Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (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: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 18x^{8} + 103x^{6} + 239x^{4} + 197x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.3 | ||
Root | \(-1.64975i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.v.4049.8 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.51466i | − 0.874489i | −0.899343 | − | 0.437244i | \(-0.855954\pi\) | ||||
0.899343 | − | 0.437244i | \(-0.144046\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.49880i | − 1.32242i | −0.750199 | − | 0.661212i | \(-0.770043\pi\) | ||||
0.750199 | − | 0.661212i | \(-0.229957\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.705809 | 0.235270 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.35556 | −1.31325 | −0.656625 | − | 0.754217i | \(-0.728016\pi\) | ||||
−0.656625 | + | 0.754217i | \(0.728016\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.67906i | − 1.02039i | −0.860059 | − | 0.510194i | \(-0.829573\pi\) | ||||
0.860059 | − | 0.510194i | \(-0.170427\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.18556i | − 1.25768i | −0.777533 | − | 0.628842i | \(-0.783529\pi\) | ||||
0.777533 | − | 0.628842i | \(-0.216471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.08538 | −0.478419 | −0.239209 | − | 0.970968i | \(-0.576888\pi\) | ||||
−0.239209 | + | 0.970968i | \(0.576888\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.29949 | −1.15644 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.61304i | − 1.08023i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.24902 | 0.231937 | 0.115968 | − | 0.993253i | \(-0.463003\pi\) | ||||
0.115968 | + | 0.993253i | \(0.463003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.82185 | 0.866029 | 0.433015 | − | 0.901387i | \(-0.357450\pi\) | ||||
0.433015 | + | 0.901387i | \(0.357450\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.59718i | 1.14842i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.04471i | 0.171749i | 0.996306 | + | 0.0858745i | \(0.0273684\pi\) | ||||
−0.996306 | + | 0.0858745i | \(0.972632\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.57253 | −0.892318 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.05578 | 1.41427 | 0.707137 | − | 0.707076i | \(-0.249986\pi\) | ||||
0.707137 | + | 0.707076i | \(0.249986\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 10.4964i | − 1.60069i | −0.599541 | − | 0.800344i | \(-0.704650\pi\) | ||||
0.599541 | − | 0.800344i | \(-0.295350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.8597i | 1.87577i | 0.346940 | + | 0.937887i | \(0.387221\pi\) | ||||
−0.346940 | + | 0.937887i | \(0.612779\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.24162 | −0.748804 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.85436 | −1.09983 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.37352i | − 1.28755i | −0.765214 | − | 0.643776i | \(-0.777367\pi\) | ||||
0.765214 | − | 0.643776i | \(-0.222633\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.15864i | 0.418372i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.1570 | −1.84309 | −0.921543 | − | 0.388276i | \(-0.873071\pi\) | ||||
−0.921543 | + | 0.388276i | \(0.873071\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.29949 | −1.19068 | −0.595339 | − | 0.803475i | \(-0.702982\pi\) | ||||
−0.595339 | + | 0.803475i | \(0.702982\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 2.46949i | − 0.311126i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.44274i | 0.542767i | 0.962471 | + | 0.271384i | \(0.0874812\pi\) | ||||
−0.962471 | + | 0.271384i | \(0.912519\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.51466 | −0.182343 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.45044 | 0.290813 | 0.145407 | − | 0.989372i | \(-0.453551\pi\) | ||||
0.145407 | + | 0.989372i | \(0.453551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.2197i | 1.54725i | 0.633643 | + | 0.773625i | \(0.281559\pi\) | ||||
−0.633643 | + | 0.773625i | \(0.718441\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.2392i | 1.73667i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.72666 | −0.869318 | −0.434659 | − | 0.900595i | \(-0.643131\pi\) | ||||
−0.434659 | + | 0.900595i | \(0.643131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.38441 | −0.709379 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.97086i | 0.326095i | 0.986618 | + | 0.163047i | \(0.0521323\pi\) | ||||
−0.986618 | + | 0.163047i | \(0.947868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1.89184i | − 0.202826i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6241 | 1.55015 | 0.775076 | − | 0.631868i | \(-0.217712\pi\) | ||||
0.775076 | + | 0.631868i | \(0.217712\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.8723 | −1.34939 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 7.30345i | − 0.757333i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.37991i | 0.952385i | 0.879341 | + | 0.476193i | \(0.157983\pi\) | ||||
−0.879341 | + | 0.476193i | \(0.842017\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.07419 | −0.308968 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.02674 | −0.102165 | −0.0510824 | − | 0.998694i | \(-0.516267\pi\) | ||||
−0.0510824 | + | 0.998694i | \(0.516267\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.71127i | 0.168617i | 0.996440 | + | 0.0843084i | \(0.0268681\pi\) | ||||
−0.996440 | + | 0.0843084i | \(0.973132\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.58418i | 0.733191i | 0.930380 | + | 0.366595i | \(0.119477\pi\) | ||||
