Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [775,2,Mod(557,775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(775, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("775.557");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 775 = 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 775.f (of order \(4\), degree \(2\), 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: | \(6.18840615665\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 743.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 775.743 |
Dual form | 775.2.f.a.557.2 |
$q$-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 \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).
\(n\) | \(251\) | \(652\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 1.22474i | 0.866025 | − | 0.866025i | −0.126004 | − | 0.992030i | \(-0.540215\pi\) |
0.992030 | + | 0.126004i | \(0.0402153\pi\) | |||||||
\(3\) | −1.00000 | + | 1.00000i | −0.577350 | + | 0.577350i | −0.934172 | − | 0.356822i | \(-0.883860\pi\) |
0.356822 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 1.00000i | ||||||||
\(7\) | 2.44949 | − | 2.44949i | 0.925820 | − | 0.925820i | −0.0716124 | − | 0.997433i | \(-0.522814\pi\) |
0.997433 | + | 0.0716124i | \(0.0228145\pi\) | |||||||
\(8\) | 1.22474 | + | 1.22474i | 0.433013 | + | 0.433013i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.89898i | − | 1.47710i | −0.674200 | − | 0.738549i | \(-0.735511\pi\) | ||
0.674200 | − | 0.738549i | \(-0.264489\pi\) | |||||||
\(12\) | 1.00000 | + | 1.00000i | 0.288675 | + | 0.288675i | ||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | − | 6.00000i | − | 1.60357i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 1.25000 | ||||||||
\(17\) | 5.00000 | + | 5.00000i | 1.21268 | + | 1.21268i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) |
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 1.22474 | + | 1.22474i | 0.288675 | + | 0.288675i | ||||
\(19\) | − | 2.00000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.89898i | 1.06904i | ||||||||
\(22\) | −6.00000 | − | 6.00000i | −1.27920 | − | 1.27920i | ||||
\(23\) | 1.00000 | − | 1.00000i | 0.208514 | − | 0.208514i | −0.595121 | − | 0.803636i | \(-0.702896\pi\) |
0.803636 | + | 0.595121i | \(0.202896\pi\) | |||||||
\(24\) | −2.44949 | −0.500000 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.34847i | 1.44115i | ||||||||
\(27\) | −4.00000 | − | 4.00000i | −0.769800 | − | 0.769800i | ||||
\(28\) | −2.44949 | − | 2.44949i | −0.462910 | − | 0.462910i | ||||
\(29\) | 9.79796 | 1.81944 | 0.909718 | − | 0.415227i | \(-0.136298\pi\) | ||||
0.909718 | + | 0.415227i | \(0.136298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | − | 2.44949i | 0.898027 | − | 0.439941i | ||||
\(32\) | 3.67423 | − | 3.67423i | 0.649519 | − | 0.649519i | ||||
\(33\) | 4.89898 | + | 4.89898i | 0.852803 | + | 0.852803i | ||||
\(34\) | 12.2474 | 2.10042 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | −2.44949 | − | 2.44949i | −0.397360 | − | 0.397360i | ||||
\(39\) | − | 6.00000i | − | 0.960769i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 6.00000 | + | 6.00000i | 0.925820 | + | 0.925820i | ||||
\(43\) | 3.00000 | − | 3.00000i | 0.457496 | − | 0.457496i | −0.440337 | − | 0.897833i | \(-0.645141\pi\) |
0.897833 | + | 0.440337i | \(0.145141\pi\) | |||||||
\(44\) | −4.89898 | −0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 2.44949i | − | 0.361158i | ||||||
\(47\) | −7.34847 | + | 7.34847i | −1.07188 | + | 1.07188i | −0.0746766 | + | 0.997208i | \(0.523792\pi\) |
−0.997208 | + | 0.0746766i | \(0.976208\pi\) | |||||||
\(48\) | −5.00000 | + | 5.00000i | −0.721688 | + | 0.721688i | ||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.0000 | −1.40028 | ||||||||
\(52\) | 3.00000 | + | 3.00000i | 0.416025 | + | 0.416025i | ||||
\(53\) | 1.00000 | − | 1.00000i | 0.137361 | − | 0.137361i | −0.635083 | − | 0.772444i | \(-0.719034\pi\) |
0.772444 | + | 0.635083i | \(0.219034\pi\) | |||||||
\(54\) | −9.79796 | −1.33333 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.00000 | 0.801784 | ||||||||
\(57\) | 2.00000 | + | 2.00000i | 0.264906 | + | 0.264906i | ||||
\(58\) | 12.0000 | − | 12.0000i | 1.57568 | − | 1.57568i | ||||
\(59\) | − | 12.0000i | − | 1.56227i | −0.624364 | − | 0.781133i | \(-0.714642\pi\) | ||
0.624364 | − | 0.781133i | \(-0.285358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.89898i | − | 0.627250i | −0.949547 | − | 0.313625i | \(-0.898457\pi\) | ||
0.949547 | − | 0.313625i | \(-0.101543\pi\) | |||||||
\(62\) | 3.12372 | − | 9.12372i | 0.396713 | − | 1.15871i | ||||
\(63\) | 2.44949 | + | 2.44949i | 0.308607 | + | 0.308607i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.0000 | 1.47710 | ||||||||
\(67\) | −2.44949 | + | 2.44949i | −0.299253 | + | 0.299253i | −0.840721 | − | 0.541468i | \(-0.817869\pi\) |
0.541468 | + | 0.840721i | \(0.317869\pi\) | |||||||
\(68\) | 5.00000 | − | 5.00000i | 0.606339 | − | 0.606339i | ||||
\(69\) | 2.00000i | 0.240772i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | −1.22474 | + | 1.22474i | −0.144338 | + | 0.144338i | ||||
\(73\) | −3.00000 | + | 3.00000i | −0.351123 | + | 0.351123i | −0.860527 | − | 0.509404i | \(-0.829866\pi\) |
0.509404 | + | 0.860527i | \(0.329866\pi\) | |||||||
\(74\) | 7.34847 | 0.854242 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | −12.0000 | − | 12.0000i | −1.36753 | − | 1.36753i | ||||
\(78\) | −7.34847 | − | 7.34847i | −0.832050 | − | 0.832050i | ||||
\(79\) | −9.79796 | −1.10236 | −0.551178 | − | 0.834388i | \(-0.685822\pi\) | ||||
−0.551178 | + | 0.834388i | \(0.685822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | −7.34847 | + | 7.34847i | −0.811503 | + | 0.811503i | ||||
\(83\) | −7.00000 | + | 7.00000i | −0.768350 | + | 0.768350i | −0.977816 | − | 0.209466i | \(-0.932827\pi\) |
0.209466 | + | 0.977816i | \(0.432827\pi\) | |||||||
\(84\) | 4.89898 | 0.534522 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 7.34847i | − | 0.792406i | ||||||
\(87\) | −9.79796 | + | 9.79796i | −1.05045 | + | 1.05045i | ||||
\(88\) | 6.00000 | − | 6.00000i | 0.639602 | − | 0.639602i | ||||
\(89\) | −9.79796 | −1.03858 | −0.519291 | − | 0.854598i | \(-0.673804\pi\) | ||||
−0.519291 | + | 0.854598i | \(0.673804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.6969i | 1.54066i | ||||||||
\(92\) | −1.00000 | − | 1.00000i | −0.104257 | − | 0.104257i | ||||
\(93\) | −2.55051 | + | 7.44949i | −0.264476 | + | 0.772476i | ||||
\(94\) | 18.0000i | 1.85656i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.34847i | 0.750000i | ||||||||
\(97\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(98\) | −6.12372 | − | 6.12372i | −0.618590 | − | 0.618590i | ||||
\(99\) | 4.89898 | 0.492366 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0000 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703650\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703650\pi\) | |||||||
\(102\) | −12.2474 | + | 12.2474i | −1.21268 | + | 1.21268i | ||||
\(103\) | −2.44949 | − | 2.44949i | −0.241355 | − | 0.241355i | 0.576055 | − | 0.817411i | \(-0.304591\pi\) |
−0.817411 | + | 0.576055i | \(0.804591\pi\) | |||||||
\(104\) | −7.34847 | −0.720577 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 2.44949i | − | 0.237915i | ||||||
\(107\) | −7.34847 | + | 7.34847i | −0.710403 | + | 0.710403i | −0.966620 | − | 0.256216i | \(-0.917524\pi\) |
0.256216 | + | 0.966620i | \(0.417524\pi\) | |||||||
\(108\) | −4.00000 | + | 4.00000i | −0.384900 | + | 0.384900i | ||||
\(109\) | 16.0000i | 1.53252i | 0.642529 | + | 0.766261i | \(0.277885\pi\) | ||||
−0.642529 | + | 0.766261i | \(0.722115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 12.2474 | − | 12.2474i | 1.15728 | − | 1.15728i | ||||
\(113\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(114\) | 4.89898 | 0.458831 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 9.79796i | − | 0.909718i | ||||||
\(117\) | −3.00000 | − | 3.00000i | −0.277350 | − | 0.277350i | ||||
