Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(176,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (of order \(2\), degree \(1\), 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: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-59}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 15 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 176.2 | ||
Root | \(0.500000 - 3.84057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.4.d.a.176.1 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 3.50000 | + | 3.84057i | 0.673575 | + | 0.739119i | ||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | − | 7.68115i | − | 0.687023i | −0.939149 | − | 0.343511i | \(-0.888384\pi\) | ||
0.939149 | − | 0.343511i | \(-0.111616\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.0000 | 1.56585 | 0.782926 | − | 0.622114i | \(-0.213726\pi\) | ||||
0.782926 | + | 0.622114i | \(0.213726\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.50000 | + | 26.8840i | −0.0925926 | + | 0.995704i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −28.0000 | − | 30.7246i | −0.673575 | − | 0.739119i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 29.5000 | − | 26.8840i | 0.507791 | − | 0.462761i | ||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | 61.4492i | 0.876683i | 0.898808 | + | 0.438342i | \(0.144434\pi\) | ||||
−0.898808 | + | 0.438342i | \(0.855566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 119.000 | 1.43687 | 0.718433 | − | 0.695596i | \(-0.244859\pi\) | ||||
0.718433 | + | 0.695596i | \(0.244859\pi\) | |||||||
\(20\) | 61.4492i | 0.687023i | ||||||||
\(21\) | 101.500 | + | 111.377i | 1.05472 | + | 1.15735i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 66.0000 | 0.528000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −112.000 | + | 84.4926i | −0.798311 | + | 0.602245i | ||||
\(28\) | −232.000 | −1.56585 | ||||||||
\(29\) | 268.840i | 1.72146i | 0.509061 | + | 0.860730i | \(0.329993\pi\) | ||||
−0.509061 | + | 0.860730i | \(0.670007\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 222.753i | − | 1.07578i | ||||||
\(36\) | 20.0000 | − | 215.072i | 0.0925926 | − | 0.995704i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.68115i | − | 0.0292584i | −0.999893 | − | 0.0146292i | \(-0.995343\pi\) | ||
0.999893 | − | 0.0146292i | \(-0.00465678\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 206.500 | + | 19.2029i | 0.684071 | + | 0.0636132i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 224.000 | + | 245.797i | 0.673575 | + | 0.739119i | ||||
\(49\) | 498.000 | 1.45190 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −236.000 | + | 215.072i | −0.647973 | + | 0.590512i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 698.984i | − | 1.81156i | −0.423744 | − | 0.905782i | \(-0.639285\pi\) | ||
0.423744 | − | 0.905782i | \(-0.360715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 416.500 | + | 457.028i | 0.967838 | + | 1.06202i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 453.188i | − | 1.00000i | ||||||
\(60\) | −236.000 | + | 215.072i | −0.507791 | + | 0.462761i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −72.5000 | + | 779.636i | −0.144986 | + | 1.55913i | ||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | − | 491.593i | − | 0.876683i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1182.90i | − | 1.97724i | −0.150437 | − | 0.988620i | \(-0.548068\pi\) | ||
0.150437 | − | 0.988620i | \(-0.451932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 231.000 | + | 253.478i | 0.355648 | + | 0.390255i | ||||
\(76\) | −952.000 | −1.43687 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −835.000 | −1.18918 | −0.594588 | − | 0.804031i | \(-0.702685\pi\) | ||||
−0.594588 | + | 0.804031i | \(0.702685\pi\) | |||||||
\(80\) | − | 491.593i | − | 0.687023i | ||||||
\(81\) | −716.500 | − | 134.420i | −0.982853 | − | 0.184390i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −812.000 | − | 891.013i | −1.05472 | − | 1.15735i | ||||
