Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,2,Mod(1324,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2205.1324");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.d (of order \(2\), degree \(1\), 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: | \(17.6070136457\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1324.3 | ||
Root | \(0.403032 - 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1324 |
Dual form | 2205.2.d.l.1324.4 |
$q$-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 \(\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times\).
\(n\) | \(442\) | \(1081\) | \(1226\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.193937i | − | 0.137134i | −0.997647 | − | 0.0685669i | \(-0.978157\pi\) | ||
0.997647 | − | 0.0685669i | \(-0.0218427\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.96239 | 0.981194 | ||||||||
\(5\) | −1.48119 | + | 1.67513i | −0.662410 | + | 0.749141i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.768452i | − | 0.271689i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.324869 | + | 0.287258i | 0.102733 | + | 0.0908389i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.35026i | 0.374495i | 0.982313 | + | 0.187248i | \(0.0599567\pi\) | ||||
−0.982313 | + | 0.187248i | \(0.940043\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.77575 | 0.943937 | ||||||||
\(17\) | − | 3.35026i | − | 0.812558i | −0.913749 | − | 0.406279i | \(-0.866826\pi\) | ||
0.913749 | − | 0.406279i | \(-0.133174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.35026 | 1.22743 | 0.613717 | − | 0.789526i | \(-0.289674\pi\) | ||||
0.613717 | + | 0.789526i | \(0.289674\pi\) | |||||||
\(20\) | −2.90668 | + | 3.28726i | −0.649953 | + | 0.735053i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.387873i | 0.0826948i | ||||||||
\(23\) | 4.96239i | 1.03473i | 0.855765 | + | 0.517365i | \(0.173087\pi\) | ||||
−0.855765 | + | 0.517365i | \(0.826913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.612127 | − | 4.96239i | −0.122425 | − | 0.992478i | ||||
\(26\) | 0.261865 | 0.0513560 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.92478 | 1.47159 | 0.735797 | − | 0.677202i | \(-0.236808\pi\) | ||||
0.735797 | + | 0.677202i | \(0.236808\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.57452 | −0.821607 | −0.410804 | − | 0.911724i | \(-0.634752\pi\) | ||||
−0.410804 | + | 0.911724i | \(0.634752\pi\) | |||||||
\(32\) | − | 2.26916i | − | 0.401134i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.649738 | −0.111429 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.775746i | − | 0.127532i | −0.997965 | − | 0.0637660i | \(-0.979689\pi\) | ||
0.997965 | − | 0.0637660i | \(-0.0203111\pi\) | |||||||
\(38\) | − | 1.03761i | − | 0.168323i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.28726 | + | 1.13823i | 0.203533 | + | 0.179969i | ||||
\(41\) | 3.73813 | 0.583799 | 0.291899 | − | 0.956449i | \(-0.405713\pi\) | ||||
0.291899 | + | 0.956449i | \(0.405713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.6253i | 1.92534i | 0.270677 | + | 0.962670i | \(0.412752\pi\) | ||||
−0.270677 | + | 0.962670i | \(0.587248\pi\) | |||||||
\(44\) | −3.92478 | −0.591682 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.962389 | 0.141896 | ||||||||
\(47\) | 9.92478i | 1.44768i | 0.689969 | + | 0.723839i | \(0.257624\pi\) | ||||
−0.689969 | + | 0.723839i | \(0.742376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.962389 | + | 0.118714i | −0.136102 | + | 0.0167887i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.64974i | 0.367453i | ||||||||
\(53\) | 8.57452i | 1.17780i | 0.808206 | + | 0.588900i | \(0.200439\pi\) | ||||
−0.808206 | + | 0.588900i | \(0.799561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.96239 | − | 3.35026i | 0.399448 | − | 0.451749i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 1.53690i | − | 0.201805i | ||||||
\(59\) | 8.62530 | 1.12292 | 0.561459 | − | 0.827504i | \(-0.310240\pi\) | ||||
0.561459 | + | 0.827504i | \(0.310240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.70052 | 1.11399 | 0.556994 | − | 0.830517i | \(-0.311955\pi\) | ||||
0.556994 | + | 0.830517i | \(0.311955\pi\) | |||||||
\(62\) | 0.887166i | 0.112670i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.11142 | 0.888927 | ||||||||
\(65\) | −2.26187 | − | 2.00000i | −0.280550 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.92478i | 1.21250i | 0.795272 | + | 0.606252i | \(0.207328\pi\) | ||||
−0.795272 | + | 0.606252i | \(0.792672\pi\) | |||||||
\(68\) | − | 6.57452i | − | 0.797277i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.35026i | − | 1.09437i | −0.837013 | − | 0.547183i | \(-0.815700\pi\) | ||
0.837013 | − | 0.547183i | \(-0.184300\pi\) | |||||||
\(74\) | −0.150446 | −0.0174889 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.4993 | 1.20435 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.7005 | −1.20390 | −0.601951 | − | 0.798533i | \(-0.705610\pi\) | ||||
−0.601951 | + | 0.798533i | \(0.705610\pi\) | |||||||
\(80\) | −5.59261 | + | 6.32487i | −0.625273 | + | 0.707142i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 0.724961i | − | 0.0800586i | ||||||
\(83\) | − | 3.22425i | − | 0.353908i | −0.984219 | − | 0.176954i | \(-0.943376\pi\) | ||
0.984219 | − | 0.176954i | \(-0.0566244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.61213 | + | 4.96239i | 0.608721 | + | 0.538247i | ||||
\(86\) | 2.44851 | 0.264029 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.53690i | 0.163835i | ||||||||
\(89\) | −1.03761 | −0.109987 | −0.0549933 | − | 0.998487i | \(-0.517514\pi\) | ||||
−0.0549933 | + | 0.998487i | \(0.517514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.73813i | 1.01527i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.92478 | 0.198526 | ||||||||
\(95\) | −7.92478 | + | 8.96239i | −0.813065 | + | 0.919522i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.4993i | 1.87832i | 0.343482 | + | 0.939159i | \(0.388394\pi\) | ||||
−0.343482 | + | 0.939159i | \(0.611606\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.20123 | − | 9.73813i | −0.120123 | − | 0.973813i | ||||
\(101\) | −17.6629 | −1.75753 | −0.878763 | − | 0.477259i | \(-0.841630\pi\) | ||||
−0.878763 | + | 0.477259i | \(0.841630\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.70052i | 0.660222i | 0.943942 | + | 0.330111i | \(0.107086\pi\) | ||||
−0.943942 | + | 0.330111i | \(0.892914\pi\) | |||||||
\(104\) | 1.03761 | 0.101746 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.66291 | 0.161516 | ||||||||
\(107\) | − | 13.7381i | − | 1.32812i | −0.747681 | − | 0.664058i | \(-0.768833\pi\) | ||
0.747681 | − | 0.664058i | \(-0.231167\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.77575 | 0.265868 | 0.132934 | − | 0.991125i | \(-0.457560\pi\) | ||||
0.132934 | + | 0.991125i | \(0.457560\pi\) | |||||||
\(110\) | −0.649738 | − | 0.574515i | −0.0619501 | − | 0.0547779i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0508i | 1.13364i | 0.823841 | + | 0.566821i | \(0.191827\pi\) | ||||
