Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(107,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.f (of order \(4\), degree \(2\), 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: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.593 |
Dual form | 1350.2.f.f.107.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.44949 | + | 1.44949i | −0.547856 | + | 0.547856i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) |
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.09638i | − | 0.330570i | −0.986246 | − | 0.165285i | \(-0.947146\pi\) | ||
0.986246 | − | 0.165285i | \(-0.0528544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.22474 | − | 4.22474i | −1.17173 | − | 1.17173i | −0.981796 | − | 0.189937i | \(-0.939172\pi\) |
−0.189937 | − | 0.981796i | \(-0.560828\pi\) | |||||||
\(14\) | 2.04989 | 0.547856 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.17121 | + | 4.17121i | 1.01167 | + | 1.01167i | 0.999931 | + | 0.0117355i | \(0.00373561\pi\) |
0.0117355 | + | 0.999931i | \(0.496264\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.44949i | 1.02078i | 0.859942 | + | 0.510391i | \(0.170499\pi\) | ||||
−0.859942 | + | 0.510391i | \(0.829501\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.775255 | + | 0.775255i | −0.165285 | + | 0.165285i | ||||
\(23\) | 4.48905 | − | 4.48905i | 0.936031 | − | 0.936031i | −0.0620428 | − | 0.998073i | \(-0.519762\pi\) |
0.998073 | + | 0.0620428i | \(0.0197615\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.97469i | 1.17173i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.44949 | − | 1.44949i | −0.273928 | − | 0.273928i | ||||
\(29\) | 3.14626 | 0.584247 | 0.292123 | − | 0.956381i | \(-0.405638\pi\) | ||||
0.292123 | + | 0.956381i | \(0.405638\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.44949 | −0.260336 | −0.130168 | − | 0.991492i | \(-0.541552\pi\) | ||||
−0.130168 | + | 0.991492i | \(0.541552\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.89898i | − | 1.01167i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 3.14626 | − | 3.14626i | 0.510391 | − | 0.510391i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.87832i | 0.761865i | 0.924603 | + | 0.380932i | \(0.124397\pi\) | ||||
−0.924603 | + | 0.380932i | \(0.875603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.22474 | + | 7.22474i | 1.10176 | + | 1.10176i | 0.994198 | + | 0.107565i | \(0.0343054\pi\) |
0.107565 | + | 0.994198i | \(0.465695\pi\) | |||||||
\(44\) | 1.09638 | 0.165285 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.34847 | −0.936031 | ||||||||
\(47\) | 7.31747 | + | 7.31747i | 1.06736 | + | 1.06736i | 0.997561 | + | 0.0698023i | \(0.0222368\pi\) |
0.0698023 | + | 0.997561i | \(0.477763\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.79796i | 0.399708i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.22474 | − | 4.22474i | 0.585867 | − | 0.585867i | ||||
\(53\) | −5.65685 | + | 5.65685i | −0.777029 | + | 0.777029i | −0.979324 | − | 0.202296i | \(-0.935160\pi\) |
0.202296 | + | 0.979324i | \(0.435160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.04989i | 0.273928i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.22474 | − | 2.22474i | −0.292123 | − | 0.292123i | ||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.44949 | −1.08185 | −0.540923 | − | 0.841072i | \(-0.681925\pi\) | ||||
−0.540923 | + | 0.841072i | \(0.681925\pi\) | |||||||
\(62\) | 1.02494 | + | 1.02494i | 0.130168 | + | 0.130168i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | + | 2.00000i | −0.244339 | + | 0.244339i | −0.818642 | − | 0.574304i | \(-0.805273\pi\) |
0.574304 | + | 0.818642i | \(0.305273\pi\) | |||||||
\(68\) | −4.17121 | + | 4.17121i | −0.505833 | + | 0.505833i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9993i | 1.66141i | 0.556714 | + | 0.830704i | \(0.312062\pi\) | ||||
−0.556714 | + | 0.830704i | \(0.687938\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.44949 | + | 4.44949i | 0.520773 | + | 0.520773i | 0.917805 | − | 0.397032i | \(-0.129960\pi\) |
−0.397032 | + | 0.917805i | \(0.629960\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.44949 | −0.510391 | ||||||||
\(77\) | 1.58919 | + | 1.58919i | 0.181105 | + | 0.181105i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.44949i | 0.613115i | 0.951852 | + | 0.306558i | \(0.0991773\pi\) | ||||
−0.951852 | + | 0.306558i | \(0.900823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.44949 | − | 3.44949i | 0.380932 | − | 0.380932i | ||||
\(83\) | 10.2173 | − | 10.2173i | 1.12150 | − | 1.12150i | 0.129981 | − | 0.991516i | \(-0.458508\pi\) |
0.991516 | − | 0.129981i | \(-0.0414918\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 10.2173i | − | 1.10176i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.775255 | − | 0.775255i | −0.0826425 | − | 0.0826425i | ||||
\(89\) | 17.4634 | 1.85111 | 0.925557 | − | 0.378609i | \(-0.123597\pi\) | ||||
0.925557 | + | 0.378609i | \(0.123597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2474 | 1.28388 | ||||||||
\(92\) | 4.48905 | + | 4.48905i | 0.468015 | + | 0.468015i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 10.3485i | − | 1.06736i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.44949 | + | 8.44949i | −0.857916 | + | 0.857916i | −0.991092 | − | 0.133177i | \(-0.957482\pi\) |
0.133177 | + | 0.991092i | \(0.457482\pi\) | |||||||
\(98\) | 1.97846 | − | 1.97846i | 0.199854 | − | 0.199854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.16744i | − | 0.812691i | −0.913719 | − | 0.406346i | \(-0.866803\pi\) | ||
0.913719 | − | 0.406346i | \(-0.133197\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.55051 | − | 1.55051i | −0.152776 | − | 0.152776i | 0.626580 | − | 0.779357i | \(-0.284454\pi\) |
−0.779357 | + | 0.626580i | \(0.784454\pi\) | |||||||
\(104\) | −5.97469 | −0.585867 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | 3.60697 | + | 3.60697i | 0.348699 | + | 0.348699i | 0.859625 | − | 0.510926i | \(-0.170697\pi\) |
−0.510926 | + | 0.859625i | \(0.670697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000i | 0.383131i | 0.981480 | + | 0.191565i | \(0.0613564\pi\) | ||||
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.44949 | − | 1.44949i | 0.136964 | − | 0.136964i | ||||
\(113\) | 5.72829 | − | 5.72829i | 0.538872 | − | 0.538872i | −0.384326 | − | 0.923198i | \(-0.625566\pi\) |
0.923198 | + | 0.384326i | \(0.125566\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.14626i | 0.292123i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000 | + | 2.00000i | 0.184115 | + | 0.184115i | ||||
\(119\) | −12.0922 | −1.10849 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.79796 | 0.890724 | ||||||||
\(122\) | 5.97469 | + | 5.97469i | 0.540923 | + | 0.540923i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 1.44949i | − | 0.130168i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.55051 | − | 4.55051i | 0.403792 | − | 0.403792i | −0.475775 | − | 0.879567i | \(-0.657832\pi\) |
