Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(493,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.493");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.f (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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.3317760000.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 17x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 493.4 | ||
Root | \(1.01575 - 1.72286i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.493 |
Dual form | 950.2.f.b.607.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | −0.472879 | − | 0.881127i | \(-0.656785\pi\) |
0.881127 | + | 0.472879i | \(0.156785\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.73861 | − | 2.73861i | 1.03510 | − | 1.03510i | 0.0357371 | − | 0.999361i | \(-0.488622\pi\) |
0.999361 | − | 0.0357371i | \(-0.0113779\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 2.00000i | 0.666667i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −0.707107 | + | 0.707107i | −0.196116 | + | 0.196116i | −0.798333 | − | 0.602217i | \(-0.794284\pi\) |
0.602217 | + | 0.798333i | \(0.294284\pi\) | |||||||
\(14\) | 3.87298 | 1.03510 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.73861 | − | 2.73861i | 0.664211 | − | 0.664211i | −0.292159 | − | 0.956370i | \(-0.594374\pi\) |
0.956370 | + | 0.292159i | \(0.0943735\pi\) | |||||||
\(18\) | −1.41421 | + | 1.41421i | −0.333333 | + | 0.333333i | ||||
\(19\) | 3.87298 | − | 2.00000i | 0.888523 | − | 0.458831i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.87298i | − | 0.845154i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.73861 | + | 2.73861i | 0.571040 | + | 0.571040i | 0.932419 | − | 0.361379i | \(-0.117694\pi\) |
−0.361379 | + | 0.932419i | \(0.617694\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 3.53553 | + | 3.53553i | 0.680414 | + | 0.680414i | ||||
\(28\) | 2.73861 | + | 2.73861i | 0.517549 | + | 0.517549i | ||||
\(29\) | −3.87298 | −0.719195 | −0.359597 | − | 0.933108i | \(-0.617086\pi\) | ||||
−0.359597 | + | 0.933108i | \(0.617086\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.87298 | 0.664211 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 1.41421 | + | 1.41421i | 0.232495 | + | 0.232495i | 0.813733 | − | 0.581238i | \(-0.197432\pi\) |
−0.581238 | + | 0.813733i | \(0.697432\pi\) | |||||||
\(38\) | 4.15283 | + | 1.32440i | 0.673677 | + | 0.214846i | ||||
\(39\) | 1.00000i | 0.160128i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.74597i | − | 1.20972i | −0.796333 | − | 0.604858i | \(-0.793230\pi\) | ||
0.796333 | − | 0.604858i | \(-0.206770\pi\) | |||||||
\(42\) | 2.73861 | − | 2.73861i | 0.422577 | − | 0.422577i | ||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.87298i | 0.571040i | ||||||||
\(47\) | 5.47723 | − | 5.47723i | 0.798935 | − | 0.798935i | −0.183992 | − | 0.982928i | \(-0.558902\pi\) |
0.982928 | + | 0.183992i | \(0.0589021\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | − | 8.00000i | − | 1.14286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3.87298i | − | 0.542326i | ||||||
\(52\) | −0.707107 | − | 0.707107i | −0.0980581 | − | 0.0980581i | ||||
\(53\) | −6.36396 | + | 6.36396i | −0.874157 | + | 0.874157i | −0.992922 | − | 0.118765i | \(-0.962106\pi\) |
0.118765 | + | 0.992922i | \(0.462106\pi\) | |||||||
\(54\) | 5.00000i | 0.680414i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.87298i | 0.517549i | ||||||||
\(57\) | 1.32440 | − | 4.15283i | 0.175421 | − | 0.550055i | ||||
\(58\) | −2.73861 | − | 2.73861i | −0.359597 | − | 0.359597i | ||||
\(59\) | −11.6190 | −1.51266 | −0.756329 | − | 0.654191i | \(-0.773009\pi\) | ||||
−0.756329 | + | 0.654191i | \(0.773009\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.47723 | + | 5.47723i | 0.690066 | + | 0.690066i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.19239 | + | 9.19239i | 1.12303 | + | 1.12303i | 0.991284 | + | 0.131745i | \(0.0420581\pi\) |
0.131745 | + | 0.991284i | \(0.457942\pi\) | |||||||
\(68\) | 2.73861 | + | 2.73861i | 0.332106 | + | 0.332106i | ||||
\(69\) | 3.87298 | 0.466252 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.74597i | 0.919277i | 0.888106 | + | 0.459639i | \(0.152021\pi\) | ||||
−0.888106 | + | 0.459639i | \(0.847979\pi\) | |||||||
\(72\) | −1.41421 | − | 1.41421i | −0.166667 | − | 0.166667i | ||||
\(73\) | −2.73861 | − | 2.73861i | −0.320530 | − | 0.320530i | 0.528440 | − | 0.848971i | \(-0.322777\pi\) |
−0.848971 | + | 0.528440i | \(0.822777\pi\) | |||||||
\(74\) | 2.00000i | 0.232495i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | + | 3.87298i | 0.229416 | + | 0.444262i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.707107 | + | 0.707107i | −0.0800641 | + | 0.0800641i | ||||
\(79\) | −15.4919 | −1.74298 | −0.871489 | − | 0.490414i | \(-0.836845\pi\) | ||||
−0.871489 | + | 0.490414i | \(0.836845\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 5.47723 | − | 5.47723i | 0.604858 | − | 0.604858i | ||||
\(83\) | 5.47723 | + | 5.47723i | 0.601204 | + | 0.601204i | 0.940632 | − | 0.339428i | \(-0.110234\pi\) |
−0.339428 | + | 0.940632i | \(0.610234\pi\) | |||||||
\(84\) | 3.87298 | 0.422577 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.73861 | + | 2.73861i | −0.293610 | + | 0.293610i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.4919 | −1.64214 | −0.821071 | − | 0.570826i | \(-0.806623\pi\) | ||||
−0.821071 | + | 0.570826i | \(0.806623\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.87298i | 0.405999i | ||||||||
\(92\) | −2.73861 | + | 2.73861i | −0.285520 | + | 0.285520i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.74597 | 0.798935 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −5.65685 | − | 5.65685i | −0.574367 | − | 0.574367i | 0.358979 | − | 0.933346i | \(-0.383125\pi\) |
−0.933346 | + | 0.358979i | \(0.883125\pi\) | |||||||
\(98\) | 5.65685 | − | 5.65685i | 0.571429 | − | 0.571429i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 2.73861 | − | 2.73861i | 0.271163 | − | 0.271163i | ||||
\(103\) | 2.82843 | − | 2.82843i | 0.278693 | − | 0.278693i | −0.553894 | − | 0.832587i | \(-0.686859\pi\) |
0.832587 | + | 0.553894i | \(0.186859\pi\) | |||||||
\(104\) | − | 1.00000i | − | 0.0980581i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | 2.12132 | + | 2.12132i | 0.205076 | + | 0.205076i | 0.802171 | − | 0.597095i | \(-0.203678\pi\) |
−0.597095 | + | 0.802171i | \(0.703678\pi\) | |||||||
\(108\) | −3.53553 | + | 3.53553i | −0.340207 | + | 0.340207i | ||||
\(109\) | 11.6190 | 1.11289 | 0.556447 | − | 0.830883i | \(-0.312164\pi\) | ||||
0.556447 | + | 0.830883i | \(0.312164\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | −2.73861 | + | 2.73861i | −0.258775 | + | 0.258775i | ||||
\(113\) | −4.24264 | + | 4.24264i | −0.399114 | + | 0.399114i | −0.877920 | − | 0.478806i | \(-0.841070\pi\) |
0.478806 | + | 0.877920i | \(0.341070\pi\) | |||||||
\(114\) | 3.87298 | − | 2.00000i | 0.362738 | − | 0.187317i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.87298i | − | 0.359597i | ||||||
\(117\) | −1.41421 | − | 1.41421i | −0.130744 | − | 0.130744i | ||||
\(118\) | −8.21584 | − | 8.21584i | −0.756329 | − | 0.756329i | ||||
\(119\) | − | 15.0000i | − | 1.37505i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 7.07107 | + | 7.07107i | 0.640184 | + | 0.640184i | ||||
