Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(274,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("325.274");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.b (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: | \(2.59513806569\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | 274.3 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.274 |
Dual form | 325.2.b.e.274.2 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | \(0.209785\pi\) | ||||
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | 0.732051i | 0.422650i | 0.977416 | + | 0.211325i | \(0.0677778\pi\) | ||||
−0.977416 | + | 0.211325i | \(0.932222\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.26795 | −0.517638 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | 2.46410 | 0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.26795 | −0.382301 | −0.191151 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191151 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(12\) | − 0.732051i | − 0.211325i | ||||||||
\(13\) | − 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 | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 4.26795i | 1.00597i | ||||||||
\(19\) | −4.19615 | −0.962663 | −0.481332 | − | 0.876539i | \(-0.659847\pi\) | ||||
−0.481332 | + | 0.876539i | \(0.659847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.46410 | −0.319493 | ||||||||
\(22\) | − 2.19615i | − 0.468221i | ||||||||
\(23\) | − 4.73205i | − 0.986701i | −0.869831 | − | 0.493350i | \(-0.835772\pi\) | ||||
0.869831 | − | 0.493350i | \(-0.164228\pi\) | |||||||
\(24\) | −1.26795 | −0.258819 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.73205 | 0.339683 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | − 2.00000i | − 0.377964i | ||||||||
\(29\) | 9.46410 | 1.75744 | 0.878720 | − | 0.477338i | \(-0.158398\pi\) | ||||
0.878720 | + | 0.477338i | \(0.158398\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | − 0.928203i | − 0.161579i | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.46410 | −0.410684 | ||||||||
\(37\) | − 4.00000i | − 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | − 7.26795i | − 1.17902i | ||||||||
\(39\) | 0.732051 | 0.117222 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.46410 | −0.541002 | −0.270501 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270501 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(42\) | − 2.53590i | − 0.391298i | ||||||||
\(43\) | − 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 | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | − 3.66025i | − 0.528312i | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.53590 | −0.355097 | ||||||||
\(52\) | 1.00000i | 0.138675i | ||||||||
\(53\) | 10.3923i | 1.42749i | 0.700404 | + | 0.713746i | \(0.253003\pi\) | ||||
−0.700404 | + | 0.713746i | \(0.746997\pi\) | |||||||
\(54\) | −6.92820 | −0.942809 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.46410 | −0.462910 | ||||||||
\(57\) | − 3.07180i | − 0.406869i | ||||||||
\(58\) | 16.3923i | 2.15242i | ||||||||
\(59\) | 15.1244 | 1.96902 | 0.984512 | − | 0.175319i | \(-0.0560957\pi\) | ||||
0.984512 | + | 0.175319i | \(0.0560957\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 4.92820i | 0.620895i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.60770 | 0.197894 | ||||||||
\(67\) | − 14.3923i | − 1.75830i | −0.476545 | − | 0.879150i | \(-0.658111\pi\) | ||||
0.476545 | − | 0.879150i | \(-0.341889\pi\) | |||||||
\(68\) | − 3.46410i | − 0.420084i | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.26795 | 0.150478 | 0.0752389 | − | 0.997166i | \(-0.476028\pi\) | ||||
0.0752389 | + | 0.997166i | \(0.476028\pi\) | |||||||
\(72\) | 4.26795i | 0.502983i | ||||||||
\(73\) | 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 | ||||||||
\(78\) | 1.26795i | 0.143567i | ||||||||
\(79\) | −12.3923 | −1.39424 | −0.697122 | − | 0.716953i | \(-0.745536\pi\) | ||||
−0.697122 | + | 0.716953i | \(0.745536\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | − 6.00000i | − 0.662589i | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 1.46410 | 0.159747 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 17.6603 | 1.90435 | ||||||||
\(87\) | 6.92820i | 0.742781i | ||||||||
\(88\) | − 2.19615i | − 0.234111i | ||||||||
\(89\) | −0.928203 | −0.0983893 | −0.0491947 | − | 0.998789i | \(-0.515665\pi\) | ||||
−0.0491947 | + | 0.998789i | \(0.515665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 4.73205i | 0.493350i | ||||||||
\(93\) | − 0.143594i | − 0.0148900i | ||||||||
\(94\) | −10.3923 | −1.07188 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.80385 | 0.388229 | ||||||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | 5.19615i | 0.524891i | ||||||||
\(99\) | −3.12436 | −0.314010 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9282 | 1.28640 | 0.643202 | − | 0.765696i | \(-0.277605\pi\) | ||||
0.643202 | + | 0.765696i | \(0.277605\pi\) | |||||||
\(102\) | − 4.39230i | − 0.434903i | ||||||||
\(103\) | − 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 | \(0.00522760\pi\) | ||||
−0.999865 | + | 0.0164222i | \(0.994772\pi\) | |||||||
\(108\) | − 4.00000i | − 0.384900i | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.92820 | 0.277933 | ||||||||
\(112\) | − 10.0000i | − 0.944911i | ||||||||
\(113\) | − 15.4641i | − 1.45474i | −0.686245 | − | 0.727370i | \(-0.740742\pi\) | ||||
0.686245 | − | 0.727370i | \(-0.259258\pi\) | |||||||
\(114\) | 5.32051 | 0.498311 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.46410 | −0.878720 | ||||||||
\(117\) | − 2.46410i | − 0.227806i | ||||||||
\(118\) | 26.1962i | 2.41155i | ||||||||
\(119\) | −6.92820 | −0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 21.4641i | 1.94327i | ||||||||
\(123\) | − 2.53590i | − 0.228654i | ||||||||
