Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(447,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.447");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.e (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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 447.4 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.447 |
Dual form | 896.2.e.b.447.1 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.73205i | 1.57735i | 0.614810 | + | 0.788675i | \(0.289233\pi\) | ||||
−0.614810 | + | 0.788675i | \(0.710767\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.732051 | 0.327383 | 0.163692 | − | 0.986512i | \(-0.447660\pi\) | ||||
0.163692 | + | 0.986512i | \(0.447660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.46410 | −1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.46410 | −1.64749 | −0.823744 | − | 0.566961i | \(-0.808119\pi\) | ||||
−0.823744 | + | 0.566961i | \(0.808119\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.73205 | −1.31243 | −0.656217 | − | 0.754572i | \(-0.727845\pi\) | ||||
−0.656217 | + | 0.754572i | \(0.727845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000i | 0.516398i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.00000i | − | 0.970143i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26795i | 0.290887i | 0.989367 | + | 0.145444i | \(0.0464610\pi\) | ||||
−0.989367 | + | 0.145444i | \(0.953539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.73205 | + | 5.46410i | −1.03262 | + | 1.19236i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.46410i | 1.13934i | 0.821872 | + | 0.569672i | \(0.192930\pi\) | ||||
−0.821872 | + | 0.569672i | \(0.807070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.46410 | −0.892820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.92820i | 1.28654i | 0.765641 | + | 0.643268i | \(0.222422\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92820 | 1.24434 | 0.622171 | − | 0.782881i | \(-0.286251\pi\) | ||||
0.622171 | + | 0.782881i | \(0.286251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 14.9282i | − | 2.59867i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.46410 | + | 1.26795i | 0.247478 | + | 0.214323i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 12.9282i | − | 2.07017i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.92820i | 0.457309i | 0.973508 | + | 0.228654i | \(0.0734325\pi\) | ||||
−0.973508 | + | 0.228654i | \(0.926567\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.53590 | 0.386721 | 0.193360 | − | 0.981128i | \(-0.438061\pi\) | ||||
0.193360 | + | 0.981128i | \(0.438061\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.26795 | −0.487157 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.92820 | −1.01058 | −0.505291 | − | 0.862949i | \(-0.668615\pi\) | ||||
−0.505291 | + | 0.862949i | \(0.668615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.9282 | 1.53025 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.92820i | 0.951662i | 0.879537 | + | 0.475831i | \(0.157853\pi\) | ||||
−0.879537 | + | 0.475831i | \(0.842147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 3.80385i | − | 0.495219i | −0.968860 | − | 0.247609i | \(-0.920355\pi\) | ||
0.968860 | − | 0.247609i | \(-0.0796450\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6603 | 1.49294 | 0.746471 | − | 0.665418i | \(-0.231747\pi\) | ||||
0.746471 | + | 0.665418i | \(0.231747\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.92820 | − | 7.73205i | −1.12485 | − | 0.974147i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.53590 | −0.309809 | −0.154905 | − | 0.987929i | \(-0.549507\pi\) | ||||
−0.154905 | + | 0.987929i | \(0.549507\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.9282 | −1.79714 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.53590i | 0.538312i | 0.963097 | + | 0.269156i | \(0.0867447\pi\) | ||||
−0.963097 | + | 0.269156i | \(0.913255\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 12.1962i | − | 1.40829i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.9282 | − | 9.46410i | −1.24538 | − | 1.07853i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.46410i | − | 0.389742i | −0.980829 | − | 0.194871i | \(-0.937571\pi\) | ||
0.980829 | − | 0.194871i | \(-0.0624288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.7321i | 1.17800i | 0.808135 | + | 0.588998i | \(0.200477\pi\) | ||||
−0.808135 | + | 0.588998i | \(0.799523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.92820i | − | 0.317608i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.9282 | −2.02932 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.9282i | − | 1.58239i | −0.611566 | − | 0.791193i | \(-0.709460\pi\) | ||
0.611566 | − | 0.791193i | \(-0.290540\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.46410 | − | 8.19615i | −0.992107 | − | 0.859190i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.9282i | 1.96276i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.928203i | 0.0952316i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000i | 1.21842i | 0.793011 | + | 0.609208i | \(0.208512\pi\) | ||||
−0.793011 | + | 0.609208i | \(0.791488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.3923 | 2.45152 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.19615 | 0.616540 | 0.308270 | − | 0.951299i | \(-0.400250\pi\) | ||||
0.308270 | + | 0.951299i | \(0.400250\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.9282 | 1.86505 | 0.932526 | − | 0.361104i | \(-0.117600\pi\) | ||||
0.932526 | + | 0.361104i | \(0.117600\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.46410 | + | 4.00000i | −0.338062 | + | 0.390360i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.39230 | −0.811315 | −0.405657 | − | 0.914025i | \(-0.632957\pi\) | ||||
−0.405657 | + | 0.914025i | \(0.632957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.92820i | − | 0.663602i | −0.943349 | − | 0.331801i | \(-0.892344\pi\) | ||
0.943349 | − | 0.331801i | \(-0.107656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.9282 | 1.03726 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.46410 | −0.890308 | −0.445154 | − | 0.895454i | \(-0.646851\pi\) | ||||
−0.445154 | + | 0.895454i | \(0.646851\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000i | 0.373002i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 21.1244 | 1.95295 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.92820 | − | 8.00000i | 0.635107 | − | 0.733359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8564 | 1.71422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.00000 | −0.721336 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.4641i | 1.90463i | 0.305115 | + | 0.952316i | \(0.401305\pi\) | ||||
