Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("1620.541");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (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: | \(12.9357651274\) |
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 | 541.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.541 |
Dual form | 1620.2.i.g.1081.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 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 | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 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 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −4.00000 | + | 6.92820i | −0.609994 | + | 1.05654i | 0.381246 | + | 0.924473i | \(0.375495\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 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 | 0.946993 | − | 0.321253i | \(-0.104104\pi\) |
−0.751710 | + | 0.659494i | \(0.770771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.00000 | + | 12.1244i | −0.896258 | + | 1.55236i | −0.0640184 | + | 0.997949i | \(0.520392\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | + | 3.46410i | −0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0000 | 1.78017 | 0.890086 | − | 0.455792i | \(-0.150644\pi\) | ||||
0.890086 | + | 0.455792i | \(0.150644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.00000 | − | 5.19615i | −0.341882 | − | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(84\) | 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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.50000 | − | 6.06218i | −0.359092 | − | 0.621966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | + | 6.92820i | −0.406138 | + | 0.703452i | −0.994453 | − | 0.105180i | \(-0.966458\pi\) |
0.588315 | + | 0.808632i | \(0.299792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50000 | − | 2.59808i | 0.149256 | − | 0.258518i | −0.781697 | − | 0.623658i | \(-0.785646\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.00000 | − | 1.73205i | −0.0985329 | − | 0.170664i | 0.812545 | − | 0.582899i | \(-0.198082\pi\) |
−0.911078 | + | 0.412235i | \(0.864748\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0000 | 1.05361 | 0.526804 | − | 0.849987i | \(-0.323390\pi\) | ||||
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.00000 | − | 15.5885i | −0.846649 | − | 1.46644i | −0.884182 | − | 0.467143i | \(-0.845283\pi\) |
0.0375328 | − | 0.999295i | \(-0.488050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | − | 5.19615i | 0.279751 | − | 0.484544i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 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 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −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 | ||||||||
\(131\) | 7.50000 | + | 12.9904i | 0.655278 | + | 1.13497i | 0.981824 | + | 0.189794i | \(0.0607819\pi\) |
−0.326546 | + | 0.945181i | \(0.605885\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.00000 | − | 12.1244i | 0.606977 | − | 1.05131i | ||||
\(134\) | 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 | ||||||||
\(139\) | 0.500000 | + | 0.866025i | 0.0424094 | + | 0.0734553i | 0.886451 | − | 0.462822i | \(-0.153163\pi\) |
−0.844042 | + | 0.536278i | \(0.819830\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00000 | −0.249136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −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 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.50000 | − | 4.33013i | 0.200805 | − | 0.347804i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | + | 3.46410i | 0.159617 | + | 0.276465i | 0.934731 | − | 0.355357i | \(-0.115641\pi\) |
−0.775113 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0000 | −1.72317 | −0.861586 | − | 0.507611i | \(-0.830529\pi\) | ||||
−0.861586 | + | 0.507611i | \(0.830529\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.00000 | + | 15.5885i | 0.696441 | + | 1.20627i | 0.969693 | + | 0.244328i | \(0.0785675\pi\) |
−0.273252 | + | 0.961943i | \(0.588099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.00000 | + | 15.5885i | −0.684257 | + | 1.18517i | 0.289412 | + | 0.957205i | \(0.406540\pi\) |
−0.973670 | + | 0.227964i | \(0.926793\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 1.73205i | −0.0755929 | − | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.0000 | −1.12115 | −0.560576 | − | 0.828103i | \(-0.689420\pi\) | ||||
−0.560576 | + | 0.828103i | \(0.689420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.0000 | 1.70958 | 0.854788 | − | 0.518977i | \(-0.173687\pi\) | ||||
