Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(107,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.107 |
Dual form | 450.2.f.c.143.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | + | 3.00000i | 1.13389 | + | 1.13389i | 0.989524 | + | 0.144370i | \(0.0461154\pi\) |
0.144370 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24264i | 1.27920i | 0.768706 | + | 0.639602i | \(0.220901\pi\) | ||||
−0.768706 | + | 0.639602i | \(0.779099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 3.00000i | 0.832050 | − | 0.832050i | −0.155747 | − | 0.987797i | \(-0.549778\pi\) |
0.987797 | + | 0.155747i | \(0.0497784\pi\) | |||||||
\(14\) | 4.24264 | 1.13389 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.24264 | − | 4.24264i | 1.02899 | − | 1.02899i | 0.0294245 | − | 0.999567i | \(-0.490633\pi\) |
0.999567 | − | 0.0294245i | \(-0.00936746\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | + | 3.00000i | 0.639602 | + | 0.639602i | ||||
\(23\) | −4.24264 | − | 4.24264i | −0.884652 | − | 0.884652i | 0.109351 | − | 0.994003i | \(-0.465123\pi\) |
−0.994003 | + | 0.109351i | \(0.965123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 4.24264i | − | 0.832050i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.00000 | − | 3.00000i | 0.566947 | − | 0.566947i | ||||
\(29\) | −8.48528 | −1.57568 | −0.787839 | − | 0.615882i | \(-0.788800\pi\) | ||||
−0.787839 | + | 0.615882i | \(0.788800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.00000i | − | 1.02899i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | 1.41421 | + | 1.41421i | 0.229416 | + | 0.229416i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.24264i | − | 0.662589i | −0.943527 | − | 0.331295i | \(-0.892515\pi\) | ||
0.943527 | − | 0.331295i | \(-0.107485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 4.24264 | 0.639602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0000i | 1.57143i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | − | 3.00000i | −0.416025 | − | 0.416025i | ||||
\(53\) | 4.24264 | + | 4.24264i | 0.582772 | + | 0.582772i | 0.935664 | − | 0.352892i | \(-0.114802\pi\) |
−0.352892 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 4.24264i | − | 0.566947i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00000 | + | 6.00000i | −0.787839 | + | 0.787839i | ||||
\(59\) | −4.24264 | −0.552345 | −0.276172 | − | 0.961108i | \(-0.589066\pi\) | ||||
−0.276172 | + | 0.961108i | \(0.589066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 2.82843 | − | 2.82843i | 0.359211 | − | 0.359211i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | − | 6.00000i | −0.733017 | − | 0.733017i | 0.238200 | − | 0.971216i | \(-0.423443\pi\) |
−0.971216 | + | 0.238200i | \(0.923443\pi\) | |||||||
\(68\) | −4.24264 | − | 4.24264i | −0.514496 | − | 0.514496i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48528i | 1.00702i | 0.863990 | + | 0.503509i | \(0.167958\pi\) | ||||
−0.863990 | + | 0.503509i | \(0.832042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | + | 6.00000i | −0.702247 | + | 0.702247i | −0.964892 | − | 0.262646i | \(-0.915405\pi\) |
0.262646 | + | 0.964892i | \(0.415405\pi\) | |||||||
\(74\) | 4.24264 | 0.493197 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −12.7279 | + | 12.7279i | −1.45048 | + | 1.45048i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.00000i | − | 0.900070i | −0.893011 | − | 0.450035i | \(-0.851411\pi\) | ||
0.893011 | − | 0.450035i | \(-0.148589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.00000 | − | 3.00000i | −0.331295 | − | 0.331295i | ||||
\(83\) | 8.48528 | + | 8.48528i | 0.931381 | + | 0.931381i | 0.997792 | − | 0.0664117i | \(-0.0211551\pi\) |
−0.0664117 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | − | 3.00000i | 0.319801 | − | 0.319801i | ||||
\(89\) | −4.24264 | −0.449719 | −0.224860 | − | 0.974391i | \(-0.572192\pi\) | ||||
−0.224860 | + | 0.974391i | \(0.572192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.0000 | 1.88691 | ||||||||
\(92\) | −4.24264 | + | 4.24264i | −0.442326 | + | 0.442326i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0000 | − | 12.0000i | −1.21842 | − | 1.21842i | −0.968187 | − | 0.250229i | \(-0.919494\pi\) |
−0.250229 | − | 0.968187i | \(-0.580506\pi\) | |||||||
\(98\) | 7.77817 | + | 7.77817i | 0.785714 | + | 0.785714i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.48528i | − | 0.844317i | −0.906522 | − | 0.422159i | \(-0.861273\pi\) | ||
0.906522 | − | 0.422159i | \(-0.138727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | + | 3.00000i | −0.295599 | + | 0.295599i | −0.839287 | − | 0.543688i | \(-0.817027\pi\) |
0.543688 | + | 0.839287i | \(0.317027\pi\) | |||||||
\(104\) | −4.24264 | −0.416025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.00000 | − | 3.00000i | −0.283473 | − | 0.283473i | ||||
\(113\) | −12.7279 | − | 12.7279i | −1.19734 | − | 1.19734i | −0.974959 | − | 0.222383i | \(-0.928617\pi\) |
−0.222383 | − | 0.974959i | \(-0.571383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.48528i | 0.787839i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.00000 | + | 3.00000i | −0.276172 | + | 0.276172i | ||||
\(119\) | 25.4558 | 2.33353 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −7.07107 | + | 7.07107i | −0.640184 | + | 0.640184i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4.00000i | − | 0.359211i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.00000 | − | 9.00000i | −0.798621 | − | 0.798621i | 0.184257 | − | 0.982878i | \(-0.441012\pi\) |
−0.982878 | + | 0.184257i | \(0.941012\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.2132i | 1.85341i | 0.375794 | + | 0.926703i | \(0.377370\pi\) | ||||
−0.375794 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 6.00000i | −0.520266 | + | 0.520266i | ||||
\(134\) | −8.48528 | −0.733017 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 4.24264 | − | 4.24264i | 0.362473 | − | 0.362473i | −0.502249 | − | 0.864723i | \(-0.667494\pi\) |
0.864723 | + | 0.502249i | \(0.167494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | + | 6.00000i | 0.503509 | + | 0.503509i | ||||
