Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,2,Mod(24,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.918279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.24 |
Dual form | 115.2.b.a.24.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | − | 2.00000i | − | 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 2.00000 | + | 1.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | 4.00000 | 1.63299 | ||||||||
\(7\) | 1.00000i | 0.377964i | 0.981981 | + | 0.188982i | \(0.0605189\pi\) | ||||
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.00000 | + | 4.00000i | −0.632456 | + | 1.26491i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 4.00000i | 1.15470i | ||||||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 2.00000 | − | 4.00000i | 0.516398 | − | 1.03280i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | − | 5.00000i | − | 1.21268i | −0.795206 | − | 0.606339i | \(-0.792637\pi\) | ||
0.795206 | − | 0.606339i | \(-0.207363\pi\) | |||||||
\(18\) | − | 2.00000i | − | 0.471405i | ||||||
\(19\) | −8.00000 | −1.83533 | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | −4.00000 | − | 2.00000i | −0.894427 | − | 0.447214i | ||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | − | 2.00000i | − | 0.377964i | ||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 8.00000 | + | 4.00000i | 1.46059 | + | 0.730297i | ||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | − | 8.00000i | − | 1.41421i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0000 | 1.71499 | ||||||||
\(35\) | −1.00000 | + | 2.00000i | −0.169031 | + | 0.338062i | ||||
\(36\) | 2.00000 | 0.333333 | ||||||||
\(37\) | 7.00000i | 1.15079i | 0.817875 | + | 0.575396i | \(0.195152\pi\) | ||||
−0.817875 | + | 0.575396i | \(0.804848\pi\) | |||||||
\(38\) | − | 16.0000i | − | 2.59554i | ||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.00000 | −1.09322 | −0.546608 | − | 0.837389i | \(-0.684081\pi\) | ||||
−0.546608 | + | 0.837389i | \(0.684081\pi\) | |||||||
\(42\) | 4.00000i | 0.617213i | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | − | 1.00000i | −0.298142 | − | 0.149071i | ||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | − | 2.00000i | − | 0.291730i | −0.989305 | − | 0.145865i | \(-0.953403\pi\) | ||
0.989305 | − | 0.145865i | \(-0.0465965\pi\) | |||||||
\(48\) | 8.00000i | 1.15470i | ||||||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | −8.00000 | + | 6.00000i | −1.13137 | + | 0.848528i | ||||
\(51\) | −10.0000 | −1.40028 | ||||||||
\(52\) | 4.00000i | 0.554700i | ||||||||
\(53\) | 1.00000i | 0.137361i | 0.997639 | + | 0.0686803i | \(0.0218788\pi\) | ||||
−0.997639 | + | 0.0686803i | \(0.978121\pi\) | |||||||
\(54\) | 8.00000 | 1.08866 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.0000i | 2.11925i | ||||||||
\(58\) | 10.0000i | 1.31306i | ||||||||
\(59\) | −3.00000 | −0.390567 | −0.195283 | − | 0.980747i | \(-0.562563\pi\) | ||||
−0.195283 | + | 0.980747i | \(0.562563\pi\) | |||||||
\(60\) | −4.00000 | + | 8.00000i | −0.516398 | + | 1.03280i | ||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | − | 10.0000i | − | 1.27000i | ||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 2.00000 | − | 4.00000i | 0.248069 | − | 0.496139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.0000i | 1.58820i | 0.607785 | + | 0.794101i | \(0.292058\pi\) | ||||
−0.607785 | + | 0.794101i | \(0.707942\pi\) | |||||||
\(68\) | 10.0000i | 1.21268i | ||||||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | −4.00000 | − | 2.00000i | −0.478091 | − | 0.239046i | ||||
\(71\) | 13.0000 | 1.54282 | 0.771408 | − | 0.636341i | \(-0.219553\pi\) | ||||
0.771408 | + | 0.636341i | \(0.219553\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.00000i | − | 0.936329i | −0.883641 | − | 0.468165i | \(-0.844915\pi\) | ||
0.883641 | − | 0.468165i | \(-0.155085\pi\) | |||||||
\(74\) | −14.0000 | −1.62747 | ||||||||
\(75\) | 8.00000 | − | 6.00000i | 0.923760 | − | 0.692820i | ||||
\(76\) | 16.0000 | 1.83533 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 8.00000i | − | 0.905822i | ||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | −8.00000 | − | 4.00000i | −0.894427 | − | 0.447214i | ||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | − | 14.0000i | − | 1.54604i | ||||||
\(83\) | 3.00000i | 0.329293i | 0.986353 | + | 0.164646i | \(0.0526483\pi\) | ||||
−0.986353 | + | 0.164646i | \(0.947352\pi\) | |||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | 5.00000 | − | 10.0000i | 0.542326 | − | 1.08465i | ||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | − | 10.0000i | − | 1.07211i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.0000 | 1.48400 | 0.741999 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(90\) | 2.00000 | − | 4.00000i | 0.210819 | − | 0.421637i | ||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | − | 2.00000i | − | 0.208514i | ||||||
\(93\) | 10.0000i | 1.03695i | ||||||||
\(94\) | 4.00000 | 0.412568 | ||||||||
\(95\) | −16.0000 | − | 8.00000i | −1.64157 | − | 0.820783i | ||||
\(96\) | −16.0000 | −1.63299 | ||||||||
\(97\) | 14.0000i | 1.42148i | 0.703452 | + | 0.710742i | \(0.251641\pi\) | ||||
−0.703452 | + | 0.710742i | \(0.748359\pi\) | |||||||
\(98\) | 12.0000i | 1.21218i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.00000 | − | 8.00000i | −0.600000 | − | 0.800000i | ||||
\(101\) | 15.0000 | 1.49256 | 0.746278 | − | 0.665635i | \(-0.231839\pi\) | ||||
0.746278 | + | 0.665635i | \(0.231839\pi\) | |||||||
\(102\) | − | 20.0000i | − | 1.98030i | ||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000 | + | 2.00000i | 0.390360 | + | 0.195180i | ||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | 9.00000i | 0.870063i | 0.900415 | + | 0.435031i | \(0.143263\pi\) | ||||
−0.900415 | + | 0.435031i | \(0.856737\pi\) | |||||||
\(108\) | 8.00000i | 0.769800i | ||||||||
\(109\) | −18.0000 | −1.72409 | −0.862044 | − | 0.506834i | \(-0.830816\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0000 | 1.32882 | ||||||||
\(112\) | − | 4.00000i | − | 0.377964i | ||||||
\(113\) | 1.00000i | 0.0940721i | 0.998893 | + | 0.0470360i | \(0.0149776\pi\) | ||||
−0.998893 | + | 0.0470360i | \(0.985022\pi\) | |||||||
\(114\) | −32.0000 | −2.99707 | ||||||||
\(115\) | −1.00000 | + | 2.00000i | −0.0932505 | + | 0.186501i | ||||
\(116\) | −10.0000 | −0.928477 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | − | 6.00000i | − | 0.552345i | ||||||
\(119\) | 5.00000 | 0.458349 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − | 12.0000i | − | 1.08643i | ||||||
\(123\) | 14.0000i | 1.26234i | ||||||||
\(124\) | 10.0000 | 0.898027 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | − | 20.0000i | − | 1.77471i | −0.461084 | − | 0.887357i | \(-0.652539\pi\) | ||
0.461084 | − | 0.887357i | \(-0.347461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 8.00000 | + | 4.00000i | 0.701646 | + | 0.350823i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 8.00000i | − | 0.693688i | ||||||
