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 | 107.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.107 |
Dual form | 1350.2.f.f.593.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) |
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09638i | 0.330570i | 0.986246 | + | 0.165285i | \(0.0528544\pi\) | ||||
−0.986246 | + | 0.165285i | \(0.947146\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.22474 | + | 4.22474i | −1.17173 | + | 1.17173i | −0.189937 | + | 0.981796i | \(0.560828\pi\) |
−0.981796 | + | 0.189937i | \(0.939172\pi\) | |||||||
\(14\) | 2.04989 | 0.547856 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.17121 | − | 4.17121i | 1.01167 | − | 1.01167i | 0.0117355 | − | 0.999931i | \(-0.496264\pi\) |
0.999931 | − | 0.0117355i | \(-0.00373561\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.44949i | − | 1.02078i | −0.859942 | − | 0.510391i | \(-0.829501\pi\) | ||
0.859942 | − | 0.510391i | \(-0.170499\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.775255 | − | 0.775255i | −0.165285 | − | 0.165285i | ||||
\(23\) | 4.48905 | + | 4.48905i | 0.936031 | + | 0.936031i | 0.998073 | − | 0.0620428i | \(-0.0197615\pi\) |
−0.0620428 | + | 0.998073i | \(0.519762\pi\) | |||||||
\(24\) | 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 | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 3.14626 | + | 3.14626i | 0.510391 | + | 0.510391i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.87832i | − | 0.761865i | −0.924603 | − | 0.380932i | \(-0.875603\pi\) | ||
0.924603 | − | 0.380932i | \(-0.124397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.22474 | − | 7.22474i | 1.10176 | − | 1.10176i | 0.107565 | − | 0.994198i | \(-0.465695\pi\) |
0.994198 | − | 0.107565i | \(-0.0343054\pi\) | |||||||
\(44\) | 1.09638 | 0.165285 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.34847 | −0.936031 | ||||||||
\(47\) | 7.31747 | − | 7.31747i | 1.06736 | − | 1.06736i | 0.0698023 | − | 0.997561i | \(-0.477763\pi\) |
0.997561 | − | 0.0698023i | \(-0.0222368\pi\) | |||||||
\(48\) | 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 | 0.202296 | − | 0.979324i | \(-0.435160\pi\) |
−0.979324 | + | 0.202296i | \(0.935160\pi\) | |||||||
\(54\) | 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 | 0.574304 | − | 0.818642i | \(-0.305273\pi\) |
−0.818642 | + | 0.574304i | \(0.805273\pi\) | |||||||
\(68\) | −4.17121 | − | 4.17121i | −0.505833 | − | 0.505833i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.9993i | − | 1.66141i | −0.556714 | − | 0.830704i | \(-0.687938\pi\) | ||
0.556714 | − | 0.830704i | \(-0.312062\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.44949 | − | 4.44949i | 0.520773 | − | 0.520773i | −0.397032 | − | 0.917805i | \(-0.629960\pi\) |
0.917805 | + | 0.397032i | \(0.129960\pi\) | |||||||
\(74\) | 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 | \(-0.900823\pi\) | ||
0.951852 | − | 0.306558i | \(-0.0991773\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.44949 | + | 3.44949i | 0.380932 | + | 0.380932i | ||||
\(83\) | 10.2173 | + | 10.2173i | 1.12150 | + | 1.12150i | 0.991516 | + | 0.129981i | \(0.0414918\pi\) |
0.129981 | + | 0.991516i | \(0.458508\pi\) | |||||||
\(84\) | 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 | 0.133177 | − | 0.991092i | \(-0.457482\pi\) |
