Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7448,2,Mod(1,7448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7448.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7448.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: | \(59.4725794254\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 15x^{6} - x^{5} + 66x^{4} + 4x^{3} - 76x^{2} + 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1064) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.912296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7448.1 |
$q$-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 | ||||||||
\(3\) | 0.912296 | 0.526714 | 0.263357 | − | 0.964698i | \(-0.415170\pi\) | ||||
0.263357 | + | 0.964698i | \(0.415170\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.66528 | −0.744737 | −0.372368 | − | 0.928085i | \(-0.621454\pi\) | ||||
−0.372368 | + | 0.928085i | \(0.621454\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.16772 | −0.722572 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.242241 | −0.0730384 | −0.0365192 | − | 0.999333i | \(-0.511627\pi\) | ||||
−0.0365192 | + | 0.999333i | \(0.511627\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.76999 | −1.60031 | −0.800154 | − | 0.599795i | \(-0.795249\pi\) | ||||
−0.800154 | + | 0.599795i | \(0.795249\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.51923 | −0.392264 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.76637 | 1.39855 | 0.699275 | − | 0.714852i | \(-0.253506\pi\) | ||||
0.699275 | + | 0.714852i | \(0.253506\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.61545 | 1.37942 | 0.689709 | − | 0.724087i | \(-0.257739\pi\) | ||||
0.689709 | + | 0.724087i | \(0.257739\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.22684 | −0.445367 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.71449 | −0.907303 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.91381 | 1.65525 | 0.827627 | − | 0.561279i | \(-0.189690\pi\) | ||||
0.827627 | + | 0.561279i | \(0.189690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.93284 | −1.06557 | −0.532785 | − | 0.846251i | \(-0.678854\pi\) | ||||
−0.532785 | + | 0.846251i | \(0.678854\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.220995 | −0.0384704 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.80371 | −1.61172 | −0.805860 | − | 0.592106i | \(-0.798297\pi\) | ||||
−0.805860 | + | 0.592106i | \(0.798297\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.26394 | −0.842905 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.83237 | −1.19443 | −0.597213 | − | 0.802083i | \(-0.703725\pi\) | ||||
−0.597213 | + | 0.802083i | \(0.703725\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.60986 | 0.538126 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.57918 | 0.230347 | 0.115173 | − | 0.993345i | \(-0.463258\pi\) | ||||
0.115173 | + | 0.993345i | \(0.463258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.26064 | 0.736637 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.48146 | 0.890297 | 0.445148 | − | 0.895457i | \(-0.353151\pi\) | ||||
0.445148 | + | 0.895457i | \(0.353151\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.403399 | 0.0543944 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.912296 | 0.120837 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.07498 | 0.139950 | 0.0699750 | − | 0.997549i | \(-0.477708\pi\) | ||||
0.0699750 | + | 0.997549i | \(0.477708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.10907 | 1.16630 | 0.583149 | − | 0.812366i | \(-0.301821\pi\) | ||||
0.583149 | + | 0.812366i | \(0.301821\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.60866 | 1.19181 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.02541 | 0.980460 | 0.490230 | − | 0.871593i | \(-0.336913\pi\) | ||||
0.490230 | + | 0.871593i | \(0.336913\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.03525 | 0.726559 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.22955 | 0.145921 | 0.0729606 | − | 0.997335i | \(-0.476755\pi\) | ||||
0.0729606 | + | 0.997335i | \(0.476755\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.801370 | 0.0937933 | 0.0468966 | − | 0.998900i | \(-0.485067\pi\) | ||||
0.0468966 | + | 0.998900i | \(0.485067\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.03153 | −0.234581 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.58202 | −0.853044 | −0.426522 | − | 0.904477i | \(-0.640261\pi\) | ||||
−0.426522 | + | 0.904477i | \(0.640261\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.20214 | 0.244682 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.91292 | −0.978320 | −0.489160 | − | 0.872194i | \(-0.662697\pi\) | ||||
−0.489160 | + | 0.872194i | \(0.662697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.60264 | −1.04155 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.13204 | 0.871846 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.1146 | −1.39015 | −0.695074 | − | 0.718938i | \(-0.744628\pi\) | ||||
−0.695074 | + | 0.718938i | \(0.744628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.41250 | −0.561250 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.66528 | −0.170854 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.11664 | 0.113377 | 0.0566886 | − | 0.998392i | \(-0.481946\pi\) | ||||
0.0566886 | + | 0.998392i | \(0.481946\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.525109 | 0.0527755 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0276 | 1.29630 | 0.648149 | − | 0.761514i | \(-0.275543\pi\) | ||||
0.648149 | + | 0.761514i | \(0.275543\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.7259 | −1.35245 | −0.676226 | − | 0.736694i | \(-0.736386\pi\) | ||||
−0.676226 | + | 0.736694i | \(0.736386\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.76847 | 0.364312 | 0.182156 | − | 0.983270i | \(-0.441692\pi\) | ||||
