Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,3,Mod(433,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.433");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.bh (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.6185790339\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.577 |
Dual form | 720.3.bh.b.433.1 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.00000 | − | 8.00000i | −1.14286 | − | 1.14286i | −0.987925 | − | 0.154932i | \(-0.950484\pi\) |
−0.154932 | − | 0.987925i | \(-0.549516\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −0.363636 | −0.181818 | − | 0.983332i | \(-0.558198\pi\) | ||||
−0.181818 | + | 0.983332i | \(0.558198\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 3.00000i | −0.230769 | + | 0.230769i | −0.813014 | − | 0.582245i | \(-0.802175\pi\) |
0.582245 | + | 0.813014i | \(0.302175\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.0000 | + | 19.0000i | 1.11765 | + | 1.11765i | 0.992086 | + | 0.125561i | \(0.0400731\pi\) |
0.125561 | + | 0.992086i | \(0.459927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.00000i | 0.421053i | 0.977588 | + | 0.210526i | \(0.0675178\pi\) | ||||
−0.977588 | + | 0.210526i | \(0.932482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.0000 | − | 20.0000i | 0.869565 | − | 0.869565i | −0.122859 | − | 0.992424i | \(-0.539206\pi\) |
0.992424 | + | 0.122859i | \(0.0392063\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 38.0000i | − | 1.31034i | −0.755479 | − | 0.655172i | \(-0.772596\pi\) | ||
0.755479 | − | 0.655172i | \(-0.227404\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.0000 | 1.41935 | 0.709677 | − | 0.704527i | \(-0.248841\pi\) | ||||
0.709677 | + | 0.704527i | \(0.248841\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 56.0000 | − | 8.00000i | 1.60000 | − | 0.228571i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.0810811 | − | 0.0810811i | 0.665403 | − | 0.746484i | \(-0.268260\pi\) |
−0.746484 | + | 0.665403i | \(0.768260\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 70.0000 | 1.70732 | 0.853659 | − | 0.520833i | \(-0.174379\pi\) | ||||
0.853659 | + | 0.520833i | \(0.174379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −36.0000 | + | 36.0000i | −0.837209 | + | 0.837209i | −0.988491 | − | 0.151281i | \(-0.951660\pi\) |
0.151281 | + | 0.988491i | \(0.451660\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 79.0000i | 1.61224i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17.0000 | − | 17.0000i | 0.320755 | − | 0.320755i | −0.528302 | − | 0.849057i | \(-0.677171\pi\) |
0.849057 | + | 0.528302i | \(0.177171\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.0000 | − | 16.0000i | 0.218182 | − | 0.290909i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 92.0000i | 1.55932i | 0.626202 | + | 0.779661i | \(0.284609\pi\) | ||||
−0.626202 | + | 0.779661i | \(0.715391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 72.0000 | 1.18033 | 0.590164 | − | 0.807283i | \(-0.299063\pi\) | ||||
0.590164 | + | 0.807283i | \(0.299063\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | − | 21.0000i | −0.0461538 | − | 0.323077i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −44.0000 | − | 44.0000i | −0.656716 | − | 0.656716i | 0.297885 | − | 0.954602i | \(-0.403719\pi\) |
−0.954602 | + | 0.297885i | \(0.903719\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 88.0000 | 1.23944 | 0.619718 | − | 0.784824i | \(-0.287247\pi\) | ||||
0.619718 | + | 0.784824i | \(0.287247\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55.0000 | − | 55.0000i | 0.753425 | − | 0.753425i | −0.221692 | − | 0.975117i | \(-0.571158\pi\) |
0.975117 | + | 0.221692i | \(0.0711580\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 32.0000 | + | 32.0000i | 0.415584 | + | 0.415584i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.0000i | − | 0.151899i | −0.997112 | − | 0.0759494i | \(-0.975801\pi\) | ||
0.997112 | − | 0.0759494i | \(-0.0241987\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 24.0000 | − | 24.0000i | 0.289157 | − | 0.289157i | −0.547590 | − | 0.836747i | \(-0.684455\pi\) |
0.836747 | + | 0.547590i | \(0.184455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −133.000 | + | 19.0000i | −1.56471 | + | 0.223529i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 26.0000i | 0.292135i | 0.989275 | + | 0.146067i | \(0.0466616\pi\) | ||||
−0.989275 | + | 0.146067i | \(0.953338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 48.0000 | 0.527473 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −32.0000 | − | 24.0000i | −0.336842 | − | 0.252632i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −57.0000 | − | 57.0000i | −0.587629 | − | 0.587629i | 0.349360 | − | 0.936989i | \(-0.386399\pi\) |
−0.936989 | + | 0.349360i | \(0.886399\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 56.0000 | 0.554455 | 0.277228 | − | 0.960804i | \(-0.410584\pi\) | ||||
0.277228 | + | 0.960804i | \(0.410584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 4.00000i | −0.0388350 | + | 0.0388350i | −0.726258 | − | 0.687423i | \(-0.758742\pi\) |
0.687423 | + | 0.726258i | \(0.258742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 68.0000 | + | 68.0000i | 0.635514 | + | 0.635514i | 0.949446 | − | 0.313932i | \(-0.101646\pi\) |
−0.313932 | + | 0.949446i | \(0.601646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 46.0000i | − | 0.422018i | −0.977484 | − | 0.211009i | \(-0.932325\pi\) | ||
0.977484 | − | 0.211009i | \(-0.0676750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 53.0000 | − | 53.0000i | 0.469027 | − | 0.469027i | −0.432573 | − | 0.901599i | \(-0.642394\pi\) |