−0.991092 | + | 0.133177i | \(0.957482\pi\) | |||||||
\(98\) | 1.97846 | + | 1.97846i | 0.199854 | + | 0.199854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.16744i | 0.812691i | 0.913719 | + | 0.406346i | \(0.133197\pi\) | ||||
−0.913719 | + | 0.406346i | \(0.866803\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.55051 | + | 1.55051i | −0.152776 | + | 0.152776i | −0.779357 | − | 0.626580i | \(-0.784454\pi\) |
0.626580 | + | 0.779357i | \(0.284454\pi\) | |||||||
\(104\) | −5.97469 | −0.585867 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | 3.60697 | − | 3.60697i | 0.348699 | − | 0.348699i | −0.510926 | − | 0.859625i | \(-0.670697\pi\) |
0.859625 | + | 0.510926i | \(0.170697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.00000i | − | 0.383131i | −0.981480 | − | 0.191565i | \(-0.938644\pi\) | ||
0.981480 | − | 0.191565i | \(-0.0613564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.44949 | + | 1.44949i | 0.136964 | + | 0.136964i | ||||
\(113\) | 5.72829 | + | 5.72829i | 0.538872 | + | 0.538872i | 0.923198 | − | 0.384326i | \(-0.125566\pi\) |
−0.384326 | + | 0.923198i | \(0.625566\pi\) | |||||||
\(114\) | 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 | 0.879567 | − | 0.475775i | \(-0.157832\pi\) |
−0.475775 | + | 0.879567i | \(0.657832\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 9.29593i | − | 0.812189i | −0.913831 | − | 0.406095i | \(-0.866890\pi\) | ||
0.913831 | − | 0.406095i | \(-0.133110\pi\) | |||||||
\(132\) | 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 | −0.400617 | + | 0.916245i | \(0.631204\pi\) |
−0.916245 | + | 0.400617i | \(0.868796\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.24745i | 0.699539i | 0.936836 | + | 0.349770i | \(0.113740\pi\) | ||||
−0.936836 | + | 0.349770i | \(0.886260\pi\) | |||||||
\(140\) | 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 | 0.310343 | − | 0.950625i | \(-0.399556\pi\) |
−0.950625 | + | 0.310343i | \(0.899556\pi\) | |||||||
\(158\) | 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 | −0.526920 | − | 0.849915i | \(-0.676653\pi\) |
0.849915 | + | 0.526920i | \(0.176653\pi\) | |||||||
\(164\) | −4.87832 | −0.380932 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4495 | −1.12150 | ||||||||
\(167\) | −5.51399 | + | 5.51399i | −0.426685 | + | 0.426685i | −0.887498 | − | 0.460812i | \(-0.847558\pi\) |
0.460812 | + | 0.887498i | \(0.347558\pi\) | |||||||
\(168\) | 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 | 0.474394 | − | 0.880312i | \(-0.342667\pi\) |
−0.880312 | + | 0.474394i | \(0.842667\pi\) | |||||||
\(174\) | 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 | \(0.197197\pi\) | ||||
−0.814162 | + | 0.580638i | \(0.802803\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.79796 | − | 6.79796i | 0.489328 | − | 0.489328i | −0.418766 | − | 0.908094i | \(-0.637537\pi\) |
0.908094 | + | 0.418766i | \(0.137537\pi\) | |||||||
\(194\) | 11.9494 | 0.857916 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.79796 | −0.199854 | ||||||||
\(197\) | 6.75323 | − | 6.75323i | 0.481148 | − | 0.481148i | −0.424350 | − | 0.905498i | \(-0.639497\pi\) |
0.905498 | + | 0.424350i | \(0.139497\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5505i | 0.889682i | 0.895610 | + | 0.444841i | \(0.146740\pi\) | ||||
