Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,2,Mod(305,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("608.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.c (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: | \(4.85490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 305.16 | ||
Root | \(1.14052 - 0.836196i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 608.305 |
Dual form | 608.2.c.b.305.1 |
$q$-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 \(\left(\mathbb{Z}/608\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.13611i | 1.81063i | 0.424735 | + | 0.905317i | \(0.360367\pi\) | ||||
−0.424735 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.594041i | 0.265663i | 0.991139 | + | 0.132832i | \(0.0424069\pi\) | ||||
−0.991139 | + | 0.132832i | \(0.957593\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.48756 | 1.31818 | 0.659088 | − | 0.752066i | \(-0.270943\pi\) | ||||
0.659088 | + | 0.752066i | \(0.270943\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.83520 | −2.27840 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.83520i | 1.45787i | 0.684585 | + | 0.728933i | \(0.259984\pi\) | ||||
−0.684585 | + | 0.728933i | \(0.740016\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.215597i | − 0.0597957i | −0.999553 | − | 0.0298979i | \(-0.990482\pi\) | ||||
0.999553 | − | 0.0298979i | \(-0.00951821\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.86298 | −0.481019 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.29720 | 0.314618 | 0.157309 | − | 0.987549i | \(-0.449718\pi\) | ||||
0.157309 | + | 0.987549i | \(0.449718\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.9374i | 2.38673i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.52815 | −0.944184 | −0.472092 | − | 0.881549i | \(-0.656501\pi\) | ||||
−0.472092 | + | 0.881549i | \(0.656501\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.64712 | 0.929423 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 12.0276i | − 2.31471i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 9.41093i | − 1.74757i | −0.486316 | − | 0.873783i | \(-0.661660\pi\) | ||||
0.486316 | − | 0.873783i | \(-0.338340\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.22031 | 0.219174 | 0.109587 | − | 0.993977i | \(-0.465047\pi\) | ||||
0.109587 | + | 0.993977i | \(0.465047\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.1637 | −2.63966 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.07176i | 0.350191i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.62653i | 0.924995i | 0.886621 | + | 0.462498i | \(0.153047\pi\) | ||||
−0.886621 | + | 0.462498i | \(0.846953\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.676135 | 0.108268 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.450021 | −0.0702815 | −0.0351407 | − | 0.999382i | \(-0.511188\pi\) | ||||
−0.0351407 | + | 0.999382i | \(0.511188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 0.794359i | − 0.121139i | −0.998164 | − | 0.0605693i | \(-0.980708\pi\) | ||||
0.998164 | − | 0.0605693i | \(-0.0192916\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 4.06039i | − 0.605287i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1986 | −1.77935 | −0.889676 | − | 0.456593i | \(-0.849070\pi\) | ||||
−0.889676 | + | 0.456593i | \(0.849070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.16310 | 0.737586 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.06817i | 0.569658i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.56409i | 0.352205i | 0.984372 | + | 0.176103i | \(0.0563490\pi\) | ||||
−0.984372 | + | 0.176103i | \(0.943651\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.87231 | −0.387302 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.13611 | −0.415388 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 2.75191i | − 0.358268i | −0.983825 | − | 0.179134i | \(-0.942670\pi\) | ||||
0.983825 | − | 0.179134i | \(-0.0573295\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 7.76665i | − 0.994417i | −0.867631 | − | 0.497209i | \(-0.834358\pi\) | ||||
0.867631 | − | 0.497209i | \(-0.165642\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −23.8382 | −3.00333 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.128073 | 0.0158855 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.11631i | − 0.502887i | −0.967872 | − | 0.251443i | \(-0.919095\pi\) | ||||
0.967872 | − | 0.251443i | \(-0.0809053\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 14.2008i | − 1.70957i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.82788 | 0.928999 | 0.464499 | − | 0.885573i | \(-0.346234\pi\) | ||||
0.464499 | + | 0.885573i | \(0.346234\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.08931 | 0.361577 | 0.180788 | − | 0.983522i | \(-0.442135\pi\) | ||||
0.180788 | + | 0.983522i | \(0.442135\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.5739i | 1.68285i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.8631i | 1.92172i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0731 | 1.13331 | 0.566654 | − | 0.823956i | \(-0.308237\pi\) | ||||
0.566654 | + | 0.823956i | \(0.308237\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.2143 | 1.91270 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6296i | 1.27651i | 0.769825 | + | 0.638255i | \(0.220343\pi\) | ||||
−0.769825 | + | 0.638255i | \(0.779657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.770591i | 0.0835823i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 29.5137 | 3.16420 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.7091 | 1.45317 | 0.726583 | − | 0.687079i | \(-0.241107\pi\) | ||||
0.726583 | + | 0.687079i | \(0.241107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 0.751907i | − 0.0788213i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.82703i | 0.396845i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.594041 | −0.0609473 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.08846 | 0.212051 | 0.106026 | − | 0.994363i | \(-0.466187\pi\) | ||||
0.106026 | + | 0.994363i | \(0.466187\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 33.0495i | − 3.32160i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.77074i | 0.275699i | 0.990453 | + | 0.137849i | \(0.0440190\pi\) | ||||
−0.990453 | + | 0.137849i | \(0.955981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.3363 | 1.41260 | 0.706301 | − | 0.707912i | \(-0.250363\pi\) | ||||
0.706301 | + | 0.707912i | \(0.250363\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.49726 | −0.634067 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.42388i | − 0.234325i | −0.993113 | − | 0.117163i | \(-0.962620\pi\) | ||||
