Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(99,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1225.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.b (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: | \(9.78167424761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 245) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.99 |
Dual form | 1225.2.b.i.99.2 |
$q$-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 \(\left(\mathbb{Z}/1225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0.414214i | 0.239146i | 0.992825 | + | 0.119573i | \(0.0381526\pi\) | ||||
−0.992825 | + | 0.119573i | \(0.961847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.585786 | −0.239146 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.171573 | −0.0517312 | −0.0258656 | − | 0.999665i | \(-0.508234\pi\) | ||||
−0.0258656 | + | 0.999665i | \(0.508234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.41421i | − 1.22428i | −0.790748 | − | 0.612141i | \(-0.790308\pi\) | ||||
0.790748 | − | 0.612141i | \(-0.209692\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 3.24264i | 0.786456i | 0.919441 | + | 0.393228i | \(0.128642\pi\) | ||||
−0.919441 | + | 0.393228i | \(0.871358\pi\) | |||||||
\(18\) | 4.00000i | 0.942809i | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 0.242641i | − 0.0517312i | ||||||||
\(23\) | 7.41421i | 1.54597i | 0.634424 | + | 0.772985i | \(0.281237\pi\) | ||||
−0.634424 | + | 0.772985i | \(0.718763\pi\) | |||||||
\(24\) | −1.17157 | −0.239146 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.24264 | 1.22428 | ||||||||
\(27\) | 2.41421i | 0.464616i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.65685 | 1.60754 | 0.803769 | − | 0.594942i | \(-0.202825\pi\) | ||||
0.803769 | + | 0.594942i | \(0.202825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2426 | −1.83963 | −0.919816 | − | 0.392349i | \(-0.871662\pi\) | ||||
−0.919816 | + | 0.392349i | \(0.871662\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 0.0710678i | − 0.0123713i | ||||||||
\(34\) | −4.58579 | −0.786456 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.24264i | − 0.368688i | −0.982862 | − | 0.184344i | \(-0.940984\pi\) | ||||
0.982862 | − | 0.184344i | \(-0.0590160\pi\) | |||||||
\(38\) | 8.48528i | 1.37649i | ||||||||
\(39\) | 1.82843 | 0.292783 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.24264 | 0.974937 | 0.487468 | − | 0.873141i | \(-0.337920\pi\) | ||||
0.487468 | + | 0.873141i | \(0.337920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.4853 | −1.54597 | ||||||||
\(47\) | − 7.24264i | − 1.05645i | −0.849105 | − | 0.528224i | \(-0.822858\pi\) | ||||
0.849105 | − | 0.528224i | \(-0.177142\pi\) | |||||||
\(48\) | − 1.65685i | − 0.239146i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.34315 | −0.188078 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24264i | 0.582772i | 0.956606 | + | 0.291386i | \(0.0941163\pi\) | ||||
−0.956606 | + | 0.291386i | \(0.905884\pi\) | |||||||
\(54\) | −3.41421 | −0.464616 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.48528i | 0.329184i | ||||||||
\(58\) | 12.2426i | 1.60754i | ||||||||
\(59\) | −2.24264 | −0.291967 | −0.145983 | − | 0.989287i | \(-0.546635\pi\) | ||||
−0.145983 | + | 0.989287i | \(0.546635\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.82843 | 0.362143 | 0.181071 | − | 0.983470i | \(-0.442043\pi\) | ||||
0.181071 | + | 0.983470i | \(0.442043\pi\) | |||||||
\(62\) | − 14.4853i | − 1.83963i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.100505 | 0.0123713 | ||||||||
\(67\) | 8.24264i | 1.00700i | 0.863996 | + | 0.503499i | \(0.167954\pi\) | ||||
−0.863996 | + | 0.503499i | \(0.832046\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.07107 | −0.369713 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.17157 | −0.376396 | −0.188198 | − | 0.982131i | \(-0.560265\pi\) | ||||
−0.188198 | + | 0.982131i | \(0.560265\pi\) | |||||||
\(72\) | 8.00000i | 0.942809i | ||||||||
\(73\) | 8.48528i | 0.993127i | 0.868000 | + | 0.496564i | \(0.165405\pi\) | ||||
−0.868000 | + | 0.496564i | \(0.834595\pi\) | |||||||
\(74\) | 3.17157 | 0.368688 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.58579i | 0.292783i | ||||||||
\(79\) | −1.48528 | −0.167107 | −0.0835536 | − | 0.996503i | \(-0.526627\pi\) | ||||
−0.0835536 | + | 0.996503i | \(0.526627\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 8.82843i | 0.974937i | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.82843 | −0.304997 | ||||||||
\(87\) | 3.58579i | 0.384437i | ||||||||
\(88\) | − 0.485281i | − 0.0517312i | ||||||||
\(89\) | −8.00000 | −0.847998 | −0.423999 | − | 0.905663i | \(-0.639374\pi\) | ||||
−0.423999 | + | 0.905663i | \(0.639374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.24264i | − 0.439941i | ||||||||
\(94\) | 10.2426 | 1.05645 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2426i | 1.34459i | 0.740285 | + | 0.672293i | \(0.234691\pi\) | ||||
−0.740285 | + | 0.672293i | \(0.765309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.485281 | −0.0487726 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.48528 | −0.247295 | −0.123647 | − | 0.992326i | \(-0.539459\pi\) | ||||
−0.123647 | + | 0.992326i | \(0.539459\pi\) | |||||||
\(102\) | − 1.89949i | − 0.188078i | ||||||||
\(103\) | − 19.2426i | − 1.89603i | −0.318220 | − | 0.948017i | \(-0.603085\pi\) | ||||
0.318220 | − | 0.948017i | \(-0.396915\pi\) | |||||||
\(104\) | 12.4853 | 1.22428 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 2.48528i | 0.240261i | 0.992758 | + | 0.120131i | \(0.0383313\pi\) | ||||
−0.992758 | + | 0.120131i | \(0.961669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.928932 | 0.0881703 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 13.0711i | − 1.22962i | −0.788674 | − | 0.614811i | \(-0.789232\pi\) | ||||
0.788674 | − | 0.614811i | \(-0.210768\pi\) | |||||||
\(114\) | −3.51472 | −0.329184 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 12.4853i | − 1.15426i | ||||||||
\(118\) | − 3.17157i | − 0.291967i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9706 | −0.997324 | ||||||||
\(122\) | 4.00000i | 0.362143i | ||||||||
