Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,3,Mod(107,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.107");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.l (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: | \(8.17440793081\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 143.2 | ||
Root | \(-0.437016 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.143 |
Dual form | 300.3.l.f.107.2 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | + | 1.41421i | −0.707107 | + | 0.707107i | ||||
\(3\) | 0.166925 | − | 2.99535i | 0.0556418 | − | 0.998451i | ||||
\(4\) | − | 4.00000i | − | 1.00000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.00000 | + | 4.47214i | 0.666667 | + | 0.745356i | ||||
\(7\) | 9.48683 | + | 9.48683i | 1.35526 | + | 1.35526i | 0.879661 | + | 0.475600i | \(0.157769\pi\) |
0.475600 | + | 0.879661i | \(0.342231\pi\) | |||||||
\(8\) | 5.65685 | + | 5.65685i | 0.707107 | + | 0.707107i | ||||
\(9\) | −8.94427 | − | 1.00000i | −0.993808 | − | 0.111111i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −11.9814 | − | 0.667701i | −0.998451 | − | 0.0556418i | ||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | −26.8328 | −1.91663 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.0000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | 14.0633 | − | 11.2349i | 0.781296 | − | 0.624161i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 30.0000 | − | 26.8328i | 1.42857 | − | 1.27775i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 31.1127 | + | 31.1127i | 1.35273 | + | 1.35273i | 0.882599 | + | 0.470128i | \(0.155792\pi\) |
0.470128 | + | 0.882599i | \(0.344208\pi\) | |||||||
\(24\) | 17.8885 | − | 16.0000i | 0.745356 | − | 0.666667i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.48838 | + | 26.6243i | −0.166236 | + | 0.986086i | ||||
\(28\) | 37.9473 | − | 37.9473i | 1.35526 | − | 1.35526i | ||||
\(29\) | 53.6656 | 1.85054 | 0.925270 | − | 0.379310i | \(-0.123839\pi\) | ||||
0.925270 | + | 0.379310i | \(0.123839\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 22.6274 | − | 22.6274i | 0.707107 | − | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.00000 | + | 35.7771i | −0.111111 | + | 0.993808i | ||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 53.6656i | − | 1.30892i | −0.756098 | − | 0.654459i | \(-0.772896\pi\) | ||
0.756098 | − | 0.654459i | \(-0.227104\pi\) | |||||||
\(42\) | −4.47907 | + | 80.3737i | −0.106645 | + | 1.91366i | ||||
\(43\) | 28.4605 | − | 28.4605i | 0.661872 | − | 0.661872i | −0.293949 | − | 0.955821i | \(-0.594970\pi\) |
0.955821 | + | 0.293949i | \(0.0949696\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −88.0000 | −1.91304 | ||||||||
\(47\) | 2.82843 | − | 2.82843i | 0.0601793 | − | 0.0601793i | −0.676377 | − | 0.736556i | \(-0.736451\pi\) |
0.736556 | + | 0.676377i | \(0.236451\pi\) | |||||||
\(48\) | −2.67080 | + | 47.9256i | −0.0556418 | + | 0.998451i | ||||
\(49\) | 131.000i | 2.67347i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | −31.3050 | − | 44.0000i | −0.579721 | − | 0.814815i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 107.331i | 1.91663i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −75.8947 | + | 75.8947i | −1.30853 | + | 1.30853i | ||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 58.0000 | 0.950820 | 0.475410 | − | 0.879764i | \(-0.342300\pi\) | ||||
0.475410 | + | 0.879764i | \(0.342300\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −75.3660 | − | 94.3396i | −1.19629 | − | 1.49745i | ||||
\(64\) | 64.0000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −47.4342 | − | 47.4342i | −0.707973 | − | 0.707973i | 0.258136 | − | 0.966109i | \(-0.416892\pi\) |
−0.966109 | + | 0.258136i | \(0.916892\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 98.3870 | − | 88.0000i | 1.42590 | − | 1.27536i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −44.9396 | − | 56.2533i | −0.624161 | − | 0.781296i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 79.0000 | + | 17.8885i | 0.975309 | + | 0.220846i | ||||
\(82\) | 75.8947 | + | 75.8947i | 0.925545 | + | 0.925545i | ||||
\(83\) | 53.7401 | + | 53.7401i | 0.647471 | + | 0.647471i | 0.952381 | − | 0.304910i | \(-0.0986264\pi\) |
−0.304910 | + | 0.952381i | \(0.598626\pi\) | |||||||
\(84\) | −107.331 | − | 120.000i | −1.27775 | − | 1.42857i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 80.4984i | 0.936028i | ||||||||
\(87\) | 8.95815 | − | 160.747i | 0.102967 | − | 1.84767i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −107.331 | −1.20597 | −0.602985 | − | 0.797753i | \(-0.706022\pi\) | ||||
−0.602985 | + | 0.797753i | \(0.706022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 124.451 | − | 124.451i | 1.35273 | − | 1.35273i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.00000i | 0.0851064i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −64.0000 | − | 71.5542i | −0.666667 | − | 0.745356i | ||||
