Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3468,2,Mod(829,3468)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3468, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3468.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3468 = 2^{2} \cdot 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3468.j (of order \(4\), degree \(2\), 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: | \(27.6921194210\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 204) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3217.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3468.3217 |
Dual form | 3468.2.j.f.829.2 |
$q$-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 \(\left(\mathbb{Z}/3468\mathbb{Z}\right)^\times\).
\(n\) | \(1157\) | \(1735\) | \(2893\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | −0.847316 | − | 0.531089i | \(-0.821783\pi\) |
0.531089 | + | 0.847316i | \(0.321783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.53553 | + | 3.53553i | 1.06600 | + | 1.06600i | 0.997662 | + | 0.0683416i | \(0.0217708\pi\) |
0.0683416 | + | 0.997662i | \(0.478229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) | ||||
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.12132 | − | 2.12132i | −0.442326 | − | 0.442326i | 0.450467 | − | 0.892793i | \(-0.351257\pi\) |
−0.892793 | + | 0.450467i | \(0.851257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000i | 0.800000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.41421 | + | 1.41421i | −0.262613 | + | 0.262613i | −0.826115 | − | 0.563502i | \(-0.809454\pi\) |
0.563502 | + | 0.826115i | \(0.309454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.41421 | − | 1.41421i | 0.254000 | − | 0.254000i | −0.568608 | − | 0.822608i | \(-0.692518\pi\) |
0.822608 | + | 0.568608i | \(0.192518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.00000 | 0.870388 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.65685 | + | 5.65685i | −0.929981 | + | 0.929981i | −0.997704 | − | 0.0677230i | \(-0.978427\pi\) |
0.0677230 | + | 0.997704i | \(0.478427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.53553 | − | 3.53553i | 0.566139 | − | 0.566139i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.53553 | + | 3.53553i | 0.552158 | + | 0.552158i | 0.927063 | − | 0.374905i | \(-0.122325\pi\) |
−0.374905 | + | 0.927063i | \(0.622325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.00000i | 1.37249i | 0.727372 | + | 0.686244i | \(0.240742\pi\) | ||||
−0.727372 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.707107 | + | 0.707107i | 0.105409 | + | 0.105409i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 7.00000i | − | 1.00000i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.707107 | + | 0.707107i | 0.0936586 | + | 0.0936586i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.00000i | − | 0.781133i | −0.920575 | − | 0.390567i | \(-0.872279\pi\) | ||
0.920575 | − | 0.390567i | \(-0.127721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.82843 | + | 2.82843i | 0.362143 | + | 0.362143i | 0.864601 | − | 0.502458i | \(-0.167571\pi\) |
−0.502458 | + | 0.864601i | \(0.667571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.53553 | + | 3.53553i | −0.438529 | + | 0.438529i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.48528 | + | 8.48528i | −1.00702 | + | 1.00702i | −0.00704243 | + | 0.999975i | \(0.502242\pi\) |
−0.999975 | + | 0.00704243i | \(0.997758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.41421 | − | 1.41421i | 0.165521 | − | 0.165521i | −0.619486 | − | 0.785007i | \(-0.712659\pi\) |
0.785007 | + | 0.619486i | \(0.212659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.82843 | + | 2.82843i | 0.326599 | + | 0.326599i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.07107 | + | 7.07107i | 0.795557 | + | 0.795557i | 0.982391 | − | 0.186834i | \(-0.0598227\pi\) |
−0.186834 | + | 0.982391i | \(0.559823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.00000i | − | 0.219529i | −0.993958 | − | 0.109764i | \(-0.964990\pi\) | ||
0.993958 | − | 0.109764i | \(-0.0350096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 2.00000i | − | 0.207390i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.707107 | − | 0.707107i | −0.0725476 | − | 0.0725476i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3137 | + | 11.3137i | −1.14873 | + | 1.14873i | −0.161931 | + | 0.986802i | \(0.551772\pi\) |
−0.986802 | + | 0.161931i | \(0.948228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.53553 | − | 3.53553i | 0.355335 | − | 0.355335i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00000 | 0.796030 | 0.398015 | − | 0.917379i | \(-0.369699\pi\) | ||||
0.398015 | + | 0.917379i | \(0.369699\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000 | 0.689730 | 0.344865 | − | 0.938652i | \(-0.387925\pi\) | ||||
0.344865 | + | 0.938652i | \(0.387925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.94975 | − | 4.94975i | 0.478510 | − | 0.478510i | −0.426145 | − | 0.904655i | \(-0.640129\pi\) |
0.904655 | + | 0.426145i | \(0.140129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.82843 | + | 2.82843i | 0.270914 | + | 0.270914i | 0.829468 | − | 0.558554i | \(-0.188644\pi\) |
−0.558554 | + | 0.829468i | \(0.688644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000i | 0.759326i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0208 | + | 12.0208i | 1.13082 | + | 1.13082i | 0.990041 | + | 0.140783i | \(0.0449619\pi\) |
0.140783 | + | 0.990041i | \(0.455038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | 0.279751 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.00000i | − | 0.462250i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.0000i | 1.27273i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.00000 | 0.450835 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.36396 | − | 6.36396i | −0.569210 | − | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.00000i | − | 0.798621i | −0.916816 | − | 0.399310i | \(-0.869250\pi\) | ||