−0.930380 | + | 0.366595i | \(0.880523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.95951 | 0.858165 | 0.429083 | − | 0.903265i | \(-0.358837\pi\) | ||||
0.429083 | + | 0.903265i | \(0.358837\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.58238 | 0.150193 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 18.8103i | − 1.76952i | −0.466047 | − | 0.884760i | \(-0.654322\pi\) | ||||
0.466047 | − | 0.884760i | \(-0.345678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.59672i | − 0.240066i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.1433 | −1.66319 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.97086 | 0.724624 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 13.7164i | − 1.23677i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 15.0385i | − 1.33445i | −0.744854 | − | 0.667227i | \(-0.767481\pi\) | ||||
0.744854 | − | 0.667227i | \(-0.232519\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.8985 | −1.39978 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.3503 | 1.77801 | 0.889007 | − | 0.457893i | \(-0.151396\pi\) | ||||
0.889007 | + | 0.457893i | \(0.151396\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.29633i | 0.632672i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.51494i | 0.129430i | 0.997904 | + | 0.0647152i | \(0.0206139\pi\) | ||||
−0.997904 | + | 0.0647152i | \(0.979386\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3658 | −1.13367 | −0.566837 | − | 0.823830i | \(-0.691833\pi\) | ||||
−0.566837 | + | 0.823830i | \(0.691833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.4780 | 1.64034 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.0244i | 1.34002i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.93927i | 0.654820i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6307 | 0.870901 | 0.435450 | − | 0.900213i | \(-0.356589\pi\) | ||||
0.435450 | + | 0.900213i | \(0.356589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.2918 | −1.81408 | −0.907041 | − | 0.421042i | \(-0.861664\pi\) | ||||
−0.907041 | + | 0.421042i | \(0.861664\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 3.66002i | − 0.295895i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2.95590i | − 0.235906i | −0.993019 | − | 0.117953i | \(-0.962367\pi\) | ||||
0.993019 | − | 0.117953i | \(-0.0376332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.1977 | −1.12595 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.49880 | −0.275744 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.40543i | − 0.345060i | −0.985004 | − | 0.172530i | \(-0.944806\pi\) | ||||
0.985004 | − | 0.172530i | \(-0.0551941\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.9252i | 1.15495i | 0.816409 | + | 0.577474i | \(0.195962\pi\) | ||||
−0.816409 | + | 0.577474i | \(0.804038\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.535514 | −0.0411934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.47188 | −0.112557 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 18.2696i | − 1.38901i | −0.719487 | − | 0.694506i | \(-0.755623\pi\) | ||||
0.719487 | − | 0.694506i | \(-0.244377\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 21.4430i | 1.61176i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.20356 | 0.463676 | 0.231838 | − | 0.972754i | \(-0.425526\pi\) | ||||
0.231838 | + | 0.972754i | \(0.425526\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.74043 | 0.426683 | 0.213341 | − | 0.976978i | \(-0.431565\pi\) | ||||
0.213341 | + | 0.976978i | \(0.431565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.0856i | 1.04123i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.5860i | 1.65165i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.6389 | −1.42852 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.4671 | −0.974445 | −0.487222 | − | 0.873278i | \(-0.661990\pi\) | ||||
−0.487222 | + | 0.873278i | \(0.661990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.295578i | 0.0212762i | 0.999943 | + | 0.0106381i | \(0.00338628\pi\) | ||||
−0.999943 | + | 0.0106381i | \(0.996614\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6206i | 0.827932i | 0.910292 | + | 0.413966i | \(0.135857\pi\) | ||||
−0.910292 | + | 0.413966i | \(0.864143\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.46949 | −0.316833 | −0.158417 | − | 0.987372i | \(-0.550639\pi\) | ||||
−0.158417 | + | 0.987372i | \(0.550639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.72924 | 0.474644 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.37007i | − 0.306719i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 0.705809i | − 0.0490571i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.08299 | 0.628283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0878 | −1.03869 | −0.519343 | − | 0.854566i | \(-0.673823\pi\) | ||||
−0.519343 | + | 0.854566i | \(0.673823\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3.71158i | − 0.254313i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 16.8707i | − 1.14526i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.0234 | 1.35305 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.0780 | −1.28333 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.2033i | 1.68774i | 0.536548 | + | 0.843870i | \(0.319728\pi\) | ||||
−0.536548 | + | 0.843870i | \(0.680272\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 20.1385i | − 1.33664i | −0.743875 | − | 0.668319i | \(-0.767014\pi\) | ||||
0.743875 | − | 0.668319i | \(-0.232986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.72411 | −0.642587 | −0.321294 | − | 0.946980i | \(-0.604118\pi\) | ||||