\(143\) | 12.7279 | + | 12.7279i | 1.06436 | + | 1.06436i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.48528i | 0.702247i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.00000 | − | 3.00000i | 0.246598 | − | 0.246598i | ||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 1.41421 | − | 1.41421i | 0.114708 | − | 0.114708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 18.0000i | 1.45048i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 9.00000i | 0.718278 | + | 0.718278i | 0.968252 | − | 0.249974i | \(-0.0804222\pi\) |
−0.249974 | + | 0.968252i | \(0.580422\pi\) | |||||||
\(158\) | −5.65685 | − | 5.65685i | −0.450035 | − | 0.450035i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 25.4558i | − | 2.00620i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | − | 6.00000i | 0.469956 | − | 0.469956i | −0.431944 | − | 0.901900i | \(-0.642172\pi\) |
0.901900 | + | 0.431944i | \(0.142172\pi\) | |||||||
\(164\) | −4.24264 | −0.331295 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | −4.24264 | + | 4.24264i | −0.328305 | + | 0.328305i | −0.851942 | − | 0.523636i | \(-0.824575\pi\) |
0.523636 | + | 0.851942i | \(0.324575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.24264 | + | 4.24264i | 0.322562 | + | 0.322562i | 0.849749 | − | 0.527187i | \(-0.176753\pi\) |
−0.527187 | + | 0.849749i | \(0.676753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.24264i | − | 0.319801i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | + | 3.00000i | −0.224860 | + | 0.224860i | ||||
\(179\) | 4.24264 | 0.317110 | 0.158555 | − | 0.987350i | \(-0.449317\pi\) | ||||
0.158555 | + | 0.987350i | \(0.449317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 12.7279 | − | 12.7279i | 0.943456 | − | 0.943456i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00000i | 0.442326i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | + | 18.0000i | 1.31629 | + | 1.31629i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.48528i | − | 0.613973i | −0.951714 | − | 0.306987i | \(-0.900679\pi\) | ||
0.951714 | − | 0.306987i | \(-0.0993207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | − | 6.00000i | 0.431889 | − | 0.431889i | −0.457381 | − | 0.889271i | \(-0.651213\pi\) |
0.889271 | + | 0.457381i | \(0.151213\pi\) | |||||||
\(194\) | −16.9706 | −1.21842 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.0000 | 0.785714 | ||||||||
\(197\) | 8.48528 | − | 8.48528i | 0.604551 | − | 0.604551i | −0.336966 | − | 0.941517i | \(-0.609401\pi\) |
0.941517 | + | 0.336966i | \(0.109401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.0000i | − | 1.41776i | −0.705328 | − | 0.708881i | \(-0.749200\pi\) | ||
0.705328 | − | 0.708881i | \(-0.250800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.00000 | − | 6.00000i | −0.422159 | − | 0.422159i | ||||
\(203\) | −25.4558 | − | 25.4558i | −1.78665 | − | 1.78665i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.24264i | 0.295599i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | + | 3.00000i | −0.208013 | + | 0.208013i | ||||
\(209\) | −8.48528 | −0.586939 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 4.24264 | − | 4.24264i | 0.291386 | − | 0.291386i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000 | + | 12.0000i | 0.814613 | + | 0.814613i | ||||
\(218\) | −1.41421 | − | 1.41421i | −0.0957826 | − | 0.0957826i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 25.4558i | − | 1.71235i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.00000 | − | 9.00000i | 0.602685 | − | 0.602685i | −0.338340 | − | 0.941024i | \(-0.609865\pi\) |
0.941024 | + | 0.338340i | \(0.109865\pi\) | |||||||
\(224\) | −4.24264 | −0.283473 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | 8.48528 | − | 8.48528i | 0.563188 | − | 0.563188i | −0.367024 | − | 0.930212i | \(-0.619623\pi\) |
0.930212 | + | 0.367024i | \(0.119623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000i | 0.925146i | 0.886581 | + | 0.462573i | \(0.153074\pi\) | ||||
−0.886581 | + | 0.462573i | \(0.846926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | + | 6.00000i | 0.393919 | + | 0.393919i | ||||
\(233\) | 12.7279 | + | 12.7279i | 0.833834 | + | 0.833834i | 0.988039 | − | 0.154205i | \(-0.0492816\pi\) |
−0.154205 | + | 0.988039i | \(0.549282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.24264i | 0.276172i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.0000 | − | 18.0000i | 1.16677 | − | 1.16677i | ||||
\(239\) | 25.4558 | 1.64660 | 0.823301 | − | 0.567605i | \(-0.192130\pi\) | ||||
0.823301 | + | 0.567605i | \(0.192130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.0000 | −1.80364 | −0.901819 | − | 0.432113i | \(-0.857768\pi\) | ||||
−0.901819 | + | 0.432113i | \(0.857768\pi\) | |||||||
\(242\) | −4.94975 | + | 4.94975i | −0.318182 | + | 0.318182i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.0000i | 0.640184i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | + | 6.00000i | 0.381771 | + | 0.381771i | ||||
\(248\) | −2.82843 | − | 2.82843i | −0.179605 | − | 0.179605i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.7279i | 0.803379i | 0.915776 | + | 0.401690i | \(0.131577\pi\) | ||||
−0.915776 | + | 0.401690i | \(0.868423\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | − | 18.0000i | 1.13165 | − | 1.13165i | ||||
\(254\) | −12.7279 | −0.798621 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.24264 | − | 4.24264i | 0.264649 | − | 0.264649i | −0.562291 | − | 0.826940i | \(-0.690080\pi\) |
0.826940 | + | 0.562291i | \(0.190080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.0000i | 1.11847i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.0000 | + | 15.0000i | 0.926703 | + | 0.926703i | ||||
\(263\) | −12.7279 | − | 12.7279i | −0.784837 | − | 0.784837i | 0.195805 | − | 0.980643i | \(-0.437268\pi\) |
−0.980643 | + | 0.195805i | \(0.937268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.48528i | 0.520266i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.00000 | + | 6.00000i | −0.366508 | + | 0.366508i | ||||
\(269\) | 8.48528 | 0.517357 | 0.258678 | − | 0.965964i | \(-0.416713\pi\) | ||||