\(124\) | 0.196152 | 0.0176150 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.53590 | −0.760438 | ||||||||
\(127\) | 5.80385i | 0.515008i | 0.966277 | + | 0.257504i | \(0.0829001\pi\) | ||||
−0.966277 | + | 0.257504i | \(0.917100\pi\) | |||||||
\(128\) | − 12.1244i | − 1.07165i | ||||||||
\(129\) | 7.46410 | 0.657178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0.928203i | 0.0807897i | ||||||||
\(133\) | − 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 | \(-0.813763\pi\) | ||||
0.833668 | − | 0.552265i | \(-0.186237\pi\) | |||||||
\(138\) | 6.00000i | 0.510754i | ||||||||
\(139\) | 8.39230 | 0.711826 | 0.355913 | − | 0.934519i | \(-0.384170\pi\) | ||||
0.355913 | + | 0.934519i | \(0.384170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.39230 | −0.369899 | ||||||||
\(142\) | 2.19615i | 0.184297i | ||||||||
\(143\) | 1.26795i | 0.106031i | ||||||||
\(144\) | −12.3205 | −1.02671 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.92820 | −0.573382 | ||||||||
\(147\) | 2.19615i | 0.181136i | ||||||||
\(148\) | 4.00000i | 0.328798i | ||||||||
\(149\) | −19.8564 | −1.62670 | −0.813350 | − | 0.581775i | \(-0.802359\pi\) | ||||
−0.813350 | + | 0.581775i | \(0.802359\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 8.53590i | 0.690086i | ||||||||
\(154\) | 4.39230 | 0.353942 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.732051 | −0.0586110 | ||||||||
\(157\) | − 10.0000i | − 0.798087i | −0.916932 | − | 0.399043i | \(-0.869342\pi\) | ||||
0.916932 | − | 0.399043i | \(-0.130658\pi\) | |||||||
\(158\) | − 21.4641i | − 1.70759i | ||||||||
\(159\) | −7.60770 | −0.603329 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.46410 | 0.745876 | ||||||||
\(162\) | 7.73205i | 0.607487i | ||||||||
\(163\) | − 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 | \(0.166743\pi\) | ||||
−0.865906 | + | 0.500207i | \(0.833257\pi\) | |||||||
\(168\) | − 2.53590i | − 0.195649i | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.3397 | −0.790700 | ||||||||
\(172\) | 10.1962i | 0.777449i | ||||||||
\(173\) | − 15.4641i | − 1.17571i | −0.808965 | − | 0.587857i | \(-0.799972\pi\) | ||||
0.808965 | − | 0.587857i | \(-0.200028\pi\) | |||||||
\(174\) | −12.0000 | −0.909718 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.33975 | 0.477876 | ||||||||
\(177\) | 11.0718i | 0.832207i | ||||||||
\(178\) | − 1.60770i | − 0.120502i | ||||||||
\(179\) | 5.07180 | 0.379084 | 0.189542 | − | 0.981873i | \(-0.439300\pi\) | ||||
0.189542 | + | 0.981873i | \(0.439300\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 9.07180i | 0.670607i | ||||||||
\(184\) | 8.19615 | 0.604228 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.248711 | 0.0182364 | ||||||||
\(187\) | − 4.39230i | − 0.321197i | ||||||||
\(188\) | − 6.00000i | − 0.437595i | ||||||||
\(189\) | −8.00000 | −0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.9282 | −1.36960 | −0.684798 | − | 0.728733i | \(-0.740110\pi\) | ||||
−0.684798 | + | 0.728733i | \(0.740110\pi\) | |||||||
\(192\) | − 0.732051i | − 0.0528312i | ||||||||
\(193\) | 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 | \(0.0105271\pi\) | ||||
−0.999453 | + | 0.0330659i | \(0.989473\pi\) | |||||||
\(198\) | − 5.41154i | − 0.384582i | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5359 | 0.743145 | ||||||||
\(202\) | 22.3923i | 1.57552i | ||||||||
\(203\) | 18.9282i | 1.32850i | ||||||||
\(204\) | 2.53590 | 0.177548 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.6603 | 1.23045 | ||||||||
\(207\) | − 11.6603i | − 0.810444i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0.928203i | 0.0635994i | ||||||||
\(214\) | −0.588457 | −0.0402261 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.92820 | −0.471405 | ||||||||
\(217\) | − 0.392305i | − 0.0266314i | ||||||||
\(218\) | − 3.46410i | − 0.234619i | ||||||||
\(219\) | −2.92820 | −0.197870 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.46410 | 0.233021 | ||||||||
\(222\) | 5.07180i | 0.340397i | ||||||||
\(223\) | − 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 | \(0.0366741\pi\) | ||||
−0.993370 | + | 0.114960i | \(0.963326\pi\) | |||||||
\(228\) | 3.07180i | 0.203435i | ||||||||
\(229\) | 14.3923 | 0.951070 | 0.475535 | − | 0.879697i | \(-0.342254\pi\) | ||||
0.475535 | + | 0.879697i | \(0.342254\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.85641 | 0.122143 | ||||||||
\(232\) | 16.3923i | 1.07621i | ||||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 4.26795 | 0.279005 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.1244 | −0.984512 | ||||||||
\(237\) | − 9.07180i | − 0.589277i | ||||||||
\(238\) | − 12.0000i | − 0.777844i | ||||||||
\(239\) | 3.80385 | 0.246050 | 0.123025 | − | 0.992404i | \(-0.460740\pi\) | ||||
0.123025 | + | 0.992404i | \(0.460740\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 15.2679i | 0.979439i | ||||||||
\(244\) | −12.3923 | −0.793336 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.39230 | 0.280043 | ||||||||
\(247\) | 4.19615i | 0.266995i | ||||||||
\(248\) | − 0.339746i | − 0.0215739i | ||||||||
\(249\) | −4.39230 | −0.278351 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.5359 | −0.917498 | −0.458749 | − | 0.888566i | \(-0.651702\pi\) | ||||
−0.458749 | + | 0.888566i | \(0.651702\pi\) | |||||||
\(252\) | − 4.92820i | − 0.310448i | ||||||||
\(253\) | 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 | \(-0.921201\pi\) | ||||
0.969514 | − | 0.245035i | \(-0.0787993\pi\) | |||||||
\(258\) | 12.9282i | 0.804875i | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.3205 | 1.44350 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 4.73205i | − 0.291791i | −0.989300 | − | 0.145895i | \(-0.953394\pi\) | ||||
0.989300 | − | 0.145895i | \(-0.0466063\pi\) | |||||||
\(264\) | 1.60770 | 0.0989468 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.5359 | 0.891253 | ||||||||
