Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(2593,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, 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("5184.2593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.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: | \(41.3944484078\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 576) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2593.12 | ||
Root | \(-0.180407 + 0.673288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.2593 |
Dual form | 5184.2.d.r.2593.6 |
$q$-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 \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205i | 0.774597i | 0.921954 | + | 0.387298i | \(0.126592\pi\) | ||||
−0.921954 | + | 0.387298i | \(0.873408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.35461 | 1.64589 | 0.822944 | − | 0.568122i | \(-0.192330\pi\) | ||||
0.822944 | + | 0.568122i | \(0.192330\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.83502i | 1.75933i | 0.475598 | + | 0.879663i | \(0.342232\pi\) | ||||
−0.475598 | + | 0.879663i | \(0.657768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.01989i | 1.11492i | 0.830205 | + | 0.557458i | \(0.188223\pi\) | ||||
−0.830205 | + | 0.557458i | \(0.811777\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.70739 | −0.414103 | −0.207051 | − | 0.978330i | \(-0.566387\pi\) | ||||
−0.207051 | + | 0.978330i | \(0.566387\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.64245 | 1.38505 | 0.692523 | − | 0.721395i | \(-0.256499\pi\) | ||||
0.692523 | + | 0.721395i | \(0.256499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.68934i | 0.870788i | 0.900240 | + | 0.435394i | \(0.143391\pi\) | ||||
−0.900240 | + | 0.435394i | \(0.856609\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.86143 | 0.873138 | 0.436569 | − | 0.899671i | \(-0.356193\pi\) | ||||
0.436569 | + | 0.899671i | \(0.356193\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.54241i | 1.27490i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.75194i | − 0.945613i | −0.881166 | − | 0.472807i | \(-0.843241\pi\) | ||||
0.881166 | − | 0.472807i | \(-0.156759\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.29261 | 0.201872 | 0.100936 | − | 0.994893i | \(-0.467816\pi\) | ||||
0.100936 | + | 0.994893i | \(0.467816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.54241i | − 0.540213i | −0.962831 | − | 0.270106i | \(-0.912941\pi\) | ||||
0.962831 | − | 0.270106i | \(-0.0870588\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.6134 | −1.54812 | −0.774060 | − | 0.633113i | \(-0.781777\pi\) | ||||
−0.774060 | + | 0.633113i | \(0.781777\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.9627 | 1.70895 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.506816i | 0.0696166i | 0.999394 | + | 0.0348083i | \(0.0110821\pi\) | ||||
−0.999394 | + | 0.0348083i | \(0.988918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.1066 | −1.36277 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.87237i | 0.243762i | 0.992545 | + | 0.121881i | \(0.0388926\pi\) | ||||
−0.992545 | + | 0.121881i | \(0.961107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.22523i | 0.156875i | 0.996919 | + | 0.0784376i | \(0.0249931\pi\) | ||||
−0.996919 | + | 0.0784376i | \(0.975007\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.96265 | −0.863611 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.57976i | 0.192998i | 0.995333 | + | 0.0964990i | \(0.0307645\pi\) | ||||
−0.995333 | + | 0.0964990i | \(0.969236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.88549 | −1.17319 | −0.586596 | − | 0.809880i | \(-0.699532\pi\) | ||||
−0.586596 | + | 0.809880i | \(0.699532\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.96265 | −0.931958 | −0.465979 | − | 0.884796i | \(-0.654298\pi\) | ||||
−0.465979 | + | 0.884796i | \(0.654298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 25.4093i | 2.89565i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.06677 | 0.232530 | 0.116265 | − | 0.993218i | \(-0.462908\pi\) | ||||
0.116265 | + | 0.993218i | \(0.462908\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.54241i | − 0.169302i | −0.996411 | − | 0.0846508i | \(-0.973023\pi\) | ||||
0.996411 | − | 0.0846508i | \(-0.0269775\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.95729i | − 0.320763i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.96265 | −0.420040 | −0.210020 | − | 0.977697i | \(-0.567353\pi\) | ||||
−0.210020 | + | 0.977697i | \(0.567353\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.5051i | 1.83503i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.46410 | −0.355409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.12217 | 0.621612 | 0.310806 | − | 0.950473i | \(-0.399401\pi\) | ||||
0.310806 | + | 0.950473i | \(0.399401\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 11.5529i | − 1.14955i | −0.818311 | − | 0.574776i | \(-0.805089\pi\) | ||||
0.818311 | − | 0.574776i | \(-0.194911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.221065 | 0.0217822 | 0.0108911 | − | 0.999941i | \(-0.496533\pi\) | ||||
0.0108911 | + | 0.999941i | \(0.496533\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.329957i | 0.0318982i | 0.999873 | + | 0.0159491i | \(0.00507697\pi\) | ||||