0.854788 | + | 0.518977i | \(0.173687\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | + | 15.5885i | −0.658145 | + | 1.13994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5000 | − | 18.1865i | 0.759753 | − | 1.31593i | −0.183223 | − | 0.983071i | \(-0.558653\pi\) |
0.942976 | − | 0.332860i | \(-0.108014\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | + | 13.8564i | 0.575853 | + | 0.997406i | 0.995948 | + | 0.0899262i | \(0.0286631\pi\) |
−0.420096 | + | 0.907480i | \(0.638004\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.0000 | 1.70993 | 0.854965 | − | 0.518686i | \(-0.173579\pi\) | ||||
0.854965 | + | 0.518686i | \(0.173579\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | −3.00000 | − | 5.19615i | −0.210559 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.50000 | − | 2.59808i | 0.104765 | − | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5000 | − | 18.1865i | 0.726300 | − | 1.25799i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.50000 | − | 4.33013i | −0.172107 | − | 0.298098i | 0.767049 | − | 0.641588i | \(-0.221724\pi\) |
−0.939156 | + | 0.343490i | \(0.888391\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0000 | 0.678844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | + | 20.7846i | 0.807207 | + | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000 | − | 24.2487i | 0.937509 | − | 1.62381i | 0.167412 | − | 0.985887i | \(-0.446459\pi\) |
0.770097 | − | 0.637927i | \(-0.220208\pi\) | |||||||
\(224\) | 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 | ||||||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0000 | −1.57229 | −0.786146 | − | 0.618041i | \(-0.787927\pi\) | ||||
−0.786146 | + | 0.618041i | \(0.787927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50000 | − | 6.06218i | 0.225455 | − | 0.390499i | −0.731001 | − | 0.682376i | \(-0.760947\pi\) |
0.956456 | + | 0.291877i | \(0.0942799\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.50000 | + | 2.59808i | −0.0958315 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0000 | − | 24.2487i | −0.890799 | − | 1.54291i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.00000 | + | 15.5885i | 0.561405 | + | 0.972381i | 0.997374 | + | 0.0724199i | \(0.0230722\pi\) |
−0.435970 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | − | 6.92820i | 0.248548 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.00000 | + | 5.19615i | −0.184988 | + | 0.320408i | −0.943572 | − | 0.331166i | \(-0.892558\pi\) |
0.758585 | + | 0.651575i | \(0.225891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | − | 5.19615i | −0.184289 | − | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0000 | −0.914566 | −0.457283 | − | 0.889321i | \(-0.651177\pi\) | ||||
−0.457283 | + | 0.889321i | \(0.651177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0000 | − | 24.2487i | 0.841178 | − | 1.45696i | −0.0477206 | − | 0.998861i | \(-0.515196\pi\) |
0.888899 | − | 0.458103i | \(-0.151471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0000 | + | 25.9808i | −0.894825 | + | 1.54988i | −0.0608039 | + | 0.998150i | \(0.519366\pi\) |
−0.834021 | + | 0.551733i | \(0.813967\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0000 | + | 19.0526i | 0.653882 | + | 1.13256i | 0.982173 | + | 0.187980i | \(0.0601941\pi\) |
−0.328291 | + | 0.944577i | \(0.606473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | 0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.0000 | − | 20.7846i | −0.701047 | − | 1.21425i | −0.968099 | − | 0.250568i | \(-0.919383\pi\) |
0.267052 | − | 0.963682i | \(-0.413951\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | −8.00000 | − | 13.8564i | −0.461112 | − | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.0000 | −0.801638 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.50000 | + | 12.9904i | 0.425286 | + | 0.736617i | 0.996447 | − | 0.0842210i | \(-0.0268402\pi\) |
−0.571161 | + | 0.820838i | \(0.693507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.00000 | − | 13.8564i | 0.452187 | − | 0.783210i | −0.546335 | − | 0.837567i | \(-0.683977\pi\) |
0.998522 | + | 0.0543564i | \(0.0173107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | − | 10.3923i | 0.336994 | − | 0.583690i | −0.646872 | − | 0.762598i | \(-0.723923\pi\) |
0.983866 | + | 0.178908i | \(0.0572566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.50000 | − | 7.79423i | −0.251952 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −42.0000 | −2.33694 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | + | 14.7224i | −0.467202 | + | 0.809218i | −0.999298 | − | 0.0374662i | \(-0.988071\pi\) |
0.532096 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.00000 | − | 1.73205i | 0.0546358 | − | 0.0946320i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | + | 24.2487i | 0.762629 | + | 1.32091i | 0.941491 | + | 0.337037i | \(0.109425\pi\) |
