Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2925,2,Mod(2224,2925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2925.2224");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2925.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.3562425912\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2224.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2925.2224 |
Dual form | 2925.2.c.v.2224.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2925\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(2251\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.73205i | − 1.22474i | −0.790569 | − | 0.612372i | \(-0.790215\pi\) | ||||
0.790569 | − | 0.612372i | \(-0.209785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | − 1.73205i | − 0.612372i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26795 | 0.382301 | 0.191151 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191151 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | 3.46410 | 0.925820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | − 3.46410i | − 0.840168i | −0.907485 | − | 0.420084i | \(-0.862001\pi\) | ||||
0.907485 | − | 0.420084i | \(-0.137999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.19615 | −0.962663 | −0.481332 | − | 0.876539i | \(-0.659847\pi\) | ||||
−0.481332 | + | 0.876539i | \(0.659847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 2.19615i | − 0.468221i | ||||||||
\(23\) | 4.73205i | 0.986701i | 0.869831 | + | 0.493350i | \(0.164228\pi\) | ||||
−0.869831 | + | 0.493350i | \(0.835772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.73205 | −0.339683 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 2.00000i | − 0.377964i | ||||||||
\(29\) | −9.46410 | −1.75744 | −0.878720 | − | 0.477338i | \(-0.841602\pi\) | ||||
−0.878720 | + | 0.477338i | \(0.841602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.196152 | −0.0352300 | −0.0176150 | − | 0.999845i | \(-0.505607\pi\) | ||||
−0.0176150 | + | 0.999845i | \(0.505607\pi\) | |||||||
\(32\) | 5.19615i | 0.918559i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4.00000i | − 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 7.26795i | 1.17902i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 10.1962i | − 1.55490i | −0.628946 | − | 0.777449i | \(-0.716513\pi\) | ||||
0.628946 | − | 0.777449i | \(-0.283487\pi\) | |||||||
\(44\) | −1.26795 | −0.191151 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.19615 | 1.20846 | ||||||||
\(47\) | − 6.00000i | − 0.875190i | −0.899172 | − | 0.437595i | \(-0.855830\pi\) | ||||
0.899172 | − | 0.437595i | \(-0.144170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000i | 0.138675i | ||||||||
\(53\) | − 10.3923i | − 1.42749i | −0.700404 | − | 0.713746i | \(-0.746997\pi\) | ||||
0.700404 | − | 0.713746i | \(-0.253003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.46410 | 0.462910 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 16.3923i | 2.15242i | ||||||||
\(59\) | −15.1244 | −1.96902 | −0.984512 | − | 0.175319i | \(-0.943904\pi\) | ||||
−0.984512 | + | 0.175319i | \(0.943904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3923 | 1.58667 | 0.793336 | − | 0.608784i | \(-0.208342\pi\) | ||||
0.793336 | + | 0.608784i | \(0.208342\pi\) | |||||||
\(62\) | 0.339746i | 0.0431478i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 14.3923i | − 1.75830i | −0.476545 | − | 0.879150i | \(-0.658111\pi\) | ||||
0.476545 | − | 0.879150i | \(-0.341889\pi\) | |||||||
\(68\) | 3.46410i | 0.420084i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.26795 | −0.150478 | −0.0752389 | − | 0.997166i | \(-0.523972\pi\) | ||||
−0.0752389 | + | 0.997166i | \(0.523972\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | −6.92820 | −0.805387 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.19615 | 0.481332 | ||||||||
\(77\) | 2.53590i | 0.288992i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3923 | −1.39424 | −0.697122 | − | 0.716953i | \(-0.745536\pi\) | ||||
−0.697122 | + | 0.716953i | \(0.745536\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 6.00000i | − 0.662589i | ||||||||
\(83\) | − 6.00000i | − 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −17.6603 | −1.90435 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 2.19615i | − 0.234111i | ||||||||
\(89\) | 0.928203 | 0.0983893 | 0.0491947 | − | 0.998789i | \(-0.484335\pi\) | ||||
0.0491947 | + | 0.998789i | \(0.484335\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | − 4.73205i | − 0.493350i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.3923 | −1.07188 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | − 5.19615i | − 0.524891i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.9282 | −1.28640 | −0.643202 | − | 0.765696i | \(-0.722395\pi\) | ||||
−0.643202 | + | 0.765696i | \(0.722395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 10.1962i | − 1.00466i | −0.864677 | − | 0.502328i | \(-0.832477\pi\) | ||||
0.864677 | − | 0.502328i | \(-0.167523\pi\) | |||||||
\(104\) | −1.73205 | −0.169842 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.0000 | −1.74831 | ||||||||
\(107\) | − 0.339746i | − 0.0328445i | −0.999865 | − | 0.0164222i | \(-0.994772\pi\) | ||||
0.999865 | − | 0.0164222i | \(-0.00522760\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 10.0000i | − 0.944911i | ||||||||
\(113\) | 15.4641i | 1.45474i | 0.686245 | + | 0.727370i | \(0.259258\pi\) | ||||
−0.686245 | + | 0.727370i | \(0.740742\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.46410 | 0.878720 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 26.1962i | 2.41155i | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | − 21.4641i | − 1.94327i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.196152 | 0.0176150 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.80385i | 0.515008i | 0.966277 | + | 0.257504i | \(0.0829001\pi\) | ||||
−0.966277 | + | 0.257504i | \(0.917100\pi\) | |||||||