0.993113 | − | 0.117163i | \(-0.0373799\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 0.00123810i | 0 0.000118589i | −1.00000 | 5.92945e-5i | \(-0.999981\pi\) | |||||
1.00000 | 5.92945e-5i | \(-1.88740e-5\pi\) | ||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.6454 | −1.67483 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.81614 | 0.170848 | 0.0854242 | − | 0.996345i | \(-0.472775\pi\) | ||||
0.0854242 | + | 0.996345i | \(0.472775\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.68990i | − 0.250835i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.47365i | 0.136239i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.52407 | 0.414721 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.3791 | −1.12538 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.41132i | − 0.127254i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.73078i | 0.512577i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.1269 | 1.43103 | 0.715517 | − | 0.698596i | \(-0.246191\pi\) | ||||
0.715517 | + | 0.698596i | \(0.246191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.49120 | 0.219338 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1477i | 0.973983i | 0.873407 | + | 0.486992i | \(0.161906\pi\) | ||||
−0.873407 | + | 0.486992i | \(0.838094\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.48756i | 0.302410i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.14489 | 0.614934 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.1666 | 0.954025 | 0.477013 | − | 0.878896i | \(-0.341720\pi\) | ||||
0.477013 | + | 0.878896i | \(0.341720\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0534i | 1.10718i | 0.832790 | + | 0.553589i | \(0.186742\pi\) | ||||
−0.832790 | + | 0.553589i | \(0.813258\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 38.2562i | − 3.22176i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.04245 | 0.0871742 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.59048 | 0.464264 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.1921i | 1.33550i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.3811i | 1.17814i | 0.808080 | + | 0.589072i | \(0.200507\pi\) | ||||
−0.808080 | + | 0.589072i | \(0.799493\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3489 | −1.41184 | −0.705918 | − | 0.708293i | \(-0.749465\pi\) | ||||
−0.705918 | + | 0.708293i | \(0.749465\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.86663 | −0.716825 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.724915i | 0.0582266i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.63293i | 0.768791i | 0.923168 | + | 0.384396i | \(0.125590\pi\) | ||||
−0.923168 | + | 0.384396i | \(0.874410\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.04128 | −0.637715 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.7922 | −1.24460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 22.5365i | − 1.76520i | −0.470129 | − | 0.882598i | \(-0.655793\pi\) | ||||
0.470129 | − | 0.882598i | \(-0.344207\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 9.00787i | − 0.701262i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.5108 | −1.27765 | −0.638823 | − | 0.769353i | \(-0.720579\pi\) | ||||
−0.638823 | + | 0.769353i | \(0.720579\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9535 | 0.996424 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 6.83520i | − 0.522701i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 5.14911i | − 0.391479i | −0.980656 | − | 0.195740i | \(-0.937289\pi\) | ||||
0.980656 | − | 0.195740i | \(-0.0627108\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.2071 | 1.22514 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.63029 | 0.648692 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 9.31580i | − 0.696295i | −0.937440 | − | 0.348148i | \(-0.886811\pi\) | ||||
0.937440 | − | 0.348148i | \(-0.113189\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 5.15517i | − 0.383180i | −0.981475 | − | 0.191590i | \(-0.938636\pi\) | ||||
0.981475 | − | 0.191590i | \(-0.0613645\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.3571 | 1.80053 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.34239 | −0.245737 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.27223i | 0.458671i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 41.9471i | − 3.05120i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.8805 | 1.07672 | 0.538359 | − | 0.842715i | \(-0.319044\pi\) | ||||
0.538359 | + | 0.842715i | \(0.319044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.2754 | −1.53144 | −0.765719 | − | 0.643175i | \(-0.777617\pi\) | ||||
−0.765719 | + | 0.643175i | \(0.777617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.401652i | 0.0287629i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3.69169i | − 0.263022i | −0.991315 | − | 0.131511i | \(-0.958017\pi\) | ||||
0.991315 | − | 0.131511i | \(-0.0419829\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.6857 | −0.828377 | −0.414188 | − | 0.910191i | \(-0.635935\pi\) | ||||
−0.414188 | + | 0.910191i | \(0.635935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.9092 | 0.910545 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 32.8212i | − 2.30360i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 0.267331i | − 0.0186712i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 30.9508 | 2.15123 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.83520 | −0.334458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 7.61611i | − 0.524315i | −0.965025 | − | 0.262157i | \(-0.915566\pi\) | ||||
0.965025 | − | 0.262157i | \(-0.0844340\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.5491i | 1.68208i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.471882 | 0.0321821 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.25591 | 0.288910 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.68844i | 0.654684i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 0.279672i | − 0.0188128i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.95477 | 0.130901 | 0.0654505 | − | 0.997856i | \(-0.479152\pi\) | ||||
0.0654505 | + | 0.997856i | \(0.479152\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.7640 | −2.11760 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 13.3709i | − 0.887461i | −0.896160 | − | 0.443730i | \(-0.853655\pi\) | ||||
0.896160 | − | 0.443730i | \(-0.146345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 11.5800i | − 0.765225i | −0.923909 | − | 0.382613i | \(-0.875024\pi\) | ||||
0.923909 | − | 0.382613i | \(-0.124976\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −52.8844 | −3.47954 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.58872 | 0.104080 | 0.0520401 | − | 0.998645i | \(-0.483428\pi\) | ||||