0.916816 | − | 0.399310i | \(-0.130750\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.36396 | + | 6.36396i | 0.560316 | + | 0.560316i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.12132 | + | 2.12132i | −0.185341 | + | 0.185341i | −0.793678 | − | 0.608338i | \(-0.791837\pi\) |
0.608338 | + | 0.793678i | \(0.291837\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.0000 | 1.87959 | 0.939793 | − | 0.341743i | \(-0.111017\pi\) | ||||
0.939793 | + | 0.341743i | \(0.111017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.89949 | − | 9.89949i | 0.839664 | − | 0.839664i | −0.149150 | − | 0.988815i | \(-0.547654\pi\) |
0.988815 | + | 0.149150i | \(0.0476538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.24264 | + | 4.24264i | −0.357295 | + | 0.357295i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.6777 | + | 17.6777i | 1.47828 | + | 1.47828i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.00000i | − | 0.166091i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.94975 | − | 4.94975i | −0.408248 | − | 0.408248i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.0000 | 1.80231 | 0.901155 | − | 0.433497i | \(-0.142720\pi\) | ||||
0.901155 | + | 0.433497i | \(0.142720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000i | 0.160644i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.0000 | 1.35675 | 0.678374 | − | 0.734717i | \(-0.262685\pi\) | ||||
0.678374 | + | 0.734717i | \(0.262685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.24264 | − | 4.24264i | −0.336463 | − | 0.336463i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.89949 | + | 9.89949i | 0.775388 | + | 0.775388i | 0.979043 | − | 0.203655i | \(-0.0652819\pi\) |
−0.203655 | + | 0.979043i | \(0.565282\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.53553 | + | 3.53553i | −0.275241 | + | 0.275241i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.2635 | + | 16.2635i | −1.25850 | + | 1.25850i | −0.306697 | + | 0.951807i | \(0.599224\pi\) |
−0.951807 | + | 0.306697i | \(0.900776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.12132 | + | 2.12132i | −0.161281 | + | 0.161281i | −0.783134 | − | 0.621853i | \(-0.786380\pi\) |
0.621853 | + | 0.783134i | \(0.286380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.24264 | − | 4.24264i | −0.318896 | − | 0.318896i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.0000i | 1.34538i | 0.739923 | + | 0.672692i | \(0.234862\pi\) | ||||
−0.739923 | + | 0.672692i | \(0.765138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.89949 | + | 9.89949i | 0.735824 | + | 0.735824i | 0.971767 | − | 0.235943i | \(-0.0758179\pi\) |
−0.235943 | + | 0.971767i | \(0.575818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.00000 | 0.295689 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 8.00000i | − | 0.588172i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.0000 | −1.88129 | −0.940647 | − | 0.339387i | \(-0.889781\pi\) | ||||
−0.940647 | + | 0.339387i | \(0.889781\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7279 | − | 12.7279i | −0.916176 | − | 0.916176i | 0.0805728 | − | 0.996749i | \(-0.474325\pi\) |
−0.996749 | + | 0.0805728i | \(0.974325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.00000i | 0.358057i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0208 | − | 12.0208i | −0.856448 | − | 0.856448i | 0.134470 | − | 0.990918i | \(-0.457067\pi\) |
−0.990918 | + | 0.134470i | \(0.957067\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.48528 | − | 8.48528i | 0.598506 | − | 0.598506i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.00000 | −0.349215 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.12132 | + | 2.12132i | −0.147442 | + | 0.147442i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.53553 | + | 3.53553i | −0.244558 | + | 0.244558i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5563 | + | 15.5563i | 1.07094 | + | 1.07094i | 0.997283 | + | 0.0736598i | \(0.0234679\pi\) |
0.0736598 | + | 0.997283i | \(0.476532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000i | 0.822226i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.36396 | − | 6.36396i | −0.434019 | − | 0.434019i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 2.00000i | − | 0.135147i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.0000i | − | 0.736614i | −0.929704 | − | 0.368307i | \(-0.879937\pi\) | ||
0.929704 | − | 0.368307i | \(-0.120063\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.53553 | − | 3.53553i | −0.234662 | − | 0.234662i | 0.579974 | − | 0.814635i | \(-0.303063\pi\) |
−0.814635 | + | 0.579974i | \(0.803063\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 22.0000i | − | 1.45380i | −0.686743 | − | 0.726900i | \(-0.740960\pi\) | ||
0.686743 | − | 0.726900i | \(-0.259040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.19239 | − | 9.19239i | 0.602213 | − | 0.602213i | −0.338686 | − | 0.940899i | \(-0.609982\pi\) |
0.940899 | + | 0.338686i | \(0.109982\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.24264 | − | 4.24264i | 0.276759 | − | 0.276759i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.0000 | 0.649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.82843 | + | 2.82843i | −0.182195 | + | 0.182195i | −0.792312 | − | 0.610117i | \(-0.791123\pi\) |
0.610117 | + | 0.792312i | \(0.291123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.94975 | + | 4.94975i | 0.316228 | + | 0.316228i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.00000i | 0.318142i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.41421 | − | 1.41421i | −0.0896221 | − | 0.0896221i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.0000 | −1.76734 | −0.883672 | − | 0.468106i | \(-0.844936\pi\) | ||||
−0.883672 | + | 0.468106i | \(0.844936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 15.0000i | − | 0.943042i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.00000i | 0.499026i | 0.968371 | + | 0.249513i | \(0.0802706\pi\) | ||||
