Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2300,2,Mod(1057,2300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2300.1057");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2300.i (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: | \(18.3655924649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.1 | ||
Root | \(-0.581861 + 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2300.1057 |
Dual form | 2300.2.i.b.1793.1 |
$q$-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 \(\left(\mathbb{Z}/2300\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(1151\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.87083 | + | 1.87083i | −1.08012 | + | 1.08012i | −0.0836263 | + | 0.996497i | \(0.526650\pi\) |
−0.996497 | + | 0.0836263i | \(0.973350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | + | 1.41421i | −0.534522 | + | 0.534522i | −0.921915 | − | 0.387392i | \(-0.873376\pi\) |
0.387392 | + | 0.921915i | \(0.373376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 4.00000i | − | 1.33333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.29150i | − | 1.59545i | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||
0.603023 | − | 0.797724i | \(-0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.87083 | + | 1.87083i | −0.518875 | + | 0.518875i | −0.917231 | − | 0.398356i | \(-0.869581\pi\) |
0.398356 | + | 0.917231i | \(0.369581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.29150 | −1.21395 | −0.606977 | − | 0.794719i | \(-0.707618\pi\) | ||||
−0.606977 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.29150i | − | 1.15470i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.69926 | + | 0.957598i | 0.979863 | + | 0.199673i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.87083 | + | 1.87083i | 0.360041 | + | 0.360041i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000i | 0.185695i | 0.995680 | + | 0.0928477i | \(0.0295970\pi\) | ||||
−0.995680 | + | 0.0928477i | \(0.970403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.89949 | + | 9.89949i | 1.72328 | + | 1.72328i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.07107 | − | 7.07107i | 1.16248 | − | 1.16248i | 0.178545 | − | 0.983932i | \(-0.442861\pi\) |
0.983932 | − | 0.178545i | \(-0.0571389\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 7.00000i | − | 1.12090i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.00000 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.24264 | − | 4.24264i | −0.646997 | − | 0.646997i | 0.305269 | − | 0.952266i | \(-0.401253\pi\) |
−0.952266 | + | 0.305269i | \(0.901253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.87083 | + | 1.87083i | 0.272888 | + | 0.272888i | 0.830262 | − | 0.557373i | \(-0.188191\pi\) |
−0.557373 | + | 0.830262i | \(0.688191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000i | 0.428571i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.82843 | − | 2.82843i | −0.388514 | − | 0.388514i | 0.485643 | − | 0.874157i | \(-0.338586\pi\) |
−0.874157 | + | 0.485643i | \(0.838586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.89949 | − | 9.89949i | 1.31122 | − | 1.31122i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.29150i | − | 0.677507i | −0.940875 | − | 0.338754i | \(-0.889995\pi\) | ||
0.940875 | − | 0.338754i | \(-0.110005\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.65685 | + | 5.65685i | 0.712697 | + | 0.712697i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.41421 | − | 1.41421i | 0.172774 | − | 0.172774i | −0.615423 | − | 0.788197i | \(-0.711015\pi\) |
0.788197 | + | 0.615423i | \(0.211015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.5830 | + | 7.00000i | −1.27404 | + | 0.842701i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | −1.06810 | −0.534052 | − | 0.845452i | \(-0.679331\pi\) | ||||
−0.534052 | + | 0.845452i | \(0.679331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.35414 | + | 9.35414i | −1.09482 | + | 1.09482i | −0.0998135 | + | 0.995006i | \(0.531825\pi\) |
−0.995006 | + | 0.0998135i | \(0.968175\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.48331 | + | 7.48331i | 0.852803 | + | 0.852803i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.29150 | −0.595341 | −0.297670 | − | 0.954669i | \(-0.596210\pi\) | ||||
−0.297670 | + | 0.954669i | \(0.596210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.48528 | + | 8.48528i | 0.931381 | + | 0.931381i | 0.997792 | − | 0.0664117i | \(-0.0211551\pi\) |
−0.0664117 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.87083 | − | 1.87083i | −0.200574 | − | 0.200574i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8745 | 1.68269 | 0.841347 | − | 0.540495i | \(-0.181763\pi\) | ||||
0.841347 | + | 0.540495i | \(0.181763\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.29150i | − | 0.554700i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.61249 | + | 5.61249i | −0.581988 | + | 0.581988i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.41421 | − | 1.41421i | 0.143592 | − | 0.143592i | −0.631657 | − | 0.775248i | \(-0.717625\pi\) |
0.775248 | + | 0.631657i | \(0.217625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −21.1660 | −2.12726 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0000 | 1.39305 | 0.696526 | − | 0.717532i | \(-0.254728\pi\) | ||||
0.696526 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.65685 | + | 5.65685i | 0.557386 | + | 0.557386i | 0.928562 | − | 0.371176i | \(-0.121045\pi\) |
−0.371176 | + | 0.928562i | \(0.621045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.24264 | + | 4.24264i | −0.410152 | + | 0.410152i | −0.881791 | − | 0.471640i | \(-0.843662\pi\) |
0.471640 | + | 0.881791i | \(0.343662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8745 | 1.52050 | 0.760251 | − | 0.649629i | \(-0.225076\pi\) | ||||
