Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.2.e.e.271.1 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 3.46410i | 0.554700 | + | 0.960769i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) |
−0.443227 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | −1.00000 | + | 1.73205i | −0.223607 | + | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.00000 | −0.755929 | ||||||||
\(29\) | 4.50000 | − | 7.79423i | 0.835629 | − | 1.44735i | −0.0578882 | − | 0.998323i | \(-0.518437\pi\) |
0.893517 | − | 0.449029i | \(-0.148230\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.0898027 | + | 0.155543i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.817625 | + | 0.575751i | \(0.804710\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | − | 3.46410i | 0.304997 | − | 0.528271i | −0.672264 | − | 0.740312i | \(-0.734678\pi\) |
0.977261 | + | 0.212041i | \(0.0680112\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | + | 10.3923i | −0.875190 | + | 1.51587i | −0.0186297 | + | 0.999826i | \(0.505930\pi\) |
−0.856560 | + | 0.516047i | \(0.827403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | + | 6.92820i | −0.554700 | + | 0.960769i | ||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50000 | − | 2.59808i | −0.195283 | − | 0.338241i | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | − | 8.66025i | 0.640184 | − | 1.10883i | −0.345207 | − | 0.938527i | \(-0.612191\pi\) |
0.985391 | − | 0.170305i | \(-0.0544754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −2.00000 | + | 3.46410i | −0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | − | 12.1244i | −0.855186 | − | 1.48123i | −0.876472 | − | 0.481452i | \(-0.840109\pi\) |
0.0212861 | − | 0.999773i | \(-0.493224\pi\) | |||||||
\(68\) | −6.00000 | − | 10.3923i | −0.727607 | − | 1.26025i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | − | 1.73205i | −0.114708 | − | 0.198680i | ||||
\(77\) | 3.00000 | + | 5.19615i | 0.341882 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | − | 13.8564i | 0.900070 | − | 1.55897i | 0.0726692 | − | 0.997356i | \(-0.476848\pi\) |
0.827401 | − | 0.561611i | \(-0.189818\pi\) | |||||||
\(80\) | −4.00000 | −0.447214 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | − | 10.3923i | 0.658586 | − | 1.14070i | −0.322396 | − | 0.946605i | \(-0.604488\pi\) |
0.980982 | − | 0.194099i | \(-0.0621783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | − | 5.19615i | −0.325396 | − | 0.563602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0000 | 1.59000 | 0.794998 | − | 0.606612i | \(-0.207472\pi\) | ||||
0.794998 | + | 0.606612i | \(0.207472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.838628 | ||||||||
\(92\) | −6.00000 | + | 10.3923i | −0.625543 | + | 1.08347i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.500000 | − | 0.866025i | −0.0512989 | − | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | − | 3.46410i | 0.203069 | − | 0.351726i | −0.746447 | − | 0.665445i | \(-0.768242\pi\) |
0.949516 | + | 0.313719i | \(0.101575\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −4.50000 | + | 7.79423i | −0.447767 | + | 0.775555i | −0.998240 | − | 0.0592978i | \(-0.981114\pi\) |
0.550474 | + | 0.834853i | \(0.314447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.00000 | − | 12.1244i | −0.689730 | − | 1.19465i | −0.971925 | − | 0.235291i | \(-0.924396\pi\) |
0.282194 | − | 0.959357i | \(-0.408938\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.0000 | −1.74013 | −0.870063 | − | 0.492941i | \(-0.835922\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | − | 6.92820i | −0.377964 | − | 0.654654i | ||||
\(113\) | −3.00000 | − | 5.19615i | −0.282216 | − | 0.488813i | 0.689714 | − | 0.724082i | \(-0.257736\pi\) |
−0.971930 | + | 0.235269i | \(0.924403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | + | 5.19615i | −0.279751 | + | 0.484544i | ||||
\(116\) | 18.0000 | 1.67126 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | − | 10.3923i | 0.550019 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50000 | + | 7.79423i | 0.393167 | + | 0.680985i | 0.992865 | − | 0.119241i | \(-0.0380462\pi\) |
−0.599699 | + | 0.800226i | \(0.704713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | − | 1.73205i | 0.0867110 | − | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.50000 | + | 6.06218i | 0.296866 | + | 0.514187i | 0.975417 | − | 0.220366i | \(-0.0707252\pi\) |
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | −2.00000 | − | 3.46410i | −0.169031 | − | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | 1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | 0.747409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000 | + | 13.8564i | 0.657596 | + | 1.13899i | ||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.500000 | − | 0.866025i | 0.0406894 | − | 0.0704761i | −0.844963 | − | 0.534824i | \(-0.820378\pi\) |
0.885653 | + | 0.464348i | \(0.153711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.500000 | + | 0.866025i | −0.0401610 | + | 0.0695608i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.00000 | + | 13.8564i | 0.638470 | + | 1.10586i | 0.985769 | + | 0.168107i | \(0.0537655\pi\) |
