Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(428,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.428");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.e (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 53x^{10} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 428.13 | ||
Root | \(1.19153 - 0.761743i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.428 |
Dual form | 429.2.e.d.428.8 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52349i | 1.07727i | 0.842540 | + | 0.538633i | \(0.181059\pi\) | ||||
−0.842540 | + | 0.538633i | \(0.818941\pi\) | |||||||
\(3\) | −1.70564 | − | 0.301340i | −0.984749 | − | 0.173979i | ||||
\(4\) | −0.321008 | −0.160504 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0.459088 | − | 2.59851i | 0.187422 | − | 1.06084i | ||||
\(7\) | −3.75874 | −1.42067 | −0.710336 | − | 0.703863i | \(-0.751457\pi\) | ||||
−0.710336 | + | 0.703863i | \(0.751457\pi\) | |||||||
\(8\) | 2.55792i | 0.904361i | ||||||||
\(9\) | 2.81839 | + | 1.02795i | 0.939463 | + | 0.342651i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.31662i | − | 1.00000i | ||||||
\(12\) | 0.547523 | + | 0.0967327i | 0.158056 | + | 0.0279243i | ||||
\(13\) | −3.60555 | −1.00000 | ||||||||
\(14\) | − | 5.72639i | − | 1.53044i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.53897 | −1.13474 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −1.56607 | + | 4.29377i | −0.369127 | + | 1.01205i | ||||
\(19\) | −2.76726 | −0.634853 | −0.317427 | − | 0.948283i | \(-0.602819\pi\) | ||||
−0.317427 | + | 0.948283i | \(0.602819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.41105 | + | 1.13266i | 1.39901 | + | 0.247167i | ||||
\(22\) | 5.05283 | 1.07727 | ||||||||
\(23\) | − | 9.31703i | − | 1.94274i | −0.237580 | − | 0.971368i | \(-0.576354\pi\) | ||
0.237580 | − | 0.971368i | \(-0.423646\pi\) | |||||||
\(24\) | 0.770804 | − | 4.36288i | 0.157340 | − | 0.890569i | ||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | − | 5.49301i | − | 1.07727i | ||||||
\(27\) | −4.49738 | − | 2.60261i | −0.865521 | − | 0.500872i | ||||
\(28\) | 1.20659 | 0.228024 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | − | 1.79922i | − | 0.318059i | ||||||
\(33\) | −0.999433 | + | 5.65695i | −0.173979 | + | 0.984749i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.904725 | − | 0.329981i | −0.150788 | − | 0.0549969i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | − | 4.21588i | − | 0.683906i | ||||||
\(39\) | 6.14976 | + | 1.08650i | 0.984749 | + | 0.173979i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.0363045i | − | 0.00566981i | −0.999996 | − | 0.00283490i | \(-0.999098\pi\) | ||
0.999996 | − | 0.00283490i | \(-0.000902379\pi\) | |||||||
\(42\) | −1.72559 | + | 9.76714i | −0.266265 | + | 1.50710i | ||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 1.06466i | 0.160504i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.1944 | 2.09284 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 7.74183 | + | 1.36777i | 1.11744 | + | 0.197421i | ||||
\(49\) | 7.12816 | 1.01831 | ||||||||
\(50\) | − | 7.61743i | − | 1.07727i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.15741 | 0.160504 | ||||||||
\(53\) | 12.7941i | 1.75740i | 0.477376 | + | 0.878699i | \(0.341588\pi\) | ||||
−0.477376 | + | 0.878699i | \(0.658412\pi\) | |||||||
\(54\) | 3.96504 | − | 6.85169i | 0.539573 | − | 0.932397i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 9.61457i | − | 1.28480i | ||||||
\(57\) | 4.71994 | + | 0.833888i | 0.625171 | + | 0.110451i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.5936 | − | 3.86382i | −1.33467 | − | 0.486795i | ||||
\(64\) | −6.33686 | −0.792108 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.61829 | − | 1.52262i | −1.06084 | − | 0.187422i | ||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.80760 | + | 15.8915i | −0.337995 | + | 1.91311i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −2.62942 | + | 7.20921i | −0.309881 | + | 0.849614i | ||||
\(73\) | −17.0656 | −1.99738 | −0.998691 | − | 0.0511455i | \(-0.983713\pi\) | ||||
−0.998691 | + | 0.0511455i | \(0.983713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.52818 | + | 1.50670i | 0.984749 | + | 0.173979i | ||||
\(76\) | 0.888313 | 0.101897 | ||||||||
\(77\) | 12.4663i | 1.42067i | ||||||||
\(78\) | −1.65526 | + | 9.36907i | −0.187422 | + | 1.06084i | ||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.88662 | + | 5.79435i | 0.765180 | + | 0.643816i | ||||
\(82\) | 0.0553094 | 0.00610790 | ||||||||
\(83\) | 11.2461i | 1.23442i | 0.786799 | + | 0.617209i | \(0.211737\pi\) | ||||
−0.786799 | + | 0.617209i | \(0.788263\pi\) | |||||||
\(84\) | −2.05800 | − | 0.363593i | −0.224546 | − | 0.0396713i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.48366 | 0.904361 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5523 | 1.42067 | ||||||||
\(92\) | 2.99084i | 0.311817i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.542176 | + | 3.06881i | −0.0553356 | + | 0.313209i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 10.8596i | 1.09699i | ||||||||
\(99\) | 3.40934 | − | 9.34754i | 0.342651 | − | 0.939463i | ||||
