Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(624,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.624");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.58140625.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 624.8 | ||
Root | \(-0.357358 + 1.86824i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.624 |
Dual form | 625.2.b.c.624.1 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.30927i | 1.63290i | 0.577414 | + | 0.816452i | \(0.304062\pi\) | ||||
−0.577414 | + | 0.816452i | \(0.695938\pi\) | |||||||
\(3\) | − 0.474903i | − 0.274185i | −0.990558 | − | 0.137093i | \(-0.956224\pi\) | ||||
0.990558 | − | 0.137093i | \(-0.0437758\pi\) | |||||||
\(4\) | −3.33275 | −1.66637 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.09668 | 0.447718 | ||||||||
\(7\) | 3.03582i | 1.14743i | 0.819055 | + | 0.573716i | \(0.194498\pi\) | ||||
−0.819055 | + | 0.573716i | \(0.805502\pi\) | |||||||
\(8\) | − 3.07768i | − 1.08813i | ||||||||
\(9\) | 2.77447 | 0.924822 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 1.58273i | 0.456895i | ||||||||
\(13\) | 1.42721i | 0.395837i | 0.980218 | + | 0.197918i | \(0.0634181\pi\) | ||||
−0.980218 | + | 0.197918i | \(0.936582\pi\) | |||||||
\(14\) | −7.01054 | −1.87364 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.441718 | 0.110430 | ||||||||
\(17\) | 1.86025i | 0.451176i | 0.974223 | + | 0.225588i | \(0.0724303\pi\) | ||||
−0.974223 | + | 0.225588i | \(0.927570\pi\) | |||||||
\(18\) | 6.40701i | 1.51015i | ||||||||
\(19\) | −0.903319 | −0.207236 | −0.103618 | − | 0.994617i | \(-0.533042\pi\) | ||||
−0.103618 | + | 0.994617i | \(0.533042\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.44172 | 0.314609 | ||||||||
\(22\) | 4.61855i | 0.984678i | ||||||||
\(23\) | 3.32932i | 0.694212i | 0.937826 | + | 0.347106i | \(0.112836\pi\) | ||||
−0.937826 | + | 0.347106i | \(0.887164\pi\) | |||||||
\(24\) | −1.46160 | −0.298348 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.29582 | −0.646364 | ||||||||
\(27\) | − 2.74231i | − 0.527758i | ||||||||
\(28\) | − 10.1176i | − 1.91205i | ||||||||
\(29\) | −3.96307 | −0.735924 | −0.367962 | − | 0.929841i | \(-0.619944\pi\) | ||||
−0.367962 | + | 0.929841i | \(0.619944\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.43997 | −1.15665 | −0.578326 | − | 0.815806i | \(-0.696294\pi\) | ||||
−0.578326 | + | 0.815806i | \(0.696294\pi\) | |||||||
\(32\) | − 5.13532i | − 0.907805i | ||||||||
\(33\) | − 0.949806i | − 0.165340i | ||||||||
\(34\) | −4.29582 | −0.736727 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.24660 | −1.54110 | ||||||||
\(37\) | 3.82022i | 0.628040i | 0.949416 | + | 0.314020i | \(0.101676\pi\) | ||||
−0.949416 | + | 0.314020i | \(0.898324\pi\) | |||||||
\(38\) | − 2.08601i | − 0.338396i | ||||||||
\(39\) | 0.677786 | 0.108533 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.83422 | −0.286457 | −0.143228 | − | 0.989690i | \(-0.545748\pi\) | ||||
−0.143228 | + | 0.989690i | \(0.545748\pi\) | |||||||
\(42\) | 3.32932i | 0.513726i | ||||||||
\(43\) | 3.59445i | 0.548149i | 0.961708 | + | 0.274074i | \(0.0883715\pi\) | ||||
−0.961708 | + | 0.274074i | \(0.911629\pi\) | |||||||
\(44\) | −6.66550 | −1.00486 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.68832 | −1.13358 | ||||||||
\(47\) | − 4.79995i | − 0.700144i | −0.936723 | − | 0.350072i | \(-0.886157\pi\) | ||||
0.936723 | − | 0.350072i | \(-0.113843\pi\) | |||||||
\(48\) | − 0.209773i | − 0.0302782i | ||||||||
\(49\) | −2.21619 | −0.316598 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.883436 | 0.123706 | ||||||||
\(52\) | − 4.75653i | − 0.659613i | ||||||||
\(53\) | 9.50473i | 1.30558i | 0.757541 | + | 0.652788i | \(0.226401\pi\) | ||||
−0.757541 | + | 0.652788i | \(0.773599\pi\) | |||||||
\(54\) | 6.33275 | 0.861778 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.34328 | 1.24855 | ||||||||
\(57\) | 0.428989i | 0.0568209i | ||||||||
\(58\) | − 9.15182i | − 1.20169i | ||||||||
\(59\) | −10.6456 | −1.38594 | −0.692971 | − | 0.720966i | \(-0.743698\pi\) | ||||
−0.692971 | + | 0.720966i | \(0.743698\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.2742 | 1.82762 | 0.913811 | − | 0.406140i | \(-0.133125\pi\) | ||||
0.913811 | + | 0.406140i | \(0.133125\pi\) | |||||||
\(62\) | − 14.8716i | − 1.88870i | ||||||||
\(63\) | 8.42278i | 1.06117i | ||||||||
\(64\) | 12.7423 | 1.59279 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.19336 | 0.269984 | ||||||||
\(67\) | − 10.6902i | − 1.30601i | −0.757352 | − | 0.653007i | \(-0.773507\pi\) | ||||
0.757352 | − | 0.653007i | \(-0.226493\pi\) | |||||||
\(68\) | − 6.19974i | − 0.751828i | ||||||||
\(69\) | 1.58111 | 0.190343 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4598 | 1.47871 | 0.739356 | − | 0.673315i | \(-0.235130\pi\) | ||||
0.739356 | + | 0.673315i | \(0.235130\pi\) | |||||||
\(72\) | − 8.53893i | − 1.00632i | ||||||||
\(73\) | − 0.267631i | − 0.0313239i | −0.999877 | − | 0.0156619i | \(-0.995014\pi\) | ||||
0.999877 | − | 0.0156619i | \(-0.00498555\pi\) | |||||||
\(74\) | −8.82193 | −1.02553 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.01054 | 0.345332 | ||||||||
\(77\) | 6.07163i | 0.691927i | ||||||||
\(78\) | 1.56519i | 0.177223i | ||||||||
\(79\) | 8.57176 | 0.964398 | 0.482199 | − | 0.876062i | \(-0.339838\pi\) | ||||
0.482199 | + | 0.876062i | \(0.339838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.02107 | 0.780119 | ||||||||
\(82\) | − 4.23572i | − 0.467757i | ||||||||
\(83\) | 12.6182i | 1.38502i | 0.721406 | + | 0.692512i | \(0.243496\pi\) | ||||
−0.721406 | + | 0.692512i | \(0.756504\pi\) | |||||||
\(84\) | −4.80489 | −0.524256 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.30058 | −0.895074 | ||||||||
\(87\) | 1.88207i | 0.201779i | ||||||||
\(88\) | − 6.15537i | − 0.656164i | ||||||||
\(89\) | 4.76796 | 0.505402 | 0.252701 | − | 0.967544i | \(-0.418681\pi\) | ||||
0.252701 | + | 0.967544i | \(0.418681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.33275 | −0.454196 | ||||||||
\(92\) | − 11.0958i | − 1.15682i | ||||||||
\(93\) | 3.05836i | 0.317137i | ||||||||
\(94\) | 11.0844 | 1.14327 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.43878 | −0.248907 | ||||||||
\(97\) | − 9.95805i | − 1.01109i | −0.862801 | − | 0.505543i | \(-0.831292\pi\) | ||||
0.862801 | − | 0.505543i | \(-0.168708\pi\) | |||||||
\(98\) | − 5.11778i | − 0.516974i | ||||||||
\(99\) | 5.54893 | 0.557689 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.34612 | 0.929974 | 0.464987 | − | 0.885318i | \(-0.346059\pi\) | ||||
0.464987 | + | 0.885318i | \(0.346059\pi\) | |||||||
\(102\) | 2.04010i | 0.202000i | ||||||||
\(103\) | − 9.08408i | − 0.895081i | −0.894264 | − | 0.447540i | \(-0.852300\pi\) | ||||
0.894264 | − | 0.447540i | \(-0.147700\pi\) | |||||||
\(104\) | 4.39250 | 0.430720 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −21.9490 | −2.13188 | ||||||||
\(107\) | 5.62871i | 0.544148i | 0.962276 | + | 0.272074i | \(0.0877096\pi\) | ||||
−0.962276 | + | 0.272074i | \(0.912290\pi\) | |||||||
\(108\) | 9.13943i | 0.879442i | ||||||||
\(109\) | 10.1130 | 0.968649 | 0.484325 | − | 0.874888i | \(-0.339065\pi\) | ||||
0.484325 | + | 0.874888i | \(0.339065\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.81423 | 0.172199 | ||||||||
\(112\) | 1.34098i | 0.126710i | ||||||||
