Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(449,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.g (of order \(2\), degree \(1\), not 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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.3 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.449 |
Dual form | 1400.2.g.k.449.2 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.56155i | 0.901563i | 0.892634 | + | 0.450781i | \(0.148855\pi\) | ||||
−0.892634 | + | 0.450781i | \(0.851145\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.561553 | 0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.56155 | 0.470826 | 0.235413 | − | 0.971895i | \(-0.424356\pi\) | ||||
0.235413 | + | 0.971895i | \(0.424356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.68466i | − 1.85399i | −0.375073 | − | 0.926995i | \(-0.622382\pi\) | ||||
0.375073 | − | 0.926995i | \(-0.377618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.56155i | 1.83395i | 0.398949 | + | 0.916973i | \(0.369375\pi\) | ||||
−0.398949 | + | 0.916973i | \(0.630625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.12311 | 1.63415 | 0.817076 | − | 0.576530i | \(-0.195593\pi\) | ||||
0.817076 | + | 0.576530i | \(0.195593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56155 | −0.340759 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3.12311i | − 0.651213i | −0.945505 | − | 0.325606i | \(-0.894432\pi\) | ||||
0.945505 | − | 0.325606i | \(-0.105568\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155i | 1.07032i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.438447 | −0.0814176 | −0.0407088 | − | 0.999171i | \(-0.512962\pi\) | ||||
−0.0407088 | + | 0.999171i | \(0.512962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.24621 | 1.12185 | 0.560926 | − | 0.827866i | \(-0.310445\pi\) | ||||
0.560926 | + | 0.827866i | \(0.310445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.43845i | 0.424479i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 8.24621i | − 1.35567i | −0.735215 | − | 0.677834i | \(-0.762919\pi\) | ||||
0.735215 | − | 0.677834i | \(-0.237081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.4384 | 1.67149 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.12311 | −0.175400 | −0.0876998 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0876998 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.12311i | 1.08626i | 0.839648 | + | 0.543132i | \(0.182762\pi\) | ||||
−0.839648 | + | 0.543132i | \(0.817238\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.43845i | 0.355684i | 0.984059 | + | 0.177842i | \(0.0569116\pi\) | ||||
−0.984059 | + | 0.177842i | \(0.943088\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.8078 | −1.65342 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.1231i | 1.80260i | 0.433198 | + | 0.901299i | \(0.357385\pi\) | ||||
−0.433198 | + | 0.901299i | \(0.642615\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.1231i | 1.47329i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.87689 | −0.880496 | −0.440248 | − | 0.897876i | \(-0.645109\pi\) | ||||
−0.440248 | + | 0.897876i | \(0.645109\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.561553i | 0.0707490i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.24621i | 0.274418i | 0.990542 | + | 0.137209i | \(0.0438133\pi\) | ||||
−0.990542 | + | 0.137209i | \(0.956187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.87689 | 0.587109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24621i | 0.496981i | 0.968634 | + | 0.248491i | \(0.0799345\pi\) | ||||
−0.968634 | + | 0.248491i | \(0.920065\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.56155i | 0.177955i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.684658 | −0.0770301 | −0.0385150 | − | 0.999258i | \(-0.512263\pi\) | ||||
−0.0385150 | + | 0.999258i | \(0.512263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 12.0000i | − 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 0.684658i | − 0.0734031i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.12311 | −0.543048 | −0.271524 | − | 0.962432i | \(-0.587528\pi\) | ||||
−0.271524 | + | 0.962432i | \(0.587528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.68466 | 0.700743 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.75379i | 1.01142i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.31534i | 0.133553i | 0.997768 | + | 0.0667764i | \(0.0212714\pi\) | ||||
−0.997768 | + | 0.0667764i | \(0.978729\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.876894 | 0.0881312 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8078i | 1.16345i | 0.813384 | + | 0.581727i | \(0.197623\pi\) | ||||
−0.813384 | + | 0.581727i | \(0.802377\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1231i | 1.46201i | 0.682374 | + | 0.731003i | \(0.260947\pi\) | ||||
−0.682374 | + | 0.731003i | \(0.739053\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.43845 | 0.425126 | 0.212563 | − | 0.977147i | \(-0.431819\pi\) | ||||
0.212563 | + | 0.977147i | \(0.431819\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.8769 | 1.22222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 8.24621i | − 0.775738i | −0.921714 | − | 0.387869i | \(-0.873211\pi\) | ||||
0.921714 | − | 0.387869i | \(-0.126789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 3.75379i | − 0.347038i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.56155 | −0.693166 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.75379i | − 0.158134i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 6.24621i | − 0.554262i | −0.960832 | − | 0.277131i | \(-0.910616\pi\) | ||||