0.760251 | + | 0.649629i | \(0.225076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.4575i | 2.51124i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24264 | + | 4.24264i | 0.399114 | + | 0.399114i | 0.877920 | − | 0.478806i | \(-0.158930\pi\) |
−0.478806 | + | 0.877920i | \(0.658930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.48331 | + | 7.48331i | 0.691833 | + | 0.691833i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.0000 | −1.54545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.8375 | + | 16.8375i | −1.51818 | + | 1.51818i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.61249 | + | 5.61249i | 0.498028 | + | 0.498028i | 0.910824 | − | 0.412796i | \(-0.135448\pi\) |
−0.412796 | + | 0.910824i | \(0.635448\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.8745 | 1.39767 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00000 | −0.0873704 | −0.0436852 | − | 0.999045i | \(-0.513910\pi\) | ||||
−0.0436852 | + | 0.999045i | \(0.513910\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.48331 | − | 7.48331i | 0.648886 | − | 0.648886i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.48528 | + | 8.48528i | −0.724947 | + | 0.724947i | −0.969608 | − | 0.244662i | \(-0.921323\pi\) |
0.244662 | + | 0.969608i | \(0.421323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000i | 0.424094i | 0.977259 | + | 0.212047i | \(0.0680131\pi\) | ||||
−0.977259 | + | 0.212047i | \(0.931987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.00000 | −0.589506 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.89949 | + | 9.89949i | 0.827837 | + | 0.827837i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.61249 | − | 5.61249i | −0.462910 | − | 0.462910i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5830 | 0.866994 | 0.433497 | − | 0.901155i | \(-0.357280\pi\) | ||||
0.433497 | + | 0.901155i | \(0.357280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.0000 | −1.87171 | −0.935857 | − | 0.352381i | \(-0.885372\pi\) | ||||
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7279 | − | 12.7279i | 1.01580 | − | 1.01580i | 0.0159256 | − | 0.999873i | \(-0.494931\pi\) |
0.999873 | − | 0.0159256i | \(-0.00506949\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.5830 | 0.839287 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | + | 5.29150i | −0.630488 | + | 0.417029i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.35414 | + | 9.35414i | −0.732673 | + | 0.732673i | −0.971149 | − | 0.238475i | \(-0.923352\pi\) |
0.238475 | + | 0.971149i | \(0.423352\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.2250 | − | 11.2250i | −0.868614 | − | 0.868614i | 0.123705 | − | 0.992319i | \(-0.460522\pi\) |
−0.992319 | + | 0.123705i | \(0.960522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000i | 0.461538i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.1660i | 1.61861i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.48331 | + | 7.48331i | −0.568946 | + | 0.568946i | −0.931833 | − | 0.362887i | \(-0.881791\pi\) |
0.362887 | + | 0.931833i | \(0.381791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5.00000i | − | 0.373718i | −0.982387 | − | 0.186859i | \(-0.940169\pi\) | ||
0.982387 | − | 0.186859i | \(-0.0598307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.29150i | 0.393314i | 0.980472 | + | 0.196657i | \(0.0630086\pi\) | ||||
−0.980472 | + | 0.196657i | \(0.936991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.89949 | + | 9.89949i | 0.731792 | + | 0.731792i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.29150 | −0.384900 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5830i | 0.765759i | 0.923798 | + | 0.382880i | \(0.125068\pi\) | ||||
−0.923798 | + | 0.382880i | \(0.874932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.35414 | − | 9.35414i | 0.673326 | − | 0.673326i | −0.285155 | − | 0.958481i | \(-0.592045\pi\) |
0.958481 | + | 0.285155i | \(0.0920452\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.35414 | + | 9.35414i | 0.666455 | + | 0.666455i | 0.956894 | − | 0.290439i | \(-0.0938012\pi\) |
−0.290439 | + | 0.956894i | \(0.593801\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.29150 | 0.375105 | 0.187552 | − | 0.982255i | \(-0.439945\pi\) | ||||
0.187552 | + | 0.982255i | \(0.439945\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.29150i | 0.373234i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.41421 | − | 1.41421i | −0.0992583 | − | 0.0992583i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.83039 | − | 18.7970i | 0.266231 | − | 1.30648i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.0000i | 1.93680i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.8375 | − | 16.8375i | 1.15368 | − | 1.15368i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.24264 | + | 4.24264i | −0.288009 | + | 0.288009i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 35.0000i | − | 2.36508i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.2250 | − | 11.2250i | 0.751680 | − | 0.751680i | −0.223113 | − | 0.974793i | \(-0.571622\pi\) |
0.974793 | + | 0.223113i | \(0.0716219\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.7279 | − | 12.7279i | 0.844782 | − | 0.844782i | −0.144695 | − | 0.989476i | \(-0.546220\pi\) |
0.989476 | + | 0.144695i | \(0.0462199\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.4575 | 1.74836 | 0.874181 | − | 0.485601i | \(-0.161399\pi\) | ||||
0.874181 | + | 0.485601i | \(0.161399\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.0000 | −1.84226 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.87083 | − | 1.87083i | 0.122562 | − | 0.122562i | −0.643165 | − | 0.765727i | \(-0.722379\pi\) |
0.765727 | + | 0.643165i | \(0.222379\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.89949 | − | 9.89949i | 0.643041 | − | 0.643041i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.00000i | − | 0.0646846i | −0.999477 | − | 0.0323423i | \(-0.989703\pi\) | ||