\(128\) | 12.1244i | 1.07165i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 8.39230i | − 0.727705i | ||||||||
\(134\) | −24.9282 | −2.15347 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 12.9282i | 1.10453i | 0.833668 | + | 0.552265i | \(0.186237\pi\) | ||||
−0.833668 | + | 0.552265i | \(0.813763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.39230 | 0.711826 | 0.355913 | − | 0.934519i | \(-0.384170\pi\) | ||||
0.355913 | + | 0.934519i | \(0.384170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.19615i | 0.184297i | ||||||||
\(143\) | − 1.26795i | − 0.106031i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.92820 | 0.573382 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.00000i | 0.328798i | ||||||||
\(149\) | 19.8564 | 1.62670 | 0.813350 | − | 0.581775i | \(-0.197641\pi\) | ||||
0.813350 | + | 0.581775i | \(0.197641\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.1962 | −0.992509 | −0.496254 | − | 0.868177i | \(-0.665292\pi\) | ||||
−0.496254 | + | 0.868177i | \(0.665292\pi\) | |||||||
\(152\) | 7.26795i | 0.589509i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.39230 | 0.353942 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.0000i | − 0.798087i | −0.916932 | − | 0.399043i | \(-0.869342\pi\) | ||||
0.916932 | − | 0.399043i | \(-0.130658\pi\) | |||||||
\(158\) | 21.4641i | 1.70759i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.46410 | −0.745876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.39230i | − 0.500684i | −0.968157 | − | 0.250342i | \(-0.919457\pi\) | ||||
0.968157 | − | 0.250342i | \(-0.0805431\pi\) | |||||||
\(164\) | −3.46410 | −0.270501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.3923 | −0.806599 | ||||||||
\(167\) | − 12.9282i | − 1.00041i | −0.865906 | − | 0.500207i | \(-0.833257\pi\) | ||||
0.865906 | − | 0.500207i | \(-0.166743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.1962i | 0.777449i | ||||||||
\(173\) | 15.4641i | 1.17571i | 0.808965 | + | 0.587857i | \(0.200028\pi\) | ||||
−0.808965 | + | 0.587857i | \(0.799972\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.33975 | −0.477876 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 1.60770i | − 0.120502i | ||||||||
\(179\) | −5.07180 | −0.379084 | −0.189542 | − | 0.981873i | \(-0.560700\pi\) | ||||
−0.189542 | + | 0.981873i | \(0.560700\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.3923 | −1.51575 | −0.757874 | − | 0.652401i | \(-0.773762\pi\) | ||||
−0.757874 | + | 0.652401i | \(0.773762\pi\) | |||||||
\(182\) | − 3.46410i | − 0.256776i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.19615 | 0.604228 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4.39230i | − 0.321197i | ||||||||
\(188\) | 6.00000i | 0.437595i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9282 | 1.36960 | 0.684798 | − | 0.728733i | \(-0.259890\pi\) | ||||
0.684798 | + | 0.728733i | \(0.259890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | 3.46410 | 0.248708 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | − 0.928203i | − 0.0661317i | −0.999453 | − | 0.0330659i | \(-0.989473\pi\) | ||||
0.999453 | − | 0.0330659i | \(-0.0105271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.3923i | 1.57552i | ||||||||
\(203\) | − 18.9282i | − 1.32850i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −17.6603 | −1.23045 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.00000i | 0.346688i | ||||||||
\(209\) | −5.32051 | −0.368027 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | 10.3923i | 0.713746i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.588457 | −0.0402261 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 0.392305i | − 0.0266314i | ||||||||
\(218\) | 3.46410i | 0.234619i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.46410 | −0.233021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.00000i | − 0.133930i | −0.997755 | − | 0.0669650i | \(-0.978668\pi\) | ||||
0.997755 | − | 0.0669650i | \(-0.0213316\pi\) | |||||||
\(224\) | −10.3923 | −0.694365 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 26.7846 | 1.78169 | ||||||||
\(227\) | − 3.46410i | − 0.229920i | −0.993370 | − | 0.114960i | \(-0.963326\pi\) | ||||
0.993370 | − | 0.114960i | \(-0.0366741\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.3923 | 0.951070 | 0.475535 | − | 0.879697i | \(-0.342254\pi\) | ||||
0.475535 | + | 0.879697i | \(0.342254\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.3923i | 1.07621i | ||||||||
\(233\) | − 6.00000i | − 0.393073i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) | ||||
0.980497 | − | 0.196537i | \(-0.0629694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15.1244 | 0.984512 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 12.0000i | − 0.777844i | ||||||||
\(239\) | −3.80385 | −0.246050 | −0.123025 | − | 0.992404i | \(-0.539260\pi\) | ||||
−0.123025 | + | 0.992404i | \(0.539260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3923 | 1.18475 | 0.592376 | − | 0.805661i | \(-0.298190\pi\) | ||||
0.592376 | + | 0.805661i | \(0.298190\pi\) | |||||||
\(242\) | 16.2679i | 1.04574i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.3923 | −0.793336 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.19615i | 0.266995i | ||||||||
\(248\) | 0.339746i | 0.0215739i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.5359 | 0.917498 | 0.458749 | − | 0.888566i | \(-0.348298\pi\) | ||||
0.458749 | + | 0.888566i | \(0.348298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000i | 0.377217i | ||||||||
\(254\) | 10.0526 | 0.630754 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 7.85641i | 0.490069i | 0.969514 | + | 0.245035i | \(0.0787993\pi\) | ||||
−0.969514 | + | 0.245035i | \(0.921201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.73205i | 0.291791i | 0.989300 | + | 0.145895i | \(0.0466063\pi\) | ||||
−0.989300 | + | 0.145895i | \(0.953394\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.5359 | −0.891253 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.3923i | 0.879150i | ||||||||