\(100\) | 1.60504 | 0.160504 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −20.2683 | −1.99710 | −0.998548 | − | 0.0538681i | \(-0.982845\pi\) | ||||
−0.998548 | + | 0.0538681i | \(0.982845\pi\) | |||||||
\(104\) | − | 9.22271i | − | 0.904361i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.4916 | −1.89319 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 1.44370 | + | 0.835458i | 0.138920 | + | 0.0803920i | ||||
\(109\) | 11.5311 | 1.10448 | 0.552240 | − | 0.833685i | \(-0.313773\pi\) | ||||
0.552240 | + | 0.833685i | \(0.313773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 17.0608 | 1.61210 | ||||||||
\(113\) | 16.4101i | 1.54374i | 0.635783 | + | 0.771868i | \(0.280677\pi\) | ||||
−0.635783 | + | 0.771868i | \(0.719323\pi\) | |||||||
\(114\) | −1.27042 | + | 7.19076i | −0.118985 | + | 0.673476i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.1618 | − | 3.70634i | −0.939463 | − | 0.342651i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0109400 | + | 0.0619223i | −0.000986427 | + | 0.00558334i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.88647 | − | 16.1392i | 0.524408 | − | 1.43779i | ||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | − | 13.2525i | − | 1.17137i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0.320826 | − | 1.81593i | 0.0279243 | − | 0.158056i | ||||
\(133\) | 10.4014 | 0.901918 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | −24.2104 | − | 4.27733i | −2.06093 | − | 0.364111i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.9583i | 1.00000i | ||||||||
\(144\) | −12.7926 | − | 4.66585i | −1.06605 | − | 0.388821i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 25.9993i | − | 2.15171i | ||||||
\(147\) | −12.1580 | − | 2.14800i | −1.00278 | − | 0.177164i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 22.3833i | − | 1.83371i | −0.399223 | − | 0.916854i | \(-0.630720\pi\) | ||
0.399223 | − | 0.916854i | \(-0.369280\pi\) | |||||||
\(150\) | −2.29544 | + | 12.9926i | −0.187422 | + | 1.06084i | ||||
\(151\) | 14.4222 | 1.17366 | 0.586831 | − | 0.809709i | \(-0.300375\pi\) | ||||
0.586831 | + | 0.809709i | \(0.300375\pi\) | |||||||
\(152\) | − | 7.07843i | − | 0.574137i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −18.9923 | −1.53044 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.97412 | − | 0.348775i | −0.158056 | − | 0.0279243i | ||||
\(157\) | 23.6263 | 1.88558 | 0.942792 | − | 0.333382i | \(-0.108190\pi\) | ||||
0.942792 | + | 0.333382i | \(0.108190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.85536 | − | 21.8220i | 0.305750 | − | 1.73060i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 35.0203i | 2.75999i | ||||||||
\(162\) | −8.82760 | + | 10.4917i | −0.693562 | + | 0.824303i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0.0116540i | 0.000910027i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.1332 | −1.32980 | ||||||||
\(167\) | − | 18.7069i | − | 1.44758i | −0.690020 | − | 0.723791i | \(-0.742398\pi\) | ||
0.690020 | − | 0.723791i | \(-0.257602\pi\) | |||||||
\(168\) | −2.89726 | + | 16.3989i | −0.223528 | + | 1.26521i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.79922 | − | 2.84462i | −0.596421 | − | 0.217533i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.7937 | 1.42067 | ||||||||
\(176\) | 15.0541i | 1.13474i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.9165i | 1.78760i | 0.448461 | + | 0.893802i | \(0.351972\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.3395 | −1.51182 | −0.755911 | − | 0.654675i | \(-0.772806\pi\) | ||||
−0.755911 | + | 0.654675i | \(0.772806\pi\) | |||||||
\(182\) | 20.6468i | 1.53044i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.8322 | 1.75693 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.9045 | + | 9.78254i | 1.22962 | + | 0.711575i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 27.3961i | − | 1.98232i | −0.132689 | − | 0.991158i | \(-0.542361\pi\) | ||
0.132689 | − | 0.991158i | \(-0.457639\pi\) | |||||||
\(192\) | 10.8084 | + | 1.90955i | 0.780028 | + | 0.137810i | ||||
\(193\) | 23.3836 | 1.68319 | 0.841595 | − | 0.540110i | \(-0.181617\pi\) | ||||
0.841595 | + | 0.540110i | \(0.181617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.28820 | −0.163443 | ||||||||
\(197\) | − | 27.8478i | − | 1.98407i | −0.125953 | − | 0.992036i | \(-0.540199\pi\) | ||
0.125953 | − | 0.992036i | \(-0.459801\pi\) | |||||||
\(198\) | 14.2408 | + | 5.19408i | 1.01205 | + | 0.369127i | ||||
\(199\) | −10.4901 | −0.743625 | −0.371813 | − | 0.928308i | \(-0.621264\pi\) | ||||
−0.371813 | + | 0.928308i | \(0.621264\pi\) | |||||||
\(200\) | − | 12.7896i | − | 0.904361i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 30.8785i | − | 2.15141i | ||||||
\(207\) | 9.57748 | − | 26.2590i | 0.665681 | − | 1.82513i | ||||
\(208\) | 16.3655 | 1.13474 | ||||||||
\(209\) | 9.17797i | 0.634853i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | − | 4.10699i | − | 0.282069i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.65727 | − | 11.5039i | 0.452970 | − | 0.782744i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.5675i | 1.18982i | ||||||||