\(85\) | 472.000 | 0.602301 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1032.50 | + | 940.940i | −1.27236 | + | 1.15953i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 914.056i | − | 0.987160i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −528.000 | −0.528000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 855.500 | − | 779.636i | 0.795126 | − | 0.724616i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2204.49i | 1.99174i | 0.0908010 | + | 0.995869i | \(0.471057\pi\) | ||||
−0.0908010 | + | 0.995869i | \(0.528943\pi\) | |||||||
\(108\) | 896.000 | − | 675.941i | 0.798311 | − | 0.602245i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1856.00 | 1.56585 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 2150.72i | − | 1.72146i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1782.03i | 1.37276i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1331.00 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 29.5000 | − | 26.8840i | 0.0216254 | − | 0.0197077i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1467.10i | − | 1.04977i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 821.000 | 0.573638 | 0.286819 | − | 0.957985i | \(-0.407402\pi\) | ||||
0.286819 | + | 0.957985i | \(0.407402\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3451.00 | 2.24992 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 649.000 | + | 860.288i | 0.413756 | + | 0.548458i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3172.31i | 1.97831i | 0.146862 | + | 0.989157i | \(0.453083\pi\) | ||||
−0.146862 | + | 0.989157i | \(0.546917\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1960.00 | −1.19601 | −0.598004 | − | 0.801493i | \(-0.704039\pi\) | ||||
−0.598004 | + | 0.801493i | \(0.704039\pi\) | |||||||
\(140\) | 1782.03i | 1.07578i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −160.000 | + | 1720.58i | −0.0925926 | + | 0.995704i | ||||
\(145\) | 2065.00 | 1.18268 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1743.00 | + | 1912.61i | 0.977961 | + | 1.07312i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1652.00 | − | 153.623i | −0.872917 | − | 0.0811744i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2684.50 | − | 2446.44i | 1.33896 | − | 1.22022i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4048.00 | −1.94518 | −0.972588 | − | 0.232533i | \(-0.925299\pi\) | ||||
−0.972588 | + | 0.232533i | \(0.925299\pi\) | |||||||
\(164\) | 61.4492i | 0.0292584i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3325.94i | − | 1.54113i | −0.637362 | − | 0.770565i | \(-0.719974\pi\) | ||
0.637362 | − | 0.770565i | \(-0.280026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2197.00 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −297.500 | + | 3199.20i | −0.133043 | + | 1.43069i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1914.00 | 0.826770 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1740.50 | − | 1586.16i | 0.739119 | − | 0.673575i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −1652.00 | − | 153.623i | −0.684071 | − | 0.0636132i | ||||
\(181\) | −4795.00 | −1.96911 | −0.984557 | − | 0.175066i | \(-0.943986\pi\) | ||||
−0.984557 | + | 0.175066i | \(0.943986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3248.00 | + | 2450.29i | −1.25004 | + | 0.943027i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −1792.00 | − | 1966.37i | −0.673575 | − | 0.739119i | ||||
\(193\) | 1937.00 | 0.722426 | 0.361213 | − | 0.932483i | \(-0.382363\pi\) | ||||
0.361213 | + | 0.932483i | \(0.382363\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3984.00 | −1.45190 | ||||||||
\(197\) | − | 4086.37i | − | 1.47788i | −0.673773 | − | 0.738939i | \(-0.735327\pi\) | ||
0.673773 | − | 0.738939i | \(-0.264673\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5411.00 | 1.92752 | 0.963758 | − | 0.266779i | \(-0.0859592\pi\) | ||||
0.963758 | + | 0.266779i | \(0.0859592\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7796.36i | 2.69555i | ||||||||
\(204\) | 1888.00 | − | 1720.58i | 0.647973 | − | 0.590512i | ||||
\(205\) | −59.0000 | −0.0201012 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 5591.87i | 1.81156i | ||||||||