−0.347299 | + | 0.937754i | \(0.612901\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | −0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | 3.00000 | − | 5.19615i | 0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | − | 5.19615i | −0.232147 | − | 0.402090i | 0.726293 | − | 0.687386i | \(-0.241242\pi\) |
−0.958440 | + | 0.285295i | \(0.907908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 1.73205i | −0.0755929 | − | 0.130931i | ||||
\(176\) | 6.00000 | + | 10.3923i | 0.452267 | + | 0.783349i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0000 | 0.817624 | 0.408812 | − | 0.912619i | \(-0.365943\pi\) | ||||
0.408812 | + | 0.912619i | \(0.365943\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | + | 6.92820i | 0.294086 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | + | 15.5885i | −0.658145 | + | 1.13994i | ||||
\(188\) | −24.0000 | −1.75038 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.50000 | − | 12.9904i | 0.542681 | − | 0.939951i | −0.456068 | − | 0.889945i | \(-0.650743\pi\) |
0.998749 | − | 0.0500060i | \(-0.0159241\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | + | 5.19615i | −0.214286 | + | 0.371154i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.00000 | + | 15.5885i | 0.631676 | + | 1.09410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.50000 | − | 2.59808i | 0.104765 | − | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.0000 | −1.10940 | ||||||||
\(209\) | −1.50000 | + | 2.59808i | −0.103757 | + | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50000 | + | 11.2583i | 0.447478 | + | 0.775055i | 0.998221 | − | 0.0596196i | \(-0.0189888\pi\) |
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.00000 | + | 5.19615i | 0.202260 | + | 0.350325i | ||||
\(221\) | −12.0000 | − | 20.7846i | −0.807207 | − | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0000 | + | 17.3205i | −0.669650 | + | 1.15987i | 0.308353 | + | 0.951272i | \(0.400222\pi\) |
−0.978002 | + | 0.208595i | \(0.933111\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.00000 | − | 15.5885i | 0.597351 | − | 1.03464i | −0.395860 | − | 0.918311i | \(-0.629553\pi\) |
0.993210 | − | 0.116331i | \(-0.0371134\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | + | 8.66025i | 0.330409 | + | 0.572286i | 0.982592 | − | 0.185776i | \(-0.0594799\pi\) |
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0000 | 0.786146 | 0.393073 | − | 0.919507i | \(-0.371412\pi\) | ||||
0.393073 | + | 0.919507i | \(0.371412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | 3.00000 | − | 5.19615i | 0.195283 | − | 0.338241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | + | 20.7846i | 0.776215 | + | 1.34444i | 0.934109 | + | 0.356988i | \(0.116196\pi\) |
−0.157893 | + | 0.987456i | \(0.550470\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | + | 14.7224i | −0.547533 | + | 0.948355i | 0.450910 | + | 0.892570i | \(0.351100\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.0000 | 1.28037 | ||||||||
\(245\) | −1.50000 | + | 2.59808i | −0.0958315 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | − | 3.46410i | −0.127257 | − | 0.220416i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | + | 13.8564i | −0.497096 | + | 0.860995i | ||||
\(260\) | −8.00000 | −0.496139 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.00000 | + | 15.5885i | −0.554964 | + | 0.961225i | 0.442943 | + | 0.896550i | \(0.353935\pi\) |
−0.997906 | + | 0.0646755i | \(0.979399\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | + | 5.19615i | 0.184289 | + | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.0000 | − | 24.2487i | 0.855186 | − | 1.48123i | ||||
\(269\) | −3.00000 | −0.182913 | −0.0914566 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914566 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 12.0000 | − | 20.7846i | 0.727607 | − | 1.26025i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.50000 | + | 2.59808i | 0.0904534 | + | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.00000 | − | 13.8564i | 0.480673 | − | 0.832551i | −0.519081 | − | 0.854725i | \(-0.673726\pi\) |
0.999754 | + | 0.0221745i | \(0.00705893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | + | 5.19615i | −0.178965 | + | 0.309976i | −0.941526 | − | 0.336939i | \(-0.890608\pi\) |
0.762561 | + | 0.646916i | \(0.223942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00000 | + | 8.66025i | 0.297219 | + | 0.514799i | 0.975499 | − | 0.220005i | \(-0.0706075\pi\) |
−0.678280 | + | 0.734804i | \(0.737274\pi\) | |||||||
\(284\) | −3.00000 | − | 5.19615i | −0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | 0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | 6.00000 | + | 10.3923i | 0.350524 | + | 0.607125i | 0.986341 | − | 0.164714i | \(-0.0526703\pi\) |
−0.635818 | + | 0.771839i | \(0.719337\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.50000 | − | 2.59808i | 0.0873334 | − | 0.151266i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 6.92820i | 0.230556 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 10.0000 | 0.572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | −6.00000 | + | 10.3923i | −0.341882 | + | 0.592157i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5000 | − | 23.3827i | −0.765515 | − | 1.32591i | −0.939974 | − | 0.341246i | \(-0.889151\pi\) |
