Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [90,3,Mod(37,90)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(90, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("90.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.g (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: | \(2.45232237924\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 90.37 |
Dual form | 90.3.g.c.73.1 |
$q$-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 \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00000 | + | 8.00000i | 1.14286 | + | 1.14286i | 0.987925 | + | 0.154932i | \(0.0495158\pi\) |
0.154932 | + | 0.987925i | \(0.450484\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.00000 | − | 1.00000i | 0.700000 | − | 0.100000i | ||||
\(11\) | −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 | \(0.302175\pi\) | |||||||
\(14\) | 16.0000i | 1.14286i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −19.0000 | − | 19.0000i | −1.11765 | − | 1.11765i | −0.992086 | − | 0.125561i | \(-0.959927\pi\) |
−0.125561 | − | 0.992086i | \(-0.540073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 8.00000i | − | 0.421053i | −0.977588 | − | 0.210526i | \(-0.932482\pi\) | ||
0.977588 | − | 0.210526i | \(-0.0675178\pi\) | |||||||
\(20\) | 8.00000 | + | 6.00000i | 0.400000 | + | 0.300000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | − | 4.00000i | −0.181818 | − | 0.181818i | ||||
\(23\) | 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 | ||||
\(26\) | −6.00000 | −0.230769 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.0000 | + | 16.0000i | −0.571429 | + | 0.571429i | ||||
\(29\) | 38.0000i | 1.31034i | 0.755479 | + | 0.655172i | \(0.227404\pi\) | ||||
−0.755479 | + | 0.655172i | \(0.772596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −44.0000 | −1.41935 | −0.709677 | − | 0.704527i | \(-0.751159\pi\) | ||||
−0.709677 | + | 0.704527i | \(0.751159\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 38.0000i | − | 1.11765i | ||||||
\(35\) | 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 | \(0.768260\pi\) | |||||||
\(38\) | 8.00000 | − | 8.00000i | 0.210526 | − | 0.210526i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00000 | + | 14.0000i | 0.0500000 | + | 0.350000i | ||||
\(41\) | −70.0000 | −1.70732 | −0.853659 | − | 0.520833i | \(-0.825621\pi\) | ||||
−0.853659 | + | 0.520833i | \(0.825621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.0000 | − | 36.0000i | 0.837209 | − | 0.837209i | −0.151281 | − | 0.988491i | \(-0.548340\pi\) |
0.988491 | + | 0.151281i | \(0.0483400\pi\) | |||||||
\(44\) | − | 8.00000i | − | 0.181818i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 40.0000 | 0.869565 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 79.0000i | 1.61224i | ||||||||
\(50\) | 17.0000 | − | 31.0000i | 0.340000 | − | 0.620000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.00000 | − | 6.00000i | −0.115385 | − | 0.115385i | ||||
\(53\) | −17.0000 | + | 17.0000i | −0.320755 | + | 0.320755i | −0.849057 | − | 0.528302i | \(-0.822829\pi\) |
0.528302 | + | 0.849057i | \(0.322829\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | + | 16.0000i | −0.218182 | + | 0.290909i | ||||
\(56\) | −32.0000 | −0.571429 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −38.0000 | + | 38.0000i | −0.655172 | + | 0.655172i | ||||
\(59\) | 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 | \(0.299063\pi\) | |||||||
\(62\) | −44.0000 | − | 44.0000i | −0.709677 | − | 0.709677i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 3.00000 | + | 21.0000i | 0.0461538 | + | 0.323077i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.0000 | + | 44.0000i | 0.656716 | + | 0.656716i | 0.954602 | − | 0.297885i | \(-0.0962813\pi\) |
−0.297885 | + | 0.954602i | \(0.596281\pi\) | |||||||
\(68\) | 38.0000 | − | 38.0000i | 0.558824 | − | 0.558824i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 64.0000 | + | 48.0000i | 0.914286 | + | 0.685714i | ||||
\(71\) | 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 | \(0.0711580\pi\) | |||||||
\(74\) | − | 6.00000i | − | 0.0810811i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.0000 | 0.210526 | ||||||||
\(77\) | −32.0000 | − | 32.0000i | −0.415584 | − | 0.415584i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000i | 0.151899i | 0.997112 | + | 0.0759494i | \(0.0241987\pi\) | ||||
−0.997112 | + | 0.0759494i | \(0.975801\pi\) | |||||||
\(80\) | −12.0000 | + | 16.0000i | −0.150000 | + | 0.200000i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −70.0000 | − | 70.0000i | −0.853659 | − | 0.853659i | ||||
\(83\) | 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 | ||||
\(86\) | 72.0000 | 0.837209 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.00000 | − | 8.00000i | 0.0909091 | − | 0.0909091i | ||||
\(89\) | − | 26.0000i | − | 0.292135i | −0.989275 | − | 0.146067i | \(-0.953338\pi\) | ||
0.989275 | − | 0.146067i | \(-0.0466616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −48.0000 | −0.527473 | ||||||||
\(92\) | 40.0000 | + | 40.0000i | 0.434783 | + | 0.434783i | ||||
\(93\) | 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 | \(0.886399\pi\) | |||||||
\(98\) | −79.0000 | + | 79.0000i | −0.806122 | + | 0.806122i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 48.0000 | − | 14.0000i | 0.480000 | − | 0.140000i | ||||
\(101\) | −56.0000 | −0.554455 | −0.277228 | − | 0.960804i | \(-0.589416\pi\) | ||||
−0.277228 | + | 0.960804i | \(0.589416\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | − | 4.00000i | 0.0388350 | − | 0.0388350i | −0.687423 | − | 0.726258i | \(-0.741258\pi\) |
0.726258 | + | 0.687423i | \(0.241258\pi\) | |||||||
\(104\) | − | 12.0000i | − | 0.115385i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −34.0000 | −0.320755 | ||||||||
\(107\) | 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 | \(-0.0676750\pi\) | |||||||
\(110\) | −28.0000 | + | 4.00000i | −0.254545 | + | 0.0363636i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −32.0000 | − | 32.0000i | −0.285714 | − | 0.285714i | ||||
\(113\) | −53.0000 | + | 53.0000i | −0.469027 | + | 0.469027i | −0.901599 | − | 0.432573i | \(-0.857606\pi\) |
0.432573 | + | 0.901599i | \(0.357606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.0000 | − | 140.000i | −0.173913 | − | 1.21739i | ||||
\(116\) | −76.0000 | −0.655172 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −92.0000 | + | 92.0000i | −0.779661 | + | 0.779661i | ||||
\(119\) | − | 304.000i | − | 2.55462i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −105.000 | −0.867769 | ||||||||
\(122\) | 72.0000 | + | 72.0000i | 0.590164 | + | 0.590164i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 88.0000i | − | 0.709677i | ||||||
