Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2300,2,Mod(1,2300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2300.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2300.a (trivial) |
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: | yes |
Analytic conductor: | \(18.3655924649\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.143376304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 12x^{4} + 22x^{2} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.16223\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2300.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −3.21923 | −1.85862 | −0.929311 | − | 0.369298i | \(-0.879598\pi\) | ||||
−0.929311 | + | 0.369298i | \(0.879598\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.43185 | 0.919152 | 0.459576 | − | 0.888138i | \(-0.348001\pi\) | ||||
0.459576 | + | 0.888138i | \(0.348001\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.36343 | 2.45448 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.884969 | −0.266828 | −0.133414 | − | 0.991060i | \(-0.542594\pi\) | ||||
−0.133414 | + | 0.991060i | \(0.542594\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.10522 | −1.41593 | −0.707967 | − | 0.706245i | \(-0.750388\pi\) | ||||
−0.707967 | + | 0.706245i | \(0.750388\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.366626 | −0.0889198 | −0.0444599 | − | 0.999011i | \(-0.514157\pi\) | ||||
−0.0444599 | + | 0.999011i | \(0.514157\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.79847 | −0.642014 | −0.321007 | − | 0.947077i | \(-0.604021\pi\) | ||||
−0.321007 | + | 0.947077i | \(0.604021\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.82867 | −1.70836 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.0469 | −2.70332 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.02431 | 1.49008 | 0.745038 | − | 0.667022i | \(-0.232431\pi\) | ||||
0.745038 | + | 0.667022i | \(0.232431\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.24179 | 1.30066 | 0.650332 | − | 0.759650i | \(-0.274630\pi\) | ||||
0.650332 | + | 0.759650i | \(0.274630\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.84892 | 0.495933 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.10036 | 0.509697 | 0.254848 | − | 0.966981i | \(-0.417974\pi\) | ||||
0.254848 | + | 0.966981i | \(0.417974\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.4349 | 2.63169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.47185 | −0.542212 | −0.271106 | − | 0.962550i | \(-0.587389\pi\) | ||||
−0.271106 | + | 0.962550i | \(0.587389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.56841 | −1.30667 | −0.653335 | − | 0.757069i | \(-0.726631\pi\) | ||||
−0.653335 | + | 0.757069i | \(0.726631\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.25528 | −0.766561 | −0.383281 | − | 0.923632i | \(-0.625206\pi\) | ||||
−0.383281 | + | 0.923632i | \(0.625206\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.08612 | −0.155160 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.18025 | 0.165268 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.6413 | 1.59905 | 0.799526 | − | 0.600632i | \(-0.205084\pi\) | ||||
0.799526 | + | 0.600632i | \(0.205084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.00892 | 1.19326 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.33209 | −1.21493 | −0.607467 | − | 0.794345i | \(-0.707814\pi\) | ||||
−0.607467 | + | 0.794345i | \(0.707814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.46699 | 0.699976 | 0.349988 | − | 0.936754i | \(-0.386186\pi\) | ||||
0.349988 | + | 0.936754i | \(0.386186\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 17.9067 | 2.25604 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.49020 | −0.182057 | −0.0910285 | − | 0.995848i | \(-0.529015\pi\) | ||||
−0.0910285 | + | 0.995848i | \(0.529015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.21923 | 0.387549 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.29949 | 0.984969 | 0.492484 | − | 0.870321i | \(-0.336089\pi\) | ||||
0.492484 | + | 0.870321i | \(0.336089\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2409 | 1.19860 | 0.599302 | − | 0.800523i | \(-0.295445\pi\) | ||||
0.599302 | + | 0.800523i | \(0.295445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.15211 | −0.245256 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.06522 | 0.682391 | 0.341195 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341195 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.1298 | 2.56998 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.2520 | −1.78389 | −0.891943 | − | 0.452148i | \(-0.850658\pi\) | ||||
−0.891943 | + | 0.452148i | \(0.850658\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −25.8321 | −2.76949 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.6033 | −1.86594 | −0.932972 | − | 0.359949i | \(-0.882794\pi\) | ||||
−0.932972 | + | 0.359949i | \(0.882794\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4151 | −1.30146 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.3130 | −2.41744 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.55618 | 0.665679 | 0.332839 | − | 0.942984i | \(-0.391993\pi\) | ||||
0.332839 | + | 0.942984i | \(0.391993\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.51641 | −0.654924 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4912 | 1.34243 | 0.671213 | − | 0.741265i | \(-0.265774\pi\) | ||||
0.671213 | + | 0.741265i | \(0.265774\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.5460 | −1.23619 | −0.618096 | − | 0.786103i | \(-0.712096\pi\) | ||||