0.174459 | − | 0.984664i | \(-0.444182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.00000 | + | 6.92820i | −0.226093 | + | 0.391605i | −0.956647 | − | 0.291250i | \(-0.905929\pi\) |
0.730554 | + | 0.682855i | \(0.239262\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.0000 | 1.80014 | ||||||||
\(317\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.5000 | − | 23.3827i | −0.755855 | − | 1.30918i | ||||
\(320\) | −4.00000 | − | 6.92820i | −0.223607 | − | 0.387298i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | − | 20.7846i | −0.661581 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5000 | − | 21.6506i | 0.687062 | − | 1.19003i | −0.285722 | − | 0.958313i | \(-0.592233\pi\) |
0.972784 | − | 0.231714i | \(-0.0744333\pi\) | |||||||
\(332\) | 24.0000 | 1.31717 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.00000 | − | 12.1244i | 0.382451 | − | 0.662424i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | + | 3.46410i | 0.108947 | + | 0.188702i | 0.915344 | − | 0.402673i | \(-0.131919\pi\) |
−0.806397 | + | 0.591375i | \(0.798585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | − | 10.3923i | 0.325396 | − | 0.563602i | ||||
\(341\) | 3.00000 | 0.162459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.00000 | − | 15.5885i | −0.483145 | − | 0.836832i | 0.516667 | − | 0.856186i | \(-0.327172\pi\) |
−0.999813 | + | 0.0193540i | \(0.993839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.50000 | + | 4.33013i | −0.133822 | + | 0.231786i | −0.925147 | − | 0.379610i | \(-0.876058\pi\) |
0.791325 | + | 0.611396i | \(0.209392\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | + | 10.3923i | −0.319348 | + | 0.553127i | −0.980352 | − | 0.197256i | \(-0.936797\pi\) |
0.661004 | + | 0.750382i | \(0.270130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.50000 | − | 2.59808i | −0.0796117 | − | 0.137892i | ||||
\(356\) | 15.0000 | + | 25.9808i | 0.794998 | + | 1.37698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0000 | −0.791670 | −0.395835 | − | 0.918322i | \(-0.629545\pi\) | ||||
−0.395835 | + | 0.918322i | \(0.629545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.00000 | − | 13.8564i | −0.419314 | − | 0.726273i | ||||
\(365\) | 1.00000 | + | 1.73205i | 0.0523424 | + | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.00000 | − | 8.66025i | 0.260998 | − | 0.452062i | −0.705509 | − | 0.708700i | \(-0.749282\pi\) |
0.966507 | + | 0.256639i | \(0.0826151\pi\) | |||||||
\(368\) | −24.0000 | −1.25109 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | + | 10.3923i | −0.311504 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0000 | − | 32.9090i | −0.983783 | − | 1.70396i | −0.647225 | − | 0.762299i | \(-0.724071\pi\) |
−0.336557 | − | 0.941663i | \(-0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 36.0000 | 1.85409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 1.00000 | − | 1.73205i | 0.0512989 | − | 0.0888523i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.00000 | + | 5.19615i | −0.152894 | + | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.00000 | 0.406138 | ||||||||
\(389\) | −15.0000 | + | 25.9808i | −0.760530 | + | 1.31728i | 0.182047 | + | 0.983290i | \(0.441728\pi\) |
−0.942578 | + | 0.333987i | \(0.891606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | − | 31.1769i | −0.910299 | − | 1.57668i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.0000 | 0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | 3.00000 | + | 5.19615i | 0.149813 | + | 0.259483i | 0.931158 | − | 0.364615i | \(-0.118800\pi\) |
−0.781345 | + | 0.624099i | \(0.785466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | −18.0000 | −0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | − | 20.7846i | 0.594818 | − | 1.03025i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00000 | − | 12.1244i | −0.346128 | − | 0.599511i | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.0000 | − | 24.2487i | 0.689730 | − | 1.19465i | ||||
\(413\) | 6.00000 | 0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | + | 10.3923i | 0.293119 | + | 0.507697i | 0.974546 | − | 0.224189i | \(-0.0719734\pi\) |
−0.681426 | + | 0.731887i | \(0.738640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.50000 | + | 4.33013i | −0.121843 | + | 0.211037i | −0.920494 | − | 0.390756i | \(-0.872214\pi\) |
0.798652 | + | 0.601793i | \(0.205547\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0000 | + | 17.3205i | 0.483934 | + | 0.838198i | ||||
\(428\) | −18.0000 | − | 31.1769i | −0.870063 | − | 1.50699i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | 0.722525 | 0.361262 | − | 0.932464i | \(-0.382346\pi\) | ||||
0.361262 | + | 0.932464i | \(0.382346\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0000 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | −3.00000 | − | 5.19615i | −0.143509 | − | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.500000 | − | 0.866025i | 0.0238637 | − | 0.0413331i | −0.853847 | − | 0.520524i | \(-0.825737\pi\) |