\(269\) | 7.85641 | 0.479014 | 0.239507 | − | 0.970895i | \(-0.423014\pi\) | ||||
0.239507 | + | 0.970895i | \(0.423014\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.9808 | −1.27449 | −0.637245 | − | 0.770661i | \(-0.719926\pi\) | ||||
−0.637245 | + | 0.770661i | \(0.719926\pi\) | |||||||
\(272\) | 17.3205i | 1.05021i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.3923 | 1.35277 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5.60770i | − 0.336934i | −0.985707 | − | 0.168467i | \(-0.946118\pi\) | ||||
0.985707 | − | 0.168467i | \(-0.0538816\pi\) | |||||||
\(278\) | − 14.5359i | − 0.871805i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.60770 | −0.0959071 | −0.0479535 | − | 0.998850i | \(-0.515270\pi\) | ||||
−0.0479535 | + | 0.998850i | \(0.515270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.41154i | − 0.0839075i | −0.999120 | − | 0.0419538i | \(-0.986642\pi\) | ||||
0.999120 | − | 0.0419538i | \(-0.0133582\pi\) | |||||||
\(284\) | 1.26795 | 0.0752389 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.19615 | −0.129861 | ||||||||
\(287\) | 6.92820i | 0.408959i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 4.00000i | − 0.234082i | ||||||||
\(293\) | − 18.9282i | − 1.10580i | −0.833248 | − | 0.552899i | \(-0.813522\pi\) | ||||
0.833248 | − | 0.552899i | \(-0.186478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.92820 | −0.402694 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 34.3923i | − 1.99229i | ||||||||
\(299\) | 4.73205 | 0.273662 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.3923 | 1.17539 | ||||||||
\(302\) | 21.1244i | 1.21557i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.9808 | 1.20333 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.7846i | 1.30039i | 0.759769 | + | 0.650193i | \(0.225312\pi\) | ||||
−0.759769 | + | 0.650193i | \(0.774688\pi\) | |||||||
\(308\) | − 2.53590i | − 0.144496i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.39230 | −0.249065 | −0.124532 | − | 0.992216i | \(-0.539743\pi\) | ||||
−0.124532 | + | 0.992216i | \(0.539743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 6.39230i | − 0.361314i | −0.983546 | − | 0.180657i | \(-0.942178\pi\) | ||||
0.983546 | − | 0.180657i | \(-0.0578225\pi\) | |||||||
\(314\) | −17.3205 | −0.977453 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.3923 | 0.697122 | ||||||||
\(317\) | − 24.0000i | − 1.34797i | −0.738743 | − | 0.673987i | \(-0.764580\pi\) | ||||
0.738743 | − | 0.673987i | \(-0.235420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 16.3923i | 0.913507i | ||||||||
\(323\) | 14.5359i | 0.808799i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.0718 | −0.613210 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 6.00000i | − 0.331295i | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.5885 | −1.57136 | −0.785682 | − | 0.618631i | \(-0.787688\pi\) | ||||
−0.785682 | + | 0.618631i | \(0.787688\pi\) | |||||||
\(332\) | 6.00000i | 0.329293i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −22.3923 | −1.22525 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 5.60770i | − 0.305471i | −0.988267 | − | 0.152735i | \(-0.951192\pi\) | ||||
0.988267 | − | 0.152735i | \(-0.0488082\pi\) | |||||||
\(338\) | 1.73205i | 0.0942111i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.248711 | −0.0134685 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | −17.6603 | −0.952177 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 26.7846 | 1.43995 | ||||||||
\(347\) | − 11.6603i | − 0.625955i | −0.949761 | − | 0.312978i | \(-0.898674\pi\) | ||||
0.949761 | − | 0.312978i | \(-0.101326\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.39230 | −0.342172 | −0.171086 | − | 0.985256i | \(-0.554728\pi\) | ||||
−0.171086 | + | 0.985256i | \(0.554728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.58846i | 0.351166i | ||||||||
\(353\) | 27.7128i | 1.47500i | 0.675345 | + | 0.737502i | \(0.263995\pi\) | ||||
−0.675345 | + | 0.737502i | \(0.736005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.928203 | −0.0491947 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.78461i | 0.464281i | ||||||||
\(359\) | 8.19615 | 0.432576 | 0.216288 | − | 0.976330i | \(-0.430605\pi\) | ||||
0.216288 | + | 0.976330i | \(0.430605\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.39230 | −0.0732792 | ||||||||
\(362\) | 35.3205i | 1.85640i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.1962i | 1.15863i | 0.815104 | + | 0.579315i | \(0.196680\pi\) | ||||
−0.815104 | + | 0.579315i | \(0.803320\pi\) | |||||||
\(368\) | − 23.6603i | − 1.23338i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.7846 | 1.07908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000i | 0.517780i | 0.965907 | + | 0.258890i | \(0.0833568\pi\) | ||||
−0.965907 | + | 0.258890i | \(0.916643\pi\) | |||||||
\(374\) | −7.60770 | −0.393385 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.3923 | −0.535942 | ||||||||
\(377\) | 9.46410i | 0.487426i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.9808 | 1.69411 | 0.847054 | − | 0.531507i | \(-0.178374\pi\) | ||||
0.847054 | + | 0.531507i | \(0.178374\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 32.7846i | − 1.67741i | ||||||||
\(383\) | − 0.928203i | − 0.0474290i | −0.999719 | − | 0.0237145i | \(-0.992451\pi\) | ||||
0.999719 | − | 0.0237145i | \(-0.00754926\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.3205 | 0.881591 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 2.00000i | − 0.101535i | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.3923 | 0.828994 | ||||||||
\(392\) | − 5.19615i | − 0.262445i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.60770 | −0.0809945 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 12.7846i | − 0.641641i | −0.947140 | − | 0.320821i | \(-0.896041\pi\) | ||||