0.901599 | + | 0.432573i | \(0.142394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.0000 | + | 140.000i | 0.173913 | + | 1.21739i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 304.000i | − | 2.55462i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −105.000 | −0.867769 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 117.000 | + | 44.0000i | 0.936000 | + | 0.352000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −68.0000 | − | 68.0000i | −0.535433 | − | 0.535433i | 0.386751 | − | 0.922184i | \(-0.373597\pi\) |
−0.922184 | + | 0.386751i | \(0.873597\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 44.0000 | 0.335878 | 0.167939 | − | 0.985797i | \(-0.446289\pi\) | ||||
0.167939 | + | 0.985797i | \(0.446289\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 64.0000 | − | 64.0000i | 0.481203 | − | 0.481203i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −69.0000 | − | 69.0000i | −0.503650 | − | 0.503650i | 0.408920 | − | 0.912570i | \(-0.365905\pi\) |
−0.912570 | + | 0.408920i | \(0.865905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 80.0000i | − | 0.575540i | −0.957700 | − | 0.287770i | \(-0.907086\pi\) | ||
0.957700 | − | 0.287770i | \(-0.0929138\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | − | 12.0000i | 0.0839161 | − | 0.0839161i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 152.000 | + | 114.000i | 1.04828 | + | 0.786207i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 168.000i | 1.12752i | 0.825940 | + | 0.563758i | \(0.190645\pi\) | ||||
−0.825940 | + | 0.563758i | \(0.809355\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | −0.0264901 | −0.0132450 | − | 0.999912i | \(-0.504216\pi\) | ||||
−0.0132450 | + | 0.999912i | \(0.504216\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −132.000 | + | 176.000i | −0.851613 | + | 1.13548i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 99.0000 | + | 99.0000i | 0.630573 | + | 0.630573i | 0.948212 | − | 0.317639i | \(-0.102890\pi\) |
−0.317639 | + | 0.948212i | \(0.602890\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −320.000 | −1.98758 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 160.000 | − | 160.000i | 0.981595 | − | 0.981595i | −0.0182386 | − | 0.999834i | \(-0.505806\pi\) |
0.999834 | + | 0.0182386i | \(0.00580584\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −56.0000 | − | 56.0000i | −0.335329 | − | 0.335329i | 0.519277 | − | 0.854606i | \(-0.326201\pi\) |
−0.854606 | + | 0.519277i | \(0.826201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 151.000i | 0.893491i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −41.0000 | + | 41.0000i | −0.236994 | + | 0.236994i | −0.815604 | − | 0.578610i | \(-0.803595\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −136.000 | + | 248.000i | −0.777143 | + | 1.41714i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 172.000i | 0.960894i | 0.877024 | + | 0.480447i | \(0.159526\pi\) | ||||
−0.877024 | + | 0.480447i | \(0.840474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 62.0000 | 0.342541 | 0.171271 | − | 0.985224i | \(-0.445213\pi\) | ||||
0.171271 | + | 0.985224i | \(0.445213\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.0000 | − | 3.00000i | 0.113514 | − | 0.0162162i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −76.0000 | − | 76.0000i | −0.406417 | − | 0.406417i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −248.000 | −1.29843 | −0.649215 | − | 0.760605i | \(-0.724902\pi\) | ||||
−0.649215 | + | 0.760605i | \(0.724902\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 135.000 | − | 135.000i | 0.699482 | − | 0.699482i | −0.264817 | − | 0.964299i | \(-0.585312\pi\) |
0.964299 | + | 0.264817i | \(0.0853115\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −153.000 | − | 153.000i | −0.776650 | − | 0.776650i | 0.202610 | − | 0.979260i | \(-0.435058\pi\) |
−0.979260 | + | 0.202610i | \(0.935058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 252.000i | 1.26633i | 0.774016 | + | 0.633166i | \(0.218245\pi\) | ||||
−0.774016 | + | 0.633166i | \(0.781755\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −304.000 | + | 304.000i | −1.49754 | + | 1.49754i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −210.000 | + | 280.000i | −1.02439 | + | 1.36585i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 32.0000i | − | 0.153110i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 64.0000 | 0.303318 | 0.151659 | − | 0.988433i | \(-0.451539\pi\) | ||||
0.151659 | + | 0.988433i | \(0.451539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −36.0000 | − | 252.000i | −0.167442 | − | 1.17209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −352.000 | − | 352.000i | −1.62212 | − | 1.62212i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −114.000 | −0.515837 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 228.000 | − | 228.000i | 1.02242 | − | 1.02242i | 0.0226787 | − | 0.999743i | \(-0.492781\pi\) |
0.999743 | − | 0.0226787i | \(-0.00721948\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 100.000 | + | 100.000i | 0.440529 | + | 0.440529i | 0.892190 | − | 0.451661i | \(-0.149168\pi\) |
−0.451661 | + | 0.892190i | \(0.649168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 312.000i | − | 1.36245i | −0.732076 | − | 0.681223i | \(-0.761449\pi\) | ||
0.732076 | − | 0.681223i | \(-0.238551\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −93.0000 | + | 93.0000i | −0.399142 | + | 0.399142i | −0.877930 | − | 0.478789i | \(-0.841076\pi\) |
0.478789 | + | 0.877930i | \(0.341076\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 96.0000i | 0.401674i | 0.979625 | + | 0.200837i | \(0.0643661\pi\) | ||||
−0.979625 | + | 0.200837i | \(0.935634\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 160.000 | 0.663900 | 0.331950 | − | 0.943297i | \(-0.392293\pi\) | ||||
