Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(783,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.783");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.f (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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 783.4 | ||
Root | \(-1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.783 |
Dual form | 784.2.f.d.783.3 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.64575 | 1.52753 | 0.763763 | − | 0.645497i | \(-0.223350\pi\) | ||||
0.763763 | + | 0.645497i | \(0.223350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205i | 0.774597i | 0.921954 | + | 0.387298i | \(0.126592\pi\) | ||||
−0.921954 | + | 0.387298i | \(0.873408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.00000 | 1.33333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.58258i | 1.38170i | 0.722999 | + | 0.690849i | \(0.242763\pi\) | ||||
−0.722999 | + | 0.690849i | \(0.757237\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.46410i | − 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.58258i | 1.18322i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.19615i | 1.26025i | 0.776493 | + | 0.630126i | \(0.216997\pi\) | ||||
−0.776493 | + | 0.630126i | \(0.783003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.64575 | 0.606977 | 0.303488 | − | 0.952835i | \(-0.401849\pi\) | ||||
0.303488 | + | 0.952835i | \(0.401849\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4.58258i | − 0.955533i | −0.878487 | − | 0.477767i | \(-0.841446\pi\) | ||||
0.878487 | − | 0.477767i | \(-0.158554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.64575 | 0.509175 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.64575 | −0.475191 | −0.237595 | − | 0.971364i | \(-0.576359\pi\) | ||||
−0.237595 | + | 0.971364i | \(0.576359\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.1244i | 2.11058i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.00000 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 9.16515i | − 1.46760i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9.16515i | − 1.39767i | −0.715282 | − | 0.698836i | \(-0.753702\pi\) | ||||
0.715282 | − | 0.698836i | \(-0.246298\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.92820i | 1.03280i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.93725 | −1.15777 | −0.578884 | − | 0.815410i | \(-0.696511\pi\) | ||||
−0.578884 | + | 0.815410i | \(0.696511\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.7477i | 1.92507i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.93725 | −1.07026 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.00000 | 0.927173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.93725 | −1.03334 | −0.516671 | − | 0.856184i | \(-0.672829\pi\) | ||||
−0.516671 | + | 0.856184i | \(0.672829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.73205i | − 0.221766i | −0.993833 | − | 0.110883i | \(-0.964632\pi\) | ||||
0.993833 | − | 0.110883i | \(-0.0353679\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.58258i | − 0.559851i | −0.960022 | − | 0.279925i | \(-0.909690\pi\) | ||||
0.960022 | − | 0.279925i | \(-0.0903097\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 12.1244i | − 1.45960i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 9.16515i | − 1.08770i | −0.839181 | − | 0.543852i | \(-0.816965\pi\) | ||||
0.839181 | − | 0.543852i | \(-0.183035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.19615i | − 0.608164i | −0.952646 | − | 0.304082i | \(-0.901650\pi\) | ||||
0.952646 | − | 0.304082i | \(-0.0983496\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.29150 | 0.611010 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 4.58258i | − 0.515580i | −0.966201 | − | 0.257790i | \(-0.917006\pi\) | ||||
0.966201 | − | 0.257790i | \(-0.0829943\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | −0.976187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.73205i | − 0.183597i | −0.995778 | − | 0.0917985i | \(-0.970738\pi\) | ||||
0.995778 | − | 0.0917985i | \(-0.0292616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.00000 | −0.725866 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.58258i | 0.470162i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.46410i | 0.351726i | 0.984415 | + | 0.175863i | \(0.0562716\pi\) | ||||
−0.984415 | + | 0.175863i | \(0.943728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.3303i | 1.84226i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.19615i | 0.517036i | 0.966006 | + | 0.258518i | \(0.0832342\pi\) | ||||
−0.966006 | + | 0.258518i | \(0.916766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.64575 | −0.260694 | −0.130347 | − | 0.991468i | \(-0.541609\pi\) | ||||
−0.130347 | + | 0.991468i | \(0.541609\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 13.7477i | − 1.32904i | −0.747269 | − | 0.664521i | \(-0.768635\pi\) | ||||
0.747269 | − | 0.664521i | \(-0.231365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.5203 | 1.75787 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000 | 1.12887 | 0.564433 | − | 0.825479i | \(-0.309095\pi\) | ||||
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.93725 | 0.740153 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 13.8564i | − 1.28103i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.16515i | 0.826394i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.16515i | 0.813276i | 0.913589 | + | 0.406638i | \(0.133299\pi\) | ||||
−0.913589 | + | 0.406638i | \(0.866701\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 24.2487i | − 2.13498i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.93725 | 0.693481 | 0.346741 | − | 0.937961i | \(-0.387288\pi\) | ||||