\(134\) | −26.0000 | −2.24606 | ||||||||
\(135\) | 4.00000 | − | 8.00000i | 0.344265 | − | 0.688530i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000i | 0.512615i | 0.966595 | + | 0.256307i | \(0.0825059\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(138\) | 4.00000i | 0.340503i | ||||||||
\(139\) | −9.00000 | −0.763370 | −0.381685 | − | 0.924292i | \(-0.624656\pi\) | ||||
−0.381685 | + | 0.924292i | \(0.624656\pi\) | |||||||
\(140\) | 2.00000 | − | 4.00000i | 0.169031 | − | 0.338062i | ||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 26.0000i | 2.18187i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 10.0000 | + | 5.00000i | 0.830455 | + | 0.415227i | ||||
\(146\) | 16.0000 | 1.32417 | ||||||||
\(147\) | − | 12.0000i | − | 0.989743i | ||||||
\(148\) | − | 14.0000i | − | 1.15079i | ||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 12.0000 | + | 16.0000i | 0.979796 | + | 1.30639i | ||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.00000i | 0.404226i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.0000 | − | 5.00000i | −0.803219 | − | 0.401610i | ||||
\(156\) | 8.00000 | 0.640513 | ||||||||
\(157\) | − | 3.00000i | − | 0.239426i | −0.992809 | − | 0.119713i | \(-0.961803\pi\) | ||
0.992809 | − | 0.119713i | \(-0.0381975\pi\) | |||||||
\(158\) | 28.0000i | 2.22756i | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 8.00000 | − | 16.0000i | 0.632456 | − | 1.26491i | ||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | − | 22.0000i | − | 1.72848i | ||||||
\(163\) | − | 24.0000i | − | 1.87983i | −0.341415 | − | 0.939913i | \(-0.610906\pi\) | ||
0.341415 | − | 0.939913i | \(-0.389094\pi\) | |||||||
\(164\) | 14.0000 | 1.09322 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | 16.0000i | 1.23812i | 0.785345 | + | 0.619059i | \(0.212486\pi\) | ||||
−0.785345 | + | 0.619059i | \(0.787514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 20.0000 | + | 10.0000i | 1.53393 | + | 0.766965i | ||||
\(171\) | 8.00000 | 0.611775 | ||||||||
\(172\) | 8.00000i | 0.609994i | ||||||||
\(173\) | − | 6.00000i | − | 0.456172i | −0.973641 | − | 0.228086i | \(-0.926753\pi\) | ||
0.973641 | − | 0.228086i | \(-0.0732467\pi\) | |||||||
\(174\) | 20.0000 | 1.51620 | ||||||||
\(175\) | −4.00000 | + | 3.00000i | −0.302372 | + | 0.226779i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | 28.0000i | 2.09869i | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 4.00000 | + | 2.00000i | 0.298142 | + | 0.149071i | ||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 4.00000i | 0.296500i | ||||||||
\(183\) | 12.0000i | 0.887066i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.00000 | + | 14.0000i | −0.514650 | + | 1.02930i | ||||
\(186\) | −20.0000 | −1.46647 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.00000i | 0.291730i | ||||||||
\(189\) | 4.00000 | 0.290957 | ||||||||
\(190\) | 16.0000 | − | 32.0000i | 1.16076 | − | 2.32152i | ||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | − | 16.0000i | − | 1.15470i | ||||||
\(193\) | 12.0000i | 0.863779i | 0.901927 | + | 0.431889i | \(0.142153\pi\) | ||||
−0.901927 | + | 0.431889i | \(0.857847\pi\) | |||||||
\(194\) | −28.0000 | −2.01028 | ||||||||
\(195\) | −8.00000 | − | 4.00000i | −0.572892 | − | 0.286446i | ||||
\(196\) | −12.0000 | −0.857143 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.0000 | 1.83390 | ||||||||
\(202\) | 30.0000i | 2.11079i | ||||||||
\(203\) | 5.00000i | 0.350931i | ||||||||
\(204\) | 20.0000 | 1.40028 | ||||||||
\(205\) | −14.0000 | − | 7.00000i | −0.977802 | − | 0.488901i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.00000i | − | 0.0695048i | ||||||
\(208\) | 8.00000i | 0.554700i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.00000 | + | 8.00000i | −0.276026 | + | 0.552052i | ||||
\(211\) | −9.00000 | −0.619586 | −0.309793 | − | 0.950804i | \(-0.600260\pi\) | ||||
−0.309793 | + | 0.950804i | \(0.600260\pi\) | |||||||
\(212\) | − | 2.00000i | − | 0.137361i | ||||||
\(213\) | − | 26.0000i | − | 1.78149i | ||||||
\(214\) | −18.0000 | −1.23045 | ||||||||
\(215\) | 4.00000 | − | 8.00000i | 0.272798 | − | 0.545595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5.00000i | − | 0.339422i | ||||||
\(218\) | − | 36.0000i | − | 2.43823i | ||||||
\(219\) | −16.0000 | −1.08118 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0000 | −0.672673 | ||||||||
\(222\) | 28.0000i | 1.87924i | ||||||||
\(223\) | 14.0000i | 0.937509i | 0.883328 | + | 0.468755i | \(0.155297\pi\) | ||||
−0.883328 | + | 0.468755i | \(0.844703\pi\) | |||||||
\(224\) | 8.00000 | 0.534522 | ||||||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | −2.00000 | −0.133038 | ||||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | − | 32.0000i | − | 2.11925i | ||||||
\(229\) | −4.00000 | −0.264327 | −0.132164 | − | 0.991228i | \(-0.542192\pi\) | ||||
−0.132164 | + | 0.991228i | \(0.542192\pi\) | |||||||
\(230\) | −4.00000 | − | 2.00000i | −0.263752 | − | 0.131876i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.00000i | − | 0.393073i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) | ||
0.980497 | − | 0.196537i | \(-0.0629694\pi\) | |||||||
\(234\) | −4.00000 | −0.261488 | ||||||||
\(235\) | 2.00000 | − | 4.00000i | 0.130466 | − | 0.260931i | ||||
\(236\) | 6.00000 | 0.390567 | ||||||||
\(237\) | − | 28.0000i | − | 1.81880i | ||||||
\(238\) | 10.0000i | 0.648204i | ||||||||
\(239\) | 1.00000 | 0.0646846 | 0.0323423 | − | 0.999477i | \(-0.489703\pi\) | ||||
0.0323423 | + | 0.999477i | \(0.489703\pi\) | |||||||
\(240\) | −8.00000 | + | 16.0000i | −0.516398 | + | 1.03280i | ||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | − | 22.0000i | − | 1.41421i | ||||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | 12.0000 | 0.768221 | ||||||||
\(245\) | 12.0000 | + | 6.00000i | 0.766652 | + | 0.383326i | ||||
\(246\) | −28.0000 | −1.78521 | ||||||||
\(247\) | 16.0000i | 1.01806i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | −22.0000 | + | 4.00000i | −1.39140 | + | 0.252982i | ||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 2.00000i | 0.125988i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 40.0000 | 2.50982 | ||||||||
\(255\) | −20.0000 | − | 10.0000i | −1.25245 | − | 0.626224i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 22.0000i | 1.37232i | 0.727450 | + | 0.686161i | \(0.240706\pi\) | ||||
−0.727450 | + | 0.686161i | \(0.759294\pi\) | |||||||
\(258\) | − | 16.0000i | − | 0.996116i | ||||||
\(259\) | −7.00000 | −0.434959 | ||||||||
\(260\) | −4.00000 | + | 8.00000i | −0.248069 | + | 0.496139i | ||||
\(261\) | −5.00000 | −0.309492 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0000i | 0.801614i | 0.916162 | + | 0.400807i | \(0.131270\pi\) | ||||
−0.916162 | + | 0.400807i | \(0.868730\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00000 | + | 2.00000i | −0.0614295 | + | 0.122859i | ||||
\(266\) | 16.0000 | 0.981023 | ||||||||