\(267\) | − 0.679492i | − 0.0415842i | ||||||||
\(268\) | 14.3923i | 0.879150i | ||||||||
\(269\) | −7.85641 | −0.479014 | −0.239507 | − | 0.970895i | \(-0.576986\pi\) | ||||
−0.239507 | + | 0.970895i | \(0.576986\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 1.46410i | 0.0886115i | ||||||||
\(274\) | 22.3923 | 1.35277 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.46410 | −0.208514 | ||||||||
\(277\) | − 5.60770i | − 0.336934i | −0.985707 | − | 0.168467i | \(-0.946118\pi\) | ||||
0.985707 | − | 0.168467i | \(-0.0538816\pi\) | |||||||
\(278\) | 14.5359i | 0.871805i | ||||||||
\(279\) | −0.483340 | −0.0289368 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.60770 | 0.0959071 | 0.0479535 | − | 0.998850i | \(-0.484730\pi\) | ||||
0.0479535 | + | 0.998850i | \(0.484730\pi\) | |||||||
\(282\) | − 7.60770i | − 0.453032i | ||||||||
\(283\) | − 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 | ||||||||
\(288\) | − 12.8038i | − 0.754474i | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.46410 | −0.0858272 | ||||||||
\(292\) | − 4.00000i | − 0.234082i | ||||||||
\(293\) | 18.9282i | 1.10580i | 0.833248 | + | 0.552899i | \(0.186478\pi\) | ||||
−0.833248 | + | 0.552899i | \(0.813522\pi\) | |||||||
\(294\) | −3.80385 | −0.221845 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.92820 | 0.402694 | ||||||||
\(297\) | − 5.07180i | − 0.294295i | ||||||||
\(298\) | − 34.3923i | − 1.99229i | ||||||||
\(299\) | −4.73205 | −0.273662 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.3923 | 1.17539 | ||||||||
\(302\) | − 21.1244i | − 1.21557i | ||||||||
\(303\) | 9.46410i | 0.543698i | ||||||||
\(304\) | 20.9808 | 1.20333 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −14.7846 | −0.845180 | ||||||||
\(307\) | 22.7846i | 1.30039i | 0.759769 | + | 0.650193i | \(0.225312\pi\) | ||||
−0.759769 | + | 0.650193i | \(0.774688\pi\) | |||||||
\(308\) | 2.53590i | 0.144496i | ||||||||
\(309\) | 7.46410 | 0.424618 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.39230 | 0.249065 | 0.124532 | − | 0.992216i | \(-0.460257\pi\) | ||||
0.124532 | + | 0.992216i | \(0.460257\pi\) | |||||||
\(312\) | 1.26795i | 0.0717835i | ||||||||
\(313\) | − 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 | \(0.235420\pi\) | ||||
−0.738743 | + | 0.673987i | \(0.764580\pi\) | |||||||
\(318\) | − 13.1769i | − 0.738925i | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.248711 | −0.0138817 | ||||||||
\(322\) | 16.3923i | 0.913507i | ||||||||
\(323\) | − 14.5359i | − 0.808799i | ||||||||
\(324\) | −4.46410 | −0.248006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.0718 | 0.613210 | ||||||||
\(327\) | − 1.46410i | − 0.0809650i | ||||||||
\(328\) | − 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 | ||||||||
\(333\) | − 9.85641i | − 0.540128i | ||||||||
\(334\) | −22.3923 | −1.22525 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.32051 | 0.399366 | ||||||||
\(337\) | − 5.60770i | − 0.305471i | −0.988267 | − | 0.152735i | \(-0.951192\pi\) | ||||
0.988267 | − | 0.152735i | \(-0.0488082\pi\) | |||||||
\(338\) | − 1.73205i | − 0.0942111i | ||||||||
\(339\) | 11.3205 | 0.614846 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.248711 | 0.0134685 | ||||||||
\(342\) | − 17.9090i | − 0.968406i | ||||||||
\(343\) | 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 | \(0.101326\pi\) | ||||
−0.949761 | + | 0.312978i | \(0.898674\pi\) | |||||||
\(348\) | − 6.92820i | − 0.371391i | ||||||||
\(349\) | −6.39230 | −0.342172 | −0.171086 | − | 0.985256i | \(-0.554728\pi\) | ||||
−0.171086 | + | 0.985256i | \(0.554728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 6.58846i | 0.351166i | ||||||||
\(353\) | − 27.7128i | − 1.47500i | −0.675345 | − | 0.737502i | \(-0.736005\pi\) | ||||
0.675345 | − | 0.737502i | \(-0.263995\pi\) | |||||||
\(354\) | −19.1769 | −1.01924 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.928203 | 0.0491947 | ||||||||
\(357\) | − 5.07180i | − 0.268428i | ||||||||
\(358\) | 8.78461i | 0.464281i | ||||||||
\(359\) | −8.19615 | −0.432576 | −0.216288 | − | 0.976330i | \(-0.569395\pi\) | ||||
−0.216288 | + | 0.976330i | \(0.569395\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.39230 | −0.0732792 | ||||||||
\(362\) | − 35.3205i | − 1.85640i | ||||||||
\(363\) | − 6.87564i | − 0.360878i | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −15.7128 | −0.821322 | ||||||||
\(367\) | 22.1962i | 1.15863i | 0.815104 | + | 0.579315i | \(0.196680\pi\) | ||||
−0.815104 | + | 0.579315i | \(0.803320\pi\) | |||||||
\(368\) | 23.6603i | 1.23338i | ||||||||
\(369\) | −8.53590 | −0.444361 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.7846 | −1.07908 | ||||||||
\(372\) | 0.143594i | 0.00744498i | ||||||||
\(373\) | 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 | ||||||||
\(378\) | − 13.8564i | − 0.712697i | ||||||||
\(379\) | 32.9808 | 1.69411 | 0.847054 | − | 0.531507i | \(-0.178374\pi\) | ||||
0.847054 | + | 0.531507i | \(0.178374\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.24871 | −0.217668 | ||||||||
\(382\) | − 32.7846i | − 1.67741i | ||||||||
\(383\) | 0.928203i | 0.0474290i | 0.999719 | + | 0.0237145i | \(0.00754926\pi\) | ||||
−0.999719 | + | 0.0237145i | \(0.992451\pi\) | |||||||
\(384\) | 8.87564 | 0.452933 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.3205 | −0.881591 | ||||||||
\(387\) | − 25.1244i | − 1.27714i | ||||||||
\(388\) | − 2.00000i | − 0.101535i | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.3923 | 0.828994 | ||||||||
\(392\) | 5.19615i | 0.262445i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.60770 | −0.0809945 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.12436 | 0.157005 | ||||||||
\(397\) | − 12.7846i | − 0.641641i | −0.947140 | − | 0.320821i | \(-0.896041\pi\) | ||||
0.947140 | − | 0.320821i | \(-0.103959\pi\) | |||||||