0.346741 | + | 0.937961i | \(0.387288\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.58258i | 0.394405i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.0000 | 1.79415 | 0.897076 | − | 0.441877i | \(-0.145687\pi\) | ||||
0.897076 | + | 0.441877i | \(0.145687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5830 | −0.897639 | −0.448819 | − | 0.893622i | \(-0.648155\pi\) | ||||
−0.448819 | + | 0.893622i | \(0.648155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.0000 | −1.76852 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.8745 | 1.32749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.0000 | −1.22885 | −0.614424 | − | 0.788976i | \(-0.710612\pi\) | ||||
−0.614424 | + | 0.788976i | \(0.710612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.9129i | 1.86462i | 0.361656 | + | 0.932312i | \(0.382212\pi\) | ||||
−0.361656 | + | 0.932312i | \(0.617788\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.7846i | 1.68034i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.58258i | − 0.368081i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.19615i | − 0.414698i | −0.978267 | − | 0.207349i | \(-0.933516\pi\) | ||||
0.978267 | − | 0.207349i | \(-0.0664836\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.93725 | 0.629465 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.58258i | − 0.358935i | −0.983764 | − | 0.179468i | \(-0.942563\pi\) | ||||
0.983764 | − | 0.179468i | \(-0.0574375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −21.0000 | −1.63485 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.8745 | −1.22841 | −0.614203 | − | 0.789148i | \(-0.710522\pi\) | ||||
−0.614203 | + | 0.789148i | \(0.710522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5830 | 0.809303 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 22.5167i | − 1.71191i | −0.517050 | − | 0.855955i | \(-0.672970\pi\) | ||||
0.517050 | − | 0.855955i | \(-0.327030\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.0000 | −1.57846 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 13.7477i | − 1.02755i | −0.857924 | − | 0.513777i | \(-0.828246\pi\) | ||||
0.857924 | − | 0.513777i | \(-0.171754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 20.7846i | − 1.54491i | −0.635071 | − | 0.772454i | \(-0.719029\pi\) | ||||
0.635071 | − | 0.772454i | \(-0.280971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 4.58258i | − 0.338754i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.1244i | 0.891400i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.8118 | −1.74129 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.9129i | 1.65792i | 0.559310 | + | 0.828959i | \(0.311066\pi\) | ||||
−0.559310 | + | 0.828959i | \(0.688934\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | −0.791797 | −0.395899 | − | 0.918294i | \(-0.629567\pi\) | ||||
−0.395899 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.8745 | 1.13680 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2288 | −0.937762 | −0.468881 | − | 0.883261i | \(-0.655343\pi\) | ||||
−0.468881 | + | 0.883261i | \(0.655343\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 12.1244i | − 0.855186i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 18.3303i | − 1.27404i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.1244i | 0.838659i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 9.16515i | − 0.630955i | −0.948933 | − | 0.315478i | \(-0.897835\pi\) | ||||
0.948933 | − | 0.315478i | \(-0.102165\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 24.2487i | − 1.66149i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.8745 | 1.08263 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 13.7477i | − 0.928985i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000 | 1.21081 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5830 | 0.708690 | 0.354345 | − | 0.935115i | \(-0.384704\pi\) | ||||
0.354345 | + | 0.935115i | \(0.384704\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.00000 | 0.533333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.8118 | −1.58044 | −0.790221 | − | 0.612822i | \(-0.790034\pi\) | ||||
−0.790221 | + | 0.612822i | \(0.790034\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.73205i | 0.114457i | 0.998361 | + | 0.0572286i | \(0.0182264\pi\) | ||||
−0.998361 | + | 0.0572286i | \(0.981774\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.0000 | 1.37576 | 0.687878 | − | 0.725826i | \(-0.258542\pi\) | ||||
0.687878 | + | 0.725826i | \(0.258542\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 13.7477i | − 0.896803i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 12.1244i | − 0.787562i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 19.0526i | − 1.22728i | −0.789585 | − | 0.613642i | \(-0.789704\pi\) | ||||
0.789585 | − | 0.613642i | \(-0.210296\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.1660 | −1.35780 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 9.16515i | − 0.583165i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.8745 | −1.00199 | −0.500995 | − | 0.865450i | \(-0.667033\pi\) | ||||
−0.500995 | + | 0.865450i | \(0.667033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.0000 | 1.32026 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.8118 | −1.49115 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.73205i | 0.108042i | 0.998540 | + | 0.0540212i | \(0.0172039\pi\) | ||||
−0.998540 | + | 0.0540212i | \(0.982796\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 4.58258i | − 0.282574i | −0.989969 | − | 0.141287i | \(-0.954876\pi\) | ||||