−0.999873 | + | 0.0159491i | \(0.994923\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 17.9253i | − 1.71693i | −0.512873 | − | 0.858465i | \(-0.671419\pi\) | ||||
0.512873 | − | 0.858465i | \(-0.328581\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0848 | 1.70128 | 0.850638 | − | 0.525751i | \(-0.176216\pi\) | ||||
0.850638 | + | 0.525751i | \(0.176216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.5051i | 1.07285i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.43502 | −0.681567 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −23.0475 | −2.09523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.57568 | −0.406026 | −0.203013 | − | 0.979176i | \(-0.565073\pi\) | ||||
−0.203013 | + | 0.979176i | \(0.565073\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 13.5424i | − 1.18321i | −0.806229 | − | 0.591603i | \(-0.798495\pi\) | ||||
0.806229 | − | 0.591603i | \(-0.201505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.70923i | 0.755186i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.3774 | 1.91183 | 0.955917 | − | 0.293639i | \(-0.0948662\pi\) | ||||
0.955917 | + | 0.293639i | \(0.0948662\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 11.5424i | − 0.979015i | −0.871999 | − | 0.489507i | \(-0.837177\pi\) | ||||
0.871999 | − | 0.489507i | \(-0.162823\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.4561 | −1.96150 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.12217 | −0.674509 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.23887i | 0.183415i | 0.995786 | + | 0.0917076i | \(0.0292325\pi\) | ||||
−0.995786 | + | 0.0917076i | \(0.970767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0348 | −1.38627 | −0.693134 | − | 0.720808i | \(-0.743771\pi\) | ||||
−0.693134 | + | 0.720808i | \(0.743771\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.42024i | 0.676330i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.0489718i | − 0.00390837i | −0.999998 | − | 0.00195419i | \(-0.999378\pi\) | ||||
0.999998 | − | 0.00195419i | \(-0.000622037\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.9253 | 2.27963 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 19.0848i | − 1.49484i | −0.664353 | − | 0.747419i | \(-0.731293\pi\) | ||||
0.664353 | − | 0.747419i | \(-0.268707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.9920 | −1.54703 | −0.773515 | − | 0.633778i | \(-0.781503\pi\) | ||||
−0.773515 | + | 0.633778i | \(0.781503\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.15951 | −0.243040 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.1244i | 0.921798i | 0.887453 | + | 0.460899i | \(0.152473\pi\) | ||||
−0.887453 | + | 0.460899i | \(0.847527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.70923 | 0.658356 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 6.00000i | − 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.75194i | 0.427538i | 0.976884 | + | 0.213769i | \(0.0685740\pi\) | ||||
−0.976884 | + | 0.213769i | \(0.931426\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.96265 | 0.732469 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 9.96265i | − 0.728541i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.221065 | 0.0159957 | 0.00799786 | − | 0.999968i | \(-0.497454\pi\) | ||||
0.00799786 | + | 0.999968i | \(0.497454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0475 | 1.29909 | 0.649543 | − | 0.760325i | \(-0.274960\pi\) | ||||
0.649543 | + | 0.760325i | \(0.274960\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 9.82080i | − 0.699703i | −0.936805 | − | 0.349852i | \(-0.886232\pi\) | ||||
0.936805 | − | 0.349852i | \(-0.113768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.604760 | 0.0428703 | 0.0214352 | − | 0.999770i | \(-0.493176\pi\) | ||||
0.0214352 | + | 0.999770i | \(0.493176\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.4202i | 1.43322i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.23887i | 0.156369i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6700 | −0.807234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.420243i | 0.0289307i | 0.999895 | + | 0.0144654i | \(0.00460462\pi\) | ||||
−0.999895 | + | 0.0144654i | \(0.995395\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.13564 | 0.418447 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.1696 | 1.43709 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 6.86352i | − 0.461690i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.7867 | 1.52591 | 0.762955 | − | 0.646452i | \(-0.223748\pi\) | ||||
0.762955 | + | 0.646452i | \(0.223748\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 11.8350i | − 0.785518i | −0.919641 | − | 0.392759i | \(-0.871521\pi\) | ||||
0.919641 | − | 0.392759i | \(-0.128479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.6864i | 1.03659i | 0.855203 | + | 0.518293i | \(0.173432\pi\) | ||||
−0.855203 | + | 0.518293i | \(0.826568\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.829557 | 0.0543461 | 0.0271731 | − | 0.999631i | \(-0.491349\pi\) | ||||
0.0271731 | + | 0.999631i | \(0.491349\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 18.3829i | − 1.19917i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.21395 | −0.466632 | −0.233316 | − | 0.972401i | \(-0.574958\pi\) | ||||
