Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(193,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(4))
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("768.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.j (of order \(4\), degree \(2\), 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: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.193 |
Dual form | 768.2.j.e.577.4 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.732051 | + | 0.732051i | 0.327383 | + | 0.327383i | 0.851591 | − | 0.524207i | \(-0.175638\pi\) |
−0.524207 | + | 0.851591i | \(0.675638\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949i | 0.925820i | 0.886405 | + | 0.462910i | \(0.153195\pi\) | ||||
−0.886405 | + | 0.462910i | \(0.846805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.86370 | + | 3.86370i | 1.16495 | + | 1.16495i | 0.983377 | + | 0.181573i | \(0.0581188\pi\) |
0.181573 | + | 0.983377i | \(0.441881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.03528 | 0.267307 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.378937 | + | 0.378937i | −0.0869342 | + | 0.0869342i | −0.749237 | − | 0.662302i | \(-0.769579\pi\) |
0.662302 | + | 0.749237i | \(0.269579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73205 | + | 1.73205i | 0.377964 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.92820i | − | 0.785641i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.19615 | + | 4.19615i | −0.779206 | + | 0.779206i | −0.979696 | − | 0.200490i | \(-0.935747\pi\) |
0.200490 | + | 0.979696i | \(0.435747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.34847 | 1.31982 | 0.659912 | − | 0.751343i | \(-0.270594\pi\) | ||||
0.659912 | + | 0.751343i | \(0.270594\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.46410 | 0.951178 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.79315 | + | 1.79315i | −0.303098 | + | 0.303098i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.46410 | + | 6.46410i | 1.06269 | + | 1.06269i | 0.997899 | + | 0.0647930i | \(0.0206387\pi\) |
0.0647930 | + | 0.997899i | \(0.479361\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.24264i | 0.679366i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.4641i | − | 1.79039i | −0.445673 | − | 0.895196i | \(-0.647036\pi\) | ||
0.445673 | − | 0.895196i | \(-0.352964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.44949 | + | 2.44949i | 0.373544 | + | 0.373544i | 0.868766 | − | 0.495222i | \(-0.164913\pi\) |
−0.495222 | + | 0.868766i | \(0.664913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.732051 | − | 0.732051i | 0.109128 | − | 0.109128i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.44949 | + | 2.44949i | −0.342997 | + | 0.342997i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.73205 | − | 6.73205i | −0.924718 | − | 0.924718i | 0.0726399 | − | 0.997358i | \(-0.476858\pi\) |
−0.997358 | + | 0.0726399i | \(0.976858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.65685i | 0.762770i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.535898i | 0.0709815i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.79796 | + | 9.79796i | 1.27559 | + | 1.27559i | 0.943113 | + | 0.332473i | \(0.107883\pi\) |
0.332473 | + | 0.943113i | \(0.392117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.46410 | − | 6.46410i | 0.827643 | − | 0.827643i | −0.159547 | − | 0.987190i | \(-0.551003\pi\) |
0.987190 | + | 0.159547i | \(0.0510033\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.44949 | 0.308607 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.39230 | −0.544798 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.757875 | − | 0.757875i | 0.0925891 | − | 0.0925891i | −0.659295 | − | 0.751884i | \(-0.729145\pi\) |
0.751884 | + | 0.659295i | \(0.229145\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | + | 2.00000i | 0.240772 | + | 0.240772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 16.2127i | − | 1.92409i | −0.272887 | − | 0.962046i | \(-0.587979\pi\) | ||
0.272887 | − | 0.962046i | \(-0.412021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.77766 | − | 2.77766i | −0.320736 | − | 0.320736i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.46410 | + | 9.46410i | −1.07853 | + | 1.07853i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.44949 | 0.275589 | 0.137795 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137795 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.03528 | − | 1.03528i | 0.113636 | − | 0.113636i | −0.648002 | − | 0.761638i | \(-0.724395\pi\) |
0.761638 | + | 0.648002i | \(0.224395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.53590 | − | 2.53590i | −0.275057 | − | 0.275057i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.93426i | 0.636219i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.92820i | 0.946388i | 0.880958 | + | 0.473194i | \(0.156899\pi\) | ||||
−0.880958 | + | 0.473194i | \(0.843101\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.34847 | − | 7.34847i | −0.770329 | − | 0.770329i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.19615 | − | 5.19615i | 0.538816 | − | 0.538816i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.554803 | −0.0569216 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9282 | 1.51573 | 0.757865 | − | 0.652412i | \(-0.226243\pi\) | ||||
0.757865 | + | 0.652412i | \(0.226243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.86370 | − | 3.86370i | 0.388317 | − | 0.388317i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.196152 | − | 0.196152i | −0.0195179 | − | 0.0195179i | 0.697280 | − | 0.716798i | \(-0.254393\pi\) |
−0.716798 | + | 0.697280i | \(0.754393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.10634i | 0.798742i | 0.916789 | + | 0.399371i | \(0.130771\pi\) | ||||
−0.916789 | + | 0.399371i | \(0.869229\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.53590i | 0.247478i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.82843 | − | 2.82843i | −0.273434 | − | 0.273434i | 0.557047 | − | 0.830481i | \(-0.311934\pi\) |
−0.830481 | + | 0.557047i | \(0.811934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | + | 1.00000i | −0.0957826 | + | 0.0957826i | −0.753374 | − | 0.657592i | \(-0.771575\pi\) |
0.657592 | + | 0.753374i | \(0.271575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.14162 | 0.867684 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.07055 | + | 2.07055i | −0.193080 | + | 0.193080i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | + | 3.00000i | 0.277350 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 8.48528i | − | 0.777844i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8564i | 1.71422i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.10634 | − | 8.10634i | −0.730924 | − | 0.730924i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.53590 | − | 6.53590i | 0.584589 | − | 0.584589i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.4201 | −1.72325 | −0.861625 | − | 0.507545i | \(-0.830553\pi\) | ||||
−0.861625 | + | 0.507545i | \(0.830553\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.46410 | 0.304997 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.757875 | + | 0.757875i | −0.0662158 | + | 0.0662158i | −0.739439 | − | 0.673223i | \(-0.764909\pi\) |