\(267\) | − | 28.0000i | − | 1.71357i | ||||||
\(268\) | − | 26.0000i | − | 1.58820i | ||||||
\(269\) | 15.0000 | 0.914566 | 0.457283 | − | 0.889321i | \(-0.348823\pi\) | ||||
0.457283 | + | 0.889321i | \(0.348823\pi\) | |||||||
\(270\) | 16.0000 | + | 8.00000i | 0.973729 | + | 0.486864i | ||||
\(271\) | −15.0000 | −0.911185 | −0.455593 | − | 0.890188i | \(-0.650573\pi\) | ||||
−0.455593 | + | 0.890188i | \(0.650573\pi\) | |||||||
\(272\) | 20.0000i | 1.21268i | ||||||||
\(273\) | − | 4.00000i | − | 0.242091i | ||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.00000 | −0.240772 | ||||||||
\(277\) | − | 26.0000i | − | 1.56219i | −0.624413 | − | 0.781094i | \(-0.714662\pi\) | ||
0.624413 | − | 0.781094i | \(-0.285338\pi\) | |||||||
\(278\) | − | 18.0000i | − | 1.07957i | ||||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | − | 8.00000i | − | 0.476393i | ||||||
\(283\) | − | 11.0000i | − | 0.653882i | −0.945045 | − | 0.326941i | \(-0.893982\pi\) | ||
0.945045 | − | 0.326941i | \(-0.106018\pi\) | |||||||
\(284\) | −26.0000 | −1.54282 | ||||||||
\(285\) | −16.0000 | + | 32.0000i | −0.947758 | + | 1.89552i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 7.00000i | − | 0.413197i | ||||||
\(288\) | 8.00000i | 0.471405i | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | −10.0000 | + | 20.0000i | −0.587220 | + | 1.17444i | ||||
\(291\) | 28.0000 | 1.64139 | ||||||||
\(292\) | 16.0000i | 0.936329i | ||||||||
\(293\) | − | 29.0000i | − | 1.69420i | −0.531435 | − | 0.847099i | \(-0.678347\pi\) | ||
0.531435 | − | 0.847099i | \(-0.321653\pi\) | |||||||
\(294\) | 24.0000 | 1.39971 | ||||||||
\(295\) | −6.00000 | − | 3.00000i | −0.349334 | − | 0.174667i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | −16.0000 | + | 12.0000i | −0.923760 | + | 0.692820i | ||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 16.0000i | 0.920697i | ||||||||
\(303\) | − | 30.0000i | − | 1.72345i | ||||||
\(304\) | 32.0000 | 1.83533 | ||||||||
\(305\) | −12.0000 | − | 6.00000i | −0.687118 | − | 0.343559i | ||||
\(306\) | −10.0000 | −0.571662 | ||||||||
\(307\) | 14.0000i | 0.799022i | 0.916728 | + | 0.399511i | \(0.130820\pi\) | ||||
−0.916728 | + | 0.399511i | \(0.869180\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.0000 | − | 20.0000i | 0.567962 | − | 1.13592i | ||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.0000i | − | 1.18699i | −0.804838 | − | 0.593495i | \(-0.797748\pi\) | ||
0.804838 | − | 0.593495i | \(-0.202252\pi\) | |||||||
\(314\) | 6.00000 | 0.338600 | ||||||||
\(315\) | 1.00000 | − | 2.00000i | 0.0563436 | − | 0.112687i | ||||
\(316\) | −28.0000 | −1.57512 | ||||||||
\(317\) | − | 24.0000i | − | 1.34797i | −0.738743 | − | 0.673987i | \(-0.764580\pi\) | ||
0.738743 | − | 0.673987i | \(-0.235420\pi\) | |||||||
\(318\) | 4.00000i | 0.224309i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 16.0000 | + | 8.00000i | 0.894427 | + | 0.447214i | ||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | − | 2.00000i | − | 0.111456i | ||||||
\(323\) | 40.0000i | 2.22566i | ||||||||
\(324\) | 22.0000 | 1.22222 | ||||||||
\(325\) | 8.00000 | − | 6.00000i | 0.443760 | − | 0.332820i | ||||
\(326\) | 48.0000 | 2.65847 | ||||||||
\(327\) | 36.0000i | 1.99080i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | −0.274825 | −0.137412 | − | 0.990514i | \(-0.543879\pi\) | ||||
−0.137412 | + | 0.990514i | \(0.543879\pi\) | |||||||
\(332\) | − | 6.00000i | − | 0.329293i | ||||||
\(333\) | − | 7.00000i | − | 0.383598i | ||||||
\(334\) | −32.0000 | −1.75096 | ||||||||
\(335\) | −13.0000 | + | 26.0000i | −0.710266 | + | 1.42053i | ||||
\(336\) | −8.00000 | −0.436436 | ||||||||
\(337\) | 26.0000i | 1.41631i | 0.706057 | + | 0.708155i | \(0.250472\pi\) | ||||
−0.706057 | + | 0.708155i | \(0.749528\pi\) | |||||||
\(338\) | 18.0000i | 0.979071i | ||||||||
\(339\) | 2.00000 | 0.108625 | ||||||||
\(340\) | −10.0000 | + | 20.0000i | −0.542326 | + | 1.08465i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 16.0000i | 0.865181i | ||||||||
\(343\) | 13.0000i | 0.701934i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | + | 2.00000i | 0.215353 | + | 0.107676i | ||||
\(346\) | 12.0000 | 0.645124 | ||||||||
\(347\) | 8.00000i | 0.429463i | 0.976673 | + | 0.214731i | \(0.0688876\pi\) | ||||
−0.976673 | + | 0.214731i | \(0.931112\pi\) | |||||||
\(348\) | 20.0000i | 1.07211i | ||||||||
\(349\) | −23.0000 | −1.23116 | −0.615581 | − | 0.788074i | \(-0.711079\pi\) | ||||
−0.615581 | + | 0.788074i | \(0.711079\pi\) | |||||||
\(350\) | −6.00000 | − | 8.00000i | −0.320713 | − | 0.427618i | ||||
\(351\) | −8.00000 | −0.427008 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | −12.0000 | −0.637793 | ||||||||
\(355\) | 26.0000 | + | 13.0000i | 1.37994 | + | 0.689968i | ||||
\(356\) | −28.0000 | −1.48400 | ||||||||
\(357\) | − | 10.0000i | − | 0.529256i | ||||||
\(358\) | 8.00000i | 0.422813i | ||||||||
\(359\) | 6.00000 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.0000 | 2.36842 | ||||||||
\(362\) | − | 28.0000i | − | 1.47165i | ||||||
\(363\) | 22.0000i | 1.15470i | ||||||||
\(364\) | −4.00000 | −0.209657 | ||||||||
\(365\) | 8.00000 | − | 16.0000i | 0.418739 | − | 0.837478i | ||||
\(366\) | −24.0000 | −1.25450 | ||||||||
\(367\) | − | 13.0000i | − | 0.678594i | −0.940679 | − | 0.339297i | \(-0.889811\pi\) | ||
0.940679 | − | 0.339297i | \(-0.110189\pi\) | |||||||
\(368\) | − | 4.00000i | − | 0.208514i | ||||||
\(369\) | 7.00000 | 0.364405 | ||||||||
\(370\) | −28.0000 | − | 14.0000i | −1.45565 | − | 0.727825i | ||||
\(371\) | −1.00000 | −0.0519174 | ||||||||
\(372\) | − | 20.0000i | − | 1.03695i | ||||||
\(373\) | 6.00000i | 0.310668i | 0.987862 | + | 0.155334i | \(0.0496454\pi\) | ||||
−0.987862 | + | 0.155334i | \(0.950355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 22.0000 | − | 4.00000i | 1.13608 | − | 0.206559i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 10.0000i | − | 0.515026i | ||||||
\(378\) | 8.00000i | 0.411476i | ||||||||
\(379\) | −6.00000 | −0.308199 | −0.154100 | − | 0.988055i | \(-0.549248\pi\) | ||||
−0.154100 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(380\) | 32.0000 | + | 16.0000i | 1.64157 | + | 0.820783i | ||||
\(381\) | −40.0000 | −2.04926 | ||||||||
\(382\) | − | 16.0000i | − | 0.818631i | ||||||
\(383\) | − | 3.00000i | − | 0.153293i | −0.997058 | − | 0.0766464i | \(-0.975579\pi\) | ||
0.997058 | − | 0.0766464i | \(-0.0244213\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.0000 | −1.22157 | ||||||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | − | 28.0000i | − | 1.42148i | ||||||
\(389\) | −22.0000 | −1.11544 | −0.557722 | − | 0.830028i | \(-0.688325\pi\) | ||||
−0.557722 | + | 0.830028i | \(0.688325\pi\) | |||||||
\(390\) | 8.00000 | − | 16.0000i | 0.405096 | − | 0.810191i | ||||
\(391\) | 5.00000 | 0.252861 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.0000 | + | 14.0000i | 1.40883 | + | 0.704416i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.0000i | 0.803017i | 0.915855 | + | 0.401508i | \(0.131514\pi\) | ||||