0.0520401 | + | 0.998645i | \(0.483428\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 7.24648i | − 0.472708i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 31.5903i | 2.05201i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.8219 | −1.54091 | −0.770455 | − | 0.637494i | \(-0.779971\pi\) | ||||
−0.770455 | + | 0.637494i | \(0.779971\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.8554 | 1.47225 | 0.736123 | − | 0.676848i | \(-0.236654\pi\) | ||||
0.736123 | + | 0.676848i | \(0.236654\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.9032i | 1.14849i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.06710i | 0.195950i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.215597 | 0.0137181 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −36.4716 | −2.31129 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.63524i | − 0.166335i | −0.996536 | − | 0.0831676i | \(-0.973496\pi\) | ||||
0.996536 | − | 0.0831676i | \(-0.0265037\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 21.8945i | − 1.37649i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.41666 | −0.151337 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.0579 | 1.25118 | 0.625588 | − | 0.780153i | \(-0.284859\pi\) | ||||
0.625588 | + | 0.780153i | \(0.284859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.6229i | 1.21931i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 64.3256i | 3.98165i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.03667 | −0.248912 | −0.124456 | − | 0.992225i | \(-0.539718\pi\) | ||||
−0.124456 | + | 0.992225i | \(0.539718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.52318 | −0.0935679 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 42.9934i | 2.63115i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 14.3095i | − 0.872467i | −0.899834 | − | 0.436233i | \(-0.856312\pi\) | ||||
0.899834 | − | 0.436233i | \(-0.143688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.85034 | −0.598366 | −0.299183 | − | 0.954196i | \(-0.596714\pi\) | ||||
−0.299183 | + | 0.954196i | \(0.596714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.35806 | 0.142717 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.4697i | 1.35498i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 16.9641i | − 1.01928i | −0.860389 | − | 0.509638i | \(-0.829779\pi\) | ||||
0.860389 | − | 0.509638i | \(-0.170221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.34107 | −0.499367 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2078 | −0.608944 | −0.304472 | − | 0.952521i | \(-0.598480\pi\) | ||||
−0.304472 | + | 0.952521i | \(0.598480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.7709i | 1.11581i | 0.829903 | + | 0.557907i | \(0.188396\pi\) | ||||
−0.829903 | + | 0.557907i | \(0.811604\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.86298i | − 0.110353i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.56948 | −0.0926433 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3173 | −0.901016 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.54966i | 0.383948i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.8271i | 1.15831i | 0.815217 | + | 0.579155i | \(0.196618\pi\) | ||||
−0.815217 | + | 0.579155i | \(0.803382\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.63475 | 0.0951786 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 58.1559 | 3.37454 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.976253i | 0.0564582i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.77038i | − 0.159682i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.68935 | −0.499190 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.61371 | 0.264180 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 18.3935i | − 1.04977i | −0.851173 | − | 0.524886i | \(-0.824108\pi\) | ||||
0.851173 | − | 0.524886i | \(-0.175892\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 44.9604i | 2.55771i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.1747 | −1.08730 | −0.543648 | − | 0.839313i | \(-0.682957\pi\) | ||||
−0.543648 | + | 0.839313i | \(0.682957\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2274 | 0.804183 | 0.402091 | − | 0.915600i | \(-0.368283\pi\) | ||||
0.402091 | + | 0.915600i | \(0.368283\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 14.1609i | − 0.797874i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 0.777938i | − 0.0436934i | −0.999761 | − | 0.0218467i | \(-0.993045\pi\) | ||||
0.999761 | − | 0.0218467i | \(-0.00695457\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 45.5037 | 2.54772 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.60156 | 0.424278 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.29720i | 0.0721782i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.00190i | − 0.0555755i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.00388283 | 0.000214721 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −42.5435 | −2.34550 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 16.3988i | − 0.901359i | −0.892686 | − | 0.450680i | \(-0.851182\pi\) | ||||
0.892686 | − | 0.450680i | \(-0.148818\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 38.4584i | − 2.10751i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.44525 | 0.133599 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.6109 | 1.34064 | 0.670320 | − | 0.742072i | \(-0.266157\pi\) | ||||
0.670320 | + | 0.742072i | \(0.266157\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.69563i | 0.309344i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.90045i | 0.319527i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.40629 | −0.345907 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.43584 | 0.454170 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.4635i | 0.722760i | 0.932419 | + | 0.361380i | \(0.117694\pi\) | ||||
−0.932419 | + | 0.361380i | \(0.882306\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.83422i | 0.151712i | 0.997119 | + | 0.0758560i | \(0.0241689\pi\) | ||||
−0.997119 | + | 0.0758560i | \(0.975831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.59311 | −0.138410 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.02227 | −0.267308 | −0.133654 | − | 0.991028i | \(-0.542671\pi\) | ||||
−0.133654 | + | 0.991028i | \(0.542671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.65008i | 0.246801i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.1880i | 0.750909i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.6898 | −1.25030 | −0.625149 | − | 0.780505i | \(-0.714962\pi\) | ||||