0.879567 | + | 0.475775i | \(0.157832\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.29593i | 0.812189i | 0.913831 | + | 0.406095i | \(0.133110\pi\) | ||||
−0.913831 | + | 0.406095i | \(0.866890\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.44949 | − | 6.44949i | −0.559242 | − | 0.559242i | ||||
\(134\) | 2.82843 | 0.244339 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.89898 | 0.505833 | ||||||||
\(137\) | −15.4135 | − | 15.4135i | −1.31686 | − | 1.31686i | −0.916245 | − | 0.400617i | \(-0.868796\pi\) |
−0.400617 | − | 0.916245i | \(-0.631204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.24745i | − | 0.699539i | −0.936836 | − | 0.349770i | \(-0.886260\pi\) | ||
0.936836 | − | 0.349770i | \(-0.113740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.89898 | − | 9.89898i | 0.830704 | − | 0.830704i | ||||
\(143\) | −4.63191 | + | 4.63191i | −0.387340 | + | 0.387340i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 6.29253i | − | 0.520773i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.41761 | −0.361905 | −0.180952 | − | 0.983492i | \(-0.557918\pi\) | ||||
−0.180952 | + | 0.983492i | \(0.557918\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.1464 | 1.96501 | 0.982504 | − | 0.186240i | \(-0.0596303\pi\) | ||||
0.982504 | + | 0.186240i | \(0.0596303\pi\) | |||||||
\(152\) | 3.14626 | + | 3.14626i | 0.255196 | + | 0.255196i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 2.24745i | − | 0.181105i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.02270 | + | 8.02270i | −0.640281 | + | 0.640281i | −0.950625 | − | 0.310343i | \(-0.899556\pi\) |
0.310343 | + | 0.950625i | \(0.399556\pi\) | |||||||
\(158\) | 3.85337 | − | 3.85337i | 0.306558 | − | 0.306558i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.0137i | 1.02562i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.12372 | + | 4.12372i | 0.322995 | + | 0.322995i | 0.849915 | − | 0.526920i | \(-0.176653\pi\) |
−0.526920 | + | 0.849915i | \(0.676653\pi\) | |||||||
\(164\) | −4.87832 | −0.380932 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4495 | −1.12150 | ||||||||
\(167\) | −5.51399 | − | 5.51399i | −0.426685 | − | 0.426685i | 0.460812 | − | 0.887498i | \(-0.347558\pi\) |
−0.887498 | + | 0.460812i | \(0.847558\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.6969i | 1.74592i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.22474 | + | 7.22474i | −0.550882 | + | 0.550882i | ||||
\(173\) | −5.33902 | + | 5.33902i | −0.405918 | + | 0.405918i | −0.880312 | − | 0.474394i | \(-0.842667\pi\) |
0.474394 | + | 0.880312i | \(0.342667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.09638i | 0.0826425i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.3485 | − | 12.3485i | −0.925557 | − | 0.925557i | ||||
\(179\) | 7.84961 | 0.586707 | 0.293354 | − | 0.956004i | \(-0.405229\pi\) | ||||
0.293354 | + | 0.956004i | \(0.405229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.24745 | −0.315710 | −0.157855 | − | 0.987462i | \(-0.550458\pi\) | ||||
−0.157855 | + | 0.987462i | \(0.550458\pi\) | |||||||
\(182\) | −8.66025 | − | 8.66025i | −0.641941 | − | 0.641941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 6.34847i | − | 0.468015i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.57321 | − | 4.57321i | 0.334427 | − | 0.334427i | ||||
\(188\) | −7.31747 | + | 7.31747i | −0.533682 | + | 0.533682i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.0492i | − | 1.16128i | −0.814162 | − | 0.580638i | \(-0.802803\pi\) | ||
0.814162 | − | 0.580638i | \(-0.197197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.79796 | + | 6.79796i | 0.489328 | + | 0.489328i | 0.908094 | − | 0.418766i | \(-0.137537\pi\) |
−0.418766 | + | 0.908094i | \(0.637537\pi\) | |||||||
\(194\) | 11.9494 | 0.857916 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.79796 | −0.199854 | ||||||||
\(197\) | 6.75323 | + | 6.75323i | 0.481148 | + | 0.481148i | 0.905498 | − | 0.424350i | \(-0.139497\pi\) |
−0.424350 | + | 0.905498i | \(0.639497\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.5505i | − | 0.889682i | −0.895610 | − | 0.444841i | \(-0.853260\pi\) | ||
0.895610 | − | 0.444841i | \(-0.146740\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.77526 | + | 5.77526i | −0.406346 | + | 0.406346i | ||||
\(203\) | −4.56048 | + | 4.56048i | −0.320083 | + | 0.320083i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.19275i | 0.152776i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.22474 | + | 4.22474i | 0.292933 | + | 0.292933i | ||||
\(209\) | 4.87832 | 0.337440 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.24745 | 0.567778 | 0.283889 | − | 0.958857i | \(-0.408375\pi\) | ||||
0.283889 | + | 0.958857i | \(0.408375\pi\) | |||||||
\(212\) | −5.65685 | − | 5.65685i | −0.388514 | − | 0.388514i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 5.10102i | − | 0.348699i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.10102 | − | 2.10102i | 0.142627 | − | 0.142627i | ||||
\(218\) | 2.82843 | − | 2.82843i | 0.191565 | − | 0.191565i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 35.2446i | − | 2.37081i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7980 | + | 12.7980i | 0.857015 | + | 0.857015i | 0.990985 | − | 0.133971i | \(-0.0427728\pi\) |
−0.133971 | + | 0.990985i | \(0.542773\pi\) | |||||||
\(224\) | −2.04989 | −0.136964 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.10102 | −0.538872 | ||||||||
\(227\) | −5.33902 | − | 5.33902i | −0.354363 | − | 0.354363i | 0.507367 | − | 0.861730i | \(-0.330619\pi\) |
−0.861730 | + | 0.507367i | \(0.830619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.65153i | − | 0.307382i | −0.988119 | − | 0.153691i | \(-0.950884\pi\) | ||
0.988119 | − | 0.153691i | \(-0.0491160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.22474 | − | 2.22474i | 0.146062 | − | 0.146062i | ||||
\(233\) | −3.46410 | + | 3.46410i | −0.226941 | + | 0.226941i | −0.811413 | − | 0.584473i | \(-0.801301\pi\) |
0.584473 | + | 0.811413i | \(0.301301\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 2.82843i | − | 0.184115i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.55051 | + | 8.55051i | 0.554247 | + | 0.554247i | ||||
\(239\) | 6.14966 | 0.397789 | 0.198894 | − | 0.980021i | \(-0.436265\pi\) | ||||
0.198894 | + | 0.980021i | \(0.436265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6969 | −1.26879 | −0.634396 | − | 0.773008i | \(-0.718751\pi\) | ||||
−0.634396 | + | 0.773008i | \(0.718751\pi\) | |||||||
\(242\) | −6.92820 | − | 6.92820i | −0.445362 | − | 0.445362i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.44949i | − | 0.540923i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.7980 | − | 18.7980i | 1.19609 | − | 1.19609i | ||||
\(248\) | −1.02494 | + | 1.02494i | −0.0650840 | + | 0.0650840i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.73205i | − | 0.109326i | −0.998505 | − | 0.0546630i | \(-0.982592\pi\) | ||