0.673223 | + | 0.739439i | \(0.264909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.928203 | − | 0.928203i | −0.0804854 | − | 0.0804854i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.03528i | − | 0.0891024i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.39230i | 0.546131i | 0.961995 | + | 0.273066i | \(0.0880377\pi\) | ||||
−0.961995 | + | 0.273066i | \(0.911962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.89898 | − | 4.89898i | −0.415526 | − | 0.415526i | 0.468132 | − | 0.883658i | \(-0.344927\pi\) |
−0.883658 | + | 0.468132i | \(0.844927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | + | 2.00000i | −0.168430 | + | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.1822 | −1.93859 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.14359 | −0.510198 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.707107 | − | 0.707107i | 0.0583212 | − | 0.0583212i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.1962 | − | 14.1962i | −1.16299 | − | 1.16299i | −0.983817 | − | 0.179177i | \(-0.942656\pi\) |
−0.179177 | − | 0.983817i | \(-0.557344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.9043i | − | 1.45703i | −0.685029 | − | 0.728516i | \(-0.740211\pi\) | ||
0.685029 | − | 0.728516i | \(-0.259789\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.46410i | 0.280056i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.37945 | + | 5.37945i | 0.432088 | + | 0.432088i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.46410 | − | 8.46410i | 0.675509 | − | 0.675509i | −0.283472 | − | 0.958981i | \(-0.591486\pi\) |
0.958981 | + | 0.283472i | \(0.0914862\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.52056 | −0.755029 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.92820 | −0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.10634 | − | 8.10634i | 0.634938 | − | 0.634938i | −0.314364 | − | 0.949302i | \(-0.601791\pi\) |
0.949302 | + | 0.314364i | \(0.101791\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.00000 | + | 4.00000i | 0.311400 | + | 0.311400i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.07055i | − | 0.160224i | −0.996786 | − | 0.0801121i | \(-0.974472\pi\) | ||
0.996786 | − | 0.0801121i | \(-0.0255278\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.378937 | + | 0.378937i | 0.0289781 | + | 0.0289781i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.80385 | − | 1.80385i | 0.137144 | − | 0.137144i | −0.635202 | − | 0.772346i | \(-0.719083\pi\) |
0.772346 | + | 0.635202i | \(0.219083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.62209 | 0.727362 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.8564 | 1.04151 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.58630 | − | 3.58630i | 0.268053 | − | 0.268053i | −0.560262 | − | 0.828315i | \(-0.689300\pi\) |
0.828315 | + | 0.560262i | \(0.189300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | + | 5.00000i | 0.371647 | + | 0.371647i | 0.868077 | − | 0.496430i | \(-0.165356\pi\) |
−0.496430 | + | 0.868077i | \(0.665356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 9.14162i | − | 0.675768i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.46410i | 0.695815i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.3843 | − | 13.3843i | −0.978754 | − | 0.978754i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.73205 | − | 1.73205i | 0.125988 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.07055 | −0.149820 | −0.0749100 | − | 0.997190i | \(-0.523867\pi\) | ||||
−0.0749100 | + | 0.997190i | \(0.523867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.10583 | + | 3.10583i | −0.222413 | + | 0.222413i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.19615 | − | 4.19615i | −0.298963 | − | 0.298963i | 0.541644 | − | 0.840608i | \(-0.317802\pi\) |
−0.840608 | + | 0.541644i | \(0.817802\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.96524i | − | 0.281088i | −0.990074 | − | 0.140544i | \(-0.955115\pi\) | ||
0.990074 | − | 0.140544i | \(-0.0448852\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1.07180i | − | 0.0755987i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.2784 | − | 10.2784i | −0.721405 | − | 0.721405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.39230 | − | 8.39230i | 0.586144 | − | 0.586144i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.92820 | −0.202548 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.89898 | − | 4.89898i | 0.337260 | − | 0.337260i | −0.518075 | − | 0.855335i | \(-0.673351\pi\) |
0.855335 | + | 0.518075i | \(0.173351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4641 | − | 11.4641i | −0.785507 | − | 0.785507i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.58630i | 0.244584i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000i | 1.22192i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.82843 | − | 2.82843i | −0.191127 | − | 0.191127i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3923 | − | 10.3923i | 0.699062 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4201 | 1.30046 | 0.650231 | − | 0.759736i | \(-0.274672\pi\) | ||||
0.650231 | + | 0.759736i | \(0.274672\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.92820 | −0.261880 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.4901 | + | 16.4901i | −1.09449 | + | 1.09449i | −0.0994423 | + | 0.995043i | \(0.531706\pi\) |
−0.995043 | + | 0.0994423i | \(0.968294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.92820 | − | 1.92820i | −0.127419 | − | 0.127419i | 0.640521 | − | 0.767940i | \(-0.278718\pi\) |
−0.767940 | + | 0.640521i | \(0.778718\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.3843i | 0.880620i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.928203i | 0.0608086i | 0.999538 | + | 0.0304043i | \(0.00967948\pi\) | ||||
−0.999538 | + | 0.0304043i | \(0.990321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.07055 | − | 2.07055i | −0.135068 | − | 0.135068i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.73205 | − | 1.73205i | 0.112509 | − | 0.112509i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.07055 | −0.133933 | −0.0669664 | − | 0.997755i | \(-0.521332\pi\) | ||||
−0.0669664 | + | 0.997755i | \(0.521332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7846 | −0.952360 | −0.476180 | − | 0.879348i | \(-0.657979\pi\) | ||||
−0.476180 | + | 0.879348i | \(0.657979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.732051 | + | 0.732051i | 0.0467690 | + | 0.0467690i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.27362i | − | 0.144667i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.46410i | − | 0.0927837i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.52056 | + | 9.52056i | 0.600932 | + | 0.600932i | 0.940560 | − | 0.339628i | \(-0.110301\pi\) |
−0.339628 | + | 0.940560i | \(0.610301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.9282 | + | 10.9282i | −0.687050 | + | 0.687050i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.58630 | −0.224583 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.7846 | 1.17175 | 0.585876 | − | 0.810401i | \(-0.300751\pi\) | ||||
0.585876 | + | 0.810401i | \(0.300751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.8338 | + | 15.8338i | −0.983861 | + | 0.983861i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.19615 | + | 4.19615i | 0.259735 | + | 0.259735i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.6274i | − | 1.39527i | −0.716455 | − | 0.697633i | \(-0.754237\pi\) | ||