\(113\) | − 10.7120i | − 1.00770i | −0.863791 | − | 0.503851i | \(-0.831916\pi\) | ||||
0.863791 | − | 0.503851i | \(-0.168084\pi\) | |||||||
\(114\) | −0.990653 | −0.0927831 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 13.2079 | 1.22632 | ||||||||
\(117\) | 3.95975i | 0.366079i | ||||||||
\(118\) | − 24.5836i | − 2.26311i | ||||||||
\(119\) | −5.64737 | −0.517693 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 32.9630i | 2.98433i | ||||||||
\(123\) | 0.871076i | 0.0785423i | ||||||||
\(124\) | 21.4628 | 1.92742 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −19.4505 | −1.73279 | ||||||||
\(127\) | − 11.3609i | − 1.00812i | −0.863669 | − | 0.504060i | \(-0.831839\pi\) | ||||
0.863669 | − | 0.504060i | \(-0.168161\pi\) | |||||||
\(128\) | 19.1548i | 1.69306i | ||||||||
\(129\) | 1.70702 | 0.150294 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.98771 | 0.697890 | 0.348945 | − | 0.937143i | \(-0.386540\pi\) | ||||
0.348945 | + | 0.937143i | \(0.386540\pi\) | |||||||
\(132\) | 3.16546i | 0.275518i | ||||||||
\(133\) | − 2.74231i | − 0.237789i | ||||||||
\(134\) | 24.6866 | 2.13259 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.72525 | 0.490936 | ||||||||
\(137\) | 9.33726i | 0.797736i | 0.917008 | + | 0.398868i | \(0.130597\pi\) | ||||
−0.917008 | + | 0.398868i | \(0.869403\pi\) | |||||||
\(138\) | 3.65121i | 0.310811i | ||||||||
\(139\) | −17.9150 | −1.51953 | −0.759767 | − | 0.650195i | \(-0.774687\pi\) | ||||
−0.759767 | + | 0.650195i | \(0.774687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.27951 | −0.191969 | ||||||||
\(142\) | 28.7732i | 2.41459i | ||||||||
\(143\) | 2.85442i | 0.238699i | ||||||||
\(144\) | 1.22553 | 0.102128 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.618034 | 0.0511489 | ||||||||
\(147\) | 1.05247i | 0.0868065i | ||||||||
\(148\) | − 12.7318i | − 1.04655i | ||||||||
\(149\) | 6.31395 | 0.517259 | 0.258629 | − | 0.965977i | \(-0.416729\pi\) | ||||
0.258629 | + | 0.965977i | \(0.416729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.71947 | 0.384065 | 0.192033 | − | 0.981389i | \(-0.438492\pi\) | ||||
0.192033 | + | 0.981389i | \(0.438492\pi\) | |||||||
\(152\) | 2.78013i | 0.225498i | ||||||||
\(153\) | 5.16119i | 0.417258i | ||||||||
\(154\) | −14.0211 | −1.12985 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.25889 | −0.180856 | ||||||||
\(157\) | 1.46908i | 0.117245i | 0.998280 | + | 0.0586225i | \(0.0186708\pi\) | ||||
−0.998280 | + | 0.0586225i | \(0.981329\pi\) | |||||||
\(158\) | 19.7945i | 1.57477i | ||||||||
\(159\) | 4.51382 | 0.357969 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.1072 | −0.796560 | ||||||||
\(162\) | 16.2136i | 1.27386i | ||||||||
\(163\) | − 4.45969i | − 0.349310i | −0.984630 | − | 0.174655i | \(-0.944119\pi\) | ||||
0.984630 | − | 0.174655i | \(-0.0558810\pi\) | |||||||
\(164\) | 6.11299 | 0.477345 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.1388 | −2.26161 | ||||||||
\(167\) | 10.4337i | 0.807381i | 0.914896 | + | 0.403691i | \(0.132273\pi\) | ||||
−0.914896 | + | 0.403691i | \(0.867727\pi\) | |||||||
\(168\) | − 4.43715i | − 0.342334i | ||||||||
\(169\) | 10.9631 | 0.843313 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.50623 | −0.191656 | ||||||||
\(172\) | − 11.9794i | − 0.913421i | ||||||||
\(173\) | 7.67619i | 0.583610i | 0.956478 | + | 0.291805i | \(0.0942559\pi\) | ||||
−0.956478 | + | 0.291805i | \(0.905744\pi\) | |||||||
\(174\) | −4.34623 | −0.329486 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.883436 | 0.0665915 | ||||||||
\(177\) | 5.05563i | 0.380005i | ||||||||
\(178\) | 11.0105i | 0.825273i | ||||||||
\(179\) | −15.5168 | −1.15978 | −0.579889 | − | 0.814696i | \(-0.696904\pi\) | ||||
−0.579889 | + | 0.814696i | \(0.696904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.59056 | −0.118225 | −0.0591126 | − | 0.998251i | \(-0.518827\pi\) | ||||
−0.0591126 | + | 0.998251i | \(0.518827\pi\) | |||||||
\(182\) | − 10.0055i | − 0.741658i | ||||||||
\(183\) | − 6.77885i | − 0.501107i | ||||||||
\(184\) | 10.2466 | 0.755390 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.06259 | −0.517854 | ||||||||
\(187\) | 3.72049i | 0.272069i | ||||||||
\(188\) | 15.9970i | 1.16670i | ||||||||
\(189\) | 8.32515 | 0.605566 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.6684 | 1.42316 | 0.711579 | − | 0.702606i | \(-0.247980\pi\) | ||||
0.711579 | + | 0.702606i | \(0.247980\pi\) | |||||||
\(192\) | − 6.05135i | − 0.436719i | ||||||||
\(193\) | − 13.1100i | − 0.943680i | −0.881684 | − | 0.471840i | \(-0.843590\pi\) | ||||
0.881684 | − | 0.471840i | \(-0.156410\pi\) | |||||||
\(194\) | 22.9959 | 1.65101 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.38599 | 0.527571 | ||||||||
\(197\) | − 3.42949i | − 0.244341i | −0.992509 | − | 0.122170i | \(-0.961015\pi\) | ||||
0.992509 | − | 0.122170i | \(-0.0389855\pi\) | |||||||
\(198\) | 12.8140i | 0.910652i | ||||||||
\(199\) | −17.6959 | −1.25443 | −0.627215 | − | 0.778846i | \(-0.715805\pi\) | ||||
−0.627215 | + | 0.778846i | \(0.715805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.07680 | −0.358090 | ||||||||
\(202\) | 21.5828i | 1.51856i | ||||||||
\(203\) | − 12.0312i | − 0.844422i | ||||||||
\(204\) | −2.94427 | −0.206140 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 20.9776 | 1.46158 | ||||||||
\(207\) | 9.23710i | 0.642023i | ||||||||
\(208\) | 0.630425i | 0.0437121i | ||||||||
\(209\) | −1.80664 | −0.124968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.24366 | −0.223303 | −0.111651 | − | 0.993747i | \(-0.535614\pi\) | ||||
−0.111651 | + | 0.993747i | \(0.535614\pi\) | |||||||
\(212\) | − 31.6769i | − 2.17558i | ||||||||
\(213\) | − 5.91722i | − 0.405441i | ||||||||
\(214\) | −12.9982 | −0.888542 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.43997 | −0.574267 | ||||||||
\(217\) | − 19.5506i | − 1.32718i | ||||||||
\(218\) | 23.3537i | 1.58171i | ||||||||
\(219\) | −0.127099 | −0.00858854 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.65496 | −0.178592 | ||||||||
\(222\) | 4.18956i | 0.281185i | ||||||||
\(223\) | − 28.7148i | − 1.92288i | −0.275010 | − | 0.961441i | \(-0.588681\pi\) | ||||
0.275010 | − | 0.961441i | \(-0.411319\pi\) | |||||||
\(224\) | 15.5899 | 1.04164 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.7370 | 1.64548 | ||||||||
\(227\) | 11.7206i | 0.777926i | 0.921253 | + | 0.388963i | \(0.127167\pi\) | ||||
−0.921253 | + | 0.388963i | \(0.872833\pi\) | |||||||
\(228\) | − 1.42971i | − 0.0946850i | ||||||||
\(229\) | 16.4013 | 1.08383 | 0.541914 | − | 0.840434i | \(-0.317700\pi\) | ||||
0.541914 | + | 0.840434i | \(0.317700\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.88344 | 0.189716 | ||||||||
\(232\) | 12.1971i | 0.800777i | ||||||||
\(233\) | − 22.5146i | − 1.47498i | −0.675358 | − | 0.737490i | \(-0.736011\pi\) | ||||
0.675358 | − | 0.737490i | \(-0.263989\pi\) | |||||||
\(234\) | −9.14415 | −0.597771 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 35.4792 | 2.30950 | ||||||||
\(237\) | − 4.07075i | − 0.264424i | ||||||||
\(238\) | − 13.0413i | − 0.845344i | ||||||||
\(239\) | 6.63333 | 0.429074 | 0.214537 | − | 0.976716i | \(-0.431176\pi\) | ||||
0.214537 | + | 0.976716i | \(0.431176\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.2261 | 1.68937 | 0.844684 | − | 0.535265i | \(-0.179788\pi\) | ||||