\(219\) | 29.1078 | + | 5.14257i | 1.96692 | + | 0.347502i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 6.76279i | 0.451858i | ||||||||
\(225\) | −14.0919 | − | 5.13977i | −0.939463 | − | 0.342651i | ||||
\(226\) | −25.0006 | −1.66302 | ||||||||
\(227\) | 12.6129i | 0.837150i | 0.908182 | + | 0.418575i | \(0.137470\pi\) | ||||
−0.908182 | + | 0.418575i | \(0.862530\pi\) | |||||||
\(228\) | −1.51514 | − | 0.267685i | −0.100343 | − | 0.0177278i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.75661 | − | 21.2630i | 0.247167 | − | 1.39901i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 5.64656 | − | 15.4814i | 0.369127 | − | 1.01205i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.8948i | 1.99842i | 0.0397962 | + | 0.999208i | \(0.487329\pi\) | ||||
−0.0397962 | + | 0.999208i | \(0.512671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.34864 | −0.537783 | −0.268892 | − | 0.963170i | \(-0.586657\pi\) | ||||
−0.268892 | + | 0.963170i | \(0.586657\pi\) | |||||||
\(242\) | − | 16.7583i | − | 1.07727i | ||||||
\(243\) | −10.0000 | − | 11.9583i | −0.641500 | − | 0.767123i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0943377 | − | 0.0166669i | −0.00601475 | − | 0.00106265i | ||||
\(247\) | 9.97750 | 0.634853 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.38890 | − | 19.1817i | 0.214763 | − | 1.21559i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.01841i | 0.190521i | 0.995452 | + | 0.0952603i | \(0.0303683\pi\) | ||||
−0.995452 | + | 0.0952603i | \(0.969632\pi\) | |||||||
\(252\) | 3.40063 | + | 1.24032i | 0.214220 | + | 0.0781325i | ||||
\(253\) | −30.9011 | −1.94274 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.51634 | 0.469771 | ||||||||
\(257\) | − | 31.1004i | − | 1.93999i | −0.243124 | − | 0.969995i | \(-0.578172\pi\) | ||
0.243124 | − | 0.969995i | \(-0.421828\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | −14.4700 | − | 2.55647i | −0.890569 | − | 0.157340i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.8464i | 0.971607i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.8018i | 1.51219i | 0.654461 | + | 0.756096i | \(0.272896\pi\) | ||||
−0.654461 | + | 0.756096i | \(0.727104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.3640 | −1.90523 | −0.952614 | − | 0.304181i | \(-0.901617\pi\) | ||||
−0.952614 | + | 0.304181i | \(0.901617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −23.1154 | − | 4.08387i | −1.39901 | − | 0.247167i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.5831i | 1.00000i | ||||||||
\(276\) | 0.901261 | − | 5.10129i | 0.0542496 | − | 0.307061i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.56596i | − | 0.570657i | −0.958430 | − | 0.285329i | \(-0.907897\pi\) | ||
0.958430 | − | 0.285329i | \(-0.0921027\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.2182 | −1.07727 | ||||||||
\(287\) | 0.136459i | 0.00805494i | ||||||||
\(288\) | 1.84951 | − | 5.07089i | 0.108983 | − | 0.298805i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.47821 | 0.320588 | ||||||||
\(293\) | − | 26.5330i | − | 1.55007i | −0.631916 | − | 0.775037i | \(-0.717731\pi\) | ||
0.631916 | − | 0.775037i | \(-0.282269\pi\) | |||||||
\(294\) | 3.27245 | − | 18.5226i | 0.190853 | − | 1.08026i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.63188 | + | 14.9161i | −0.500872 | + | 0.865521i | ||||
\(298\) | 34.1006 | 1.97539 | ||||||||
\(299\) | 33.5930i | 1.94274i | ||||||||
\(300\) | −2.73761 | − | 0.483663i | −0.158056 | − | 0.0279243i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 21.9720i | 1.26435i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.5605 | 0.720395 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.8444 | −1.64624 | −0.823119 | − | 0.567869i | \(-0.807768\pi\) | ||||
−0.823119 | + | 0.567869i | \(0.807768\pi\) | |||||||
\(308\) | − | 4.00180i | − | 0.228024i | ||||||
\(309\) | 34.5704 | + | 6.10766i | 1.96664 | + | 0.347453i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.0122i | − | 1.75854i | −0.476322 | − | 0.879271i | \(-0.658030\pi\) | ||
0.476322 | − | 0.879271i | \(-0.341970\pi\) | |||||||
\(312\) | −2.77917 | + | 15.7306i | −0.157340 | + | 0.890569i | ||||
\(313\) | 3.47839 | 0.196610 | 0.0983052 | − | 0.995156i | \(-0.468658\pi\) | ||||
0.0983052 | + | 0.995156i | \(0.468658\pi\) | |||||||
\(314\) | 35.9943i | 2.03128i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 33.2455 | + | 5.87359i | 1.86431 | + | 0.329375i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −53.3530 | −2.97325 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.21066 | − | 1.86003i | −0.122814 | − | 0.103335i | ||||
\(325\) | 18.0278 | 1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.6679 | − | 3.47479i | −1.08764 | − | 0.192156i | ||||
\(328\) | 0.0928640 | 0.00512756 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | − | 3.61008i | − | 0.198129i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 28.4996 | 1.55943 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −29.0996 | − | 5.14111i | −1.58751 | − | 0.280471i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 19.8053i | 1.07727i | ||||||||