\(125\) | −117.000 | − | 44.0000i | −0.936000 | − | 0.352000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 68.0000 | + | 68.0000i | 0.535433 | + | 0.535433i | 0.922184 | − | 0.386751i | \(-0.126403\pi\) |
−0.386751 | + | 0.922184i | \(0.626403\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.0000 | + | 24.0000i | −0.138462 | + | 0.184615i | ||||
\(131\) | 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 | ||||
\(134\) | 88.0000i | 0.656716i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 76.0000 | 0.558824 | ||||||||
\(137\) | 69.0000 | + | 69.0000i | 0.503650 | + | 0.503650i | 0.912570 | − | 0.408920i | \(-0.134095\pi\) |
−0.408920 | + | 0.912570i | \(0.634095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 80.0000i | 0.575540i | 0.957700 | + | 0.287770i | \(0.0929138\pi\) | ||||
−0.957700 | + | 0.287770i | \(0.907086\pi\) | |||||||
\(140\) | 16.0000 | + | 112.000i | 0.114286 | + | 0.800000i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 88.0000 | + | 88.0000i | 0.619718 | + | 0.619718i | ||||
\(143\) | 12.0000 | − | 12.0000i | 0.0839161 | − | 0.0839161i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 152.000 | + | 114.000i | 1.04828 | + | 0.786207i | ||||
\(146\) | 110.000 | 0.753425 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | − | 6.00000i | 0.0405405 | − | 0.0405405i | ||||
\(149\) | − | 168.000i | − | 1.12752i | −0.825940 | − | 0.563758i | \(-0.809355\pi\) | ||
0.825940 | − | 0.563758i | \(-0.190645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.0264901 | 0.0132450 | − | 0.999912i | \(-0.495784\pi\) | ||||
0.0132450 | + | 0.999912i | \(0.495784\pi\) | |||||||
\(152\) | 16.0000 | + | 16.0000i | 0.105263 | + | 0.105263i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 64.0000i | − | 0.415584i | ||||||
\(155\) | −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 | \(0.602890\pi\) | |||||||
\(158\) | −12.0000 | + | 12.0000i | −0.0759494 | + | 0.0759494i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −28.0000 | + | 4.00000i | −0.175000 | + | 0.0250000i | ||||
\(161\) | 320.000 | 1.98758 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −160.000 | + | 160.000i | −0.981595 | + | 0.981595i | −0.999834 | − | 0.0182386i | \(-0.994194\pi\) |
0.0182386 | + | 0.999834i | \(0.494194\pi\) | |||||||
\(164\) | − | 140.000i | − | 0.853659i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 48.0000 | 0.289157 | ||||||||
\(167\) | −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 | ||||||||
\(170\) | −152.000 | − | 114.000i | −0.894118 | − | 0.670588i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 72.0000 | + | 72.0000i | 0.418605 | + | 0.418605i | ||||
\(173\) | 41.0000 | − | 41.0000i | 0.236994 | − | 0.236994i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.815604 | + | 0.578610i | \(0.196405\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 136.000 | − | 248.000i | 0.777143 | − | 1.41714i | ||||
\(176\) | 16.0000 | 0.0909091 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 26.0000 | − | 26.0000i | 0.146067 | − | 0.146067i | ||||
\(179\) | 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 | \(0.445213\pi\) | |||||||
\(182\) | −48.0000 | − | 48.0000i | −0.263736 | − | 0.263736i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 80.0000i | 0.434783i | ||||||||
\(185\) | −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 | ||||||||
\(190\) | −8.00000 | − | 56.0000i | −0.0421053 | − | 0.294737i | ||||
\(191\) | −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 | \(0.0853115\pi\) | |||||||
\(194\) | − | 114.000i | − | 0.587629i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −158.000 | −0.806122 | ||||||||
\(197\) | 153.000 | + | 153.000i | 0.776650 | + | 0.776650i | 0.979260 | − | 0.202610i | \(-0.0649423\pi\) |
−0.202610 | + | 0.979260i | \(0.564942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 252.000i | − | 1.26633i | −0.774016 | − | 0.633166i | \(-0.781755\pi\) | ||
0.774016 | − | 0.633166i | \(-0.218245\pi\) | |||||||
\(200\) | 62.0000 | + | 34.0000i | 0.310000 | + | 0.170000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −56.0000 | − | 56.0000i | −0.277228 | − | 0.277228i | ||||
\(203\) | −304.000 | + | 304.000i | −1.49754 | + | 1.49754i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −210.000 | + | 280.000i | −1.02439 | + | 1.36585i | ||||
\(206\) | 8.00000 | 0.0388350 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.0000 | − | 12.0000i | 0.0576923 | − | 0.0576923i | ||||
\(209\) | 32.0000i | 0.153110i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −64.0000 | −0.303318 | −0.151659 | − | 0.988433i | \(-0.548461\pi\) | ||||
−0.151659 | + | 0.988433i | \(0.548461\pi\) | |||||||
\(212\) | −34.0000 | − | 34.0000i | −0.160377 | − | 0.160377i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 136.000i | 0.635514i | ||||||||
\(215\) | −36.0000 | − | 252.000i | −0.167442 | − | 1.17209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −352.000 | − | 352.000i | −1.62212 | − | 1.62212i | ||||
\(218\) | 46.0000 | − | 46.0000i | 0.211009 | − | 0.211009i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −32.0000 | − | 24.0000i | −0.145455 | − | 0.109091i | ||||
\(221\) | 114.000 | 0.515837 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −228.000 | + | 228.000i | −1.02242 | + | 1.02242i | −0.0226787 | + | 0.999743i | \(0.507219\pi\) |
−0.999743 | + | 0.0226787i | \(0.992781\pi\) | |||||||
\(224\) | − | 64.0000i | − | 0.285714i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −106.000 | −0.469027 | ||||||||
\(227\) | 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 | \(-0.238551\pi\) | |||||||
\(230\) | 120.000 | − | 160.000i | 0.521739 | − | 0.695652i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −76.0000 | − | 76.0000i | −0.327586 | − | 0.327586i | ||||
\(233\) | 93.0000 | − | 93.0000i | 0.399142 | − | 0.399142i | −0.478789 | − | 0.877930i | \(-0.658924\pi\) |
0.877930 | + | 0.478789i | \(0.158924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −184.000 | −0.779661 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 304.000 | − | 304.000i | 1.27731 | − | 1.27731i | ||||
\(239\) | 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 | \(0.392293\pi\) | |||||||
\(242\) | −105.000 | − | 105.000i | −0.433884 | − | 0.433884i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 144.000i | 0.590164i | ||||||||
\(245\) | 316.000 | + | 237.000i | 1.28980 | + | 0.967347i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.0000 | + | 24.0000i | 0.0971660 | + | 0.0971660i | ||||
\(248\) | 88.0000 | − | 88.0000i | 0.354839 | − | 0.354839i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −73.0000 | − | 161.000i | −0.292000 | − | 0.644000i | ||||