0.999477 | − | 0.0323423i | \(-0.0102967\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 21.1660i | − | 1.36342i | −0.731621 | − | 0.681711i | \(-0.761236\pi\) | ||
0.731621 | − | 0.681711i | \(-0.238764\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.9666 | + | 14.9666i | −0.960110 | + | 0.960110i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.89949 | − | 9.89949i | 0.629890 | − | 0.629890i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.7490 | −2.01201 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.1660i | − | 1.33599i | −0.744167 | − | 0.667993i | \(-0.767153\pi\) | ||
0.744167 | − | 0.667993i | \(-0.232847\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.06713 | − | 24.8661i | 0.318568 | − | 1.56332i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.8375 | + | 16.8375i | 1.05029 | + | 1.05029i | 0.998667 | + | 0.0516253i | \(0.0164401\pi\) |
0.0516253 | + | 0.998667i | \(0.483560\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0000i | 1.24274i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | 0.247594 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.3848 | − | 18.3848i | −1.13365 | − | 1.13365i | −0.989565 | − | 0.144089i | \(-0.953975\pi\) |
−0.144089 | − | 0.989565i | \(-0.546025\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −29.6985 | + | 29.6985i | −1.81752 | + | 1.81752i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.00000i | − | 0.182913i | −0.995809 | − | 0.0914566i | \(-0.970848\pi\) | ||
0.995809 | − | 0.0914566i | \(-0.0291523\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.89949 | + | 9.89949i | 0.599145 | + | 0.599145i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.61249 | + | 5.61249i | 0.337222 | + | 0.337222i | 0.855321 | − | 0.518099i | \(-0.173360\pi\) |
−0.518099 | + | 0.855321i | \(0.673360\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 12.0000i | − | 0.718421i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8745i | 0.946994i | 0.880795 | + | 0.473497i | \(0.157008\pi\) | ||||
−0.880795 | + | 0.473497i | \(0.842992\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.9706 | + | 16.9706i | 1.00880 | + | 1.00880i | 0.999961 | + | 0.00883427i | \(0.00281207\pi\) |
0.00883427 | + | 0.999961i | \(0.497188\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.7279 | + | 12.7279i | −0.751305 | + | 0.751305i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.29150i | 0.310193i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.3137 | − | 11.3137i | −0.660954 | − | 0.660954i | 0.294651 | − | 0.955605i | \(-0.404797\pi\) |
−0.955605 | + | 0.294651i | \(0.904797\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.89949 | − | 9.89949i | 0.574427 | − | 0.574427i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5830 | + | 7.00000i | −0.612031 | + | 0.404820i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.1916 | + | 26.1916i | −1.50467 | + | 1.50467i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.2250 | + | 11.2250i | 0.640643 | + | 0.640643i | 0.950714 | − | 0.310071i | \(-0.100353\pi\) |
−0.310071 | + | 0.950714i | \(0.600353\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.1660 | −1.20409 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.0000 | 1.19080 | 0.595400 | − | 0.803429i | \(-0.296993\pi\) | ||||
0.595400 | + | 0.803429i | \(0.296993\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.1421 | − | 14.1421i | −0.799361 | − | 0.799361i | 0.183634 | − | 0.982995i | \(-0.441214\pi\) |
−0.982995 | + | 0.183634i | \(0.941214\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.4499 | − | 22.4499i | −1.26091 | − | 1.26091i | −0.950650 | − | 0.310264i | \(-0.899583\pi\) |
−0.310264 | − | 0.950650i | \(-0.600417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.29150 | 0.296267 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 15.8745i | − | 0.886029i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.6985 | + | 29.6985i | −1.64233 | + | 1.64233i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.29150 | −0.291730 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.0000 | 1.59398 | 0.796992 | − | 0.603990i | \(-0.206423\pi\) | ||||
0.796992 | + | 0.603990i | \(0.206423\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −28.2843 | − | 28.2843i | −1.54997 | − | 1.54997i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.41421 | − | 1.41421i | 0.0770371 | − | 0.0770371i | −0.667538 | − | 0.744575i | \(-0.732652\pi\) |
0.744575 | + | 0.667538i | \(0.232652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.8745 | −0.862185 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 15.8745i | − | 0.859653i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.1421 | − | 14.1421i | −0.763604 | − | 0.763604i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.2250 | − | 11.2250i | −0.602588 | − | 0.602588i | 0.338411 | − | 0.940999i | \(-0.390111\pi\) |
−0.940999 | + | 0.338411i | \(0.890111\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 23.0000i | − | 1.23116i | −0.788074 | − | 0.615581i | \(-0.788921\pi\) | ||
0.788074 | − | 0.615581i | \(-0.211079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.00000 | −0.373632 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.8375 | + | 16.8375i | −0.896167 | + | 0.896167i | −0.995095 | − | 0.0989272i | \(-0.968459\pi\) |
0.0989272 | + | 0.995095i | \(0.468459\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.8745 | 0.837824 | 0.418912 | − | 0.908027i | \(-0.362411\pi\) | ||||
0.418912 | + | 0.908027i | \(0.362411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | 0.473684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.8041 | − | 31.8041i | 1.66928 | − | 1.66928i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.82843 | − | 2.82843i | 0.147643 | − | 0.147643i | −0.629421 | − | 0.777064i | \(-0.716708\pi\) |