−0.625149 | + | 0.780505i | \(0.714962\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 38.8223i | − 2.03764i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.83518i | 0.0960577i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.9338 | 0.883938 | 0.441969 | − | 0.897030i | \(-0.354280\pi\) | ||||
0.441969 | + | 0.897030i | \(0.354280\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.07598 | 0.160129 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.94244i | 0.464268i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12.8599i | − 0.665860i | −0.942952 | − | 0.332930i | \(-0.891963\pi\) | ||||
0.942952 | − | 0.332930i | \(-0.108037\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.9724 | −0.928089 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.02896 | −0.104497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 20.7810i | − 1.06745i | −0.845659 | − | 0.533723i | \(-0.820793\pi\) | ||||
0.845659 | − | 0.533723i | \(-0.179207\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 50.5758i | 2.59108i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.6170 | 0.797993 | 0.398996 | − | 0.916953i | \(-0.369359\pi\) | ||||
0.398996 | + | 0.916953i | \(0.369359\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0173 | −0.510531 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.42960i | 0.276002i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 10.1133i | − 0.512764i | −0.966576 | − | 0.256382i | \(-0.917470\pi\) | ||||
0.966576 | − | 0.256382i | \(-0.0825304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.87392 | −0.297057 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.9606 | −1.76353 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.98381i | 0.301078i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.60677i | − 0.231207i | −0.993295 | − | 0.115604i | \(-0.963120\pi\) | ||||
0.993295 | − | 0.115604i | \(-0.0368802\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.9374 | −0.547554 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.00112 | −0.199806 | −0.0999032 | − | 0.994997i | \(-0.531853\pi\) | ||||
−0.0999032 | + | 0.994997i | \(0.531853\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.263095i | − 0.0131057i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.2260i | 0.508135i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.2054 | −1.34852 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.5111 | −0.717529 | −0.358765 | − | 0.933428i | \(-0.616802\pi\) | ||||
−0.358765 | + | 0.933428i | \(0.616802\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.0196i | 1.72739i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 9.59745i | − 0.472260i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.90843 | −0.339122 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −40.9370 | −2.00470 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 5.02078i | − 0.245281i | −0.992451 | − | 0.122641i | \(-0.960864\pi\) | ||||
0.992451 | − | 0.122641i | \(-0.0391362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4.10152i | − 0.199896i | −0.994993 | − | 0.0999479i | \(-0.968132\pi\) | ||||
0.994993 | − | 0.0999479i | \(-0.0318676\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 83.3800 | 4.05407 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.02825 | 0.292413 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 27.0867i | − 1.31082i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.26925i | 0.157841i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.2920 | 0.784760 | 0.392380 | − | 0.919803i | \(-0.371652\pi\) | ||||
0.392380 | + | 0.919803i | \(0.371652\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.44858 | 0.357956 | 0.178978 | − | 0.983853i | \(-0.442721\pi\) | ||||
0.178978 | + | 0.983853i | \(0.442721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.5324i | 0.840612i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.52815i | − 0.216611i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.8898 | −0.758379 | −0.379189 | − | 0.925319i | \(-0.623797\pi\) | ||||
−0.379189 | + | 0.925319i | \(0.623797\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −35.2908 | −1.68052 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.1742i | 0.720949i | 0.932769 | + | 0.360474i | \(0.117385\pi\) | ||||
−0.932769 | + | 0.360474i | \(0.882615\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.14379i | 0.386053i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −45.1007 | −2.13319 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.3909 | −1.15108 | −0.575538 | − | 0.817775i | \(-0.695207\pi\) | ||||
−0.575538 | + | 0.817775i | \(0.695207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.17594i | − 0.102461i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 54.4082i | − 2.55632i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.446664 | 0.0209399 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.6860 | −0.499869 | −0.249934 | − | 0.968263i | \(-0.580409\pi\) | ||||
−0.249934 | + | 0.968263i | \(0.580409\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 15.6022i | − 0.728250i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 21.8232i | − 1.01641i | −0.861236 | − | 0.508205i | \(-0.830309\pi\) | ||||
0.861236 | − | 0.508205i | \(-0.169691\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0258442 | −0.00120108 | −0.000600541 | − | 1.00000i | \(-0.500191\pi\) | ||||
−0.000600541 | 1.00000i | \(0.500191\pi\) | ||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.27341 | −0.105427 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.66985i | 0.216095i | 0.994146 | + | 0.108047i | \(0.0344598\pi\) | ||||
−0.994146 | + | 0.108047i | \(0.965540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 14.3559i | − 0.662893i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.2099 | −1.39200 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.84088 | 0.176604 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.64712i | 0.213224i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 17.5261i | − 0.802464i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.5428 | 1.39554 | 0.697768 | − | 0.716324i | \(-0.254177\pi\) | ||||
0.697768 | + | 0.716324i | \(0.254177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.21306 | 0.0553108 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 49.5261i | − 2.25352i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.24063i | 0.0563342i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.37133 | 0.107455 | 0.0537277 | − | 0.998556i | \(-0.482890\pi\) | ||||
0.0537277 | + | 0.998556i | \(0.482890\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 70.6770 | 3.19613 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 41.3206i | − 1.86477i | −0.361466 | − | 0.932385i | \(-0.617724\pi\) | ||||
