Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(449,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, 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("2240.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.3 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.449 |
Dual form | 2240.2.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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | 0.957427 | + | 0.288675i | \(0.0932147\pi\) | ||||
−0.957427 | + | 0.288675i | \(0.906785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.23607i | − 1.00000i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23607 | 0.674200 | 0.337100 | − | 0.941469i | \(-0.390554\pi\) | ||||
0.337100 | + | 0.941469i | \(0.390554\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.23607i | − 0.620174i | −0.950708 | − | 0.310087i | \(-0.899642\pi\) | ||||
0.950708 | − | 0.310087i | \(-0.100358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23607 | 0.577350 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23607i | 0.542326i | 0.962533 | + | 0.271163i | \(0.0874083\pi\) | ||||
−0.962533 | + | 0.271163i | \(0.912592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.47214 | 1.02598 | 0.512989 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512989 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.23607i | 0.389249i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.23607 | 0.377964 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 8.94427i | − 1.47043i | −0.677834 | − | 0.735215i | \(-0.737081\pi\) | ||||
0.677834 | − | 0.735215i | \(-0.262919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.23607 | 0.358057 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 6.00000i | − 0.914991i | −0.889212 | − | 0.457496i | \(-0.848747\pi\) | ||||
0.889212 | − | 0.457496i | \(-0.151253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 4.47214i | − 0.666667i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 3.00000i | − 0.437595i | −0.975770 | − | 0.218797i | \(-0.929787\pi\) | ||||
0.975770 | − | 0.218797i | \(-0.0702134\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.23607 | −0.313112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.47214i | − 0.614295i | −0.951662 | − | 0.307148i | \(-0.900625\pi\) | ||||
0.951662 | − | 0.307148i | \(-0.0993745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 5.00000i | − 0.674200i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.47214i | 0.592349i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.47214 | 0.582223 | 0.291111 | − | 0.956689i | \(-0.405975\pi\) | ||||
0.291111 | + | 0.956689i | \(0.405975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000i | 0.251976i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.00000 | −0.620174 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.94427 | 1.06149 | 0.530745 | − | 0.847532i | \(-0.321912\pi\) | ||||
0.530745 | + | 0.847532i | \(0.321912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4164i | 1.57027i | 0.619324 | + | 0.785136i | \(0.287407\pi\) | ||||
−0.619324 | + | 0.785136i | \(0.712593\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 5.00000i | − 0.577350i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.23607i | 0.254824i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.6525 | 1.76104 | 0.880521 | − | 0.474008i | \(-0.157193\pi\) | ||||
0.880521 | + | 0.474008i | \(0.157193\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | 0.542326 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1.00000i | − 0.107211i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.0000 | 1.48400 | 0.741999 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.23607 | 0.234404 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 10.0000i | − 1.02598i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.23607i | 0.227038i | 0.993536 | + | 0.113519i | \(0.0362123\pi\) | ||||
−0.993536 | + | 0.113519i | \(0.963788\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.47214 | 0.449467 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0000i | 1.08386i | 0.840423 | + | 0.541931i | \(0.182307\pi\) | ||||
−0.840423 | + | 0.541931i | \(0.817693\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.23607i | 0.218218i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.0000i | − 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.0000 | −1.43674 | −0.718370 | − | 0.695662i | \(-0.755111\pi\) | ||||
−0.718370 | + | 0.695662i | \(0.755111\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.94427 | 0.848953 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 8.94427i | − 0.841406i | −0.907198 | − | 0.420703i | \(-0.861783\pi\) | ||||
0.907198 | − | 0.420703i | \(-0.138217\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.94427 | 0.834058 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.47214i | − 0.413449i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.23607 | −0.204980 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 1.00000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.00000i | − 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.8885 | 1.56293 | 0.781465 | − | 0.623949i | \(-0.214473\pi\) | ||||
0.781465 | + | 0.623949i | \(0.214473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.47214i | 0.387783i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.1803 | 0.962250 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 13.4164i | − 1.14624i | −0.819471 | − | 0.573121i | \(-0.805733\pi\) | ||||
0.819471 | − | 0.573121i | \(-0.194267\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.4164 | −1.13796 | −0.568982 | − | 0.822350i | \(-0.692663\pi\) | ||||