\(398\) | − 34.6410i | − 1.73640i | ||||||||
\(399\) | 6.14359 | 0.307564 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0718 | −1.15215 | −0.576075 | − | 0.817397i | \(-0.695416\pi\) | ||||
−0.576075 | + | 0.817397i | \(0.695416\pi\) | |||||||
\(402\) | 18.2487i | 0.910163i | ||||||||
\(403\) | 0.196152i | 0.00977105i | ||||||||
\(404\) | −12.9282 | −0.643202 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −32.7846 | −1.62707 | ||||||||
\(407\) | 5.07180i | 0.251400i | ||||||||
\(408\) | − 4.39230i | − 0.217451i | ||||||||
\(409\) | 38.3923 | 1.89838 | 0.949189 | − | 0.314708i | \(-0.101906\pi\) | ||||
0.949189 | + | 0.314708i | \(0.101906\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.46410 | 0.466830 | ||||||||
\(412\) | 10.1962i | 0.502328i | ||||||||
\(413\) | 30.2487i | 1.48844i | ||||||||
\(414\) | 20.1962 | 0.992587 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.19615 | −0.254762 | ||||||||
\(417\) | 6.14359i | 0.300853i | ||||||||
\(418\) | 9.21539i | 0.450739i | ||||||||
\(419\) | 9.46410 | 0.462352 | 0.231176 | − | 0.972912i | \(-0.425743\pi\) | ||||
0.231176 | + | 0.972912i | \(0.425743\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 14.7846i | 0.718852i | ||||||||
\(424\) | −18.0000 | −0.874157 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.60770 | −0.0778931 | ||||||||
\(427\) | 24.7846i | 1.19941i | ||||||||
\(428\) | − 0.339746i | − 0.0164222i | ||||||||
\(429\) | −0.928203 | −0.0448141 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.5167 | 0.940084 | 0.470042 | − | 0.882644i | \(-0.344239\pi\) | ||||
0.470042 | + | 0.882644i | \(0.344239\pi\) | |||||||
\(432\) | − 20.0000i | − 0.962250i | ||||||||
\(433\) | 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 | ||||||||
\(438\) | − 5.07180i | − 0.242340i | ||||||||
\(439\) | −32.0000 | −1.52728 | −0.763638 | − | 0.645644i | \(-0.776589\pi\) | ||||
−0.763638 | + | 0.645644i | \(0.776589\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.39230 | 0.352015 | ||||||||
\(442\) | 6.00000i | 0.285391i | ||||||||
\(443\) | − 34.9808i | − 1.66199i | −0.556283 | − | 0.830993i | \(-0.687773\pi\) | ||||
0.556283 | − | 0.830993i | \(-0.312227\pi\) | |||||||
\(444\) | −2.92820 | −0.138966 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.46410 | 0.164030 | ||||||||
\(447\) | − 14.5359i | − 0.687524i | ||||||||
\(448\) | − 2.00000i | − 0.0944911i | ||||||||
\(449\) | −27.4641 | −1.29611 | −0.648056 | − | 0.761593i | \(-0.724418\pi\) | ||||
−0.648056 | + | 0.761593i | \(0.724418\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.39230 | 0.206826 | ||||||||
\(452\) | 15.4641i | 0.727370i | ||||||||
\(453\) | − 8.92820i | − 0.419484i | ||||||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.32051 | 0.249156 | ||||||||
\(457\) | − 30.7846i | − 1.44004i | −0.693952 | − | 0.720022i | \(-0.744132\pi\) | ||||
0.693952 | − | 0.720022i | \(-0.255868\pi\) | |||||||
\(458\) | 24.9282i | 1.16482i | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.46410 | 0.161339 | 0.0806696 | − | 0.996741i | \(-0.474294\pi\) | ||||
0.0806696 | + | 0.996741i | \(0.474294\pi\) | |||||||
\(462\) | 3.21539i | 0.149593i | ||||||||
\(463\) | − 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 | \(0.344992\pi\) | ||||
−0.467953 | + | 0.883754i | \(0.655008\pi\) | |||||||
\(468\) | 2.46410i | 0.113903i | ||||||||
\(469\) | 28.7846 | 1.32915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.32051 | 0.337311 | ||||||||
\(472\) | 26.1962i | 1.20578i | ||||||||
\(473\) | 12.9282i | 0.594439i | ||||||||
\(474\) | 15.7128 | 0.721713 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.92820 | 0.317554 | ||||||||
\(477\) | 25.6077i | 1.17250i | ||||||||
\(478\) | 6.58846i | 0.301349i | ||||||||
\(479\) | −18.3397 | −0.837964 | −0.418982 | − | 0.907994i | \(-0.637613\pi\) | ||||
−0.418982 | + | 0.907994i | \(0.637613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 31.8564i | 1.45102i | ||||||||
\(483\) | 6.92820i | 0.315244i | ||||||||
\(484\) | 9.39230 | 0.426923 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −26.4449 | −1.19956 | ||||||||
\(487\) | − 5.60770i | − 0.254109i | −0.991896 | − | 0.127054i | \(-0.959448\pi\) | ||||
0.991896 | − | 0.127054i | \(-0.0405523\pi\) | |||||||
\(488\) | 21.4641i | 0.971634i | ||||||||
\(489\) | 4.67949 | 0.211614 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.46410 | −0.427109 | −0.213554 | − | 0.976931i | \(-0.568504\pi\) | ||||
−0.213554 | + | 0.976931i | \(0.568504\pi\) | |||||||
\(492\) | 2.53590i | 0.114327i | ||||||||
\(493\) | 32.7846i | 1.47654i | ||||||||
\(494\) | −7.26795 | −0.327000 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.980762 | 0.0440375 | ||||||||
\(497\) | 2.53590i | 0.113751i | ||||||||
\(498\) | − 7.60770i | − 0.340909i | ||||||||
\(499\) | −12.9808 | −0.581099 | −0.290549 | − | 0.956860i | \(-0.593838\pi\) | ||||
−0.290549 | + | 0.956860i | \(0.593838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.46410 | −0.422825 | ||||||||
\(502\) | − 25.1769i | − 1.12370i | ||||||||
\(503\) | 25.5167i | 1.13773i | 0.822430 | + | 0.568866i | \(0.192618\pi\) | ||||
−0.822430 | + | 0.568866i | \(0.807382\pi\) | |||||||
\(504\) | −8.53590 | −0.380219 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.3923 | −0.461994 | ||||||||
\(507\) | − 0.732051i | − 0.0325115i | ||||||||
\(508\) | − 5.80385i | − 0.257504i | ||||||||
\(509\) | −32.5359 | −1.44213 | −0.721064 | − | 0.692868i | \(-0.756347\pi\) | ||||
−0.721064 | + | 0.692868i | \(0.756347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | − 16.7846i | − 0.741059i | ||||||||
\(514\) | 13.6077 | 0.600210 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.46410 | −0.328589 | ||||||||
\(517\) | − 7.60770i | − 0.334586i | ||||||||
\(518\) | 13.8564i | 0.608816i | ||||||||