−0.968371 | + | 0.249513i | \(0.919729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.41421 | + | 1.41421i | 0.0875376 | + | 0.0875376i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.0000i | − | 0.986602i | −0.869859 | − | 0.493301i | \(-0.835790\pi\) | ||
0.869859 | − | 0.493301i | \(-0.164210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.24264 | + | 4.24264i | 0.260623 | + | 0.260623i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.48528 | + | 8.48528i | −0.519291 | + | 0.519291i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8492 | + | 14.8492i | −0.905374 | + | 0.905374i | −0.995895 | − | 0.0905203i | \(-0.971147\pi\) |
0.0905203 | + | 0.995895i | \(0.471147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.0000 | 1.51864 | 0.759321 | − | 0.650716i | \(-0.225531\pi\) | ||||
0.759321 | + | 0.650716i | \(0.225531\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.1421 | + | 14.1421i | −0.852803 | + | 0.852803i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7279 | − | 12.7279i | 0.764747 | − | 0.764747i | −0.212430 | − | 0.977176i | \(-0.568138\pi\) |
0.977176 | + | 0.212430i | \(0.0681376\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.41421 | − | 1.41421i | −0.0846668 | − | 0.0846668i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.0000i | − | 1.43172i | −0.698244 | − | 0.715860i | \(-0.746035\pi\) | ||
0.698244 | − | 0.715860i | \(-0.253965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.2132 | − | 21.2132i | −1.26099 | − | 1.26099i | −0.950612 | − | 0.310382i | \(-0.899543\pi\) |
−0.310382 | − | 0.950612i | \(-0.600457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.0000i | 0.937937i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.00000 | −0.233682 | −0.116841 | − | 0.993151i | \(-0.537277\pi\) | ||||
−0.116841 | + | 0.993151i | \(0.537277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.24264 | + | 4.24264i | 0.247016 | + | 0.247016i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.00000i | − | 0.290129i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.6066 | − | 10.6066i | −0.613396 | − | 0.613396i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.65685 | − | 5.65685i | 0.324978 | − | 0.324978i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.94975 | − | 4.94975i | 0.281581 | − | 0.281581i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.9706 | + | 16.9706i | −0.962312 | + | 0.962312i | −0.999315 | − | 0.0370028i | \(-0.988219\pi\) |
0.0370028 | + | 0.999315i | \(0.488219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3137 | − | 11.3137i | −0.639489 | − | 0.639489i | 0.310941 | − | 0.950429i | \(-0.399356\pi\) |
−0.950429 | + | 0.310941i | \(0.899356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.2132 | + | 21.2132i | 1.19145 | + | 1.19145i | 0.976660 | + | 0.214792i | \(0.0689075\pi\) |
0.214792 | + | 0.976660i | \(0.431092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0000 | −0.559893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 7.00000i | − | 0.390702i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.0000i | 1.10940i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.00000 | 0.221201 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0000i | 0.604615i | 0.953211 | + | 0.302307i | \(0.0977569\pi\) | ||||
−0.953211 | + | 0.302307i | \(0.902243\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.65685 | + | 5.65685i | 0.309994 | + | 0.309994i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.48528 | + | 8.48528i | −0.463600 | + | 0.463600i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.41421 | + | 1.41421i | −0.0770371 | + | 0.0770371i | −0.744575 | − | 0.667538i | \(-0.767348\pi\) |
0.667538 | + | 0.744575i | \(0.267348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.0000 | 0.923313 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.0000 | 0.541530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.12132 | − | 2.12132i | 0.114208 | − | 0.114208i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.82843 | − | 2.82843i | −0.151838 | − | 0.151838i | 0.627100 | − | 0.778938i | \(-0.284242\pi\) |
−0.778938 | + | 0.627100i | \(0.784242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.00000i | 0.374701i | 0.982293 | + | 0.187351i | \(0.0599901\pi\) | ||||
−0.982293 | + | 0.187351i | \(0.940010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.53553 | − | 3.53553i | −0.188713 | − | 0.188713i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 12.0000i | − | 0.636894i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 36.0000i | − | 1.90001i | −0.312239 | − | 0.950004i | \(-0.601079\pi\) | ||
0.312239 | − | 0.950004i | \(-0.398921\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.89949 | + | 9.89949i | 0.519589 | + | 0.519589i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000i | 0.104685i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.48528 | − | 8.48528i | −0.442928 | − | 0.442928i | 0.450067 | − | 0.892995i | \(-0.351400\pi\) |
−0.892995 | + | 0.450067i | \(0.851400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.53553 | − | 3.53553i | 0.184053 | − | 0.184053i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.00000 | −0.464758 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.07107 | + | 7.07107i | −0.364179 | + | 0.364179i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.82843 | − | 2.82843i | 0.145287 | − | 0.145287i | −0.630722 | − | 0.776009i | \(-0.717241\pi\) |
0.776009 | + | 0.630722i | \(0.217241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.36396 | − | 6.36396i | −0.326036 | − | 0.326036i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 20.0000i | − | 1.02195i | −0.859595 | − | 0.510976i | \(-0.829284\pi\) | ||
0.859595 | − | 0.510976i | \(-0.170716\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.00000 | 0.457496 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 8.00000i | − | 0.405616i | −0.979219 | − | 0.202808i | \(-0.934993\pi\) | ||