\(213\) | 4543.00 | − | 4140.14i | 1.46141 | − | 1.33182i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5852.00 | 1.75730 | 0.878652 | − | 0.477462i | \(-0.158443\pi\) | ||||
0.878652 | + | 0.477462i | \(0.158443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −165.000 | + | 1774.34i | −0.0488889 | + | 0.525732i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | −3332.00 | − | 3656.23i | −0.967838 | − | 1.06202i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3625.50i | 1.00000i | ||||||||
\(237\) | −2922.50 | − | 3206.88i | −0.800999 | − | 0.878941i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7043.61i | 1.90633i | 0.302448 | + | 0.953166i | \(0.402196\pi\) | ||||
−0.302448 | + | 0.953166i | \(0.597804\pi\) | |||||||
\(240\) | 1888.00 | − | 1720.58i | 0.507791 | − | 0.462761i | ||||
\(241\) | −5803.00 | −1.55105 | −0.775527 | − | 0.631314i | \(-0.782516\pi\) | ||||
−0.775527 | + | 0.631314i | \(0.782516\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1991.50 | − | 3222.24i | −0.525740 | − | 0.850645i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3825.21i | − | 0.997485i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7750.28i | − | 1.94898i | −0.224439 | − | 0.974488i | \(-0.572055\pi\) | ||
0.224439 | − | 0.974488i | \(-0.427945\pi\) | |||||||
\(252\) | 580.000 | − | 6237.09i | 0.144986 | − | 1.55913i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1652.00 | + | 1812.75i | 0.405695 | + | 0.445172i | ||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | − | 3325.94i | − | 0.807261i | −0.914922 | − | 0.403631i | \(-0.867748\pi\) | ||
0.914922 | − | 0.403631i | \(-0.132252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7227.50 | − | 672.100i | −1.71407 | − | 0.159394i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8441.58i | − | 1.97920i | −0.143840 | − | 0.989601i | \(-0.545945\pi\) | ||
0.143840 | − | 0.989601i | \(-0.454055\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5369.00 | −1.24459 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8575.00 | −1.92212 | −0.961059 | − | 0.276342i | \(-0.910878\pi\) | ||||
−0.961059 | + | 0.276342i | \(0.910878\pi\) | |||||||
\(272\) | 3932.75i | 0.876683i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9151.00 | −1.98495 | −0.992473 | − | 0.122460i | \(-0.960922\pi\) | ||||
−0.992473 | + | 0.122460i | \(0.960922\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 268.840i | 0.0570735i | 0.999593 | + | 0.0285368i | \(0.00908476\pi\) | ||||
−0.999593 | + | 0.0285368i | \(0.990915\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 9463.17i | 1.97724i | ||||||||
\(285\) | 3510.50 | − | 3199.20i | 0.729628 | − | 0.664927i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 222.753i | − | 0.0458143i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1137.00 | 0.231427 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5384.48i | 1.07360i | 0.843709 | + | 0.536800i | \(0.180367\pi\) | ||||
−0.843709 | + | 0.536800i | \(0.819633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3481.00 | −0.687023 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1848.00 | − | 2027.82i | −0.355648 | − | 0.390255i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7616.00 | 1.43687 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3661.00 | −0.680600 | −0.340300 | − | 0.940317i | \(-0.610529\pi\) | ||||
−0.340300 | + | 0.940317i | \(0.610529\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8718.10i | − | 1.58958i | −0.606887 | − | 0.794788i | \(-0.707582\pi\) | ||
0.606887 | − | 0.794788i | \(-0.292418\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5988.50 | + | 556.883i | 1.07115 | + | 0.0996089i | ||||
\(316\) | 6680.00 | 1.18918 | ||||||||
\(317\) | − | 215.072i | − | 0.0381062i | −0.999818 | − | 0.0190531i | \(-0.993935\pi\) | ||
0.999818 | − | 0.0190531i | \(-0.00606515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3932.75i | 0.687023i | ||||||||
\(321\) | −8466.50 | + | 7715.71i | −1.47213 | + | 1.34159i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7312.45i | 1.25968i | ||||||||