−0.233316 | + | 0.972401i | \(0.574958\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.9253 | −1.34792 | −0.673959 | − | 0.738769i | \(-0.735407\pi\) | ||||
−0.673959 | + | 0.738769i | \(0.735407\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.7199i | 1.32375i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.03978 | −0.511559 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.2553i | 1.27850i | 0.768999 | + | 0.639250i | \(0.220755\pi\) | ||||
−0.768999 | + | 0.639250i | \(0.779245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 38.7588i | 2.43675i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.74474 | 0.420725 | 0.210363 | − | 0.977623i | \(-0.432536\pi\) | ||||
0.210363 | + | 0.977623i | \(0.432536\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 25.0475i | − 1.55637i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.4134 | −1.62872 | −0.814361 | − | 0.580359i | \(-0.802912\pi\) | ||||
−0.814361 | + | 0.580359i | \(0.802912\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.877832 | −0.0539248 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.1704i | 1.41272i | 0.707851 | + | 0.706362i | \(0.249665\pi\) | ||||
−0.707851 | + | 0.706362i | \(0.750335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.7626 | 1.07900 | 0.539502 | − | 0.841984i | \(-0.318613\pi\) | ||||
0.539502 | + | 0.841984i | \(0.318613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.6700i | 0.703730i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 10.4413i | − 0.627356i | −0.949529 | − | 0.313678i | \(-0.898439\pi\) | ||||
0.949529 | − | 0.313678i | \(-0.101561\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.8880 | 1.60400 | 0.802001 | − | 0.597323i | \(-0.203769\pi\) | ||||
0.802001 | + | 0.597323i | \(0.203769\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.6272i | 1.10727i | 0.832758 | + | 0.553637i | \(0.186760\pi\) | ||||
−0.832758 | + | 0.553637i | \(0.813240\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.62882 | 0.332259 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0848 | −0.828519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.16055i | − 0.0678000i | −0.999425 | − | 0.0339000i | \(-0.989207\pi\) | ||||
0.999425 | − | 0.0339000i | \(-0.0107928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.24304 | −0.188817 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.7019i | 1.54421i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 15.4258i | − 0.889130i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.12217 | −0.121515 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0848i | 1.08923i | 0.838687 | + | 0.544614i | \(0.183324\pi\) | ||||
−0.838687 | + | 0.544614i | \(0.816676\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.1202 | −0.630568 | −0.315284 | − | 0.948997i | \(-0.602100\pi\) | ||||
−0.315284 | + | 0.948997i | \(0.602100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.9253 | 1.52191 | 0.760954 | − | 0.648806i | \(-0.224731\pi\) | ||||
0.760954 | + | 0.648806i | \(0.224731\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4520i | 1.26103i | 0.776178 | + | 0.630514i | \(0.217156\pi\) | ||||
−0.776178 | + | 0.630514i | \(0.782844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.3624 | −1.53200 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.41478i | − 0.190003i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.03978i | 0.445967i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −46.2171 | −2.54803 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.5899i | 1.24165i | 0.783948 | + | 0.620826i | \(0.213203\pi\) | ||||
−0.783948 | + | 0.620826i | \(0.786797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.73622 | −0.149496 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0848 | −0.767249 | −0.383625 | − | 0.923489i | \(-0.625324\pi\) | ||||
−0.383625 | + | 0.923489i | \(0.625324\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.3665i | 1.53613i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21.6104 | 1.16685 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.99454i | 0.375486i | 0.982218 | + | 0.187743i | \(0.0601173\pi\) | ||||
−0.982218 | + | 0.187743i | \(0.939883\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 9.42764i | − 0.504650i | −0.967643 | − | 0.252325i | \(-0.918805\pi\) | ||||
0.967643 | − | 0.252325i | \(-0.0811952\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.62257 | 0.405708 | 0.202854 | − | 0.979209i | \(-0.434978\pi\) | ||||
0.202854 | + | 0.979209i | \(0.434978\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 17.1222i | − 0.908750i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.8344 | −0.571820 | −0.285910 | − | 0.958257i | \(-0.592296\pi\) | ||||
−0.285910 | + | 0.958257i | \(0.592296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 13.7917i | − 0.721892i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.9493 | −1.19795 | −0.598973 | − | 0.800770i | \(-0.704424\pi\) | ||||
−0.598973 | + | 0.800770i | \(0.704424\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.20699i | 0.114581i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.113658i | 0.00588498i | 0.999996 | + | 0.00294249i | \(0.000936625\pi\) | ||||