0.844684 | + | 0.535265i | \(0.179788\pi\) | |||||||
\(242\) | − 16.1649i | − 1.03912i | ||||||||
\(243\) | − 11.5613i | − 0.741655i | ||||||||
\(244\) | −47.5723 | −3.04550 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.01155 | −0.128252 | ||||||||
\(247\) | − 1.28923i | − 0.0820315i | ||||||||
\(248\) | 19.8202i | 1.25858i | ||||||||
\(249\) | 5.99241 | 0.379753 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.9121 | −0.688766 | −0.344383 | − | 0.938829i | \(-0.611912\pi\) | ||||
−0.344383 | + | 0.938829i | \(0.611912\pi\) | |||||||
\(252\) | − 28.0710i | − 1.76831i | ||||||||
\(253\) | 6.65865i | 0.418626i | ||||||||
\(254\) | 26.2355 | 1.64616 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −18.7492 | −1.17182 | ||||||||
\(257\) | 6.58051i | 0.410481i | 0.978712 | + | 0.205240i | \(0.0657976\pi\) | ||||
−0.978712 | + | 0.205240i | \(0.934202\pi\) | |||||||
\(258\) | 3.94197i | 0.245416i | ||||||||
\(259\) | −11.5975 | −0.720632 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.9954 | −0.680599 | ||||||||
\(262\) | 18.4458i | 1.13959i | ||||||||
\(263\) | 27.1073i | 1.67151i | 0.549106 | + | 0.835753i | \(0.314968\pi\) | ||||
−0.549106 | + | 0.835753i | \(0.685032\pi\) | |||||||
\(264\) | −2.92320 | −0.179911 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.33275 | 0.388286 | ||||||||
\(267\) | − 2.26432i | − 0.138574i | ||||||||
\(268\) | 35.6277i | 2.17631i | ||||||||
\(269\) | −1.00945 | −0.0615474 | −0.0307737 | − | 0.999526i | \(-0.509797\pi\) | ||||
−0.0307737 | + | 0.999526i | \(0.509797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.25203 | 0.379784 | 0.189892 | − | 0.981805i | \(-0.439186\pi\) | ||||
0.189892 | + | 0.981805i | \(0.439186\pi\) | |||||||
\(272\) | 0.821705i | 0.0498232i | ||||||||
\(273\) | 2.05763i | 0.124534i | ||||||||
\(274\) | −21.5623 | −1.30263 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.26943 | −0.317182 | ||||||||
\(277\) | − 24.6703i | − 1.48230i | −0.671342 | − | 0.741148i | \(-0.734282\pi\) | ||||
0.671342 | − | 0.741148i | \(-0.265718\pi\) | |||||||
\(278\) | − 41.3708i | − 2.48125i | ||||||||
\(279\) | −17.8675 | −1.06970 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.83891 | 0.109700 | 0.0548502 | − | 0.998495i | \(-0.482532\pi\) | ||||
0.0548502 | + | 0.998495i | \(0.482532\pi\) | |||||||
\(282\) | − 5.26401i | − 0.313467i | ||||||||
\(283\) | 8.64116i | 0.513664i | 0.966456 | + | 0.256832i | \(0.0826786\pi\) | ||||
−0.966456 | + | 0.256832i | \(0.917321\pi\) | |||||||
\(284\) | −41.5255 | −2.46409 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.59164 | −0.389772 | ||||||||
\(287\) | − 5.56835i | − 0.328690i | ||||||||
\(288\) | − 14.2478i | − 0.839558i | ||||||||
\(289\) | 13.5395 | 0.796440 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.72910 | −0.277225 | ||||||||
\(292\) | 0.891948i | 0.0521973i | ||||||||
\(293\) | − 6.29156i | − 0.367557i | −0.982968 | − | 0.183779i | \(-0.941167\pi\) | ||||
0.982968 | − | 0.183779i | \(-0.0588329\pi\) | |||||||
\(294\) | −2.43045 | −0.141747 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.7574 | 0.683386 | ||||||||
\(297\) | − 5.48462i | − 0.318250i | ||||||||
\(298\) | 14.5806i | 0.844634i | ||||||||
\(299\) | −4.75164 | −0.274795 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.9121 | −0.628963 | ||||||||
\(302\) | 10.8986i | 0.627142i | ||||||||
\(303\) | − 4.43850i | − 0.254985i | ||||||||
\(304\) | −0.399012 | −0.0228849 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.9186 | −0.681342 | ||||||||
\(307\) | − 28.6661i | − 1.63606i | −0.575175 | − | 0.818030i | \(-0.695066\pi\) | ||||
0.575175 | − | 0.818030i | \(-0.304934\pi\) | |||||||
\(308\) | − 20.2352i | − 1.15301i | ||||||||
\(309\) | −4.31405 | −0.245418 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.83649 | −0.444367 | −0.222183 | − | 0.975005i | \(-0.571318\pi\) | ||||
−0.222183 | + | 0.975005i | \(0.571318\pi\) | |||||||
\(312\) | − 2.08601i | − 0.118097i | ||||||||
\(313\) | − 21.4093i | − 1.21012i | −0.796179 | − | 0.605061i | \(-0.793149\pi\) | ||||
0.796179 | − | 0.605061i | \(-0.206851\pi\) | |||||||
\(314\) | −3.39250 | −0.191450 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −28.5675 | −1.60705 | ||||||||
\(317\) | 4.01983i | 0.225776i | 0.993608 | + | 0.112888i | \(0.0360102\pi\) | ||||
−0.993608 | + | 0.112888i | \(0.963990\pi\) | |||||||
\(318\) | 10.4237i | 0.584530i | ||||||||
\(319\) | −7.92614 | −0.443779 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.67309 | 0.149197 | ||||||||
\(322\) | − 23.3403i | − 1.30071i | ||||||||
\(323\) | − 1.68040i | − 0.0934997i | ||||||||
\(324\) | −23.3995 | −1.29997 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.2987 | 0.570390 | ||||||||
\(327\) | − 4.80269i | − 0.265589i | ||||||||
\(328\) | 5.64515i | 0.311701i | ||||||||
\(329\) | 14.5718 | 0.803367 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6439 | 0.640005 | 0.320002 | − | 0.947417i | \(-0.396316\pi\) | ||||
0.320002 | + | 0.947417i | \(0.396316\pi\) | |||||||
\(332\) | − 42.0532i | − 2.30797i | ||||||||
\(333\) | 10.5991i | 0.580825i | ||||||||
\(334\) | −24.0942 | −1.31838 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.636833 | 0.0347421 | ||||||||
\(337\) | − 21.5348i | − 1.17307i | −0.809922 | − | 0.586537i | \(-0.800491\pi\) | ||||
0.809922 | − | 0.586537i | \(-0.199509\pi\) | |||||||
\(338\) | 25.3167i | 1.37705i | ||||||||
\(339\) | −5.08716 | −0.276297 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.8799 | −0.697487 | ||||||||
\(342\) | − 5.78757i | − 0.312956i | ||||||||
\(343\) | 14.5228i | 0.784157i | ||||||||
\(344\) | 11.0626 | 0.596455 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.7264 | −0.952979 | ||||||||
\(347\) | 15.5972i | 0.837303i | 0.908147 | + | 0.418652i | \(0.137497\pi\) | ||||
−0.908147 | + | 0.418652i | \(0.862503\pi\) | |||||||
\(348\) | − 6.27248i | − 0.336240i | ||||||||
\(349\) | −5.56598 | −0.297940 | −0.148970 | − | 0.988842i | \(-0.547596\pi\) | ||||
−0.148970 | + | 0.988842i | \(0.547596\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.91385 | 0.208906 | ||||||||
\(352\) | − 10.2706i | − 0.547427i | ||||||||
\(353\) | − 8.02216i | − 0.426977i | −0.976946 | − | 0.213488i | \(-0.931517\pi\) | ||||
0.976946 | − | 0.213488i | \(-0.0684825\pi\) | |||||||
\(354\) | −11.6748 | −0.620511 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.8904 | −0.842190 | ||||||||
\(357\) | 2.68195i | 0.141944i | ||||||||
\(358\) | − 35.8325i | − 1.89380i | ||||||||
\(359\) | 12.3427 | 0.651424 | 0.325712 | − | 0.945469i | \(-0.394396\pi\) | ||||
0.325712 | + | 0.945469i | \(0.394396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1840 | −0.957053 | ||||||||
\(362\) | − 3.67303i | − 0.193050i | ||||||||
\(363\) | 3.32432i | 0.174482i | ||||||||
\(364\) | 14.4400 | 0.756860 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 15.6542 | 0.818260 | ||||||||
\(367\) | 26.8749i | 1.40286i | 0.712738 | + | 0.701430i | \(0.247455\pi\) | ||||
−0.712738 | + | 0.701430i | \(0.752545\pi\) | |||||||
\(368\) | 1.47062i | 0.0766615i | ||||||||
\(369\) | −5.08898 | −0.264922 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.8546 | −1.49806 | ||||||||
\(372\) | − 10.1927i | − 0.528469i | ||||||||
\(373\) | 27.6389i | 1.43109i | 0.698567 | + | 0.715544i | \(0.253821\pi\) | ||||
−0.698567 | + | 0.715544i | \(0.746179\pi\) | |||||||
