Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(191,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.13251087523\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 191.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.191 |
Dual form | 768.2.k.c.575.2 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.70711 | + | 0.292893i | 0.985599 | + | 0.169102i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421 | + | 1.41421i | 0.632456 | + | 0.632456i | 0.948683 | − | 0.316228i | \(-0.102416\pi\) |
−0.316228 | + | 0.948683i | \(0.602416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421 | 0.534522 | 0.267261 | − | 0.963624i | \(-0.413881\pi\) | ||||
0.267261 | + | 0.963624i | \(0.413881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | + | 1.00000i | 0.942809 | + | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | − | 4.00000i | 1.20605 | − | 1.20605i | 0.233748 | − | 0.972297i | \(-0.424901\pi\) |
0.972297 | − | 0.233748i | \(-0.0750991\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | − | 3.00000i | −0.832050 | − | 0.832050i | 0.155747 | − | 0.987797i | \(-0.450222\pi\) |
−0.987797 | + | 0.155747i | \(0.950222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | + | 2.82843i | 0.516398 | + | 0.730297i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.82843i | − | 0.685994i | −0.939336 | − | 0.342997i | \(-0.888558\pi\) | ||
0.939336 | − | 0.342997i | \(-0.111442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82843 | + | 2.82843i | −0.648886 | + | 0.648886i | −0.952724 | − | 0.303838i | \(-0.901732\pi\) |
0.303838 | + | 0.952724i | \(0.401732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.41421 | + | 0.414214i | 0.526825 | + | 0.0903888i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.53553 | + | 2.53553i | 0.872864 | + | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.07107 | + | 7.07107i | −1.31306 | + | 1.31306i | −0.393919 | + | 0.919145i | \(0.628881\pi\) |
−0.919145 | + | 0.393919i | \(0.871119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.24264i | 0.762001i | 0.924575 | + | 0.381000i | \(0.124420\pi\) | ||||
−0.924575 | + | 0.381000i | \(0.875580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.00000 | − | 5.65685i | 1.39262 | − | 0.984732i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | + | 2.00000i | 0.338062 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | + | 5.00000i | −0.821995 | + | 0.821995i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.24264 | − | 6.00000i | −0.679366 | − | 0.960769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82843 | 0.441726 | 0.220863 | − | 0.975305i | \(-0.429113\pi\) | ||||
0.220863 | + | 0.975305i | \(0.429113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.82843 | + | 2.82843i | 0.431331 | + | 0.431331i | 0.889081 | − | 0.457750i | \(-0.151344\pi\) |
−0.457750 | + | 0.889081i | \(0.651344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.58579 | + | 5.41421i | 0.385466 | + | 0.807103i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0000 | 1.75038 | 0.875190 | − | 0.483779i | \(-0.160736\pi\) | ||||
0.875190 | + | 0.483779i | \(0.160736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.828427 | − | 4.82843i | 0.116003 | − | 0.676115i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.24264 | − | 4.24264i | −0.582772 | − | 0.582772i | 0.352892 | − | 0.935664i | \(-0.385198\pi\) |
−0.935664 | + | 0.352892i | \(0.885198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.3137 | 1.52554 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.65685 | + | 4.00000i | −0.749269 | + | 0.529813i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 2.00000i | −0.260378 | + | 0.260378i | −0.825208 | − | 0.564830i | \(-0.808942\pi\) |
0.564830 | + | 0.825208i | \(0.308942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.00000 | − | 9.00000i | −1.15233 | − | 1.15233i | −0.986084 | − | 0.166248i | \(-0.946835\pi\) |
−0.166248 | − | 0.986084i | \(-0.553165\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.00000 | + | 1.41421i | 0.503953 | + | 0.178174i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 8.48528i | − | 1.05247i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.07107 | + | 7.07107i | −0.863868 | + | 0.863868i | −0.991785 | − | 0.127917i | \(-0.959171\pi\) |
0.127917 | + | 0.991785i | \(0.459171\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.00000i | − | 0.474713i | −0.971423 | − | 0.237356i | \(-0.923719\pi\) | ||
0.971423 | − | 0.237356i | \(-0.0762809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.292893 | − | 1.70711i | 0.0338204 | − | 0.197120i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65685 | − | 5.65685i | 0.644658 | − | 0.644658i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.89949i | − | 1.11378i | −0.830586 | − | 0.556890i | \(-0.811994\pi\) | ||
0.830586 | − | 0.556890i | \(-0.188006\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | − | 4.00000i | 0.433861 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.1421 | + | 10.0000i | −1.51620 | + | 1.07211i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.65685 | −0.599625 | −0.299813 | − | 0.953998i | \(-0.596924\pi\) | ||||
−0.299813 | + | 0.953998i | \(0.596924\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.24264 | − | 4.24264i | −0.444750 | − | 0.444750i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.24264 | + | 7.24264i | −0.128856 | + | 0.751027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.3137 | − | 7.31371i | 1.53909 | − | 0.735055i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.89949 | + | 9.89949i | 0.985037 | + | 0.985037i | 0.999890 | − | 0.0148531i | \(-0.00472807\pi\) |
−0.0148531 | + | 0.999890i | \(0.504728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.24264 | 0.418040 | 0.209020 | − | 0.977911i | \(-0.432973\pi\) | ||||
0.209020 | + | 0.977911i | \(0.432973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.82843 | + | 4.00000i | 0.276026 | + | 0.390360i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.00000 | + | 2.00000i | −0.193347 | + | 0.193347i | −0.797141 | − | 0.603793i | \(-0.793655\pi\) |
0.603793 | + | 0.797141i | \(0.293655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.00000 | + | 3.00000i | 0.287348 | + | 0.287348i | 0.836031 | − | 0.548683i | \(-0.184871\pi\) |
−0.548683 | + | 0.836031i | \(0.684871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | + | 7.07107i | −0.949158 | + | 0.671156i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.9706i | 1.59646i | 0.602355 | + | 0.798228i | \(0.294229\pi\) | ||||
−0.602355 | + | 0.798228i | \(0.705771\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.48528 | − | 11.4853i | −0.507114 | − | 1.06181i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.00000i | − | 0.366679i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 21.0000i | − | 1.90909i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.82843 | + | 0.828427i | 0.435365 | + | 0.0746968i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.48528 | − | 8.48528i | 0.758947 | − | 0.758947i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.24264i | − | 0.376473i | −0.982124 | − | 0.188237i | \(-0.939723\pi\) | ||