\(118\) | −14.6969 | − | 14.6969i | −1.35296 | − | 1.35296i | ||||
\(119\) | 24.4949 | 2.24544 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.0000 | −1.18182 | ||||||||
\(122\) | −6.00000 | − | 6.00000i | −0.543214 | − | 0.543214i | ||||
\(123\) | 6.00000 | − | 6.00000i | 0.541002 | − | 0.541002i | ||||
\(124\) | −2.44949 | − | 5.00000i | −0.219971 | − | 0.449013i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.00000 | 0.534522 | ||||||||
\(127\) | 3.00000 | + | 3.00000i | 0.266207 | + | 0.266207i | 0.827570 | − | 0.561363i | \(-0.189723\pi\) |
−0.561363 | + | 0.827570i | \(0.689723\pi\) | |||||||
\(128\) | 8.57321 | + | 8.57321i | 0.757772 | + | 0.757772i | ||||
\(129\) | 6.00000i | 0.528271i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 4.89898 | − | 4.89898i | 0.426401 | − | 0.426401i | ||||
\(133\) | −4.89898 | − | 4.89898i | −0.424795 | − | 0.424795i | ||||
\(134\) | 6.00000i | 0.518321i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.2474i | 1.05021i | ||||||||
\(137\) | −5.00000 | − | 5.00000i | −0.427179 | − | 0.427179i | 0.460487 | − | 0.887666i | \(-0.347675\pi\) |
−0.887666 | + | 0.460487i | \(0.847675\pi\) | |||||||
\(138\) | 2.44949 | + | 2.44949i | 0.208514 | + | 0.208514i | ||||
\(139\) | −14.6969 | −1.24658 | −0.623289 | − | 0.781992i | \(-0.714204\pi\) | ||||
−0.623289 | + | 0.781992i | \(0.714204\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 14.6969i | − | 1.23771i | ||||||
\(142\) | 7.34847 | − | 7.34847i | 0.616670 | − | 0.616670i | ||||
\(143\) | 14.6969 | + | 14.6969i | 1.22902 | + | 1.22902i | ||||
\(144\) | 5.00000i | 0.416667i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.34847i | 0.608164i | ||||||||
\(147\) | 5.00000 | + | 5.00000i | 0.412393 | + | 0.412393i | ||||
\(148\) | 3.00000 | − | 3.00000i | 0.246598 | − | 0.246598i | ||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.6969i | − | 1.19602i | −0.801489 | − | 0.598010i | \(-0.795958\pi\) | ||
0.801489 | − | 0.598010i | \(-0.204042\pi\) | |||||||
\(152\) | 2.44949 | − | 2.44949i | 0.198680 | − | 0.198680i | ||||
\(153\) | −5.00000 | + | 5.00000i | −0.404226 | + | 0.404226i | ||||
\(154\) | −29.3939 | −2.36863 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.00000 | −0.480384 | ||||||||
\(157\) | 9.79796 | − | 9.79796i | 0.781962 | − | 0.781962i | −0.198199 | − | 0.980162i | \(-0.563509\pi\) |
0.980162 | + | 0.198199i | \(0.0635094\pi\) | |||||||
\(158\) | −12.0000 | + | 12.0000i | −0.954669 | + | 0.954669i | ||||
\(159\) | 2.00000i | 0.158610i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.89898i | − | 0.386094i | ||||||
\(162\) | 6.12372 | − | 6.12372i | 0.481125 | − | 0.481125i | ||||
\(163\) | −12.2474 | − | 12.2474i | −0.959294 | − | 0.959294i | 0.0399091 | − | 0.999203i | \(-0.487293\pi\) |
−0.999203 | + | 0.0399091i | \(0.987293\pi\) | |||||||
\(164\) | 6.00000i | 0.468521i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.1464i | 1.33082i | ||||||||
\(167\) | 7.00000 | + | 7.00000i | 0.541676 | + | 0.541676i | 0.924020 | − | 0.382344i | \(-0.124883\pi\) |
−0.382344 | + | 0.924020i | \(0.624883\pi\) | |||||||
\(168\) | −6.00000 | + | 6.00000i | −0.462910 | + | 0.462910i | ||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | −3.00000 | − | 3.00000i | −0.228748 | − | 0.228748i | ||||
\(173\) | 4.89898 | + | 4.89898i | 0.372463 | + | 0.372463i | 0.868373 | − | 0.495911i | \(-0.165166\pi\) |
−0.495911 | + | 0.868373i | \(0.665166\pi\) | |||||||
\(174\) | 24.0000i | 1.81944i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 24.4949i | − | 1.84637i | ||||||
\(177\) | 12.0000 | + | 12.0000i | 0.901975 | + | 0.901975i | ||||
\(178\) | −12.0000 | + | 12.0000i | −0.899438 | + | 0.899438i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.79796i | − | 0.728277i | −0.931345 | − | 0.364138i | \(-0.881364\pi\) | ||
0.931345 | − | 0.364138i | \(-0.118636\pi\) | |||||||
\(182\) | 18.0000 | + | 18.0000i | 1.33425 | + | 1.33425i | ||||
\(183\) | 4.89898 | + | 4.89898i | 0.362143 | + | 0.362143i | ||||
\(184\) | 2.44949 | 0.180579 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | + | 12.2474i | 0.439941 | + | 0.898027i | ||||
\(187\) | 24.4949 | − | 24.4949i | 1.79124 | − | 1.79124i | ||||
\(188\) | 7.34847 | + | 7.34847i | 0.535942 | + | 0.535942i | ||||
\(189\) | −19.5959 | −1.42539 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.0000 | −1.73658 | −0.868290 | − | 0.496058i | \(-0.834780\pi\) | ||||
−0.868290 | + | 0.496058i | \(0.834780\pi\) | |||||||
\(192\) | −1.00000 | − | 1.00000i | −0.0721688 | − | 0.0721688i | ||||
\(193\) | 9.79796 | + | 9.79796i | 0.705273 | + | 0.705273i | 0.965537 | − | 0.260265i | \(-0.0838099\pi\) |
−0.260265 | + | 0.965537i | \(0.583810\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | −0.357143 | ||||||||
\(197\) | −17.0000 | − | 17.0000i | −1.21120 | − | 1.21120i | −0.970632 | − | 0.240567i | \(-0.922666\pi\) |
−0.240567 | − | 0.970632i | \(-0.577334\pi\) | |||||||
\(198\) | 6.00000 | − | 6.00000i | 0.426401 | − | 0.426401i | ||||
\(199\) | 14.6969 | 1.04184 | 0.520919 | − | 0.853606i | \(-0.325589\pi\) | ||||
0.520919 | + | 0.853606i | \(0.325589\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.89898i | − | 0.345547i | ||||||
\(202\) | −14.6969 | + | 14.6969i | −1.03407 | + | 1.03407i | ||||
\(203\) | 24.0000 | − | 24.0000i | 1.68447 | − | 1.68447i | ||||
\(204\) | 10.0000i | 0.700140i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.00000 | −0.418040 | ||||||||
\(207\) | 1.00000 | + | 1.00000i | 0.0695048 | + | 0.0695048i | ||||
\(208\) | −15.0000 | + | 15.0000i | −1.04006 | + | 1.04006i | ||||
\(209\) | −9.79796 | −0.677739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | 0.688428 | 0.344214 | − | 0.938891i | \(-0.388145\pi\) | ||||
0.344214 | + | 0.938891i | \(0.388145\pi\) | |||||||
\(212\) | −1.00000 | − | 1.00000i | −0.0686803 | − | 0.0686803i | ||||
\(213\) | −6.00000 | + | 6.00000i | −0.411113 | + | 0.411113i | ||||
\(214\) | 18.0000i | 1.23045i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 9.79796i | − | 0.666667i | ||||||
\(217\) | 6.24745 | − | 18.2474i | 0.424104 | − | 1.23872i | ||||
\(218\) | 19.5959 | + | 19.5959i | 1.32720 | + | 1.32720i | ||||
\(219\) | − | 6.00000i | − | 0.405442i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.0000 | −2.01802 | ||||||||
\(222\) | −7.34847 | + | 7.34847i | −0.493197 | + | 0.493197i | ||||
\(223\) | 3.00000 | − | 3.00000i | 0.200895 | − | 0.200895i | −0.599489 | − | 0.800383i | \(-0.704629\pi\) |
0.800383 | + | 0.599489i | \(0.204629\pi\) | |||||||
\(224\) | − | 18.0000i | − | 1.20268i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.44949 | + | 2.44949i | −0.162578 | + | 0.162578i | −0.783708 | − | 0.621130i | \(-0.786674\pi\) |
0.621130 | + | 0.783708i | \(0.286674\pi\) | |||||||
\(228\) | 2.00000 | − | 2.00000i | 0.132453 | − | 0.132453i | ||||
\(229\) | 19.5959 | 1.29493 | 0.647467 | − | 0.762093i | \(-0.275828\pi\) | ||||
0.647467 | + | 0.762093i | \(0.275828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.0000 | 1.57908 | ||||||||
\(232\) | 12.0000 | + | 12.0000i | 0.787839 | + | 0.787839i | ||||
\(233\) | −14.6969 | − | 14.6969i | −0.962828 | − | 0.962828i | 0.0365050 | − | 0.999333i | \(-0.488378\pi\) |
−0.999333 | + | 0.0365050i | \(0.988378\pi\) | |||||||
\(234\) | −7.34847 | −0.480384 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12.0000 | −0.781133 | ||||||||
\(237\) | 9.79796 | − | 9.79796i | 0.636446 | − | 0.636446i | ||||
\(238\) | 30.0000 | − | 30.0000i | 1.94461 | − | 1.94461i | ||||
\(239\) | 4.89898 | 0.316889 | 0.158444 | − | 0.987368i | \(-0.449352\pi\) | ||||
0.158444 | + | 0.987368i | \(0.449352\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.4949i | 1.57786i | 0.614486 | + | 0.788928i | \(0.289363\pi\) | ||||
−0.614486 | + | 0.788928i | \(0.710637\pi\) | |||||||
\(242\) | −15.9217 | + | 15.9217i | −1.02348 | + | 1.02348i | ||||
\(243\) | 7.00000 | − | 7.00000i | 0.449050 | − | 0.449050i | ||||