0.777064 | + | 0.629421i | \(0.216708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 36.0000i | − | 1.87409i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.00000 | 0.415339 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.82843 | − | 2.82843i | −0.146450 | − | 0.146450i | 0.630080 | − | 0.776530i | \(-0.283022\pi\) |
−0.776530 | + | 0.630080i | \(0.783022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.87083 | − | 1.87083i | −0.0963526 | − | 0.0963526i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5830 | −0.543612 | −0.271806 | − | 0.962352i | \(-0.587621\pi\) | ||||
−0.271806 | + | 0.962352i | \(0.587621\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.0000 | −1.07586 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0416 | + | 24.0416i | 1.22847 | + | 1.22847i | 0.964543 | + | 0.263927i | \(0.0850179\pi\) |
0.263927 | + | 0.964543i | \(0.414982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.9706 | + | 16.9706i | −0.862662 | + | 0.862662i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5830 | 0.536580 | 0.268290 | − | 0.963338i | \(-0.413542\pi\) | ||||
0.268290 | + | 0.963338i | \(0.413542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.87083 | − | 1.87083i | 0.0943708 | − | 0.0943708i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.61249 | + | 5.61249i | 0.281683 | + | 0.281683i | 0.833780 | − | 0.552097i | \(-0.186172\pi\) |
−0.552097 | + | 0.833780i | \(0.686172\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 28.0000i | 1.40175i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.7490i | − | 1.58547i | −0.609566 | − | 0.792735i | \(-0.708656\pi\) | ||
0.609566 | − | 0.792735i | \(-0.291344\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.61249 | + | 5.61249i | −0.279578 | + | 0.279578i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.4166 | − | 37.4166i | −1.85467 | − | 1.85467i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.00000i | 0.346128i | 0.984911 | + | 0.173064i | \(0.0553667\pi\) | ||||
−0.984911 | + | 0.173064i | \(0.944633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 31.7490i | − | 1.56606i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.35414 | − | 9.35414i | −0.458074 | − | 0.458074i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.8745 | −0.775520 | −0.387760 | − | 0.921760i | \(-0.626751\pi\) | ||||
−0.387760 | + | 0.921760i | \(0.626751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.29150i | 0.257892i | 0.991652 | + | 0.128946i | \(0.0411594\pi\) | ||||
−0.991652 | + | 0.128946i | \(0.958841\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.48331 | − | 7.48331i | 0.363851 | − | 0.363851i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.48331 | + | 7.48331i | 0.362143 | + | 0.362143i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −37.0405 | −1.78833 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.8745i | − | 0.764648i | −0.924028 | − | 0.382324i | \(-0.875124\pi\) | ||
0.924028 | − | 0.382324i | \(-0.124876\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.48528 | − | 8.48528i | −0.407777 | − | 0.407777i | 0.473186 | − | 0.880963i | \(-0.343104\pi\) |
−0.880963 | + | 0.473186i | \(0.843104\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.8661 | − | 5.06713i | −1.18951 | − | 0.242394i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0000i | 0.715911i | 0.933739 | + | 0.357955i | \(0.116526\pi\) | ||||
−0.933739 | + | 0.357955i | \(0.883474\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.5791 | − | 20.5791i | 0.977743 | − | 0.977743i | −0.0220144 | − | 0.999758i | \(-0.507008\pi\) |
0.999758 | + | 0.0220144i | \(0.00700796\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.7990 | + | 19.7990i | −0.936460 | + | 0.936460i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 26.0000i | − | 1.22702i | −0.789689 | − | 0.613508i | \(-0.789758\pi\) | ||
0.789689 | − | 0.613508i | \(-0.210242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 47.6235i | − | 2.24250i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 43.0291 | − | 43.0291i | 2.02168 | − | 2.02168i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.4558 | − | 25.4558i | 1.19077 | − | 1.19077i | 0.213924 | − | 0.976850i | \(-0.431376\pi\) |
0.976850 | − | 0.213924i | \(-0.0686244\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.0000 | −0.884918 | −0.442459 | − | 0.896789i | \(-0.645894\pi\) | ||||
−0.442459 | + | 0.896789i | \(0.645894\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1916 | − | 26.1916i | 1.21723 | − | 1.21723i | 0.248628 | − | 0.968599i | \(-0.420020\pi\) |
0.968599 | − | 0.248628i | \(-0.0799796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7990 | + | 19.7990i | −0.916188 | + | 0.916188i | −0.996750 | − | 0.0805616i | \(-0.974329\pi\) |
0.0805616 | + | 0.996750i | \(0.474329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000i | 0.184703i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 47.6235i | 2.19438i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.4499 | + | 22.4499i | −1.03225 | + | 1.03225i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.3137 | + | 11.3137i | −0.518019 | + | 0.518019i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.7490 | 1.45065 | 0.725325 | − | 0.688407i | \(-0.241690\pi\) | ||||
0.725325 | + | 0.688407i | \(0.241690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.4575i | 1.20636i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.06713 | − | 24.8661i | 0.230563 | − | 1.13145i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.5791 | + | 20.5791i | 0.932529 | + | 0.932529i | 0.997863 | − | 0.0653347i | \(-0.0208115\pi\) |
−0.0653347 | + | 0.997863i | \(0.520811\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 35.0000i | − | 1.58275i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.0000 | 1.03798 | 0.518988 | − | 0.854782i | \(-0.326309\pi\) | ||||
0.518988 | + | 0.854782i | \(0.326309\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7279 | − | 12.7279i | 0.570925 | − | 0.570925i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 39.0000i | − | 1.74588i | −0.487828 | − | 0.872940i | \(-0.662211\pi\) | ||