0.960832 | − | 0.277131i | \(-0.0893835\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.1231 | −0.979335 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.1231 | 1.32131 | 0.660656 | − | 0.750689i | \(-0.270278\pi\) | ||||
0.660656 | + | 0.750689i | \(0.270278\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.12311i | 0.617652i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 7.36932i | − 0.629603i | −0.949157 | − | 0.314802i | \(-0.898062\pi\) | ||||
0.949157 | − | 0.314802i | \(-0.101938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.3693 | 1.81252 | 0.906261 | − | 0.422719i | \(-0.138924\pi\) | ||||
0.906261 | + | 0.422719i | \(0.138924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.80776 | −0.320672 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 10.4384i | − 0.872907i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.56155i | − 0.128795i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.246211 | 0.0201704 | 0.0100852 | − | 0.999949i | \(-0.496790\pi\) | ||||
0.0100852 | + | 0.999949i | \(0.496790\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.8078 | −1.61193 | −0.805966 | − | 0.591961i | \(-0.798354\pi\) | ||||
−0.805966 | + | 0.591961i | \(0.798354\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.24621i | 0.343286i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.24621i | 0.338885i | 0.985540 | + | 0.169442i | \(0.0541966\pi\) | ||||
−0.985540 | + | 0.169442i | \(0.945803\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.4924 | −1.62515 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.12311 | 0.246135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 19.6155i | − 1.53641i | −0.640206 | − | 0.768203i | \(-0.721151\pi\) | ||||
0.640206 | − | 0.768203i | \(-0.278849\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.19224i | 0.324405i | 0.986757 | + | 0.162202i | \(0.0518598\pi\) | ||||
−0.986757 | + | 0.162202i | \(0.948140\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −31.6847 | −2.43728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.1771i | 1.76212i | 0.473004 | + | 0.881060i | \(0.343170\pi\) | ||||
−0.473004 | + | 0.881060i | \(0.656830\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.24621i | 0.469494i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.12311 | −0.380797 | −0.190399 | − | 0.981707i | \(-0.560978\pi\) | ||||
−0.190399 | + | 0.981707i | \(0.560978\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 10.7386i | − 0.793823i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.8078i | 0.863469i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.56155 | −0.404543 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.684658 | −0.0495401 | −0.0247701 | − | 0.999693i | \(-0.507885\pi\) | ||||
−0.0247701 | + | 0.999693i | \(0.507885\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 13.1231i | − 0.944622i | −0.881432 | − | 0.472311i | \(-0.843420\pi\) | ||||
0.881432 | − | 0.472311i | \(-0.156580\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 13.1231i | − 0.934983i | −0.883998 | − | 0.467491i | \(-0.845158\pi\) | ||||
0.883998 | − | 0.467491i | \(-0.154842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2462 | 1.00989 | 0.504944 | − | 0.863152i | \(-0.331513\pi\) | ||||
0.504944 | + | 0.863152i | \(0.331513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.50758 | −0.247405 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.438447i | − 0.0307730i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1.75379i | − 0.121897i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.1231 | 0.769401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.5616 | −1.20899 | −0.604494 | − | 0.796610i | \(-0.706624\pi\) | ||||
−0.604494 | + | 0.796610i | \(0.706624\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.24621i | 0.424020i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.63068 | −0.448060 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 50.5464 | 3.40012 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 24.6847i | − 1.65301i | −0.562932 | − | 0.826503i | \(-0.690327\pi\) | ||||
0.562932 | − | 0.826503i | \(-0.309673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 11.3153i | − 0.751026i | −0.926817 | − | 0.375513i | \(-0.877467\pi\) | ||||
0.926817 | − | 0.375513i | \(-0.122533\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3693 | 0.751306 | 0.375653 | − | 0.926760i | \(-0.377419\pi\) | ||||
0.375653 | + | 0.926760i | \(0.377419\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.43845 | −0.160438 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8769i | 0.712569i | 0.934378 | + | 0.356285i | \(0.115957\pi\) | ||||
−0.934378 | + | 0.356285i | \(0.884043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.06913i | − 0.0694475i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0540 | 1.16781 | 0.583907 | − | 0.811820i | \(-0.301523\pi\) | ||||
0.583907 | + | 0.811820i | \(0.301523\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.75379i | 0.369106i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 47.6155i | − 3.02970i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.7386 | 1.18751 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3693 | 0.843864 | 0.421932 | − | 0.906628i | \(-0.361352\pi\) | ||||