−0.999996 | + | 0.00294249i | \(0.999063\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.8506 | −0.970856 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 16.2070i | − 0.832497i | −0.909251 | − | 0.416249i | \(-0.863345\pi\) | ||||
0.909251 | − | 0.416249i | \(-0.136655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.0775 | −0.719325 | −0.359663 | − | 0.933082i | \(-0.617108\pi\) | ||||
−0.359663 | + | 0.933082i | \(0.617108\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −44.0101 | −2.24296 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.8734i | 1.46394i | 0.681338 | + | 0.731969i | \(0.261398\pi\) | ||||
−0.681338 | + | 0.731969i | \(0.738602\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.3413 | −0.573552 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.57976i | 0.180117i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.85934i | − 0.143506i | −0.997422 | − | 0.0717531i | \(-0.977141\pi\) | ||||
0.997422 | − | 0.0717531i | \(-0.0228594\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.5479 | −1.07605 | −0.538025 | − | 0.842929i | \(-0.680829\pi\) | ||||
−0.538025 | + | 0.842929i | \(0.680829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.5424i | 0.973477i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.5627 | 1.66364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.9253 | −1.03469 | −0.517345 | − | 0.855777i | \(-0.673080\pi\) | ||||
−0.517345 | + | 0.855777i | \(0.673080\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.15344i | 0.401204i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.67153 | 0.131140 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6646i | 0.618705i | 0.950947 | + | 0.309353i | \(0.100112\pi\) | ||||
−0.950947 | + | 0.309353i | \(0.899888\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 26.6835i | − 1.30047i | −0.759732 | − | 0.650236i | \(-0.774670\pi\) | ||||
0.759732 | − | 0.650236i | \(-0.225330\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.41478 | −0.165641 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.33542i | 0.258199i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.6772 | 1.14049 | 0.570246 | − | 0.821474i | \(-0.306848\pi\) | ||||
0.570246 | + | 0.821474i | \(0.306848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.96265 | 0.382661 | 0.191330 | − | 0.981526i | \(-0.438720\pi\) | ||||
0.191330 | + | 0.981526i | \(0.438720\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.2849i | 0.635503i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.6781 | 0.509636 | 0.254818 | − | 0.966989i | \(-0.417984\pi\) | ||||
0.254818 | + | 0.966989i | \(0.417984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 12.8825i | − 0.612066i | −0.952021 | − | 0.306033i | \(-0.900998\pi\) | ||||
0.952021 | − | 0.306033i | \(-0.0990018\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 6.86352i | − 0.325362i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.547875 | 0.0258558 | 0.0129279 | − | 0.999916i | \(-0.495885\pi\) | ||||
0.0129279 | + | 0.999916i | \(0.495885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.54241i | 0.355158i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.3197 | −1.42141 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.8031 | 0.926352 | 0.463176 | − | 0.886266i | \(-0.346710\pi\) | ||||
0.463176 | + | 0.886266i | \(0.346710\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 14.0680i | − 0.655212i | −0.944814 | − | 0.327606i | \(-0.893758\pi\) | ||||
0.944814 | − | 0.327606i | \(-0.106242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.4591 | 0.579022 | 0.289511 | − | 0.957175i | \(-0.406507\pi\) | ||||
0.289511 | + | 0.957175i | \(0.406507\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 29.3401i | − 1.35770i | −0.734278 | − | 0.678849i | \(-0.762479\pi\) | ||||
0.734278 | − | 0.678849i | \(-0.237521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.87923i | 0.317653i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.6700 | 0.950410 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000i | 0.183533i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.9274 | 0.910504 | 0.455252 | − | 0.890363i | \(-0.349549\pi\) | ||||
0.455252 | + | 0.890363i | \(0.349549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.1222 | 1.05428 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.6039i | 0.481499i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.46828 | −0.338420 | −0.169210 | − | 0.985580i | \(-0.554122\pi\) | ||||
−0.169210 | + | 0.985580i | \(0.554122\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.8934i | 1.57472i | 0.616495 | + | 0.787359i | \(0.288552\pi\) | ||||
−0.616495 | + | 0.787359i | \(0.711448\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.00652i | − 0.360596i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.0475 | −1.93094 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.4677i | 1.67729i | 0.544682 | + | 0.838643i | \(0.316650\pi\) | ||||
−0.544682 | + | 0.838643i | \(0.683350\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.8991 | −0.485968 | −0.242984 | − | 0.970030i | \(-0.578126\pi\) | ||||