\(123\) | −5.47723 | − | 5.47723i | −0.493865 | − | 0.493865i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.74597i | 0.690066i | ||||||||
\(127\) | −5.65685 | − | 5.65685i | −0.501965 | − | 0.501965i | 0.410083 | − | 0.912048i | \(-0.365500\pi\) |
−0.912048 | + | 0.410083i | \(0.865500\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0000 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.12938 | − | 16.0838i | 0.444773 | − | 1.39464i | ||||
\(134\) | 13.0000i | 1.12303i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.87298i | 0.332106i | ||||||||
\(137\) | −8.21584 | + | 8.21584i | −0.701926 | + | 0.701926i | −0.964824 | − | 0.262897i | \(-0.915322\pi\) |
0.262897 | + | 0.964824i | \(0.415322\pi\) | |||||||
\(138\) | 2.73861 | + | 2.73861i | 0.233126 | + | 0.233126i | ||||
\(139\) | − | 10.0000i | − | 0.848189i | −0.905618 | − | 0.424094i | \(-0.860592\pi\) | ||
0.905618 | − | 0.424094i | \(-0.139408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 7.74597i | − | 0.652328i | ||||||
\(142\) | −5.47723 | + | 5.47723i | −0.459639 | + | 0.459639i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 2.00000i | − | 0.166667i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 3.87298i | − | 0.320530i | ||||||
\(147\) | −5.65685 | − | 5.65685i | −0.466569 | − | 0.466569i | ||||
\(148\) | −1.41421 | + | 1.41421i | −0.116248 | + | 0.116248i | ||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.74597i | 0.630358i | 0.949032 | + | 0.315179i | \(0.102065\pi\) | ||||
−0.949032 | + | 0.315179i | \(0.897935\pi\) | |||||||
\(152\) | −1.32440 | + | 4.15283i | −0.107423 | + | 0.336839i | ||||
\(153\) | 5.47723 | + | 5.47723i | 0.442807 | + | 0.442807i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | −10.9545 | − | 10.9545i | −0.871489 | − | 0.871489i | ||||
\(159\) | 9.00000i | 0.713746i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0000 | 1.18217 | ||||||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −10.9545 | − | 10.9545i | −0.858019 | − | 0.858019i | 0.133086 | − | 0.991105i | \(-0.457511\pi\) |
−0.991105 | + | 0.133086i | \(0.957511\pi\) | |||||||
\(164\) | 7.74597 | 0.604858 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.74597i | 0.601204i | ||||||||
\(167\) | −12.7279 | − | 12.7279i | −0.984916 | − | 0.984916i | 0.0149717 | − | 0.999888i | \(-0.495234\pi\) |
−0.999888 | + | 0.0149717i | \(0.995234\pi\) | |||||||
\(168\) | 2.73861 | + | 2.73861i | 0.211289 | + | 0.211289i | ||||
\(169\) | 12.0000i | 0.923077i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | + | 7.74597i | 0.305888 | + | 0.592349i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.24264 | + | 4.24264i | −0.322562 | + | 0.322562i | −0.849749 | − | 0.527187i | \(-0.823247\pi\) |
0.527187 | + | 0.849749i | \(0.323247\pi\) | |||||||
\(174\) | −3.87298 | −0.293610 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.21584 | + | 8.21584i | −0.617540 | + | 0.617540i | ||||
\(178\) | −10.9545 | − | 10.9545i | −0.821071 | − | 0.821071i | ||||
\(179\) | −7.74597 | −0.578961 | −0.289480 | − | 0.957184i | \(-0.593482\pi\) | ||||
−0.289480 | + | 0.957184i | \(0.593482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.4919i | − | 1.15151i | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||
0.817624 | − | 0.575753i | \(-0.195291\pi\) | |||||||
\(182\) | −2.73861 | + | 2.73861i | −0.202999 | + | 0.202999i | ||||
\(183\) | 7.07107 | − | 7.07107i | 0.522708 | − | 0.522708i | ||||
\(184\) | −3.87298 | −0.285520 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.47723 | + | 5.47723i | 0.399468 | + | 0.399468i | ||||
\(189\) | 19.3649 | 1.40859 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | 0.217072 | 0.108536 | − | 0.994092i | \(-0.465384\pi\) | ||||
0.108536 | + | 0.994092i | \(0.465384\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 18.3848 | − | 18.3848i | 1.32337 | − | 1.32337i | 0.412331 | − | 0.911034i | \(-0.364715\pi\) |
0.911034 | − | 0.412331i | \(-0.135285\pi\) | |||||||
\(194\) | − | 8.00000i | − | 0.574367i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.00000 | 0.571429 | ||||||||
\(197\) | −16.4317 | + | 16.4317i | −1.17071 | + | 1.17071i | −0.188667 | + | 0.982041i | \(0.560417\pi\) |
−0.982041 | + | 0.188667i | \(0.939583\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0000i | 0.779769i | 0.920864 | + | 0.389885i | \(0.127485\pi\) | ||||
−0.920864 | + | 0.389885i | \(0.872515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.0000 | 0.916949 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.6066 | + | 10.6066i | −0.744438 | + | 0.744438i | ||||
\(204\) | 3.87298 | 0.271163 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | −5.47723 | + | 5.47723i | −0.380693 | + | 0.380693i | ||||
\(208\) | 0.707107 | − | 0.707107i | 0.0490290 | − | 0.0490290i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.87298i | 0.266627i | 0.991074 | + | 0.133314i | \(0.0425617\pi\) | ||||
−0.991074 | + | 0.133314i | \(0.957438\pi\) | |||||||
\(212\) | −6.36396 | − | 6.36396i | −0.437079 | − | 0.437079i | ||||
\(213\) | 5.47723 | + | 5.47723i | 0.375293 | + | 0.375293i | ||||
\(214\) | 3.00000i | 0.205076i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.21584 | + | 8.21584i | 0.556447 | + | 0.556447i | ||||
\(219\) | −3.87298 | −0.261712 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.87298i | 0.260525i | ||||||||
\(222\) | 1.41421 | + | 1.41421i | 0.0949158 | + | 0.0949158i | ||||
\(223\) | −9.89949 | + | 9.89949i | −0.662919 | + | 0.662919i | −0.956067 | − | 0.293148i | \(-0.905297\pi\) |
0.293148 | + | 0.956067i | \(0.405297\pi\) | |||||||
\(224\) | −3.87298 | −0.258775 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 2.12132 | + | 2.12132i | 0.140797 | + | 0.140797i | 0.773992 | − | 0.633195i | \(-0.218257\pi\) |
−0.633195 | + | 0.773992i | \(0.718257\pi\) | |||||||
\(228\) | 4.15283 | + | 1.32440i | 0.275028 | + | 0.0877105i | ||||
\(229\) | 20.0000i | 1.32164i | 0.750546 | + | 0.660819i | \(0.229791\pi\) | ||||
−0.750546 | + | 0.660819i | \(0.770209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.73861 | − | 2.73861i | 0.179799 | − | 0.179799i | ||||
\(233\) | −10.9545 | − | 10.9545i | −0.717650 | − | 0.717650i | 0.250473 | − | 0.968123i | \(-0.419414\pi\) |
−0.968123 | + | 0.250473i | \(0.919414\pi\) | |||||||
\(234\) | − | 2.00000i | − | 0.130744i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 11.6190i | − | 0.756329i | ||||||
\(237\) | −10.9545 | + | 10.9545i | −0.711568 | + | 0.711568i | ||||
\(238\) | 10.6066 | − | 10.6066i | 0.687524 | − | 0.687524i | ||||
\(239\) | − | 21.0000i | − | 1.35838i | −0.733964 | − | 0.679189i | \(-0.762332\pi\) | ||
0.733964 | − | 0.679189i | \(-0.237668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.4919i | − | 0.997923i | −0.866624 | − | 0.498962i | \(-0.833715\pi\) | ||
0.866624 | − | 0.498962i | \(-0.166285\pi\) | |||||||
\(242\) | −7.77817 | − | 7.77817i | −0.500000 | − | 0.500000i | ||||
\(243\) | −11.3137 | + | 11.3137i | −0.725775 | + | 0.725775i | ||||
\(244\) | 10.0000i | 0.640184i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 7.74597i | − | 0.493865i | ||||||