−0.915855 | + | 0.401508i | \(0.868486\pi\) | |||||||
\(398\) | − | 4.00000i | − | 0.200502i | ||||||
\(399\) | −16.0000 | −0.801002 | ||||||||
\(400\) | −12.0000 | − | 16.0000i | −0.600000 | − | 0.800000i | ||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 52.0000i | 2.59352i | ||||||||
\(403\) | 10.0000i | 0.498135i | ||||||||
\(404\) | −30.0000 | −1.49256 | ||||||||
\(405\) | −22.0000 | − | 11.0000i | −1.09319 | − | 0.546594i | ||||
\(406\) | −10.0000 | −0.496292 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0000 | 0.939490 | 0.469745 | − | 0.882802i | \(-0.344346\pi\) | ||||
0.469745 | + | 0.882802i | \(0.344346\pi\) | |||||||
\(410\) | 14.0000 | − | 28.0000i | 0.691411 | − | 1.38282i | ||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.00000i | − | 0.147620i | ||||||
\(414\) | 2.00000 | 0.0982946 | ||||||||
\(415\) | −3.00000 | + | 6.00000i | −0.147264 | + | 0.294528i | ||||
\(416\) | −16.0000 | −0.784465 | ||||||||
\(417\) | 18.0000i | 0.881464i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.00000 | 0.0977064 | 0.0488532 | − | 0.998806i | \(-0.484443\pi\) | ||||
0.0488532 | + | 0.998806i | \(0.484443\pi\) | |||||||
\(420\) | −8.00000 | − | 4.00000i | −0.390360 | − | 0.195180i | ||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | − | 18.0000i | − | 0.876226i | ||||||
\(423\) | 2.00000i | 0.0972433i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.0000 | − | 15.0000i | 0.970143 | − | 0.727607i | ||||
\(426\) | 52.0000 | 2.51941 | ||||||||
\(427\) | − | 6.00000i | − | 0.290360i | ||||||
\(428\) | − | 18.0000i | − | 0.870063i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.0000 | + | 8.00000i | 0.771589 | + | 0.385794i | ||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 16.0000i | 0.769800i | ||||||||
\(433\) | − | 19.0000i | − | 0.913082i | −0.889702 | − | 0.456541i | \(-0.849088\pi\) | ||
0.889702 | − | 0.456541i | \(-0.150912\pi\) | |||||||
\(434\) | 10.0000 | 0.480015 | ||||||||
\(435\) | 10.0000 | − | 20.0000i | 0.479463 | − | 0.958927i | ||||
\(436\) | 36.0000 | 1.72409 | ||||||||
\(437\) | − | 8.00000i | − | 0.382692i | ||||||
\(438\) | − | 32.0000i | − | 1.52902i | ||||||
\(439\) | 28.0000 | 1.33637 | 0.668184 | − | 0.743996i | \(-0.267072\pi\) | ||||
0.668184 | + | 0.743996i | \(0.267072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | − | 20.0000i | − | 0.951303i | ||||||
\(443\) | 24.0000i | 1.14027i | 0.821549 | + | 0.570137i | \(0.193110\pi\) | ||||
−0.821549 | + | 0.570137i | \(0.806890\pi\) | |||||||
\(444\) | −28.0000 | −1.32882 | ||||||||
\(445\) | 28.0000 | + | 14.0000i | 1.32733 | + | 0.663664i | ||||
\(446\) | −28.0000 | −1.32584 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000i | 0.377964i | ||||||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 8.00000 | − | 6.00000i | 0.377124 | − | 0.282843i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 2.00000i | − | 0.0940721i | ||||||
\(453\) | − | 16.0000i | − | 0.751746i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.00000 | + | 2.00000i | 0.187523 | + | 0.0937614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00000i | 0.0467780i | 0.999726 | + | 0.0233890i | \(0.00744563\pi\) | ||||
−0.999726 | + | 0.0233890i | \(0.992554\pi\) | |||||||
\(458\) | − | 8.00000i | − | 0.373815i | ||||||
\(459\) | −20.0000 | −0.933520 | ||||||||
\(460\) | 2.00000 | − | 4.00000i | 0.0932505 | − | 0.186501i | ||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000i | 0.185896i | 0.995671 | + | 0.0929479i | \(0.0296290\pi\) | ||||
−0.995671 | + | 0.0929479i | \(0.970371\pi\) | |||||||
\(464\) | −20.0000 | −0.928477 | ||||||||
\(465\) | −10.0000 | + | 20.0000i | −0.463739 | + | 0.927478i | ||||
\(466\) | 12.0000 | 0.555889 | ||||||||
\(467\) | − | 27.0000i | − | 1.24941i | −0.780860 | − | 0.624705i | \(-0.785219\pi\) | ||
0.780860 | − | 0.624705i | \(-0.214781\pi\) | |||||||
\(468\) | − | 4.00000i | − | 0.184900i | ||||||
\(469\) | −13.0000 | −0.600284 | ||||||||
\(470\) | 8.00000 | + | 4.00000i | 0.369012 | + | 0.184506i | ||||
\(471\) | −6.00000 | −0.276465 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 56.0000 | 2.57217 | ||||||||
\(475\) | −24.0000 | − | 32.0000i | −1.10120 | − | 1.46826i | ||||
\(476\) | −10.0000 | −0.458349 | ||||||||
\(477\) | − | 1.00000i | − | 0.0457869i | ||||||
\(478\) | 2.00000i | 0.0914779i | ||||||||
\(479\) | 28.0000 | 1.27935 | 0.639676 | − | 0.768644i | \(-0.279068\pi\) | ||||
0.639676 | + | 0.768644i | \(0.279068\pi\) | |||||||
\(480\) | −32.0000 | − | 16.0000i | −1.46059 | − | 0.730297i | ||||
\(481\) | 14.0000 | 0.638345 | ||||||||
\(482\) | 12.0000i | 0.546585i | ||||||||
\(483\) | 2.00000i | 0.0910032i | ||||||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | −14.0000 | + | 28.0000i | −0.635707 | + | 1.27141i | ||||
\(486\) | −20.0000 | −0.907218 | ||||||||
\(487\) | − | 32.0000i | − | 1.45006i | −0.688718 | − | 0.725029i | \(-0.741826\pi\) | ||
0.688718 | − | 0.725029i | \(-0.258174\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −48.0000 | −2.17064 | ||||||||
\(490\) | −12.0000 | + | 24.0000i | −0.542105 | + | 1.08421i | ||||
\(491\) | −31.0000 | −1.39901 | −0.699505 | − | 0.714628i | \(-0.746596\pi\) | ||||
−0.699505 | + | 0.714628i | \(0.746596\pi\) | |||||||
\(492\) | − | 28.0000i | − | 1.26234i | ||||||
\(493\) | − | 25.0000i | − | 1.12594i | ||||||
\(494\) | −32.0000 | −1.43975 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | 13.0000i | 0.583130i | ||||||||
\(498\) | 12.0000i | 0.537733i | ||||||||
\(499\) | 11.0000 | 0.492428 | 0.246214 | − | 0.969216i | \(-0.420813\pi\) | ||||
0.246214 | + | 0.969216i | \(0.420813\pi\) | |||||||
\(500\) | −4.00000 | − | 22.0000i | −0.178885 | − | 0.983870i | ||||
\(501\) | 32.0000 | 1.42965 | ||||||||
\(502\) | 36.0000i | 1.60676i | ||||||||
\(503\) | 9.00000i | 0.401290i | 0.979664 | + | 0.200645i | \(0.0643038\pi\) | ||||
−0.979664 | + | 0.200645i | \(0.935696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.0000 | + | 15.0000i | 1.33498 | + | 0.667491i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 18.0000i | − | 0.799408i | ||||||
\(508\) | 40.0000i | 1.77471i | ||||||||
\(509\) | −26.0000 | −1.15243 | −0.576215 | − | 0.817298i | \(-0.695471\pi\) | ||||
−0.576215 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(510\) | 20.0000 | − | 40.0000i | 0.885615 | − | 1.77123i | ||||
\(511\) | 8.00000 | 0.353899 | ||||||||
\(512\) | 32.0000i | 1.41421i | ||||||||
\(513\) | 32.0000i | 1.41283i | ||||||||
\(514\) | −44.0000 | −1.94076 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 16.0000 | 0.704361 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 14.0000i | − | 0.615125i | ||||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.0000 | −0.876216 | −0.438108 | − | 0.898922i | \(-0.644351\pi\) | ||||
−0.438108 | + | 0.898922i | \(0.644351\pi\) | |||||||