0.947140 | − | 0.320821i | \(-0.103959\pi\) | |||||||
\(398\) | 34.6410i | 1.73640i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.0718 | 1.15215 | 0.576075 | − | 0.817397i | \(-0.304584\pi\) | ||||
0.576075 | + | 0.817397i | \(0.304584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.196152i | 0.00977105i | ||||||||
\(404\) | 12.9282 | 0.643202 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −32.7846 | −1.62707 | ||||||||
\(407\) | − 5.07180i | − 0.251400i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.3923 | 1.89838 | 0.949189 | − | 0.314708i | \(-0.101906\pi\) | ||||
0.949189 | + | 0.314708i | \(0.101906\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.1962i | 0.502328i | ||||||||
\(413\) | − 30.2487i | − 1.48844i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.19615 | 0.254762 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.21539i | 0.450739i | ||||||||
\(419\) | −9.46410 | −0.462352 | −0.231176 | − | 0.972912i | \(-0.574257\pi\) | ||||
−0.231176 | + | 0.972912i | \(0.574257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7846 | 0.525610 | 0.262805 | − | 0.964849i | \(-0.415352\pi\) | ||||
0.262805 | + | 0.964849i | \(0.415352\pi\) | |||||||
\(422\) | − 13.8564i | − 0.674519i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.0000 | −0.874157 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.7846i | 1.19941i | ||||||||
\(428\) | 0.339746i | 0.0164222i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.5167 | −0.940084 | −0.470042 | − | 0.882644i | \(-0.655761\pi\) | ||||
−0.470042 | + | 0.882644i | \(0.655761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.78461i | 0.326048i | 0.986622 | + | 0.163024i | \(0.0521247\pi\) | ||||
−0.986622 | + | 0.163024i | \(0.947875\pi\) | |||||||
\(434\) | −0.679492 | −0.0326167 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | − 19.8564i | − 0.949861i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.0000 | −1.52728 | −0.763638 | − | 0.645644i | \(-0.776589\pi\) | ||||
−0.763638 | + | 0.645644i | \(0.776589\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.00000i | 0.285391i | ||||||||
\(443\) | 34.9808i | 1.66199i | 0.556283 | + | 0.830993i | \(0.312227\pi\) | ||||
−0.556283 | + | 0.830993i | \(0.687773\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.46410 | −0.164030 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 2.00000i | − 0.0944911i | ||||||||
\(449\) | 27.4641 | 1.29611 | 0.648056 | − | 0.761593i | \(-0.275582\pi\) | ||||
0.648056 | + | 0.761593i | \(0.275582\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.39230 | 0.206826 | ||||||||
\(452\) | − 15.4641i | − 0.727370i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 30.7846i | − 1.44004i | −0.693952 | − | 0.720022i | \(-0.744132\pi\) | ||||
0.693952 | − | 0.720022i | \(-0.255868\pi\) | |||||||
\(458\) | − 24.9282i | − 1.16482i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.46410 | −0.161339 | −0.0806696 | − | 0.996741i | \(-0.525706\pi\) | ||||
−0.0806696 | + | 0.996741i | \(0.525706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 18.3923i | − 0.854763i | −0.904071 | − | 0.427381i | \(-0.859436\pi\) | ||||
0.904071 | − | 0.427381i | \(-0.140564\pi\) | |||||||
\(464\) | 47.3205 | 2.19680 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.3923 | −0.481414 | ||||||||
\(467\) | − 38.1962i | − 1.76751i | −0.467953 | − | 0.883754i | \(-0.655008\pi\) | ||||
0.467953 | − | 0.883754i | \(-0.344992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.7846 | 1.32915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 26.1962i | 1.20578i | ||||||||
\(473\) | − 12.9282i | − 0.594439i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.92820 | −0.317554 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.58846i | 0.301349i | ||||||||
\(479\) | 18.3397 | 0.837964 | 0.418982 | − | 0.907994i | \(-0.362387\pi\) | ||||
0.418982 | + | 0.907994i | \(0.362387\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | − 31.8564i | − 1.45102i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.39230 | 0.426923 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.60770i | − 0.254109i | −0.991896 | − | 0.127054i | \(-0.959448\pi\) | ||||
0.991896 | − | 0.127054i | \(-0.0405523\pi\) | |||||||
\(488\) | − 21.4641i | − 0.971634i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.46410 | 0.427109 | 0.213554 | − | 0.976931i | \(-0.431496\pi\) | ||||
0.213554 | + | 0.976931i | \(0.431496\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.7846i | 1.47654i | ||||||||
\(494\) | 7.26795 | 0.327000 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.980762 | 0.0440375 | ||||||||
\(497\) | − 2.53590i | − 0.113751i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.9808 | −0.581099 | −0.290549 | − | 0.956860i | \(-0.593838\pi\) | ||||
−0.290549 | + | 0.956860i | \(0.593838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 25.1769i | − 1.12370i | ||||||||
\(503\) | − 25.5167i | − 1.13773i | −0.822430 | − | 0.568866i | \(-0.807382\pi\) | ||||
0.822430 | − | 0.568866i | \(-0.192618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.3923 | 0.461994 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 5.80385i | − 0.257504i | ||||||||
\(509\) | 32.5359 | 1.44213 | 0.721064 | − | 0.692868i | \(-0.243653\pi\) | ||||
0.721064 | + | 0.692868i | \(0.243653\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | − 8.66025i | − 0.382733i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.6077 | 0.600210 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7.60770i | − 0.334586i | ||||||||
\(518\) | − 13.8564i | − 0.608816i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.60770 | 0.333299 | 0.166650 | − | 0.986016i | \(-0.446705\pi\) | ||||
0.166650 | + | 0.986016i | \(0.446705\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8038i | 0.603600i | 0.953371 | + | 0.301800i | \(0.0975875\pi\) | ||||
−0.953371 | + | 0.301800i | \(0.902412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.19615 | 0.357369 | ||||||||
