Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1749,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1749");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.c (of order \(2\), degree \(1\), not 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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1749.4 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1749 |
Dual form | 1900.2.c.e.1749.1 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.73205i | 1.57735i | 0.614810 | + | 0.788675i | \(0.289233\pi\) | ||||
−0.614810 | + | 0.788675i | \(0.710767\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.00000i | − 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.46410 | −1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | −1.04447 | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.73205i | − 0.757735i | −0.925451 | − | 0.378867i | \(-0.876314\pi\) | ||||
0.925451 | − | 0.378867i | \(-0.123686\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.46410 | 1.19236 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3.46410i | − 0.722315i | −0.932505 | − | 0.361158i | \(-0.882382\pi\) | ||||
0.932505 | − | 0.361158i | \(-0.117618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 4.00000i | − 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.46410 | −0.643268 | −0.321634 | − | 0.946864i | \(-0.604232\pi\) | ||||
−0.321634 | + | 0.946864i | \(0.604232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.46410 | −0.262960 | −0.131480 | − | 0.991319i | \(-0.541973\pi\) | ||||
−0.131480 | + | 0.991319i | \(0.541973\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 9.46410i | − 1.64749i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.73205i | − 1.10674i | −0.832935 | − | 0.553371i | \(-0.813341\pi\) | ||||
0.832935 | − | 0.553371i | \(-0.186659\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.46410 | 1.19521 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.92820i | − 0.751544i | −0.926712 | − | 0.375772i | \(-0.877378\pi\) | ||||
0.926712 | − | 0.375772i | \(-0.122622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 12.9282i | − 1.88577i | −0.333115 | − | 0.942886i | \(-0.608100\pi\) | ||||
0.333115 | − | 0.942886i | \(-0.391900\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.46410 | −1.32524 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.7321i | − 1.47416i | −0.675805 | − | 0.737080i | \(-0.736204\pi\) | ||||
0.675805 | − | 0.737080i | \(-0.263796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 2.73205i | − 0.361869i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.92820 | −0.901975 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3923 | 1.58667 | 0.793336 | − | 0.608784i | \(-0.208342\pi\) | ||||
0.793336 | + | 0.608784i | \(0.208342\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.92820i | 1.12485i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.73205i | − 0.822451i | −0.911534 | − | 0.411225i | \(-0.865101\pi\) | ||||
0.911534 | − | 0.411225i | \(-0.134899\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.46410 | 1.13934 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.53590 | −0.300956 | −0.150478 | − | 0.988613i | \(-0.548081\pi\) | ||||
−0.150478 | + | 0.988613i | \(0.548081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 0.535898i | − 0.0627222i | −0.999508 | − | 0.0313611i | \(-0.990016\pi\) | ||||
0.999508 | − | 0.0313611i | \(-0.00998418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.92820i | 0.789542i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.92820 | −0.329449 | −0.164724 | − | 0.986340i | \(-0.552673\pi\) | ||||
−0.164724 | + | 0.986340i | \(0.552673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.46410i | 0.380235i | 0.981761 | + | 0.190117i | \(0.0608868\pi\) | ||||
−0.981761 | + | 0.190117i | \(0.939113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 9.46410i | − 1.01466i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4641 | 1.63919 | 0.819596 | − | 0.572942i | \(-0.194198\pi\) | ||||
0.819596 | + | 0.572942i | \(0.194198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.46410 | −0.572793 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.00000i | − 0.414781i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.5885i | 1.68430i | 0.539241 | + | 0.842151i | \(0.318711\pi\) | ||||
−0.539241 | + | 0.842151i | \(0.681289\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.4641 | 1.55420 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.3923 | −1.63110 | −0.815548 | − | 0.578690i | \(-0.803564\pi\) | ||||
−0.815548 | + | 0.578690i | \(0.803564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.6603i | 1.34598i | 0.739649 | + | 0.672992i | \(0.234991\pi\) | ||||
−0.739649 | + | 0.672992i | \(0.765009\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.66025i | 0.547197i | 0.961844 | + | 0.273599i | \(0.0882140\pi\) | ||||
−0.961844 | + | 0.273599i | \(0.911786\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.3923 | 1.37853 | 0.689266 | − | 0.724508i | \(-0.257933\pi\) | ||||
0.689266 | + | 0.724508i | \(0.257933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.3923 | 1.74572 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.5885i | 1.18422i | 0.805856 | + | 0.592111i | \(0.201705\pi\) | ||||