\(123\) | 2.58579i | 0.233153i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 8.24264i | − 0.731416i | −0.930730 | − | 0.365708i | \(-0.880827\pi\) | ||||
0.930730 | − | 0.365708i | \(-0.119173\pi\) | |||||||
\(128\) | − 11.3137i | − 1.00000i | ||||||||
\(129\) | −0.828427 | −0.0729389 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2426 | −1.06964 | −0.534822 | − | 0.844965i | \(-0.679621\pi\) | ||||
−0.534822 | + | 0.844965i | \(0.679621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.6569 | −1.00700 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.17157 | −0.786456 | ||||||||
\(137\) | − 12.0000i | − 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | − 4.34315i | − 0.369713i | ||||||||
\(139\) | 7.75736 | 0.657971 | 0.328985 | − | 0.944335i | \(-0.393293\pi\) | ||||
0.328985 | + | 0.944335i | \(0.393293\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | − 4.48528i | − 0.376396i | ||||||||
\(143\) | 0.757359i | 0.0633336i | ||||||||
\(144\) | −11.3137 | −0.942809 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.0000 | −0.993127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.17157 | 0.751365 | 0.375682 | − | 0.926749i | \(-0.377408\pi\) | ||||
0.375682 | + | 0.926749i | \(0.377408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.48528 | −0.609144 | −0.304572 | − | 0.952489i | \(-0.598513\pi\) | ||||
−0.304572 | + | 0.952489i | \(0.598513\pi\) | |||||||
\(152\) | 16.9706i | 1.37649i | ||||||||
\(153\) | 9.17157i | 0.741478i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 15.1716i | − 1.21082i | −0.795913 | − | 0.605412i | \(-0.793008\pi\) | ||||
0.795913 | − | 0.605412i | \(-0.206992\pi\) | |||||||
\(158\) | − 2.10051i | − 0.167107i | ||||||||
\(159\) | −1.75736 | −0.139368 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 10.5858i | 0.831698i | ||||||||
\(163\) | − 10.2426i | − 0.802266i | −0.916020 | − | 0.401133i | \(-0.868617\pi\) | ||||
0.916020 | − | 0.401133i | \(-0.131383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.757359i | 0.0586062i | 0.999571 | + | 0.0293031i | \(0.00932881\pi\) | ||||
−0.999571 | + | 0.0293031i | \(0.990671\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.48528 | −0.498868 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.9706 | 1.29777 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.24264i | 0.550648i | 0.961352 | + | 0.275324i | \(0.0887851\pi\) | ||||
−0.961352 | + | 0.275324i | \(0.911215\pi\) | |||||||
\(174\) | −5.07107 | −0.384437 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.686292 | 0.0517312 | ||||||||
\(177\) | − 0.928932i | − 0.0698228i | ||||||||
\(178\) | − 11.3137i | − 0.847998i | ||||||||
\(179\) | 14.4853 | 1.08268 | 0.541340 | − | 0.840804i | \(-0.317917\pi\) | ||||
0.541340 | + | 0.840804i | \(0.317917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7279 | 1.39204 | 0.696018 | − | 0.718025i | \(-0.254953\pi\) | ||||
0.696018 | + | 0.718025i | \(0.254953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.17157i | 0.0866052i | ||||||||
\(184\) | −20.9706 | −1.54597 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | − 0.556349i | − 0.0406843i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.9706 | 1.01087 | 0.505437 | − | 0.862863i | \(-0.331331\pi\) | ||||
0.505437 | + | 0.862863i | \(0.331331\pi\) | |||||||
\(192\) | − 3.31371i | − 0.239146i | ||||||||
\(193\) | − 16.0000i | − 1.15171i | −0.817554 | − | 0.575853i | \(-0.804670\pi\) | ||||
0.817554 | − | 0.575853i | \(-0.195330\pi\) | |||||||
\(194\) | −18.7279 | −1.34459 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 13.4142i | − 0.955723i | −0.878435 | − | 0.477862i | \(-0.841412\pi\) | ||||
0.878435 | − | 0.477862i | \(-0.158588\pi\) | |||||||
\(198\) | − 0.686292i | − 0.0487726i | ||||||||
\(199\) | −7.41421 | −0.525580 | −0.262790 | − | 0.964853i | \(-0.584643\pi\) | ||||
−0.262790 | + | 0.964853i | \(0.584643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.41421 | −0.240820 | ||||||||
\(202\) | − 3.51472i | − 0.247295i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 27.2132 | 1.89603 | ||||||||
\(207\) | 20.9706i | 1.45755i | ||||||||
\(208\) | 17.6569i | 1.22428i | ||||||||
\(209\) | −1.02944 | −0.0712077 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000 | 0.619586 | 0.309793 | − | 0.950804i | \(-0.399740\pi\) | ||||
0.309793 | + | 0.950804i | \(0.399740\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.31371i | − 0.0900138i | ||||||||
\(214\) | −3.51472 | −0.240261 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.82843 | −0.464616 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 7.07107i | − 0.478913i | ||||||||
\(219\) | −3.51472 | −0.237503 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.3137 | 0.962844 | ||||||||
\(222\) | 1.31371i | 0.0881703i | ||||||||
\(223\) | 24.2132i | 1.62144i | 0.585437 | + | 0.810718i | \(0.300923\pi\) | ||||
−0.585437 | + | 0.810718i | \(0.699077\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.4853 | 1.22962 | ||||||||
\(227\) | 15.7279i | 1.04390i | 0.852976 | + | 0.521949i | \(0.174795\pi\) | ||||
−0.852976 | + | 0.521949i | \(0.825205\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0416 | 1.19222 | 0.596112 | − | 0.802901i | \(-0.296711\pi\) | ||||
0.596112 | + | 0.802901i | \(0.296711\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 24.4853i | 1.60754i | ||||||||
\(233\) | − 9.17157i | − 0.600850i | −0.953805 | − | 0.300425i | \(-0.902872\pi\) | ||||
0.953805 | − | 0.300425i | \(-0.0971285\pi\) | |||||||
\(234\) | 17.6569 | 1.15426 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 0.615224i | − 0.0399631i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.4853 | 1.13103 | 0.565514 | − | 0.824738i | \(-0.308678\pi\) | ||||
0.565514 | + | 0.824738i | \(0.308678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.727922 | 0.0468896 | 0.0234448 | − | 0.999725i | \(-0.492537\pi\) | ||||
0.0234448 | + | 0.999725i | \(0.492537\pi\) | |||||||
\(242\) | − 15.5147i | − 0.997324i | ||||||||
\(243\) | 10.3431i | 0.663513i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.65685 | −0.233153 | ||||||||
\(247\) | − 26.4853i | − 1.68522i | ||||||||