0.982124 | − | 0.188237i | \(-0.0602772\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | + | 5.65685i | 0.352180 | + | 0.498058i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | − | 6.00000i | −0.524222 | − | 0.524222i | 0.394621 | − | 0.918844i | \(-0.370876\pi\) |
−0.918844 | + | 0.394621i | \(0.870876\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 4.00000i | −0.346844 | + | 0.346844i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.82843 | + | 10.0000i | 0.243432 | + | 0.860663i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.1421 | 1.20824 | 0.604122 | − | 0.796892i | \(-0.293524\pi\) | ||||
0.604122 | + | 0.796892i | \(0.293524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.89949 | − | 9.89949i | −0.839664 | − | 0.839664i | 0.149150 | − | 0.988815i | \(-0.452346\pi\) |
−0.988815 | + | 0.149150i | \(0.952346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.4853 | + | 3.51472i | 1.72517 | + | 0.295993i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.0000 | −2.00698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.0000 | −1.66091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.53553 | − | 1.46447i | −0.703999 | − | 0.120787i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.24264 | − | 4.24264i | −0.347571 | − | 0.347571i | 0.511633 | − | 0.859204i | \(-0.329041\pi\) |
−0.859204 | + | 0.511633i | \(0.829041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.24264 | 0.345261 | 0.172631 | − | 0.984987i | \(-0.444773\pi\) | ||||
0.172631 | + | 0.984987i | \(0.444773\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.82843 | − | 8.00000i | 0.228665 | − | 0.646762i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | + | 6.00000i | −0.481932 | + | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00000 | − | 3.00000i | −0.239426 | − | 0.239426i | 0.577186 | − | 0.816612i | \(-0.304151\pi\) |
−0.816612 | + | 0.577186i | \(0.804151\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | − | 8.48528i | −0.475831 | − | 0.672927i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.48528 | + | 8.48528i | −0.664619 | + | 0.664619i | −0.956465 | − | 0.291847i | \(-0.905730\pi\) |
0.291847 | + | 0.956465i | \(0.405730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.3137 | + | 3.31371i | 1.50357 | + | 0.257972i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.0000i | 1.23812i | 0.785345 | + | 0.619059i | \(0.212486\pi\) | ||||
−0.785345 | + | 0.619059i | \(0.787514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.8284 | + | 5.17157i | −0.828071 | + | 0.395480i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.07107 | − | 7.07107i | 0.537603 | − | 0.537603i | −0.385221 | − | 0.922824i | \(-0.625875\pi\) |
0.922824 | + | 0.385221i | \(0.125875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.41421i | − | 0.106904i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | + | 2.82843i | −0.300658 | + | 0.212598i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | + | 6.00000i | 0.448461 | + | 0.448461i | 0.894843 | − | 0.446382i | \(-0.147288\pi\) |
−0.446382 | + | 0.894843i | \(0.647288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.00000 | + | 3.00000i | −0.222988 | + | 0.222988i | −0.809756 | − | 0.586767i | \(-0.800400\pi\) |
0.586767 | + | 0.809756i | \(0.300400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.7279 | − | 18.0000i | −0.940875 | − | 1.33060i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.1421 | −1.03975 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3137 | − | 11.3137i | −0.827340 | − | 0.827340i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.41421 | + | 3.58579i | 0.466565 | + | 0.260828i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.48528 | − | 14.4853i | 0.177975 | − | 1.03731i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7279 | − | 12.7279i | −0.906827 | − | 0.906827i | 0.0891879 | − | 0.996015i | \(-0.471573\pi\) |
−0.996015 | + | 0.0891879i | \(0.971573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.5563 | −1.10276 | −0.551380 | − | 0.834254i | \(-0.685899\pi\) | ||||
−0.551380 | + | 0.834254i | \(0.685899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.1421 | + | 10.0000i | −0.997509 | + | 0.705346i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.0000 | + | 10.0000i | −0.701862 | + | 0.701862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | + | 4.00000i | 0.279372 | + | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.6274i | 1.56517i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7279 | − | 12.7279i | 0.876226 | − | 0.876226i | −0.116916 | − | 0.993142i | \(-0.537301\pi\) |
0.993142 | + | 0.116916i | \(0.0373007\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.17157 | − | 6.82843i | 0.0802749 | − | 0.467876i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000i | 0.545595i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000i | 0.407307i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.17157 | + | 6.82843i | −0.0791676 | + | 0.461422i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.48528 | + | 8.48528i | −0.570782 | + | 0.570782i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 12.7279i | − | 0.852325i | −0.904647 | − | 0.426162i | \(-0.859865\pi\) | ||
0.904647 | − | 0.426162i | \(-0.140135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | − | 2.82843i | 0.0666667 | − | 0.188562i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.00000 | − | 8.00000i | −0.530979 | − | 0.530979i | 0.389885 | − | 0.920864i | \(-0.372515\pi\) |
−0.920864 | + | 0.389885i | \(0.872515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | − | 5.00000i | 0.330409 | − | 0.330409i | −0.522333 | − | 0.852742i | \(-0.674938\pi\) |
0.852742 | + | 0.522333i | \(0.174938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3137 | − | 8.00000i | 0.744387 | − | 0.526361i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.3137 | −0.741186 | −0.370593 | − | 0.928795i | \(-0.620845\pi\) | ||||
−0.370593 | + | 0.928795i | \(0.620845\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9706 | + | 16.9706i | 1.10704 | + | 1.10704i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.89949 | − | 16.8995i | 0.188342 | − | 1.09774i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.2929 | + | 11.7071i | 0.660289 | + | 0.751011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.07107 | − | 7.07107i | −0.451754 | − | 0.451754i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.9706 | 1.07981 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.00000 | − | 8.00000i | 0.504956 | − | 0.504956i | −0.408018 | − | 0.912974i | \(-0.633780\pi\) |
0.912974 | + | 0.408018i | \(0.133780\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.00000 | − | 5.65685i | 0.500979 | − | 0.354246i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.3137i | − | 0.705730i | −0.935674 | − | 0.352865i | \(-0.885208\pi\) | ||