0.361466 | − | 0.932385i | \(-0.382276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 12.2079i | − 0.549815i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.6328 | 0.882427 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.3002 | 1.22458 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.8610i | 0.710035i | 0.934860 | + | 0.355018i | \(0.115525\pi\) | ||||
−0.934860 | + | 0.355018i | \(0.884475\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 51.7798i | − 2.31335i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.6879 | 0.833254 | 0.416627 | − | 0.909078i | \(-0.363212\pi\) | ||||
0.416627 | + | 0.909078i | \(0.363212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.64593 | −0.0732431 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 40.6237i | 1.80416i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 33.2172i | − 1.47233i | −0.676804 | − | 0.736163i | \(-0.736636\pi\) | ||||
0.676804 | − | 0.736163i | \(-0.263364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.7742 | 0.476622 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.0276 | 0.531032 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.51637i | 0.375276i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 58.9827i | − 2.59406i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.1482 | 0.708826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.9831 | −0.481178 | −0.240589 | − | 0.970627i | \(-0.577341\pi\) | ||||
−0.240589 | + | 0.970627i | \(0.577341\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8.00433i | − 0.350005i | −0.984568 | − | 0.175002i | \(-0.944007\pi\) | ||||
0.984568 | − | 0.175002i | \(-0.0559933\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 50.8273i | 2.21829i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.58299 | 0.0689561 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.49589 | −0.108517 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.8098i | 0.816277i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0970230i | 0.00420253i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.43988 | 0.0622516 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.2154 | 1.26074 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.9646i | 1.07530i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.4359i | 1.05058i | 0.850923 | + | 0.525291i | \(0.176044\pi\) | ||||
−0.850923 | + | 0.525291i | \(0.823956\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.1672 | 0.693800 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.000735485 0 | 3.15047e−5 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.25284i | 0.224595i | 0.993675 | + | 0.112298i | \(0.0358210\pi\) | ||||
−0.993675 | + | 0.112298i | \(0.964179\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 53.0866i | 2.26568i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.41093 | 0.400919 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.1305 | 1.49390 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 10.4821i | − 0.444940i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.56791i | 0.151177i | 0.997139 | + | 0.0755886i | \(0.0240836\pi\) | ||||
−0.997139 | + | 0.0755886i | \(0.975916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.171261 | −0.00724357 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.6704 | −0.830485 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.0555i | 0.718805i | 0.933183 | + | 0.359403i | \(0.117020\pi\) | ||||
−0.933183 | + | 0.359403i | \(0.882980\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.07886i | 0.0453881i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 60.0361 | 2.52128 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.858816 | −0.0360034 | −0.0180017 | − | 0.999838i | \(-0.505730\pi\) | ||||
−0.0180017 | + | 0.999838i | \(0.505730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 40.5440i | − 1.69671i | −0.529426 | − | 0.848356i | \(-0.677593\pi\) | ||||
0.529426 | − | 0.848356i | \(-0.322407\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 46.6671i | 1.94954i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.0428 | −0.877546 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.5405 | 1.52120 | 0.760600 | − | 0.649220i | \(-0.224905\pi\) | ||||
0.760600 | + | 0.649220i | \(0.224905\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 66.7221i | − 2.77288i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.5588i | 1.68266i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.3979 | −0.513468 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.875406 | −0.0361936 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 30.4022i | − 1.25483i | −0.778684 | − | 0.627416i | \(-0.784113\pi\) | ||||
0.778684 | − | 0.627416i | \(-0.215887\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.22031i | 0.0502821i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.5776 | 0.476237 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.3814 | −0.672703 | −0.336351 | − | 0.941737i | \(-0.609193\pi\) | ||||
−0.336351 | + | 0.941737i | \(0.609193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.68749i | 0.110176i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 36.6476i | − 1.49989i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.24749 | 0.0918298 | 0.0459149 | − | 0.998945i | \(-0.485380\pi\) | ||||
0.0459149 | + | 0.998945i | \(0.485380\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.1805 | −1.35346 | −0.676730 | − | 0.736231i | \(-0.736604\pi\) | ||||
−0.676730 | + | 0.736231i | \(0.736604\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.1358i | 1.14578i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 7.35371i | − 0.298971i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.7847 | −1.45246 | −0.726228 | − | 0.687454i | \(-0.758728\pi\) | ||||
−0.726228 | + | 0.687454i | \(0.758728\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 102.931 | 4.17098 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.62998i | 0.106398i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.2856i | 1.70790i | 0.520355 | + | 0.853950i | \(0.325800\pi\) | ||||
−0.520355 | + | 0.853950i | \(0.674200\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.838380 | 0.0338067 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.2079 | −1.05509 | −0.527545 | − | 0.849527i | \(-0.676887\pi\) | ||||
−0.527545 | + | 0.849527i | \(0.676887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.7494i | 1.63786i | 0.573896 | + | 0.818929i | \(0.305432\pi\) | ||||