−0.823841 | + | 0.566821i | \(0.808173\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.31265 | − | 7.35026i | −0.775159 | − | 0.685415i | ||||
\(116\) | 15.5515 | 1.44392 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.67276i | − | 0.153990i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | − | 1.68735i | − | 0.152765i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.97698 | −0.806156 | ||||||||
\(125\) | 9.21933 | + | 6.32487i | 0.824602 | + | 0.565713i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.70052i | 0.239633i | 0.992796 | + | 0.119816i | \(0.0382306\pi\) | ||||
−0.992796 | + | 0.119816i | \(0.961769\pi\) | |||||||
\(128\) | − | 5.91748i | − | 0.523037i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.387873 | + | 0.438658i | −0.0340187 | + | 0.0384729i | ||||
\(131\) | 20.6253 | 1.80204 | 0.901020 | − | 0.433777i | \(-0.142819\pi\) | ||||
0.901020 | + | 0.433777i | \(0.142819\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.92478 | 0.166275 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.57452 | −0.220763 | ||||||||
\(137\) | − | 22.4993i | − | 1.92224i | −0.276124 | − | 0.961122i | \(-0.589050\pi\) | ||
0.276124 | − | 0.961122i | \(-0.410950\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.27504 | −0.277785 | −0.138893 | − | 0.990307i | \(-0.544354\pi\) | ||||
−0.138893 | + | 0.990307i | \(0.544354\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.387873i | 0.0325496i | ||||||||
\(143\) | − | 2.70052i | − | 0.225829i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.7381 | + | 13.2750i | −0.974799 | + | 1.10243i | ||||
\(146\) | −1.81336 | −0.150075 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.52232i | − | 0.125134i | ||||||
\(149\) | −4.44851 | −0.364436 | −0.182218 | − | 0.983258i | \(-0.558328\pi\) | ||||
−0.182218 | + | 0.983258i | \(0.558328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.29948 | 0.105750 | 0.0528749 | − | 0.998601i | \(-0.483162\pi\) | ||||
0.0528749 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(152\) | − | 4.11142i | − | 0.333480i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.77575 | − | 7.66291i | 0.544241 | − | 0.615500i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.64974i | 0.211472i | 0.994394 | + | 0.105736i | \(0.0337199\pi\) | ||||
−0.994394 | + | 0.105736i | \(0.966280\pi\) | |||||||
\(158\) | 2.07522i | 0.165096i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.80114 | + | 3.36107i | 0.300506 | + | 0.265716i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.29948i | − | 0.415087i | −0.978226 | − | 0.207544i | \(-0.933453\pi\) | ||
0.978226 | − | 0.207544i | \(-0.0665469\pi\) | |||||||
\(164\) | 7.33567 | 0.572820 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.625301 | −0.0485327 | ||||||||
\(167\) | − | 14.5501i | − | 1.12592i | −0.826485 | − | 0.562959i | \(-0.809663\pi\) | ||
0.826485 | − | 0.562959i | \(-0.190337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1768 | 0.859753 | ||||||||
\(170\) | 0.962389 | − | 1.08840i | 0.0738118 | − | 0.0834762i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 24.7757i | 1.88913i | ||||||||
\(173\) | 4.49929i | 0.342075i | 0.985265 | + | 0.171037i | \(0.0547119\pi\) | ||||
−0.985265 | + | 0.171037i | \(0.945288\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.55149 | −0.569215 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.201231i | 0.0150829i | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6253 | −0.789772 | −0.394886 | − | 0.918730i | \(-0.629216\pi\) | ||||
−0.394886 | + | 0.918730i | \(0.629216\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.81336 | 0.281124 | ||||||||
\(185\) | 1.29948 | + | 1.14903i | 0.0955394 | + | 0.0844784i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.70052i | 0.489991i | ||||||||
\(188\) | 19.4763i | 1.42045i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.73813 | + | 1.53690i | 0.126098 | + | 0.111499i | ||||
\(191\) | 13.8496 | 1.00212 | 0.501059 | − | 0.865413i | \(-0.332944\pi\) | ||||
0.501059 | + | 0.865413i | \(0.332944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 15.3258i | − | 1.10318i | −0.834116 | − | 0.551588i | \(-0.814022\pi\) | ||
0.834116 | − | 0.551588i | \(-0.185978\pi\) | |||||||
\(194\) | 3.58769 | 0.257581 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.574515i | 0.0409325i | 0.999791 | + | 0.0204663i | \(0.00651507\pi\) | ||||
−0.999791 | + | 0.0204663i | \(0.993485\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.201231 | −0.0142649 | −0.00713244 | − | 0.999975i | \(-0.502270\pi\) | ||||
−0.00713244 | + | 0.999975i | \(0.502270\pi\) | |||||||
\(200\) | −3.81336 | + | 0.470390i | −0.269645 | + | 0.0332616i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.42548i | 0.241016i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.53690 | + | 6.26187i | −0.386714 | + | 0.437348i | ||||
\(206\) | 1.29948 | 0.0905388 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.09825i | 0.353500i | ||||||||
\(209\) | −10.7005 | −0.740171 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.44851 | 0.443934 | 0.221967 | − | 0.975054i | \(-0.428752\pi\) | ||||
0.221967 | + | 0.975054i | \(0.428752\pi\) | |||||||
\(212\) | 16.8265i | 1.15565i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.66433 | −0.182130 | ||||||||
\(215\) | −21.1490 | − | 18.7005i | −1.44235 | − | 1.27537i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 0.538319i | − | 0.0364595i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.81336 | − | 6.57452i | 0.391936 | − | 0.443254i | ||||
\(221\) | 4.52373 | 0.304299 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.55149i | 0.103896i | 0.998650 | + | 0.0519478i | \(0.0165429\pi\) | ||||
−0.998650 | + | 0.0519478i | \(0.983457\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.33709 | 0.155461 | ||||||||
\(227\) | − | 13.1490i | − | 0.872732i | −0.899769 | − | 0.436366i | \(-0.856265\pi\) | ||
0.899769 | − | 0.436366i | \(-0.143735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.77575 | 0.183426 | 0.0917132 | − | 0.995785i | \(-0.470766\pi\) | ||||
0.0917132 | + | 0.995785i | \(0.470766\pi\) | |||||||
\(230\) | −1.42548 | + | 1.61213i | −0.0939937 | + | 0.106300i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.08981i | − | 0.399816i | ||||||
\(233\) | − | 0.0507852i | − | 0.00332705i | −0.999999 | − | 0.00166353i | \(-0.999470\pi\) | ||
0.999999 | − | 0.00166353i | \(-0.000529517\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.6253 | − | 14.7005i | −1.08452 | − | 0.958956i | ||||
\(236\) | 16.9262 | 1.10180 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.84955 | 0.378376 | 0.189188 | − | 0.981941i | \(-0.439414\pi\) | ||||
0.189188 | + | 0.981941i | \(0.439414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0752228 | 0.00484553 | 0.00242276 | − | 0.999997i | \(-0.499229\pi\) | ||||
0.00242276 | + | 0.999997i | \(0.499229\pi\) | |||||||