\(527\) | 0.679492i | 0.0295991i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.607695 | 0.0264215 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.39230i | 0.363853i | ||||||||
\(533\) | − 3.46410i | − 0.150047i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −24.9282 | −1.07673 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 13.6077i | − 0.586669i | ||||||||
\(539\) | 3.80385 | 0.163843 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.60770 | −0.241094 | −0.120547 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120547 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(542\) | 36.3397i | 1.56093i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.0000 | 0.771744 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.80385i | − 0.0771270i | −0.999256 | − | 0.0385635i | \(-0.987722\pi\) | ||||
0.999256 | − | 0.0385635i | \(-0.0122782\pi\) | |||||||
\(548\) | − 12.9282i | − 0.552265i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 39.7128 | 1.69182 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 24.7846i | − 1.05395i | ||||||||
\(554\) | −9.71281 | −0.412658 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.39230 | −0.355913 | ||||||||
\(557\) | 25.8564i | 1.09557i | 0.836619 | + | 0.547786i | \(0.184529\pi\) | ||||
−0.836619 | + | 0.547786i | \(0.815471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1962 | −0.431251 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.78461i | 0.117462i | ||||||||
\(563\) | 16.0526i | 0.676535i | 0.941050 | + | 0.338267i | \(0.109841\pi\) | ||||
−0.941050 | + | 0.338267i | \(0.890159\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.44486 | −0.102765 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.19615i | 0.0921485i | ||||||||
\(569\) | −9.46410 | −0.396756 | −0.198378 | − | 0.980126i | \(-0.563567\pi\) | ||||
−0.198378 | + | 0.980126i | \(0.563567\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.6077 | 0.653162 | 0.326581 | − | 0.945169i | \(-0.394103\pi\) | ||||
0.326581 | + | 0.945169i | \(0.394103\pi\) | |||||||
\(572\) | 1.26795i | 0.0530156i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 4.00000i | − 0.166522i | −0.996528 | − | 0.0832611i | \(-0.973466\pi\) | ||||
0.996528 | − | 0.0832611i | \(-0.0265335\pi\) | |||||||
\(578\) | − 8.66025i | − 0.360219i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 13.1769i | − 0.545732i | ||||||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.7846 | −1.35432 | ||||||||
\(587\) | 15.4641i | 0.638272i | 0.947709 | + | 0.319136i | \(0.103393\pi\) | ||||
−0.947709 | + | 0.319136i | \(0.896607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.823085 | 0.0339146 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 20.0000i | 0.821995i | ||||||||
\(593\) | − 14.7846i | − 0.607131i | −0.952811 | − | 0.303566i | \(-0.901823\pi\) | ||||
0.952811 | − | 0.303566i | \(-0.0981771\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.8564 | −0.813350 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 8.19615i | − 0.335166i | ||||||||
\(599\) | −28.3923 | −1.16008 | −0.580039 | − | 0.814589i | \(-0.696963\pi\) | ||||
−0.580039 | + | 0.814589i | \(0.696963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.5692 | −1.61406 | −0.807031 | − | 0.590509i | \(-0.798927\pi\) | ||||
−0.807031 | + | 0.590509i | \(0.798927\pi\) | |||||||
\(602\) | − 35.3205i | − 1.43956i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.1962 | 0.496254 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 26.9808i | − 1.09512i | −0.836768 | − | 0.547558i | \(-0.815558\pi\) | ||||
0.836768 | − | 0.547558i | \(-0.184442\pi\) | |||||||
\(608\) | − 21.8038i | − 0.884263i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00000 | −0.242734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 26.0000i | − 1.05013i | −0.851062 | − | 0.525065i | \(-0.824041\pi\) | ||||
0.851062 | − | 0.525065i | \(-0.175959\pi\) | |||||||
\(614\) | 39.4641 | 1.59264 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.39230 | 0.176971 | ||||||||
\(617\) | 21.7128i | 0.874125i | 0.899431 | + | 0.437062i | \(0.143981\pi\) | ||||
−0.899431 | + | 0.437062i | \(0.856019\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.9808 | 1.80793 | 0.903965 | − | 0.427607i | \(-0.140643\pi\) | ||||
0.903965 | + | 0.427607i | \(0.140643\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.60770i | 0.305041i | ||||||||
\(623\) | 1.85641i | 0.0743754i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.0718 | −0.442518 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.0000i | 0.399043i | ||||||||
\(629\) | −13.8564 | −0.552491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.1962 | 0.644759 | 0.322379 | − | 0.946611i | \(-0.395517\pi\) | ||||
0.322379 | + | 0.946611i | \(0.395517\pi\) | |||||||
\(632\) | 21.4641i | 0.853796i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −41.5692 | −1.65092 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.00000i | − 0.118864i | ||||||||
\(638\) | 20.7846i | 0.822871i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.928203 | 0.0366618 | 0.0183309 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183309 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 34.7846i | − 1.37177i | −0.727709 | − | 0.685886i | \(-0.759415\pi\) | ||||
0.727709 | − | 0.685886i | \(-0.240585\pi\) | |||||||
\(644\) | 9.46410 | 0.372938 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.1769 | 0.990572 | ||||||||
\(647\) | 16.0526i | 0.631091i | 0.948910 | + | 0.315546i | \(0.102188\pi\) | ||||
−0.948910 | + | 0.315546i | \(0.897812\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.1769 | −0.752760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.39230i | 0.250342i | ||||||||
\(653\) | − 19.8564i | − 0.777041i | −0.921440 | − | 0.388521i | \(-0.872986\pi\) | ||||