\(247\) | −1.32440 | + | 4.15283i | −0.0842695 | + | 0.264238i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.74597 | 0.490881 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | −5.47723 | + | 5.47723i | −0.345033 | + | 0.345033i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 8.00000i | − | 0.501965i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.48528 | + | 8.48528i | 0.529297 | + | 0.529297i | 0.920363 | − | 0.391066i | \(-0.127893\pi\) |
−0.391066 | + | 0.920363i | \(0.627893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.74597 | 0.481311 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 7.74597i | − | 0.479463i | ||||||
\(262\) | −12.7279 | − | 12.7279i | −0.786334 | − | 0.786334i | ||||
\(263\) | 5.47723 | + | 5.47723i | 0.337740 | + | 0.337740i | 0.855516 | − | 0.517776i | \(-0.173240\pi\) |
−0.517776 | + | 0.855516i | \(0.673240\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.0000 | − | 7.74597i | 0.919709 | − | 0.474936i | ||||
\(267\) | −10.9545 | + | 10.9545i | −0.670402 | + | 0.670402i | ||||
\(268\) | −9.19239 | + | 9.19239i | −0.561514 | + | 0.561514i | ||||
\(269\) | 15.4919 | 0.944560 | 0.472280 | − | 0.881449i | \(-0.343431\pi\) | ||||
0.472280 | + | 0.881449i | \(0.343431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.0000 | −1.51864 | −0.759321 | − | 0.650716i | \(-0.774469\pi\) | ||||
−0.759321 | + | 0.650716i | \(0.774469\pi\) | |||||||
\(272\) | −2.73861 | + | 2.73861i | −0.166053 | + | 0.166053i | ||||
\(273\) | 2.73861 | + | 2.73861i | 0.165748 | + | 0.165748i | ||||
\(274\) | −11.6190 | −0.701926 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.87298i | 0.233126i | ||||||||
\(277\) | 16.4317 | − | 16.4317i | 0.987284 | − | 0.987284i | −0.0126364 | − | 0.999920i | \(-0.504022\pi\) |
0.999920 | + | 0.0126364i | \(0.00402239\pi\) | |||||||
\(278\) | 7.07107 | − | 7.07107i | 0.424094 | − | 0.424094i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.74597i | − | 0.462086i | −0.972944 | − | 0.231043i | \(-0.925786\pi\) | ||
0.972944 | − | 0.231043i | \(-0.0742137\pi\) | |||||||
\(282\) | 5.47723 | − | 5.47723i | 0.326164 | − | 0.326164i | ||||
\(283\) | −16.4317 | − | 16.4317i | −0.976762 | − | 0.976762i | 0.0229743 | − | 0.999736i | \(-0.492686\pi\) |
−0.999736 | + | 0.0229743i | \(0.992686\pi\) | |||||||
\(284\) | −7.74597 | −0.459639 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.2132 | − | 21.2132i | −1.25218 | − | 1.25218i | ||||
\(288\) | 1.41421 | − | 1.41421i | 0.0833333 | − | 0.0833333i | ||||
\(289\) | 2.00000i | 0.117647i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.00000 | −0.468968 | ||||||||
\(292\) | 2.73861 | − | 2.73861i | 0.160265 | − | 0.160265i | ||||
\(293\) | 14.8492 | − | 14.8492i | 0.867502 | − | 0.867502i | −0.124693 | − | 0.992195i | \(-0.539795\pi\) |
0.992195 | + | 0.124693i | \(0.0397947\pi\) | |||||||
\(294\) | − | 8.00000i | − | 0.466569i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.87298 | −0.223980 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.47723 | + | 5.47723i | −0.315179 | + | 0.315179i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.87298 | + | 2.00000i | −0.222131 | + | 0.114708i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.74597i | 0.442807i | ||||||||
\(307\) | 19.7990 | + | 19.7990i | 1.12999 | + | 1.12999i | 0.990178 | + | 0.139810i | \(0.0446491\pi\) |
0.139810 | + | 0.990178i | \(0.455351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.00000i | − | 0.227552i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | −0.850572 | −0.425286 | − | 0.905059i | \(-0.639826\pi\) | ||||
−0.425286 | + | 0.905059i | \(0.639826\pi\) | |||||||
\(312\) | −0.707107 | − | 0.707107i | −0.0400320 | − | 0.0400320i | ||||
\(313\) | −19.1703 | − | 19.1703i | −1.08357 | − | 1.08357i | −0.996174 | − | 0.0873951i | \(-0.972146\pi\) |
−0.0873951 | − | 0.996174i | \(-0.527854\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 15.4919i | − | 0.871489i | ||||||
\(317\) | 2.12132 | + | 2.12132i | 0.119145 | + | 0.119145i | 0.764165 | − | 0.645020i | \(-0.223151\pi\) |
−0.645020 | + | 0.764165i | \(0.723151\pi\) | |||||||
\(318\) | −6.36396 | + | 6.36396i | −0.356873 | + | 0.356873i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.00000 | 0.167444 | ||||||||
\(322\) | 10.6066 | + | 10.6066i | 0.591083 | + | 0.591083i | ||||
\(323\) | 5.12938 | − | 16.0838i | 0.285406 | − | 0.894928i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 15.4919i | − | 0.858019i | ||||||
\(327\) | 8.21584 | − | 8.21584i | 0.454337 | − | 0.454337i | ||||
\(328\) | 5.47723 | + | 5.47723i | 0.302429 | + | 0.302429i | ||||
\(329\) | − | 30.0000i | − | 1.65395i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3649i | 1.06439i | 0.846621 | + | 0.532196i | \(0.178633\pi\) | ||||
−0.846621 | + | 0.532196i | \(0.821367\pi\) | |||||||
\(332\) | −5.47723 | + | 5.47723i | −0.300602 | + | 0.300602i | ||||
\(333\) | −2.82843 | + | 2.82843i | −0.154997 | + | 0.154997i | ||||
\(334\) | − | 18.0000i | − | 0.984916i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.87298i | 0.211289i | ||||||||
\(337\) | 5.65685 | + | 5.65685i | 0.308148 | + | 0.308148i | 0.844191 | − | 0.536043i | \(-0.180081\pi\) |
−0.536043 | + | 0.844191i | \(0.680081\pi\) | |||||||
\(338\) | −8.48528 | + | 8.48528i | −0.461538 | + | 0.461538i | ||||
\(339\) | 6.00000i | 0.325875i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.64880 | + | 8.30565i | −0.143231 | + | 0.449118i | ||||
\(343\) | −2.73861 | − | 2.73861i | −0.147871 | − | 0.147871i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | 10.9545 | − | 10.9545i | 0.588066 | − | 0.588066i | −0.349042 | − | 0.937107i | \(-0.613493\pi\) |
0.937107 | + | 0.349042i | \(0.113493\pi\) | |||||||
\(348\) | −2.73861 | − | 2.73861i | −0.146805 | − | 0.146805i | ||||
\(349\) | 16.0000i | 0.856460i | 0.903670 | + | 0.428230i | \(0.140863\pi\) | ||||
−0.903670 | + | 0.428230i | \(0.859137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.6475 | + | 24.6475i | 1.31185 | + | 1.31185i | 0.920047 | + | 0.391808i | \(0.128150\pi\) |
0.391808 | + | 0.920047i | \(0.371850\pi\) | |||||||
\(354\) | −11.6190 | −0.617540 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 15.4919i | − | 0.821071i | ||||||
\(357\) | −10.6066 | − | 10.6066i | −0.561361 | − | 0.561361i | ||||
\(358\) | −5.47723 | − | 5.47723i | −0.289480 | − | 0.289480i | ||||
\(359\) | 15.0000i | 0.791670i | 0.918322 | + | 0.395835i | \(0.129545\pi\) | ||||
−0.918322 | + | 0.395835i | \(0.870455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | − | 15.4919i | 0.578947 | − | 0.815365i | ||||
\(362\) | 10.9545 | − | 10.9545i | 0.575753 | − | 0.575753i | ||||
\(363\) | −7.77817 | + | 7.77817i | −0.408248 | + | 0.408248i | ||||
\(364\) | −3.87298 | −0.202999 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.0000 | 0.522708 | ||||||||
\(367\) | −5.47723 | + | 5.47723i | −0.285909 | + | 0.285909i | −0.835460 | − | 0.549551i | \(-0.814799\pi\) |
0.549551 | + | 0.835460i | \(0.314799\pi\) | |||||||
\(368\) | −2.73861 | − | 2.73861i | −0.142760 | − | 0.142760i | ||||
\(369\) | 15.4919 | 0.806478 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.8569i | 1.80968i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.9203 | − | 21.9203i | 1.13499 | − | 1.13499i | 0.145655 | − | 0.989335i | \(-0.453471\pi\) |