\(242\) | 1.35756i | 0.0872670i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 17.0738 | 1.09304 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.22425i | 0.459668i | ||||||||
\(248\) | 3.51530i | 0.223222i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.22662 | − | 1.78797i | 0.0775785 | − | 0.113081i | ||||
\(251\) | 19.2243 | 1.21342 | 0.606712 | − | 0.794922i | \(-0.292488\pi\) | ||||
0.606712 | + | 0.794922i | \(0.292488\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.92478i | − | 0.623965i | ||||||
\(254\) | 0.523730 | 0.0328618 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.0752 | 0.817201 | ||||||||
\(257\) | 7.35026i | 0.458497i | 0.973368 | + | 0.229248i | \(0.0736268\pi\) | ||||
−0.973368 | + | 0.229248i | \(0.926373\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.43866 | − | 3.92478i | −0.275274 | − | 0.243404i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 4.00000i | − | 0.247121i | ||||||
\(263\) | − | 12.9624i | − | 0.799295i | −0.916669 | − | 0.399648i | \(-0.869133\pi\) | ||
0.916669 | − | 0.399648i | \(-0.130867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.3634 | − | 12.7005i | −0.882339 | − | 0.780187i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.4763i | 1.18970i | ||||||||
\(269\) | −4.11142 | −0.250678 | −0.125339 | − | 0.992114i | \(-0.540002\pi\) | ||||
−0.125339 | + | 0.992114i | \(0.540002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4241 | 0.997691 | 0.498846 | − | 0.866691i | \(-0.333757\pi\) | ||||
0.498846 | + | 0.866691i | \(0.333757\pi\) | |||||||
\(272\) | − | 12.6497i | − | 0.767003i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.36344 | −0.263605 | ||||||||
\(275\) | 1.22425 | + | 9.92478i | 0.0738253 | + | 0.598487i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 11.0738i | − | 0.665361i | −0.943040 | − | 0.332680i | \(-0.892047\pi\) | ||
0.943040 | − | 0.332680i | \(-0.107953\pi\) | |||||||
\(278\) | 0.635150i | 0.0380938i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.3733 | −0.857438 | −0.428719 | − | 0.903438i | \(-0.641035\pi\) | ||||
−0.428719 | + | 0.903438i | \(0.641035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.14903i | 0.0683028i | 0.999417 | + | 0.0341514i | \(0.0108728\pi\) | ||||
−0.999417 | + | 0.0341514i | \(0.989127\pi\) | |||||||
\(284\) | −3.92478 | −0.232893 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.523730 | −0.0309688 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.77575 | 0.339750 | ||||||||
\(290\) | 2.57452 | + | 2.27645i | 0.151181 | + | 0.133678i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 18.3488i | − | 1.07379i | ||||||
\(293\) | − | 0.649738i | − | 0.0379581i | −0.999820 | − | 0.0189791i | \(-0.993958\pi\) | ||
0.999820 | − | 0.0189791i | \(-0.00604158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.7757 | + | 14.4485i | −0.743833 | + | 0.841225i | ||||
\(296\) | −0.596124 | −0.0346490 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.862728i | 0.0499765i | ||||||||
\(299\) | −6.70052 | −0.387501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 0.252016i | − | 0.0145019i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.2012 | 1.15862 | ||||||||
\(305\) | −12.8872 | + | 14.5745i | −0.737917 | + | 0.834534i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.1016i | − | 1.37555i | −0.725924 | − | 0.687775i | \(-0.758588\pi\) | ||
0.725924 | − | 0.687775i | \(-0.241412\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.48612 | − | 1.31406i | −0.0844059 | − | 0.0746339i | ||||
\(311\) | 8.25202 | 0.467929 | 0.233964 | − | 0.972245i | \(-0.424830\pi\) | ||||
0.233964 | + | 0.972245i | \(0.424830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.9018i | − | 0.842297i | −0.906992 | − | 0.421148i | \(-0.861627\pi\) | ||
0.906992 | − | 0.421148i | \(-0.138373\pi\) | |||||||
\(314\) | 0.513881 | 0.0290000 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.9986 | −1.18126 | ||||||||
\(317\) | − | 10.1260i | − | 0.568733i | −0.958716 | − | 0.284367i | \(-0.908217\pi\) | ||
0.958716 | − | 0.284367i | \(-0.0917833\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.8496 | −0.887405 | ||||||||
\(320\) | −10.5334 | + | 11.9126i | −0.588835 | + | 0.665932i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 17.9248i | − | 0.997361i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.70052 | − | 0.826531i | 0.371678 | − | 0.0458477i | ||||
\(326\) | −1.02776 | −0.0569225 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 2.87258i | − | 0.158612i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.8496 | 1.53075 | 0.765375 | − | 0.643585i | \(-0.222554\pi\) | ||||
0.765375 | + | 0.643585i | \(0.222554\pi\) | |||||||
\(332\) | − | 6.32724i | − | 0.347252i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.82179 | −0.154402 | ||||||||
\(335\) | −16.6253 | − | 14.7005i | −0.908337 | − | 0.803175i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.84955i | − | 0.209699i | −0.994488 | − | 0.104849i | \(-0.966564\pi\) | ||
0.994488 | − | 0.104849i | \(-0.0334360\pi\) | |||||||
\(338\) | − | 2.16759i | − | 0.117901i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.0132 | + | 9.73813i | 0.597273 | + | 0.528125i | ||||
\(341\) | 9.14903 | 0.495448 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.70194 | 0.523093 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.872577 | 0.0469101 | ||||||||
\(347\) | − | 9.58769i | − | 0.514694i | −0.966319 | − | 0.257347i | \(-0.917152\pi\) | ||
0.966319 | − | 0.257347i | \(-0.0828484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.1490 | −0.810909 | −0.405455 | − | 0.914115i | \(-0.632887\pi\) | ||||
−0.405455 | + | 0.914115i | \(0.632887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.53832i | 0.241893i | ||||||||
\(353\) | 20.3488i | 1.08306i | 0.840681 | + | 0.541530i | \(0.182155\pi\) | ||||
−0.840681 | + | 0.541530i | \(0.817845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.96239 | − | 3.35026i | 0.157227 | − | 0.177813i | ||||
\(356\) | −2.03620 | −0.107918 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 1.93937i | − | 0.102499i | ||||||
\(359\) | −31.4010 | −1.65728 | −0.828642 | − | 0.559779i | \(-0.810886\pi\) | ||||
−0.828642 | + | 0.559779i | \(0.810886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.62530 | 0.506595 | ||||||||
\(362\) | 2.06063i | 0.108305i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.6629 | + | 13.8496i | 0.819834 | + | 0.724919i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.4010i | 1.53472i | 0.641215 | + | 0.767361i | \(0.278431\pi\) | ||||
−0.641215 | + | 0.767361i | \(0.721569\pi\) | |||||||
\(368\) | 18.7367i | 0.976719i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.222839 | − | 0.252016i | 0.0115849 | − | 0.0131017i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.0000i | − | 0.828449i | −0.910175 | − | 0.414224i | \(-0.864053\pi\) | ||
0.910175 | − | 0.414224i | \(-0.135947\pi\) | |||||||