−0.242984 | + | 0.970030i | \(0.578126\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0101 | 0.890439 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 4.68934i | − 0.207851i | −0.994585 | − | 0.103926i | \(-0.966860\pi\) | ||||
0.994585 | − | 0.103926i | \(-0.0331404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.6743 | −1.53390 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.382896i | 0.0168724i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 61.9292i | − 2.72364i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.4249 | 1.15770 | 0.578848 | − | 0.815435i | \(-0.303502\pi\) | ||||
0.578848 | + | 0.815435i | \(0.303502\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 13.8880i | − 0.607278i | −0.952787 | − | 0.303639i | \(-0.901798\pi\) | ||||
0.952787 | − | 0.303639i | \(-0.0982017\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.30035 | −0.361569 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1222 | 0.918355 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.19615i | 0.225070i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.571503 | −0.0247082 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 69.8023i | 3.00660i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 25.0161i | − 1.07553i | −0.843096 | − | 0.537763i | \(-0.819269\pi\) | ||||
0.843096 | − | 0.537763i | \(-0.180731\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.0475 | 1.32993 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 14.3455i | − 0.613371i | −0.951811 | − | 0.306686i | \(-0.900780\pi\) | ||||
0.951811 | − | 0.306686i | \(-0.0992200\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.37867 | −0.399545 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.00000 | 0.382719 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 32.9912i | − 1.39788i | −0.715179 | − | 0.698941i | \(-0.753655\pi\) | ||||
0.715179 | − | 0.698941i | \(-0.246345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.2401 | 0.602292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 24.9945i | − 1.05339i | −0.850053 | − | 0.526697i | \(-0.823430\pi\) | ||||
0.850053 | − | 0.526697i | \(-0.176570\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.3238i | 1.31780i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.58522 | 0.234145 | 0.117072 | − | 0.993123i | \(-0.462649\pi\) | ||||
0.117072 | + | 0.993123i | \(0.462649\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.57976i | 0.233506i | 0.993161 | + | 0.116753i | \(0.0372485\pi\) | ||||
−0.993161 | + | 0.116753i | \(0.962751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.2849 | 0.554019 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.04748 | −0.376651 | −0.188326 | − | 0.982107i | \(-0.560306\pi\) | ||||
−0.188326 | + | 0.982107i | \(0.560306\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.71660i | − 0.278652i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.95729 | −0.122478 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 7.21245i | − 0.297690i | −0.988861 | − | 0.148845i | \(-0.952444\pi\) | ||||
0.988861 | − | 0.148845i | \(-0.0475555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.72286i | 0.400623i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.0475 | 1.02858 | 0.514288 | − | 0.857617i | \(-0.328056\pi\) | ||||
0.514288 | + | 0.857617i | \(0.328056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 12.8778i | − 0.527940i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.2051 | 1.64274 | 0.821369 | − | 0.570397i | \(-0.193211\pi\) | ||||
0.821369 | + | 0.570397i | \(0.193211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.9627 | −0.447176 | −0.223588 | − | 0.974684i | \(-0.571777\pi\) | ||||
−0.223588 | + | 0.974684i | \(0.571777\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 39.9194i | − 1.62295i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.4740 | 1.15572 | 0.577861 | − | 0.816135i | \(-0.303888\pi\) | ||||
0.577861 | + | 0.816135i | \(0.303888\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 42.6646i | − 1.72602i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 14.3632i | − 0.580125i | −0.957008 | − | 0.290063i | \(-0.906324\pi\) | ||||
0.957008 | − | 0.290063i | \(-0.0936761\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.632696 | 0.0254714 | 0.0127357 | − | 0.999919i | \(-0.495946\pi\) | ||||
0.0127357 | + | 0.999919i | \(0.495946\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.4304i | 1.34368i | 0.740696 | + | 0.671840i | \(0.234496\pi\) | ||||
−0.740696 | + | 0.671840i | \(0.765504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.2558 | −0.691340 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.82080i | 0.391581i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.59765 | −0.302458 | −0.151229 | − | 0.988499i | \(-0.548323\pi\) | ||||
−0.151229 | + | 0.988499i | \(0.548323\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 7.92531i | − 0.314506i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 48.0885i | 1.90534i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.7549 | 0.938261 | 0.469130 | − | 0.883129i | \(-0.344567\pi\) | ||||
0.469130 | + | 0.883129i | \(0.344567\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 14.3455i | − 0.565733i | −0.959159 | − | 0.282867i | \(-0.908715\pi\) | ||||