0.989969 | − | 0.141287i | \(-0.0451240\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.19615i | 0.319197i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 4.58258i | − 0.280449i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.4449i | 1.79529i | 0.440724 | + | 0.897643i | \(0.354722\pi\) | ||||
−0.440724 | + | 0.897643i | \(0.645278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.1033 | 1.76790 | 0.883949 | − | 0.467584i | \(-0.154875\pi\) | ||||
0.883949 | + | 0.467584i | \(0.154875\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.16515i | 0.552679i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.0000 | −1.02143 | −0.510716 | − | 0.859750i | \(-0.670619\pi\) | ||||
−0.510716 | + | 0.859750i | \(0.670619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.5830 | −0.633588 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.2288 | −0.786368 | −0.393184 | − | 0.919460i | \(-0.628626\pi\) | ||||
−0.393184 | + | 0.919460i | \(0.628626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.1244i | 0.718185i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0000 | −0.588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.16515i | 0.537271i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.7846i | 1.21425i | 0.794606 | + | 0.607125i | \(0.207677\pi\) | ||||
−0.794606 | + | 0.607125i | \(0.792323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 13.7477i | − 0.800424i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.1244i | 0.703526i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.8745 | −0.918046 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.7477i | 0.789786i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.00000 | 0.171780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.5830 | 0.604004 | 0.302002 | − | 0.953307i | \(-0.402345\pi\) | ||||
0.302002 | + | 0.953307i | \(0.402345\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00000 | −0.398216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8118 | 1.35024 | 0.675121 | − | 0.737707i | \(-0.264092\pi\) | ||||
0.675121 | + | 0.737707i | \(0.264092\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.9808i | 1.46852i | 0.678869 | + | 0.734260i | \(0.262471\pi\) | ||||
−0.678869 | + | 0.734260i | \(0.737529\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0000 | 0.842484 | 0.421242 | − | 0.906948i | \(-0.361594\pi\) | ||||
0.421242 | + | 0.906948i | \(0.361594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 36.3731i | − 2.03015i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.7477i | 0.764944i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 6.92820i | − 0.384308i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.5203 | −1.02417 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.7477i | 0.755643i | 0.925878 | + | 0.377822i | \(0.123327\pi\) | ||||
−0.925878 | + | 0.377822i | \(0.876673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 28.0000 | 1.53439 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.93725 | 0.433659 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.0000 | −1.52526 | −0.762629 | − | 0.646837i | \(-0.776092\pi\) | ||||
−0.762629 | + | 0.646837i | \(0.776092\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.7490 | 1.72437 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 12.1244i | − 0.656571i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.0000 | 1.13060 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4.58258i | − 0.246006i | −0.992406 | − | 0.123003i | \(-0.960748\pi\) | ||||
0.992406 | − | 0.123003i | \(-0.0392524\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.46410i | 0.185429i | 0.995693 | + | 0.0927146i | \(0.0295544\pi\) | ||||
−0.995693 | + | 0.0927146i | \(0.970446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 9.16515i | − 0.489200i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.0526i | 1.01407i | 0.861927 | + | 0.507033i | \(0.169258\pi\) | ||||
−0.861927 | + | 0.507033i | \(0.830742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.8745 | 0.842531 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 13.7477i | − 0.725577i | −0.931871 | − | 0.362789i | \(-0.881825\pi\) | ||||
0.931871 | − | 0.362789i | \(-0.118175\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0000 | −0.631579 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.4575 | −1.38866 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.00000 | 0.471082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.3948 | 1.79539 | 0.897696 | − | 0.440615i | \(-0.145240\pi\) | ||||
0.897696 | + | 0.440615i | \(0.145240\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.8564i | 0.721336i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | −0.0517780 | −0.0258890 | − | 0.999665i | \(-0.508242\pi\) | ||||
−0.0258890 | + | 0.999665i | \(0.508242\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 32.0780i | 1.65650i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3303i | 0.941564i | 0.882249 | + | 0.470782i | \(0.156028\pi\) | ||||
−0.882249 | + | 0.470782i | \(0.843972\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.2487i | 1.24230i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.93725 | −0.405575 | −0.202787 | − | 0.979223i | \(-0.565000\pi\) | ||||
−0.202787 | + | 0.979223i | \(0.565000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 36.6606i | − 1.86356i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0000 | 1.06474 | 0.532371 | − | 0.846511i | \(-0.321301\pi\) | ||||