\(374\) | 1.29948 | 0.0671943 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.62672 | 0.393318 | ||||||||
\(377\) | 10.7005i | 0.551105i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7005 | −0.549649 | −0.274824 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274824 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(380\) | −15.5515 | + | 17.5877i | −0.797775 | + | 0.902229i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 2.68594i | − | 0.137424i | ||||||
\(383\) | 16.7757i | 0.857201i | 0.903494 | + | 0.428600i | \(0.140993\pi\) | ||||
−0.903494 | + | 0.428600i | \(0.859007\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.97224 | −0.151283 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 36.3028i | 1.84300i | ||||||||
\(389\) | −29.3258 | −1.48688 | −0.743439 | − | 0.668804i | \(-0.766807\pi\) | ||||
−0.743439 | + | 0.668804i | \(0.766807\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.6253 | 0.840778 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.111420 | 0.00561324 | ||||||||
\(395\) | 15.8496 | − | 17.9248i | 0.797478 | − | 0.901893i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 18.3488i | − | 0.920902i | −0.887685 | − | 0.460451i | \(-0.847688\pi\) | ||
0.887685 | − | 0.460451i | \(-0.152312\pi\) | |||||||
\(398\) | 0.0390260i | 0.00195620i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.31124 | − | 18.7367i | −0.115562 | − | 0.936836i | ||||
\(401\) | 37.3258 | 1.86396 | 0.931981 | − | 0.362506i | \(-0.118079\pi\) | ||||
0.931981 | + | 0.362506i | \(0.118079\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.17679i | − | 0.307688i | ||||||
\(404\) | −34.6615 | −1.72447 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.55149i | 0.0769046i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.3733 | −1.10629 | −0.553144 | − | 0.833086i | \(-0.686572\pi\) | ||||
−0.553144 | + | 0.833086i | \(0.686572\pi\) | |||||||
\(410\) | 1.21440 | + | 1.07381i | 0.0599752 | + | 0.0530316i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.1490i | 0.647806i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.40105 | + | 4.77575i | 0.265127 | + | 0.234432i | ||||
\(416\) | 3.06396 | 0.150223 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.07522i | 0.101502i | ||||||||
\(419\) | −23.4763 | −1.14689 | −0.573445 | − | 0.819244i | \(-0.694394\pi\) | ||||
−0.573445 | + | 0.819244i | \(0.694394\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2243 | −1.22935 | −0.614677 | − | 0.788779i | \(-0.710714\pi\) | ||||
−0.614677 | + | 0.788779i | \(0.710714\pi\) | |||||||
\(422\) | − | 1.25060i | − | 0.0608783i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.58910 | 0.319995 | ||||||||
\(425\) | −16.6253 | + | 2.05079i | −0.806446 | + | 0.0994777i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 26.9596i | − | 1.30314i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.62672 | + | 4.10157i | −0.174896 | + | 0.197795i | ||||
\(431\) | 19.4010 | 0.934516 | 0.467258 | − | 0.884121i | \(-0.345242\pi\) | ||||
0.467258 | + | 0.884121i | \(0.345242\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.49929i | 0.312336i | 0.987731 | + | 0.156168i | \(0.0499141\pi\) | ||||
−0.987731 | + | 0.156168i | \(0.950086\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.44709 | 0.260868 | ||||||||
\(437\) | 26.5501i | 1.27006i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.6497 | −0.699194 | −0.349597 | − | 0.936900i | \(-0.613681\pi\) | ||||
−0.349597 | + | 0.936900i | \(0.613681\pi\) | |||||||
\(440\) | −2.57452 | − | 2.27645i | −0.122735 | − | 0.108526i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 0.877317i | − | 0.0417297i | ||||||
\(443\) | 19.1392i | 0.909330i | 0.890663 | + | 0.454665i | \(0.150241\pi\) | ||||
−0.890663 | + | 0.454665i | \(0.849759\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.53690 | − | 1.73813i | 0.0728562 | − | 0.0823955i | ||||
\(446\) | 0.300891 | 0.0142476 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.8021 | −1.54803 | −0.774013 | − | 0.633169i | \(-0.781754\pi\) | ||||
−0.774013 | + | 0.633169i | \(0.781754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.47627 | −0.352044 | ||||||||
\(452\) | 23.6483i | 1.11232i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.55008 | −0.119681 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 18.7005i | − | 0.874774i | −0.899273 | − | 0.437387i | \(-0.855904\pi\) | ||
0.899273 | − | 0.437387i | \(-0.144096\pi\) | |||||||
\(458\) | − | 0.538319i | − | 0.0251540i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.3127 | − | 14.4241i | −0.760581 | − | 0.672526i | ||||
\(461\) | −6.96239 | −0.324271 | −0.162135 | − | 0.986769i | \(-0.551838\pi\) | ||||
−0.162135 | + | 0.986769i | \(0.551838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.29948i | − | 0.246288i | −0.992389 | − | 0.123144i | \(-0.960702\pi\) | ||
0.992389 | − | 0.123144i | \(-0.0392976\pi\) | |||||||
\(464\) | 29.9219 | 1.38909 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.00984911 | −0.000456251 | ||||||||
\(467\) | − | 13.1490i | − | 0.608465i | −0.952598 | − | 0.304232i | \(-0.901600\pi\) | ||
0.952598 | − | 0.304232i | \(-0.0983999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.85097 | + | 3.22425i | −0.131505 | + | 0.148724i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 6.62813i | − | 0.305084i | ||||||
\(473\) | − | 25.2506i | − | 1.16102i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.27504 | − | 26.5501i | −0.150269 | − | 1.21820i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 1.13444i | − | 0.0518882i | ||||||
\(479\) | −5.14903 | −0.235265 | −0.117633 | − | 0.993057i | \(-0.537531\pi\) | ||||
−0.117633 | + | 0.993057i | \(0.537531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.04746 | 0.0477601 | ||||||||
\(482\) | − | 0.0145884i | − | 0.000664486i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.7367 | −0.624396 | ||||||||
\(485\) | −30.9887 | − | 27.4010i | −1.40713 | − | 1.24422i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.1768i | − | 1.00493i | −0.864599 | − | 0.502463i | \(-0.832427\pi\) | ||
0.864599 | − | 0.502463i | \(-0.167573\pi\) | |||||||
\(488\) | − | 6.68594i | − | 0.302658i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.00000 | −0.0902587 | −0.0451294 | − | 0.998981i | \(-0.514370\pi\) | ||||
−0.0451294 | + | 0.998981i | \(0.514370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 26.5501i | − | 1.19576i | ||||||
\(494\) | 1.40105 | 0.0630361 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.2722 | −0.775545 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.55008 | 0.293222 | 0.146611 | − | 0.989194i | \(-0.453163\pi\) | ||||
0.146611 | + | 0.989194i | \(0.453163\pi\) | |||||||
\(500\) | 18.0919 | + | 12.4119i | 0.809095 | + | 0.555075i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 3.72829i | − | 0.166402i | ||||||
\(503\) | − | 8.77575i | − | 0.391291i | −0.980675 | − | 0.195646i | \(-0.937320\pi\) | ||
