Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(2017,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.2017");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.c (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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.897122304.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 51x^{4} - 104x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2017.3 | ||
Root | \(-2.07341 - 1.19709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.2017 |
Dual form | 4032.2.c.r.2017.6 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | − 1.75265i | − 0.783811i | −0.920006 | − | 0.391905i | \(-0.871816\pi\) | ||||
0.920006 | − | 0.391905i | \(-0.128184\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.75265i | − 0.528445i | −0.964462 | − | 0.264223i | \(-0.914885\pi\) | ||||
0.964462 | − | 0.264223i | \(-0.0851153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.46410i | − 0.406069i | −0.979172 | − | 0.203034i | \(-0.934920\pi\) | ||||
0.979172 | − | 0.203034i | \(-0.0650803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.54099 | 1.58642 | 0.793212 | − | 0.608945i | \(-0.208407\pi\) | ||||
0.793212 | + | 0.608945i | \(0.208407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.46410i | − 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.03569 | 0.632984 | 0.316492 | − | 0.948595i | \(-0.397495\pi\) | ||||
0.316492 | + | 0.948595i | \(0.397495\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.92820 | 0.385641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.57668i | 1.77834i | 0.457572 | + | 0.889172i | \(0.348719\pi\) | ||||
−0.457572 | + | 0.889172i | \(0.651281\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.75265i | − 0.296253i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4.53590i | − 0.745697i | −0.927892 | − | 0.372849i | \(-0.878381\pi\) | ||||
0.927892 | − | 0.372849i | \(-0.121619\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.54099 | −1.02153 | −0.510766 | − | 0.859720i | \(-0.670638\pi\) | ||||
−0.510766 | + | 0.859720i | \(0.670638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.92820i | − 0.751544i | −0.926712 | − | 0.375772i | \(-0.877378\pi\) | ||||
0.926712 | − | 0.375772i | \(-0.122622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.57668 | 1.39690 | 0.698451 | − | 0.715658i | \(-0.253873\pi\) | ||||
0.698451 | + | 0.715658i | \(0.253873\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.07180 | −0.414201 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.57668i | 1.24678i | 0.781912 | + | 0.623389i | \(0.214245\pi\) | ||||
−0.781912 | + | 0.623389i | \(0.785755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.46410i | 0.187459i | 0.995598 | + | 0.0937295i | \(0.0298789\pi\) | ||||
−0.995598 | + | 0.0937295i | \(0.970121\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.56606 | −0.318281 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.0000i | − 1.22169i | −0.791748 | − | 0.610847i | \(-0.790829\pi\) | ||||
0.791748 | − | 0.610847i | \(-0.209171\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0463 | −1.19228 | −0.596138 | − | 0.802882i | \(-0.703299\pi\) | ||||
−0.596138 | + | 0.802882i | \(0.703299\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9282 | 1.51313 | 0.756566 | − | 0.653917i | \(-0.226876\pi\) | ||||
0.756566 | + | 0.653917i | \(0.226876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.75265i | − 0.199733i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9282 | −1.22952 | −0.614759 | − | 0.788715i | \(-0.710747\pi\) | ||||
−0.614759 | + | 0.788715i | \(0.710747\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 6.07137i | − 0.666420i | −0.942853 | − | 0.333210i | \(-0.891868\pi\) | ||||
0.942853 | − | 0.333210i | \(-0.108132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 11.4641i | − 1.24346i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.469622 | −0.0497799 | −0.0248899 | − | 0.999690i | \(-0.507924\pi\) | ||||
−0.0248899 | + | 0.999690i | \(0.507924\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.46410i | − 0.153480i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.07137 | −0.622910 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.92820 | 0.906522 | 0.453261 | − | 0.891378i | \(-0.350261\pi\) | ||||
0.453261 | + | 0.891378i | \(0.350261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.75265i | − 0.174396i | −0.996191 | − | 0.0871978i | \(-0.972209\pi\) | ||||
0.996191 | − | 0.0871978i | \(-0.0277912\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.92820 | −0.485590 | −0.242795 | − | 0.970078i | \(-0.578064\pi\) | ||||
−0.242795 | + | 0.970078i | \(0.578064\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 17.4007i | − 1.68219i | −0.540888 | − | 0.841095i | \(-0.681912\pi\) | ||||