−0.178863 | + | 0.983874i | \(0.557242\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0000 | 0.812296 | ||||||||
\(342\) | 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 | ||||||||
\(349\) | 3.50000 | − | 6.06218i | 0.187351 | − | 0.324501i | −0.757015 | − | 0.653397i | \(-0.773343\pi\) |
0.944366 | + | 0.328896i | \(0.106677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000 | − | 20.7846i | 0.638696 | − | 1.10625i | −0.347024 | − | 0.937856i | \(-0.612808\pi\) |
0.985719 | − | 0.168397i | \(-0.0538590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.50000 | + | 12.9904i | 0.398059 | + | 0.689458i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.0000 | 1.42501 | 0.712503 | − | 0.701669i | \(-0.247562\pi\) | ||||
0.712503 | + | 0.701669i | \(0.247562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.00000 | − | 8.66025i | −0.261712 | − | 0.453298i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0000 | − | 19.0526i | 0.574195 | − | 0.994535i | −0.421933 | − | 0.906627i | \(-0.638648\pi\) |
0.996129 | − | 0.0879086i | \(-0.0280183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | − | 10.3923i | 0.311504 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.0000 | 1.64373 | 0.821865 | − | 0.569683i | \(-0.192934\pi\) | ||||
0.821865 | + | 0.569683i | \(0.192934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | + | 20.7846i | 0.613171 | + | 1.06204i | 0.990702 | + | 0.136047i | \(0.0434398\pi\) |
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.00000 | − | 5.19615i | 0.152894 | − | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.00000 | + | 5.19615i | −0.152106 | + | 0.263455i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.779895 | + | 0.625910i | \(0.215272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | − | 31.1769i | −0.910299 | − | 1.57668i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 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 | ||||||||
\(403\) | 10.0000 | − | 17.3205i | 0.498135 | − | 0.862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | − | 10.3923i | 0.297409 | − | 0.515127i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.00000 | −0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000 | + | 31.1769i | 0.879358 | + | 1.52309i | 0.852047 | + | 0.523465i | \(0.175361\pi\) |
0.0273103 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.50000 | − | 6.06218i | 0.170580 | − | 0.295452i | −0.768043 | − | 0.640398i | \(-0.778769\pi\) |
0.938623 | + | 0.344946i | \(0.112103\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | + | 5.19615i | −0.145521 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.0000 | − | 24.2487i | −0.677507 | − | 1.17348i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | −0.144505 | −0.0722525 | − | 0.997386i | \(-0.523019\pi\) | ||||
−0.0722525 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.0000 | + | 36.3731i | 1.00457 | + | 1.73996i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.50000 | − | 16.4545i | 0.453410 | − | 0.785330i | −0.545185 | − | 0.838316i | \(-0.683541\pi\) |
0.998595 | + | 0.0529862i | \(0.0168739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.50000 | + | 12.9904i | 0.355534 | + | 0.615803i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | 0.423793 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | − | 6.92820i | −0.187523 | − | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.00000 | + | 6.92820i | −0.187112 | + | 0.324088i | −0.944286 | − | 0.329125i | \(-0.893246\pi\) |
0.757174 | + | 0.653213i | \(0.226579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.50000 | − | 12.9904i | 0.349310 | − | 0.605022i | −0.636817 | − | 0.771015i | \(-0.719749\pi\) |
0.986127 | + | 0.165992i | \(0.0530827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.00000 | − | 12.1244i | −0.325318 | − | 0.563467i | 0.656259 | − | 0.754536i | \(-0.272138\pi\) |
−0.981577 | + | 0.191069i | \(0.938805\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 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 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.0000 | − | 20.7846i | −0.551761 | − | 0.955677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.50000 | − | 6.06218i | 0.160591 | − | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.5000 | + | 23.3827i | −0.616831 | + | 1.06838i | 0.373230 | + | 0.927739i | \(0.378250\pi\) |
−0.990060 | + | 0.140643i | \(0.955083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | − | 13.8564i | −0.364769 | − | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.00000 | −0.363261 | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 19.5000 | + | 33.7750i | 0.880023 | + | 1.52424i | 0.851314 | + | 0.524656i | \(0.175806\pi\) |