0.532371 | + | 0.846511i | \(0.321301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.8118 | 1.20421 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.0000 | 1.05931 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.93725 | 0.399367 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.5167i | 1.13008i | 0.825064 | + | 0.565039i | \(0.191139\pi\) | ||||
−0.825064 | + | 0.565039i | \(0.808861\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0000 | 1.04869 | 0.524345 | − | 0.851506i | \(-0.324310\pi\) | ||||
0.524345 | + | 0.851506i | \(0.324310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.16515i | 0.456549i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 8.66025i | − 0.430331i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.0780i | 1.59005i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0526i | 0.942088i | 0.882110 | + | 0.471044i | \(0.156123\pi\) | ||||
−0.882110 | + | 0.471044i | \(0.843877\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 55.5608 | 2.74061 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.0000 | −1.37117 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.7490 | 1.55104 | 0.775520 | − | 0.631322i | \(-0.217488\pi\) | ||||
0.775520 | + | 0.631322i | \(0.217488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.7490 | −1.54369 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.3923i | 0.504101i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 42.0000 | 2.02778 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.9129i | 1.10367i | 0.833952 | + | 0.551837i | \(0.186073\pi\) | ||||
−0.833952 | + | 0.551837i | \(0.813927\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 3.46410i | − 0.166474i | −0.996530 | − | 0.0832370i | \(-0.973474\pi\) | ||||
0.996530 | − | 0.0832370i | \(-0.0265259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 12.1244i | − 0.579987i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.1033 | −1.38902 | −0.694512 | − | 0.719482i | \(-0.744379\pi\) | ||||
−0.694512 | + | 0.719482i | \(0.744379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.58258i | 0.217725i | 0.994057 | + | 0.108862i | \(0.0347208\pi\) | ||||
−0.994057 | + | 0.108862i | \(0.965279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | 0.142214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −39.6863 | −1.87710 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.8745 | −0.747501 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 60.6218i | 2.84826i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | −0.0467780 | −0.0233890 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233890 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.7477i | 0.641689i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.46410i | 0.161339i | 0.996741 | + | 0.0806696i | \(0.0257059\pi\) | ||||
−0.996741 | + | 0.0806696i | \(0.974294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4955i | 1.27782i | 0.769281 | + | 0.638911i | \(0.220615\pi\) | ||||
−0.769281 | + | 0.638911i | \(0.779385\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 12.1244i | − 0.562254i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.93725 | 0.367292 | 0.183646 | − | 0.982992i | \(-0.441210\pi\) | ||||
0.183646 | + | 0.982992i | \(0.441210\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 13.7477i | − 0.633462i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 42.0000 | 1.93116 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.29150 | 0.242791 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.93725 | −0.362662 | −0.181331 | − | 0.983422i | \(-0.558041\pi\) | ||||
−0.181331 | + | 0.983422i | \(0.558041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 24.2487i | − 1.10565i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.00000 | −0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 41.2432i | − 1.86891i | −0.356085 | − | 0.934453i | \(-0.615889\pi\) | ||||
0.356085 | − | 0.934453i | \(-0.384111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 12.1244i | − 0.548282i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 18.3303i | − 0.827235i | −0.910451 | − | 0.413617i | \(-0.864265\pi\) | ||||
0.910451 | − | 0.413617i | \(-0.135735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31.7490 | −1.42701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0780i | 1.43601i | 0.696038 | + | 0.718005i | \(0.254944\pi\) | ||||
−0.696038 | + | 0.718005i | \(0.745056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.0000 | −1.87642 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.7490 | 1.41562 | 0.707809 | − | 0.706404i | \(-0.249684\pi\) | ||||
0.707809 | + | 0.706404i | \(0.249684\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.64575 | 0.117502 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 25.9808i | − 1.15158i | −0.817599 | − | 0.575789i | \(-0.804695\pi\) | ||||
0.817599 | − | 0.575789i | \(-0.195305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.00000 | 0.309058 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.58258i | − 0.201932i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 36.3731i | − 1.59969i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 59.5735i | − 2.61499i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 43.3013i | 1.89706i | 0.316683 | + | 0.948532i | \(0.397431\pi\) | ||||
−0.316683 | + | 0.948532i | \(0.602569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.2288 | 0.578453 | 0.289227 | − | 0.957261i | \(-0.406602\pi\) | ||||