0.540888 | − | 0.841095i | \(-0.318088\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 4.00000i | − 0.383131i | −0.981480 | − | 0.191565i | \(-0.938644\pi\) | ||||
0.981480 | − | 0.191565i | \(-0.0613564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.50531 | 0.329752 | 0.164876 | − | 0.986314i | \(-0.447278\pi\) | ||||
0.164876 | + | 0.986314i | \(0.447278\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 5.32051i | − 0.496140i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.54099 | 0.599612 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.92820 | 0.720746 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 12.1427i | − 1.08608i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.07180 | −0.0951066 | −0.0475533 | − | 0.998869i | \(-0.515142\pi\) | ||||
−0.0475533 | + | 0.998869i | \(0.515142\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.07137i | 0.530458i | 0.964185 | + | 0.265229i | \(0.0854476\pi\) | ||||
−0.964185 | + | 0.265229i | \(0.914552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.46410i | − 0.300376i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.07137 | 0.518712 | 0.259356 | − | 0.965782i | \(-0.416490\pi\) | ||||
0.259356 | + | 0.965782i | \(0.416490\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 9.85641i | − 0.836009i | −0.908445 | − | 0.418005i | \(-0.862730\pi\) | ||||
0.908445 | − | 0.418005i | \(-0.137270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.56606 | −0.214585 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.7846 | 1.39389 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.01062i | 0.574332i | 0.957881 | + | 0.287166i | \(0.0927132\pi\) | ||||
−0.957881 | + | 0.287166i | \(0.907287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | −0.325515 | −0.162758 | − | 0.986666i | \(-0.552039\pi\) | ||||
−0.162758 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.50531i | 0.281553i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3923i | 0.989014i | 0.869174 | + | 0.494507i | \(0.164651\pi\) | ||||
−0.869174 | + | 0.494507i | \(0.835349\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.03569 | 0.239246 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 11.8564i | − 0.928665i | −0.885661 | − | 0.464333i | \(-0.846294\pi\) | ||||
0.885661 | − | 0.464333i | \(-0.153706\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.07137 | −0.469817 | −0.234908 | − | 0.972018i | \(-0.575479\pi\) | ||||
−0.234908 | + | 0.972018i | \(0.575479\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8564 | 0.835108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 5.25796i | − 0.399755i | −0.979821 | − | 0.199878i | \(-0.935945\pi\) | ||||
0.979821 | − | 0.199878i | \(-0.0640545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.92820 | 0.145758 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.4113i | 1.82459i | 0.409536 | + | 0.912294i | \(0.365691\pi\) | ||||
−0.409536 | + | 0.912294i | \(0.634309\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 21.4641i | − 1.59541i | −0.603045 | − | 0.797707i | \(-0.706046\pi\) | ||||
0.603045 | − | 0.797707i | \(-0.293954\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.94986 | −0.584485 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 11.4641i | − 0.838338i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.0569 | −1.23420 | −0.617098 | − | 0.786887i | \(-0.711692\pi\) | ||||
−0.617098 | + | 0.786887i | \(0.711692\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.07180 | −0.0771496 | −0.0385748 | − | 0.999256i | \(-0.512282\pi\) | ||||
−0.0385748 | + | 0.999256i | \(0.512282\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 6.07137i | − 0.432567i | −0.976331 | − | 0.216284i | \(-0.930606\pi\) | ||||
0.976331 | − | 0.216284i | \(-0.0693936\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.7846 | −1.75693 | −0.878467 | − | 0.477803i | \(-0.841433\pi\) | ||||
−0.878467 | + | 0.477803i | \(0.841433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.57668i | 0.672151i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.4641i | 0.800688i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.07137 | −0.419966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 10.0000i | − 0.688428i | −0.938891 | − | 0.344214i | \(-0.888145\pi\) | ||||
0.938891 | − | 0.344214i | \(-0.111855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.63744 | −0.589068 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 9.57668i | − 0.644197i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.07180 | 0.339633 | 0.169816 | − | 0.985476i | \(-0.445683\pi\) | ||||
0.169816 | + | 0.985476i | \(0.445683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 10.5159i | − 0.697966i | −0.937129 | − | 0.348983i | \(-0.886527\pi\) | ||||
0.937129 | − | 0.348983i | \(-0.113473\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 10.5359i | − 0.696232i | −0.937452 | − | 0.348116i | \(-0.886822\pi\) | ||||