\(97\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(98\) | −185.262 | − | 185.262i | −1.89043 | − | 1.89043i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 160.997i | − | 1.59403i | −0.603960 | − | 0.797014i | \(-0.706411\pi\) | ||
0.603960 | − | 0.797014i | \(-0.293589\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −142.302 | + | 142.302i | −1.38158 | + | 1.38158i | −0.539756 | + | 0.841821i | \(0.681484\pi\) |
−0.841821 | + | 0.539756i | \(0.818516\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −87.6812 | + | 87.6812i | −0.819451 | + | 0.819451i | −0.986028 | − | 0.166578i | \(-0.946728\pi\) |
0.166578 | + | 0.986028i | \(0.446728\pi\) | |||||||
\(108\) | 106.497 | + | 17.9535i | 0.986086 | + | 0.166236i | ||||
\(109\) | 38.0000i | 0.348624i | 0.984690 | + | 0.174312i | \(0.0557701\pi\) | ||||
−0.984690 | + | 0.174312i | \(0.944230\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −151.789 | − | 151.789i | −1.35526 | − | 1.35526i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 214.663i | − | 1.85054i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −121.000 | −1.00000 | ||||||||
\(122\) | −82.0244 | + | 82.0244i | −0.672331 | + | 0.672331i | ||||
\(123\) | −160.747 | − | 8.95815i | −1.30689 | − | 0.0728305i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 240.000 | + | 26.8328i | 1.90476 | + | 0.212959i | ||||
\(127\) | 66.4078 | + | 66.4078i | 0.522896 | + | 0.522896i | 0.918445 | − | 0.395549i | \(-0.129446\pi\) |
−0.395549 | + | 0.918445i | \(0.629446\pi\) | |||||||
\(128\) | −90.5097 | − | 90.5097i | −0.707107 | − | 0.707107i | ||||
\(129\) | −80.4984 | − | 90.0000i | −0.624019 | − | 0.697674i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 134.164 | 1.00122 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(138\) | −14.6894 | + | 263.591i | −0.106445 | + | 1.91008i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | − | 8.94427i | −0.0567376 | − | 0.0634346i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 143.108 | + | 16.0000i | 0.993808 | + | 0.111111i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 392.391 | + | 21.8672i | 2.66933 | + | 0.148757i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 107.331 | 0.720344 | 0.360172 | − | 0.932886i | \(-0.382718\pi\) | ||||
0.360172 | + | 0.932886i | \(0.382718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 590.322i | 3.66660i | ||||||||
\(162\) | −137.021 | + | 86.4247i | −0.845809 | + | 0.533485i | ||||
\(163\) | 199.223 | − | 199.223i | 1.22223 | − | 1.22223i | 0.255393 | − | 0.966837i | \(-0.417795\pi\) |
0.966837 | − | 0.255393i | \(-0.0822047\pi\) | |||||||
\(164\) | −214.663 | −1.30892 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −152.000 | −0.915663 | ||||||||
\(167\) | −172.534 | + | 172.534i | −1.03314 | + | 1.03314i | −0.0337063 | + | 0.999432i | \(0.510731\pi\) |
−0.999432 | + | 0.0337063i | \(0.989269\pi\) | |||||||
\(168\) | 321.495 | + | 17.9163i | 1.91366 | + | 0.106645i | ||||
\(169\) | − | 169.000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −113.842 | − | 113.842i | −0.661872 | − | 0.661872i | ||||
\(173\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(174\) | 214.663 | + | 240.000i | 1.23369 | + | 1.37931i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 151.789 | − | 151.789i | 0.852749 | − | 0.852749i | ||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −358.000 | −1.97790 | −0.988950 | − | 0.148248i | \(-0.952637\pi\) | ||||
−0.988950 | + | 0.148248i | \(0.952637\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.68167 | − | 173.730i | 0.0529053 | − | 0.949347i | ||||
\(184\) | 352.000i | 1.91304i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −11.3137 | − | 11.3137i | −0.0601793 | − | 0.0601793i | ||||
\(189\) | −295.161 | + | 210.000i | −1.56170 | + | 1.11111i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 191.703 | + | 10.6832i | 0.998451 | + | 0.0556418i | ||||
\(193\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 524.000 | 2.67347 | ||||||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −150.000 | + | 134.164i | −0.746269 | + | 0.667483i | ||||
\(202\) | 227.684 | + | 227.684i | 1.12715 | + | 1.12715i | ||||
\(203\) | 509.117 | + | 509.117i | 2.50796 | + | 2.50796i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 402.492i | − | 1.95385i | ||||||
\(207\) | −247.168 | − | 309.393i | −1.19405 | − | 1.49465i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 248.000i | − | 1.15888i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −176.000 | + | 125.220i | −0.814815 | + | 0.579721i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −53.7401 | − | 53.7401i | −0.246514 | − | 0.246514i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −66.4078 | + | 66.4078i | −0.297793 | + | 0.297793i | −0.840149 | − | 0.542356i | \(-0.817532\pi\) |
0.542356 | + | 0.840149i | \(0.317532\pi\) | |||||||