−0.305115 | + | 0.952316i | \(0.598695\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.92820i | 0.609994i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7321i | 0.937664i | 0.883287 | + | 0.468832i | \(0.155325\pi\) | ||||
−0.883287 | + | 0.468832i | \(0.844675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.19615 | + | 2.53590i | −0.190431 | + | 0.219890i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.92820i | − | 0.252020i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.8564 | 1.69645 | 0.848224 | − | 0.529638i | \(-0.177672\pi\) | ||||
0.848224 | + | 0.529638i | \(0.177672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.19615i | 0.355913i | 0.984038 | + | 0.177957i | \(0.0569486\pi\) | ||||
−0.984038 | + | 0.177957i | \(0.943051\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 18.9282i | − | 1.59404i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.8564 | 2.16222 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.07180i | 0.421190i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.9282 | + | 2.73205i | −1.56117 | + | 0.225336i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.0000i | − | 0.983078i | −0.870855 | − | 0.491539i | \(-0.836434\pi\) | ||
0.870855 | − | 0.491539i | \(-0.163566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3205i | 0.921250i | 0.887595 | + | 0.460625i | \(0.152375\pi\) | ||||
−0.887595 | + | 0.460625i | \(0.847625\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.8564i | 1.44360i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.07180 | 0.407377 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.2679 | 1.53775 | 0.768875 | − | 0.639399i | \(-0.220817\pi\) | ||||
0.768875 | + | 0.639399i | \(0.220817\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.9282 | −1.50110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.46410 | + | 10.9282i | −0.745876 | + | 0.861263i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.3923 | −1.28394 | −0.641972 | − | 0.766728i | \(-0.721884\pi\) | ||||
−0.641972 | + | 0.766728i | \(0.721884\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 10.9282i | − | 0.850759i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.07180 | 0.392467 | 0.196234 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196234 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.39230 | 0.722485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.66025i | − | 0.432850i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.26795 | 0.248458 | 0.124229 | − | 0.992254i | \(-0.460354\pi\) | ||||
0.124229 | + | 0.992254i | \(0.460354\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.92820 | − | 7.73205i | −0.674909 | − | 0.584488i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3923 | 0.781133 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.392305 | 0.0293222 | 0.0146611 | − | 0.999893i | \(-0.495333\pi\) | ||||
0.0146611 | + | 0.999893i | \(0.495333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7321 | 1.24368 | 0.621842 | − | 0.783143i | \(-0.286385\pi\) | ||||
0.621842 | + | 0.783143i | \(0.286385\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.8564i | 2.35489i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.92820i | − | 0.215286i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.8564i | 1.59830i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.92820 | − | 8.00000i | 0.503953 | − | 0.581914i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.4641i | 0.829513i | 0.909932 | + | 0.414757i | \(0.136133\pi\) | ||||
−0.909932 | + | 0.414757i | \(0.863867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.39230 | 0.316165 | 0.158083 | − | 0.987426i | \(-0.449469\pi\) | ||||
0.158083 | + | 0.987426i | \(0.449469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 9.46410i | − | 0.677738i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7846 | −1.18983 | −0.594915 | − | 0.803789i | \(-0.702814\pi\) | ||||
−0.594915 | + | 0.803789i | \(0.702814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.92820i | − | 0.488678i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.0000 | + | 13.8564i | −0.842235 | + | 0.972529i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.14359i | 0.149715i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 24.3923i | − | 1.69538i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.92820i | − | 0.479234i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.60770 | 0.523735 | 0.261868 | − | 0.965104i | \(-0.415662\pi\) | ||||
0.261868 | + | 0.965104i | \(0.415662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.3923 | −0.849107 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.85641 | 0.126606 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.8564 | + | 12.0000i | 0.940634 | + | 0.814613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.9282 | 1.27905 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.9282i | 1.27325i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.9282 | 1.32855 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.26795i | 0.0841567i | 0.999114 | + | 0.0420784i | \(0.0133979\pi\) | ||||
−0.999114 | + | 0.0420784i | \(0.986602\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.339746 | 0.0224510 | 0.0112255 | − | 0.999937i | \(-0.496427\pi\) | ||||
0.0112255 | + | 0.999937i | \(0.496427\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 25.8564 | − | 29.8564i | 1.70123 | − | 1.96441i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.8564 | −1.30084 | −0.650418 | − | 0.759576i | \(-0.725406\pi\) | ||||
−0.650418 | + | 0.759576i | \(0.725406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.07180 | −0.330848 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.46410 | 0.614759 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 0.392305i | − | 0.0253761i | −0.999920 | − | 0.0126880i | \(-0.995961\pi\) | ||
0.999920 | − | 0.0126880i | \(-0.00403884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0000i | 0.772988i | 0.922292 | + | 0.386494i | \(0.126314\pi\) | ||||
−0.922292 | + | 0.386494i | \(0.873686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 18.7321i | − | 1.20166i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.732051 | + | 5.07180i | 0.0467690 | + | 0.324025i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.00000i | − | 0.381771i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.3205 | −1.85811 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 22.0526i | − | 1.39195i | −0.718068 | − | 0.695973i | \(-0.754973\pi\) | ||