0.487828 | − | 0.872940i | \(-0.337789\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.0000 | 1.87642 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.7990 | − | 19.7990i | −0.882793 | − | 0.882793i | 0.111024 | − | 0.993818i | \(-0.464587\pi\) |
−0.993818 | + | 0.111024i | \(0.964587\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.2250 | − | 11.2250i | −0.498519 | − | 0.498519i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.0000i | 0.930809i | 0.885098 | + | 0.465404i | \(0.154091\pi\) | ||||
−0.885098 | + | 0.465404i | \(0.845909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 26.4575i | − | 1.17041i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.89949 | − | 9.89949i | −0.437073 | − | 0.437073i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.89949 | − | 9.89949i | 0.435379 | − | 0.435379i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 28.0000i | − | 1.22906i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.5830i | 0.463650i | 0.972758 | + | 0.231825i | \(0.0744697\pi\) | ||||
−0.972758 | + | 0.231825i | \(0.925530\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0416 | − | 24.0416i | −1.05127 | − | 1.05127i | −0.998613 | − | 0.0526543i | \(-0.983232\pi\) |
−0.0526543 | − | 0.998613i | \(-0.516768\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1660 | + | 9.00000i | 0.920261 | + | 0.391304i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.8375 | + | 16.8375i | −0.729311 | + | 0.729311i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.35414 | + | 9.35414i | 0.403661 | + | 0.403661i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.8745 | 0.683763 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.0000 | −1.07483 | −0.537417 | − | 0.843317i | \(-0.680600\pi\) | ||||
−0.537417 | + | 0.843317i | \(0.680600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.89949 | − | 9.89949i | −0.424828 | − | 0.424828i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.87083 | − | 1.87083i | −0.0799909 | − | 0.0799909i | 0.665979 | − | 0.745970i | \(-0.268014\pi\) |
−0.745970 | + | 0.665979i | \(0.768014\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.1660 | −0.903343 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 5.29150i | − | 0.225426i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.48331 | − | 7.48331i | 0.318223 | − | 0.318223i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.41421 | − | 1.41421i | 0.0599222 | − | 0.0599222i | −0.676511 | − | 0.736433i | \(-0.736509\pi\) |
0.736433 | + | 0.676511i | \(0.236509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8745 | 0.671420 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.82843 | + | 2.82843i | 0.119204 | + | 0.119204i | 0.764192 | − | 0.644988i | \(-0.223138\pi\) |
−0.644988 | + | 0.764192i | \(0.723138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.07107 | + | 7.07107i | −0.296957 | + | 0.296957i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.7490 | −1.33099 | −0.665494 | − | 0.746403i | \(-0.731779\pi\) | ||||
−0.665494 | + | 0.746403i | \(0.731779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10.5830i | − | 0.442885i | −0.975173 | − | 0.221442i | \(-0.928923\pi\) | ||
0.975173 | − | 0.221442i | \(-0.0710765\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.7990 | − | 19.7990i | −0.827115 | − | 0.827115i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.5791 | + | 20.5791i | 0.856720 | + | 0.856720i | 0.990950 | − | 0.134230i | \(-0.0428562\pi\) |
−0.134230 | + | 0.990950i | \(0.542856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.0000i | 1.45455i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | −0.995688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.9666 | + | 14.9666i | −0.619854 | + | 0.619854i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.35414 | + | 9.35414i | 0.386087 | + | 0.386087i | 0.873289 | − | 0.487202i | \(-0.161983\pi\) |
−0.487202 | + | 0.873289i | \(0.661983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.8745 | −0.654098 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.0000 | −1.43971 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.4499 | − | 22.4499i | 0.921909 | − | 0.921909i | −0.0752556 | − | 0.997164i | \(-0.523977\pi\) |
0.997164 | + | 0.0752556i | \(0.0239773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.89949 | + | 9.89949i | −0.405159 | + | 0.405159i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000i | 0.490307i | 0.969484 | + | 0.245153i | \(0.0788383\pi\) | ||||
−0.969484 | + | 0.245153i | \(0.921162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.00000 | −0.367118 | −0.183559 | − | 0.983009i | \(-0.558762\pi\) | ||||
−0.183559 | + | 0.983009i | \(0.558762\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.65685 | − | 5.65685i | −0.230365 | − | 0.230365i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.74166 | − | 3.74166i | −0.151869 | − | 0.151869i | 0.627083 | − | 0.778952i | \(-0.284249\pi\) |
−0.778952 | + | 0.627083i | \(0.784249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.29150 | 0.214423 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.00000 | −0.283190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.6274 | − | 22.6274i | −0.913913 | − | 0.913913i | 0.0826647 | − | 0.996577i | \(-0.473657\pi\) |
−0.996577 | + | 0.0826647i | \(0.973657\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5563 | − | 15.5563i | 0.626275 | − | 0.626275i | −0.320854 | − | 0.947129i | \(-0.603970\pi\) |
0.947129 | + | 0.320854i | \(0.103970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1660 | 0.850734 | 0.425367 | − | 0.905021i | \(-0.360145\pi\) | ||||