\(224\) | 429.325 | 1.91663 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −251.730 | + | 251.730i | −1.10894 | + | 1.10894i | −0.115653 | + | 0.993290i | \(0.536896\pi\) |
−0.993290 | + | 0.115653i | \(0.963104\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 262.000i | − | 1.14410i | −0.820217 | − | 0.572052i | \(-0.806147\pi\) | ||
0.820217 | − | 0.572052i | \(-0.193853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 303.579 | + | 303.579i | 1.30853 | + | 1.30853i | ||||
\(233\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 302.000 | 1.25311 | 0.626556 | − | 0.779376i | \(-0.284464\pi\) | ||||
0.626556 | + | 0.779376i | \(0.284464\pi\) | |||||||
\(242\) | 171.120 | − | 171.120i | 0.707107 | − | 0.707107i | ||||
\(243\) | 66.7696 | − | 233.647i | 0.274772 | − | 0.961509i | ||||
\(244\) | − | 232.000i | − | 0.950820i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 240.000 | − | 214.663i | 0.975610 | − | 0.872612i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 169.941 | − | 152.000i | 0.682495 | − | 0.610442i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −377.359 | + | 301.464i | −1.49745 | + | 1.19629i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −187.830 | −0.739487 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 241.121 | + | 13.4372i | 0.934578 | + | 0.0520823i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −480.000 | − | 53.6656i | −1.83908 | − | 0.205615i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −200.818 | − | 200.818i | −0.763568 | − | 0.763568i | 0.213398 | − | 0.976965i | \(-0.431547\pi\) |
−0.976965 | + | 0.213398i | \(0.931547\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.9163 | + | 321.495i | −0.0671022 | + | 1.20410i | ||||
\(268\) | −189.737 | + | 189.737i | −0.707973 | + | 0.707973i | ||||
\(269\) | −536.656 | −1.99500 | −0.997502 | − | 0.0706320i | \(-0.977498\pi\) | ||||
−0.997502 | + | 0.0706320i | \(0.977498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −352.000 | − | 393.548i | −1.27536 | − | 1.42590i | ||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 375.659i | − | 1.33687i | −0.743772 | − | 0.668433i | \(-0.766965\pi\) | ||
0.743772 | − | 0.668433i | \(-0.233035\pi\) | |||||||
\(282\) | 23.9628 | + | 1.33540i | 0.0849745 | + | 0.00473547i | ||||
\(283\) | 332.039 | − | 332.039i | 1.17328 | − | 1.17328i | 0.191861 | − | 0.981422i | \(-0.438548\pi\) |
0.981422 | − | 0.191861i | \(-0.0614523\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 509.117 | − | 509.117i | 1.77393 | − | 1.77393i | ||||
\(288\) | −225.013 | + | 179.758i | −0.781296 | + | 0.624161i | ||||
\(289\) | − | 289.000i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | −585.850 | + | 524.000i | −1.99269 | + | 1.78231i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −151.789 | + | 151.789i | −0.509360 | + | 0.509360i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 540.000 | 1.79402 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −482.242 | − | 26.8744i | −1.59156 | − | 0.0886946i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −104.355 | − | 104.355i | −0.339919 | − | 0.339919i | 0.516418 | − | 0.856337i | \(-0.327265\pi\) |
−0.856337 | + | 0.516418i | \(0.827265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 402.492 | + | 450.000i | 1.30256 | + | 1.45631i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 248.000 | + | 277.272i | 0.772586 | + | 0.863777i | ||||
\(322\) | −834.841 | − | 834.841i | −2.59267 | − | 2.59267i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 71.5542 | − | 316.000i | 0.220846 | − | 0.975309i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 563.489i | 1.72849i | ||||||||
\(327\) | 113.823 | + | 6.34316i | 0.348084 | + | 0.0193980i | ||||
\(328\) | 303.579 | − | 303.579i | 0.925545 | − | 0.925545i | ||||
\(329\) | 53.6656 | 0.163117 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 214.960 | − | 214.960i | 0.647471 | − | 0.647471i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 488.000i | − | 1.46108i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −480.000 | + | 429.325i | −1.42857 | + | 1.27775i | ||||
\(337\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | 239.002 | + | 239.002i | 0.707107 | + | 0.707107i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −777.920 | + | 777.920i | −2.26799 | + | 2.26799i | ||||
\(344\) | 321.994 | 0.936028 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 82.0244 | − | 82.0244i | 0.236382 | − | 0.236382i | −0.578968 | − | 0.815350i | \(-0.696545\pi\) |
0.815350 | + | 0.578968i | \(0.196545\pi\) | |||||||
\(348\) | −642.990 | − | 35.8326i | −1.84767 | − | 0.102967i | ||||
\(349\) | 22.0000i | 0.0630372i | 0.999503 | + | 0.0315186i | \(0.0100344\pi\) | ||||
−0.999503 | + | 0.0315186i | \(0.989966\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 429.325i | 1.20597i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −361.000 | −1.00000 | ||||||||
\(362\) | 506.288 | − | 506.288i | 1.39859 | − | 1.39859i | ||||