0.331950 | + | 0.943297i | \(0.392293\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −316.000 | − | 237.000i | −1.28980 | − | 0.967347i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.0000 | − | 24.0000i | −0.0971660 | − | 0.0971660i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.0478088 | −0.0239044 | − | 0.999714i | \(-0.507610\pi\) | ||||
−0.0239044 | + | 0.999714i | \(0.507610\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −80.0000 | + | 80.0000i | −0.316206 | + | 0.316206i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 101.000 | + | 101.000i | 0.392996 | + | 0.392996i | 0.875754 | − | 0.482758i | \(-0.160365\pi\) |
−0.482758 | + | 0.875754i | \(0.660365\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 48.0000i | 0.185328i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 208.000 | − | 208.000i | 0.790875 | − | 0.790875i | −0.190762 | − | 0.981636i | \(-0.561096\pi\) |
0.981636 | + | 0.190762i | \(0.0610958\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.0000 | + | 119.000i | 0.0641509 | + | 0.449057i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 296.000i | − | 1.10037i | −0.835042 | − | 0.550186i | \(-0.814557\pi\) | ||
0.835042 | − | 0.550186i | \(-0.185443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −108.000 | −0.398524 | −0.199262 | − | 0.979946i | \(-0.563854\pi\) | ||||
−0.199262 | + | 0.979946i | \(0.563854\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.0000 | + | 96.0000i | 0.101818 | + | 0.349091i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −243.000 | − | 243.000i | −0.877256 | − | 0.877256i | 0.115994 | − | 0.993250i | \(-0.462995\pi\) |
−0.993250 | + | 0.115994i | \(0.962995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 378.000 | 1.34520 | 0.672598 | − | 0.740008i | \(-0.265178\pi\) | ||||
0.672598 | + | 0.740008i | \(0.265178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −92.0000 | + | 92.0000i | −0.325088 | + | 0.325088i | −0.850715 | − | 0.525627i | \(-0.823831\pi\) |
0.525627 | + | 0.850715i | \(0.323831\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −560.000 | − | 560.000i | −1.95122 | − | 1.95122i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 433.000i | 1.49827i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −279.000 | + | 279.000i | −0.952218 | + | 0.952218i | −0.998909 | − | 0.0466910i | \(-0.985132\pi\) |
0.0466910 | + | 0.998909i | \(0.485132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −368.000 | − | 276.000i | −1.24746 | − | 0.935593i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 120.000i | 0.401338i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 576.000 | 1.91362 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −216.000 | + | 288.000i | −0.708197 | + | 0.944262i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −216.000 | − | 216.000i | −0.703583 | − | 0.703583i | 0.261595 | − | 0.965178i | \(-0.415752\pi\) |
−0.965178 | + | 0.261595i | \(0.915752\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −272.000 | −0.874598 | −0.437299 | − | 0.899316i | \(-0.644065\pi\) | ||||
−0.437299 | + | 0.899316i | \(0.644065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0000 | − | 15.0000i | 0.0479233 | − | 0.0479233i | −0.682739 | − | 0.730662i | \(-0.739211\pi\) |
0.730662 | + | 0.682739i | \(0.239211\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 87.0000 | + | 87.0000i | 0.274448 | + | 0.274448i | 0.830888 | − | 0.556440i | \(-0.187833\pi\) |
−0.556440 | + | 0.830888i | \(0.687833\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 152.000i | 0.476489i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −152.000 | + | 152.000i | −0.470588 | + | 0.470588i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 93.0000 | + | 51.0000i | 0.286154 | + | 0.156923i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 584.000 | 1.76435 | 0.882175 | − | 0.470921i | \(-0.156078\pi\) | ||||
0.882175 | + | 0.470921i | \(0.156078\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 308.000 | − | 44.0000i | 0.919403 | − | 0.131343i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −129.000 | − | 129.000i | −0.382789 | − | 0.382789i | 0.489317 | − | 0.872106i | \(-0.337246\pi\) |
−0.872106 | + | 0.489317i | \(0.837246\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −176.000 | −0.516129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 240.000 | − | 240.000i | 0.699708 | − | 0.699708i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 260.000 | + | 260.000i | 0.749280 | + | 0.749280i | 0.974344 | − | 0.225064i | \(-0.0722592\pi\) |
−0.225064 | + | 0.974344i | \(0.572259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 136.000i | 0.389685i | 0.980835 | + | 0.194842i | \(0.0624195\pi\) | ||||
−0.980835 | + | 0.194842i | \(0.937580\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −75.0000 | + | 75.0000i | −0.212465 | + | 0.212465i | −0.805314 | − | 0.592849i | \(-0.798003\pi\) |
0.592849 | + | 0.805314i | \(0.298003\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −264.000 | + | 352.000i | −0.743662 | + | 0.991549i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 32.0000i | − | 0.0891365i | −0.999006 | − | 0.0445682i | \(-0.985809\pi\) | ||
0.999006 | − | 0.0445682i | \(-0.0141912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 297.000 | 0.822715 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 55.0000 | + | 385.000i | 0.150685 | + | 1.05479i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | + | 16.0000i | 0.0435967 | + | 0.0435967i | 0.728569 | − | 0.684972i | \(-0.240186\pi\) |