−0.805856 | + | 0.592111i | \(0.798295\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.1962i | 1.12753i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 16.3923i | − 1.47804i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 20.5885i | − 1.82693i | −0.406917 | − | 0.913465i | \(-0.633396\pi\) | ||||
0.406917 | − | 0.913465i | \(-0.366604\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.4641 | 1.18545 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.9282 | −1.65376 | −0.826882 | − | 0.562375i | \(-0.809888\pi\) | ||||
−0.826882 | + | 0.562375i | \(0.809888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000i | 0.173422i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 17.3205i | − 1.47979i | −0.672722 | − | 0.739895i | \(-0.734875\pi\) | ||||
0.672722 | − | 0.739895i | \(-0.265125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.4641 | −0.972372 | −0.486186 | − | 0.873855i | \(-0.661612\pi\) | ||||
−0.486186 | + | 0.873855i | \(0.661612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 35.3205 | 2.97452 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.46410i | 0.791428i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.19615i | 0.676007i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.39230 | 0.359832 | 0.179916 | − | 0.983682i | \(-0.442417\pi\) | ||||
0.179916 | + | 0.983682i | \(0.442417\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.39230 | −0.682956 | −0.341478 | − | 0.939890i | \(-0.610927\pi\) | ||||
−0.341478 | + | 0.939890i | \(0.610927\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 15.4641i | − 1.25020i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 23.4641i | − 1.87264i | −0.351149 | − | 0.936320i | \(-0.614209\pi\) | ||||
0.351149 | − | 0.936320i | \(-0.385791\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 29.3205 | 2.32527 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.92820 | −0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.07180i | 0.553906i | 0.960883 | + | 0.276953i | \(0.0893246\pi\) | ||||
−0.960883 | + | 0.276953i | \(0.910675\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.7321i | 0.830471i | 0.909714 | + | 0.415236i | \(0.136301\pi\) | ||||
−0.909714 | + | 0.415236i | \(0.863699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.53590 | 0.425838 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.46410 | 0.341378 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.80385i | 0.289201i | 0.989490 | + | 0.144601i | \(0.0461897\pi\) | ||||
−0.989490 | + | 0.144601i | \(0.953810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 18.9282i | − 1.42273i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.7846 | −1.55351 | −0.776757 | − | 0.629800i | \(-0.783137\pi\) | ||||
−0.776757 | + | 0.629800i | \(0.783137\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 33.8564i | 2.50274i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 12.0000i | − 0.877527i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.00000 | −0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.92820 | 0.501307 | 0.250654 | − | 0.968077i | \(-0.419354\pi\) | ||||
0.250654 | + | 0.968077i | \(0.419354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 7.80385i | − 0.561733i | −0.959747 | − | 0.280867i | \(-0.909378\pi\) | ||||
0.959747 | − | 0.280867i | \(-0.0906219\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 0.928203i | − 0.0661317i | −0.999453 | − | 0.0330659i | \(-0.989473\pi\) | ||||
0.999453 | − | 0.0330659i | \(-0.0105271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.9282 | −1.90889 | −0.954445 | − | 0.298387i | \(-0.903551\pi\) | ||||
−0.954445 | + | 0.298387i | \(0.903551\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.3923 | 1.29729 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.92820i | 0.486265i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.4641i | 1.07483i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.46410 | 0.239617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.3205 | 1.33008 | 0.665039 | − | 0.746808i | \(-0.268415\pi\) | ||||
0.665039 | + | 0.746808i | \(0.268415\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6.92820i | − 0.474713i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.92820i | 0.198779i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.46410 | 0.0989348 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.46410 | 0.636624 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 9.66025i | − 0.646898i | −0.946246 | − | 0.323449i | \(-0.895158\pi\) | ||||
0.946246 | − | 0.323449i | \(-0.104842\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8.19615i | − 0.543998i | −0.962298 | − | 0.271999i | \(-0.912315\pi\) | ||||
0.962298 | − | 0.271999i | \(-0.0876847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.4641 | −1.15406 | −0.577030 | − | 0.816723i | \(-0.695788\pi\) | ||||
−0.577030 | + | 0.816723i | \(0.695788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.9282 | −1.24538 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 0.928203i | − 0.0608086i | −0.999538 | − | 0.0304043i | \(-0.990321\pi\) | ||||
0.999538 | − | 0.0304043i | \(-0.00967948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8.00000i | − 0.519656i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8564 | 0.896296 | 0.448148 | − | 0.893959i | \(-0.352084\pi\) | ||||
0.448148 | + | 0.893959i | \(0.352084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.8564 | −0.763738 | −0.381869 | − | 0.924216i | \(-0.624719\pi\) | ||||