\(363\) | −20.1980 | + | 362.438i | −0.0556418 | + | 0.998451i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 232.000 | + | 259.384i | 0.633880 | + | 0.708699i | ||||
\(367\) | −85.3815 | − | 85.3815i | −0.232647 | − | 0.232647i | 0.581150 | − | 0.813797i | \(-0.302603\pi\) |
−0.813797 | + | 0.581150i | \(0.802603\pi\) | |||||||
\(368\) | −497.803 | − | 497.803i | −1.35273 | − | 1.35273i | ||||
\(369\) | −53.6656 | + | 480.000i | −0.145435 | + | 1.30081i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.0000 | 0.0851064 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 120.436 | − | 714.405i | 0.318613 | − | 1.88996i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 210.000 | − | 187.830i | 0.551181 | − | 0.492991i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.1127 | − | 31.1127i | −0.0812342 | − | 0.0812342i | 0.665322 | − | 0.746556i | \(-0.268294\pi\) |
−0.746556 | + | 0.665322i | \(0.768294\pi\) | |||||||
\(384\) | −286.217 | + | 256.000i | −0.745356 | + | 0.666667i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −283.019 | + | 226.098i | −0.731315 | + | 0.584232i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 751.319 | 1.93141 | 0.965705 | − | 0.259640i | \(-0.0836039\pi\) | ||||
0.965705 | + | 0.259640i | \(0.0836039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −741.048 | + | 741.048i | −1.89043 | + | 1.89043i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 643.988i | − | 1.60595i | −0.596010 | − | 0.802977i | \(-0.703248\pi\) | ||
0.596010 | − | 0.802977i | \(-0.296752\pi\) | |||||||
\(402\) | 22.3954 | − | 401.869i | 0.0557099 | − | 0.999673i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −643.988 | −1.59403 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1440.00 | −3.54680 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 802.000i | 1.96088i | 0.196818 | + | 0.980440i | \(0.436939\pi\) | ||||
−0.196818 | + | 0.980440i | \(0.563061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 569.210 | + | 569.210i | 1.38158 | + | 1.38158i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 787.096 | + | 88.0000i | 1.90120 | + | 0.212560i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 778.000 | 1.84798 | 0.923990 | − | 0.382415i | \(-0.124908\pi\) | ||||
0.923990 | + | 0.382415i | \(0.124908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.1266 | + | 22.4698i | −0.0664933 | + | 0.0531201i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 550.236 | + | 550.236i | 1.28861 | + | 1.28861i | ||||
\(428\) | 350.725 | + | 350.725i | 0.819451 | + | 0.819451i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 71.8140 | − | 425.989i | 0.166236 | − | 0.986086i | ||||
\(433\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 152.000 | 0.348624 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 131.000 | − | 1171.70i | 0.297052 | − | 2.65692i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −562.857 | − | 562.857i | −1.27056 | − | 1.27056i | −0.945796 | − | 0.324762i | \(-0.894716\pi\) |
−0.324762 | − | 0.945796i | \(-0.605284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 187.830i | − | 0.421143i | ||||||
\(447\) | 17.9163 | − | 321.495i | 0.0400812 | − | 0.719228i | ||||
\(448\) | −607.157 | + | 607.157i | −1.35526 | + | 1.35526i | ||||
\(449\) | 804.984 | 1.79284 | 0.896419 | − | 0.443207i | \(-0.146159\pi\) | ||||
0.896419 | + | 0.443207i | \(0.146159\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 712.000i | − | 1.56828i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(458\) | 370.524 | + | 370.524i | 0.809004 | + | 0.809004i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 375.659i | 0.814879i | 0.913232 | + | 0.407440i | \(0.133578\pi\) | ||||
−0.913232 | + | 0.407440i | \(0.866422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 369.986 | − | 369.986i | 0.799107 | − | 0.799107i | −0.183848 | − | 0.982955i | \(-0.558855\pi\) |
0.982955 | + | 0.183848i | \(0.0588554\pi\) | |||||||
\(464\) | −858.650 | −1.85054 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 87.6812 | − | 87.6812i | 0.187754 | − | 0.187754i | −0.606970 | − | 0.794725i | \(-0.707615\pi\) |
0.794725 | + | 0.606970i | \(0.207615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 900.000i | − | 1.91898i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −427.092 | + | 427.092i | −0.886084 | + | 0.886084i | ||||
\(483\) | 1768.22 | + | 98.5396i | 3.66092 | + | 0.204016i | ||||
\(484\) | 484.000i | 1.00000i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 236.000 | + | 424.853i | 0.485597 | + | 0.874183i | ||||
\(487\) | −597.670 | − | 597.670i | −1.22725 | − | 1.22725i | −0.965000 | − | 0.262249i | \(-0.915536\pi\) |
−0.262249 | − | 0.965000i | \(-0.584464\pi\) | |||||||
\(488\) | 328.098 | + | 328.098i | 0.672331 | + | 0.672331i | ||||