−0.321294 | + | 0.946980i | \(0.604118\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.0822 | 1.51870 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.37957i | 0.417940i | 0.977922 | + | 0.208970i | \(0.0670110\pi\) | ||||
−0.977922 | + | 0.208970i | \(0.932989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.7033i | 0.760208i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.07706 | 0.199039 | 0.0995194 | − | 0.995036i | \(-0.468269\pi\) | ||||
0.0995194 | + | 0.995036i | \(0.468269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.6341 | −1.84448 | −0.922242 | − | 0.386612i | \(-0.873645\pi\) | ||||
−0.922242 | + | 0.386612i | \(0.873645\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 7.16891i | − 0.459886i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.67225i | 0.488173i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.49984 | 0.285166 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.728308 | 0.0459704 | 0.0229852 | − | 0.999736i | \(-0.492683\pi\) | ||||
0.0229852 | + | 0.999736i | \(0.492683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.35556i | 0.273831i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.1681i | 1.81945i | 0.415206 | + | 0.909727i | \(0.363710\pi\) | ||||
−0.415206 | + | 0.909727i | \(0.636290\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.65523 | 0.227125 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.881568 | 0.0545677 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 2.79631i | − 0.172428i | −0.996277 | − | 0.0862139i | \(-0.972523\pi\) | ||||
0.996277 | − | 0.0862139i | \(-0.0274769\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 22.1505i | − 1.35559i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.662454 | 0.0403905 | 0.0201953 | − | 0.999796i | \(-0.493571\pi\) | ||||
0.0201953 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5266 | 0.882428 | 0.441214 | − | 0.897402i | \(-0.354548\pi\) | ||||
0.441214 | + | 0.897402i | \(0.354548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.4972i | 1.18002i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.15432i | − 0.0693562i | −0.999399 | − | 0.0346781i | \(-0.988959\pi\) | ||||
0.999399 | − | 0.0346781i | \(-0.0110406\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.40330 | 0.203750 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.2977 | −0.852930 | −0.426465 | − | 0.904504i | \(-0.640241\pi\) | ||||
−0.426465 | + | 0.904504i | \(0.640241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 31.2654i | − 1.85854i | −0.369407 | − | 0.929268i | \(-0.620439\pi\) | ||||
0.369407 | − | 0.929268i | \(-0.379561\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 31.6844i | − 1.87027i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.89006 | −0.581768 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.2074 | 0.832850 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 4.59477i | − 0.268429i | −0.990952 | − | 0.134215i | \(-0.957149\pi\) | ||||
0.990952 | − | 0.134215i | \(-0.0428512\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.4479i | 1.41861i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.67906 | −0.212766 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.7249 | −2.11679 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.55517i | 0.0893420i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.96103i | 0.568506i | 0.958749 | + | 0.284253i | \(0.0917455\pi\) | ||||
−0.958749 | + | 0.284253i | \(0.908254\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.59200 | 0.147453 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7520 | −0.723102 | −0.361551 | − | 0.932352i | \(-0.617753\pi\) | ||||
−0.361551 | + | 0.932352i | \(0.617753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5585i | 1.10551i | 0.833343 | + | 0.552756i | \(0.186424\pi\) | ||||
−0.833343 | + | 0.552756i | \(0.813576\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.5493i | 1.82815i | 0.405542 | + | 0.914076i | \(0.367083\pi\) | ||||
−0.405542 | + | 0.914076i | \(0.632917\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.44017 | −0.304591 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.4874 | 0.641167 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8139i | 0.601700i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 13.5706i | − 0.750456i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 44.9934 | 2.48057 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.9704 | 1.31753 | 0.658767 | − | 0.752347i | \(-0.271078\pi\) | ||||
0.658767 | + | 0.752347i | \(0.271078\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.737364i | 0.0404073i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.88246i | 0.320438i | 0.987082 | + | 0.160219i | \(0.0512200\pi\) | ||||
−0.987082 | + | 0.160219i | \(0.948780\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.4911 | −1.54743 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.0018 | −1.13731 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6.15221i | − 0.332188i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.7454i | 1.38209i | 0.722814 | + | 0.691043i | \(0.242849\pi\) | ||||
−0.722814 | + | 0.691043i | \(0.757151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.7758 | 0.951517 | 0.475758 | − | 0.879576i | \(-0.342174\pi\) | ||||
0.475758 | + | 0.879576i | \(0.342174\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.6507 | −1.10225 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 20.4426i | − 1.08805i | −0.839068 | − | 0.544026i | \(-0.816899\pi\) | ||||
0.839068 | − | 0.544026i | \(-0.183101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.4809i | 1.45444i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.5323 | 0.766987 | 0.383494 | − | 0.923543i | \(-0.374721\pi\) | ||||