\(324\) | 5732.00 | + | 1075.36i | 0.982853 | + | 0.184390i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12017.0 | 1.99551 | 0.997755 | − | 0.0669643i | \(-0.0213314\pi\) | ||||
0.997755 | + | 0.0669643i | \(0.0213314\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6496.00 | + | 7128.10i | 1.05472 | + | 1.15735i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3776.00 | −0.602301 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4495.00 | 0.707601 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 8260.00 | − | 7527.52i | 1.27236 | − | 1.15953i | ||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9086.00 | −1.35841 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6844.00 | + | 6237.09i | −1.01463 | + | 0.924655i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8011.44i | 1.17779i | 0.808209 | + | 0.588896i | \(0.200437\pi\) | ||||
−0.808209 | + | 0.588896i | \(0.799563\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7302.00 | 1.06459 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4658.50 | − | 5111.80i | −0.673575 | − | 0.739119i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 206.500 | + | 19.2029i | 0.0291327 | + | 0.00270911i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 20270.5i | − | 2.83664i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4898.00 | 0.679916 | 0.339958 | − | 0.940441i | \(-0.389587\pi\) | ||||
0.339958 | + | 0.940441i | \(0.389587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5634.50 | − | 5134.85i | 0.775905 | − | 0.707099i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13025.0 | 1.76530 | 0.882651 | − | 0.470029i | \(-0.155757\pi\) | ||||
0.882651 | + | 0.470029i | \(0.155757\pi\) | |||||||
\(380\) | 7312.45i | 0.987160i | ||||||||
\(381\) | 2873.50 | + | 3153.11i | 0.386388 | + | 0.423986i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14025.8i | 1.87124i | 0.353014 | + | 0.935618i | \(0.385157\pi\) | ||||
−0.353014 | + | 0.935618i | \(0.614843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 11829.0i | − | 1.54178i | −0.636968 | − | 0.770890i | \(-0.719812\pi\) | ||
0.636968 | − | 0.770890i | \(-0.280188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6413.76i | 0.816990i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12078.5 | + | 13253.8i | 1.51549 | + | 1.66296i | ||||
\(400\) | 4224.00 | 0.528000 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1032.50 | + | 5503.54i | −0.126680 | + | 0.675242i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12183.5 | + | 11103.1i | −1.46221 | + | 1.33254i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 13142.4i | − | 1.56585i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6860.00 | − | 7527.52i | −0.805601 | − | 0.883991i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | −6844.00 | + | 6237.09i | −0.795126 | + | 0.724616i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4055.64i | 0.462889i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 17635.9i | − | 1.99174i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −7168.00 | + | 5407.53i | −0.798311 | + | 0.602245i | ||||
\(433\) | −14623.0 | −1.62295 | −0.811474 | − | 0.584388i | \(-0.801334\pi\) | ||||
−0.811474 | + | 0.584388i | \(0.801334\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7227.50 | + | 7930.78i | 0.796626 | + | 0.874142i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3220.00 | −0.350073 | −0.175037 | − | 0.984562i | \(-0.556004\pi\) | ||||
−0.175037 | + | 0.984562i | \(0.556004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1245.00 | + | 13388.2i | −0.134435 | + | 1.44566i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14848.0 | −1.56585 | ||||||||
\(449\) | − | 9409.40i | − | 0.988992i | −0.869180 | − | 0.494496i | \(-0.835353\pi\) | ||
0.869180 | − | 0.494496i | \(-0.164647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5192.00 | − | 6882.31i | −0.527978 | − | 0.699866i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13488.1i | − | 1.36270i | −0.731959 | − | 0.681348i | \(-0.761394\pi\) | ||
0.731959 | − | 0.681348i | \(-0.238606\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 17205.8i | 1.72146i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7854.00 | 0.758666 | ||||||||