0.716455 | − | 0.697633i | \(-0.245763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.85641i | − | 0.605474i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.31319 | + | 6.31319i | 0.386361 | + | 0.386361i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.7321 | + | 10.7321i | −0.654345 | + | 0.654345i | −0.954036 | − | 0.299691i | \(-0.903116\pi\) |
0.299691 | + | 0.954036i | \(0.403116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.10634 | −0.492425 | −0.246213 | − | 0.969216i | \(-0.579186\pi\) | ||||
−0.246213 | + | 0.969216i | \(0.579186\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.3923 | −0.628971 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.1774 | − | 15.1774i | 0.915232 | − | 0.915232i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.8564 | − | 18.8564i | −1.13297 | − | 1.13297i | −0.989681 | − | 0.143291i | \(-0.954231\pi\) |
−0.143291 | − | 0.989681i | \(-0.545769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 7.34847i | − | 0.439941i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.9282i | − | 0.771232i | −0.922659 | − | 0.385616i | \(-0.873989\pi\) | ||
0.922659 | − | 0.385616i | \(-0.126011\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.6264 | + | 12.6264i | 0.750561 | + | 0.750561i | 0.974584 | − | 0.224023i | \(-0.0719191\pi\) |
−0.224023 | + | 0.974584i | \(0.571919\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.392305 | + | 0.392305i | −0.0232381 | + | 0.0232381i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.0812 | 1.65758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.5558 | − | 10.5558i | 0.618794 | − | 0.618794i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.66025 | + | 9.66025i | 0.564358 | + | 0.564358i | 0.930542 | − | 0.366184i | \(-0.119336\pi\) |
−0.366184 | + | 0.930542i | \(0.619336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3452i | 0.835210i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.46410i | − | 0.317059i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.48528 | − | 8.48528i | −0.490716 | − | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | + | 6.00000i | −0.345834 | + | 0.345834i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.277401 | −0.0159363 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.46410 | 0.541913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.41473 | + | 6.41473i | −0.366108 | + | 0.366108i | −0.866056 | − | 0.499948i | \(-0.833353\pi\) |
0.499948 | + | 0.866056i | \(0.333353\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.73205 | + | 5.73205i | 0.326085 | + | 0.326085i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.8295i | 0.727492i | 0.931498 | + | 0.363746i | \(0.118502\pi\) | ||||
−0.931498 | + | 0.363746i | \(0.881498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.8564i | − | 1.34844i | −0.738529 | − | 0.674222i | \(-0.764479\pi\) | ||
0.738529 | − | 0.674222i | \(-0.235521\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.79315 | + | 1.79315i | 0.101033 | + | 0.101033i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.26795 | − | 1.26795i | 0.0712151 | − | 0.0712151i | −0.670602 | − | 0.741817i | \(-0.733964\pi\) |
0.741817 | + | 0.670602i | \(0.233964\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.4254 | −1.81547 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.31268 | − | 1.31268i | 0.0730393 | − | 0.0730393i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7846 | + | 11.7846i | 0.653693 | + | 0.653693i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.41421i | 0.0782062i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.92820i | − | 0.381964i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.5558 | + | 10.5558i | 0.580201 | + | 0.580201i | 0.934958 | − | 0.354757i | \(-0.115437\pi\) |
−0.354757 | + | 0.934958i | \(0.615437\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.46410 | − | 6.46410i | 0.354231 | − | 0.354231i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.10961 | 0.0606242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.8564 | 0.972700 | 0.486350 | − | 0.873764i | \(-0.338328\pi\) | ||||
0.486350 | + | 0.873764i | \(0.338328\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.7279 | + | 12.7279i | −0.691286 | + | 0.691286i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.3923 | + | 28.3923i | 1.53753 | + | 1.53753i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959i | 1.05808i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.92820i | 0.157649i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.69213 | − | 6.69213i | −0.359252 | − | 0.359252i | 0.504285 | − | 0.863537i | \(-0.331756\pi\) |
−0.863537 | + | 0.504285i | \(0.831756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.39230 | + | 1.39230i | −0.0745284 | + | 0.0745284i | −0.743388 | − | 0.668860i | \(-0.766783\pi\) |
0.668860 | + | 0.743388i | \(0.266783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.24264 | 0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9282 | 0.688099 | 0.344049 | − | 0.938952i | \(-0.388201\pi\) | ||||
0.344049 | + | 0.938952i | \(0.388201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.8685 | − | 11.8685i | 0.629915 | − | 0.629915i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | − | 6.00000i | −0.317554 | − | 0.317554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.1518i | 1.59135i | 0.605725 | + | 0.795674i | \(0.292883\pi\) | ||||
−0.605725 | + | 0.795674i | \(0.707117\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7128i | 0.984885i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.3335 | + | 13.3335i | 0.699827 | + | 0.699827i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.92820 | − | 2.92820i | 0.153269 | − | 0.153269i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.7023 | 1.44605 | 0.723023 | − | 0.690824i | \(-0.242752\pi\) | ||||
0.723023 | + | 0.690824i | \(0.242752\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.4641 | −0.596797 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4901 | − | 16.4901i | 0.856123 | − | 0.856123i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3923 | + | 11.3923i | 0.589871 | + | 0.589871i | 0.937596 | − | 0.347725i | \(-0.113046\pi\) |
−0.347725 | + | 0.937596i | \(0.613046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 9.24316i | − | 0.477315i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 25.1769i | − | 1.29668i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0759 | + | 15.0759i | 0.774396 | + | 0.774396i | 0.978872 | − | 0.204476i | \(-0.0655490\pi\) |
−0.204476 | + | 0.978872i | \(0.565549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.7321 | + | 13.7321i | −0.703514 | + | 0.703514i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.554803 | 0.0283491 | 0.0141746 | − | 0.999900i | \(-0.495488\pi\) | ||||
0.0141746 | + | 0.999900i | \(0.495488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.8564 | −0.706188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.44949 | − | 2.44949i | 0.124515 | − | 0.124515i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.26795 | − | 3.26795i | −0.165692 | − | 0.165692i | 0.619391 | − | 0.785083i | \(-0.287380\pi\) |