0.258678 | + | 0.965964i | \(0.416713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | −4.24264 | + | 4.24264i | −0.257248 | + | 0.257248i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 6.00000i | − | 0.362473i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.00000 | − | 9.00000i | −0.540758 | − | 0.540758i | 0.382993 | − | 0.923751i | \(-0.374893\pi\) |
−0.923751 | + | 0.382993i | \(0.874893\pi\) | |||||||
\(278\) | −2.82843 | − | 2.82843i | −0.169638 | − | 0.169638i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7279i | 0.759284i | 0.925133 | + | 0.379642i | \(0.123953\pi\) | ||||
−0.925133 | + | 0.379642i | \(0.876047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0000 | + | 18.0000i | −1.06999 | + | 1.06999i | −0.0726300 | + | 0.997359i | \(0.523139\pi\) |
−0.997359 | + | 0.0726300i | \(0.976861\pi\) | |||||||
\(284\) | 8.48528 | 0.503509 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.0000 | 1.06436 | ||||||||
\(287\) | 12.7279 | − | 12.7279i | 0.751305 | − | 0.751305i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 19.0000i | − | 1.11765i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.00000 | + | 6.00000i | 0.351123 | + | 0.351123i | ||||
\(293\) | −8.48528 | − | 8.48528i | −0.495715 | − | 0.495715i | 0.414386 | − | 0.910101i | \(-0.363996\pi\) |
−0.910101 | + | 0.414386i | \(0.863996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 4.24264i | − | 0.246598i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.4558 | −1.47215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.65685 | + | 5.65685i | −0.325515 | + | 0.325515i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 2.00000i | − | 0.114708i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 12.7279 | + | 12.7279i | 0.725241 | + | 0.725241i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.48528i | − | 0.481156i | −0.970630 | − | 0.240578i | \(-0.922663\pi\) | ||
0.970630 | − | 0.240578i | \(-0.0773370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | − | 6.00000i | 0.339140 | − | 0.339140i | −0.516904 | − | 0.856044i | \(-0.672915\pi\) |
0.856044 | + | 0.516904i | \(0.172915\pi\) | |||||||
\(314\) | 12.7279 | 0.718278 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 8.48528 | − | 8.48528i | 0.476581 | − | 0.476581i | −0.427456 | − | 0.904036i | \(-0.640590\pi\) |
0.904036 | + | 0.427456i | \(0.140590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36.0000i | − | 2.01561i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −18.0000 | − | 18.0000i | −1.00310 | − | 1.00310i | ||||
\(323\) | 8.48528 | + | 8.48528i | 0.472134 | + | 0.472134i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 8.48528i | − | 0.469956i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.00000 | + | 3.00000i | −0.165647 | + | 0.165647i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0000 | 1.42909 | 0.714545 | − | 0.699590i | \(-0.246634\pi\) | ||||
0.714545 | + | 0.699590i | \(0.246634\pi\) | |||||||
\(332\) | 8.48528 | − | 8.48528i | 0.465690 | − | 0.465690i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.00000i | 0.328305i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000 | + | 6.00000i | 0.326841 | + | 0.326841i | 0.851384 | − | 0.524543i | \(-0.175764\pi\) |
−0.524543 | + | 0.851384i | \(0.675764\pi\) | |||||||
\(338\) | −3.53553 | − | 3.53553i | −0.192308 | − | 0.192308i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706i | 0.919007i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | −25.4558 | + | 25.4558i | −1.36654 | + | 1.36654i | −0.501223 | + | 0.865318i | \(0.667117\pi\) |
−0.865318 | + | 0.501223i | \(0.832883\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0000i | 1.39175i | 0.718164 | + | 0.695874i | \(0.244983\pi\) | ||||
−0.718164 | + | 0.695874i | \(0.755017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.00000 | − | 3.00000i | −0.159901 | − | 0.159901i | ||||
\(353\) | 12.7279 | + | 12.7279i | 0.677439 | + | 0.677439i | 0.959420 | − | 0.281981i | \(-0.0909915\pi\) |
−0.281981 | + | 0.959420i | \(0.590992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.24264i | 0.224860i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.00000 | − | 3.00000i | 0.158555 | − | 0.158555i | ||||
\(359\) | 16.9706 | 0.895672 | 0.447836 | − | 0.894116i | \(-0.352195\pi\) | ||||
0.447836 | + | 0.894116i | \(0.352195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | −1.41421 | + | 1.41421i | −0.0743294 | + | 0.0743294i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 18.0000i | − | 0.943456i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.00000 | − | 3.00000i | −0.156599 | − | 0.156599i | 0.624459 | − | 0.781058i | \(-0.285320\pi\) |
−0.781058 | + | 0.624459i | \(0.785320\pi\) | |||||||
\(368\) | 4.24264 | + | 4.24264i | 0.221163 | + | 0.221163i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.4558i | 1.32160i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.0000 | + | 15.0000i | −0.776671 | + | 0.776671i | −0.979263 | − | 0.202593i | \(-0.935063\pi\) |
0.202593 | + | 0.979263i | \(0.435063\pi\) | |||||||
\(374\) | 25.4558 | 1.31629 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.4558 | + | 25.4558i | −1.31104 | + | 1.31104i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000i | 1.02733i | 0.857991 | + | 0.513665i | \(0.171713\pi\) | ||||
−0.857991 | + | 0.513665i | \(0.828287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.00000 | − | 6.00000i | −0.306987 | − | 0.306987i | ||||
\(383\) | 16.9706 | + | 16.9706i | 0.867155 | + | 0.867155i | 0.992157 | − | 0.125001i | \(-0.0398935\pi\) |
−0.125001 | + | 0.992157i | \(0.539894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 8.48528i | − | 0.431889i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.0000 | + | 12.0000i | −0.609208 | + | 0.609208i | ||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.0000 | −1.82060 | ||||||||
\(392\) | 7.77817 | − | 7.77817i | 0.392857 | − | 0.392857i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 12.0000i | − | 0.604551i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.0000 | − | 27.0000i | −1.35509 | − | 1.35509i | −0.879862 | − | 0.475229i | \(-0.842365\pi\) |