\(339\) | 4.94504 | − | 27.9897i | 0.268577 | − | 1.52019i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.33373 | − | 11.8820i | 0.234341 | − | 0.642505i | ||||
\(343\) | −0.481706 | −0.0260097 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.831151 | 0.0444905 | 0.0222453 | − | 0.999753i | \(-0.492919\pi\) | ||||
0.0222453 | + | 0.999753i | \(0.492919\pi\) | |||||||
\(350\) | 28.6320i | 1.53044i | ||||||||
\(351\) | 16.2155 | + | 9.38384i | 0.865521 | + | 0.500872i | ||||
\(352\) | −5.96732 | −0.318059 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −36.4365 | −1.92573 | ||||||||
\(359\) | − | 33.6656i | − | 1.77681i | −0.459065 | − | 0.888403i | \(-0.651816\pi\) | ||
0.459065 | − | 0.888403i | \(-0.348184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3423 | −0.596961 | ||||||||
\(362\) | − | 30.9869i | − | 1.62864i | ||||||
\(363\) | 18.7620 | + | 3.31474i | 0.984749 | + | 0.173979i | ||||
\(364\) | −4.35041 | −0.228024 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.9578 | −1.61598 | −0.807991 | − | 0.589195i | \(-0.799445\pi\) | ||||
−0.807991 | + | 0.589195i | \(0.799445\pi\) | |||||||
\(368\) | 42.2897i | 2.20450i | ||||||||
\(369\) | 0.0373193 | − | 0.102320i | 0.00194277 | − | 0.00532657i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 48.0896i | − | 2.49669i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −14.9036 | + | 25.7538i | −0.766556 | + | 1.32463i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 41.7376 | 2.13548 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | −3.99353 | + | 22.6040i | −0.203794 | + | 1.15351i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 35.6246i | 1.81324i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.0262i | 1.01537i | 0.861543 | + | 0.507685i | \(0.169499\pi\) | ||||
−0.861543 | + | 0.507685i | \(0.830501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 18.2333i | 0.920918i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 42.4257 | 2.13738 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.09442 | + | 3.00063i | −0.0549969 | + | 0.150788i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | − | 15.9816i | − | 0.801083i | ||||||
\(399\) | −17.7410 | − | 3.13437i | −0.888163 | − | 0.156915i | ||||
\(400\) | 22.6948 | 1.13474 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.21110 | −0.356566 | −0.178283 | − | 0.983979i | \(-0.557054\pi\) | ||||
−0.178283 | + | 0.983979i | \(0.557054\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.50629 | 0.320542 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 40.0052 | + | 14.5912i | 1.96615 | + | 0.717116i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.48716i | 0.318059i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.9825 | −0.683906 | ||||||||
\(419\) | 34.2497i | 1.67321i | 0.547808 | + | 0.836604i | \(0.315462\pi\) | ||||
−0.547808 | + | 0.836604i | \(0.684538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −32.7262 | −1.58932 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.60351 | − | 20.3964i | 0.173979 | − | 0.984749i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 11.3187i | − | 0.545202i | −0.962127 | − | 0.272601i | \(-0.912116\pi\) | ||
0.962127 | − | 0.272601i | \(-0.0878840\pi\) | |||||||
\(432\) | 20.4135 | + | 11.8132i | 0.982144 | + | 0.568361i | ||||
\(433\) | 41.0634 | 1.97338 | 0.986691 | − | 0.162607i | \(-0.0519901\pi\) | ||||
0.986691 | + | 0.162607i | \(0.0519901\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.70158 | −0.177274 | ||||||||
\(437\) | 25.7827i | 1.23335i | ||||||||
\(438\) | −7.83463 | + | 44.3453i | −0.374353 | + | 2.11890i | ||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.0899 | + | 7.32742i | 0.956662 | + | 0.348925i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 21.6525i | − | 1.02874i | −0.857568 | − | 0.514370i | \(-0.828026\pi\) | ||
0.857568 | − | 0.514370i | \(-0.171974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.74498 | + | 38.1777i | −0.319027 | + | 1.80574i | ||||
\(448\) | 23.8186 | 1.12533 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 7.83036 | − | 21.4689i | 0.369127 | − | 1.01205i | ||||
\(451\) | −0.120408 | −0.00566981 | ||||||||
\(452\) | − | 5.26779i | − | 0.247776i | ||||||
\(453\) | −24.5990 | − | 4.34599i | −1.15576 | − | 0.204193i | ||||
\(454\) | −19.2156 | −0.901834 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.13302 | + | 12.0732i | −0.0998877 | + | 0.565381i | ||||
\(457\) | 28.1347 | 1.31609 | 0.658043 | − | 0.752981i | \(-0.271385\pi\) | ||||
0.658043 | + | 0.752981i | \(0.271385\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.0357i | 1.86465i | 0.361625 | + | 0.932323i | \(0.382222\pi\) | ||||
−0.361625 | + | 0.932323i | \(0.617778\pi\) | |||||||
\(462\) | 32.3939 | + | 5.72314i | 1.50710 | + | 0.266265i | ||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.9165i | 1.10672i | 0.832941 | + | 0.553362i | \(0.186655\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 3.26203 | + | 1.18976i | 0.150788 | + | 0.0549969i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −40.2979 | − | 7.11956i | −1.85683 | − | 0.328052i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.8363 | 0.634853 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.1517 | + | 36.0586i | −0.602175 | + | 1.65101i | ||||