\(244\) | −4.89898 | −0.313625 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 14.6969i | − | 0.937043i | ||||||
\(247\) | 6.00000 | + | 6.00000i | 0.381771 | + | 0.381771i | ||||
\(248\) | 9.12372 | + | 3.12372i | 0.579357 | + | 0.198357i | ||||
\(249\) | − | 14.0000i | − | 0.887214i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.79796i | 0.618442i | 0.950990 | + | 0.309221i | \(0.100068\pi\) | ||||
−0.950990 | + | 0.309221i | \(0.899932\pi\) | |||||||
\(252\) | 2.44949 | − | 2.44949i | 0.154303 | − | 0.154303i | ||||
\(253\) | −4.89898 | − | 4.89898i | −0.307996 | − | 0.307996i | ||||
\(254\) | 7.34847 | 0.461084 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −4.89898 | + | 4.89898i | −0.305590 | + | 0.305590i | −0.843196 | − | 0.537606i | \(-0.819329\pi\) |
0.537606 | + | 0.843196i | \(0.319329\pi\) | |||||||
\(258\) | 7.34847 | + | 7.34847i | 0.457496 | + | 0.457496i | ||||
\(259\) | 14.6969 | 0.913223 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.79796i | 0.606478i | ||||||||
\(262\) | −7.34847 | + | 7.34847i | −0.453990 | + | 0.453990i | ||||
\(263\) | −17.0000 | + | 17.0000i | −1.04826 | + | 1.04826i | −0.0494903 | + | 0.998775i | \(0.515760\pi\) |
−0.998775 | + | 0.0494903i | \(0.984240\pi\) | |||||||
\(264\) | 12.0000i | 0.738549i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.0000 | −0.735767 | ||||||||
\(267\) | 9.79796 | − | 9.79796i | 0.599625 | − | 0.599625i | ||||
\(268\) | 2.44949 | + | 2.44949i | 0.149626 | + | 0.149626i | ||||
\(269\) | −24.4949 | −1.49348 | −0.746740 | − | 0.665116i | \(-0.768382\pi\) | ||||
−0.746740 | + | 0.665116i | \(0.768382\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.79796i | − | 0.595184i | −0.954693 | − | 0.297592i | \(-0.903817\pi\) | ||
0.954693 | − | 0.297592i | \(-0.0961834\pi\) | |||||||
\(272\) | 25.0000 | + | 25.0000i | 1.51585 | + | 1.51585i | ||||
\(273\) | −14.6969 | − | 14.6969i | −0.889499 | − | 0.889499i | ||||
\(274\) | −12.2474 | −0.739895 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.00000 | 0.120386 | ||||||||
\(277\) | 3.00000 | + | 3.00000i | 0.180253 | + | 0.180253i | 0.791466 | − | 0.611213i | \(-0.209318\pi\) |
−0.611213 | + | 0.791466i | \(0.709318\pi\) | |||||||
\(278\) | −18.0000 | + | 18.0000i | −1.07957 | + | 1.07957i | ||||
\(279\) | 2.44949 | + | 5.00000i | 0.146647 | + | 0.299342i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | −18.0000 | − | 18.0000i | −1.07188 | − | 1.07188i | ||||
\(283\) | −2.44949 | − | 2.44949i | −0.145607 | − | 0.145607i | 0.630545 | − | 0.776152i | \(-0.282831\pi\) |
−0.776152 | + | 0.630545i | \(0.782831\pi\) | |||||||
\(284\) | − | 6.00000i | − | 0.356034i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 36.0000 | 2.12872 | ||||||||
\(287\) | −14.6969 | + | 14.6969i | −0.867533 | + | 0.867533i | ||||
\(288\) | 3.67423 | + | 3.67423i | 0.216506 | + | 0.216506i | ||||
\(289\) | 33.0000i | 1.94118i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.00000 | + | 3.00000i | 0.175562 | + | 0.175562i | ||||
\(293\) | −4.89898 | − | 4.89898i | −0.286201 | − | 0.286201i | 0.549375 | − | 0.835576i | \(-0.314866\pi\) |
−0.835576 | + | 0.549375i | \(0.814866\pi\) | |||||||
\(294\) | 12.2474 | 0.714286 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.34847i | 0.427121i | ||||||||
\(297\) | −19.5959 | + | 19.5959i | −1.13707 | + | 1.13707i | ||||
\(298\) | −7.34847 | − | 7.34847i | −0.425685 | − | 0.425685i | ||||
\(299\) | 6.00000i | 0.346989i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 14.6969i | − | 0.847117i | ||||||
\(302\) | −18.0000 | − | 18.0000i | −1.03578 | − | 1.03578i | ||||
\(303\) | 12.0000 | − | 12.0000i | 0.689382 | − | 0.689382i | ||||
\(304\) | − | 10.0000i | − | 0.573539i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 12.2474i | 0.700140i | ||||||||
\(307\) | 12.2474 | − | 12.2474i | 0.698999 | − | 0.698999i | −0.265196 | − | 0.964195i | \(-0.585437\pi\) |
0.964195 | + | 0.265196i | \(0.0854366\pi\) | |||||||
\(308\) | −12.0000 | + | 12.0000i | −0.683763 | + | 0.683763i | ||||
\(309\) | 4.89898 | 0.278693 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 7.34847 | − | 7.34847i | 0.416025 | − | 0.416025i | ||||
\(313\) | 15.0000 | − | 15.0000i | 0.847850 | − | 0.847850i | −0.142014 | − | 0.989865i | \(-0.545358\pi\) |
0.989865 | + | 0.142014i | \(0.0453579\pi\) | |||||||
\(314\) | − | 24.0000i | − | 1.35440i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.79796i | 0.551178i | ||||||||
\(317\) | 24.4949 | − | 24.4949i | 1.37577 | − | 1.37577i | 0.524136 | − | 0.851635i | \(-0.324388\pi\) |
0.851635 | − | 0.524136i | \(-0.175612\pi\) | |||||||
\(318\) | 2.44949 | + | 2.44949i | 0.137361 | + | 0.137361i | ||||
\(319\) | − | 48.0000i | − | 2.68748i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 14.6969i | − | 0.820303i | ||||||
\(322\) | −6.00000 | − | 6.00000i | −0.334367 | − | 0.334367i | ||||
\(323\) | 10.0000 | − | 10.0000i | 0.556415 | − | 0.556415i | ||||
\(324\) | − | 5.00000i | − | 0.277778i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.0000 | −1.66155 | ||||||||
\(327\) | −16.0000 | − | 16.0000i | −0.884802 | − | 0.884802i | ||||
\(328\) | −7.34847 | − | 7.34847i | −0.405751 | − | 0.405751i | ||||
\(329\) | 36.0000i | 1.98474i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.3939i | 1.61563i | 0.589434 | + | 0.807817i | \(0.299351\pi\) | ||||
−0.589434 | + | 0.807817i | \(0.700649\pi\) | |||||||
\(332\) | 7.00000 | + | 7.00000i | 0.384175 | + | 0.384175i | ||||
\(333\) | −3.00000 | + | 3.00000i | −0.164399 | + | 0.164399i | ||||
\(334\) | 17.1464 | 0.938211 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 24.4949i | 1.33631i | ||||||||
\(337\) | 9.00000 | + | 9.00000i | 0.490261 | + | 0.490261i | 0.908388 | − | 0.418127i | \(-0.137313\pi\) |
−0.418127 | + | 0.908388i | \(0.637313\pi\) | |||||||
\(338\) | −6.12372 | − | 6.12372i | −0.333087 | − | 0.333087i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | − | 24.4949i | −0.649836 | − | 1.32647i | ||||
\(342\) | 2.44949 | − | 2.44949i | 0.132453 | − | 0.132453i | ||||
\(343\) | 4.89898 | + | 4.89898i | 0.264520 | + | 0.264520i | ||||
\(344\) | 7.34847 | 0.396203 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.0000 | 0.645124 | ||||||||
\(347\) | −5.00000 | − | 5.00000i | −0.268414 | − | 0.268414i | 0.560047 | − | 0.828461i | \(-0.310783\pi\) |
−0.828461 | + | 0.560047i | \(0.810783\pi\) | |||||||
\(348\) | 9.79796 | + | 9.79796i | 0.525226 | + | 0.525226i | ||||
\(349\) | − | 10.0000i | − | 0.535288i | −0.963518 | − | 0.267644i | \(-0.913755\pi\) | ||
0.963518 | − | 0.267644i | \(-0.0862451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.0000 | 1.28103 | ||||||||
\(352\) | −18.0000 | − | 18.0000i | −0.959403 | − | 0.959403i | ||||
\(353\) | −11.0000 | + | 11.0000i | −0.585471 | + | 0.585471i | −0.936401 | − | 0.350931i | \(-0.885865\pi\) |
0.350931 | + | 0.936401i | \(0.385865\pi\) | |||||||
\(354\) | 29.3939 | 1.56227 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.79796i | 0.519291i | ||||||||
\(357\) | −24.4949 | + | 24.4949i | −1.29641 | + | 1.29641i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.00000i | − | 0.316668i | −0.987386 | − | 0.158334i | \(-0.949388\pi\) | ||
0.987386 | − | 0.158334i | \(-0.0506123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | −12.0000 | − | 12.0000i | −0.630706 | − | 0.630706i | ||||
\(363\) | 13.0000 | − | 13.0000i | 0.682323 | − | 0.682323i | ||||
\(364\) | 14.6969 | 0.770329 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.0000 | 0.627250 | ||||||||
\(367\) | 15.0000 | + | 15.0000i | 0.782994 | + | 0.782994i | 0.980335 | − | 0.197341i | \(-0.0632307\pi\) |
−0.197341 | + | 0.980335i | \(0.563231\pi\) | |||||||
\(368\) | 5.00000 | − | 5.00000i | 0.260643 | − | 0.260643i | ||||
\(369\) | − | 6.00000i | − | 0.312348i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.89898i | − | 0.254342i | ||||||