0.989335 | − | 0.145655i | \(-0.0465290\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.74597i | 0.399468i | ||||||||
\(377\) | 2.73861 | − | 2.73861i | 0.141046 | − | 0.141046i | ||||
\(378\) | 13.6931 | + | 13.6931i | 0.704295 | + | 0.704295i | ||||
\(379\) | −19.3649 | −0.994709 | −0.497354 | − | 0.867547i | \(-0.665695\pi\) | ||||
−0.497354 | + | 0.867547i | \(0.665695\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.00000 | −0.409852 | ||||||||
\(382\) | 2.12132 | + | 2.12132i | 0.108536 | + | 0.108536i | ||||
\(383\) | 16.9706 | − | 16.9706i | 0.867155 | − | 0.867155i | −0.125001 | − | 0.992157i | \(-0.539894\pi\) |
0.992157 | + | 0.125001i | \(0.0398935\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.0000 | 1.32337 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.65685 | − | 5.65685i | 0.287183 | − | 0.287183i | ||||
\(389\) | 24.0000i | 1.21685i | 0.793612 | + | 0.608424i | \(0.208198\pi\) | ||||
−0.793612 | + | 0.608424i | \(0.791802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.0000 | 0.758583 | ||||||||
\(392\) | 5.65685 | + | 5.65685i | 0.285714 | + | 0.285714i | ||||
\(393\) | −12.7279 | + | 12.7279i | −0.642039 | + | 0.642039i | ||||
\(394\) | −23.2379 | −1.17071 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4317 | − | 16.4317i | 0.824682 | − | 0.824682i | −0.162093 | − | 0.986775i | \(-0.551825\pi\) |
0.986775 | + | 0.162093i | \(0.0518245\pi\) | |||||||
\(398\) | −7.77817 | + | 7.77817i | −0.389885 | + | 0.389885i | ||||
\(399\) | −7.74597 | − | 15.0000i | −0.387783 | − | 0.750939i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7.74597i | − | 0.386815i | −0.981119 | − | 0.193408i | \(-0.938046\pi\) | ||
0.981119 | − | 0.193408i | \(-0.0619540\pi\) | |||||||
\(402\) | 9.19239 | + | 9.19239i | 0.458475 | + | 0.458475i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | −0.744438 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.73861 | + | 2.73861i | 0.135582 | + | 0.135582i | ||||
\(409\) | 15.4919 | 0.766027 | 0.383013 | − | 0.923743i | \(-0.374886\pi\) | ||||
0.383013 | + | 0.923743i | \(0.374886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.6190i | 0.573121i | ||||||||
\(412\) | 2.82843 | + | 2.82843i | 0.139347 | + | 0.139347i | ||||
\(413\) | −31.8198 | + | 31.8198i | −1.56575 | + | 1.56575i | ||||
\(414\) | −7.74597 | −0.380693 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −7.07107 | − | 7.07107i | −0.346272 | − | 0.346272i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000i | 1.17248i | 0.810139 | + | 0.586238i | \(0.199392\pi\) | ||||
−0.810139 | + | 0.586238i | \(0.800608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.1109i | 1.32130i | 0.750692 | + | 0.660652i | \(0.229720\pi\) | ||||
−0.750692 | + | 0.660652i | \(0.770280\pi\) | |||||||
\(422\) | −2.73861 | + | 2.73861i | −0.133314 | + | 0.133314i | ||||
\(423\) | 10.9545 | + | 10.9545i | 0.532624 | + | 0.532624i | ||||
\(424\) | − | 9.00000i | − | 0.437079i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.74597i | 0.375293i | ||||||||
\(427\) | 27.3861 | − | 27.3861i | 1.32531 | − | 1.32531i | ||||
\(428\) | −2.12132 | + | 2.12132i | −0.102538 | + | 0.102538i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.7298i | 1.86555i | 0.360459 | + | 0.932775i | \(0.382620\pi\) | ||||
−0.360459 | + | 0.932775i | \(0.617380\pi\) | |||||||
\(432\) | −3.53553 | − | 3.53553i | −0.170103 | − | 0.170103i | ||||
\(433\) | −11.3137 | + | 11.3137i | −0.543702 | + | 0.543702i | −0.924612 | − | 0.380910i | \(-0.875611\pi\) |
0.380910 | + | 0.924612i | \(0.375611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.6190i | 0.556447i | ||||||||
\(437\) | 16.0838 | + | 5.12938i | 0.769394 | + | 0.245371i | ||||
\(438\) | −2.73861 | − | 2.73861i | −0.130856 | − | 0.130856i | ||||
\(439\) | 23.2379 | 1.10908 | 0.554542 | − | 0.832156i | \(-0.312893\pi\) | ||||
0.554542 | + | 0.832156i | \(0.312893\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.0000 | 0.761905 | ||||||||
\(442\) | −2.73861 | + | 2.73861i | −0.130263 | + | 0.130263i | ||||
\(443\) | 10.9545 | + | 10.9545i | 0.520462 | + | 0.520462i | 0.917711 | − | 0.397249i | \(-0.130035\pi\) |
−0.397249 | + | 0.917711i | \(0.630035\pi\) | |||||||
\(444\) | 2.00000i | 0.0949158i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0000 | −0.662919 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.73861 | − | 2.73861i | −0.129387 | − | 0.129387i | ||||
\(449\) | −23.2379 | −1.09666 | −0.548332 | − | 0.836261i | \(-0.684737\pi\) | ||||
−0.548332 | + | 0.836261i | \(0.684737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.24264 | − | 4.24264i | −0.199557 | − | 0.199557i | ||||
\(453\) | 5.47723 | + | 5.47723i | 0.257343 | + | 0.257343i | ||||
\(454\) | 3.00000i | 0.140797i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | + | 3.87298i | 0.0936586 | + | 0.181369i | ||||
\(457\) | 24.6475 | − | 24.6475i | 1.15296 | − | 1.15296i | 0.167006 | − | 0.985956i | \(-0.446590\pi\) |
0.985956 | − | 0.167006i | \(-0.0534100\pi\) | |||||||
\(458\) | −14.1421 | + | 14.1421i | −0.660819 | + | 0.660819i | ||||
\(459\) | 19.3649 | 0.903877 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.47723 | + | 5.47723i | 0.254548 | + | 0.254548i | 0.822832 | − | 0.568284i | \(-0.192393\pi\) |
−0.568284 | + | 0.822832i | \(0.692393\pi\) | |||||||
\(464\) | 3.87298 | 0.179799 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 15.4919i | − | 0.717650i | ||||||
\(467\) | −16.4317 | + | 16.4317i | −0.760367 | + | 0.760367i | −0.976389 | − | 0.216021i | \(-0.930692\pi\) |
0.216021 | + | 0.976389i | \(0.430692\pi\) | |||||||
\(468\) | 1.41421 | − | 1.41421i | 0.0653720 | − | 0.0653720i | ||||
\(469\) | 50.3488 | 2.32489 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.21584 | − | 8.21584i | 0.378165 | − | 0.378165i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −15.4919 | −0.711568 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 15.0000 | 0.687524 | ||||||||
\(477\) | −12.7279 | − | 12.7279i | −0.582772 | − | 0.582772i | ||||
\(478\) | 14.8492 | − | 14.8492i | 0.679189 | − | 0.679189i | ||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 10.9545 | − | 10.9545i | 0.498962 | − | 0.498962i | ||||
\(483\) | 10.6066 | − | 10.6066i | 0.482617 | − | 0.482617i | ||||
\(484\) | − | 11.0000i | − | 0.500000i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −16.0000 | −0.725775 | ||||||||
\(487\) | 26.8701 | + | 26.8701i | 1.21760 | + | 1.21760i | 0.968471 | + | 0.249128i | \(0.0801440\pi\) |
0.249128 | + | 0.968471i | \(0.419856\pi\) | |||||||
\(488\) | −7.07107 | + | 7.07107i | −0.320092 | + | 0.320092i | ||||
\(489\) | −15.4919 | −0.700569 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.0000 | −1.89543 | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||||
−0.947717 | + | 0.319113i | \(0.896615\pi\) | |||||||
\(492\) | 5.47723 | − | 5.47723i | 0.246932 | − | 0.246932i | ||||
\(493\) | −10.6066 | + | 10.6066i | −0.477697 | + | 0.477697i | ||||
\(494\) | −3.87298 | + | 2.00000i | −0.174254 | + | 0.0899843i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.2132 | + | 21.2132i | 0.951542 | + | 0.951542i | ||||
\(498\) | 5.47723 | + | 5.47723i | 0.245440 | + | 0.245440i | ||||
\(499\) | − | 20.0000i | − | 0.895323i | −0.894203 | − | 0.447661i | \(-0.852257\pi\) | ||