0.937452 | − | 0.348116i | \(-0.113178\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.7300 | −1.88217 | −0.941084 | − | 0.338173i | \(-0.890191\pi\) | ||||
−0.941084 | + | 0.338173i | \(0.890191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 16.7846i | − 1.09491i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.1283 | 1.49604 | 0.748022 | − | 0.663673i | \(-0.231004\pi\) | ||||
0.748022 | + | 0.663673i | \(0.231004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.75265i | − 0.111973i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.07180 | −0.322711 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5159i | 0.663759i | 0.943322 | + | 0.331880i | \(0.107683\pi\) | ||||
−0.943322 | + | 0.331880i | \(0.892317\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.32051i | − 0.334497i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.6230 | 1.22405 | 0.612024 | − | 0.790839i | \(-0.290356\pi\) | ||||
0.612024 | + | 0.790839i | \(0.290356\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 4.53590i | − 0.281847i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.1177 | 0.993858 | 0.496929 | − | 0.867791i | \(-0.334461\pi\) | ||||
0.496929 | + | 0.867791i | \(0.334461\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5.25796i | − 0.320584i | −0.987070 | − | 0.160292i | \(-0.948756\pi\) | ||||
0.987070 | − | 0.160292i | \(-0.0512435\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0718 | −0.915546 | −0.457773 | − | 0.889069i | \(-0.651353\pi\) | ||||
−0.457773 | + | 0.889069i | \(0.651353\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 3.37947i | − 0.203790i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 30.3923i | − 1.82610i | −0.407851 | − | 0.913048i | \(-0.633722\pi\) | ||||
0.407851 | − | 0.913048i | \(-0.366278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.56606 | −0.153079 | −0.0765393 | − | 0.997067i | \(-0.524387\pi\) | ||||
−0.0765393 | + | 0.997067i | \(0.524387\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.3923i | 0.855534i | 0.903889 | + | 0.427767i | \(0.140700\pi\) | ||||
−0.903889 | + | 0.427767i | \(0.859300\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.54099 | −0.386103 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.7846 | 1.51674 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.9060i | 1.22134i | 0.791884 | + | 0.610671i | \(0.209100\pi\) | ||||
−0.791884 | + | 0.610671i | \(0.790900\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.7846 | 0.977238 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.44455i | − 0.257035i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 4.92820i | − 0.284057i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.56606 | 0.146932 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 18.3923i | − 1.04970i | −0.851193 | − | 0.524852i | \(-0.824121\pi\) | ||||
0.851193 | − | 0.524852i | \(-0.175879\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.57668 | 0.543044 | 0.271522 | − | 0.962432i | \(-0.412473\pi\) | ||||
0.271522 | + | 0.962432i | \(0.412473\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.928203 | −0.0524651 | −0.0262326 | − | 0.999656i | \(-0.508351\pi\) | ||||
−0.0262326 | + | 0.999656i | \(0.508351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.1640i | 1.46952i | 0.678330 | + | 0.734758i | \(0.262704\pi\) | ||||
−0.678330 | + | 0.734758i | \(0.737296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.7846 | 0.939758 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 22.6587i | − 1.26076i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2.82309i | − 0.156597i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.57668 | 0.527979 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000i | 0.329790i | 0.986311 | + | 0.164895i | \(0.0527285\pi\) | ||||
−0.986311 | + | 0.164895i | \(0.947272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.5265 | −0.957577 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.50531i | 0.189823i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 27.9166i | − 1.49864i | −0.662206 | − | 0.749322i | \(-0.730380\pi\) | ||||
0.662206 | − | 0.749322i | \(-0.269620\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.4641i | 0.720717i | 0.932814 | + | 0.360358i | \(0.117346\pi\) | ||||
−0.932814 | + | 0.360358i | \(0.882654\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.5516 | 0.721279 | 0.360640 | − | 0.932705i | \(-0.382558\pi\) | ||||
0.360640 | + | 0.932705i | \(0.382558\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.6077i | 0.934519i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.03569 | 0.160217 | 0.0801087 | − | 0.996786i | \(-0.474473\pi\) | ||||
0.0801087 | + | 0.996786i | \(0.474473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 22.6587i | − 1.18601i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.7846 | −1.71134 | −0.855671 | − | 0.517520i | \(-0.826855\pi\) | ||||