0.383494 | + | 0.923543i | \(0.374721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.6512 | −0.771115 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 12.0731i | − 0.633675i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 12.2205i | − 0.637906i | −0.947771 | − | 0.318953i | \(-0.896669\pi\) | ||||
0.947771 | − | 0.318953i | \(-0.103331\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.39165 | 0.332736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −32.7961 | −1.70269 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.78846i | 0.0926029i | 0.998928 | + | 0.0463015i | \(0.0147435\pi\) | ||||
−0.998928 | + | 0.0463015i | \(0.985257\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 4.59522i | − 0.236666i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.02119 | −0.360654 | −0.180327 | − | 0.983607i | \(-0.557716\pi\) | ||||
−0.180327 | + | 0.983607i | \(0.557716\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.7782 | −1.16697 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 13.0896i | − 0.668846i | −0.942423 | − | 0.334423i | \(-0.891459\pi\) | ||||
0.942423 | − | 0.334423i | \(-0.108541\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 7.40846i | − 0.376593i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.5395 | 1.09210 | 0.546048 | − | 0.837754i | \(-0.316132\pi\) | ||||
0.546048 | + | 0.837754i | \(0.316132\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.18556 | −0.262245 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 30.8238i | − 1.55485i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 31.2045i | − 1.56611i | −0.621953 | − | 0.783055i | \(-0.713660\pi\) | ||||
0.621953 | − | 0.783055i | \(-0.286340\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.0515 | 0.553265 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.7592 | 0.687100 | 0.343550 | − | 0.939134i | \(-0.388371\pi\) | ||||
0.343550 | + | 0.939134i | \(0.388371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 17.7399i | − 0.883687i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 4.55028i | − 0.225549i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.9730 | −1.08649 | −0.543247 | − | 0.839573i | \(-0.682805\pi\) | ||||
−0.543247 | + | 0.839573i | \(0.682805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.29462 | 0.113185 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 49.5326i | 2.43734i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.2447i | 0.991385i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.3024 | 0.649867 | 0.324934 | − | 0.945737i | \(-0.394658\pi\) | ||||
0.324934 | + | 0.945737i | \(0.394658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.32759 | −0.357125 | −0.178562 | − | 0.983929i | \(-0.557145\pi\) | ||||
−0.178562 | + | 0.983929i | \(0.557145\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.07646i | 0.441313i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.5371i | 1.57458i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.2715 | 1.17184 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.4301 | 1.41760 | 0.708800 | − | 0.705409i | \(-0.249237\pi\) | ||||
0.708800 | + | 0.705409i | \(0.249237\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 10.5491i | − 0.506960i | −0.967341 | − | 0.253480i | \(-0.918425\pi\) | ||||
0.967341 | − | 0.253480i | \(-0.0815752\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.08538i | 0.0997572i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.04921 | −0.0500761 | −0.0250380 | − | 0.999686i | \(-0.507971\pi\) | ||||
−0.0250380 | + | 0.999686i | \(0.507971\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.69958 | −0.176171 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 9.57098i | − 0.454731i | −0.973810 | − | 0.227365i | \(-0.926989\pi\) | ||||
0.973810 | − | 0.227365i | \(-0.0730112\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 16.1019i | − 0.761593i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.10079 | −0.382300 | −0.191150 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191150 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.4429 | −1.85730 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.7645i | 1.58639i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.5867i | 1.61790i | 0.587880 | + | 0.808948i | \(0.299963\pi\) | ||||
−0.587880 | + | 0.808948i | \(0.700037\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.1068 | −1.35859 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.3497 | −1.08750 | −0.543752 | − | 0.839246i | \(-0.682997\pi\) | ||||
−0.543752 | + | 0.839246i | \(0.682997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 36.7512i | − 1.70797i | −0.520295 | − | 0.853987i | \(-0.674178\pi\) | ||||
0.520295 | − | 0.853987i | \(-0.325822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.5786i | 1.36874i | 0.729137 | + | 0.684368i | \(0.239922\pi\) | ||||
−0.729137 | + | 0.684368i | \(0.760078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.5443 | 0.717768 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.47717 | −0.206297 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 45.7177i | 2.10210i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 6.61591i | − 0.302922i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.23409 | −0.330534 | −0.165267 | − | 0.986249i | \(-0.552849\pi\) | ||||
−0.165267 | + | 0.986249i | \(0.552849\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.84355 | 0.175251 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.29949i | 0.241135i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.99593i | 0.407645i | 0.979008 | + | 0.203822i | \(0.0653365\pi\) | ||||