−0.568982 | + | 0.822350i | \(0.692663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 5.00000i | − 0.418121i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.23607i | 0.185695i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.00000i | − 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.6525 | −1.27378 | −0.636890 | − | 0.770955i | \(-0.719780\pi\) | ||||
−0.636890 | + | 0.770955i | \(0.719780\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.47214i | 0.361551i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.47214i | 0.356915i | 0.983948 | + | 0.178458i | \(0.0571108\pi\) | ||||
−0.983948 | + | 0.178458i | \(0.942889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.47214 | 0.354663 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0000i | 1.09656i | 0.836293 | + | 0.548282i | \(0.184718\pi\) | ||||
−0.836293 | + | 0.548282i | \(0.815282\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.00000 | 0.389249 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 7.00000i | − 0.541676i | −0.962625 | − | 0.270838i | \(-0.912699\pi\) | ||||
0.962625 | − | 0.270838i | \(-0.0873008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.00000 | 0.615385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.94427 | 0.683986 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.23607i | 0.170005i | 0.996381 | + | 0.0850026i | \(0.0270898\pi\) | ||||
−0.996381 | + | 0.0850026i | \(0.972910\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 5.00000i | − 0.377964i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.47214i | 0.336146i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.8885 | 1.33705 | 0.668526 | − | 0.743689i | \(-0.266925\pi\) | ||||
0.668526 | + | 0.743689i | \(0.266925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0000i | 0.739221i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.0000 | −1.47043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.00000i | 0.365636i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.00000 | −0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.5967 | 1.77976 | 0.889879 | − | 0.456196i | \(-0.150789\pi\) | ||||
0.889879 | + | 0.456196i | \(0.150789\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 13.4164i | − 0.965734i | −0.875694 | − | 0.482867i | \(-0.839595\pi\) | ||||
0.875694 | − | 0.482867i | \(-0.160405\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 5.00000i | − 0.358057i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.8885i | 1.27451i | 0.770655 | + | 0.637253i | \(0.219929\pi\) | ||||
−0.770655 | + | 0.637253i | \(0.780071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.3607 | −1.58511 | −0.792553 | − | 0.609803i | \(-0.791249\pi\) | ||||
−0.792553 | + | 0.609803i | \(0.791249\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.00000 | −0.141069 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.00000i | − 0.0701862i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.00000i | 0.556038i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0000 | 0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.70820 | 0.461812 | 0.230906 | − | 0.972976i | \(-0.425831\pi\) | ||||
0.230906 | + | 0.972976i | \(0.425831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.94427i | 0.612851i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.4164 | −0.914991 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.4164 | −0.906597 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.00000 | 0.336336 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0000i | 1.27233i | 0.771551 | + | 0.636167i | \(0.219481\pi\) | ||||
−0.771551 | + | 0.636167i | \(0.780519\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.0000 | −0.666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 17.0000i | − 1.12833i | −0.825662 | − | 0.564165i | \(-0.809198\pi\) | ||||
0.825662 | − | 0.564165i | \(-0.190802\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.00000 | −0.264327 | −0.132164 | − | 0.991228i | \(-0.542192\pi\) | ||||
−0.132164 | + | 0.991228i | \(0.542192\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.23607 | −0.147122 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 17.8885i | − 1.17192i | −0.810341 | − | 0.585959i | \(-0.800718\pi\) | ||||
0.810341 | − | 0.585959i | \(-0.199282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.70820 | −0.437595 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.6525i | 1.01674i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.70820 | 0.433918 | 0.216959 | − | 0.976181i | \(-0.430386\pi\) | ||||
0.216959 | + | 0.976181i | \(0.430386\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000i | 1.02640i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.23607i | 0.142857i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 10.0000i | − 0.636285i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.3607 | −1.41139 | −0.705697 | − | 0.708514i | \(-0.749366\pi\) | ||||
−0.705697 | + | 0.708514i | \(0.749366\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.94427i | 0.562322i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.00000i | 0.313112i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 22.3607i | − 1.39482i | −0.716672 | − | 0.697410i | \(-0.754335\pi\) | ||||
0.716672 | − | 0.697410i | \(-0.245665\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.94427 | 0.555770 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0000i | 0.986602i | 0.869859 | + | 0.493301i | \(0.164210\pi\) | ||||