0.980675 | − | 0.195646i | \(-0.0626802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.1622 | − | 29.5877i | 1.16420 | − | 1.31663i | ||||
\(506\) | −1.92478 | −0.0855668 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.29948i | 0.235126i | ||||||||
\(509\) | −13.1392 | −0.582384 | −0.291192 | − | 0.956665i | \(-0.594052\pi\) | ||||
−0.291192 | + | 0.956665i | \(0.594052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 14.3707i | − | 0.635103i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.42548 | 0.0628754 | ||||||||
\(515\) | −11.2243 | − | 9.92478i | −0.494600 | − | 0.437338i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 19.8496i | − | 0.872982i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.53690 | + | 1.73813i | −0.0673977 | + | 0.0762223i | ||||
\(521\) | −37.6629 | −1.65004 | −0.825021 | − | 0.565102i | \(-0.808837\pi\) | ||||
−0.825021 | + | 0.565102i | \(0.808837\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.00000i | − | 0.174908i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) | ||
0.996169 | − | 0.0874539i | \(-0.0278730\pi\) | |||||||
\(524\) | 40.4749 | 1.76815 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.51388 | −0.109610 | ||||||||
\(527\) | 15.3258i | 0.667603i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.62530 | −0.0706652 | ||||||||
\(530\) | −2.46310 | + | 2.78560i | −0.106990 | + | 0.120999i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.04746i | 0.218630i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.0132 | + | 20.3488i | 0.994946 | + | 0.879757i | ||||
\(536\) | 7.62672 | 0.329424 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.797355i | 0.0343764i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.4749 | −0.966269 | −0.483135 | − | 0.875546i | \(-0.660502\pi\) | ||||
−0.483135 | + | 0.875546i | \(0.660502\pi\) | |||||||
\(542\) | − | 3.18523i | − | 0.136817i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.60228 | −0.325945 | ||||||||
\(545\) | −4.11142 | + | 4.64974i | −0.176114 | + | 0.199173i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.9248i | − | 1.10846i | −0.832362 | − | 0.554232i | \(-0.813012\pi\) | ||
0.832362 | − | 0.554232i | \(-0.186988\pi\) | |||||||
\(548\) | − | 44.1524i | − | 1.88610i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.92478 | − | 0.237428i | 0.0820728 | − | 0.0101239i | ||||
\(551\) | 42.3996 | 1.80629 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.14762 | −0.0912435 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.42690 | −0.272561 | ||||||||
\(557\) | 28.5256i | 1.20867i | 0.796730 | + | 0.604335i | \(0.206561\pi\) | ||||
−0.796730 | + | 0.604335i | \(0.793439\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.0475 | −0.721031 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.78751i | 0.117584i | ||||||||
\(563\) | 11.6267i | 0.490008i | 0.969522 | + | 0.245004i | \(0.0787892\pi\) | ||||
−0.969522 | + | 0.245004i | \(0.921211\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.1866 | − | 17.8496i | −0.849258 | − | 0.750936i | ||||
\(566\) | 0.222839 | 0.00936663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.53690i | 0.0644871i | ||||||||
\(569\) | 9.32582 | 0.390959 | 0.195479 | − | 0.980708i | \(-0.437374\pi\) | ||||
0.195479 | + | 0.980708i | \(0.437374\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.6991 | −0.824382 | −0.412191 | − | 0.911097i | \(-0.635236\pi\) | ||||
−0.412191 | + | 0.911097i | \(0.635236\pi\) | |||||||
\(572\) | − | 5.29948i | − | 0.221582i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.6253 | − | 3.03761i | 1.02695 | − | 0.126677i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.7974i | − | 1.36537i | −0.730712 | − | 0.682686i | \(-0.760812\pi\) | ||
0.730712 | − | 0.682686i | \(-0.239188\pi\) | |||||||
\(578\) | − | 1.12013i | − | 0.0465912i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −23.0348 | + | 26.0508i | −0.956467 | + | 1.08170i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 17.1490i | − | 0.710240i | ||||||
\(584\) | −7.18523 | −0.297327 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.126008 | −0.00520534 | ||||||||
\(587\) | 18.8218i | 0.776859i | 0.921479 | + | 0.388429i | \(0.126982\pi\) | ||||
−0.921479 | + | 0.388429i | \(0.873018\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.4749 | −1.00847 | ||||||||
\(590\) | 2.80209 | + | 2.47768i | 0.115360 | + | 0.102005i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 2.92902i | − | 0.120382i | ||||||
\(593\) | − | 33.7499i | − | 1.38594i | −0.720965 | − | 0.692971i | \(-0.756301\pi\) | ||
0.720965 | − | 0.692971i | \(-0.243699\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.72970 | −0.357582 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.29948i | 0.0531395i | ||||||||
\(599\) | −20.2981 | −0.829356 | −0.414678 | − | 0.909968i | \(-0.636106\pi\) | ||||
−0.414678 | + | 0.909968i | \(0.636106\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.8496 | 0.564935 | 0.282468 | − | 0.959277i | \(-0.408847\pi\) | ||||
0.282468 | + | 0.959277i | \(0.408847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.55008 | 0.103761 | ||||||||
\(605\) | 10.3684 | − | 11.7259i | 0.421534 | − | 0.476726i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.2506i | 1.02489i | 0.858720 | + | 0.512445i | \(0.171260\pi\) | ||||
−0.858720 | + | 0.512445i | \(0.828740\pi\) | |||||||
\(608\) | − | 12.1406i | − | 0.492366i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.82653 | + | 2.49929i | 0.114443 | + | 0.101193i | ||||
\(611\) | −13.4010 | −0.542148 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.14903i | 0.369526i | 0.982783 | + | 0.184763i | \(0.0591517\pi\) | ||||
−0.982783 | + | 0.184763i | \(0.940848\pi\) | |||||||
\(614\) | −4.67418 | −0.188634 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.9492i | − | 0.642091i | −0.947064 | − | 0.321046i | \(-0.895966\pi\) | ||
0.947064 | − | 0.321046i | \(-0.104034\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1735 | 0.449100 | 0.224550 | − | 0.974463i | \(-0.427909\pi\) | ||||
0.224550 | + | 0.974463i | \(0.427909\pi\) | |||||||
\(620\) | 13.2966 | − | 15.0376i | 0.534006 | − | 0.603925i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 1.60037i | − | 0.0641689i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2506 | + | 6.07522i | −0.970024 | + | 0.243009i | ||||
\(626\) | −2.89000 | −0.115507 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.19982i | 0.207495i | ||||||||
\(629\) | −2.59895 | −0.103627 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.5501 | −0.579229 | −0.289615 | − | 0.957143i | \(-0.593527\pi\) | ||||
−0.289615 | + | 0.957143i | \(0.593527\pi\) | |||||||
\(632\) | 8.22284i | 0.327087i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.96380 | −0.0779926 | ||||||||
\(635\) | −4.52373 | − | 4.00000i | −0.179519 | − | 0.158735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.07381i | 0.121693i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.91256 | + | 8.76494i | 0.391828 | + | 0.346465i | ||||