−0.785083 | + | 0.619391i | \(0.787380\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.79796i | − | 0.495504i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.07180i | 0.0540650i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.79315 | + | 1.79315i | 0.0902232 | + | 0.0902232i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3205 | + | 18.3205i | −0.919480 | + | 0.919480i | −0.996991 | − | 0.0775115i | \(-0.975303\pi\) |
0.0775115 | + | 0.996991i | \(0.475303\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.31268 | −0.0657161 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.39230 | −0.119466 | −0.0597330 | − | 0.998214i | \(-0.519025\pi\) | ||||
−0.0597330 | + | 0.998214i | \(0.519025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0454 | + | 22.0454i | −1.09816 | + | 1.09816i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.732051 | − | 0.732051i | −0.0363759 | − | 0.0363759i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 49.9507i | 2.47597i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.9282i | − | 1.13373i | −0.823812 | − | 0.566863i | \(-0.808157\pi\) | ||
0.823812 | − | 0.566863i | \(-0.191843\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.52004 | + | 4.52004i | 0.222957 | + | 0.222957i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0000 | + | 24.0000i | −1.18096 | + | 1.18096i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.51575 | 0.0744052 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.92820 | −0.339276 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.4195 | + | 14.4195i | −0.704440 | + | 0.704440i | −0.965360 | − | 0.260920i | \(-0.915974\pi\) |
0.260920 | + | 0.965360i | \(0.415974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0717968 | − | 0.0717968i | −0.00349916 | − | 0.00349916i | 0.705355 | − | 0.708854i | \(-0.250788\pi\) |
−0.708854 | + | 0.705355i | \(0.750788\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843i | 0.137523i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.6077i | 0.660070i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.8338 | + | 15.8338i | 0.766249 | + | 0.766249i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.3923 | + | 16.3923i | −0.791428 | + | 0.791428i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.9401 | 1.15315 | 0.576577 | − | 0.817043i | \(-0.304388\pi\) | ||||
0.576577 | + | 0.817043i | \(0.304388\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.14359 | 0.103015 | 0.0515073 | − | 0.998673i | \(-0.483597\pi\) | ||||
0.0515073 | + | 0.998673i | \(0.483597\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.34418 | + | 4.34418i | −0.208287 | + | 0.208287i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.07180 | − | 1.07180i | −0.0512710 | − | 0.0512710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 28.4601i | − | 1.35833i | −0.733986 | − | 0.679164i | \(-0.762342\pi\) | ||
0.733986 | − | 0.679164i | \(-0.237658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 1.00000i | − | 0.0476190i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.480473 | + | 0.480473i | 0.0228280 | + | 0.0228280i | 0.718429 | − | 0.695601i | \(-0.244862\pi\) |
−0.695601 | + | 0.718429i | \(0.744862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.53590 | + | 6.53590i | −0.309831 | + | 0.309831i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.0764 | −0.949581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.3923 | 0.679215 | 0.339607 | − | 0.940567i | \(-0.389706\pi\) | ||||
0.339607 | + | 0.940567i | \(0.389706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.2939 | − | 44.2939i | 2.08572 | − | 2.08572i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.6603 | − | 12.6603i | −0.594831 | − | 0.594831i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 10.7589i | − | 0.504385i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 20.7846i | − | 0.972263i | −0.873886 | − | 0.486132i | \(-0.838408\pi\) | ||
0.873886 | − | 0.486132i | \(-0.161592\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.44949 | + | 2.44949i | 0.114332 | + | 0.114332i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.0526 | − | 16.0526i | 0.747642 | − | 0.747642i | −0.226394 | − | 0.974036i | \(-0.572694\pi\) |
0.974036 | + | 0.226394i | \(0.0726936\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.72311 | −0.219502 | −0.109751 | − | 0.993959i | \(-0.535005\pi\) | ||||
−0.109751 | + | 0.993959i | \(0.535005\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.60770 | 0.352798 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.9038 | + | 12.9038i | −0.597116 | + | 0.597116i | −0.939544 | − | 0.342428i | \(-0.888751\pi\) |
0.342428 | + | 0.939544i | \(0.388751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.85641 | + | 1.85641i | 0.0857209 | + | 0.0857209i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 11.9700i | − | 0.551551i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.9282i | 0.870320i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.48854 | + | 1.48854i | 0.0682990 | + | 0.0682990i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.73205 | + | 6.73205i | −0.308239 | + | 0.308239i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.8401 | 1.77465 | 0.887325 | − | 0.461145i | \(-0.152561\pi\) | ||||
0.887325 | + | 0.461145i | \(0.152561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.7846 | −1.76843 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.89898 | + | 4.89898i | −0.222911 | + | 0.222911i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9282 | + | 10.9282i | 0.496224 | + | 0.496224i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.8033i | 1.03332i | 0.856192 | + | 0.516658i | \(0.172824\pi\) | ||||
−0.856192 | + | 0.516658i | \(0.827176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 11.4641i | − | 0.518425i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.4548 | − | 15.4548i | −0.697466 | − | 0.697466i | 0.266397 | − | 0.963863i | \(-0.414167\pi\) |
−0.963863 | + | 0.266397i | \(0.914167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.5359 | − | 14.5359i | 0.654664 | − | 0.654664i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | 0.254257 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 39.7128 | 1.78136 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.82843 | + | 2.82843i | −0.126618 | + | 0.126618i | −0.767576 | − | 0.640958i | \(-0.778537\pi\) |
0.640958 | + | 0.767576i | \(0.278537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.46410 | − | 1.46410i | −0.0654112 | − | 0.0654112i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.1833i | 1.47957i | 0.672844 | + | 0.739784i | \(0.265072\pi\) | ||||
−0.672844 | + | 0.739784i | \(0.734928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.287187i | − | 0.0127797i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.53553 | − | 3.53553i | −0.157019 | − | 0.157019i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.1244 | − | 19.1244i | 0.847672 | − | 0.847672i | −0.142170 | − | 0.989842i | \(-0.545408\pi\) |
0.989842 | + | 0.142170i | \(0.0454080\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79796 | 0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.535898 | 0.0236605 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.93426 | + | 5.93426i | −0.261495 | + | 0.261495i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.9282 | − | 10.9282i | −0.480622 | − | 0.480622i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.55103i | − | 0.111978i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.3205i | − | 0.583582i | −0.956482 | − | 0.291791i | \(-0.905749\pi\) | ||