−0.381869 | + | 0.924216i | \(0.624719\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 18.7321i | − 1.20166i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.73205i | 0.173836i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.46410 | −0.599763 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000i | 0.754434i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.1244i | 0.943431i | 0.881751 | + | 0.471716i | \(0.156365\pi\) | ||||
−0.881751 | + | 0.471716i | \(0.843635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.4641 | −0.836619 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.4641 | 0.957204 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.53590i | 0.526346i | 0.964749 | + | 0.263173i | \(0.0847690\pi\) | ||||
−0.964749 | + | 0.263173i | \(0.915231\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 42.2487i | 2.58558i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.3923 | −0.633630 | −0.316815 | − | 0.948487i | \(-0.602613\pi\) | ||||
−0.316815 | + | 0.948487i | \(0.602613\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.39230 | −0.145322 | −0.0726611 | − | 0.997357i | \(-0.523149\pi\) | ||||
−0.0726611 | + | 0.997357i | \(0.523149\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 14.9282i | − 0.903496i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 18.3923i | − 1.10509i | −0.833484 | − | 0.552543i | \(-0.813657\pi\) | ||||
0.833484 | − | 0.552543i | \(-0.186343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.53590 | 0.391294 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.928203 | 0.0553720 | 0.0276860 | − | 0.999617i | \(-0.491186\pi\) | ||||
0.0276860 | + | 0.999617i | \(0.491186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.3923i | 1.09331i | 0.837358 | + | 0.546655i | \(0.184099\pi\) | ||||
−0.837358 | + | 0.546655i | \(0.815901\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000i | 0.708338i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −45.3205 | −2.65674 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5.66025i | − 0.330676i | −0.986237 | − | 0.165338i | \(-0.947129\pi\) | ||||
0.986237 | − | 0.165338i | \(-0.0528714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.8564i | 0.804030i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.46410 | −0.547323 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.85641 | −0.568114 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 44.7846i | − 2.57281i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.80385i | 0.445389i | 0.974888 | + | 0.222695i | \(0.0714853\pi\) | ||||
−0.974888 | + | 0.222695i | \(0.928515\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37.3205 | −2.12309 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.60770 | −0.0911640 | −0.0455820 | − | 0.998961i | \(-0.514514\pi\) | ||||
−0.0455820 | + | 0.998961i | \(0.514514\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.7846i | 0.609582i | 0.952419 | + | 0.304791i | \(0.0985866\pi\) | ||||
−0.952419 | + | 0.304791i | \(0.901413\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.12436i | − 0.175481i | −0.996143 | − | 0.0877406i | \(-0.972035\pi\) | ||||
0.996143 | − | 0.0877406i | \(-0.0279647\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.4641 | −0.863122 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.46410i | − 0.192748i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 39.3205i | 2.17443i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.8564 | −1.42551 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2487 | −1.22290 | −0.611450 | − | 0.791283i | \(-0.709413\pi\) | ||||
−0.611450 | + | 0.791283i | \(0.709413\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.0526i | 1.64687i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.2679i | 0.940645i | 0.882495 | + | 0.470323i | \(0.155862\pi\) | ||||
−0.882495 | + | 0.470323i | \(0.844138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −34.3923 | −1.86793 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.07180 | 0.274653 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 20.0000i | − 1.07990i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 31.1769i | − 1.67366i | −0.547459 | − | 0.836832i | \(-0.684405\pi\) | ||||
0.547459 | − | 0.836832i | \(-0.315595\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.9282 | −1.12026 | −0.560131 | − | 0.828404i | \(-0.689249\pi\) | ||||
−0.560131 | + | 0.828404i | \(0.689249\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.9282 | −0.583304 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.60770i | 0.0855690i | 0.999084 | + | 0.0427845i | \(0.0136229\pi\) | ||||
−0.999084 | + | 0.0427845i | \(0.986377\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.9282i | 1.00179i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.53590 | 0.450507 | 0.225254 | − | 0.974300i | \(-0.427679\pi\) | ||||
0.225254 | + | 0.974300i | \(0.427679\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.73205i | 0.143395i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.85641i | − 0.201303i | −0.994922 | − | 0.100651i | \(-0.967907\pi\) | ||||
0.994922 | − | 0.100651i | \(-0.0320927\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.7846 | 1.39435 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.4641 | −1.11436 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 16.5885i | − 0.858918i | −0.903086 | − | 0.429459i | \(-0.858704\pi\) | ||||