0.979219 | − | 0.202808i | \(-0.0650067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00000i | 0.151330i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.0000 | −0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.82843 | + | 2.82843i | 0.141955 | + | 0.141955i | 0.774513 | − | 0.632558i | \(-0.217995\pi\) |
−0.632558 | + | 0.774513i | \(0.717995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0208 | + | 12.0208i | 0.600291 | + | 0.600291i | 0.940390 | − | 0.340099i | \(-0.110461\pi\) |
−0.340099 | + | 0.940390i | \(0.610461\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.07107 | − | 7.07107i | 0.352235 | − | 0.352235i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.707107 | − | 0.707107i | 0.0351364 | − | 0.0351364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −40.0000 | −1.98273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | 0.247234 | 0.123617 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123617 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.5563 | − | 15.5563i | 0.767338 | − | 0.767338i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.41421 | + | 1.41421i | 0.0694210 | + | 0.0694210i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 14.0000i | − | 0.685583i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7990 | + | 19.7990i | 0.967244 | + | 0.967244i | 0.999480 | − | 0.0322363i | \(-0.0102629\pi\) |
−0.0322363 | + | 0.999480i | \(0.510263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.0000 | 1.41337 | 0.706687 | − | 0.707527i | \(-0.250189\pi\) | ||||
0.706687 | + | 0.707527i | \(0.250189\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000i | 0.291730i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.0000 | 1.20701 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.6274 | − | 22.6274i | −1.08992 | − | 1.08992i | −0.995535 | − | 0.0943889i | \(-0.969910\pi\) |
−0.0943889 | − | 0.995535i | \(-0.530090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 41.0000i | 1.97033i | 0.171598 | + | 0.985167i | \(0.445107\pi\) | ||||
−0.171598 | + | 0.985167i | \(0.554893\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41421 | − | 1.41421i | −0.0678064 | − | 0.0678064i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.12132 | − | 2.12132i | 0.101477 | − | 0.101477i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7990 | − | 19.7990i | 0.944954 | − | 0.944954i | −0.0536078 | − | 0.998562i | \(-0.517072\pi\) |
0.998562 | + | 0.0536078i | \(0.0170721\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.00000 | 0.0950229 | 0.0475114 | − | 0.998871i | \(-0.484871\pi\) | ||||
0.0475114 | + | 0.998871i | \(0.484871\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.48528 | − | 8.48528i | 0.402241 | − | 0.402241i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.5563 | − | 15.5563i | 0.735790 | − | 0.735790i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.07107 | + | 7.07107i | 0.333704 | + | 0.333704i | 0.853991 | − | 0.520287i | \(-0.174175\pi\) |
−0.520287 | + | 0.853991i | \(0.674175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.0000i | 1.17720i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0000i | 0.608114i | 0.952654 | + | 0.304057i | \(0.0983414\pi\) | ||||
−0.952654 | + | 0.304057i | \(0.901659\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.00000i | − | 0.279448i | −0.990190 | − | 0.139724i | \(-0.955378\pi\) | ||
0.990190 | − | 0.139724i | \(-0.0446215\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.41421 | + | 1.41421i | 0.0655826 | + | 0.0655826i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 18.0000i | − | 0.832941i | −0.909149 | − | 0.416470i | \(-0.863267\pi\) | ||
0.909149 | − | 0.416470i | \(-0.136733\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0208 | − | 12.0208i | 0.553890 | − | 0.553890i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.8198 | + | 31.8198i | −1.46308 | + | 1.46308i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.36396 | − | 6.36396i | 0.290777 | − | 0.290777i | −0.546610 | − | 0.837387i | \(-0.684082\pi\) |
0.837387 | + | 0.546610i | \(0.184082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.2843 | + | 28.2843i | −1.28965 | + | 1.28965i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 16.0000i | − | 0.726523i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.0416 | − | 24.0416i | −1.08943 | − | 1.08943i | −0.995587 | − | 0.0938433i | \(-0.970085\pi\) |
−0.0938433 | − | 0.995587i | \(-0.529915\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.0000 | 0.633102 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0000i | 1.35388i | 0.736038 | + | 0.676941i | \(0.236695\pi\) | ||||
−0.736038 | + | 0.676941i | \(0.763305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.00000i | 0.224733i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.07107 | + | 7.07107i | 0.316544 | + | 0.316544i | 0.847438 | − | 0.530894i | \(-0.178144\pi\) |
−0.530894 | + | 0.847438i | \(0.678144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.0000i | 1.02756i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.0919 | − | 19.0919i | −0.851265 | − | 0.851265i | 0.139024 | − | 0.990289i | \(-0.455603\pi\) |
−0.990289 | + | 0.139024i | \(0.955603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.65685 | + | 5.65685i | −0.251727 | + | 0.251727i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.48528 | − | 8.48528i | 0.376845 | − | 0.376845i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.0000 | −1.59567 | −0.797836 | − | 0.602875i | \(-0.794022\pi\) | ||||
−0.797836 | + | 0.602875i | \(0.794022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.707107 | − | 0.707107i | 0.0312195 | − | 0.0312195i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.94975 | + | 4.94975i | −0.218112 | + | 0.218112i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.2132 | − | 21.2132i | −0.932956 | − | 0.932956i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.00000i | 0.131685i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.19239 | − | 9.19239i | −0.402726 | − | 0.402726i | 0.476467 | − | 0.879193i | \(-0.341917\pi\) |