0.956482 | − | 0.291791i | \(-0.0942512\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3495 | + | 17.3495i | 0.758641 | + | 0.758641i | 0.976075 | − | 0.217434i | \(-0.0697688\pi\) |
−0.217434 | + | 0.976075i | \(0.569769\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.80385 | − | 6.80385i | 0.296944 | − | 0.296944i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.4558 | −1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.79796 | − | 9.79796i | 0.425195 | − | 0.425195i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.3923 | + | 34.3923i | 1.48970 | + | 1.48970i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.14110i | − | 0.179036i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5.07180i | − | 0.218864i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.86370 | + | 3.86370i | 0.166421 | + | 0.166421i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.07180 | + | 6.07180i | −0.261047 | + | 0.261047i | −0.825479 | − | 0.564432i | \(-0.809095\pi\) |
0.564432 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.07107 | 0.303449 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.46410 | −0.0627152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.7023 | + | 27.7023i | −1.18446 | + | 1.18446i | −0.205888 | + | 0.978576i | \(0.566008\pi\) |
−0.978576 | + | 0.205888i | \(0.933992\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.46410 | − | 6.46410i | −0.275881 | − | 0.275881i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.18016i | − | 0.135479i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000i | 0.255146i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.69213 | + | 6.69213i | 0.284065 | + | 0.284065i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.1962 | − | 30.1962i | 1.27945 | − | 1.27945i | 0.338478 | − | 0.940974i | \(-0.390088\pi\) |
0.940974 | − | 0.338478i | \(-0.109912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6969 | −0.621614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.9282 | −0.799149 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.86370 | − | 3.86370i | 0.162836 | − | 0.162836i | −0.620986 | − | 0.783822i | \(-0.713268\pi\) |
0.783822 | + | 0.620986i | \(0.213268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.1769 | − | 13.1769i | −0.554357 | − | 0.554357i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.44949i | − | 0.102869i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.46410i | 0.145223i | 0.997360 | + | 0.0726113i | \(0.0231333\pi\) | ||||
−0.997360 | + | 0.0726113i | \(0.976867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.7675 | − | 16.7675i | −0.701698 | − | 0.701698i | 0.263077 | − | 0.964775i | \(-0.415263\pi\) |
−0.964775 | + | 0.263077i | \(0.915263\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.46410 | + | 1.46410i | −0.0611637 | + | 0.0611637i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.1106 | 0.463346 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.85641 | 0.243805 | 0.121903 | − | 0.992542i | \(-0.461100\pi\) | ||||
0.121903 | + | 0.992542i | \(0.461100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.24264 | − | 4.24264i | 0.176318 | − | 0.176318i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.53590 | + | 2.53590i | 0.105207 | + | 0.105207i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 52.0213i | − | 2.15450i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.39230i | 0.181599i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.5569 | − | 20.5569i | −0.848473 | − | 0.848473i | 0.141470 | − | 0.989943i | \(-0.454817\pi\) |
−0.989943 | + | 0.141470i | \(0.954817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.78461 | + | 2.78461i | −0.114738 | + | 0.114738i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.93426 | −0.244103 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.7128 | 0.727378 | 0.363689 | − | 0.931520i | \(-0.381517\pi\) | ||||
0.363689 | + | 0.931520i | \(0.381517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.21166 | − | 6.21166i | 0.254653 | − | 0.254653i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.80385 | − | 2.80385i | −0.114754 | − | 0.114754i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.6264i | − | 0.515900i | −0.966158 | − | 0.257950i | \(-0.916953\pi\) | ||
0.966158 | − | 0.257950i | \(-0.0830470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 35.7128i | − | 1.45676i | −0.685176 | − | 0.728378i | \(-0.740275\pi\) | ||
0.685176 | − | 0.728378i | \(-0.259725\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.757875 | − | 0.757875i | −0.0308630 | − | 0.0308630i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.8038 | + | 13.8038i | −0.561206 | + | 0.561206i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8434 | −1.29248 | −0.646241 | − | 0.763133i | \(-0.723660\pi\) | ||||
−0.646241 | + | 0.763133i | \(0.723660\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.5359 | −0.589024 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.48528 | − | 8.48528i | 0.343278 | − | 0.343278i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.3205 | − | 30.3205i | −1.22463 | − | 1.22463i | −0.965966 | − | 0.258667i | \(-0.916717\pi\) |
−0.258667 | − | 0.965966i | \(-0.583283\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 11.8685i | − | 0.478585i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1436i | 0.488883i | 0.969664 | + | 0.244441i | \(0.0786046\pi\) | ||||
−0.969664 | + | 0.244441i | \(0.921395\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.48528 | − | 8.48528i | −0.341052 | − | 0.341052i | 0.515711 | − | 0.856763i | \(-0.327528\pi\) |
−0.856763 | + | 0.515711i | \(0.827528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | − | 2.00000i | 0.0802572 | − | 0.0802572i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.8695 | −0.876185 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.0718 | −0.402872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.07055 | + | 2.07055i | −0.0826899 | + | 0.0826899i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.3923 | − | 22.3923i | −0.892840 | − | 0.892840i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.933740i | 0.0371716i | 0.999827 | + | 0.0185858i | \(0.00591639\pi\) | ||||
−0.999827 | + | 0.0185858i | \(0.994084\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.92820i | − | 0.275371i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.2165 | − | 14.2165i | −0.564163 | − | 0.564163i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | + | 3.00000i | −0.118864 | + | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.2127 | −0.641364 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.3923 | −1.83239 | −0.916193 | − | 0.400737i | \(-0.868754\pi\) | ||||
−0.916193 | + | 0.400737i | \(0.868754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0769 | + | 25.0769i | −0.988937 | + | 0.988937i | −0.999939 | − | 0.0110028i | \(-0.996498\pi\) |
0.0110028 | + | 0.999939i | \(0.496498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.53590 | + | 2.53590i | 0.0998509 | + | 0.0998509i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 21.3147i | − | 0.837969i | −0.907993 | − | 0.418984i | \(-0.862386\pi\) | ||