0.903086 | − | 0.429459i | \(-0.141296\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.46410i | 0.487426i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9282 | −0.766810 | −0.383405 | − | 0.923580i | \(-0.625249\pi\) | ||||
−0.383405 | + | 0.923580i | \(0.625249\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 56.2487 | 2.88171 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.33975i | 0.323946i | 0.986795 | + | 0.161973i | \(0.0517857\pi\) | ||||
−0.986795 | + | 0.161973i | \(0.948214\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.0000i | 1.11832i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 51.7128i | − 2.60857i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.4641i | 0.976875i | 0.872599 | + | 0.488438i | \(0.162433\pi\) | ||||
−0.872599 | + | 0.488438i | \(0.837567\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.46410 | −0.273547 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.7846 | 1.93681 | 0.968405 | − | 0.249381i | \(-0.0802271\pi\) | ||||
0.968405 | + | 0.249381i | \(0.0802271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000i | 0.199254i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.3205i | 1.15595i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3923 | 0.711654 | 0.355827 | − | 0.934552i | \(-0.384199\pi\) | ||||
0.355827 | + | 0.934552i | \(0.384199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 47.3205 | 2.33415 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.8564i | 0.681829i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 31.3205i | − 1.53377i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 57.7128i | 2.80609i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 24.7846i | − 1.19941i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25.8564 | −1.24836 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.4641 | −1.61191 | −0.805955 | − | 0.591977i | \(-0.798347\pi\) | ||||
−0.805955 | + | 0.591977i | \(0.798347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 22.3397i | − 1.07358i | −0.843716 | − | 0.536790i | \(-0.819637\pi\) | ||||
0.843716 | − | 0.536790i | \(-0.180363\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.46410i | 0.165710i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.7128 | 1.51357 | 0.756785 | − | 0.653664i | \(-0.226769\pi\) | ||||
0.756785 | + | 0.653664i | \(0.226769\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.3923 | −0.637729 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.6077i | 0.646521i | 0.946310 | + | 0.323261i | \(0.104779\pi\) | ||||
−0.946310 | + | 0.323261i | \(0.895221\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000i | 0.567581i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.46410 | 0.163481 | 0.0817405 | − | 0.996654i | \(-0.473952\pi\) | ||||
0.0817405 | + | 0.996654i | \(0.473952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.7846 | 0.978709 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 22.9282i | − 1.07726i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 34.7846i | − 1.62716i | −0.581456 | − | 0.813578i | \(-0.697517\pi\) | ||||
0.581456 | − | 0.813578i | \(-0.302483\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.8564 | 0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.7128 | −1.01127 | −0.505633 | − | 0.862749i | \(-0.668741\pi\) | ||||
−0.505633 | + | 0.862749i | \(0.668741\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.53590i | 0.210801i | 0.994430 | + | 0.105401i | \(0.0336125\pi\) | ||||
−0.994430 | + | 0.105401i | \(0.966388\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.3205i | 1.35679i | 0.734697 | + | 0.678396i | \(0.237324\pi\) | ||||
−0.734697 | + | 0.678396i | \(0.762676\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.4641 | −0.621714 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 64.1051 | 2.95381 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.0718i | 0.784962i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 47.9090i | 2.19360i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.3923 | 1.02313 | 0.511565 | − | 0.859244i | \(-0.329066\pi\) | ||||
0.511565 | + | 0.859244i | \(0.329066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.3923 | −0.838617 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 18.9282i | − 0.861263i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1962i | 0.552660i | 0.961063 | + | 0.276330i | \(0.0891183\pi\) | ||||
−0.961063 | + | 0.276330i | \(0.910882\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.3205 | −0.873704 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.9282 | 0.854218 | 0.427109 | − | 0.904200i | \(-0.359532\pi\) | ||||
0.427109 | + | 0.904200i | \(0.359532\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 12.0000i | − 0.540453i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.07180i | 0.227501i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.4641 | −1.05040 | −0.525199 | − | 0.850980i | \(-0.676009\pi\) | ||||
−0.525199 | + | 0.850980i | \(0.676009\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.3205 | −1.30994 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.4641i | 0.689510i | 0.938693 | + | 0.344755i | \(0.112038\pi\) | ||||
−0.938693 | + | 0.344755i | \(0.887962\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.1244i | 0.671696i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.32051 | 0.235827 | 0.117914 | − | 0.993024i | \(-0.462379\pi\) | ||||