−0.895610 | + | 0.444841i | \(0.853260\pi\) | |||||||
\(200\) | 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 | −0.133971 | − | 0.990985i | \(-0.542773\pi\) |
0.990985 | + | 0.133971i | \(0.0427728\pi\) | |||||||
\(224\) | −2.04989 | −0.136964 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.10102 | −0.538872 | ||||||||
\(227\) | −5.33902 | + | 5.33902i | −0.354363 | + | 0.354363i | −0.861730 | − | 0.507367i | \(-0.830619\pi\) |
0.507367 | + | 0.861730i | \(0.330619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.65153i | 0.307382i | 0.988119 | + | 0.153691i | \(0.0491160\pi\) | ||||
−0.988119 | + | 0.153691i | \(0.950884\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.22474 | + | 2.22474i | 0.146062 | + | 0.146062i | ||||
\(233\) | −3.46410 | − | 3.46410i | −0.226941 | − | 0.226941i | 0.584473 | − | 0.811413i | \(-0.301301\pi\) |
−0.811413 | + | 0.584473i | \(0.801301\pi\) | |||||||
\(234\) | 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 | \(0.0174085\pi\) | ||||
−0.998505 | + | 0.0546630i | \(0.982592\pi\) | |||||||
\(252\) | 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 | −0.783923 | − | 0.620858i | \(-0.786784\pi\) |
0.620858 | + | 0.783923i | \(0.286784\pi\) | |||||||
\(258\) | 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 | 0.734944 | − | 0.678128i | \(-0.237208\pi\) |
−0.678128 | + | 0.734944i | \(0.737208\pi\) | |||||||
\(264\) | 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 | 0.359363 | − | 0.933198i | \(-0.382994\pi\) |
−0.933198 | + | 0.359363i | \(0.882994\pi\) | |||||||
\(278\) | −5.83183 | − | 5.83183i | −0.349770 | − | 0.349770i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.83523i | − | 0.527065i | −0.964650 | − | 0.263533i | \(-0.915112\pi\) | ||
0.964650 | − | 0.263533i | \(-0.0848877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.898979 | + | 0.898979i | −0.0534388 | + | 0.0534388i | −0.733321 | − | 0.679882i | \(-0.762031\pi\) |
0.679882 | + | 0.733321i | \(0.262031\pi\) | |||||||
\(284\) | −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 | 0.572233 | − | 0.820091i | \(-0.306077\pi\) |
−0.820091 | + | 0.572233i | \(0.806077\pi\) | |||||||
\(294\) | 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 | −0.961216 | − | 0.275798i | \(-0.911058\pi\) |
−0.275798 | − | 0.961216i | \(-0.588942\pi\) | |||||||
\(308\) | −1.58919 | − | 1.58919i | −0.0905523 | − | 0.0905523i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.2412i | 1.82823i | 0.405455 | + | 0.914115i | \(0.367113\pi\) | ||||
−0.405455 | + | 0.914115i | \(0.632887\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.24745 | + | 3.24745i | −0.183557 | + | 0.183557i | −0.792904 | − | 0.609347i | \(-0.791432\pi\) |
0.609347 | + | 0.792904i | \(0.291432\pi\) | |||||||
\(314\) | 11.3458 | 0.640281 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.44949 | −0.306558 | ||||||||
\(317\) | 1.55708 | − | 1.55708i | 0.0874542 | − | 0.0874542i | −0.662026 | − | 0.749481i | \(-0.730303\pi\) |
0.749481 | + | 0.662026i | \(0.230303\pi\) | |||||||
\(318\) | 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 | 0.873551 | − | 0.486733i | \(-0.161812\pi\) |
−0.486733 | + | 0.873551i | \(0.661812\pi\) | |||||||
\(338\) | 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 | −0.923771 | − | 0.382945i | \(-0.874910\pi\) |