0.182156 | + | 0.983270i | \(0.441692\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.674254 | −0.0645819 | −0.0322909 | − | 0.999479i | \(-0.510280\pi\) | ||||
−0.0322909 | + | 0.999479i | \(0.510280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.94388 | −0.848916 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1480 | 0.954646 | 0.477323 | − | 0.878728i | \(-0.341607\pi\) | ||||
0.477323 | + | 0.878728i | \(0.341607\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.0166 | −1.02730 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.5077 | 1.15634 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9413 | −0.994665 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.82459 | −0.164518 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0347 | 1.07642 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.5974 | 1.65025 | 0.825126 | − | 0.564949i | \(-0.191104\pi\) | ||||
0.825126 | + | 0.564949i | \(0.191104\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.14544 | −0.629121 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.97141 | 0.696465 | 0.348233 | − | 0.937408i | \(-0.386782\pi\) | ||||
0.348233 | + | 0.937408i | \(0.386782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.85095 | 0.675702 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.318763 | −0.0272338 | −0.0136169 | − | 0.999907i | \(-0.504335\pi\) | ||||
−0.0136169 | + | 0.999907i | \(0.504335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.80115 | −0.492047 | −0.246024 | − | 0.969264i | \(-0.579124\pi\) | ||||
−0.246024 | + | 0.969264i | \(0.579124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.44068 | 0.121327 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.39773 | 0.116884 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.8440 | −1.23273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.6701 | 1.11990 | 0.559948 | − | 0.828528i | \(-0.310821\pi\) | ||||
0.559948 | + | 0.828528i | \(0.310821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0282 | 0.897464 | 0.448732 | − | 0.893666i | \(-0.351876\pi\) | ||||
0.448732 | + | 0.893666i | \(0.351876\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.4999 | −1.01055 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.87985 | 0.793568 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.8566 | 1.42511 | 0.712556 | − | 0.701616i | \(-0.247538\pi\) | ||||
0.712556 | + | 0.701616i | \(0.247538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.91301 | 0.468932 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.1970 | 0.877018 | 0.438509 | − | 0.898727i | \(-0.355507\pi\) | ||||
0.438509 | + | 0.898727i | \(0.355507\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.368020 | 0.0286503 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.44712 | 0.111981 | 0.0559906 | − | 0.998431i | \(-0.482168\pi\) | ||||
0.0559906 | + | 0.998431i | \(0.482168\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.2928 | 1.56098 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.16772 | −0.165769 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8941 | 0.904292 | 0.452146 | − | 0.891944i | \(-0.350659\pi\) | ||||
0.452146 | + | 0.891944i | \(0.350659\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.980697 | 0.0737137 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.1728 | 1.88150 | 0.940751 | − | 0.339098i | \(-0.110122\pi\) | ||||
0.940751 | + | 0.339098i | \(0.110122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7410 | 1.39301 | 0.696503 | − | 0.717554i | \(-0.254738\pi\) | ||||
0.696503 | + | 0.717554i | \(0.254738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.31017 | 0.614305 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.3259 | 1.20031 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.39685 | −0.102148 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.356002 | 0.0257594 | 0.0128797 | − | 0.999917i | \(-0.495900\pi\) | ||||
0.0128797 | + | 0.999917i | \(0.495900\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.0988 | 1.23080 | 0.615398 | − | 0.788216i | \(-0.288995\pi\) | ||||
0.615398 | + | 0.788216i | \(0.288995\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.76594 | 0.627742 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.1088 | 0.933964 | 0.466982 | − | 0.884267i | \(-0.345341\pi\) | ||||
0.466982 | + | 0.884267i | \(0.345341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.76977 | 0.338120 | 0.169060 | − | 0.985606i | \(-0.445927\pi\) | ||||
0.169060 | + | 0.985606i | \(0.445927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.32155 | 0.516422 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.33056 | 0.232617 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.3404 | −0.996728 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.242241 | −0.0167561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.0442 | 1.51759 | 0.758794 | − | 0.651331i | \(-0.225789\pi\) | ||||
0.758794 | + | 0.651331i | \(0.225789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.12172 | 0.0768588 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.0431 | 0.889533 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.731087 | 0.0494023 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.2719 | −2.23811 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.5836 | 1.31142 | 0.655708 | − | 0.755014i | \(-0.272370\pi\) | ||||
0.655708 | + | 0.755014i | \(0.272370\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.82715 | 0.321810 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.78829 | −0.384182 | −0.192091 | − | 0.981377i | \(-0.561527\pi\) | ||||
−0.192091 | + | 0.981377i | \(0.561527\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.1074 | −1.26266 | −0.631328 | − | 0.775516i | \(-0.717490\pi\) | ||||