\(251\) | −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 | ||||
\(254\) | 136.000i | 0.535433i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −101.000 | − | 101.000i | −0.392996 | − | 0.392996i | 0.482758 | − | 0.875754i | \(-0.339635\pi\) |
−0.875754 | + | 0.482758i | \(0.839635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 48.0000i | − | 0.185328i | ||||||
\(260\) | −42.0000 | + | 6.00000i | −0.161538 | + | 0.0230769i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 44.0000 | + | 44.0000i | 0.167939 | + | 0.167939i | ||||
\(263\) | 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 | ||||
\(266\) | 128.000 | 0.481203 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −88.0000 | + | 88.0000i | −0.328358 | + | 0.328358i | ||||
\(269\) | 296.000i | 1.10037i | 0.835042 | + | 0.550186i | \(0.185443\pi\) | ||||
−0.835042 | + | 0.550186i | \(0.814557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 108.000 | 0.398524 | 0.199262 | − | 0.979946i | \(-0.436146\pi\) | ||||
0.199262 | + | 0.979946i | \(0.436146\pi\) | |||||||
\(272\) | 76.0000 | + | 76.0000i | 0.279412 | + | 0.279412i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 138.000i | 0.503650i | ||||||||
\(275\) | 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 | \(0.962995\pi\) | |||||||
\(278\) | −80.0000 | + | 80.0000i | −0.287770 | + | 0.287770i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −96.0000 | + | 128.000i | −0.342857 | + | 0.457143i | ||||
\(281\) | −378.000 | −1.34520 | −0.672598 | − | 0.740008i | \(-0.734822\pi\) | ||||
−0.672598 | + | 0.740008i | \(0.734822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 92.0000 | − | 92.0000i | 0.325088 | − | 0.325088i | −0.525627 | − | 0.850715i | \(-0.676169\pi\) |
0.850715 | + | 0.525627i | \(0.176169\pi\) | |||||||
\(284\) | 176.000i | 0.619718i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0000 | 0.0839161 | ||||||||
\(287\) | −560.000 | − | 560.000i | −1.95122 | − | 1.95122i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 433.000i | 1.49827i | ||||||||
\(290\) | 38.0000 | + | 266.000i | 0.131034 | + | 0.917241i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 110.000 | + | 110.000i | 0.376712 | + | 0.376712i | ||||
\(293\) | 279.000 | − | 279.000i | 0.952218 | − | 0.952218i | −0.0466910 | − | 0.998909i | \(-0.514868\pi\) |
0.998909 | + | 0.0466910i | \(0.0148676\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 368.000 | + | 276.000i | 1.24746 | + | 0.935593i | ||||
\(296\) | 12.0000 | 0.0405405 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 168.000 | − | 168.000i | 0.563758 | − | 0.563758i | ||||
\(299\) | 120.000i | 0.401338i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 576.000 | 1.91362 | ||||||||
\(302\) | 4.00000 | + | 4.00000i | 0.0132450 | + | 0.0132450i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 32.0000i | 0.105263i | ||||||||
\(305\) | 216.000 | − | 288.000i | 0.708197 | − | 0.944262i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 216.000 | + | 216.000i | 0.703583 | + | 0.703583i | 0.965178 | − | 0.261595i | \(-0.0842484\pi\) |
−0.261595 | + | 0.965178i | \(0.584248\pi\) | |||||||
\(308\) | 64.0000 | − | 64.0000i | 0.207792 | − | 0.207792i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −308.000 | + | 44.0000i | −0.993548 | + | 0.141935i | ||||
\(311\) | −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 | \(0.239211\pi\) | |||||||
\(314\) | 198.000i | 0.630573i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.0000 | −0.0759494 | ||||||||
\(317\) | −87.0000 | − | 87.0000i | −0.274448 | − | 0.274448i | 0.556440 | − | 0.830888i | \(-0.312167\pi\) |
−0.830888 | + | 0.556440i | \(0.812167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 152.000i | − | 0.476489i | ||||||
\(320\) | −32.0000 | − | 24.0000i | −0.100000 | − | 0.0750000i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 320.000 | + | 320.000i | 0.993789 | + | 0.993789i | ||||
\(323\) | −152.000 | + | 152.000i | −0.470588 | + | 0.470588i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 93.0000 | + | 51.0000i | 0.286154 | + | 0.156923i | ||||
\(326\) | −320.000 | −0.981595 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 140.000 | − | 140.000i | 0.426829 | − | 0.426829i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −584.000 | −1.76435 | −0.882175 | − | 0.470921i | \(-0.843922\pi\) | ||||
−0.882175 | + | 0.470921i | \(0.843922\pi\) | |||||||
\(332\) | 48.0000 | + | 48.0000i | 0.144578 | + | 0.144578i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 112.000i | − | 0.335329i | ||||||
\(335\) | 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 | \(0.837246\pi\) | |||||||
\(338\) | −151.000 | + | 151.000i | −0.446746 | + | 0.446746i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −38.0000 | − | 266.000i | −0.111765 | − | 0.782353i | ||||
\(341\) | 176.000 | 0.516129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −240.000 | + | 240.000i | −0.699708 | + | 0.699708i | ||||
\(344\) | 144.000i | 0.418605i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 82.0000 | 0.236994 | ||||||||
\(347\) | 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 | \(0.937580\pi\) | |||||||
\(350\) | 384.000 | − | 112.000i | 1.09714 | − | 0.320000i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.0000 | + | 16.0000i | 0.0454545 | + | 0.0454545i | ||||
\(353\) | 75.0000 | − | 75.0000i | 0.212465 | − | 0.212465i | −0.592849 | − | 0.805314i | \(-0.701997\pi\) |
0.805314 | + | 0.592849i | \(0.201997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 264.000 | − | 352.000i | 0.743662 | − | 0.991549i | ||||
\(356\) | 52.0000 | 0.146067 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −172.000 | + | 172.000i | −0.480447 | + | 0.480447i | ||||
\(359\) | − | 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 | ||||||||
\(362\) | 62.0000 | + | 62.0000i | 0.171271 | + | 0.171271i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 96.0000i | − | 0.263736i | ||||||
\(365\) | −55.0000 | − | 385.000i | −0.150685 | − | 1.05479i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | − | 16.0000i | −0.0435967 | − | 0.0435967i | 0.684972 | − | 0.728569i | \(-0.259814\pi\) |
−0.728569 | + | 0.684972i | \(0.759814\pi\) | |||||||
\(368\) | −80.0000 | + | 80.0000i | −0.217391 | + | 0.217391i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24.0000 | − | 18.0000i | −0.0648649 | − | 0.0486486i | ||||
\(371\) | −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 | \(0.407851\pi\) | |||||||
\(374\) | 152.000i | 0.406417i | ||||||||
\(375\) | 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 | \(-0.735399\pi\) | ||
0.673940 | − | 0.738786i | \(-0.264601\pi\) | |||||||