0.382945 | + | 0.923771i | \(0.374910\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0454i | 1.07301i | 0.843898 | + | 0.536503i | \(0.180255\pi\) | ||||
−0.843898 | + | 0.536503i | \(0.819745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.775255 | + | 0.775255i | 0.0413212 | + | 0.0413212i | ||||
\(353\) | −1.34278 | − | 1.34278i | −0.0714690 | − | 0.0714690i | 0.670469 | − | 0.741938i | \(-0.266093\pi\) |
−0.741938 | + | 0.670469i | \(0.766093\pi\) | |||||||
\(354\) | 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 | −0.998280 | − | 0.0586283i | \(-0.981327\pi\) |
−0.0586283 | − | 0.998280i | \(-0.518673\pi\) | |||||||
\(368\) | −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 | −0.00300584 | + | 0.999995i | \(0.500957\pi\) |
−0.999995 | + | 0.00300584i | \(0.999043\pi\) | |||||||
\(374\) | −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 | \(0.0327588\pi\) | ||||
−0.994709 | + | 0.102733i | \(0.967241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.3485 | − | 11.3485i | −0.580638 | − | 0.580638i | ||||
\(383\) | −14.2457 | − | 14.2457i | −0.727920 | − | 0.727920i | 0.242285 | − | 0.970205i | \(-0.422103\pi\) |
−0.970205 | + | 0.242285i | \(0.922103\pi\) | |||||||
\(384\) | 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 | 0.999847 | − | 0.0174955i | \(-0.00556927\pi\) |
−0.0174955 | + | 0.999847i | \(0.505569\pi\) | |||||||
\(398\) | −8.87455 | − | 8.87455i | −0.444841 | − | 0.444841i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.0424i | − | 0.501492i | −0.968053 | − | 0.250746i | \(-0.919324\pi\) | ||
0.968053 | − | 0.250746i | \(-0.0806758\pi\) | |||||||
\(402\) | 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 | \(-0.724497\pi\) | ||
0.648247 | − | 0.761431i | \(-0.275503\pi\) | |||||||
\(410\) | 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 | \(-0.816544\pi\) | ||
0.838461 | − | 0.544962i | \(-0.183456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2474 | + | 14.2474i | −0.684689 | + | 0.684689i | −0.961053 | − | 0.276364i | \(-0.910870\pi\) |
0.276364 | + | 0.961053i | \(0.410870\pi\) | |||||||
\(434\) | −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 | \(0.0273484\pi\) | ||||
−0.996311 | + | 0.0858119i | \(0.972652\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.9217 | − | 24.9217i | −1.18540 | − | 1.18540i | ||||
\(443\) | 4.41761 | + | 4.41761i | 0.209887 | + | 0.209887i | 0.804220 | − | 0.594332i | \(-0.202584\pi\) |
−0.594332 | + | 0.804220i | \(0.702584\pi\) | |||||||
\(444\) | 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 | 0.274184 | − | 0.961677i | \(-0.411592\pi\) |
−0.961677 | + | 0.274184i | \(0.911592\pi\) | |||||||
\(458\) | −3.28913 | − | 3.28913i | −0.153691 | − | 0.153691i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.82843i | 0.131733i | 0.997828 | + | 0.0658665i | \(0.0209811\pi\) | ||||
−0.997828 | + | 0.0658665i | \(0.979019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3485 | − | 11.3485i | 0.527408 | − | 0.527408i | −0.392391 | − | 0.919799i | \(-0.628352\pi\) |
0.919799 | + | 0.392391i | \(0.128352\pi\) | |||||||
\(464\) | −3.14626 | −0.146062 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.89898 | 0.226941 | ||||||||
\(467\) | −6.61037 | + | 6.61037i | −0.305891 | + | 0.305891i | −0.843313 | − | 0.537422i | \(-0.819398\pi\) |