0.894203 | − | 0.447661i | \(-0.147743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0000 | −0.804181 | ||||||||
\(502\) | 12.7279 | + | 12.7279i | 0.568075 | + | 0.568075i | ||||
\(503\) | 24.6475 | + | 24.6475i | 1.09898 | + | 1.09898i | 0.994530 | + | 0.104448i | \(0.0333076\pi\) |
0.104448 | + | 0.994530i | \(0.466692\pi\) | |||||||
\(504\) | −7.74597 | −0.345033 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.48528 | + | 8.48528i | 0.376845 | + | 0.376845i | ||||
\(508\) | 5.65685 | − | 5.65685i | 0.250982 | − | 0.250982i | ||||
\(509\) | 15.4919 | 0.686668 | 0.343334 | − | 0.939213i | \(-0.388444\pi\) | ||||
0.343334 | + | 0.939213i | \(0.388444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0000 | −0.663561 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 20.7641 | + | 6.62200i | 0.916759 | + | 0.292368i | ||||
\(514\) | 12.0000i | 0.529297i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5.47723 | + | 5.47723i | 0.240655 | + | 0.240655i | ||||
\(519\) | 6.00000i | 0.263371i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 5.47723 | − | 5.47723i | 0.239732 | − | 0.239732i | ||||
\(523\) | 7.77817 | − | 7.77817i | 0.340116 | − | 0.340116i | −0.516295 | − | 0.856411i | \(-0.672689\pi\) |
0.856411 | + | 0.516295i | \(0.172689\pi\) | |||||||
\(524\) | − | 18.0000i | − | 0.786334i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.74597i | 0.337740i | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 8.00000i | − | 0.347826i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 23.2379i | − | 1.00844i | ||||||
\(532\) | 16.0838 | + | 5.12938i | 0.697322 | + | 0.222387i | ||||
\(533\) | 5.47723 | + | 5.47723i | 0.237245 | + | 0.237245i | ||||
\(534\) | −15.4919 | −0.670402 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.0000 | −0.561514 | ||||||||
\(537\) | −5.47723 | + | 5.47723i | −0.236360 | + | 0.236360i | ||||
\(538\) | 10.9545 | + | 10.9545i | 0.472280 | + | 0.472280i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | −17.6777 | − | 17.6777i | −0.759321 | − | 0.759321i | ||||
\(543\) | −10.9545 | − | 10.9545i | −0.470100 | − | 0.470100i | ||||
\(544\) | −3.87298 | −0.166053 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.87298i | 0.165748i | ||||||||
\(547\) | −19.7990 | − | 19.7990i | −0.846544 | − | 0.846544i | 0.143156 | − | 0.989700i | \(-0.454275\pi\) |
−0.989700 | + | 0.143156i | \(0.954275\pi\) | |||||||
\(548\) | −8.21584 | − | 8.21584i | −0.350963 | − | 0.350963i | ||||
\(549\) | 20.0000i | 0.853579i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0000 | + | 7.74597i | −0.639021 | + | 0.329989i | ||||
\(552\) | −2.73861 | + | 2.73861i | −0.116563 | + | 0.116563i | ||||
\(553\) | −42.4264 | + | 42.4264i | −1.80415 | + | 1.80415i | ||||
\(554\) | 23.2379 | 0.987284 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.0000 | 0.424094 | ||||||||
\(557\) | 27.3861 | − | 27.3861i | 1.16039 | − | 1.16039i | 0.175997 | − | 0.984391i | \(-0.443685\pi\) |
0.984391 | − | 0.175997i | \(-0.0563148\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.47723 | − | 5.47723i | 0.231043 | − | 0.231043i | ||||
\(563\) | 25.4558 | − | 25.4558i | 1.07284 | − | 1.07284i | 0.0757057 | − | 0.997130i | \(-0.475879\pi\) |
0.997130 | − | 0.0757057i | \(-0.0241210\pi\) | |||||||
\(564\) | 7.74597 | 0.326164 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 23.2379i | − | 0.976762i | ||||||
\(567\) | −2.73861 | + | 2.73861i | −0.115011 | + | 0.115011i | ||||
\(568\) | −5.47723 | − | 5.47723i | −0.229819 | − | 0.229819i | ||||
\(569\) | −30.9839 | −1.29891 | −0.649456 | − | 0.760399i | \(-0.725003\pi\) | ||||
−0.649456 | + | 0.760399i | \(0.725003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | −0.418487 | −0.209243 | − | 0.977864i | \(-0.567100\pi\) | ||||
−0.209243 | + | 0.977864i | \(0.567100\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.12132 | − | 2.12132i | 0.0886194 | − | 0.0886194i | ||||
\(574\) | − | 30.0000i | − | 1.25218i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.00000 | 0.0833333 | ||||||||
\(577\) | 13.6931 | − | 13.6931i | 0.570050 | − | 0.570050i | −0.362092 | − | 0.932142i | \(-0.617938\pi\) |
0.932142 | + | 0.362092i | \(0.117938\pi\) | |||||||
\(578\) | −1.41421 | + | 1.41421i | −0.0588235 | + | 0.0588235i | ||||
\(579\) | − | 26.0000i | − | 1.08052i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.0000 | 1.24461 | ||||||||
\(582\) | −5.65685 | − | 5.65685i | −0.234484 | − | 0.234484i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.87298 | 0.160265 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.0000 | 0.867502 | ||||||||
\(587\) | −5.47723 | + | 5.47723i | −0.226069 | + | 0.226069i | −0.811048 | − | 0.584979i | \(-0.801103\pi\) |
0.584979 | + | 0.811048i | \(0.301103\pi\) | |||||||
\(588\) | 5.65685 | − | 5.65685i | 0.233285 | − | 0.233285i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.2379i | 0.955879i | ||||||||
\(592\) | −1.41421 | − | 1.41421i | −0.0581238 | − | 0.0581238i | ||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.77817 | + | 7.77817i | 0.318339 | + | 0.318339i | ||||
\(598\) | −2.73861 | − | 2.73861i | −0.111990 | − | 0.111990i | ||||
\(599\) | 7.74597 | 0.316492 | 0.158246 | − | 0.987400i | \(-0.449416\pi\) | ||||
0.158246 | + | 0.987400i | \(0.449416\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 46.4758i | − | 1.89579i | −0.318587 | − | 0.947894i | \(-0.603208\pi\) | ||
0.318587 | − | 0.947894i | \(-0.396792\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.3848 | + | 18.3848i | −0.748686 | + | 0.748686i | ||||
\(604\) | −7.74597 | −0.315179 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.65685 | + | 5.65685i | 0.229605 | + | 0.229605i | 0.812527 | − | 0.582923i | \(-0.198091\pi\) |
−0.582923 | + | 0.812527i | \(0.698091\pi\) | |||||||
\(608\) | −4.15283 | − | 1.32440i | −0.168419 | − | 0.0537115i | ||||
\(609\) | 15.0000i | 0.607831i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.74597i | 0.313368i | ||||||||
\(612\) | −5.47723 | + | 5.47723i | −0.221404 | + | 0.221404i | ||||
\(613\) | −10.9545 | − | 10.9545i | −0.442446 | − | 0.442446i | 0.450387 | − | 0.892833i | \(-0.351286\pi\) |
−0.892833 | + | 0.450387i | \(0.851286\pi\) | |||||||
\(614\) | 28.0000i | 1.12999i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.9089 | + | 21.9089i | −0.882019 | + | 0.882019i | −0.993740 | − | 0.111720i | \(-0.964364\pi\) |
0.111720 | + | 0.993740i | \(0.464364\pi\) | |||||||
\(618\) | 2.82843 | − | 2.82843i | 0.113776 | − | 0.113776i | ||||
\(619\) | 10.0000i | 0.401934i | 0.979598 | + | 0.200967i | \(0.0644084\pi\) | ||||
−0.979598 | + | 0.200967i | \(0.935592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.3649i | 0.777087i | ||||||||
\(622\) | −10.6066 | − | 10.6066i | −0.425286 | − | 0.425286i | ||||
\(623\) | −42.4264 | + | 42.4264i | −1.69978 | + | 1.69978i | ||||
\(624\) | − | 1.00000i | − | 0.0400320i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 27.1109i | − | 1.08357i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.74597 | 0.308852 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 10.9545 | − | 10.9545i | 0.435745 | − | 0.435745i | ||||
\(633\) | 2.73861 | + | 2.73861i | 0.108850 | + | 0.108850i | ||||