0.421932 | + | 0.906628i | \(0.361352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.87689i | − 0.306608i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 18.4924i | − 1.15353i | −0.816912 | − | 0.576763i | \(-0.804316\pi\) | ||||
0.816912 | − | 0.576763i | \(-0.195684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.24621 | 0.512395 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.246211 | −0.0152401 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 9.36932i | − 0.577737i | −0.957369 | − | 0.288868i | \(-0.906721\pi\) | ||||
0.957369 | − | 0.288868i | \(-0.0932790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 8.00000i | − 0.489592i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.24621 | −0.258896 | −0.129448 | − | 0.991586i | \(-0.541321\pi\) | ||||
−0.129448 | + | 0.991586i | \(0.541321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.24621 | −0.379430 | −0.189715 | − | 0.981839i | \(-0.560756\pi\) | ||||
−0.189715 | + | 0.981839i | \(0.560756\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.4384i | 0.631764i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 8.24621i | − 0.495467i | −0.968828 | − | 0.247733i | \(-0.920314\pi\) | ||||
0.968828 | − | 0.247733i | \(-0.0796857\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.50758 | 0.209993 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.5616 | −1.16694 | −0.583472 | − | 0.812133i | \(-0.698306\pi\) | ||||
−0.583472 | + | 0.812133i | \(0.698306\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.68466i | 0.278474i | 0.990259 | + | 0.139237i | \(0.0444650\pi\) | ||||
−0.990259 | + | 0.139237i | \(0.955535\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.12311i | − 0.0662948i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −40.1771 | −2.36336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.05398 | −0.120406 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 32.0540i | − 1.87261i | −0.351184 | − | 0.936307i | \(-0.614221\pi\) | ||||
0.351184 | − | 0.936307i | \(-0.385779\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.68466i | 0.503935i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.8769 | −1.20734 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.12311 | −0.410569 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.36932i | 0.538253i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 28.6847i | − 1.63712i | −0.574421 | − | 0.818560i | \(-0.694773\pi\) | ||||
0.574421 | − | 0.818560i | \(-0.305227\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4384 | −1.04893 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.8769 | −0.730182 | −0.365091 | − | 0.930972i | \(-0.618962\pi\) | ||||
−0.365091 | + | 0.930972i | \(0.618962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 26.6847i | − 1.50831i | −0.656699 | − | 0.754153i | \(-0.728048\pi\) | ||||
0.656699 | − | 0.754153i | \(-0.271952\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 10.0000i | − 0.561656i | −0.959758 | − | 0.280828i | \(-0.909391\pi\) | ||||
0.959758 | − | 0.280828i | \(-0.0906090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.684658 | −0.0383335 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.6155 | −1.31809 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 53.8617i | 2.99695i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.93087i | 0.383278i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.43845 | −0.134436 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 4.63068i | − 0.253760i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000i | 0.108947i | 0.998515 | + | 0.0544735i | \(0.0173480\pi\) | ||||
−0.998515 | + | 0.0544735i | \(0.982652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.8769 | 0.699377 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.75379 | 0.528197 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.1231i | 0.811851i | 0.913906 | + | 0.405925i | \(0.133051\pi\) | ||||
−0.913906 | + | 0.405925i | \(0.866949\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.7538 | 0.629166 | 0.314583 | − | 0.949230i | \(-0.398135\pi\) | ||||
0.314583 | + | 0.949230i | \(0.398135\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.1771 | 1.98437 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.19224i | 0.116681i | 0.998297 | + | 0.0583405i | \(0.0185809\pi\) | ||||
−0.998297 | + | 0.0583405i | \(0.981419\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 11.8078i | − 0.624933i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.0000 | −1.68890 | −0.844448 | − | 0.535638i | \(-0.820071\pi\) | ||||
−0.844448 | + | 0.535638i | \(0.820071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.7386 | 1.67045 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 13.3693i | − 0.701707i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.9309i | 0.779385i | 0.920945 | + | 0.389693i | \(0.127419\pi\) | ||||
−0.920945 | + | 0.389693i | \(0.872581\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.630683 | −0.0328321 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.1231 | −0.681318 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 15.3693i | − 0.795793i | −0.917430 | − | 0.397897i | \(-0.869740\pi\) | ||||
0.917430 | − | 0.397897i | \(-0.130260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.93087i | 0.150947i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.4924 | −1.66902 | −0.834512 | − | 0.550990i | \(-0.814250\pi\) | ||||