\(489\) | −563.489 | − | 630.000i | −1.15233 | − | 1.28834i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | −35.8326 | + | 642.990i | −0.0728305 | + | 1.30689i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −25.3726 | + | 455.294i | −0.0509491 | + | 0.914244i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 488.000 | + | 545.601i | 0.974052 | + | 1.08902i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −647.710 | − | 647.710i | −1.28769 | − | 1.28769i | −0.936185 | − | 0.351509i | \(-0.885669\pi\) |
−0.351509 | − | 0.936185i | \(-0.614331\pi\) | |||||||
\(504\) | 107.331 | − | 960.000i | 0.212959 | − | 1.90476i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −506.215 | − | 28.2104i | −0.998451 | − | 0.0556418i | ||||
\(508\) | 265.631 | − | 265.631i | 0.522896 | − | 0.522896i | ||||
\(509\) | −268.328 | −0.527167 | −0.263584 | − | 0.964637i | \(-0.584905\pi\) | ||||
−0.263584 | + | 0.964637i | \(0.584905\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −362.039 | + | 362.039i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −360.000 | + | 321.994i | −0.697674 | + | 0.624019i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 751.319i | − | 1.44207i | −0.692898 | − | 0.721035i | \(-0.743667\pi\) | ||
0.692898 | − | 0.721035i | \(-0.256333\pi\) | |||||||
\(522\) | 754.717 | − | 602.928i | 1.44582 | − | 1.15503i | ||||
\(523\) | 730.486 | − | 730.486i | 1.39672 | − | 1.39672i | 0.587496 | − | 0.809227i | \(-0.300114\pi\) |
0.809227 | − | 0.587496i | \(-0.199886\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 568.000 | 1.07985 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1407.00i | 2.65974i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −429.325 | − | 480.000i | −0.803979 | − | 0.898876i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 536.656i | − | 1.00122i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 758.947 | − | 758.947i | 1.41068 | − | 1.41068i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −362.000 | −0.669131 | −0.334566 | − | 0.942372i | \(-0.608590\pi\) | ||||
−0.334566 | + | 0.942372i | \(0.608590\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −59.7592 | + | 1072.34i | −0.110054 | + | 1.97484i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 104.355 | + | 104.355i | 0.190777 | + | 0.190777i | 0.796032 | − | 0.605255i | \(-0.206929\pi\) |
−0.605255 | + | 0.796032i | \(0.706929\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −518.768 | − | 58.0000i | −0.944932 | − | 0.105647i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1054.36 | + | 58.7577i | 1.91008 | + | 0.106445i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 531.263 | + | 531.263i | 0.945307 | + | 0.945307i | ||||
\(563\) | 794.788 | + | 794.788i | 1.41170 | + | 1.41170i | 0.747977 | + | 0.663725i | \(0.231025\pi\) |
0.663725 | + | 0.747977i | \(0.268975\pi\) | |||||||
\(564\) | −35.7771 | + | 32.0000i | −0.0634346 | + | 0.0567376i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 939.149i | 1.65927i | ||||||||
\(567\) | 579.754 | + | 919.165i | 1.02249 | + | 1.62110i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1126.98 | −1.98063 | −0.990315 | − | 0.138840i | \(-0.955663\pi\) | ||||
−0.990315 | + | 0.138840i | \(0.955663\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1440.00i | 2.50871i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 64.0000 | − | 572.433i | 0.111111 | − | 0.993808i | ||||
\(577\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(578\) | 408.708 | + | 408.708i | 0.707107 | + | 0.707107i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1019.65i | 1.75499i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −760.847 | + | 760.847i | −1.29616 | + | 1.29616i | −0.365254 | + | 0.930908i | \(0.619018\pi\) |
−0.930908 | + | 0.365254i | \(0.880982\pi\) | |||||||
\(588\) | 87.4688 | − | 1569.56i | 0.148757 | − | 2.66933i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 429.325i | − | 0.720344i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −418.000 | −0.695507 | −0.347754 | − | 0.937586i | \(-0.613055\pi\) | ||||
−0.347754 | + | 0.937586i | \(0.613055\pi\) | |||||||
\(602\) | −763.675 | + | 763.675i | −1.26856 | + | 1.26856i | ||||
\(603\) | 376.830 | + | 471.698i | 0.624925 | + | 0.782252i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 720.000 | − | 643.988i | 1.18812 | − | 1.06269i | ||||
\(607\) | −521.776 | − | 521.776i | −0.859598 | − | 0.859598i | 0.131693 | − | 0.991291i | \(-0.457959\pi\) |
−0.991291 | + | 0.131693i | \(0.957959\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1609.97 | − | 1440.00i | 2.64363 | − | 2.36453i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(614\) | 295.161 | 0.480718 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(618\) | −1205.61 | − | 67.1861i | −1.95082 | − | 0.108715i | ||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −968.000 | + | 688.709i | −1.55878 | + | 1.10903i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1018.23 | − | 1018.23i | −1.63440 | − | 1.63440i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 590.322i | 0.920939i | 0.887676 | + | 0.460470i | \(0.152319\pi\) | ||||