0.289227 | + | 0.957261i | \(0.406602\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 13.7477i | − 0.598860i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | 0.0869565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.7490 | −1.37779 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.8118 | 1.02947 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 36.3731i | − 1.56961i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0000 | 0.558914 | 0.279457 | − | 0.960158i | \(-0.409846\pi\) | ||||
0.279457 | + | 0.960158i | \(0.409846\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 54.9909i | − 2.35989i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 12.1244i | − 0.519350i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 18.3303i | − 0.783747i | −0.920019 | − | 0.391874i | \(-0.871827\pi\) | ||||
0.920019 | − | 0.391874i | \(-0.128173\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 6.92820i | − 0.295689i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 32.0780i | 1.36164i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.00000 | −0.127114 | −0.0635570 | − | 0.997978i | \(-0.520244\pi\) | ||||
−0.0635570 | + | 0.997978i | \(0.520244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.7490 | −1.34284 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −63.0000 | −2.65986 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.93725 | −0.334515 | −0.167258 | − | 0.985913i | \(-0.553491\pi\) | ||||
−0.167258 | + | 0.985913i | \(0.553491\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.7846i | 0.874415i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.0000 | −0.880366 | −0.440183 | − | 0.897908i | \(-0.645086\pi\) | ||||
−0.440183 | + | 0.897908i | \(0.645086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 13.7477i | − 0.575324i | −0.957732 | − | 0.287662i | \(-0.907122\pi\) | ||||
0.957732 | − | 0.287662i | \(-0.0928781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 60.6218i | 2.53251i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 9.16515i | − 0.382213i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 19.0526i | − 0.793168i | −0.917998 | − | 0.396584i | \(-0.870195\pi\) | ||||
0.917998 | − | 0.396584i | \(-0.129805\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.1033 | −1.20949 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.7477i | 0.569373i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.0000 | 0.992278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.7490 | 1.31042 | 0.655211 | − | 0.755446i | \(-0.272580\pi\) | ||||
0.655211 | + | 0.755446i | \(0.272580\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.00000 | −0.288430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.7490 | −1.30598 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.5167i | 0.924648i | 0.886711 | + | 0.462324i | \(0.152984\pi\) | ||||
−0.886711 | + | 0.462324i | \(0.847016\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −35.0000 | −1.43245 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 4.58258i | − 0.187239i | −0.995608 | − | 0.0936195i | \(-0.970156\pi\) | ||||
0.995608 | − | 0.0936195i | \(-0.0298437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.46410i | 0.141304i | 0.997501 | + | 0.0706518i | \(0.0225079\pi\) | ||||
−0.997501 | + | 0.0706518i | \(0.977492\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 18.3303i | − 0.746468i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 17.3205i | − 0.704179i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.64575 | 0.107388 | 0.0536939 | − | 0.998557i | \(-0.482900\pi\) | ||||
0.0536939 | + | 0.998557i | \(0.482900\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.4955i | 1.11235i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.00000 | −0.282727 | −0.141364 | − | 0.989958i | \(-0.545149\pi\) | ||||
−0.141364 | + | 0.989958i | \(0.545149\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.8745 | −0.640122 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.5203 | −0.744392 | −0.372196 | − | 0.928154i | \(-0.621395\pi\) | ||||
−0.372196 | + | 0.928154i | \(0.621395\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 12.1244i | − 0.486534i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 32.0780i | 1.28107i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.3731i | 1.45029i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.8258i | 1.82429i | 0.409863 | + | 0.912147i | \(0.365577\pi\) | ||||
−0.409863 | + | 0.912147i | \(0.634423\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 24.2487i | − 0.963800i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.8745 | −0.629961 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 36.6606i | − 1.45027i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.0000 | −0.829450 | −0.414725 | − | 0.909947i | \(-0.636122\pi\) | ||||
−0.414725 | + | 0.909947i | \(0.636122\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.1660 | −0.834706 | −0.417353 | − | 0.908744i | \(-0.637042\pi\) | ||||
−0.417353 | + | 0.908744i | \(0.637042\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 42.0000 | 1.65375 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.6863 | −1.56023 | −0.780114 | − | 0.625637i | \(-0.784839\pi\) | ||||
−0.780114 | + | 0.625637i | \(0.784839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 36.3731i | − 1.42777i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.0000 | −0.821794 | −0.410897 | − | 0.911682i | \(-0.634784\pi\) | ||||
−0.410897 | + | 0.911682i | \(0.634784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.7477i | 0.537168i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 20.7846i | − 0.810885i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 9.16515i | − 0.357024i | −0.983938 | − | 0.178512i | \(-0.942872\pi\) | ||||