−0.631328 | + | 0.775516i | \(0.717490\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.17125 | −0.404292 | −0.202146 | − | 0.979355i | \(-0.564792\pi\) | ||||
−0.202146 | + | 0.979355i | \(0.564792\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.62978 | −0.171548 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.91705 | −0.449311 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1425 | 1.69101 | 0.845507 | − | 0.533964i | \(-0.179298\pi\) | ||||
0.845507 | + | 0.533964i | \(0.179298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5916 | −1.26201 | −0.631003 | − | 0.775780i | \(-0.717357\pi\) | ||||
−0.631003 | + | 0.775780i | \(0.717357\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1525 | 1.03618 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.76999 | −0.367136 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.13122 | −0.515295 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.39080 | −0.403384 | −0.201692 | − | 0.979449i | \(-0.564644\pi\) | ||||
−0.201692 | + | 0.979449i | \(0.564644\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.60253 | −0.100750 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.76045 | −0.548600 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.8742 | 1.36448 | 0.682238 | − | 0.731130i | \(-0.261007\pi\) | ||||
0.682238 | + | 0.731130i | \(0.261007\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.3226 | −1.19604 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.7237 | −1.83284 | −0.916420 | − | 0.400218i | \(-0.868934\pi\) | ||||
−0.916420 | + | 0.400218i | \(0.868934\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.7935 | −0.663037 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.9644 | −0.732211 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.3856 | 0.816133 | 0.408067 | − | 0.912952i | \(-0.366203\pi\) | ||||
0.408067 | + | 0.912952i | \(0.366203\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.7732 | −1.56561 | −0.782805 | − | 0.622267i | \(-0.786212\pi\) | ||||
−0.782805 | + | 0.622267i | \(0.786212\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.539431 | 0.0325289 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.97402 | −0.178692 | −0.0893458 | − | 0.996001i | \(-0.528478\pi\) | ||||
−0.0893458 | + | 0.996001i | \(0.528478\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.8607 | 0.769950 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.8947 | −1.12716 | −0.563582 | − | 0.826060i | \(-0.690577\pi\) | ||||
−0.563582 | + | 0.826060i | \(0.690577\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.8300 | 1.35710 | 0.678551 | − | 0.734554i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734554i | \(0.262608\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.51923 | −0.0899914 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.2510 | 0.955944 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.01870 | 0.0597174 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.3710 | 0.664299 | 0.332150 | − | 0.943227i | \(-0.392226\pi\) | ||||
0.332150 | + | 0.943227i | \(0.392226\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.79014 | −0.104226 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.14204 | 0.0662680 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38.1711 | −2.20749 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.8851 | 0.682779 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.1692 | −0.868584 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.87636 | −0.221236 | −0.110618 | − | 0.993863i | \(-0.535283\pi\) | ||||
−0.110618 | + | 0.993863i | \(0.535283\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.5221 | −0.712356 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.0561 | 1.25069 | 0.625344 | − | 0.780349i | \(-0.284959\pi\) | ||||
0.625344 | + | 0.780349i | \(0.284959\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.0643 | −1.75586 | −0.877930 | − | 0.478790i | \(-0.841076\pi\) | ||||
−0.877930 | + | 0.478790i | \(0.841076\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.2863 | 1.86954 | 0.934772 | − | 0.355249i | \(-0.115604\pi\) | ||||
0.934772 | + | 0.355249i | \(0.115604\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.15929 | −0.120897 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.43796 | 0.191888 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.76637 | 0.320850 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8488 | 0.712724 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.615120 | −0.0340162 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.37379 | 0.460265 | 0.230133 | − | 0.973159i | \(-0.426084\pi\) | ||||
0.230133 | + | 0.973159i | \(0.426084\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.2517 | 1.16458 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.3646 | −0.730184 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.87908 | −0.102360 | −0.0511799 | − | 0.998689i | \(-0.516298\pi\) | ||||
−0.0511799 | + | 0.998689i | \(0.516298\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.25801 | 0.502826 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.43718 | 0.0778274 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.0504 | −0.541095 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.13726 | −0.329465 | −0.164733 | − | 0.986338i | \(-0.552676\pi\) | ||||
−0.164733 | + | 0.986338i | \(0.552676\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.9103 | −1.01225 | −0.506123 | − | 0.862461i | \(-0.668922\pi\) | ||||
−0.506123 | + | 0.862461i | \(0.668922\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.2025 | 1.45196 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.94453 | −0.529294 | −0.264647 | − | 0.964345i | \(-0.585255\pi\) | ||||