−0.618096 | + | 0.786103i | \(0.712096\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.46269 | −0.141404 | −0.0707020 | − | 0.997497i | \(-0.522524\pi\) | ||||
−0.0707020 | + | 0.997497i | \(0.522524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.2173 | −1.84069 | −0.920343 | − | 0.391113i | \(-0.872090\pi\) | ||||
−0.920343 | + | 0.391113i | \(0.872090\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.98078 | −0.947334 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.834901 | 0.0785409 | 0.0392705 | − | 0.999229i | \(-0.487497\pi\) | ||||
0.0392705 | + | 0.999229i | \(0.487497\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −37.5920 | −3.47538 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.891578 | −0.0817308 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2168 | −0.928803 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.1767 | 1.00777 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.87453 | −0.698751 | −0.349376 | − | 0.936983i | \(-0.613606\pi\) | ||||
−0.349376 | + | 0.936983i | \(0.613606\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 27.5837 | 2.42861 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.8740 | −1.12481 | −0.562403 | − | 0.826863i | \(-0.690123\pi\) | ||||
−0.562403 | + | 0.826863i | \(0.690123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.80546 | −0.590108 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.26675 | −0.279097 | −0.139549 | − | 0.990215i | \(-0.544565\pi\) | ||||
−0.139549 | + | 0.990215i | \(0.544565\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.5578 | −1.06514 | −0.532570 | − | 0.846386i | \(-0.678774\pi\) | ||||
−0.532570 | + | 0.846386i | \(0.678774\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.9179 | 1.42475 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.51797 | 0.377811 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.49647 | 0.288384 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.188265 | −0.0154233 | −0.00771164 | − | 0.999970i | \(-0.502455\pi\) | ||||
−0.00771164 | + | 0.999970i | \(0.502455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.6708 | −1.51941 | −0.759704 | − | 0.650269i | \(-0.774656\pi\) | ||||
−0.759704 | + | 0.650269i | \(0.774656\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.69962 | −0.218252 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0277 | −1.59839 | −0.799193 | − | 0.601074i | \(-0.794740\pi\) | ||||
−0.799193 | + | 0.601074i | \(0.794740\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −37.4759 | −2.97203 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.43185 | −0.191656 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.35607 | −0.262867 | −0.131434 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131434 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.57745 | 0.199449 | 0.0997246 | − | 0.995015i | \(-0.468204\pi\) | ||||
0.0997246 | + | 0.995015i | \(0.468204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0633 | 1.00487 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.6064 | −1.57581 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.4182 | 1.47634 | 0.738170 | − | 0.674615i | \(-0.235690\pi\) | ||||
0.738170 | + | 0.674615i | \(0.235690\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30.0421 | 2.25810 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.3628 | −1.52199 | −0.760993 | − | 0.648760i | \(-0.775288\pi\) | ||||
−0.760993 | + | 0.648760i | \(0.775288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.5629 | −1.67709 | −0.838543 | − | 0.544835i | \(-0.816592\pi\) | ||||
−0.838543 | + | 0.544835i | \(0.816592\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.5995 | −1.30099 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.324453 | 0.0237263 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −34.1598 | −2.48476 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6554 | −1.20514 | −0.602571 | − | 0.798065i | \(-0.705857\pi\) | ||||
−0.602571 | + | 0.798065i | \(0.705857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.5214 | −1.04527 | −0.522636 | − | 0.852556i | \(-0.675051\pi\) | ||||
−0.522636 | + | 0.852556i | \(0.675051\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.3479 | 0.950995 | 0.475498 | − | 0.879717i | \(-0.342268\pi\) | ||||
0.475498 | + | 0.879717i | \(0.342268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7856 | 1.33168 | 0.665838 | − | 0.746097i | \(-0.268074\pi\) | ||||
0.665838 | + | 0.746097i | \(0.268074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.79730 | 0.338375 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.5139 | 1.36961 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.36343 | −0.511794 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.47656 | 0.171307 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1078 | 1.17775 | 0.588874 | − | 0.808225i | \(-0.299571\pi\) | ||||
0.588874 | + | 0.808225i | \(0.299571\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −26.7180 | −1.83068 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.6109 | 1.19551 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −32.9677 | −2.22775 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.87171 | 0.125905 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.5184 | 0.905262 | 0.452631 | − | 0.891698i | \(-0.350485\pi\) | ||||
0.452631 | + | 0.891698i | \(0.350485\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.29581 | −0.550612 | −0.275306 | − | 0.961357i | \(-0.588779\pi\) | ||||
−0.275306 | + | 0.961357i | \(0.588779\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.22318 | −0.411239 | −0.205620 | − | 0.978632i | \(-0.565921\pi\) | ||||