\(248\) | − 28.9706i | − 1.83963i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.2132 | −1.08649 | −0.543244 | − | 0.839575i | \(-0.682804\pi\) | ||||
−0.543244 | + | 0.839575i | \(0.682804\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.27208i | − 0.0799749i | ||||||||
\(254\) | 11.6569 | 0.731416 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 9.51472i | − 0.593512i | −0.954953 | − | 0.296756i | \(-0.904095\pi\) | ||||
0.954953 | − | 0.296756i | \(-0.0959048\pi\) | |||||||
\(258\) | − 1.17157i | − 0.0729389i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.4853 | 1.51560 | ||||||||
\(262\) | − 17.3137i | − 1.06964i | ||||||||
\(263\) | − 16.6274i | − 1.02529i | −0.858601 | − | 0.512645i | \(-0.828666\pi\) | ||||
0.858601 | − | 0.512645i | \(-0.171334\pi\) | |||||||
\(264\) | 0.201010 | 0.0123713 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3.31371i | − 0.202796i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.2426 | −0.990331 | −0.495166 | − | 0.868799i | \(-0.664893\pi\) | ||||
−0.495166 | + | 0.868799i | \(0.664893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.686292 | 0.0416892 | 0.0208446 | − | 0.999783i | \(-0.493364\pi\) | ||||
0.0208446 | + | 0.999783i | \(0.493364\pi\) | |||||||
\(272\) | − 12.9706i | − 0.786456i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.9706 | 1.02523 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 15.2132i | − 0.914073i | −0.889448 | − | 0.457036i | \(-0.848911\pi\) | ||||
0.889448 | − | 0.457036i | \(-0.151089\pi\) | |||||||
\(278\) | 10.9706i | 0.657971i | ||||||||
\(279\) | −28.9706 | −1.73442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.31371 | 0.138024 | 0.0690121 | − | 0.997616i | \(-0.478015\pi\) | ||||
0.0690121 | + | 0.997616i | \(0.478015\pi\) | |||||||
\(282\) | 4.24264i | 0.252646i | ||||||||
\(283\) | − 24.5563i | − 1.45972i | −0.683595 | − | 0.729862i | \(-0.739584\pi\) | ||||
0.683595 | − | 0.729862i | \(-0.260416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.07107 | −0.0633336 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.48528 | 0.381487 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.48528 | −0.321553 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 25.7279i | − 1.50304i | −0.659710 | − | 0.751521i | \(-0.729321\pi\) | ||||
0.659710 | − | 0.751521i | \(-0.270679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.34315 | 0.368688 | ||||||||
\(297\) | − 0.414214i | − 0.0240351i | ||||||||
\(298\) | 12.9706i | 0.751365i | ||||||||
\(299\) | 32.7279 | 1.89270 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 10.5858i | − 0.609144i | ||||||||
\(303\) | − 1.02944i | − 0.0591396i | ||||||||
\(304\) | −24.0000 | −1.37649 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.9706 | −0.741478 | ||||||||
\(307\) | 30.8995i | 1.76353i | 0.471691 | + | 0.881764i | \(0.343644\pi\) | ||||
−0.471691 | + | 0.881764i | \(0.656356\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.97056 | 0.453429 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0000 | 0.567048 | 0.283524 | − | 0.958965i | \(-0.408496\pi\) | ||||
0.283524 | + | 0.958965i | \(0.408496\pi\) | |||||||
\(312\) | 5.17157i | 0.292783i | ||||||||
\(313\) | 18.2132i | 1.02947i | 0.857349 | + | 0.514736i | \(0.172110\pi\) | ||||
−0.857349 | + | 0.514736i | \(0.827890\pi\) | |||||||
\(314\) | 21.4558 | 1.21082 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.343146i | 0.0192730i | 0.999954 | + | 0.00963649i | \(0.00306744\pi\) | ||||
−0.999954 | + | 0.00963649i | \(0.996933\pi\) | |||||||
\(318\) | − 2.48528i | − 0.139368i | ||||||||
\(319\) | −1.48528 | −0.0831598 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.02944 | −0.0574576 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4558i | 1.08255i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.4853 | 0.802266 | ||||||||
\(327\) | − 2.07107i | − 0.114530i | ||||||||
\(328\) | 17.6569i | 0.974937i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.4558 | −1.50911 | −0.754555 | − | 0.656237i | \(-0.772147\pi\) | ||||
−0.754555 | + | 0.656237i | \(0.772147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.34315i | − 0.347602i | ||||||||
\(334\) | −1.07107 | −0.0586062 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 22.2426i | − 1.21163i | −0.795604 | − | 0.605817i | \(-0.792846\pi\) | ||||
0.795604 | − | 0.605817i | \(-0.207154\pi\) | |||||||
\(338\) | − 9.17157i | − 0.498868i | ||||||||
\(339\) | 5.41421 | 0.294060 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.75736 | 0.0951663 | ||||||||
\(342\) | 24.0000i | 1.29777i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.65685 | −0.304997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.2426 | −0.550648 | ||||||||
\(347\) | − 13.0711i | − 0.701692i | −0.936433 | − | 0.350846i | \(-0.885894\pi\) | ||||
0.936433 | − | 0.350846i | \(-0.114106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.9706 | −0.587241 | −0.293620 | − | 0.955922i | \(-0.594860\pi\) | ||||
−0.293620 | + | 0.955922i | \(0.594860\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.6569 | 0.568821 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.21320i | 0.330695i | 0.986235 | + | 0.165348i | \(0.0528746\pi\) | ||||
−0.986235 | + | 0.165348i | \(0.947125\pi\) | |||||||
\(354\) | 1.31371 | 0.0698228 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.4853i | 1.08268i | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 26.4853i | 1.39204i | ||||||||
\(363\) | − 4.54416i | − 0.238506i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.65685 | −0.0866052 | ||||||||
\(367\) | − 23.8701i | − 1.24601i | −0.782219 | − | 0.623003i | \(-0.785912\pi\) | ||||
0.782219 | − | 0.623003i | \(-0.214088\pi\) | |||||||
\(368\) | − 29.6569i | − 1.54597i | ||||||||
\(369\) | 17.6569 | 0.919179 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 16.4853i | − 0.853576i | −0.904352 | − | 0.426788i | \(-0.859645\pi\) | ||||
0.904352 | − | 0.426788i | \(-0.140355\pi\) | |||||||
\(374\) | 0.786797 | 0.0406843 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.4853 | 1.05645 | ||||||||
\(377\) | − 38.2132i | − 1.96808i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.00000 | −0.102733 | −0.0513665 | − | 0.998680i | \(-0.516358\pi\) | ||||