−0.869859 | + | 0.493301i | \(0.835790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0000 | −0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.0000i | 0.856786i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.47214 | −0.271663 | −0.135831 | − | 0.990732i | \(-0.543371\pi\) | ||||
−0.135831 | + | 0.990732i | \(0.543371\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.23607i | 0.135333i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.1803 | −0.674200 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 13.4164i | − 0.806114i | −0.915175 | − | 0.403057i | \(-0.867948\pi\) | ||||
0.915175 | − | 0.403057i | \(-0.132052\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0000 | 0.894825 | 0.447412 | − | 0.894328i | \(-0.352346\pi\) | ||||
0.447412 | + | 0.894328i | \(0.352346\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.0000i | 1.84276i | 0.388664 | + | 0.921379i | \(0.372937\pi\) | ||||
−0.388664 | + | 0.921379i | \(0.627063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.0000 | 0.592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.0000 | 0.705882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.23607 | −0.131081 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.1803i | 0.653162i | 0.945169 | + | 0.326581i | \(0.105897\pi\) | ||||
−0.945169 | + | 0.326581i | \(0.894103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 10.0000i | − 0.582223i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1803i | 0.648749i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.94427 | 0.517261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.00000i | − 0.114897i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 22.3607i | − 1.28037i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 23.0000i | − 1.31268i | −0.754466 | − | 0.656340i | \(-0.772104\pi\) | ||||
0.754466 | − | 0.656340i | \(-0.227896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.0000 | −0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.3607 | −1.26796 | −0.633979 | − | 0.773350i | \(-0.718579\pi\) | ||||
−0.633979 | + | 0.773350i | \(0.718579\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 15.6525i | − 0.884730i | −0.896835 | − | 0.442365i | \(-0.854140\pi\) | ||||
0.896835 | − | 0.442365i | \(-0.145860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.47214 | 0.251976 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.8885i | 1.00472i | 0.864658 | + | 0.502360i | \(0.167535\pi\) | ||||
−0.864658 | + | 0.502360i | \(0.832465\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.23607 | −0.125196 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0000i | 0.556415i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.1803i | 0.620174i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 15.0000i | − 0.829502i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.00000 | 0.165395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.7771 | −1.96649 | −0.983243 | − | 0.182298i | \(-0.941646\pi\) | ||||
−0.983243 | + | 0.182298i | \(0.941646\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 17.8885i | − 0.980286i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.47214 | 0.244339 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4164i | 0.730838i | 0.930843 | + | 0.365419i | \(0.119074\pi\) | ||||
−0.930843 | + | 0.365419i | \(0.880926\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.94427 | 0.485786 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.94427i | 0.481543i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8.00000i | − 0.429463i | −0.976673 | − | 0.214731i | \(-0.931112\pi\) | ||||
0.976673 | − | 0.214731i | \(-0.0688876\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.1803 | 0.596762 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 11.1803i | − 0.595069i | −0.954711 | − | 0.297535i | \(-0.903836\pi\) | ||||
0.954711 | − | 0.297535i | \(-0.0961644\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 20.0000i | − 1.06149i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2.23607i | − 0.118345i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.8885 | 0.944121 | 0.472061 | − | 0.881566i | \(-0.343510\pi\) | ||||
0.472061 | + | 0.881566i | \(0.343510\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 6.00000i | − 0.314918i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.0000 | 1.57027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.0000i | 0.887393i | 0.896177 | + | 0.443696i | \(0.146333\pi\) | ||||
−0.896177 | + | 0.443696i | \(0.853667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.47214 | 0.232182 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 13.4164i | − 0.694675i | −0.937740 | − | 0.347338i | \(-0.887086\pi\) | ||||
0.937740 | − | 0.347338i | \(-0.112914\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1803 | −0.577350 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.23607i | 0.115163i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.8328 | −1.37831 | −0.689155 | − | 0.724614i | \(-0.742018\pi\) | ||||
−0.689155 | + | 0.724614i | \(0.742018\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.00000 | 0.102463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 16.0000i | − 0.817562i | −0.912633 | − | 0.408781i | \(-0.865954\pi\) | ||||
0.912633 | − | 0.408781i | \(-0.134046\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.00000 | 0.254824 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 12.0000i | − 0.609994i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.00000 | 0.253510 | 0.126755 | − | 0.991934i | \(-0.459544\pi\) | ||||