−0.855671 | + | 0.517520i | \(0.826855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.92820i | 0.358729i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) | ||||
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.0212 | 0.722130 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 27.8564i | − 1.43089i | −0.698670 | − | 0.715444i | \(-0.746225\pi\) | ||||
0.698670 | − | 0.715444i | \(-0.253775\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.5159 | −0.537339 | −0.268669 | − | 0.963232i | \(-0.586584\pi\) | ||||
−0.268669 | + | 0.963232i | \(0.586584\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.07180 | −0.156553 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 4.44455i | − 0.225348i | −0.993632 | − | 0.112674i | \(-0.964058\pi\) | ||||
0.993632 | − | 0.112674i | \(-0.0359415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.8564 | 1.00418 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.1534i | 0.963710i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.5359i | 0.930290i | 0.885234 | + | 0.465145i | \(0.153998\pi\) | ||||
−0.885234 | + | 0.465145i | \(0.846002\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.939245 | 0.0469036 | 0.0234518 | − | 0.999725i | \(-0.492534\pi\) | ||||
0.0234518 | + | 0.999725i | \(0.492534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.92820i | 0.145864i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.94986 | −0.394060 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.92820 | 0.441471 | 0.220736 | − | 0.975334i | \(-0.429154\pi\) | ||||
0.220736 | + | 0.975334i | \(0.429154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.57668i | 0.471238i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.6410 | −0.522347 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 23.5979i | − 1.15283i | −0.817156 | − | 0.576417i | \(-0.804450\pi\) | ||||
0.817156 | − | 0.576417i | \(-0.195550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 29.3205i | − 1.42899i | −0.699638 | − | 0.714497i | \(-0.746656\pi\) | ||||
0.699638 | − | 0.714497i | \(-0.253344\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.6124 | 0.611790 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.46410i | 0.0708528i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.1177 | 0.776361 | 0.388181 | − | 0.921583i | \(-0.373104\pi\) | ||||
0.388181 | + | 0.921583i | \(0.373104\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.14359 | −0.391356 | −0.195678 | − | 0.980668i | \(-0.562691\pi\) | ||||
−0.195678 | + | 0.980668i | \(0.562691\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 10.5159i | − 0.503045i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8564 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.25796i | 0.249813i | 0.992168 | + | 0.124907i | \(0.0398631\pi\) | ||||
−0.992168 | + | 0.124907i | \(0.960137\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.823085i | 0.0390180i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.6799 | −1.73103 | −0.865516 | − | 0.500882i | \(-0.833009\pi\) | ||||
−0.865516 | + | 0.500882i | \(0.833009\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.4641i | 0.539823i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.56606 | −0.120299 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.85641 | −0.180395 | −0.0901975 | − | 0.995924i | \(-0.528750\pi\) | ||||
−0.0901975 | + | 0.995924i | \(0.528750\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.5541i | 1.70249i | 0.524766 | + | 0.851246i | \(0.324153\pi\) | ||||
−0.524766 | + | 0.851246i | \(0.675847\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.6693i | 1.37293i | 0.727162 | + | 0.686465i | \(0.240839\pi\) | ||||
−0.727162 | + | 0.686465i | \(0.759161\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10.0000i | − 0.461757i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.63744 | −0.397150 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 6.67949i | − 0.306476i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.7407 | 1.63303 | 0.816516 | − | 0.577323i | \(-0.195902\pi\) | ||||
0.816516 | + | 0.577323i | \(0.195902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.64102 | −0.302804 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 15.6481i | − 0.710541i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.7846 | 1.12310 | 0.561549 | − | 0.827444i | \(-0.310206\pi\) | ||||
0.561549 | + | 0.827444i | \(0.310206\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 5.25796i | − 0.237289i | −0.992937 | − | 0.118644i | \(-0.962145\pi\) | ||||
0.992937 | − | 0.118644i | \(-0.0378548\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 62.6410i | 2.82121i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.0463 | −0.450638 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9282i | 0.757810i | 0.925435 | + | 0.378905i | \(0.123699\pi\) | ||||