−0.684972 | + | 0.728569i | \(0.740186\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −272.000 | −0.733154 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −251.000 | + | 251.000i | −0.672922 | + | 0.672922i | −0.958389 | − | 0.285466i | \(-0.907851\pi\) |
0.285466 | + | 0.958389i | \(0.407851\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 114.000 | + | 114.000i | 0.302387 | + | 0.302387i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 560.000i | 1.47757i | 0.673940 | + | 0.738786i | \(0.264601\pi\) | ||||
−0.673940 | + | 0.738786i | \(0.735399\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 300.000 | − | 300.000i | 0.783290 | − | 0.783290i | −0.197095 | − | 0.980384i | \(-0.563151\pi\) |
0.980384 | + | 0.197095i | \(0.0631506\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −224.000 | + | 32.0000i | −0.581818 | + | 0.0831169i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 24.0000i | − | 0.0616967i | −0.999524 | − | 0.0308483i | \(-0.990179\pi\) | ||
0.999524 | − | 0.0308483i | \(-0.00982089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 760.000 | 1.94373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 48.0000 | + | 36.0000i | 0.121519 | + | 0.0911392i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −299.000 | − | 299.000i | −0.753149 | − | 0.753149i | 0.221917 | − | 0.975066i | \(-0.428769\pi\) |
−0.975066 | + | 0.221917i | \(0.928769\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −144.000 | −0.359102 | −0.179551 | − | 0.983749i | \(-0.557465\pi\) | ||||
−0.179551 | + | 0.983749i | \(0.557465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −132.000 | + | 132.000i | −0.327543 | + | 0.327543i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | + | 12.0000i | 0.0294840 | + | 0.0294840i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 354.000i | − | 0.865526i | −0.901508 | − | 0.432763i | \(-0.857539\pi\) | ||
0.901508 | − | 0.432763i | \(-0.142461\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 736.000 | − | 736.000i | 1.78208 | − | 1.78208i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.0000 | + | 168.000i | 0.0578313 | + | 0.404819i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 468.000i | 1.11695i | 0.829523 | + | 0.558473i | \(0.188612\pi\) | ||||
−0.829523 | + | 0.558473i | \(0.811388\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 104.000 | 0.247031 | 0.123515 | − | 0.992343i | \(-0.460583\pi\) | ||||
0.123515 | + | 0.992343i | \(0.460583\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 323.000 | − | 589.000i | 0.760000 | − | 1.38588i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −576.000 | − | 576.000i | −1.34895 | − | 1.34895i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 680.000 | 1.57773 | 0.788863 | − | 0.614569i | \(-0.210670\pi\) | ||||
0.788863 | + | 0.614569i | \(0.210670\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 41.0000 | − | 41.0000i | 0.0946882 | − | 0.0946882i | −0.658176 | − | 0.752864i | \(-0.728672\pi\) |
0.752864 | + | 0.658176i | \(0.228672\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 160.000 | + | 160.000i | 0.366133 | + | 0.366133i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 364.000i | 0.829157i | 0.910014 | + | 0.414579i | \(0.136071\pi\) | ||||
−0.910014 | + | 0.414579i | \(0.863929\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 372.000 | − | 372.000i | 0.839729 | − | 0.839729i | −0.149094 | − | 0.988823i | \(-0.547636\pi\) |
0.988823 | + | 0.149094i | \(0.0476357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −104.000 | − | 78.0000i | −0.233708 | − | 0.175281i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 176.000i | − | 0.391982i | −0.980606 | − | 0.195991i | \(-0.937208\pi\) | ||
0.980606 | − | 0.195991i | \(-0.0627924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −280.000 | −0.620843 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −144.000 | + | 192.000i | −0.316484 | + | 0.421978i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 129.000 | + | 129.000i | 0.282276 | + | 0.282276i | 0.834016 | − | 0.551740i | \(-0.186036\pi\) |
−0.551740 | + | 0.834016i | \(0.686036\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 568.000 | 1.23210 | 0.616052 | − | 0.787705i | \(-0.288731\pi\) | ||||
0.616052 | + | 0.787705i | \(0.288731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 568.000 | − | 568.000i | 1.22678 | − | 1.22678i | 0.261608 | − | 0.965174i | \(-0.415747\pi\) |
0.965174 | − | 0.261608i | \(-0.0842526\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 272.000 | + | 272.000i | 0.582441 | + | 0.582441i | 0.935573 | − | 0.353132i | \(-0.114883\pi\) |
−0.353132 | + | 0.935573i | \(0.614883\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 704.000i | 1.50107i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 144.000 | − | 144.000i | 0.304440 | − | 0.304440i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 192.000 | − | 56.0000i | 0.404211 | − | 0.117895i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 928.000i | − | 1.93737i | −0.248294 | − | 0.968685i | \(-0.579870\pi\) | ||
0.248294 | − | 0.968685i | \(-0.420130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.0374220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 399.000 | − | 57.0000i | 0.822680 | − | 0.117526i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −252.000 | − | 252.000i | −0.517454 | − | 0.517454i | 0.399346 | − | 0.916800i | \(-0.369237\pi\) |
−0.916800 | + | 0.399346i | \(0.869237\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 844.000 | 1.71894 | 0.859470 | − | 0.511185i | \(-0.170793\pi\) | ||||
