | 1.15137i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.6274 | −0.766701 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.0000 | −0.473828 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 16.0000i | − 0.540899i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 11.3137i | − 0.382037i | −0.981586 | − | 0.191018i | \(-0.938821\pi\) | ||||
0.981586 | − | 0.191018i | \(-0.0611790\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.7990 | −0.667803 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.0000 | −1.54978 | −0.774890 | − | 0.632096i | \(-0.782195\pi\) | ||||
−0.774890 | + | 0.632096i | \(0.782195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0000i | 0.403832i | 0.979403 | + | 0.201916i | \(0.0647168\pi\) | ||||
−0.979403 | + | 0.201916i | \(0.935283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.3137i | 0.380306i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0000 | −0.804934 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.00000i | 0.134005i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.6274i | 0.757198i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.9411 | 1.13453 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.0000 | 1.06845 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 24.0000i | − 0.800445i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 5.65685i | − 0.188457i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.9411 | 1.12949 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.0000 | −0.531858 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.0000i | 1.46100i | 0.682915 | + | 0.730498i | \(0.260712\pi\) | ||||
−0.682915 | + | 0.730498i | \(0.739288\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 14.1421i | − 0.469065i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.6274 | 0.749680 | 0.374840 | − | 0.927090i | \(-0.377698\pi\) | ||||
0.374840 | + | 0.927090i | \(0.377698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.0000 | −0.529523 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 32.0000i | − 1.05789i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.9411i | 1.12083i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.82843 | 0.0933012 | 0.0466506 | − | 0.998911i | \(-0.485145\pi\) | ||||
0.0466506 | + | 0.998911i | \(0.485145\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.00000 | −0.131804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 32.0000i | − 1.05329i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.82843 | 0.0928977 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4.00000i | − 0.131095i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.3137i | 0.370394i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.6274 | −0.739996 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.0000 | −1.37208 | −0.686040 | − | 0.727564i | \(-0.740653\pi\) | ||||
−0.686040 | + | 0.727564i | \(0.740653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000i | 0.456873i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.1421i | 0.461020i | 0.973070 | + | 0.230510i | \(0.0740395\pi\) | ||||
−0.973070 | + | 0.230510i | \(0.925960\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.5685 | −1.84213 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.00000 | 0.260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 36.0000i | − 1.16984i | −0.811090 | − | 0.584921i | \(-0.801125\pi\) | ||||
0.811090 | − | 0.584921i | \(-0.198875\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.3137i | 0.367259i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.48528 | 0.275154 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.0000 | 1.36051 | 0.680257 | − | 0.732974i | \(-0.261868\pi\) | ||||
0.680257 | + | 0.732974i | \(0.261868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 32.0000i | − 1.03550i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 11.3137i | − 0.365720i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.2843 | 0.913347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0000 | 1.32258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 12.0000i | − 0.386695i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 16.9706i | − 0.546302i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.1421 | −0.454780 | −0.227390 | − | 0.973804i | \(-0.573019\pi\) | ||||
−0.227390 | + | 0.973804i | \(0.573019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.00000 | 0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 12.0000i | − 0.385098i | −0.981287 | − | 0.192549i | \(-0.938325\pi\) | ||||
0.981287 | − | 0.192549i | \(-0.0616755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 11.3137i | − 0.362701i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.9706 | 0.543493 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.00000 | −0.0639857 | −0.0319928 | − | 0.999488i | \(-0.510185\pi\) | ||||
−0.0319928 | + | 0.999488i | \(0.510185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000i | 0.767043i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 5.65685i | − 0.180609i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0000 | −0.764704 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.0000i | 0.509286i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 67.8823i | − 2.15853i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4558 | −0.808632 | −0.404316 | − | 0.914619i | \(-0.632490\pi\) | ||||
−0.404316 | + | 0.914619i | \(0.632490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.0000 | −0.634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.00000i | 0.253617i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 33.9411i | − 1.07493i | −0.843287 | − | 0.537463i | \(-0.819383\pi\) | ||||
0.843287 | − | 0.537463i | \(-0.180617\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.2.d.c.193.1 | ✓ | 4 | |
3.2 | odd | 2 | 1152.2.d.h.577.4 | 4 | |||
4.3 | odd | 2 | inner | 384.2.d.c.193.3 | yes | 4 | |
8.3 | odd | 2 | inner | 384.2.d.c.193.2 | yes | 4 | |
8.5 | even | 2 | inner | 384.2.d.c.193.4 | yes | 4 | |
12.11 | even | 2 | 1152.2.d.h.577.3 | 4 | |||
16.3 | odd | 4 | 768.2.a.i.1.1 | 2 | |||
16.5 | even | 4 | 768.2.a.i.1.2 | 2 | |||
16.11 | odd | 4 | 768.2.a.l.1.2 | 2 | |||
16.13 | even | 4 | 768.2.a.l.1.1 | 2 | |||
24.5 | odd | 2 | 1152.2.d.h.577.2 | 4 | |||
24.11 | even | 2 | 1152.2.d.h.577.1 | 4 | |||
48.5 | odd | 4 | 2304.2.a.x.1.1 | 2 | |||
48.11 | even | 4 | 2304.2.a.r.1.1 | 2 | |||
48.29 | odd | 4 | 2304.2.a.r.1.2 | 2 | |||
48.35 | even | 4 | 2304.2.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.2.d.c.193.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
384.2.d.c.193.2 | yes | 4 | 8.3 | odd | 2 | inner | |
384.2.d.c.193.3 | yes | 4 | 4.3 | odd | 2 | inner | |
384.2.d.c.193.4 | yes | 4 | 8.5 | even | 2 | inner | |
768.2.a.i.1.1 | 2 | 16.3 | odd | 4 | |||
768.2.a.i.1.2 | 2 | 16.5 | even | 4 | |||
768.2.a.l.1.1 | 2 | 16.13 | even | 4 | |||
768.2.a.l.1.2 | 2 | 16.11 | odd | 4 | |||
1152.2.d.h.577.1 | 4 | 24.11 | even | 2 | |||
1152.2.d.h.577.2 | 4 | 24.5 | odd | 2 | |||
1152.2.d.h.577.3 | 4 | 12.11 | even | 2 | |||
1152.2.d.h.577.4 | 4 | 3.2 | odd | 2 | |||
2304.2.a.r.1.1 | 2 | 48.11 | even | 4 | |||
2304.2.a.r.1.2 | 2 | 48.29 | odd | 4 | |||
2304.2.a.x.1.1 | 2 | 48.5 | odd | 4 | |||
2304.2.a.x.1.2 | 2 | 48.35 | even | 4 |