\(478\) | −47.0677 | −2.15283 | ||||||||
\(479\) | − | 6.63325i | − | 0.303081i | −0.988451 | − | 0.151540i | \(-0.951577\pi\) | ||
0.988451 | − | 0.151540i | \(-0.0484234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 12.7190i | − | 0.579336i | ||||||
\(483\) | 10.5530 | − | 59.7320i | 0.480180 | − | 2.71790i | ||||
\(484\) | 3.53109 | 0.160504 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 18.2182 | − | 15.2349i | 0.826396 | − | 0.691067i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0.00351183 | − | 0.0198775i | 0.000158326 | − | 0.000896149i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 15.2006i | 0.683906i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 29.2231 | + | 5.16294i | 1.30952 | + | 0.231357i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.63714 | + | 31.9071i | −0.251849 | + | 1.42550i | ||||
\(502\) | −4.59851 | −0.205241 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 9.88333 | − | 27.0976i | 0.440238 | − | 1.20702i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 47.0774i | − | 2.09284i | ||||||
\(507\) | −22.1733 | − | 3.91742i | −0.984749 | − | 0.173979i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 64.1454 | 2.83762 | ||||||||
\(512\) | − | 15.0541i | − | 0.665302i | ||||||
\(513\) | 12.4454 | + | 7.20210i | 0.549479 | + | 0.317980i | ||||
\(514\) | 47.3810 | 2.08989 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 18.7650i | − | 0.822108i | −0.911611 | − | 0.411054i | \(-0.865161\pi\) | ||
0.911611 | − | 0.411054i | \(-0.134839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −32.0552 | − | 5.66331i | −1.39901 | − | 0.247167i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 4.53640 | − | 25.6767i | 0.197421 | − | 1.11744i | ||||
\(529\) | −63.8071 | −2.77422 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.33894 | −0.144761 | ||||||||
\(533\) | 0.130898i | 0.00566981i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.20701 | − | 40.7929i | 0.311006 | − | 1.76034i | ||||
\(538\) | −37.7852 | −1.62903 | ||||||||
\(539\) | − | 23.6414i | − | 1.01831i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.9361 | 1.97495 | 0.987473 | − | 0.157787i | \(-0.0504360\pi\) | ||||
0.987473 | + | 0.157787i | \(0.0504360\pi\) | |||||||
\(542\) | − | 47.7826i | − | 2.05244i | ||||||
\(543\) | 34.6917 | + | 6.12910i | 1.48877 | + | 0.263025i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.22171 | − | 35.2159i | 0.266265 | − | 1.50710i | ||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −25.2641 | −1.07727 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −40.6491 | − | 7.18161i | −1.73014 | − | 0.305670i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.5285i | 0.954562i | 0.878751 | + | 0.477281i | \(0.158378\pi\) | ||||
−0.878751 | + | 0.477281i | \(0.841622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.5736 | 0.614750 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −25.8850 | − | 21.7795i | −1.08707 | − | 0.914651i | ||||
\(568\) | 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 | \(\pi\) | |||||||||
\(572\) | − | 3.83870i | − | 0.160504i | ||||||
\(573\) | −8.25556 | + | 46.7279i | −0.344881 | + | 1.95208i | ||||
\(574\) | −0.207894 | −0.00867732 | ||||||||
\(575\) | 46.5852i | 1.94274i | ||||||||
\(576\) | −17.8597 | − | 6.51400i | −0.744156 | − | 0.271417i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | − | 25.8993i | − | 1.07727i | ||||||
\(579\) | −39.8839 | − | 7.04643i | −1.65752 | − | 0.292839i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 42.2712i | − | 1.75370i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.4331 | 1.75740 | ||||||||
\(584\) | − | 43.6525i | − | 1.80636i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 40.4226 | 1.66984 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 3.90283 | + | 0.689526i | 0.160950 | + | 0.0284356i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.39166 | + | 47.4982i | −0.345187 | + | 1.95381i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.8754i | 1.84281i | 0.388600 | + | 0.921407i | \(0.372959\pi\) | ||||
−0.388600 | + | 0.921407i | \(0.627041\pi\) | |||||||
\(594\) | −22.7245 | − | 13.1505i | −0.932397 | − | 0.539573i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.18521i | 0.294318i | ||||||||
\(597\) | 17.8923 | + | 3.16110i | 0.732285 | + | 0.129375i | ||||
\(598\) | −51.1785 | −2.09284 | ||||||||
\(599\) | − | 20.1640i | − | 0.823878i | −0.911211 | − | 0.411939i | \(-0.864852\pi\) | ||
0.911211 | − | 0.411939i | \(-0.135148\pi\) | |||||||
\(600\) | −3.85402 | + | 21.8144i | −0.157340 | + | 0.890569i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.62964 | −0.188378 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 4.97890i | 0.201921i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.6624 | −1.84429 | −0.922144 | − | 0.386848i | \(-0.873564\pi\) | ||||
−0.922144 | + | 0.386848i | \(0.873564\pi\) | |||||||