\(519\) | 11.3205 | 0.496915 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.60770 | −0.333299 | −0.166650 | − | 0.986016i | \(-0.553295\pi\) | ||||
−0.166650 | + | 0.986016i | \(0.553295\pi\) | |||||||
\(522\) | 40.3923i | 1.76792i | ||||||||
\(523\) | 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 | ||||||||
\(528\) | 4.64102i | 0.201974i | ||||||||
\(529\) | 0.607695 | 0.0264215 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 37.2679 | 1.61729 | ||||||||
\(532\) | 8.39230i | 0.363853i | ||||||||
\(533\) | 3.46410i | 0.150047i | ||||||||
\(534\) | 1.17691 | 0.0509301 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 24.9282 | 1.07673 | ||||||||
\(537\) | 3.71281i | 0.160220i | ||||||||
\(538\) | − 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 | ||||||||
\(543\) | − 14.9282i | − 0.640631i | ||||||||
\(544\) | 18.0000 | 0.771744 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.53590 | −0.108526 | ||||||||
\(547\) | − 1.80385i | − 0.0771270i | −0.999256 | − | 0.0385635i | \(-0.987722\pi\) | ||||
0.999256 | − | 0.0385635i | \(-0.0122782\pi\) | |||||||
\(548\) | 12.9282i | 0.552265i | ||||||||
\(549\) | 30.5359 | 1.30324 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.7128 | −1.69182 | ||||||||
\(552\) | 6.00000i | 0.255377i | ||||||||
\(553\) | − 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 | \(-0.815471\pi\) | ||||
0.836619 | − | 0.547786i | \(-0.184529\pi\) | |||||||
\(558\) | − 0.837169i | − 0.0354402i | ||||||||
\(559\) | −10.1962 | −0.431251 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.21539 | 0.135754 | ||||||||
\(562\) | 2.78461i | 0.117462i | ||||||||
\(563\) | − 16.0526i | − 0.676535i | −0.941050 | − | 0.338267i | \(-0.890159\pi\) | ||||
0.941050 | − | 0.338267i | \(-0.109841\pi\) | |||||||
\(564\) | 4.39230 | 0.184949 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.44486 | 0.102765 | ||||||||
\(567\) | 8.92820i | 0.374949i | ||||||||
\(568\) | 2.19615i | 0.0921485i | ||||||||
\(569\) | 9.46410 | 0.396756 | 0.198378 | − | 0.980126i | \(-0.436433\pi\) | ||||
0.198378 | + | 0.980126i | \(0.436433\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | − 13.8564i | − 0.578860i | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.46410 | −0.102671 | ||||||||
\(577\) | − 4.00000i | − 0.166522i | −0.996528 | − | 0.0832611i | \(-0.973466\pi\) | ||||
0.996528 | − | 0.0832611i | \(-0.0265335\pi\) | |||||||
\(578\) | 8.66025i | 0.360219i | ||||||||
\(579\) | −7.32051 | −0.304230 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | − 2.53590i | − 0.105116i | ||||||||
\(583\) | − 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 | \(-0.896607\pi\) | ||||
0.947709 | − | 0.319136i | \(-0.103393\pi\) | |||||||
\(588\) | − 2.19615i | − 0.0905678i | ||||||||
\(589\) | 0.823085 | 0.0339146 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.679492 | −0.0279506 | ||||||||
\(592\) | 20.0000i | 0.821995i | ||||||||
\(593\) | 14.7846i | 0.607131i | 0.952811 | + | 0.303566i | \(0.0981771\pi\) | ||||
−0.952811 | + | 0.303566i | \(0.901823\pi\) | |||||||
\(594\) | 8.78461 | 0.360437 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.8564 | 0.813350 | ||||||||
\(597\) | − 14.6410i | − 0.599217i | ||||||||
\(598\) | − 8.19615i | − 0.335166i | ||||||||
\(599\) | 28.3923 | 1.16008 | 0.580039 | − | 0.814589i | \(-0.303037\pi\) | ||||
0.580039 | + | 0.814589i | \(0.303037\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | − 35.4641i | − 1.44421i | ||||||||
\(604\) | 12.1962 | 0.496254 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.3923 | −0.665892 | ||||||||
\(607\) | − 26.9808i | − 1.09512i | −0.836768 | − | 0.547558i | \(-0.815558\pi\) | ||||
0.836768 | − | 0.547558i | \(-0.184442\pi\) | |||||||
\(608\) | 21.8038i | 0.884263i | ||||||||
\(609\) | −13.8564 | −0.561490 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | − 8.53590i | − 0.345043i | ||||||||
\(613\) | − 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 | \(-0.856019\pi\) | ||||
0.899431 | − | 0.437062i | \(-0.143981\pi\) | |||||||
\(618\) | 12.9282i | 0.520049i | ||||||||
\(619\) | 44.9808 | 1.80793 | 0.903965 | − | 0.427607i | \(-0.140643\pi\) | ||||
0.903965 | + | 0.427607i | \(0.140643\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9282 | 0.759563 | ||||||||
\(622\) | 7.60770i | 0.305041i | ||||||||
\(623\) | − 1.85641i | − 0.0743754i | ||||||||
\(624\) | −3.66025 | −0.146527 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.0718 | 0.442518 | ||||||||
\(627\) | 3.89488i | 0.155547i | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 5.85641i | 0.232771i | ||||||||
\(634\) | −41.5692 | −1.65092 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.60770 | 0.301665 | ||||||||
\(637\) | − 3.00000i | − 0.118864i | ||||||||
\(638\) | − 20.7846i | − 0.822871i | ||||||||
\(639\) | 3.12436 | 0.123598 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.928203 | −0.0366618 | −0.0183309 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183309 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(642\) | − 0.430781i | − 0.0170016i | ||||||||
\(643\) | − 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 | \(-0.897812\pi\) | ||||
0.948910 | − | 0.315546i | \(-0.102188\pi\) | |||||||
\(648\) | 7.73205i | 0.303744i | ||||||||
\(649\) | −19.1769 | −0.752760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.287187 | 0.0112557 | ||||||||
\(652\) | 6.39230i | 0.250342i | ||||||||
\(653\) | 19.8564i | 0.777041i | 0.921440 | + | 0.388521i | \(0.127014\pi\) | ||||
−0.921440 | + | 0.388521i | \(0.872986\pi\) | |||||||
\(654\) | 2.53590 | 0.0991615 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17.3205 | 0.676252 | ||||||||
\(657\) | 9.85641i | 0.384535i | ||||||||
\(658\) | − 20.7846i | − 0.810268i | ||||||||
\(659\) | 14.5359 | 0.566238 | 0.283119 | − | 0.959085i | \(-0.408631\pi\) | ||||