0.959159 | − | 0.282867i | \(-0.0912854\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.5781 | −1.12352 | −0.561761 | − | 0.827299i | \(-0.689876\pi\) | ||||
−0.561761 | + | 0.827299i | \(0.689876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9253 | −0.428856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 17.0253i | − 0.666251i | −0.942882 | − | 0.333126i | \(-0.891897\pi\) | ||||
0.942882 | − | 0.333126i | \(-0.108103\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.4561 | 0.916507 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 12.4949i | − 0.486734i | −0.969934 | − | 0.243367i | \(-0.921748\pi\) | ||||
0.969934 | − | 0.243367i | \(-0.0782519\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.7879i | 1.35309i | 0.736400 | + | 0.676547i | \(0.236524\pi\) | ||||
−0.736400 | + | 0.676547i | \(0.763476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.0848 | −0.584964 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.1487i | 1.20608i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.14927 | −0.275994 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0475 | 1.00406 | 0.502028 | − | 0.864851i | \(-0.332587\pi\) | ||||
0.502028 | + | 0.864851i | \(0.332587\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 33.3511i | − 1.28179i | −0.767630 | − | 0.640893i | \(-0.778564\pi\) | ||||
0.767630 | − | 0.640893i | \(-0.221436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.6597 | 1.02310 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 26.4249i | − 1.01112i | −0.862791 | − | 0.505560i | \(-0.831286\pi\) | ||||
0.862791 | − | 0.505560i | \(-0.168714\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.7588i | 1.48090i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.03735 | −0.0776167 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.3829i | 0.775402i | 0.921785 | + | 0.387701i | \(0.126731\pi\) | ||||
−0.921785 | + | 0.387701i | \(0.873269\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.9920 | 0.758341 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.20699 | −0.0835957 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 49.8696i | − 1.88355i | −0.336247 | − | 0.941774i | \(-0.609158\pi\) | ||||
0.336247 | − | 0.941774i | \(-0.390842\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.5039 | 0.433877 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 50.3082i | − 1.89203i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 9.90120i | − 0.371847i | −0.982564 | − | 0.185924i | \(-0.940472\pi\) | ||||
0.982564 | − | 0.185924i | \(-0.0595277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.2918 | 1.20934 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 40.6272i | − 1.51937i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5562 | −0.953084 | −0.476542 | − | 0.879152i | \(-0.658110\pi\) | ||||
−0.476542 | + | 0.879152i | \(0.658110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.962653 | 0.0358511 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.37867i | 0.348315i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.1405 | 1.48873 | 0.744364 | − | 0.667774i | \(-0.232753\pi\) | ||||
0.744364 | + | 0.667774i | \(0.232753\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.04827i | 0.223704i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.3387i | 1.74849i | 0.485481 | + | 0.874247i | \(0.338645\pi\) | ||||
−0.485481 | + | 0.874247i | \(0.661355\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.21792 | −0.339546 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.9627i | 1.39648i | 0.715864 | + | 0.698239i | \(0.246033\pi\) | ||||
−0.715864 | + | 0.698239i | \(0.753967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.5196 | 0.532673 | 0.266336 | − | 0.963880i | \(-0.414187\pi\) | ||||
0.266336 | + | 0.963880i | \(0.414187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.87783 | −0.142073 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.43684i | 0.0525008i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.6431 | −1.33713 | −0.668563 | − | 0.743656i | \(-0.733090\pi\) | ||||
−0.668563 | + | 0.743656i | \(0.733090\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 29.5051i | − 1.07380i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 2.02727i | − 0.0736822i | −0.999321 | − | 0.0368411i | \(-0.988270\pi\) | ||||
0.999321 | − | 0.0368411i | \(-0.0117295\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.2070 | 0.623753 | 0.311876 | − | 0.950123i | \(-0.399042\pi\) | ||||
0.311876 | + | 0.950123i | \(0.399042\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 78.0576i | − 2.82587i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.52671 | −0.271774 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.8506 | 0.968258 | 0.484129 | − | 0.874997i | \(-0.339137\pi\) | ||||
0.484129 | + | 0.874997i | \(0.339137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.41305i | 0.158726i | 0.996846 | + | 0.0793632i | \(0.0252887\pi\) | ||||
−0.996846 | + | 0.0793632i | \(0.974711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.72286 | 0.349255 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.58522i | 0.0926252i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 57.6820i | − 2.06403i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0848216 | 0.00302741 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34.3829i | − 1.22562i | −0.790231 | − | 0.612809i | \(-0.790040\pi\) | ||||