\(522\) | − | 10.0000i | − | 0.437688i | ||||||
\(523\) | 28.0000i | 1.22435i | 0.790721 | + | 0.612177i | \(0.209706\pi\) | ||||
−0.790721 | + | 0.612177i | \(0.790294\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.00000 | + | 8.00000i | 0.261861 | + | 0.349149i | ||||
\(526\) | −26.0000 | −1.13365 | ||||||||
\(527\) | 25.0000i | 1.08902i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | −4.00000 | − | 2.00000i | −0.173749 | − | 0.0868744i | ||||
\(531\) | 3.00000 | 0.130189 | ||||||||
\(532\) | 16.0000i | 0.693688i | ||||||||
\(533\) | 14.0000i | 0.606407i | ||||||||
\(534\) | 56.0000 | 2.42336 | ||||||||
\(535\) | −9.00000 | + | 18.0000i | −0.389104 | + | 0.778208i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 8.00000i | − | 0.345225i | ||||||
\(538\) | 30.0000i | 1.29339i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.00000 | + | 16.0000i | −0.344265 | + | 0.688530i | ||||
\(541\) | 14.0000 | 0.601907 | 0.300954 | − | 0.953639i | \(-0.402695\pi\) | ||||
0.300954 | + | 0.953639i | \(0.402695\pi\) | |||||||
\(542\) | − | 30.0000i | − | 1.28861i | ||||||
\(543\) | 28.0000i | 1.20160i | ||||||||
\(544\) | −40.0000 | −1.71499 | ||||||||
\(545\) | −36.0000 | − | 18.0000i | −1.54207 | − | 0.771035i | ||||
\(546\) | 8.00000 | 0.342368 | ||||||||
\(547\) | − | 4.00000i | − | 0.171028i | −0.996337 | − | 0.0855138i | \(-0.972747\pi\) | ||
0.996337 | − | 0.0855138i | \(-0.0272532\pi\) | |||||||
\(548\) | − | 12.0000i | − | 0.512615i | ||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.0000 | −1.70406 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0000i | 0.595341i | ||||||||
\(554\) | 52.0000 | 2.20927 | ||||||||
\(555\) | 28.0000 | + | 14.0000i | 1.18853 | + | 0.594267i | ||||
\(556\) | 18.0000 | 0.763370 | ||||||||
\(557\) | − | 33.0000i | − | 1.39825i | −0.714997 | − | 0.699127i | \(-0.753572\pi\) | ||
0.714997 | − | 0.699127i | \(-0.246428\pi\) | |||||||
\(558\) | 10.0000i | 0.423334i | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 4.00000 | − | 8.00000i | 0.169031 | − | 0.338062i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 24.0000i | − | 1.01238i | ||||||
\(563\) | 25.0000i | 1.05362i | 0.849982 | + | 0.526812i | \(0.176613\pi\) | ||||
−0.849982 | + | 0.526812i | \(0.823387\pi\) | |||||||
\(564\) | 8.00000 | 0.336861 | ||||||||
\(565\) | −1.00000 | + | 2.00000i | −0.0420703 | + | 0.0841406i | ||||
\(566\) | 22.0000 | 0.924729 | ||||||||
\(567\) | − | 11.0000i | − | 0.461957i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0000 | 0.503066 | 0.251533 | − | 0.967849i | \(-0.419065\pi\) | ||||
0.251533 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(570\) | −64.0000 | − | 32.0000i | −2.68067 | − | 1.34033i | ||||
\(571\) | 18.0000 | 0.753277 | 0.376638 | − | 0.926360i | \(-0.377080\pi\) | ||||
0.376638 | + | 0.926360i | \(0.377080\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0000i | 0.668410i | ||||||||
\(574\) | 14.0000 | 0.584349 | ||||||||
\(575\) | −4.00000 | + | 3.00000i | −0.166812 | + | 0.125109i | ||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | 22.0000i | 0.915872i | 0.888985 | + | 0.457936i | \(0.151411\pi\) | ||||
−0.888985 | + | 0.457936i | \(0.848589\pi\) | |||||||
\(578\) | − | 16.0000i | − | 0.665512i | ||||||
\(579\) | 24.0000 | 0.997406 | ||||||||
\(580\) | −20.0000 | − | 10.0000i | −0.830455 | − | 0.415227i | ||||
\(581\) | −3.00000 | −0.124461 | ||||||||
\(582\) | 56.0000i | 2.32127i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | + | 4.00000i | −0.0826898 | + | 0.165380i | ||||
\(586\) | 58.0000 | 2.39596 | ||||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 24.0000i | 0.989743i | ||||||||
\(589\) | 40.0000 | 1.64817 | ||||||||
\(590\) | 6.00000 | − | 12.0000i | 0.247016 | − | 0.494032i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 28.0000i | − | 1.15079i | ||||||
\(593\) | − | 30.0000i | − | 1.23195i | −0.787765 | − | 0.615976i | \(-0.788762\pi\) | ||
0.787765 | − | 0.615976i | \(-0.211238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | + | 5.00000i | 0.409960 | + | 0.204980i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.00000i | 0.163709i | ||||||||
\(598\) | 4.00000i | 0.163572i | ||||||||
\(599\) | 48.0000 | 1.96123 | 0.980613 | − | 0.195952i | \(-0.0627798\pi\) | ||||
0.980613 | + | 0.195952i | \(0.0627798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.0000 | −1.01977 | −0.509886 | − | 0.860242i | \(-0.670312\pi\) | ||||
−0.509886 | + | 0.860242i | \(0.670312\pi\) | |||||||
\(602\) | 8.00000i | 0.326056i | ||||||||
\(603\) | − | 13.0000i | − | 0.529401i | ||||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | −22.0000 | − | 11.0000i | −0.894427 | − | 0.447214i | ||||
\(606\) | 60.0000 | 2.43733 | ||||||||
\(607\) | − | 38.0000i | − | 1.54237i | −0.636610 | − | 0.771186i | \(-0.719664\pi\) | ||
0.636610 | − | 0.771186i | \(-0.280336\pi\) | |||||||
\(608\) | 64.0000i | 2.59554i | ||||||||
\(609\) | 10.0000 | 0.405220 | ||||||||
\(610\) | 12.0000 | − | 24.0000i | 0.485866 | − | 0.971732i | ||||
\(611\) | −4.00000 | −0.161823 | ||||||||
\(612\) | − | 10.0000i | − | 0.404226i | ||||||
\(613\) | − | 6.00000i | − | 0.242338i | −0.992632 | − | 0.121169i | \(-0.961336\pi\) | ||
0.992632 | − | 0.121169i | \(-0.0386643\pi\) | |||||||
\(614\) | −28.0000 | −1.12999 | ||||||||
\(615\) | −14.0000 | + | 28.0000i | −0.564534 | + | 1.12907i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 47.0000i | − | 1.89215i | −0.323949 | − | 0.946074i | \(-0.605011\pi\) | ||
0.323949 | − | 0.946074i | \(-0.394989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(620\) | 20.0000 | + | 10.0000i | 0.803219 | + | 0.401610i | ||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 8.00000i | 0.320771i | ||||||||
\(623\) | 14.0000i | 0.560898i | ||||||||
\(624\) | 16.0000 | 0.640513 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 42.0000 | 1.67866 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.00000i | 0.239426i | ||||||||
\(629\) | 35.0000 | 1.39554 | ||||||||
\(630\) | 4.00000 | + | 2.00000i | 0.159364 | + | 0.0796819i | ||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.0000i | 0.715436i | ||||||||
\(634\) | 48.0000 | 1.90632 | ||||||||
\(635\) | 20.0000 | − | 40.0000i | 0.793676 | − | 1.58735i | ||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | − | 12.0000i | − | 0.475457i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.0000 | −0.514272 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.0000 | −0.947943 | −0.473972 | − | 0.880540i | \(-0.657180\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(642\) | 36.0000i | 1.42081i | ||||||||
\(643\) | − | 37.0000i | − | 1.45914i | −0.683907 | − | 0.729569i | \(-0.739721\pi\) | ||
0.683907 | − | 0.729569i | \(-0.260279\pi\) | |||||||
\(644\) | 2.00000 | 0.0788110 | ||||||||
\(645\) | −16.0000 | − | 8.00000i | −0.629999 | − | 0.315000i | ||||
\(646\) | −80.0000 | −3.14756 | ||||||||
\(647\) | − | 18.0000i | − | 0.707653i | −0.935311 | − | 0.353827i | \(-0.884880\pi\) | ||