0.877711 | + | 0.479191i | \(0.159070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00000 | − | 10.3923i | 0.285069 | − | 0.493753i | −0.687557 | − | 0.726130i | \(-0.741317\pi\) |
0.972626 | + | 0.232377i | \(0.0746503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.50000 | + | 12.9904i | 0.355534 | + | 0.615803i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | − | 13.8564i | 0.377964 | − | 0.654654i | ||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | −0.423793 | ||||||||
\(452\) | 6.00000 | − | 10.3923i | 0.282216 | − | 0.488813i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | − | 6.92820i | −0.187523 | − | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.0000 | − | 24.2487i | 0.654892 | − | 1.13431i | −0.327028 | − | 0.945015i | \(-0.606047\pi\) |
0.981921 | − | 0.189292i | \(-0.0606194\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.0000 | −0.559503 | ||||||||
\(461\) | −10.5000 | + | 18.1865i | −0.489034 | + | 0.847031i | −0.999920 | − | 0.0126168i | \(-0.995984\pi\) |
0.510887 | + | 0.859648i | \(0.329317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.0000 | − | 22.5167i | −0.604161 | − | 1.04644i | −0.992183 | − | 0.124788i | \(-0.960175\pi\) |
0.388022 | − | 0.921650i | \(-0.373158\pi\) | |||||||
\(464\) | 18.0000 | + | 31.1769i | 0.835629 | + | 1.44735i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.00000 | −0.277647 | −0.138823 | − | 0.990317i | \(-0.544332\pi\) | ||||
−0.138823 | + | 0.990317i | \(0.544332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.0000 | 1.29292 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | − | 10.3923i | −0.275880 | − | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.500000 | − | 0.866025i | 0.0229416 | − | 0.0397360i | ||||
\(476\) | 24.0000 | 1.10004 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.5000 | + | 28.5788i | −0.753904 | + | 1.30580i | 0.192013 | + | 0.981392i | \(0.438498\pi\) |
−0.945917 | + | 0.324408i | \(0.894835\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | + | 27.7128i | 0.729537 | + | 1.26360i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | + | 3.46410i | −0.0909091 | + | 0.157459i | ||||
\(485\) | 4.00000 | 0.181631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.50000 | + | 7.79423i | 0.203082 | + | 0.351749i | 0.949520 | − | 0.313707i | \(-0.101571\pi\) |
−0.746438 | + | 0.665455i | \(0.768237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.0000 | + | 46.7654i | −1.21602 | + | 2.10621i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 3.00000 | − | 5.19615i | 0.134568 | − | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.50000 | + | 11.2583i | 0.290980 | + | 0.503992i | 0.974042 | − | 0.226369i | \(-0.0726854\pi\) |
−0.683062 | + | 0.730361i | \(0.739352\pi\) | |||||||
\(500\) | −1.00000 | − | 1.73205i | −0.0447214 | − | 0.0774597i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | + | 3.46410i | 0.0887357 | + | 0.153695i | ||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | + | 3.46410i | −0.0884748 | + | 0.153243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.00000 | − | 12.1244i | 0.308457 | − | 0.534263i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | + | 31.1769i | 0.791639 | + | 1.37116i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | −9.00000 | + | 15.5885i | −0.393167 | + | 0.680985i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.00000 | − | 5.19615i | −0.130682 | − | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.00000 | 0.173422 | ||||||||
\(533\) | 6.00000 | − | 10.3923i | 0.259889 | − | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00000 | − | 15.5885i | −0.389104 | − | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.00000 | 0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0000 | 0.988847 | 0.494424 | − | 0.869221i | \(-0.335379\pi\) | ||||
0.494424 | + | 0.869221i | \(0.335379\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.500000 | − | 0.866025i | −0.0214176 | − | 0.0370965i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | + | 6.92820i | −0.171028 | + | 0.296229i | −0.938779 | − | 0.344519i | \(-0.888042\pi\) |
0.767752 | + | 0.640747i | \(0.221375\pi\) | |||||||
\(548\) | −24.0000 | −1.02523 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.50000 | + | 7.79423i | −0.191706 | + | 0.332045i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | + | 27.7128i | 0.680389 | + | 1.17847i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.00000 | + | 12.1244i | −0.296866 | + | 0.514187i | ||||
\(557\) | 24.0000 | 1.01691 | 0.508456 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508456 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 4.00000 | − | 6.92820i | 0.169031 | − | 0.292770i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000 | + | 20.7846i | 0.505740 | + | 0.875967i | 0.999978 | + | 0.00664037i | \(0.00211371\pi\) |
−0.494238 | + | 0.869326i | \(0.664553\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | − | 5.19615i | 0.126211 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5000 | − | 23.3827i | 0.565949 | − | 0.980253i | −0.431011 | − | 0.902347i | \(-0.641843\pi\) |