−0.573896 | + | 0.818929i | \(0.694568\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 54.4628i | 2.18552i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.8115 | 1.91553 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.8313 | 0.793250 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 15.1637i | − 0.605581i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.29874i | 0.291020i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.3804 | −1.68714 | −0.843569 | − | 0.537021i | \(-0.819550\pi\) | ||||
−0.843569 | + | 0.537021i | \(0.819550\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.8850 | 0.949343 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.58005i | 0.380173i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.11315i | − 0.0441045i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −53.5051 | −2.11663 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.0356 | −1.58131 | −0.790656 | − | 0.612261i | \(-0.790260\pi\) | ||||
−0.790656 | + | 0.612261i | \(0.790260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.25369i | 0.0888767i | 0.999012 | + | 0.0444384i | \(0.0141498\pi\) | ||||
−0.999012 | + | 0.0444384i | \(0.985850\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.47987i | 0.0582700i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.89272 | 0.270981 | 0.135490 | − | 0.990779i | \(-0.456739\pi\) | ||||
0.135490 | + | 0.990779i | \(0.456739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.3060 | 0.522307 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.3470i | 0.523111i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.75398i | 0.225170i | 0.993642 | + | 0.112585i | \(0.0359131\pi\) | ||||
−0.993642 | + | 0.112585i | \(0.964087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.62222 | −0.258751 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.1161 | −0.823817 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 34.1024i | − 1.32844i | −0.747537 | − | 0.664220i | \(-0.768764\pi\) | ||||
0.747537 | − | 0.664220i | \(-0.231236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.3767i | 1.80384i | 0.431900 | + | 0.901922i | \(0.357843\pi\) | ||||
−0.431900 | + | 0.901922i | \(0.642157\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.877084 | 0.0340631 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.07176 | −0.0803392 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.6141i | 1.65002i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.13038i | 0.237014i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.5533 | 1.44973 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.1579 | −1.12395 | −0.561977 | − | 0.827153i | \(-0.689959\pi\) | ||||
−0.561977 | + | 0.827153i | \(0.689959\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 55.8937i | − 2.15135i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 10.0436i | − 0.386006i | −0.981198 | − | 0.193003i | \(-0.938177\pi\) | ||||
0.981198 | − | 0.193003i | \(-0.0618228\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.28365 | 0.279521 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.9328 | 1.60687 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.5866i | 0.979042i | 0.871991 | + | 0.489521i | \(0.162828\pi\) | ||||
−0.871991 | + | 0.489521i | \(0.837172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.63341i | 0.253449i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.3161 | 1.38554 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.552809 | 0.0210604 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 42.2386i | − 1.60683i | −0.595417 | − | 0.803417i | \(-0.703013\pi\) | ||||
0.595417 | − | 0.803417i | \(-0.296987\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 115.262i | − 4.37845i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.75428 | −0.294136 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.583768 | −0.0221118 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.98239i | 0.188451i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 43.9811i | − 1.66114i | −0.556911 | − | 0.830572i | \(-0.688014\pi\) | ||||
0.556911 | − | 0.830572i | \(-0.311986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.62653 | −0.212208 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.7258 | 0.855902 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.66314i | 0.363420i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 11.1307i | − 0.418023i | −0.977913 | − | 0.209012i | \(-0.932975\pi\) | ||||
0.977913 | − | 0.209012i | \(-0.0670246\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −68.8514 | −2.58213 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.52575 | −0.206941 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.619259i | 0.0231590i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 74.7081i | − 2.79003i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.8961 | −0.667413 | −0.333706 | − | 0.942677i | \(-0.608299\pi\) | ||||
−0.333706 | + | 0.942677i | \(0.608299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.9989 | 1.86206 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 71.6771i | 2.66570i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 43.7337i | − 1.62423i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.8772 | 1.33061 | 0.665306 | − | 0.746571i | \(-0.268301\pi\) | ||||
0.665306 | + | 0.746571i | \(0.268301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.50357 | −0.166799 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.03044i | − 0.0381123i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.4618i | 0.903516i | 0.892141 | + | 0.451758i | \(0.149203\pi\) | ||||
−0.892141 | + | 0.451758i | \(0.850797\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.61875 | −0.354793 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.9032 | 0.733142 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 26.7820i | − 0.985193i | −0.870258 | − | 0.492596i | \(-0.836048\pi\) | ||||
0.870258 | − | 0.492596i | \(-0.163952\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.676135i | 0.0248384i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.7835 | −0.872534 | −0.436267 | − | 0.899817i | \(-0.643700\pi\) | ||||
−0.436267 | + | 0.899817i | \(0.643700\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.54295 | −0.312990 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 79.4903i | − 2.90840i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 8.45344i | − 0.308882i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.4303 | −0.818494 | −0.409247 | − | 0.912424i | \(-0.634209\pi\) | ||||
−0.409247 | + | 0.912424i | \(0.634209\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.26442 | 0.301172 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 10.3060i | − 0.375073i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2421i | 1.17186i | 0.810362 | + | 0.585930i | \(0.199271\pi\) | ||||