\(372\) | 7.44949 | + | 2.55051i | 0.386238 | + | 0.132238i | ||||
\(373\) | −14.6969 | − | 14.6969i | −0.760979 | − | 0.760979i | 0.215521 | − | 0.976499i | \(-0.430855\pi\) |
−0.976499 | + | 0.215521i | \(0.930855\pi\) | |||||||
\(374\) | − | 60.0000i | − | 3.10253i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.0000 | −0.928279 | ||||||||
\(377\) | −29.3939 | + | 29.3939i | −1.51386 | + | 1.51386i | ||||
\(378\) | −24.0000 | + | 24.0000i | −1.23443 | + | 1.23443i | ||||
\(379\) | − | 20.0000i | − | 1.02733i | −0.857991 | − | 0.513665i | \(-0.828287\pi\) | ||
0.857991 | − | 0.513665i | \(-0.171713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | −0.307389 | ||||||||
\(382\) | −29.3939 | + | 29.3939i | −1.50392 | + | 1.50392i | ||||
\(383\) | −19.0000 | + | 19.0000i | −0.970855 | + | 0.970855i | −0.999587 | − | 0.0287325i | \(-0.990853\pi\) |
0.0287325 | + | 0.999587i | \(0.490853\pi\) | |||||||
\(384\) | −17.1464 | −0.875000 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.0000 | 1.22157 | ||||||||
\(387\) | 3.00000 | + | 3.00000i | 0.152499 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.89898 | 0.248388 | 0.124194 | − | 0.992258i | \(-0.460365\pi\) | ||||
0.124194 | + | 0.992258i | \(0.460365\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0000 | 0.505722 | ||||||||
\(392\) | 6.12372 | − | 6.12372i | 0.309295 | − | 0.309295i | ||||
\(393\) | 6.00000 | − | 6.00000i | 0.302660 | − | 0.302660i | ||||
\(394\) | −41.6413 | −2.09786 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − | 4.89898i | − | 0.246183i | ||||||
\(397\) | −19.5959 | + | 19.5959i | −0.983491 | + | 0.983491i | −0.999866 | − | 0.0163750i | \(-0.994787\pi\) |
0.0163750 | + | 0.999866i | \(0.494787\pi\) | |||||||
\(398\) | 18.0000 | − | 18.0000i | 0.902258 | − | 0.902258i | ||||
\(399\) | 9.79796 | 0.490511 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | −6.00000 | − | 6.00000i | −0.299253 | − | 0.299253i | ||||
\(403\) | −7.65153 | + | 22.3485i | −0.381150 | + | 1.11326i | ||||
\(404\) | 12.0000i | 0.597022i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 58.7878i | − | 2.91759i | ||||||
\(407\) | 14.6969 | − | 14.6969i | 0.728500 | − | 0.728500i | ||||
\(408\) | −12.2474 | − | 12.2474i | −0.606339 | − | 0.606339i | ||||
\(409\) | −4.89898 | −0.242239 | −0.121119 | − | 0.992638i | \(-0.538648\pi\) | ||||
−0.121119 | + | 0.992638i | \(0.538648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0000 | 0.493264 | ||||||||
\(412\) | −2.44949 | + | 2.44949i | −0.120678 | + | 0.120678i | ||||
\(413\) | −29.3939 | − | 29.3939i | −1.44638 | − | 1.44638i | ||||
\(414\) | 2.44949 | 0.120386 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 22.0454i | 1.08087i | ||||||||
\(417\) | 14.6969 | − | 14.6969i | 0.719712 | − | 0.719712i | ||||
\(418\) | −12.0000 | + | 12.0000i | −0.586939 | + | 0.586939i | ||||
\(419\) | 12.0000i | 0.586238i | 0.956076 | + | 0.293119i | \(0.0946933\pi\) | ||||
−0.956076 | + | 0.293119i | \(0.905307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 12.2474 | − | 12.2474i | 0.596196 | − | 0.596196i | ||||
\(423\) | −7.34847 | − | 7.34847i | −0.357295 | − | 0.357295i | ||||
\(424\) | 2.44949 | 0.118958 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 14.6969i | 0.712069i | ||||||||
\(427\) | −12.0000 | − | 12.0000i | −0.580721 | − | 0.580721i | ||||
\(428\) | 7.34847 | + | 7.34847i | 0.355202 | + | 0.355202i | ||||
\(429\) | −29.3939 | −1.41915 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | 0.289010 | 0.144505 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144505 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(432\) | −20.0000 | − | 20.0000i | −0.962250 | − | 0.962250i | ||||
\(433\) | 15.0000 | − | 15.0000i | 0.720854 | − | 0.720854i | −0.247925 | − | 0.968779i | \(-0.579749\pi\) |
0.968779 | + | 0.247925i | \(0.0797487\pi\) | |||||||
\(434\) | −14.6969 | − | 30.0000i | −0.705476 | − | 1.44005i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.0000 | 0.766261 | ||||||||
\(437\) | −2.00000 | − | 2.00000i | −0.0956730 | − | 0.0956730i | ||||
\(438\) | −7.34847 | − | 7.34847i | −0.351123 | − | 0.351123i | ||||
\(439\) | − | 8.00000i | − | 0.381819i | −0.981608 | − | 0.190910i | \(-0.938856\pi\) | ||
0.981608 | − | 0.190910i | \(-0.0611437\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | −36.7423 | + | 36.7423i | −1.74766 | + | 1.74766i | ||||
\(443\) | −12.2474 | − | 12.2474i | −0.581894 | − | 0.581894i | 0.353530 | − | 0.935423i | \(-0.384981\pi\) |
−0.935423 | + | 0.353530i | \(0.884981\pi\) | |||||||
\(444\) | 6.00000i | 0.284747i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 7.34847i | − | 0.347960i | ||||||
\(447\) | 6.00000 | + | 6.00000i | 0.283790 | + | 0.283790i | ||||
\(448\) | 2.44949 | + | 2.44949i | 0.115728 | + | 0.115728i | ||||
\(449\) | 34.2929 | 1.61838 | 0.809190 | − | 0.587547i | \(-0.199906\pi\) | ||||
0.809190 | + | 0.587547i | \(0.199906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.3939i | 1.38410i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.6969 | + | 14.6969i | 0.690522 | + | 0.690522i | ||||
\(454\) | 6.00000i | 0.281594i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.89898i | 0.229416i | ||||||||
\(457\) | −21.0000 | − | 21.0000i | −0.982339 | − | 0.982339i | 0.0175082 | − | 0.999847i | \(-0.494427\pi\) |
−0.999847 | + | 0.0175082i | \(0.994427\pi\) | |||||||
\(458\) | 24.0000 | − | 24.0000i | 1.12145 | − | 1.12145i | ||||
\(459\) | − | 40.0000i | − | 1.86704i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.5959i | 0.912673i | 0.889807 | + | 0.456336i | \(0.150839\pi\) | ||||
−0.889807 | + | 0.456336i | \(0.849161\pi\) | |||||||
\(462\) | 29.3939 | − | 29.3939i | 1.36753 | − | 1.36753i | ||||
\(463\) | −21.0000 | + | 21.0000i | −0.975953 | + | 0.975953i | −0.999718 | − | 0.0237648i | \(-0.992435\pi\) |
0.0237648 | + | 0.999718i | \(0.492435\pi\) | |||||||
\(464\) | 48.9898 | 2.27429 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −36.0000 | −1.66767 | ||||||||
\(467\) | −12.2474 | + | 12.2474i | −0.566744 | + | 0.566744i | −0.931215 | − | 0.364471i | \(-0.881250\pi\) |
0.364471 | + | 0.931215i | \(0.381250\pi\) | |||||||
\(468\) | −3.00000 | + | 3.00000i | −0.138675 | + | 0.138675i | ||||
\(469\) | 12.0000i | 0.554109i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.5959i | 0.902932i | ||||||||
\(472\) | 14.6969 | − | 14.6969i | 0.676481 | − | 0.676481i | ||||
\(473\) | −14.6969 | − | 14.6969i | −0.675766 | − | 0.675766i | ||||
\(474\) | − | 24.0000i | − | 1.10236i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 24.4949i | − | 1.12272i | ||||||
\(477\) | 1.00000 | + | 1.00000i | 0.0457869 | + | 0.0457869i | ||||
\(478\) | 6.00000 | − | 6.00000i | 0.274434 | − | 0.274434i | ||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0000 | −0.820729 | ||||||||
\(482\) | 30.0000 | + | 30.0000i | 1.36646 | + | 1.36646i | ||||
\(483\) | 4.89898 | + | 4.89898i | 0.222911 | + | 0.222911i | ||||
\(484\) | 13.0000i | 0.590909i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 17.1464i | − | 0.777778i | ||||||
\(487\) | −15.0000 | − | 15.0000i | −0.679715 | − | 0.679715i | 0.280221 | − | 0.959936i | \(-0.409592\pi\) |
−0.959936 | + | 0.280221i | \(0.909592\pi\) | |||||||
\(488\) | 6.00000 | − | 6.00000i | 0.271607 | − | 0.271607i | ||||
\(489\) | 24.4949 | 1.10770 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.5959i | − | 0.884351i | −0.896928 | − | 0.442176i | \(-0.854207\pi\) | ||
0.896928 | − | 0.442176i | \(-0.145793\pi\) | |||||||
\(492\) | −6.00000 | − | 6.00000i | −0.270501 | − | 0.270501i | ||||
\(493\) | 48.9898 | + | 48.9898i | 2.20639 | + | 2.20639i | ||||
\(494\) | 14.6969 | 0.661247 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25.0000 | − | 12.2474i | 1.12253 | − | 0.549927i | ||||
\(497\) | 14.6969 | − | 14.6969i | 0.659248 | − | 0.659248i | ||||
\(498\) | −17.1464 | − | 17.1464i | −0.768350 | − | 0.768350i | ||||
\(499\) | 19.5959 | 0.877234 | 0.438617 | − | 0.898674i | \(-0.355469\pi\) | ||||