0.718068 | − | 0.695973i | \(-0.245027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 29.8564i | − | 1.87706i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.00000 | 0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.8564i | 1.36337i | 0.731648 | + | 0.681683i | \(0.238751\pi\) | ||||
−0.731648 | + | 0.681683i | \(0.761249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.92820 | − | 8.00000i | 0.430498 | − | 0.497096i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 30.9282i | − | 1.91441i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.4641i | − | 0.706907i | −0.935452 | − | 0.353453i | \(-0.885007\pi\) | ||
0.935452 | − | 0.353453i | \(-0.114993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.07180i | 0.311558i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40.7846 | 2.49598 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.12436 | 0.0685532 | 0.0342766 | − | 0.999412i | \(-0.489087\pi\) | ||||
0.0342766 | + | 0.999412i | \(0.489087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.3923 | − | 25.8564i | 1.35524 | − | 1.56490i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.3923 | 1.47091 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.7846i | − | 1.72950i | −0.502203 | − | 0.864750i | \(-0.667477\pi\) | ||
0.502203 | − | 0.864750i | \(-0.332523\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.9282 | −1.85162 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.8038i | 0.939441i | 0.882815 | + | 0.469721i | \(0.155645\pi\) | ||||
−0.882815 | + | 0.469721i | \(0.844355\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.53590 | −0.150214 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.07180 | + | 5.85641i | −0.299379 | + | 0.345693i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.7846 | −1.92187 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.80385 | −0.105382 | −0.0526910 | − | 0.998611i | \(-0.516780\pi\) | ||||
−0.0526910 | + | 0.998611i | \(0.516780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.78461i | − | 0.162126i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.8564i | 1.26824i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 25.8564i | − | 1.49531i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.07180 | + | 4.39230i | 0.292334 | + | 0.253168i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.9282i | 0.972500i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.53590 | 0.488764 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.2679i | − | 0.757242i | −0.925552 | − | 0.378621i | \(-0.876398\pi\) | ||
0.925552 | − | 0.378621i | \(-0.123602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 51.7128i | 2.94184i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.8564 | −1.46618 | −0.733091 | − | 0.680130i | \(-0.761923\pi\) | ||||
−0.733091 | + | 0.680130i | \(0.761923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.7846i | 1.85310i | 0.376177 | + | 0.926548i | \(0.377238\pi\) | ||||
−0.376177 | + | 0.926548i | \(0.622762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.53590 | − | 5.66025i | −0.368256 | − | 0.318919i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.85641i | − | 0.104266i | −0.998640 | − | 0.0521331i | \(-0.983398\pi\) | ||
0.998640 | − | 0.0521331i | \(-0.0166020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 37.8564i | − | 2.11955i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 22.9282i | − | 1.27973i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.07180 | 0.282202 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.1244 | 1.17177 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.9282 | 1.04673 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.8564 | − | 12.0000i | −0.763928 | − | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3205 | 0.622231 | 0.311116 | − | 0.950372i | \(-0.399297\pi\) | ||||
0.311116 | + | 0.950372i | \(0.399297\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.8564i | 0.978525i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.85641 | −0.101426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.60770 | −0.196524 | −0.0982618 | − | 0.995161i | \(-0.531328\pi\) | ||||
−0.0982618 | + | 0.995161i | \(0.531328\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 25.8564i | − | 1.40433i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −37.8564 | −2.05004 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.9282 | −0.588355 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.4641 | −0.722791 | −0.361395 | − | 0.932413i | \(-0.617700\pi\) | ||||
−0.361395 | + | 0.932413i | \(0.617700\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.6603 | 0.624159 | 0.312080 | − | 0.950056i | \(-0.398974\pi\) | ||||
0.312080 | + | 0.950056i | \(0.398974\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9282i | 1.01031i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 29.8564i | − | 1.58910i | −0.607201 | − | 0.794548i | \(-0.707708\pi\) | ||
0.607201 | − | 0.794548i | \(-0.292292\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.32051i | 0.176234i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.8564 | + | 18.9282i | 1.15676 | + | 1.00179i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 0.392305i | − | 0.0207051i | −0.999946 | − | 0.0103525i | \(-0.996705\pi\) | ||
0.999946 | − | 0.0103525i | \(-0.00329537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3923 | 0.915384 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 51.5167i | 2.70392i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 5.07180i | − | 0.265470i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 13.0718i | − | 0.680491i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | + | 13.8564i | −0.623009 | + | 0.719389i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.0718i | − | 0.883944i | −0.897029 | − | 0.441972i | \(-0.854279\pi\) | ||
0.897029 | − | 0.441972i | \(-0.145721\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 18.9282i | − | 0.977448i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 32.7846i | − | 1.68849i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.4641 | 1.10254 | 0.551268 | − | 0.834328i | \(-0.314144\pi\) | ||||
0.551268 | + | 0.834328i | \(0.314144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −58.6410 | −3.00427 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.92820 | −0.354015 | −0.177007 | − | 0.984210i | \(-0.556642\pi\) | ||||