0.907993 | − | 0.418984i | \(-0.137614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 75.7128i | 2.97199i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.7279 | + | 12.7279i | 0.498847 | + | 0.498847i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.339746 | − | 0.339746i | 0.0132953 | − | 0.0132953i | −0.700428 | − | 0.713723i | \(-0.747007\pi\) |
0.713723 | + | 0.700428i | \(0.247007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.10961 | −0.0433559 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9706 | − | 16.9706i | 0.661079 | − | 0.661079i | −0.294555 | − | 0.955634i | \(-0.595171\pi\) |
0.955634 | + | 0.294555i | \(0.0951715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.3923 | + | 25.3923i | 0.987646 | + | 0.987646i | 0.999925 | − | 0.0122784i | \(-0.00390844\pi\) |
−0.0122784 | + | 0.999925i | \(0.503908\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 14.6969i | − | 0.570782i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.35898i | − | 0.0526991i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.8685 | − | 11.8685i | −0.459551 | − | 0.459551i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.7321 | − | 13.7321i | 0.530912 | − | 0.530912i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.9507 | 1.92833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00000 | 0.308377 | 0.154189 | − | 0.988041i | \(-0.450724\pi\) | ||||
0.154189 | + | 0.988041i | \(0.450724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.77766 | + | 2.77766i | −0.106912 | + | 0.106912i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.6603 | − | 19.6603i | −0.755605 | − | 0.755605i | 0.219914 | − | 0.975519i | \(-0.429422\pi\) |
−0.975519 | + | 0.219914i | \(0.929422\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.5665i | 1.40329i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.3205i | 0.893644i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.2880 | − | 26.2880i | −1.00588 | − | 1.00588i | −0.999983 | − | 0.00590163i | \(-0.998121\pi\) |
−0.00590163 | − | 0.999983i | \(-0.501879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.67949 | + | 4.67949i | −0.178794 | + | 0.178794i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.72689 | −0.104037 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.3923 | 1.53882 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.96524 | + | 3.96524i | −0.150845 | + | 0.150845i | −0.778495 | − | 0.627650i | \(-0.784017\pi\) |
0.627650 | + | 0.778495i | \(0.284017\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.46410 | + | 9.46410i | 0.359511 | + | 0.359511i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7.17260i | − | 0.272072i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.7128i | 1.50423i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.656339 | + | 0.656339i | 0.0248250 | + | 0.0248250i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.5885 | − | 20.5885i | 0.777615 | − | 0.777615i | −0.201809 | − | 0.979425i | \(-0.564682\pi\) |
0.979425 | + | 0.201809i | \(0.0646822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.89898 | −0.184769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.92820 | −0.110283 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.480473 | − | 0.480473i | 0.0180701 | − | 0.0180701i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.7128 | − | 20.7128i | −0.777886 | − | 0.777886i | 0.201585 | − | 0.979471i | \(-0.435391\pi\) |
−0.979471 | + | 0.201585i | \(0.935391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2.44949i | − | 0.0918630i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7846i | 0.778390i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.9706 | − | 16.9706i | −0.634663 | − | 0.634663i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.46410 | + | 1.46410i | −0.0546779 | + | 0.0546779i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.6675 | −1.18100 | −0.590499 | − | 0.807038i | \(-0.701069\pi\) | ||||
−0.590499 | + | 0.807038i | \(0.701069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.8564 | −0.739491 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.4543 | + | 10.4543i | −0.388800 | + | 0.388800i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.4833 | + | 16.4833i | 0.612176 | + | 0.612176i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.20736i | − | 0.118955i | −0.998230 | − | 0.0594773i | \(-0.981057\pi\) | ||
0.998230 | − | 0.0594773i | \(-0.0189434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.48528 | − | 8.48528i | −0.313839 | − | 0.313839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.00000 | − | 5.00000i | 0.184679 | − | 0.184679i | −0.608712 | − | 0.793391i | \(-0.708314\pi\) |
0.793391 | + | 0.608712i | \(0.208314\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.03528 | 0.0381867 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.85641 | 0.215724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4558 | − | 25.4558i | 0.936408 | − | 0.936408i | −0.0616872 | − | 0.998096i | \(-0.519648\pi\) |
0.998096 | + | 0.0616872i | \(0.0196481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.60770 | − | 1.60770i | −0.0590602 | − | 0.0590602i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.6665i | 0.794866i | 0.917631 | + | 0.397433i | \(0.130099\pi\) | ||||
−0.917631 | + | 0.397433i | \(0.869901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 20.7846i | − | 0.761489i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.03528 | − | 1.03528i | −0.0378788 | − | 0.0378788i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.92820 | − | 6.92820i | 0.253151 | − | 0.253151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6937 | 0.791614 | 0.395807 | − | 0.918334i | \(-0.370465\pi\) | ||||
0.395807 | + | 0.918334i | \(0.370465\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.4641 | 0.490659 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.1069 | − | 13.1069i | 0.477007 | − | 0.477007i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7846 | + | 17.7846i | 0.646393 | + | 0.646393i | 0.952119 | − | 0.305727i | \(-0.0988994\pi\) |
−0.305727 | + | 0.952119i | \(0.598899\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.4548i | 0.560974i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.75129i | − | 0.135984i | −0.997686 | − | 0.0679921i | \(-0.978341\pi\) | ||
0.997686 | − | 0.0679921i | \(-0.0216593\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.44949 | − | 2.44949i | −0.0886775 | − | 0.0886775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.53590 | + | 2.53590i | −0.0916856 | + | 0.0916856i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −58.7878 | −2.12270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.2827 | − | 13.2827i | 0.478366 | − | 0.478366i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.41154 | − | 3.41154i | −0.122705 | − | 0.122705i | 0.643088 | − | 0.765792i | \(-0.277653\pi\) |
−0.765792 | + | 0.643088i | \(0.777653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 28.8663i | − | 1.03691i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.3923i | 0.803319i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.34418 | + | 4.34418i | 0.155646 | + | 0.155646i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62.6410 | − | 62.6410i | 2.24147 | − | 2.24147i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.93426 | 0.212073 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.3923 | 0.442300 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.6926 | − | 11.6926i | 0.416798 | − | 0.416798i | −0.467301 | − | 0.884098i | \(-0.654773\pi\) |