−0.0513665 | + | 0.998680i | \(0.516358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.41421 | 0.174915 | ||||||||
\(382\) | 19.7574i | 1.01087i | ||||||||
\(383\) | − 4.48528i | − 0.229187i | −0.993412 | − | 0.114594i | \(-0.963443\pi\) | ||||
0.993412 | − | 0.114594i | \(-0.0365566\pi\) | |||||||
\(384\) | 4.68629 | 0.239146 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.6274 | 1.15171 | ||||||||
\(387\) | 5.65685i | 0.287554i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.85786 | 0.347708 | 0.173854 | − | 0.984771i | \(-0.444378\pi\) | ||||
0.173854 | + | 0.984771i | \(0.444378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0416 | −1.21584 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 5.07107i | − 0.255802i | ||||||||
\(394\) | 18.9706 | 0.955723 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.58579i | 0.0795883i | 0.999208 | + | 0.0397942i | \(0.0126702\pi\) | ||||
−0.999208 | + | 0.0397942i | \(0.987330\pi\) | |||||||
\(398\) | − 10.4853i | − 0.525580i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8284 | 0.590683 | 0.295342 | − | 0.955392i | \(-0.404566\pi\) | ||||
0.295342 | + | 0.955392i | \(0.404566\pi\) | |||||||
\(402\) | − 4.82843i | − 0.240820i | ||||||||
\(403\) | 45.2132i | 2.25223i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.384776i | 0.0190727i | ||||||||
\(408\) | − 3.79899i | − 0.188078i | ||||||||
\(409\) | 2.48528 | 0.122889 | 0.0614446 | − | 0.998110i | \(-0.480429\pi\) | ||||
0.0614446 | + | 0.998110i | \(0.480429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.97056 | 0.245180 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −29.6569 | −1.45755 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.21320i | 0.157351i | ||||||||
\(418\) | − 1.45584i | − 0.0712077i | ||||||||
\(419\) | 18.7279 | 0.914919 | 0.457459 | − | 0.889230i | \(-0.348759\pi\) | ||||
0.457459 | + | 0.889230i | \(0.348759\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 12.7279i | 0.619586i | ||||||||
\(423\) | − 20.4853i | − 0.996028i | ||||||||
\(424\) | −12.0000 | −0.582772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.85786 | 0.0900138 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.313708 | −0.0151460 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.7990 | −1.38720 | −0.693599 | − | 0.720361i | \(-0.743976\pi\) | ||||
−0.693599 | + | 0.720361i | \(0.743976\pi\) | |||||||
\(432\) | − 9.65685i | − 0.464616i | ||||||||
\(433\) | − 10.9706i | − 0.527212i | −0.964630 | − | 0.263606i | \(-0.915088\pi\) | ||||
0.964630 | − | 0.263606i | \(-0.0849118\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 44.4853i | 2.12802i | ||||||||
\(438\) | − 4.97056i | − 0.237503i | ||||||||
\(439\) | −30.3848 | −1.45019 | −0.725093 | − | 0.688651i | \(-0.758203\pi\) | ||||
−0.725093 | + | 0.688651i | \(0.758203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.2426i | 0.962844i | ||||||||
\(443\) | 15.1716i | 0.720823i | 0.932793 | + | 0.360412i | \(0.117364\pi\) | ||||
−0.932793 | + | 0.360412i | \(0.882636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −34.2426 | −1.62144 | ||||||||
\(447\) | 3.79899i | 0.179686i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.1716 | 1.14073 | 0.570364 | − | 0.821392i | \(-0.306802\pi\) | ||||
0.570364 | + | 0.821392i | \(0.306802\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.07107 | −0.0504346 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3.10051i | − 0.145674i | ||||||||
\(454\) | −22.2426 | −1.04390 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.02944 | −0.329184 | ||||||||
\(457\) | 11.7574i | 0.549986i | 0.961446 | + | 0.274993i | \(0.0886756\pi\) | ||||
−0.961446 | + | 0.274993i | \(0.911324\pi\) | |||||||
\(458\) | 25.5147i | 1.19222i | ||||||||
\(459\) | −7.82843 | −0.365400 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.02944 | −0.141095 | −0.0705475 | − | 0.997508i | \(-0.522475\pi\) | ||||
−0.0705475 | + | 0.997508i | \(0.522475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 21.4558i | − 0.997138i | −0.866850 | − | 0.498569i | \(-0.833859\pi\) | ||||
0.866850 | − | 0.498569i | \(-0.166141\pi\) | |||||||
\(464\) | −34.6274 | −1.60754 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.9706 | 0.600850 | ||||||||
\(467\) | − 5.72792i | − 0.265057i | −0.991179 | − | 0.132528i | \(-0.957690\pi\) | ||||
0.991179 | − | 0.132528i | \(-0.0423095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.28427 | 0.289564 | ||||||||
\(472\) | − 6.34315i | − 0.291967i | ||||||||
\(473\) | − 0.343146i | − 0.0157779i | ||||||||
\(474\) | 0.870058 | 0.0399631 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000i | 0.549442i | ||||||||
\(478\) | 24.7279i | 1.13103i | ||||||||
\(479\) | 11.7574 | 0.537207 | 0.268604 | − | 0.963251i | \(-0.413438\pi\) | ||||
0.268604 | + | 0.963251i | \(0.413438\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.89949 | −0.451378 | ||||||||
\(482\) | 1.02944i | 0.0468896i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.6274 | −0.663513 | ||||||||
\(487\) | − 27.6985i | − 1.25514i | −0.778561 | − | 0.627569i | \(-0.784050\pi\) | ||||
0.778561 | − | 0.627569i | \(-0.215950\pi\) | |||||||
\(488\) | 8.00000i | 0.362143i | ||||||||
\(489\) | 4.24264 | 0.191859 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.2843 | −1.68262 | −0.841308 | − | 0.540556i | \(-0.818214\pi\) | ||||
−0.841308 | + | 0.540556i | \(0.818214\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.0711i | 1.26426i | ||||||||
\(494\) | 37.4558 | 1.68522 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 40.9706 | 1.83963 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.00000 | −0.134298 | −0.0671492 | − | 0.997743i | \(-0.521390\pi\) | ||||
−0.0671492 | + | 0.997743i | \(0.521390\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.313708 | −0.0140155 | ||||||||
\(502\) | − 24.3431i | − 1.08649i | ||||||||
\(503\) | 41.2426i | 1.83892i | 0.393185 | + | 0.919459i | \(0.371373\pi\) | ||||
−0.393185 | + | 0.919459i | \(0.628627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.79899 | 0.0799749 | ||||||||