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.75379 | 0.499702 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.75379i | 0.498395i | 0.968453 | + | 0.249198i | \(0.0801669\pi\) | ||||
−0.968453 | + | 0.249198i | \(0.919833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.3002 | −1.13066 | −0.565332 | − | 0.824863i | \(-0.691252\pi\) | ||||
−0.565332 | + | 0.824863i | \(0.691252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.6155 | 1.19429 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.6155i | 1.19125i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 23.1771i | − 1.16322i | −0.813466 | − | 0.581612i | \(-0.802422\pi\) | ||||
0.813466 | − | 0.581612i | \(-0.197578\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.1231 | −0.556852 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.9309 | −0.645737 | −0.322868 | − | 0.946444i | \(-0.604647\pi\) | ||||
−0.322868 | + | 0.946444i | \(0.604647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 41.7538i | − 2.07990i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 12.8769i | − 0.638284i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4924 | 0.914391 | 0.457196 | − | 0.889366i | \(-0.348854\pi\) | ||||
0.457196 | + | 0.889366i | \(0.348854\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.5076 | 0.567627 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.3693i | 1.63410i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.2462 | 0.891386 | 0.445693 | − | 0.895186i | \(-0.352957\pi\) | ||||
0.445693 | + | 0.895186i | \(0.352957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.56155 | 0.173579 | 0.0867897 | − | 0.996227i | \(-0.472339\pi\) | ||||
0.0867897 | + | 0.996227i | \(0.472339\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.36932i | 0.0665785i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.87689i | − 0.332796i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.3002 | 0.786980 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.9309 | −1.10454 | −0.552271 | − | 0.833665i | \(-0.686238\pi\) | ||||
−0.552271 | + | 0.833665i | \(0.686238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 19.7538i | − 0.949307i | −0.880173 | − | 0.474653i | \(-0.842573\pi\) | ||||
0.880173 | − | 0.474653i | \(-0.157427\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 22.2462i | − 1.06418i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.1231 | −0.912696 | −0.456348 | − | 0.889801i | \(-0.650843\pi\) | ||||
−0.456348 | + | 0.889801i | \(0.650843\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.561553 | −0.0267406 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6155i | 0.931962i | 0.884795 | + | 0.465981i | \(0.154298\pi\) | ||||
−0.884795 | + | 0.465981i | \(0.845702\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.384472i | 0.0181849i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.3153 | 1.00593 | 0.502967 | − | 0.864306i | \(-0.332242\pi\) | ||||
0.502967 | + | 0.864306i | \(0.332242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.75379 | −0.0825827 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 30.9309i | − 1.45326i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.63068i | 0.403726i | 0.979414 | + | 0.201863i | \(0.0646996\pi\) | ||||
−0.979414 | + | 0.201863i | \(0.935300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −42.0540 | −1.96291 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.8769 | 0.879185 | 0.439592 | − | 0.898197i | \(-0.355123\pi\) | ||||
0.439592 | + | 0.898197i | \(0.355123\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.24621i | 0.290286i | 0.989411 | + | 0.145143i | \(0.0463642\pi\) | ||||
−0.989411 | + | 0.145143i | \(0.953636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.5616i | 1.18285i | 0.806361 | + | 0.591424i | \(0.201434\pi\) | ||||
−0.806361 | + | 0.591424i | \(0.798566\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.24621 | −0.103720 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.63068 | −0.305526 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.1231i | 0.511441i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.36932i | 0.337418i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.3693 | −0.793624 | −0.396812 | − | 0.917900i | \(-0.629884\pi\) | ||||
−0.396812 | + | 0.917900i | \(0.629884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −55.1231 | −2.51340 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.87689i | 0.221906i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.12311i | 0.141521i | 0.997493 | + | 0.0707607i | \(0.0225427\pi\) | ||||
−0.997493 | + | 0.0707607i | \(0.977457\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30.6307 | 1.38517 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.31534 | −0.149619 | −0.0748096 | − | 0.997198i | \(-0.523835\pi\) | ||||
−0.0748096 | + | 0.997198i | \(0.523835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 3.31534i | − 0.149315i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.192236 | 0.00860566 | 0.00430283 | − | 0.999991i | \(-0.498630\pi\) | ||||
0.00430283 | + | 0.999991i | \(0.498630\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.54640 | −0.292471 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.1771i | 1.30094i | 0.759531 | + | 0.650471i | \(0.225428\pi\) | ||||
−0.759531 | + | 0.650471i | \(0.774572\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 49.4773i | − 2.19736i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.7386 | −1.45111 | −0.725557 | − | 0.688162i | \(-0.758418\pi\) | ||||