−0.177007 | + | 0.984210i | \(0.556642\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | − | 6.92820i | −0.407718 | − | 0.353094i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.3205 | −0.575454 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.85641i | 0.0941235i | 0.998892 | + | 0.0470618i | \(0.0149858\pi\) | ||||
−0.998892 | + | 0.0470618i | \(0.985014\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.8564 | 1.10533 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.3205 | −1.47902 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2.53590i | − | 0.127595i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.9090 | −1.50109 | −0.750544 | − | 0.660821i | \(-0.770208\pi\) | ||||
−0.750544 | + | 0.660821i | \(0.770208\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | − | 6.00000i | −0.346844 | − | 0.300376i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.3205 | −1.16457 | −0.582285 | − | 0.812985i | \(-0.697841\pi\) | ||||
−0.582285 | + | 0.812985i | \(0.697841\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.7846 | −1.63312 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.80385 | −0.0896339 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.8564i | 1.08338i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.07180i | − | 0.250784i | −0.992107 | − | 0.125392i | \(-0.959981\pi\) | ||
0.992107 | − | 0.125392i | \(-0.0400189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 54.2487i | 2.67589i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.58846 | − | 7.60770i | 0.324197 | − | 0.374350i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.85641i | 0.385656i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.4641 | −0.561399 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3.12436i | − | 0.152635i | −0.997084 | − | 0.0763174i | \(-0.975684\pi\) | ||
0.997084 | − | 0.0763174i | \(-0.0243162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000i | 0.974740i | 0.873195 | + | 0.487370i | \(0.162044\pi\) | ||||
−0.873195 | + | 0.487370i | \(0.837956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.9282 | 1.50378 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.8564i | 0.866163i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.3205 | + | 20.1962i | 1.12856 | + | 0.977360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 70.6410i | 3.41058i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.46410i | 0.263197i | 0.991303 | + | 0.131598i | \(0.0420109\pi\) | ||||
−0.991303 | + | 0.131598i | \(0.957989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.85641i | 0.0892132i | 0.999005 | + | 0.0446066i | \(0.0142034\pi\) | ||||
−0.999005 | + | 0.0446066i | \(0.985797\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.8564 | −0.664364 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.92820 | −0.331421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | −0.190910 | −0.0954548 | − | 0.995434i | \(-0.530431\pi\) | ||||
−0.0954548 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.46410 | − | 30.9282i | −0.212576 | − | 1.47277i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.46410 | 0.259607 | 0.129804 | − | 0.991540i | \(-0.458565\pi\) | ||||
0.129804 | + | 0.991540i | \(0.458565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 10.9282i | − | 0.518047i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 32.7846 | 1.55066 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.14359 | 0.195548 | 0.0977741 | − | 0.995209i | \(-0.468828\pi\) | ||||
0.0977741 | + | 0.995209i | \(0.468828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.0000i | − | 0.753411i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.9282 | −1.45313 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.92820 | − | 6.00000i | −0.324799 | − | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.3923 | 0.579688 | 0.289844 | − | 0.957074i | \(-0.406397\pi\) | ||||
0.289844 | + | 0.957074i | \(0.406397\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.0000 | −0.746816 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5167 | 0.815832 | 0.407916 | − | 0.913019i | \(-0.366256\pi\) | ||||
0.407916 | + | 0.913019i | \(0.366256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4641i | 1.27637i | 0.769885 | + | 0.638183i | \(0.220313\pi\) | ||||
−0.769885 | + | 0.638183i | \(0.779687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.8564i | 0.642575i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.5885i | − | 0.582524i | −0.956643 | − | 0.291262i | \(-0.905925\pi\) | ||
0.956643 | − | 0.291262i | \(-0.0940752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.07180 | − | 4.39230i | −0.234194 | − | 0.202818i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 52.6410i | 2.42557i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.8564 | −0.637118 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.66025i | − | 0.259710i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 30.9282i | − | 1.41611i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0718 | −0.780030 | −0.390015 | − | 0.920808i | \(-0.627530\pi\) | ||||
−0.390015 | + | 0.920808i | \(0.627530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9282i | 0.863052i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −29.8564 | − | 25.8564i | −1.35851 | − | 1.17651i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.78461i | 0.398889i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.3923i | − | 0.742806i | −0.928472 | − | 0.371403i | \(-0.878877\pi\) | ||
0.928472 | − | 0.371403i | \(-0.121123\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 44.7846i | − | 2.02523i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.3205 | −0.871922 | −0.435961 | − | 0.899965i | \(-0.643591\pi\) | ||||
−0.435961 | + | 0.899965i | \(0.643591\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.7128 | 1.24812 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.8564 | 0.802586 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.85641 | + | 9.07180i | −0.352408 | + | 0.406926i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.3923 | −0.733820 | −0.366910 | − | 0.930256i | \(-0.619584\pi\) | ||||
−0.366910 | + | 0.930256i | \(0.619584\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.8564i | 0.619059i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.53590 | 0.201845 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.6603i | 1.13961i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.1962 | −1.87031 | −0.935156 | − | 0.354237i | \(-0.884741\pi\) | ||||