\(614\) | − | 43.9440i | − | 1.77344i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −31.8879 | −1.28480 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | −9.30493 | + | 52.6674i | −0.374299 | + | 2.11860i | ||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.2486 | + | 41.9022i | −0.973063 | + | 1.68148i | ||||
\(622\) | 47.2467 | 1.89442 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −27.9136 | − | 4.93158i | −1.11744 | − | 0.197421i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 5.29928i | 0.211802i | ||||||||
\(627\) | 2.76569 | − | 15.6543i | 0.110451 | − | 0.625171i | ||||
\(628\) | −7.58423 | −0.302644 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.23760 | + | 7.00504i | −0.0490741 | + | 0.277768i | ||||
\(637\) | −25.7009 | −1.01831 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 43.4359i | − | 1.71561i | −0.513973 | − | 0.857807i | \(-0.671827\pi\) | ||
0.513973 | − | 0.857807i | \(-0.328173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | − | 11.2418i | − | 0.442989i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 34.6283i | − | 1.36138i | −0.732572 | − | 0.680690i | \(-0.761680\pi\) | ||
0.732572 | − | 0.680690i | \(-0.238320\pi\) | |||||||
\(648\) | −14.8215 | + | 17.6154i | −0.582242 | + | 0.691999i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 27.4650i | 1.07727i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 47.8330i | − | 1.87185i | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||
0.352197 | − | 0.935926i | \(-0.385435\pi\) | |||||||
\(654\) | 5.29379 | − | 29.9637i | 0.207004 | − | 1.17168i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.164785i | 0.00643377i | ||||||||
\(657\) | −48.0976 | − | 17.5427i | −1.87647 | − | 0.684406i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −28.7666 | −1.11636 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.00506i | 0.232343i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.03790 | − | 11.5349i | 0.0786137 | − | 0.444967i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 22.4869 | + | 13.0130i | 0.865521 | + | 0.500872i | ||||
\(676\) | −4.17310 | −0.160504 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 42.6419 | + | 7.53369i | 1.63765 | + | 0.289330i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.80078 | − | 21.5131i | 0.145646 | − | 0.824383i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 2.50361 | + | 0.913145i | 0.0957280 | + | 0.0349150i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 0.733873i | − | 0.0280194i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 46.1296i | − | 1.75740i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.8148 | + | 35.1350i | −0.486795 | + | 1.33467i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.26625i | 0.0479282i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.03294 | −0.228024 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | −14.2961 | + | 24.7041i | −0.539573 | + | 0.932397i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 21.0170i | 0.792108i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 7.67740i | − | 0.286918i | ||||||
\(717\) | 9.30984 | − | 52.6952i | 0.347682 | − | 1.96794i | ||||
\(718\) | 51.2891 | 1.91409 | ||||||||
\(719\) | 23.9165i | 0.891936i | 0.895049 | + | 0.445968i | \(0.147140\pi\) | ||||
−0.895049 | + | 0.445968i | \(0.852860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 76.1834 | 2.83722 | ||||||||
\(722\) | − | 17.2798i | − | 0.643087i | ||||||
\(723\) | 14.2397 | + | 2.51578i | 0.529582 | + | 0.0935629i | ||||
\(724\) | 6.52913 | 0.242653 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.04996 | + | 28.5836i | −0.187422 | + | 1.06084i | ||||
\(727\) | 47.3730 | 1.75697 | 0.878484 | − | 0.477772i | \(-0.158556\pi\) | ||||
0.878484 | + | 0.477772i | \(0.158556\pi\) | |||||||
\(728\) | 34.6658i | 1.28480i | ||||||||
\(729\) | 13.4529 | + | 23.4098i | 0.498254 | + | 0.867031i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.2038 | 0.524630 | 0.262315 | − | 0.964982i | \(-0.415514\pi\) | ||||
0.262315 | + | 0.964982i | \(0.415514\pi\) | |||||||
\(734\) | − | 47.1637i | − | 1.74084i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.7633 | −0.617905 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.155883 | + | 0.0568555i | 0.00573814 | + | 0.00209288i | ||||
\(739\) | −35.4910 | −1.30556 | −0.652779 | − | 0.757549i | \(-0.726397\pi\) | ||||
−0.652779 | + | 0.757549i | \(0.726397\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.0180 | − | 3.00662i | −0.625171 | − | 0.110451i | ||||
\(742\) | 73.2638 | 2.68960 | ||||||||
\(743\) | 33.1662i | 1.21675i | 0.793649 | + | 0.608376i | \(0.208179\pi\) | ||||
−0.793649 | + | 0.608376i | \(0.791821\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.5605 | + | 31.6958i | −0.422975 | + | 1.15969i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.4254 | −1.87654 | −0.938270 | − | 0.345905i | \(-0.887572\pi\) | ||||
−0.938270 | + | 0.345905i | \(0.887572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.909569 | − | 5.14831i | 0.0331466 | − | 0.187615i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.42648 | − | 3.14027i | −0.197359 | − | 0.114211i | ||||