0.0287085 | + | 0.999588i | \(0.490861\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | + | 15.5885i | −0.405340 | + | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.0000 | + | 25.9808i | −0.672842 | + | 1.16540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.50000 | − | 4.33013i | −0.111915 | − | 0.193843i | 0.804627 | − | 0.593780i | \(-0.202365\pi\) |
−0.916542 | + | 0.399937i | \(0.869032\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0000 | −1.60516 | −0.802580 | − | 0.596544i | \(-0.796540\pi\) | ||||
−0.802580 | + | 0.596544i | \(0.796540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00000 | 0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −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 | ||||||||
\(511\) | 10.0000 | − | 17.3205i | 0.442374 | − | 0.766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.00000 | − | 1.73205i | 0.0440653 | − | 0.0763233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.0000 | 1.84005 | 0.920027 | − | 0.391856i | \(-0.128167\pi\) | ||||
0.920027 | + | 0.391856i | \(0.128167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.0000 | −1.22435 | −0.612177 | − | 0.790721i | \(-0.709706\pi\) | ||||
−0.612177 | + | 0.790721i | \(0.709706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.0000 | − | 25.9808i | −0.653410 | − | 1.13174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | − | 10.3923i | 0.259889 | − | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.00000 | − | 5.19615i | −0.129701 | − | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.00000 | −0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.0000 | −0.558914 | −0.279457 | − | 0.960158i | \(-0.590154\pi\) | ||||
−0.279457 | + | 0.960158i | \(0.590154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.50000 | + | 9.52628i | 0.235594 | + | 0.408061i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | + | 27.7128i | −0.684111 | + | 1.18491i | 0.289605 | + | 0.957146i | \(0.406476\pi\) |
−0.973715 | + | 0.227768i | \(0.926857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.5000 | − | 18.1865i | 0.447315 | − | 0.774772i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | − | 13.8564i | −0.340195 | − | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.0000 | 1.01691 | 0.508456 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508456 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.0000 | −1.35346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | − | 31.1769i | −0.758610 | − | 1.31395i | −0.943560 | − | 0.331202i | \(-0.892546\pi\) |
0.184950 | − | 0.982748i | \(-0.440788\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | − | 15.5885i | 0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.50000 | − | 2.59808i | 0.0628833 | − | 0.108917i | −0.832870 | − | 0.553469i | \(-0.813304\pi\) |
0.895753 | + | 0.444552i | \(0.146637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.5000 | + | 32.0429i | 0.774201 | + | 1.34096i | 0.935243 | + | 0.354008i | \(0.115181\pi\) |
−0.161042 | + | 0.986948i | \(0.551485\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000 | 0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0000 | 1.08239 | 0.541197 | − | 0.840896i | \(-0.317971\pi\) | ||||
0.541197 | + | 0.840896i | \(0.317971\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | − | 15.5885i | 0.372742 | − | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.00000 | − | 10.3923i | 0.247647 | − | 0.428936i | −0.715226 | − | 0.698893i | \(-0.753676\pi\) |
0.962872 | + | 0.269957i | \(0.0870095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.5000 | + | 30.3109i | 0.721075 | + | 1.24894i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.0000 | −1.23195 | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.5000 | + | 33.7750i | 0.796748 | + | 1.38001i | 0.921723 | + | 0.387849i | \(0.126782\pi\) |
−0.124975 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.50000 | + | 14.7224i | −0.346722 | + | 0.600541i | −0.985665 | − | 0.168714i | \(-0.946039\pi\) |
0.638943 | + | 0.769254i | \(0.279372\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | − | 6.92820i | −0.162355 | − | 0.281207i | 0.773358 | − | 0.633970i | \(-0.218576\pi\) |
−0.935713 | + | 0.352763i | \(0.885242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | 0.323117 | 0.161558 | − | 0.986863i | \(-0.448348\pi\) | ||||
0.161558 | + | 0.986863i | \(0.448348\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 2.00000 | − | 3.46410i | 0.0803868 | − | 0.139234i | −0.823029 | − | 0.567999i | \(-0.807718\pi\) |