0.537422 | + | 0.843313i | \(0.319398\pi\) | |||||||
\(468\) | 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 | 0.956783 | − | 0.290802i | \(-0.0939219\pi\) |
−0.290802 | + | 0.956783i | \(0.593922\pi\) | |||||||
\(488\) | −5.97469 | − | 5.97469i | −0.270462 | − | 0.270462i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 25.1701i | − | 1.13591i | −0.823059 | − | 0.567956i | \(-0.807734\pi\) | ||
0.823059 | − | 0.567956i | \(-0.192266\pi\) | |||||||
\(492\) | 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 | \(0.0414259\pi\) | ||||
−0.991543 | + | 0.129776i | \(0.958574\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.22474 | − | 1.22474i | −0.0546630 | − | 0.0546630i | ||||
\(503\) | 26.1951 | + | 26.1951i | 1.16798 | + | 1.16798i | 0.982682 | + | 0.185297i | \(0.0593249\pi\) |
0.185297 | + | 0.982682i | \(0.440675\pi\) | |||||||
\(504\) | 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 | \(-0.967923\pi\) | ||
0.994927 | − | 0.100602i | \(-0.0320770\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.77526 | + | 4.77526i | −0.208807 | + | 0.208807i | −0.803760 | − | 0.594953i | \(-0.797171\pi\) |
0.594953 | + | 0.803760i | \(0.297171\pi\) | |||||||
\(524\) | −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 | 0.933807 | − | 0.357777i | \(-0.116465\pi\) |
−0.357777 | + | 0.933807i | \(0.616465\pi\) | |||||||
\(548\) | 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 | −0.401940 | − | 0.915666i | \(-0.631664\pi\) |
0.915666 | + | 0.401940i | \(0.131664\pi\) | |||||||
\(558\) | 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 | 0.357362 | − | 0.933966i | \(-0.383676\pi\) |
−0.933966 | + | 0.357362i | \(0.883676\pi\) | |||||||
\(564\) | 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 | 0.618927 | − | 0.785449i | \(-0.287568\pi\) |
−0.785449 | + | 0.618927i | \(0.787568\pi\) | |||||||
\(578\) | 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 | −0.00635031 | − | 0.999980i | \(-0.502021\pi\) |
0.999980 | + | 0.00635031i | \(0.00202138\pi\) | |||||||
\(588\) | 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 | 0.999879 | − | 0.0155412i | \(-0.00494711\pi\) |
−0.0155412 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(594\) | 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 | 0.959062 | − | 0.283197i | \(-0.0913950\pi\) |
−0.283197 | + | 0.959062i | \(0.591395\pi\) | |||||||
\(608\) | −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 | −0.463256 | − | 0.886224i | \(-0.653319\pi\) |
0.886224 | + | 0.463256i | \(0.153319\pi\) | |||||||
\(614\) | 30.6520 | 1.23701 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.24745 | 0.0905523 | ||||||||
\(617\) | −3.67840 | + | 3.67840i | −0.148087 | + | 0.148087i | −0.777263 | − | 0.629176i | \(-0.783392\pi\) |
0.629176 | + | 0.777263i | \(0.283392\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.69694i | 0.349559i | 0.984608 | + | 0.174780i | \(0.0559213\pi\) | ||||
−0.984608 | + | 0.174780i | \(0.944079\pi\) | |||||||
\(620\) | 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 | \(-0.814583\pi\) | ||
0.835088 | − | 0.550117i | \(-0.185417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.8207 | − | 32.8207i | 1.29432 | − | 1.29432i | 0.362233 | − | 0.932088i | \(-0.382014\pi\) |