0.935674 | − | 0.352865i | \(-0.114792\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.07107 | + | 7.07107i | −0.439375 | + | 0.439375i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.0711 | + | 12.9289i | −1.67566 | + | 0.800281i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.00000i | 0.246651i | 0.992366 | + | 0.123325i | \(0.0393559\pi\) | ||||
−0.992366 | + | 0.123325i | \(0.960644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 12.0000i | − | 0.737154i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.65685 | − | 1.65685i | −0.590990 | − | 0.101398i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.24264 | + | 4.24264i | −0.258678 | + | 0.258678i | −0.824516 | − | 0.565838i | \(-0.808553\pi\) |
0.565838 | + | 0.824516i | \(0.308553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 21.2132i | − | 1.28861i | −0.764768 | − | 0.644305i | \(-0.777147\pi\) | ||
0.764768 | − | 0.644305i | \(-0.222853\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | − | 8.48528i | −0.363137 | − | 0.513553i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00000 | − | 4.00000i | −0.241209 | − | 0.241209i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00000 | − | 3.00000i | 0.180253 | − | 0.180253i | −0.611213 | − | 0.791466i | \(-0.709318\pi\) |
0.791466 | + | 0.611213i | \(0.209318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.24264 | + | 12.0000i | −0.254000 | + | 0.718421i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.9706 | −1.01238 | −0.506189 | − | 0.862422i | \(-0.668946\pi\) | ||||
−0.506189 | + | 0.862422i | \(0.668946\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.89949 | − | 9.89949i | −0.588464 | − | 0.588464i | 0.348751 | − | 0.937215i | \(-0.386606\pi\) |
−0.937215 | + | 0.348751i | \(0.886606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.6569 | − | 2.34315i | −0.808962 | − | 0.138796i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.6569 | − | 2.34315i | −0.800579 | − | 0.137358i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.89949 | + | 9.89949i | 0.578335 | + | 0.578335i | 0.934444 | − | 0.356110i | \(-0.115897\pi\) |
−0.356110 | + | 0.934444i | \(0.615897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.65685 | −0.329355 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.2843 | − | 8.00000i | 1.64122 | − | 0.464207i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 4.00000i | 0.230556 | + | 0.230556i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.0000 | + | 19.7990i | 0.804279 | + | 1.13742i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 25.4558i | − | 1.45760i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.41421 | − | 1.41421i | 0.0807134 | − | 0.0807134i | −0.665597 | − | 0.746311i | \(-0.731823\pi\) |
0.746311 | + | 0.665597i | \(0.231823\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.24264 | + | 1.24264i | 0.412019 | + | 0.0706914i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 28.0000i | − | 1.58773i | −0.608091 | − | 0.793867i | \(-0.708065\pi\) | ||
0.608091 | − | 0.793867i | \(-0.291935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0000i | 1.24351i | 0.783210 | + | 0.621757i | \(0.213581\pi\) | ||||
−0.783210 | + | 0.621757i | \(0.786419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.65685 | + | 7.65685i | 0.206040 | + | 0.431415i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.24264 | + | 4.24264i | −0.238290 | + | 0.238290i | −0.816142 | − | 0.577851i | \(-0.803891\pi\) |
0.577851 | + | 0.816142i | \(0.303891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 56.5685i | 3.16723i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | + | 2.82843i | −0.223258 | + | 0.157867i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | + | 8.00000i | 0.445132 | + | 0.445132i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.00000 | + | 3.00000i | −0.166410 | + | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.24264 | + | 6.00000i | 0.234619 | + | 0.331801i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.9706 | 0.935617 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.2132 | + | 21.2132i | 1.16598 | + | 1.16598i | 0.983143 | + | 0.182841i | \(0.0585292\pi\) |
0.182841 | + | 0.983143i | \(0.441471\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.1421 | + | 9.14214i | −1.04898 | + | 0.500986i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.0000 | −1.09272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0000 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.97056 | + | 28.9706i | −0.269964 | + | 1.57346i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706 | + | 16.9706i | 0.919007 | + | 0.919007i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.0000 | − | 20.0000i | 1.07366 | − | 1.07366i | 0.0765939 | − | 0.997062i | \(-0.475596\pi\) |
0.997062 | − | 0.0765939i | \(-0.0244045\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.00000 | + | 9.00000i | 0.481759 | + | 0.481759i | 0.905693 | − | 0.423934i | \(-0.139351\pi\) |
−0.423934 | + | 0.905693i | \(0.639351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.00000 | − | 21.2132i | −0.320256 | − | 1.13228i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.3137i | 0.602168i | 0.953598 | + | 0.301084i | \(0.0973484\pi\) | ||||
−0.953598 | + | 0.301084i | \(0.902652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.65685 | − | 5.65685i | 0.300235 | − | 0.300235i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.17157 | − | 6.82843i | 0.0620062 | − | 0.361399i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 20.0000i | − | 1.05556i | −0.849381 | − | 0.527780i | \(-0.823025\pi\) | ||
0.849381 | − | 0.527780i | \(-0.176975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000i | 0.157895i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.15076 | − | 35.8492i | 0.322831 | − | 1.88160i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.65685 | + | 5.65685i | −0.296093 | + | 0.296093i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3848i | 0.959678i | 0.877357 | + | 0.479839i | \(0.159305\pi\) | ||||
−0.877357 | + | 0.479839i | \(0.840695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.00000 | + | 2.82843i | 0.416463 | + | 0.147242i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | − | 6.00000i | −0.311504 | − | 0.311504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.00000 | − | 9.00000i | 0.466002 | − | 0.466002i | −0.434614 | − | 0.900617i | \(-0.643115\pi\) |
0.900617 | + | 0.434614i | \(0.143115\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.9706 | − | 12.0000i | 0.876356 | − | 0.619677i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 42.4264 | 2.18507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1421 | + | 14.1421i | 0.726433 | + | 0.726433i | 0.969907 | − | 0.243475i | \(-0.0782872\pi\) |
−0.243475 | + | 0.969907i | \(0.578287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.24264 | − | 7.24264i | 0.0636624 | − | 0.371052i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.0000 | 1.43073 | 0.715367 | − | 0.698749i | \(-0.246260\pi\) | ||||