0.983938 | − | 0.178512i | \(-0.0571283\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 5.19615i | − 0.202107i | −0.994881 | − | 0.101053i | \(-0.967779\pi\) | ||||
0.994881 | − | 0.101053i | \(-0.0322213\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 47.6235 | 1.84954 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.0000 | 1.08254 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.93725 | 0.306414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.0000 | 1.07932 | 0.539660 | − | 0.841883i | \(-0.318553\pi\) | ||||
0.539660 | + | 0.841883i | \(0.318553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.29150 | 0.203670 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.73205i | 0.0665681i | 0.999446 | + | 0.0332841i | \(0.0105966\pi\) | ||||
−0.999446 | + | 0.0332841i | \(0.989403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −63.0000 | −2.41417 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.58258i | 0.175347i | 0.996149 | + | 0.0876737i | \(0.0279433\pi\) | ||||
−0.996149 | + | 0.0876737i | \(0.972057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.3731i | 1.38974i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.58258i | 0.174836i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 10.3923i | − 0.395915i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.64575 | −0.100649 | −0.0503246 | − | 0.998733i | \(-0.516026\pi\) | ||||
−0.0503246 | + | 0.998733i | \(0.516026\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 18.3303i | − 0.695308i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | −0.681799 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 55.5608 | 2.10150 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5203 | 0.698505 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 36.3731i | − 1.36989i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.0000 | 1.31445 | 0.657226 | − | 0.753693i | \(-0.271730\pi\) | ||||
0.657226 | + | 0.753693i | \(0.271730\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 18.3303i | − 0.687440i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.1244i | 0.454061i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.4955i | 1.02827i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.93725 | 0.296010 | 0.148005 | − | 0.988987i | \(-0.452715\pi\) | ||||
0.148005 | + | 0.988987i | \(0.452715\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 50.4083i | − 1.87471i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.1660 | 0.785004 | 0.392502 | − | 0.919751i | \(-0.371610\pi\) | ||||
0.392502 | + | 0.919751i | \(0.371610\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.0000 | −1.51852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.6235 | 1.76142 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 22.5167i | − 0.831672i | −0.909440 | − | 0.415836i | \(-0.863489\pi\) | ||||
0.909440 | − | 0.415836i | \(-0.136511\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.0000 | 0.773545 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.9129i | 0.842864i | 0.906860 | + | 0.421432i | \(0.138472\pi\) | ||||
−0.906860 | + | 0.421432i | \(0.861528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 24.2487i | − 0.890799i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.8258i | 1.68118i | 0.541669 | + | 0.840592i | \(0.317793\pi\) | ||||
−0.541669 | + | 0.840592i | \(0.682207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 25.9808i | − 0.951861i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 13.7477i | − 0.501662i | −0.968031 | − | 0.250831i | \(-0.919296\pi\) | ||||
0.968031 | − | 0.250831i | \(-0.0807038\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −42.0000 | −1.53057 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.6863 | −1.44433 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.0000 | −1.01768 | −0.508839 | − | 0.860862i | \(-0.669925\pi\) | ||||
−0.508839 | + | 0.860862i | \(0.669925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 55.5608 | 2.01673 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 25.9808i | − 0.941802i | −0.882186 | − | 0.470901i | \(-0.843929\pi\) | ||||
0.882186 | − | 0.470901i | \(-0.156071\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −36.0000 | −1.30158 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.4955i | 0.992803i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 51.9615i | − 1.87378i | −0.349624 | − | 0.936890i | \(-0.613691\pi\) | ||||
0.349624 | − | 0.936890i | \(-0.386309\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.58258i | 0.165037i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 29.4449i | − 1.05906i | −0.848292 | − | 0.529529i | \(-0.822369\pi\) | ||||
0.848292 | − | 0.529529i | \(-0.177631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.29150 | −0.190076 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.16515i | 0.328376i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42.0000 | 1.50288 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.00000 | 0.321224 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.2288 | 0.471554 | 0.235777 | − | 0.971807i | \(-0.424236\pi\) | ||||
0.235777 | + | 0.971807i | \(0.424236\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 12.1244i | − 0.431638i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.00000 | −0.213066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.7477i | 0.487582i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3.46410i | − 0.122705i | −0.998116 | − | 0.0613524i | \(-0.980459\pi\) | ||||