−0.205620 | + | 0.978632i | \(0.565921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.92813 | 0.455838 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.6347 | 0.893242 | 0.446621 | − | 0.894723i | \(-0.352627\pi\) | ||||
0.446621 | + | 0.894723i | \(0.352627\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.5253 | −1.26831 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.5281 | 0.745693 | 0.372847 | − | 0.927893i | \(-0.378382\pi\) | ||||
0.372847 | + | 0.927893i | \(0.378382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.5952 | −1.13341 | −0.566704 | − | 0.823921i | \(-0.691782\pi\) | ||||
−0.566704 | + | 0.823921i | \(0.691782\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −32.3195 | −2.07329 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2868 | 0.909049 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 52.3188 | 3.31557 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.5471 | 0.791968 | 0.395984 | − | 0.918257i | \(-0.370404\pi\) | ||||
0.395984 | + | 0.918257i | \(0.370404\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.884969 | 0.0556375 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.88072 | −0.304451 | −0.152225 | − | 0.988346i | \(-0.548644\pi\) | ||||
−0.152225 | + | 0.988346i | \(0.548644\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.53961 | 0.468489 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 59.0864 | 3.65736 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.6045 | 0.715566 | 0.357783 | − | 0.933805i | \(-0.383533\pi\) | ||||
0.357783 | + | 0.933805i | \(0.383533\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 56.6690 | 3.46808 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.04327 | −0.368465 | −0.184232 | − | 0.982883i | \(-0.558980\pi\) | ||||
−0.184232 | + | 0.982883i | \(0.558980\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.93401 | 0.238974 | 0.119487 | − | 0.992836i | \(-0.461875\pi\) | ||||
0.119487 | + | 0.992836i | \(0.461875\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39.9671 | 2.41892 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.92174 | −0.475971 | −0.237986 | − | 0.971269i | \(-0.576487\pi\) | ||||
−0.237986 | + | 0.971269i | \(0.576487\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 53.3244 | 3.19245 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00419 | −0.358180 | −0.179090 | − | 0.983833i | \(-0.557315\pi\) | ||||
−0.179090 | + | 0.983833i | \(0.557315\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.65299 | −0.454923 | −0.227461 | − | 0.973787i | \(-0.573043\pi\) | ||||
−0.227461 | + | 0.973787i | \(0.573043\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.44301 | −0.498375 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8656 | −0.992093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.1058 | −1.23725 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.5480 | 0.791485 | 0.395743 | − | 0.918361i | \(-0.370487\pi\) | ||||
0.395743 | + | 0.918361i | \(0.370487\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.4310 | 0.721323 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.10522 | 0.295243 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.8371 | −1.20103 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.4313 | −2.49506 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0870 | −0.575697 | −0.287848 | − | 0.957676i | \(-0.592940\pi\) | ||||
−0.287848 | + | 0.957676i | \(0.592940\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.3883 | 2.29761 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.2481 | −1.60180 | −0.800902 | − | 0.598795i | \(-0.795646\pi\) | ||||
−0.800902 | + | 0.598795i | \(0.795646\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4504 | 0.816786 | 0.408393 | − | 0.912806i | \(-0.366089\pi\) | ||||
0.408393 | + | 0.912806i | \(0.366089\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.7835 | −0.830324 | −0.415162 | − | 0.909748i | \(-0.636275\pi\) | ||||
−0.415162 | + | 0.909748i | \(0.636275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.10127 | −0.397595 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.70875 | 0.262817 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.02599 | 0.0570877 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 61.8649 | 3.42114 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.7800 | −0.704586 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.1494 | −1.10751 | −0.553757 | − | 0.832679i | \(-0.686806\pi\) | ||||
−0.553757 | + | 0.832679i | \(0.686806\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.8293 | 1.25104 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.0660 | −1.31096 | −0.655479 | − | 0.755214i | \(-0.727533\pi\) | ||||
−0.655479 | + | 0.755214i | \(0.727533\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.68774 | −0.145978 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.40876 | −0.347054 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.6642 | −1.06177 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.3788 | 1.41609 | 0.708045 | − | 0.706168i | \(-0.249578\pi\) | ||||
0.708045 | + | 0.706168i | \(0.249578\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.535518 | 0.0286656 | 0.0143328 | − | 0.999897i | \(-0.495438\pi\) | ||||
0.0143328 | + | 0.999897i | \(0.495438\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 71.7124 | 3.82773 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.27606 | 0.280816 | 0.140408 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140408 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.87019 | 0.151907 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.4351 | 1.07852 | 0.539261 | − | 0.842139i | \(-0.318704\pi\) | ||||