0.438617 | + | 0.898674i | \(0.355469\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.0000 | −0.625474 | ||||||||
\(502\) | 12.0000 | + | 12.0000i | 0.535586 | + | 0.535586i | ||||
\(503\) | 2.44949 | + | 2.44949i | 0.109217 | + | 0.109217i | 0.759604 | − | 0.650386i | \(-0.225393\pi\) |
−0.650386 | + | 0.759604i | \(0.725393\pi\) | |||||||
\(504\) | 6.00000i | 0.267261i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | 5.00000 | + | 5.00000i | 0.222058 | + | 0.222058i | ||||
\(508\) | 3.00000 | − | 3.00000i | 0.133103 | − | 0.133103i | ||||
\(509\) | −19.5959 | −0.868574 | −0.434287 | − | 0.900775i | \(-0.643000\pi\) | ||||
−0.434287 | + | 0.900775i | \(0.643000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6969i | 0.650154i | ||||||||
\(512\) | 6.12372 | − | 6.12372i | 0.270633 | − | 0.270633i | ||||
\(513\) | −8.00000 | + | 8.00000i | −0.353209 | + | 0.353209i | ||||
\(514\) | 12.0000i | 0.529297i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.00000 | 0.264135 | ||||||||
\(517\) | 36.0000 | + | 36.0000i | 1.58328 | + | 1.58328i | ||||
\(518\) | 18.0000 | − | 18.0000i | 0.790875 | − | 0.790875i | ||||
\(519\) | −9.79796 | −0.430083 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0000 | 1.05146 | 0.525730 | − | 0.850652i | \(-0.323792\pi\) | ||||
0.525730 | + | 0.850652i | \(0.323792\pi\) | |||||||
\(522\) | 12.0000 | + | 12.0000i | 0.525226 | + | 0.525226i | ||||
\(523\) | 9.00000 | − | 9.00000i | 0.393543 | − | 0.393543i | −0.482405 | − | 0.875948i | \(-0.660237\pi\) |
0.875948 | + | 0.482405i | \(0.160237\pi\) | |||||||
\(524\) | 6.00000i | 0.262111i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 41.6413i | 1.81565i | ||||||||
\(527\) | 37.2474 | + | 12.7526i | 1.62252 | + | 0.555510i | ||||
\(528\) | 24.4949 | + | 24.4949i | 1.06600 | + | 1.06600i | ||||
\(529\) | 21.0000i | 0.913043i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | −4.89898 | + | 4.89898i | −0.212398 | + | 0.212398i | ||||
\(533\) | 18.0000 | − | 18.0000i | 0.779667 | − | 0.779667i | ||||
\(534\) | − | 24.0000i | − | 1.03858i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.00000 | −0.259161 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.0000 | + | 30.0000i | −1.29339 | + | 1.29339i | ||||
\(539\) | −24.4949 | −1.05507 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.0000 | 1.89171 | 0.945854 | − | 0.324593i | \(-0.105227\pi\) | ||||
0.945854 | + | 0.324593i | \(0.105227\pi\) | |||||||
\(542\) | −12.0000 | − | 12.0000i | −0.515444 | − | 0.515444i | ||||
\(543\) | 9.79796 | + | 9.79796i | 0.420471 | + | 0.420471i | ||||
\(544\) | 36.7423 | 1.57532 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −36.0000 | −1.54066 | ||||||||
\(547\) | 22.0454 | − | 22.0454i | 0.942594 | − | 0.942594i | −0.0558458 | − | 0.998439i | \(-0.517786\pi\) |
0.998439 | + | 0.0558458i | \(0.0177855\pi\) | |||||||
\(548\) | −5.00000 | + | 5.00000i | −0.213589 | + | 0.213589i | ||||
\(549\) | 4.89898 | 0.209083 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 19.5959i | − | 0.834814i | ||||||
\(552\) | −2.44949 | + | 2.44949i | −0.104257 | + | 0.104257i | ||||
\(553\) | −24.0000 | + | 24.0000i | −1.02058 | + | 1.02058i | ||||
\(554\) | 7.34847 | 0.312207 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.6969i | 0.623289i | ||||||||
\(557\) | 11.0000 | + | 11.0000i | 0.466085 | + | 0.466085i | 0.900644 | − | 0.434559i | \(-0.143096\pi\) |
−0.434559 | + | 0.900644i | \(0.643096\pi\) | |||||||
\(558\) | 9.12372 | + | 3.12372i | 0.386238 | + | 0.132238i | ||||
\(559\) | 18.0000i | 0.761319i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 48.9898i | 2.06835i | ||||||||
\(562\) | 14.6969 | − | 14.6969i | 0.619953 | − | 0.619953i | ||||
\(563\) | −7.34847 | − | 7.34847i | −0.309701 | − | 0.309701i | 0.535092 | − | 0.844794i | \(-0.320277\pi\) |
−0.844794 | + | 0.535092i | \(0.820277\pi\) | |||||||
\(564\) | −14.6969 | −0.618853 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.00000 | −0.252199 | ||||||||
\(567\) | 12.2474 | − | 12.2474i | 0.514344 | − | 0.514344i | ||||
\(568\) | 7.34847 | + | 7.34847i | 0.308335 | + | 0.308335i | ||||
\(569\) | −24.4949 | −1.02688 | −0.513440 | − | 0.858126i | \(-0.671629\pi\) | ||||
−0.513440 | + | 0.858126i | \(0.671629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 9.79796i | − | 0.410032i | −0.978759 | − | 0.205016i | \(-0.934275\pi\) | ||
0.978759 | − | 0.205016i | \(-0.0657246\pi\) | |||||||
\(572\) | 14.6969 | − | 14.6969i | 0.614510 | − | 0.614510i | ||||
\(573\) | 24.0000 | − | 24.0000i | 1.00261 | − | 1.00261i | ||||
\(574\) | 36.0000i | 1.50261i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 4.89898 | − | 4.89898i | 0.203947 | − | 0.203947i | −0.597742 | − | 0.801689i | \(-0.703935\pi\) |
0.801689 | + | 0.597742i | \(0.203935\pi\) | |||||||
\(578\) | 40.4166 | + | 40.4166i | 1.68111 | + | 1.68111i | ||||
\(579\) | −19.5959 | −0.814379 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.2929i | 1.42271i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.89898 | − | 4.89898i | −0.202895 | − | 0.202895i | ||||
\(584\) | −7.34847 | −0.304082 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0000 | −0.495715 | ||||||||
\(587\) | 11.0000 | + | 11.0000i | 0.454019 | + | 0.454019i | 0.896686 | − | 0.442667i | \(-0.145968\pi\) |
−0.442667 | + | 0.896686i | \(0.645968\pi\) | |||||||
\(588\) | 5.00000 | − | 5.00000i | 0.206197 | − | 0.206197i | ||||
\(589\) | −4.89898 | − | 10.0000i | −0.201859 | − | 0.412043i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.0000 | 1.39857 | ||||||||
\(592\) | 15.0000 | + | 15.0000i | 0.616496 | + | 0.616496i | ||||
\(593\) | 24.4949 | + | 24.4949i | 1.00588 | + | 1.00588i | 0.999983 | + | 0.00590230i | \(0.00187877\pi\) |
0.00590230 | + | 0.999983i | \(0.498121\pi\) | |||||||
\(594\) | 48.0000i | 1.96946i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −14.6969 | + | 14.6969i | −0.601506 | + | 0.601506i | ||||
\(598\) | 7.34847 | + | 7.34847i | 0.300501 | + | 0.300501i | ||||
\(599\) | 18.0000i | 0.735460i | 0.929933 | + | 0.367730i | \(0.119865\pi\) | ||||
−0.929933 | + | 0.367730i | \(0.880135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.2929i | − | 1.39883i | −0.714713 | − | 0.699417i | \(-0.753443\pi\) | ||
0.714713 | − | 0.699417i | \(-0.246557\pi\) | |||||||
\(602\) | −18.0000 | − | 18.0000i | −0.733625 | − | 0.733625i | ||||
\(603\) | −2.44949 | − | 2.44949i | −0.0997509 | − | 0.0997509i | ||||
\(604\) | −14.6969 | −0.598010 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 29.3939i | − | 1.19404i | ||||||
\(607\) | −22.0454 | + | 22.0454i | −0.894795 | + | 0.894795i | −0.994970 | − | 0.100174i | \(-0.968060\pi\) |
0.100174 | + | 0.994970i | \(0.468060\pi\) | |||||||
\(608\) | −7.34847 | − | 7.34847i | −0.298020 | − | 0.298020i | ||||
\(609\) | 48.0000i | 1.94506i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 44.0908i | − | 1.78372i | ||||||
\(612\) | 5.00000 | + | 5.00000i | 0.202113 | + | 0.202113i | ||||
\(613\) | 3.00000 | − | 3.00000i | 0.121169 | − | 0.121169i | −0.643922 | − | 0.765091i | \(-0.722694\pi\) |
0.765091 | + | 0.643922i | \(0.222694\pi\) | |||||||
\(614\) | − | 30.0000i | − | 1.21070i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 29.3939i | − | 1.18431i | ||||||
\(617\) | 24.4949 | − | 24.4949i | 0.986127 | − | 0.986127i | −0.0137776 | − | 0.999905i | \(-0.504386\pi\) |
0.999905 | + | 0.0137776i | \(0.00438570\pi\) | |||||||
\(618\) | 6.00000 | − | 6.00000i | 0.241355 | − | 0.241355i | ||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.00000 | −0.321029 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.0000 | + | 24.0000i | −0.961540 | + | 0.961540i | ||||
\(624\) | − | 30.0000i | − | 1.20096i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 36.7423i | − | 1.46852i | ||||||
\(627\) | 9.79796 | − | 9.79796i | 0.391293 | − | 0.391293i | ||||
\(628\) | −9.79796 | − | 9.79796i | −0.390981 | − | 0.390981i | ||||