−0.979008 | + | 0.203822i | \(0.934664\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.67272 | −0.301751 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.71762 | 0.438550 | 0.219275 | − | 0.975663i | \(-0.429631\pi\) | ||||
0.219275 | + | 0.975663i | \(0.429631\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6.47686i | − 0.291703i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 8.57360i | − 0.384578i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.3758 | −1.49410 | −0.747052 | − | 0.664765i | \(-0.768532\pi\) | ||||
−0.747052 | + | 0.664765i | \(0.768532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.6066 | 1.00999 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 22.1147i | − 0.986046i | −0.870016 | − | 0.493023i | \(-0.835892\pi\) | ||||
0.870016 | − | 0.493023i | \(-0.164108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.811121i | 0.0360232i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.8182 | −0.479507 | −0.239753 | − | 0.970834i | \(-0.577067\pi\) | ||||
−0.239753 | + | 0.970834i | \(0.577067\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 46.2532 | 2.04612 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.7053i | 0.516802i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 56.0110i | − 2.46336i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.6722 | −1.21467 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.20820 | −0.140554 | −0.0702770 | − | 0.997528i | \(-0.522388\pi\) | ||||
−0.0702770 | + | 0.997528i | \(0.522388\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 23.7159i | − 1.03702i | −0.855071 | − | 0.518512i | \(-0.826486\pi\) | ||||
0.855071 | − | 0.518512i | \(-0.173514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 25.0040i | − 1.08919i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.99214 | −0.433622 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 33.3168i | − 1.44311i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 9.39628i | − 0.405479i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.8302 | 0.983366 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.46616 | −0.278002 | −0.139001 | − | 0.990292i | \(-0.544389\pi\) | ||||
−0.139001 | + | 0.990292i | \(0.544389\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 8.69479i | − 0.373129i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.48526i | 0.320047i | 0.987113 | + | 0.160023i | \(0.0511570\pi\) | ||||
−0.987113 | + | 0.160023i | \(0.948843\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.56366 | −0.280130 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.60468 | −0.110963 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.0341i | 1.14961i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 22.2922i | − 0.944553i | −0.881451 | − | 0.472276i | \(-0.843432\pi\) | ||||
0.881451 | − | 0.472276i | \(-0.156568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.6170 | −1.63332 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.2101 | 1.44435 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.93402i | 0.418669i | 0.977844 | + | 0.209335i | \(0.0671298\pi\) | ||||
−0.977844 | + | 0.209335i | \(0.932870\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.3378i | 0.938099i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.8239 | 1.12452 | 0.562258 | − | 0.826962i | \(-0.309933\pi\) | ||||
0.562258 | + | 0.826962i | \(0.309933\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.0260 | 1.25655 | 0.628274 | − | 0.777992i | \(-0.283762\pi\) | ||||
0.628274 | + | 0.777992i | \(0.283762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.3981i | 0.852141i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 23.5058i | − 0.978559i | −0.872127 | − | 0.489279i | \(-0.837260\pi\) | ||||
0.872127 | − | 0.489279i | \(-0.162740\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.447701 | 0.0186058 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3945 | 0.431235 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.8269i | 1.69088i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 5.05879i | − 0.208799i | −0.994535 | − | 0.104399i | \(-0.966708\pi\) | ||||
0.994535 | − | 0.104399i | \(-0.0332920\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0554 | −0.414325 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.6012 | 0.724017 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 15.0522i | − 0.618120i | −0.951043 | − | 0.309060i | \(-0.899986\pi\) | ||||
0.951043 | − | 0.309060i | \(-0.100014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.76975i | 0.277067i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.9863 | 0.653181 | 0.326590 | − | 0.945166i | \(-0.394100\pi\) | ||||
0.326590 | + | 0.945166i | \(0.394100\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.7941 | 1.33770 | 0.668851 | − | 0.743397i | \(-0.266787\pi\) | ||||
0.668851 | + | 0.743397i | \(0.266787\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.13573i | 0.127697i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 38.4884i | − 1.56220i | −0.624409 | − | 0.781098i | \(-0.714660\pi\) | ||||
0.624409 | − | 0.781098i | \(-0.285340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.61916 | −0.268222 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 47.3115 | 1.91402 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 6.47626i | − 0.261574i | −0.991411 | − | 0.130787i | \(-0.958250\pi\) | ||||
0.991411 | − | 0.130787i | \(-0.0417503\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.8193i | 1.36152i | 0.732509 | + | 0.680758i | \(0.238349\pi\) | ||||