−0.935156 | + | 0.354237i | \(0.884741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | − | 13.8564i | 0.530849 | − | 0.612971i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.07180 | 0.223925 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.8564 | 0.610586 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.8564 | 1.66492 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.92820i | 0.391905i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.0718i | − | 0.572686i | −0.958127 | − | 0.286343i | \(-0.907560\pi\) | ||
0.958127 | − | 0.286343i | \(-0.0924397\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 29.3731i | − | 1.28439i | −0.766539 | − | 0.642197i | \(-0.778023\pi\) | ||
0.766539 | − | 0.642197i | \(-0.221977\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.1244 | − | 24.3923i | 0.921942 | − | 1.06457i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 27.7128i | − | 1.20719i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.85641 | −0.298105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.9808i | 0.736902i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 13.8564i | − | 0.600188i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.14359 | −0.265611 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.07180i | 0.0462514i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.46410 | − | 37.8564i | −0.235356 | − | 1.63059i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.0000i | 1.20381i | 0.798566 | + | 0.601907i | \(0.205592\pi\) | ||||
−0.798566 | + | 0.601907i | \(0.794408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.7128i | 1.96172i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 5.07180i | − | 0.217252i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4641 | 0.917739 | 0.458869 | − | 0.888504i | \(-0.348255\pi\) | ||||
0.458869 | + | 0.888504i | \(0.348255\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −52.0526 | −2.22155 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.78461 | −0.374237 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | − | 6.92820i | 0.255146 | − | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.00000 | 0.339581 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.9282i | 1.31047i | 0.755425 | + | 0.655235i | \(0.227430\pi\) | ||||
−0.755425 | + | 0.655235i | \(0.772570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −59.7128 | −2.52108 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.9808i | 1.22139i | 0.791865 | + | 0.610697i | \(0.209111\pi\) | ||||
−0.791865 | + | 0.610697i | \(0.790889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.92820 | −0.291472 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.92820 | − | 4.26795i | −0.206965 | − | 0.179237i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.3923 | 1.19027 | 0.595134 | − | 0.803627i | \(-0.297099\pi\) | ||||
0.595134 | + | 0.803627i | \(0.297099\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.2487 | 1.26587 | 0.632935 | − | 0.774205i | \(-0.281850\pi\) | ||||
0.632935 | + | 0.774205i | \(0.281850\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.3205 | −1.30843 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 24.3923i | − | 1.01723i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.1436i | 0.422283i | 0.977455 | + | 0.211142i | \(0.0677181\pi\) | ||||
−0.977455 | + | 0.211142i | \(0.932282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0000i | 0.498703i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.5885 | + | 21.4641i | −0.771179 | + | 0.890481i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 37.8564i | − | 1.56785i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.4641 | 0.639362 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3.80385i | − | 0.157002i | −0.996914 | − | 0.0785008i | \(-0.974987\pi\) | ||
0.996914 | − | 0.0785008i | \(-0.0250133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.78461i | 0.361964i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.7846 | −1.34858 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.7128i | 0.809508i | 0.914426 | + | 0.404754i | \(0.132643\pi\) | ||||
−0.914426 | + | 0.404754i | \(0.867357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.07180 | − | 5.85641i | 0.207923 | − | 0.240089i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 45.8564i | − | 1.87678i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.5359i | − | 0.512203i | −0.966650 | − | 0.256101i | \(-0.917562\pi\) | ||
0.966650 | − | 0.256101i | \(-0.0824381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.6410i | − | 1.41304i | −0.707695 | − | 0.706518i | \(-0.750265\pi\) | ||
0.707695 | − | 0.706518i | \(-0.249735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3205 | 0.461007 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.8038 | 0.561206 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.00000 | −0.324710 | −0.162355 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −37.8564 | − | 32.7846i | −1.53402 | − | 1.32850i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.7846 | 1.32632 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.8564i | 1.04433i | 0.852844 | + | 0.522165i | \(0.174876\pi\) | ||||
−0.852844 | + | 0.522165i | \(0.825124\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.85641 | −0.236153 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.39230 | 0.176828 | 0.0884138 | − | 0.996084i | \(-0.471820\pi\) | ||||
0.0884138 | + | 0.996084i | \(0.471820\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 24.1962i | − | 0.972525i | −0.873813 | − | 0.486263i | \(-0.838360\pi\) | ||
0.873813 | − | 0.486263i | \(-0.161640\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.8564 | 0.877067 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.8564 | − | 29.8564i | 1.03592 | − | 1.19617i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.9282 | 0.755920 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 24.2487i | − | 0.965326i | −0.875806 | − | 0.482663i | \(-0.839670\pi\) | ||
0.875806 | − | 0.482663i | \(-0.160330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.7846i | 0.826114i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.7128i | 0.623544i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.73205 | − | 32.7846i | −0.187491 | − | 1.29897i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 20.2487i | − | 0.801027i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.4641 | −1.32175 | −0.660876 | − | 0.750495i | \(-0.729815\pi\) | ||||
−0.660876 | + | 0.750495i | \(0.729815\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 22.7321i | − | 0.896465i | −0.893917 | − | 0.448232i | \(-0.852054\pi\) | ||