0.425367 | + | 0.905021i | \(0.360145\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.00000 | + | 10.5830i | 0.280900 | + | 0.424681i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.4499 | + | 22.4499i | −0.899438 | + | 0.899438i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −52.3832 | − | 52.3832i | −2.09198 | − | 2.09198i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.0405i | 1.47456i | 0.675587 | + | 0.737280i | \(0.263890\pi\) | ||||
−0.675587 | + | 0.737280i | \(0.736110\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.4166 | + | 37.4166i | −1.48718 | + | 1.48718i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.61249 | − | 5.61249i | −0.222375 | − | 0.222375i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.0000i | 1.42414i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.8745i | 0.627005i | 0.949587 | + | 0.313503i | \(0.101502\pi\) | ||||
−0.949587 | + | 0.313503i | \(0.898498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.48528 | − | 8.48528i | −0.334627 | − | 0.334627i | 0.519714 | − | 0.854341i | \(-0.326039\pi\) |
−0.854341 | + | 0.519714i | \(0.826039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.35414 | − | 9.35414i | −0.367749 | − | 0.367749i | 0.498906 | − | 0.866656i | \(-0.333735\pi\) |
−0.866656 | + | 0.498906i | \(0.833735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 15.8745i | − | 0.622171i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.35414 | − | 9.35414i | 0.366056 | − | 0.366056i | −0.499981 | − | 0.866037i | \(-0.666660\pi\) |
0.866037 | + | 0.499981i | \(0.166660\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 37.4166 | + | 37.4166i | 1.45976 | + | 1.45976i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.3320 | 1.64902 | 0.824511 | − | 0.565846i | \(-0.191450\pi\) | ||||
0.824511 | + | 0.565846i | \(0.191450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.1660i | 0.823262i | 0.911351 | + | 0.411631i | \(0.135041\pi\) | ||||
−0.911351 | + | 0.411631i | \(0.864959\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.957598 | + | 4.69926i | −0.0370784 | + | 0.181956i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.0000i | 1.62381i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.0000 | −1.08093 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.5457 | − | 35.5457i | 1.37019 | − | 1.37019i | 0.510033 | − | 0.860155i | \(-0.329633\pi\) |
0.860155 | − | 0.510033i | \(-0.170367\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.65685 | + | 5.65685i | −0.217411 | + | 0.217411i | −0.807406 | − | 0.589996i | \(-0.799129\pi\) |
0.589996 | + | 0.807406i | \(0.299129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000i | 0.153506i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 47.6235i | 1.82494i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.3208 | − | 24.3208i | 0.930609 | − | 0.930609i | −0.0671354 | − | 0.997744i | \(-0.521386\pi\) |
0.997744 | + | 0.0671354i | \(0.0213859\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −49.4975 | + | 49.4975i | −1.88845 | + | 1.88845i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.5830 | 0.403180 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.0000 | 1.36950 | 0.684752 | − | 0.728776i | \(-0.259910\pi\) | ||||
0.684752 | + | 0.728776i | \(0.259910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 29.9333 | − | 29.9333i | 1.13707 | − | 1.13707i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.00000i | 0.264764i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.8745i | 0.599572i | 0.954006 | + | 0.299786i | \(0.0969153\pi\) | ||||
−0.954006 | + | 0.299786i | \(0.903085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.4166 | + | 37.4166i | −1.41119 | + | 1.41119i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.7990 | + | 19.7990i | −0.744618 | + | 0.744618i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.29150 | −0.198727 | −0.0993633 | − | 0.995051i | \(-0.531681\pi\) | ||||
−0.0993633 | + | 0.995051i | \(0.531681\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.1660i | 0.793787i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.0978 | + | 2.87280i | 0.527966 | + | 0.107587i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.87083 | + | 1.87083i | 0.0698674 | + | 0.0698674i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | −0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.5980 | + | 39.5980i | 1.47266 | + | 1.47266i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.7990 | − | 19.7990i | 0.734304 | − | 0.734304i | −0.237165 | − | 0.971469i | \(-0.576218\pi\) |
0.971469 | + | 0.237165i | \(0.0762183\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 41.0000i | − | 1.51852i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.4558 | − | 25.4558i | −0.940233 | − | 0.940233i | 0.0580789 | − | 0.998312i | \(-0.481502\pi\) |
−0.998312 | + | 0.0580789i | \(0.981502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.48331 | − | 7.48331i | −0.275651 | − | 0.275651i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 3.00000i | − | 0.110357i | −0.998477 | − | 0.0551784i | \(-0.982427\pi\) | ||
0.998477 | − | 0.0551784i | \(-0.0175728\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 37.0405i | 1.36072i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.9411 | − | 33.9411i | −1.24518 | − | 1.24518i | −0.957824 | − | 0.287355i | \(-0.907224\pi\) |
−0.287355 | − | 0.957824i | \(-0.592776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 33.9411 | − | 33.9411i | 1.24184 | − | 1.24184i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 12.0000i | − | 0.438470i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.0405i | 1.35163i | 0.737072 | + | 0.675814i | \(0.236208\pi\) | ||||
−0.737072 | + | 0.675814i | \(0.763792\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39.5980 | + | 39.5980i | 1.44303 | + | 1.44303i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.0416 | + | 24.0416i | −0.873808 | + | 0.873808i | −0.992885 | − | 0.119077i | \(-0.962006\pi\) |