−0.732509 | + | 0.680758i | \(0.761651\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.02686 | −0.0814663 | −0.0407331 | − | 0.999170i | \(-0.512969\pi\) | ||||
−0.0407331 | + | 0.999170i | \(0.512969\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.61304 | −0.225243 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 51.1669i | − 2.04996i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 13.7576i | − 0.549427i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.41740 | 0.216006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.45649 | −0.137601 | −0.0688003 | − | 0.997630i | \(-0.521917\pi\) | ||||
−0.0688003 | + | 0.997630i | \(0.521917\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.8529i | 0.908319i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.2843i | 0.764071i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.72954 | 0.0684195 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.2630 | 1.86678 | 0.933388 | − | 0.358869i | \(-0.116837\pi\) | ||||
0.933388 | + | 0.358869i | \(0.116837\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.6052i | 0.930899i | 0.885075 | + | 0.465449i | \(0.154107\pi\) | ||||
−0.885075 | + | 0.465449i | \(0.845893\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 20.3090i | − 0.798430i | −0.916857 | − | 0.399215i | \(-0.869283\pi\) | ||||
0.916857 | − | 0.399215i | \(-0.130717\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.6617 | 2.42043 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.5533 | −1.00151 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.8982i | 0.622146i | 0.950386 | + | 0.311073i | \(0.100688\pi\) | ||||
−0.950386 | + | 0.311073i | \(0.899312\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.33059i | 0.364021i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.6170 | −0.530441 | −0.265221 | − | 0.964188i | \(-0.585445\pi\) | ||||
−0.265221 | + | 0.964188i | \(0.585445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.8049 | 1.08148 | 0.540742 | − | 0.841188i | \(-0.318143\pi\) | ||||
0.540742 | + | 0.841188i | \(0.318143\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.8967i | 1.12225i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.24902i | − 0.0483622i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.1744 | 1.47591 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.5045 | 1.56366 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.92071i | 0.189679i | 0.995493 | + | 0.0948396i | \(0.0302338\pi\) | ||||
−0.995493 | + | 0.0948396i | \(0.969766\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 48.4096i | − 1.86053i | −0.366886 | − | 0.930266i | \(-0.619576\pi\) | ||||
0.366886 | − | 0.930266i | \(-0.380424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.8184 | 1.25946 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.5029 | −1.16887 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.1788i | 1.38434i | 0.721732 | + | 0.692172i | \(0.243346\pi\) | ||||
−0.721732 | + | 0.692172i | \(0.756654\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.7287i | 0.561935i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.4858 | −1.31380 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.1568 | 1.22330 | 0.611651 | − | 0.791127i | \(-0.290506\pi\) | ||||
0.611651 | + | 0.791127i | \(0.290506\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.7560i | 0.408586i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 46.9593i | − 1.77871i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.66287 | 0.365483 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.9408 | 0.677614 | 0.338807 | − | 0.940856i | \(-0.389977\pi\) | ||||
0.338807 | + | 0.940856i | \(0.389977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.17861i | − 0.0821680i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.59238i | 0.135105i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.4153 | −1.70561 | −0.852804 | − | 0.522231i | \(-0.825100\pi\) | ||||
−0.852804 | + | 0.522231i | \(0.825100\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.45355 | −0.204524 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4.82185i | − 0.180580i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 4.66070i | − 0.174057i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.90426 | −0.220192 | −0.110096 | − | 0.993921i | \(-0.535116\pi\) | ||||
−0.110096 | + | 0.993921i | \(0.535116\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.98741 | 0.222983 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.3709i | 1.61298i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 34.8037i | − 1.29080i | −0.763846 | − | 0.645398i | \(-0.776691\pi\) | ||||
0.763846 | − | 0.645398i | \(-0.223309\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30.0117 | −1.11154 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.4298 | −2.01316 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.6346i | 0.799093i | 0.916713 | + | 0.399547i | \(0.130832\pi\) | ||||
−0.916713 | + | 0.399547i | \(0.869168\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 19.3506i | − 0.712789i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.53418 | 0.166792 | 0.0833962 | − | 0.996516i | \(-0.473423\pi\) | ||||
0.0833962 | + | 0.996516i | \(0.473423\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6208 | 0.426902 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 17.9137i | − 0.657192i | −0.944471 | − | 0.328596i | \(-0.893425\pi\) | ||||
0.944471 | − | 0.328596i | \(-0.106575\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.09686i | 0.0767201i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.5356 | 0.969588 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.1812 | −0.918875 | −0.459438 | − | 0.888210i | \(-0.651949\pi\) | ||||