0.126755 | + | 0.991934i | \(0.459544\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.94427 | −0.452331 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.8885i | 0.902358i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 35.0000i | − 1.76104i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 29.0689i | − 1.45893i | −0.684021 | − | 0.729463i | \(-0.739770\pi\) | ||||
0.684021 | − | 0.729463i | \(-0.260230\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.47214 | −0.223887 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.0000 | −1.34832 | −0.674158 | − | 0.738587i | \(-0.735493\pi\) | ||||
−0.674158 | + | 0.738587i | \(0.735493\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 2.23607i | − 0.111111i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 20.0000i | − 0.991363i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.0000 | 0.988936 | 0.494468 | − | 0.869196i | \(-0.335363\pi\) | ||||
0.494468 | + | 0.869196i | \(0.335363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.4164 | 0.661783 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.47214i | 0.220059i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.94427 | 0.439057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 13.4164i | − 0.657004i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.3607 | −1.09239 | −0.546195 | − | 0.837658i | \(-0.683924\pi\) | ||||
−0.546195 | + | 0.837658i | \(0.683924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0000 | −1.21843 | −0.609213 | − | 0.793007i | \(-0.708514\pi\) | ||||
−0.609213 | + | 0.793007i | \(0.708514\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 6.00000i | − 0.291730i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 11.1803i | − 0.542326i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0000i | 0.483934i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.00000 | 0.241402 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.1246 | −0.969368 | −0.484684 | − | 0.874689i | \(-0.661065\pi\) | ||||
−0.484684 | + | 0.874689i | \(0.661065\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.3050i | 1.50442i | 0.658923 | + | 0.752210i | \(0.271012\pi\) | ||||
−0.658923 | + | 0.752210i | \(0.728988\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.23607 | −0.107211 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.8885i | 0.855725i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.2492 | −1.92099 | −0.960495 | − | 0.278296i | \(-0.910230\pi\) | ||||
−0.960495 | + | 0.278296i | \(0.910230\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.0000i | 1.61539i | 0.589601 | + | 0.807694i | \(0.299285\pi\) | ||||
−0.589601 | + | 0.807694i | \(0.700715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 31.3050i | − 1.48400i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 10.0000i | − 0.472984i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 15.6525i | − 0.735417i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 5.00000i | − 0.234404i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 26.8328i | − 1.25519i | −0.778542 | − | 0.627593i | \(-0.784040\pi\) | ||||
0.778542 | − | 0.627593i | \(-0.215960\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.1803 | −0.521854 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000i | 1.20832i | 0.796862 | + | 0.604161i | \(0.206492\pi\) | ||||
−0.796862 | + | 0.604161i | \(0.793508\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 3.00000i | − 0.138823i | −0.997588 | − | 0.0694117i | \(-0.977888\pi\) | ||||
0.997588 | − | 0.0694117i | \(-0.0221122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.47214 | −0.206065 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 13.4164i | − 0.616887i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.3607 | −1.02598 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 8.94427i | − 0.409530i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.94427 | 0.408674 | 0.204337 | − | 0.978901i | \(-0.434496\pi\) | ||||
0.204337 | + | 0.978901i | \(0.434496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.00000i | − 0.182006i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.00000 | 0.227038 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 18.0000i | − 0.815658i | −0.913058 | − | 0.407829i | \(-0.866286\pi\) | ||||
0.913058 | − | 0.407829i | \(-0.133714\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.0000 | −0.633102 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.1246 | −0.908211 | −0.454106 | − | 0.890948i | \(-0.650041\pi\) | ||||
−0.454106 | + | 0.890948i | \(0.650041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.23607i | − 0.100707i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 10.0000i | − 0.449467i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.94427i | 0.401205i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.1246 | −0.900901 | −0.450451 | − | 0.892801i | \(-0.648737\pi\) | ||||
−0.450451 | + | 0.892801i | \(0.648737\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.00000 | 0.312737 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0000i | 0.936344i | 0.883637 | + | 0.468172i | \(0.155087\pi\) | ||||
−0.883637 | + | 0.468172i | \(0.844913\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.47214i | 0.199007i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.00000i | 0.355292i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.00000 | −0.265945 | −0.132973 | − | 0.991120i | \(-0.542452\pi\) | ||||