−0.879193 | + | 0.476467i | \(0.841917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 14.0000i | − | 0.608696i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.6777 | + | 17.6777i | 0.765705 | + | 0.765705i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.00000i | 0.302636i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.7279 | + | 12.7279i | 0.549250 | + | 0.549250i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.7487 | − | 24.7487i | 1.06600 | − | 1.06600i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.1127 | − | 31.1127i | 1.33764 | − | 1.33764i | 0.439298 | − | 0.898341i | \(-0.355227\pi\) |
0.898341 | − | 0.439298i | \(-0.144773\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.0000 | 0.600798 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00000 | −0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.48528 | + | 8.48528i | −0.362804 | + | 0.362804i | −0.864844 | − | 0.502040i | \(-0.832583\pi\) |
0.502040 | + | 0.864844i | \(0.332583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.82843 | − | 2.82843i | 0.120714 | − | 0.120714i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.41421 | − | 1.41421i | −0.0602475 | − | 0.0602475i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.65685 | − | 5.65685i | −0.240120 | − | 0.240120i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.0000i | 1.90330i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 18.0000i | − | 0.758610i | −0.925272 | − | 0.379305i | \(-0.876163\pi\) | ||
0.925272 | − | 0.379305i | \(-0.123837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.0000 | −0.715195 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000i | 1.00613i | 0.864248 | + | 0.503066i | \(0.167795\pi\) | ||||
−0.864248 | + | 0.503066i | \(0.832205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.3137 | − | 11.3137i | −0.473464 | − | 0.473464i | 0.429570 | − | 0.903034i | \(-0.358665\pi\) |
−0.903034 | + | 0.429570i | \(0.858665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.3848 | + | 18.3848i | −0.768035 | + | 0.768035i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.48528 | − | 8.48528i | 0.353861 | − | 0.353861i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.00000 | −0.291414 | −0.145707 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145707 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.0000 | −0.748054 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.2132 | − | 21.2132i | 0.878561 | − | 0.878561i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.53553 | + | 3.53553i | 0.146176 | + | 0.146176i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.00000i | − | 0.165098i | −0.996587 | − | 0.0825488i | \(-0.973694\pi\) | ||
0.996587 | − | 0.0825488i | \(-0.0263060\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.41421 | + | 1.41421i | 0.0582717 | + | 0.0582717i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.0000 | −0.699287 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.0000i | 0.903432i | 0.892162 | + | 0.451716i | \(0.149188\pi\) | ||||
−0.892162 | + | 0.451716i | \(0.850812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.0000 | −0.408589 | −0.204294 | − | 0.978909i | \(-0.565490\pi\) | ||||
−0.204294 | + | 0.978909i | \(0.565490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.6985 | + | 29.6985i | 1.21143 | + | 1.21143i | 0.970558 | + | 0.240869i | \(0.0774323\pi\) |
0.240869 | + | 0.970558i | \(0.422568\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.89949 | − | 9.89949i | −0.402472 | − | 0.402472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.24264 | − | 4.24264i | 0.172203 | − | 0.172203i | −0.615743 | − | 0.787947i | \(-0.711144\pi\) |
0.787947 | + | 0.615743i | \(0.211144\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.0000 | −1.21367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.0000 | −1.00974 | −0.504870 | − | 0.863195i | \(-0.668460\pi\) | ||||
−0.504870 | + | 0.863195i | \(0.668460\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.53553 | + | 3.53553i | −0.142566 | + | 0.142566i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.7279 | − | 12.7279i | 0.512407 | − | 0.512407i | −0.402856 | − | 0.915263i | \(-0.631983\pi\) |
0.915263 | + | 0.402856i | \(0.131983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.0416 | − | 24.0416i | −0.966315 | − | 0.966315i | 0.0331361 | − | 0.999451i | \(-0.489451\pi\) |
−0.999451 | + | 0.0331361i | \(0.989451\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000i | 0.120386i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.00000i | 0.199681i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.00000i | 0.358284i | 0.983823 | + | 0.179142i | \(0.0573322\pi\) | ||||
−0.983823 | + | 0.179142i | \(0.942668\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.0000 | 0.874421 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.36396 | + | 6.36396i | 0.252546 | + | 0.252546i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 35.0000i | − | 1.38675i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.48528 | + | 8.48528i | 0.335673 | + | 0.335673i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.94975 | − | 4.94975i | 0.195503 | − | 0.195503i | −0.602566 | − | 0.798069i | \(-0.705855\pi\) |
0.798069 | + | 0.602566i | \(0.205855\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.65685 | − | 5.65685i | 0.223085 | − | 0.223085i | −0.586711 | − | 0.809796i | \(-0.699578\pi\) |
0.809796 | + | 0.586711i | \(0.199578\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.00000 | −0.354375 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.0000 | −0.864909 | −0.432455 | − | 0.901656i | \(-0.642352\pi\) | ||||