−0.475229 | − | 0.879862i | \(-0.657635\pi\) | |||||||
\(398\) | −14.1421 | − | 14.1421i | −0.708881 | − | 0.708881i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7279i | 0.635602i | 0.948157 | + | 0.317801i | \(0.102944\pi\) | ||||
−0.948157 | + | 0.317801i | \(0.897056\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000 | − | 12.0000i | 0.597763 | − | 0.597763i | ||||
\(404\) | −8.48528 | −0.422159 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −36.0000 | −1.78665 | ||||||||
\(407\) | −12.7279 | + | 12.7279i | −0.630900 | + | 0.630900i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000i | 0.692255i | 0.938187 | + | 0.346128i | \(0.112504\pi\) | ||||
−0.938187 | + | 0.346128i | \(0.887496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.00000 | + | 3.00000i | 0.147799 | + | 0.147799i | ||||
\(413\) | −12.7279 | − | 12.7279i | −0.626300 | − | 0.626300i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.24264i | 0.208013i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.00000 | + | 6.00000i | −0.293470 | + | 0.293470i | ||||
\(419\) | −38.1838 | −1.86540 | −0.932700 | − | 0.360654i | \(-0.882553\pi\) | ||||
−0.932700 | + | 0.360654i | \(0.882553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | −2.82843 | + | 2.82843i | −0.137686 | + | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 6.00000i | − | 0.291386i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.0000 | − | 30.0000i | −1.45180 | − | 1.45180i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16.9706i | − | 0.817443i | −0.912659 | − | 0.408722i | \(-0.865975\pi\) | ||
0.912659 | − | 0.408722i | \(-0.134025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.0000 | + | 18.0000i | −0.865025 | + | 0.865025i | −0.991917 | − | 0.126892i | \(-0.959500\pi\) |
0.126892 | + | 0.991917i | \(0.459500\pi\) | |||||||
\(434\) | 16.9706 | 0.814613 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | −0.0957826 | ||||||||
\(437\) | 8.48528 | − | 8.48528i | 0.405906 | − | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0000i | 1.33637i | 0.743996 | + | 0.668184i | \(0.232928\pi\) | ||||
−0.743996 | + | 0.668184i | \(0.767072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.0000 | − | 18.0000i | −0.856173 | − | 0.856173i | ||||
\(443\) | 16.9706 | + | 16.9706i | 0.806296 | + | 0.806296i | 0.984071 | − | 0.177775i | \(-0.0568900\pi\) |
−0.177775 | + | 0.984071i | \(0.556890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 12.7279i | − | 0.602685i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.00000 | + | 3.00000i | −0.141737 | + | 0.141737i | ||||
\(449\) | −29.6985 | −1.40156 | −0.700779 | − | 0.713378i | \(-0.747164\pi\) | ||||
−0.700779 | + | 0.713378i | \(0.747164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.0000 | 0.847587 | ||||||||
\(452\) | −12.7279 | + | 12.7279i | −0.598671 | + | 0.598671i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 12.0000i | − | 0.563188i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(458\) | 9.89949 | + | 9.89949i | 0.462573 | + | 0.462573i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 16.9706i | − | 0.790398i | −0.918596 | − | 0.395199i | \(-0.870676\pi\) | ||
0.918596 | − | 0.395199i | \(-0.129324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0000 | − | 21.0000i | 0.975953 | − | 0.975953i | −0.0237648 | − | 0.999718i | \(-0.507565\pi\) |
0.999718 | + | 0.0237648i | \(0.00756529\pi\) | |||||||
\(464\) | 8.48528 | 0.393919 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.0000 | 0.833834 | ||||||||
\(467\) | 8.48528 | − | 8.48528i | 0.392652 | − | 0.392652i | −0.482980 | − | 0.875632i | \(-0.660445\pi\) |
0.875632 | + | 0.482980i | \(0.160445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 36.0000i | − | 1.66233i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.00000 | + | 3.00000i | 0.138086 | + | 0.138086i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 25.4558i | − | 1.16677i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0000 | − | 18.0000i | 0.823301 | − | 0.823301i | ||||
\(479\) | 8.48528 | 0.387702 | 0.193851 | − | 0.981031i | \(-0.437902\pi\) | ||||
0.193851 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | −19.7990 | + | 19.7990i | −0.901819 | + | 0.901819i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000i | 0.318182i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.00000 | + | 3.00000i | 0.135943 | + | 0.135943i | 0.771804 | − | 0.635861i | \(-0.219355\pi\) |
−0.635861 | + | 0.771804i | \(0.719355\pi\) | |||||||
\(488\) | 7.07107 | + | 7.07107i | 0.320092 | + | 0.320092i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.24264i | − | 0.191468i | −0.995407 | − | 0.0957338i | \(-0.969480\pi\) | ||
0.995407 | − | 0.0957338i | \(-0.0305198\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.0000 | + | 36.0000i | −1.62136 | + | 1.62136i | ||||
\(494\) | 8.48528 | 0.381771 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −25.4558 | + | 25.4558i | −1.14185 | + | 1.14185i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.0000i | 0.984855i | 0.870353 | + | 0.492428i | \(0.163890\pi\) | ||||
−0.870353 | + | 0.492428i | \(0.836110\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.00000 | + | 9.00000i | 0.401690 | + | 0.401690i | ||||
\(503\) | −16.9706 | − | 16.9706i | −0.756680 | − | 0.756680i | 0.219037 | − | 0.975717i | \(-0.429709\pi\) |
−0.975717 | + | 0.219037i | \(0.929709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 25.4558i | − | 1.13165i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.00000 | + | 9.00000i | −0.399310 | + | 0.399310i | ||||
\(509\) | −25.4558 | −1.12831 | −0.564155 | − | 0.825669i | \(-0.690798\pi\) | ||||
−0.564155 | + | 0.825669i | \(0.690798\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.0000 | −1.59255 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 6.00000i | − | 0.264649i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 12.7279 | + | 12.7279i | 0.559233 | + | 0.559233i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.7279i | 0.557620i | 0.960346 | + | 0.278810i | \(0.0899400\pi\) | ||||