−0.132973 | + | 0.991120i | \(0.542452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.4164 | −0.593507 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.3607i | 0.987248i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.5967 | 1.08386 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.70820i | − 0.295026i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.23607 | −0.0981525 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.00000 | 0.0876216 | 0.0438108 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438108 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4.00000i | − 0.174908i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) | ||||
0.996169 | − | 0.0874539i | \(-0.0278730\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.00000 | 0.218218 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.94427 | 0.388148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.8328 | −1.16008 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.8885i | 0.771948i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.23607 | −0.0963143 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | 0.730887 | 0.365444 | − | 0.930834i | \(-0.380917\pi\) | ||||
0.365444 | + | 0.930834i | \(0.380917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.0000i | 0.944110i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.5410i | 1.43674i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 22.0000i | − 0.940652i | −0.882493 | − | 0.470326i | \(-0.844136\pi\) | ||||
0.882493 | − | 0.470326i | \(-0.155864\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.0000 | 0.853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.47214 | −0.190519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.6525i | 0.665611i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 20.0000i | − 0.848953i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 44.7214i | − 1.89490i | −0.319897 | − | 0.947452i | \(-0.603648\pi\) | ||||
0.319897 | − | 0.947452i | \(-0.396352\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.4164 | −0.567454 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.00000 | −0.211100 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.0000i | 1.51722i | 0.651546 | + | 0.758610i | \(0.274121\pi\) | ||||
−0.651546 | + | 0.758610i | \(0.725879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0000 | −0.841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.8885 | −0.748612 | −0.374306 | − | 0.927305i | \(-0.622119\pi\) | ||||
−0.374306 | + | 0.927305i | \(0.622119\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.5967i | 1.02754i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 20.0000i | − 0.834058i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.6525i | 0.651621i | 0.945435 | + | 0.325811i | \(0.105637\pi\) | ||||
−0.945435 | + | 0.325811i | \(0.894363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.4164 | 0.557567 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 10.0000i | − 0.414158i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.0000 | −0.413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.00000i | 0.330195i | 0.986277 | + | 0.165098i | \(0.0527939\pi\) | ||||
−0.986277 | + | 0.165098i | \(0.947206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.8885 | −0.735836 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 6.70820i | − 0.275473i | −0.990469 | − | 0.137736i | \(-0.956017\pi\) | ||||
0.990469 | − | 0.137736i | \(-0.0439827\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.00000i | 0.204980i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 22.3607i | − 0.915162i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.5967 | −1.00500 | −0.502498 | − | 0.864578i | \(-0.667586\pi\) | ||||
−0.502498 | + | 0.864578i | \(0.667586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.0000 | −0.815817 | −0.407909 | − | 0.913023i | \(-0.633742\pi\) | ||||
−0.407909 | + | 0.913023i | \(0.633742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.4164i | 0.545455i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.0000i | 1.90767i | 0.300329 | + | 0.953836i | \(0.402903\pi\) | ||||
−0.300329 | + | 0.953836i | \(0.597097\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.00000 | 0.0405220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.70820 | −0.271385 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 26.8328i | − 1.08377i | −0.840454 | − | 0.541884i | \(-0.817711\pi\) | ||||
0.840454 | − | 0.541884i | \(-0.182289\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.47214i | 0.180041i | 0.995940 | + | 0.0900207i | \(0.0286933\pi\) | ||||
−0.995940 | + | 0.0900207i | \(0.971307\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.0000 | −0.802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.0000i | 0.560898i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.0000i | 0.399362i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.1246 | −0.801148 | −0.400574 | − | 0.916264i | \(-0.631189\pi\) | ||||
−0.400574 | + | 0.916264i | \(0.631189\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.70820i | 0.266627i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.47214 | −0.177471 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.23607i | 0.0885962i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.8885 | 0.707660 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.0000i | 0.828159i | 0.910241 | + | 0.414080i | \(0.135896\pi\) | ||||
−0.910241 | + | 0.414080i | \(0.864104\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 13.4164i | − 0.528271i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000i | 0.471769i | 0.971781 | + | 0.235884i | \(0.0757987\pi\) | ||||
−0.971781 | + | 0.235884i | \(0.924201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000 | 0.392534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.47214i | 0.175008i | 0.996164 | + | 0.0875041i | \(0.0278891\pi\) | ||||