−0.432455 | + | 0.901656i | \(0.642352\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.2132 | − | 21.2132i | 0.832691 | − | 0.832691i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.3345 | − | 23.3345i | −0.913150 | − | 0.913150i | 0.0833683 | − | 0.996519i | \(-0.473432\pi\) |
−0.996519 | + | 0.0833683i | \(0.973432\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.00000i | − | 0.117220i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.41421 | − | 1.41421i | −0.0551737 | − | 0.0551737i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.00000i | − | 0.116686i | −0.998297 | − | 0.0583432i | \(-0.981418\pi\) | ||
0.998297 | − | 0.0583432i | \(-0.0185818\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.00000 | 0.232321 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.77817 | − | 7.77817i | −0.300722 | − | 0.300722i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.0000i | 0.772091i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0416 | + | 24.0416i | 0.926737 | + | 0.926737i | 0.997494 | − | 0.0707568i | \(-0.0225414\pi\) |
−0.0707568 | + | 0.997494i | \(0.522541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.82843 | − | 2.82843i | 0.108866 | − | 0.108866i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.9914 | + | 28.9914i | −1.11423 | + | 1.11423i | −0.121657 | + | 0.992572i | \(0.538821\pi\) |
−0.992572 | + | 0.121657i | \(0.961179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.00000 | −0.191600 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.53553 | + | 3.53553i | −0.135283 | + | 0.135283i | −0.771506 | − | 0.636222i | \(-0.780496\pi\) |
0.636222 | + | 0.771506i | \(0.280496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.5563 | + | 15.5563i | −0.594378 | + | 0.594378i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.5563 | − | 15.5563i | −0.593512 | − | 0.593512i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 30.0000i | − | 1.14291i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7990 | − | 19.7990i | −0.753189 | − | 0.753189i | 0.221884 | − | 0.975073i | \(-0.428779\pi\) |
−0.975073 | + | 0.221884i | \(0.928779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.0000i | 0.531050i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 13.0000i | − | 0.491705i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.0000 | −1.51078 | −0.755390 | − | 0.655276i | \(-0.772552\pi\) | ||||
−0.755390 | + | 0.655276i | \(0.772552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.65685 | − | 5.65685i | −0.213352 | − | 0.213352i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 6.00000i | − | 0.225973i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.07107 | + | 7.07107i | −0.265560 | + | 0.265560i | −0.827308 | − | 0.561749i | \(-0.810129\pi\) |
0.561749 | + | 0.827308i | \(0.310129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.07107 | − | 7.07107i | 0.265186 | − | 0.265186i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.0000 | −0.934947 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.48528 | − | 8.48528i | 0.316889 | − | 0.316889i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.94975 | + | 4.94975i | −0.184594 | + | 0.184594i | −0.793354 | − | 0.608760i | \(-0.791667\pi\) |
0.608760 | + | 0.793354i | \(0.291667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.00000i | 0.148762i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.65685 | − | 5.65685i | −0.210090 | − | 0.210090i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.0000 | −0.593407 | −0.296704 | − | 0.954970i | \(-0.595887\pi\) | ||||
−0.296704 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0000i | 0.369358i | 0.982799 | + | 0.184679i | \(0.0591246\pi\) | ||||
−0.982799 | + | 0.184679i | \(0.940875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.00000 | 0.258199 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.4264 | + | 42.4264i | 1.56280 | + | 1.56280i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.0000i | 0.846069i | 0.906114 | + | 0.423034i | \(0.139035\pi\) | ||||
−0.906114 | + | 0.423034i | \(0.860965\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.53553 | + | 3.53553i | 0.129881 | + | 0.129881i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.3137 | − | 11.3137i | 0.415060 | − | 0.415060i | −0.468437 | − | 0.883497i | \(-0.655183\pi\) |
0.883497 | + | 0.468437i | \(0.155183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.5563 | + | 15.5563i | −0.569941 | + | 0.569941i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.00000 | −0.0731762 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.5563 | + | 15.5563i | −0.567659 | + | 0.567659i | −0.931472 | − | 0.363813i | \(-0.881475\pi\) |
0.363813 | + | 0.931472i | \(0.381475\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.7990 | + | 19.7990i | −0.721515 | + | 0.721515i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 41.0000i | − | 1.49017i | −0.666969 | − | 0.745085i | \(-0.732409\pi\) | ||
0.666969 | − | 0.745085i | \(-0.267591\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.6066 | − | 10.6066i | −0.384995 | − | 0.384995i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000 | 1.52250 | 0.761249 | − | 0.648459i | \(-0.224586\pi\) | ||||
0.761249 | + | 0.648459i | \(0.224586\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 30.0000i | − | 1.08324i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.0000 | 1.40638 | 0.703188 | − | 0.711004i | \(-0.251759\pi\) | ||||
0.703188 | + | 0.711004i | \(0.251759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.65685 | + | 5.65685i | 0.203727 | + | 0.203727i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.0000i | 0.575480i | 0.957709 | + | 0.287740i | \(0.0929039\pi\) | ||||
−0.957709 | + | 0.287740i | \(0.907096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65685 | + | 5.65685i | 0.203200 | + | 0.203200i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.53553 | + | 3.53553i | −0.126674 | + | 0.126674i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.0000 | −2.14697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.0208 | + | 12.0208i | −0.429041 | + | 0.429041i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.6274 | − | 22.6274i | 0.806580 | − | 0.806580i | −0.177534 | − | 0.984115i | \(-0.556812\pi\) |