\(380\) | 48.0000 | − | 64.0000i | 0.126316 | − | 0.168421i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −248.000 | − | 248.000i | −0.649215 | − | 0.649215i | ||||
\(383\) | 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 | ||||
\(386\) | 270.000 | 0.699482 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 114.000 | − | 114.000i | 0.293814 | − | 0.293814i | ||||
\(389\) | 24.0000i | 0.0616967i | 0.999524 | + | 0.0308483i | \(0.00982089\pi\) | ||||
−0.999524 | + | 0.0308483i | \(0.990179\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −760.000 | −1.94373 | ||||||||
\(392\) | −158.000 | − | 158.000i | −0.403061 | − | 0.403061i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 306.000i | 0.776650i | ||||||||
\(395\) | 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 | \(0.928769\pi\) | |||||||
\(398\) | 252.000 | − | 252.000i | 0.633166 | − | 0.633166i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.0000 | + | 96.0000i | 0.0700000 | + | 0.240000i | ||||
\(401\) | 144.000 | 0.359102 | 0.179551 | − | 0.983749i | \(-0.442535\pi\) | ||||
0.179551 | + | 0.983749i | \(0.442535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 132.000 | − | 132.000i | 0.327543 | − | 0.327543i | ||||
\(404\) | − | 112.000i | − | 0.277228i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −608.000 | −1.49754 | ||||||||
\(407\) | 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 | \(-0.142461\pi\) | |||||||
\(410\) | −490.000 | + | 70.0000i | −1.19512 | + | 0.170732i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000 | + | 8.00000i | 0.0194175 | + | 0.0194175i | ||||
\(413\) | −736.000 | + | 736.000i | −1.78208 | + | 1.78208i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.0000 | − | 168.000i | −0.0578313 | − | 0.404819i | ||||
\(416\) | 24.0000 | 0.0576923 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −32.0000 | + | 32.0000i | −0.0765550 | + | 0.0765550i | ||||
\(419\) | 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 | \(0.460583\pi\) | |||||||
\(422\) | −64.0000 | − | 64.0000i | −0.151659 | − | 0.151659i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 68.0000i | − | 0.160377i | ||||||
\(425\) | −323.000 | + | 589.000i | −0.760000 | + | 1.38588i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 576.000 | + | 576.000i | 1.34895 | + | 1.34895i | ||||
\(428\) | −136.000 | + | 136.000i | −0.317757 | + | 0.317757i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 216.000 | − | 288.000i | 0.502326 | − | 0.669767i | ||||
\(431\) | 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 | \(0.228672\pi\) | |||||||
\(434\) | − | 704.000i | − | 1.62212i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 92.0000 | 0.211009 | ||||||||
\(437\) | −160.000 | − | 160.000i | −0.366133 | − | 0.366133i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 364.000i | − | 0.829157i | −0.910014 | − | 0.414579i | \(-0.863929\pi\) | ||
0.910014 | − | 0.414579i | \(-0.136071\pi\) | |||||||
\(440\) | −8.00000 | − | 56.0000i | −0.0181818 | − | 0.127273i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 114.000 | + | 114.000i | 0.257919 | + | 0.257919i | ||||
\(443\) | 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 | ||||
\(446\) | −456.000 | −1.02242 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 64.0000 | − | 64.0000i | 0.142857 | − | 0.142857i | ||||
\(449\) | 176.000i | 0.391982i | 0.980606 | + | 0.195991i | \(0.0627924\pi\) | ||||
−0.980606 | + | 0.195991i | \(0.937208\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 280.000 | 0.620843 | ||||||||
\(452\) | −106.000 | − | 106.000i | −0.234513 | − | 0.234513i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 200.000i | 0.440529i | ||||||||
\(455\) | −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 | \(0.686036\pi\) | |||||||
\(458\) | 312.000 | − | 312.000i | 0.681223 | − | 0.681223i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 280.000 | − | 40.0000i | 0.608696 | − | 0.0869565i | ||||
\(461\) | −568.000 | −1.23210 | −0.616052 | − | 0.787705i | \(-0.711269\pi\) | ||||
−0.616052 | + | 0.787705i | \(0.711269\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −568.000 | + | 568.000i | −1.22678 | + | 1.22678i | −0.261608 | + | 0.965174i | \(0.584253\pi\) |
−0.965174 | + | 0.261608i | \(0.915747\pi\) | |||||||
\(464\) | − | 152.000i | − | 0.327586i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 186.000 | 0.399142 | ||||||||
\(467\) | 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 | ||||||||
\(472\) | −184.000 | − | 184.000i | −0.389831 | − | 0.389831i | ||||
\(473\) | −144.000 | + | 144.000i | −0.304440 | + | 0.304440i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −192.000 | + | 56.0000i | −0.404211 | + | 0.117895i | ||||
\(476\) | 608.000 | 1.27731 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −96.0000 | + | 96.0000i | −0.200837 | + | 0.200837i | ||||
\(479\) | − | 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 | ||||||||
\(482\) | 160.000 | + | 160.000i | 0.331950 | + | 0.331950i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 210.000i | − | 0.433884i | ||||||
\(485\) | −399.000 | + | 57.0000i | −0.822680 | + | 0.117526i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 252.000 | + | 252.000i | 0.517454 | + | 0.517454i | 0.916800 | − | 0.399346i | \(-0.130763\pi\) |
−0.399346 | + | 0.916800i | \(0.630763\pi\) | |||||||
\(488\) | −144.000 | + | 144.000i | −0.295082 | + | 0.295082i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 79.0000 | + | 553.000i | 0.161224 | + | 1.12857i | ||||
\(491\) | 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 | ||||
\(494\) | 48.0000i | 0.0971660i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 176.000 | 0.354839 | ||||||||
\(497\) | 704.000 | + | 704.000i | 1.41650 | + | 1.41650i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 872.000i | 1.74749i | 0.486380 | + | 0.873747i | \(0.338317\pi\) | ||||
−0.486380 | + | 0.873747i | \(0.661683\pi\) | |||||||
\(500\) | 88.0000 | − | 234.000i | 0.176000 | − | 0.468000i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.0000 | − | 12.0000i | −0.0239044 | − | 0.0239044i | ||||
\(503\) | −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 | ||||
\(506\) | −160.000 | −0.316206 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −136.000 | + | 136.000i | −0.267717 | + | 0.267717i | ||||
\(509\) | − | 694.000i | − | 1.36346i | −0.731605 | − | 0.681729i | \(-0.761228\pi\) | ||
0.731605 | − | 0.681729i | \(-0.238772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 880.000 | 1.72211 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 202.000i | − | 0.392996i | ||||||