0.283119 | + | 0.959085i | \(0.408631\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 2.53590i | 0.0984861i | ||||||||
\(664\) | −10.3923 | −0.403300 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.0718 | 0.661519 | ||||||||
\(667\) | − 44.7846i | − 1.73407i | ||||||||
\(668\) | − 12.9282i | − 0.500207i | ||||||||
\(669\) | 1.46410 | 0.0566054 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.7128 | −0.606586 | ||||||||
\(672\) | 7.60770i | 0.293473i | ||||||||
\(673\) | − 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 | \(-0.936002\pi\) | ||||
0.979856 | − | 0.199704i | \(-0.0639982\pi\) | |||||||
\(678\) | 19.6077i | 0.753029i | ||||||||
\(679\) | −4.00000 | −0.153506 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.53590 | −0.0971758 | ||||||||
\(682\) | 0.430781i | 0.0164954i | ||||||||
\(683\) | − 39.4641i | − 1.51005i | −0.655695 | − | 0.755026i | \(-0.727624\pi\) | ||||
0.655695 | − | 0.755026i | \(-0.272376\pi\) | |||||||
\(684\) | 10.3397 | 0.395350 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −34.6410 | −1.32260 | ||||||||
\(687\) | 10.5359i | 0.401970i | ||||||||
\(688\) | 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 | ||||||||
\(693\) | − 6.24871i | − 0.237369i | ||||||||
\(694\) | −20.1962 | −0.766635 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.0000 | −0.454859 | ||||||||
\(697\) | − 12.0000i | − 0.454532i | ||||||||
\(698\) | − 11.0718i | − 0.419074i | ||||||||
\(699\) | −4.39230 | −0.166132 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 6.92820i | 0.261488i | ||||||||
\(703\) | 16.7846i | 0.633044i | ||||||||
\(704\) | 1.26795 | 0.0477876 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 48.0000 | 1.80650 | ||||||||
\(707\) | 25.8564i | 0.972430i | ||||||||
\(708\) | − 11.0718i | − 0.416104i | ||||||||
\(709\) | −9.60770 | −0.360825 | −0.180412 | − | 0.983591i | \(-0.557743\pi\) | ||||
−0.180412 | + | 0.983591i | \(0.557743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.5359 | −1.14519 | ||||||||
\(712\) | − 1.60770i | − 0.0602509i | ||||||||
\(713\) | 0.928203i | 0.0347615i | ||||||||
\(714\) | 8.78461 | 0.328756 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.07180 | −0.189542 | ||||||||
\(717\) | 2.78461i | 0.103993i | ||||||||
\(718\) | − 14.1962i | − 0.529796i | ||||||||
\(719\) | −1.85641 | −0.0692323 | −0.0346161 | − | 0.999401i | \(-0.511021\pi\) | ||||
−0.0346161 | + | 0.999401i | \(0.511021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.3923 | 0.759449 | ||||||||
\(722\) | − 2.41154i | − 0.0897483i | ||||||||
\(723\) | 13.4641i | 0.500735i | ||||||||
\(724\) | 20.3923 | 0.757874 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.9090 | 0.441983 | ||||||||
\(727\) | 13.4115i | 0.497407i | 0.968580 | + | 0.248703i | \(0.0800044\pi\) | ||||
−0.968580 | + | 0.248703i | \(0.919996\pi\) | |||||||
\(728\) | 3.46410i | 0.128388i | ||||||||
\(729\) | 2.21539 | 0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.3205 | 1.30638 | ||||||||
\(732\) | − 9.07180i | − 0.335303i | ||||||||
\(733\) | − 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 | ||||||||
\(738\) | − 14.7846i | − 0.544229i | ||||||||
\(739\) | 7.80385 | 0.287069 | 0.143535 | − | 0.989645i | \(-0.454153\pi\) | ||||
0.143535 | + | 0.989645i | \(0.454153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.07180 | −0.112845 | ||||||||
\(742\) | − 36.0000i | − 1.32160i | ||||||||
\(743\) | 43.8564i | 1.60894i | 0.593996 | + | 0.804468i | \(0.297549\pi\) | ||||
−0.593996 | + | 0.804468i | \(0.702451\pi\) | |||||||
\(744\) | 0.248711 | 0.00911820 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.3205 | −0.634149 | ||||||||
\(747\) | 14.7846i | 0.540941i | ||||||||
\(748\) | 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 | ||||||||
\(753\) | − 10.6410i | − 0.387780i | ||||||||
\(754\) | 16.3923 | 0.596973 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.00000 | 0.290957 | ||||||||
\(757\) | 18.3923i | 0.668480i | 0.942488 | + | 0.334240i | \(0.108480\pi\) | ||||
−0.942488 | + | 0.334240i | \(0.891520\pi\) | |||||||
\(758\) | 57.1244i | 2.07485i | ||||||||
\(759\) | −4.39230 | −0.159431 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.85641 | 0.284795 | 0.142397 | − | 0.989810i | \(-0.454519\pi\) | ||||
0.142397 | + | 0.989810i | \(0.454519\pi\) | |||||||
\(762\) | − 7.35898i | − 0.266588i | ||||||||
\(763\) | − 4.00000i | − 0.144810i | ||||||||
\(764\) | 18.9282 | 0.684798 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.60770 | −0.0580884 | ||||||||
\(767\) | − 15.1244i | − 0.546109i | ||||||||
\(768\) | 13.9090i | 0.501897i | ||||||||
\(769\) | 6.78461 | 0.244659 | 0.122330 | − | 0.992490i | \(-0.460963\pi\) | ||||
0.122330 | + | 0.992490i | \(0.460963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.75129 | 0.207128 | ||||||||
\(772\) | − 10.0000i | − 0.359908i | ||||||||
\(773\) | 6.92820i | 0.249190i | 0.992208 | + | 0.124595i | \(0.0397632\pi\) | ||||
−0.992208 | + | 0.124595i | \(0.960237\pi\) | |||||||
\(774\) | 43.5167 | 1.56417 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.46410 | −0.124354 | ||||||||
\(777\) | 5.85641i | 0.210097i | ||||||||
\(778\) | − 10.3923i | − 0.372582i | ||||||||
\(779\) | 14.5359 | 0.520803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.60770 | −0.0575279 | ||||||||
\(782\) | 28.3923i | 1.01531i | ||||||||
\(783\) | 37.8564i | 1.35288i | ||||||||
\(784\) | −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 | ||||||||
\(789\) | 3.46410 | 0.123325 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.9282 | 1.09968 | ||||||||
\(792\) | − 5.41154i | − 0.192291i | ||||||||
\(793\) | − 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 | \(0.169341\pi\) | ||||
−0.861794 | + | 0.507258i | \(0.830659\pi\) | |||||||
\(798\) | 10.6410i | 0.376688i | ||||||||