0.935311 | − | 0.353827i | \(-0.115120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 12.0000 | + | 16.0000i | 0.470679 | + | 0.627572i | ||||
\(651\) | −10.0000 | −0.391931 | ||||||||
\(652\) | 48.0000i | 1.87983i | ||||||||
\(653\) | − | 2.00000i | − | 0.0782660i | −0.999234 | − | 0.0391330i | \(-0.987540\pi\) | ||
0.999234 | − | 0.0391330i | \(-0.0124596\pi\) | |||||||
\(654\) | −72.0000 | −2.81542 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 28.0000 | 1.09322 | ||||||||
\(657\) | 8.00000i | 0.312110i | ||||||||
\(658\) | 4.00000i | 0.155936i | ||||||||
\(659\) | −22.0000 | −0.856998 | −0.428499 | − | 0.903542i | \(-0.640958\pi\) | ||||
−0.428499 | + | 0.903542i | \(0.640958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | −0.622328 | −0.311164 | − | 0.950356i | \(-0.600719\pi\) | ||||
−0.311164 | + | 0.950356i | \(0.600719\pi\) | |||||||
\(662\) | − | 10.0000i | − | 0.388661i | ||||||
\(663\) | 20.0000i | 0.776736i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | − | 16.0000i | 0.310227 | − | 0.620453i | ||||
\(666\) | 14.0000 | 0.542489 | ||||||||
\(667\) | 5.00000i | 0.193601i | ||||||||
\(668\) | − | 32.0000i | − | 1.23812i | ||||||
\(669\) | 28.0000 | 1.08254 | ||||||||
\(670\) | −52.0000 | − | 26.0000i | −2.00894 | − | 1.00447i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 16.0000i | − | 0.617213i | ||||||
\(673\) | − | 24.0000i | − | 0.925132i | −0.886585 | − | 0.462566i | \(-0.846929\pi\) | ||
0.886585 | − | 0.462566i | \(-0.153071\pi\) | |||||||
\(674\) | −52.0000 | −2.00297 | ||||||||
\(675\) | 16.0000 | − | 12.0000i | 0.615840 | − | 0.461880i | ||||
\(676\) | −18.0000 | −0.692308 | ||||||||
\(677\) | − | 3.00000i | − | 0.115299i | −0.998337 | − | 0.0576497i | \(-0.981639\pi\) | ||
0.998337 | − | 0.0576497i | \(-0.0183606\pi\) | |||||||
\(678\) | 4.00000i | 0.153619i | ||||||||
\(679\) | −14.0000 | −0.537271 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 46.0000i | − | 1.76014i | −0.474843 | − | 0.880071i | \(-0.657495\pi\) | ||
0.474843 | − | 0.880071i | \(-0.342505\pi\) | |||||||
\(684\) | −16.0000 | −0.611775 | ||||||||
\(685\) | −6.00000 | + | 12.0000i | −0.229248 | + | 0.458496i | ||||
\(686\) | −26.0000 | −0.992685 | ||||||||
\(687\) | 8.00000i | 0.305219i | ||||||||
\(688\) | 16.0000i | 0.609994i | ||||||||
\(689\) | 2.00000 | 0.0761939 | ||||||||
\(690\) | −4.00000 | + | 8.00000i | −0.152277 | + | 0.304555i | ||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | 12.0000i | 0.456172i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | −18.0000 | − | 9.00000i | −0.682779 | − | 0.341389i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.0000i | 1.32572i | ||||||||
\(698\) | − | 46.0000i | − | 1.74113i | ||||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | 8.00000 | − | 6.00000i | 0.302372 | − | 0.226779i | ||||
\(701\) | −28.0000 | −1.05755 | −0.528773 | − | 0.848763i | \(-0.677348\pi\) | ||||
−0.528773 | + | 0.848763i | \(0.677348\pi\) | |||||||
\(702\) | − | 16.0000i | − | 0.603881i | ||||||
\(703\) | − | 56.0000i | − | 2.11208i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | − | 4.00000i | −0.301297 | − | 0.150649i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.0000i | 0.564133i | ||||||||
\(708\) | − | 12.0000i | − | 0.450988i | ||||||
\(709\) | −4.00000 | −0.150223 | −0.0751116 | − | 0.997175i | \(-0.523931\pi\) | ||||
−0.0751116 | + | 0.997175i | \(0.523931\pi\) | |||||||
\(710\) | −26.0000 | + | 52.0000i | −0.975763 | + | 1.95153i | ||||
\(711\) | −14.0000 | −0.525041 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.00000i | − | 0.187251i | ||||||
\(714\) | 20.0000 | 0.748481 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.00000 | −0.298974 | ||||||||
\(717\) | − | 2.00000i | − | 0.0746914i | ||||||
\(718\) | 12.0000i | 0.447836i | ||||||||
\(719\) | 45.0000 | 1.67822 | 0.839108 | − | 0.543964i | \(-0.183077\pi\) | ||||
0.839108 | + | 0.543964i | \(0.183077\pi\) | |||||||
\(720\) | 8.00000 | + | 4.00000i | 0.298142 | + | 0.149071i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 90.0000i | 3.34945i | ||||||||
\(723\) | − | 12.0000i | − | 0.446285i | ||||||
\(724\) | 28.0000 | 1.04061 | ||||||||
\(725\) | 15.0000 | + | 20.0000i | 0.557086 | + | 0.742781i | ||||
\(726\) | −44.0000 | −1.63299 | ||||||||
\(727\) | 27.0000i | 1.00137i | 0.865628 | + | 0.500687i | \(0.166919\pi\) | ||||
−0.865628 | + | 0.500687i | \(0.833081\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 32.0000 | + | 16.0000i | 1.18437 | + | 0.592187i | ||||
\(731\) | −20.0000 | −0.739727 | ||||||||
\(732\) | − | 24.0000i | − | 0.887066i | ||||||
\(733\) | − | 7.00000i | − | 0.258551i | −0.991609 | − | 0.129275i | \(-0.958735\pi\) | ||
0.991609 | − | 0.129275i | \(-0.0412651\pi\) | |||||||
\(734\) | 26.0000 | 0.959678 | ||||||||
\(735\) | 12.0000 | − | 24.0000i | 0.442627 | − | 0.885253i | ||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 14.0000i | 0.515347i | ||||||||
\(739\) | −7.00000 | −0.257499 | −0.128750 | − | 0.991677i | \(-0.541096\pi\) | ||||
−0.128750 | + | 0.991677i | \(0.541096\pi\) | |||||||
\(740\) | 14.0000 | − | 28.0000i | 0.514650 | − | 1.02930i | ||||
\(741\) | 32.0000 | 1.17555 | ||||||||
\(742\) | − | 2.00000i | − | 0.0734223i | ||||||
\(743\) | 32.0000i | 1.17397i | 0.809599 | + | 0.586983i | \(0.199684\pi\) | ||||
−0.809599 | + | 0.586983i | \(0.800316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.0000 | −0.439351 | ||||||||
\(747\) | − | 3.00000i | − | 0.109764i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.00000 | −0.328853 | ||||||||
\(750\) | 8.00000 | + | 44.0000i | 0.292119 | + | 1.60665i | ||||
\(751\) | 14.0000 | 0.510867 | 0.255434 | − | 0.966827i | \(-0.417782\pi\) | ||||
0.255434 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(752\) | 8.00000i | 0.291730i | ||||||||
\(753\) | − | 36.0000i | − | 1.31191i | ||||||
\(754\) | 20.0000 | 0.728357 | ||||||||
\(755\) | 16.0000 | + | 8.00000i | 0.582300 | + | 0.291150i | ||||
\(756\) | −8.00000 | −0.290957 | ||||||||
\(757\) | − | 35.0000i | − | 1.27210i | −0.771649 | − | 0.636048i | \(-0.780568\pi\) | ||
0.771649 | − | 0.636048i | \(-0.219432\pi\) | |||||||
\(758\) | − | 12.0000i | − | 0.435860i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.0000 | 0.906249 | 0.453125 | − | 0.891447i | \(-0.350309\pi\) | ||||
0.453125 | + | 0.891447i | \(0.350309\pi\) | |||||||
\(762\) | − | 80.0000i | − | 2.89809i | ||||||
\(763\) | − | 18.0000i | − | 0.651644i | ||||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | −5.00000 | + | 10.0000i | −0.180775 | + | 0.361551i | ||||
\(766\) | 6.00000 | 0.216789 | ||||||||
\(767\) | 6.00000i | 0.216647i | ||||||||
\(768\) | − | 32.0000i | − | 1.15470i | ||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.0000 | 1.58462 | ||||||||
\(772\) | − | 24.0000i | − | 0.863779i | ||||||
\(773\) | 42.0000i | 1.51064i | 0.655359 | + | 0.755318i | \(0.272517\pi\) | ||||