−0.264647 | + | 0.964345i | \(0.585255\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.04755 | −0.108673 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.3900 | 0.970590 | 0.485295 | − | 0.874351i | \(-0.338712\pi\) | ||||
0.485295 | + | 0.874351i | \(0.338712\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.98172 | −0.523905 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.33451 | −0.0698513 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.2152 | −0.742029 | −0.371014 | − | 0.928627i | \(-0.620990\pi\) | ||||
−0.371014 | + | 0.928627i | \(0.620990\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.33543 | 0.225694 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.6016 | 1.32560 | 0.662800 | − | 0.748796i | \(-0.269368\pi\) | ||||
0.662800 | + | 0.748796i | \(0.269368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.9792 | 0.566965 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −51.4326 | −2.64891 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.51685 | −0.437481 | −0.218741 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218741 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.9663 | 0.869211 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0169 | −0.511841 | −0.255921 | − | 0.966698i | \(-0.582379\pi\) | ||||
−0.255921 | + | 0.966698i | \(0.582379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.9784 | 0.863059 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.2802 | −1.02825 | −0.514123 | − | 0.857717i | \(-0.671882\pi\) | ||||
−0.514123 | + | 0.857717i | \(0.671882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.1472 | 1.92918 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.27229 | 0.366838 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.6262 | 0.635293 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.8275 | −1.34643 | −0.673216 | − | 0.739446i | \(-0.735088\pi\) | ||||
−0.673216 | + | 0.739446i | \(0.735088\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.8582 | −0.692047 | −0.346023 | − | 0.938226i | \(-0.612468\pi\) | ||||
−0.346023 | + | 0.938226i | \(0.612468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.2324 | 1.70524 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.66719 | −0.182224 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.37486 | 0.117717 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.19430 | −0.306288 | −0.153144 | − | 0.988204i | \(-0.548940\pi\) | ||||
−0.153144 | + | 0.988204i | \(0.548940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.290807 | −0.0143444 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.8425 | 0.728591 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.29237 | −0.259168 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4938 | 0.708068 | 0.354034 | − | 0.935233i | \(-0.384810\pi\) | ||||
0.354034 | + | 0.935233i | \(0.384810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.8753 | 1.45603 | 0.728016 | − | 0.685560i | \(-0.240443\pi\) | ||||
0.728016 | + | 0.685560i | \(0.240443\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.42321 | −0.166442 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.8408 | −0.622868 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.27514 | 0.0615644 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.8609 | 1.05300 | 0.526501 | − | 0.850175i | \(-0.323504\pi\) | ||||
0.526501 | + | 0.850175i | \(0.323504\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.1847 | −0.537500 | −0.268750 | − | 0.963210i | \(-0.586611\pi\) | ||||
−0.268750 | + | 0.963210i | \(0.586611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.5421 | −0.649296 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.61545 | 0.316460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.4187 | −0.735896 | −0.367948 | − | 0.929846i | \(-0.619940\pi\) | ||||
−0.367948 | + | 0.929846i | \(0.619940\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.939483 | −0.0446362 | −0.0223181 | − | 0.999751i | \(-0.507105\pi\) | ||||
−0.0223181 | + | 0.999751i | \(0.507105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.8396 | 1.03529 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4711 | 0.589865 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.2058 | −1.33112 | −0.665558 | − | 0.746346i | \(-0.731806\pi\) | ||||
−0.665558 | + | 0.746346i | \(0.731806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.484482 | 0.0228134 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.0610 | 0.472707 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.777826 | 0.0363852 | 0.0181926 | − | 0.999835i | \(-0.494209\pi\) | ||||
0.0181926 | + | 0.999835i | \(0.494209\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.1855 | −1.26891 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.3614 | −0.901751 | −0.450875 | − | 0.892587i | \(-0.648888\pi\) | ||||
−0.450875 | + | 0.892587i | \(0.648888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.5688 | 1.60655 | 0.803275 | − | 0.595608i | \(-0.203089\pi\) | ||||
0.803275 | + | 0.595608i | \(0.203089\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.01335 | 0.417984 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.8545 | −1.38150 | −0.690750 | − | 0.723094i | \(-0.742719\pi\) | ||||
−0.690750 | + | 0.723094i | \(0.742719\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.2905 | 0.750626 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.89732 | 0.0872389 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.22684 | −0.102174 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.0500 | −0.643303 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.8865 | −1.27416 | −0.637082 | − | 0.770796i | \(-0.719859\pi\) | ||||
−0.637082 | + | 0.770796i | \(0.719859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.5673 | 2.57925 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.85951 | −0.0844361 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.6224 | 0.526660 | 0.263330 | − | 0.964706i | \(-0.415179\pi\) | ||||