\(476\) | − | 14256.2i | − | 1.37276i | ||||||
\(477\) | 18791.5 | + | 1747.46i | 1.80378 | + | 0.167737i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1459.42i | − | 0.139212i | −0.997575 | − | 0.0696059i | \(-0.977826\pi\) | ||
0.997575 | − | 0.0696059i | \(-0.0221742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10648.0 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19721.0 | 1.83500 | 0.917499 | − | 0.397739i | \(-0.130205\pi\) | ||||
0.917499 | + | 0.397739i | \(0.130205\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14168.0 | − | 15546.6i | −1.31022 | − | 1.43772i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9947.08i | 0.914268i | 0.889398 | + | 0.457134i | \(0.151124\pi\) | ||||
−0.889398 | + | 0.457134i | \(0.848876\pi\) | |||||||
\(492\) | −236.000 | + | 215.072i | −0.0216254 | + | 0.0197077i | ||||
\(493\) | −16520.0 | −1.50918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 34304.0i | − | 3.09607i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9511.00 | −0.853248 | −0.426624 | − | 0.904429i | \(-0.640297\pi\) | ||||
−0.426624 | + | 0.904429i | \(0.640297\pi\) | |||||||
\(500\) | 11736.8i | 1.04977i | ||||||||
\(501\) | 12773.5 | − | 11640.8i | 1.13908 | − | 1.03807i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7689.50 | + | 8437.74i | 0.673575 | + | 0.739119i | ||||
\(508\) | −6568.00 | −0.573638 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13328.0 | + | 10054.6i | −1.14707 | + | 0.865346i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11552.4i | − | 0.971443i | −0.874114 | − | 0.485721i | \(-0.838557\pi\) | ||
0.874114 | − | 0.485721i | \(-0.161443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6167.00 | 0.515610 | 0.257805 | − | 0.966197i | \(-0.417001\pi\) | ||||
0.257805 | + | 0.966197i | \(0.417001\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6699.00 | + | 7350.86i | 0.556892 | + | 0.611081i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12183.5 | + | 1132.97i | 0.995704 | + | 0.0925926i | ||||
\(532\) | −27608.0 | −2.24992 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16933.0 | 1.36837 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5192.00 | − | 6882.31i | −0.413756 | − | 0.548458i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16782.5 | − | 18415.5i | −1.32635 | − | 1.45541i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12616.0 | −0.986145 | −0.493072 | − | 0.869988i | \(-0.664126\pi\) | ||||
−0.493072 | + | 0.869988i | \(0.664126\pi\) | |||||||
\(548\) | − | 25378.5i | − | 1.97831i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31992.0i | 2.47351i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24215.0 | −1.86207 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15680.0 | 1.19601 | ||||||||
\(557\) | 8011.44i | 0.609435i | 0.952443 | + | 0.304718i | \(0.0985621\pi\) | ||||
−0.952443 | + | 0.304718i | \(0.901438\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | − | 14256.2i | − | 1.07578i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20778.5 | − | 3898.18i | −1.53900 | − | 0.288727i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1280.00 | − | 13764.6i | 0.0925926 | − | 0.995704i | ||||
\(577\) | 9569.00 | 0.690403 | 0.345202 | − | 0.938529i | \(-0.387811\pi\) | ||||
0.345202 | + | 0.938529i | \(0.387811\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6779.50 | + | 7439.19i | 0.486609 | + | 0.533959i | ||||
\(580\) | −16520.0 | −1.18268 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −13944.0 | − | 15300.8i | −0.977961 | − | 1.07312i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15694.0 | − | 14302.3i | 1.09233 | − | 0.995461i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6767.09i | 0.468619i | 0.972162 | + | 0.234309i | \(0.0752829\pi\) | ||||
−0.972162 | + | 0.234309i | \(0.924717\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13688.0 | 0.943115 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18938.5 | + | 20781.3i | 1.29833 | + | 1.42466i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24464.4i | 1.66877i | 0.551186 | + | 0.834383i | \(0.314176\pi\) | ||||