0.998505 | − | 0.0546630i | \(-0.0174085\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.92168 | − | 4.92168i | −0.309424 | − | 0.309424i | ||||
\(254\) | −6.43539 | −0.403792 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.61413 | − | 2.61413i | −0.163065 | − | 0.163065i | 0.620858 | − | 0.783923i | \(-0.286784\pi\) |
−0.783923 | + | 0.620858i | \(0.786784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.57321 | − | 6.57321i | 0.406095 | − | 0.406095i | ||||
\(263\) | 0.921404 | − | 0.921404i | 0.0568162 | − | 0.0568162i | −0.678128 | − | 0.734944i | \(-0.737208\pi\) |
0.734944 | + | 0.678128i | \(0.237208\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.12096i | 0.559242i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.00000 | − | 2.00000i | −0.122169 | − | 0.122169i | ||||
\(269\) | −24.5665 | −1.49785 | −0.748924 | − | 0.662655i | \(-0.769429\pi\) | ||||
−0.748924 | + | 0.662655i | \(0.769429\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.00000 | −0.364474 | −0.182237 | − | 0.983255i | \(-0.558334\pi\) | ||||
−0.182237 | + | 0.983255i | \(0.558334\pi\) | |||||||
\(272\) | −4.17121 | − | 4.17121i | −0.252917 | − | 0.252917i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.7980i | 1.31686i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.55051 | + | 9.55051i | −0.573835 | + | 0.573835i | −0.933198 | − | 0.359363i | \(-0.882994\pi\) |
0.359363 | + | 0.933198i | \(0.382994\pi\) | |||||||
\(278\) | −5.83183 | + | 5.83183i | −0.349770 | + | 0.349770i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.83523i | 0.527065i | 0.964650 | + | 0.263533i | \(0.0848877\pi\) | ||||
−0.964650 | + | 0.263533i | \(0.915112\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.898979 | − | 0.898979i | −0.0534388 | − | 0.0534388i | 0.679882 | − | 0.733321i | \(-0.262031\pi\) |
−0.733321 | + | 0.679882i | \(0.762031\pi\) | |||||||
\(284\) | −13.9993 | −0.830704 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.55051 | 0.387340 | ||||||||
\(287\) | −7.07107 | − | 7.07107i | −0.417392 | − | 0.417392i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.7980i | 1.04694i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.44949 | + | 4.44949i | −0.260387 | + | 0.260387i | ||||
\(293\) | −4.24264 | + | 4.24264i | −0.247858 | + | 0.247858i | −0.820091 | − | 0.572233i | \(-0.806077\pi\) |
0.572233 | + | 0.820091i | \(0.306077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.12372 | + | 3.12372i | 0.180952 | + | 0.180952i | ||||
\(299\) | −37.9301 | −2.19356 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.9444 | −1.20721 | ||||||||
\(302\) | −17.0741 | − | 17.0741i | −0.982504 | − | 0.982504i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.44949i | − | 0.255196i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.6742 | + | 21.6742i | −1.23701 | + | 1.23701i | −0.275798 | + | 0.961216i | \(0.588942\pi\) |
−0.961216 | + | 0.275798i | \(0.911058\pi\) | |||||||
\(308\) | −1.58919 | + | 1.58919i | −0.0905523 | + | 0.0905523i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 32.2412i | − | 1.82823i | −0.405455 | − | 0.914115i | \(-0.632887\pi\) | ||
0.405455 | − | 0.914115i | \(-0.367113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.24745 | − | 3.24745i | −0.183557 | − | 0.183557i | 0.609347 | − | 0.792904i | \(-0.291432\pi\) |
−0.792904 | + | 0.609347i | \(0.791432\pi\) | |||||||
\(314\) | 11.3458 | 0.640281 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.44949 | −0.306558 | ||||||||
\(317\) | 1.55708 | + | 1.55708i | 0.0874542 | + | 0.0874542i | 0.749481 | − | 0.662026i | \(-0.230303\pi\) |
−0.662026 | + | 0.749481i | \(0.730303\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.44949i | − | 0.193134i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.20204 | − | 9.20204i | 0.512810 | − | 0.512810i | ||||
\(323\) | −18.5597 | + | 18.5597i | −1.03269 | + | 1.03269i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 5.83183i | − | 0.322995i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.44949 | + | 3.44949i | 0.190466 | + | 0.190466i | ||||
\(329\) | −21.2132 | −1.16952 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.1010 | −1.15982 | −0.579908 | − | 0.814682i | \(-0.696912\pi\) | ||||
−0.579908 | + | 0.814682i | \(0.696912\pi\) | |||||||
\(332\) | 10.2173 | + | 10.2173i | 0.560749 | + | 0.560749i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.79796i | 0.426685i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.10102 | − | 7.10102i | 0.386817 | − | 0.386817i | −0.486733 | − | 0.873551i | \(-0.661812\pi\) |
0.873551 | + | 0.486733i | \(0.161812\pi\) | |||||||
\(338\) | 16.0492 | − | 16.0492i | 0.872959 | − | 0.872959i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.58919i | 0.0860593i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2020 | − | 14.2020i | −0.766838 | − | 0.766838i | ||||
\(344\) | 10.2173 | 0.550882 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.55051 | 0.405918 | ||||||||
\(347\) | −10.0745 | − | 10.0745i | −0.540826 | − | 0.540826i | 0.382945 | − | 0.923771i | \(-0.374910\pi\) |
−0.923771 | + | 0.382945i | \(0.874910\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.0454i | − | 1.07301i | −0.843898 | − | 0.536503i | \(-0.819745\pi\) | ||
0.843898 | − | 0.536503i | \(-0.180255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.775255 | − | 0.775255i | 0.0413212 | − | 0.0413212i | ||||
\(353\) | −1.34278 | + | 1.34278i | −0.0714690 | + | 0.0714690i | −0.741938 | − | 0.670469i | \(-0.766093\pi\) |
0.670469 | + | 0.741938i | \(0.266093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 17.4634i | 0.925557i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.55051 | − | 5.55051i | −0.293354 | − | 0.293354i | ||||
\(359\) | 24.0416 | 1.26887 | 0.634434 | − | 0.772977i | \(-0.281233\pi\) | ||||
0.634434 | + | 0.772977i | \(0.281233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.797959 | −0.0419978 | ||||||||
\(362\) | 3.00340 | + | 3.00340i | 0.157855 | + | 0.157855i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.2474i | 0.641941i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.2474 | + | 20.2474i | −1.05691 | + | 1.05691i | −0.0586283 | + | 0.998280i | \(0.518673\pi\) |
−0.998280 | + | 0.0586283i | \(0.981327\pi\) | |||||||
\(368\) | −4.48905 | + | 4.48905i | −0.234008 | + | 0.234008i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 16.3991i | − | 0.851399i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.3712 | − | 19.3712i | −1.00300 | − | 1.00300i | −0.999995 | − | 0.00300584i | \(-0.999043\pi\) |
−0.00300584 | − | 0.999995i | \(-0.500957\pi\) | |||||||
\(374\) | −6.46750 | −0.334427 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3485 | 0.533682 | ||||||||
\(377\) | −13.2922 | − | 13.2922i | −0.684581 | − | 0.684581i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.00000i | − | 0.205466i | −0.994709 | − | 0.102733i | \(-0.967241\pi\) | ||