\(629\) | 30.0000i | 1.19618i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.1918i | 1.56020i | 0.625653 | + | 0.780101i | \(0.284832\pi\) | ||||
−0.625653 | + | 0.780101i | \(0.715168\pi\) | |||||||
\(632\) | −12.0000 | − | 12.0000i | −0.477334 | − | 0.477334i | ||||
\(633\) | −10.0000 | + | 10.0000i | −0.397464 | + | 0.397464i | ||||
\(634\) | − | 60.0000i | − | 2.38290i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.00000 | 0.0793052 | ||||||||
\(637\) | 15.0000 | + | 15.0000i | 0.594322 | + | 0.594322i | ||||
\(638\) | −58.7878 | − | 58.7878i | −2.32743 | − | 2.32743i | ||||
\(639\) | 6.00000i | 0.237356i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 14.6969i | − | 0.580494i | −0.956952 | − | 0.290247i | \(-0.906263\pi\) | ||
0.956952 | − | 0.290247i | \(-0.0937375\pi\) | |||||||
\(642\) | −18.0000 | − | 18.0000i | −0.710403 | − | 0.710403i | ||||
\(643\) | −27.0000 | + | 27.0000i | −1.06478 | + | 1.06478i | −0.0670247 | + | 0.997751i | \(0.521351\pi\) |
−0.997751 | + | 0.0670247i | \(0.978649\pi\) | |||||||
\(644\) | −4.89898 | −0.193047 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 24.4949i | − | 0.963739i | ||||||
\(647\) | −23.0000 | − | 23.0000i | −0.904223 | − | 0.904223i | 0.0915749 | − | 0.995798i | \(-0.470810\pi\) |
−0.995798 | + | 0.0915749i | \(0.970810\pi\) | |||||||
\(648\) | 6.12372 | + | 6.12372i | 0.240563 | + | 0.240563i | ||||
\(649\) | −58.7878 | −2.30762 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0000 | + | 24.4949i | 0.470317 | + | 0.960031i | ||||
\(652\) | −12.2474 | + | 12.2474i | −0.479647 | + | 0.479647i | ||||
\(653\) | −9.79796 | − | 9.79796i | −0.383424 | − | 0.383424i | 0.488910 | − | 0.872334i | \(-0.337395\pi\) |
−0.872334 | + | 0.488910i | \(0.837395\pi\) | |||||||
\(654\) | −39.1918 | −1.53252 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −30.0000 | −1.17130 | ||||||||
\(657\) | −3.00000 | − | 3.00000i | −0.117041 | − | 0.117041i | ||||
\(658\) | 44.0908 | + | 44.0908i | 1.71884 | + | 1.71884i | ||||
\(659\) | − | 30.0000i | − | 1.16863i | −0.811525 | − | 0.584317i | \(-0.801362\pi\) | ||
0.811525 | − | 0.584317i | \(-0.198638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.0000 | −1.55582 | −0.777910 | − | 0.628376i | \(-0.783720\pi\) | ||||
−0.777910 | + | 0.628376i | \(0.783720\pi\) | |||||||
\(662\) | 36.0000 | + | 36.0000i | 1.39918 | + | 1.39918i | ||||
\(663\) | 30.0000 | − | 30.0000i | 1.16510 | − | 1.16510i | ||||
\(664\) | −17.1464 | −0.665410 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.34847i | 0.284747i | ||||||||
\(667\) | 9.79796 | − | 9.79796i | 0.379378 | − | 0.379378i | ||||
\(668\) | 7.00000 | − | 7.00000i | 0.270838 | − | 0.270838i | ||||
\(669\) | 6.00000i | 0.231973i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0000 | −0.926510 | ||||||||
\(672\) | 18.0000 | + | 18.0000i | 0.694365 | + | 0.694365i | ||||
\(673\) | −15.0000 | + | 15.0000i | −0.578208 | + | 0.578208i | −0.934409 | − | 0.356202i | \(-0.884072\pi\) |
0.356202 | + | 0.934409i | \(0.384072\pi\) | |||||||
\(674\) | 22.0454 | 0.849157 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | −1.00000 | − | 1.00000i | −0.0384331 | − | 0.0384331i | 0.687629 | − | 0.726062i | \(-0.258652\pi\) |
−0.726062 | + | 0.687629i | \(0.758652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.89898i | − | 0.187729i | ||||||
\(682\) | −44.6969 | − | 15.3031i | −1.71153 | − | 0.585985i | ||||
\(683\) | 2.44949 | + | 2.44949i | 0.0937271 | + | 0.0937271i | 0.752416 | − | 0.658689i | \(-0.228889\pi\) |
−0.658689 | + | 0.752416i | \(0.728889\pi\) | |||||||
\(684\) | − | 2.00000i | − | 0.0764719i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.0000 | 0.458162 | ||||||||
\(687\) | −19.5959 | + | 19.5959i | −0.747631 | + | 0.747631i | ||||
\(688\) | 15.0000 | − | 15.0000i | 0.571870 | − | 0.571870i | ||||
\(689\) | 6.00000i | 0.228582i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | 4.89898 | − | 4.89898i | 0.186231 | − | 0.186231i | ||||
\(693\) | 12.0000 | − | 12.0000i | 0.455842 | − | 0.455842i | ||||
\(694\) | −12.2474 | −0.464907 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −24.0000 | −0.909718 | ||||||||
\(697\) | −30.0000 | − | 30.0000i | −1.13633 | − | 1.13633i | ||||
\(698\) | −12.2474 | − | 12.2474i | −0.463573 | − | 0.463573i | ||||
\(699\) | 29.3939 | 1.11178 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 29.3939 | − | 29.3939i | 1.10940 | − | 1.10940i | ||||
\(703\) | 6.00000 | − | 6.00000i | 0.226294 | − | 0.226294i | ||||
\(704\) | 4.89898 | 0.184637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.9444i | 1.01407i | ||||||||
\(707\) | −29.3939 | + | 29.3939i | −1.10547 | + | 1.10547i | ||||
\(708\) | 12.0000 | − | 12.0000i | 0.450988 | − | 0.450988i | ||||
\(709\) | 29.3939 | 1.10391 | 0.551955 | − | 0.833874i | \(-0.313882\pi\) | ||||
0.551955 | + | 0.833874i | \(0.313882\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 9.79796i | − | 0.367452i | ||||||
\(712\) | −12.0000 | − | 12.0000i | −0.449719 | − | 0.449719i | ||||
\(713\) | 2.55051 | − | 7.44949i | 0.0955174 | − | 0.278986i | ||||
\(714\) | 60.0000i | 2.24544i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.89898 | + | 4.89898i | −0.182956 | + | 0.182956i | ||||
\(718\) | −7.34847 | − | 7.34847i | −0.274242 | − | 0.274242i | ||||
\(719\) | −4.89898 | −0.182701 | −0.0913506 | − | 0.995819i | \(-0.529118\pi\) | ||||
−0.0913506 | + | 0.995819i | \(0.529118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0000 | −0.446903 | ||||||||
\(722\) | 18.3712 | − | 18.3712i | 0.683704 | − | 0.683704i | ||||
\(723\) | −24.4949 | − | 24.4949i | −0.910975 | − | 0.910975i | ||||
\(724\) | −9.79796 | −0.364138 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 31.8434i | − | 1.18182i | ||||||
\(727\) | −17.1464 | + | 17.1464i | −0.635926 | + | 0.635926i | −0.949548 | − | 0.313622i | \(-0.898458\pi\) |
0.313622 | + | 0.949548i | \(0.398458\pi\) | |||||||
\(728\) | −18.0000 | + | 18.0000i | −0.667124 | + | 0.667124i | ||||
\(729\) | 29.0000i | 1.07407i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.0000 | 1.10959 | ||||||||
\(732\) | 4.89898 | − | 4.89898i | 0.181071 | − | 0.181071i | ||||
\(733\) | 9.79796 | + | 9.79796i | 0.361896 | + | 0.361896i | 0.864511 | − | 0.502615i | \(-0.167629\pi\) |
−0.502615 | + | 0.864511i | \(0.667629\pi\) | |||||||
\(734\) | 36.7423 | 1.35618 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.34847i | − | 0.270868i | ||||||
\(737\) | 12.0000 | + | 12.0000i | 0.442026 | + | 0.442026i | ||||
\(738\) | −7.34847 | − | 7.34847i | −0.270501 | − | 0.270501i | ||||
\(739\) | 24.4949 | 0.901059 | 0.450530 | − | 0.892761i | \(-0.351235\pi\) | ||||
0.450530 | + | 0.892761i | \(0.351235\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.0000 | −0.440831 | ||||||||
\(742\) | −6.00000 | − | 6.00000i | −0.220267 | − | 0.220267i | ||||
\(743\) | −23.0000 | + | 23.0000i | −0.843788 | + | 0.843788i | −0.989349 | − | 0.145561i | \(-0.953501\pi\) |
0.145561 | + | 0.989349i | \(0.453501\pi\) | |||||||
\(744\) | −12.2474 | + | 6.00000i | −0.449013 | + | 0.219971i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −36.0000 | −1.31805 | ||||||||
\(747\) | −7.00000 | − | 7.00000i | −0.256117 | − | 0.256117i | ||||
\(748\) | −24.4949 | − | 24.4949i | −0.895622 | − | 0.895622i | ||||
\(749\) | 36.0000i | 1.31541i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0000 | −0.510867 | −0.255434 | − | 0.966827i | \(-0.582218\pi\) | ||||
−0.255434 | + | 0.966827i | \(0.582218\pi\) | |||||||
\(752\) | −36.7423 | + | 36.7423i | −1.33986 | + | 1.33986i | ||||
\(753\) | −9.79796 | − | 9.79796i | −0.357057 | − | 0.357057i | ||||
\(754\) | 72.0000i | 2.62209i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19.5959i | 0.712697i | ||||||||
\(757\) | 9.00000 | + | 9.00000i | 0.327111 | + | 0.327111i | 0.851487 | − | 0.524376i | \(-0.175701\pi\) |
−0.524376 | + | 0.851487i | \(0.675701\pi\) | |||||||