0.903416 | + | 0.428765i | \(0.141051\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 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 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.00000 | 0.199047 | 0.0995234 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995234 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(632\) | 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 | ||||||||
\(643\) | 20.0000 | + | 34.6410i | 0.788723 | + | 1.36611i | 0.926750 | + | 0.375680i | \(0.122591\pi\) |
−0.138027 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0000 | 0.707653 | 0.353827 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353827 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.0000 | − | 20.7846i | −0.469596 | − | 0.813365i | 0.529799 | − | 0.848123i | \(-0.322267\pi\) |
−0.999396 | + | 0.0347583i | \(0.988934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.50000 | + | 12.9904i | −0.293049 | + | 0.507576i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | + | 20.7846i | −0.467454 | + | 0.809653i | −0.999309 | − | 0.0371821i | \(-0.988162\pi\) |
0.531855 | + | 0.846836i | \(0.321495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.50000 | + | 6.06218i | 0.136134 | + | 0.235791i | 0.926030 | − | 0.377450i | \(-0.123199\pi\) |
−0.789896 | + | 0.613241i | \(0.789865\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.0000 | 0.542897 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0000 | 0.696963 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.0000 | − | 36.3731i | −0.810696 | − | 1.40417i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | − | 8.66025i | 0.192736 | − | 0.333828i | −0.753420 | − | 0.657539i | \(-0.771597\pi\) |
0.946156 | + | 0.323711i | \(0.104931\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | + | 5.19615i | −0.115299 | + | 0.199704i | −0.917899 | − | 0.396813i | \(-0.870116\pi\) |
0.802600 | + | 0.596518i | \(0.203449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.00000 | − | 13.8564i | −0.307012 | − | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −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 | \(0.851021\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.500000 | + | 0.866025i | −0.0189661 | + | 0.0328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | − | 15.5885i | −0.340899 | − | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.00000 | 0.113308 | 0.0566542 | − | 0.998394i | \(-0.481957\pi\) | ||||
0.0566542 | + | 0.998394i | \(0.481957\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.0000 | 1.05604 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.00000 | + | 5.19615i | 0.112827 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.0000 | + | 25.9808i | −0.561754 | + | 0.972987i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | − | 10.3923i | −0.224387 | − | 0.388650i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.00000 | 0.335643 | 0.167822 | − | 0.985817i | \(-0.446327\pi\) | ||||
0.167822 | + | 0.985817i | \(0.446327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.50000 | − | 2.59808i | −0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0000 | + | 38.1051i | −0.815935 | + | 1.41324i | 0.0927199 | + | 0.995692i | \(0.470444\pi\) |
−0.908655 | + | 0.417548i | \(0.862889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.0000 | + | 41.5692i | −0.887672 | + | 1.53749i | ||||
\(732\) | 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 | ||||||||
\(737\) | 6.00000 | 0.221013 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.0000 | −0.919640 | −0.459820 | − | 0.888012i | \(-0.652086\pi\) | ||||
−0.459820 | + | 0.888012i | \(0.652086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.0000 | − | 46.7654i | −0.990534 | − | 1.71566i | −0.614145 | − | 0.789193i | \(-0.710499\pi\) |
−0.376389 | − | 0.926462i | \(-0.622834\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00000 | − | 5.19615i | 0.109911 | − | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000 | − | 10.3923i | 0.219235 | − | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | − | 6.92820i | −0.145962 | − | 0.252814i | 0.783769 | − | 0.621052i | \(-0.213294\pi\) |
−0.929731 | + | 0.368238i | \(0.879961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.00000 | −0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.0000 | −1.01768 | −0.508839 | − | 0.860862i | \(-0.669925\pi\) | ||||
−0.508839 | + | 0.860862i | \(0.669925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.50000 | − | 7.79423i | −0.163125 | − | 0.282541i | 0.772863 | − | 0.634573i | \(-0.218824\pi\) |