−0.810362 | + | 0.585930i | \(0.800729\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 68.6635 | 2.49233 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.3559 | 0.592902 | 0.296451 | − | 0.955048i | \(-0.404197\pi\) | ||||
0.296451 | + | 0.955048i | \(0.404197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 0.00431797i | 0 0.000156321i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 5.26714i | − 0.190434i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.593302 | −0.0214229 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.6832 | −0.709794 | −0.354897 | − | 0.934905i | \(-0.615484\pi\) | ||||
−0.354897 | + | 0.934905i | \(0.615484\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 62.9038i | 2.26542i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.0819i | 1.18987i | 0.803773 | + | 0.594936i | \(0.202823\pi\) | ||||
−0.803773 | + | 0.594936i | \(0.797177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.67093 | 0.203706 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −61.5395 | −2.20772 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 0.450021i | − 0.0161237i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.8494i | 1.35436i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −113.191 | −4.04512 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.72235 | −0.204240 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.1617i | 1.25338i | 0.779269 | + | 0.626690i | \(0.215591\pi\) | ||||
−0.779269 | + | 0.626690i | \(0.784409\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 12.6594i | − 0.450688i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.33392 | 0.225208 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.67446 | −0.0594619 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 4.77685i | − 0.169417i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3.75101i | − 0.132868i | −0.997791 | − | 0.0664338i | \(-0.978838\pi\) | ||||
0.997791 | − | 0.0664338i | \(-0.0211621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.8241 | −0.559815 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −93.7046 | −3.31089 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.9374i | 0.527131i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 9.38121i | − 0.330644i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.8763 | 1.57972 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.9158 | 0.840836 | 0.420418 | − | 0.907331i | \(-0.361883\pi\) | ||||
0.420418 | + | 0.907331i | \(0.361883\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0538i | 1.82785i | 0.405878 | + | 0.913927i | \(0.366966\pi\) | ||||
−0.405878 | + | 0.913927i | \(0.633034\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 30.8918i | − 1.08342i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.3876 | 0.468947 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.794359 | 0.0277911 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.13943i | 0.179586i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 0.703590i | − 0.0245555i | −0.999925 | − | 0.0122777i | \(-0.996092\pi\) | ||||
0.999925 | − | 0.0122777i | \(-0.00390822\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.4559 | −0.817622 | −0.408811 | − | 0.912619i | \(-0.634057\pi\) | ||||
−0.408811 | + | 0.912619i | \(0.634057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −70.4676 | −2.45337 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 29.5282i | − 1.02680i | −0.858150 | − | 0.513399i | \(-0.828386\pi\) | ||||
0.858150 | − | 0.513399i | \(-0.171614\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.42946i | 0.153841i | 0.997037 | + | 0.0769207i | \(0.0245088\pi\) | ||||
−0.997037 | + | 0.0769207i | \(0.975491\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 53.2014 | 1.84554 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.69759 | 0.232058 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 9.80811i | − 0.339424i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 14.6774i | − 0.507326i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.4506 | 1.25841 | 0.629207 | − | 0.777237i | \(-0.283380\pi\) | ||||
0.629207 | + | 0.777237i | \(0.283380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −59.5656 | −2.05399 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 32.0127i | − 1.10257i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.69492i | 0.264713i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.1730 | −1.48344 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −58.8677 | −2.02033 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 25.4777i | − 0.873366i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.7043i | 1.80456i | 0.431149 | + | 0.902281i | \(0.358108\pi\) | ||||
−0.431149 | + | 0.902281i | \(0.641892\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.06039 | 0.138862 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.7199 | 0.468662 | 0.234331 | − | 0.972157i | \(-0.424710\pi\) | ||||
0.234331 | + | 0.972157i | \(0.424710\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 55.0757i | − 1.87916i | −0.342330 | − | 0.939580i | \(-0.611216\pi\) | ||||
0.342330 | − | 0.939580i | \(-0.388784\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 4.92206i | − 0.167743i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.3384 | −1.30505 | −0.652527 | − | 0.757766i | \(-0.726291\pi\) | ||||
−0.652527 | + | 0.757766i | \(0.726291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.05878 | 0.104002 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 48.0367i | − 1.63141i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.7053i | 1.65221i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.887462 | −0.0300705 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.2751 | −0.483138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.9865i | 0.675666i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 21.4788i | − 0.725288i | −0.931928 | − | 0.362644i | \(-0.881874\pi\) | ||||
0.931928 | − | 0.362644i | \(-0.118126\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −62.1800 | −2.09728 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.2383 | −0.378629 | −0.189314 | − | 0.981917i | \(-0.560627\pi\) | ||||
−0.189314 | + | 0.981917i | \(0.560627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.7137i | 0.528809i | 0.964412 | + | 0.264405i | \(0.0851755\pi\) | ||||
−0.964412 | + | 0.264405i | \(0.914825\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.12674i | 0.172334i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.48008 | −0.150426 | −0.0752131 | − | 0.997167i | \(-0.523964\pi\) | ||||