0.859470 | + | 0.511185i | \(0.170793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 722.000 | − | 722.000i | 1.46450 | − | 1.46450i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −704.000 | − | 704.000i | −1.41650 | − | 1.41650i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 872.000i | − | 1.74749i | −0.486380 | − | 0.873747i | \(-0.661683\pi\) | ||
0.486380 | − | 0.873747i | \(-0.338317\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −480.000 | + | 480.000i | −0.954274 | + | 0.954274i | −0.998999 | − | 0.0447250i | \(-0.985759\pi\) |
0.0447250 | + | 0.998999i | \(0.485759\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −168.000 | + | 224.000i | −0.332673 | + | 0.443564i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 694.000i | 1.36346i | 0.731605 | + | 0.681729i | \(0.238772\pi\) | ||||
−0.731605 | + | 0.681729i | \(0.761228\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −880.000 | −1.72211 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.00000 | − | 28.0000i | −0.00776699 | − | 0.0543689i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 528.000 | 1.01344 | 0.506718 | − | 0.862112i | \(-0.330859\pi\) | ||||
0.506718 | + | 0.862112i | \(0.330859\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −552.000 | + | 552.000i | −1.05545 | + | 1.05545i | −0.0570797 | + | 0.998370i | \(0.518179\pi\) |
−0.998370 | + | 0.0570797i | \(0.981821\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 836.000 | + | 836.000i | 1.58634 | + | 1.58634i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 271.000i | − | 0.512287i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −210.000 | + | 210.000i | −0.393996 | + | 0.393996i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −476.000 | + | 68.0000i | −0.889720 | + | 0.127103i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 316.000i | − | 0.586271i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −782.000 | −1.44547 | −0.722736 | − | 0.691125i | \(-0.757116\pi\) | ||||
−0.722736 | + | 0.691125i | \(0.757116\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 184.000 | + | 138.000i | 0.337615 | + | 0.253211i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 420.000 | + | 420.000i | 0.767824 | + | 0.767824i | 0.977723 | − | 0.209899i | \(-0.0673134\pi\) |
−0.209899 | + | 0.977723i | \(0.567313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 304.000 | 0.551724 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −96.0000 | + | 96.0000i | −0.173599 | + | 0.173599i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 417.000 | + | 417.000i | 0.748654 | + | 0.748654i | 0.974226 | − | 0.225573i | \(-0.0724254\pi\) |
−0.225573 | + | 0.974226i | \(0.572425\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 216.000i | − | 0.386404i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −228.000 | + | 228.000i | −0.404973 | + | 0.404973i | −0.879981 | − | 0.475008i | \(-0.842445\pi\) |
0.475008 | + | 0.879981i | \(0.342445\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 53.0000 | + | 371.000i | 0.0938053 | + | 0.656637i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 368.000i | 0.646749i | 0.946271 | + | 0.323374i | \(0.104817\pi\) | ||||
−0.946271 | + | 0.323374i | \(0.895183\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 736.000 | 1.28897 | 0.644483 | − | 0.764618i | \(-0.277072\pi\) | ||||
0.644483 | + | 0.764618i | \(0.277072\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −620.000 | − | 340.000i | −1.07826 | − | 0.591304i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −113.000 | − | 113.000i | −0.195841 | − | 0.195841i | 0.602374 | − | 0.798214i | \(-0.294222\pi\) |
−0.798214 | + | 0.602374i | \(0.794222\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −384.000 | −0.660929 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −68.0000 | + | 68.0000i | −0.116638 | + | 0.116638i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −684.000 | − | 684.000i | −1.16525 | − | 1.16525i | −0.983310 | − | 0.181937i | \(-0.941763\pi\) |
−0.181937 | − | 0.983310i | \(-0.558237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 352.000i | 0.597623i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −149.000 | + | 149.000i | −0.251265 | + | 0.251265i | −0.821489 | − | 0.570224i | \(-0.806856\pi\) |
0.570224 | + | 0.821489i | \(0.306856\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1216.00 | + | 912.000i | 2.04370 | + | 1.53277i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 152.000i | 0.253756i | 0.991918 | + | 0.126878i | \(0.0404957\pi\) | ||||
−0.991918 | + | 0.126878i | \(0.959504\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 320.000 | 0.532446 | 0.266223 | − | 0.963911i | \(-0.414224\pi\) | ||||
0.266223 | + | 0.963911i | \(0.414224\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 315.000 | − | 420.000i | 0.520661 | − | 0.694215i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 528.000 | + | 528.000i | 0.869852 | + | 0.869852i | 0.992456 | − | 0.122604i | \(-0.0391245\pi\) |
−0.122604 | + | 0.992456i | \(0.539124\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 771.000 | − | 771.000i | 1.25775 | − | 1.25775i | 0.305583 | − | 0.952165i | \(-0.401148\pi\) |
0.952165 | − | 0.305583i | \(-0.0988515\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 675.000 | + | 675.000i | 1.09400 | + | 1.09400i | 0.995097 | + | 0.0989065i | \(0.0315345\pi\) |
0.0989065 | + | 0.995097i | \(0.468466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 600.000i | − | 0.969305i | −0.874707 | − | 0.484653i | \(-0.838946\pi\) | ||
0.874707 | − | 0.484653i | \(-0.161054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 208.000 | − | 208.000i | 0.333868 | − | 0.333868i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −527.000 | + | 336.000i | −0.843200 | + | 0.537600i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 114.000i | − | 0.181240i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.0316957 | 0.0158479 | − | 0.999874i | \(-0.494955\pi\) | ||||