\(507\) | − 2.68629i | − 0.119302i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.2132 | −1.11756 | −0.558778 | − | 0.829317i | \(-0.688730\pi\) | ||||
−0.558778 | + | 0.829317i | \(0.688730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 22.6274i | − 1.00000i | ||||||||
\(513\) | 14.4853i | 0.639541i | ||||||||
\(514\) | 13.4558 | 0.593512 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.24264i | 0.0546513i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.00000 | −0.131685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.9706 | −0.655872 | −0.327936 | − | 0.944700i | \(-0.606353\pi\) | ||||
−0.327936 | + | 0.944700i | \(0.606353\pi\) | |||||||
\(522\) | 34.6274i | 1.51560i | ||||||||
\(523\) | − 32.4853i | − 1.42048i | −0.703959 | − | 0.710241i | \(-0.748586\pi\) | ||||
0.703959 | − | 0.710241i | \(-0.251414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.5147 | 1.02529 | ||||||||
\(527\) | − 33.2132i | − 1.44679i | ||||||||
\(528\) | 0.284271i | 0.0123713i | ||||||||
\(529\) | −31.9706 | −1.39002 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.34315 | −0.275269 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 27.5563i | − 1.19360i | ||||||||
\(534\) | 4.68629 | 0.202796 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −23.3137 | −1.00700 | ||||||||
\(537\) | 6.00000i | 0.258919i | ||||||||
\(538\) | − 22.9706i | − 0.990331i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9706 | −0.944588 | −0.472294 | − | 0.881441i | \(-0.656574\pi\) | ||||
−0.472294 | + | 0.881441i | \(0.656574\pi\) | |||||||
\(542\) | 0.970563i | 0.0416892i | ||||||||
\(543\) | 7.75736i | 0.332900i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4853i | 1.04692i | 0.852052 | + | 0.523458i | \(0.175358\pi\) | ||||
−0.852052 | + | 0.523458i | \(0.824642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.00000 | 0.341432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 51.9411 | 2.21277 | ||||||||
\(552\) | − 8.68629i | − 0.369713i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.5147 | 0.914073 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.79899i | 0.330454i | 0.986256 | + | 0.165227i | \(0.0528356\pi\) | ||||
−0.986256 | + | 0.165227i | \(0.947164\pi\) | |||||||
\(558\) | − 40.9706i | − 1.73442i | ||||||||
\(559\) | 8.82843 | 0.373403 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.230447 | 0.00972950 | ||||||||
\(562\) | 3.27208i | 0.138024i | ||||||||
\(563\) | 31.9411i | 1.34616i | 0.739571 | + | 0.673079i | \(0.235029\pi\) | ||||
−0.739571 | + | 0.673079i | \(0.764971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 34.7279 | 1.45972 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 8.97056i | − 0.376396i | ||||||||
\(569\) | −26.1421 | −1.09594 | −0.547968 | − | 0.836500i | \(-0.684598\pi\) | ||||
−0.547968 | + | 0.836500i | \(0.684598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5147 | −0.732968 | −0.366484 | − | 0.930424i | \(-0.619439\pi\) | ||||
−0.366484 | + | 0.930424i | \(0.619439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.78680i | 0.241747i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −22.6274 | −0.942809 | ||||||||
\(577\) | 15.7279i | 0.654762i | 0.944892 | + | 0.327381i | \(0.106166\pi\) | ||||
−0.944892 | + | 0.327381i | \(0.893834\pi\) | |||||||
\(578\) | 9.17157i | 0.381487i | ||||||||
\(579\) | 6.62742 | 0.275426 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − 7.75736i | − 0.321553i | ||||||||
\(583\) | − 0.727922i | − 0.0301475i | ||||||||
\(584\) | −24.0000 | −0.993127 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.3848 | 1.50304 | ||||||||
\(587\) | − 37.4558i | − 1.54597i | −0.634425 | − | 0.772984i | \(-0.718763\pi\) | ||||
0.634425 | − | 0.772984i | \(-0.281237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −61.4558 | −2.53224 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.55635 | 0.228558 | ||||||||
\(592\) | 8.97056i | 0.368688i | ||||||||
\(593\) | − 19.2426i | − 0.790201i | −0.918638 | − | 0.395100i | \(-0.870710\pi\) | ||||
0.918638 | − | 0.395100i | \(-0.129290\pi\) | |||||||
\(594\) | 0.585786 | 0.0240351 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.07107i | − 0.125690i | ||||||||
\(598\) | 46.2843i | 1.89270i | ||||||||
\(599\) | 17.8284 | 0.728450 | 0.364225 | − | 0.931311i | \(-0.381334\pi\) | ||||
0.364225 | + | 0.931311i | \(0.381334\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.9706 | 0.447499 | 0.223749 | − | 0.974647i | \(-0.428170\pi\) | ||||
0.223749 | + | 0.974647i | \(0.428170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.3137i | 0.949408i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.45584 | 0.0591396 | ||||||||
\(607\) | − 5.10051i | − 0.207023i | −0.994628 | − | 0.103512i | \(-0.966992\pi\) | ||||
0.994628 | − | 0.103512i | \(-0.0330079\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.9706 | −1.29339 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 23.9411i | − 0.966973i | −0.875352 | − | 0.483486i | \(-0.839370\pi\) | ||||
0.875352 | − | 0.483486i | \(-0.160630\pi\) | |||||||
\(614\) | −43.6985 | −1.76353 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 4.58579i | − 0.184617i | −0.995730 | − | 0.0923084i | \(-0.970575\pi\) | ||||
0.995730 | − | 0.0923084i | \(-0.0294246\pi\) | |||||||
\(618\) | 11.2721i | 0.453429i | ||||||||
\(619\) | 16.9289 | 0.680431 | 0.340216 | − | 0.940347i | \(-0.389500\pi\) | ||||
0.340216 | + | 0.940347i | \(0.389500\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.8995 | −0.718282 | ||||||||
\(622\) | 14.1421i | 0.567048i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.31371 | −0.292783 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25.7574 | −1.02947 | ||||||||
\(627\) | − 0.426407i | − 0.0170291i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.27208 | 0.289957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.4558 | −1.69014 | −0.845070 | − | 0.534655i | \(-0.820441\pi\) | ||||
−0.845070 | + | 0.534655i | \(0.820441\pi\) | |||||||
\(632\) | − 4.20101i | − 0.167107i | ||||||||
\(633\) | 3.72792i | 0.148172i | ||||||||
\(634\) | −0.485281 | −0.0192730 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 2.10051i | − 0.0831598i | ||||||||