0.539261 | + | 0.842139i | \(0.318704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.1685 | −0.587818 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.8903 | 1.72629 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.4382 | −0.649268 | −0.324634 | − | 0.945840i | \(-0.605241\pi\) | ||||
−0.324634 | + | 0.945840i | \(0.605241\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.5647 | −1.33085 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.3098 | 1.46977 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.99999 | −0.155334 | −0.0776669 | − | 0.996979i | \(-0.524747\pi\) | ||||
−0.0776669 | + | 0.996979i | \(0.524747\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.9659 | −2.10985 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.02165 | −0.155212 | −0.0776059 | − | 0.996984i | \(-0.524728\pi\) | ||||
−0.0776059 | + | 0.996984i | \(0.524728\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.3499 | 1.29871 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.15719 | −0.416813 | −0.208406 | − | 0.978042i | \(-0.566828\pi\) | ||||
−0.208406 | + | 0.978042i | \(0.566828\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −63.0929 | −3.20719 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.7789 | 0.597214 | 0.298607 | − | 0.954376i | \(-0.403478\pi\) | ||||
0.298607 | + | 0.954376i | \(0.403478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.366626 | 0.0185411 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.4443 | 2.09059 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.7004 | 0.838167 | 0.419083 | − | 0.907948i | \(-0.362351\pi\) | ||||
0.419083 | + | 0.907948i | \(0.362351\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.9083 | 1.09679 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.99936 | 0.499344 | 0.249672 | − | 0.968330i | \(-0.419677\pi\) | ||||
0.249672 | + | 0.968330i | \(0.419677\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.9710 | −1.84165 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.74373 | −0.136002 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.20305 | 0.108934 | 0.0544668 | − | 0.998516i | \(-0.482654\pi\) | ||||
0.0544668 | + | 0.998516i | \(0.482654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.5164 | 0.518736 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.6942 | −1.11671 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.4264 | 1.97969 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.12814 | 0.201673 | 0.100836 | − | 0.994903i | \(-0.467848\pi\) | ||||
0.100836 | + | 0.994903i | \(0.467848\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7354 | −0.766899 | −0.383449 | − | 0.923562i | \(-0.625264\pi\) | ||||
−0.383449 | + | 0.923562i | \(0.625264\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −38.6969 | −1.88151 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.2949 | 0.643385 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.5444 | −0.702209 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.35158 | −0.0651034 | −0.0325517 | − | 0.999470i | \(-0.510363\pi\) | ||||
−0.0325517 | + | 0.999470i | \(0.510363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.4114 | −1.89399 | −0.946996 | − | 0.321244i | \(-0.895899\pi\) | ||||
−0.946996 | + | 0.321244i | \(0.895899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.79847 | 0.133869 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1059 | 0.482326 | 0.241163 | − | 0.970485i | \(-0.422471\pi\) | ||||
0.241163 | + | 0.970485i | \(0.422471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.99756 | −0.380836 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.25526 | −0.297197 | −0.148598 | − | 0.988898i | \(-0.547476\pi\) | ||||
−0.148598 | + | 0.988898i | \(0.547476\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.606068 | 0.0286660 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.28779 | 0.107968 | 0.0539839 | − | 0.998542i | \(-0.482808\pi\) | ||||
0.0539839 | + | 0.998542i | \(0.482808\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.07248 | 0.144677 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 60.1055 | 2.82400 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3062 | 0.669217 | 0.334609 | − | 0.942357i | \(-0.391396\pi\) | ||||
0.334609 | + | 0.942357i | \(0.391396\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.14995 | 0.240379 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.38995 | −0.111311 | −0.0556556 | − | 0.998450i | \(-0.517725\pi\) | ||||
−0.0556556 | + | 0.998450i | \(0.517725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.52232 | 0.442540 | 0.221270 | − | 0.975213i | \(-0.428980\pi\) | ||||
0.221270 | + | 0.975213i | \(0.428980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.14501 | 0.284357 | 0.142178 | − | 0.989841i | \(-0.454589\pi\) | ||||
0.142178 | + | 0.989841i | \(0.454589\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.62394 | −0.167338 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 64.4738 | 2.97080 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.58278 | 0.348657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 85.7197 | 3.92483 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.40986 | −0.0644180 | −0.0322090 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322090 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.8281 | −0.721697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.82867 | 0.356217 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.2993 | −1.41831 | −0.709154 | − | 0.705054i | \(-0.750923\pi\) | ||||