0.994709 | − | 0.102733i | \(-0.0327588\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.3485 | + | 11.3485i | −0.580638 | + | 0.580638i | ||||
\(383\) | −14.2457 | + | 14.2457i | −0.727920 | + | 0.727920i | −0.970205 | − | 0.242285i | \(-0.922103\pi\) |
0.242285 | + | 0.970205i | \(0.422103\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 9.61377i | − | 0.489328i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.44949 | − | 8.44949i | −0.428958 | − | 0.428958i | ||||
\(389\) | 9.43879 | 0.478566 | 0.239283 | − | 0.970950i | \(-0.423088\pi\) | ||||
0.239283 | + | 0.970950i | \(0.423088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.4495 | 1.89390 | ||||||||
\(392\) | 1.97846 | + | 1.97846i | 0.0999271 | + | 0.0999271i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 9.55051i | − | 0.481148i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.5732 | − | 19.5732i | 0.982351 | − | 0.982351i | −0.0174955 | − | 0.999847i | \(-0.505569\pi\) |
0.999847 | + | 0.0174955i | \(0.00556927\pi\) | |||||||
\(398\) | −8.87455 | + | 8.87455i | −0.444841 | + | 0.444841i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0424i | 0.501492i | 0.968053 | + | 0.250746i | \(0.0806758\pi\) | ||||
−0.968053 | + | 0.250746i | \(0.919324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.12372 | + | 6.12372i | 0.305044 | + | 0.305044i | ||||
\(404\) | 8.16744 | 0.406346 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.44949 | 0.320083 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.7980i | 1.52286i | 0.648247 | + | 0.761431i | \(0.275503\pi\) | ||||
−0.648247 | + | 0.761431i | \(0.724497\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.55051 | − | 1.55051i | 0.0763882 | − | 0.0763882i | ||||
\(413\) | 4.09978 | − | 4.09978i | 0.201737 | − | 0.201737i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 5.97469i | − | 0.292933i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.44949 | − | 3.44949i | −0.168720 | − | 0.168720i | ||||
\(419\) | 34.1161 | 1.66668 | 0.833340 | − | 0.552760i | \(-0.186426\pi\) | ||||
0.833340 | + | 0.552760i | \(0.186426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5505 | −0.660411 | −0.330206 | − | 0.943909i | \(-0.607118\pi\) | ||||
−0.330206 | + | 0.943909i | \(0.607118\pi\) | |||||||
\(422\) | −5.83183 | − | 5.83183i | −0.283889 | − | 0.283889i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.00000i | 0.388514i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.2474 | − | 12.2474i | 0.592696 | − | 0.592696i | ||||
\(428\) | −3.60697 | + | 3.60697i | −0.174349 | + | 0.174349i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.6274i | 1.08992i | 0.838461 | + | 0.544962i | \(0.183456\pi\) | ||||
−0.838461 | + | 0.544962i | \(0.816544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2474 | − | 14.2474i | −0.684689 | − | 0.684689i | 0.276364 | − | 0.961053i | \(-0.410870\pi\) |
−0.961053 | + | 0.276364i | \(0.910870\pi\) | |||||||
\(434\) | −2.97129 | −0.142627 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | 19.9740 | + | 19.9740i | 0.955484 | + | 0.955484i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.59592i | − | 0.171624i | −0.996311 | − | 0.0858119i | \(-0.972652\pi\) | ||
0.996311 | − | 0.0858119i | \(-0.0273484\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.9217 | + | 24.9217i | −1.18540 | + | 1.18540i | ||||
\(443\) | 4.41761 | − | 4.41761i | 0.209887 | − | 0.209887i | −0.594332 | − | 0.804220i | \(-0.702584\pi\) |
0.804220 | + | 0.594332i | \(0.202584\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 18.0990i | − | 0.857015i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.44949 | + | 1.44949i | 0.0684820 | + | 0.0684820i | ||||
\(449\) | −15.5563 | −0.734150 | −0.367075 | − | 0.930191i | \(-0.619641\pi\) | ||||
−0.367075 | + | 0.930191i | \(0.619641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.34847 | 0.251850 | ||||||||
\(452\) | 5.72829 | + | 5.72829i | 0.269436 | + | 0.269436i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.55051i | 0.354363i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.6969 | + | 14.6969i | −0.687494 | + | 0.687494i | −0.961677 | − | 0.274184i | \(-0.911592\pi\) |
0.274184 | + | 0.961677i | \(0.411592\pi\) | |||||||
\(458\) | −3.28913 | + | 3.28913i | −0.153691 | + | 0.153691i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.82843i | − | 0.131733i | −0.997828 | − | 0.0658665i | \(-0.979019\pi\) | ||
0.997828 | − | 0.0658665i | \(-0.0209811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3485 | + | 11.3485i | 0.527408 | + | 0.527408i | 0.919799 | − | 0.392391i | \(-0.128352\pi\) |
−0.392391 | + | 0.919799i | \(0.628352\pi\) | |||||||
\(464\) | −3.14626 | −0.146062 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.89898 | 0.226941 | ||||||||
\(467\) | −6.61037 | − | 6.61037i | −0.305891 | − | 0.305891i | 0.537422 | − | 0.843313i | \(-0.319398\pi\) |
−0.843313 | + | 0.537422i | \(0.819398\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.79796i | − | 0.267725i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00000 | + | 2.00000i | −0.0920575 | + | 0.0920575i | ||||
\(473\) | 7.92104 | − | 7.92104i | 0.364210 | − | 0.364210i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 12.0922i | − | 0.554247i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.34847 | − | 4.34847i | −0.198894 | − | 0.198894i | ||||
\(479\) | 18.3848 | 0.840022 | 0.420011 | − | 0.907519i | \(-0.362026\pi\) | ||||
0.420011 | + | 0.907519i | \(0.362026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 13.9278 | + | 13.9278i | 0.634396 | + | 0.634396i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.79796i | 0.445362i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.6969 | − | 14.6969i | 0.665982 | − | 0.665982i | −0.290802 | − | 0.956783i | \(-0.593922\pi\) |
0.956783 | + | 0.290802i | \(0.0939219\pi\) | |||||||
\(488\) | −5.97469 | + | 5.97469i | −0.270462 | + | 0.270462i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.1701i | 1.13591i | 0.823059 | + | 0.567956i | \(0.192266\pi\) | ||||
−0.823059 | + | 0.567956i | \(0.807734\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.1237 | + | 13.1237i | 0.591063 | + | 0.591063i | ||||
\(494\) | −26.5843 | −1.19609 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.44949 | 0.0650840 | ||||||||
\(497\) | −20.2918 | − | 20.2918i | −0.910212 | − | 0.910212i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 5.79796i | − | 0.259552i | −0.991543 | − | 0.129776i | \(-0.958574\pi\) | ||
0.991543 | − | 0.129776i | \(-0.0414259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.22474 | + | 1.22474i | −0.0546630 | + | 0.0546630i | ||||
\(503\) | 26.1951 | − | 26.1951i | 1.16798 | − | 1.16798i | 0.185297 | − | 0.982682i | \(-0.440675\pi\) |