\(758\) | −24.4949 | − | 24.4949i | −0.889695 | − | 0.889695i | ||||
\(759\) | 9.79796 | 0.355643 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.3939i | 1.06553i | 0.846264 | + | 0.532764i | \(0.178847\pi\) | ||||
−0.846264 | + | 0.532764i | \(0.821153\pi\) | |||||||
\(762\) | −7.34847 | + | 7.34847i | −0.266207 | + | 0.266207i | ||||
\(763\) | 39.1918 | + | 39.1918i | 1.41884 | + | 1.41884i | ||||
\(764\) | 24.0000i | 0.868290i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 46.5403i | 1.68157i | ||||||||
\(767\) | 36.0000 | + | 36.0000i | 1.29988 | + | 1.29988i | ||||
\(768\) | −19.0000 | + | 19.0000i | −0.685603 | + | 0.685603i | ||||
\(769\) | 10.0000i | 0.360609i | 0.983611 | + | 0.180305i | \(0.0577084\pi\) | ||||
−0.983611 | + | 0.180305i | \(0.942292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 9.79796i | − | 0.352865i | ||||||
\(772\) | 9.79796 | − | 9.79796i | 0.352636 | − | 0.352636i | ||||
\(773\) | 1.00000 | − | 1.00000i | 0.0359675 | − | 0.0359675i | −0.688894 | − | 0.724862i | \(-0.741904\pi\) |
0.724862 | + | 0.688894i | \(0.241904\pi\) | |||||||
\(774\) | 7.34847 | 0.264135 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.6969 | + | 14.6969i | −0.527250 | + | 0.527250i | ||||
\(778\) | 6.00000 | − | 6.00000i | 0.215110 | − | 0.215110i | ||||
\(779\) | 12.0000i | 0.429945i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 29.3939i | − | 1.05180i | ||||||
\(782\) | 12.2474 | − | 12.2474i | 0.437968 | − | 0.437968i | ||||
\(783\) | −39.1918 | − | 39.1918i | −1.40060 | − | 1.40060i | ||||
\(784\) | − | 25.0000i | − | 0.892857i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 14.6969i | − | 0.524222i | ||||||
\(787\) | 3.00000 | + | 3.00000i | 0.106938 | + | 0.106938i | 0.758552 | − | 0.651613i | \(-0.225907\pi\) |
−0.651613 | + | 0.758552i | \(0.725907\pi\) | |||||||
\(788\) | −17.0000 | + | 17.0000i | −0.605600 | + | 0.605600i | ||||
\(789\) | − | 34.0000i | − | 1.21043i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.00000 | + | 6.00000i | 0.213201 | + | 0.213201i | ||||
\(793\) | 14.6969 | + | 14.6969i | 0.521904 | + | 0.521904i | ||||
\(794\) | 48.0000i | 1.70346i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 14.6969i | − | 0.520919i | ||||||
\(797\) | −19.0000 | − | 19.0000i | −0.673015 | − | 0.673015i | 0.285395 | − | 0.958410i | \(-0.407875\pi\) |
−0.958410 | + | 0.285395i | \(0.907875\pi\) | |||||||
\(798\) | 12.0000 | − | 12.0000i | 0.424795 | − | 0.424795i | ||||
\(799\) | −73.4847 | −2.59970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 9.79796i | − | 0.346194i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.6969 | + | 14.6969i | 0.518644 | + | 0.518644i | ||||
\(804\) | −4.89898 | −0.172774 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.0000 | + | 36.7423i | 0.634023 | + | 1.29419i | ||||
\(807\) | 24.4949 | − | 24.4949i | 0.862261 | − | 0.862261i | ||||
\(808\) | −14.6969 | − | 14.6969i | −0.517036 | − | 0.517036i | ||||
\(809\) | −29.3939 | −1.03343 | −0.516717 | − | 0.856156i | \(-0.672846\pi\) | ||||
−0.516717 | + | 0.856156i | \(0.672846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.0000 | 1.54505 | 0.772524 | − | 0.634985i | \(-0.218994\pi\) | ||||
0.772524 | + | 0.634985i | \(0.218994\pi\) | |||||||
\(812\) | −24.0000 | − | 24.0000i | −0.842235 | − | 0.842235i | ||||
\(813\) | 9.79796 | + | 9.79796i | 0.343629 | + | 0.343629i | ||||
\(814\) | − | 36.0000i | − | 1.26180i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −50.0000 | −1.75035 | ||||||||
\(817\) | −6.00000 | − | 6.00000i | −0.209913 | − | 0.209913i | ||||
\(818\) | −6.00000 | + | 6.00000i | −0.209785 | + | 0.209785i | ||||
\(819\) | −14.6969 | −0.513553 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 14.6969i | − | 0.512927i | −0.966554 | − | 0.256463i | \(-0.917443\pi\) | ||
0.966554 | − | 0.256463i | \(-0.0825573\pi\) | |||||||
\(822\) | 12.2474 | − | 12.2474i | 0.427179 | − | 0.427179i | ||||
\(823\) | −27.0000 | + | 27.0000i | −0.941161 | + | 0.941161i | −0.998363 | − | 0.0572018i | \(-0.981782\pi\) |
0.0572018 | + | 0.998363i | \(0.481782\pi\) | |||||||
\(824\) | − | 6.00000i | − | 0.209020i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −72.0000 | −2.50520 | ||||||||
\(827\) | −35.0000 | − | 35.0000i | −1.21707 | − | 1.21707i | −0.968654 | − | 0.248416i | \(-0.920090\pi\) |
−0.248416 | − | 0.968654i | \(-0.579910\pi\) | |||||||
\(828\) | 1.00000 | − | 1.00000i | 0.0347524 | − | 0.0347524i | ||||
\(829\) | 44.0908 | 1.53134 | 0.765669 | − | 0.643235i | \(-0.222408\pi\) | ||||
0.765669 | + | 0.643235i | \(0.222408\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.00000 | −0.208138 | ||||||||
\(832\) | −3.00000 | − | 3.00000i | −0.104006 | − | 0.104006i | ||||
\(833\) | 25.0000 | − | 25.0000i | 0.866199 | − | 0.866199i | ||||
\(834\) | − | 36.0000i | − | 1.24658i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.79796i | 0.338869i | ||||||||
\(837\) | −29.7980 | − | 10.2020i | −1.02997 | − | 0.352634i | ||||
\(838\) | 14.6969 | + | 14.6969i | 0.507697 | + | 0.507697i | ||||
\(839\) | − | 42.0000i | − | 1.45000i | −0.688748 | − | 0.725001i | \(-0.741839\pi\) | ||
0.688748 | − | 0.725001i | \(-0.258161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 67.0000 | 2.31034 | ||||||||
\(842\) | −12.2474 | + | 12.2474i | −0.422075 | + | 0.422075i | ||||
\(843\) | −12.0000 | + | 12.0000i | −0.413302 | + | 0.413302i | ||||
\(844\) | − | 10.0000i | − | 0.344214i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.0000 | −0.618853 | ||||||||
\(847\) | −31.8434 | + | 31.8434i | −1.09415 | + | 1.09415i | ||||
\(848\) | 5.00000 | − | 5.00000i | 0.171701 | − | 0.171701i | ||||
\(849\) | 4.89898 | 0.168133 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | 0.205677 | ||||||||
\(852\) | 6.00000 | + | 6.00000i | 0.205557 | + | 0.205557i | ||||
\(853\) | −9.79796 | − | 9.79796i | −0.335476 | − | 0.335476i | 0.519186 | − | 0.854661i | \(-0.326235\pi\) |
−0.854661 | + | 0.519186i | \(0.826235\pi\) | |||||||
\(854\) | −29.3939 | −1.00584 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.0000 | −0.615227 | ||||||||
\(857\) | 24.4949 | − | 24.4949i | 0.836730 | − | 0.836730i | −0.151697 | − | 0.988427i | \(-0.548474\pi\) |
0.988427 | + | 0.151697i | \(0.0484739\pi\) | |||||||
\(858\) | −36.0000 | + | 36.0000i | −1.22902 | + | 1.22902i | ||||
\(859\) | 39.1918 | 1.33721 | 0.668604 | − | 0.743619i | \(-0.266892\pi\) | ||||
0.668604 | + | 0.743619i | \(0.266892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 29.3939i | − | 1.00174i | ||||||
\(862\) | 7.34847 | − | 7.34847i | 0.250290 | − | 0.250290i | ||||
\(863\) | 31.0000 | − | 31.0000i | 1.05525 | − | 1.05525i | 0.0568707 | − | 0.998382i | \(-0.481888\pi\) |
0.998382 | − | 0.0568707i | \(-0.0181123\pi\) | |||||||
\(864\) | −29.3939 | −1.00000 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 36.7423i | − | 1.24856i | ||||||
\(867\) | −33.0000 | − | 33.0000i | −1.12074 | − | 1.12074i | ||||
\(868\) | −18.2474 | − | 6.24745i | −0.619359 | − | 0.212052i | ||||
\(869\) | 48.0000i | 1.62829i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.6969i | − | 0.497987i | ||||||
\(872\) | −19.5959 | + | 19.5959i | −0.663602 | + | 0.663602i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.89898 | −0.165710 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(878\) | −9.79796 | − | 9.79796i | −0.330665 | − | 0.330665i | ||||
\(879\) | 9.79796 | 0.330477 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.89898i | − | 0.165051i | −0.996589 | − | 0.0825254i | \(-0.973701\pi\) | ||
0.996589 | − | 0.0825254i | \(-0.0262986\pi\) | |||||||
\(882\) | 6.12372 | − | 6.12372i | 0.206197 | − | 0.206197i | ||||
\(883\) | 9.00000 | − | 9.00000i | 0.302874 | − | 0.302874i | −0.539263 | − | 0.842137i | \(-0.681297\pi\) |
0.842137 | + | 0.539263i | \(0.181297\pi\) | |||||||
\(884\) | 30.0000i | 1.00901i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.0000 | −1.00787 | ||||||||