\(634\) | 3.00000i | 0.119145i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.00000 | −0.356873 | ||||||||
\(637\) | 5.65685 | + | 5.65685i | 0.224133 | + | 0.224133i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.4919 | −0.612851 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 15.4919i | − | 0.611895i | −0.952048 | − | 0.305947i | \(-0.901027\pi\) | ||
0.952048 | − | 0.305947i | \(-0.0989731\pi\) | |||||||
\(642\) | 2.12132 | + | 2.12132i | 0.0837218 | + | 0.0837218i | ||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 15.0000i | 0.591083i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.0000 | − | 7.74597i | 0.590167 | − | 0.304761i | ||||
\(647\) | −24.6475 | + | 24.6475i | −0.968994 | + | 0.968994i | −0.999534 | − | 0.0305397i | \(-0.990277\pi\) |
0.0305397 | + | 0.999534i | \(0.490277\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.9545 | − | 10.9545i | 0.429009 | − | 0.429009i | ||||
\(653\) | 5.47723 | + | 5.47723i | 0.214340 | + | 0.214340i | 0.806108 | − | 0.591768i | \(-0.201570\pi\) |
−0.591768 | + | 0.806108i | \(0.701570\pi\) | |||||||
\(654\) | 11.6190 | 0.454337 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.74597i | 0.302429i | ||||||||
\(657\) | 5.47723 | − | 5.47723i | 0.213687 | − | 0.213687i | ||||
\(658\) | 21.2132 | − | 21.2132i | 0.826977 | − | 0.826977i | ||||
\(659\) | 19.3649 | 0.754350 | 0.377175 | − | 0.926142i | \(-0.376896\pi\) | ||||
0.377175 | + | 0.926142i | \(0.376896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.87298i | 0.150642i | 0.997159 | + | 0.0753208i | \(0.0239981\pi\) | ||||
−0.997159 | + | 0.0753208i | \(0.976002\pi\) | |||||||
\(662\) | −13.6931 | + | 13.6931i | −0.532196 | + | 0.532196i | ||||
\(663\) | 2.73861 | + | 2.73861i | 0.106359 | + | 0.106359i | ||||
\(664\) | −7.74597 | −0.300602 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | −10.6066 | − | 10.6066i | −0.410689 | − | 0.410689i | ||||
\(668\) | 12.7279 | − | 12.7279i | 0.492458 | − | 0.492458i | ||||
\(669\) | 14.0000i | 0.541271i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.73861 | + | 2.73861i | −0.105644 | + | 0.105644i | ||||
\(673\) | 31.1127 | − | 31.1127i | 1.19931 | − | 1.19931i | 0.224932 | − | 0.974374i | \(-0.427784\pi\) |
0.974374 | − | 0.224932i | \(-0.0722160\pi\) | |||||||
\(674\) | 8.00000i | 0.308148i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | 19.0919 | + | 19.0919i | 0.733761 | + | 0.733761i | 0.971363 | − | 0.237602i | \(-0.0763614\pi\) |
−0.237602 | + | 0.971363i | \(0.576361\pi\) | |||||||
\(678\) | −4.24264 | + | 4.24264i | −0.162938 | + | 0.162938i | ||||
\(679\) | −30.9839 | −1.18905 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | 0.114960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.4558 | − | 25.4558i | 0.974041 | − | 0.974041i | −0.0256307 | − | 0.999671i | \(-0.508159\pi\) |
0.999671 | + | 0.0256307i | \(0.00815939\pi\) | |||||||
\(684\) | −7.74597 | + | 4.00000i | −0.296174 | + | 0.152944i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 3.87298i | − | 0.147871i | ||||||
\(687\) | 14.1421 | + | 14.1421i | 0.539556 | + | 0.539556i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9.00000i | − | 0.342873i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.0000 | 1.52167 | 0.760836 | − | 0.648944i | \(-0.224789\pi\) | ||||
0.760836 | + | 0.648944i | \(0.224789\pi\) | |||||||
\(692\) | −4.24264 | − | 4.24264i | −0.161281 | − | 0.161281i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.4919 | 0.588066 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 3.87298i | − | 0.146805i | ||||||
\(697\) | −21.2132 | − | 21.2132i | −0.803507 | − | 0.803507i | ||||
\(698\) | −11.3137 | + | 11.3137i | −0.428230 | + | 0.428230i | ||||
\(699\) | −15.4919 | −0.585959 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | −3.53553 | − | 3.53553i | −0.133440 | − | 0.133440i | ||||
\(703\) | 8.30565 | + | 2.64880i | 0.313254 | + | 0.0999013i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34.8569i | 1.31185i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.21584 | − | 8.21584i | −0.308770 | − | 0.308770i | ||||
\(709\) | − | 44.0000i | − | 1.65245i | −0.563337 | − | 0.826227i | \(-0.690483\pi\) | ||
0.563337 | − | 0.826227i | \(-0.309517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 30.9839i | − | 1.16199i | ||||||
\(712\) | 10.9545 | − | 10.9545i | 0.410535 | − | 0.410535i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | − | 15.0000i | − | 0.561361i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 7.74597i | − | 0.289480i | ||||||
\(717\) | −14.8492 | − | 14.8492i | −0.554555 | − | 0.554555i | ||||
\(718\) | −10.6066 | + | 10.6066i | −0.395835 | + | 0.395835i | ||||
\(719\) | 15.0000i | 0.559406i | 0.960087 | + | 0.279703i | \(0.0902359\pi\) | ||||
−0.960087 | + | 0.279703i | \(0.909764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 15.4919i | − | 0.576950i | ||||||
\(722\) | 18.7326 | − | 3.17628i | 0.697156 | − | 0.118209i | ||||
\(723\) | −10.9545 | − | 10.9545i | −0.407400 | − | 0.407400i | ||||
\(724\) | 15.4919 | 0.575753 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.0000 | −0.408248 | ||||||||
\(727\) | 8.21584 | − | 8.21584i | 0.304709 | − | 0.304709i | −0.538144 | − | 0.842853i | \(-0.680874\pi\) |
0.842853 | + | 0.538144i | \(0.180874\pi\) | |||||||
\(728\) | −2.73861 | − | 2.73861i | −0.101500 | − | 0.101500i | ||||
\(729\) | 13.0000i | 0.481481i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 7.07107 | + | 7.07107i | 0.261354 | + | 0.261354i | ||||
\(733\) | −16.4317 | − | 16.4317i | −0.606918 | − | 0.606918i | 0.335222 | − | 0.942139i | \(-0.391189\pi\) |
−0.942139 | + | 0.335222i | \(0.891189\pi\) | |||||||
\(734\) | −7.74597 | −0.285909 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.87298i | − | 0.142760i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 10.9545 | + | 10.9545i | 0.403239 | + | 0.403239i | ||||
\(739\) | 26.0000i | 0.956425i | 0.878244 | + | 0.478213i | \(0.158715\pi\) | ||||
−0.878244 | + | 0.478213i | \(0.841285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00000 | + | 3.87298i | 0.0734718 | + | 0.142278i | ||||
\(742\) | −24.6475 | + | 24.6475i | −0.904839 | + | 0.904839i | ||||
\(743\) | −16.9706 | + | 16.9706i | −0.622590 | + | 0.622590i | −0.946193 | − | 0.323603i | \(-0.895106\pi\) |
0.323603 | + | 0.946193i | \(0.395106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 31.0000 | 1.13499 | ||||||||
\(747\) | −10.9545 | + | 10.9545i | −0.400802 | + | 0.400802i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.6190 | 0.424547 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 38.7298i | − | 1.41327i | −0.707577 | − | 0.706636i | \(-0.750212\pi\) | ||
0.707577 | − | 0.706636i | \(-0.249788\pi\) | |||||||
\(752\) | −5.47723 | + | 5.47723i | −0.199734 | + | 0.199734i | ||||
\(753\) | 12.7279 | − | 12.7279i | 0.463831 | − | 0.463831i | ||||
\(754\) | 3.87298 | 0.141046 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19.3649i | 0.704295i | ||||||||
\(757\) | −21.9089 | + | 21.9089i | −0.796293 | + | 0.796293i | −0.982509 | − | 0.186216i | \(-0.940378\pi\) |
0.186216 | + | 0.982509i | \(0.440378\pi\) | |||||||
\(758\) | −13.6931 | − | 13.6931i | −0.497354 | − | 0.497354i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | −0.543750 | −0.271875 | − | 0.962333i | \(-0.587644\pi\) | ||||