0.884098 | + | 0.467301i | \(0.154773\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.0000 | − | 16.0000i | −0.569615 | − | 0.569615i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 44.0908i | − | 1.56769i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.7846i | 1.37728i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.96953 | − | 6.96953i | −0.247184 | − | 0.247184i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.5167 | + | 29.5167i | −1.04553 | + | 1.04553i | −0.0466211 | + | 0.998913i | \(0.514845\pi\) |
−0.998913 | + | 0.0466211i | \(0.985155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.79796 | 0.346627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.92820 | 0.315463 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.4548 | − | 15.4548i | 0.545389 | − | 0.545389i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.07180 | − | 5.07180i | −0.178757 | − | 0.178757i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.1774i | 0.534270i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.3205i | 1.45275i | 0.687298 | + | 0.726376i | \(0.258797\pi\) | ||||
−0.687298 | + | 0.726376i | \(0.741203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.7642 | + | 23.7642i | 0.834475 | + | 0.834475i | 0.988125 | − | 0.153650i | \(-0.0491029\pi\) |
−0.153650 | + | 0.988125i | \(0.549103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.73205 | + | 5.73205i | −0.201032 | + | 0.201032i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.8685 | 0.415736 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.85641 | −0.0649474 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.34847 | + | 7.34847i | −0.256776 | + | 0.256776i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.1962 | − | 28.1962i | −0.984053 | − | 0.984053i | 0.0158223 | − | 0.999875i | \(-0.494963\pi\) |
−0.999875 | + | 0.0158223i | \(0.994963\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 43.9149i | − | 1.53078i | −0.643567 | − | 0.765389i | \(-0.722546\pi\) | ||
0.643567 | − | 0.765389i | \(-0.277454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 21.4641i | − | 0.747284i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.27362 | − | 2.27362i | −0.0790617 | − | 0.0790617i | 0.666470 | − | 0.745532i | \(-0.267804\pi\) |
−0.745532 | + | 0.666470i | \(0.767804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.8564 | + | 28.8564i | −1.00222 | + | 1.00222i | −0.00222690 | + | 0.999998i | \(0.500709\pi\) |
−0.999998 | + | 0.00222690i | \(0.999291\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.6670 | −0.925067 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.46410 | −0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.51575 | − | 1.51575i | 0.0524547 | − | 0.0524547i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.19615 | − | 5.19615i | −0.179605 | − | 0.179605i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.38323i | − | 0.116802i | −0.998293 | − | 0.0584010i | \(-0.981400\pi\) | ||
0.998293 | − | 0.0584010i | \(-0.0186002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 6.21539i | − | 0.214324i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.14162 | − | 9.14162i | −0.314854 | − | 0.314854i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.66025 | − | 3.66025i | 0.125917 | − | 0.125917i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.1886 | −1.58706 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.8564 | 0.612830 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.2832 | + | 18.2832i | −0.626741 | + | 0.626741i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.2487 | − | 15.2487i | −0.522106 | − | 0.522106i | 0.396101 | − | 0.918207i | \(-0.370363\pi\) |
−0.918207 | + | 0.396101i | \(0.870363\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.554803i | 0.0189739i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.1769i | − | 0.655071i | −0.944839 | − | 0.327535i | \(-0.893782\pi\) | ||
0.944839 | − | 0.327535i | \(-0.106218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.4896 | − | 11.4896i | −0.392019 | − | 0.392019i | 0.483387 | − | 0.875407i | \(-0.339406\pi\) |
−0.875407 | + | 0.483387i | \(0.839406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.8564 | − | 19.8564i | 0.676705 | − | 0.676705i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.4644 | −1.07106 | −0.535531 | − | 0.844516i | \(-0.679888\pi\) | ||||
−0.535531 | + | 0.844516i | \(0.679888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.64102 | 0.0897972 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.53553 | + | 3.53553i | −0.120073 | + | 0.120073i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.46410 | + | 9.46410i | 0.321048 | + | 0.321048i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.54725i | 0.154078i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 14.9282i | − | 0.505243i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.0096 | + | 16.0096i | 0.541224 | + | 0.541224i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.2487 | + | 23.2487i | −0.785053 | + | 0.785053i | −0.980679 | − | 0.195625i | \(-0.937326\pi\) |
0.195625 | + | 0.980679i | \(0.437326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.6617 | 0.460796 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.6410 | −1.09970 | −0.549852 | − | 0.835262i | \(-0.685316\pi\) | ||||
−0.549852 | + | 0.835262i | \(0.685316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.6622 | − | 18.6622i | 0.628032 | − | 0.628032i | −0.319540 | − | 0.947573i | \(-0.603529\pi\) |
0.947573 | + | 0.319540i | \(0.103529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.1436 | + | 10.1436i | 0.340973 | + | 0.340973i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.62536i | 0.0881508i | 0.999028 | + | 0.0440754i | \(0.0140342\pi\) | ||||
−0.999028 | + | 0.0440754i | \(0.985966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 47.5692i | − | 1.59542i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.86370 | − | 3.86370i | −0.129439 | − | 0.129439i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.07180 | − | 1.07180i | 0.0358663 | − | 0.0358663i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.25071 | 0.175512 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.8353 | + | 30.8353i | −1.02841 | + | 1.02841i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.3205 | + | 23.3205i | 0.776919 | + | 0.776919i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.48528i | 0.282372i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.32051i | 0.243342i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.2789 | − | 15.2789i | −0.507329 | − | 0.507329i | 0.406377 | − | 0.913706i | \(-0.366792\pi\) |
−0.913706 | + | 0.406377i | \(0.866792\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.196152 | + | 0.196152i | −0.00650597 | + | 0.00650597i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.4665 | 1.70516 | 0.852580 | − | 0.522596i | \(-0.175036\pi\) | ||||