−0.459438 | + | 0.888210i | \(0.651949\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 1.10314i | − 0.0402006i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.7079i | 1.11610i | 0.829809 | + | 0.558048i | \(0.188450\pi\) | ||||
−0.829809 | + | 0.558048i | \(0.811550\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.59718 | 0.239462 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.58720 | 0.347536 | 0.173768 | − | 0.984787i | \(-0.444406\pi\) | ||||
0.173768 | + | 0.984787i | \(0.444406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 31.3476i | − 1.13486i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52.0846i | 1.88066i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.31547 | 0.227742 | 0.113871 | − | 0.993496i | \(-0.463675\pi\) | ||||
0.113871 | + | 0.993496i | \(0.463675\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.1797 | 1.59109 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 47.4787i | − 1.70769i | −0.520528 | − | 0.853845i | \(-0.674265\pi\) | ||||
0.520528 | − | 0.853845i | \(-0.325735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 5.53642i | − 0.198618i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.8847 | −0.676616 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.6730 | −0.381910 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 7.01078i | − 0.250545i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 47.0588i | − 1.67747i | −0.544543 | − | 0.838733i | \(-0.683297\pi\) | ||||
0.544543 | − | 0.838733i | \(-0.316703\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.23546 | −0.150786 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −65.8134 | −2.34005 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.2134i | 1.21495i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 22.8819i | − 0.810517i | −0.914202 | − | 0.405259i | \(-0.867181\pi\) | ||||
0.914202 | − | 0.405259i | \(-0.132819\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 66.6846 | 2.35913 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.3218 | 0.364704 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 57.5792i | − 2.03193i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1.00339i | − 0.0353211i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.6918 | −0.762643 | −0.381322 | − | 0.924442i | \(-0.624531\pi\) | ||||
−0.381322 | + | 0.924442i | \(0.624531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.84992 | 0.205418 | 0.102709 | − | 0.994711i | \(-0.467249\pi\) | ||||
0.102709 | + | 0.994711i | \(0.467249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 22.0028i | − 0.771674i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.8890i | 0.765799i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.08540 | −0.317469 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.98613 | 0.208917 | 0.104459 | − | 0.994529i | \(-0.466689\pi\) | ||||
0.104459 | + | 0.994529i | \(0.466689\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 27.4906i | − 0.958261i | −0.877744 | − | 0.479131i | \(-0.840952\pi\) | ||||
0.877744 | − | 0.479131i | \(-0.159048\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.85519i | − 0.0992848i | −0.998767 | − | 0.0496424i | \(-0.984192\pi\) | ||||
0.998767 | − | 0.0496424i | \(-0.0158082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.63982 | 0.265342 | 0.132671 | − | 0.991160i | \(-0.457645\pi\) | ||||
0.132671 | + | 0.991160i | \(0.457645\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.74840 | −0.0606512 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.1808i | 0.941758i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 27.0652i | − 0.935510i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.41078 | 0.290372 | 0.145186 | − | 0.989404i | \(-0.453622\pi\) | ||||
0.145186 | + | 0.989404i | \(0.453622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4400 | −0.946205 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.6561i | 0.745877i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 27.8885i | − 0.958260i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −47.3564 | −1.62527 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.04471 | 0.0358121 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 35.6430i | − 1.22039i | −0.792250 | − | 0.610197i | \(-0.791090\pi\) | ||||
0.792250 | − | 0.610197i | \(-0.208910\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.66046i | 0.0908794i | 0.998967 | + | 0.0454397i | \(0.0144689\pi\) | ||||
−0.998967 | + | 0.0454397i | \(0.985531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0909 | −0.480774 | −0.240387 | − | 0.970677i | \(-0.577274\pi\) | ||||
−0.240387 | + | 0.970677i | \(0.577274\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −47.9910 | −1.63553 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 48.1228i | − 1.63812i | −0.573708 | − | 0.819060i | \(-0.694496\pi\) | ||||
0.573708 | − | 0.819060i | \(-0.305504\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.9801i | 0.508750i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.6539 | 1.14163 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.3451 | 0.553834 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.62042i | 0.224067i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 26.3172i | − 0.888668i | −0.895861 | − | 0.444334i | \(-0.853440\pi\) | ||||
0.895861 | − | 0.444334i | \(-0.146560\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.95951 | −0.234738 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.59556 | 0.255901 | 0.127951 | − | 0.991781i | \(-0.459160\pi\) | ||||