−0.655359 | + | 0.755318i | \(0.727483\pi\) | |||||||
\(774\) | −8.00000 | −0.287554 | ||||||||
\(775\) | −15.0000 | − | 20.0000i | −0.538816 | − | 0.718421i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.0000i | 0.502247i | ||||||||
\(778\) | − | 44.0000i | − | 1.57748i | ||||||
\(779\) | 56.0000 | 2.00641 | ||||||||
\(780\) | 16.0000 | + | 8.00000i | 0.572892 | + | 0.286446i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 10.0000i | 0.357599i | ||||||||
\(783\) | − | 20.0000i | − | 0.714742i | ||||||
\(784\) | −24.0000 | −0.857143 | ||||||||
\(785\) | 3.00000 | − | 6.00000i | 0.107075 | − | 0.214149i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.0000i | 0.605985i | 0.952993 | + | 0.302992i | \(0.0979856\pi\) | ||||
−0.952993 | + | 0.302992i | \(0.902014\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.0000 | 0.925625 | ||||||||
\(790\) | −28.0000 | + | 56.0000i | −0.996195 | + | 1.99239i | ||||
\(791\) | −1.00000 | −0.0355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000i | 0.426132i | ||||||||
\(794\) | −32.0000 | −1.13564 | ||||||||
\(795\) | 4.00000 | + | 2.00000i | 0.141865 | + | 0.0709327i | ||||
\(796\) | 4.00000 | 0.141776 | ||||||||
\(797\) | − | 15.0000i | − | 0.531327i | −0.964066 | − | 0.265664i | \(-0.914409\pi\) | ||
0.964066 | − | 0.265664i | \(-0.0855911\pi\) | |||||||
\(798\) | − | 32.0000i | − | 1.13279i | ||||||
\(799\) | −10.0000 | −0.353775 | ||||||||
\(800\) | 32.0000 | − | 24.0000i | 1.13137 | − | 0.848528i | ||||
\(801\) | −14.0000 | −0.494666 | ||||||||
\(802\) | 4.00000i | 0.141245i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −52.0000 | −1.83390 | ||||||||
\(805\) | −2.00000 | − | 1.00000i | −0.0704907 | − | 0.0352454i | ||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | − | 30.0000i | − | 1.05605i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.0000 | 0.878953 | 0.439477 | − | 0.898254i | \(-0.355164\pi\) | ||||
0.439477 | + | 0.898254i | \(0.355164\pi\) | |||||||
\(810\) | 22.0000 | − | 44.0000i | 0.773001 | − | 1.54600i | ||||
\(811\) | 31.0000 | 1.08856 | 0.544279 | − | 0.838905i | \(-0.316803\pi\) | ||||
0.544279 | + | 0.838905i | \(0.316803\pi\) | |||||||
\(812\) | − | 10.0000i | − | 0.350931i | ||||||
\(813\) | 30.0000i | 1.05215i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0000 | − | 48.0000i | 0.840683 | − | 1.68137i | ||||
\(816\) | 40.0000 | 1.40028 | ||||||||
\(817\) | 32.0000i | 1.11954i | ||||||||
\(818\) | 38.0000i | 1.32864i | ||||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | 28.0000 | + | 14.0000i | 0.977802 | + | 0.488901i | ||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | 24.0000i | 0.837096i | ||||||||
\(823\) | 34.0000i | 1.18517i | 0.805510 | + | 0.592583i | \(0.201892\pi\) | ||||
−0.805510 | + | 0.592583i | \(0.798108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | 0.208767 | ||||||||
\(827\) | − | 9.00000i | − | 0.312961i | −0.987681 | − | 0.156480i | \(-0.949985\pi\) | ||
0.987681 | − | 0.156480i | \(-0.0500148\pi\) | |||||||
\(828\) | 2.00000i | 0.0695048i | ||||||||
\(829\) | −37.0000 | −1.28506 | −0.642532 | − | 0.766259i | \(-0.722116\pi\) | ||||
−0.642532 | + | 0.766259i | \(0.722116\pi\) | |||||||
\(830\) | −12.0000 | − | 6.00000i | −0.416526 | − | 0.208263i | ||||
\(831\) | −52.0000 | −1.80386 | ||||||||
\(832\) | − | 16.0000i | − | 0.554700i | ||||||
\(833\) | − | 30.0000i | − | 1.03944i | ||||||
\(834\) | −36.0000 | −1.24658 | ||||||||
\(835\) | −16.0000 | + | 32.0000i | −0.553703 | + | 1.10741i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.0000i | 0.691301i | ||||||||
\(838\) | 4.00000i | 0.138178i | ||||||||
\(839\) | −14.0000 | −0.483334 | −0.241667 | − | 0.970359i | \(-0.577694\pi\) | ||||
−0.241667 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 20.0000i | 0.689246i | ||||||||
\(843\) | 24.0000i | 0.826604i | ||||||||
\(844\) | 18.0000 | 0.619586 | ||||||||
\(845\) | 18.0000 | + | 9.00000i | 0.619219 | + | 0.309609i | ||||
\(846\) | −4.00000 | −0.137523 | ||||||||
\(847\) | − | 11.0000i | − | 0.377964i | ||||||
\(848\) | − | 4.00000i | − | 0.137361i | ||||||
\(849\) | −22.0000 | −0.755038 | ||||||||
\(850\) | 30.0000 | + | 40.0000i | 1.02899 | + | 1.37199i | ||||
\(851\) | −7.00000 | −0.239957 | ||||||||
\(852\) | 52.0000i | 1.78149i | ||||||||
\(853\) | − | 8.00000i | − | 0.273915i | −0.990577 | − | 0.136957i | \(-0.956268\pi\) | ||
0.990577 | − | 0.136957i | \(-0.0437323\pi\) | |||||||
\(854\) | 12.0000 | 0.410632 | ||||||||
\(855\) | 16.0000 | + | 8.00000i | 0.547188 | + | 0.273594i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0000i | 0.819824i | 0.912125 | + | 0.409912i | \(0.134441\pi\) | ||||
−0.912125 | + | 0.409912i | \(0.865559\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.0000 | −1.46714 | −0.733571 | − | 0.679613i | \(-0.762148\pi\) | ||||
−0.733571 | + | 0.679613i | \(0.762148\pi\) | |||||||
\(860\) | −8.00000 | + | 16.0000i | −0.272798 | + | 0.545595i | ||||
\(861\) | −14.0000 | −0.477119 | ||||||||
\(862\) | − | 24.0000i | − | 0.817443i | ||||||
\(863\) | 18.0000i | 0.612727i | 0.951915 | + | 0.306364i | \(0.0991123\pi\) | ||||
−0.951915 | + | 0.306364i | \(0.900888\pi\) | |||||||
\(864\) | −32.0000 | −1.08866 | ||||||||
\(865\) | 6.00000 | − | 12.0000i | 0.204006 | − | 0.408012i | ||||
\(866\) | 38.0000 | 1.29129 | ||||||||
\(867\) | 16.0000i | 0.543388i | ||||||||
\(868\) | 10.0000i | 0.339422i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 40.0000 | + | 20.0000i | 1.35613 | + | 0.678064i | ||||
\(871\) | 26.0000 | 0.880976 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 14.0000i | − | 0.473828i | ||||||
\(874\) | 16.0000 | 0.541208 | ||||||||
\(875\) | −11.0000 | + | 2.00000i | −0.371868 | + | 0.0676123i | ||||
\(876\) | 32.0000 | 1.08118 | ||||||||
\(877\) | 8.00000i | 0.270141i | 0.990836 | + | 0.135070i | \(0.0431261\pi\) | ||||
−0.990836 | + | 0.135070i | \(0.956874\pi\) | |||||||
\(878\) | 56.0000i | 1.88991i | ||||||||
\(879\) | −58.0000 | −1.95629 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.0000 | 1.81931 | 0.909653 | − | 0.415369i | \(-0.136347\pi\) | ||||
0.909653 | + | 0.415369i | \(0.136347\pi\) | |||||||
\(882\) | − | 12.0000i | − | 0.404061i | ||||||
\(883\) | 20.0000i | 0.673054i | 0.941674 | + | 0.336527i | \(0.109252\pi\) | ||||
−0.941674 | + | 0.336527i | \(0.890748\pi\) | |||||||
\(884\) | 20.0000 | 0.672673 | ||||||||
\(885\) | −6.00000 | + | 12.0000i | −0.201688 | + | 0.403376i | ||||
\(886\) | −48.0000 | −1.61259 | ||||||||
\(887\) | 42.0000i | 1.41022i | 0.709097 | + | 0.705111i | \(0.249103\pi\) | ||||
−0.709097 | + | 0.705111i | \(0.750897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | 0.670778 | ||||||||
\(890\) | −28.0000 | + | 56.0000i | −0.938562 | + | 1.87712i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 28.0000i | − | 0.937509i | ||||||
\(893\) | 16.0000i | 0.535420i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | + | 4.00000i | 0.267411 | + | 0.133705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 4.00000i | − | 0.133556i | ||||||