0.715367 | + | 0.698749i | \(0.246260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.17157 | + | 10.8284i | 0.262886 | + | 0.550440i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.07107 | + | 7.07107i | 0.358517 | + | 0.358517i | 0.863266 | − | 0.504749i | \(-0.168415\pi\) |
−0.504749 | + | 0.863266i | \(0.668415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.48528 | − | 12.0000i | −0.428026 | − | 0.605320i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.0000 | − | 14.0000i | 0.704416 | − | 0.704416i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | − | 13.0000i | −0.652451 | − | 0.652451i | 0.301131 | − | 0.953583i | \(-0.402636\pi\) |
−0.953583 | + | 0.301131i | \(0.902636\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.00000 | + | 5.65685i | −0.400501 | + | 0.283197i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.1127i | − | 1.55369i | −0.629689 | − | 0.776847i | \(-0.716818\pi\) | ||
0.629689 | − | 0.776847i | \(-0.283182\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.7279 | − | 12.7279i | 0.634023 | − | 0.634023i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.89949 | + | 17.8995i | 0.0943867 | + | 0.889433i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.0000i | 1.98273i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.00000i | − | 0.395575i | −0.980245 | − | 0.197787i | \(-0.936624\pi\) | ||
0.980245 | − | 0.197787i | \(-0.0633755\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.1421 | + | 4.14214i | 1.19084 | + | 0.204316i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.82843 | + | 2.82843i | −0.139178 | + | 0.139178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.0000 | − | 19.7990i | −0.685583 | − | 0.969561i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000 | + | 24.0000i | 1.17248 | + | 1.17248i | 0.981617 | + | 0.190859i | \(0.0611274\pi\) |
0.190859 | + | 0.981617i | \(0.438873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | + | 11.0000i | −0.536107 | + | 0.536107i | −0.922383 | − | 0.386276i | \(-0.873761\pi\) |
0.386276 | + | 0.922383i | \(0.373761\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 33.9411 | + | 12.0000i | 1.65027 | + | 0.583460i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.82843 | −0.137199 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.7279 | − | 12.7279i | −0.615947 | − | 0.615947i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −40.9706 | − | 7.02944i | −1.97808 | − | 0.339384i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.0000 | 1.34871 | 0.674356 | − | 0.738406i | \(-0.264421\pi\) | ||||
0.674356 | + | 0.738406i | \(0.264421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0000 | 0.768911 | 0.384455 | − | 0.923144i | \(-0.374389\pi\) | ||||
0.384455 | + | 0.923144i | \(0.374389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34.1421 | − | 5.85786i | −1.63699 | − | 0.280863i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.24264 | 0.202490 | 0.101245 | − | 0.994862i | \(-0.467717\pi\) | ||||
0.101245 | + | 0.994862i | \(0.467717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.1421 | − | 5.00000i | −0.673435 | − | 0.238095i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.00000 | + | 8.00000i | −0.380091 | + | 0.380091i | −0.871135 | − | 0.491044i | \(-0.836616\pi\) |
0.491044 | + | 0.871135i | \(0.336616\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | − | 8.00000i | −0.379236 | − | 0.379236i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.00000 | − | 8.48528i | −0.283790 | − | 0.401340i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.82843i | 0.133482i | 0.997770 | + | 0.0667409i | \(0.0212601\pi\) | ||||
−0.997770 | + | 0.0667409i | \(0.978740\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3137 | − | 11.3137i | 0.532742 | − | 0.532742i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.24264 | + | 1.24264i | 0.340289 | + | 0.0583844i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 12.0000i | − | 0.562569i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.0000i | 0.748448i | 0.927338 | + | 0.374224i | \(0.122091\pi\) | ||||
−0.927338 | + | 0.374224i | \(0.877909\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.17157 | − | 12.8284i | 0.334740 | − | 0.598780i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.24264 | − | 4.24264i | 0.197599 | − | 0.197599i | −0.601371 | − | 0.798970i | \(-0.705378\pi\) |
0.798970 | + | 0.601371i | \(0.205378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.07107i | − | 0.328620i | −0.986409 | − | 0.164310i | \(-0.947460\pi\) | ||
0.986409 | − | 0.164310i | \(-0.0525398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.0000 | + | 8.48528i | −0.556487 | + | 0.393496i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.00000 | + | 8.00000i | 0.370196 | + | 0.370196i | 0.867548 | − | 0.497353i | \(-0.165694\pi\) |
−0.497353 | + | 0.867548i | \(0.665694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | + | 10.0000i | −0.461757 | + | 0.461757i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.24264 | − | 6.00000i | −0.195491 | − | 0.276465i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.6274 | 1.04041 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.82843 | + | 2.82843i | 0.129777 | + | 0.129777i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.75736 | − | 16.2426i | −0.355185 | − | 0.743699i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.00000 | −0.365529 | −0.182765 | − | 0.983157i | \(-0.558505\pi\) | ||||
−0.182765 | + | 0.983157i | \(0.558505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.0000 | 1.36788 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.3137 | − | 11.3137i | −0.513729 | − | 0.513729i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.3553 | −1.60210 | −0.801052 | − | 0.598595i | \(-0.795726\pi\) | ||||
−0.801052 | + | 0.598595i | \(0.795726\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.9706 | + | 12.0000i | −0.767435 | + | 0.542659i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00000 | − | 2.00000i | 0.0902587 | − | 0.0902587i | −0.660536 | − | 0.750795i | \(-0.729671\pi\) |
0.750795 | + | 0.660536i | \(0.229671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | + | 20.0000i | 0.900755 | + | 0.900755i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 32.0000 | + | 11.3137i | 1.43829 | + | 0.508513i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.65685i | − | 0.253745i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.89949 | − | 9.89949i | 0.443162 | − | 0.443162i | −0.449911 | − | 0.893073i | \(-0.648544\pi\) |
0.893073 | + | 0.449911i | \(0.148544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.68629 | + | 27.3137i | −0.209368 | + | 1.22029i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.0000i | − | 0.535054i | −0.963550 | − | 0.267527i | \(-0.913794\pi\) | ||
0.963550 | − | 0.267527i | \(-0.0862064\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.0000i | 1.24598i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.46447 | + | 8.53553i | −0.0650392 | + | 0.379076i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.24264 | + | 4.24264i | −0.188052 | + | 0.188052i | −0.794853 | − | 0.606802i | \(-0.792452\pi\) |