\(374\) | −8.59164 | −0.444263 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.7727 | −0.761845 | ||||||||
\(377\) | − 5.65614i | − 0.291306i | ||||||||
\(378\) | 19.2251i | 0.988831i | ||||||||
\(379\) | 3.47462 | 0.178479 | 0.0892397 | − | 0.996010i | \(-0.471556\pi\) | ||||
0.0892397 | + | 0.996010i | \(0.471556\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.39534 | −0.276412 | ||||||||
\(382\) | 45.4198i | 2.32388i | ||||||||
\(383\) | − 27.3719i | − 1.39864i | −0.714810 | − | 0.699319i | \(-0.753487\pi\) | ||||
0.714810 | − | 0.699319i | \(-0.246513\pi\) | |||||||
\(384\) | 9.09668 | 0.464213 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 30.2746 | 1.54094 | ||||||||
\(387\) | 9.97269i | 0.506940i | ||||||||
\(388\) | 33.1877i | 1.68485i | ||||||||
\(389\) | −10.8845 | −0.551867 | −0.275934 | − | 0.961177i | \(-0.588987\pi\) | ||||
−0.275934 | + | 0.961177i | \(0.588987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.19336 | −0.313212 | ||||||||
\(392\) | 6.82072i | 0.344498i | ||||||||
\(393\) | − 3.79339i | − 0.191351i | ||||||||
\(394\) | 7.91963 | 0.398985 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.4932 | −0.929319 | ||||||||
\(397\) | 16.2212i | 0.814120i | 0.913401 | + | 0.407060i | \(0.133446\pi\) | ||||
−0.913401 | + | 0.407060i | \(0.866554\pi\) | |||||||
\(398\) | − 40.8647i | − 2.04836i | ||||||||
\(399\) | −1.30233 | −0.0651981 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.78686 | 0.189107 | 0.0945534 | − | 0.995520i | \(-0.469858\pi\) | ||||
0.0945534 | + | 0.995520i | \(0.469858\pi\) | |||||||
\(402\) | − 11.7237i | − 0.584726i | ||||||||
\(403\) | − 9.19118i | − 0.457845i | ||||||||
\(404\) | −31.1483 | −1.54968 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 27.7832 | 1.37886 | ||||||||
\(407\) | 7.64044i | 0.378722i | ||||||||
\(408\) | − 2.71894i | − 0.134607i | ||||||||
\(409\) | −1.85585 | −0.0917661 | −0.0458831 | − | 0.998947i | \(-0.514610\pi\) | ||||
−0.0458831 | + | 0.998947i | \(0.514610\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.43429 | 0.218728 | ||||||||
\(412\) | 30.2750i | 1.49154i | ||||||||
\(413\) | − 32.3181i | − 1.59027i | ||||||||
\(414\) | −21.3310 | −1.04836 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.32918 | 0.359343 | ||||||||
\(417\) | 8.50790i | 0.416634i | ||||||||
\(418\) | − 4.17202i | − 0.204060i | ||||||||
\(419\) | −14.3472 | −0.700907 | −0.350453 | − | 0.936580i | \(-0.613972\pi\) | ||||
−0.350453 | + | 0.936580i | \(0.613972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.4545 | 0.753207 | 0.376604 | − | 0.926374i | \(-0.377092\pi\) | ||||
0.376604 | + | 0.926374i | \(0.377092\pi\) | |||||||
\(422\) | − 7.49051i | − 0.364632i | ||||||||
\(423\) | − 13.3173i | − 0.647509i | ||||||||
\(424\) | 29.2525 | 1.42063 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.6645 | 0.662046 | ||||||||
\(427\) | 43.3338i | 2.09707i | ||||||||
\(428\) | − 18.7591i | − 0.906755i | ||||||||
\(429\) | 1.35557 | 0.0654477 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.5043 | 0.602311 | 0.301156 | − | 0.953575i | \(-0.402628\pi\) | ||||
0.301156 | + | 0.953575i | \(0.402628\pi\) | |||||||
\(432\) | − 1.21133i | − 0.0582801i | ||||||||
\(433\) | 22.4951i | 1.08105i | 0.841329 | + | 0.540524i | \(0.181774\pi\) | ||||
−0.841329 | + | 0.540524i | \(0.818226\pi\) | |||||||
\(434\) | 45.1476 | 2.16715 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −33.7041 | −1.61413 | ||||||||
\(437\) | − 3.00744i | − 0.143865i | ||||||||
\(438\) | − 0.293506i | − 0.0140243i | ||||||||
\(439\) | −12.1776 | −0.581204 | −0.290602 | − | 0.956844i | \(-0.593855\pi\) | ||||
−0.290602 | + | 0.956844i | \(0.593855\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.14873 | −0.292797 | ||||||||
\(442\) | − 6.13104i | − 0.291624i | ||||||||
\(443\) | 20.7101i | 0.983968i | 0.870604 | + | 0.491984i | \(0.163728\pi\) | ||||
−0.870604 | + | 0.491984i | \(0.836272\pi\) | |||||||
\(444\) | −6.04638 | −0.286949 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 66.3103 | 3.13988 | ||||||||
\(447\) | − 2.99851i | − 0.141825i | ||||||||
\(448\) | 38.6833i | 1.82761i | ||||||||
\(449\) | 25.9539 | 1.22484 | 0.612420 | − | 0.790533i | \(-0.290196\pi\) | ||||
0.612420 | + | 0.790533i | \(0.290196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.66844 | −0.172740 | ||||||||
\(452\) | 35.7004i | 1.67921i | ||||||||
\(453\) | − 2.24129i | − 0.105305i | ||||||||
\(454\) | −27.0662 | −1.27028 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.32029 | 0.0618283 | ||||||||
\(457\) | − 8.50150i | − 0.397684i | −0.980032 | − | 0.198842i | \(-0.936282\pi\) | ||||
0.980032 | − | 0.198842i | \(-0.0637180\pi\) | |||||||
\(458\) | 37.8751i | 1.76979i | ||||||||
\(459\) | 5.10137 | 0.238112 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.7851 | 0.688609 | 0.344305 | − | 0.938858i | \(-0.388115\pi\) | ||||
0.344305 | + | 0.938858i | \(0.388115\pi\) | |||||||
\(462\) | 6.65865i | 0.309788i | ||||||||
\(463\) | 22.1921i | 1.03135i | 0.856783 | + | 0.515677i | \(0.172460\pi\) | ||||
−0.856783 | + | 0.515677i | \(0.827540\pi\) | |||||||
\(464\) | −1.75056 | −0.0812677 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 51.9924 | 2.40850 | ||||||||
\(467\) | − 28.5014i | − 1.31889i | −0.751754 | − | 0.659443i | \(-0.770792\pi\) | ||||
0.751754 | − | 0.659443i | \(-0.229208\pi\) | |||||||
\(468\) | − 13.1968i | − 0.610024i | ||||||||
\(469\) | 32.4534 | 1.49856 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.697669 | 0.0321469 | ||||||||
\(472\) | 32.7638i | 1.50808i | ||||||||
\(473\) | 7.18891i | 0.330546i | ||||||||
\(474\) | 9.40048 | 0.431779 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 18.8213 | 0.862671 | ||||||||
\(477\) | 26.3706i | 1.20743i | ||||||||
\(478\) | 15.3182i | 0.700637i | ||||||||
\(479\) | −25.0569 | −1.14488 | −0.572440 | − | 0.819947i | \(-0.694003\pi\) | ||||
−0.572440 | + | 0.819947i | \(0.694003\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.45225 | −0.248601 | ||||||||
\(482\) | 60.5632i | 2.75858i | ||||||||
\(483\) | 4.79995i | 0.218405i | ||||||||
\(484\) | 23.3292 | 1.06042 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 26.6981 | 1.21105 | ||||||||
\(487\) | − 1.46479i | − 0.0663758i | −0.999449 | − | 0.0331879i | \(-0.989434\pi\) | ||||
0.999449 | − | 0.0331879i | \(-0.0105660\pi\) | |||||||
\(488\) | − 43.9314i | − 1.98868i | ||||||||
\(489\) | −2.11792 | −0.0957757 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0686 | −0.905685 | −0.452843 | − | 0.891591i | \(-0.649590\pi\) | ||||
−0.452843 | + | 0.891591i | \(0.649590\pi\) | |||||||
\(492\) | − 2.90308i | − 0.130881i | ||||||||
\(493\) | − 7.37229i | − 0.332031i | ||||||||
\(494\) | 2.97718 | 0.133950 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.84465 | −0.127729 | ||||||||
\(497\) | 37.8258i | 1.69672i | ||||||||
\(498\) | 13.8381i | 0.620101i | ||||||||
\(499\) | −0.624999 | −0.0279788 | −0.0139894 | − | 0.999902i | \(-0.504453\pi\) | ||||
−0.0139894 | + | 0.999902i | \(0.504453\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.95498 | 0.221372 | ||||||||
\(502\) | − 25.1990i | − 1.12469i | ||||||||
\(503\) | 19.3052i | 0.860776i | 0.902644 | + | 0.430388i | \(0.141623\pi\) | ||||
−0.902644 | + | 0.430388i | \(0.858377\pi\) | |||||||