\(639\) | −8.97056 | −0.354870 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3137 | −0.920836 | −0.460418 | − | 0.887702i | \(-0.652300\pi\) | ||||
−0.460418 | + | 0.887702i | \(0.652300\pi\) | |||||||
\(642\) | − 1.45584i | − 0.0574576i | ||||||||
\(643\) | − 2.27208i | − 0.0896020i | −0.998996 | − | 0.0448010i | \(-0.985735\pi\) | ||||
0.998996 | − | 0.0448010i | \(-0.0142654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.5147 | −1.08255 | ||||||||
\(647\) | − 11.5147i | − 0.452690i | −0.974047 | − | 0.226345i | \(-0.927322\pi\) | ||||
0.974047 | − | 0.226345i | \(-0.0726777\pi\) | |||||||
\(648\) | 21.1716i | 0.831698i | ||||||||
\(649\) | 0.384776 | 0.0151038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.9706i | 1.36850i | 0.729246 | + | 0.684252i | \(0.239871\pi\) | ||||
−0.729246 | + | 0.684252i | \(0.760129\pi\) | |||||||
\(654\) | 2.92893 | 0.114530 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.9706 | −0.974937 | ||||||||
\(657\) | 24.0000i | 0.936329i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.9706 | −0.777943 | −0.388971 | − | 0.921250i | \(-0.627169\pi\) | ||||
−0.388971 | + | 0.921250i | \(0.627169\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.4558 | −0.523372 | −0.261686 | − | 0.965153i | \(-0.584278\pi\) | ||||
−0.261686 | + | 0.965153i | \(0.584278\pi\) | |||||||
\(662\) | − 38.8284i | − 1.50911i | ||||||||
\(663\) | 5.92893i | 0.230261i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.97056 | 0.347602 | ||||||||
\(667\) | 64.1838i | 2.48521i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.0294 | −0.387760 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.485281 | −0.0187341 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.51472i | 0.135482i | 0.997703 | + | 0.0677412i | \(0.0215792\pi\) | ||||
−0.997703 | + | 0.0677412i | \(0.978421\pi\) | |||||||
\(674\) | 31.4558 | 1.21163 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.2132i | 1.69925i | 0.527386 | + | 0.849626i | \(0.323172\pi\) | ||||
−0.527386 | + | 0.849626i | \(0.676828\pi\) | |||||||
\(678\) | 7.65685i | 0.294060i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.51472 | −0.249645 | ||||||||
\(682\) | 2.48528i | 0.0951663i | ||||||||
\(683\) | 31.7990i | 1.21675i | 0.793648 | + | 0.608377i | \(0.208179\pi\) | ||||
−0.793648 | + | 0.608377i | \(0.791821\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.47309i | 0.285116i | ||||||||
\(688\) | − 8.00000i | − 0.304997i | ||||||||
\(689\) | 18.7279 | 0.713477 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.8284 | −0.564100 | −0.282050 | − | 0.959400i | \(-0.591014\pi\) | ||||
−0.282050 | + | 0.959400i | \(0.591014\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.4853 | 0.701692 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.1421 | −0.384437 | ||||||||
\(697\) | 20.2426i | 0.766745i | ||||||||
\(698\) | − 15.5147i | − 0.587241i | ||||||||
\(699\) | 3.79899 | 0.143691 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.4558 | 1.75461 | 0.877307 | − | 0.479931i | \(-0.159338\pi\) | ||||
0.877307 | + | 0.479931i | \(0.159338\pi\) | |||||||
\(702\) | 15.0711i | 0.568821i | ||||||||
\(703\) | − 13.4558i | − 0.507497i | ||||||||
\(704\) | 1.37258 | 0.0517312 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.78680 | −0.330695 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0000 | −0.638448 | −0.319224 | − | 0.947679i | \(-0.603422\pi\) | ||||
−0.319224 | + | 0.947679i | \(0.603422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.20101 | −0.157550 | ||||||||
\(712\) | − 22.6274i | − 0.847998i | ||||||||
\(713\) | − 75.9411i | − 2.84402i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.24264i | 0.270481i | ||||||||
\(718\) | 16.0000i | 0.597115i | ||||||||
\(719\) | −25.2132 | −0.940294 | −0.470147 | − | 0.882588i | \(-0.655799\pi\) | ||||
−0.470147 | + | 0.882588i | \(0.655799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.0416i | 0.894737i | ||||||||
\(723\) | 0.301515i | 0.0112135i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.42641 | 0.238506 | ||||||||
\(727\) | − 6.68629i | − 0.247981i | −0.992283 | − | 0.123990i | \(-0.960431\pi\) | ||||
0.992283 | − | 0.123990i | \(-0.0395692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.1716 | 0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.48528 | −0.239867 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 14.6985i | − 0.542901i | −0.962452 | − | 0.271450i | \(-0.912497\pi\) | ||||
0.962452 | − | 0.271450i | \(-0.0875033\pi\) | |||||||
\(734\) | 33.7574 | 1.24601 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.41421i | − 0.0520932i | ||||||||
\(738\) | 24.9706i | 0.919179i | ||||||||
\(739\) | −29.9706 | −1.10248 | −0.551242 | − | 0.834345i | \(-0.685846\pi\) | ||||
−0.551242 | + | 0.834345i | \(0.685846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.9706 | 0.403014 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.2721i | 0.413532i | 0.978390 | + | 0.206766i | \(0.0662940\pi\) | ||||
−0.978390 | + | 0.206766i | \(0.933706\pi\) | |||||||
\(744\) | 12.0000 | 0.439941 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23.3137 | 0.853576 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.4853 | 1.07593 | 0.537967 | − | 0.842966i | \(-0.319193\pi\) | ||||
0.537967 | + | 0.842966i | \(0.319193\pi\) | |||||||
\(752\) | 28.9706i | 1.05645i | ||||||||
\(753\) | − 7.12994i | − 0.259830i | ||||||||
\(754\) | 54.0416 | 1.96808 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 0.485281i | − 0.0176379i | −0.999961 | − | 0.00881893i | \(-0.997193\pi\) | ||||
0.999961 | − | 0.00881893i | \(-0.00280719\pi\) | |||||||
\(758\) | − 2.82843i | − 0.102733i | ||||||||
\(759\) | 0.526912 | 0.0191257 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.7279 | 0.461387 | 0.230693 | − | 0.973026i | \(-0.425901\pi\) | ||||
0.230693 | + | 0.973026i | \(0.425901\pi\) | |||||||
\(762\) | 4.82843i | 0.174915i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.34315 | 0.229187 | ||||||||
\(767\) | 9.89949i | 0.357450i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.82843 | −0.318361 | −0.159181 | − | 0.987249i | \(-0.550885\pi\) | ||||