−0.960346 | + | 0.278810i | \(0.910060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.00000 | + | 6.00000i | −0.262362 | + | 0.262362i | −0.826013 | − | 0.563651i | \(-0.809396\pi\) |
0.563651 | + | 0.826013i | \(0.309396\pi\) | |||||||
\(524\) | 21.2132 | 0.926703 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.0000 | −0.784837 | ||||||||
\(527\) | 16.9706 | − | 16.9706i | 0.739249 | − | 0.739249i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000i | 0.565217i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.00000 | + | 6.00000i | 0.260133 | + | 0.260133i | ||||
\(533\) | −12.7279 | − | 12.7279i | −0.551308 | − | 0.551308i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.48528i | 0.366508i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.00000 | − | 6.00000i | 0.258678 | − | 0.258678i | ||||
\(539\) | −46.6690 | −2.01018 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 14.1421 | − | 14.1421i | 0.607457 | − | 0.607457i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.00000i | 0.257248i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | − | 12.0000i | −0.513083 | − | 0.513083i | 0.402387 | − | 0.915470i | \(-0.368181\pi\) |
−0.915470 | + | 0.402387i | \(0.868181\pi\) | |||||||
\(548\) | −4.24264 | − | 4.24264i | −0.181237 | − | 0.181237i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 16.9706i | − | 0.722970i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.0000 | − | 24.0000i | 1.02058 | − | 1.02058i | ||||
\(554\) | −12.7279 | −0.540758 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | 12.7279 | − | 12.7279i | 0.539299 | − | 0.539299i | −0.384024 | − | 0.923323i | \(-0.625462\pi\) |
0.923323 | + | 0.384024i | \(0.125462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00000 | + | 9.00000i | 0.379642 | + | 0.379642i | ||||
\(563\) | 25.4558 | + | 25.4558i | 1.07284 | + | 1.07284i | 0.997130 | + | 0.0757057i | \(0.0241210\pi\) |
0.0757057 | + | 0.997130i | \(0.475879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.4558i | 1.06999i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | − | 6.00000i | 0.251754 | − | 0.251754i | ||||
\(569\) | 46.6690 | 1.95647 | 0.978234 | − | 0.207504i | \(-0.0665341\pi\) | ||||
0.978234 | + | 0.207504i | \(0.0665341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | 12.7279 | − | 12.7279i | 0.532181 | − | 0.532181i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 18.0000i | − | 0.751305i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.0000 | + | 24.0000i | 0.999133 | + | 0.999133i | 1.00000 | 0.000866551i | \(-0.000275832\pi\) | |
−0.000866551 | 1.00000i | \(0.500276\pi\) | ||||||||
\(578\) | −13.4350 | − | 13.4350i | −0.558824 | − | 0.558824i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.9117i | 2.11217i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | + | 18.0000i | −0.745484 | + | 0.745484i | ||||
\(584\) | 8.48528 | 0.351123 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0000 | −0.495715 | ||||||||
\(587\) | 16.9706 | − | 16.9706i | 0.700450 | − | 0.700450i | −0.264057 | − | 0.964507i | \(-0.585061\pi\) |
0.964507 | + | 0.264057i | \(0.0850607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000i | 0.329634i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.00000 | − | 3.00000i | −0.123299 | − | 0.123299i | ||||
\(593\) | −4.24264 | − | 4.24264i | −0.174224 | − | 0.174224i | 0.614608 | − | 0.788833i | \(-0.289314\pi\) |
−0.788833 | + | 0.614608i | \(0.789314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.0000 | + | 18.0000i | −0.736075 | + | 0.736075i | ||||
\(599\) | 16.9706 | 0.693398 | 0.346699 | − | 0.937976i | \(-0.387302\pi\) | ||||
0.346699 | + | 0.937976i | \(0.387302\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.0000 | 1.14214 | 0.571072 | − | 0.820900i | \(-0.306528\pi\) | ||||
0.571072 | + | 0.820900i | \(0.306528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000i | 0.325515i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.0000 | + | 21.0000i | 0.852364 | + | 0.852364i | 0.990424 | − | 0.138060i | \(-0.0440867\pi\) |
−0.138060 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(608\) | −1.41421 | − | 1.41421i | −0.0573539 | − | 0.0573539i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.0000 | − | 33.0000i | 1.33286 | − | 1.33286i | 0.430055 | − | 0.902803i | \(-0.358494\pi\) |
0.902803 | − | 0.430055i | \(-0.141506\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.0000 | 0.725241 | ||||||||
\(617\) | 4.24264 | − | 4.24264i | 0.170802 | − | 0.170802i | −0.616530 | − | 0.787332i | \(-0.711462\pi\) |
0.787332 | + | 0.616530i | \(0.211462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0000i | 1.12542i | 0.826656 | + | 0.562708i | \(0.190240\pi\) | ||||
−0.826656 | + | 0.562708i | \(0.809760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.00000 | − | 6.00000i | −0.240578 | − | 0.240578i | ||||
\(623\) | −12.7279 | − | 12.7279i | −0.509933 | − | 0.509933i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 8.48528i | − | 0.339140i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.00000 | − | 9.00000i | 0.359139 | − | 0.359139i | ||||
\(629\) | 25.4558 | 1.01499 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | −5.65685 | + | 5.65685i | −0.225018 | + | 0.225018i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 12.0000i | − | 0.476581i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.0000 | + | 33.0000i | 1.30751 | + | 1.30751i | ||||
\(638\) | −25.4558 | − | 25.4558i | −1.00781 | − | 1.00781i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.24264i | − | 0.167574i | −0.996484 | − | 0.0837871i | \(-0.973298\pi\) | ||
0.996484 | − | 0.0837871i | \(-0.0267016\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0000 | − | 18.0000i | 0.709851 | − | 0.709851i | −0.256653 | − | 0.966504i | \(-0.582620\pi\) |
0.966504 | + | 0.256653i | \(0.0826197\pi\) | |||||||
\(644\) | −25.4558 | −1.00310 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | −16.9706 | + | 16.9706i | −0.667182 | + | 0.667182i | −0.957063 | − | 0.289881i | \(-0.906384\pi\) |