−0.709154 | + | 0.705054i | \(0.750923\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.8039 | 0.488571 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.9254 | −1.17000 | −0.584999 | − | 0.811034i | \(-0.698905\pi\) | ||||
−0.584999 | + | 0.811034i | \(0.698905\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.94192 | −0.132497 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.1831 | 0.905336 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.04562 | −0.360172 | −0.180086 | − | 0.983651i | \(-0.557638\pi\) | ||||
−0.180086 | + | 0.983651i | \(0.557638\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.29740 | −0.370701 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.50490 | 0.245451 | 0.122726 | − | 0.992441i | \(-0.460836\pi\) | ||||
0.122726 | + | 0.992441i | \(0.460836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −42.0538 | −1.86767 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.26586 | −0.366378 | −0.183189 | − | 0.983078i | \(-0.558642\pi\) | ||||
−0.183189 | + | 0.983078i | \(0.558642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.9043 | 1.10170 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 39.3098 | 1.73557 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.65076 | 0.204540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −62.5116 | −2.74396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.9776 | 0.524747 | 0.262374 | − | 0.964966i | \(-0.415495\pi\) | ||||
0.262374 | + | 0.964966i | \(0.415495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.711546 | 0.0311137 | 0.0155569 | − | 0.999879i | \(-0.495048\pi\) | ||||
0.0155569 | + | 0.999879i | \(0.495048\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.65503 | −0.115655 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −68.7162 | −2.98203 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.7246 | 0.767737 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 65.5524 | 2.82880 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.961182 | 0.0414011 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.9533 | 1.50276 | 0.751381 | − | 0.659869i | \(-0.229388\pi\) | ||||
0.751381 | + | 0.659869i | \(0.229388\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 72.6351 | 3.11707 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8478 | −0.763118 | −0.381559 | − | 0.924345i | \(-0.624613\pi\) | ||||
−0.381559 | + | 0.924345i | \(0.624613\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 40.2558 | 1.71808 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.4558 | −0.956650 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.7497 | 0.627221 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.29661 | −0.139682 | −0.0698410 | − | 0.997558i | \(-0.522249\pi\) | ||||
−0.0698410 | + | 0.997558i | \(0.522249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.7437 | 1.85016 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.04449 | −0.0440983 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.44153 | −0.187188 | −0.0935941 | − | 0.995610i | \(-0.529836\pi\) | ||||
−0.0935941 | + | 0.995610i | \(0.529836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 56.2481 | 2.36220 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00088 | −0.251570 | −0.125785 | − | 0.992058i | \(-0.540145\pi\) | ||||
−0.125785 | + | 0.992058i | \(0.540145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1609 | 0.760008 | 0.380004 | − | 0.924985i | \(-0.375923\pi\) | ||||
0.380004 | + | 0.924985i | \(0.375923\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 53.6175 | 2.23990 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.0474 | 0.418279 | 0.209140 | − | 0.977886i | \(-0.432934\pi\) | ||||
0.209140 | + | 0.977886i | \(0.432934\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 46.7476 | 1.94277 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.5223 | −1.63966 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.3022 | −0.426672 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.3593 | 1.74836 | 0.874178 | − | 0.485605i | \(-0.161401\pi\) | ||||
0.874178 | + | 0.485605i | \(0.161401\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.2660 | −0.835044 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −42.9698 | −1.76754 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.6741 | −0.807917 | −0.403958 | − | 0.914777i | \(-0.632366\pi\) | ||||
−0.403958 | + | 0.914777i | \(0.632366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −60.4751 | −2.47508 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.2740 | −0.746655 | −0.373328 | − | 0.927700i | \(-0.621783\pi\) | ||||
−0.373328 | + | 0.927700i | \(0.621783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.17793 | −0.333585 | −0.166792 | − | 0.985992i | \(-0.553341\pi\) | ||||
−0.166792 | + | 0.985992i | \(0.553341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9730 | −0.446855 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.7927 | −0.884538 | −0.442269 | − | 0.896883i | \(-0.645826\pi\) | ||||
−0.442269 | + | 0.896883i | \(0.645826\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −62.8197 | −2.54558 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.8294 | 1.08540 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.2379 | 0.615455 | 0.307727 | − | 0.951475i | \(-0.400432\pi\) | ||||
0.307727 | + | 0.951475i | \(0.400432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.2945 | −0.817024 | −0.408512 | − | 0.912753i | \(-0.633952\pi\) | ||||
−0.408512 | + | 0.912753i | \(0.633952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.08510 | 0.0838073 | 0.0419037 | − | 0.999122i | \(-0.486658\pi\) | ||||