0.119077 | + | 0.992885i | \(0.462006\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.0405 | + | 56.0000i | 1.34449 | + | 2.03267i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.0000 | 0.978749 | 0.489375 | − | 0.872074i | \(-0.337225\pi\) | ||||
0.489375 | + | 0.872074i | \(0.337225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.4499 | + | 22.4499i | −0.812743 | + | 0.812743i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.5830 | 0.381633 | 0.190816 | − | 0.981626i | \(-0.438886\pi\) | ||||
0.190816 | + | 0.981626i | \(0.438886\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −63.0000 | −2.26889 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.8701 | + | 26.8701i | 0.966449 | + | 0.966449i | 0.999455 | − | 0.0330063i | \(-0.0105082\pi\) |
−0.0330063 | + | 0.999455i | \(0.510508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −37.4166 | − | 37.4166i | −1.34231 | − | 1.34231i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47.6235 | −1.70629 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.6235i | 1.70410i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.87083 | + | 1.87083i | −0.0668580 | + | 0.0668580i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7990 | − | 19.7990i | 0.705758 | − | 0.705758i | −0.259882 | − | 0.965640i | \(-0.583684\pi\) |
0.965640 | + | 0.259882i | \(0.0836838\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 68.7895 | 2.44897 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.89949 | + | 9.89949i | 0.351541 | + | 0.351541i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.3848 | + | 18.3848i | −0.651222 | + | 0.651222i | −0.953287 | − | 0.302065i | \(-0.902324\pi\) |
0.302065 | + | 0.953287i | \(0.402324\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 63.4980i | − | 2.24359i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 49.4975 | + | 49.4975i | 1.74673 | + | 1.74673i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.61249 | + | 5.61249i | 0.197569 | + | 0.197569i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.0000i | 0.351581i | 0.984428 | + | 0.175791i | \(0.0562482\pi\) | ||||
−0.984428 | + | 0.175791i | \(0.943752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.00000 | 0.316033 | 0.158016 | − | 0.987436i | \(-0.449490\pi\) | ||||
0.158016 | + | 0.987436i | \(0.449490\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.9666 | + | 14.9666i | −0.524903 | + | 0.524903i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.4499 | + | 22.4499i | 0.785424 | + | 0.785424i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.1660 | −0.739600 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.0000 | −1.32621 | −0.663105 | − | 0.748527i | \(-0.730762\pi\) | ||||
−0.663105 | + | 0.748527i | \(0.730762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.5457 | − | 35.5457i | 1.23905 | − | 1.23905i | 0.278656 | − | 0.960391i | \(-0.410111\pi\) |
0.960391 | − | 0.278656i | \(-0.0898888\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.9411 | + | 33.9411i | −1.18025 | + | 1.18025i | −0.200569 | + | 0.979680i | \(0.564279\pi\) |
−0.979680 | + | 0.200569i | \(0.935721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 38.0000i | − | 1.31979i | −0.751356 | − | 0.659897i | \(-0.770600\pi\) | ||
0.751356 | − | 0.659897i | \(-0.229400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.0000 | −0.728482 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.61249 | + | 5.61249i | 0.193996 | + | 0.193996i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.29150 | 0.182683 | 0.0913415 | − | 0.995820i | \(-0.470885\pi\) | ||||
0.0913415 | + | 0.995820i | \(0.470885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.0000 | 0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.6985 | − | 29.6985i | −1.02287 | − | 1.02287i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.0416 | − | 24.0416i | 0.826080 | − | 0.826080i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −63.4980 | −2.17925 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.0000 | − | 26.4575i | 1.37118 | − | 0.906952i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.48331 | − | 7.48331i | 0.256224 | − | 0.256224i | −0.567293 | − | 0.823516i | \(-0.692009\pi\) |
0.823516 | + | 0.567293i | \(0.192009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.8041 | + | 31.8041i | 1.08641 | + | 1.08641i | 0.995895 | + | 0.0905115i | \(0.0288502\pi\) |
0.0905115 | + | 0.995895i | \(0.471150\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.0000i | 1.46714i | 0.679613 | + | 0.733571i | \(0.262148\pi\) | ||||
−0.679613 | + | 0.733571i | \(0.737852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 47.6235i | − | 1.62301i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.5791 | + | 20.5791i | −0.700521 | + | 0.700521i | −0.964522 | − | 0.264001i | \(-0.914958\pi\) |
0.264001 | + | 0.964522i | \(0.414958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.8041 | − | 31.8041i | −1.08012 | − | 1.08012i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.0000i | 0.949835i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.29150i | 0.179296i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.65685 | − | 5.65685i | −0.191456 | − | 0.191456i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.4166 | − | 37.4166i | −1.26347 | − | 1.26347i | −0.949401 | − | 0.314067i | \(-0.898308\pi\) |
−0.314067 | − | 0.949401i | \(-0.601692\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.3320 | 1.42782 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.7490i | 1.06965i | 0.844962 | + | 0.534826i | \(0.179623\pi\) | ||||
−0.844962 | + | 0.534826i | \(0.820377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.7083 | + | 18.7083i | −0.629584 | + | 0.629584i | −0.947963 | − | 0.318379i | \(-0.896861\pi\) |
0.318379 | + | 0.947963i | \(0.396861\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.61249 | + | 5.61249i | 0.188449 | + | 0.188449i | 0.795025 | − | 0.606576i | \(-0.207458\pi\) |