−0.0752131 | + | 0.997167i | \(0.523964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 56.2437 | 1.88635 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 83.2347i | 2.78847i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 12.1986i | − 0.408211i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.53396 | 0.184980 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.06164 | −0.102225 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 11.4843i | − 0.383022i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.32614i | 0.110810i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.68822 | 0.289126 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.06238 | 0.101797 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 6.37021i | − 0.211519i | −0.994392 | − | 0.105760i | \(-0.966273\pi\) | ||||
0.994392 | − | 0.105760i | \(-0.0337274\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 18.9386i | − 0.628152i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.5275 | 1.01142 | 0.505711 | − | 0.862703i | \(-0.331230\pi\) | ||||
0.505711 | + | 0.862703i | \(0.331230\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56.2312 | −1.86098 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.4691i | 0.478334i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.8785i | 1.28388i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.0650 | 1.58552 | 0.792758 | − | 0.609536i | \(-0.208644\pi\) | ||||
0.792758 | + | 0.609536i | \(0.208644\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 57.6840 | 1.90075 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.68767i | − 0.0555502i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.1471i | 0.859712i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −97.9917 | −3.21847 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.2953 | 1.55171 | 0.775854 | − | 0.630912i | \(-0.217319\pi\) | ||||
0.775854 | + | 0.630912i | \(0.217319\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.16310i | 0.169214i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 60.1339i | − 1.96870i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.72596 | −0.121852 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.30237 | −0.271227 | −0.135613 | − | 0.990762i | \(-0.543301\pi\) | ||||
−0.135613 | + | 0.990762i | \(0.543301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 44.6189i | 1.45608i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.3955i | 1.02347i | 0.859145 | + | 0.511733i | \(0.170996\pi\) | ||||
−0.859145 | + | 0.511733i | \(0.829004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.03776 | 0.0663586 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.9183 | 0.810591 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.14805i | 0.0698024i | 0.999391 | + | 0.0349012i | \(0.0111117\pi\) | ||||
−0.999391 | + | 0.0349012i | \(0.988888\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 0.666046i | − 0.0216208i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.43970 | 0.0791127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.3661 | 0.821689 | 0.410844 | − | 0.911705i | \(-0.365234\pi\) | ||||
0.410844 | + | 0.911705i | \(0.365234\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.83965i | 0.286044i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 142.705i | 4.61299i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.9442 | 1.25757 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5108 | −0.951963 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.5677i | 0.533887i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 12.6385i | − 0.406847i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8395 | 0.412892 | 0.206446 | − | 0.978458i | \(-0.433810\pi\) | ||||
0.206446 | + | 0.978458i | \(0.433810\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.06817 | −0.130688 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.77909i | 0.281734i | 0.990028 | + | 0.140867i | \(0.0449891\pi\) | ||||
−0.990028 | + | 0.140867i | \(0.955011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.5247i | 1.45945i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.14208 | 0.100627 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.9701 | −1.47071 | −0.735357 | − | 0.677680i | \(-0.762986\pi\) | ||||
−0.735357 | + | 0.677680i | \(0.762986\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66.2864i | 2.11852i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.00846269i | 0 0.000270193i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.4992 | 1.64257 | 0.821284 | − | 0.570519i | \(-0.193258\pi\) | ||||
0.821284 | + | 0.570519i | \(0.193258\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.19302 | 0.0698753 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 133.421i | − 4.24684i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.59697i | 0.114377i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.4762 | 0.936343 | 0.468171 | − | 0.883638i | \(-0.344913\pi\) | ||||
0.468171 | + | 0.883638i | \(0.344913\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 51.4284 | 1.63203 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 6.94178i | − 0.220069i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 54.3591i | − 1.72157i | −0.508968 | − | 0.860786i | \(-0.669973\pi\) | ||||
0.508968 | − | 0.860786i | \(-0.330027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 67.6737 | 2.14110 |
(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 | 608.2.c.b.305.16 | 16 | ||
3.2 | odd | 2 | 5472.2.g.b.2737.8 | 16 | |||
4.3 | odd | 2 | 152.2.c.b.77.6 | yes | 16 | ||
8.3 | odd | 2 | 152.2.c.b.77.5 | ✓ | 16 | ||
8.5 | even | 2 | inner | 608.2.c.b.305.1 | 16 | ||
12.11 | even | 2 | 1368.2.g.b.685.11 | 16 | |||
16.3 | odd | 4 | 4864.2.a.bq.1.8 | 8 | |||
16.5 | even | 4 | 4864.2.a.bn.1.8 | 8 | |||
16.11 | odd | 4 | 4864.2.a.bo.1.1 | 8 | |||
16.13 | even | 4 | 4864.2.a.bp.1.1 | 8 | |||
24.5 | odd | 2 | 5472.2.g.b.2737.9 | 16 | |||
24.11 | even | 2 | 1368.2.g.b.685.12 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.5 | ✓ | 16 | 8.3 | odd | 2 | ||
152.2.c.b.77.6 | yes | 16 | 4.3 | odd | 2 | ||
608.2.c.b.305.1 | 16 | 8.5 | even | 2 | inner | ||
608.2.c.b.305.16 | 16 | 1.1 | even | 1 | trivial | ||
1368.2.g.b.685.11 | 16 | 12.11 | even | 2 | |||
1368.2.g.b.685.12 | 16 | 24.11 | even | 2 | |||
4864.2.a.bn.1.8 | 8 | 16.5 | even | 4 | |||
4864.2.a.bo.1.1 | 8 | 16.11 | odd | 4 | |||
4864.2.a.bp.1.1 | 8 | 16.13 | even | 4 | |||
4864.2.a.bq.1.8 | 8 | 16.3 | odd | 4 | |||
5472.2.g.b.2737.8 | 16 | 3.2 | odd | 2 | |||
5472.2.g.b.2737.9 | 16 | 24.5 | odd | 2 |