−0.271875 | + | 0.962333i | \(0.587644\pi\) | |||||||
\(762\) | −5.65685 | − | 5.65685i | −0.204926 | − | 0.204926i | ||||
\(763\) | 31.8198 | − | 31.8198i | 1.15195 | − | 1.15195i | ||||
\(764\) | 3.00000i | 0.108536i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | 8.21584 | − | 8.21584i | 0.296657 | − | 0.296657i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 5.00000i | − | 0.180305i | −0.995928 | − | 0.0901523i | \(-0.971265\pi\) | ||
0.995928 | − | 0.0901523i | \(-0.0287354\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | 18.3848 | + | 18.3848i | 0.661683 | + | 0.661683i | ||||
\(773\) | 6.36396 | − | 6.36396i | 0.228896 | − | 0.228896i | −0.583336 | − | 0.812231i | \(-0.698253\pi\) |
0.812231 | + | 0.583336i | \(0.198253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.00000 | 0.287183 | ||||||||
\(777\) | 5.47723 | − | 5.47723i | 0.196494 | − | 0.196494i | ||||
\(778\) | −16.9706 | + | 16.9706i | −0.608424 | + | 0.608424i | ||||
\(779\) | −15.4919 | − | 30.0000i | −0.555056 | − | 1.07486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 10.6066 | + | 10.6066i | 0.379291 | + | 0.379291i | ||||
\(783\) | −13.6931 | − | 13.6931i | −0.489350 | − | 0.489350i | ||||
\(784\) | 8.00000i | 0.285714i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.0000 | −0.642039 | ||||||||
\(787\) | −16.2635 | − | 16.2635i | −0.579730 | − | 0.579730i | 0.355099 | − | 0.934829i | \(-0.384447\pi\) |
−0.934829 | + | 0.355099i | \(0.884447\pi\) | |||||||
\(788\) | −16.4317 | − | 16.4317i | −0.585354 | − | 0.585354i | ||||
\(789\) | 7.74597 | 0.275764 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.2379i | 0.826245i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.07107 | + | 7.07107i | −0.251101 | + | 0.251101i | ||||
\(794\) | 23.2379 | 0.824682 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0000 | −0.389885 | ||||||||
\(797\) | −23.3345 | − | 23.3345i | −0.826551 | − | 0.826551i | 0.160487 | − | 0.987038i | \(-0.448694\pi\) |
−0.987038 | + | 0.160487i | \(0.948694\pi\) | |||||||
\(798\) | 5.12938 | − | 16.0838i | 0.181578 | − | 0.569361i | ||||
\(799\) | − | 30.0000i | − | 1.06132i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 30.9839i | − | 1.09476i | ||||||
\(802\) | 5.47723 | − | 5.47723i | 0.193408 | − | 0.193408i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.0000i | 0.458475i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.9545 | − | 10.9545i | 0.385615 | − | 0.385615i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.0000i | 0.738321i | 0.929366 | + | 0.369160i | \(0.120355\pi\) | ||||
−0.929366 | + | 0.369160i | \(0.879645\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 34.8569i | − | 1.22399i | −0.790862 | − | 0.611995i | \(-0.790367\pi\) | ||
0.790862 | − | 0.611995i | \(-0.209633\pi\) | |||||||
\(812\) | −10.6066 | − | 10.6066i | −0.372219 | − | 0.372219i | ||||
\(813\) | −17.6777 | + | 17.6777i | −0.619983 | + | 0.619983i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.87298i | 0.135582i | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 10.9545 | + | 10.9545i | 0.383013 | + | 0.383013i | ||||
\(819\) | −7.74597 | −0.270666 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | −8.21584 | + | 8.21584i | −0.286560 | + | 0.286560i | ||||
\(823\) | −35.6020 | − | 35.6020i | −1.24101 | − | 1.24101i | −0.959584 | − | 0.281423i | \(-0.909194\pi\) |
−0.281423 | − | 0.959584i | \(-0.590806\pi\) | |||||||
\(824\) | 4.00000i | 0.139347i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −45.0000 | −1.56575 | ||||||||
\(827\) | −2.12132 | − | 2.12132i | −0.0737655 | − | 0.0737655i | 0.669261 | − | 0.743027i | \(-0.266611\pi\) |
−0.743027 | + | 0.669261i | \(0.766611\pi\) | |||||||
\(828\) | −5.47723 | − | 5.47723i | −0.190347 | − | 0.190347i | ||||
\(829\) | 27.1109 | 0.941600 | 0.470800 | − | 0.882240i | \(-0.343965\pi\) | ||||
0.470800 | + | 0.882240i | \(0.343965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 23.2379i | − | 0.806114i | ||||||
\(832\) | 0.707107 | + | 0.707107i | 0.0245145 | + | 0.0245145i | ||||
\(833\) | −21.9089 | − | 21.9089i | −0.759098 | − | 0.759098i | ||||
\(834\) | − | 10.0000i | − | 0.346272i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.9706 | + | 16.9706i | −0.586238 | + | 0.586238i | ||||
\(839\) | 7.74597 | 0.267420 | 0.133710 | − | 0.991020i | \(-0.457311\pi\) | ||||
0.133710 | + | 0.991020i | \(0.457311\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0000 | −0.482759 | ||||||||
\(842\) | −19.1703 | + | 19.1703i | −0.660652 | + | 0.660652i | ||||
\(843\) | −5.47723 | − | 5.47723i | −0.188646 | − | 0.188646i | ||||
\(844\) | −3.87298 | −0.133314 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.4919i | 0.532624i | ||||||||
\(847\) | −30.1247 | + | 30.1247i | −1.03510 | + | 1.03510i | ||||
\(848\) | 6.36396 | − | 6.36396i | 0.218539 | − | 0.218539i | ||||
\(849\) | −23.2379 | −0.797523 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.74597i | 0.265528i | ||||||||
\(852\) | −5.47723 | + | 5.47723i | −0.187647 | + | 0.187647i | ||||
\(853\) | 38.3406 | + | 38.3406i | 1.31276 | + | 1.31276i | 0.919376 | + | 0.393381i | \(0.128695\pi\) |
0.393381 | + | 0.919376i | \(0.371305\pi\) | |||||||
\(854\) | 38.7298 | 1.32531 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | −33.9411 | − | 33.9411i | −1.15941 | − | 1.15941i | −0.984603 | − | 0.174803i | \(-0.944071\pi\) |
−0.174803 | − | 0.984603i | \(-0.555929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000i | 0.136478i | 0.997669 | + | 0.0682391i | \(0.0217381\pi\) | ||||
−0.997669 | + | 0.0682391i | \(0.978262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.0000 | −1.02240 | ||||||||
\(862\) | −27.3861 | + | 27.3861i | −0.932775 | + | 0.932775i | ||||
\(863\) | 4.24264 | − | 4.24264i | 0.144421 | − | 0.144421i | −0.631199 | − | 0.775621i | \(-0.717437\pi\) |
0.775621 | + | 0.631199i | \(0.217437\pi\) | |||||||
\(864\) | − | 5.00000i | − | 0.170103i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.0000 | −0.543702 | ||||||||
\(867\) | 1.41421 | + | 1.41421i | 0.0480292 | + | 0.0480292i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.0000 | −0.440488 | ||||||||
\(872\) | −8.21584 | + | 8.21584i | −0.278223 | + | 0.278223i | ||||
\(873\) | 11.3137 | − | 11.3137i | 0.382911 | − | 0.382911i | ||||
\(874\) | 7.74597 | + | 15.0000i | 0.262011 | + | 0.507383i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 3.87298i | − | 0.130856i | ||||||
\(877\) | 26.1630 | + | 26.1630i | 0.883460 | + | 0.883460i | 0.993885 | − | 0.110424i | \(-0.0352210\pi\) |
−0.110424 | + | 0.993885i | \(0.535221\pi\) | |||||||
\(878\) | 16.4317 | + | 16.4317i | 0.554542 | + | 0.554542i | ||||
\(879\) | − | 21.0000i | − | 0.708312i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 11.3137 | + | 11.3137i | 0.380952 | + | 0.380952i | ||||
\(883\) | 10.9545 | + | 10.9545i | 0.368647 | + | 0.368647i | 0.866983 | − | 0.498337i | \(-0.166056\pi\) |
−0.498337 | + | 0.866983i | \(0.666056\pi\) | |||||||
\(884\) | −3.87298 | −0.130263 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.4919i | 0.520462i | ||||||||
\(887\) | −29.6985 | − | 29.6985i | −0.997178 | − | 0.997178i | 0.00281850 | − | 0.999996i | \(-0.499103\pi\) |