0.606802 | + | 0.794853i | \(0.292452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.65685i | 0.250244i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.0000 | + | 5.65685i | −0.883022 | + | 0.249756i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.00000 | + | 6.00000i | 0.264392 | + | 0.264392i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.0000 | − | 48.0000i | 2.11104 | − | 2.11104i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.1421 | − | 10.0000i | 0.620771 | − | 0.438951i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.7696 | −1.61090 | −0.805452 | − | 0.592661i | \(-0.798077\pi\) | ||||
−0.805452 | + | 0.592661i | \(0.798077\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.4558 | + | 25.4558i | 1.11311 | + | 1.11311i | 0.992728 | + | 0.120378i | \(0.0384107\pi\) |
0.120378 | + | 0.992728i | \(0.461589\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.414214 | − | 2.41421i | 0.0180778 | − | 0.105365i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | 0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.65685 | + | 3.65685i | −0.332279 | + | 0.158694i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.48528 | − | 8.48528i | −0.367538 | − | 0.367538i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.65685 | −0.244567 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.48528 | + | 12.0000i | 0.366167 | + | 0.517838i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.0000 | + | 20.0000i | −0.861461 | + | 0.861461i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.0000 | + | 31.0000i | 1.33279 | + | 1.33279i | 0.902861 | + | 0.429934i | \(0.141463\pi\) |
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.00000 | + | 4.24264i | −0.257485 | + | 0.182069i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.48528i | 0.363470i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.7990 | + | 19.7990i | −0.846544 | + | 0.846544i | −0.989700 | − | 0.143156i | \(-0.954275\pi\) |
0.143156 | + | 0.989700i | \(0.454275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.4558 | − | 34.4558i | −0.702318 | − | 1.47054i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 40.0000i | − | 1.70406i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.0000i | − | 0.595341i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.1421 | − | 4.14214i | −1.02478 | − | 0.175824i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.3848 | + | 18.3848i | −0.778988 | + | 0.778988i | −0.979659 | − | 0.200671i | \(-0.935688\pi\) |
0.200671 | + | 0.979659i | \(0.435688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16.9706i | − | 0.717778i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.0000 | − | 22.6274i | −0.675521 | − | 0.955330i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.0000 | − | 20.0000i | −0.842900 | − | 0.842900i | 0.146336 | − | 0.989235i | \(-0.453252\pi\) |
−0.989235 | + | 0.146336i | \(0.953252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.0000 | + | 24.0000i | −1.00969 | + | 1.00969i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.89949 | + | 8.00000i | 0.415740 | + | 0.335968i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.82843 | −0.118574 | −0.0592869 | − | 0.998241i | \(-0.518883\pi\) | ||||
−0.0592869 | + | 0.998241i | \(0.518883\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.3848 | − | 18.3848i | −0.769379 | − | 0.769379i | 0.208618 | − | 0.977997i | \(-0.433103\pi\) |
−0.977997 | + | 0.208618i | \(0.933103\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.82843 | + | 1.17157i | 0.285262 | + | 0.0489432i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.0000 | −1.16566 | −0.582828 | − | 0.812596i | \(-0.698054\pi\) | ||||
−0.582828 | + | 0.812596i | \(0.698054\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.41421 | + | 0.585786i | 0.141890 | + | 0.0243445i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.9411 | −1.40570 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.48528 | − | 24.0000i | 0.350823 | − | 0.992278i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0000 | + | 14.0000i | −0.577842 | + | 0.577842i | −0.934308 | − | 0.356466i | \(-0.883981\pi\) |
0.356466 | + | 0.934308i | \(0.383981\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | − | 12.0000i | −0.494451 | − | 0.494451i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | − | 25.4558i | −0.740421 | − | 1.04711i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.65685 | − | 5.65685i | 0.231908 | − | 0.231908i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.5563 | − | 4.55635i | −1.08688 | − | 0.186479i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0000i | 1.30748i | 0.756717 | + | 0.653742i | \(0.226802\pi\) | ||||
−0.756717 | + | 0.653742i | \(0.773198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.0000i | − | 0.815817i | −0.913023 | − | 0.407909i | \(-0.866258\pi\) | ||
0.913023 | − | 0.407909i | \(-0.133742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.0711 | + | 12.9289i | −1.10242 | + | 0.526507i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.6985 | − | 29.6985i | 1.20742 | − | 1.20742i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.6985i | 1.20542i | 0.797959 | + | 0.602712i | \(0.205913\pi\) | ||||
−0.797959 | + | 0.602712i | \(0.794087\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.0000 | + | 14.1421i | −0.810441 | + | 0.573068i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.0000 | − | 36.0000i | −1.45640 | − | 1.45640i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.0000 | + | 25.0000i | −1.00974 | + | 1.00974i | −0.00978840 | + | 0.999952i | \(0.503116\pi\) |
−0.999952 | + | 0.00978840i | \(0.996884\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.65685 | + | 8.00000i | 0.228106 | + | 0.322591i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.2843 | −1.13868 | −0.569341 | − | 0.822102i | \(-0.692802\pi\) | ||||
−0.569341 | + | 0.822102i | \(0.692802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.89949 | + | 9.89949i | 0.397894 | + | 0.397894i | 0.877490 | − | 0.479595i | \(-0.159217\pi\) |
−0.479595 | + | 0.877490i | \(0.659217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0000 | 0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.62742 | + | 38.6274i | −0.264674 | + | 1.54263i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.1421 | + | 14.1421i | 0.563884 | + | 0.563884i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.3553 | 1.40747 | 0.703737 | − | 0.710461i | \(-0.251513\pi\) | ||||
0.703737 | + | 0.710461i | \(0.251513\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.4558 | − | 18.0000i | 1.01178 | − | 0.715436i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.00000 | − | 6.00000i | 0.238103 | − | 0.238103i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | + | 15.0000i | 0.594322 | + | 0.594322i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.00000 | − | 11.3137i | 0.158238 | − | 0.447563i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.82843i | 0.111716i | 0.998439 | + | 0.0558581i | \(0.0177894\pi\) | ||||