−0.887676 | + | 0.460470i | \(0.847681\pi\) | |||||||
\(642\) | −742.847 | − | 41.3975i | −1.15708 | − | 0.0644820i | ||||
\(643\) | −863.302 | + | 863.302i | −1.34262 | + | 1.34262i | −0.449168 | + | 0.893447i | \(0.648280\pi\) |
−0.893447 | + | 0.449168i | \(0.851720\pi\) | |||||||
\(644\) | 2361.29 | 3.66660 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 675.994 | − | 675.994i | 1.04481 | − | 1.04481i | 0.0458655 | − | 0.998948i | \(-0.485395\pi\) |
0.998948 | − | 0.0458655i | \(-0.0146046\pi\) | |||||||
\(648\) | 345.699 | + | 548.084i | 0.533485 | + | 0.845809i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −796.894 | − | 796.894i | −1.22223 | − | 1.22223i | ||||
\(653\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | −169.941 | + | 152.000i | −0.259849 | + | 0.232416i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 858.650i | 1.30892i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −75.8947 | + | 75.8947i | −0.115341 | + | 0.115341i | ||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −298.000 | −0.450832 | −0.225416 | − | 0.974263i | \(-0.572374\pi\) | ||||
−0.225416 | + | 0.974263i | \(0.572374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 608.000i | 0.915663i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1669.68 | + | 1669.68i | 2.50327 | + | 2.50327i | ||||
\(668\) | 690.136 | + | 690.136i | 1.03314 | + | 1.03314i | ||||
\(669\) | 187.830 | + | 210.000i | 0.280762 | + | 0.313901i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 71.6652 | − | 1285.98i | 0.106645 | − | 1.91366i | ||||
\(673\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −676.000 | −1.00000 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 712.000 | + | 796.040i | 1.04552 | + | 1.16893i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −393.151 | − | 393.151i | −0.575624 | − | 0.575624i | 0.358070 | − | 0.933695i | \(-0.383435\pi\) |
−0.933695 | + | 0.358070i | \(0.883435\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 2200.29i | − | 3.20742i | ||||||
\(687\) | −784.782 | − | 43.7344i | −1.14233 | − | 0.0636600i | ||||
\(688\) | −455.368 | + | 455.368i | −0.661872 | + | 0.661872i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 232.000i | 0.334294i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 960.000 | − | 858.650i | 1.37931 | − | 1.23369i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −31.1127 | − | 31.1127i | −0.0445741 | − | 0.0445741i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1073.31i | − | 1.53112i | −0.643367 | − | 0.765558i | \(-0.722463\pi\) | ||
0.643367 | − | 0.765558i | \(-0.277537\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1527.35 | − | 1527.35i | 2.16033 | − | 2.16033i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 698.000i | 0.984485i | 0.870458 | + | 0.492243i | \(0.163823\pi\) | ||||
−0.870458 | + | 0.492243i | \(0.836177\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −607.157 | − | 607.157i | −0.852749 | − | 0.852749i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2700.00 | −3.74480 | ||||||||
\(722\) | 510.531 | − | 510.531i | 0.707107 | − | 0.707107i | ||||
\(723\) | 50.4114 | − | 904.596i | 0.0697254 | − | 1.25117i | ||||
\(724\) | 1432.00i | 1.97790i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −484.000 | − | 541.128i | −0.666667 | − | 0.745356i | ||||
\(727\) | −161.276 | − | 161.276i | −0.221838 | − | 0.221838i | 0.587434 | − | 0.809272i | \(-0.300138\pi\) |
−0.809272 | + | 0.587434i | \(0.800138\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −688.709 | − | 239.000i | −0.944731 | − | 0.327846i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −694.922 | − | 38.7267i | −0.949347 | − | 0.0529053i | ||||
\(733\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(734\) | 241.495 | 0.329013 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1408.00 | 1.91304 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −602.928 | − | 754.717i | −0.816975 | − | 1.02265i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −540.230 | − | 540.230i | −0.727092 | − | 0.727092i | 0.242947 | − | 0.970040i | \(-0.421886\pi\) |
−0.970040 | + | 0.242947i | \(0.921886\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −426.926 | − | 534.406i | −0.571521 | − | 0.715403i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1663.63 | −2.22114 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | −45.2548 | + | 45.2548i | −0.0601793 | + | 0.0601793i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 840.000 | + | 1180.64i | 1.11111 | + | 1.56170i | ||||
\(757\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1502.64i | 1.97456i | 0.159001 | + | 0.987278i | \(0.449173\pi\) | ||||
−0.159001 | + | 0.987278i | \(0.550827\pi\) | |||||||
\(762\) | −31.3535 | + | 562.616i | −0.0411464 | + | 0.738341i | ||||