0.984115 | + | 0.177534i | \(0.0568121\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.3137 | − | 11.3137i | −0.402779 | − | 0.402779i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.1421 | + | 14.1421i | 0.502202 | + | 0.502202i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.00000 | 0.212798 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.00000i | 0.283375i | 0.989911 | + | 0.141687i | \(0.0452527\pi\) | ||||
−0.989911 | + | 0.141687i | \(0.954747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0000i | 0.423999i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.0000 | 0.352892 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.0000i | 0.739235i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.77817 | − | 7.77817i | −0.273466 | − | 0.273466i | 0.557028 | − | 0.830494i | \(-0.311942\pi\) |
−0.830494 | + | 0.557028i | \(0.811942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.3848 | − | 18.3848i | 0.645577 | − | 0.645577i | −0.306344 | − | 0.951921i | \(-0.599106\pi\) |
0.951921 | + | 0.306344i | \(0.0991058\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.6777 | − | 17.6777i | 0.619983 | − | 0.619983i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.0000 | −0.490399 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.00000 | −0.314870 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.9203 | − | 21.9203i | 0.765024 | − | 0.765024i | −0.212202 | − | 0.977226i | \(-0.568063\pi\) |
0.977226 | + | 0.212202i | \(0.0680634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.65685 | − | 5.65685i | −0.197186 | − | 0.197186i | 0.601607 | − | 0.798792i | \(-0.294527\pi\) |
−0.798792 | + | 0.601607i | \(0.794527\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.0000i | 0.696311i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.53553 | − | 3.53553i | −0.122943 | − | 0.122943i | 0.642958 | − | 0.765901i | \(-0.277707\pi\) |
−0.765901 | + | 0.642958i | \(0.777707\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0000 | 0.347314 | 0.173657 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 18.0000i | − | 0.624413i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 23.0000i | − | 0.795948i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.8492 | − | 14.8492i | −0.512653 | − | 0.512653i | 0.402686 | − | 0.915338i | \(-0.368077\pi\) |
−0.915338 | + | 0.402686i | \(0.868077\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000i | 0.862069i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.9706 | − | 16.9706i | −0.584497 | − | 0.584497i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.48528 | + | 8.48528i | −0.291903 | + | 0.291903i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.0000 | −1.02960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000 | 0.822709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.0122 | − | 41.0122i | 1.40423 | − | 1.40423i | 0.618246 | − | 0.785984i | \(-0.287843\pi\) |
0.785984 | − | 0.618246i | \(-0.212157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.707107 | + | 0.707107i | −0.0241825 | + | 0.0241825i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.24264 | + | 4.24264i | 0.144926 | + | 0.144926i | 0.775847 | − | 0.630921i | \(-0.217323\pi\) |
−0.630921 | + | 0.775847i | \(0.717323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 36.0000i | − | 1.22830i | −0.789188 | − | 0.614152i | \(-0.789498\pi\) | ||
0.789188 | − | 0.614152i | \(-0.210502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.00000 | −0.136162 | −0.0680808 | − | 0.997680i | \(-0.521688\pi\) | ||||
−0.0680808 | + | 0.997680i | \(0.521688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 3.00000i | − | 0.102003i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.0000i | 1.69613i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60.0000 | 2.03302 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.3137 | + | 11.3137i | 0.382911 | + | 0.382911i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.3848 | + | 18.3848i | 0.620810 | + | 0.620810i | 0.945739 | − | 0.324929i | \(-0.105340\pi\) |
−0.324929 | + | 0.945739i | \(0.605340\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.82843 | + | 2.82843i | −0.0954005 | + | 0.0954005i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.89949 | − | 9.89949i | 0.333522 | − | 0.333522i | −0.520400 | − | 0.853923i | \(-0.674217\pi\) |
0.853923 | + | 0.520400i | \(0.174217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.0000 | −0.908622 | −0.454311 | − | 0.890843i | \(-0.650115\pi\) | ||||
−0.454311 | + | 0.890843i | \(0.650115\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.00000 | 0.201688 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.0919 | − | 19.0919i | 0.641043 | − | 0.641043i | −0.309769 | − | 0.950812i | \(-0.600252\pi\) |
0.950812 | + | 0.309769i | \(0.100252\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.53553 | − | 3.53553i | −0.118445 | − | 0.118445i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 6.00000i | − | 0.200782i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.7279 | − | 12.7279i | −0.425448 | − | 0.425448i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.0000 | −0.500835 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00000i | 0.133407i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.0000 | −0.465376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.41421 | − | 1.41421i | −0.0469582 | − | 0.0469582i | 0.683238 | − | 0.730196i | \(-0.260571\pi\) |
−0.730196 | + | 0.683238i | \(0.760571\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 8.00000i | − | 0.265343i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0208 | − | 12.0208i | −0.398267 | − | 0.398267i | 0.479354 | − | 0.877622i | \(-0.340871\pi\) |