\(515\) | −4.00000 | − | 28.0000i | −0.00776699 | − | 0.0543689i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 48.0000 | − | 48.0000i | 0.0926641 | − | 0.0926641i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −48.0000 | − | 36.0000i | −0.0923077 | − | 0.0692308i | ||||
\(521\) | −528.000 | −1.01344 | −0.506718 | − | 0.862112i | \(-0.669141\pi\) | ||||
−0.506718 | + | 0.862112i | \(0.669141\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 552.000 | − | 552.000i | 1.05545 | − | 1.05545i | 0.0570797 | − | 0.998370i | \(-0.481821\pi\) |
0.998370 | − | 0.0570797i | \(-0.0181789\pi\) | |||||||
\(524\) | 88.0000i | 0.167939i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 416.000 | 0.790875 | ||||||||
\(527\) | 836.000 | + | 836.000i | 1.58634 | + | 1.58634i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 271.000i | − | 0.512287i | ||||||
\(530\) | −102.000 | + | 136.000i | −0.192453 | + | 0.256604i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 128.000 | + | 128.000i | 0.240602 | + | 0.240602i | ||||
\(533\) | 210.000 | − | 210.000i | 0.393996 | − | 0.393996i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 476.000 | − | 68.0000i | 0.889720 | − | 0.127103i | ||||
\(536\) | −176.000 | −0.328358 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −296.000 | + | 296.000i | −0.550186 | + | 0.550186i | ||||
\(539\) | − | 316.000i | − | 0.586271i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −782.000 | −1.44547 | −0.722736 | − | 0.691125i | \(-0.757116\pi\) | ||||
−0.722736 | + | 0.691125i | \(0.757116\pi\) | |||||||
\(542\) | 108.000 | + | 108.000i | 0.199262 | + | 0.199262i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 152.000i | 0.279412i | ||||||||
\(545\) | −184.000 | − | 138.000i | −0.337615 | − | 0.253211i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −420.000 | − | 420.000i | −0.767824 | − | 0.767824i | 0.209899 | − | 0.977723i | \(-0.432687\pi\) |
−0.977723 | + | 0.209899i | \(0.932687\pi\) | |||||||
\(548\) | −138.000 | + | 138.000i | −0.251825 | + | 0.251825i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −68.0000 | + | 124.000i | −0.123636 | + | 0.225455i | ||||
\(551\) | 304.000 | 0.551724 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −96.0000 | + | 96.0000i | −0.173599 | + | 0.173599i | ||||
\(554\) | − | 486.000i | − | 0.877256i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −160.000 | −0.287770 | ||||||||
\(557\) | −417.000 | − | 417.000i | −0.748654 | − | 0.748654i | 0.225573 | − | 0.974226i | \(-0.427575\pi\) |
−0.974226 | + | 0.225573i | \(0.927575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 216.000i | 0.386404i | ||||||||
\(560\) | −224.000 | + | 32.0000i | −0.400000 | + | 0.0571429i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −378.000 | − | 378.000i | −0.672598 | − | 0.672598i | ||||
\(563\) | −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 | ||||
\(566\) | 184.000 | 0.325088 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −176.000 | + | 176.000i | −0.309859 | + | 0.309859i | ||||
\(569\) | − | 368.000i | − | 0.646749i | −0.946271 | − | 0.323374i | \(-0.895183\pi\) | ||
0.946271 | − | 0.323374i | \(-0.104817\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −736.000 | −1.28897 | −0.644483 | − | 0.764618i | \(-0.722928\pi\) | ||||
−0.644483 | + | 0.764618i | \(0.722928\pi\) | |||||||
\(572\) | 24.0000 | + | 24.0000i | 0.0419580 | + | 0.0419580i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1120.00i | − | 1.95122i | ||||||
\(575\) | −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 | \(0.794222\pi\) | |||||||
\(578\) | −433.000 | + | 433.000i | −0.749135 | + | 0.749135i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −228.000 | + | 304.000i | −0.393103 | + | 0.524138i | ||||
\(581\) | 384.000 | 0.660929 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 68.0000 | − | 68.0000i | 0.116638 | − | 0.116638i | ||||
\(584\) | 220.000i | 0.376712i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 558.000 | 0.952218 | ||||||||
\(587\) | −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 | ||||||||
\(590\) | 92.0000 | + | 644.000i | 0.155932 | + | 1.09153i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.0000 | + | 12.0000i | 0.0202703 | + | 0.0202703i | ||||
\(593\) | 149.000 | − | 149.000i | 0.251265 | − | 0.251265i | −0.570224 | − | 0.821489i | \(-0.693144\pi\) |
0.821489 | + | 0.570224i | \(0.193144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1216.00 | − | 912.000i | −2.04370 | − | 1.53277i | ||||
\(596\) | 336.000 | 0.563758 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −120.000 | + | 120.000i | −0.200669 | + | 0.200669i | ||||
\(599\) | 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 | \(0.414224\pi\) | |||||||
\(602\) | 576.000 | + | 576.000i | 0.956811 | + | 0.956811i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000i | 0.0132450i | ||||||||
\(605\) | −315.000 | + | 420.000i | −0.520661 | + | 0.694215i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −528.000 | − | 528.000i | −0.869852 | − | 0.869852i | 0.122604 | − | 0.992456i | \(-0.460876\pi\) |
−0.992456 | + | 0.122604i | \(0.960876\pi\) | |||||||
\(608\) | −32.0000 | + | 32.0000i | −0.0526316 | + | 0.0526316i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 504.000 | − | 72.0000i | 0.826230 | − | 0.118033i | ||||
\(611\) | 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 | \(-0.0988515\pi\) | |||||||
\(614\) | 432.000i | 0.703583i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 128.000 | 0.207792 | ||||||||
\(617\) | −675.000 | − | 675.000i | −1.09400 | − | 1.09400i | −0.995097 | − | 0.0989065i | \(-0.968466\pi\) |
−0.0989065 | − | 0.995097i | \(-0.531534\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 600.000i | 0.969305i | 0.874707 | + | 0.484653i | \(0.161054\pi\) | ||||
−0.874707 | + | 0.484653i | \(0.838946\pi\) | |||||||
\(620\) | −352.000 | − | 264.000i | −0.567742 | − | 0.425806i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −272.000 | − | 272.000i | −0.437299 | − | 0.437299i | ||||
\(623\) | 208.000 | − | 208.000i | 0.333868 | − | 0.333868i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −527.000 | + | 336.000i | −0.843200 | + | 0.537600i | ||||
\(626\) | 30.0000 | 0.0479233 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −198.000 | + | 198.000i | −0.315287 | + | 0.315287i | ||||
\(629\) | 114.000i | 0.181240i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.0316957 | −0.0158479 | − | 0.999874i | \(-0.505045\pi\) | ||||
−0.0158479 | + | 0.999874i | \(0.505045\pi\) | |||||||
\(632\) | −24.0000 | − | 24.0000i | −0.0379747 | − | 0.0379747i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 174.000i | − | 0.274448i | ||||||