0.893917 | − | 0.448232i | \(-0.147946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.07180i | 0.199702i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.6410 | 0.890110 | 0.445055 | − | 0.895503i | \(-0.353184\pi\) | ||||
0.445055 | + | 0.895503i | \(0.353184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.7846i | 0.815867i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.7846 | + | 37.8564i | −1.28493 | + | 1.48371i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0000i | 0.469596i | 0.972044 | + | 0.234798i | \(0.0754429\pi\) | ||||
−0.972044 | + | 0.234798i | \(0.924557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.85641i | 0.306975i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.9282i | 1.20662i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.1051 | 1.40646 | 0.703228 | − | 0.710965i | \(-0.251741\pi\) | ||||
0.703228 | + | 0.710965i | \(0.251741\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.1962 | 0.552166 | 0.276083 | − | 0.961134i | \(-0.410963\pi\) | ||||
0.276083 | + | 0.961134i | \(0.410963\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −51.7128 | −2.00836 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.60770 | + | 1.85641i | −0.0623437 | + | 0.0719884i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.8564 | −1.46581 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 21.8564i | − | 0.845017i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −63.7128 | −2.45961 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0000 | 1.15642 | 0.578208 | − | 0.815890i | \(-0.303752\pi\) | ||||
0.578208 | + | 0.815890i | \(0.303752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.8564i | 0.687293i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.8756 | 0.725450 | 0.362725 | − | 0.931896i | \(-0.381846\pi\) | ||||
0.362725 | + | 0.931896i | \(0.381846\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.7846 | + | 24.0000i | −0.797640 | + | 0.921035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.46410 | −0.132745 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.4641 | 1.12741 | 0.563706 | − | 0.825975i | \(-0.309375\pi\) | ||||
0.563706 | + | 0.825975i | \(0.309375\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.5359 | 0.555388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.928203i | 0.0354132i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 32.7846i | − | 1.24899i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32.9808i | − | 1.25465i | −0.778759 | − | 0.627324i | \(-0.784150\pi\) | ||
0.778759 | − | 0.627324i | \(-0.215850\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 48.7846 | + | 42.2487i | 1.85317 | + | 1.60490i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.07180i | 0.116520i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.7128 | 0.443654 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 54.2487i | − | 2.05187i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.85641i | 0.0701155i | 0.999385 | + | 0.0350578i | \(0.0111615\pi\) | ||||
−0.999385 | + | 0.0350578i | \(0.988838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.07180 | 0.191286 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 13.8564i | − | 0.521862i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.3923 | + | 10.7321i | 0.466061 | + | 0.403620i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 30.9282i | − | 1.16153i | −0.814070 | − | 0.580767i | \(-0.802753\pi\) | ||
0.814070 | − | 0.580767i | \(-0.197247\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.4641i | 0.579949i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.8564i | 1.41773i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.9282 | 0.707875 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.07180 | 0.0400270 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.0718 | 0.636671 | 0.318335 | − | 0.947978i | \(-0.396876\pi\) | ||||
0.318335 | + | 0.947978i | \(0.396876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.8564 | + | 32.7846i | 1.40985 | + | 1.22096i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −32.7846 | −1.21927 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 30.9282i | − | 1.14864i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.78461 | 0.325803 | 0.162902 | − | 0.986642i | \(-0.447915\pi\) | ||||
0.162902 | + | 0.986642i | \(0.447915\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.7846 | 1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 10.1436i | − | 0.375174i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.19615 | −0.0811167 | −0.0405584 | − | 0.999177i | \(-0.512914\pi\) | ||||
−0.0405584 | + | 0.999177i | \(0.512914\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.8564 | + | 2.00000i | −0.511101 | + | 0.0737711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.8564 | 0.510407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3205 | 0.416432 | 0.208216 | − | 0.978083i | \(-0.433234\pi\) | ||||
0.208216 | + | 0.978083i | \(0.433234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.3923 | 0.602186 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 10.5359i | − | 0.386525i | −0.981147 | − | 0.193262i | \(-0.938093\pi\) | ||
0.981147 | − | 0.193262i | \(-0.0619068\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 8.78461i | − | 0.321843i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 47.9090i | − | 1.75290i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.7846 | − | 14.5359i | −0.613296 | − | 0.531130i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 26.5359i | − | 0.968309i | −0.874983 | − | 0.484154i | \(-0.839127\pi\) | ||
0.874983 | − | 0.484154i | \(-0.160873\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 60.2487 | 2.19559 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.28719i | 0.301602i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 29.5692i | − | 1.07471i | −0.843356 | − | 0.537356i | \(-0.819423\pi\) | ||
0.843356 | − | 0.537356i | \(-0.180577\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 81.5692 | 2.96078 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 16.7846i | − | 0.608442i | −0.952602 | − | 0.304221i | \(-0.901604\pi\) | ||
0.952602 | − | 0.304221i | \(-0.0983961\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0000 | − | 13.8564i | 0.434429 | − | 0.501636i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.0718i | 0.472612i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.0000i | 0.649942i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.85641i | 0.0669437i | 0.999440 | + | 0.0334719i | \(0.0106564\pi\) | ||||