0.263330 | + | 0.964706i | \(0.415179\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.2150 | 0.461938 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.4037 | −1.14645 | −0.573225 | − | 0.819398i | \(-0.694308\pi\) | ||||
−0.573225 | + | 0.819398i | \(0.694308\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 51.4004 | 2.31496 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.874455 | −0.0393038 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.67840 | 0.119902 | 0.0599509 | − | 0.998201i | \(-0.480906\pi\) | ||||
0.0599509 | + | 0.998201i | \(0.480906\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32020 | 0.0589821 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.0893 | −1.65373 | −0.826866 | − | 0.562399i | \(-0.809879\pi\) | ||||
−0.826866 | + | 0.562399i | \(0.809879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.6947 | −0.965401 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.5130 | 0.822192 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.8243 | 0.657075 | 0.328537 | − | 0.944491i | \(-0.393444\pi\) | ||||
0.328537 | + | 0.944491i | \(0.393444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.71449 | −0.208150 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.8575 | 1.00722 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.382542 | −0.0168242 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.8509 | 0.476303 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.4922 | −0.459670 | −0.229835 | − | 0.973230i | \(-0.573819\pi\) | ||||
−0.229835 | + | 0.973230i | \(0.573819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.4757 | −0.676707 | −0.338353 | − | 0.941019i | \(-0.609870\pi\) | ||||
−0.338353 | + | 0.941019i | \(0.609870\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.2109 | −1.49025 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.7642 | 0.902792 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.33024 | −0.101124 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.5400 | 0.499852 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.27557 | −0.271316 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.9650 | 0.991014 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7927 | −0.807961 | −0.403980 | − | 0.914768i | \(-0.632374\pi\) | ||||
−0.403980 | + | 0.914768i | \(0.632374\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.0973 | 0.733716 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.12282 | 0.0480965 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.809060 | −0.0345929 | −0.0172965 | − | 0.999850i | \(-0.505506\pi\) | ||||
−0.0172965 | + | 0.999850i | \(0.505506\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.7459 | −0.842734 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.91381 | 0.379741 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.8941 | 0.632219 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.4536 | −0.739533 | −0.369767 | − | 0.929125i | \(-0.620562\pi\) | ||||
−0.369767 | + | 0.929125i | \(0.620562\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.1927 | 1.91145 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.27434 | −0.0538027 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.68375 | −0.155251 | −0.0776257 | − | 0.996983i | \(-0.524734\pi\) | ||||
−0.0776257 | + | 0.996983i | \(0.524734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.8993 | −0.710960 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.13224 | −0.382843 | −0.191422 | − | 0.981508i | \(-0.561310\pi\) | ||||
−0.191422 | + | 0.981508i | \(0.561310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.1247 | 0.884039 | 0.442020 | − | 0.897005i | \(-0.354262\pi\) | ||||
0.442020 | + | 0.897005i | \(0.354262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.324779 | 0.0135678 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.7315 | −0.614347 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.24274 | 0.218258 | 0.109129 | − | 0.994028i | \(-0.465194\pi\) | ||||
0.109129 | + | 0.994028i | \(0.465194\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.5991 | 0.648278 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.57007 | −0.0650258 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20.8288 | −0.861167 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.26045 | −0.134573 | −0.0672865 | − | 0.997734i | \(-0.521434\pi\) | ||||
−0.0672865 | + | 0.997734i | \(0.521434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.93284 | −0.244458 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.9591 | 0.491932 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.9230 | 0.818141 | 0.409070 | − | 0.912503i | \(-0.365853\pi\) | ||||
0.409070 | + | 0.912503i | \(0.365853\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.35144 | 0.178093 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.4649 | 1.81679 | 0.908394 | − | 0.418116i | \(-0.137309\pi\) | ||||
0.908394 | + | 0.418116i | \(0.137309\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3392 | 0.911233 | 0.455617 | − | 0.890176i | \(-0.349419\pi\) | ||||
0.455617 | + | 0.890176i | \(0.349419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.3968 | −0.708453 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.2204 | 0.740764 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.4089 | 1.39661 | 0.698306 | − | 0.715799i | \(-0.253937\pi\) | ||||
0.698306 | + | 0.715799i | \(0.253937\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.11184 | −0.368626 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.2940 | −0.981226 | −0.490613 | − | 0.871378i | \(-0.663227\pi\) | ||||