−0.159181 | + | 0.987249i | \(0.550885\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.94113 | 0.141936 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.21320i | 0.223473i | 0.993738 | + | 0.111737i | \(0.0356413\pi\) | ||||
−0.993738 | + | 0.111737i | \(0.964359\pi\) | |||||||
\(774\) | −8.00000 | −0.287554 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −37.4558 | −1.34459 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.69848i | 0.347708i | ||||||||
\(779\) | 37.4558 | 1.34199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.544156 | 0.0194714 | ||||||||
\(782\) | − 34.0000i | − 1.21584i | ||||||||
\(783\) | 20.8995i | 0.746887i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.17157 | 0.255802 | ||||||||
\(787\) | 20.2721i | 0.722622i | 0.932445 | + | 0.361311i | \(0.117671\pi\) | ||||
−0.932445 | + | 0.361311i | \(0.882329\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.88730 | 0.245194 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − 1.37258i | − 0.0487726i | ||||||||
\(793\) | − 12.4853i | − 0.443365i | ||||||||
\(794\) | −2.24264 | −0.0795883 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 21.1838i | − 0.750367i | −0.926950 | − | 0.375184i | \(-0.877580\pi\) | ||||
0.926950 | − | 0.375184i | \(-0.122420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.4853 | 0.830850 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.6274 | −0.799500 | ||||||||
\(802\) | 16.7279i | 0.590683i | ||||||||
\(803\) | − 1.45584i | − 0.0513756i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −63.9411 | −2.25223 | ||||||||
\(807\) | − 6.72792i | − 0.236834i | ||||||||
\(808\) | − 7.02944i | − 0.247295i | ||||||||
\(809\) | 48.5980 | 1.70861 | 0.854307 | − | 0.519769i | \(-0.173982\pi\) | ||||
0.854307 | + | 0.519769i | \(0.173982\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.3553 | −1.66287 | −0.831435 | − | 0.555621i | \(-0.812480\pi\) | ||||
−0.831435 | + | 0.555621i | \(0.812480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.284271i | 0.00996983i | ||||||||
\(814\) | −0.544156 | −0.0190727 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.37258 | 0.188078 | ||||||||
\(817\) | 12.0000i | 0.419827i | ||||||||
\(818\) | 3.51472i | 0.122889i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.4853 | −0.819642 | −0.409821 | − | 0.912166i | \(-0.634409\pi\) | ||||
−0.409821 | + | 0.912166i | \(0.634409\pi\) | |||||||
\(822\) | 7.02944i | 0.245180i | ||||||||
\(823\) | 16.7279i | 0.583099i | 0.956556 | + | 0.291549i | \(0.0941708\pi\) | ||||
−0.956556 | + | 0.291549i | \(0.905829\pi\) | |||||||
\(824\) | 54.4264 | 1.89603 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 42.0416i | − 1.46193i | −0.682415 | − | 0.730965i | \(-0.739070\pi\) | ||||
0.682415 | − | 0.730965i | \(-0.260930\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.95837 | 0.206943 | 0.103471 | − | 0.994632i | \(-0.467005\pi\) | ||||
0.103471 | + | 0.994632i | \(0.467005\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.30152 | 0.218597 | ||||||||
\(832\) | 35.3137i | 1.22428i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.54416 | −0.157351 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 24.7279i | − 0.854722i | ||||||||
\(838\) | 26.4853i | 0.914919i | ||||||||
\(839\) | −23.2721 | −0.803441 | −0.401721 | − | 0.915762i | \(-0.631588\pi\) | ||||
−0.401721 | + | 0.915762i | \(0.631588\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.9411 | 1.58418 | ||||||||
\(842\) | − 26.8701i | − 0.926003i | ||||||||
\(843\) | 0.958369i | 0.0330080i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 28.9706 | 0.996028 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 16.9706i | − 0.582772i | ||||||||
\(849\) | 10.1716 | 0.349087 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.6274 | 0.569981 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 10.9706i | − 0.375625i | −0.982205 | − | 0.187812i | \(-0.939860\pi\) | ||||
0.982205 | − | 0.187812i | \(-0.0601397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.02944 | −0.240261 | ||||||||
\(857\) | − 22.4853i | − 0.768083i | −0.923316 | − | 0.384041i | \(-0.874532\pi\) | ||||
0.923316 | − | 0.384041i | \(-0.125468\pi\) | |||||||
\(858\) | − 0.443651i | − 0.0151460i | ||||||||
\(859\) | −24.7696 | −0.845126 | −0.422563 | − | 0.906334i | \(-0.638870\pi\) | ||||
−0.422563 | + | 0.906334i | \(0.638870\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 40.7279i | − 1.38720i | ||||||||
\(863\) | 18.3848i | 0.625825i | 0.949782 | + | 0.312913i | \(0.101305\pi\) | ||||
−0.949782 | + | 0.312913i | \(0.898695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.5147 | 0.527212 | ||||||||
\(867\) | 2.68629i | 0.0912312i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.254834 | 0.00864465 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.3848 | 1.23285 | ||||||||
\(872\) | − 14.1421i | − 0.478913i | ||||||||
\(873\) | 37.4558i | 1.26769i | ||||||||
\(874\) | −62.9117 | −2.12802 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 13.0294i | − 0.439973i | −0.975503 | − | 0.219986i | \(-0.929399\pi\) | ||||
0.975503 | − | 0.219986i | \(-0.0706013\pi\) | |||||||
\(878\) | − 42.9706i | − 1.45019i | ||||||||
\(879\) | 10.6569 | 0.359447 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.9706 | 1.78462 | 0.892312 | − | 0.451420i | \(-0.149082\pi\) | ||||
0.892312 | + | 0.451420i | \(0.149082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.5147i | 1.06055i | 0.847824 | + | 0.530277i | \(0.177912\pi\) | ||||
−0.847824 | + | 0.530277i | \(0.822088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.4558 | −0.720823 | ||||||||
\(887\) | 2.97056i | 0.0997417i | 0.998756 | + | 0.0498709i | \(0.0158810\pi\) | ||||
−0.998756 | + | 0.0498709i | \(0.984119\pi\) | |||||||
\(888\) | 2.62742i | 0.0881703i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.28427 | −0.0430247 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 43.4558i | − 1.45419i | ||||||||
\(894\) | −5.37258 | −0.179686 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.5563i | 0.452633i | ||||||||
\(898\) | 34.1838i | 1.14073i | ||||||||
\(899\) | −88.6690 | −2.95728 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.7574 | −0.458324 | ||||||||