−0.925435 | + | 0.378905i | \(0.876301\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.6587 | 1.01030 | 0.505150 | − | 0.863032i | \(-0.331437\pi\) | ||||
0.505150 | + | 0.863032i | \(0.331437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.07180 | −0.136693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.4007i | 0.771273i | 0.922651 | + | 0.385636i | \(0.126018\pi\) | ||||
−0.922651 | + | 0.385636i | \(0.873982\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.9282 | 0.571910 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.63744i | 0.380611i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16.7846i | − 0.738186i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.6230 | 0.859699 | 0.429849 | − | 0.902901i | \(-0.358567\pi\) | ||||
0.429849 | + | 0.902901i | \(0.358567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8.00000i | − 0.349816i | −0.984585 | − | 0.174908i | \(-0.944037\pi\) | ||||
0.984585 | − | 0.174908i | \(-0.0559627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.0820 | −0.569860 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.7846 | −0.599331 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.57668i | 0.414812i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.4974 | −1.31852 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.75265i | − 0.0754922i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.1769i | 1.51237i | 0.654356 | + | 0.756187i | \(0.272940\pi\) | ||||
−0.654356 | + | 0.756187i | \(0.727060\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.01062 | −0.300302 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.92820i | 0.381742i | 0.981615 | + | 0.190871i | \(0.0611313\pi\) | ||||
−0.981615 | + | 0.190871i | \(0.938869\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.1746 | 1.41329 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9282 | −0.464714 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.1534i | 0.811554i | 0.913972 | + | 0.405777i | \(0.132999\pi\) | ||||
−0.913972 | + | 0.405777i | \(0.867001\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.21539 | −0.305178 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.5873i | 0.699071i | 0.936923 | + | 0.349536i | \(0.113661\pi\) | ||||
−0.936923 | + | 0.349536i | \(0.886339\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 6.14359i | − 0.258463i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.7407 | 1.49833 | 0.749163 | − | 0.662385i | \(-0.230456\pi\) | ||||
0.749163 | + | 0.662385i | \(0.230456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7846i | 1.12090i | 0.828188 | + | 0.560451i | \(0.189372\pi\) | ||||
−0.828188 | + | 0.560451i | \(0.810628\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.85342 | 0.244104 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.9282 | 0.704730 | 0.352365 | − | 0.935863i | \(-0.385378\pi\) | ||||
0.352365 | + | 0.935863i | \(0.385378\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.07137i | − 0.251883i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 3.50531i | − 0.144680i | −0.997380 | − | 0.0723398i | \(-0.976953\pi\) | ||||
0.997380 | − | 0.0723398i | \(-0.0230466\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.92820i | 0.285472i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.5622 | −0.844390 | −0.422195 | − | 0.906505i | \(-0.638740\pi\) | ||||
−0.422195 | + | 0.906505i | \(0.638740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 11.4641i | − 0.469982i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.2103 | −1.47951 | −0.739756 | − | 0.672875i | \(-0.765059\pi\) | ||||
−0.739756 | + | 0.672875i | \(0.765059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 13.8954i | − 0.564928i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.0718 | 1.17999 | 0.589994 | − | 0.807408i | \(-0.299130\pi\) | ||||
0.589994 | + | 0.807408i | \(0.299130\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 14.0212i | − 0.567238i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 31.7128i | − 1.28087i | −0.768013 | − | 0.640434i | \(-0.778754\pi\) | ||||
0.768013 | − | 0.640434i | \(-0.221246\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.0820 | 0.526661 | 0.263331 | − | 0.964706i | \(-0.415179\pi\) | ||||
0.263331 | + | 0.964706i | \(0.415179\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.0000i | 1.28619i | 0.765787 | + | 0.643094i | \(0.222350\pi\) | ||||
−0.765787 | + | 0.643094i | \(0.777650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.469622 | −0.0188150 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.6410 | −0.465641 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 29.6693i | − 1.18299i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.7846 | 0.508947 | 0.254474 | − | 0.967080i | \(-0.418098\pi\) | ||||