−0.551186 | + | 0.834383i | \(0.685824\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10223.6i | 0.687023i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25319.0 | 1.69303 | 0.846513 | − | 0.532368i | \(-0.178698\pi\) | ||||
0.846513 | + | 0.532368i | \(0.178698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29942.5 | + | 27287.3i | −1.99233 | + | 1.81566i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 13216.0 | + | 1228.98i | 0.872917 | + | 0.0811744i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −206.500 | − | 226.594i | −0.0135396 | − | 0.0148571i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 16184.2i | − | 1.05600i | −0.849245 | − | 0.527999i | \(-0.822943\pi\) | ||
0.849245 | − | 0.527999i | \(-0.177057\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30485.0 | 1.97948 | 0.989738 | − | 0.142894i | \(-0.0456409\pi\) | ||||
0.989738 | + | 0.142894i | \(0.0456409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3019.00 | −0.193216 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29860.0 | −1.88385 | −0.941924 | − | 0.335827i | \(-0.890984\pi\) | ||||
−0.941924 | + | 0.335827i | \(0.890984\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 6306.22i | − | 0.394102i | ||||||
\(636\) | −21476.0 | + | 19571.6i | −1.33896 | + | 1.22022i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 31801.0 | + | 2957.24i | 1.96875 | + | 0.183078i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17205.8i | 1.06020i | 0.847936 | + | 0.530099i | \(0.177845\pi\) | ||||
−0.847936 | + | 0.530099i | \(0.822155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18907.0 | −1.15959 | −0.579797 | − | 0.814761i | \(-0.696868\pi\) | ||||
−0.579797 | + | 0.814761i | \(0.696868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32898.3i | 1.99902i | 0.0312629 | + | 0.999511i | \(0.490047\pi\) | ||||
−0.0312629 | + | 0.999511i | \(0.509953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32384.0 | 1.94518 | ||||||||
\(653\) | − | 24894.6i | − | 1.49188i | −0.666011 | − | 0.745942i | \(-0.731999\pi\) | ||
0.666011 | − | 0.745942i | \(-0.268001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 491.593i | − | 0.0292584i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31745.0 | 1.86798 | 0.933992 | − | 0.357294i | \(-0.116301\pi\) | ||||
0.933992 | + | 0.357294i | \(0.116301\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 26507.6i | − | 1.54575i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 26607.5i | 1.54113i | ||||||||
\(669\) | 20482.0 | + | 22475.0i | 1.18368 | + | 1.29886i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7392.00 | + | 5576.51i | −0.421508 | + | 0.317985i | ||||
\(676\) | −17576.0 | −1.00000 | ||||||||
\(677\) | − | 33397.6i | − | 1.89597i | −0.318308 | − | 0.947987i | \(-0.603115\pi\) | ||
0.318308 | − | 0.947987i | \(-0.396885\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 2380.00 | − | 25593.6i | 0.133043 | − | 1.43069i | ||||
\(685\) | 24367.0 | 1.35915 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15055.0i | 0.821684i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 472.000 | 0.0256503 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15312.0 | −0.826770 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13924.0 | + | 12689.3i | −0.739119 | + | 0.673575i | ||||
\(709\) | −14929.0 | −0.790790 | −0.395395 | − | 0.918511i | \(-0.629392\pi\) | ||||
−0.395395 | + | 0.918511i | \(0.629392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2087.50 | − | 22448.1i | 0.110109 | − | 1.18407i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27051.5 | + | 24652.6i | −1.40901 | + | 1.28406i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 13216.0 | + | 1228.98i | 0.684071 | + | 0.0636132i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20310.5 | − | 22286.8i | −1.04475 | − | 1.14641i | ||||
\(724\) | 38360.0 | 1.96911 | ||||||||
\(725\) | 17743.4i | 0.908931i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39116.0 | 1.99551 | 0.997753 | − | 0.0670071i | \(-0.0213450\pi\) | ||||