0.982682 | − | 0.185297i | \(-0.0593249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.96031i | 0.309424i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.55051 | + | 4.55051i | 0.201896 | + | 0.201896i | ||||
\(509\) | −18.8455 | −0.835311 | −0.417656 | − | 0.908605i | \(-0.637148\pi\) | ||||
−0.417656 | + | 0.908605i | \(0.637148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.8990 | −0.570617 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.69694i | 0.163065i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.02270 | − | 8.02270i | 0.352838 | − | 0.352838i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.59259i | 0.201205i | 0.994927 | + | 0.100602i | \(0.0320770\pi\) | ||||
−0.994927 | + | 0.100602i | \(0.967923\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.77526 | − | 4.77526i | −0.208807 | − | 0.208807i | 0.594953 | − | 0.803760i | \(-0.297171\pi\) |
−0.803760 | + | 0.594953i | \(0.797171\pi\) | |||||||
\(524\) | −9.29593 | −0.406095 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.30306 | −0.0568162 | ||||||||
\(527\) | −6.04612 | − | 6.04612i | −0.263373 | − | 0.263373i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 17.3031i | − | 0.752307i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.44949 | − | 6.44949i | 0.279621 | − | 0.279621i | ||||
\(533\) | 20.6096 | − | 20.6096i | 0.892702 | − | 0.892702i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.82843i | 0.122169i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.3712 | + | 17.3712i | 0.748924 | + | 0.748924i | ||||
\(539\) | 3.06762 | 0.132132 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.59592 | −0.412561 | −0.206280 | − | 0.978493i | \(-0.566136\pi\) | ||||
−0.206280 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(542\) | 4.24264 | + | 4.24264i | 0.182237 | + | 0.182237i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.89898i | 0.252917i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.4722 | − | 13.4722i | 0.576029 | − | 0.576029i | −0.357777 | − | 0.933807i | \(-0.616465\pi\) |
0.933807 | + | 0.357777i | \(0.116465\pi\) | |||||||
\(548\) | 15.4135 | − | 15.4135i | 0.658431 | − | 0.658431i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.9993i | 0.596389i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.89898 | − | 7.89898i | −0.335899 | − | 0.335899i | ||||
\(554\) | 13.5065 | 0.573835 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.24745 | 0.349770 | ||||||||
\(557\) | 12.1244 | + | 12.1244i | 0.513725 | + | 0.513725i | 0.915666 | − | 0.401940i | \(-0.131664\pi\) |
−0.401940 | + | 0.915666i | \(0.631664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 61.0454i | − | 2.58195i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.24745 | − | 6.24745i | 0.263533 | − | 0.263533i | ||||
\(563\) | −13.6814 | + | 13.6814i | −0.576604 | + | 0.576604i | −0.933966 | − | 0.357362i | \(-0.883676\pi\) |
0.357362 | + | 0.933966i | \(0.383676\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.27135i | 0.0534388i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.89898 | + | 9.89898i | 0.415352 | + | 0.415352i | ||||
\(569\) | 22.0560 | 0.924634 | 0.462317 | − | 0.886715i | \(-0.347018\pi\) | ||||
0.462317 | + | 0.886715i | \(0.347018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.55051 | −0.0648868 | −0.0324434 | − | 0.999474i | \(-0.510329\pi\) | ||||
−0.0324434 | + | 0.999474i | \(0.510329\pi\) | |||||||
\(572\) | −4.63191 | − | 4.63191i | −0.193670 | − | 0.193670i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.0000i | 0.417392i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.00000 | + | 4.00000i | −0.166522 | + | 0.166522i | −0.785449 | − | 0.618927i | \(-0.787568\pi\) |
0.618927 | + | 0.785449i | \(0.287568\pi\) | |||||||
\(578\) | 12.5851 | − | 12.5851i | 0.523469 | − | 0.523469i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.6198i | 1.22884i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.20204 | + | 6.20204i | 0.256862 | + | 0.256862i | ||||
\(584\) | 6.29253 | 0.260387 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | 24.0737 | + | 24.0737i | 0.993630 | + | 0.993630i | 0.999980 | − | 0.00635031i | \(-0.00202138\pi\) |
−0.00635031 | + | 0.999980i | \(0.502021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6.44949i | − | 0.265747i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.9702 | − | 23.9702i | 0.984338 | − | 0.984338i | −0.0155412 | − | 0.999879i | \(-0.504947\pi\) |
0.999879 | + | 0.0155412i | \(0.00494711\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 4.41761i | − | 0.180952i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.8207 | + | 26.8207i | 1.09678 | + | 1.09678i | ||||
\(599\) | −18.5919 | −0.759643 | −0.379821 | − | 0.925060i | \(-0.624015\pi\) | ||||
−0.379821 | + | 0.925060i | \(0.624015\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.3939 | −0.750302 | −0.375151 | − | 0.926964i | \(-0.622409\pi\) | ||||
−0.375151 | + | 0.926964i | \(0.622409\pi\) | |||||||
\(602\) | 14.8099 | + | 14.8099i | 0.603607 | + | 0.603607i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.1464i | 0.982504i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.6515 | − | 16.6515i | 0.675865 | − | 0.675865i | −0.283197 | − | 0.959062i | \(-0.591395\pi\) |
0.959062 | + | 0.283197i | \(0.0913950\pi\) | |||||||
\(608\) | −3.14626 | + | 3.14626i | −0.127598 | + | 0.127598i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 61.8289i | − | 2.50133i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.4722 | + | 10.4722i | 0.422968 | + | 0.422968i | 0.886224 | − | 0.463256i | \(-0.153319\pi\) |
−0.463256 | + | 0.886224i | \(0.653319\pi\) | |||||||
\(614\) | 30.6520 | 1.23701 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.24745 | 0.0905523 | ||||||||
\(617\) | −3.67840 | − | 3.67840i | −0.148087 | − | 0.148087i | 0.629176 | − | 0.777263i | \(-0.283392\pi\) |
−0.777263 | + | 0.629176i | \(0.783392\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.69694i | − | 0.349559i | −0.984608 | − | 0.174780i | \(-0.944079\pi\) | ||
0.984608 | − | 0.174780i | \(-0.0559213\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.7980 | + | 22.7980i | −0.914115 | + | 0.914115i | ||||
\(623\) | −25.3130 | + | 25.3130i | −1.01414 | + | 1.01414i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.59259i | 0.183557i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.02270 | − | 8.02270i | −0.320141 | − | 0.320141i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.49490 | 0.178939 | 0.0894695 | − | 0.995990i | \(-0.471483\pi\) | ||||
0.0894695 | + | 0.995990i | \(0.471483\pi\) | |||||||
\(632\) | 3.85337 | + | 3.85337i | 0.153279 | + | 0.153279i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 2.20204i | − | 0.0874542i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.8207 | − | 11.8207i | 0.468352 | − | 0.468352i | ||||
\(638\) | −2.43916 | + | 2.43916i | −0.0965672 | + | 0.0965672i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.8557i | 1.10023i | 0.835088 | + | 0.550117i | \(0.185417\pi\) | ||||