0.998116 | − | 0.0613524i | \(-0.0195413\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 41.2432i | − 1.45908i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 6.92820i | − 0.244796i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.8118 | 0.840299 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 77.9038i | 2.74234i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.0000 | −1.58212 | −0.791058 | − | 0.611741i | \(-0.790469\pi\) | ||||
−0.791058 | + | 0.611741i | \(0.790469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.1660 | 0.743239 | 0.371620 | − | 0.928385i | \(-0.378803\pi\) | ||||
0.371620 | + | 0.928385i | \(0.378803\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 77.0000 | 2.70051 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.93725 | 0.278030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 24.2487i | − 0.848355i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.0000 | −0.942306 | −0.471153 | − | 0.882051i | \(-0.656162\pi\) | ||||
−0.471153 | + | 0.882051i | \(0.656162\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.0780i | 1.11817i | 0.829110 | + | 0.559085i | \(0.188847\pi\) | ||||
−0.829110 | + | 0.559085i | \(0.811153\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.2487i | 0.844232i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.16515i | 0.318704i | 0.987222 | + | 0.159352i | \(0.0509404\pi\) | ||||
−0.987222 | + | 0.159352i | \(0.949060\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.19615i | 0.180470i | 0.995921 | + | 0.0902349i | \(0.0287618\pi\) | ||||
−0.995921 | + | 0.0902349i | \(0.971238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −44.9778 | −1.56026 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 27.4955i | − 0.951519i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.00000 | −0.241955 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.7490 | −1.09610 | −0.548049 | − | 0.836446i | \(-0.684629\pi\) | ||||
−0.548049 | + | 0.836446i | \(0.684629\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.73205i | 0.0595844i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −35.0000 | −1.20120 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 32.0780i | − 1.09962i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.9615i | 1.77913i | 0.456810 | + | 0.889564i | \(0.348992\pi\) | ||||
−0.456810 | + | 0.889564i | \(0.651008\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.3303i | 0.626883i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.4449i | 1.00582i | 0.864340 | + | 0.502909i | \(0.167737\pi\) | ||||
−0.864340 | + | 0.502909i | \(0.832263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.64575 | 0.0902719 | 0.0451359 | − | 0.998981i | \(-0.485628\pi\) | ||||
0.0451359 | + | 0.998981i | \(0.485628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.7477i | 0.467978i | 0.972239 | + | 0.233989i | \(0.0751780\pi\) | ||||
−0.972239 | + | 0.233989i | \(0.924822\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.0000 | 1.32604 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.4575 | −0.898544 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0000 | 0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.8745 | −0.537887 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.8564i | 0.468968i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.00000 | −0.236373 | −0.118187 | − | 0.992991i | \(-0.537708\pi\) | ||||
−0.118187 | + | 0.992991i | \(0.537708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 54.9909i | 1.85480i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 27.7128i | − 0.933668i | −0.884345 | − | 0.466834i | \(-0.845394\pi\) | ||||
0.884345 | − | 0.466834i | \(-0.154606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 27.4955i | − 0.925296i | −0.886542 | − | 0.462648i | \(-0.846899\pi\) | ||||
0.886542 | − | 0.462648i | \(-0.153101\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 36.3731i | − 1.22267i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.8118 | 0.799521 | 0.399760 | − | 0.916620i | \(-0.369093\pi\) | ||||
0.399760 | + | 0.916620i | \(0.369093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 22.9129i | − 0.767610i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.0000 | −0.702738 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.8118 | 0.795939 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.0000 | −1.40234 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.5885i | 0.519327i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.0000 | 1.19668 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 22.9129i | − 0.760810i | −0.924820 | − | 0.380405i | \(-0.875785\pi\) | ||||
0.924820 | − | 0.380405i | \(-0.124215\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.7846i | 0.689382i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 27.4955i | − 0.910965i | −0.890245 | − | 0.455483i | \(-0.849467\pi\) | ||||
0.890245 | − | 0.455483i | \(-0.150533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.93725 | 0.262398 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.9129i | 0.755826i | 0.925841 | + | 0.377913i | \(0.123358\pi\) | ||||
−0.925841 | + | 0.377913i | \(0.876642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.0000 | 0.922631 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.7490 | −1.04503 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | 0.460317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.5830 | −0.347591 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.7654i | 1.53432i | 0.641455 | + | 0.767161i | \(0.278331\pi\) | ||||