\(902\) | − 1.51472i | − 0.0504346i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 36.9706 | 1.22962 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.38478 | 0.145674 | ||||||||
\(907\) | 44.1838i | 1.46710i | 0.679637 | + | 0.733549i | \(0.262137\pi\) | ||||
−0.679637 | + | 0.733549i | \(0.737863\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.02944 | −0.233152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.65685 | 0.187420 | 0.0937100 | − | 0.995600i | \(-0.470127\pi\) | ||||
0.0937100 | + | 0.995600i | \(0.470127\pi\) | |||||||
\(912\) | − 9.94113i | − 0.329184i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −16.6274 | −0.549986 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − 11.0711i | − 0.365400i | ||||||||
\(919\) | −12.4558 | −0.410880 | −0.205440 | − | 0.978670i | \(-0.565863\pi\) | ||||
−0.205440 | + | 0.978670i | \(0.565863\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.7990 | −0.421741 | ||||||||
\(922\) | − 4.28427i | − 0.141095i | ||||||||
\(923\) | 14.0000i | 0.460816i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30.3431 | 0.997138 | ||||||||
\(927\) | − 54.4264i | − 1.78760i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.2721 | 0.960386 | 0.480193 | − | 0.877163i | \(-0.340567\pi\) | ||||
0.480193 | + | 0.877163i | \(0.340567\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.14214i | 0.135607i | ||||||||
\(934\) | 8.10051 | 0.265057 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 35.3137 | 1.15426 | ||||||||
\(937\) | − 48.5563i | − 1.58627i | −0.609048 | − | 0.793133i | \(-0.708448\pi\) | ||||
0.609048 | − | 0.793133i | \(-0.291552\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.54416 | −0.246194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.9706 | −0.944413 | −0.472207 | − | 0.881488i | \(-0.656542\pi\) | ||||
−0.472207 | + | 0.881488i | \(0.656542\pi\) | |||||||
\(942\) | 8.88730i | 0.289564i | ||||||||
\(943\) | 46.2843i | 1.50722i | ||||||||
\(944\) | 8.97056 | 0.291967 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.485281 | 0.0157779 | ||||||||
\(947\) | 52.2426i | 1.69766i | 0.528668 | + | 0.848829i | \(0.322692\pi\) | ||||
−0.528668 | + | 0.848829i | \(0.677308\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.4558 | 1.21587 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.142136 | −0.00460906 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.0122i | 1.71723i | 0.512618 | + | 0.858617i | \(0.328676\pi\) | ||||
−0.512618 | + | 0.858617i | \(0.671324\pi\) | |||||||
\(954\) | −16.9706 | −0.549442 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 0.615224i | − 0.0198874i | ||||||||
\(958\) | 16.6274i | 0.537207i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9117 | 2.38425 | ||||||||
\(962\) | − 14.0000i | − 0.451378i | ||||||||
\(963\) | 7.02944i | 0.226520i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.4264i | 1.94318i | 0.236666 | + | 0.971591i | \(0.423945\pi\) | ||||
−0.236666 | + | 0.971591i | \(0.576055\pi\) | |||||||
\(968\) | − 31.0294i | − 0.997324i | ||||||||
\(969\) | −8.05887 | −0.258888 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.2721 | 0.554287 | 0.277144 | − | 0.960828i | \(-0.410612\pi\) | ||||
0.277144 | + | 0.960828i | \(0.410612\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 39.1716 | 1.25514 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.3137 | −0.362143 | ||||||||
\(977\) | − 42.7696i | − 1.36832i | −0.729332 | − | 0.684160i | \(-0.760169\pi\) | ||||
0.729332 | − | 0.684160i | \(-0.239831\pi\) | |||||||
\(978\) | 6.00000i | 0.191859i | ||||||||
\(979\) | 1.37258 | 0.0438679 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.1421 | −0.451524 | ||||||||
\(982\) | − 52.7279i | − 1.68262i | ||||||||
\(983\) | − 0.213203i | − 0.00680013i | −0.999994 | − | 0.00340007i | \(-0.998918\pi\) | ||||
0.999994 | − | 0.00340007i | \(-0.00108228\pi\) | |||||||
\(984\) | −7.31371 | −0.233153 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −39.6985 | −1.26426 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.8284 | −0.471517 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.9411 | 0.633451 | 0.316725 | − | 0.948517i | \(-0.397417\pi\) | ||||
0.316725 | + | 0.948517i | \(0.397417\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 11.3726i | − 0.360898i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 21.7279i | − 0.688130i | −0.938946 | − | 0.344065i | \(-0.888196\pi\) | ||||
0.938946 | − | 0.344065i | \(-0.111804\pi\) | |||||||
\(998\) | − 4.24264i | − 0.134298i | ||||||||
\(999\) | 5.41421 | 0.171298 |
(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 | 1225.2.b.i.99.3 | 4 | ||
5.2 | odd | 4 | 245.2.a.e.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1225.2.a.r.1.2 | 2 | |||
5.4 | even | 2 | inner | 1225.2.b.i.99.2 | 4 | ||
7.6 | odd | 2 | 1225.2.b.j.99.4 | 4 | |||
15.2 | even | 4 | 2205.2.a.v.1.2 | 2 | |||
20.7 | even | 4 | 3920.2.a.bw.1.1 | 2 | |||
35.2 | odd | 12 | 245.2.e.g.116.2 | 4 | |||
35.12 | even | 12 | 245.2.e.f.116.2 | 4 | |||
35.13 | even | 4 | 1225.2.a.p.1.2 | 2 | |||
35.17 | even | 12 | 245.2.e.f.226.2 | 4 | |||
35.27 | even | 4 | 245.2.a.f.1.1 | yes | 2 | ||
35.32 | odd | 12 | 245.2.e.g.226.2 | 4 | |||
35.34 | odd | 2 | 1225.2.b.j.99.1 | 4 | |||
105.62 | odd | 4 | 2205.2.a.t.1.2 | 2 | |||
140.27 | odd | 4 | 3920.2.a.br.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.2.a.e.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
245.2.a.f.1.1 | yes | 2 | 35.27 | even | 4 | ||
245.2.e.f.116.2 | 4 | 35.12 | even | 12 | |||
245.2.e.f.226.2 | 4 | 35.17 | even | 12 | |||
245.2.e.g.116.2 | 4 | 35.2 | odd | 12 | |||
245.2.e.g.226.2 | 4 | 35.32 | odd | 12 | |||
1225.2.a.p.1.2 | 2 | 35.13 | even | 4 | |||
1225.2.a.r.1.2 | 2 | 5.3 | odd | 4 | |||
1225.2.b.i.99.2 | 4 | 5.4 | even | 2 | inner | ||
1225.2.b.i.99.3 | 4 | 1.1 | even | 1 | trivial | ||
1225.2.b.j.99.1 | 4 | 35.34 | odd | 2 | |||
1225.2.b.j.99.4 | 4 | 7.6 | odd | 2 | |||
2205.2.a.t.1.2 | 2 | 105.62 | odd | 4 | |||
2205.2.a.v.1.2 | 2 | 15.2 | even | 4 | |||
3920.2.a.br.1.2 | 2 | 140.27 | odd | 4 | |||
3920.2.a.bw.1.1 | 2 | 20.7 | even | 4 |