−0.999440 | + | 0.0334719i | \(0.989344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −59.7128 | −2.15050 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.4449 | 1.31083 | 0.655415 | − | 0.755269i | \(-0.272494\pi\) | ||||
0.655415 | + | 0.755269i | \(0.272494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.9282 | −1.11097 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.8564 | + | 18.9282i | 0.784094 | + | 0.679046i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.71281 | −0.133025 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 24.7846i | − | 0.886863i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.7128 | 0.990375 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.1051 | 0.503433 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 20.5885i | − | 0.733899i | −0.930241 | − | 0.366950i | \(-0.880402\pi\) | ||
0.930241 | − | 0.366950i | \(-0.119598\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.3205 | 1.11504 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.9282 | − | 16.3923i | −0.673009 | − | 0.582843i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.1769 | −1.95939 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.8564 | −0.491436 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.1244 | 1.45670 | 0.728350 | − | 0.685206i | \(-0.240288\pi\) | ||||
0.728350 | + | 0.685206i | \(0.240288\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.7128i | 0.980409i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 66.6410i | 2.35464i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.8564i | 1.33592i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.92820 | + | 8.00000i | −0.244187 | + | 0.281963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.07180i | 0.108132i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.1769 | −1.30707 | −0.653535 | − | 0.756896i | \(-0.726715\pi\) | ||||
−0.653535 | + | 0.756896i | \(0.726715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.3731i | 1.73372i | 0.498549 | + | 0.866861i | \(0.333866\pi\) | ||||
−0.498549 | + | 0.866861i | \(0.666134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | −0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.21539i | 0.112492i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 42.2487 | + | 36.5885i | 1.47629 | + | 1.27850i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.92820i | − | 0.241796i | −0.992665 | − | 0.120898i | \(-0.961423\pi\) | ||
0.992665 | − | 0.120898i | \(-0.0385774\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.5359i | 0.715836i | 0.933753 | + | 0.357918i | \(0.116513\pi\) | ||||
−0.933753 | + | 0.357918i | \(0.883487\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 66.6410i | 2.32014i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.3205 | −1.50640 | −0.753201 | − | 0.657791i | \(-0.771491\pi\) | ||||
−0.753201 | + | 0.657791i | \(0.771491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.19615 | −0.0762755 | −0.0381378 | − | 0.999272i | \(-0.512143\pi\) | ||||
−0.0381378 | + | 0.999272i | \(0.512143\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 78.6410 | 2.72803 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.7128 | − | 4.00000i | 0.960192 | − | 0.138592i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.71281 | 0.128487 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 27.7128i | − | 0.957895i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.07180 | −0.175098 | −0.0875489 | − | 0.996160i | \(-0.527903\pi\) | ||||
−0.0875489 | + | 0.996160i | \(0.527903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.3923i | 0.564581i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.87564 | 0.236529 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.7128 | + | 32.6603i | 1.29583 | + | 1.12222i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.1769 | −1.48183 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.8564 | 0.749228 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.3731 | −1.75898 | −0.879490 | − | 0.475917i | \(-0.842116\pi\) | ||||
−0.879490 | + | 0.475917i | \(0.842116\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4.14359i | − | 0.141708i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0718i | 0.719799i | 0.932991 | + | 0.359899i | \(0.117189\pi\) | ||||
−0.932991 | + | 0.359899i | \(0.882811\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.5167i | 0.665900i | 0.942945 | + | 0.332950i | \(0.108044\pi\) | ||||
−0.942945 | + | 0.332950i | \(0.891956\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0000 | − | 13.8564i | −0.545279 | − | 0.472225i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.1769i | 1.33360i | 0.745238 | + | 0.666799i | \(0.232336\pi\) | ||||
−0.745238 | + | 0.666799i | \(0.767664\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.39230 | 0.0813408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.73205i | 0.0927853i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.9282i | 0.642095i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | 0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 53.5692i | − | 1.81304i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.8564 | − | 12.0000i | −0.468432 | − | 0.405674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 29.5692i | − | 0.998482i | −0.866463 | − | 0.499241i | \(-0.833612\pi\) | ||
0.866463 | − | 0.499241i | \(-0.166388\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 4.92820i | − | 0.166224i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 35.7128i | − | 1.20320i | −0.798799 | − | 0.601598i | \(-0.794531\pi\) | ||
0.798799 | − | 0.601598i | \(-0.205469\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.53590 | 0.0853398 | 0.0426699 | − | 0.999089i | \(-0.486414\pi\) | ||||
0.0426699 | + | 0.999089i | \(0.486414\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.60770 | 0.255730 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.0718 | 0.976135 | 0.488068 | − | 0.872806i | \(-0.337702\pi\) | ||||
0.488068 | + | 0.872806i | \(0.337702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.1769 | + | 42.9282i | −1.24687 | + | 1.43977i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.4641 | 0.451064 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 8.78461i | − | 0.293966i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.287187 | 0.00959961 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 70.6410 | 2.35863 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.0000i | 1.60089i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.7128 | 0.923248 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.0000 | + | 13.8564i | −0.399335 | + | 0.461112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.2487 | 0.407161 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.1051 | −1.46449 | −0.732243 | − | 0.681043i | \(-0.761527\pi\) | ||||