−0.725557 | + | 0.688162i | \(0.758418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.24621 | −0.187841 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 39.6155i | 1.74907i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.80776i | 0.167465i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −36.1922 | −1.58866 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.2462 | −0.536516 | −0.268258 | − | 0.963347i | \(-0.586448\pi\) | ||||
−0.268258 | + | 0.963347i | \(0.586448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0000i | 0.524723i | 0.964970 | + | 0.262362i | \(0.0845013\pi\) | ||||
−0.964970 | + | 0.262362i | \(0.915499\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.2311i | 2.05742i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.2462 | 0.575922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.24621 | 0.0974773 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.50758i | 0.325189i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.24621i | 0.269544i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.56155 | −0.0672608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.4233 | 1.78093 | 0.890463 | − | 0.455055i | \(-0.150380\pi\) | ||||
0.890463 | + | 0.455055i | \(0.150380\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 8.00000i | − 0.343313i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000i | 0.513083i | 0.966533 | + | 0.256541i | \(0.0825830\pi\) | ||||
−0.966533 | + | 0.256541i | \(0.917417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.86174 | −0.164815 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.12311 | −0.133049 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 0.684658i | − 0.0291146i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 17.6155i | − 0.746394i | −0.927752 | − | 0.373197i | \(-0.878262\pi\) | ||||
0.927752 | − | 0.373197i | \(-0.121738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.6155 | 2.01392 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.4384 | −0.778472 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.50758i | 0.316407i | 0.987407 | + | 0.158203i | \(0.0505701\pi\) | ||||
−0.987407 | + | 0.158203i | \(0.949430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 7.00000i | − 0.293972i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.9848 | −0.795886 | −0.397943 | − | 0.917410i | \(-0.630276\pi\) | ||||
−0.397943 | + | 0.917410i | \(0.630276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.06913i | − 0.0446636i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 3.56155i | − 0.148269i | −0.997248 | − | 0.0741347i | \(-0.976381\pi\) | ||||
0.997248 | − | 0.0741347i | \(-0.0236195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.4924 | 0.851636 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.4924i | 0.848709i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.2462i | 0.422906i | 0.977388 | + | 0.211453i | \(0.0678196\pi\) | ||||
−0.977388 | + | 0.211453i | \(0.932180\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.4924 | 1.83328 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.4924 | 0.842946 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 37.4233i | − 1.53679i | −0.639976 | − | 0.768395i | \(-0.721056\pi\) | ||||
0.639976 | − | 0.768395i | \(-0.278944\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.2462i | 0.910477i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.9309 | 1.91754 | 0.958772 | − | 0.284178i | \(-0.0917205\pi\) | ||||
0.958772 | + | 0.284178i | \(0.0917205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.26137i | 0.0513668i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 8.68466i | − 0.352499i | −0.984345 | − | 0.176250i | \(-0.943603\pi\) | ||||
0.984345 | − | 0.176250i | \(-0.0563966\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.684658 | 0.0277438 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.3002 | 0.659435 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 16.7386i | − 0.676067i | −0.941134 | − | 0.338034i | \(-0.890238\pi\) | ||||
0.941134 | − | 0.338034i | \(-0.109762\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 15.7538i | − 0.634224i | −0.948388 | − | 0.317112i | \(-0.897287\pi\) | ||||
0.948388 | − | 0.317112i | \(-0.102713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6307 | −0.427283 | −0.213642 | − | 0.976912i | \(-0.568532\pi\) | ||||
−0.213642 | + | 0.976912i | \(0.568532\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.3693 | 0.697007 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5.12311i | − 0.205253i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.3693i | 0.693664i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 62.3542 | 2.48622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.4233 | −1.09170 | −0.545852 | − | 0.837882i | \(-0.683794\pi\) | ||||
−0.545852 | + | 0.837882i | \(0.683794\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 27.4233i | − 1.08998i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.68466i | 0.264856i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.9848 | −0.907847 | −0.453923 | − | 0.891041i | \(-0.649976\pi\) | ||||
−0.453923 | + | 0.891041i | \(0.649976\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.0540i | 1.18521i | 0.805492 | + | 0.592607i | \(0.201901\pi\) | ||||