\(504\) | 25.9226 | 1.15469 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.3766 | −0.683575 | ||||||||
\(507\) | − 5.20639i | − 0.231224i | ||||||||
\(508\) | 37.8631i | 1.67990i | ||||||||
\(509\) | 10.5202 | 0.466298 | 0.233149 | − | 0.972441i | \(-0.425097\pi\) | ||||
0.233149 | + | 0.972441i | \(0.425097\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.812479 | 0.0359420 | ||||||||
\(512\) | − 4.98730i | − 0.220410i | ||||||||
\(513\) | 2.47718i | 0.109370i | ||||||||
\(514\) | −15.1962 | −0.670276 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.68906 | −0.250447 | ||||||||
\(517\) | − 9.59989i | − 0.422203i | ||||||||
\(518\) | − 26.7818i | − 1.17672i | ||||||||
\(519\) | 3.64545 | 0.160017 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0070 | −0.438413 | −0.219207 | − | 0.975678i | \(-0.570347\pi\) | ||||
−0.219207 | + | 0.975678i | \(0.570347\pi\) | |||||||
\(522\) | − 25.3914i | − 1.11135i | ||||||||
\(523\) | − 22.7830i | − 0.996233i | −0.867110 | − | 0.498117i | \(-0.834025\pi\) | ||||
0.867110 | − | 0.498117i | \(-0.165975\pi\) | |||||||
\(524\) | −26.6210 | −1.16295 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −62.5981 | −2.72941 | ||||||||
\(527\) | − 11.9799i | − 0.521854i | ||||||||
\(528\) | − 0.419546i | − 0.0182584i | ||||||||
\(529\) | 11.9156 | 0.518070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.5359 | −1.28175 | ||||||||
\(532\) | 9.13943i | 0.396245i | ||||||||
\(533\) | − 2.61782i | − 0.113390i | ||||||||
\(534\) | 5.22893 | 0.226278 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −32.9010 | −1.42111 | ||||||||
\(537\) | 7.36896i | 0.317994i | ||||||||
\(538\) | − 2.33110i | − 0.100501i | ||||||||
\(539\) | −4.43237 | −0.190916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.25900 | 0.140115 | 0.0700576 | − | 0.997543i | \(-0.477682\pi\) | ||||
0.0700576 | + | 0.997543i | \(0.477682\pi\) | |||||||
\(542\) | 14.4377i | 0.620150i | ||||||||
\(543\) | 0.755360i | 0.0324156i | ||||||||
\(544\) | 9.55296 | 0.409580 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.75164 | −0.203352 | ||||||||
\(547\) | − 13.5883i | − 0.580993i | −0.956876 | − | 0.290497i | \(-0.906179\pi\) | ||||
0.956876 | − | 0.290497i | \(-0.0938205\pi\) | |||||||
\(548\) | − 31.1188i | − 1.32933i | ||||||||
\(549\) | 39.6033 | 1.69023 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.57992 | 0.152510 | ||||||||
\(552\) | − 4.86614i | − 0.207117i | ||||||||
\(553\) | 26.0223i | 1.10658i | ||||||||
\(554\) | 56.9706 | 2.42045 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 59.7063 | 2.53211 | ||||||||
\(557\) | − 27.6399i | − 1.17114i | −0.810621 | − | 0.585571i | \(-0.800870\pi\) | ||||
0.810621 | − | 0.585571i | \(-0.199130\pi\) | |||||||
\(558\) | − 41.2609i | − 1.74671i | ||||||||
\(559\) | −5.13004 | −0.216978 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.76687 | 0.0745974 | ||||||||
\(562\) | 4.24656i | 0.179130i | ||||||||
\(563\) | 1.65925i | 0.0699291i | 0.999389 | + | 0.0349646i | \(0.0111318\pi\) | ||||
−0.999389 | + | 0.0349646i | \(0.988868\pi\) | |||||||
\(564\) | 7.59703 | 0.319893 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19.9548 | −0.838763 | ||||||||
\(567\) | 21.3147i | 0.895133i | ||||||||
\(568\) | − 38.3475i | − 1.60902i | ||||||||
\(569\) | −17.8828 | −0.749686 | −0.374843 | − | 0.927088i | \(-0.622303\pi\) | ||||
−0.374843 | + | 0.927088i | \(0.622303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.8723 | −1.54306 | −0.771530 | − | 0.636193i | \(-0.780508\pi\) | ||||
−0.771530 | + | 0.636193i | \(0.780508\pi\) | |||||||
\(572\) | − 9.51307i | − 0.397761i | ||||||||
\(573\) | − 9.34060i | − 0.390209i | ||||||||
\(574\) | 12.8589 | 0.536718 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 35.3531 | 1.47305 | ||||||||
\(577\) | − 22.8137i | − 0.949746i | −0.880054 | − | 0.474873i | \(-0.842494\pi\) | ||||
0.880054 | − | 0.474873i | \(-0.157506\pi\) | |||||||
\(578\) | 31.2664i | 1.30051i | ||||||||
\(579\) | −6.22599 | −0.258743 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.3065 | −1.58922 | ||||||||
\(582\) | − 10.9208i | − 0.452682i | ||||||||
\(583\) | 19.0095i | 0.787291i | ||||||||
\(584\) | −0.823684 | −0.0340843 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5289 | 0.600185 | ||||||||
\(587\) | − 11.0855i | − 0.457546i | −0.973480 | − | 0.228773i | \(-0.926529\pi\) | ||||
0.973480 | − | 0.228773i | \(-0.0734714\pi\) | |||||||
\(588\) | − 3.50763i | − 0.144652i | ||||||||
\(589\) | 5.81734 | 0.239699 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.62867 | −0.0669947 | ||||||||
\(592\) | 1.68746i | 0.0693542i | ||||||||
\(593\) | − 11.1321i | − 0.457139i | −0.973528 | − | 0.228570i | \(-0.926595\pi\) | ||||
0.973528 | − | 0.228570i | \(-0.0734049\pi\) | |||||||
\(594\) | 12.6655 | 0.519672 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.0428 | −0.861947 | ||||||||
\(597\) | 8.40384i | 0.343946i | ||||||||
\(598\) | − 10.9729i | − 0.448713i | ||||||||
\(599\) | −36.2736 | −1.48210 | −0.741049 | − | 0.671451i | \(-0.765671\pi\) | ||||
−0.741049 | + | 0.671451i | \(0.765671\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.1051 | −0.616150 | −0.308075 | − | 0.951362i | \(-0.599685\pi\) | ||||
−0.308075 | + | 0.951362i | \(0.599685\pi\) | |||||||
\(602\) | − 25.1990i | − 1.02704i | ||||||||
\(603\) | − 29.6596i | − 1.20783i | ||||||||
\(604\) | −15.7288 | −0.639997 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.2497 | 0.416366 | ||||||||
\(607\) | − 33.5066i | − 1.35999i | −0.733216 | − | 0.679996i | \(-0.761982\pi\) | ||||
0.733216 | − | 0.679996i | \(-0.238018\pi\) | |||||||
\(608\) | 4.63883i | 0.188129i | ||||||||
\(609\) | −5.71363 | −0.231528 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.85053 | 0.277143 | ||||||||
\(612\) | − 17.2010i | − 0.695308i | ||||||||
\(613\) | 28.0289i | 1.13208i | 0.824379 | + | 0.566038i | \(0.191524\pi\) | ||||
−0.824379 | + | 0.566038i | \(0.808476\pi\) | |||||||
\(614\) | 66.1979 | 2.67153 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.6866 | 0.752903 | ||||||||
\(617\) | 30.5223i | 1.22878i | 0.789002 | + | 0.614391i | \(0.210598\pi\) | ||||
−0.789002 | + | 0.614391i | \(0.789402\pi\) | |||||||
\(618\) | − 9.96234i | − 0.400744i | ||||||||
\(619\) | 21.6971 | 0.872080 | 0.436040 | − | 0.899927i | \(-0.356381\pi\) | ||||
0.436040 | + | 0.899927i | \(0.356381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.13004 | 0.366376 | ||||||||
\(622\) | − 18.0966i | − 0.725608i | ||||||||
\(623\) | 14.4746i | 0.579914i | ||||||||
\(624\) | 0.299391 | 0.0119852 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 49.4399 | 1.97601 | ||||||||
\(627\) | 0.857977i | 0.0342643i | ||||||||
\(628\) | − 4.89606i | − 0.195374i | ||||||||
\(629\) | −7.10655 | −0.283357 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.2277 | −0.646015 | −0.323007 | − | 0.946396i | \(-0.604694\pi\) | ||||
−0.323007 | + | 0.946396i | \(0.604694\pi\) | |||||||
\(632\) | − 26.3812i | − 1.04939i | ||||||||
\(633\) | 1.54042i | 0.0612264i | ||||||||
\(634\) | −9.28290 | −0.368671 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −15.0434 | −0.596511 | ||||||||
\(637\) | − 3.16296i | − 0.125321i | ||||||||
\(638\) | − 18.3036i | − 0.724648i | ||||||||
\(639\) | 34.5694 | 1.36755 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.1774 | −0.875956 | −0.437978 | − | 0.898986i | \(-0.644305\pi\) | ||||