0.921440 | − | 0.388521i | \(-0.127014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.3205 | −0.676252 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 20.7846i | − 0.810268i | ||||||||
\(659\) | −14.5359 | −0.566238 | −0.283119 | − | 0.959085i | \(-0.591369\pi\) | ||||
−0.283119 | + | 0.959085i | \(0.591369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.7846 | −1.19738 | −0.598691 | − | 0.800980i | \(-0.704312\pi\) | ||||
−0.598691 | + | 0.800980i | \(0.704312\pi\) | |||||||
\(662\) | 49.5167i | 1.92452i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.3923 | −0.403300 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 44.7846i | − 1.73407i | ||||||||
\(668\) | 12.9282i | 0.500207i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.7128 | 0.606586 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 6.39230i | − 0.246405i | −0.992382 | − | 0.123203i | \(-0.960683\pi\) | ||||
0.992382 | − | 0.123203i | \(-0.0393165\pi\) | |||||||
\(674\) | −9.71281 | −0.374124 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 10.3923i | 0.399409i | 0.979856 | + | 0.199704i | \(0.0639982\pi\) | ||||
−0.979856 | + | 0.199704i | \(0.936002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.00000 | −0.153506 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.430781i | 0.0164954i | ||||||||
\(683\) | 39.4641i | 1.51005i | 0.655695 | + | 0.755026i | \(0.272376\pi\) | ||||
−0.655695 | + | 0.755026i | \(0.727624\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 34.6410 | 1.32260 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 50.9808i | 1.94362i | ||||||||
\(689\) | −10.3923 | −0.395915 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.7654 | 1.74100 | 0.870498 | − | 0.492171i | \(-0.163797\pi\) | ||||
0.870498 | + | 0.492171i | \(0.163797\pi\) | |||||||
\(692\) | − 15.4641i | − 0.587857i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.1962 | −0.766635 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 12.0000i | − 0.454532i | ||||||||
\(698\) | 11.0718i | 0.419074i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7846i | 0.633044i | ||||||||
\(704\) | −1.26795 | −0.0477876 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 48.0000 | 1.80650 | ||||||||
\(707\) | − 25.8564i | − 0.972430i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.60770 | −0.360825 | −0.180412 | − | 0.983591i | \(-0.557743\pi\) | ||||
−0.180412 | + | 0.983591i | \(0.557743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 1.60770i | − 0.0602509i | ||||||||
\(713\) | − 0.928203i | − 0.0347615i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.07180 | 0.189542 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 14.1962i | − 0.529796i | ||||||||
\(719\) | 1.85641 | 0.0692323 | 0.0346161 | − | 0.999401i | \(-0.488979\pi\) | ||||
0.0346161 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.3923 | 0.759449 | ||||||||
\(722\) | 2.41154i | 0.0897483i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.3923 | 0.757874 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.4115i | 0.497407i | 0.968580 | + | 0.248703i | \(0.0800044\pi\) | ||||
−0.968580 | + | 0.248703i | \(0.919996\pi\) | |||||||
\(728\) | − 3.46410i | − 0.128388i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.3205 | −1.30638 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 38.0000i | − 1.40356i | −0.712393 | − | 0.701781i | \(-0.752388\pi\) | ||||
0.712393 | − | 0.701781i | \(-0.247612\pi\) | |||||||
\(734\) | 38.4449 | 1.41903 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.5885 | −0.906343 | ||||||||
\(737\) | − 18.2487i | − 0.672200i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.80385 | 0.287069 | 0.143535 | − | 0.989645i | \(-0.454153\pi\) | ||||
0.143535 | + | 0.989645i | \(0.454153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 36.0000i | − 1.32160i | ||||||||
\(743\) | − 43.8564i | − 1.60894i | −0.593996 | − | 0.804468i | \(-0.702451\pi\) | ||||
0.593996 | − | 0.804468i | \(-0.297549\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.3205 | 0.634149 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.39230i | 0.160599i | ||||||||
\(749\) | 0.679492 | 0.0248281 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6077 | 0.569533 | 0.284766 | − | 0.958597i | \(-0.408084\pi\) | ||||
0.284766 | + | 0.958597i | \(0.408084\pi\) | |||||||
\(752\) | 30.0000i | 1.09399i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.3923 | 0.596973 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.3923i | 0.668480i | 0.942488 | + | 0.334240i | \(0.108480\pi\) | ||||
−0.942488 | + | 0.334240i | \(0.891520\pi\) | |||||||
\(758\) | − 57.1244i | − 2.07485i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.85641 | −0.284795 | −0.142397 | − | 0.989810i | \(-0.545481\pi\) | ||||
−0.142397 | + | 0.989810i | \(0.545481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4.00000i | − 0.144810i | ||||||||
\(764\) | −18.9282 | −0.684798 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.60770 | −0.0580884 | ||||||||
\(767\) | 15.1244i | 0.546109i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.78461 | 0.244659 | 0.122330 | − | 0.992490i | \(-0.460963\pi\) | ||||
0.122330 | + | 0.992490i | \(0.460963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 10.0000i | − 0.359908i | ||||||||
\(773\) | − 6.92820i | − 0.249190i | −0.992208 | − | 0.124595i | \(-0.960237\pi\) | ||||
0.992208 | − | 0.124595i | \(-0.0397632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.46410 | 0.124354 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 10.3923i | − 0.372582i | ||||||||
\(779\) | −14.5359 | −0.520803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.60770 | −0.0575279 | ||||||||
\(782\) | − 28.3923i | − 1.01531i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.0000 | −0.535714 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 51.5692i | − 1.83824i | −0.393973 | − | 0.919122i | \(-0.628900\pi\) | ||||
0.393973 | − | 0.919122i | \(-0.371100\pi\) | |||||||