0.117914 | + | 0.993024i | \(0.462379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.07180 | −0.0474135 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000i | 0.176604i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.7846i | 1.96962i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3923 | −0.456172 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.7846 | −0.647726 | −0.323863 | − | 0.946104i | \(-0.604982\pi\) | ||||
−0.323863 | + | 0.946104i | \(0.604982\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 37.3731i | − 1.63421i | −0.576489 | − | 0.817105i | \(-0.695578\pi\) | ||||
0.576489 | − | 0.817105i | \(-0.304422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 5.07180i | − 0.220931i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.9282 | 1.34217 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.3923i | 0.710030i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 56.7846i | − 2.45044i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.3923 | −0.447628 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.1769 | −1.25441 | −0.627207 | − | 0.778853i | \(-0.715802\pi\) | ||||
−0.627207 | + | 0.778853i | \(0.715802\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 38.2487i | 1.64141i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 6.73205i | − 0.287842i | −0.989589 | − | 0.143921i | \(-0.954029\pi\) | ||||
0.989589 | − | 0.143921i | \(-0.0459711\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −55.3205 | −2.36102 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.46410 | 0.147576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.85641i | 0.249040i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.32051i | − 0.225437i | −0.993627 | − | 0.112719i | \(-0.964044\pi\) | ||||
0.993627 | − | 0.112719i | \(-0.0359559\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.4641 | −0.569471 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.7846 | 1.38417 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.1962i | 1.86265i | 0.364195 | + | 0.931323i | \(0.381344\pi\) | ||||
−0.364195 | + | 0.931323i | \(0.618656\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.92820i | 0.206965i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.3205 | 1.22918 | 0.614590 | − | 0.788847i | \(-0.289322\pi\) | ||||
0.614590 | + | 0.788847i | \(0.289322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3923 | 0.769694 | 0.384847 | − | 0.922980i | \(-0.374254\pi\) | ||||
0.384847 | + | 0.922980i | \(0.374254\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.9282i | 0.790737i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.78461i | 0.282447i | 0.989978 | + | 0.141223i | \(0.0451036\pi\) | ||||
−0.989978 | + | 0.141223i | \(0.954896\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.3205 | 0.886050 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.92820 | 0.287430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.1769i | 1.53971i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 43.1769i | − 1.78210i | −0.453903 | − | 0.891051i | \(-0.649969\pi\) | ||||
0.453903 | − | 0.891051i | \(-0.350031\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.46410 | 0.0603273 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.53590 | 0.104313 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.8564i | 1.30819i | 0.756414 | + | 0.654093i | \(0.226949\pi\) | ||||
−0.756414 | + | 0.654093i | \(0.773051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 73.5692i | − 3.01099i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.7846 | 0.849236 | 0.424618 | − | 0.905373i | \(-0.360408\pi\) | ||||
0.424618 | + | 0.905373i | \(0.360408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.6410 | 1.00513 | 0.502564 | − | 0.864540i | \(-0.332390\pi\) | ||||
0.502564 | + | 0.864540i | \(0.332390\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.0526i | 1.22383i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.9090i | 1.61985i | 0.586530 | + | 0.809927i | \(0.300494\pi\) | ||||
−0.586530 | + | 0.809927i | \(0.699506\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.9282 | −0.767010 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.3205 | −1.42891 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.39230i | 0.258183i | 0.991633 | + | 0.129091i | \(0.0412061\pi\) | ||||
−0.991633 | + | 0.129091i | \(0.958794\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1.60770i | − 0.0647234i | −0.999476 | − | 0.0323617i | \(-0.989697\pi\) | ||||
0.999476 | − | 0.0323617i | \(-0.0103028\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.39230 | 0.0961549 | 0.0480774 | − | 0.998844i | \(-0.484691\pi\) | ||||
0.0480774 | + | 0.998844i | \(0.484691\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.8564 | −0.556038 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 30.9282i | − 1.23911i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.46410i | 0.377960i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.3205 | 0.929850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.4641 | 0.456379 | 0.228189 | − | 0.973617i | \(-0.426719\pi\) | ||||
0.228189 | + | 0.973617i | \(0.426719\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 52.7846i | 2.09800i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 8.19615i | − 0.324743i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.3205 | 0.447832 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.9282 | −0.984605 | −0.492302 | − | 0.870424i | \(-0.663845\pi\) | ||||