0.997753 | + | 0.0670071i | \(0.0213450\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5405.00 | − | 18926.3i | 0.274602 | − | 0.961558i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9898.00 | −0.498760 | −0.249380 | − | 0.968406i | \(-0.580227\pi\) | ||||
−0.249380 | + | 0.968406i | \(0.580227\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14691.0 | − | 13388.2i | 0.737259 | − | 0.671881i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35594.4i | 1.75751i | 0.477269 | + | 0.878757i | \(0.341627\pi\) | ||||
−0.477269 | + | 0.878757i | \(0.658373\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 63930.2i | 3.11877i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29765.5 | − | 27126.0i | 1.44052 | − | 1.31278i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 25984.0 | − | 19602.3i | 1.25004 | − | 0.943027i | ||||
\(757\) | −19861.0 | −0.953580 | −0.476790 | − | 0.879017i | \(-0.658200\pi\) | ||||
−0.476790 | + | 0.879017i | \(0.658200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34419.2i | 1.63955i | 0.572688 | + | 0.819774i | \(0.305901\pi\) | ||||
−0.572688 | + | 0.819774i | \(0.694099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1180.00 | + | 12689.3i | −0.0557686 | + | 0.599714i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 14336.0 | + | 15731.0i | 0.673575 | + | 0.739119i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12773.5 | − | 11640.8i | 0.596662 | − | 0.543751i | ||||
\(772\) | −15496.0 | −0.722426 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 914.056i | − | 0.0420404i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22715.0 | − | 30110.1i | −1.03674 | − | 1.37426i | ||||
\(784\) | 31872.0 | 1.45190 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42784.0 | −1.93785 | −0.968923 | − | 0.247362i | \(-0.920436\pi\) | ||||
−0.968923 | + | 0.247362i | \(0.920436\pi\) | |||||||
\(788\) | 32691.0i | 1.47788i | ||||||||
\(789\) | 32420.5 | − | 29545.5i | 1.46286 | − | 1.33314i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18791.5 | − | 20620.0i | −0.838322 | − | 0.919896i | ||||
\(796\) | −43288.0 | −1.92752 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | − | 62370.9i | − | 2.69555i | ||||||
\(813\) | −30012.5 | − | 32932.9i | −1.29469 | − | 1.42067i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31093.3i | 1.33638i | ||||||||
\(816\) | −15104.0 | + | 13764.6i | −0.647973 | + | 0.590512i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 472.000 | 0.0201012 | ||||||||
\(821\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18603.7i | − | 0.782243i | −0.920339 | − | 0.391122i | \(-0.872087\pi\) | ||
0.920339 | − | 0.391122i | \(-0.127913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28091.0 | 1.17689 | 0.588444 | − | 0.808538i | \(-0.299741\pi\) | ||||
0.588444 | + | 0.808538i | \(0.299741\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32028.5 | − | 35145.1i | −1.33701 | − | 1.46711i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30601.7i | 1.27285i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25547.0 | −1.05879 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −47886.0 | −1.96343 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1032.50 | + | 940.940i | −0.0421841 | + | 0.0384433i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 16875.5i | − | 0.687023i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38599.0 | −1.56585 | ||||||||
\(848\) | − | 44735.0i | − | 1.81156i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −36344.0 | + | 33121.1i | −1.46141 | + | 1.33182i | ||||
\(853\) | 13853.0 | 0.556058 | 0.278029 | − | 0.960573i | \(-0.410319\pi\) | ||||
0.278029 | + | 0.960573i | \(0.410319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24573.5 | + | 2285.14i | 0.982919 | + | 0.0914037i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 855.500 | − | 779.636i | 0.0338622 | − | 0.0308594i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3979.50 | + | 4366.73i | 0.155883 | + | 0.171052i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 42545.9i | − | 1.64379i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50591.0 | 1.94793 | 0.973966 | − | 0.226693i | \(-0.0727915\pi\) | ||||