−0.490613 | + | 0.871378i | \(0.663227\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.03846 | 0.122523 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.0255 | −0.685422 | −0.342711 | − | 0.939441i | \(-0.611345\pi\) | ||||
−0.342711 | + | 0.939441i | \(0.611345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.6795 | 1.15273 | 0.576363 | − | 0.817194i | \(-0.304472\pi\) | ||||
0.576363 | + | 0.817194i | \(0.304472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −31.1885 | −1.25155 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.90703 | −0.356281 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.220995 | −0.00882570 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −56.5318 | −2.25407 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4675 | −1.17308 | −0.586542 | − | 0.809919i | \(-0.699511\pi\) | ||||
−0.586542 | + | 0.809919i | \(0.699511\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.1109 | 0.799335 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.9699 | −1.22900 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.66532 | −0.105439 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.1367 | −0.637363 | −0.318681 | − | 0.947862i | \(-0.603240\pi\) | ||||
−0.318681 | + | 0.947862i | \(0.603240\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8353 | 0.900535 | 0.450267 | − | 0.892894i | \(-0.351329\pi\) | ||||
0.450267 | + | 0.892894i | \(0.351329\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.8992 | 0.468530 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7399 | 0.815370 | 0.407685 | − | 0.913123i | \(-0.366336\pi\) | ||||
0.407685 | + | 0.913123i | \(0.366336\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.260403 | −0.0102217 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.3767 | −0.758268 | −0.379134 | − | 0.925342i | \(-0.623778\pi\) | ||||
−0.379134 | + | 0.925342i | \(0.623778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.2746 | −0.518683 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.73714 | −0.0677724 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.33347 | 0.285672 | 0.142836 | − | 0.989746i | \(-0.454378\pi\) | ||||
0.142836 | + | 0.989746i | \(0.454378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.7069 | −1.46663 | −0.733315 | − | 0.679889i | \(-0.762028\pi\) | ||||
−0.733315 | + | 0.679889i | \(0.762028\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −30.3538 | −1.17884 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 58.9689 | 2.28329 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.8661 | 0.690742 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.20659 | −0.0851844 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.4005 | 1.86570 | 0.932851 | − | 0.360263i | \(-0.117313\pi\) | ||||
0.932851 | + | 0.360263i | \(0.117313\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.4984 | 0.404083 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8658 | 0.609772 | 0.304886 | − | 0.952389i | \(-0.401382\pi\) | ||||
0.304886 | + | 0.952389i | \(0.401382\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.28063 | −0.202354 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.2671 | 0.660707 | 0.330353 | − | 0.943857i | \(-0.392832\pi\) | ||||
0.330353 | + | 0.943857i | \(0.392832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.530831 | 0.0202820 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.4316 | −0.665059 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.3979 | −1.42475 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −49.2612 | −1.87398 | −0.936992 | − | 0.349351i | \(-0.886402\pi\) | ||||
−0.936992 | + | 0.349351i | \(0.886402\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.66056 | 0.366446 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.5327 | −0.436834 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.63001 | −0.212947 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.1609 | 0.383770 | 0.191885 | − | 0.981417i | \(-0.438540\pi\) | ||||
0.191885 | + | 0.981417i | \(0.438540\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.80371 | −0.369754 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.39914 | −0.0903567 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.73019 | 0.290313 | 0.145157 | − | 0.989409i | \(-0.453631\pi\) | ||||
0.145157 | + | 0.989409i | \(0.453631\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.4357 | 0.616386 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.2484 | −1.46986 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.32761 | −0.0870477 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.8497 | 0.890682 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.3207 | 0.944303 | 0.472152 | − | 0.881517i | \(-0.343477\pi\) | ||||
0.472152 | + | 0.881517i | \(0.343477\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.8733 | −0.664717 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.8496 | −0.737196 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.5601 | 0.910884 | 0.455442 | − | 0.890266i | \(-0.349481\pi\) | ||||
0.455442 | + | 0.890266i | \(0.349481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.12941 | 0.301089 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −45.1644 | −1.67046 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.3033 | −1.00847 | −0.504235 | − | 0.863567i | \(-0.668225\pi\) | ||||
−0.504235 | + | 0.863567i | \(0.668225\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.94408 | −0.0716112 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.0375 | 1.76709 | 0.883544 | − | 0.468348i | \(-0.155151\pi\) | ||||
0.883544 | + | 0.468348i | \(0.155151\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.26394 | −0.193376 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.8539 | 0.398190 | 0.199095 | − | 0.979980i | \(-0.436200\pi\) | ||||