0.932088 | − | 0.362233i | \(-0.117986\pi\) | |||||||
\(644\) | −13.0137 | −0.512810 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.2474 | 1.03269 | ||||||||
\(647\) | 6.00680 | − | 6.00680i | 0.236152 | − | 0.236152i | −0.579103 | − | 0.815254i | \(-0.696597\pi\) |
0.815254 | + | 0.579103i | \(0.196597\pi\) | |||||||
\(648\) | 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 | 0.882966 | − | 0.469437i | \(-0.155543\pi\) |
−0.469437 | + | 0.882966i | \(0.655543\pi\) | |||||||
\(654\) | 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 | −0.446658 | + | 0.894705i | \(0.647386\pi\) |
−0.894705 | + | 0.446658i | \(0.852614\pi\) | |||||||
\(674\) | −10.0424 | −0.386817 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.6969 | −0.872959 | ||||||||
\(677\) | 33.6554 | − | 33.6554i | 1.29348 | − | 1.29348i | 0.360863 | − | 0.932619i | \(-0.382482\pi\) |
0.932619 | − | 0.360863i | \(-0.117518\pi\) | |||||||
\(678\) | 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 | 0.562022 | − | 0.827122i | \(-0.310024\pi\) |
−0.827122 | + | 0.562022i | \(0.810024\pi\) | |||||||
\(684\) | 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 | \(0.0840748\pi\) | ||||
−0.965320 | + | 0.261068i | \(0.915925\pi\) | |||||||
\(702\) | 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 | \(-0.952001\pi\) | ||
0.988652 | − | 0.150223i | \(-0.0479992\pi\) | |||||||
\(710\) | 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 | 0.996148 | − | 0.0876830i | \(-0.0279462\pi\) |
−0.0876830 | + | 0.996148i | \(0.527946\pi\) | |||||||
\(728\) | 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 | −0.992640 | − | 0.121105i | \(-0.961356\pi\) |
0.121105 | + | 0.992640i | \(0.461356\pi\) | |||||||
\(734\) | 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 | \(0.0579486\pi\) | ||||
−0.983474 | + | 0.181047i | \(0.942051\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.5959 | − | 11.5959i | −0.425700 | − | 0.425700i | ||||
\(743\) | 19.7597 | + | 19.7597i | 0.724912 | + | 0.724912i | 0.969601 | − | 0.244690i | \(-0.0786861\pi\) |
−0.244690 | + | 0.969601i | \(0.578686\pi\) | |||||||
\(744\) | 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 | 0.669393 | − | 0.742909i | \(-0.266554\pi\) |
−0.742909 | + | 0.669393i | \(0.766554\pi\) | |||||||
\(758\) | −2.82843 | − | 2.82843i | −0.102733 | − | 0.102733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.52837i | − | 0.164153i | −0.996626 | − | 0.0820766i | \(-0.973845\pi\) | ||
0.996626 | − | 0.0820766i | \(-0.0261552\pi\) | |||||||
\(762\) | 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 | \(0.193642\pi\) | ||||
−0.820595 | + | 0.571510i | \(0.806358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.79796 | − | 6.79796i | −0.244664 | − | 0.244664i | ||||
\(773\) | −1.12848 | − | 1.12848i | −0.0405888 | − | 0.0405888i | 0.686521 | − | 0.727110i | \(-0.259137\pi\) |
−0.727110 | + | 0.686521i | \(0.759137\pi\) | |||||||
\(774\) | 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 | 0.446565 | − | 0.894751i | \(-0.352647\pi\) |
−0.894751 | + | 0.446565i | \(0.852647\pi\) | |||||||
\(788\) | −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 | −0.293484 | − | 0.955964i | \(-0.594815\pi\) |
0.955964 | + | 0.293484i | \(0.0948146\pi\) | |||||||