0.254474 | + | 0.967080i | \(0.418098\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.87849i | 0.0745456i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.46410i | − 0.0580098i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.939245 | −0.0370979 | −0.0185490 | − | 0.999828i | \(-0.505905\pi\) | ||||
−0.0185490 | + | 0.999828i | \(0.505905\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.1051i | 1.34497i | 0.740109 | + | 0.672487i | \(0.234774\pi\) | ||||
−0.740109 | + | 0.672487i | \(0.765226\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.1032 | −1.06554 | −0.532769 | − | 0.846261i | \(-0.678848\pi\) | ||||
−0.532769 | + | 0.846261i | \(0.678848\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.7846 | 0.658854 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 34.8014i | − 1.36188i | −0.732337 | − | 0.680942i | \(-0.761570\pi\) | ||||
0.732337 | − | 0.680942i | \(-0.238430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.6410 | 0.415779 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.2686i | 0.477916i | 0.971030 | + | 0.238958i | \(0.0768058\pi\) | ||||
−0.971030 | + | 0.238958i | \(0.923194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.1769i | 1.91276i | 0.292125 | + | 0.956380i | \(0.405638\pi\) | ||||
−0.292125 | + | 0.956380i | \(0.594362\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.07137 | −0.235438 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.0718i | 1.12566i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.56606 | 0.0990618 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.6410 | −1.33531 | −0.667657 | − | 0.744469i | \(-0.732703\pi\) | ||||
−0.667657 | + | 0.744469i | \(0.732703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 27.9166i | − 1.07292i | −0.843925 | − | 0.536462i | \(-0.819761\pi\) | ||||
0.843925 | − | 0.536462i | \(-0.180239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.92820 | 0.342633 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.75265i | − 0.0670634i | −0.999438 | − | 0.0335317i | \(-0.989325\pi\) | ||||
0.999438 | − | 0.0335317i | \(-0.0106755\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 10.6410i | − 0.406572i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.7128i | 1.81508i | 0.419965 | + | 0.907540i | \(0.362042\pi\) | ||||
−0.419965 | + | 0.907540i | \(0.637958\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.2749 | −0.655273 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.7846 | −1.62058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.5159i | 0.397181i | 0.980083 | + | 0.198591i | \(0.0636364\pi\) | ||||
−0.980083 | + | 0.198591i | \(0.936364\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.7128 | −0.592620 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.75265i | − 0.0659153i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 14.1436i | − 0.531174i | −0.964087 | − | 0.265587i | \(-0.914434\pi\) | ||||
0.964087 | − | 0.265587i | \(-0.0855657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.07137 | −0.227375 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.49742i | 0.168194i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.8226 | −1.82078 | −0.910389 | − | 0.413754i | \(-0.864217\pi\) | ||||
−0.910389 | + | 0.413754i | \(0.864217\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.92820 | −0.183536 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.4658i | 0.685802i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9282 | 0.627832 | 0.313916 | − | 0.949451i | \(-0.398359\pi\) | ||||
0.313916 | + | 0.949451i | \(0.398359\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 32.2354i | − 1.19227i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.2487i | 1.85598i | 0.372607 | + | 0.927989i | \(0.378464\pi\) | ||||
−0.372607 | + | 0.927989i | \(0.621536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.5265 | −0.645598 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 49.7128i | − 1.82872i | −0.404907 | − | 0.914358i | \(-0.632696\pi\) | ||||
0.404907 | − | 0.914358i | \(-0.367304\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.1495 | −1.36288 | −0.681442 | − | 0.731872i | \(-0.738647\pi\) | ||||
−0.681442 | + | 0.731872i | \(0.738647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2872 | 0.450168 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 17.4007i | − 0.635808i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.7128 | −1.01125 | −0.505627 | − | 0.862752i | \(-0.668739\pi\) | ||||
−0.505627 | + | 0.862752i | \(0.668739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.01062i | 0.255142i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 47.7128i | − 1.73415i | −0.498176 | − | 0.867076i | \(-0.665997\pi\) | ||||