\(898\) | − | 30.0000i | − | 1.00111i | ||||||
\(899\) | −25.0000 | −0.833797 | ||||||||
\(900\) | 6.00000 | + | 8.00000i | 0.200000 | + | 0.266667i | ||||
\(901\) | 5.00000 | 0.166574 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 8.00000i | − | 0.266223i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.0000 | − | 14.0000i | −0.930751 | − | 0.465376i | ||||
\(906\) | 32.0000 | 1.06313 | ||||||||
\(907\) | 9.00000i | 0.298840i | 0.988774 | + | 0.149420i | \(0.0477407\pi\) | ||||
−0.988774 | + | 0.149420i | \(0.952259\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.0000 | −0.497519 | ||||||||
\(910\) | −4.00000 | + | 8.00000i | −0.132599 | + | 0.265197i | ||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | − | 64.0000i | − | 2.11925i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.00000 | −0.0661541 | ||||||||
\(915\) | −12.0000 | + | 24.0000i | −0.396708 | + | 0.793416i | ||||
\(916\) | 8.00000 | 0.264327 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 40.0000i | − | 1.32020i | ||||||
\(919\) | −4.00000 | −0.131948 | −0.0659739 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659739 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.0000 | 0.922631 | ||||||||
\(922\) | − | 36.0000i | − | 1.18560i | ||||||
\(923\) | − | 26.0000i | − | 0.855800i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.0000 | + | 21.0000i | −0.920634 | + | 0.690476i | ||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 40.0000i | − | 1.31306i | ||||||
\(929\) | −35.0000 | −1.14831 | −0.574156 | − | 0.818746i | \(-0.694670\pi\) | ||||
−0.574156 | + | 0.818746i | \(0.694670\pi\) | |||||||
\(930\) | −40.0000 | − | 20.0000i | −1.31165 | − | 0.655826i | ||||
\(931\) | −48.0000 | −1.57314 | ||||||||
\(932\) | 12.0000i | 0.393073i | ||||||||
\(933\) | − | 8.00000i | − | 0.261908i | ||||||
\(934\) | 54.0000 | 1.76693 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.0000i | 1.76410i | 0.471153 | + | 0.882052i | \(0.343838\pi\) | ||||
−0.471153 | + | 0.882052i | \(0.656162\pi\) | |||||||
\(938\) | − | 26.0000i | − | 0.848930i | ||||||
\(939\) | −42.0000 | −1.37062 | ||||||||
\(940\) | −4.00000 | + | 8.00000i | −0.130466 | + | 0.260931i | ||||
\(941\) | 2.00000 | 0.0651981 | 0.0325991 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325991 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(942\) | − | 12.0000i | − | 0.390981i | ||||||
\(943\) | − | 7.00000i | − | 0.227951i | ||||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 8.00000 | + | 4.00000i | 0.260240 | + | 0.130120i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.0000i | 0.454939i | 0.973785 | + | 0.227469i | \(0.0730452\pi\) | ||||
−0.973785 | + | 0.227469i | \(0.926955\pi\) | |||||||
\(948\) | 56.0000i | 1.81880i | ||||||||
\(949\) | −16.0000 | −0.519382 | ||||||||
\(950\) | 64.0000 | − | 48.0000i | 2.07643 | − | 1.55733i | ||||
\(951\) | −48.0000 | −1.55651 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 54.0000i | − | 1.74923i | −0.484817 | − | 0.874616i | \(-0.661114\pi\) | ||
0.484817 | − | 0.874616i | \(-0.338886\pi\) | |||||||
\(954\) | 2.00000 | 0.0647524 | ||||||||
\(955\) | −16.0000 | − | 8.00000i | −0.517748 | − | 0.258874i | ||||
\(956\) | −2.00000 | −0.0646846 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 56.0000i | 1.80928i | ||||||||
\(959\) | −6.00000 | −0.193750 | ||||||||
\(960\) | 16.0000 | − | 32.0000i | 0.516398 | − | 1.03280i | ||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 28.0000i | 0.902756i | ||||||||
\(963\) | − | 9.00000i | − | 0.290021i | ||||||
\(964\) | −12.0000 | −0.386494 | ||||||||
\(965\) | −12.0000 | + | 24.0000i | −0.386294 | + | 0.772587i | ||||
\(966\) | −4.00000 | −0.128698 | ||||||||
\(967\) | − | 18.0000i | − | 0.578841i | −0.957202 | − | 0.289420i | \(-0.906537\pi\) | ||
0.957202 | − | 0.289420i | \(-0.0934626\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 80.0000 | 2.56997 | ||||||||
\(970\) | −56.0000 | − | 28.0000i | −1.79805 | − | 0.899026i | ||||
\(971\) | −6.00000 | −0.192549 | −0.0962746 | − | 0.995355i | \(-0.530693\pi\) | ||||
−0.0962746 | + | 0.995355i | \(0.530693\pi\) | |||||||
\(972\) | − | 20.0000i | − | 0.641500i | ||||||
\(973\) | − | 9.00000i | − | 0.288527i | ||||||
\(974\) | 64.0000 | 2.05069 | ||||||||
\(975\) | −12.0000 | − | 16.0000i | −0.384308 | − | 0.512410i | ||||
\(976\) | 24.0000 | 0.768221 | ||||||||
\(977\) | − | 39.0000i | − | 1.24772i | −0.781536 | − | 0.623860i | \(-0.785563\pi\) | ||
0.781536 | − | 0.623860i | \(-0.214437\pi\) | |||||||
\(978\) | − | 96.0000i | − | 3.06974i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −24.0000 | − | 12.0000i | −0.766652 | − | 0.383326i | ||||
\(981\) | 18.0000 | 0.574696 | ||||||||
\(982\) | − | 62.0000i | − | 1.97850i | ||||||
\(983\) | − | 21.0000i | − | 0.669796i | −0.942254 | − | 0.334898i | \(-0.891298\pi\) | ||
0.942254 | − | 0.334898i | \(-0.108702\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 50.0000 | 1.59232 | ||||||||
\(987\) | − | 4.00000i | − | 0.127321i | ||||||
\(988\) | − | 32.0000i | − | 1.01806i | ||||||
\(989\) | 4.00000 | 0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0000 | 0.603555 | 0.301777 | − | 0.953378i | \(-0.402420\pi\) | ||||
0.301777 | + | 0.953378i | \(0.402420\pi\) | |||||||
\(992\) | 40.0000i | 1.27000i | ||||||||
\(993\) | 10.0000i | 0.317340i | ||||||||
\(994\) | −26.0000 | −0.824670 | ||||||||
\(995\) | −4.00000 | − | 2.00000i | −0.126809 | − | 0.0634043i | ||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 20.0000i | 0.633406i | 0.948525 | + | 0.316703i | \(0.102576\pi\) | ||||
−0.948525 | + | 0.316703i | \(0.897424\pi\) | |||||||
\(998\) | 22.0000i | 0.696398i | ||||||||
\(999\) | 28.0000 | 0.885881 |
(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 | 115.2.b.a.24.2 | yes | 2 | |
3.2 | odd | 2 | 1035.2.b.a.829.1 | 2 | |||
4.3 | odd | 2 | 1840.2.e.b.369.2 | 2 | |||
5.2 | odd | 4 | 575.2.a.a.1.1 | 1 | |||
5.3 | odd | 4 | 575.2.a.e.1.1 | 1 | |||
5.4 | even | 2 | inner | 115.2.b.a.24.1 | ✓ | 2 | |
15.2 | even | 4 | 5175.2.a.z.1.1 | 1 | |||
15.8 | even | 4 | 5175.2.a.a.1.1 | 1 | |||
15.14 | odd | 2 | 1035.2.b.a.829.2 | 2 | |||
20.3 | even | 4 | 9200.2.a.g.1.1 | 1 | |||
20.7 | even | 4 | 9200.2.a.bg.1.1 | 1 | |||
20.19 | odd | 2 | 1840.2.e.b.369.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.b.a.24.1 | ✓ | 2 | 5.4 | even | 2 | inner | |
115.2.b.a.24.2 | yes | 2 | 1.1 | even | 1 | trivial | |
575.2.a.a.1.1 | 1 | 5.2 | odd | 4 | |||
575.2.a.e.1.1 | 1 | 5.3 | odd | 4 | |||
1035.2.b.a.829.1 | 2 | 3.2 | odd | 2 | |||
1035.2.b.a.829.2 | 2 | 15.14 | odd | 2 | |||
1840.2.e.b.369.1 | 2 | 20.19 | odd | 2 | |||
1840.2.e.b.369.2 | 2 | 4.3 | odd | 2 | |||
5175.2.a.a.1.1 | 1 | 15.8 | even | 4 | |||
5175.2.a.z.1.1 | 1 | 15.2 | even | 4 | |||
9200.2.a.g.1.1 | 1 | 20.3 | even | 4 | |||
9200.2.a.bg.1.1 | 1 | 20.7 | even | 4 |