\(763\) | −360.500 | + | 360.500i | −0.472477 | + | 0.472477i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 88.0000 | 0.114883 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 42.7329 | − | 766.810i | 0.0556418 | − | 0.998451i | ||||
\(769\) | − | 1342.00i | − | 1.74512i | −0.488504 | − | 0.872562i | \(-0.662457\pi\) | ||
0.488504 | − | 0.872562i | \(-0.337543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(774\) | 80.4984 | − | 720.000i | 0.104003 | − | 0.930233i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1062.53 | + | 1062.53i | −1.36571 | + | 1.36571i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −240.872 | + | 1428.81i | −0.307627 | + | 1.82479i | ||||
\(784\) | − | 2096.00i | − | 2.67347i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1109.96 | − | 1109.96i | −1.41037 | − | 1.41037i | −0.757296 | − | 0.653072i | \(-0.773480\pi\) |
−0.653072 | − | 0.757296i | \(-0.726520\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −635.043 | + | 568.000i | −0.804871 | + | 0.719899i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 960.000 | + | 107.331i | 1.19850 | + | 0.133997i | ||||
\(802\) | 910.736 | + | 910.736i | 1.13558 | + | 1.13558i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 536.656 | + | 600.000i | 0.667483 | + | 0.746269i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −89.5815 | + | 1607.47i | −0.111006 | + | 1.99191i | ||||
\(808\) | 910.736 | − | 910.736i | 1.12715 | − | 1.12715i | ||||
\(809\) | 965.981 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296351\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 2036.47 | − | 2036.47i | 2.50796 | − | 2.50796i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1134.20 | − | 1134.20i | −1.38655 | − | 1.38655i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1502.64i | 1.83025i | 0.403167 | + | 0.915126i | \(0.367909\pi\) | ||||
−0.403167 | + | 0.915126i | \(0.632091\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −616.644 | + | 616.644i | −0.749264 | + | 0.749264i | −0.974341 | − | 0.225077i | \(-0.927737\pi\) |
0.225077 | + | 0.974341i | \(0.427737\pi\) | |||||||
\(824\) | −1609.97 | −1.95385 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −421.436 | + | 421.436i | −0.509596 | + | 0.509596i | −0.914402 | − | 0.404807i | \(-0.867339\pi\) |
0.404807 | + | 0.914402i | \(0.367339\pi\) | |||||||
\(828\) | −1237.57 | + | 988.671i | −1.49465 | + | 1.19405i | ||||
\(829\) | − | 1478.00i | − | 1.78287i | −0.453148 | − | 0.891435i | \(-0.649699\pi\) | ||
0.453148 | − | 0.891435i | \(-0.350301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2039.00 | 2.42449 | ||||||||
\(842\) | −1100.26 | + | 1100.26i | −1.30672 | + | 1.30672i | ||||
\(843\) | −1125.23 | − | 62.7070i | −1.33480 | − | 0.0743856i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.00000 | − | 71.5542i | 0.00945626 | − | 0.0845794i | ||||
\(847\) | −1147.91 | − | 1147.91i | −1.35526 | − | 1.35526i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −939.149 | − | 1050.00i | −1.10618 | − | 1.23675i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | −1556.30 | −1.82237 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −992.000 | −1.15888 | ||||||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1440.00 | − | 1609.97i | −1.67247 | − | 1.86988i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1156.83 | + | 1156.83i | 1.34047 | + | 1.34047i | 0.895589 | + | 0.444882i | \(0.146754\pi\) |
0.444882 | + | 0.895589i | \(0.353246\pi\) | |||||||
\(864\) | 500.879 | + | 704.000i | 0.579721 | + | 0.814815i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −865.657 | − | 48.2414i | −0.998451 | − | 0.0556418i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −214.960 | + | 214.960i | −0.246514 | + | 0.246514i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 697.653i | − | 0.791888i | −0.918275 | − | 0.395944i | \(-0.870417\pi\) | ||
0.918275 | − | 0.395944i | \(-0.129583\pi\) | |||||||
\(882\) | 1471.77 | + | 1842.30i | 1.66868 | + | 2.08877i | ||||
\(883\) | 863.302 | − | 863.302i | 0.977692 | − | 0.977692i | −0.0220648 | − | 0.999757i | \(-0.507024\pi\) |
0.999757 | + | 0.0220648i | \(0.00702402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1592.00 | 1.79684 | ||||||||
\(887\) | 681.651 | − | 681.651i | 0.768490 | − | 0.768490i | −0.209350 | − | 0.977841i | \(-0.567135\pi\) |
0.977841 | + | 0.209350i | \(0.0671349\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1260.00i | 1.41732i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 265.631 | + | 265.631i | 0.297793 | + | 0.297793i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 429.325 | + | 480.000i | 0.480229 | + | 0.536913i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1717.30i | − | 1.91663i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1138.42 | + | 1138.42i | −1.26773 | + | 1.26773i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 90.1396 | − | 1617.49i | 0.0998224 | − | 1.79124i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 180.250 | + | 180.250i | 0.198732 | + | 0.198732i | 0.799456 | − | 0.600724i | \(-0.205121\pi\) |