−0.492302 | + | 0.870424i | \(0.663845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 14.3923i | − 0.567577i | −0.958887 | − | 0.283789i | \(-0.908409\pi\) | ||||
0.958887 | − | 0.283789i | \(-0.0915914\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 15.4641i | − 0.607957i | −0.952679 | − | 0.303978i | \(-0.901685\pi\) | ||||
0.952679 | − | 0.303978i | \(-0.0983150\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.4641i | 1.07475i | 0.843342 | + | 0.537377i | \(0.180585\pi\) | ||||
−0.843342 | + | 0.537377i | \(0.819415\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.39230i | 0.0933327i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.78461 | −0.342200 | −0.171100 | − | 0.985254i | \(-0.554732\pi\) | ||||
−0.171100 | + | 0.985254i | \(0.554732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.21539 | 0.202855 | 0.101428 | − | 0.994843i | \(-0.467659\pi\) | ||||
0.101428 | + | 0.994843i | \(0.467659\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.8564i | 1.00418i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000i | 0.464642i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.3923 | 1.02039 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.9282 | −1.65722 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 50.7321i | − 1.95558i | −0.209594 | − | 0.977788i | \(-0.567214\pi\) | ||||
0.209594 | − | 0.977788i | \(-0.432786\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 16.9808i | − 0.652624i | −0.945262 | − | 0.326312i | \(-0.894194\pi\) | ||||
0.945262 | − | 0.326312i | \(-0.105806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.1769 | 1.27321 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.3923 | 0.858075 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 17.6603i | − 0.675751i | −0.941191 | − | 0.337875i | \(-0.890292\pi\) | ||||
0.941191 | − | 0.337875i | \(-0.109708\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 47.7128i | − 1.82036i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.3205 | −1.11702 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.1769 | 1.94686 | 0.973431 | − | 0.228981i | \(-0.0735395\pi\) | ||||
0.973431 | + | 0.228981i | \(0.0735395\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 30.9282i | − 1.17487i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 20.7846i | − 0.787273i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.53590 | 0.0959165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.5359 | −1.00225 | −0.501124 | − | 0.865376i | \(-0.667080\pi\) | ||||
−0.501124 | + | 0.865376i | \(0.667080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.73205i | 0.253904i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 32.7846i | 1.23299i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.7846 | 1.15614 | 0.578070 | − | 0.815987i | \(-0.303806\pi\) | ||||
0.578070 | + | 0.815987i | \(0.303806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.0718 | 0.490231 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.07180i | 0.189940i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 37.8564i | 1.41377i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.3205 | −0.645946 | −0.322973 | − | 0.946408i | \(-0.604682\pi\) | ||||
−0.322973 | + | 0.946408i | \(0.604682\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.3205 | 1.01747 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 32.3923i | − 1.20468i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 0.143594i | − 0.00532559i | −0.999996 | − | 0.00266279i | \(-0.999152\pi\) | ||||
0.999996 | − | 0.00266279i | \(-0.000847595\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.7846 | 1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.0718 | 0.631423 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.7846i | 0.398339i | 0.979965 | + | 0.199169i | \(0.0638244\pi\) | ||||
−0.979965 | + | 0.199169i | \(0.936176\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.3205i | 0.859022i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.0000 | 1.03000 | 0.514998 | − | 0.857191i | \(-0.327793\pi\) | ||||
0.514998 | + | 0.857191i | \(0.327793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.46410 | −0.274201 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.8756i | 0.765853i | 0.923779 | + | 0.382927i | \(0.125084\pi\) | ||||
−0.923779 | + | 0.382927i | \(0.874916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 15.4641i | − 0.565802i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.3205 | 0.413642 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.4641 | −0.929198 | −0.464599 | − | 0.885521i | \(-0.653802\pi\) | ||||
−0.464599 | + | 0.885521i | \(0.653802\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 65.5692i | − 2.38948i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000i | 0.363456i | 0.983349 | + | 0.181728i | \(0.0581691\pi\) | ||||
−0.983349 | + | 0.181728i | \(0.941831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −32.7846 | −1.19001 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.6077 | 0.710778 | 0.355389 | − | 0.934718i | \(-0.384348\pi\) | ||||