0.289881 | + | 0.957063i | \(0.406384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18.0000i | − | 0.706562i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.00000 | − | 6.00000i | −0.234978 | − | 0.234978i | ||||
\(653\) | 16.9706 | + | 16.9706i | 0.664109 | + | 0.664109i | 0.956346 | − | 0.292237i | \(-0.0943995\pi\) |
−0.292237 | + | 0.956346i | \(0.594399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.24264i | 0.165647i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.1838 | −1.48743 | −0.743714 | − | 0.668498i | \(-0.766938\pi\) | ||||
−0.743714 | + | 0.668498i | \(0.766938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 18.3848 | − | 18.3848i | 0.714545 | − | 0.714545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 12.0000i | − | 0.465690i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.0000 | + | 36.0000i | 1.39393 | + | 1.39393i | ||||
\(668\) | 4.24264 | + | 4.24264i | 0.164153 | + | 0.164153i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 42.4264i | − | 1.63785i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0000 | − | 30.0000i | 1.15642 | − | 1.15642i | 0.171174 | − | 0.985241i | \(-0.445244\pi\) |
0.985241 | − | 0.171174i | \(-0.0547561\pi\) | |||||||
\(674\) | 8.48528 | 0.326841 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 72.0000i | − | 2.76311i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0000 | + | 12.0000i | 0.459504 | + | 0.459504i | ||||
\(683\) | −33.9411 | − | 33.9411i | −1.29872 | − | 1.29872i | −0.929237 | − | 0.369484i | \(-0.879534\pi\) |
−0.369484 | − | 0.929237i | \(-0.620466\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.9706i | 0.647939i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.4558 | 0.969790 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | 0.380418 | 0.190209 | − | 0.981744i | \(-0.439083\pi\) | ||||
0.190209 | + | 0.981744i | \(0.439083\pi\) | |||||||
\(692\) | 4.24264 | − | 4.24264i | 0.161281 | − | 0.161281i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.0000i | 1.36654i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | − | 18.0000i | −0.681799 | − | 0.681799i | ||||
\(698\) | 18.3848 | + | 18.3848i | 0.695874 | + | 0.695874i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.4264i | 1.60242i | 0.598381 | + | 0.801212i | \(0.295811\pi\) | ||||
−0.598381 | + | 0.801212i | \(0.704189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | + | 6.00000i | −0.226294 | + | 0.226294i | ||||
\(704\) | −4.24264 | −0.159901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.0000 | 0.677439 | ||||||||
\(707\) | 25.4558 | − | 25.4558i | 0.957366 | − | 0.957366i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 46.0000i | − | 1.72757i | −0.503864 | − | 0.863783i | \(-0.668089\pi\) | ||
0.503864 | − | 0.863783i | \(-0.331911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.00000 | + | 3.00000i | 0.112430 | + | 0.112430i | ||||
\(713\) | −16.9706 | − | 16.9706i | −0.635553 | − | 0.635553i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 4.24264i | − | 0.158555i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.0000 | − | 12.0000i | 0.447836 | − | 0.447836i | ||||
\(719\) | 33.9411 | 1.26579 | 0.632895 | − | 0.774237i | \(-0.281866\pi\) | ||||
0.632895 | + | 0.774237i | \(0.281866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.0000 | −0.670355 | ||||||||
\(722\) | 10.6066 | − | 10.6066i | 0.394737 | − | 0.394737i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.00000i | 0.0743294i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.00000 | − | 9.00000i | −0.333792 | − | 0.333792i | 0.520233 | − | 0.854024i | \(-0.325845\pi\) |
−0.854024 | + | 0.520233i | \(0.825845\pi\) | |||||||
\(728\) | −12.7279 | − | 12.7279i | −0.471728 | − | 0.471728i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.00000 | + | 9.00000i | −0.332423 | + | 0.332423i | −0.853506 | − | 0.521083i | \(-0.825528\pi\) |
0.521083 | + | 0.853506i | \(0.325528\pi\) | |||||||
\(734\) | −4.24264 | −0.156599 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 25.4558 | − | 25.4558i | 0.937678 | − | 0.937678i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.0000i | 1.39785i | 0.715194 | + | 0.698926i | \(0.246338\pi\) | ||||
−0.715194 | + | 0.698926i | \(0.753662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.0000 | + | 18.0000i | 0.660801 | + | 0.660801i | ||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21.2132i | 0.776671i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.0000 | − | 18.0000i | 0.658145 | − | 0.658145i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 36.0000i | 1.31104i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | − | 15.0000i | −0.545184 | − | 0.545184i | 0.379860 | − | 0.925044i | \(-0.375972\pi\) |
−0.925044 | + | 0.379860i | \(0.875972\pi\) | |||||||
\(758\) | 14.1421 | + | 14.1421i | 0.513665 | + | 0.513665i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.6985i | 1.07657i | 0.842763 | + | 0.538285i | \(0.180927\pi\) | ||||
−0.842763 | + | 0.538285i | \(0.819073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.00000 | − | 6.00000i | 0.217215 | − | 0.217215i | ||||
\(764\) | −8.48528 | −0.306987 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | −12.7279 | + | 12.7279i | −0.459579 | + | 0.459579i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.0000i | 1.44244i | 0.692708 | + | 0.721218i | \(0.256418\pi\) | ||||
−0.692708 | + | 0.721218i | \(0.743582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.00000 | − | 6.00000i | −0.215945 | − | 0.215945i | ||||
\(773\) | 8.48528 | + | 8.48528i | 0.305194 | + | 0.305194i | 0.843042 | − | 0.537848i | \(-0.180762\pi\) |
−0.537848 | + | 0.843042i | \(0.680762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.9706i | 0.609208i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.48528 | 0.304017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | −25.4558 | + | 25.4558i | −0.910299 | + | 0.910299i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 11.0000i | − | 0.392857i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.0000 | + | 30.0000i | 1.06938 | + | 1.06938i | 0.997406 | + | 0.0719783i | \(0.0229312\pi\) |