−0.999996 | + | 0.00281850i | \(0.999103\pi\) | |||||||
\(888\) | −1.41421 | + | 1.41421i | −0.0474579 | + | 0.0474579i | ||||
\(889\) | −30.9839 | −1.03917 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.89949 | − | 9.89949i | −0.331460 | − | 0.331460i | ||||
\(893\) | 10.2588 | − | 32.1677i | 0.343296 | − | 1.07645i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 3.87298i | − | 0.129387i | ||||||
\(897\) | −2.73861 | + | 2.73861i | −0.0914396 | + | 0.0914396i | ||||
\(898\) | −16.4317 | − | 16.4317i | −0.548332 | − | 0.548332i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.8569i | 1.16125i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 6.00000i | − | 0.199557i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.74597i | 0.257343i | ||||||||
\(907\) | −12.0208 | − | 12.0208i | −0.399145 | − | 0.399145i | 0.478787 | − | 0.877931i | \(-0.341077\pi\) |
−0.877931 | + | 0.478787i | \(0.841077\pi\) | |||||||
\(908\) | −2.12132 | + | 2.12132i | −0.0703985 | + | 0.0703985i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.2379i | 0.769906i | 0.922936 | + | 0.384953i | \(0.125782\pi\) | ||||
−0.922936 | + | 0.384953i | \(0.874218\pi\) | |||||||
\(912\) | −1.32440 | + | 4.15283i | −0.0438552 | + | 0.137514i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 34.8569 | 1.15296 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.0000 | −0.660819 | ||||||||
\(917\) | −49.2950 | + | 49.2950i | −1.62787 | + | 1.62787i | ||||
\(918\) | 13.6931 | + | 13.6931i | 0.451938 | + | 0.451938i | ||||
\(919\) | − | 1.00000i | − | 0.0329870i | −0.999864 | − | 0.0164935i | \(-0.994750\pi\) | ||
0.999864 | − | 0.0164935i | \(-0.00525028\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.0000 | 0.922631 | ||||||||
\(922\) | −12.7279 | − | 12.7279i | −0.419172 | − | 0.419172i | ||||
\(923\) | −5.47723 | − | 5.47723i | −0.180285 | − | 0.180285i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.74597i | 0.254548i | ||||||||
\(927\) | 5.65685 | + | 5.65685i | 0.185795 | + | 0.185795i | ||||
\(928\) | 2.73861 | + | 2.73861i | 0.0898994 | + | 0.0898994i | ||||
\(929\) | − | 39.0000i | − | 1.27955i | −0.768563 | − | 0.639774i | \(-0.779028\pi\) | ||
0.768563 | − | 0.639774i | \(-0.220972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.0000 | − | 30.9839i | −0.524379 | − | 1.01546i | ||||
\(932\) | 10.9545 | − | 10.9545i | 0.358825 | − | 0.358825i | ||||
\(933\) | −10.6066 | + | 10.6066i | −0.347245 | + | 0.347245i | ||||
\(934\) | −23.2379 | −0.760367 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | −19.1703 | + | 19.1703i | −0.626266 | + | 0.626266i | −0.947126 | − | 0.320860i | \(-0.896028\pi\) |
0.320860 | + | 0.947126i | \(0.396028\pi\) | |||||||
\(938\) | 35.6020 | + | 35.6020i | 1.16245 | + | 1.16245i | ||||
\(939\) | −27.1109 | −0.884730 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.1109i | 0.883790i | 0.897067 | + | 0.441895i | \(0.145694\pi\) | ||||
−0.897067 | + | 0.441895i | \(0.854306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.2132 | − | 21.2132i | 0.690797 | − | 0.690797i | ||||
\(944\) | 11.6190 | 0.378165 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.3861 | − | 27.3861i | 0.889930 | − | 0.889930i | −0.104586 | − | 0.994516i | \(-0.533352\pi\) |
0.994516 | + | 0.104586i | \(0.0333518\pi\) | |||||||
\(948\) | −10.9545 | − | 10.9545i | −0.355784 | − | 0.355784i | ||||
\(949\) | 3.87298 | 0.125722 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.00000 | 0.0972817 | ||||||||
\(952\) | 10.6066 | + | 10.6066i | 0.343762 | + | 0.343762i | ||||
\(953\) | 25.4558 | − | 25.4558i | 0.824596 | − | 0.824596i | −0.162168 | − | 0.986763i | \(-0.551849\pi\) |
0.986763 | + | 0.162168i | \(0.0518485\pi\) | |||||||
\(954\) | − | 18.0000i | − | 0.582772i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21.0000 | 0.679189 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.0000i | 1.45313i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | −1.41421 | − | 1.41421i | −0.0455961 | − | 0.0455961i | ||||
\(963\) | −4.24264 | + | 4.24264i | −0.136717 | + | 0.136717i | ||||
\(964\) | 15.4919 | 0.498962 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.0000 | 0.482617 | ||||||||
\(967\) | −38.3406 | + | 38.3406i | −1.23295 | + | 1.23295i | −0.270124 | + | 0.962825i | \(0.587065\pi\) |
−0.962825 | + | 0.270124i | \(0.912935\pi\) | |||||||
\(968\) | 7.77817 | − | 7.77817i | 0.250000 | − | 0.250000i | ||||
\(969\) | −7.74597 | − | 15.0000i | −0.248836 | − | 0.481869i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.74597i | 0.248580i | 0.992246 | + | 0.124290i | \(0.0396653\pi\) | ||||
−0.992246 | + | 0.124290i | \(0.960335\pi\) | |||||||
\(972\) | −11.3137 | − | 11.3137i | −0.362887 | − | 0.362887i | ||||
\(973\) | −27.3861 | − | 27.3861i | −0.877959 | − | 0.877959i | ||||
\(974\) | 38.0000i | 1.21760i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | 33.9411 | + | 33.9411i | 1.08587 | + | 1.08587i | 0.995949 | + | 0.0899242i | \(0.0286625\pi\) |
0.0899242 | + | 0.995949i | \(0.471338\pi\) | |||||||
\(978\) | −10.9545 | − | 10.9545i | −0.350285 | − | 0.350285i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.2379i | 0.741929i | ||||||||
\(982\) | −29.6985 | − | 29.6985i | −0.947717 | − | 0.947717i | ||||
\(983\) | −25.4558 | + | 25.4558i | −0.811915 | + | 0.811915i | −0.984921 | − | 0.173006i | \(-0.944652\pi\) |
0.173006 | + | 0.984921i | \(0.444652\pi\) | |||||||
\(984\) | 7.74597 | 0.246932 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15.0000 | −0.477697 | ||||||||
\(987\) | −21.2132 | − | 21.2132i | −0.675224 | − | 0.675224i | ||||
\(988\) | −4.15283 | − | 1.32440i | −0.132119 | − | 0.0421348i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.4919i | 0.492117i | 0.969255 | + | 0.246059i | \(0.0791356\pi\) | ||||
−0.969255 | + | 0.246059i | \(0.920864\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.6931 | + | 13.6931i | 0.434536 | + | 0.434536i | ||||
\(994\) | 30.0000i | 0.951542i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.74597i | 0.245440i | ||||||||
\(997\) | −32.8634 | + | 32.8634i | −1.04079 | + | 1.04079i | −0.0416610 | + | 0.999132i | \(0.513265\pi\) |
−0.999132 | + | 0.0416610i | \(0.986735\pi\) | |||||||
\(998\) | 14.1421 | − | 14.1421i | 0.447661 | − | 0.447661i | ||||
\(999\) | 10.0000i | 0.316386i |
(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 | 950.2.f.b.493.4 | yes | 8 | |
5.2 | odd | 4 | inner | 950.2.f.b.607.2 | yes | 8 | |
5.3 | odd | 4 | inner | 950.2.f.b.607.3 | yes | 8 | |
5.4 | even | 2 | inner | 950.2.f.b.493.1 | ✓ | 8 | |
19.18 | odd | 2 | inner | 950.2.f.b.493.2 | yes | 8 | |
95.18 | even | 4 | inner | 950.2.f.b.607.1 | yes | 8 | |
95.37 | even | 4 | inner | 950.2.f.b.607.4 | yes | 8 | |
95.94 | odd | 2 | inner | 950.2.f.b.493.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.f.b.493.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
950.2.f.b.493.2 | yes | 8 | 19.18 | odd | 2 | inner | |
950.2.f.b.493.3 | yes | 8 | 95.94 | odd | 2 | inner | |
950.2.f.b.493.4 | yes | 8 | 1.1 | even | 1 | trivial | |
950.2.f.b.607.1 | yes | 8 | 95.18 | even | 4 | inner | |
950.2.f.b.607.2 | yes | 8 | 5.2 | odd | 4 | inner | |
950.2.f.b.607.3 | yes | 8 | 5.3 | odd | 4 | inner | |
950.2.f.b.607.4 | yes | 8 | 95.37 | even | 4 | inner |