\(635\) | 476.000 | − | 68.0000i | 0.749606 | − | 0.107087i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −237.000 | − | 237.000i | −0.372057 | − | 0.372057i | ||||
\(638\) | 152.000 | − | 152.000i | 0.238245 | − | 0.238245i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.00000 | − | 56.0000i | −0.0125000 | − | 0.0875000i | ||||
\(641\) | 694.000 | 1.08268 | 0.541342 | − | 0.840803i | \(-0.317917\pi\) | ||||
0.541342 | + | 0.840803i | \(0.317917\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −168.000 | + | 168.000i | −0.261275 | + | 0.261275i | −0.825572 | − | 0.564297i | \(-0.809147\pi\) |
0.564297 | + | 0.825572i | \(0.309147\pi\) | |||||||
\(644\) | 640.000i | 0.993789i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −304.000 | −0.470588 | ||||||||
\(647\) | 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 | ||||||
\(650\) | 42.0000 | + | 144.000i | 0.0646154 | + | 0.221538i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −320.000 | − | 320.000i | −0.490798 | − | 0.490798i | ||||
\(653\) | −81.0000 | + | 81.0000i | −0.124043 | + | 0.124043i | −0.766403 | − | 0.642360i | \(-0.777955\pi\) |
0.642360 | + | 0.766403i | \(0.277955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 132.000 | − | 176.000i | 0.201527 | − | 0.268702i | ||||
\(656\) | 280.000 | 0.426829 | ||||||||
\(657\) | 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 | \(0.641364\pi\) | |||||||
\(662\) | −584.000 | − | 584.000i | −0.882175 | − | 0.882175i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 96.0000i | 0.144578i | ||||||||
\(665\) | −64.0000 | − | 448.000i | −0.0962406 | − | 0.673684i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 760.000 | + | 760.000i | 1.13943 | + | 1.13943i | ||||
\(668\) | 112.000 | − | 112.000i | 0.167665 | − | 0.167665i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 352.000 | + | 264.000i | 0.525373 | + | 0.394030i | ||||
\(671\) | −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 | \(0.225562\pi\) | |||||||
\(674\) | − | 258.000i | − | 0.382789i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −302.000 | −0.446746 | ||||||||
\(677\) | 839.000 | + | 839.000i | 1.23929 | + | 1.23929i | 0.960291 | + | 0.279000i | \(0.0900029\pi\) |
0.279000 | + | 0.960291i | \(0.409997\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 912.000i | − | 1.34315i | ||||||
\(680\) | 228.000 | − | 304.000i | 0.335294 | − | 0.447059i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 176.000 | + | 176.000i | 0.258065 | + | 0.258065i | ||||
\(683\) | 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 | ||||
\(686\) | −480.000 | −0.699708 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −144.000 | + | 144.000i | −0.209302 | + | 0.209302i | ||||
\(689\) | − | 102.000i | − | 0.148041i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 504.000 | 0.729378 | 0.364689 | − | 0.931129i | \(-0.381175\pi\) | ||||
0.364689 | + | 0.931129i | \(0.381175\pi\) | |||||||
\(692\) | 82.0000 | + | 82.0000i | 0.118497 | + | 0.118497i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 520.000i | 0.749280i | ||||||||
\(695\) | 320.000 | + | 240.000i | 0.460432 | + | 0.345324i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1330.00 | + | 1330.00i | 1.90818 | + | 1.90818i | ||||
\(698\) | −136.000 | + | 136.000i | −0.194842 | + | 0.194842i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 496.000 | + | 272.000i | 0.708571 | + | 0.388571i | ||||
\(701\) | −298.000 | −0.425107 | −0.212553 | − | 0.977149i | \(-0.568178\pi\) | ||||
−0.212553 | + | 0.977149i | \(0.568178\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.0000 | + | 24.0000i | −0.0341394 | + | 0.0341394i | ||||
\(704\) | 32.0000i | 0.0454545i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 150.000 | 0.212465 | ||||||||
\(707\) | −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 | \(0.891985\pi\) | |||||||
\(710\) | 616.000 | − | 88.0000i | 0.867606 | − | 0.123944i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 52.0000 | + | 52.0000i | 0.0730337 | + | 0.0730337i | ||||
\(713\) | −880.000 | + | 880.000i | −1.23422 | + | 1.23422i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | − | 84.0000i | −0.0167832 | − | 0.117483i | ||||
\(716\) | −344.000 | −0.480447 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32.0000 | − | 32.0000i | 0.0445682 | − | 0.0445682i | ||||
\(719\) | 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 | ||||||||
\(722\) | 297.000 | + | 297.000i | 0.411357 | + | 0.411357i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 124.000i | 0.171271i | ||||||||
\(725\) | 912.000 | − | 266.000i | 1.25793 | − | 0.366897i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −60.0000 | − | 60.0000i | −0.0825309 | − | 0.0825309i | 0.664636 | − | 0.747167i | \(-0.268587\pi\) |
−0.747167 | + | 0.664636i | \(0.768587\pi\) | |||||||
\(728\) | 96.0000 | − | 96.0000i | 0.131868 | − | 0.131868i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 330.000 | − | 440.000i | 0.452055 | − | 0.602740i | ||||
\(731\) | −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 | \(0.439382\pi\) | |||||||
\(734\) | − | 32.0000i | − | 0.0435967i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −160.000 | −0.217391 | ||||||||
\(737\) | −176.000 | − | 176.000i | −0.238806 | − | 0.238806i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1160.00i | 1.56969i | 0.619693 | + | 0.784844i | \(0.287257\pi\) | ||||
−0.619693 | + | 0.784844i | \(0.712743\pi\) | |||||||
\(740\) | −6.00000 | − | 42.0000i | −0.00810811 | − | 0.0567568i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −272.000 | − | 272.000i | −0.366577 | − | 0.366577i | ||||
\(743\) | −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 | ||||
\(746\) | −502.000 | −0.672922 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −152.000 | + | 152.000i | −0.203209 | + | 0.203209i | ||||
\(749\) | 1088.00i | 1.45260i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 780.000 | 1.03862 | 0.519308 | − | 0.854587i | \(-0.326190\pi\) | ||||
0.519308 | + | 0.854587i | \(0.326190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 228.000i | − | 0.302387i | ||||||
\(755\) | 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 | \(0.664227\pi\) | |||||||
\(758\) | 560.000 | − | 560.000i | 0.738786 | − | 0.738786i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 112.000 | − | 16.0000i | 0.147368 | − | 0.0210526i | ||||
\(761\) | −304.000 | −0.399474 | −0.199737 | − | 0.979850i | \(-0.564009\pi\) | ||||
−0.199737 | + | 0.979850i | \(0.564009\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 368.000 | − | 368.000i | 0.482307 | − | 0.482307i | ||||
\(764\) | − | 496.000i | − | 0.649215i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 600.000 | 0.783290 | ||||||||