−0.805492 | + | 0.592607i | \(0.798099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.00000i | 0.314512i | 0.987558 | + | 0.157256i | \(0.0502649\pi\) | ||||
−0.987558 | + | 0.157256i | \(0.949735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.24621 | 0.245185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.75379 | −0.382281 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.4924i | 1.50632i | 0.657835 | + | 0.753162i | \(0.271473\pi\) | ||||
−0.657835 | + | 0.753162i | \(0.728527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.38447i | 0.0930271i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.192236 | 0.00748845 | 0.00374422 | − | 0.999993i | \(-0.498808\pi\) | ||||
0.00374422 | + | 0.999993i | \(0.498808\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.6155 | −0.685165 | −0.342582 | − | 0.939488i | \(-0.611302\pi\) | ||||
−0.342582 | + | 0.939488i | \(0.611302\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 78.9309i | 3.06542i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.36932i | 0.0530202i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.5464 | 1.49029 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.7386 | −0.414560 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 41.6155i | − 1.60416i | −0.597216 | − | 0.802080i | \(-0.703727\pi\) | ||||
0.597216 | − | 0.802080i | \(-0.296273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.31534i | − 0.0505527i | −0.999681 | − | 0.0252763i | \(-0.991953\pi\) | ||||
0.999681 | − | 0.0252763i | \(-0.00804657\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.31534 | −0.0504782 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6695 | 0.677097 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 44.9848i | − 1.72130i | −0.509199 | − | 0.860649i | \(-0.670058\pi\) | ||||
0.509199 | − | 0.860649i | \(-0.329942\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.7538i | 0.677349i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 87.7235 | 3.34200 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.4924 | 0.627401 | 0.313701 | − | 0.949522i | \(-0.398431\pi\) | ||||
0.313701 | + | 0.949522i | \(0.398431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.876894i | 0.0333105i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 8.49242i | − 0.321673i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.9848 | −0.642426 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.31534 | −0.351836 | −0.175918 | − | 0.984405i | \(-0.556289\pi\) | ||||
−0.175918 | + | 0.984405i | \(0.556289\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 58.7386i | − 2.21537i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000i | 0.225653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.05398 | 0.152250 | 0.0761251 | − | 0.997098i | \(-0.475745\pi\) | ||||
0.0761251 | + | 0.997098i | \(0.475745\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.384472 | −0.0144188 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 19.5076i | − 0.730565i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.1922i | 1.05286i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.6155 | 0.880711 | 0.440355 | − | 0.897824i | \(-0.354852\pi\) | ||||
0.440355 | + | 0.897824i | \(0.354852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.8078 | −0.439744 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.12311i | 0.116150i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.9848i | 1.81675i | 0.418159 | + | 0.908374i | \(0.362675\pi\) | ||||
−0.418159 | + | 0.908374i | \(0.637325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9848 | −1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.8617 | −1.99215 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16.4384i | − 0.607168i | −0.952805 | − | 0.303584i | \(-0.901817\pi\) | ||||
0.952805 | − | 0.303584i | \(-0.0981833\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.50758i | 0.129203i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.43845 | 0.236842 | 0.118421 | − | 0.992963i | \(-0.462217\pi\) | ||||
0.118421 | + | 0.992963i | \(0.462217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 74.3542 | 2.73147 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000i | 0.880475i | 0.897881 | + | 0.440237i | \(0.145106\pi\) | ||||
−0.897881 | + | 0.440237i | \(0.854894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 6.73863i | − 0.246554i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.1231 | −0.552586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.3153 | −1.14271 | −0.571357 | − | 0.820702i | \(-0.693583\pi\) | ||||
−0.571357 | + | 0.820702i | \(0.693583\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.8769i | 0.760796i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.3693i | 0.558607i | 0.960203 | + | 0.279304i | \(0.0901036\pi\) | ||||
−0.960203 | + | 0.279304i | \(0.909896\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.61553 | 0.276426 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.0000 | 0.942499 | 0.471250 | − | 0.882000i | \(-0.343803\pi\) | ||||
0.471250 | + | 0.882000i | \(0.343803\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.43845i | 0.160683i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 26.7386i | − 0.965476i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.9848 | −1.55007 | −0.775037 | − | 0.631916i | \(-0.782269\pi\) | ||||
−0.775037 | + | 0.631916i | \(0.782269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.8769 | 1.03998 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.8078i | 1.07211i | 0.844183 | + | 0.536055i | \(0.180086\pi\) | ||||