−0.935988 | + | 0.352032i | \(0.885491\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.0000 | + | 19.0526i | −0.398227 | + | 0.689749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 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 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.0000 | 1.29483 | 0.647415 | − | 0.762138i | \(-0.275850\pi\) | ||||
0.647415 | + | 0.762138i | \(0.275850\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.00000 | 0.179605 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.5000 | + | 18.1865i | 0.376202 | + | 0.651600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.5000 | + | 38.9711i | −0.805113 | + | 1.39450i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | + | 3.46410i | −0.0713831 | + | 0.123639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.0000 | + | 29.4449i | 0.605985 | + | 1.04960i | 0.991895 | + | 0.127060i | \(0.0405540\pi\) |
−0.385911 | + | 0.922536i | \(0.626113\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.0000 | 1.28001 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.0000 | −1.98862 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.0000 | − | 25.9808i | 0.529339 | − | 0.916841i | ||||
\(804\) | 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 | ||||||||
\(811\) | −7.00000 | −0.245803 | −0.122902 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122902 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.0000 | − | 19.0526i | −0.385313 | − | 0.667382i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0000 | − | 48.4974i | 0.979596 | − | 1.69671i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.50000 | + | 12.9904i | −0.261752 | + | 0.453367i | −0.966708 | − | 0.255884i | \(-0.917634\pi\) |
0.704956 | + | 0.709251i | \(0.250967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.00000 | − | 12.1244i | −0.244005 | − | 0.422628i | 0.717847 | − | 0.696201i | \(-0.245128\pi\) |
−0.961851 | + | 0.273573i | \(0.911795\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.0000 | −0.868286 | −0.434143 | − | 0.900844i | \(-0.642949\pi\) | ||||
−0.434143 | + | 0.900844i | \(0.642949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.00000 | + | 15.5885i | 0.311832 | + | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.00000 | + | 15.5885i | −0.311458 | + | 0.539461i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.50000 | − | 7.79423i | 0.155357 | − | 0.269087i | −0.777832 | − | 0.628473i | \(-0.783680\pi\) |
0.933189 | + | 0.359386i | \(0.117014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.00000 | −0.137442 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000 | + | 20.7846i | 0.411355 | + | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.00000 | + | 12.1244i | −0.239675 | + | 0.415130i | −0.960621 | − | 0.277862i | \(-0.910374\pi\) |
0.720946 | + | 0.692992i | \(0.243708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.5000 | + | 47.6314i | 0.938288 | + | 1.62516i | 0.768663 | + | 0.639654i | \(0.220922\pi\) |
0.169625 | + | 0.985509i | \(0.445745\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000 | 0.204242 | 0.102121 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102121 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | − | 20.7846i | −0.407072 | − | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | − | 6.92820i | 0.135535 | − | 0.234753i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | − | 1.73205i | 0.0338062 | − | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | + | 24.2487i | 0.472746 | + | 0.818821i | 0.999514 | − | 0.0311889i | \(-0.00992933\pi\) |
−0.526767 | + | 0.850010i | \(0.676596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.0000 | −1.11180 | −0.555899 | − | 0.831250i | \(-0.687626\pi\) | ||||
−0.555899 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.0000 | − | 41.5692i | −0.805841 | − | 1.39576i | −0.915722 | − | 0.401813i | \(-0.868380\pi\) |
0.109881 | − | 0.993945i | \(-0.464953\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.00000 | + | 3.46410i | −0.0670778 | + | 0.116182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.50000 | − | 12.9904i | −0.250697 | − | 0.434221i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.0000 | 0.500278 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.5000 | + | 19.9186i | 0.382273 | + | 0.662116i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0000 | + | 22.5167i | −0.431658 | + | 0.747653i | −0.997016 | − | 0.0771920i | \(-0.975405\pi\) |
0.565358 | + | 0.824845i | \(0.308738\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.5000 | + | 38.9711i | −0.745458 | + | 1.29117i | 0.204522 | + | 0.978862i | \(0.434436\pi\) |