−0.996164 | + | 0.0875041i | \(0.972111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 40.0000i | − 1.56293i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.8328i | 1.04685i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.70820 | 0.261315 | 0.130657 | − | 0.991428i | \(-0.458291\pi\) | ||||
0.130657 | + | 0.991428i | \(0.458291\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.00000i | 0.194184i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.0000 | 0.387783 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.00000i | − 0.154881i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.0000 | −0.734582 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.3607 | 0.863224 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.2492i | 1.55149i | 0.631044 | + | 0.775747i | \(0.282627\pi\) | ||||
−0.631044 | + | 0.775747i | \(0.717373\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 25.0000i | − 0.962250i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.1246i | 0.773452i | 0.922195 | + | 0.386726i | \(0.126394\pi\) | ||||
−0.922195 | + | 0.386726i | \(0.873606\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.23607 | −0.0858124 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.0000 | 0.651441 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 6.00000i | − 0.229584i | −0.993390 | − | 0.114792i | \(-0.963380\pi\) | ||||
0.993390 | − | 0.114792i | \(-0.0366201\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.0000 | −1.14624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 4.00000i | − 0.152610i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.0000 | −0.380970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.8328 | −1.02077 | −0.510384 | − | 0.859946i | \(-0.670497\pi\) | ||||
−0.510384 | + | 0.859946i | \(0.670497\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.47214i | 0.169882i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.0000i | 1.13796i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.8885 | 0.676607 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.0000 | −1.32193 | −0.660966 | − | 0.750416i | \(-0.729853\pi\) | ||||
−0.660966 | + | 0.750416i | \(0.729853\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 40.0000i | − 1.50863i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 6.70820i | − 0.252646i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.00000i | − 0.0752177i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0000 | 0.713560 | 0.356780 | − | 0.934188i | \(-0.383875\pi\) | ||||
0.356780 | + | 0.934188i | \(0.383875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.3050 | 1.17403 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.1803 | −0.418121 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.70820i | 0.250522i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.94427 | −0.333565 | −0.166783 | − | 0.985994i | \(-0.553338\pi\) | ||||
−0.166783 | + | 0.985994i | \(0.553338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.0000 | −0.409661 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.00000 | 0.185695 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 12.0000i | − 0.445055i | −0.974926 | − | 0.222528i | \(-0.928569\pi\) | ||||
0.974926 | − | 0.222528i | \(-0.0714308\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.4164 | 0.496224 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 20.1246i | − 0.743319i | −0.928369 | − | 0.371660i | \(-0.878789\pi\) | ||||
0.928369 | − | 0.371660i | \(-0.121211\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.23607 | −0.0824786 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.47214i | 0.164733i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.1803 | −0.411275 | −0.205638 | − | 0.978628i | \(-0.565927\pi\) | ||||
−0.205638 | + | 0.978628i | \(0.565927\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.0000 | 0.367359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 54.0000i | 1.98107i | 0.137268 | + | 0.990534i | \(0.456168\pi\) | ||||
−0.137268 | + | 0.990534i | \(0.543832\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.3607i | 0.819232i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.00000i | 0.292705i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.1803 | 0.407976 | 0.203988 | − | 0.978973i | \(-0.434610\pi\) | ||||
0.203988 | + | 0.978973i | \(0.434610\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 22.3607i | − 0.814868i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.0000i | 1.27378i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.94427i | 0.325085i | 0.986702 | + | 0.162543i | \(0.0519695\pi\) | ||||
−0.986702 | + | 0.162543i | \(0.948031\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.94427 | −0.324657 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.0000 | −1.74000 | −0.869999 | − | 0.493053i | \(-0.835881\pi\) | ||||
−0.869999 | + | 0.493053i | \(0.835881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 15.0000i | − 0.543036i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.0000 | 0.361551 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 10.0000i | − 0.361079i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.00000 | −0.144244 | −0.0721218 | − | 0.997396i | \(-0.522977\pi\) | ||||
−0.0721218 | + | 0.997396i | \(0.522977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.3607 | 0.805300 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.4853i | 1.52809i | 0.645163 | + | 0.764045i | \(0.276789\pi\) | ||||