−0.844183 | + | 0.536055i | \(0.819914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.8769i | 0.461956i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | −0.286630 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2.43845i | − 0.0871430i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.1771i | 1.18264i | 0.806439 | + | 0.591318i | \(0.201392\pi\) | ||||
−0.806439 | + | 0.591318i | \(0.798608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.6307 | 0.520866 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.24621 | 0.293202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.9697i | 1.63243i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.8078i | 0.630783i | 0.948962 | + | 0.315392i | \(0.102136\pi\) | ||||
−0.948962 | + | 0.315392i | \(0.897864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.4384 | −0.652305 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.87689 | −0.101650 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.63068i | 0.233992i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 6.63068i | − 0.233411i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.05398 | −0.142530 | −0.0712651 | − | 0.997457i | \(-0.522704\pi\) | ||||
−0.0712651 | + | 0.997457i | \(0.522704\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.6155 | −0.969712 | −0.484856 | − | 0.874594i | \(-0.661128\pi\) | ||||
−0.484856 | + | 0.874594i | \(0.661128\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 9.75379i | − 0.342080i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.7386i | 1.77512i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.75379 | 0.131168 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.3002 | 1.89509 | 0.947545 | − | 0.319623i | \(-0.103556\pi\) | ||||
0.947545 | + | 0.319623i | \(0.103556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.7538i | 0.618858i | 0.950923 | + | 0.309429i | \(0.100138\pi\) | ||||
−0.950923 | + | 0.309429i | \(0.899862\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.8769i | 0.865054i | 0.901621 | + | 0.432527i | \(0.142378\pi\) | ||||
−0.901621 | + | 0.432527i | \(0.857622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.61553 | −0.195035 | −0.0975177 | − | 0.995234i | \(-0.531090\pi\) | ||||
−0.0975177 | + | 0.995234i | \(0.531090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.8769 | 0.446695 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 7.56155i | − 0.261992i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.7386i | 1.20074i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.1231 | −0.660203 | −0.330101 | − | 0.943945i | \(-0.607083\pi\) | ||||
−0.330101 | + | 0.943945i | \(0.607083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8078 | −0.993371 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 30.5464i | − 1.05207i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 8.56155i | − 0.294178i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.31534 | −0.251062 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.7538 | −0.882829 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 15.7538i | − 0.539399i | −0.962944 | − | 0.269700i | \(-0.913076\pi\) | ||||
0.962944 | − | 0.269700i | \(-0.0869244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.7386i | 1.80152i | 0.434320 | + | 0.900759i | \(0.356989\pi\) | ||||
−0.434320 | + | 0.900759i | \(0.643011\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.9848 | −1.26191 | −0.630953 | − | 0.775821i | \(-0.717336\pi\) | ||||
−0.630953 | + | 0.775821i | \(0.717336\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.75379 | 0.0597690 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 28.4924i | − 0.969893i | −0.874544 | − | 0.484947i | \(-0.838839\pi\) | ||||
0.874544 | − | 0.484947i | \(-0.161161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 62.7386i | − 2.13072i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.06913 | −0.0362678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.0152 | 0.508769 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.738634i | 0.0249990i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 13.5076i | − 0.456118i | −0.973647 | − | 0.228059i | \(-0.926762\pi\) | ||||
0.973647 | − | 0.228059i | \(-0.0732380\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50.0540 | 1.68828 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.1080 | 1.82294 | 0.911472 | − | 0.411363i | \(-0.134947\pi\) | ||||
0.911472 | + | 0.411363i | \(0.134947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 21.7538i | − 0.732073i | −0.930600 | − | 0.366037i | \(-0.880714\pi\) | ||||
0.930600 | − | 0.366037i | \(-0.119286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 36.4924i | − 1.22530i | −0.790356 | − | 0.612648i | \(-0.790104\pi\) | ||||
0.790356 | − | 0.612648i | \(-0.209896\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.24621 | 0.209491 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.9309 | −0.366198 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.3693i | 0.581242i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 32.6004i | − 1.08849i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.73863 | −0.0913385 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −99.2311 | −3.30587 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 11.1231i | − 0.370154i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 48.1080i | − 1.59740i | −0.601731 | − | 0.798699i | \(-0.705522\pi\) | ||||