−0.998439 | + | 0.0558581i | \(0.982211\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.7990 | − | 19.7990i | 0.780796 | − | 0.780796i | −0.199169 | − | 0.979965i | \(-0.563824\pi\) |
0.979965 | + | 0.199169i | \(0.0638243\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.34315 | + | 13.6569i | −0.0922613 | + | 0.537738i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.0000i | 1.57256i | 0.617869 | + | 0.786281i | \(0.287996\pi\) | ||||
−0.617869 | + | 0.786281i | \(0.712004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000i | 0.628055i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.75736 | + | 10.2426i | −0.0688763 | + | 0.401441i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.07107 | + | 7.07107i | −0.276712 | + | 0.276712i | −0.831795 | − | 0.555083i | \(-0.812687\pi\) |
0.555083 | + | 0.831795i | \(0.312687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 16.9706i | − | 0.663095i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.00000 | + | 11.3137i | −0.156055 | + | 0.441390i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.00000 | − | 2.00000i | −0.0779089 | − | 0.0779089i | 0.667078 | − | 0.744987i | \(-0.267545\pi\) |
−0.744987 | + | 0.667078i | \(0.767545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.0000 | − | 23.0000i | 0.894596 | − | 0.894596i | −0.100355 | − | 0.994952i | \(-0.531998\pi\) |
0.994952 | + | 0.100355i | \(0.0319980\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.9706 | + | 12.0000i | −0.659082 | + | 0.466041i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.3137 | −0.438727 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.72792 | − | 21.7279i | 0.144130 | − | 0.840050i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −72.0000 | −2.77953 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.0000 | −1.85026 | −0.925132 | − | 0.379646i | \(-0.876046\pi\) | ||||
−0.925132 | + | 0.379646i | \(0.876046\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.53553 | − | 4.53553i | 0.0975927 | − | 0.174573i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.6985 | − | 29.6985i | −1.14141 | − | 1.14141i | −0.988193 | − | 0.153212i | \(-0.951038\pi\) |
−0.153212 | − | 0.988193i | \(-0.548962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.3137 | −0.434180 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3137 | − | 16.0000i | −0.433542 | − | 0.613121i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.00000 | − | 8.00000i | 0.306111 | − | 0.306111i | −0.537288 | − | 0.843399i | \(-0.680551\pi\) |
0.843399 | + | 0.537288i | \(0.180551\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.0000 | + | 20.0000i | 0.764161 | + | 0.764161i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0000 | − | 7.07107i | 0.381524 | − | 0.269778i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.4558i | 0.969790i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4558 | − | 25.4558i | 0.968386 | − | 0.968386i | −0.0311294 | − | 0.999515i | \(-0.509910\pi\) |
0.999515 | + | 0.0311294i | \(0.00991040\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 21.6569 | − | 10.3431i | 0.822676 | − | 0.392904i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 28.0000i | − | 1.06210i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.00000i | − | 0.303022i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.3137 | − | 3.31371i | −0.730512 | − | 0.125336i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.2132 | − | 21.2132i | 0.801212 | − | 0.801212i | −0.182073 | − | 0.983285i | \(-0.558281\pi\) |
0.983285 | + | 0.182073i | \(0.0582808\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 28.2843i | − | 1.06676i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.0000 | + | 33.9411i | 0.903892 | + | 1.27830i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.0000 | + | 14.0000i | 0.526524 | + | 0.526524i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.0000 | − | 27.0000i | 1.01401 | − | 1.01401i | 0.0141058 | − | 0.999901i | \(-0.495510\pi\) |
0.999901 | − | 0.0141058i | \(-0.00449016\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.89949 | − | 28.0000i | 0.371260 | − | 1.05008i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.9411 | − | 33.9411i | −1.26933 | − | 1.26933i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.4853 | + | 3.51472i | 0.765037 | + | 0.131260i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.41421 | − | 0.585786i | −0.126976 | − | 0.0217856i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.07107 | + | 7.07107i | 0.262613 | + | 0.262613i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.1838 | −1.41616 | −0.708079 | − | 0.706133i | \(-0.750438\pi\) | ||||
−0.708079 | + | 0.706133i | \(0.750438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1421 | + | 23.0000i | 0.523783 | + | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | − | 8.00000i | 0.295891 | − | 0.295891i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00000 | + | 1.00000i | 0.0369358 | + | 0.0369358i | 0.725333 | − | 0.688398i | \(-0.241686\pi\) |
−0.688398 | + | 0.725333i | \(0.741686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.0000 | − | 14.1421i | −0.368856 | − | 0.521641i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 56.5685i | 2.08373i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.41421 | + | 1.41421i | −0.0520227 | + | 0.0520227i | −0.732640 | − | 0.680617i | \(-0.761712\pi\) |
0.680617 | + | 0.732640i | \(0.261712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.9706 | + | 4.97056i | 1.06426 | + | 0.182598i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.0000i | 1.17397i | 0.809599 | + | 0.586983i | \(0.199684\pi\) | ||||
−0.809599 | + | 0.586983i | \(0.800316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 12.0000i | − | 0.439646i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.82843 | + | 2.82843i | −0.103348 | + | 0.103348i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.5269i | 1.18692i | 0.804862 | + | 0.593462i | \(0.202239\pi\) | ||||
−0.804862 | + | 0.593462i | \(0.797761\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.0000 | − | 11.3137i | 0.583072 | − | 0.412294i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.00000 | + | 6.00000i | 0.218362 | + | 0.218362i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.00000 | − | 5.00000i | 0.181728 | − | 0.181728i | −0.610380 | − | 0.792108i | \(-0.708983\pi\) |
0.792108 | + | 0.610380i | \(0.208983\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.48528 | −0.307591 | −0.153796 | − | 0.988103i | \(-0.549150\pi\) | ||||
−0.153796 | + | 0.988103i | \(0.549150\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.24264 | + | 4.24264i | 0.153594 | + | 0.153594i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.3137 | − | 7.31371i | 0.553668 | − | 0.264428i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.0000 | 0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.0000 | −0.649097 | −0.324548 | − | 0.945869i | \(-0.605212\pi\) | ||||