−0.732243 | + | 0.681043i | \(0.761527\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.6603 | −0.917433 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.3923i | − | 1.07320i | −0.843835 | − | 0.536602i | \(-0.819707\pi\) | ||
0.843835 | − | 0.536602i | \(-0.180293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 58.6410i | − | 1.94073i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.3205i | 0.770952i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.5885 | + | 21.4641i | −0.613845 | + | 0.708807i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.4641i | − | 0.905957i | −0.891521 | − | 0.452979i | \(-0.850361\pi\) | ||
0.891521 | − | 0.452979i | \(-0.149639\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.2487 | 1.19444 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 21.4641i | − | 0.706500i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.8564i | 0.587115i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −84.4974 | −2.77526 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.00000i | 0.131236i | 0.997845 | + | 0.0656179i | \(0.0209018\pi\) | ||||
−0.997845 | + | 0.0656179i | \(0.979098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.78461 | + | 1.26795i | −0.287904 | + | 0.0415554i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 70.6410i | − | 2.31268i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.0000i | 0.523256i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.9282i | 1.01038i | 0.863008 | + | 0.505190i | \(0.168578\pi\) | ||||
−0.863008 | + | 0.505190i | \(0.831422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −89.5692 | −2.92298 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.1244 | 0.558238 | 0.279119 | − | 0.960257i | \(-0.409958\pi\) | ||||
0.279119 | + | 0.960257i | \(0.409958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.07180 | − | 5.85641i | 0.164986 | − | 0.190509i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.4641 | −0.437525 | −0.218762 | − | 0.975778i | \(-0.570202\pi\) | ||||
−0.218762 | + | 0.975778i | \(0.570202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.7846i | 1.06423i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.07180 | 0.164464 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.7128 | −1.09207 | −0.546033 | − | 0.837764i | \(-0.683863\pi\) | ||||
−0.546033 | + | 0.837764i | \(0.683863\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.39230i | 0.271569i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 103.426 | 3.34328 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.7128 | + | 34.3923i | 1.28239 | + | 1.11059i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.4641 | 1.20726 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.21539 | 0.103507 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.3205i | 0.364043i | 0.983295 | + | 0.182021i | \(0.0582640\pi\) | ||||
−0.983295 | + | 0.182021i | \(0.941736\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.8564i | 0.445132i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 55.5167i | − | 1.78161i | −0.454381 | − | 0.890807i | \(-0.650140\pi\) | ||
0.454381 | − | 0.890807i | \(-0.349860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.26795 | + | 8.39230i | −0.233000 | + | 0.269045i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 57.7128i | 1.84829i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.8564 | 1.01918 | 0.509588 | − | 0.860418i | \(-0.329798\pi\) | ||||
0.509588 | + | 0.860418i | \(0.329798\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 81.5692i | 2.60696i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.9282i | 0.987462i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.07180 | 0.161765 | 0.0808826 | − | 0.996724i | \(-0.474226\pi\) | ||||
0.0808826 | + | 0.996724i | \(0.474226\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.78461i | 0.279901i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32.7846 | − | 37.8564i | 1.04355 | − | 1.20498i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.8564i | 0.440608i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 31.1769i | − | 0.990367i | −0.868788 | − | 0.495184i | \(-0.835101\pi\) | ||
0.868788 | − | 0.495184i | \(-0.164899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.9282i | 0.981477i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.2872 | −0.389530 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.87564 | 0.0910726 | 0.0455363 | − | 0.998963i | \(-0.485500\pi\) | ||||
0.0455363 | + | 0.998963i | \(0.485500\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.0000 | −0.506218 |
(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 | 896.2.e.b.447.4 | yes | 4 | |
4.3 | odd | 2 | 896.2.e.a.447.1 | ✓ | 4 | ||
7.6 | odd | 2 | 896.2.e.e.447.1 | yes | 4 | ||
8.3 | odd | 2 | 896.2.e.e.447.4 | yes | 4 | ||
8.5 | even | 2 | 896.2.e.f.447.1 | yes | 4 | ||
16.3 | odd | 4 | 1792.2.f.i.1791.3 | 4 | |||
16.5 | even | 4 | 1792.2.f.h.1791.4 | 4 | |||
16.11 | odd | 4 | 1792.2.f.b.1791.2 | 4 | |||
16.13 | even | 4 | 1792.2.f.a.1791.1 | 4 | |||
28.27 | even | 2 | 896.2.e.f.447.4 | yes | 4 | ||
56.13 | odd | 2 | 896.2.e.a.447.4 | yes | 4 | ||
56.27 | even | 2 | inner | 896.2.e.b.447.1 | yes | 4 | |
112.13 | odd | 4 | 1792.2.f.i.1791.4 | 4 | |||
112.27 | even | 4 | 1792.2.f.h.1791.3 | 4 | |||
112.69 | odd | 4 | 1792.2.f.b.1791.1 | 4 | |||
112.83 | even | 4 | 1792.2.f.a.1791.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.e.a.447.1 | ✓ | 4 | 4.3 | odd | 2 | ||
896.2.e.a.447.4 | yes | 4 | 56.13 | odd | 2 | ||
896.2.e.b.447.1 | yes | 4 | 56.27 | even | 2 | inner | |
896.2.e.b.447.4 | yes | 4 | 1.1 | even | 1 | trivial | |
896.2.e.e.447.1 | yes | 4 | 7.6 | odd | 2 | ||
896.2.e.e.447.4 | yes | 4 | 8.3 | odd | 2 | ||
896.2.e.f.447.1 | yes | 4 | 8.5 | even | 2 | ||
896.2.e.f.447.4 | yes | 4 | 28.27 | even | 2 | ||
1792.2.f.a.1791.1 | 4 | 16.13 | even | 4 | |||
1792.2.f.a.1791.2 | 4 | 112.83 | even | 4 | |||
1792.2.f.b.1791.1 | 4 | 112.69 | odd | 4 | |||
1792.2.f.b.1791.2 | 4 | 16.11 | odd | 4 | |||
1792.2.f.h.1791.3 | 4 | 112.27 | even | 4 | |||
1792.2.f.h.1791.4 | 4 | 16.5 | even | 4 | |||
1792.2.f.i.1791.3 | 4 | 16.3 | odd | 4 | |||
1792.2.f.i.1791.4 | 4 | 112.13 | odd | 4 |