0.498176 | − | 0.867076i | \(-0.334003\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.7657 | −1.15151 | −0.575753 | − | 0.817623i | \(-0.695291\pi\) | ||||
−0.575753 | + | 0.817623i | \(0.695291\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4.00000i | − 0.144810i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.0212 | 0.506277 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.5692 | −1.13842 | −0.569208 | − | 0.822194i | \(-0.692750\pi\) | ||||
−0.569208 | + | 0.822194i | \(0.692750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.4326i | 1.38232i | 0.722700 | + | 0.691162i | \(0.242901\pi\) | ||||
−0.722700 | + | 0.691162i | \(0.757099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.85641 | −0.138526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.6587i | 0.811831i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.6077i | 0.630053i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.7194 | 0.775200 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.5692i | 1.33920i | 0.742723 | + | 0.669599i | \(0.233534\pi\) | ||||
−0.742723 | + | 0.669599i | \(0.766466\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.50531 | 0.124634 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.14359 | 0.0761212 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 31.4219i | − 1.11302i | −0.830840 | − | 0.556511i | \(-0.812140\pi\) | ||||
0.830840 | − | 0.556511i | \(-0.187860\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.6410 | 2.21608 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 22.6587i | − 0.799607i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 5.32051i | − 0.187523i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.6905 | 1.53608 | 0.768038 | − | 0.640404i | \(-0.221233\pi\) | ||||
0.768038 | + | 0.640404i | \(0.221233\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 10.1436i | − 0.356190i | −0.984013 | − | 0.178095i | \(-0.943007\pi\) | ||||
0.984013 | − | 0.178095i | \(-0.0569934\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.7802 | −0.727898 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.0718 | −0.597267 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.1427i | 0.423785i | 0.977293 | + | 0.211892i | \(0.0679626\pi\) | ||||
−0.977293 | + | 0.211892i | \(0.932037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.8564 | 1.45902 | 0.729511 | − | 0.683969i | \(-0.239748\pi\) | ||||
0.729511 | + | 0.683969i | \(0.239748\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.4326i | 1.33643i | 0.743968 | + | 0.668215i | \(0.232942\pi\) | ||||
−0.743968 | + | 0.668215i | \(0.767058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.1769i | 1.70798i | 0.520285 | + | 0.853992i | \(0.325826\pi\) | ||||
−0.520285 | + | 0.853992i | \(0.674174\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.54099 | 0.226632 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.6410i | 0.368248i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.1032 | 0.935707 | 0.467854 | − | 0.883806i | \(-0.345027\pi\) | ||||
0.467854 | + | 0.883806i | \(0.345027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −62.7128 | −2.16251 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 19.0275i | − 0.654567i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.92820 | 0.272416 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 13.7696i | − 0.472015i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7.60770i | − 0.260483i | −0.991482 | − | 0.130241i | \(-0.958425\pi\) | ||||
0.991482 | − | 0.130241i | \(-0.0415752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −50.9191 | −1.73936 | −0.869681 | − | 0.493613i | \(-0.835676\pi\) | ||||
−0.869681 | + | 0.493613i | \(0.835676\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.32051i | 0.0450552i | 0.999746 | + | 0.0225276i | \(0.00717136\pi\) | ||||
−0.999746 | + | 0.0225276i | \(0.992829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.3530 | 1.64596 | 0.822978 | − | 0.568073i | \(-0.192311\pi\) | ||||
0.822978 | + | 0.568073i | \(0.192311\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.21539 | −0.313333 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.1534i | 0.649733i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.6410 | −0.496092 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 12.1427i | − 0.410500i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.0000i | 1.48577i | 0.669417 | + | 0.742887i | \(0.266544\pi\) | ||||
−0.669417 | + | 0.742887i | \(0.733456\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.40887 | −0.0474659 | −0.0237330 | − | 0.999718i | \(-0.507555\pi\) | ||||
−0.0237330 | + | 0.999718i | \(0.507555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.0718i | 0.372596i | 0.982493 | + | 0.186298i | \(0.0596489\pi\) | ||||
−0.982493 | + | 0.186298i | \(0.940351\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.3887 | 1.72546 | 0.862732 | − | 0.505661i | \(-0.168751\pi\) | ||||