−0.606576 | + | 0.795025i | \(0.707458\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.8745 | −0.532414 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 26.4575i | − | 0.886360i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.89949 | − | 9.89949i | −0.331274 | − | 0.331274i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.70319 | − | 32.8948i | 0.223813 | − | 1.09833i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.00000i | 0.100056i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.4499 | + | 22.4499i | −0.747087 | + | 0.747087i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.5269 | − | 32.5269i | 1.08004 | − | 1.08004i | 0.0835334 | − | 0.996505i | \(-0.473379\pi\) |
0.996505 | − | 0.0835334i | \(-0.0266205\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 56.0000i | − | 1.85740i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.8745i | 0.525946i | 0.964803 | + | 0.262973i | \(0.0847030\pi\) | ||||
−0.964803 | + | 0.262973i | \(0.915297\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.8999 | − | 44.8999i | 1.48597 | − | 1.48597i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.41421 | − | 1.41421i | 0.0467014 | − | 0.0467014i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.6235 | −1.57096 | −0.785478 | − | 0.618890i | \(-0.787583\pi\) | ||||
−0.785478 | + | 0.618890i | \(0.787583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42.0000 | −1.38395 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.8375 | − | 16.8375i | 0.554212 | − | 0.554212i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.6274 | − | 22.6274i | 0.743182 | − | 0.743182i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.0000i | 1.60764i | 0.594874 | + | 0.803819i | \(0.297202\pi\) | ||||
−0.594874 | + | 0.803819i | \(0.702798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 15.8745i | − | 0.520266i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.2874 | + | 39.2874i | −1.28621 | + | 1.28621i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.0122 | − | 41.0122i | 1.33981 | − | 1.33981i | 0.443570 | − | 0.896240i | \(-0.353712\pi\) |
0.896240 | − | 0.443570i | \(-0.146288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52.9150 | 1.72682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5830i | 0.344996i | 0.985010 | + | 0.172498i | \(0.0551839\pi\) | ||||
−0.985010 | + | 0.172498i | \(0.944816\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.2933 | + | 8.61839i | 1.37726 | + | 0.280653i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.3208 | + | 24.3208i | 0.790319 | + | 0.790319i | 0.981546 | − | 0.191227i | \(-0.0612466\pi\) |
−0.191227 | + | 0.981546i | \(0.561247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 35.0000i | − | 1.13615i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 84.0000 | 2.72389 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.65685 | − | 5.65685i | −0.183243 | − | 0.183243i | 0.609524 | − | 0.792768i | \(-0.291361\pi\) |
−0.792768 | + | 0.609524i | \(0.791361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.89949 | + | 9.89949i | −0.320005 | + | 0.320005i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 24.0000i | − | 0.775000i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.9706 | + | 16.9706i | 0.546869 | + | 0.546869i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.8041 | + | 31.8041i | 1.02275 | + | 1.02275i | 0.999735 | + | 0.0230154i | \(0.00732668\pi\) |
0.0230154 | + | 0.999735i | \(0.492673\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 21.1660i | − | 0.679250i | −0.940561 | − | 0.339625i | \(-0.889700\pi\) | ||
0.940561 | − | 0.339625i | \(-0.110300\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.07107 | − | 7.07107i | −0.226688 | − | 0.226688i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.8701 | + | 26.8701i | −0.859649 | + | 0.859649i | −0.991297 | − | 0.131647i | \(-0.957973\pi\) |
0.131647 | + | 0.991297i | \(0.457973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 84.0000i | − | 2.68465i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 63.4980i | − | 2.02734i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.9706 | + | 16.9706i | 0.541277 | + | 0.541277i | 0.923903 | − | 0.382626i | \(-0.124980\pi\) |
−0.382626 | + | 0.923903i | \(0.624980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.89949 | − | 9.89949i | 0.315104 | − | 0.315104i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.8745 | − | 24.0000i | −0.504780 | − | 0.763156i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −54.2540 | + | 54.2540i | −1.72170 | + | 1.72170i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.4166 | + | 37.4166i | 1.18499 | + | 1.18499i | 0.978434 | + | 0.206561i | \(0.0662272\pi\) |
0.206561 | + | 0.978434i | \(0.433773\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.4575 | 0.837079 |
(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 | 2300.2.i.b.1057.1 | ✓ | 8 | |
5.2 | odd | 4 | inner | 2300.2.i.b.1793.3 | yes | 8 | |
5.3 | odd | 4 | inner | 2300.2.i.b.1793.2 | yes | 8 | |
5.4 | even | 2 | inner | 2300.2.i.b.1057.4 | yes | 8 | |
23.22 | odd | 2 | inner | 2300.2.i.b.1057.2 | yes | 8 | |
115.22 | even | 4 | inner | 2300.2.i.b.1793.4 | yes | 8 | |
115.68 | even | 4 | inner | 2300.2.i.b.1793.1 | yes | 8 | |
115.114 | odd | 2 | inner | 2300.2.i.b.1057.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2300.2.i.b.1057.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
2300.2.i.b.1057.2 | yes | 8 | 23.22 | odd | 2 | inner | |
2300.2.i.b.1057.3 | yes | 8 | 115.114 | odd | 2 | inner | |
2300.2.i.b.1057.4 | yes | 8 | 5.4 | even | 2 | inner | |
2300.2.i.b.1793.1 | yes | 8 | 115.68 | even | 4 | inner | |
2300.2.i.b.1793.2 | yes | 8 | 5.3 | odd | 4 | inner | |
2300.2.i.b.1793.3 | yes | 8 | 5.2 | odd | 4 | inner | |
2300.2.i.b.1793.4 | yes | 8 | 115.22 | even | 4 | inner |