\(799\) | −20.7846 | −0.735307 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.28719 | −0.0808138 | ||||||||
\(802\) | − 39.9615i | − 1.41109i | ||||||||
\(803\) | − 5.07180i | − 0.178980i | ||||||||
\(804\) | −10.5359 | −0.371572 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.339746 | −0.0119670 | ||||||||
\(807\) | − 5.75129i | − 0.202455i | ||||||||
\(808\) | 22.3923i | 0.787759i | ||||||||
\(809\) | 9.46410 | 0.332740 | 0.166370 | − | 0.986063i | \(-0.446795\pi\) | ||||
0.166370 | + | 0.986063i | \(0.446795\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | − 15.3590i | − 0.538663i | ||||||||
\(814\) | −8.78461 | −0.307900 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.6795 | 0.443871 | ||||||||
\(817\) | 42.7846i | 1.49684i | ||||||||
\(818\) | 66.4974i | 2.32503i | ||||||||
\(819\) | 4.92820 | 0.172205 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.6410 | −1.41838 | −0.709191 | − | 0.705017i | \(-0.750939\pi\) | ||||
−0.709191 | + | 0.705017i | \(0.750939\pi\) | |||||||
\(822\) | 16.3923i | 0.571747i | ||||||||
\(823\) | 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 | \(0.101321\pi\) | ||||
−0.949766 | + | 0.312961i | \(0.898679\pi\) | |||||||
\(828\) | 11.6603i | 0.405222i | ||||||||
\(829\) | 20.3923 | 0.708254 | 0.354127 | − | 0.935197i | \(-0.384778\pi\) | ||||
0.354127 | + | 0.935197i | \(0.384778\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.10512 | 0.142405 | ||||||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | 10.3923i | 0.360072i | ||||||||
\(834\) | −10.6410 | −0.368468 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.32051 | −0.184014 | ||||||||
\(837\) | − 0.784610i | − 0.0271201i | ||||||||
\(838\) | 16.3923i | 0.566263i | ||||||||
\(839\) | −17.6603 | −0.609700 | −0.304850 | − | 0.952400i | \(-0.598606\pi\) | ||||
−0.304850 | + | 0.952400i | \(0.598606\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.5692 | 2.08859 | ||||||||
\(842\) | 18.6795i | 0.643738i | ||||||||
\(843\) | 1.17691i | 0.0405351i | ||||||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.6077 | −0.880411 | ||||||||
\(847\) | − 18.7846i | − 0.645447i | ||||||||
\(848\) | − 51.9615i | − 1.78437i | ||||||||
\(849\) | 1.03332 | 0.0354635 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.9282 | −0.648850 | ||||||||
\(852\) | − 0.928203i | − 0.0317997i | ||||||||
\(853\) | − 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 | \(0.301876\pi\) | ||||
−0.583007 | + | 0.812467i | \(0.698124\pi\) | |||||||
\(858\) | − 1.60770i | − 0.0548858i | ||||||||
\(859\) | −45.1769 | −1.54142 | −0.770708 | − | 0.637188i | \(-0.780097\pi\) | ||||
−0.770708 | + | 0.637188i | \(0.780097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.07180 | 0.172846 | ||||||||
\(862\) | 33.8038i | 1.15136i | ||||||||
\(863\) | − 2.78461i | − 0.0947892i | −0.998876 | − | 0.0473946i | \(-0.984908\pi\) | ||||
0.998876 | − | 0.0473946i | \(-0.0150918\pi\) | |||||||
\(864\) | 20.7846 | 0.707107 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.7513 | −0.399325 | ||||||||
\(867\) | 3.66025i | 0.124309i | ||||||||
\(868\) | 0.392305i | 0.0133157i | ||||||||
\(869\) | 15.7128 | 0.533021 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.3923 | −0.487665 | ||||||||
\(872\) | − 3.46410i | − 0.117309i | ||||||||
\(873\) | 4.92820i | 0.166794i | ||||||||
\(874\) | −34.3923 | −1.16334 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.92820 | 0.0989348 | ||||||||
\(877\) | 2.00000i | 0.0675352i | 0.999430 | + | 0.0337676i | \(0.0107506\pi\) | ||||
−0.999430 | + | 0.0337676i | \(0.989249\pi\) | |||||||
\(878\) | − 55.4256i | − 1.87052i | ||||||||
\(879\) | −13.8564 | −0.467365 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.6795 | −0.427183 | −0.213591 | − | 0.976923i | \(-0.568516\pi\) | ||||
−0.213591 | + | 0.976923i | \(0.568516\pi\) | |||||||
\(882\) | 12.8038i | 0.431128i | ||||||||
\(883\) | − 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 | \(0.0972076\pi\) | ||||
−0.953731 | + | 0.300662i | \(0.902792\pi\) | |||||||
\(888\) | 5.07180i | 0.170198i | ||||||||
\(889\) | −11.6077 | −0.389310 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.66025 | −0.189626 | ||||||||
\(892\) | 2.00000i | 0.0669650i | ||||||||
\(893\) | − 25.1769i | − 0.842513i | ||||||||
\(894\) | 25.1769 | 0.842042 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.2487 | 0.810093 | ||||||||
\(897\) | − 3.46410i | − 0.115663i | ||||||||
\(898\) | − 47.5692i | − 1.58741i | ||||||||
\(899\) | −1.85641 | −0.0619146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 7.60770i | 0.253309i | ||||||||
\(903\) | 14.9282i | 0.496779i | ||||||||
\(904\) | 26.7846 | 0.890843 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 15.4641 | 0.513760 | ||||||||
\(907\) | 39.7654i | 1.32039i | 0.751095 | + | 0.660194i | \(0.229526\pi\) | ||||
−0.751095 | + | 0.660194i | \(0.770474\pi\) | |||||||
\(908\) | − 3.46410i | − 0.114960i | ||||||||
\(909\) | 31.8564 | 1.05661 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 15.3590i | 0.508587i | ||||||||
\(913\) | − 7.60770i | − 0.251778i | ||||||||
\(914\) | 53.3205 | 1.76369 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.3923 | −0.475535 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − 24.0000i | − 0.792118i | ||||||||
\(919\) | 53.1769 | 1.75414 | 0.877072 | − | 0.480358i | \(-0.159493\pi\) | ||||
0.877072 | + | 0.480358i | \(0.159493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.6795 | −0.549608 | ||||||||
\(922\) | 6.00000i | 0.197599i | ||||||||
\(923\) | − 1.26795i | − 0.0417351i | ||||||||
\(924\) | −1.85641 | −0.0610713 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.8564 | 1.04687 | ||||||||
\(927\) | − 25.1244i | − 0.825192i | ||||||||
\(928\) | − 49.1769i | − 1.61431i | ||||||||
\(929\) | −51.4641 | −1.68848 | −0.844241 | − | 0.535963i | \(-0.819948\pi\) | ||||