−0.437978 | + | 0.898986i | \(0.644305\pi\) | |||||||
\(642\) | 6.17290i | 0.243625i | ||||||||
\(643\) | 13.2767i | 0.523583i | 0.965124 | + | 0.261792i | \(0.0843133\pi\) | ||||
−0.965124 | + | 0.261792i | \(0.915687\pi\) | |||||||
\(644\) | 33.6848 | 1.32737 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.88050 | 0.152676 | ||||||||
\(647\) | − 11.2853i | − 0.443671i | −0.975084 | − | 0.221835i | \(-0.928795\pi\) | ||||
0.975084 | − | 0.221835i | \(-0.0712047\pi\) | |||||||
\(648\) | − 21.6086i | − 0.848867i | ||||||||
\(649\) | −21.2912 | −0.835754 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.28462 | −0.363893 | ||||||||
\(652\) | 14.8630i | 0.582082i | ||||||||
\(653\) | 35.8134i | 1.40149i | 0.713414 | + | 0.700743i | \(0.247148\pi\) | ||||
−0.713414 | + | 0.700743i | \(0.752852\pi\) | |||||||
\(654\) | 11.0907 | 0.433682 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.810208 | −0.0316333 | ||||||||
\(657\) | − 0.742534i | − 0.0289690i | ||||||||
\(658\) | 33.6502i | 1.31182i | ||||||||
\(659\) | −39.7655 | −1.54905 | −0.774523 | − | 0.632546i | \(-0.782010\pi\) | ||||
−0.774523 | + | 0.632546i | \(0.782010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.24734 | −0.242993 | −0.121497 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121497 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(662\) | 26.8889i | 1.04507i | ||||||||
\(663\) | 1.26085i | 0.0489673i | ||||||||
\(664\) | 38.8347 | 1.50708 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.4762 | −0.948432 | ||||||||
\(667\) | − 13.1943i | − 0.510887i | ||||||||
\(668\) | − 34.7728i | − 1.34540i | ||||||||
\(669\) | −13.6367 | −0.527226 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.5484 | 1.10210 | ||||||||
\(672\) | − 7.40368i | − 0.285603i | ||||||||
\(673\) | 41.4627i | 1.59827i | 0.601151 | + | 0.799135i | \(0.294709\pi\) | ||||
−0.601151 | + | 0.799135i | \(0.705291\pi\) | |||||||
\(674\) | 49.7297 | 1.91552 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −36.5372 | −1.40528 | ||||||||
\(677\) | − 1.43915i | − 0.0553112i | −0.999618 | − | 0.0276556i | \(-0.991196\pi\) | ||||
0.999618 | − | 0.0276556i | \(-0.00880417\pi\) | |||||||
\(678\) | − 11.7477i | − 0.451166i | ||||||||
\(679\) | 30.2308 | 1.16015 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.56616 | 0.213296 | ||||||||
\(682\) | − 29.7433i | − 1.13893i | ||||||||
\(683\) | 8.48623i | 0.324716i | 0.986732 | + | 0.162358i | \(0.0519100\pi\) | ||||
−0.986732 | + | 0.162358i | \(0.948090\pi\) | |||||||
\(684\) | 8.35263 | 0.319371 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −33.5371 | −1.28045 | ||||||||
\(687\) | − 7.78902i | − 0.297170i | ||||||||
\(688\) | 1.58774i | 0.0605318i | ||||||||
\(689\) | −13.5652 | −0.516795 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.7797 | −1.66546 | −0.832730 | − | 0.553679i | \(-0.813223\pi\) | ||||
−0.832730 | + | 0.553679i | \(0.813223\pi\) | |||||||
\(692\) | − 25.5828i | − 0.972513i | ||||||||
\(693\) | 16.8456i | 0.639910i | ||||||||
\(694\) | −36.0183 | −1.36724 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.79243 | 0.219561 | ||||||||
\(697\) | − 3.41210i | − 0.129243i | ||||||||
\(698\) | − 12.8534i | − 0.486508i | ||||||||
\(699\) | −10.6922 | −0.404418 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.840795 | 0.0317564 | 0.0158782 | − | 0.999874i | \(-0.494946\pi\) | ||||
0.0158782 | + | 0.999874i | \(0.494946\pi\) | |||||||
\(702\) | 9.03816i | 0.341124i | ||||||||
\(703\) | − 3.45087i | − 0.130152i | ||||||||
\(704\) | 25.4846 | 0.960487 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.5254 | 0.697212 | ||||||||
\(707\) | 28.3731i | 1.06708i | ||||||||
\(708\) | − 16.8492i | − 0.633230i | ||||||||
\(709\) | 13.3812 | 0.502543 | 0.251271 | − | 0.967917i | \(-0.419151\pi\) | ||||
0.251271 | + | 0.967917i | \(0.419151\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.7821 | 0.891897 | ||||||||
\(712\) | − 14.6743i | − 0.549941i | ||||||||
\(713\) | − 21.4407i | − 0.802962i | ||||||||
\(714\) | −6.19336 | −0.231781 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 51.7135 | 1.93262 | ||||||||
\(717\) | − 3.15019i | − 0.117646i | ||||||||
\(718\) | 28.5027i | 1.06371i | ||||||||
\(719\) | −43.4148 | −1.61910 | −0.809550 | − | 0.587051i | \(-0.800289\pi\) | ||||
−0.809550 | + | 0.587051i | \(0.800289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5776 | 1.02704 | ||||||||
\(722\) | − 41.9919i | − 1.56278i | ||||||||
\(723\) | − 12.4548i | − 0.463200i | ||||||||
\(724\) | 5.30093 | 0.197007 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.67677 | −0.284912 | ||||||||
\(727\) | − 32.0480i | − 1.18859i | −0.804245 | − | 0.594297i | \(-0.797430\pi\) | ||||
0.804245 | − | 0.594297i | \(-0.202570\pi\) | |||||||
\(728\) | 13.3348i | 0.494222i | ||||||||
\(729\) | 15.5727 | 0.576768 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.68657 | −0.247312 | ||||||||
\(732\) | 22.5922i | 0.835032i | ||||||||
\(733\) | − 8.13928i | − 0.300631i | −0.988638 | − | 0.150316i | \(-0.951971\pi\) | ||||
0.988638 | − | 0.150316i | \(-0.0480289\pi\) | |||||||
\(734\) | −62.0616 | −2.29074 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.0971 | 0.630209 | ||||||||
\(737\) | − 21.3804i | − 0.787556i | ||||||||
\(738\) | − 11.7519i | − 0.432592i | ||||||||
\(739\) | 7.12714 | 0.262176 | 0.131088 | − | 0.991371i | \(-0.458153\pi\) | ||||
0.131088 | + | 0.991371i | \(0.458153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.612257 | −0.0224918 | ||||||||
\(742\) | − 66.6332i | − 2.44618i | ||||||||
\(743\) | − 21.9040i | − 0.803578i | −0.915732 | − | 0.401789i | \(-0.868388\pi\) | ||||
0.915732 | − | 0.401789i | \(-0.131612\pi\) | |||||||
\(744\) | 9.41266 | 0.345085 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −63.8258 | −2.33683 | ||||||||
\(747\) | 35.0087i | 1.28090i | ||||||||
\(748\) | − 12.3995i | − 0.453370i | ||||||||
\(749\) | −17.0877 | −0.624373 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.21909 | 0.336409 | 0.168205 | − | 0.985752i | \(-0.446203\pi\) | ||||
0.168205 | + | 0.985752i | \(0.446203\pi\) | |||||||
\(752\) | − 2.12022i | − 0.0773166i | ||||||||
\(753\) | 5.18219i | 0.188849i | ||||||||
\(754\) | 13.0616 | 0.475674 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −27.7457 | −1.00910 | ||||||||
\(757\) | 45.6524i | 1.65926i | 0.558311 | + | 0.829632i | \(0.311450\pi\) | ||||
−0.558311 | + | 0.829632i | \(0.688550\pi\) | |||||||
\(758\) | 8.02386i | 0.291440i | ||||||||
\(759\) | 3.16221 | 0.114781 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.9058 | 1.44658 | 0.723291 | − | 0.690543i | \(-0.242628\pi\) | ||||
0.723291 | + | 0.690543i | \(0.242628\pi\) | |||||||
\(762\) | − 12.4593i | − 0.451353i | ||||||||
\(763\) | 30.7012i | 1.11146i | ||||||||
\(764\) | −65.5500 | −2.37151 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 63.2092 | 2.28384 | ||||||||
\(767\) | − 15.1935i | − 0.548607i | ||||||||
\(768\) | 8.90403i | 0.321296i | ||||||||
\(769\) | 44.3420 | 1.59901 | 0.799506 | − | 0.600658i | \(-0.205094\pi\) | ||||
0.799506 | + | 0.600658i | \(0.205094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.12510 | 0.112548 | ||||||||
\(772\) | 43.6924i | 1.57252i | ||||||||
\(773\) | 38.4944i | 1.38455i | 0.721635 | + | 0.692273i | \(0.243391\pi\) | ||||