0.0158479 | + | 0.999874i | \(0.494955\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 476.000 | − | 68.0000i | 0.749606 | − | 0.107087i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −237.000 | − | 237.000i | −0.372057 | − | 0.372057i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −694.000 | −1.08268 | −0.541342 | − | 0.840803i | \(-0.682083\pi\) | ||||
−0.541342 | + | 0.840803i | \(0.682083\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 168.000 | − | 168.000i | 0.261275 | − | 0.261275i | −0.564297 | − | 0.825572i | \(-0.690853\pi\) |
0.825572 | + | 0.564297i | \(0.190853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 328.000 | + | 328.000i | 0.506955 | + | 0.506955i | 0.913591 | − | 0.406635i | \(-0.133298\pi\) |
−0.406635 | + | 0.913591i | \(0.633298\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 368.000i | − | 0.567026i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 81.0000 | − | 81.0000i | 0.124043 | − | 0.124043i | −0.642360 | − | 0.766403i | \(-0.722045\pi\) |
0.766403 | + | 0.642360i | \(0.222045\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −132.000 | + | 176.000i | −0.201527 | + | 0.268702i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 500.000i | − | 0.758725i | −0.925248 | − | 0.379363i | \(-0.876143\pi\) | ||
0.925248 | − | 0.379363i | \(-0.123857\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −568.000 | −0.859304 | −0.429652 | − | 0.902995i | \(-0.641364\pi\) | ||||
−0.429652 | + | 0.902995i | \(0.641364\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 64.0000 | + | 448.000i | 0.0962406 | + | 0.673684i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −760.000 | − | 760.000i | −1.13943 | − | 1.13943i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −288.000 | −0.429210 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 73.0000 | − | 73.0000i | 0.108470 | − | 0.108470i | −0.650789 | − | 0.759259i | \(-0.725562\pi\) |
0.759259 | + | 0.650789i | \(0.225562\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −839.000 | − | 839.000i | −1.23929 | − | 1.23929i | −0.960291 | − | 0.279000i | \(-0.909997\pi\) |
−0.279000 | − | 0.960291i | \(-0.590003\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 912.000i | 1.34315i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 744.000 | − | 744.000i | 1.08931 | − | 1.08931i | 0.0937126 | − | 0.995599i | \(-0.470127\pi\) |
0.995599 | − | 0.0937126i | \(-0.0298735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 483.000 | − | 69.0000i | 0.705109 | − | 0.100730i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 102.000i | 0.148041i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −504.000 | −0.729378 | −0.364689 | − | 0.931129i | \(-0.618825\pi\) | ||||
−0.364689 | + | 0.931129i | \(0.618825\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 320.000 | + | 240.000i | 0.460432 | + | 0.345324i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1330.00 | + | 1330.00i | 1.90818 | + | 1.90818i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 298.000 | 0.425107 | 0.212553 | − | 0.977149i | \(-0.431822\pi\) | ||||
0.212553 | + | 0.977149i | \(0.431822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | − | 24.0000i | 0.0341394 | − | 0.0341394i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −448.000 | − | 448.000i | −0.633663 | − | 0.633663i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 472.000i | 0.665726i | 0.942975 | + | 0.332863i | \(0.108015\pi\) | ||||
−0.942975 | + | 0.332863i | \(0.891985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 880.000 | − | 880.000i | 1.23422 | − | 1.23422i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | + | 84.0000i | 0.0167832 | + | 0.117483i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 872.000i | 1.21280i | 0.795161 | + | 0.606398i | \(0.207386\pi\) | ||||
−0.795161 | + | 0.606398i | \(0.792614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 64.0000 | 0.0887656 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −912.000 | + | 266.000i | −1.25793 | + | 0.366897i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 60.0000 | + | 60.0000i | 0.0825309 | + | 0.0825309i | 0.747167 | − | 0.664636i | \(-0.231413\pi\) |
−0.664636 | + | 0.747167i | \(0.731413\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1368.00 | −1.87141 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −581.000 | + | 581.000i | −0.792633 | + | 0.792633i | −0.981922 | − | 0.189289i | \(-0.939382\pi\) |
0.189289 | + | 0.981922i | \(0.439382\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 176.000 | + | 176.000i | 0.238806 | + | 0.238806i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1160.00i | − | 1.56969i | −0.619693 | − | 0.784844i | \(-0.712743\pi\) | ||
0.619693 | − | 0.784844i | \(-0.287257\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −380.000 | + | 380.000i | −0.511440 | + | 0.511440i | −0.914968 | − | 0.403527i | \(-0.867784\pi\) |
0.403527 | + | 0.914968i | \(0.367784\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −672.000 | − | 504.000i | −0.902013 | − | 0.676510i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1088.00i | − | 1.45260i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −780.000 | −1.03862 | −0.519308 | − | 0.854587i | \(-0.673810\pi\) | ||||
−0.519308 | + | 0.854587i | \(0.673810\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | − | 16.0000i | 0.0158940 | − | 0.0211921i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 285.000 | + | 285.000i | 0.376486 | + | 0.376486i | 0.869833 | − | 0.493347i | \(-0.164227\pi\) |