\(887\) | −26.9444 | + | 26.9444i | −0.904704 | + | 0.904704i | −0.995839 | − | 0.0911346i | \(-0.970951\pi\) |
0.0911346 | + | 0.995839i | \(0.470951\pi\) | |||||||
\(888\) | −7.34847 | − | 7.34847i | −0.246598 | − | 0.246598i | ||||
\(889\) | 14.6969 | 0.492919 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 24.4949i | − | 0.820610i | ||||||
\(892\) | −3.00000 | − | 3.00000i | −0.100447 | − | 0.100447i | ||||
\(893\) | 14.6969 | + | 14.6969i | 0.491814 | + | 0.491814i | ||||
\(894\) | 14.6969 | 0.491539 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 42.0000 | 1.40312 | ||||||||
\(897\) | −6.00000 | − | 6.00000i | −0.200334 | − | 0.200334i | ||||
\(898\) | 42.0000 | − | 42.0000i | 1.40156 | − | 1.40156i | ||||
\(899\) | 48.9898 | − | 24.0000i | 1.63390 | − | 0.800445i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | 0.333148 | ||||||||
\(902\) | 36.0000 | + | 36.0000i | 1.19867 | + | 1.19867i | ||||
\(903\) | 14.6969 | + | 14.6969i | 0.489083 | + | 0.489083i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 36.0000 | 1.19602 | ||||||||
\(907\) | −31.8434 | + | 31.8434i | −1.05734 | + | 1.05734i | −0.0590889 | + | 0.998253i | \(0.518820\pi\) |
−0.998253 | + | 0.0590889i | \(0.981180\pi\) | |||||||
\(908\) | 2.44949 | + | 2.44949i | 0.0812892 | + | 0.0812892i | ||||
\(909\) | − | 12.0000i | − | 0.398015i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.4949i | 0.811552i | 0.913973 | + | 0.405776i | \(0.132999\pi\) | ||||
−0.913973 | + | 0.405776i | \(0.867001\pi\) | |||||||
\(912\) | 10.0000 | + | 10.0000i | 0.331133 | + | 0.331133i | ||||
\(913\) | 34.2929 | + | 34.2929i | 1.13493 | + | 1.13493i | ||||
\(914\) | −51.4393 | −1.70146 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 19.5959i | − | 0.647467i | ||||||
\(917\) | −14.6969 | + | 14.6969i | −0.485336 | + | 0.485336i | ||||
\(918\) | −48.9898 | − | 48.9898i | −1.61690 | − | 1.61690i | ||||
\(919\) | 10.0000i | 0.329870i | 0.986304 | + | 0.164935i | \(0.0527414\pi\) | ||||
−0.986304 | + | 0.164935i | \(0.947259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.4949i | 0.807134i | ||||||||
\(922\) | 24.0000 | + | 24.0000i | 0.790398 | + | 0.790398i | ||||
\(923\) | −18.0000 | + | 18.0000i | −0.592477 | + | 0.592477i | ||||
\(924\) | − | 24.0000i | − | 0.789542i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 51.4393i | 1.69040i | ||||||||
\(927\) | 2.44949 | − | 2.44949i | 0.0804518 | − | 0.0804518i | ||||
\(928\) | 36.0000 | − | 36.0000i | 1.18176 | − | 1.18176i | ||||
\(929\) | −24.4949 | −0.803652 | −0.401826 | − | 0.915716i | \(-0.631624\pi\) | ||||
−0.401826 | + | 0.915716i | \(0.631624\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.0000 | −0.327737 | ||||||||
\(932\) | −14.6969 | + | 14.6969i | −0.481414 | + | 0.481414i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.0000i | 0.981630i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 7.34847i | − | 0.240192i | ||||||
\(937\) | 19.5959 | − | 19.5959i | 0.640171 | − | 0.640171i | −0.310427 | − | 0.950597i | \(-0.600472\pi\) |
0.950597 | + | 0.310427i | \(0.100472\pi\) | |||||||
\(938\) | 14.6969 | + | 14.6969i | 0.479872 | + | 0.479872i | ||||
\(939\) | 30.0000i | 0.979013i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.3939i | 0.958213i | 0.877757 | + | 0.479107i | \(0.159039\pi\) | ||||
−0.877757 | + | 0.479107i | \(0.840961\pi\) | |||||||
\(942\) | 24.0000 | + | 24.0000i | 0.781962 | + | 0.781962i | ||||
\(943\) | −6.00000 | + | 6.00000i | −0.195387 | + | 0.195387i | ||||
\(944\) | − | 60.0000i | − | 1.95283i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.0000 | −1.17046 | ||||||||
\(947\) | −31.0000 | − | 31.0000i | −1.00736 | − | 1.00736i | −0.999973 | − | 0.00739197i | \(-0.997647\pi\) |
−0.00739197 | − | 0.999973i | \(-0.502353\pi\) | |||||||
\(948\) | −9.79796 | − | 9.79796i | −0.318223 | − | 0.318223i | ||||
\(949\) | − | 18.0000i | − | 0.584305i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.9898i | 1.58860i | ||||||||
\(952\) | 30.0000 | + | 30.0000i | 0.972306 | + | 0.972306i | ||||
\(953\) | 5.00000 | − | 5.00000i | 0.161966 | − | 0.161966i | −0.621471 | − | 0.783437i | \(-0.713465\pi\) |
0.783437 | + | 0.621471i | \(0.213465\pi\) | |||||||
\(954\) | 2.44949 | 0.0793052 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 4.89898i | − | 0.158444i | ||||||
\(957\) | 48.0000 | + | 48.0000i | 1.55162 | + | 1.55162i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.4949 | −0.790981 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | − | 24.4949i | 0.612903 | − | 0.790158i | ||||
\(962\) | −22.0454 | + | 22.0454i | −0.710772 | + | 0.710772i | ||||
\(963\) | −7.34847 | − | 7.34847i | −0.236801 | − | 0.236801i | ||||
\(964\) | 24.4949 | 0.788928 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 12.0000 | 0.386094 | ||||||||
\(967\) | −3.00000 | − | 3.00000i | −0.0964735 | − | 0.0964735i | 0.657223 | − | 0.753696i | \(-0.271731\pi\) |
−0.753696 | + | 0.657223i | \(0.771731\pi\) | |||||||
\(968\) | −15.9217 | − | 15.9217i | −0.511742 | − | 0.511742i | ||||
\(969\) | 20.0000i | 0.642493i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.0000 | −1.15529 | −0.577647 | − | 0.816286i | \(-0.696029\pi\) | ||||
−0.577647 | + | 0.816286i | \(0.696029\pi\) | |||||||
\(972\) | −7.00000 | − | 7.00000i | −0.224525 | − | 0.224525i | ||||
\(973\) | −36.0000 | + | 36.0000i | −1.15411 | + | 1.15411i | ||||
\(974\) | −36.7423 | −1.17730 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 24.4949i | − | 0.784063i | ||||||
\(977\) | −14.6969 | + | 14.6969i | −0.470197 | + | 0.470197i | −0.901978 | − | 0.431782i | \(-0.857885\pi\) |
0.431782 | + | 0.901978i | \(0.357885\pi\) | |||||||
\(978\) | 30.0000 | − | 30.0000i | 0.959294 | − | 0.959294i | ||||
\(979\) | 48.0000i | 1.53409i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | −24.0000 | − | 24.0000i | −0.765871 | − | 0.765871i | ||||
\(983\) | −7.00000 | + | 7.00000i | −0.223265 | + | 0.223265i | −0.809872 | − | 0.586607i | \(-0.800463\pi\) |
0.586607 | + | 0.809872i | \(0.300463\pi\) | |||||||
\(984\) | 14.6969 | 0.468521 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 120.000 | 3.82158 | ||||||||
\(987\) | −36.0000 | − | 36.0000i | −1.14589 | − | 1.14589i | ||||
\(988\) | 6.00000 | − | 6.00000i | 0.190885 | − | 0.190885i | ||||
\(989\) | − | 6.00000i | − | 0.190789i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.79796i | 0.311242i | 0.987817 | + | 0.155621i | \(0.0497379\pi\) | ||||
−0.987817 | + | 0.155621i | \(0.950262\pi\) | |||||||
\(992\) | 9.37117 | − | 27.3712i | 0.297535 | − | 0.869036i | ||||
\(993\) | −29.3939 | − | 29.3939i | −0.932786 | − | 0.932786i | ||||
\(994\) | − | 36.0000i | − | 1.14185i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −14.0000 | −0.443607 | ||||||||
\(997\) | −9.79796 | + | 9.79796i | −0.310304 | + | 0.310304i | −0.845027 | − | 0.534723i | \(-0.820416\pi\) |
0.534723 | + | 0.845027i | \(0.320416\pi\) | |||||||
\(998\) | 24.0000 | − | 24.0000i | 0.759707 | − | 0.759707i | ||||
\(999\) | − | 24.0000i | − | 0.759326i |
(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 | 775.2.f.a.743.2 | yes | 4 | |
5.2 | odd | 4 | 775.2.f.b.557.2 | yes | 4 | ||
5.3 | odd | 4 | inner | 775.2.f.a.557.1 | ✓ | 4 | |
5.4 | even | 2 | 775.2.f.b.743.1 | yes | 4 | ||
31.30 | odd | 2 | 775.2.f.b.743.2 | yes | 4 | ||
155.92 | even | 4 | inner | 775.2.f.a.557.2 | yes | 4 | |
155.123 | even | 4 | 775.2.f.b.557.1 | yes | 4 | ||
155.154 | odd | 2 | inner | 775.2.f.a.743.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
775.2.f.a.557.1 | ✓ | 4 | 5.3 | odd | 4 | inner | |
775.2.f.a.557.2 | yes | 4 | 155.92 | even | 4 | inner | |
775.2.f.a.743.1 | yes | 4 | 155.154 | odd | 2 | inner | |
775.2.f.a.743.2 | yes | 4 | 1.1 | even | 1 | trivial | |
775.2.f.b.557.1 | yes | 4 | 155.123 | even | 4 | ||
775.2.f.b.557.2 | yes | 4 | 5.2 | odd | 4 | ||
775.2.f.b.743.1 | yes | 4 | 5.4 | even | 2 | ||
775.2.f.b.743.2 | yes | 4 | 31.30 | odd | 2 |