−0.844241 | + | 0.535963i | \(0.819948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.5885 | −0.412570 | ||||||||
\(932\) | − 6.00000i | − 0.196537i | ||||||||
\(933\) | 3.21539i | 0.105267i | ||||||||
\(934\) | −66.1577 | −2.16475 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.26795 | 0.139502 | ||||||||
\(937\) | − 6.78461i | − 0.221644i | −0.993840 | − | 0.110822i | \(-0.964652\pi\) | ||||
0.993840 | − | 0.110822i | \(-0.0353483\pi\) | |||||||
\(938\) | 49.8564i | 1.62787i | ||||||||
\(939\) | 4.67949 | 0.152709 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.1769 | −1.01634 | −0.508169 | − | 0.861257i | \(-0.669678\pi\) | ||||
−0.508169 | + | 0.861257i | \(0.669678\pi\) | |||||||
\(942\) | 12.6795i | 0.413120i | ||||||||
\(943\) | 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 | \(-0.845927\pi\) | ||||
0.885125 | − | 0.465354i | \(-0.154073\pi\) | |||||||
\(948\) | 9.07180i | 0.294638i | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.5692 | −0.569721 | ||||||||
\(952\) | − 12.0000i | − 0.388922i | ||||||||
\(953\) | 12.9282i | 0.418786i | 0.977832 | + | 0.209393i | \(0.0671487\pi\) | ||||
−0.977832 | + | 0.209393i | \(0.932851\pi\) | |||||||
\(954\) | −44.3538 | −1.43601 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.80385 | −0.123025 | ||||||||
\(957\) | − 8.78461i | − 0.283966i | ||||||||
\(958\) | − 31.7654i | − 1.02629i | ||||||||
\(959\) | 25.8564 | 0.834947 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9615 | −0.998759 | ||||||||
\(962\) | − 6.92820i | − 0.223374i | ||||||||
\(963\) | 0.837169i | 0.0269774i | ||||||||
\(964\) | −18.3923 | −0.592376 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.0000 | −0.386094 | ||||||||
\(967\) | − 29.6077i | − 0.952119i | −0.879413 | − | 0.476060i | \(-0.842065\pi\) | ||||
0.879413 | − | 0.476060i | \(-0.157935\pi\) | |||||||
\(968\) | − 16.2679i | − 0.522872i | ||||||||
\(969\) | 10.6410 | 0.341839 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.07180 | 0.162762 | 0.0813809 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813809 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(972\) | − 15.2679i | − 0.489720i | ||||||||
\(973\) | 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 | \(0.219108\pi\) | ||||
−0.772296 | + | 0.635263i | \(0.780892\pi\) | |||||||
\(978\) | 8.10512i | 0.259173i | ||||||||
\(979\) | 1.17691 | 0.0376144 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.92820 | −0.157345 | ||||||||
\(982\) | − 16.3923i | − 0.523099i | ||||||||
\(983\) | 13.6077i | 0.434018i | 0.976170 | + | 0.217009i | \(0.0696301\pi\) | ||||
−0.976170 | + | 0.217009i | \(0.930370\pi\) | |||||||
\(984\) | 4.39230 | 0.140022 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −56.7846 | −1.80839 | ||||||||
\(987\) | − 8.78461i | − 0.279617i | ||||||||
\(988\) | − 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 | ||||||||
\(993\) | − 20.9282i | − 0.664136i | ||||||||
\(994\) | −4.39230 | −0.139315 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.39230 | 0.139176 | ||||||||
\(997\) | 54.3923i | 1.72262i | 0.508078 | + | 0.861311i | \(0.330356\pi\) | ||||
−0.508078 | + | 0.861311i | \(0.669644\pi\) | |||||||
\(998\) | − 22.4833i | − 0.711698i | ||||||||
\(999\) | 16.0000 | 0.506218 |
(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 | 325.2.b.e.274.3 | 4 | ||
3.2 | odd | 2 | 2925.2.c.v.2224.2 | 4 | |||
5.2 | odd | 4 | 325.2.a.g.1.1 | 2 | |||
5.3 | odd | 4 | 65.2.a.c.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 325.2.b.e.274.2 | 4 | ||
15.2 | even | 4 | 2925.2.a.z.1.2 | 2 | |||
15.8 | even | 4 | 585.2.a.k.1.1 | 2 | |||
15.14 | odd | 2 | 2925.2.c.v.2224.3 | 4 | |||
20.3 | even | 4 | 1040.2.a.h.1.2 | 2 | |||
20.7 | even | 4 | 5200.2.a.ca.1.1 | 2 | |||
35.13 | even | 4 | 3185.2.a.k.1.2 | 2 | |||
40.3 | even | 4 | 4160.2.a.bj.1.1 | 2 | |||
40.13 | odd | 4 | 4160.2.a.y.1.2 | 2 | |||
55.43 | even | 4 | 7865.2.a.h.1.1 | 2 | |||
60.23 | odd | 4 | 9360.2.a.cm.1.2 | 2 | |||
65.3 | odd | 12 | 845.2.e.e.191.1 | 4 | |||
65.8 | even | 4 | 845.2.c.e.506.3 | 4 | |||
65.12 | odd | 4 | 4225.2.a.w.1.2 | 2 | |||
65.18 | even | 4 | 845.2.c.e.506.1 | 4 | |||
65.23 | odd | 12 | 845.2.e.f.191.2 | 4 | |||
65.28 | even | 12 | 845.2.m.c.316.2 | 4 | |||
65.33 | even | 12 | 845.2.m.c.361.2 | 4 | |||
65.38 | odd | 4 | 845.2.a.d.1.1 | 2 | |||
65.43 | odd | 12 | 845.2.e.f.146.2 | 4 | |||
65.48 | odd | 12 | 845.2.e.e.146.1 | 4 | |||
65.58 | even | 12 | 845.2.m.a.361.2 | 4 | |||
65.63 | even | 12 | 845.2.m.a.316.2 | 4 | |||
195.38 | even | 4 | 7605.2.a.be.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.c.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
325.2.a.g.1.1 | 2 | 5.2 | odd | 4 | |||
325.2.b.e.274.2 | 4 | 5.4 | even | 2 | inner | ||
325.2.b.e.274.3 | 4 | 1.1 | even | 1 | trivial | ||
585.2.a.k.1.1 | 2 | 15.8 | even | 4 | |||
845.2.a.d.1.1 | 2 | 65.38 | odd | 4 | |||
845.2.c.e.506.1 | 4 | 65.18 | even | 4 | |||
845.2.c.e.506.3 | 4 | 65.8 | even | 4 | |||
845.2.e.e.146.1 | 4 | 65.48 | odd | 12 | |||
845.2.e.e.191.1 | 4 | 65.3 | odd | 12 | |||
845.2.e.f.146.2 | 4 | 65.43 | odd | 12 | |||
845.2.e.f.191.2 | 4 | 65.23 | odd | 12 | |||
845.2.m.a.316.2 | 4 | 65.63 | even | 12 | |||
845.2.m.a.361.2 | 4 | 65.58 | even | 12 | |||
845.2.m.c.316.2 | 4 | 65.28 | even | 12 | |||
845.2.m.c.361.2 | 4 | 65.33 | even | 12 | |||
1040.2.a.h.1.2 | 2 | 20.3 | even | 4 | |||
2925.2.a.z.1.2 | 2 | 15.2 | even | 4 | |||
2925.2.c.v.2224.2 | 4 | 3.2 | odd | 2 | |||
2925.2.c.v.2224.3 | 4 | 15.14 | odd | 2 | |||
3185.2.a.k.1.2 | 2 | 35.13 | even | 4 | |||
4160.2.a.y.1.2 | 2 | 40.13 | odd | 4 | |||
4160.2.a.bj.1.1 | 2 | 40.3 | even | 4 | |||
4225.2.a.w.1.2 | 2 | 65.12 | odd | 4 | |||
5200.2.a.ca.1.1 | 2 | 20.7 | even | 4 | |||
7605.2.a.be.1.2 | 2 | 195.38 | even | 4 | |||
7865.2.a.h.1.1 | 2 | 55.43 | even | 4 | |||
9360.2.a.cm.1.2 | 2 | 60.23 | odd | 4 |