0.996961 | − | 0.0779066i | \(-0.0248236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.50000 | + | 16.4545i | 0.397563 | + | 0.688599i | 0.993425 | − | 0.114488i | \(-0.0365228\pi\) |
−0.595862 | + | 0.803087i | \(0.703189\pi\) | |||||||
\(572\) | 12.0000 | + | 20.7846i | 0.501745 | + | 0.869048i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.0000 | −1.41544 | −0.707719 | − | 0.706494i | \(-0.750276\pi\) | ||||
−0.707719 | + | 0.706494i | \(0.750276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.00000 | + | 15.5885i | 0.373705 | + | 0.647275i | ||||
\(581\) | 12.0000 | + | 20.7846i | 0.497844 | + | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | − | 15.5885i | 0.372742 | − | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.0000 | − | 41.5692i | 0.990586 | − | 1.71575i | 0.376741 | − | 0.926319i | \(-0.377045\pi\) |
0.613845 | − | 0.789427i | \(-0.289622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.500000 | − | 0.866025i | −0.0206021 | − | 0.0356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.0000 | + | 27.7128i | −0.657596 | + | 1.13899i | ||||
\(593\) | 18.0000 | 0.739171 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | 0.491952 | ||||||||
\(596\) | 6.00000 | − | 10.3923i | 0.245770 | − | 0.425685i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5000 | + | 18.1865i | 0.429018 | + | 0.743082i | 0.996786 | − | 0.0801071i | \(-0.0255262\pi\) |
−0.567768 | + | 0.823189i | \(0.692193\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5000 | − | 26.8468i | 0.632258 | − | 1.09510i | −0.354831 | − | 0.934931i | \(-0.615462\pi\) |
0.987089 | − | 0.160173i | \(-0.0512051\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.00000 | 0.0813788 | ||||||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0000 | − | 17.3205i | −0.405887 | − | 0.703018i | 0.588537 | − | 0.808470i | \(-0.299704\pi\) |
−0.994424 | + | 0.105453i | \(0.966371\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0000 | + | 20.7846i | 0.483102 | + | 0.836757i | 0.999812 | − | 0.0194037i | \(-0.00617676\pi\) |
−0.516710 | + | 0.856161i | \(0.672843\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.0000 | + | 38.1051i | −0.884255 | + | 1.53157i | −0.0376891 | + | 0.999290i | \(0.512000\pi\) |
−0.846566 | + | 0.532284i | \(0.821334\pi\) | |||||||
\(620\) | −2.00000 | −0.0803219 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.0000 | + | 25.9808i | −0.600962 | + | 1.04090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.0000 | + | 27.7128i | −0.638470 | + | 1.10586i | ||||
\(629\) | −48.0000 | −1.91389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.0000 | −0.995234 | −0.497617 | − | 0.867397i | \(-0.665792\pi\) | ||||
−0.497617 | + | 0.867397i | \(0.665792\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.00000 | + | 1.73205i | 0.0396838 | + | 0.0687343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.00000 | + | 10.3923i | −0.237729 | + | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | − | 28.5788i | 0.651711 | − | 1.12880i | −0.330997 | − | 0.943632i | \(-0.607385\pi\) |
0.982708 | − | 0.185164i | \(-0.0592817\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | + | 3.46410i | 0.0788723 | + | 0.136611i | 0.902764 | − | 0.430137i | \(-0.141535\pi\) |
−0.823891 | + | 0.566748i | \(0.808201\pi\) | |||||||
\(644\) | −12.0000 | − | 20.7846i | −0.472866 | − | 0.819028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00000 | 0.235884 | 0.117942 | − | 0.993020i | \(-0.462370\pi\) | ||||
0.117942 | + | 0.993020i | \(0.462370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00000 | + | 3.46410i | 0.0783260 | + | 0.135665i | ||||
\(653\) | 12.0000 | + | 20.7846i | 0.469596 | + | 0.813365i | 0.999396 | − | 0.0347583i | \(-0.0110661\pi\) |
−0.529799 | + | 0.848123i | \(0.677733\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.50000 | + | 7.79423i | −0.175830 | + | 0.304546i | ||||
\(656\) | 12.0000 | 0.468521 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | − | 20.7846i | 0.467454 | − | 0.809653i | −0.531855 | − | 0.846836i | \(-0.678505\pi\) |
0.999309 | + | 0.0371821i | \(0.0118382\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.50000 | − | 4.33013i | −0.0972387 | − | 0.168422i | 0.813302 | − | 0.581842i | \(-0.197668\pi\) |
−0.910541 | + | 0.413419i | \(0.864334\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00000 | 0.0775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.0000 | 2.09089 | ||||||||
\(668\) | 6.00000 | − | 10.3923i | 0.232147 | − | 0.402090i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0000 | − | 25.9808i | −0.579069 | − | 1.00298i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0000 | − | 29.4449i | 0.655302 | − | 1.13502i | −0.326516 | − | 0.945192i | \(-0.605875\pi\) |
0.981818 | − | 0.189824i | \(-0.0607919\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | −0.230769 | ||||||||
\(677\) | −15.0000 | + | 25.9808i | −0.576497 | + | 0.998522i | 0.419380 | + | 0.907811i | \(0.362247\pi\) |