−0.324548 | + | 0.945869i | \(0.605212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.31371 | − | 19.3137i | 0.119340 | − | 0.695566i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.24264 | + | 4.24264i | 0.152597 | + | 0.152597i | 0.779277 | − | 0.626680i | \(-0.215587\pi\) |
−0.626680 | + | 0.779277i | \(0.715587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.24264 | 0.152400 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.1421 | + | 10.0000i | −0.507346 | + | 0.358748i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | + | 8.00000i | −0.286630 | + | 0.286630i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | − | 16.0000i | −0.572525 | − | 0.572525i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −50.0000 | + | 14.1421i | −1.78685 | + | 0.505399i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 8.48528i | − | 0.302853i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.48528 | − | 8.48528i | 0.302468 | − | 0.302468i | −0.539511 | − | 0.841979i | \(-0.681391\pi\) |
0.841979 | + | 0.539511i | \(0.181391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.17157 | + | 6.82843i | −0.0417091 | + | 0.243098i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0000i | 0.853342i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.0000i | 1.91760i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.51472 | − | 20.4853i | 0.124654 | − | 0.726538i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.5269 | − | 32.5269i | 1.15216 | − | 1.15216i | 0.166044 | − | 0.986118i | \(-0.446901\pi\) |
0.986118 | − | 0.166044i | \(-0.0530994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 33.9411i | − | 1.20075i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.0000 | − | 5.65685i | −0.565332 | − | 0.199875i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.0000 | + | 16.0000i | 0.564628 | + | 0.564628i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.48528 | + | 6.00000i | −0.298696 | + | 0.211210i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.7696 | 1.29275 | 0.646374 | − | 0.763020i | \(-0.276284\pi\) | ||||
0.646374 | + | 0.763020i | \(0.276284\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1421 | − | 14.1421i | −0.496598 | − | 0.496598i | 0.413780 | − | 0.910377i | \(-0.364208\pi\) |
−0.910377 | + | 0.413780i | \(0.864208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.21320 | − | 36.2132i | 0.217907 | − | 1.27005i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.0000 | −0.840683 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.75736 | − | 16.2426i | −0.271064 | − | 0.567564i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.8701 | + | 26.8701i | 0.937771 | + | 0.937771i | 0.998174 | − | 0.0604026i | \(-0.0192385\pi\) |
−0.0604026 | + | 0.998174i | \(0.519238\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.3553 | 1.23241 | 0.616205 | − | 0.787586i | \(-0.288669\pi\) | ||||
0.616205 | + | 0.787586i | \(0.288669\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.65685 | − | 8.00000i | −0.196946 | − | 0.278524i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.0000 | + | 30.0000i | −1.04320 | + | 1.04320i | −0.0441786 | + | 0.999024i | \(0.514067\pi\) |
−0.999024 | + | 0.0441786i | \(0.985933\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0000 | + | 13.0000i | 0.451509 | + | 0.451509i | 0.895855 | − | 0.444346i | \(-0.146564\pi\) |
−0.444346 | + | 0.895855i | \(0.646564\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.00000 | − | 4.24264i | 0.208138 | − | 0.147176i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.1421i | 0.489996i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.6274 | + | 22.6274i | −0.783054 | + | 0.783054i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.7574 | + | 19.2426i | −0.371829 | + | 0.665123i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.0000i | 1.24286i | 0.783470 | + | 0.621429i | \(0.213448\pi\) | ||||
−0.783470 | + | 0.621429i | \(0.786552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 71.0000i | − | 2.44828i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.9706 | − | 4.97056i | −0.997799 | − | 0.171195i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.07107 | + | 7.07107i | −0.243252 | + | 0.243252i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 29.6985i | − | 1.02045i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.0000 | − | 19.7990i | −0.480479 | − | 0.679500i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0000 | + | 15.0000i | −0.513590 | + | 0.513590i | −0.915625 | − | 0.402034i | \(-0.868303\pi\) |
0.402034 | + | 0.915625i | \(0.368303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.6274 | − | 8.00000i | −0.773841 | − | 0.273594i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.4558 | 0.869555 | 0.434778 | − | 0.900538i | \(-0.356827\pi\) | ||||
0.434778 | + | 0.900538i | \(0.356827\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.1421 | − | 14.1421i | −0.482523 | − | 0.482523i | 0.423413 | − | 0.905937i | \(-0.360832\pi\) |
−0.905937 | + | 0.423413i | \(0.860832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.82843 | + | 1.17157i | 0.232712 | + | 0.0399271i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.0000 | 0.953131 | 0.476566 | − | 0.879139i | \(-0.341881\pi\) | ||||
0.476566 | + | 0.879139i | \(0.341881\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.0000 | 0.680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.3640 | + | 2.63604i | 0.521787 | + | 0.0895246i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.5980 | − | 39.5980i | −1.34327 | − | 1.34327i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.4264 | 1.43756 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.6274 | − | 8.00000i | −0.765822 | − | 0.270759i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0000 | − | 12.0000i | 0.405674 | − | 0.405674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.0000 | − | 15.0000i | −0.506514 | − | 0.506514i | 0.406941 | − | 0.913455i | \(-0.366596\pi\) |
−0.913455 | + | 0.406941i | \(0.866596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.0000 | + | 19.7990i | 0.472208 | + | 0.667803i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.9706i | 0.571753i | 0.958267 | + | 0.285876i | \(0.0922847\pi\) | ||||
−0.958267 | + | 0.285876i | \(0.907715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.1127 | + | 31.1127i | −1.04703 | + | 1.04703i | −0.0481873 | + | 0.998838i | \(0.515344\pi\) |
−0.998838 | + | 0.0481873i | \(0.984656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.65685 | − | 1.65685i | −0.324612 | − | 0.0556945i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 44.0000i | − | 1.47738i | −0.674048 | − | 0.738688i | \(-0.735446\pi\) | ||
0.674048 | − | 0.738688i | \(-0.264554\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.00000i | − | 0.201234i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 50.6274 | − | 5.37258i | 1.69608 | − | 0.179988i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.9411 | + | 33.9411i | −1.13580 | + | 1.13580i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.9706i | 0.567263i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.0000 | − | 30.0000i | −1.00056 | − | 1.00056i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | + | 12.0000i | −0.399778 | + | 0.399778i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.65685 | + | 8.00000i | 0.188248 | + | 0.266223i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.48528 | −0.282060 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.1127 | + | 31.1127i | 1.03308 | + | 1.03308i | 0.999434 | + | 0.0336464i | \(0.0107120\pi\) |