\(767\) | −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 | \(-0.245486\pi\) | |||||||
\(770\) | −256.000 | − | 192.000i | −0.332468 | − | 0.249351i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 270.000 | + | 270.000i | 0.349741 | + | 0.349741i | ||||
\(773\) | 897.000 | − | 897.000i | 1.16041 | − | 1.16041i | 0.176029 | − | 0.984385i | \(-0.443675\pi\) |
0.984385 | − | 0.176029i | \(-0.0563252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 308.000 | + | 1056.00i | 0.397419 | + | 1.36258i | ||||
\(776\) | 228.000 | 0.293814 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.0000 | + | 24.0000i | −0.0308483 | + | 0.0308483i | ||||
\(779\) | 560.000i | 0.718870i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −352.000 | −0.450704 | ||||||||
\(782\) | −760.000 | − | 760.000i | −0.971867 | − | 0.971867i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 316.000i | − | 0.403061i | ||||||
\(785\) | 693.000 | − | 99.0000i | 0.882803 | − | 0.126115i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 328.000 | + | 328.000i | 0.416773 | + | 0.416773i | 0.884090 | − | 0.467317i | \(-0.154779\pi\) |
−0.467317 | + | 0.884090i | \(0.654779\pi\) | |||||||
\(788\) | −306.000 | + | 306.000i | −0.388325 | + | 0.388325i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0000 | + | 84.0000i | 0.0151899 | + | 0.106329i | ||||
\(791\) | −848.000 | −1.07206 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −216.000 | + | 216.000i | −0.272383 | + | 0.272383i | ||||
\(794\) | − | 598.000i | − | 0.753149i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 504.000 | 0.633166 | ||||||||
\(797\) | 87.0000 | + | 87.0000i | 0.109159 | + | 0.109159i | 0.759577 | − | 0.650418i | \(-0.225406\pi\) |
−0.650418 | + | 0.759577i | \(0.725406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −68.0000 | + | 124.000i | −0.0850000 | + | 0.155000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 144.000 | + | 144.000i | 0.179551 | + | 0.179551i | ||||
\(803\) | −220.000 | + | 220.000i | −0.273973 | + | 0.273973i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 960.000 | − | 1280.00i | 1.19255 | − | 1.59006i | ||||
\(806\) | 264.000 | 0.327543 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 112.000 | − | 112.000i | 0.138614 | − | 0.138614i | ||||
\(809\) | 922.000i | 1.13968i | 0.821756 | + | 0.569839i | \(0.192995\pi\) | ||||
−0.821756 | + | 0.569839i | \(0.807005\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1312.00 | −1.61776 | −0.808878 | − | 0.587977i | \(-0.799925\pi\) | ||||
−0.808878 | + | 0.587977i | \(0.799925\pi\) | |||||||
\(812\) | −608.000 | − | 608.000i | −0.748768 | − | 0.748768i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24.0000i | 0.0294840i | ||||||||
\(815\) | 160.000 | + | 1120.00i | 0.196319 | + | 1.37423i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −288.000 | − | 288.000i | −0.352509 | − | 0.352509i | ||||
\(818\) | 354.000 | − | 354.000i | 0.432763 | − | 0.432763i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −560.000 | − | 420.000i | −0.682927 | − | 0.512195i | ||||
\(821\) | 950.000 | 1.15713 | 0.578563 | − | 0.815638i | \(-0.303614\pi\) | ||||
0.578563 | + | 0.815638i | \(0.303614\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 68.0000 | − | 68.0000i | 0.0826245 | − | 0.0826245i | −0.664587 | − | 0.747211i | \(-0.731392\pi\) |
0.747211 | + | 0.664587i | \(0.231392\pi\) | |||||||
\(824\) | 16.0000i | 0.0194175i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1472.00 | −1.78208 | ||||||||
\(827\) | −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 | \(-0.0342392\pi\) | |||||||
\(830\) | 144.000 | − | 192.000i | 0.173494 | − | 0.231325i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.0000 | + | 24.0000i | 0.0288462 | + | 0.0288462i | ||||
\(833\) | 1501.00 | − | 1501.00i | 1.80192 | − | 1.80192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −392.000 | + | 56.0000i | −0.469461 | + | 0.0670659i | ||||
\(836\) | −64.0000 | −0.0765550 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −468.000 | + | 468.000i | −0.558473 | + | 0.558473i | ||||
\(839\) | 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 | ||||||||
\(842\) | 104.000 | + | 104.000i | 0.123515 | + | 0.123515i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 128.000i | − | 0.151659i | ||||||
\(845\) | 604.000 | + | 453.000i | 0.714793 | + | 0.536095i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −840.000 | − | 840.000i | −0.991736 | − | 0.991736i | ||||
\(848\) | 68.0000 | − | 68.0000i | 0.0801887 | − | 0.0801887i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −912.000 | + | 266.000i | −1.07294 | + | 0.312941i | ||||
\(851\) | −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 | \(0.388652\pi\) | |||||||
\(854\) | 1152.00i | 1.34895i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −272.000 | −0.317757 | ||||||||
\(857\) | −357.000 | − | 357.000i | −0.416569 | − | 0.416569i | 0.467450 | − | 0.884019i | \(-0.345173\pi\) |
−0.884019 | + | 0.467450i | \(0.845173\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 520.000i | − | 0.605355i | −0.953093 | − | 0.302678i | \(-0.902119\pi\) | ||
0.953093 | − | 0.302678i | \(-0.0978805\pi\) | |||||||
\(860\) | 504.000 | − | 72.0000i | 0.586047 | − | 0.0837209i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 680.000 | + | 680.000i | 0.788863 | + | 0.788863i | ||||
\(863\) | −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 | ||||
\(866\) | 82.0000 | 0.0946882 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 704.000 | − | 704.000i | 0.811060 | − | 0.811060i | ||||
\(869\) | − | 48.0000i | − | 0.0552359i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −264.000 | −0.303100 | ||||||||
\(872\) | 92.0000 | + | 92.0000i | 0.105505 | + | 0.105505i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 320.000i | − | 0.366133i | ||||||
\(875\) | −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 | \(0.946206\pi\) | |||||||
\(878\) | 364.000 | − | 364.000i | 0.414579 | − | 0.414579i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 48.0000 | − | 64.0000i | 0.0545455 | − | 0.0727273i | ||||
\(881\) | 554.000 | 0.628831 | 0.314415 | − | 0.949285i | \(-0.398192\pi\) | ||||
0.314415 | + | 0.949285i | \(0.398192\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 952.000 | − | 952.000i | 1.07814 | − | 1.07814i | 0.0814666 | − | 0.996676i | \(-0.474040\pi\) |
0.996676 | − | 0.0814666i | \(-0.0259604\pi\) | |||||||
\(884\) | 228.000i | 0.257919i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 744.000 | 0.839729 | ||||||||
\(887\) | −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 | ||||||||