−0.835088 | + | 0.550117i | \(0.814583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.8207 | + | 32.8207i | 1.29432 | + | 1.29432i | 0.932088 | + | 0.362233i | \(0.117986\pi\) |
0.362233 | + | 0.932088i | \(0.382014\pi\) | |||||||
\(644\) | −13.0137 | −0.512810 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.2474 | 1.03269 | ||||||||
\(647\) | 6.00680 | + | 6.00680i | 0.236152 | + | 0.236152i | 0.815254 | − | 0.579103i | \(-0.196597\pi\) |
−0.579103 | + | 0.815254i | \(0.696597\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.10102i | 0.121726i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.12372 | + | 4.12372i | −0.161498 | + | 0.161498i | ||||
\(653\) | 10.5673 | − | 10.5673i | 0.413530 | − | 0.413530i | −0.469437 | − | 0.882966i | \(-0.655543\pi\) |
0.882966 | + | 0.469437i | \(0.155543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 4.87832i | − | 0.190466i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.0000 | + | 15.0000i | 0.584761 | + | 0.584761i | ||||
\(659\) | 32.0983 | 1.25037 | 0.625186 | − | 0.780475i | \(-0.285023\pi\) | ||||
0.625186 | + | 0.780475i | \(0.285023\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0454 | −0.779676 | −0.389838 | − | 0.920883i | \(-0.627469\pi\) | ||||
−0.389838 | + | 0.920883i | \(0.627469\pi\) | |||||||
\(662\) | 14.9207 | + | 14.9207i | 0.579908 | + | 0.579908i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.4495i | − | 0.560749i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.1237 | − | 14.1237i | 0.546873 | − | 0.546873i | ||||
\(668\) | 5.51399 | − | 5.51399i | 0.213343 | − | 0.213343i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.26382i | 0.357626i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.7980 | − | 34.7980i | −1.34136 | − | 1.34136i | −0.894705 | − | 0.446658i | \(-0.852614\pi\) |
−0.446658 | − | 0.894705i | \(-0.647386\pi\) | |||||||
\(674\) | −10.0424 | −0.386817 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.6969 | −0.872959 | ||||||||
\(677\) | 33.6554 | + | 33.6554i | 1.29348 | + | 1.29348i | 0.932619 | + | 0.360863i | \(0.117518\pi\) |
0.360863 | + | 0.932619i | \(0.382482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 24.4949i | − | 0.940028i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.12372 | − | 1.12372i | 0.0430296 | − | 0.0430296i | ||||
\(683\) | −6.92820 | + | 6.92820i | −0.265100 | + | 0.265100i | −0.827122 | − | 0.562022i | \(-0.810024\pi\) |
0.562022 | + | 0.827122i | \(0.310024\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.0847i | 0.766838i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.22474 | − | 7.22474i | −0.275441 | − | 0.275441i | ||||
\(689\) | 47.7975 | 1.82094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.8990 | 0.871118 | 0.435559 | − | 0.900160i | \(-0.356551\pi\) | ||||
0.435559 | + | 0.900160i | \(0.356551\pi\) | |||||||
\(692\) | −5.33902 | − | 5.33902i | −0.202959 | − | 0.202959i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2474i | 0.540826i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.3485 | + | 20.3485i | −0.770753 | + | 0.770753i | ||||
\(698\) | −14.1742 | + | 14.1742i | −0.536503 | + | 0.536503i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.8243i | − | 0.522137i | −0.965320 | − | 0.261068i | \(-0.915925\pi\) | ||
0.965320 | − | 0.261068i | \(-0.0840748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.09638 | −0.0413212 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.89898 | 0.0714690 | ||||||||
\(707\) | 11.8386 | + | 11.8386i | 0.445237 | + | 0.445237i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00000i | 0.300446i | 0.988652 | + | 0.150223i | \(0.0479992\pi\) | ||||
−0.988652 | + | 0.150223i | \(0.952001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.3485 | − | 12.3485i | 0.462778 | − | 0.462778i | ||||
\(713\) | −6.50683 | + | 6.50683i | −0.243683 | + | 0.243683i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.84961i | 0.293354i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.0000 | − | 17.0000i | −0.634434 | − | 0.634434i | ||||
\(719\) | −29.7627 | −1.10996 | −0.554981 | − | 0.831863i | \(-0.687274\pi\) | ||||
−0.554981 | + | 0.831863i | \(0.687274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.49490 | 0.167399 | ||||||||
\(722\) | 0.564242 | + | 0.564242i | 0.0209989 | + | 0.0209989i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 4.24745i | − | 0.157855i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.4949 | − | 24.4949i | 0.908465 | − | 0.908465i | −0.0876830 | − | 0.996148i | \(-0.527946\pi\) |
0.996148 | + | 0.0876830i | \(0.0279462\pi\) | |||||||
\(728\) | 8.66025 | − | 8.66025i | 0.320970 | − | 0.320970i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 60.2718i | 2.22923i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.5959 | − | 23.5959i | −0.871535 | − | 0.871535i | 0.121105 | − | 0.992640i | \(-0.461356\pi\) |
−0.992640 | + | 0.121105i | \(0.961356\pi\) | |||||||
\(734\) | 28.6342 | 1.05691 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.34847 | 0.234008 | ||||||||
\(737\) | 2.19275 | + | 2.19275i | 0.0807711 | + | 0.0807711i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 9.84337i | − | 0.362094i | −0.983474 | − | 0.181047i | \(-0.942051\pi\) | ||
0.983474 | − | 0.181047i | \(-0.0579486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.5959 | + | 11.5959i | −0.425700 | + | 0.425700i | ||||
\(743\) | 19.7597 | − | 19.7597i | 0.724912 | − | 0.724912i | −0.244690 | − | 0.969601i | \(-0.578686\pi\) |
0.969601 | + | 0.244690i | \(0.0786861\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 27.3950i | 1.00300i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.57321 | + | 4.57321i | 0.167213 | + | 0.167213i | ||||
\(749\) | −10.4565 | −0.382073 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0454 | 0.913920 | 0.456960 | − | 0.889487i | \(-0.348938\pi\) | ||||
0.456960 | + | 0.889487i | \(0.348938\pi\) | |||||||
\(752\) | −7.31747 | − | 7.31747i | −0.266841 | − | 0.266841i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.7980i | 0.684581i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.02270 | + | 2.02270i | −0.0735164 | + | 0.0735164i | −0.742909 | − | 0.669393i | \(-0.766554\pi\) |
0.669393 | + | 0.742909i | \(0.266554\pi\) | |||||||
\(758\) | −2.82843 | + | 2.82843i | −0.102733 | + | 0.102733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.52837i | 0.164153i | 0.996626 | + | 0.0820766i | \(0.0261552\pi\) | ||||
−0.996626 | + | 0.0820766i | \(0.973845\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.79796 | − | 5.79796i | −0.209900 | − | 0.209900i | ||||
\(764\) | 16.0492 | 0.580638 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.1464 | 0.727920 | ||||||||
\(767\) | 11.9494 | + | 11.9494i | 0.431467 | + | 0.431467i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.6969i | − | 1.14302i | −0.820595 | − | 0.571510i | \(-0.806358\pi\) | ||