0.199095 | + | 0.979980i | \(0.436200\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.7645 | −0.834027 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.3207 | 0.706906 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.9144 | 0.653705 | 0.326852 | − | 0.945075i | \(-0.394012\pi\) | ||||
0.326852 | + | 0.945075i | \(0.394012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.83030 | −0.212468 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.3651 | −0.668374 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.7888 | 0.719235 | 0.359617 | − | 0.933100i | \(-0.382907\pi\) | ||||
0.359617 | + | 0.933100i | \(0.382907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.46198 | −0.0530667 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 51.4603 | 1.86543 | 0.932717 | − | 0.360609i | \(-0.117431\pi\) | ||||
0.932717 | + | 0.360609i | \(0.117431\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.8158 | 0.752596 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.20260 | −0.223963 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.2468 | −0.946485 | −0.473243 | − | 0.880932i | \(-0.656917\pi\) | ||||
−0.473243 | + | 0.880932i | \(0.656917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.9558 | 0.718689 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.05223 | 0.217684 | 0.108842 | − | 0.994059i | \(-0.465286\pi\) | ||||
0.108842 | + | 0.994059i | \(0.465286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.2115 | 0.474569 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.00000 | −0.0716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.297848 | −0.0106578 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −42.0241 | −1.50182 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.7363 | −1.06133 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.4576 | −0.444064 | −0.222032 | − | 0.975039i | \(-0.571269\pi\) | ||||
−0.222032 | + | 0.975039i | \(0.571269\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.1168 | −0.965383 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −52.5592 | −1.86643 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.84682 | −0.349231 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.13423 | 0.252707 | 0.126354 | − | 0.991985i | \(-0.459673\pi\) | ||||
0.126354 | + | 0.991985i | \(0.459673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.10613 | 0.322152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.4288 | 1.00448 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.194125 | −0.00685051 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.2116 | 0.429869 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.75801 | 0.343074 | 0.171537 | − | 0.985178i | \(-0.445127\pi\) | ||||
0.171537 | + | 0.985178i | \(0.445127\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.23879 | −0.0434998 | −0.0217499 | − | 0.999763i | \(-0.506924\pi\) | ||||
−0.0217499 | + | 0.999763i | \(0.506924\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.5128 | −0.824630 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.6462 | −0.653148 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.83237 | −0.274020 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.8811 | 1.49656 | 0.748281 | − | 0.663382i | \(-0.230880\pi\) | ||||
0.748281 | + | 0.663382i | \(0.230880\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.7541 | −0.444579 | −0.222290 | − | 0.974981i | \(-0.571353\pi\) | ||||
−0.222290 | + | 0.974981i | \(0.571353\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.492120 | 0.0171334 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.6536 | 1.83095 | 0.915473 | − | 0.402380i | \(-0.131817\pi\) | ||||
0.915473 | + | 0.402380i | \(0.131817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.121544 | −0.00422139 | −0.00211070 | − | 0.999998i | \(-0.500672\pi\) | ||||
−0.00211070 | + | 0.999998i | \(0.500672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.71319 | −0.0941194 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.40986 | −0.0833966 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.9703 | 0.966794 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.8707 | 1.58363 | 0.791816 | − | 0.610759i | \(-0.209136\pi\) | ||||
0.791816 | + | 0.610759i | \(0.209136\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.4561 | 1.73987 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.2376 | −0.593693 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33.7932 | −1.16252 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.8277 | 0.714805 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −64.8560 | −2.22323 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.8106 | −0.644064 | −0.322032 | − | 0.946729i | \(-0.604366\pi\) | ||||
−0.322032 | + | 0.946729i | \(0.604366\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.60986 | 0.123455 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.9936 | −0.751288 | −0.375644 | − | 0.926764i | \(-0.622578\pi\) | ||||
−0.375644 | + | 0.926764i | \(0.622578\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.9757 | 1.15924 | 0.579619 | − | 0.814888i | \(-0.303202\pi\) | ||||
0.579619 | + | 0.814888i | \(0.303202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.0442 | −1.12484 | −0.562419 | − | 0.826852i | \(-0.690129\pi\) | ||||
−0.562419 | + | 0.826852i | \(0.690129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.8070 | −0.673459 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.8258 | 0.503509 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.83668 | 0.0623049 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.3065 | −1.56904 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.42055 | −0.0819232 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.7266 | −0.902494 | −0.451247 | − | 0.892399i | \(-0.649021\pi\) | ||||