\(757\) | −44.0150 | −1.59975 | −0.799876 | − | 0.600165i | \(-0.795102\pi\) | ||||
−0.799876 | + | 0.600165i | \(0.795102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 52.7060 | + | 9.31175i | 1.91311 | + | 0.337995i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 44.7302i | − | 1.62147i | −0.585414 | − | 0.810734i | \(-0.699068\pi\) | ||
0.585414 | − | 0.810734i | \(-0.300932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.3425 | −1.56910 | ||||||||
\(764\) | 8.79438i | 0.318170i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12.8201 | − | 2.26498i | −0.462607 | − | 0.0817303i | ||||
\(769\) | −53.4536 | −1.92758 | −0.963792 | − | 0.266654i | \(-0.914082\pi\) | ||||
−0.963792 | + | 0.266654i | \(0.914082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.37181 | + | 53.0460i | −0.337517 | + | 1.91040i | ||||
\(772\) | −7.50633 | −0.270159 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30.5097 | −1.09382 | ||||||||
\(779\) | 0.100464i | 0.00359950i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −32.3545 | −1.15552 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.9735 | 0.997148 | 0.498574 | − | 0.866847i | \(-0.333857\pi\) | ||||
0.498574 | + | 0.866847i | \(0.333857\pi\) | |||||||
\(788\) | 8.93936i | 0.318452i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 61.6815i | − | 2.19314i | ||||||
\(792\) | 23.9102 | + | 8.72081i | 0.849614 | + | 0.309881i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.36742 | 0.119355 | ||||||||
\(797\) | − | 47.8330i | − | 1.69433i | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||
0.531327 | − | 0.847167i | \(-0.321693\pi\) | |||||||
\(798\) | 4.77517 | − | 27.0282i | 0.169039 | − | 0.956789i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 8.99608i | 0.318059i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56.6003i | 1.99738i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.47378 | − | 42.3028i | 0.263089 | − | 1.48913i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.5260 | 1.77421 | 0.887103 | − | 0.461571i | \(-0.152714\pi\) | ||||
0.887103 | + | 0.461571i | \(0.152714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 53.4956 | + | 9.45125i | 1.87617 | + | 0.331470i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 10.9860i | − | 0.384117i | ||||||
\(819\) | 38.1958 | + | 13.9312i | 1.33467 | + | 0.486795i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.0660i | 1.85202i | 0.377504 | + | 0.926008i | \(0.376783\pi\) | ||||
−0.377504 | + | 0.926008i | \(0.623217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.59556 | −0.229907 | −0.114953 | − | 0.993371i | \(-0.536672\pi\) | ||||
−0.114953 | + | 0.993371i | \(0.536672\pi\) | |||||||
\(824\) | − | 51.8447i | − | 1.80610i | ||||||
\(825\) | 4.99716 | − | 28.2848i | 0.173979 | − | 0.984749i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.1766i | 1.71004i | 0.518597 | + | 0.855019i | \(0.326454\pi\) | ||||
−0.518597 | + | 0.855019i | \(0.673546\pi\) | |||||||
\(828\) | −3.07445 | + | 8.42935i | −0.106844 | + | 0.292940i | ||||
\(829\) | 57.4470 | 1.99522 | 0.997608 | − | 0.0691315i | \(-0.0220228\pi\) | ||||
0.997608 | + | 0.0691315i | \(0.0220228\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 22.8479 | 0.792108 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 2.94620i | − | 0.101897i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52.1790 | −1.80249 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.88261 | + | 16.3160i | −0.0992823 | + | 0.561954i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.3462 | 1.42067 | ||||||||
\(848\) | − | 58.0718i | − | 1.99419i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.7315 | 1.94245 | 0.971224 | − | 0.238168i | \(-0.0765469\pi\) | ||||
0.971224 | + | 0.238168i | \(0.0765469\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 31.0737 | + | 5.48989i | 1.06084 | + | 0.187422i | ||||
\(859\) | −9.72119 | −0.331683 | −0.165841 | − | 0.986152i | \(-0.553034\pi\) | ||||
−0.165841 | + | 0.986152i | \(0.553034\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0411207 | − | 0.232750i | 0.00140139 | − | 0.00793210i | ||||
\(862\) | 17.2439 | 0.587328 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | −4.68265 | + | 8.09175i | −0.159307 | + | 0.275287i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 62.5595i | 2.12586i | ||||||||
\(867\) | 28.9958 | + | 5.12279i | 0.984749 | + | 0.173979i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 29.4957i | 0.998850i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −39.2795 | −1.32865 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.34383 | − | 1.65081i | −0.315699 | − | 0.0557755i | ||||
\(877\) | −33.6692 | −1.13693 | −0.568464 | − | 0.822708i | \(-0.692462\pi\) | ||||
−0.568464 | + | 0.822708i | \(0.692462\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.99546 | + | 45.2556i | −0.269680 | + | 1.52643i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.6423i | 0.796529i | 0.917271 | + | 0.398265i | \(0.130387\pi\) | ||||
−0.917271 | + | 0.398265i | \(0.869613\pi\) | |||||||