\(641\) | 38.7269 | 1.52962 | 0.764810 | − | 0.644256i | \(-0.222833\pi\) | ||||
0.764810 | + | 0.644256i | \(0.222833\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.9511i | − | 0.471306i | −0.971837 | − | 0.235653i | \(-0.924277\pi\) | ||
0.971837 | − | 0.235653i | \(-0.0757229\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.47627 | −0.136772 | ||||||||
\(647\) | − | 14.5501i | − | 0.572023i | −0.958226 | − | 0.286011i | \(-0.907671\pi\) | ||
0.958226 | − | 0.286011i | \(-0.0923295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.2506 | −0.677145 | ||||||||
\(650\) | −0.160295 | − | 1.29948i | −0.00628727 | − | 0.0509697i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 10.3996i | − | 0.407281i | ||||||
\(653\) | 49.9756i | 1.95569i | 0.209319 | + | 0.977847i | \(0.432875\pi\) | ||||
−0.209319 | + | 0.977847i | \(0.567125\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.5501 | + | 34.5501i | −1.19369 | + | 1.34998i | ||||
\(656\) | 14.1142 | 0.551069 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9525 | −0.660377 | −0.330189 | − | 0.943915i | \(-0.607112\pi\) | ||||
−0.330189 | + | 0.943915i | \(0.607112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6531 | 0.608834 | 0.304417 | − | 0.952539i | \(-0.401538\pi\) | ||||
0.304417 | + | 0.952539i | \(0.401538\pi\) | |||||||
\(662\) | − | 5.40105i | − | 0.209918i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.47768 | −0.0961528 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.3258i | 1.52270i | ||||||||
\(668\) | − | 28.5529i | − | 1.10475i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.85097 | + | 3.22425i | −0.110143 | + | 0.124564i | ||||
\(671\) | −17.4010 | −0.671760 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 26.0263i | − | 1.00324i | −0.865088 | − | 0.501621i | \(-0.832737\pi\) | ||
0.865088 | − | 0.501621i | \(-0.167263\pi\) | |||||||
\(674\) | −0.746569 | −0.0287568 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.9332 | 0.843585 | ||||||||
\(677\) | − | 35.4518i | − | 1.36252i | −0.732039 | − | 0.681262i | \(-0.761431\pi\) | ||
0.732039 | − | 0.681262i | \(-0.238569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.81336 | − | 4.31265i | 0.146236 | − | 0.165383i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 1.77433i | − | 0.0679427i | ||||||
\(683\) | − | 23.6629i | − | 0.905436i | −0.891654 | − | 0.452718i | \(-0.850454\pi\) | ||
0.891654 | − | 0.452718i | \(-0.149546\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.6893 | + | 33.3258i | 1.44003 | + | 1.27331i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 47.6699i | 1.81740i | ||||||||
\(689\) | −11.5778 | −0.441081 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.574515 | 0.0218556 | 0.0109278 | − | 0.999940i | \(-0.496522\pi\) | ||||
0.0109278 | + | 0.999940i | \(0.496522\pi\) | |||||||
\(692\) | 8.82936i | 0.335642i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.85940 | −0.0705820 | ||||||||
\(695\) | 4.85097 | − | 5.48612i | 0.184008 | − | 0.208100i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.5237i | − | 0.474370i | ||||||
\(698\) | 2.93795i | 0.111203i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.7269 | −1.61377 | −0.806886 | − | 0.590707i | \(-0.798849\pi\) | ||||
−0.806886 | + | 0.590707i | \(0.798849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.15045i | − | 0.156537i | ||||||
\(704\) | −14.2228 | −0.536043 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.94639 | 0.148524 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.2506 | −1.02342 | −0.511709 | − | 0.859159i | \(-0.670987\pi\) | ||||
−0.511709 | + | 0.859159i | \(0.670987\pi\) | |||||||
\(710\) | −0.649738 | − | 0.574515i | −0.0243842 | − | 0.0215612i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.797355i | 0.0298821i | ||||||||
\(713\) | − | 22.7005i | − | 0.850141i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.52373 | + | 4.00000i | 0.169178 | + | 0.149592i | ||||
\(716\) | 19.6239 | 0.733379 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.08981i | 0.227270i | ||||||||
\(719\) | 10.7005 | 0.399062 | 0.199531 | − | 0.979891i | \(-0.436058\pi\) | ||||
0.199531 | + | 0.979891i | \(0.436058\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.86670i | − | 0.0694713i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.8510 | −0.774920 | ||||||||
\(725\) | −4.85097 | − | 39.3258i | −0.180160 | − | 1.46052i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 39.9511i | − | 1.48171i | −0.671668 | − | 0.740853i | \(-0.734422\pi\) | ||
0.671668 | − | 0.740853i | \(-0.265578\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.68594 | − | 3.03761i | 0.0994109 | − | 0.112427i | ||||
\(731\) | 42.2981 | 1.56445 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30.3488i | − | 1.12096i | −0.828168 | − | 0.560480i | \(-0.810617\pi\) | ||
0.828168 | − | 0.560480i | \(-0.189383\pi\) | |||||||
\(734\) | 5.70194 | 0.210462 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.2605 | 0.415066 | ||||||||
\(737\) | − | 19.8496i | − | 0.731168i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.2506 | −1.37029 | −0.685143 | − | 0.728409i | \(-0.740260\pi\) | ||||
−0.685143 | + | 0.728409i | \(0.740260\pi\) | |||||||
\(740\) | 2.55008 | + | 2.25485i | 0.0937427 | + | 0.0828898i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.3634i | 0.967181i | 0.875294 | + | 0.483590i | \(0.160668\pi\) | ||||
−0.875294 | + | 0.483590i | \(0.839332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.58910 | − | 7.45183i | 0.241406 | − | 0.273014i | ||||
\(746\) | −3.10299 | −0.113608 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.1490i | 0.480776i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.6516 | 1.84830 | 0.924152 | − | 0.382024i | \(-0.124773\pi\) | ||||
0.924152 | + | 0.382024i | \(0.124773\pi\) | |||||||
\(752\) | 37.4734i | 1.36652i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.07522 | 0.0755752 | ||||||||
\(755\) | −1.92478 | + | 2.17679i | −0.0700498 | + | 0.0792216i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.9525i | 1.41575i | 0.706336 | + | 0.707877i | \(0.250347\pi\) | ||||
−0.706336 | + | 0.707877i | \(0.749653\pi\) | |||||||
\(758\) | 2.07522i | 0.0753755i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.88717 | + | 6.08981i | 0.249824 | + | 0.220901i | ||||
\(761\) | 48.2130 | 1.74772 | 0.873860 | − | 0.486178i | \(-0.161609\pi\) | ||||
0.873860 | + | 0.486178i | \(0.161609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.1782 | 0.983273 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.25343 | 0.117551 | ||||||||
\(767\) | 11.6464i | 0.420528i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.44851 | 0.160417 | 0.0802086 | − | 0.996778i | \(-0.474441\pi\) | ||||
0.0802086 | + | 0.996778i | \(0.474441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 30.0752i | − | 1.08243i | ||||||
\(773\) | − | 39.3014i | − | 1.41357i | −0.707427 | − | 0.706786i | \(-0.750144\pi\) | ||