−0.949980 | + | 0.312310i | \(0.898897\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.0000 | −0.990687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.0000 | 0.362857 | 0.181428 | − | 0.983404i | \(-0.441928\pi\) | ||||
0.181428 | + | 0.983404i | \(0.441928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.0000 | + | 51.9615i | 0.987462 | + | 1.71033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | − | 3.46410i | 0.0657596 | − | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.50000 | + | 7.79423i | −0.147640 | + | 0.255720i | −0.930355 | − | 0.366660i | \(-0.880501\pi\) |
0.782715 | + | 0.622381i | \(0.213834\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.5000 | − | 18.1865i | −0.344124 | − | 0.596040i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.0000 | −0.588663 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −58.0000 | −1.89478 | −0.947389 | − | 0.320085i | \(-0.896288\pi\) | ||||
−0.947389 | + | 0.320085i | \(0.896288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.00000 | − | 5.19615i | −0.0977972 | − | 0.169390i | 0.812975 | − | 0.582298i | \(-0.197846\pi\) |
−0.910773 | + | 0.412908i | \(0.864513\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.00000 | + | 15.5885i | −0.293080 | + | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0000 | − | 46.7654i | 0.877382 | − | 1.51967i | 0.0231788 | − | 0.999731i | \(-0.492621\pi\) |
0.854203 | − | 0.519939i | \(-0.174045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0000 | − | 34.6410i | −0.649227 | − | 1.12449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.0000 | 0.679544 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.0000 | − | 20.7846i | −0.387500 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.00000 | + | 13.8564i | −0.257529 | + | 0.446054i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.00000 | − | 1.73205i | −0.0321578 | − | 0.0556990i | 0.849499 | − | 0.527591i | \(-0.176905\pi\) |
−0.881656 | + | 0.471892i | \(0.843571\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.0000 | −1.44412 | −0.722059 | − | 0.691831i | \(-0.756804\pi\) | ||||
−0.722059 | + | 0.691831i | \(0.756804\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.00000 | −0.0641171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.0000 | − | 20.7846i | −0.383914 | − | 0.664959i | 0.607704 | − | 0.794164i | \(-0.292091\pi\) |
−0.991618 | + | 0.129205i | \(0.958757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.5000 | + | 38.9711i | −0.719103 | + | 1.24552i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.0000 | + | 36.3731i | −0.669796 | + | 1.16012i | 0.308165 | + | 0.951333i | \(0.400285\pi\) |
−0.977961 | + | 0.208788i | \(0.933048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | + | 20.7846i | 0.382352 | + | 0.662253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.0000 | 1.52631 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.0000 | −0.603555 | −0.301777 | − | 0.953378i | \(-0.597580\pi\) | ||||
−0.301777 | + | 0.953378i | \(0.597580\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.00000 | − | 13.8564i | −0.253617 | − | 0.439278i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0000 | + | 22.5167i | −0.411714 | + | 0.713110i | −0.995077 | − | 0.0991016i | \(-0.968403\pi\) |
0.583363 | + | 0.812211i | \(0.301736\pi\) | |||||||
\(998\) | 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 | 1620.2.i.g.541.1 | 2 | ||
3.2 | odd | 2 | 1620.2.i.c.541.1 | 2 | |||
9.2 | odd | 6 | 1620.2.a.f.1.1 | yes | 1 | ||
9.4 | even | 3 | inner | 1620.2.i.g.1081.1 | 2 | ||
9.5 | odd | 6 | 1620.2.i.c.1081.1 | 2 | |||
9.7 | even | 3 | 1620.2.a.c.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 6480.2.a.b.1.1 | 1 | |||
36.11 | even | 6 | 6480.2.a.p.1.1 | 1 | |||
45.2 | even | 12 | 8100.2.d.d.649.2 | 2 | |||
45.7 | odd | 12 | 8100.2.d.i.649.2 | 2 | |||
45.29 | odd | 6 | 8100.2.a.b.1.1 | 1 | |||
45.34 | even | 6 | 8100.2.a.e.1.1 | 1 | |||
45.38 | even | 12 | 8100.2.d.d.649.1 | 2 | |||
45.43 | odd | 12 | 8100.2.d.i.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.2.a.c.1.1 | ✓ | 1 | 9.7 | even | 3 | ||
1620.2.a.f.1.1 | yes | 1 | 9.2 | odd | 6 | ||
1620.2.i.c.541.1 | 2 | 3.2 | odd | 2 | |||
1620.2.i.c.1081.1 | 2 | 9.5 | odd | 6 | |||
1620.2.i.g.541.1 | 2 | 1.1 | even | 1 | trivial | ||
1620.2.i.g.1081.1 | 2 | 9.4 | even | 3 | inner | ||
6480.2.a.b.1.1 | 1 | 36.7 | odd | 6 | |||
6480.2.a.p.1.1 | 1 | 36.11 | even | 6 | |||
8100.2.a.b.1.1 | 1 | 45.29 | odd | 6 | |||
8100.2.a.e.1.1 | 1 | 45.34 | even | 6 | |||
8100.2.d.d.649.1 | 2 | 45.38 | even | 12 | |||
8100.2.d.d.649.2 | 2 | 45.2 | even | 12 | |||
8100.2.d.i.649.1 | 2 | 45.43 | odd | 12 | |||
8100.2.d.i.649.2 | 2 | 45.7 | odd | 12 |