−0.600724 | + | 0.799456i | \(0.705121\pi\) | |||||||
\(908\) | 1006.92 | + | 1006.92i | 1.10894 | + | 1.10894i | ||||
\(909\) | −160.997 | + | 1440.00i | −0.177114 | + | 1.58416i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1048.00 | −1.14410 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −330.000 | + | 295.161i | −0.358306 | + | 0.320479i | ||||
\(922\) | −531.263 | − | 531.263i | −0.576207 | − | 0.576207i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1046.48i | 1.13011i | ||||||||
\(927\) | 1415.09 | − | 1130.49i | 1.52653 | − | 1.21951i | ||||
\(928\) | 1214.31 | − | 1214.31i | 1.30853 | − | 1.30853i | ||||
\(929\) | 1770.97 | 1.90631 | 0.953157 | − | 0.302476i | \(-0.0978131\pi\) | ||||
0.953157 | + | 0.302476i | \(0.0978131\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 248.000i | 0.265525i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(938\) | 1272.79 | + | 1272.79i | 1.35692 | + | 1.35692i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1878.30i | − | 1.99606i | −0.0626993 | − | 0.998032i | \(-0.519971\pi\) | ||
0.0626993 | − | 0.998032i | \(-0.480029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1669.68 | − | 1669.68i | 1.77061 | − | 1.77061i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1275.62 | + | 1275.62i | −1.34701 | + | 1.34701i | −0.458124 | + | 0.888888i | \(0.651478\pi\) |
−0.888888 | + | 0.458124i | \(0.848522\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 961.000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 871.926 | − | 696.564i | 0.905427 | − | 0.723327i | ||||
\(964\) | − | 1208.00i | − | 1.25311i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2640.00 | + | 2361.29i | −2.73292 | + | 2.44440i | ||||
\(967\) | 1356.62 | + | 1356.62i | 1.40291 | + | 1.40291i | 0.790668 | + | 0.612246i | \(0.209734\pi\) |
0.612246 | + | 0.790668i | \(0.290266\pi\) | |||||||
\(968\) | −684.479 | − | 684.479i | −0.707107 | − | 0.707107i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −934.587 | − | 267.078i | −0.961509 | − | 0.274772i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1690.47 | 1.73559 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −928.000 | −0.950820 | ||||||||
\(977\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 1687.85 | + | 94.0606i | 1.72582 | + | 0.0961765i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.0000 | − | 339.882i | 0.0387360 | − | 0.346465i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 200.818 | + | 200.818i | 0.204291 | + | 0.204291i | 0.801836 | − | 0.597544i | \(-0.203857\pi\) |
−0.597544 | + | 0.801836i | \(0.703857\pi\) | |||||||
\(984\) | −858.650 | − | 960.000i | −0.872612 | − | 0.975610i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.95815 | − | 160.747i | 0.00907614 | − | 0.162865i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1770.97 | 1.79066 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −608.000 | − | 679.765i | −0.610442 | − | 0.682495i | ||||
\(997\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 300.3.l.f.143.2 | yes | 8 | |
3.2 | odd | 2 | inner | 300.3.l.f.143.4 | yes | 8 | |
4.3 | odd | 2 | inner | 300.3.l.f.143.3 | yes | 8 | |
5.2 | odd | 4 | inner | 300.3.l.f.107.1 | ✓ | 8 | |
5.3 | odd | 4 | inner | 300.3.l.f.107.4 | yes | 8 | |
5.4 | even | 2 | inner | 300.3.l.f.143.3 | yes | 8 | |
12.11 | even | 2 | inner | 300.3.l.f.143.1 | yes | 8 | |
15.2 | even | 4 | inner | 300.3.l.f.107.3 | yes | 8 | |
15.8 | even | 4 | inner | 300.3.l.f.107.2 | yes | 8 | |
15.14 | odd | 2 | inner | 300.3.l.f.143.1 | yes | 8 | |
20.3 | even | 4 | inner | 300.3.l.f.107.1 | ✓ | 8 | |
20.7 | even | 4 | inner | 300.3.l.f.107.4 | yes | 8 | |
20.19 | odd | 2 | CM | 300.3.l.f.143.2 | yes | 8 | |
60.23 | odd | 4 | inner | 300.3.l.f.107.3 | yes | 8 | |
60.47 | odd | 4 | inner | 300.3.l.f.107.2 | yes | 8 | |
60.59 | even | 2 | inner | 300.3.l.f.143.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.3.l.f.107.1 | ✓ | 8 | 5.2 | odd | 4 | inner | |
300.3.l.f.107.1 | ✓ | 8 | 20.3 | even | 4 | inner | |
300.3.l.f.107.2 | yes | 8 | 15.8 | even | 4 | inner | |
300.3.l.f.107.2 | yes | 8 | 60.47 | odd | 4 | inner | |
300.3.l.f.107.3 | yes | 8 | 15.2 | even | 4 | inner | |
300.3.l.f.107.3 | yes | 8 | 60.23 | odd | 4 | inner | |
300.3.l.f.107.4 | yes | 8 | 5.3 | odd | 4 | inner | |
300.3.l.f.107.4 | yes | 8 | 20.7 | even | 4 | inner | |
300.3.l.f.143.1 | yes | 8 | 12.11 | even | 2 | inner | |
300.3.l.f.143.1 | yes | 8 | 15.14 | odd | 2 | inner | |
300.3.l.f.143.2 | yes | 8 | 1.1 | even | 1 | trivial | |
300.3.l.f.143.2 | yes | 8 | 20.19 | odd | 2 | CM | |
300.3.l.f.143.3 | yes | 8 | 4.3 | odd | 2 | inner | |
300.3.l.f.143.3 | yes | 8 | 5.4 | even | 2 | inner | |
300.3.l.f.143.4 | yes | 8 | 3.2 | odd | 2 | inner | |
300.3.l.f.143.4 | yes | 8 | 60.59 | even | 2 | inner |