0.820595 | − | 0.571510i | \(-0.193642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.79796 | + | 6.79796i | −0.244664 | + | 0.244664i | ||||
\(773\) | −1.12848 | + | 1.12848i | −0.0405888 | + | 0.0405888i | −0.727110 | − | 0.686521i | \(-0.759137\pi\) |
0.686521 | + | 0.727110i | \(0.259137\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.9494i | 0.428958i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.67423 | − | 6.67423i | −0.239283 | − | 0.239283i | ||||
\(779\) | −21.7060 | −0.777699 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.3485 | 0.549211 | ||||||||
\(782\) | −26.4808 | − | 26.4808i | −0.946951 | − | 0.946951i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 2.79796i | − | 0.0999271i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.5732 | + | 12.5732i | −0.448187 | + | 0.448187i | −0.894751 | − | 0.446565i | \(-0.852647\pi\) |
0.446565 | + | 0.894751i | \(0.352647\pi\) | |||||||
\(788\) | −6.75323 | + | 6.75323i | −0.240574 | + | 0.240574i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.6062i | 0.590448i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.6969 | + | 35.6969i | 1.26764 | + | 1.26764i | ||||
\(794\) | −27.6807 | −0.982351 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.5505 | 0.444841 | ||||||||
\(797\) | 18.7026 | + | 18.7026i | 0.662481 | + | 0.662481i | 0.955964 | − | 0.293484i | \(-0.0948146\pi\) |
−0.293484 | + | 0.955964i | \(0.594815\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.0454i | 2.15963i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.10102 | − | 7.10102i | 0.250746 | − | 0.250746i | ||||
\(803\) | 4.87832 | − | 4.87832i | 0.172152 | − | 0.172152i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 8.66025i | − | 0.305044i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.77526 | − | 5.77526i | −0.203173 | − | 0.203173i | ||||
\(809\) | −15.6992 | −0.551955 | −0.275977 | − | 0.961164i | \(-0.589002\pi\) | ||||
−0.275977 | + | 0.961164i | \(0.589002\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.8990 | 1.08501 | 0.542505 | − | 0.840053i | \(-0.317476\pi\) | ||||
0.542505 | + | 0.840053i | \(0.317476\pi\) | |||||||
\(812\) | −4.56048 | − | 4.56048i | −0.160041 | − | 0.160041i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.1464 | + | 32.1464i | −1.12466 | + | 1.12466i | ||||
\(818\) | 21.7774 | − | 21.7774i | 0.761431 | − | 0.761431i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 5.08540i | − | 0.177482i | −0.996055 | − | 0.0887408i | \(-0.971716\pi\) | ||
0.996055 | − | 0.0887408i | \(-0.0282843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000 | + | 4.00000i | 0.139431 | + | 0.139431i | 0.773377 | − | 0.633946i | \(-0.218566\pi\) |
−0.633946 | + | 0.773377i | \(0.718566\pi\) | |||||||
\(824\) | −2.19275 | −0.0763882 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.79796 | −0.201737 | ||||||||
\(827\) | 17.7491 | + | 17.7491i | 0.617197 | + | 0.617197i | 0.944811 | − | 0.327615i | \(-0.106245\pi\) |
−0.327615 | + | 0.944811i | \(0.606245\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.7980i | 0.896000i | 0.894034 | + | 0.448000i | \(0.147864\pi\) | ||||
−0.894034 | + | 0.448000i | \(0.852136\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.22474 | + | 4.22474i | −0.146467 | + | 0.146467i | ||||
\(833\) | −11.6709 | + | 11.6709i | −0.404372 | + | 0.404372i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.87832i | 0.168720i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.1237 | − | 24.1237i | −0.833340 | − | 0.833340i | ||||
\(839\) | 8.54950 | 0.295161 | 0.147581 | − | 0.989050i | \(-0.452851\pi\) | ||||
0.147581 | + | 0.989050i | \(0.452851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.1010 | −0.658656 | ||||||||
\(842\) | 9.58166 | + | 9.58166i | 0.330206 | + | 0.330206i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.24745i | 0.283889i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.2020 | + | 14.2020i | −0.487988 | + | 0.487988i | ||||
\(848\) | 5.65685 | − | 5.65685i | 0.194257 | − | 0.194257i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.4268 | − | 16.4268i | −0.562442 | − | 0.562442i | 0.367558 | − | 0.930001i | \(-0.380194\pi\) |
−0.930001 | + | 0.367558i | \(0.880194\pi\) | |||||||
\(854\) | −17.3205 | −0.592696 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.10102 | 0.174349 | ||||||||
\(857\) | 24.2487 | + | 24.2487i | 0.828320 | + | 0.828320i | 0.987284 | − | 0.158964i | \(-0.0508154\pi\) |
−0.158964 | + | 0.987284i | \(0.550815\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.89898i | 0.0989119i | 0.998776 | + | 0.0494560i | \(0.0157487\pi\) | ||||
−0.998776 | + | 0.0494560i | \(0.984251\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.0000 | − | 16.0000i | 0.544962 | − | 0.544962i | ||||
\(863\) | 7.95315 | − | 7.95315i | 0.270728 | − | 0.270728i | −0.558665 | − | 0.829393i | \(-0.688686\pi\) |
0.829393 | + | 0.558665i | \(0.188686\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20.1489i | 0.684689i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.10102 | + | 2.10102i | 0.0713133 | + | 0.0713133i | ||||
\(869\) | 5.97469 | 0.202678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.8990 | 0.572600 | ||||||||
\(872\) | 2.82843 | + | 2.82843i | 0.0957826 | + | 0.0957826i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 28.2474i | − | 0.955484i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.9217 | − | 24.9217i | 0.841545 | − | 0.841545i | −0.147514 | − | 0.989060i | \(-0.547127\pi\) |
0.989060 | + | 0.147514i | \(0.0471273\pi\) | |||||||
\(878\) | −2.54270 | + | 2.54270i | −0.0858119 | + | 0.0858119i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 40.2337i | − | 1.35551i | −0.735290 | − | 0.677753i | \(-0.762954\pi\) | ||
0.735290 | − | 0.677753i | \(-0.237046\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.1464 | − | 33.1464i | −1.11547 | − | 1.11547i | −0.992398 | − | 0.123068i | \(-0.960727\pi\) |
−0.123068 | − | 0.992398i | \(-0.539273\pi\) | |||||||
\(884\) | 35.2446 | 1.18540 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.24745 | −0.209887 | ||||||||
\(887\) | 10.4316 | + | 10.4316i | 0.350260 | + | 0.350260i | 0.860206 | − | 0.509946i | \(-0.170335\pi\) |
−0.509946 | + | 0.860206i | \(0.670335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.1918i | 0.442440i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.7980 | + | 12.7980i | −0.428507 | + | 0.428507i | ||||
\(893\) | −32.5590 | + | 32.5590i | −1.08955 | + | 1.08955i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 2.04989i | − | 0.0684820i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.0000 | + | 11.0000i | 0.367075 | + | 0.367075i | ||||
\(899\) | −4.56048 | −0.152100 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.1918 | −1.57219 | ||||||||