−0.995877 | + | 0.0907112i | \(0.971086\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000 | + | 6.92820i | 0.153506 | + | 0.265880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.00000 | + | 13.8564i | 0.304997 | + | 0.528271i | ||||
\(689\) | 12.0000 | + | 20.7846i | 0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0000 | + | 38.1051i | −0.836919 | + | 1.44959i | 0.0555386 | + | 0.998457i | \(0.482312\pi\) |
−0.892458 | + | 0.451130i | \(0.851021\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.50000 | + | 6.06218i | −0.132763 | + | 0.229952i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | + | 15.5885i | 0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.00000 | − | 3.46410i | 0.0755929 | − | 0.130931i | ||||
\(701\) | 15.0000 | 0.566542 | 0.283271 | − | 0.959040i | \(-0.408580\pi\) | ||||
0.283271 | + | 0.959040i | \(0.408580\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | −12.0000 | + | 20.7846i | −0.452267 | + | 0.783349i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.00000 | − | 15.5885i | −0.338480 | − | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.0000 | − | 19.0526i | 0.413114 | − | 0.715534i | −0.582115 | − | 0.813107i | \(-0.697775\pi\) |
0.995228 | + | 0.0975728i | \(0.0311079\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.00000 | + | 5.19615i | −0.112351 | + | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | + | 10.3923i | 0.224387 | + | 0.388650i | ||||
\(716\) | −9.00000 | − | 15.5885i | −0.336346 | − | 0.582568i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.0000 | 1.00693 | 0.503465 | − | 0.864016i | \(-0.332058\pi\) | ||||
0.503465 | + | 0.864016i | \(0.332058\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.0000 | 1.04277 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.0000 | + | 19.0526i | 0.408812 | + | 0.708083i | ||||
\(725\) | 4.50000 | + | 7.79423i | 0.167126 | + | 0.289470i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0000 | − | 24.2487i | 0.519231 | − | 0.899335i | −0.480519 | − | 0.876984i | \(-0.659552\pi\) |
0.999750 | − | 0.0223506i | \(-0.00711500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.00000 | − | 12.1244i | −0.258551 | − | 0.447823i | 0.707303 | − | 0.706910i | \(-0.249912\pi\) |
−0.965854 | + | 0.259087i | \(0.916578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.0000 | −1.54709 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.00000 | −0.257499 | −0.128750 | − | 0.991677i | \(-0.541096\pi\) | ||||
−0.128750 | + | 0.991677i | \(0.541096\pi\) | |||||||
\(740\) | −8.00000 | + | 13.8564i | −0.294086 | + | 0.509372i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.00000 | + | 15.5885i | 0.330178 | + | 0.571885i | 0.982547 | − | 0.186017i | \(-0.0595579\pi\) |
−0.652369 | + | 0.757902i | \(0.726225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00000 | − | 5.19615i | 0.109911 | − | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −36.0000 | −1.31629 | ||||||||
\(749\) | 18.0000 | − | 31.1769i | 0.657706 | − | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | −24.0000 | − | 41.5692i | −0.875190 | − | 1.51587i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.0000 | 0.726912 | 0.363456 | − | 0.931611i | \(-0.381597\pi\) | ||||
0.363456 | + | 0.931611i | \(0.381597\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.5000 | − | 28.5788i | −0.598125 | − | 1.03598i | −0.993098 | − | 0.117289i | \(-0.962579\pi\) |
0.394973 | − | 0.918693i | \(-0.370754\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00000 | − | 1.73205i | 0.0362024 | − | 0.0627044i | ||||
\(764\) | 30.0000 | 1.08536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000 | − | 10.3923i | 0.216647 | − | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.5000 | − | 35.5070i | −0.739249 | − | 1.28042i | −0.952834 | − | 0.303492i | \(-0.901847\pi\) |
0.213585 | − | 0.976924i | \(-0.431486\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.00000 | + | 6.92820i | −0.143963 | + | 0.249351i | ||||
\(773\) | 24.0000 | 0.863220 | 0.431610 | − | 0.902060i | \(-0.357946\pi\) | ||||
0.431610 | + | 0.902060i | \(0.357946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.50000 | + | 2.59808i | 0.0537431 | + | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.50000 | + | 7.79423i | −0.161023 | + | 0.278899i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.0000 | −0.428571 | ||||||||
\(785\) | −8.00000 | + | 13.8564i | −0.285532 | + | 0.494556i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.00000 | − | 12.1244i | −0.249523 | − | 0.432187i | 0.713871 | − | 0.700278i | \(-0.246941\pi\) |
−0.963394 | + | 0.268091i | \(0.913607\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000 | 0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.0000 | 1.42044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.0000 | − | 27.7128i | −0.567105 | − | 0.982255i | ||||
\(797\) | 12.0000 | + | 20.7846i | 0.425062 | + | 0.736229i | 0.996426 | − | 0.0844678i | \(-0.0269190\pi\) |