\(788\) | 0.928203i | 0.0330659i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.9282 | −1.09968 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 12.3923i | − 0.440064i | ||||||||
\(794\) | −22.1436 | −0.785847 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.0000 | 0.708881 | ||||||||
\(797\) | − 28.6410i | − 1.01452i | −0.861794 | − | 0.507258i | \(-0.830659\pi\) | ||||
0.861794 | − | 0.507258i | \(-0.169341\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.7846 | −0.735307 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 39.9615i | − 1.41109i | ||||||||
\(803\) | 5.07180i | 0.178980i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.339746 | 0.0119670 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.3923i | 0.787759i | ||||||||
\(809\) | −9.46410 | −0.332740 | −0.166370 | − | 0.986063i | \(-0.553205\pi\) | ||||
−0.166370 | + | 0.986063i | \(0.553205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.1962 | 0.990101 | 0.495050 | − | 0.868864i | \(-0.335150\pi\) | ||||
0.495050 | + | 0.868864i | \(0.335150\pi\) | |||||||
\(812\) | 18.9282i | 0.664250i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.78461 | −0.307900 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.7846i | 1.49684i | ||||||||
\(818\) | − 66.4974i | − 2.32503i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.6410 | 1.41838 | 0.709191 | − | 0.705017i | \(-0.249061\pi\) | ||||
0.709191 | + | 0.705017i | \(0.249061\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.5885i | 1.62397i | 0.583677 | + | 0.811986i | \(0.301613\pi\) | ||||
−0.583677 | + | 0.811986i | \(0.698387\pi\) | |||||||
\(824\) | −17.6603 | −0.615224 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −52.3923 | −1.82296 | ||||||||
\(827\) | − 18.0000i | − 0.625921i | −0.949766 | − | 0.312961i | \(-0.898679\pi\) | ||||
0.949766 | − | 0.312961i | \(-0.101321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.3923 | 0.708254 | 0.354127 | − | 0.935197i | \(-0.384778\pi\) | ||||
0.354127 | + | 0.935197i | \(0.384778\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | − 10.3923i | − 0.360072i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.32051 | 0.184014 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.3923i | 0.566263i | ||||||||
\(839\) | 17.6603 | 0.609700 | 0.304850 | − | 0.952400i | \(-0.401394\pi\) | ||||
0.304850 | + | 0.952400i | \(0.401394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.5692 | 2.08859 | ||||||||
\(842\) | − 18.6795i | − 0.643738i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 18.7846i | − 0.645447i | ||||||||
\(848\) | 51.9615i | 1.78437i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.9282 | 0.648850 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 8.00000i | − 0.273915i | −0.990577 | − | 0.136957i | \(-0.956268\pi\) | ||||
0.990577 | − | 0.136957i | \(-0.0437323\pi\) | |||||||
\(854\) | 42.9282 | 1.46897 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.588457 | −0.0201131 | ||||||||
\(857\) | − 47.5692i | − 1.62493i | −0.583007 | − | 0.812467i | \(-0.698124\pi\) | ||||
0.583007 | − | 0.812467i | \(-0.301876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.1769 | −1.54142 | −0.770708 | − | 0.637188i | \(-0.780097\pi\) | ||||
−0.770708 | + | 0.637188i | \(0.780097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.8038i | 1.15136i | ||||||||
\(863\) | 2.78461i | 0.0947892i | 0.998876 | + | 0.0473946i | \(0.0150918\pi\) | ||||
−0.998876 | + | 0.0473946i | \(0.984908\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.7513 | 0.399325 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.392305i | 0.0133157i | ||||||||
\(869\) | −15.7128 | −0.533021 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.3923 | −0.487665 | ||||||||
\(872\) | 3.46410i | 0.117309i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34.3923 | −1.16334 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.00000i | 0.0675352i | 0.999430 | + | 0.0337676i | \(0.0107506\pi\) | ||||
−0.999430 | + | 0.0337676i | \(0.989249\pi\) | |||||||
\(878\) | 55.4256i | 1.87052i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.6795 | 0.427183 | 0.213591 | − | 0.976923i | \(-0.431484\pi\) | ||||
0.213591 | + | 0.976923i | \(0.431484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 34.1962i | − 1.15079i | −0.817875 | − | 0.575396i | \(-0.804848\pi\) | ||||
0.817875 | − | 0.575396i | \(-0.195152\pi\) | |||||||
\(884\) | 3.46410 | 0.116510 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 60.5885 | 2.03551 | ||||||||
\(887\) | − 17.9090i | − 0.601324i | −0.953731 | − | 0.300662i | \(-0.902792\pi\) | ||||
0.953731 | − | 0.300662i | \(-0.0972076\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.6077 | −0.389310 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.00000i | 0.0669650i | ||||||||
\(893\) | 25.1769i | 0.842513i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −24.2487 | −0.810093 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 47.5692i | − 1.58741i | ||||||||
\(899\) | 1.85641 | 0.0619146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | − 7.60770i | − 0.253309i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.7846 | 0.890843 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.7654i | 1.32039i | 0.751095 | + | 0.660194i | \(0.229526\pi\) | ||||
−0.751095 | + | 0.660194i | \(0.770474\pi\) | |||||||
\(908\) | 3.46410i | 0.114960i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.0000 | 1.19273 | 0.596367 | − | 0.802712i | \(-0.296610\pi\) | ||||
0.596367 | + | 0.802712i | \(0.296610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 7.60770i | − 0.251778i | ||||||||
\(914\) | −53.3205 | −1.76369 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.3923 | −0.475535 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.1769 | 1.75414 | 0.877072 | − | 0.480358i | \(-0.159493\pi\) | ||||
0.877072 | + | 0.480358i | \(0.159493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.00000i | 0.197599i | ||||||||