\(882\) | −11.1632 | + | 30.6067i | −0.375885 | + | 1.03058i | ||||
\(883\) | 31.2141 | 1.05044 | 0.525219 | − | 0.850967i | \(-0.323984\pi\) | ||||
0.525219 | + | 0.850967i | \(0.323984\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.9872 | 1.10823 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.2177 | − | 22.8403i | 0.643816 | − | 0.765180i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −58.1632 | − | 10.2759i | −1.94527 | − | 0.343677i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 49.8129i | 1.66413i | ||||||||
\(897\) | 10.1229 | − | 57.2975i | 0.337995 | − | 1.91311i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 4.52363 | + | 1.64991i | 0.150788 | + | 0.0549969i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 0.183440i | − | 0.00610790i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41.9758 | −1.39609 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.62106 | − | 37.4763i | 0.219970 | − | 1.24507i | ||||
\(907\) | −40.4162 | −1.34200 | −0.670999 | − | 0.741458i | \(-0.734135\pi\) | ||||
−0.670999 | + | 0.741458i | \(0.734135\pi\) | |||||||
\(908\) | − | 4.04885i | − | 0.134366i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.9143i | 0.726052i | 0.931779 | + | 0.363026i | \(0.118256\pi\) | ||||
−0.931779 | + | 0.363026i | \(0.881744\pi\) | |||||||
\(912\) | −21.4237 | − | 3.78499i | −0.709409 | − | 0.125334i | ||||
\(913\) | 37.2990 | 1.23442 | ||||||||
\(914\) | 42.8628i | 1.41778i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 49.1981 | + | 8.69198i | 1.62113 | + | 0.286411i | ||||
\(922\) | −60.9938 | −2.00872 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.20590 | + | 6.82561i | −0.0396713 | + | 0.224546i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −57.1240 | − | 20.8349i | −1.87620 | − | 0.684308i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.7255 | −0.646476 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.34524 | + | 52.8956i | −0.305949 | + | 1.73172i | ||||
\(934\) | −36.4365 | −1.19224 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.48052 | − | 25.9932i | 0.309881 | − | 0.849614i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.93287 | − | 1.04818i | −0.193612 | − | 0.0342061i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.71587i | 0.284129i | 0.989857 | + | 0.142065i | \(0.0453741\pi\) | ||||
−0.989857 | + | 0.142065i | \(0.954626\pi\) | |||||||
\(942\) | 10.8465 | − | 61.3932i | 0.353399 | − | 2.00030i | ||||
\(943\) | −0.338250 | −0.0110149 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61.5311 | 1.99738 | ||||||||
\(950\) | 21.0794i | 0.683906i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | −54.9348 | − | 20.0364i | −1.77858 | − | 0.648703i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 9.91746i | − | 0.320754i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.1057 | 0.326499 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.67998 | 0.0863164 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 91.0008 | + | 16.0774i | 2.92790 | + | 0.517282i | ||||
\(967\) | −47.9676 | −1.54253 | −0.771267 | − | 0.636512i | \(-0.780377\pi\) | ||||
−0.771267 | + | 0.636512i | \(0.780377\pi\) | |||||||
\(968\) | − | 28.1371i | − | 0.904361i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.3682i | 1.58430i | 0.610327 | + | 0.792150i | \(0.291038\pi\) | ||||
−0.610327 | + | 0.792150i | \(0.708962\pi\) | |||||||
\(972\) | 3.21008 | + | 3.83870i | 0.102963 | + | 0.123126i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30.7488 | − | 5.43249i | −0.984749 | − | 0.173979i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.4992 | + | 11.8535i | 1.03762 | + | 0.378452i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | −0.158392 | − | 0.0279837i | −0.00504936 | − | 0.000892087i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.20286 | −0.101897 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.9128 | 1.61730 | 0.808649 | − | 0.588292i | \(-0.200199\pi\) | ||||
0.808649 | + | 0.588292i | \(0.200199\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.08786 | + | 6.15749i | −0.0344703 | + | 0.195108i | ||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 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 | 429.2.e.d.428.13 | yes | 20 | |
3.2 | odd | 2 | inner | 429.2.e.d.428.8 | yes | 20 | |
11.10 | odd | 2 | inner | 429.2.e.d.428.7 | ✓ | 20 | |
13.12 | even | 2 | inner | 429.2.e.d.428.7 | ✓ | 20 | |
33.32 | even | 2 | inner | 429.2.e.d.428.14 | yes | 20 | |
39.38 | odd | 2 | inner | 429.2.e.d.428.14 | yes | 20 | |
143.142 | odd | 2 | CM | 429.2.e.d.428.13 | yes | 20 | |
429.428 | even | 2 | inner | 429.2.e.d.428.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.e.d.428.7 | ✓ | 20 | 11.10 | odd | 2 | inner | |
429.2.e.d.428.7 | ✓ | 20 | 13.12 | even | 2 | inner | |
429.2.e.d.428.8 | yes | 20 | 3.2 | odd | 2 | inner | |
429.2.e.d.428.8 | yes | 20 | 429.428 | even | 2 | inner | |
429.2.e.d.428.13 | yes | 20 | 1.1 | even | 1 | trivial | |
429.2.e.d.428.13 | yes | 20 | 143.142 | odd | 2 | CM | |
429.2.e.d.428.14 | yes | 20 | 33.32 | even | 2 | inner | |
429.2.e.d.428.14 | yes | 20 | 39.38 | odd | 2 | inner |