−0.721635 | + | 0.692273i | \(0.756609\pi\) | |||||||
\(774\) | −23.0297 | −0.827785 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −30.6477 | −1.10019 | ||||||||
\(777\) | 5.50768i | 0.197587i | ||||||||
\(778\) | − 25.1353i | − 0.901146i | ||||||||
\(779\) | 1.65689 | 0.0593641 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.9197 | 0.891697 | ||||||||
\(782\) | − 14.3022i | − 0.511445i | ||||||||
\(783\) | 10.8680i | 0.388390i | ||||||||
\(784\) | −0.978929 | −0.0349618 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.75997 | 0.312458 | ||||||||
\(787\) | − 53.0202i | − 1.88997i | −0.327120 | − | 0.944983i | \(-0.606078\pi\) | ||||
0.327120 | − | 0.944983i | \(-0.393922\pi\) | |||||||
\(788\) | 11.4296i | 0.407164i | ||||||||
\(789\) | 12.8733 | 0.458302 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.5197 | 1.15627 | ||||||||
\(792\) | − 17.0779i | − 0.606835i | ||||||||
\(793\) | 20.3723i | 0.723440i | ||||||||
\(794\) | −37.4593 | −1.32938 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 58.9760 | 2.09035 | ||||||||
\(797\) | − 12.6769i | − 0.449037i | −0.974470 | − | 0.224519i | \(-0.927919\pi\) | ||||
0.974470 | − | 0.224519i | \(-0.0720810\pi\) | |||||||
\(798\) | − 3.00744i | − 0.106462i | ||||||||
\(799\) | 8.92908 | 0.315888 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.2285 | 0.467407 | ||||||||
\(802\) | 8.74490i | 0.308793i | ||||||||
\(803\) | − 0.535262i | − 0.0188890i | ||||||||
\(804\) | 16.9197 | 0.596712 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.2250 | 0.747618 | ||||||||
\(807\) | 0.479392i | 0.0168754i | ||||||||
\(808\) | − 28.7644i | − 1.01193i | ||||||||
\(809\) | 41.8935 | 1.47290 | 0.736449 | − | 0.676493i | \(-0.236501\pi\) | ||||
0.736449 | + | 0.676493i | \(0.236501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.5486 | −1.21317 | −0.606583 | − | 0.795020i | \(-0.707460\pi\) | ||||
−0.606583 | + | 0.795020i | \(0.707460\pi\) | |||||||
\(812\) | 40.0968i | 1.40712i | ||||||||
\(813\) | − 2.96911i | − 0.104131i | ||||||||
\(814\) | −17.6439 | −0.618417 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.390230 | 0.0136608 | ||||||||
\(817\) | − 3.24694i | − 0.113596i | ||||||||
\(818\) | − 4.28568i | − 0.149845i | ||||||||
\(819\) | −12.0211 | −0.420050 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.1349 | −0.737612 | −0.368806 | − | 0.929506i | \(-0.620233\pi\) | ||||
−0.368806 | + | 0.929506i | \(0.620233\pi\) | |||||||
\(822\) | 10.2400i | 0.357161i | ||||||||
\(823\) | − 3.17714i | − 0.110748i | −0.998466 | − | 0.0553740i | \(-0.982365\pi\) | ||||
0.998466 | − | 0.0553740i | \(-0.0176351\pi\) | |||||||
\(824\) | −27.9579 | −0.973960 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 74.6315 | 2.59676 | ||||||||
\(827\) | 9.74482i | 0.338860i | 0.985542 | + | 0.169430i | \(0.0541927\pi\) | ||||
−0.985542 | + | 0.169430i | \(0.945807\pi\) | |||||||
\(828\) | − 30.7849i | − 1.06985i | ||||||||
\(829\) | −23.4352 | −0.813938 | −0.406969 | − | 0.913442i | \(-0.633414\pi\) | ||||
−0.406969 | + | 0.913442i | \(0.633414\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.7160 | −0.406424 | ||||||||
\(832\) | 18.1859i | 0.630484i | ||||||||
\(833\) | − 4.12265i | − 0.142841i | ||||||||
\(834\) | −19.6471 | −0.680323 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.02107 | 0.208243 | ||||||||
\(837\) | 17.6604i | 0.610432i | ||||||||
\(838\) | − 33.1316i | − 1.14451i | ||||||||
\(839\) | −42.6819 | −1.47354 | −0.736771 | − | 0.676142i | \(-0.763650\pi\) | ||||
−0.736771 | + | 0.676142i | \(0.763650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2941 | −0.458416 | ||||||||
\(842\) | 35.6887i | 1.22992i | ||||||||
\(843\) | − 0.873305i | − 0.0300782i | ||||||||
\(844\) | 10.8103 | 0.372106 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 30.7533 | 1.05732 | ||||||||
\(847\) | − 21.2507i | − 0.730183i | ||||||||
\(848\) | 4.19841i | 0.144174i | ||||||||
\(849\) | 4.10371 | 0.140839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.7187 | −0.435993 | ||||||||
\(852\) | 19.7206i | 0.675617i | ||||||||
\(853\) | − 16.9610i | − 0.580733i | −0.956915 | − | 0.290367i | \(-0.906223\pi\) | ||||
0.956915 | − | 0.290367i | \(-0.0937773\pi\) | |||||||
\(854\) | −100.070 | −3.42431 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.3234 | 0.592102 | ||||||||
\(857\) | − 39.3176i | − 1.34306i | −0.740976 | − | 0.671531i | \(-0.765637\pi\) | ||||
0.740976 | − | 0.671531i | \(-0.234363\pi\) | |||||||
\(858\) | 3.13039i | 0.106870i | ||||||||
\(859\) | −0.707056 | −0.0241244 | −0.0120622 | − | 0.999927i | \(-0.503840\pi\) | ||||
−0.0120622 | + | 0.999927i | \(0.503840\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.64443 | −0.0901219 | ||||||||
\(862\) | 28.8759i | 0.983516i | ||||||||
\(863\) | − 0.909409i | − 0.0309567i | −0.999880 | − | 0.0154783i | \(-0.995073\pi\) | ||||
0.999880 | − | 0.0154783i | \(-0.00492710\pi\) | |||||||
\(864\) | −14.0826 | −0.479101 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −51.9474 | −1.76525 | ||||||||
\(867\) | − 6.42994i | − 0.218372i | ||||||||
\(868\) | 65.1571i | 2.21158i | ||||||||
\(869\) | 17.1435 | 0.581554 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2571 | 0.516968 | ||||||||
\(872\) | − 31.1246i | − 1.05401i | ||||||||
\(873\) | − 27.6283i | − 0.935075i | ||||||||
\(874\) | 6.94501 | 0.234918 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.423589 | 0.0143117 | ||||||||
\(877\) | 33.6613i | 1.13666i | 0.822800 | + | 0.568331i | \(0.192411\pi\) | ||||
−0.822800 | + | 0.568331i | \(0.807589\pi\) | |||||||
\(878\) | − 28.1213i | − 0.949050i | ||||||||
\(879\) | −2.98788 | −0.100779 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.9283 | −0.671402 | −0.335701 | − | 0.941969i | \(-0.608973\pi\) | ||||
−0.335701 | + | 0.941969i | \(0.608973\pi\) | |||||||
\(882\) | − 14.1991i | − 0.478109i | ||||||||
\(883\) | − 15.6081i | − 0.525255i | −0.964897 | − | 0.262627i | \(-0.915411\pi\) | ||||
0.964897 | − | 0.262627i | \(-0.0845890\pi\) | |||||||
\(884\) | 8.84833 | 0.297601 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −47.8254 | −1.60673 | ||||||||
\(887\) | 46.8968i | 1.57464i | 0.616544 | + | 0.787320i | \(0.288532\pi\) | ||||
−0.616544 | + | 0.787320i | \(0.711468\pi\) | |||||||
\(888\) | − 5.58363i | − 0.187374i | ||||||||
\(889\) | 34.4897 | 1.15675 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.0421 | 0.470429 | ||||||||
\(892\) | 95.6991i | 3.20424i | ||||||||
\(893\) | 4.33588i | 0.145095i | ||||||||
\(894\) | 6.92439 | 0.231586 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −58.1505 | −1.94267 | ||||||||
\(897\) | 2.25657i | 0.0753447i | ||||||||
\(898\) | 59.9347i | 2.00005i | ||||||||
\(899\) | 25.5220 | 0.851208 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.6811 | −0.589044 | ||||||||
\(902\) | − 8.47143i | − 0.282068i | ||||||||
\(903\) | 5.18219i | 0.172452i | ||||||||
\(904\) | −32.9682 | −1.09651 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.17576 | 0.171953 | ||||||||
\(907\) | 1.43447i | 0.0476308i | 0.999716 | + | 0.0238154i | \(0.00758139\pi\) | ||||
−0.999716 | + | 0.0238154i | \(0.992419\pi\) | |||||||
\(908\) | − 39.0619i | − 1.29632i | ||||||||
\(909\) | 25.9305 | 0.860061 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.81129 | −0.0931422 | −0.0465711 | − | 0.998915i | \(-0.514829\pi\) | ||||