0.0719783 | + | 0.997406i | \(0.477069\pi\) | |||||||
\(788\) | −8.48528 | − | 8.48528i | −0.302276 | − | 0.302276i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 76.3675i | − | 2.71532i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.0000 | + | 30.0000i | −1.06533 | + | 1.06533i | ||||
\(794\) | −38.1838 | −1.35509 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | 21.2132 | − | 21.2132i | 0.751410 | − | 0.751410i | −0.223332 | − | 0.974742i | \(-0.571693\pi\) |
0.974742 | + | 0.223332i | \(0.0716935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.00000 | + | 9.00000i | 0.317801 | + | 0.317801i | ||||
\(803\) | −25.4558 | − | 25.4558i | −0.898317 | − | 0.898317i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 16.9706i | − | 0.597763i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.00000 | + | 6.00000i | −0.211079 | + | 0.211079i | ||||
\(809\) | 29.6985 | 1.04414 | 0.522072 | − | 0.852902i | \(-0.325159\pi\) | ||||
0.522072 | + | 0.852902i | \(0.325159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | −25.4558 | + | 25.4558i | −0.893325 | + | 0.893325i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.0000i | 0.630900i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 9.89949 | + | 9.89949i | 0.346128 | + | 0.346128i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.48528i | 0.296138i | 0.988977 | + | 0.148069i | \(0.0473058\pi\) | ||||
−0.988977 | + | 0.148069i | \(0.952694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.00000 | + | 3.00000i | −0.104573 | + | 0.104573i | −0.757458 | − | 0.652884i | \(-0.773559\pi\) |
0.652884 | + | 0.757458i | \(0.273559\pi\) | |||||||
\(824\) | 4.24264 | 0.147799 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0000 | −0.626300 | ||||||||
\(827\) | −33.9411 | + | 33.9411i | −1.18025 | + | 1.18025i | −0.200569 | + | 0.979680i | \(0.564279\pi\) |
−0.979680 | + | 0.200569i | \(0.935721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.0000i | − | 1.18087i | −0.807086 | − | 0.590434i | \(-0.798956\pi\) | ||
0.807086 | − | 0.590434i | \(-0.201044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.00000 | + | 3.00000i | 0.104006 | + | 0.104006i | ||||
\(833\) | 46.6690 | + | 46.6690i | 1.61699 | + | 1.61699i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.48528i | 0.293470i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.0000 | + | 27.0000i | −0.932700 | + | 0.932700i | ||||
\(839\) | −16.9706 | −0.585889 | −0.292944 | − | 0.956129i | \(-0.594635\pi\) | ||||
−0.292944 | + | 0.956129i | \(0.594635\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 7.07107 | − | 7.07107i | 0.243685 | − | 0.243685i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000i | 0.137686i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0000 | − | 21.0000i | −0.721569 | − | 0.721569i | ||||
\(848\) | −4.24264 | − | 4.24264i | −0.145693 | − | 0.145693i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 25.4558i | − | 0.872615i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.0000 | − | 21.0000i | 0.719026 | − | 0.719026i | −0.249380 | − | 0.968406i | \(-0.580227\pi\) |
0.968406 | + | 0.249380i | \(0.0802267\pi\) | |||||||
\(854\) | −42.4264 | −1.45180 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.6985 | − | 29.6985i | 1.01448 | − | 1.01448i | 0.0145873 | − | 0.999894i | \(-0.495357\pi\) |
0.999894 | − | 0.0145873i | \(-0.00464345\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000i | 0.136478i | 0.997669 | + | 0.0682391i | \(0.0217381\pi\) | ||||
−0.997669 | + | 0.0682391i | \(0.978262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.0000 | − | 12.0000i | −0.408722 | − | 0.408722i | ||||
\(863\) | 4.24264 | + | 4.24264i | 0.144421 | + | 0.144421i | 0.775621 | − | 0.631199i | \(-0.217437\pi\) |
−0.631199 | + | 0.775621i | \(0.717437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25.4558i | 0.865025i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.0000 | − | 12.0000i | 0.407307 | − | 0.407307i | ||||
\(869\) | 33.9411 | 1.15137 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.0000 | −1.21981 | ||||||||
\(872\) | −1.41421 | + | 1.41421i | −0.0478913 | + | 0.0478913i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 12.0000i | − | 0.405906i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.0000 | − | 15.0000i | −0.506514 | − | 0.506514i | 0.406941 | − | 0.913455i | \(-0.366596\pi\) |
−0.913455 | + | 0.406941i | \(0.866596\pi\) | |||||||
\(878\) | 19.7990 | + | 19.7990i | 0.668184 | + | 0.668184i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 46.6690i | − | 1.57232i | −0.618023 | − | 0.786160i | \(-0.712066\pi\) | ||
0.618023 | − | 0.786160i | \(-0.287934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.00000 | + | 6.00000i | −0.201916 | + | 0.201916i | −0.800821 | − | 0.598904i | \(-0.795603\pi\) |
0.598904 | + | 0.800821i | \(0.295603\pi\) | |||||||
\(884\) | −25.4558 | −0.856173 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.0000 | 0.806296 | ||||||||
\(887\) | 4.24264 | − | 4.24264i | 0.142454 | − | 0.142454i | −0.632283 | − | 0.774737i | \(-0.717882\pi\) |
0.774737 | + | 0.632283i | \(0.217882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 54.0000i | − | 1.81110i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.00000 | − | 9.00000i | −0.301342 | − | 0.301342i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.24264i | 0.141737i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.0000 | + | 21.0000i | −0.700779 | + | 0.700779i | ||||
\(899\) | −33.9411 | −1.13200 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 12.7279 | − | 12.7279i | 0.423793 | − | 0.423793i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.0000i | 0.598671i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.0000 | − | 24.0000i | −0.796907 | − | 0.796907i | 0.185700 | − | 0.982607i | \(-0.440545\pi\) |
−0.982607 | + | 0.185700i | \(0.940545\pi\) | |||||||
\(908\) | −8.48528 | − | 8.48528i | −0.281594 | − | 0.281594i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 16.9706i | − | 0.562260i | −0.959670 | − | 0.281130i | \(-0.909291\pi\) | ||