−0.493347 | + | 0.869833i | \(0.664227\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 304.000 | 0.399474 | 0.199737 | − | 0.979850i | \(-0.435991\pi\) | ||||
0.199737 | + | 0.979850i | \(0.435991\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −368.000 | + | 368.000i | −0.482307 | + | 0.482307i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −276.000 | − | 276.000i | −0.359844 | − | 0.359844i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1072.00i | − | 1.39402i | −0.717062 | − | 0.697009i | \(-0.754514\pi\) | ||
0.717062 | − | 0.697009i | \(-0.245486\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −897.000 | + | 897.000i | −1.16041 | + | 1.16041i | −0.176029 | + | 0.984385i | \(0.556325\pi\) |
−0.984385 | + | 0.176029i | \(0.943675\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −308.000 | − | 1056.00i | −0.397419 | − | 1.36258i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 560.000i | 0.718870i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −352.000 | −0.450704 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −693.000 | + | 99.0000i | −0.882803 | + | 0.126115i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −328.000 | − | 328.000i | −0.416773 | − | 0.416773i | 0.467317 | − | 0.884090i | \(-0.345221\pi\) |
−0.884090 | + | 0.467317i | \(0.845221\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −848.000 | −1.07206 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −216.000 | + | 216.000i | −0.272383 | + | 0.272383i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −87.0000 | − | 87.0000i | −0.109159 | − | 0.109159i | 0.650418 | − | 0.759577i | \(-0.274594\pi\) |
−0.759577 | + | 0.650418i | \(0.774594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −220.000 | + | 220.000i | −0.273973 | + | 0.273973i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 960.000 | − | 1280.00i | 1.19255 | − | 1.59006i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 922.000i | − | 1.13968i | −0.821756 | − | 0.569839i | \(-0.807005\pi\) | ||
0.821756 | − | 0.569839i | \(-0.192995\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1312.00 | 1.61776 | 0.808878 | − | 0.587977i | \(-0.200075\pi\) | ||||
0.808878 | + | 0.587977i | \(0.200075\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 160.000 | + | 1120.00i | 0.196319 | + | 1.37423i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −288.000 | − | 288.000i | −0.352509 | − | 0.352509i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −950.000 | −1.15713 | −0.578563 | − | 0.815638i | \(-0.696386\pi\) | ||||
−0.578563 | + | 0.815638i | \(0.696386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −68.0000 | + | 68.0000i | −0.0826245 | + | 0.0826245i | −0.747211 | − | 0.664587i | \(-0.768608\pi\) |
0.664587 | + | 0.747211i | \(0.268608\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −264.000 | − | 264.000i | −0.319226 | − | 0.319226i | 0.529244 | − | 0.848470i | \(-0.322476\pi\) |
−0.848470 | + | 0.529244i | \(0.822476\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 178.000i | − | 0.214717i | −0.994220 | − | 0.107358i | \(-0.965761\pi\) | ||
0.994220 | − | 0.107358i | \(-0.0342392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1501.00 | + | 1501.00i | −1.80192 | + | 1.80192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 392.000 | − | 56.0000i | 0.469461 | − | 0.0670659i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1576.00i | 1.87843i | 0.343334 | + | 0.939213i | \(0.388444\pi\) | ||||
−0.343334 | + | 0.939213i | \(0.611556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −603.000 | −0.717004 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −604.000 | − | 453.000i | −0.714793 | − | 0.536095i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 840.000 | + | 840.000i | 0.991736 | + | 0.991736i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −120.000 | −0.141011 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −509.000 | + | 509.000i | −0.596717 | + | 0.596717i | −0.939438 | − | 0.342720i | \(-0.888652\pi\) |
0.342720 | + | 0.939438i | \(0.388652\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 357.000 | + | 357.000i | 0.416569 | + | 0.416569i | 0.884019 | − | 0.467450i | \(-0.154827\pi\) |
−0.467450 | + | 0.884019i | \(0.654827\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 520.000i | 0.605355i | 0.953093 | + | 0.302678i | \(0.0978805\pi\) | ||||
−0.953093 | + | 0.302678i | \(0.902119\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −952.000 | + | 952.000i | −1.10313 | + | 1.10313i | −0.109098 | + | 0.994031i | \(0.534796\pi\) |
−0.994031 | + | 0.109098i | \(0.965204\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −41.0000 | − | 287.000i | −0.0473988 | − | 0.331792i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.0000i | 0.0552359i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 264.000 | 0.303100 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −584.000 | − | 1288.00i | −0.667429 | − | 1.47200i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −717.000 | − | 717.000i | −0.817560 | − | 0.817560i | 0.168194 | − | 0.985754i | \(-0.446206\pi\) |
−0.985754 | + | 0.168194i | \(0.946206\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −554.000 | −0.628831 | −0.314415 | − | 0.949285i | \(-0.601808\pi\) | ||||
−0.314415 | + | 0.949285i | \(0.601808\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −952.000 | + | 952.000i | −1.07814 | + | 1.07814i | −0.0814666 | + | 0.996676i | \(0.525960\pi\) |
−0.996676 | + | 0.0814666i | \(0.974040\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −648.000 | − | 648.000i | −0.730552 | − | 0.730552i | 0.240177 | − | 0.970729i | \(-0.422795\pi\) |