0.707427 | − | 0.706786i | \(-0.249856\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.80018 | + | 22.7005i | 0.100586 | + | 0.815427i | ||||
\(776\) | 14.2158 | 0.510318 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.68735i | 0.203901i | ||||||||
\(779\) | 20.0000 | 0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | − | 3.22425i | − | 0.115299i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.43866 | − | 3.92478i | −0.158423 | − | 0.140081i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 0.897015i | − | 0.0319751i | −0.999872 | − | 0.0159876i | \(-0.994911\pi\) | ||
0.999872 | − | 0.0159876i | \(-0.00508922\pi\) | |||||||
\(788\) | 1.12742i | 0.0401628i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.47627 | − | 3.07381i | −0.123680 | − | 0.109361i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.7480i | 0.417183i | ||||||||
\(794\) | −3.55851 | −0.126287 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.394893 | −0.0139966 | ||||||||
\(797\) | 3.19982i | 0.113343i | 0.998393 | + | 0.0566717i | \(0.0180488\pi\) | ||||
−0.998393 | + | 0.0566717i | \(0.981951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.2506 | 1.17632 | ||||||||
\(800\) | −11.2605 | + | 1.38901i | −0.398117 | + | 0.0491090i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 7.23884i | − | 0.255612i | ||||||
\(803\) | 18.7005i | 0.659927i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.19791 | −0.0421944 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.5731i | 0.477500i | ||||||||
\(809\) | 4.44851 | 0.156401 | 0.0782006 | − | 0.996938i | \(-0.475083\pi\) | ||||
0.0782006 | + | 0.996938i | \(0.475083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.6747 | −1.32294 | −0.661468 | − | 0.749973i | \(-0.730066\pi\) | ||||
−0.661468 | + | 0.749973i | \(0.730066\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.300891 | 0.0105462 | ||||||||
\(815\) | 8.87732 | + | 7.84955i | 0.310959 | + | 0.274958i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 67.5487i | 2.36323i | ||||||||
\(818\) | 4.33900i | 0.151710i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.8656 | + | 12.2882i | −0.379442 | + | 0.429123i | ||||
\(821\) | 0.749399 | 0.0261542 | 0.0130771 | − | 0.999914i | \(-0.495837\pi\) | ||||
0.0130771 | + | 0.999914i | \(0.495837\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.3996i | 0.920233i | 0.887858 | + | 0.460117i | \(0.152192\pi\) | ||||
−0.887858 | + | 0.460117i | \(0.847808\pi\) | |||||||
\(824\) | 5.14903 | 0.179375 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.43724i | − | 0.189071i | −0.995521 | − | 0.0945357i | \(-0.969863\pi\) | ||
0.995521 | − | 0.0945357i | \(-0.0301367\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.7757 | 0.791034 | 0.395517 | − | 0.918459i | \(-0.370565\pi\) | ||||
0.395517 | + | 0.918459i | \(0.370565\pi\) | |||||||
\(830\) | 0.926192 | − | 1.04746i | 0.0321486 | − | 0.0363579i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.60228i | 0.332899i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.3733 | + | 21.5515i | 0.843472 | + | 0.745820i | ||||
\(836\) | −20.9986 | −0.726251 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.55291i | 0.157278i | ||||||||
\(839\) | −15.8496 | −0.547187 | −0.273594 | − | 0.961845i | \(-0.588212\pi\) | ||||
−0.273594 | + | 0.961845i | \(0.588212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8021 | 1.16559 | ||||||||
\(842\) | 4.89191i | 0.168586i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.6545 | 0.435585 | ||||||||
\(845\) | −16.5550 | + | 18.7226i | −0.569509 | + | 0.644077i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 32.3752i | 1.11177i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.397722 | + | 3.22425i | 0.0136418 | + | 0.110591i | ||||
\(851\) | 3.84955 | 0.131961 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 21.0494i | − | 0.720717i | −0.932814 | − | 0.360358i | \(-0.882654\pi\) | ||
0.932814 | − | 0.360358i | \(-0.117346\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.5571 | −0.360834 | ||||||||
\(857\) | 50.1524i | 1.71317i | 0.516004 | + | 0.856586i | \(0.327419\pi\) | ||||
−0.516004 | + | 0.856586i | \(0.672581\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.35026 | −0.182549 | −0.0912743 | − | 0.995826i | \(-0.529094\pi\) | ||||
−0.0912743 | + | 0.995826i | \(0.529094\pi\) | |||||||
\(860\) | −41.5026 | − | 36.6977i | −1.41523 | − | 1.25138i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 3.76257i | − | 0.128154i | ||||||
\(863\) | − | 33.6893i | − | 1.14680i | −0.819277 | − | 0.573398i | \(-0.805625\pi\) | ||
0.819277 | − | 0.573398i | \(-0.194375\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.53690 | − | 6.66433i | −0.256262 | − | 0.226594i | ||||
\(866\) | 1.26045 | 0.0428319 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.4010 | 0.725981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.4010 | −0.454077 | ||||||||
\(872\) | − | 2.13303i | − | 0.0722334i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.14903 | 0.174169 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 21.5026i | − | 0.726092i | −0.931771 | − | 0.363046i | \(-0.881737\pi\) | ||
0.931771 | − | 0.363046i | \(-0.118263\pi\) | |||||||
\(878\) | 2.84112i | 0.0958832i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11.1852 | − | 12.6497i | 0.377054 | − | 0.426423i | ||||
\(881\) | 32.3634 | 1.09035 | 0.545176 | − | 0.838322i | \(-0.316463\pi\) | ||||
0.545176 | + | 0.838322i | \(0.316463\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.59895i | 0.0874617i | 0.999043 | + | 0.0437309i | \(0.0139244\pi\) | ||||
−0.999043 | + | 0.0437309i | \(0.986076\pi\) | |||||||
\(884\) | 8.87732 | 0.298576 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.71179 | 0.124700 | ||||||||
\(887\) | 38.2784i | 1.28526i | 0.766176 | + | 0.642631i | \(0.222157\pi\) | ||||
−0.766176 | + | 0.642631i | \(0.777843\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.337088 | − | 0.298062i | −0.0112992 | − | 0.00999106i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.04463i | 0.101942i | ||||||||
\(893\) | 53.1002i | 1.77693i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.8119 | + | 16.7513i | −0.495109 | + | 0.559934i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.36153i | 0.212287i | ||||||||
\(899\) | −36.2520 | −1.20907 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.7269 | 0.957031 | ||||||||
\(902\) | 1.44992i | 0.0482771i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.26045 | 0.307998 | ||||||||
\(905\) | 15.7381 | − | 17.7988i | 0.523153 | − | 0.591651i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 49.9972i | − | 1.66013i | −0.557668 | − | 0.830064i | \(-0.688304\pi\) | ||
0.557668 | − | 0.830064i | \(-0.311696\pi\) | |||||||
\(908\) | − | 25.8035i | − | 0.856320i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9525 | 0.826715 | 0.413357 | − | 0.910569i | \(-0.364356\pi\) | ||||