0.790231 | − | 0.612809i | \(-0.209960\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 78.7524 | 2.80011 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.92531 | −0.174903 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.8941i | 0.810951i | 0.914106 | + | 0.405475i | \(0.132894\pi\) | ||||
−0.914106 | + | 0.405475i | \(0.867106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.1212 | 0.641080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 46.4623i | − 1.63962i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 50.1001i | 1.76580i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.7922 | −1.22323 | −0.611614 | − | 0.791156i | \(-0.709480\pi\) | ||||
−0.611614 | + | 0.791156i | \(0.709480\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 11.6810i | − 0.410174i | −0.978744 | − | 0.205087i | \(-0.934252\pi\) | ||||
0.978744 | − | 0.205087i | \(-0.0657478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.0559 | 1.15790 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.08482 | 0.247867 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 16.0953i | − 0.561729i | −0.959747 | − | 0.280864i | \(-0.909379\pi\) | ||||
0.959747 | − | 0.280864i | \(-0.0906211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8033 | 0.446294 | 0.223147 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223147 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.9253i | 0.901511i | 0.892647 | + | 0.450756i | \(0.148845\pi\) | ||||
−0.892647 | + | 0.450756i | \(0.851155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 49.0708i | − 1.70430i | −0.523299 | − | 0.852149i | \(-0.675299\pi\) | ||||
0.523299 | − | 0.852149i | \(-0.324701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.4249 | −0.707681 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 34.6272i | − 1.19832i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.2550 | −1.04452 | −0.522259 | − | 0.852787i | \(-0.674911\pi\) | ||||
−0.522259 | + | 0.852787i | \(0.674911\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.01013 | 0.241729 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 5.47244i | − 0.188258i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −100.363 | −3.44851 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 38.2070i | − 1.30972i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.9517i | 1.02553i | 0.858530 | + | 0.512763i | \(0.171378\pi\) | ||||
−0.858530 | + | 0.512763i | \(0.828622\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.8031 | −0.813100 | −0.406550 | − | 0.913629i | \(-0.633268\pi\) | ||||
−0.406550 | + | 0.913629i | \(0.633268\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.9089i | 1.12284i | 0.827532 | + | 0.561419i | \(0.189744\pi\) | ||||
−0.827532 | + | 0.561419i | \(0.810256\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.3906 | −1.23875 | −0.619375 | − | 0.785095i | \(-0.712614\pi\) | ||||
−0.619375 | + | 0.785095i | \(0.712614\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | −0.714021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0597i | 0.409096i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.35045 | −0.215177 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 52.7969i | 1.78486i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 48.9049i | − 1.65140i | −0.564108 | − | 0.825701i | \(-0.690780\pi\) | ||||
0.564108 | − | 0.825701i | \(-0.309220\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.9627 | −1.34638 | −0.673188 | − | 0.739471i | \(-0.735076\pi\) | ||||
−0.673188 | + | 0.739471i | \(0.735076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 10.0000i | − 0.336527i | −0.985742 | − | 0.168263i | \(-0.946184\pi\) | ||||
0.985742 | − | 0.168263i | \(-0.0538159\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.1897 | 1.51732 | 0.758661 | − | 0.651486i | \(-0.225854\pi\) | ||||
0.758661 | + | 0.651486i | \(0.225854\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.9253 | −0.668273 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 21.2267i | − 0.710326i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.3923 | 0.347376 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.7969i | 0.760318i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 0.865333i | − 0.0288284i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.96265 | −0.331170 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.3829i | 1.34089i | 0.741958 | + | 0.670446i | \(0.233897\pi\) | ||||
−0.741958 | + | 0.670446i | \(0.766103\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.52142 | −0.282327 | −0.141164 | − | 0.989986i | \(-0.545084\pi\) | ||||
−0.141164 | + | 0.989986i | \(0.545084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00000 | 0.297857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 58.9720i | − 1.94743i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.00834 | 0.0662490 | 0.0331245 | − | 0.999451i | \(-0.489454\pi\) | ||||