−0.645163 | + | 0.764045i | \(0.723211\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.94427i | 0.320874i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0000 | 0.715656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 5.00000i | − 0.178685i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.00000i | 0.106938i | 0.998569 | + | 0.0534692i | \(0.0170279\pi\) | ||||
−0.998569 | + | 0.0534692i | \(0.982972\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.0000 | −0.569615 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.94427 | 0.318022 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 22.3607i | − 0.794051i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 10.0000i | − 0.354663i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.6525i | 0.554439i | 0.960807 | + | 0.277220i | \(0.0894129\pi\) | ||||
−0.960807 | + | 0.277220i | \(0.910587\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.70820 | 0.237319 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.0000 | 0.989331 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.0000i | 1.05868i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.94427i | 0.315244i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 10.0000i | − 0.352017i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.00000 | −0.316423 | −0.158212 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158212 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.47214 | −0.157038 | −0.0785190 | − | 0.996913i | \(-0.525019\pi\) | ||||
−0.0785190 | + | 0.996913i | \(0.525019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 4.47214i | − 0.156845i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.3050 | 1.09656 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 26.8328i | − 0.938761i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.47214 | 0.156269 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.0000 | −1.57051 | −0.785255 | − | 0.619172i | \(-0.787468\pi\) | ||||
−0.785255 | + | 0.619172i | \(0.787468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000i | 0.836587i | 0.908312 | + | 0.418294i | \(0.137372\pi\) | ||||
−0.908312 | + | 0.418294i | \(0.862628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 11.1803i | − 0.389249i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 18.0000i | − 0.625921i | −0.949766 | − | 0.312961i | \(-0.898679\pi\) | ||||
0.949766 | − | 0.312961i | \(-0.101321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.0000 | 1.38926 | 0.694629 | − | 0.719368i | \(-0.255569\pi\) | ||||
0.694629 | + | 0.719368i | \(0.255569\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.4164 | 0.465410 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 2.23607i | − 0.0774752i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.6525 | −0.541676 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.6656 | 1.85274 | 0.926372 | − | 0.376611i | \(-0.122911\pi\) | ||||
0.926372 | + | 0.376611i | \(0.122911\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.0000i | 0.516627i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 17.8885i | − 0.615385i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 6.00000i | − 0.206162i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.0000 | −1.06392 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.7771 | 1.22642 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.47214i | 0.153123i | 0.997065 | + | 0.0765615i | \(0.0243942\pi\) | ||||
−0.997065 | + | 0.0765615i | \(0.975606\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 20.0000i | − 0.683986i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.47214i | 0.152765i | 0.997079 | + | 0.0763826i | \(0.0243370\pi\) | ||||
−0.997079 | + | 0.0763826i | \(0.975663\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.7771 | −1.22070 | −0.610349 | − | 0.792132i | \(-0.708971\pi\) | ||||
−0.610349 | + | 0.792132i | \(0.708971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000i | 0.816970i | 0.912765 | + | 0.408485i | \(0.133943\pi\) | ||||
−0.912765 | + | 0.408485i | \(0.866057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.00000 | 0.170005 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.0000i | 0.407541i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.0000 | 1.18729 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.47214 | 0.151533 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.47214i | 0.151359i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1803 | −0.377964 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.47214i | 0.151013i | 0.997145 | + | 0.0755067i | \(0.0240574\pi\) | ||||
−0.997145 | + | 0.0755067i | \(0.975943\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.1803 | −0.377104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.0000 | 1.34763 | 0.673817 | − | 0.738898i | \(-0.264654\pi\) | ||||
0.673817 | + | 0.738898i | \(0.264654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 34.0000i | − 1.14419i | −0.820187 | − | 0.572096i | \(-0.806131\pi\) | ||||
0.820187 | − | 0.572096i | \(-0.193869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.0000 | 0.336146 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.00000i | 0.268614i | 0.990940 | + | 0.134307i | \(0.0428808\pi\) | ||||
−0.990940 | + | 0.134307i | \(0.957119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | 0.0670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.23607 | 0.0749111 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 13.4164i | − 0.448963i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 40.0000i | − 1.33705i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.94427i | 0.298641i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | 0.333148 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.00000i | 0.199667i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 49.1935i | − 1.63525i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.0000i | 1.06254i | 0.847202 | + | 0.531271i | \(0.178286\pi\) | ||||