0.413357 | + | 0.910569i | \(0.364356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.44851i | 0.213414i | ||||||||
\(914\) | −3.62672 | −0.119961 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.44709 | 0.179977 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.6991 | 0.385918 | 0.192959 | − | 0.981207i | \(-0.438192\pi\) | ||||
0.192959 | + | 0.981207i | \(0.438192\pi\) | |||||||
\(920\) | −5.64832 | + | 6.38787i | −0.186220 | + | 0.210602i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.35026i | 0.0444685i | ||||||||
\(923\) | − | 2.70052i | − | 0.0888888i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.84955 | + | 0.474855i | −0.126573 | + | 0.0156131i | ||||
\(926\) | −1.02776 | −0.0337744 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 17.9826i | − | 0.590307i | ||||||
\(929\) | −23.7090 | −0.777866 | −0.388933 | − | 0.921266i | \(-0.627156\pi\) | ||||
−0.388933 | + | 0.921266i | \(0.627156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 0.0996603i | − | 0.00326448i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.55008 | −0.0834411 | ||||||||
\(935\) | −11.2243 | − | 9.92478i | −0.367072 | − | 0.324575i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.9003i | 0.650116i | 0.945694 | + | 0.325058i | \(0.105384\pi\) | ||||
−0.945694 | + | 0.325058i | \(0.894616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −32.6253 | − | 28.8481i | −1.06412 | − | 0.940923i | ||||
\(941\) | −6.28821 | −0.204990 | −0.102495 | − | 0.994734i | \(-0.532683\pi\) | ||||
−0.102495 | + | 0.994734i | \(0.532683\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.5501i | 0.604074i | ||||||||
\(944\) | 32.5669 | 1.05996 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.89701 | −0.159216 | ||||||||
\(947\) | 40.0362i | 1.30100i | 0.759506 | + | 0.650501i | \(0.225441\pi\) | ||||
−0.759506 | + | 0.650501i | \(0.774559\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.6253 | 0.409835 | ||||||||
\(950\) | −5.14903 | + | 0.635150i | −0.167057 | + | 0.0206070i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.9478i | 1.32643i | 0.748429 | + | 0.663215i | \(0.230808\pi\) | ||||
−0.748429 | + | 0.663215i | \(0.769192\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.5139 | + | 23.1998i | −0.663814 | + | 0.750728i | ||||
\(956\) | 11.4791 | 0.371261 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.998585i | 0.0322628i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.0738 | −0.324962 | ||||||||
\(962\) | − | 0.203141i | − | 0.00654953i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.147616 | 0.00475440 | ||||||||
\(965\) | 25.6728 | + | 22.7005i | 0.826435 | + | 0.730756i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.2784i | 1.23095i | 0.788157 | + | 0.615475i | \(0.211036\pi\) | ||||
−0.788157 | + | 0.615475i | \(0.788964\pi\) | |||||||
\(968\) | 5.37916i | 0.172893i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.31406 | + | 6.00985i | −0.170624 | + | 0.192965i | ||||
\(971\) | −28.7269 | −0.921889 | −0.460945 | − | 0.887429i | \(-0.652489\pi\) | ||||
−0.460945 | + | 0.887429i | \(0.652489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.30089 | −0.137809 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.8510 | 1.05153 | ||||||||
\(977\) | 41.3014i | 1.32135i | 0.750673 | + | 0.660674i | \(0.229730\pi\) | ||||
−0.750673 | + | 0.660674i | \(0.770270\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.07522 | 0.0663244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.387873i | 0.0123775i | ||||||||
\(983\) | 24.0000i | 0.765481i | 0.923856 | + | 0.382741i | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.962389 | − | 0.850969i | −0.0306643 | − | 0.0271141i | ||||
\(986\) | −5.14903 | −0.163979 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.1768i | 0.451024i | ||||||||
\(989\) | −62.6516 | −1.99221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.1002 | 0.797333 | 0.398666 | − | 0.917096i | \(-0.369473\pi\) | ||||
0.398666 | + | 0.917096i | \(0.369473\pi\) | |||||||
\(992\) | 10.3803i | 0.329575i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.298062 | − | 0.337088i | 0.00944920 | − | 0.0106864i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 32.7974i | − | 1.03870i | −0.854561 | − | 0.519351i | \(-0.826174\pi\) | ||
0.854561 | − | 0.519351i | \(-0.173826\pi\) | |||||||
\(998\) | − | 1.27030i | − | 0.0402106i | ||||||
\(999\) | 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 | 2205.2.d.l.1324.3 | 6 | ||
3.2 | odd | 2 | 735.2.d.b.589.4 | 6 | |||
5.4 | even | 2 | inner | 2205.2.d.l.1324.4 | 6 | ||
7.6 | odd | 2 | 315.2.d.e.64.3 | 6 | |||
15.2 | even | 4 | 3675.2.a.bi.1.2 | 3 | |||
15.8 | even | 4 | 3675.2.a.bj.1.2 | 3 | |||
15.14 | odd | 2 | 735.2.d.b.589.3 | 6 | |||
21.2 | odd | 6 | 735.2.q.f.214.4 | 12 | |||
21.5 | even | 6 | 735.2.q.e.214.4 | 12 | |||
21.11 | odd | 6 | 735.2.q.f.79.3 | 12 | |||
21.17 | even | 6 | 735.2.q.e.79.3 | 12 | |||
21.20 | even | 2 | 105.2.d.b.64.4 | yes | 6 | ||
28.27 | even | 2 | 5040.2.t.v.1009.5 | 6 | |||
35.13 | even | 4 | 1575.2.a.w.1.2 | 3 | |||
35.27 | even | 4 | 1575.2.a.x.1.2 | 3 | |||
35.34 | odd | 2 | 315.2.d.e.64.4 | 6 | |||
84.83 | odd | 2 | 1680.2.t.k.1009.1 | 6 | |||
105.44 | odd | 6 | 735.2.q.f.214.3 | 12 | |||
105.59 | even | 6 | 735.2.q.e.79.4 | 12 | |||
105.62 | odd | 4 | 525.2.a.j.1.2 | 3 | |||
105.74 | odd | 6 | 735.2.q.f.79.4 | 12 | |||
105.83 | odd | 4 | 525.2.a.k.1.2 | 3 | |||
105.89 | even | 6 | 735.2.q.e.214.3 | 12 | |||
105.104 | even | 2 | 105.2.d.b.64.3 | ✓ | 6 | ||
140.139 | even | 2 | 5040.2.t.v.1009.6 | 6 | |||
420.83 | even | 4 | 8400.2.a.dj.1.3 | 3 | |||
420.167 | even | 4 | 8400.2.a.dg.1.1 | 3 | |||
420.419 | odd | 2 | 1680.2.t.k.1009.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.3 | ✓ | 6 | 105.104 | even | 2 | ||
105.2.d.b.64.4 | yes | 6 | 21.20 | even | 2 | ||
315.2.d.e.64.3 | 6 | 7.6 | odd | 2 | |||
315.2.d.e.64.4 | 6 | 35.34 | odd | 2 | |||
525.2.a.j.1.2 | 3 | 105.62 | odd | 4 | |||
525.2.a.k.1.2 | 3 | 105.83 | odd | 4 | |||
735.2.d.b.589.3 | 6 | 15.14 | odd | 2 | |||
735.2.d.b.589.4 | 6 | 3.2 | odd | 2 | |||
735.2.q.e.79.3 | 12 | 21.17 | even | 6 | |||
735.2.q.e.79.4 | 12 | 105.59 | even | 6 | |||
735.2.q.e.214.3 | 12 | 105.89 | even | 6 | |||
735.2.q.e.214.4 | 12 | 21.5 | even | 6 | |||
735.2.q.f.79.3 | 12 | 21.11 | odd | 6 | |||
735.2.q.f.79.4 | 12 | 105.74 | odd | 6 | |||
735.2.q.f.214.3 | 12 | 105.44 | odd | 6 | |||
735.2.q.f.214.4 | 12 | 21.2 | odd | 6 | |||
1575.2.a.w.1.2 | 3 | 35.13 | even | 4 | |||
1575.2.a.x.1.2 | 3 | 35.27 | even | 4 | |||
1680.2.t.k.1009.1 | 6 | 84.83 | odd | 2 | |||
1680.2.t.k.1009.4 | 6 | 420.419 | odd | 2 | |||
2205.2.d.l.1324.3 | 6 | 1.1 | even | 1 | trivial | ||
2205.2.d.l.1324.4 | 6 | 5.4 | even | 2 | inner | ||
3675.2.a.bi.1.2 | 3 | 15.2 | even | 4 | |||
3675.2.a.bj.1.2 | 3 | 15.8 | even | 4 | |||
5040.2.t.v.1009.5 | 6 | 28.27 | even | 2 | |||
5040.2.t.v.1009.6 | 6 | 140.139 | even | 2 | |||
8400.2.a.dg.1.1 | 3 | 420.167 | even | 4 | |||
8400.2.a.dj.1.3 | 3 | 420.83 | even | 4 |