0.127951 | + | 0.991781i | \(0.459160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 11.8772i | − 0.399699i | −0.979827 | − | 0.199849i | \(-0.935955\pi\) | ||||
0.979827 | − | 0.199849i | \(-0.0640453\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 35.9421i | − 1.20682i | −0.797432 | − | 0.603409i | \(-0.793809\pi\) | ||||
0.797432 | − | 0.603409i | \(-0.206191\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.6169 | −1.76471 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.8076 | 0.931591 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 26.8173i | − 0.897406i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.57253i | 0.186061i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.02258 | 0.200864 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.6070 | −1.61933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 55.6257i | 1.85111i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.9912i | 1.89236i | 0.323637 | + | 0.946181i | \(0.395094\pi\) | ||||
−0.323637 | + | 0.946181i | \(0.604906\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.724685 | −0.0240363 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.5339 | −1.21042 | −0.605212 | − | 0.796065i | \(-0.706912\pi\) | ||||
−0.605212 | + | 0.796065i | \(0.706912\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 12.9398i | − 0.428243i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 71.2017i | − 2.35129i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.65041 | 0.0544419 | 0.0272210 | − | 0.999629i | \(-0.491334\pi\) | ||||
0.0272210 | + | 0.999629i | \(0.491334\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.0876 | 0.497152 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 9.01531i | − 0.296743i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.20783i | 0.0396704i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.24062 | −0.106321 | −0.0531606 | − | 0.998586i | \(-0.516930\pi\) | ||||
−0.0531606 | + | 0.998586i | \(0.516930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9308 | 0.358242 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.3150i | 0.632344i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 4.26930i | − 0.139472i | −0.997565 | − | 0.0697360i | \(-0.977784\pi\) | ||||
0.997565 | − | 0.0697360i | \(-0.0222157\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.6244 | 0.966757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −57.0889 | −1.86105 | −0.930523 | − | 0.366234i | \(-0.880647\pi\) | ||||
−0.930523 | + | 0.366234i | \(0.880647\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 9.05578i | − 0.294897i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 50.1371i | − 1.62924i | −0.579997 | − | 0.814618i | \(-0.696946\pi\) | ||||
0.579997 | − | 0.814618i | \(-0.303054\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.6362 | 1.57880 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 49.3011 | 1.59870 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 6.17257i | − 0.199949i | −0.994990 | − | 0.0999745i | \(-0.968124\pi\) | ||||
0.994990 | − | 0.0999745i | \(-0.0318761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.24000i | 0.266361i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.30049 | 0.171162 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.74979 | −0.249993 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.35298i | 0.172497i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.04066i | 0.226412i | 0.993572 | + | 0.113206i | \(0.0361121\pi\) | ||||
−0.993572 | + | 0.113206i | \(0.963888\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.3793 | 0.526180 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.91622 | −0.189861 | −0.0949303 | − | 0.995484i | \(-0.530263\pi\) | ||||
−0.0949303 | + | 0.995484i | \(0.530263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46.7644i | 1.49920i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 14.7695i | − 0.472517i | −0.971690 | − | 0.236259i | \(-0.924079\pi\) | ||||
0.971690 | − | 0.236259i | \(-0.0759213\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −63.6961 | −2.03574 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.32370 | 0.201900 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.8892i | 0.730054i | 0.930997 | + | 0.365027i | \(0.118940\pi\) | ||||
−0.930997 | + | 0.365027i | \(0.881060\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 68.1497i | − 2.16923i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.4964 | −0.333766 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.4611 | 0.713500 | 0.356750 | − | 0.934200i | \(-0.383885\pi\) | ||||
0.356750 | + | 0.934200i | \(0.383885\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 36.3070i | − 1.15217i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 43.9293i | − 1.39125i | −0.718403 | − | 0.695627i | \(-0.755127\pi\) | ||||
0.718403 | − | 0.695627i | \(-0.244873\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.86398 | 0.185528 |
(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 | 4600.2.e.v.4049.3 | 10 | ||
5.2 | odd | 4 | 4600.2.a.bc.1.2 | ✓ | 5 | ||
5.3 | odd | 4 | 4600.2.a.bg.1.4 | yes | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.v.4049.8 | 10 | ||
20.3 | even | 4 | 9200.2.a.cs.1.2 | 5 | |||
20.7 | even | 4 | 9200.2.a.cw.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bc.1.2 | ✓ | 5 | 5.2 | odd | 4 | ||
4600.2.a.bg.1.4 | yes | 5 | 5.3 | odd | 4 | ||
4600.2.e.v.4049.3 | 10 | 1.1 | even | 1 | trivial | ||
4600.2.e.v.4049.8 | 10 | 5.4 | even | 2 | inner | ||
9200.2.a.cs.1.2 | 5 | 20.3 | even | 4 | |||
9200.2.a.cw.1.4 | 5 | 20.7 | even | 4 |