\(902\) | −3.78194 | − | 3.78194i | −0.125925 | − | 0.125925i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 8.10102i | − | 0.269436i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.62883 | − | 1.62883i | 0.0540843 | − | 0.0540843i | −0.679547 | − | 0.733632i | \(-0.737824\pi\) |
0.733632 | + | 0.679547i | \(0.237824\pi\) | |||||||
\(908\) | 5.33902 | − | 5.33902i | 0.177182 | − | 0.177182i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 43.4120i | − | 1.43830i | −0.694852 | − | 0.719152i | \(-0.744530\pi\) | ||
0.694852 | − | 0.719152i | \(-0.255470\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2020 | − | 11.2020i | −0.370733 | − | 0.370733i | ||||
\(914\) | 20.7846 | 0.687494 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.65153 | 0.153691 | ||||||||
\(917\) | −13.4744 | − | 13.4744i | −0.444962 | − | 0.444962i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.65153i | 0.186427i | 0.995646 | + | 0.0932134i | \(0.0297139\pi\) | ||||
−0.995646 | + | 0.0932134i | \(0.970286\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.00000 | + | 2.00000i | −0.0658665 | + | 0.0658665i | ||||
\(923\) | 59.1433 | − | 59.1433i | 1.94673 | − | 1.94673i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 16.0492i | − | 0.527408i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.22474 | + | 2.22474i | 0.0730308 | + | 0.0730308i | ||||
\(929\) | −39.8051 | −1.30596 | −0.652981 | − | 0.757374i | \(-0.726482\pi\) | ||||
−0.652981 | + | 0.757374i | \(0.726482\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.4495 | −0.408016 | ||||||||
\(932\) | −3.46410 | − | 3.46410i | −0.113470 | − | 0.113470i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.34847i | 0.305891i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.4949 | + | 19.4949i | −0.636871 | + | 0.636871i | −0.949782 | − | 0.312912i | \(-0.898696\pi\) |
0.312912 | + | 0.949782i | \(0.398696\pi\) | |||||||
\(938\) | −4.09978 | + | 4.09978i | −0.133862 | + | 0.133862i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.3376i | 1.08677i | 0.839483 | + | 0.543387i | \(0.182858\pi\) | ||||
−0.839483 | + | 0.543387i | \(0.817142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.8990 | + | 21.8990i | 0.713129 | + | 0.713129i | ||||
\(944\) | 2.82843 | 0.0920575 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.2020 | −0.364210 | ||||||||
\(947\) | −33.4804 | − | 33.4804i | −1.08797 | − | 1.08797i | −0.995738 | − | 0.0922298i | \(-0.970601\pi\) |
−0.0922298 | − | 0.995738i | \(-0.529399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 37.5959i | − | 1.22042i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.55051 | + | 8.55051i | −0.277124 | + | 0.277124i | ||||
\(953\) | 3.67840 | − | 3.67840i | 0.119155 | − | 0.119155i | −0.645015 | − | 0.764170i | \(-0.723149\pi\) |
0.764170 | + | 0.645015i | \(0.223149\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.14966i | 0.198894i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.0000 | − | 13.0000i | −0.420011 | − | 0.420011i | ||||
\(959\) | 44.6834 | 1.44290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8990 | −0.932225 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 19.6969i | − | 0.634396i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.3485 | + | 11.3485i | −0.364942 | + | 0.364942i | −0.865629 | − | 0.500687i | \(-0.833081\pi\) |
0.500687 | + | 0.865629i | \(0.333081\pi\) | |||||||
\(968\) | 6.92820 | − | 6.92820i | 0.222681 | − | 0.222681i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 37.8659i | − | 1.21518i | −0.794253 | − | 0.607588i | \(-0.792137\pi\) | ||
0.794253 | − | 0.607588i | \(-0.207863\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.9546 | + | 11.9546i | 0.383247 | + | 0.383247i | ||||
\(974\) | −20.7846 | −0.665982 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.44949 | 0.270462 | ||||||||
\(977\) | −14.0707 | − | 14.0707i | −0.450162 | − | 0.450162i | 0.445246 | − | 0.895408i | \(-0.353116\pi\) |
−0.895408 | + | 0.445246i | \(0.853116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 19.1464i | − | 0.611922i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.7980 | − | 17.7980i | 0.567956 | − | 0.567956i | ||||
\(983\) | −12.1958 | + | 12.1958i | −0.388985 | + | 0.388985i | −0.874325 | − | 0.485340i | \(-0.838696\pi\) |
0.485340 | + | 0.874325i | \(0.338696\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 18.5597i | − | 0.591063i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.7980 | + | 18.7980i | 0.598043 | + | 0.598043i | ||||
\(989\) | 64.8644 | 2.06257 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.7423 | −1.32599 | −0.662995 | − | 0.748624i | \(-0.730715\pi\) | ||||
−0.662995 | + | 0.748624i | \(0.730715\pi\) | |||||||
\(992\) | −1.02494 | − | 1.02494i | −0.0325420 | − | 0.0325420i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 28.6969i | 0.910212i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.9217 | − | 14.9217i | 0.472574 | − | 0.472574i | −0.430172 | − | 0.902747i | \(-0.641547\pi\) |
0.902747 | + | 0.430172i | \(0.141547\pi\) | |||||||
\(998\) | −4.09978 | + | 4.09978i | −0.129776 | + | 0.129776i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.2.f.f.593.1 | 8 | ||
3.2 | odd | 2 | inner | 1350.2.f.f.593.3 | 8 | ||
5.2 | odd | 4 | inner | 1350.2.f.f.107.3 | 8 | ||
5.3 | odd | 4 | 270.2.f.a.107.1 | yes | 8 | ||
5.4 | even | 2 | 270.2.f.a.53.3 | yes | 8 | ||
15.2 | even | 4 | inner | 1350.2.f.f.107.1 | 8 | ||
15.8 | even | 4 | 270.2.f.a.107.4 | yes | 8 | ||
15.14 | odd | 2 | 270.2.f.a.53.2 | ✓ | 8 | ||
20.3 | even | 4 | 2160.2.w.f.1457.1 | 8 | |||
20.19 | odd | 2 | 2160.2.w.f.593.3 | 8 | |||
45.4 | even | 6 | 810.2.m.a.593.1 | 8 | |||
45.13 | odd | 12 | 810.2.m.a.107.1 | 8 | |||
45.14 | odd | 6 | 810.2.m.h.593.2 | 8 | |||
45.23 | even | 12 | 810.2.m.h.107.2 | 8 | |||
45.29 | odd | 6 | 810.2.m.a.53.1 | 8 | |||
45.34 | even | 6 | 810.2.m.h.53.2 | 8 | |||
45.38 | even | 12 | 810.2.m.a.377.1 | 8 | |||
45.43 | odd | 12 | 810.2.m.h.377.2 | 8 | |||
60.23 | odd | 4 | 2160.2.w.f.1457.4 | 8 | |||
60.59 | even | 2 | 2160.2.w.f.593.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.2.f.a.53.2 | ✓ | 8 | 15.14 | odd | 2 | ||
270.2.f.a.53.3 | yes | 8 | 5.4 | even | 2 | ||
270.2.f.a.107.1 | yes | 8 | 5.3 | odd | 4 | ||
270.2.f.a.107.4 | yes | 8 | 15.8 | even | 4 | ||
810.2.m.a.53.1 | 8 | 45.29 | odd | 6 | |||
810.2.m.a.107.1 | 8 | 45.13 | odd | 12 | |||
810.2.m.a.377.1 | 8 | 45.38 | even | 12 | |||
810.2.m.a.593.1 | 8 | 45.4 | even | 6 | |||
810.2.m.h.53.2 | 8 | 45.34 | even | 6 | |||
810.2.m.h.107.2 | 8 | 45.23 | even | 12 | |||
810.2.m.h.377.2 | 8 | 45.43 | odd | 12 | |||
810.2.m.h.593.2 | 8 | 45.14 | odd | 6 | |||
1350.2.f.f.107.1 | 8 | 15.2 | even | 4 | inner | ||
1350.2.f.f.107.3 | 8 | 5.2 | odd | 4 | inner | ||
1350.2.f.f.593.1 | 8 | 1.1 | even | 1 | trivial | ||
1350.2.f.f.593.3 | 8 | 3.2 | odd | 2 | inner | ||
2160.2.w.f.593.2 | 8 | 60.59 | even | 2 | |||
2160.2.w.f.593.3 | 8 | 20.19 | odd | 2 | |||
2160.2.w.f.1457.1 | 8 | 20.3 | even | 4 | |||
2160.2.w.f.1457.4 | 8 | 60.23 | odd | 4 |