−0.970729 | + | 0.240177i | \(0.922795\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1088.00i | 1.22385i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −688.000 | − | 516.000i | −0.768715 | − | 0.576536i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1672.00i | − | 1.85984i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 646.000 | 0.716981 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −186.000 | + | 248.000i | −0.205525 | + | 0.274033i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 740.000 | + | 740.000i | 0.815877 | + | 0.815877i | 0.985508 | − | 0.169631i | \(-0.0542576\pi\) |
−0.169631 | + | 0.985508i | \(0.554258\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 520.000 | 0.570801 | 0.285401 | − | 0.958408i | \(-0.407873\pi\) | ||||
0.285401 | + | 0.958408i | \(0.407873\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −96.0000 | + | 96.0000i | −0.105148 | + | 0.105148i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −352.000 | − | 352.000i | −0.383860 | − | 0.383860i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 844.000i | 0.918390i | 0.888336 | + | 0.459195i | \(0.151862\pi\) | ||||
−0.888336 | + | 0.459195i | \(0.848138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −264.000 | + | 264.000i | −0.286024 | + | 0.286024i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51.0000 | + | 93.0000i | −0.0551351 | + | 0.100541i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 208.000i | 0.223897i | 0.993714 | + | 0.111948i | \(0.0357091\pi\) | ||||
−0.993714 | + | 0.111948i | \(0.964291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −632.000 | −0.678840 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 532.000 | − | 76.0000i | 0.568984 | − | 0.0812834i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.00000 | + | 7.00000i | 0.00747065 | + | 0.00747065i | 0.710832 | − | 0.703362i | \(-0.248319\pi\) |
−0.703362 | + | 0.710832i | \(0.748319\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1752.00 | 1.86185 | 0.930925 | − | 0.365212i | \(-0.119003\pi\) | ||||
0.930925 | + | 0.365212i | \(0.119003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1400.00 | − | 1400.00i | 1.48462 | − | 1.48462i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −224.000 | − | 224.000i | −0.236536 | − | 0.236536i | 0.578878 | − | 0.815414i | \(-0.303491\pi\) |
−0.815414 | + | 0.578878i | \(0.803491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 330.000i | 0.347734i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 645.000 | − | 645.000i | 0.676810 | − | 0.676810i | −0.282467 | − | 0.959277i | \(-0.591153\pi\) |
0.959277 | + | 0.282467i | \(0.0911528\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 744.000 | − | 992.000i | 0.779058 | − | 1.03874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1104.00i | 1.15120i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 975.000 | 1.01457 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 135.000 | + | 945.000i | 0.139896 | + | 0.979275i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 92.0000 | + | 92.0000i | 0.0951396 | + | 0.0951396i | 0.753075 | − | 0.657935i | \(-0.228570\pi\) |
−0.657935 | + | 0.753075i | \(0.728570\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000 | 0.00411946 | 0.00205973 | − | 0.999998i | \(-0.499344\pi\) | ||||
0.00205973 | + | 0.999998i | \(0.499344\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −640.000 | + | 640.000i | −0.657760 | + | 0.657760i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1011.00 | − | 1011.00i | −1.03480 | − | 1.03480i | −0.999372 | − | 0.0354282i | \(-0.988720\pi\) |
−0.0354282 | − | 0.999372i | \(-0.511280\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 104.000i | − | 0.106231i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 604.000 | − | 604.000i | 0.614446 | − | 0.614446i | −0.329656 | − | 0.944101i | \(-0.606933\pi\) |
0.944101 | + | 0.329656i | \(0.106933\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1071.00 | − | 153.000i | 1.08731 | − | 0.155330i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1440.00i | 1.45602i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −652.000 | −0.657921 | −0.328961 | − | 0.944344i | \(-0.606698\pi\) | ||||
−0.328961 | + | 0.944344i | \(0.606698\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1008.00 | − | 756.000i | −1.01307 | − | 0.759799i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1051.00 | + | 1051.00i | 1.05416 | + | 1.05416i | 0.998447 | + | 0.0557158i | \(0.0177441\pi\) |
0.0557158 | + | 0.998447i | \(0.482256\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 720.3.bh.b.577.1 | 2 | ||
3.2 | odd | 2 | 720.3.bh.d.577.1 | 2 | |||
4.3 | odd | 2 | 90.3.g.a.37.1 | ✓ | 2 | ||
5.3 | odd | 4 | inner | 720.3.bh.b.433.1 | 2 | ||
12.11 | even | 2 | 90.3.g.c.37.1 | yes | 2 | ||
15.8 | even | 4 | 720.3.bh.d.433.1 | 2 | |||
20.3 | even | 4 | 90.3.g.a.73.1 | yes | 2 | ||
20.7 | even | 4 | 450.3.g.d.343.1 | 2 | |||
20.19 | odd | 2 | 450.3.g.d.307.1 | 2 | |||
60.23 | odd | 4 | 90.3.g.c.73.1 | yes | 2 | ||
60.47 | odd | 4 | 450.3.g.a.343.1 | 2 | |||
60.59 | even | 2 | 450.3.g.a.307.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.3.g.a.37.1 | ✓ | 2 | 4.3 | odd | 2 | ||
90.3.g.a.73.1 | yes | 2 | 20.3 | even | 4 | ||
90.3.g.c.37.1 | yes | 2 | 12.11 | even | 2 | ||
90.3.g.c.73.1 | yes | 2 | 60.23 | odd | 4 | ||
450.3.g.a.307.1 | 2 | 60.59 | even | 2 | |||
450.3.g.a.343.1 | 2 | 60.47 | odd | 4 | |||
450.3.g.d.307.1 | 2 | 20.19 | odd | 2 | |||
450.3.g.d.343.1 | 2 | 20.7 | even | 4 | |||
720.3.bh.b.433.1 | 2 | 5.3 | odd | 4 | inner | ||
720.3.bh.b.577.1 | 2 | 1.1 | even | 1 | trivial | ||
720.3.bh.d.433.1 | 2 | 15.8 | even | 4 | |||
720.3.bh.d.577.1 | 2 | 3.2 | odd | 2 |