\(798\) | 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 | \(0.0282843\pi\) | ||||
−0.996055 | + | 0.0887408i | \(0.971716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000 | − | 4.00000i | 0.139431 | − | 0.139431i | −0.633946 | − | 0.773377i | \(-0.718566\pi\) |
0.773377 | + | 0.633946i | \(0.218566\pi\) | |||||||
\(824\) | −2.19275 | −0.0763882 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.79796 | −0.201737 | ||||||||
\(827\) | 17.7491 | − | 17.7491i | 0.617197 | − | 0.617197i | −0.327615 | − | 0.944811i | \(-0.606245\pi\) |
0.944811 | + | 0.327615i | \(0.106245\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 25.7980i | − | 0.896000i | −0.894034 | − | 0.448000i | \(-0.852136\pi\) | ||
0.894034 | − | 0.448000i | \(-0.147864\pi\) | |||||||
\(830\) | 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 | −0.930001 | − | 0.367558i | \(-0.880194\pi\) |
0.367558 | + | 0.930001i | \(0.380194\pi\) | |||||||
\(854\) | −17.3205 | −0.592696 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.10102 | 0.174349 | ||||||||
\(857\) | 24.2487 | − | 24.2487i | 0.828320 | − | 0.828320i | −0.158964 | − | 0.987284i | \(-0.550815\pi\) |
0.987284 | + | 0.158964i | \(0.0508154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.89898i | − | 0.0989119i | −0.998776 | − | 0.0494560i | \(-0.984251\pi\) | ||
0.998776 | − | 0.0494560i | \(-0.0157487\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.0000 | + | 16.0000i | 0.544962 | + | 0.544962i | ||||
\(863\) | 7.95315 | + | 7.95315i | 0.270728 | + | 0.270728i | 0.829393 | − | 0.558665i | \(-0.188686\pi\) |
−0.558665 | + | 0.829393i | \(0.688686\pi\) | |||||||
\(864\) | 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 | 0.989060 | − | 0.147514i | \(-0.0471273\pi\) |
−0.147514 | + | 0.989060i | \(0.547127\pi\) | |||||||
\(878\) | −2.54270 | − | 2.54270i | −0.0858119 | − | 0.0858119i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.2337i | 1.35551i | 0.735290 | + | 0.677753i | \(0.237046\pi\) | ||||
−0.735290 | + | 0.677753i | \(0.762954\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.1464 | + | 33.1464i | −1.11547 | + | 1.11547i | −0.123068 | + | 0.992398i | \(0.539273\pi\) |
−0.992398 | + | 0.123068i | \(0.960727\pi\) | |||||||
\(884\) | 35.2446 | 1.18540 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.24745 | −0.209887 | ||||||||
\(887\) | 10.4316 | − | 10.4316i | 0.350260 | − | 0.350260i | −0.509946 | − | 0.860206i | \(-0.670335\pi\) |
0.860206 | + | 0.509946i | \(0.170335\pi\) | |||||||
\(888\) | 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 | 0.733632 | − | 0.679547i | \(-0.237824\pi\) |
−0.679547 | + | 0.733632i | \(0.737824\pi\) | |||||||
\(908\) | 5.33902 | + | 5.33902i | 0.177182 | + | 0.177182i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.4120i | 1.43830i | 0.694852 | + | 0.719152i | \(0.255470\pi\) | ||||
−0.694852 | + | 0.719152i | \(0.744530\pi\) | |||||||
\(912\) | 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 | \(-0.970286\pi\) | ||
0.995646 | − | 0.0932134i | \(-0.0297139\pi\) | |||||||
\(920\) | 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 | 0.312912 | − | 0.949782i | \(-0.398696\pi\) |
−0.949782 | + | 0.312912i | \(0.898696\pi\) | |||||||
\(938\) | −4.09978 | − | 4.09978i | −0.133862 | − | 0.133862i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 33.3376i | − | 1.08677i | −0.839483 | − | 0.543387i | \(-0.817142\pi\) | ||