\(890\) | −26.0000 | − | 182.000i | −0.0292135 | − | 0.204494i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −456.000 | − | 456.000i | −0.511211 | − | 0.511211i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 688.000 | + | 516.000i | 0.768715 | + | 0.576536i | ||||
\(896\) | 128.000 | 0.142857 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −176.000 | + | 176.000i | −0.195991 | + | 0.195991i | ||||
\(899\) | − | 1672.00i | − | 1.85984i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 646.000 | 0.716981 | ||||||||
\(902\) | 280.000 | + | 280.000i | 0.310421 | + | 0.310421i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 212.000i | − | 0.234513i | ||||||
\(905\) | 186.000 | − | 248.000i | 0.205525 | − | 0.274033i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −740.000 | − | 740.000i | −0.815877 | − | 0.815877i | 0.169631 | − | 0.985508i | \(-0.445742\pi\) |
−0.985508 | + | 0.169631i | \(0.945742\pi\) | |||||||
\(908\) | −200.000 | + | 200.000i | −0.220264 | + | 0.220264i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −336.000 | + | 48.0000i | −0.369231 | + | 0.0527473i | ||||
\(911\) | 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 | ||||
\(914\) | 258.000i | 0.282276i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 624.000 | 0.681223 | ||||||||
\(917\) | 352.000 | + | 352.000i | 0.383860 | + | 0.383860i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 844.000i | − | 0.918390i | −0.888336 | − | 0.459195i | \(-0.848138\pi\) | ||
0.888336 | − | 0.459195i | \(-0.151862\pi\) | |||||||
\(920\) | 320.000 | + | 240.000i | 0.347826 | + | 0.260870i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −568.000 | − | 568.000i | −0.616052 | − | 0.616052i | ||||
\(923\) | −264.000 | + | 264.000i | −0.286024 | + | 0.286024i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51.0000 | + | 93.0000i | −0.0551351 | + | 0.100541i | ||||
\(926\) | −1136.00 | −1.22678 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 152.000 | − | 152.000i | 0.163793 | − | 0.163793i | ||||
\(929\) | − | 208.000i | − | 0.223897i | −0.993714 | − | 0.111948i | \(-0.964291\pi\) | ||
0.993714 | − | 0.111948i | \(-0.0357091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 632.000 | 0.678840 | ||||||||
\(932\) | 186.000 | + | 186.000i | 0.199571 | + | 0.199571i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 544.000i | 0.582441i | ||||||||
\(935\) | 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 | \(0.748319\pi\) | |||||||
\(938\) | −704.000 | + | 704.000i | −0.750533 | + | 0.750533i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1752.00 | −1.86185 | −0.930925 | − | 0.365212i | \(-0.880997\pi\) | ||||
−0.930925 | + | 0.365212i | \(0.880997\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1400.00 | + | 1400.00i | −1.48462 | + | 1.48462i | ||||
\(944\) | − | 368.000i | − | 0.389831i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −288.000 | −0.304440 | ||||||||
\(947\) | −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 | ||||||||
\(950\) | −248.000 | − | 136.000i | −0.261053 | − | 0.143158i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 608.000 | + | 608.000i | 0.638655 | + | 0.638655i | ||||
\(953\) | −645.000 | + | 645.000i | −0.676810 | + | 0.676810i | −0.959277 | − | 0.282467i | \(-0.908847\pi\) |
0.282467 | + | 0.959277i | \(0.408847\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −744.000 | + | 992.000i | −0.779058 | + | 1.03874i | ||||
\(956\) | −192.000 | −0.200837 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 928.000 | − | 928.000i | 0.968685 | − | 0.968685i | ||||
\(959\) | 1104.00i | 1.15120i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 975.000 | 1.01457 | ||||||||
\(962\) | 18.0000 | + | 18.0000i | 0.0187110 | + | 0.0187110i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 320.000i | 0.331950i | ||||||||
\(965\) | −135.000 | − | 945.000i | −0.139896 | − | 0.979275i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −92.0000 | − | 92.0000i | −0.0951396 | − | 0.0951396i | 0.657935 | − | 0.753075i | \(-0.271430\pi\) |
−0.753075 | + | 0.657935i | \(0.771430\pi\) | |||||||
\(968\) | 210.000 | − | 210.000i | 0.216942 | − | 0.216942i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −456.000 | − | 342.000i | −0.470103 | − | 0.352577i | ||||
\(971\) | 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 | ||||
\(974\) | 504.000i | 0.517454i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −288.000 | −0.295082 | ||||||||
\(977\) | 1011.00 | + | 1011.00i | 1.03480 | + | 1.03480i | 0.999372 | + | 0.0354282i | \(0.0112795\pi\) |
0.0354282 | + | 0.999372i | \(0.488720\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 104.000i | 0.106231i | ||||||||
\(980\) | −474.000 | + | 632.000i | −0.483673 | + | 0.644898i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 844.000 | + | 844.000i | 0.859470 | + | 0.859470i | ||||
\(983\) | 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 | ||||
\(986\) | 1444.00 | 1.46450 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −48.0000 | + | 48.0000i | −0.0485830 | + | 0.0485830i | ||||
\(989\) | − | 1440.00i | − | 1.45602i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 652.000 | 0.657921 | 0.328961 | − | 0.944344i | \(-0.393302\pi\) | ||||
0.328961 | + | 0.944344i | \(0.393302\pi\) | |||||||
\(992\) | 176.000 | + | 176.000i | 0.177419 | + | 0.177419i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1408.00i | 1.41650i | ||||||||
\(995\) | −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 | \(0.482256\pi\) | |||||||
\(998\) | −872.000 | + | 872.000i | −0.873747 | + | 0.873747i | ||||
\(999\) | 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 | 90.3.g.c.37.1 | yes | 2 | |
3.2 | odd | 2 | 90.3.g.a.37.1 | ✓ | 2 | ||
4.3 | odd | 2 | 720.3.bh.d.577.1 | 2 | |||
5.2 | odd | 4 | 450.3.g.a.343.1 | 2 | |||
5.3 | odd | 4 | inner | 90.3.g.c.73.1 | yes | 2 | |
5.4 | even | 2 | 450.3.g.a.307.1 | 2 | |||
12.11 | even | 2 | 720.3.bh.b.577.1 | 2 | |||
15.2 | even | 4 | 450.3.g.d.343.1 | 2 | |||
15.8 | even | 4 | 90.3.g.a.73.1 | yes | 2 | ||
15.14 | odd | 2 | 450.3.g.d.307.1 | 2 | |||
20.3 | even | 4 | 720.3.bh.d.433.1 | 2 | |||
60.23 | odd | 4 | 720.3.bh.b.433.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.3.g.a.37.1 | ✓ | 2 | 3.2 | odd | 2 | ||
90.3.g.a.73.1 | yes | 2 | 15.8 | even | 4 | ||
90.3.g.c.37.1 | yes | 2 | 1.1 | even | 1 | trivial | |
90.3.g.c.73.1 | yes | 2 | 5.3 | odd | 4 | inner | |
450.3.g.a.307.1 | 2 | 5.4 | even | 2 | |||
450.3.g.a.343.1 | 2 | 5.2 | odd | 4 | |||
450.3.g.d.307.1 | 2 | 15.14 | odd | 2 | |||
450.3.g.d.343.1 | 2 | 15.2 | even | 4 | |||
720.3.bh.b.433.1 | 2 | 60.23 | odd | 4 | |||
720.3.bh.b.577.1 | 2 | 12.11 | even | 2 | |||
720.3.bh.d.433.1 | 2 | 20.3 | even | 4 | |||
720.3.bh.d.577.1 | 2 | 4.3 | odd | 2 |