−0.571364 | + | 0.820696i | \(0.693586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0000 | − | 62.3538i | 1.27359 | − | 2.20592i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.00000 | − | 5.19615i | 0.105868 | − | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.00000 | − | 10.3923i | −0.211472 | − | 0.366281i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.0000 | 0.527372 | 0.263686 | − | 0.964609i | \(-0.415062\pi\) | ||||
0.263686 | + | 0.964609i | \(0.415062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.0000 | 0.807639 | 0.403820 | − | 0.914839i | \(-0.367682\pi\) | ||||
0.403820 | + | 0.914839i | \(0.367682\pi\) | |||||||
\(812\) | −18.0000 | + | 31.1769i | −0.631676 | + | 1.09410i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.00000 | + | 1.73205i | 0.0350285 | + | 0.0606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00000 | + | 3.46410i | −0.0699711 | + | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 22.5000 | − | 38.9711i | 0.785255 | − | 1.36010i | −0.143591 | − | 0.989637i | \(-0.545865\pi\) |
0.928846 | − | 0.370465i | \(-0.120802\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0000 | + | 19.0526i | 0.383436 | + | 0.664130i | 0.991551 | − | 0.129719i | \(-0.0414074\pi\) |
−0.608115 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0000 | −0.451509 | −0.225754 | − | 0.974184i | \(-0.572485\pi\) | ||||
−0.225754 | + | 0.974184i | \(0.572485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.0000 | − | 27.7128i | −0.554700 | − | 0.960769i | ||||
\(833\) | −9.00000 | − | 15.5885i | −0.311832 | − | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.00000 | − | 5.19615i | 0.103819 | − | 0.179820i | ||||
\(836\) | −6.00000 | −0.207514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.5000 | + | 38.9711i | −0.776786 | + | 1.34543i | 0.156999 | + | 0.987599i | \(0.449818\pi\) |
−0.933785 | + | 0.357834i | \(0.883515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | − | 45.0333i | −0.896552 | − | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.0000 | + | 22.5167i | −0.447478 | + | 0.775055i | ||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.00000 | −0.137442 | ||||||||
\(848\) | −12.0000 | + | 20.7846i | −0.412082 | + | 0.713746i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000 | + | 41.5692i | 0.822709 | + | 1.42497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0000 | − | 39.8372i | 0.787505 | − | 1.36400i | −0.139986 | − | 0.990153i | \(-0.544706\pi\) |
0.927491 | − | 0.373845i | \(-0.121961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.0000 | + | 41.5692i | −0.819824 | + | 1.41998i | 0.0859870 | + | 0.996296i | \(0.472596\pi\) |
−0.905811 | + | 0.423681i | \(0.860738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.5000 | + | 21.6506i | 0.426494 | + | 0.738710i | 0.996559 | − | 0.0828900i | \(-0.0264150\pi\) |
−0.570064 | + | 0.821600i | \(0.693082\pi\) | |||||||
\(860\) | 4.00000 | + | 6.92820i | 0.136399 | + | 0.236250i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.0000 | 1.02121 | 0.510606 | − | 0.859815i | \(-0.329421\pi\) | ||||
0.510606 | + | 0.859815i | \(0.329421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.00000 | 0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.00000 | − | 3.46410i | −0.0678844 | − | 0.117579i | ||||
\(869\) | −24.0000 | − | 41.5692i | −0.814144 | − | 1.41014i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.0000 | − | 48.4974i | 0.948744 | − | 1.64327i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | − | 1.73205i | 0.0338062 | − | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.0000 | − | 38.1051i | −0.742887 | − | 1.28672i | −0.951175 | − | 0.308651i | \(-0.900123\pi\) |
0.208288 | − | 0.978068i | \(-0.433211\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00000 | + | 10.3923i | −0.202260 | + | 0.350325i | ||||
\(881\) | 39.0000 | 1.31394 | 0.656972 | − | 0.753915i | \(-0.271837\pi\) | ||||
0.656972 | + | 0.753915i | \(0.271837\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.0000 | −1.54802 | −0.774012 | − | 0.633171i | \(-0.781753\pi\) | ||||
−0.774012 | + | 0.633171i | \(0.781753\pi\) | |||||||
\(884\) | 24.0000 | − | 41.5692i | 0.807207 | − | 1.39812i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.0000 | − | 31.1769i | −0.604381 | − | 1.04682i | −0.992149 | − | 0.125061i | \(-0.960087\pi\) |
0.387768 | − | 0.921757i | \(-0.373246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.00000 | + | 3.46410i | −0.0670778 | + | 0.116182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −40.0000 | −1.33930 | ||||||||
\(893\) | 6.00000 | − | 10.3923i | 0.200782 | − | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.50000 | − | 7.79423i | −0.150418 | − | 0.260532i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.00000 | 0.300167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.50000 | + | 9.52628i | 0.182826 | + | 0.316664i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.0000 | + | 32.9090i | −0.630885 | + | 1.09272i | 0.356487 | + | 0.934300i | \(0.383975\pi\) |
−0.987371 | + | 0.158424i | \(0.949359\pi\) | |||||||
\(908\) | 36.0000 | 1.19470 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.50000 | − | 7.79423i | 0.149092 | − | 0.258234i | −0.781800 | − | 0.623529i | \(-0.785698\pi\) |