0.852580 | + | 0.522596i | \(0.175036\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.00000 | 0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.69213 | − | 6.69213i | 0.221235 | − | 0.221235i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.85641 | − | 1.85641i | −0.0613039 | − | 0.0613039i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.6728i | 1.47362i | 0.676100 | + | 0.736810i | \(0.263669\pi\) | ||||
−0.676100 | + | 0.736810i | \(0.736331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.07180i | 0.298926i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.6381 | + | 48.6381i | 1.60094 | + | 1.60094i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.3923 | − | 25.3923i | 0.834894 | − | 0.834894i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.10634 | 0.266247 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.6795 | −0.350383 | −0.175191 | − | 0.984534i | \(-0.556054\pi\) | ||||
−0.175191 | + | 0.984534i | \(0.556054\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.378937 | + | 0.378937i | −0.0124192 | + | 0.0124192i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.07180 | + | 9.07180i | 0.296997 | + | 0.296997i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 19.5959i | − | 0.640855i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.00000i | − | 0.0653372i | −0.999466 | − | 0.0326686i | \(-0.989599\pi\) | ||
0.999466 | − | 0.0326686i | \(-0.0104006\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.8690 | − | 16.8690i | −0.550500 | − | 0.550500i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.33975 | − | 8.33975i | 0.271868 | − | 0.271868i | −0.557984 | − | 0.829852i | \(-0.688425\pi\) |
0.829852 | + | 0.557984i | \(0.188425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.4254 | 1.05592 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.53590 | 0.0824928 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.3548 | + | 30.3548i | −0.986399 | + | 0.986399i | −0.999909 | − | 0.0135095i | \(-0.995700\pi\) |
0.0135095 | + | 0.999909i | \(0.495700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | + | 12.0000i | 0.389536 | + | 0.389536i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.79315i | − | 0.0581469i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.6077i | 0.829515i | 0.909932 | + | 0.414757i | \(0.136134\pi\) | ||||
−0.909932 | + | 0.414757i | \(0.863866\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.51575 | − | 1.51575i | −0.0490485 | − | 0.0490485i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.9282 | + | 22.9282i | −0.741164 | + | 0.741164i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.6579 | −0.505619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.82843 | + | 2.82843i | −0.0911448 | + | 0.0911448i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.39230 | + | 4.39230i | 0.141393 | + | 0.141393i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.8749i | 1.12150i | 0.827985 | + | 0.560750i | \(0.189487\pi\) | ||||
−0.827985 | + | 0.560750i | \(0.810513\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.85641i | − | 0.0596364i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.5606 | − | 18.5606i | −0.595639 | − | 0.595639i | 0.343510 | − | 0.939149i | \(-0.388384\pi\) |
−0.939149 | + | 0.343510i | \(0.888384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | − | 12.0000i | 0.384702 | − | 0.384702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.6660 | 0.533738 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.1769 | −0.869467 | −0.434733 | − | 0.900559i | \(-0.643157\pi\) | ||||
−0.434733 | + | 0.900559i | \(0.643157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.4959 | + | 34.4959i | −1.10249 | + | 1.10249i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.00000 | + | 1.00000i | 0.0319275 | + | 0.0319275i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.0507i | 1.11794i | 0.829186 | + | 0.558972i | \(0.188804\pi\) | ||||
−0.829186 | + | 0.558972i | \(0.811196\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.14359i | − | 0.195751i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.89898 | − | 4.89898i | −0.155936 | − | 0.155936i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.92820 | + | 6.92820i | −0.220304 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.2474 | 0.389053 | 0.194527 | − | 0.980897i | \(-0.437683\pi\) | ||||
0.194527 | + | 0.980897i | \(0.437683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.9282 | 0.473732 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.90276 | − | 2.90276i | 0.0920236 | − | 0.0920236i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.53590 | − | 5.53590i | −0.175324 | − | 0.175324i | 0.613990 | − | 0.789314i | \(-0.289563\pi\) |
−0.789314 | + | 0.613990i | \(0.789563\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 9.14162i | − | 0.289228i |
(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 | 768.2.j.e.193.4 | yes | 8 | |
3.2 | odd | 2 | 2304.2.k.l.1729.2 | 8 | |||
4.3 | odd | 2 | inner | 768.2.j.e.193.2 | ✓ | 8 | |
8.3 | odd | 2 | 768.2.j.f.193.3 | yes | 8 | ||
8.5 | even | 2 | 768.2.j.f.193.1 | yes | 8 | ||
12.11 | even | 2 | 2304.2.k.l.1729.1 | 8 | |||
16.3 | odd | 4 | inner | 768.2.j.e.577.2 | yes | 8 | |
16.5 | even | 4 | 768.2.j.f.577.1 | yes | 8 | ||
16.11 | odd | 4 | 768.2.j.f.577.3 | yes | 8 | ||
16.13 | even | 4 | inner | 768.2.j.e.577.4 | yes | 8 | |
24.5 | odd | 2 | 2304.2.k.e.1729.4 | 8 | |||
24.11 | even | 2 | 2304.2.k.e.1729.3 | 8 | |||
32.3 | odd | 8 | 3072.2.a.l.1.2 | 4 | |||
32.5 | even | 8 | 3072.2.d.h.1537.7 | 8 | |||
32.11 | odd | 8 | 3072.2.d.h.1537.6 | 8 | |||
32.13 | even | 8 | 3072.2.a.l.1.3 | 4 | |||
32.19 | odd | 8 | 3072.2.a.r.1.3 | 4 | |||
32.21 | even | 8 | 3072.2.d.h.1537.2 | 8 | |||
32.27 | odd | 8 | 3072.2.d.h.1537.3 | 8 | |||
32.29 | even | 8 | 3072.2.a.r.1.2 | 4 | |||
48.5 | odd | 4 | 2304.2.k.e.577.3 | 8 | |||
48.11 | even | 4 | 2304.2.k.e.577.4 | 8 | |||
48.29 | odd | 4 | 2304.2.k.l.577.1 | 8 | |||
48.35 | even | 4 | 2304.2.k.l.577.2 | 8 | |||
96.29 | odd | 8 | 9216.2.a.bc.1.3 | 4 | |||
96.35 | even | 8 | 9216.2.a.bi.1.3 | 4 | |||
96.77 | odd | 8 | 9216.2.a.bi.1.2 | 4 | |||
96.83 | even | 8 | 9216.2.a.bc.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.e.193.2 | ✓ | 8 | 4.3 | odd | 2 | inner | |
768.2.j.e.193.4 | yes | 8 | 1.1 | even | 1 | trivial | |
768.2.j.e.577.2 | yes | 8 | 16.3 | odd | 4 | inner | |
768.2.j.e.577.4 | yes | 8 | 16.13 | even | 4 | inner | |
768.2.j.f.193.1 | yes | 8 | 8.5 | even | 2 | ||
768.2.j.f.193.3 | yes | 8 | 8.3 | odd | 2 | ||
768.2.j.f.577.1 | yes | 8 | 16.5 | even | 4 | ||
768.2.j.f.577.3 | yes | 8 | 16.11 | odd | 4 | ||
2304.2.k.e.577.3 | 8 | 48.5 | odd | 4 | |||
2304.2.k.e.577.4 | 8 | 48.11 | even | 4 | |||
2304.2.k.e.1729.3 | 8 | 24.11 | even | 2 | |||
2304.2.k.e.1729.4 | 8 | 24.5 | odd | 2 | |||
2304.2.k.l.577.1 | 8 | 48.29 | odd | 4 | |||
2304.2.k.l.577.2 | 8 | 48.35 | even | 4 | |||
2304.2.k.l.1729.1 | 8 | 12.11 | even | 2 | |||
2304.2.k.l.1729.2 | 8 | 3.2 | odd | 2 | |||
3072.2.a.l.1.2 | 4 | 32.3 | odd | 8 | |||
3072.2.a.l.1.3 | 4 | 32.13 | even | 8 | |||
3072.2.a.r.1.2 | 4 | 32.29 | even | 8 | |||
3072.2.a.r.1.3 | 4 | 32.19 | odd | 8 | |||
3072.2.d.h.1537.2 | 8 | 32.21 | even | 8 | |||
3072.2.d.h.1537.3 | 8 | 32.27 | odd | 8 | |||
3072.2.d.h.1537.6 | 8 | 32.11 | odd | 8 | |||
3072.2.d.h.1537.7 | 8 | 32.5 | even | 8 | |||
9216.2.a.bc.1.2 | 4 | 96.83 | even | 8 | |||
9216.2.a.bc.1.3 | 4 | 96.29 | odd | 8 | |||
9216.2.a.bi.1.2 | 4 | 96.77 | odd | 8 | |||
9216.2.a.bi.1.3 | 4 | 96.35 | even | 8 |