0.839483 | − | 0.543387i | \(-0.182858\pi\) | |||||||
\(942\) | 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 | −0.0922298 | + | 0.995738i | \(0.529399\pi\) |
−0.995738 | + | 0.0922298i | \(0.970601\pi\) | |||||||
\(948\) | 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 | 0.764170 | − | 0.645015i | \(-0.223149\pi\) |
−0.645015 | + | 0.764170i | \(0.723149\pi\) | |||||||
\(954\) | 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 | 0.500687 | − | 0.865629i | \(-0.333081\pi\) |
−0.865629 | + | 0.500687i | \(0.833081\pi\) | |||||||
\(968\) | 6.92820 | + | 6.92820i | 0.222681 | + | 0.222681i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.8659i | 1.21518i | 0.794253 | + | 0.607588i | \(0.207863\pi\) | ||||
−0.794253 | + | 0.607588i | \(0.792137\pi\) | |||||||
\(972\) | 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 | −0.895408 | − | 0.445246i | \(-0.853116\pi\) |
0.445246 | + | 0.895408i | \(0.353116\pi\) | |||||||
\(978\) | 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 | 0.485340 | − | 0.874325i | \(-0.338696\pi\) |
−0.874325 | + | 0.485340i | \(0.838696\pi\) | |||||||
\(984\) | 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 | 0.902747 | − | 0.430172i | \(-0.141547\pi\) |
−0.430172 | + | 0.902747i | \(0.641547\pi\) | |||||||
\(998\) | −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.107.1 | 8 | ||
3.2 | odd | 2 | inner | 1350.2.f.f.107.3 | 8 | ||
5.2 | odd | 4 | 270.2.f.a.53.2 | ✓ | 8 | ||
5.3 | odd | 4 | inner | 1350.2.f.f.593.3 | 8 | ||
5.4 | even | 2 | 270.2.f.a.107.4 | yes | 8 | ||
15.2 | even | 4 | 270.2.f.a.53.3 | yes | 8 | ||
15.8 | even | 4 | inner | 1350.2.f.f.593.1 | 8 | ||
15.14 | odd | 2 | 270.2.f.a.107.1 | yes | 8 | ||
20.7 | even | 4 | 2160.2.w.f.593.2 | 8 | |||
20.19 | odd | 2 | 2160.2.w.f.1457.4 | 8 | |||
45.2 | even | 12 | 810.2.m.h.53.2 | 8 | |||
45.4 | even | 6 | 810.2.m.h.107.2 | 8 | |||
45.7 | odd | 12 | 810.2.m.a.53.1 | 8 | |||
45.14 | odd | 6 | 810.2.m.a.107.1 | 8 | |||
45.22 | odd | 12 | 810.2.m.h.593.2 | 8 | |||
45.29 | odd | 6 | 810.2.m.h.377.2 | 8 | |||
45.32 | even | 12 | 810.2.m.a.593.1 | 8 | |||
45.34 | even | 6 | 810.2.m.a.377.1 | 8 | |||
60.47 | odd | 4 | 2160.2.w.f.593.3 | 8 | |||
60.59 | even | 2 | 2160.2.w.f.1457.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.2.f.a.53.2 | ✓ | 8 | 5.2 | odd | 4 | ||
270.2.f.a.53.3 | yes | 8 | 15.2 | even | 4 | ||
270.2.f.a.107.1 | yes | 8 | 15.14 | odd | 2 | ||
270.2.f.a.107.4 | yes | 8 | 5.4 | even | 2 | ||
810.2.m.a.53.1 | 8 | 45.7 | odd | 12 | |||
810.2.m.a.107.1 | 8 | 45.14 | odd | 6 | |||
810.2.m.a.377.1 | 8 | 45.34 | even | 6 | |||
810.2.m.a.593.1 | 8 | 45.32 | even | 12 | |||
810.2.m.h.53.2 | 8 | 45.2 | even | 12 | |||
810.2.m.h.107.2 | 8 | 45.4 | even | 6 | |||
810.2.m.h.377.2 | 8 | 45.29 | odd | 6 | |||
810.2.m.h.593.2 | 8 | 45.22 | odd | 12 | |||
1350.2.f.f.107.1 | 8 | 1.1 | even | 1 | trivial | ||
1350.2.f.f.107.3 | 8 | 3.2 | odd | 2 | inner | ||
1350.2.f.f.593.1 | 8 | 15.8 | even | 4 | inner | ||
1350.2.f.f.593.3 | 8 | 5.3 | odd | 4 | inner | ||
2160.2.w.f.593.2 | 8 | 20.7 | even | 4 | |||
2160.2.w.f.593.3 | 8 | 60.47 | odd | 4 | |||
2160.2.w.f.1457.1 | 8 | 60.59 | even | 2 | |||
2160.2.w.f.1457.4 | 8 | 20.19 | odd | 2 |