0.355389 | + | 0.934718i | \(0.384348\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 28.7846i | − 1.04207i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.9282i | 0.683458i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.5359 | 1.10115 | 0.550576 | − | 0.834785i | \(-0.314408\pi\) | ||||
0.550576 | + | 0.834785i | \(0.314408\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.3205 | −1.48812 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.0526i | 0.793175i | 0.917997 | + | 0.396588i | \(0.129806\pi\) | ||||
−0.917997 | + | 0.396588i | \(0.870194\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 36.7846i | − 1.31964i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.78461 | 0.314338 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.8564i | 0.495188i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.1962i | 0.434746i | 0.976089 | + | 0.217373i | \(0.0697488\pi\) | ||||
−0.976089 | + | 0.217373i | \(0.930251\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.3205 | −0.830232 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.1769 | 0.895188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 33.8564i | − 1.20228i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.66025i | 0.200496i | 0.994962 | + | 0.100248i | \(0.0319637\pi\) | ||||
−0.994962 | + | 0.100248i | \(0.968036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.7846 | 1.58437 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −69.0333 | −2.43917 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.85641i | 0.0655112i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 28.3923i | − 0.999456i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.71281 | −0.341484 | −0.170742 | − | 0.985316i | \(-0.554617\pi\) | ||||
−0.170742 | + | 0.985316i | \(0.554617\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.6077 | 0.548060 | 0.274030 | − | 0.961721i | \(-0.411643\pi\) | ||||
0.274030 | + | 0.961721i | \(0.411643\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.53590i | − 0.229224i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.92820i | 0.172416i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.3923 | 0.852336 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.1436 | −0.563415 | −0.281708 | − | 0.959500i | \(-0.590901\pi\) | ||||
−0.281708 | + | 0.959500i | \(0.590901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 39.5692i | − 1.37930i | −0.724145 | − | 0.689648i | \(-0.757765\pi\) | ||||
0.724145 | − | 0.689648i | \(-0.242235\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.6603i | 1.03139i | 0.856773 | + | 0.515694i | \(0.172466\pi\) | ||||
−0.856773 | + | 0.515694i | \(0.827534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.24871 | −0.286490 | −0.143245 | − | 0.989687i | \(-0.545754\pi\) | ||||
−0.143245 | + | 0.989687i | \(0.545754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.2487 | 1.74311 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.3923i | 0.360072i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.85641i | 0.202427i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.9282 | −0.653474 | −0.326737 | − | 0.945115i | \(-0.605949\pi\) | ||||
−0.326737 | + | 0.945115i | \(0.605949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0000 | −0.586207 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.53590i | 0.0873410i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.00000i | − 0.0687208i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −50.2487 | −1.72453 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.3205 | −0.799417 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 44.6410i | − 1.52848i | −0.644932 | − | 0.764240i | \(-0.723114\pi\) | ||||
0.644932 | − | 0.764240i | \(-0.276886\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 3.80385i | − 0.129937i | −0.997887 | − | 0.0649685i | \(-0.979305\pi\) | ||||
0.997887 | − | 0.0649685i | \(-0.0206947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.7128 | −1.62794 | −0.813970 | − | 0.580907i | \(-0.802698\pi\) | ||||
−0.813970 | + | 0.580907i | \(0.802698\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.7846 | −1.11730 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 37.2679i | − 1.26862i | −0.773081 | − | 0.634308i | \(-0.781285\pi\) | ||||
0.773081 | − | 0.634308i | \(-0.218715\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.6603i | 0.463927i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.1436 | 0.344098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.3923 | −0.623199 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 74.0526i | − 2.50630i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 0.980762i | − 0.0331180i | −0.999863 | − | 0.0165590i | \(-0.994729\pi\) | ||||
0.999863 | − | 0.0165590i | \(-0.00527113\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.4641 | 0.521591 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.679492 | −0.0228927 | −0.0114463 | − | 0.999934i | \(-0.503644\pi\) | ||||
−0.0114463 | + | 0.999934i | \(0.503644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 22.0000i | − 0.740359i | −0.928960 | − | 0.370179i | \(-0.879296\pi\) | ||||
0.928960 | − | 0.370179i | \(-0.120704\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 23.4115i | − 0.786083i | −0.919521 | − | 0.393041i | \(-0.871423\pi\) | ||||