0.862732 | + | 0.505661i | \(0.168751\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.07180 | −0.0359469 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 33.1746i | − 1.11015i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.7846 | 1.43013 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 19.1534i | − 0.638800i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −37.6191 | −1.25050 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.6410i | 0.818192i | 0.912491 | + | 0.409096i | \(0.134156\pi\) | ||||
−0.912491 | + | 0.409096i | \(0.865844\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.16781 | −0.270612 | −0.135306 | − | 0.990804i | \(-0.543202\pi\) | ||||
−0.135306 | + | 0.990804i | \(0.543202\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.6410 | −0.352166 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.07137i | 0.200494i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.7846 | −1.60926 | −0.804628 | − | 0.593779i | \(-0.797635\pi\) | ||||
−0.804628 | + | 0.593779i | \(0.797635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.7088i | 0.484146i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 8.74613i | − 0.287571i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.6124 | −0.413798 | −0.206899 | − | 0.978362i | \(-0.566337\pi\) | ||||
−0.206899 | + | 0.978362i | \(0.566337\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 3.46410i | − 0.113531i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.0926 | −0.657098 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.07180 | 0.100351 | 0.0501756 | − | 0.998740i | \(-0.484022\pi\) | ||||
0.0501756 | + | 0.998740i | \(0.484022\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.5541i | 1.19163i | 0.803122 | + | 0.595814i | \(0.203171\pi\) | ||||
−0.803122 | + | 0.595814i | \(0.796829\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.8564 | −0.646614 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.0381i | 0.846126i | 0.906100 | + | 0.423063i | \(0.139045\pi\) | ||||
−0.906100 | + | 0.423063i | \(0.860955\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 18.9282i | − 0.614435i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.1746 | 1.07463 | 0.537315 | − | 0.843381i | \(-0.319439\pi\) | ||||
0.537315 | + | 0.843381i | \(0.319439\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.8949i | 0.967376i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.07137 | 0.196055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.87849i | 0.0604707i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.7846 | 1.18291 | 0.591457 | − | 0.806337i | \(-0.298553\pi\) | ||||
0.591457 | + | 0.806337i | \(0.298553\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 33.1746i | − 1.06462i | −0.846548 | − | 0.532312i | \(-0.821323\pi\) | ||||
0.846548 | − | 0.532312i | \(-0.178677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9.85641i | − 0.315982i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.8728 | −1.30764 | −0.653818 | − | 0.756652i | \(-0.726834\pi\) | ||||
−0.653818 | + | 0.756652i | \(0.726834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.823085i | 0.0263059i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −59.3386 | −1.89261 | −0.946303 | − | 0.323280i | \(-0.895214\pi\) | ||||
−0.946303 | + | 0.323280i | \(0.895214\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.6410 | −0.339051 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 14.9605i | − 0.475716i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.0000 | 1.65183 | 0.825917 | − | 0.563791i | \(-0.190658\pi\) | ||||
0.825917 | + | 0.563791i | \(0.190658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.4389i | 1.37710i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.0333i | 0.982835i | 0.870924 | + | 0.491418i | \(0.163521\pi\) | ||||
−0.870924 | + | 0.491418i | \(0.836479\pi\) | |||||||
\(998\) | 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 | 4032.2.c.r.2017.3 | yes | 8 | |
3.2 | odd | 2 | inner | 4032.2.c.r.2017.5 | yes | 8 | |
4.3 | odd | 2 | 4032.2.c.q.2017.3 | ✓ | 8 | ||
8.3 | odd | 2 | 4032.2.c.q.2017.6 | yes | 8 | ||
8.5 | even | 2 | inner | 4032.2.c.r.2017.6 | yes | 8 | |
12.11 | even | 2 | 4032.2.c.q.2017.5 | yes | 8 | ||
24.5 | odd | 2 | inner | 4032.2.c.r.2017.4 | yes | 8 | |
24.11 | even | 2 | 4032.2.c.q.2017.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4032.2.c.q.2017.3 | ✓ | 8 | 4.3 | odd | 2 | ||
4032.2.c.q.2017.4 | yes | 8 | 24.11 | even | 2 | ||
4032.2.c.q.2017.5 | yes | 8 | 12.11 | even | 2 | ||
4032.2.c.q.2017.6 | yes | 8 | 8.3 | odd | 2 | ||
4032.2.c.r.2017.3 | yes | 8 | 1.1 | even | 1 | trivial | |
4032.2.c.r.2017.4 | yes | 8 | 24.5 | odd | 2 | inner | |
4032.2.c.r.2017.5 | yes | 8 | 3.2 | odd | 2 | inner | |
4032.2.c.r.2017.6 | yes | 8 | 8.5 | even | 2 | inner |