−0.641455 | + | 0.767161i | \(0.721669\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 63.0000 | 2.06253 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 41.2432i | − 1.34880i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.7128i | 0.905338i | 0.891679 | + | 0.452669i | \(0.149528\pi\) | ||||
−0.891679 | + | 0.452669i | \(0.850472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 68.7386i | 2.24320i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 19.0526i | − 0.621096i | −0.950558 | − | 0.310548i | \(-0.899488\pi\) | ||||
0.950558 | − | 0.310548i | \(-0.100512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.8745 | 0.516945 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.58258i | − 0.148914i | −0.997224 | − | 0.0744569i | \(-0.976278\pi\) | ||||
0.997224 | − | 0.0744569i | \(-0.0237223\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | −0.584305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.6863 | 1.28692 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.0000 | −0.388718 | −0.194359 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194359 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.6863 | −1.28422 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.0000 | −0.774194 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 54.9909i | − 1.77206i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 19.0526i | − 0.613324i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 45.8258i | − 1.47366i | −0.676080 | − | 0.736828i | \(-0.736323\pi\) | ||||
0.676080 | − | 0.736828i | \(-0.263677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.3731i | 1.16847i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55.5608 | −1.78303 | −0.891515 | − | 0.452991i | \(-0.850357\pi\) | ||||
−0.891515 | + | 0.452991i | \(0.850357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 18.3303i | − 0.587040i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0000 | 0.671850 | 0.335925 | − | 0.941889i | \(-0.390951\pi\) | ||||
0.335925 | + | 0.941889i | \(0.390951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.93725 | 0.253676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.0000 | −0.893971 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.93725 | 0.253159 | 0.126580 | − | 0.991956i | \(-0.459600\pi\) | ||||
0.126580 | + | 0.991956i | \(0.459600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 20.7846i | − 0.662253i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.0000 | −1.33552 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 4.58258i | − 0.145570i | −0.997348 | − | 0.0727852i | \(-0.976811\pi\) | ||||
0.997348 | − | 0.0727852i | \(-0.0231887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36.3731i | 1.15426i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 22.9129i | − 0.726387i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.3013i | 1.37136i | 0.727901 | + | 0.685682i | \(0.240496\pi\) | ||||
−0.727901 | + | 0.685682i | \(0.759504\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.5203 | 0.585955 |
(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 | 784.2.f.d.783.4 | 4 | ||
3.2 | odd | 2 | 7056.2.b.s.1567.1 | 4 | |||
4.3 | odd | 2 | inner | 784.2.f.d.783.2 | 4 | ||
7.2 | even | 3 | 784.2.p.g.31.1 | 4 | |||
7.3 | odd | 6 | 784.2.p.g.607.2 | 4 | |||
7.4 | even | 3 | 112.2.p.c.47.1 | yes | 4 | ||
7.5 | odd | 6 | 112.2.p.c.31.2 | yes | 4 | ||
7.6 | odd | 2 | inner | 784.2.f.d.783.1 | 4 | ||
8.3 | odd | 2 | 3136.2.f.f.3135.3 | 4 | |||
8.5 | even | 2 | 3136.2.f.f.3135.1 | 4 | |||
12.11 | even | 2 | 7056.2.b.s.1567.2 | 4 | |||
21.5 | even | 6 | 1008.2.cs.q.703.2 | 4 | |||
21.11 | odd | 6 | 1008.2.cs.q.271.1 | 4 | |||
21.20 | even | 2 | 7056.2.b.s.1567.3 | 4 | |||
28.3 | even | 6 | 784.2.p.g.607.1 | 4 | |||
28.11 | odd | 6 | 112.2.p.c.47.2 | yes | 4 | ||
28.19 | even | 6 | 112.2.p.c.31.1 | ✓ | 4 | ||
28.23 | odd | 6 | 784.2.p.g.31.2 | 4 | |||
28.27 | even | 2 | inner | 784.2.f.d.783.3 | 4 | ||
56.5 | odd | 6 | 448.2.p.c.255.1 | 4 | |||
56.11 | odd | 6 | 448.2.p.c.383.1 | 4 | |||
56.13 | odd | 2 | 3136.2.f.f.3135.4 | 4 | |||
56.19 | even | 6 | 448.2.p.c.255.2 | 4 | |||
56.27 | even | 2 | 3136.2.f.f.3135.2 | 4 | |||
56.53 | even | 6 | 448.2.p.c.383.2 | 4 | |||
84.11 | even | 6 | 1008.2.cs.q.271.2 | 4 | |||
84.47 | odd | 6 | 1008.2.cs.q.703.1 | 4 | |||
84.83 | odd | 2 | 7056.2.b.s.1567.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.p.c.31.1 | ✓ | 4 | 28.19 | even | 6 | ||
112.2.p.c.31.2 | yes | 4 | 7.5 | odd | 6 | ||
112.2.p.c.47.1 | yes | 4 | 7.4 | even | 3 | ||
112.2.p.c.47.2 | yes | 4 | 28.11 | odd | 6 | ||
448.2.p.c.255.1 | 4 | 56.5 | odd | 6 | |||
448.2.p.c.255.2 | 4 | 56.19 | even | 6 | |||
448.2.p.c.383.1 | 4 | 56.11 | odd | 6 | |||
448.2.p.c.383.2 | 4 | 56.53 | even | 6 | |||
784.2.f.d.783.1 | 4 | 7.6 | odd | 2 | inner | ||
784.2.f.d.783.2 | 4 | 4.3 | odd | 2 | inner | ||
784.2.f.d.783.3 | 4 | 28.27 | even | 2 | inner | ||
784.2.f.d.783.4 | 4 | 1.1 | even | 1 | trivial | ||
784.2.p.g.31.1 | 4 | 7.2 | even | 3 | |||
784.2.p.g.31.2 | 4 | 28.23 | odd | 6 | |||
784.2.p.g.607.1 | 4 | 28.3 | even | 6 | |||
784.2.p.g.607.2 | 4 | 7.3 | odd | 6 | |||
1008.2.cs.q.271.1 | 4 | 21.11 | odd | 6 | |||
1008.2.cs.q.271.2 | 4 | 84.11 | even | 6 | |||
1008.2.cs.q.703.1 | 4 | 84.47 | odd | 6 | |||
1008.2.cs.q.703.2 | 4 | 21.5 | even | 6 | |||
3136.2.f.f.3135.1 | 4 | 8.5 | even | 2 | |||
3136.2.f.f.3135.2 | 4 | 56.27 | even | 2 | |||
3136.2.f.f.3135.3 | 4 | 8.3 | odd | 2 | |||
3136.2.f.f.3135.4 | 4 | 56.13 | odd | 2 | |||
7056.2.b.s.1567.1 | 4 | 3.2 | odd | 2 | |||
7056.2.b.s.1567.2 | 4 | 12.11 | even | 2 | |||
7056.2.b.s.1567.3 | 4 | 21.20 | even | 2 | |||
7056.2.b.s.1567.4 | 4 | 84.83 | odd | 2 |