0.973966 | + | 0.226693i | \(0.0727915\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20679.5 | + | 18845.7i | −0.793518 | + | 0.723151i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52477.0 | −1.99999 | −0.999995 | − | 0.00307379i | \(-0.999022\pi\) | ||||
−0.999995 | + | 0.00307379i | \(0.999022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12183.5 | − | 13369.0i | −0.462761 | − | 0.507791i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23809.0 | 0.898232 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −46816.0 | −1.75730 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1320.00 | − | 14194.8i | 0.0488889 | − | 0.525732i | ||||
\(901\) | 42952.0 | 1.58817 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36831.1i | 1.35283i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20869.0 | −0.763995 | −0.381998 | − | 0.924163i | \(-0.624764\pi\) | ||||
−0.381998 | + | 0.924163i | \(0.624764\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8979.26i | 0.326560i | 0.986580 | + | 0.163280i | \(0.0522074\pi\) | ||||
−0.986580 | + | 0.163280i | \(0.947793\pi\) | |||||||
\(912\) | 26656.0 | + | 29249.8i | 0.967838 | + | 1.06202i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12813.5 | − | 14060.3i | −0.458436 | − | 0.503044i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 59262.0 | 2.08618 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33482.5 | − | 30513.4i | 1.17489 | − | 1.07070i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 29004.0i | − | 1.00000i | ||||||
\(945\) | 18821.0 | + | 24948.4i | 0.647881 | + | 0.858805i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 54897.1i | − | 1.88376i | −0.335954 | − | 0.941878i | \(-0.609059\pi\) | ||
0.335954 | − | 0.941878i | \(-0.390941\pi\) | |||||||
\(948\) | 23380.0 | + | 25655.0i | 0.800999 | + | 0.878941i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 826.000 | − | 752.752i | 0.0281650 | − | 0.0256674i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 56348.9i | − | 1.91534i | −0.287868 | − | 0.957670i | \(-0.592946\pi\) | ||
0.287868 | − | 0.957670i | \(-0.407054\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 56348.9i | − | 1.90633i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 91997.1i | 3.09775i | ||||||||
\(960\) | −15104.0 | + | 13764.6i | −0.507791 | + | 0.462761i | ||||
\(961\) | 29791.0 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −59265.5 | − | 5511.22i | −1.98318 | − | 0.184420i | ||||
\(964\) | 46424.0 | 1.55105 | ||||||||
\(965\) | − | 14878.4i | − | 0.496323i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28084.0 | + | 25593.6i | −0.931051 | + | 0.848487i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 57109.3i | − | 1.88746i | −0.330715 | − | 0.943731i | \(-0.607290\pi\) | ||
0.330715 | − | 0.943731i | \(-0.392710\pi\) | |||||||
\(972\) | 15932.0 | + | 25777.9i | 0.525740 | + | 0.850645i | ||||
\(973\) | −56840.0 | −1.87277 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 30601.7i | 0.997485i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31388.0 | −1.01533 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42059.5 | + | 46152.2i | 1.34413 | + | 1.47492i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 41562.7i | − | 1.32425i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61859.0 | 1.96499 | 0.982495 | − | 0.186291i | \(-0.0596468\pi\) | ||||
0.982495 | + | 0.186291i | \(0.0596468\pi\) | |||||||
\(998\) | 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 | 177.4.d.a.176.2 | yes | 2 | |
3.2 | odd | 2 | inner | 177.4.d.a.176.1 | ✓ | 2 | |
59.58 | odd | 2 | CM | 177.4.d.a.176.2 | yes | 2 | |
177.176 | even | 2 | inner | 177.4.d.a.176.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.d.a.176.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
177.4.d.a.176.1 | ✓ | 2 | 177.176 | even | 2 | inner | |
177.4.d.a.176.2 | yes | 2 | 1.1 | even | 1 | trivial | |
177.4.d.a.176.2 | yes | 2 | 59.58 | odd | 2 | CM |