0.930892 | + | 0.365295i | \(0.119032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | + | 17.3205i | −0.330409 | + | 0.572286i | ||||
\(917\) | −18.0000 | −0.594412 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.00000 | −0.230909 | −0.115454 | − | 0.993313i | \(-0.536832\pi\) | ||||
−0.115454 | + | 0.993313i | \(0.536832\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.00000 | − | 10.3923i | −0.197492 | − | 0.342067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | + | 6.92820i | −0.131519 | + | 0.227798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.5000 | − | 33.7750i | 0.639774 | − | 1.10812i | −0.345708 | − | 0.938342i | \(-0.612361\pi\) |
0.985482 | − | 0.169779i | \(-0.0543055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.50000 | − | 2.59808i | −0.0491605 | − | 0.0851485i | ||||
\(932\) | 12.0000 | + | 20.7846i | 0.393073 | + | 0.680823i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.0000 | −0.588663 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0000 | 0.457360 | 0.228680 | − | 0.973502i | \(-0.426559\pi\) | ||||
0.228680 | + | 0.973502i | \(0.426559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0000 | − | 20.7846i | −0.391397 | − | 0.677919i | ||||
\(941\) | −15.0000 | − | 25.9808i | −0.488986 | − | 0.846949i | 0.510934 | − | 0.859620i | \(-0.329300\pi\) |
−0.999920 | + | 0.0126715i | \(0.995966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | − | 15.5885i | 0.293080 | − | 0.507630i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.0000 | + | 25.9808i | −0.487435 | + | 0.844261i | −0.999896 | − | 0.0144491i | \(-0.995401\pi\) |
0.512461 | + | 0.858710i | \(0.328734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | + | 6.92820i | 0.129845 | + | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.0000 | −1.55487 | −0.777436 | − | 0.628962i | \(-0.783480\pi\) | ||||
−0.777436 | + | 0.628962i | \(0.783480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0000 | 0.485389 | ||||||||
\(956\) | −24.0000 | + | 41.5692i | −0.776215 | + | 1.34444i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.0000 | − | 20.7846i | −0.387500 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −34.0000 | −1.09507 | ||||||||
\(965\) | −2.00000 | + | 3.46410i | −0.0643823 | + | 0.111513i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.0000 | − | 43.3013i | −0.803946 | − | 1.39247i | −0.917000 | − | 0.398886i | \(-0.869397\pi\) |
0.113055 | − | 0.993589i | \(-0.463936\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.00000 | −0.0962746 | −0.0481373 | − | 0.998841i | \(-0.515328\pi\) | ||||
−0.0481373 | + | 0.998841i | \(0.515328\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.0000 | −0.448819 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.0000 | + | 34.6410i | 0.640184 | + | 1.10883i | ||||
\(977\) | 24.0000 | + | 41.5692i | 0.767828 | + | 1.32992i | 0.938738 | + | 0.344631i | \(0.111996\pi\) |
−0.170910 | + | 0.985287i | \(0.554671\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.5000 | − | 38.9711i | 0.719103 | − | 1.24552i | ||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.00000 | − | 5.19615i | 0.0956851 | − | 0.165732i | −0.814209 | − | 0.580572i | \(-0.802829\pi\) |
0.909894 | + | 0.414840i | \(0.136162\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | − | 6.92820i | 0.127257 | − | 0.220416i | ||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0000 | 1.49300 | 0.746502 | − | 0.665383i | \(-0.231732\pi\) | ||||
0.746502 | + | 0.665383i | \(0.231732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.00000 | − | 13.8564i | −0.253617 | − | 0.439278i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | − | 8.66025i | 0.158352 | − | 0.274273i | −0.775923 | − | 0.630828i | \(-0.782715\pi\) |
0.934274 | + | 0.356555i | \(0.116049\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 405.2.e.e.136.1 | 2 | ||
3.2 | odd | 2 | 405.2.e.d.136.1 | 2 | |||
9.2 | odd | 6 | 405.2.a.d.1.1 | yes | 1 | ||
9.4 | even | 3 | inner | 405.2.e.e.271.1 | 2 | ||
9.5 | odd | 6 | 405.2.e.d.271.1 | 2 | |||
9.7 | even | 3 | 405.2.a.c.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 6480.2.a.c.1.1 | 1 | |||
36.11 | even | 6 | 6480.2.a.o.1.1 | 1 | |||
45.2 | even | 12 | 2025.2.b.f.649.2 | 2 | |||
45.7 | odd | 12 | 2025.2.b.e.649.2 | 2 | |||
45.29 | odd | 6 | 2025.2.a.d.1.1 | 1 | |||
45.34 | even | 6 | 2025.2.a.c.1.1 | 1 | |||
45.38 | even | 12 | 2025.2.b.f.649.1 | 2 | |||
45.43 | odd | 12 | 2025.2.b.e.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.a.c.1.1 | ✓ | 1 | 9.7 | even | 3 | ||
405.2.a.d.1.1 | yes | 1 | 9.2 | odd | 6 | ||
405.2.e.d.136.1 | 2 | 3.2 | odd | 2 | |||
405.2.e.d.271.1 | 2 | 9.5 | odd | 6 | |||
405.2.e.e.136.1 | 2 | 1.1 | even | 1 | trivial | ||
405.2.e.e.271.1 | 2 | 9.4 | even | 3 | inner | ||
2025.2.a.c.1.1 | 1 | 45.34 | even | 6 | |||
2025.2.a.d.1.1 | 1 | 45.29 | odd | 6 | |||
2025.2.b.e.649.1 | 2 | 45.43 | odd | 12 | |||
2025.2.b.e.649.2 | 2 | 45.7 | odd | 12 | |||
2025.2.b.f.649.1 | 2 | 45.38 | even | 12 | |||
2025.2.b.f.649.2 | 2 | 45.2 | even | 12 | |||
6480.2.a.c.1.1 | 1 | 36.7 | odd | 6 | |||
6480.2.a.o.1.1 | 1 | 36.11 | even | 6 |