0.0419037 | + | 0.999122i | \(0.486658\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.0469 | 0.563681 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −42.8085 | −1.71509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.97262 | −0.318396 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.13667 | −0.0453221 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.0512 | 1.55461 | 0.777303 | − | 0.629127i | \(-0.216587\pi\) | ||||
0.777303 | + | 0.629127i | \(0.216587\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −55.0738 | −2.18899 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.54488 | 0.219696 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 61.1127 | 2.41758 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.8361 | −0.862475 | −0.431238 | − | 0.902238i | \(-0.641923\pi\) | ||||
−0.431238 | + | 0.902238i | \(0.641923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.3727 | 0.645676 | 0.322838 | − | 0.946454i | \(-0.395363\pi\) | ||||
0.322838 | + | 0.946454i | \(0.395363\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.9991 | 0.825560 | 0.412780 | − | 0.910831i | \(-0.364558\pi\) | ||||
0.412780 | + | 0.910831i | \(0.364558\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.25861 | 0.324179 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −56.6936 | −2.22200 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.2756 | 0.910846 | 0.455423 | − | 0.890275i | \(-0.349488\pi\) | ||||
0.455423 | + | 0.890275i | \(0.349488\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 75.4080 | 2.94195 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.09639 | −0.0816637 | −0.0408318 | − | 0.999166i | \(-0.513001\pi\) | ||||
−0.0408318 | + | 0.999166i | \(0.513001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.3184 | −1.21814 | −0.609072 | − | 0.793115i | \(-0.708458\pi\) | ||||
−0.609072 | + | 0.793115i | \(0.708458\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.02545 | −0.234009 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.02431 | −0.310703 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −43.5190 | −1.68254 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.83812 | −0.186773 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.3377 | −1.70909 | −0.854545 | − | 0.519377i | \(-0.826164\pi\) | ||||
−0.854545 | + | 0.519377i | \(0.826164\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.03772 | −0.116749 | −0.0583746 | − | 0.998295i | \(-0.518592\pi\) | ||||
−0.0583746 | + | 0.998295i | \(0.518592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.9436 | 0.611860 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.7061 | 1.02338 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.6750 | 0.867635 | 0.433817 | − | 0.901001i | \(-0.357166\pi\) | ||||
0.433817 | + | 0.901001i | \(0.357166\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.0338 | 0.764338 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −59.4313 | −2.26415 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2394 | −0.693860 | −0.346930 | − | 0.937891i | \(-0.612776\pi\) | ||||
−0.346930 | + | 0.937891i | \(0.612776\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.8469 | −0.601974 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.27287 | 0.0482134 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −43.8934 | −1.66020 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4315 | 0.658378 | 0.329189 | − | 0.944264i | \(-0.393225\pi\) | ||||
0.329189 | + | 0.944264i | \(0.393225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.67629 | −0.327232 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 32.8086 | 1.23389 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.4207 | −1.21758 | −0.608792 | − | 0.793330i | \(-0.708346\pi\) | ||||
−0.608792 | + | 0.793330i | \(0.708346\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 44.6608 | 1.67491 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.24179 | −0.271207 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.1117 | −1.38596 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.494269 | 0.0184331 | 0.00921656 | − | 0.999958i | \(-0.497066\pi\) | ||||
0.00921656 | + | 0.999958i | \(0.497066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.5099 | −1.13625 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 56.6430 | 2.10658 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.25774 | 0.157911 | 0.0789555 | − | 0.996878i | \(-0.474842\pi\) | ||||
0.0789555 | + | 0.996878i | \(0.474842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 34.6543 | 1.28349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.14140 | 0.116189 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.8525 | −0.548589 | −0.274295 | − | 0.961646i | \(-0.588444\pi\) | ||||
−0.274295 | + | 0.961646i | \(0.588444\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.31878 | 0.0485780 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.1389 | −1.55010 | −0.775052 | − | 0.631898i | \(-0.782276\pi\) | ||||
−0.775052 | + | 0.631898i | \(0.782276\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.9926 | −1.68958 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.97014 | −0.145650 | −0.0728252 | − | 0.997345i | \(-0.523202\pi\) | ||||
−0.0728252 | + | 0.997345i | \(0.523202\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −119.670 | −4.37851 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.55705 | −0.129972 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.5382 | 1.88066 | 0.940328 | − | 0.340269i | \(-0.110518\pi\) | ||||