−0.847202 | + | 0.531271i | \(0.821714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.00000 | −0.132672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.94427 | −0.296337 | −0.148168 | − | 0.988962i | \(-0.547338\pi\) | ||||
−0.148168 | + | 0.988962i | \(0.547338\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.94427i | 0.296012i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.3607 | 0.739221 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.8885i | 0.590732i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.9574 | −1.54898 | −0.774491 | − | 0.632585i | \(-0.781994\pi\) | ||||
−0.774491 | + | 0.632585i | \(0.781994\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.0000 | 0.757876 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 20.0000i | − 0.658308i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.7214i | 1.47043i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.0000i | 0.722575i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.47214 | −0.146568 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 22.3607i | − 0.732056i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.1803 | 0.365636 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.1246i | 0.657442i | 0.944427 | + | 0.328721i | \(0.106618\pi\) | ||||
−0.944427 | + | 0.328721i | \(0.893382\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.6525 | 0.510799 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.0000 | −1.23876 | −0.619382 | − | 0.785090i | \(-0.712617\pi\) | ||||
−0.619382 | + | 0.785090i | \(0.712617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.1803i | 0.363696i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 48.0000i | − 1.55979i | −0.625910 | − | 0.779895i | \(-0.715272\pi\) | ||||
0.625910 | − | 0.779895i | \(-0.284728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.0000 | 0.973841 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.8885 | −0.580076 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 26.8328i | − 0.869200i | −0.900624 | − | 0.434600i | \(-0.856890\pi\) | ||||
0.900624 | − | 0.434600i | \(-0.143110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 55.0000i | − 1.77976i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.23607i | − 0.0722818i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.4164 | 0.433238 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 24.0000i | − 0.773389i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.0000 | −0.965734 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 28.0000i | − 0.900419i | −0.892923 | − | 0.450210i | \(-0.851349\pi\) | ||||
0.892923 | − | 0.450210i | \(-0.148651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.0000 | −0.321246 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.8328 | 0.861106 | 0.430553 | − | 0.902565i | \(-0.358319\pi\) | ||||
0.430553 | + | 0.902565i | \(0.358319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 13.4164i | − 0.430110i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.1803 | −0.358057 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 49.1935i | − 1.57384i | −0.617055 | − | 0.786920i | \(-0.711675\pi\) | ||||
0.617055 | − | 0.786920i | \(-0.288325\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.3050 | 1.00051 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.0000 | −0.957826 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 39.0000i | − 1.24391i | −0.783054 | − | 0.621953i | \(-0.786339\pi\) | ||||
0.783054 | − | 0.621953i | \(-0.213661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.0000 | 1.27451 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.00000i | 0.0954911i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.8328 | 0.852372 | 0.426186 | − | 0.904635i | \(-0.359857\pi\) | ||||
0.426186 | + | 0.904635i | \(0.359857\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 35.7771i | − 1.13535i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50.0000i | 1.58511i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.5410i | 1.06225i | 0.847292 | + | 0.531127i | \(0.178231\pi\) | ||||
−0.847292 | + | 0.531127i | \(0.821769\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.7214 | 1.41492 |
(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 | 2240.2.g.k.449.3 | 4 | ||
4.3 | odd | 2 | inner | 2240.2.g.k.449.1 | 4 | ||
5.4 | even | 2 | inner | 2240.2.g.k.449.2 | 4 | ||
8.3 | odd | 2 | 1120.2.g.a.449.4 | yes | 4 | ||
8.5 | even | 2 | 1120.2.g.a.449.2 | yes | 4 | ||
20.19 | odd | 2 | inner | 2240.2.g.k.449.4 | 4 | ||
40.3 | even | 4 | 5600.2.a.w.1.2 | 2 | |||
40.13 | odd | 4 | 5600.2.a.bl.1.1 | 2 | |||
40.19 | odd | 2 | 1120.2.g.a.449.1 | ✓ | 4 | ||
40.27 | even | 4 | 5600.2.a.bl.1.2 | 2 | |||
40.29 | even | 2 | 1120.2.g.a.449.3 | yes | 4 | ||
40.37 | odd | 4 | 5600.2.a.w.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.g.a.449.1 | ✓ | 4 | 40.19 | odd | 2 | ||
1120.2.g.a.449.2 | yes | 4 | 8.5 | even | 2 | ||
1120.2.g.a.449.3 | yes | 4 | 40.29 | even | 2 | ||
1120.2.g.a.449.4 | yes | 4 | 8.3 | odd | 2 | ||
2240.2.g.k.449.1 | 4 | 4.3 | odd | 2 | inner | ||
2240.2.g.k.449.2 | 4 | 5.4 | even | 2 | inner | ||
2240.2.g.k.449.3 | 4 | 1.1 | even | 1 | trivial | ||
2240.2.g.k.449.4 | 4 | 20.19 | odd | 2 | inner | ||
5600.2.a.w.1.1 | 2 | 40.37 | odd | 4 | |||
5600.2.a.w.1.2 | 2 | 40.3 | even | 4 | |||
5600.2.a.bl.1.1 | 2 | 40.13 | odd | 4 | |||
5600.2.a.bl.1.2 | 2 | 40.27 | even | 4 |