0.601731 | − | 0.798699i | \(-0.294478\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.36932 | 0.111753 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 18.7386i | − 0.620158i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.1231i | 0.499409i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.43845 | −0.0804370 | −0.0402185 | − | 0.999191i | \(-0.512805\pi\) | ||||
−0.0402185 | + | 0.999191i | \(0.512805\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.7926 | 1.47597 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.63068i | 0.217780i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.87689 | 0.0943878 | 0.0471939 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471939 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.12311 | −0.233450 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 20.1080i | − 0.658305i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.8078i | 1.23513i | 0.786521 | + | 0.617563i | \(0.211880\pi\) | ||||
−0.786521 | + | 0.617563i | \(0.788120\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.6695 | 1.35983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.6307 | 0.933334 | 0.466667 | − | 0.884433i | \(-0.345455\pi\) | ||||
0.466667 | + | 0.884433i | \(0.345455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.50758i | 0.114222i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 35.2311i | − 1.14486i | −0.819955 | − | 0.572428i | \(-0.806002\pi\) | ||||
0.819955 | − | 0.572428i | \(-0.193998\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.3845 | 0.921399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.6155 | 0.506368 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.8617i | 1.67997i | 0.542612 | + | 0.839983i | \(0.317435\pi\) | ||||
−0.542612 | + | 0.839983i | \(0.682565\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.06913i | − 0.0345601i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.36932 | 0.237968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.01515 | 0.258553 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.49242i | 0.273664i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.1080i | 1.41842i | 0.704999 | + | 0.709208i | \(0.250947\pi\) | ||||
−0.704999 | + | 0.709208i | \(0.749053\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −84.1080 | −2.70194 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.7386 | −0.729717 | −0.364859 | − | 0.931063i | \(-0.618883\pi\) | ||||
−0.364859 | + | 0.931063i | \(0.618883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.3693i | 0.685069i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.9848i | 0.351436i | 0.984441 | + | 0.175718i | \(0.0562247\pi\) | ||||
−0.984441 | + | 0.175718i | \(0.943775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.49242 | 0.0795769 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.1771i | 0.930604i | 0.885152 | + | 0.465302i | \(0.154054\pi\) | ||||
−0.885152 | + | 0.465302i | \(0.845946\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 3.80776i | − 0.121202i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.2462 | 0.707388 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4924 | −0.650963 | −0.325482 | − | 0.945548i | \(-0.605526\pi\) | ||||
−0.325482 | + | 0.945548i | \(0.605526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 18.7386i | − 0.594653i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 56.9309i | − 1.80302i | −0.432760 | − | 0.901509i | \(-0.642460\pi\) | ||||
0.432760 | − | 0.901509i | \(-0.357540\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.8617 | 1.45100 |
(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 | 1400.2.g.k.449.3 | 4 | ||
4.3 | odd | 2 | 2800.2.g.u.449.2 | 4 | |||
5.2 | odd | 4 | 1400.2.a.p.1.2 | 2 | |||
5.3 | odd | 4 | 280.2.a.d.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1400.2.g.k.449.2 | 4 | ||
15.8 | even | 4 | 2520.2.a.w.1.1 | 2 | |||
20.3 | even | 4 | 560.2.a.g.1.2 | 2 | |||
20.7 | even | 4 | 2800.2.a.bn.1.1 | 2 | |||
20.19 | odd | 2 | 2800.2.g.u.449.3 | 4 | |||
35.3 | even | 12 | 1960.2.q.u.961.1 | 4 | |||
35.13 | even | 4 | 1960.2.a.r.1.2 | 2 | |||
35.18 | odd | 12 | 1960.2.q.s.961.2 | 4 | |||
35.23 | odd | 12 | 1960.2.q.s.361.2 | 4 | |||
35.27 | even | 4 | 9800.2.a.by.1.1 | 2 | |||
35.33 | even | 12 | 1960.2.q.u.361.1 | 4 | |||
40.3 | even | 4 | 2240.2.a.bi.1.1 | 2 | |||
40.13 | odd | 4 | 2240.2.a.be.1.2 | 2 | |||
60.23 | odd | 4 | 5040.2.a.bq.1.2 | 2 | |||
140.83 | odd | 4 | 3920.2.a.bu.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.d.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
560.2.a.g.1.2 | 2 | 20.3 | even | 4 | |||
1400.2.a.p.1.2 | 2 | 5.2 | odd | 4 | |||
1400.2.g.k.449.2 | 4 | 5.4 | even | 2 | inner | ||
1400.2.g.k.449.3 | 4 | 1.1 | even | 1 | trivial | ||
1960.2.a.r.1.2 | 2 | 35.13 | even | 4 | |||
1960.2.q.s.361.2 | 4 | 35.23 | odd | 12 | |||
1960.2.q.s.961.2 | 4 | 35.18 | odd | 12 | |||
1960.2.q.u.361.1 | 4 | 35.33 | even | 12 | |||
1960.2.q.u.961.1 | 4 | 35.3 | even | 12 | |||
2240.2.a.be.1.2 | 2 | 40.13 | odd | 4 | |||
2240.2.a.bi.1.1 | 2 | 40.3 | even | 4 | |||
2520.2.a.w.1.1 | 2 | 15.8 | even | 4 | |||
2800.2.a.bn.1.1 | 2 | 20.7 | even | 4 | |||
2800.2.g.u.449.2 | 4 | 4.3 | odd | 2 | |||
2800.2.g.u.449.3 | 4 | 20.19 | odd | 2 | |||
3920.2.a.bu.1.1 | 2 | 140.83 | odd | 4 | |||
5040.2.a.bq.1.2 | 2 | 60.23 | odd | 4 | |||
9800.2.a.by.1.1 | 2 | 35.27 | even | 4 |