−0.451247 | + | 0.892399i | \(0.649021\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.3737 | 0.349896 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.6752 | 1.13454 | 0.567272 | − | 0.823530i | \(-0.307999\pi\) | ||||
0.567272 | + | 0.823530i | \(0.307999\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6753 | −0.527516 | −0.263758 | − | 0.964589i | \(-0.584962\pi\) | ||||
−0.263758 | + | 0.964589i | \(0.584962\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.63314 | −0.0548973 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.19711 | 0.174502 | 0.0872510 | − | 0.996186i | \(-0.472192\pi\) | ||||
0.0872510 | + | 0.996186i | \(0.472192\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.533448 | −0.0178712 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.57918 | 0.0528452 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.9198 | −1.40122 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.8233 | −1.16272 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −52.8842 | −1.76379 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.3745 | 1.24512 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.2090 | −1.03742 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.5830 | −1.24792 | −0.623962 | − | 0.781455i | \(-0.714478\pi\) | ||||
−0.623962 | + | 0.781455i | \(0.714478\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.2402 | −0.936669 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.9982 | 0.662571 | 0.331286 | − | 0.943530i | \(-0.392518\pi\) | ||||
0.331286 | + | 0.943530i | \(0.392518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.15907 | 0.0714549 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.8388 | −0.457496 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.6251 | −1.37309 | −0.686543 | − | 0.727089i | \(-0.740873\pi\) | ||||
−0.686543 | + | 0.727089i | \(0.740873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.53639 | −0.116528 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.09451 | −0.233519 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.8312 | 0.717807 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.7538 | 0.977244 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.3223 | −1.06046 | −0.530229 | − | 0.847854i | \(-0.677894\pi\) | ||||
−0.530229 | + | 0.847854i | \(0.677894\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.1217 | 0.658755 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.32615 | 0.0760733 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.8754 | −0.779975 | −0.389988 | − | 0.920820i | \(-0.627521\pi\) | ||||
−0.389988 | + | 0.920820i | \(0.627521\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.3399 | −0.924836 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.6962 | −1.00067 | −0.500334 | − | 0.865833i | \(-0.666789\pi\) | ||||
−0.500334 | + | 0.865833i | \(0.666789\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.2309 | −0.430858 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.7378 | 0.901357 | 0.450678 | − | 0.892686i | \(-0.351182\pi\) | ||||
0.450678 | + | 0.892686i | \(0.351182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.62390 | −0.150098 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.3669 | 0.984715 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.9634 | −0.970611 | −0.485305 | − | 0.874345i | \(-0.661292\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.592844 | −0.0191840 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.96991 | −0.0636782 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.19856 | 0.135437 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.16897 | −0.263241 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.4743 | −0.916619 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.2270 | −0.618299 | −0.309150 | − | 0.951013i | \(-0.600044\pi\) | ||||
−0.309150 | + | 0.951013i | \(0.600044\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.26064 | 0.168996 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.2936 | 0.522887 | 0.261443 | − | 0.965219i | \(-0.415802\pi\) | ||||
0.261443 | + | 0.965219i | \(0.415802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.7219 | 0.375402 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.3065 | −0.681655 | −0.340828 | − | 0.940126i | \(-0.610707\pi\) | ||||
−0.340828 | + | 0.940126i | \(0.610707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.17690 | 0.101534 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.46159 | 0.0466650 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.27409 | −0.232007 | −0.116004 | − | 0.993249i | \(-0.537008\pi\) | ||||
−0.116004 | + | 0.993249i | \(0.537008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.8299 | −0.695558 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.8147 | −1.64761 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.2758 | −1.24764 | −0.623818 | − | 0.781569i | \(-0.714419\pi\) | ||||
−0.623818 | + | 0.781569i | \(0.714419\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.63938 | 0.242428 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.94301 | −0.251811 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.97292 | 0.284175 | 0.142088 | − | 0.989854i | \(-0.454619\pi\) | ||||
0.142088 | + | 0.989854i | \(0.454619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 46.2195 | 1.46232 |
(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 | 7448.2.a.bq.1.6 | 8 | ||
7.2 | even | 3 | 1064.2.q.n.305.3 | ✓ | 16 | ||
7.4 | even | 3 | 1064.2.q.n.457.3 | yes | 16 | ||
7.6 | odd | 2 | 7448.2.a.br.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.q.n.305.3 | ✓ | 16 | 7.2 | even | 3 | ||
1064.2.q.n.457.3 | yes | 16 | 7.4 | even | 3 | ||
7448.2.a.bq.1.6 | 8 | 1.1 | even | 1 | trivial | ||
7448.2.a.br.1.3 | 8 | 7.6 | odd | 2 |