−0.877622 | + | 0.479354i | \(0.840871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.07107 | − | 7.07107i | 0.234018 | − | 0.234018i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.82843 | + | 2.82843i | −0.0935049 | + | 0.0935049i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.0000 | −0.494804 | −0.247402 | − | 0.968913i | \(-0.579577\pi\) | ||||
−0.247402 | + | 0.968913i | \(0.579577\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.48528 | + | 8.48528i | −0.279600 | + | 0.279600i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.4264 | + | 42.4264i | −1.39648 | + | 1.39648i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.6274 | − | 22.6274i | −0.743985 | − | 0.743985i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 7.00000i | − | 0.229910i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.9203 | − | 21.9203i | −0.719182 | − | 0.719182i | 0.249256 | − | 0.968438i | \(-0.419814\pi\) |
−0.968438 | + | 0.249256i | \(0.919814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.00000 | 0.229416 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.0000i | 0.785725i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.0000i | − | 0.718709i | −0.933201 | − | 0.359354i | \(-0.882997\pi\) | ||
0.933201 | − | 0.359354i | \(-0.117003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0000 | −0.522140 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.0416 | − | 24.0416i | −0.783735 | − | 0.783735i | 0.196724 | − | 0.980459i | \(-0.436970\pi\) |
−0.980459 | + | 0.196724i | \(0.936970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 15.0000i | − | 0.488467i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.7990 | − | 19.7990i | 0.643381 | − | 0.643381i | −0.308004 | − | 0.951385i | \(-0.599661\pi\) |
0.951385 | + | 0.308004i | \(0.0996611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.07107 | − | 7.07107i | 0.229537 | − | 0.229537i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.0000 | 0.972817 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0000 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.3848 | − | 18.3848i | 0.594917 | − | 0.594917i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.07107 | + | 7.07107i | −0.228575 | + | 0.228575i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000i | 0.870968i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.94975 | − | 4.94975i | −0.159503 | − | 0.159503i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.0000 | 0.579441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0000i | 0.610999i | 0.952192 | + | 0.305499i | \(0.0988234\pi\) | ||||
−0.952192 | + | 0.305499i | \(0.901177\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 22.0000i | − | 0.706014i | −0.935621 | − | 0.353007i | \(-0.885159\pi\) | ||
0.935621 | − | 0.353007i | \(-0.114841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.1421 | + | 14.1421i | 0.452911 | + | 0.452911i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 14.0000i | − | 0.447900i | −0.974601 | − | 0.223950i | \(-0.928105\pi\) | ||
0.974601 | − | 0.223950i | \(-0.0718952\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.4264 | − | 42.4264i | −1.35595 | − | 1.35595i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.82843 | − | 2.82843i | 0.0903047 | − | 0.0903047i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0624 | − | 36.0624i | 1.15021 | − | 1.15021i | 0.163704 | − | 0.986510i | \(-0.447656\pi\) |
0.986510 | − | 0.163704i | \(-0.0523442\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.0000 | 0.541665 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.0919 | − | 19.0919i | 0.607087 | − | 0.607087i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.1421 | + | 14.1421i | −0.449240 | + | 0.449240i | −0.895102 | − | 0.445862i | \(-0.852897\pi\) |
0.445862 | + | 0.895102i | \(0.352897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.77817 | + | 7.77817i | 0.246833 | + | 0.246833i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.41421 | − | 1.41421i | −0.0447886 | − | 0.0447886i | 0.684358 | − | 0.729146i | \(-0.260083\pi\) |
−0.729146 | + | 0.684358i | \(0.760083\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.00000 | 0.253109 |
(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 | 3468.2.j.f.3217.2 | 4 | ||
17.2 | even | 8 | 3468.2.b.a.577.1 | 2 | |||
17.4 | even | 4 | inner | 3468.2.j.f.829.1 | 4 | ||
17.8 | even | 8 | 3468.2.a.a.1.1 | 1 | |||
17.9 | even | 8 | 204.2.a.b.1.1 | ✓ | 1 | ||
17.13 | even | 4 | inner | 3468.2.j.f.829.2 | 4 | ||
17.15 | even | 8 | 3468.2.b.a.577.2 | 2 | |||
17.16 | even | 2 | inner | 3468.2.j.f.3217.1 | 4 | ||
51.26 | odd | 8 | 612.2.a.b.1.1 | 1 | |||
68.43 | odd | 8 | 816.2.a.e.1.1 | 1 | |||
85.9 | even | 8 | 5100.2.a.f.1.1 | 1 | |||
85.43 | odd | 8 | 5100.2.g.l.2449.2 | 2 | |||
85.77 | odd | 8 | 5100.2.g.l.2449.1 | 2 | |||
119.111 | odd | 8 | 9996.2.a.b.1.1 | 1 | |||
136.43 | odd | 8 | 3264.2.a.u.1.1 | 1 | |||
136.77 | even | 8 | 3264.2.a.f.1.1 | 1 | |||
204.179 | even | 8 | 2448.2.a.e.1.1 | 1 | |||
408.77 | odd | 8 | 9792.2.a.bo.1.1 | 1 | |||
408.179 | even | 8 | 9792.2.a.bn.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
204.2.a.b.1.1 | ✓ | 1 | 17.9 | even | 8 | ||
612.2.a.b.1.1 | 1 | 51.26 | odd | 8 | |||
816.2.a.e.1.1 | 1 | 68.43 | odd | 8 | |||
2448.2.a.e.1.1 | 1 | 204.179 | even | 8 | |||
3264.2.a.f.1.1 | 1 | 136.77 | even | 8 | |||
3264.2.a.u.1.1 | 1 | 136.43 | odd | 8 | |||
3468.2.a.a.1.1 | 1 | 17.8 | even | 8 | |||
3468.2.b.a.577.1 | 2 | 17.2 | even | 8 | |||
3468.2.b.a.577.2 | 2 | 17.15 | even | 8 | |||
3468.2.j.f.829.1 | 4 | 17.4 | even | 4 | inner | ||
3468.2.j.f.829.2 | 4 | 17.13 | even | 4 | inner | ||
3468.2.j.f.3217.1 | 4 | 17.16 | even | 2 | inner | ||
3468.2.j.f.3217.2 | 4 | 1.1 | even | 1 | trivial | ||
5100.2.a.f.1.1 | 1 | 85.9 | even | 8 | |||
5100.2.g.l.2449.1 | 2 | 85.77 | odd | 8 | |||
5100.2.g.l.2449.2 | 2 | 85.43 | odd | 8 | |||
9792.2.a.bn.1.1 | 1 | 408.179 | even | 8 | |||
9792.2.a.bo.1.1 | 1 | 408.77 | odd | 8 | |||
9996.2.a.b.1.1 | 1 | 119.111 | odd | 8 |