0.959670 | − | 0.281130i | \(-0.0907092\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.0000 | + | 36.0000i | −1.19143 | + | 1.19143i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | −63.6396 | + | 63.6396i | −2.10157 | + | 2.10157i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000i | 0.659739i | 0.944027 | + | 0.329870i | \(0.107005\pi\) | ||||
−0.944027 | + | 0.329870i | \(0.892995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.0000 | − | 12.0000i | −0.395199 | − | 0.395199i | ||||
\(923\) | 25.4558 | + | 25.4558i | 0.837889 | + | 0.837889i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 29.6985i | − | 0.975953i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.00000 | − | 6.00000i | 0.196960 | − | 0.196960i | ||||
\(929\) | 4.24264 | 0.139197 | 0.0695983 | − | 0.997575i | \(-0.477828\pi\) | ||||
0.0695983 | + | 0.997575i | \(0.477828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.0000 | −0.721021 | ||||||||
\(932\) | 12.7279 | − | 12.7279i | 0.416917 | − | 0.416917i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 12.0000i | − | 0.392652i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.0000 | − | 24.0000i | −0.784046 | − | 0.784046i | 0.196465 | − | 0.980511i | \(-0.437054\pi\) |
−0.980511 | + | 0.196465i | \(0.937054\pi\) | |||||||
\(938\) | −25.4558 | − | 25.4558i | −0.831163 | − | 0.831163i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 50.9117i | − | 1.65967i | −0.558006 | − | 0.829837i | \(-0.688433\pi\) | ||
0.558006 | − | 0.829837i | \(-0.311567\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | + | 18.0000i | −0.586161 | + | 0.586161i | ||||
\(944\) | 4.24264 | 0.138086 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.9411 | + | 33.9411i | −1.10294 | + | 1.10294i | −0.108884 | + | 0.994054i | \(0.534728\pi\) |
−0.994054 | + | 0.108884i | \(0.965272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.0000i | 1.16861i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18.0000 | − | 18.0000i | −0.583383 | − | 0.583383i | ||||
\(953\) | −38.1838 | − | 38.1838i | −1.23689 | − | 1.23689i | −0.961264 | − | 0.275630i | \(-0.911114\pi\) |
−0.275630 | − | 0.961264i | \(-0.588886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 25.4558i | − | 0.823301i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.00000 | − | 6.00000i | 0.193851 | − | 0.193851i | ||||
\(959\) | 25.4558 | 0.822012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 12.7279 | − | 12.7279i | 0.410365 | − | 0.410365i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 28.0000i | 0.901819i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.0000 | − | 15.0000i | −0.482367 | − | 0.482367i | 0.423520 | − | 0.905887i | \(-0.360795\pi\) |
−0.905887 | + | 0.423520i | \(0.860795\pi\) | |||||||
\(968\) | 4.94975 | + | 4.94975i | 0.159091 | + | 0.159091i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.6985i | 0.953070i | 0.879156 | + | 0.476535i | \(0.158107\pi\) | ||||
−0.879156 | + | 0.476535i | \(0.841893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | − | 12.0000i | 0.384702 | − | 0.384702i | ||||
\(974\) | 4.24264 | 0.135943 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | −12.7279 | + | 12.7279i | −0.407202 | + | 0.407202i | −0.880762 | − | 0.473560i | \(-0.842969\pi\) |
0.473560 | + | 0.880762i | \(0.342969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 18.0000i | − | 0.575282i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.00000 | − | 3.00000i | −0.0957338 | − | 0.0957338i | ||||
\(983\) | 33.9411 | + | 33.9411i | 1.08255 | + | 1.08255i | 0.996271 | + | 0.0862831i | \(0.0274990\pi\) |
0.0862831 | + | 0.996271i | \(0.472501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 50.9117i | 1.62136i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.00000 | − | 6.00000i | 0.190885 | − | 0.190885i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.0000 | −1.65183 | −0.825917 | − | 0.563791i | \(-0.809342\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(992\) | −2.82843 | + | 2.82843i | −0.0898027 | + | 0.0898027i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 36.0000i | 1.14185i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.0000 | + | 27.0000i | 0.855099 | + | 0.855099i | 0.990756 | − | 0.135657i | \(-0.0433146\pi\) |
−0.135657 | + | 0.990756i | \(0.543315\pi\) | |||||||
\(998\) | 15.5563 | + | 15.5563i | 0.492428 | + | 0.492428i | ||||
\(999\) | 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 | 450.2.f.c.107.2 | yes | 4 | |
3.2 | odd | 2 | inner | 450.2.f.c.107.1 | yes | 4 | |
4.3 | odd | 2 | 3600.2.w.a.1457.1 | 4 | |||
5.2 | odd | 4 | 450.2.f.a.143.2 | yes | 4 | ||
5.3 | odd | 4 | inner | 450.2.f.c.143.1 | yes | 4 | |
5.4 | even | 2 | 450.2.f.a.107.1 | ✓ | 4 | ||
12.11 | even | 2 | 3600.2.w.a.1457.2 | 4 | |||
15.2 | even | 4 | 450.2.f.a.143.1 | yes | 4 | ||
15.8 | even | 4 | inner | 450.2.f.c.143.2 | yes | 4 | |
15.14 | odd | 2 | 450.2.f.a.107.2 | yes | 4 | ||
20.3 | even | 4 | 3600.2.w.a.593.1 | 4 | |||
20.7 | even | 4 | 3600.2.w.h.593.1 | 4 | |||
20.19 | odd | 2 | 3600.2.w.h.1457.1 | 4 | |||
60.23 | odd | 4 | 3600.2.w.a.593.2 | 4 | |||
60.47 | odd | 4 | 3600.2.w.h.593.2 | 4 | |||
60.59 | even | 2 | 3600.2.w.h.1457.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.f.a.107.1 | ✓ | 4 | 5.4 | even | 2 | ||
450.2.f.a.107.2 | yes | 4 | 15.14 | odd | 2 | ||
450.2.f.a.143.1 | yes | 4 | 15.2 | even | 4 | ||
450.2.f.a.143.2 | yes | 4 | 5.2 | odd | 4 | ||
450.2.f.c.107.1 | yes | 4 | 3.2 | odd | 2 | inner | |
450.2.f.c.107.2 | yes | 4 | 1.1 | even | 1 | trivial | |
450.2.f.c.143.1 | yes | 4 | 5.3 | odd | 4 | inner | |
450.2.f.c.143.2 | yes | 4 | 15.8 | even | 4 | inner | |
3600.2.w.a.593.1 | 4 | 20.3 | even | 4 | |||
3600.2.w.a.593.2 | 4 | 60.23 | odd | 4 | |||
3600.2.w.a.1457.1 | 4 | 4.3 | odd | 2 | |||
3600.2.w.a.1457.2 | 4 | 12.11 | even | 2 | |||
3600.2.w.h.593.1 | 4 | 20.7 | even | 4 | |||
3600.2.w.h.593.2 | 4 | 60.47 | odd | 4 | |||
3600.2.w.h.1457.1 | 4 | 20.19 | odd | 2 | |||
3600.2.w.h.1457.2 | 4 | 60.59 | even | 2 |