0.919521 | − | 0.393041i | \(-0.128577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.1769 | −1.38103 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.53590 | 0.285963 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.9282i | 0.432626i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 25.8564i | − 0.863320i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.07180 | 0.169154 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.1769 | 1.23854 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 26.9282i | − 0.896114i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 7.41154i | − 0.246096i | −0.992401 | − | 0.123048i | \(-0.960733\pi\) | ||||
0.992401 | − | 0.123048i | \(-0.0392670\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 73.1769 | 2.42713 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5359 | 0.481596 | 0.240798 | − | 0.970575i | \(-0.422591\pi\) | ||||
0.240798 | + | 0.970575i | \(0.422591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 12.0000i | − 0.397142i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.8564i | 1.25013i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.4974 | −1.46783 | −0.733917 | − | 0.679239i | \(-0.762310\pi\) | ||||
−0.733917 | + | 0.679239i | \(0.762310\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.3205 | −0.702535 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.92820i | 0.228045i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 60.9808i | − 2.00287i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.5692 | 1.56070 | 0.780348 | − | 0.625346i | \(-0.215042\pi\) | ||||
0.780348 | + | 0.625346i | \(0.215042\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | −0.0983210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 4.39230i | − 0.143798i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 51.1769i | − 1.67188i | −0.548823 | − | 0.835938i | \(-0.684924\pi\) | ||||
0.548823 | − | 0.835938i | \(-0.315076\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.4641 | −0.961525 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.6410 | 1.71605 | 0.858024 | − | 0.513610i | \(-0.171692\pi\) | ||||
0.858024 | + | 0.513610i | \(0.171692\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.7846i | 0.676840i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 6.67949i | − 0.217054i | −0.994093 | − | 0.108527i | \(-0.965387\pi\) | ||||
0.994093 | − | 0.108527i | \(-0.0346134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.46410 | −0.0475267 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.53590 | 0.276795 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.5885i | 1.96265i | 0.192350 | + | 0.981326i | \(0.438389\pi\) | ||||
−0.192350 | + | 0.981326i | \(0.561611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.7846i | 1.05978i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.6410 | −1.11862 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8564 | −0.930852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 25.2679i | − 0.814248i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.3205i | 1.45741i | 0.684828 | + | 0.728705i | \(0.259877\pi\) | ||||
−0.684828 | + | 0.728705i | \(0.740123\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.46410 | 0.304031 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.5359 | −0.466479 | −0.233240 | − | 0.972419i | \(-0.574933\pi\) | ||||
−0.233240 | + | 0.972419i | \(0.574933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.9282i | 0.735044i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 32.1962i | − 1.03005i | −0.857176 | − | 0.515023i | \(-0.827783\pi\) | ||||
0.857176 | − | 0.515023i | \(-0.172217\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.5692 | −1.71208 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −64.2487 | −2.05130 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 2.44486i | − 0.0779790i | −0.999240 | − | 0.0389895i | \(-0.987586\pi\) | ||||
0.999240 | − | 0.0389895i | \(-0.0124139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 70.6410i | − 2.24853i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.0718 | −0.542852 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.39230 | −0.266590 | −0.133295 | − | 0.991076i | \(-0.542556\pi\) | ||||
−0.133295 | + | 0.991076i | \(0.542556\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 60.7846i | − 1.92894i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 30.3923i | − 0.962534i | −0.876574 | − | 0.481267i | \(-0.840177\pi\) | ||||
0.876574 | − | 0.481267i | \(-0.159823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.9282 | −0.851971 |
(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 | 1900.2.c.e.1749.4 | 4 | ||
5.2 | odd | 4 | 380.2.a.d.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 1900.2.a.d.1.1 | 2 | |||
5.4 | even | 2 | inner | 1900.2.c.e.1749.1 | 4 | ||
15.2 | even | 4 | 3420.2.a.h.1.2 | 2 | |||
20.3 | even | 4 | 7600.2.a.bf.1.2 | 2 | |||
20.7 | even | 4 | 1520.2.a.l.1.1 | 2 | |||
40.27 | even | 4 | 6080.2.a.bj.1.2 | 2 | |||
40.37 | odd | 4 | 6080.2.a.z.1.1 | 2 | |||
95.37 | even | 4 | 7220.2.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.a.d.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
1520.2.a.l.1.1 | 2 | 20.7 | even | 4 | |||
1900.2.a.d.1.1 | 2 | 5.3 | odd | 4 | |||
1900.2.c.e.1749.1 | 4 | 5.4 | even | 2 | inner | ||
1900.2.c.e.1749.4 | 4 | 1.1 | even | 1 | trivial | ||
3420.2.a.h.1.2 | 2 | 15.2 | even | 4 | |||
6080.2.a.z.1.1 | 2 | 40.37 | odd | 4 | |||
6080.2.a.bj.1.2 | 2 | 40.27 | even | 4 | |||
7220.2.a.h.1.1 | 2 | 95.37 | even | 4 | |||
7600.2.a.bf.1.2 | 2 | 20.3 | even | 4 |