\(923\) | 1.26795i | 0.0417351i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.8564 | −1.04687 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 49.1769i | − 1.61431i | ||||||||
\(929\) | 51.4641 | 1.68848 | 0.844241 | − | 0.535963i | \(-0.180052\pi\) | ||||
0.844241 | + | 0.535963i | \(0.180052\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.5885 | −0.412570 | ||||||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −66.1577 | −2.16475 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 6.78461i | − 0.221644i | −0.993840 | − | 0.110822i | \(-0.964652\pi\) | ||||
0.993840 | − | 0.110822i | \(-0.0353483\pi\) | |||||||
\(938\) | − 49.8564i | − 1.62787i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.1769 | 1.01634 | 0.508169 | − | 0.861257i | \(-0.330322\pi\) | ||||
0.508169 | + | 0.861257i | \(0.330322\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.3923i | 0.533807i | ||||||||
\(944\) | 75.6218 | 2.46128 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.3923 | −0.728037 | ||||||||
\(947\) | 28.6410i | 0.930708i | 0.885125 | + | 0.465354i | \(0.154073\pi\) | ||||
−0.885125 | + | 0.465354i | \(0.845927\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 12.0000i | − 0.388922i | ||||||||
\(953\) | − 12.9282i | − 0.418786i | −0.977832 | − | 0.209393i | \(-0.932851\pi\) | ||||
0.977832 | − | 0.209393i | \(-0.0671487\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.80385 | 0.123025 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 31.7654i | − 1.02629i | ||||||||
\(959\) | −25.8564 | −0.834947 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9615 | −0.998759 | ||||||||
\(962\) | 6.92820i | 0.223374i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.3923 | −0.592376 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 29.6077i | − 0.952119i | −0.879413 | − | 0.476060i | \(-0.842065\pi\) | ||||
0.879413 | − | 0.476060i | \(-0.157935\pi\) | |||||||
\(968\) | 16.2679i | 0.522872i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.07180 | −0.162762 | −0.0813809 | − | 0.996683i | \(-0.525933\pi\) | ||||
−0.0813809 | + | 0.996683i | \(0.525933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.7846i | 0.538090i | ||||||||
\(974\) | −9.71281 | −0.311219 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −61.9615 | −1.98334 | ||||||||
\(977\) | − 39.7128i | − 1.27053i | −0.772296 | − | 0.635263i | \(-0.780892\pi\) | ||||
0.772296 | − | 0.635263i | \(-0.219108\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.17691 | 0.0376144 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 16.3923i | − 0.523099i | ||||||||
\(983\) | − 13.6077i | − 0.434018i | −0.976170 | − | 0.217009i | \(-0.930370\pi\) | ||||
0.976170 | − | 0.217009i | \(-0.0696301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 56.7846 | 1.80839 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 4.19615i | − 0.133497i | ||||||||
\(989\) | 48.2487 | 1.53422 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | − 1.01924i | − 0.0323608i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.39230 | −0.139315 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.3923i | 1.72262i | 0.508078 | + | 0.861311i | \(0.330356\pi\) | ||||
−0.508078 | + | 0.861311i | \(0.669644\pi\) | |||||||
\(998\) | 22.4833i | 0.711698i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2925.2.c.v.2224.2 | 4 | ||
3.2 | odd | 2 | 325.2.b.e.274.3 | 4 | |||
5.2 | odd | 4 | 2925.2.a.z.1.2 | 2 | |||
5.3 | odd | 4 | 585.2.a.k.1.1 | 2 | |||
5.4 | even | 2 | inner | 2925.2.c.v.2224.3 | 4 | ||
15.2 | even | 4 | 325.2.a.g.1.1 | 2 | |||
15.8 | even | 4 | 65.2.a.c.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 325.2.b.e.274.2 | 4 | |||
20.3 | even | 4 | 9360.2.a.cm.1.2 | 2 | |||
60.23 | odd | 4 | 1040.2.a.h.1.2 | 2 | |||
60.47 | odd | 4 | 5200.2.a.ca.1.1 | 2 | |||
65.38 | odd | 4 | 7605.2.a.be.1.2 | 2 | |||
105.83 | odd | 4 | 3185.2.a.k.1.2 | 2 | |||
120.53 | even | 4 | 4160.2.a.y.1.2 | 2 | |||
120.83 | odd | 4 | 4160.2.a.bj.1.1 | 2 | |||
165.98 | odd | 4 | 7865.2.a.h.1.1 | 2 | |||
195.8 | odd | 4 | 845.2.c.e.506.3 | 4 | |||
195.23 | even | 12 | 845.2.e.f.191.2 | 4 | |||
195.38 | even | 4 | 845.2.a.d.1.1 | 2 | |||
195.68 | even | 12 | 845.2.e.e.191.1 | 4 | |||
195.77 | even | 4 | 4225.2.a.w.1.2 | 2 | |||
195.83 | odd | 4 | 845.2.c.e.506.1 | 4 | |||
195.98 | odd | 12 | 845.2.m.c.361.2 | 4 | |||
195.113 | even | 12 | 845.2.e.e.146.1 | 4 | |||
195.128 | odd | 12 | 845.2.m.a.316.2 | 4 | |||
195.158 | odd | 12 | 845.2.m.c.316.2 | 4 | |||
195.173 | even | 12 | 845.2.e.f.146.2 | 4 | |||
195.188 | odd | 12 | 845.2.m.a.361.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.c.1.2 | ✓ | 2 | 15.8 | even | 4 | ||
325.2.a.g.1.1 | 2 | 15.2 | even | 4 | |||
325.2.b.e.274.2 | 4 | 15.14 | odd | 2 | |||
325.2.b.e.274.3 | 4 | 3.2 | odd | 2 | |||
585.2.a.k.1.1 | 2 | 5.3 | odd | 4 | |||
845.2.a.d.1.1 | 2 | 195.38 | even | 4 | |||
845.2.c.e.506.1 | 4 | 195.83 | odd | 4 | |||
845.2.c.e.506.3 | 4 | 195.8 | odd | 4 | |||
845.2.e.e.146.1 | 4 | 195.113 | even | 12 | |||
845.2.e.e.191.1 | 4 | 195.68 | even | 12 | |||
845.2.e.f.146.2 | 4 | 195.173 | even | 12 | |||
845.2.e.f.191.2 | 4 | 195.23 | even | 12 | |||
845.2.m.a.316.2 | 4 | 195.128 | odd | 12 | |||
845.2.m.a.361.2 | 4 | 195.188 | odd | 12 | |||
845.2.m.c.316.2 | 4 | 195.158 | odd | 12 | |||
845.2.m.c.361.2 | 4 | 195.98 | odd | 12 | |||
1040.2.a.h.1.2 | 2 | 60.23 | odd | 4 | |||
2925.2.a.z.1.2 | 2 | 5.2 | odd | 4 | |||
2925.2.c.v.2224.2 | 4 | 1.1 | even | 1 | trivial | ||
2925.2.c.v.2224.3 | 4 | 5.4 | even | 2 | inner | ||
3185.2.a.k.1.2 | 2 | 105.83 | odd | 4 | |||
4160.2.a.y.1.2 | 2 | 120.53 | even | 4 | |||
4160.2.a.bj.1.1 | 2 | 120.83 | odd | 4 | |||
4225.2.a.w.1.2 | 2 | 195.77 | even | 4 | |||
5200.2.a.ca.1.1 | 2 | 60.47 | odd | 4 | |||
7605.2.a.be.1.2 | 2 | 65.38 | odd | 4 | |||
7865.2.a.h.1.1 | 2 | 165.98 | odd | 4 | |||
9360.2.a.cm.1.2 | 2 | 20.3 | even | 4 |