0.940328 | + | 0.340269i | \(0.110518\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −40.3921 | −1.47197 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.9808 | 1.45313 | 0.726564 | − | 0.687099i | \(-0.241116\pi\) | ||||
0.726564 | + | 0.687099i | \(0.241116\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.84892 | −0.103409 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.6683 | −0.749226 | −0.374613 | − | 0.927181i | \(-0.622224\pi\) | ||||
−0.374613 | + | 0.927181i | \(0.622224\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.7336 | −1.69187 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.6424 | 1.72027 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.0670558 | −0.00241809 | −0.00120905 | − | 0.999999i | \(-0.500385\pi\) | ||||
−0.00120905 | + | 0.999999i | \(0.500385\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.7121 | 0.565859 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.2074 | −0.762778 | −0.381389 | − | 0.924415i | \(-0.624554\pi\) | ||||
−0.381389 | + | 0.924415i | \(0.624554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.2717 | −0.870744 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.71588 | 0.348108 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.34480 | −0.262817 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −112.716 | −4.02816 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.1047 | −0.681010 | −0.340505 | − | 0.940243i | \(-0.610598\pi\) | ||||
−0.340505 | + | 0.940243i | \(0.610598\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.3577 | −1.32997 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.03035 | 0.0721910 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.9102 | −0.991121 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.0751 | 1.80917 | 0.904587 | − | 0.426290i | \(-0.140180\pi\) | ||||
0.904587 | + | 0.426290i | \(0.140180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.92672 | 0.0681625 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −129.621 | −4.57992 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.06286 | −0.319822 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.4547 | 0.684837 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.02800 | −0.176775 | −0.0883876 | − | 0.996086i | \(-0.528171\pi\) | ||||
−0.0883876 | + | 0.996086i | \(0.528171\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.3571 | 1.80339 | 0.901696 | − | 0.432371i | \(-0.142323\pi\) | ||||
0.901696 | + | 0.432371i | \(0.142323\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.6645 | −0.444162 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.9785 | 0.838900 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −91.4179 | −3.19440 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7483 | 0.479818 | 0.239909 | − | 0.970795i | \(-0.422882\pi\) | ||||
0.239909 | + | 0.970795i | \(0.422882\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.07220 | 0.316237 | 0.158119 | − | 0.987420i | \(-0.449457\pi\) | ||||
0.158119 | + | 0.987420i | \(0.449457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.2010 | 1.67611 | 0.838057 | − | 0.545583i | \(-0.183692\pi\) | ||||
0.838057 | + | 0.545583i | \(0.183692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.0601 | 1.42608 | 0.713038 | − | 0.701125i | \(-0.247319\pi\) | ||||
0.713038 | + | 0.701125i | \(0.247319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.5019 | 0.884651 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.398199 | 0.0137968 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −101.724 | −3.51611 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.3970 | 1.01490 | 0.507449 | − | 0.861682i | \(-0.330588\pi\) | ||||
0.507449 | + | 0.861682i | \(0.330588\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.3895 | 1.22033 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.3288 | 0.665721 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.8458 | −0.853711 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.6367 | 0.845530 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.10036 | −0.106279 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.39913 | 0.0479053 | 0.0239527 | − | 0.999713i | \(-0.492375\pi\) | ||||
0.0239527 | + | 0.999713i | \(0.492375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.68808 | 0.125982 | 0.0629912 | − | 0.998014i | \(-0.479936\pi\) | ||||
0.0629912 | + | 0.998014i | \(0.479936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.0281 | 0.546871 | 0.273435 | − | 0.961890i | \(-0.411840\pi\) | ||||
0.273435 | + | 0.961890i | \(0.411840\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.1800 | 0.926291 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.0979 | 1.19475 | 0.597374 | − | 0.801963i | \(-0.296211\pi\) | ||||
0.597374 | + | 0.801963i | \(0.296211\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 54.2942 | 1.84393 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.36753 | −0.182081 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.60781 | 0.257781 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 48.2759 | 1.63389 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.2491 | −1.79809 | −0.899046 | − | 0.437853i | \(-0.855739\pi\) | ||||
−0.899046 | + | 0.437853i | \(0.855739\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −43.6142 | −1.47107 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.8449 | 1.37610 | 0.688050 | − | 0.725663i | \(-0.258467\pi\) | ||||
0.688050 | + | 0.725663i | \(0.258467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.9288 | 0.502393 | 0.251196 | − | 0.967936i | \(-0.419176\pi\) | ||||