0.0336464 | + | 0.999434i | \(0.489288\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.1005 | + | 37.8995i | 0.600356 | + | 1.25705i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.45584 | − | 43.4558i | 0.246483 | − | 1.43661i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.48528 | − | 8.48528i | −0.280209 | − | 0.280209i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.2132 | −0.699759 | −0.349880 | − | 0.936795i | \(-0.613777\pi\) | ||||
−0.349880 | + | 0.936795i | \(0.613777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.82843 | − | 2.00000i | 0.0931998 | − | 0.0659022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.0000 | + | 12.0000i | −0.394985 | + | 0.394985i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00000 | + | 5.00000i | 0.164399 | + | 0.164399i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.0000 | + | 4.24264i | 0.394132 | + | 0.139347i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 59.3970i | − | 1.94875i | −0.224927 | − | 0.974376i | \(-0.572214\pi\) | ||
0.224927 | − | 0.974376i | \(-0.427786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.1421 | − | 14.1421i | 0.463490 | − | 0.463490i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.20101 | − | 47.7990i | 0.268489 | − | 1.56487i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 32.0000i | − | 1.04651i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.0000i | 0.588034i | 0.955800 | + | 0.294017i | \(0.0949923\pi\) | ||||
−0.955800 | + | 0.294017i | \(0.905008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.44365 | + | 37.5563i | −0.210281 | + | 1.22561i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.2132 | − | 21.2132i | 0.691531 | − | 0.691531i | −0.271038 | − | 0.962569i | \(-0.587367\pi\) |
0.962569 | + | 0.271038i | \(0.0873669\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00000 | + | 14.1421i | 0.130120 | + | 0.460044i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.0000 | + | 34.0000i | 1.10485 | + | 1.10485i | 0.993816 | + | 0.111035i | \(0.0354166\pi\) |
0.111035 | + | 0.993816i | \(0.464583\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | − | 12.0000i | 0.389536 | − | 0.389536i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.48528 | + | 6.00000i | −0.275154 | + | 0.194563i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.1421 | −0.458109 | −0.229054 | − | 0.973414i | \(-0.573563\pi\) | ||||
−0.229054 | + | 0.973414i | \(0.573563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.65685 | + | 5.65685i | 0.183052 | + | 0.183052i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.5685 | + | 96.5685i | −0.535585 | + | 3.12162i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.0000 | 0.645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.0000 | 0.419355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.65685 | + | 3.65685i | −0.246739 | + | 0.117840i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.82843 | + | 2.82843i | 0.0910503 | + | 0.0910503i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.41421 | −0.0454780 | −0.0227390 | − | 0.999741i | \(-0.507239\pi\) | ||||
−0.0227390 | + | 0.999741i | \(0.507239\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.3137 | + | 16.0000i | 0.363449 | + | 0.513994i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0000 | + | 12.0000i | −0.385098 | + | 0.385098i | −0.872935 | − | 0.487837i | \(-0.837786\pi\) |
0.487837 | + | 0.872935i | \(0.337786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.0000 | − | 14.0000i | −0.448819 | − | 0.448819i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.00000 | + | 4.24264i | −0.192154 | + | 0.135873i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 19.7990i | − | 0.633426i | −0.948521 | − | 0.316713i | \(-0.897421\pi\) | ||
0.948521 | − | 0.316713i | \(-0.102579\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.6274 | + | 22.6274i | −0.723175 | + | 0.723175i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.48528 | + | 11.4853i | 0.175132 | + | 0.366697i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 28.0000i | − | 0.893061i | −0.894768 | − | 0.446531i | \(-0.852659\pi\) | ||
0.894768 | − | 0.446531i | \(-0.147341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 36.0000i | − | 1.14706i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.9706 | + | 4.97056i | 0.922143 | + | 0.158215i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.7279i | 0.404316i | 0.979353 | + | 0.202158i | \(0.0647954\pi\) | ||||
−0.979353 | + | 0.202158i | \(0.935205\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.0000 | + | 42.4264i | 0.952021 | + | 1.34636i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.0000 | − | 22.0000i | −0.697447 | − | 0.697447i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.0000 | + | 21.0000i | −0.665077 | + | 0.665077i | −0.956572 | − | 0.291496i | \(-0.905847\pi\) |
0.291496 | + | 0.956572i | \(0.405847\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35.3553 | + | 10.0000i | −1.11859 | + | 0.316386i |
(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 | 768.2.k.c.191.2 | yes | 4 | |
3.2 | odd | 2 | 768.2.k.a.191.2 | yes | 4 | ||
4.3 | odd | 2 | 768.2.k.a.191.1 | ✓ | 4 | ||
8.3 | odd | 2 | 768.2.k.d.191.2 | yes | 4 | ||
8.5 | even | 2 | 768.2.k.b.191.1 | yes | 4 | ||
12.11 | even | 2 | inner | 768.2.k.c.191.1 | yes | 4 | |
16.3 | odd | 4 | 768.2.k.d.575.1 | yes | 4 | ||
16.5 | even | 4 | inner | 768.2.k.c.575.1 | yes | 4 | |
16.11 | odd | 4 | 768.2.k.a.575.2 | yes | 4 | ||
16.13 | even | 4 | 768.2.k.b.575.2 | yes | 4 | ||
24.5 | odd | 2 | 768.2.k.d.191.1 | yes | 4 | ||
24.11 | even | 2 | 768.2.k.b.191.2 | yes | 4 | ||
48.5 | odd | 4 | 768.2.k.a.575.1 | yes | 4 | ||
48.11 | even | 4 | inner | 768.2.k.c.575.2 | yes | 4 | |
48.29 | odd | 4 | 768.2.k.d.575.2 | yes | 4 | ||
48.35 | even | 4 | 768.2.k.b.575.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.k.a.191.1 | ✓ | 4 | 4.3 | odd | 2 | ||
768.2.k.a.191.2 | yes | 4 | 3.2 | odd | 2 | ||
768.2.k.a.575.1 | yes | 4 | 48.5 | odd | 4 | ||
768.2.k.a.575.2 | yes | 4 | 16.11 | odd | 4 | ||
768.2.k.b.191.1 | yes | 4 | 8.5 | even | 2 | ||
768.2.k.b.191.2 | yes | 4 | 24.11 | even | 2 | ||
768.2.k.b.575.1 | yes | 4 | 48.35 | even | 4 | ||
768.2.k.b.575.2 | yes | 4 | 16.13 | even | 4 | ||
768.2.k.c.191.1 | yes | 4 | 12.11 | even | 2 | inner | |
768.2.k.c.191.2 | yes | 4 | 1.1 | even | 1 | trivial | |
768.2.k.c.575.1 | yes | 4 | 16.5 | even | 4 | inner | |
768.2.k.c.575.2 | yes | 4 | 48.11 | even | 4 | inner | |
768.2.k.d.191.1 | yes | 4 | 24.5 | odd | 2 | ||
768.2.k.d.191.2 | yes | 4 | 8.3 | odd | 2 | ||
768.2.k.d.575.1 | yes | 4 | 16.3 | odd | 4 | ||
768.2.k.d.575.2 | yes | 4 | 48.29 | odd | 4 |