−0.0465711 | + | 0.998915i | \(0.514829\pi\) | |||||||
\(912\) | 0.189492i | 0.00627471i | ||||||||
\(913\) | 25.2363i | 0.835201i | ||||||||
\(914\) | 19.6323 | 0.649379 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −54.6614 | −1.80606 | ||||||||
\(917\) | 24.2492i | 0.800780i | ||||||||
\(918\) | 11.7805i | 0.388814i | ||||||||
\(919\) | −0.992236 | −0.0327308 | −0.0163654 | − | 0.999866i | \(-0.505210\pi\) | ||||
−0.0163654 | + | 0.999866i | \(0.505210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.6136 | −0.448584 | ||||||||
\(922\) | 34.1428i | 1.12443i | ||||||||
\(923\) | 17.7828i | 0.585329i | ||||||||
\(924\) | −9.60977 | −0.316138 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −51.2477 | −1.68410 | ||||||||
\(927\) | − 25.2035i | − 0.827791i | ||||||||
\(928\) | 20.3516i | 0.668075i | ||||||||
\(929\) | −33.3227 | −1.09328 | −0.546642 | − | 0.837367i | \(-0.684094\pi\) | ||||
−0.546642 | + | 0.837367i | \(0.684094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00192 | 0.0656104 | ||||||||
\(932\) | 75.0355i | 2.45787i | ||||||||
\(933\) | 3.72157i | 0.121839i | ||||||||
\(934\) | 65.8175 | 2.15361 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.1869 | 0.398340 | ||||||||
\(937\) | 13.3675i | 0.436698i | 0.975871 | + | 0.218349i | \(0.0700671\pi\) | ||||
−0.975871 | + | 0.218349i | \(0.929933\pi\) | |||||||
\(938\) | 74.9439i | 2.44701i | ||||||||
\(939\) | −10.1673 | −0.331798 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.14982 | −0.0700820 | −0.0350410 | − | 0.999386i | \(-0.511156\pi\) | ||||
−0.0350410 | + | 0.999386i | \(0.511156\pi\) | |||||||
\(942\) | 1.61111i | 0.0524928i | ||||||||
\(943\) | − 6.10671i | − 0.198862i | ||||||||
\(944\) | −4.70236 | −0.153049 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.6012 | −0.539750 | ||||||||
\(947\) | 34.9183i | 1.13469i | 0.823479 | + | 0.567346i | \(0.192030\pi\) | ||||
−0.823479 | + | 0.567346i | \(0.807970\pi\) | |||||||
\(948\) | 13.5668i | 0.440629i | ||||||||
\(949\) | 0.381966 | 0.0123991 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.90903 | 0.0619046 | ||||||||
\(952\) | 17.3808i | 0.563315i | ||||||||
\(953\) | 8.27883i | 0.268178i | 0.990969 | + | 0.134089i | \(0.0428108\pi\) | ||||
−0.990969 | + | 0.134089i | \(0.957189\pi\) | |||||||
\(954\) | −60.8969 | −1.97161 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.1072 | −0.714998 | ||||||||
\(957\) | 3.76415i | 0.121678i | ||||||||
\(958\) | − 57.8633i | − 1.86948i | ||||||||
\(959\) | −28.3462 | −0.915347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.4732 | 0.337844 | ||||||||
\(962\) | − 12.5908i | − 0.405942i | ||||||||
\(963\) | 15.6167i | 0.503241i | ||||||||
\(964\) | −87.4048 | −2.81512 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.0844 | −0.356635 | ||||||||
\(967\) | 29.4871i | 0.948241i | 0.880460 | + | 0.474121i | \(0.157234\pi\) | ||||
−0.880460 | + | 0.474121i | \(0.842766\pi\) | |||||||
\(968\) | 21.5438i | 0.692443i | ||||||||
\(969\) | −0.798025 | −0.0256363 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.8666 | 0.701733 | 0.350867 | − | 0.936425i | \(-0.385887\pi\) | ||||
0.350867 | + | 0.936425i | \(0.385887\pi\) | |||||||
\(972\) | 38.5308i | 1.23588i | ||||||||
\(973\) | − 54.3868i | − 1.74356i | ||||||||
\(974\) | 3.38260 | 0.108385 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.30517 | 0.201823 | ||||||||
\(977\) | 13.8482i | 0.443043i | 0.975155 | + | 0.221521i | \(0.0711023\pi\) | ||||
−0.975155 | + | 0.221521i | \(0.928898\pi\) | |||||||
\(978\) | − 4.89086i | − 0.156392i | ||||||||
\(979\) | 9.53591 | 0.304769 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.0582 | 0.895828 | ||||||||
\(982\) | − 46.3440i | − 1.47890i | ||||||||
\(983\) | − 2.93538i | − 0.0936241i | −0.998904 | − | 0.0468120i | \(-0.985094\pi\) | ||||
0.998904 | − | 0.0468120i | \(-0.0149062\pi\) | |||||||
\(984\) | 2.68090 | 0.0854639 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17.0246 | 0.542175 | ||||||||
\(987\) | − 6.92017i | − 0.220271i | ||||||||
\(988\) | 4.29667i | 0.136695i | ||||||||
\(989\) | −11.9671 | −0.380531 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.6137 | 1.00424 | 0.502122 | − | 0.864797i | \(-0.332553\pi\) | ||||
0.502122 | + | 0.864797i | \(0.332553\pi\) | |||||||
\(992\) | 33.0713i | 1.05001i | ||||||||
\(993\) | − 5.52970i | − 0.175480i | ||||||||
\(994\) | −87.3502 | −2.77058 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −19.9712 | −0.632811 | ||||||||
\(997\) | − 12.0885i | − 0.382845i | −0.981508 | − | 0.191423i | \(-0.938690\pi\) | ||||
0.981508 | − | 0.191423i | \(-0.0613101\pi\) | |||||||
\(998\) | − 1.44329i | − 0.0456867i | ||||||||
\(999\) | 10.4762 | 0.331453 |
(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 | 625.2.b.c.624.8 | 8 | ||
5.2 | odd | 4 | 625.2.a.f.1.1 | 8 | |||
5.3 | odd | 4 | 625.2.a.f.1.8 | 8 | |||
5.4 | even | 2 | inner | 625.2.b.c.624.1 | 8 | ||
15.2 | even | 4 | 5625.2.a.x.1.8 | 8 | |||
15.8 | even | 4 | 5625.2.a.x.1.1 | 8 | |||
20.3 | even | 4 | 10000.2.a.bj.1.4 | 8 | |||
20.7 | even | 4 | 10000.2.a.bj.1.5 | 8 | |||
25.2 | odd | 20 | 625.2.d.o.501.1 | 16 | |||
25.3 | odd | 20 | 125.2.d.b.76.1 | 16 | |||
25.4 | even | 10 | 25.2.e.a.9.1 | ✓ | 8 | ||
25.6 | even | 5 | 25.2.e.a.14.1 | yes | 8 | ||
25.8 | odd | 20 | 125.2.d.b.51.1 | 16 | |||
25.9 | even | 10 | 625.2.e.a.499.2 | 8 | |||
25.11 | even | 5 | 625.2.e.a.124.2 | 8 | |||
25.12 | odd | 20 | 625.2.d.o.126.1 | 16 | |||
25.13 | odd | 20 | 625.2.d.o.126.4 | 16 | |||
25.14 | even | 10 | 625.2.e.i.124.1 | 8 | |||
25.16 | even | 5 | 625.2.e.i.499.1 | 8 | |||
25.17 | odd | 20 | 125.2.d.b.51.4 | 16 | |||
25.19 | even | 10 | 125.2.e.b.74.2 | 8 | |||
25.21 | even | 5 | 125.2.e.b.49.2 | 8 | |||
25.22 | odd | 20 | 125.2.d.b.76.4 | 16 | |||
25.23 | odd | 20 | 625.2.d.o.501.4 | 16 | |||
75.29 | odd | 10 | 225.2.m.a.109.2 | 8 | |||
75.56 | odd | 10 | 225.2.m.a.64.2 | 8 | |||
100.31 | odd | 10 | 400.2.y.c.289.1 | 8 | |||
100.79 | odd | 10 | 400.2.y.c.209.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.e.a.9.1 | ✓ | 8 | 25.4 | even | 10 | ||
25.2.e.a.14.1 | yes | 8 | 25.6 | even | 5 | ||
125.2.d.b.51.1 | 16 | 25.8 | odd | 20 | |||
125.2.d.b.51.4 | 16 | 25.17 | odd | 20 | |||
125.2.d.b.76.1 | 16 | 25.3 | odd | 20 | |||
125.2.d.b.76.4 | 16 | 25.22 | odd | 20 | |||
125.2.e.b.49.2 | 8 | 25.21 | even | 5 | |||
125.2.e.b.74.2 | 8 | 25.19 | even | 10 | |||
225.2.m.a.64.2 | 8 | 75.56 | odd | 10 | |||
225.2.m.a.109.2 | 8 | 75.29 | odd | 10 | |||
400.2.y.c.209.1 | 8 | 100.79 | odd | 10 | |||
400.2.y.c.289.1 | 8 | 100.31 | odd | 10 | |||
625.2.a.f.1.1 | 8 | 5.2 | odd | 4 | |||
625.2.a.f.1.8 | 8 | 5.3 | odd | 4 | |||
625.2.b.c.624.1 | 8 | 5.4 | even | 2 | inner | ||
625.2.b.c.624.8 | 8 | 1.1 | even | 1 | trivial | ||
625.2.d.o.126.1 | 16 | 25.12 | odd | 20 | |||
625.2.d.o.126.4 | 16 | 25.13 | odd | 20 | |||
625.2.d.o.501.1 | 16 | 25.2 | odd | 20 | |||
625.2.d.o.501.4 | 16 | 25.23 | odd | 20 | |||
625.2.e.a.124.2 | 8 | 25.11 | even | 5 | |||
625.2.e.a.499.2 | 8 | 25.9 | even | 10 | |||
625.2.e.i.124.1 | 8 | 25.14 | even | 10 | |||
625.2.e.i.499.1 | 8 | 25.16 | even | 5 | |||
5625.2.a.x.1.1 | 8 | 15.8 | even | 4 | |||
5625.2.a.x.1.8 | 8 | 15.2 | even | 4 | |||
10000.2.a.bj.1.4 | 8 | 20.3 | even | 4 | |||
10000.2.a.bj.1.5 | 8 | 20.7 | even | 4 |