0.251196 | + | 0.967936i | \(0.419176\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.9975 | −1.17510 | −0.587550 | − | 0.809188i | \(-0.699908\pi\) | ||||
−0.587550 | + | 0.809188i | \(0.699908\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.1496 | −0.642259 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.4692 | −0.685742 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.7068 | 0.492143 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.4349 | −0.548745 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.1104 | 1.93809 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.26799 | −0.142187 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 67.0793 | 2.23226 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.3920 | 0.544288 | 0.272144 | − | 0.962257i | \(-0.412267\pi\) | ||||
0.272144 | + | 0.962257i | \(0.412267\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 99.3416 | 3.29495 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.1111 | −1.46147 | −0.730733 | − | 0.682663i | \(-0.760822\pi\) | ||||
−0.730733 | + | 0.682663i | \(0.760822\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.3825 | 0.475991 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.3076 | −1.03387 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.5629 | 0.942203 | 0.471101 | − | 0.882079i | \(-0.343857\pi\) | ||||
0.471101 | + | 0.882079i | \(0.343857\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.4724 | 1.07000 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.3708 | −1.39465 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −92.3813 | −3.03420 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.2273 | 0.532400 | 0.266200 | − | 0.963918i | \(-0.414232\pi\) | ||||
0.266200 | + | 0.963918i | \(0.414232\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.03948 | 0.0996148 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 90.9372 | 2.97715 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.65418 | 0.184714 | 0.0923571 | − | 0.995726i | \(-0.470560\pi\) | ||||
0.0923571 | + | 0.995726i | \(0.470560\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46.5192 | −1.51810 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.6246 | −0.835338 | −0.417669 | − | 0.908599i | \(-0.637153\pi\) | ||||
−0.417669 | + | 0.908599i | \(0.637153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.47185 | 0.113059 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.248718 | −0.00808223 | −0.00404112 | − | 0.999992i | \(-0.501286\pi\) | ||||
−0.00404112 | + | 0.999992i | \(0.501286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −52.2820 | −1.69715 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 47.5914 | 1.54326 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.1737 | 1.26896 | 0.634481 | − | 0.772939i | \(-0.281214\pi\) | ||||
0.634481 | + | 0.772939i | \(0.281214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.8606 | 0.738978 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.94423 | −0.256533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.4435 | 0.691726 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.7704 | −0.347073 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.04114 | −0.0656386 | −0.0328193 | − | 0.999461i | \(-0.510449\pi\) | ||||
−0.0328193 | + | 0.999461i | \(0.510449\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.30290 | −0.106105 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.6713 | −0.438734 | −0.219367 | − | 0.975642i | \(-0.570399\pi\) | ||||
−0.219367 | + | 0.975642i | \(0.570399\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.5387 | −0.979025 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.8777 | −1.46776 | −0.733878 | − | 0.679281i | \(-0.762292\pi\) | ||||
−0.733878 | + | 0.679281i | \(0.762292\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.5784 | 0.497887 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −141.505 | −4.51792 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59.6356 | 1.90208 | 0.951039 | − | 0.309070i | \(-0.100018\pi\) | ||||
0.951039 | + | 0.309070i | \(0.100018\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 41.1418 | 1.30956 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.56841 | 0.272460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.3396 | −1.34496 | −0.672480 | − | 0.740115i | \(-0.734771\pi\) | ||||
−0.672480 | + | 0.740115i | \(0.734771\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 64.8656 | 2.05845 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.02379 | 0.222446 | 0.111223 | − | 0.993795i | \(-0.464523\pi\) | ||||
0.111223 | + | 0.993795i | \(0.464523\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.5504 | −1.37787 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2300.2.a.n.1.1 | 6 | ||
4.3 | odd | 2 | 9200.2.a.cy.1.6 | 6 | |||
5.2 | odd | 4 | 460.2.c.a.369.12 | yes | 12 | ||
5.3 | odd | 4 | 460.2.c.a.369.1 | ✓ | 12 | ||
5.4 | even | 2 | 2300.2.a.o.1.6 | 6 | |||
15.2 | even | 4 | 4140.2.f.b.829.4 | 12 | |||
15.8 | even | 4 | 4140.2.f.b.829.3 | 12 | |||
20.3 | even | 4 | 1840.2.e.f.369.12 | 12 | |||
20.7 | even | 4 | 1840.2.e.f.369.1 | 12 | |||
20.19 | odd | 2 | 9200.2.a.cx.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.1 | ✓ | 12 | 5.3 | odd | 4 | ||
460.2.c.a.369.12 | yes | 12 | 5.2 | odd | 4 | ||
1840.2.e.f.369.1 | 12 | 20.7 | even | 4 | |||
1840.2.e.f.369.12 | 12 | 20.3 | even | 4 | |||
2300.2.a.n.1.1 | 6 | 1.1 | even | 1 | trivial | ||
2300.2.a.o.1.6 | 6 | 5.4 | even | 2 | |||
4140.2.f.b.829.3 | 12 | 15.8 | even | 4 | |||
4140.2.f.b.829.4 | 12 | 15.2 | even | 4 | |||
9200.2.a.cx.1.1 | 6 | 20.19 | odd | 2 | |||
9200.2.a.cy.1.6 | 6 | 4.3 | odd | 2 |