0.0331245 | + | 0.999451i | \(0.489454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 39.7386i | − 1.30801i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 11.5039i | − 0.378245i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.9728 | −0.983375 | −0.491688 | − | 0.870772i | \(-0.663620\pi\) | ||||
−0.491688 | + | 0.870772i | \(0.663620\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.9253i | 0.784120i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.2558 | 0.564326 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.0475 | −1.47164 | −0.735818 | − | 0.677179i | \(-0.763202\pi\) | ||||
−0.735818 | + | 0.677179i | \(0.763202\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 53.5642i | − 1.74614i | −0.487592 | − | 0.873072i | \(-0.662125\pi\) | ||||
0.487592 | − | 0.873072i | \(-0.337875\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.58610 | 0.279602 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 23.8350i | − 0.774534i | −0.921968 | − | 0.387267i | \(-0.873419\pi\) | ||||
0.921968 | − | 0.387267i | \(-0.126581\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 32.0090i | − 1.03906i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.4732 | 1.05191 | 0.525955 | − | 0.850513i | \(-0.323708\pi\) | ||||
0.525955 | + | 0.850513i | \(0.323708\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.382896i | 0.0123902i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 97.4451 | 3.14666 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.36650 | −0.237629 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.2591i | 1.00627i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.66442 | −0.310787 | −0.155393 | − | 0.987853i | \(-0.549665\pi\) | ||||
−0.155393 | + | 0.987853i | \(0.549665\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 49.8133i | − 1.59858i | −0.600943 | − | 0.799292i | \(-0.705208\pi\) | ||||
0.600943 | − | 0.799292i | \(-0.294792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 50.2627i | − 1.61135i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.18057 | 0.229727 | 0.114863 | − | 0.993381i | \(-0.463357\pi\) | ||||
0.114863 | + | 0.993381i | \(0.463357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 23.1222i | − 0.738988i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.76349 | −0.151932 | −0.0759658 | − | 0.997110i | \(-0.524204\pi\) | ||||
−0.0759658 | + | 0.997110i | \(0.524204\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.0101 | 0.541988 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 23.5303i | − 0.748220i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.5781 | −0.907815 | −0.453907 | − | 0.891049i | \(-0.649970\pi\) | ||||
−0.453907 | + | 0.891049i | \(0.649970\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.04748i | 0.0332072i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.2384i | 1.17935i | 0.807640 | + | 0.589676i | \(0.200745\pi\) | ||||
−0.807640 | + | 0.589676i | \(0.799255\pi\) | |||||||
\(998\) | 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 | 5184.2.d.r.2593.12 | 12 | ||
3.2 | odd | 2 | 5184.2.d.q.2593.6 | 12 | |||
4.3 | odd | 2 | inner | 5184.2.d.r.2593.7 | 12 | ||
8.3 | odd | 2 | inner | 5184.2.d.r.2593.1 | 12 | ||
8.5 | even | 2 | inner | 5184.2.d.r.2593.6 | 12 | ||
9.2 | odd | 6 | 576.2.r.f.481.3 | yes | 12 | ||
9.4 | even | 3 | 1728.2.r.f.289.1 | 12 | |||
9.5 | odd | 6 | 576.2.r.e.97.4 | yes | 12 | ||
9.7 | even | 3 | 1728.2.r.e.1441.1 | 12 | |||
12.11 | even | 2 | 5184.2.d.q.2593.1 | 12 | |||
24.5 | odd | 2 | 5184.2.d.q.2593.12 | 12 | |||
24.11 | even | 2 | 5184.2.d.q.2593.7 | 12 | |||
36.7 | odd | 6 | 1728.2.r.e.1441.6 | 12 | |||
36.11 | even | 6 | 576.2.r.f.481.4 | yes | 12 | ||
36.23 | even | 6 | 576.2.r.e.97.3 | ✓ | 12 | ||
36.31 | odd | 6 | 1728.2.r.f.289.6 | 12 | |||
72.5 | odd | 6 | 576.2.r.f.97.3 | yes | 12 | ||
72.11 | even | 6 | 576.2.r.e.481.3 | yes | 12 | ||
72.13 | even | 6 | 1728.2.r.e.289.1 | 12 | |||
72.29 | odd | 6 | 576.2.r.e.481.4 | yes | 12 | ||
72.43 | odd | 6 | 1728.2.r.f.1441.6 | 12 | |||
72.59 | even | 6 | 576.2.r.f.97.4 | yes | 12 | ||
72.61 | even | 6 | 1728.2.r.f.1441.1 | 12 | |||
72.67 | odd | 6 | 1728.2.r.e.289.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.e.97.3 | ✓ | 12 | 36.23 | even | 6 | ||
576.2.r.e.97.4 | yes | 12 | 9.5 | odd | 6 | ||
576.2.r.e.481.3 | yes | 12 | 72.11 | even | 6 | ||
576.2.r.e.481.4 | yes | 12 | 72.29 | odd | 6 | ||
576.2.r.f.97.3 | yes | 12 | 72.5 | odd | 6 | ||
576.2.r.f.97.4 | yes | 12 | 72.59 | even | 6 | ||
576.2.r.f.481.3 | yes | 12 | 9.2 | odd | 6 | ||
576.2.r.f.481.4 | yes | 12 | 36.11 | even | 6 | ||
1728.2.r.e.289.1 | 12 | 72.13 | even | 6 | |||
1728.2.r.e.289.6 | 12 | 72.67 | odd | 6 | |||
1728.2.r.e.1441.1 | 12 | 9.7 | even | 3 | |||
1728.2.r.e.1441.6 | 12 | 36.7 | odd | 6 | |||
1728.2.r.f.289.1 | 12 | 9.4 | even | 3 | |||
1728.2.r.f.289.6 | 12 | 36.31 | odd | 6 | |||
1728.2.r.f.1441.1 | 12 | 72.61 | even | 6 | |||
1728.2.r.f.1441.6 | 12 | 72.43 | odd | 6 | |||
5184.2.d.q.2593.1 | 12 | 12.11 | even | 2 | |||
5184.2.d.q.2593.6 | 12 | 3.2 | odd | 2 | |||
5184.2.d.q.2593.7 | 12 | 24.11 | even | 2 | |||
5184.2.d.q.2593.12 | 12 | 24.5 | odd | 2 | |||
5184.2.d.r.2593.1 | 12 | 8.3 | odd | 2 | inner | ||
5184.2.d.r.2593.6 | 12 | 8.5 | even | 2 | inner | ||
5184.2.d.r.2593.7 | 12 | 4.3 | odd | 2 | inner | ||
5184.2.d.r.2593.12 | 12 | 1.1 | even | 1 | trivial |