Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(193,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.j (of order \(4\), degree \(2\), 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: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.193 |
Dual form | 768.2.j.c.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.41421i | − | 0.534522i | −0.963624 | − | 0.267261i | \(-0.913881\pi\) | ||
0.963624 | − | 0.267261i | \(-0.0861187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.00000i | 0.277350 | − | 0.277350i | −0.554700 | − | 0.832050i | \(-0.687167\pi\) |
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24264 | + | 4.24264i | −0.973329 | + | 0.973329i | −0.999653 | − | 0.0263249i | \(-0.991620\pi\) |
0.0263249 | + | 0.999653i | \(0.491620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | + | 1.00000i | 0.218218 | + | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.48528i | − | 1.76930i | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||
0.466252 | − | 0.884652i | \(-0.345604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 1.00000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | − | 6.00000i | 1.11417 | − | 1.11417i | 0.121592 | − | 0.992580i | \(-0.461200\pi\) |
0.992580 | − | 0.121592i | \(-0.0387999\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.41421 | 0.254000 | 0.127000 | − | 0.991903i | \(-0.459465\pi\) | ||||
0.127000 | + | 0.991903i | \(0.459465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | + | 5.00000i | 0.821995 | + | 0.821995i | 0.986394 | − | 0.164399i | \(-0.0525685\pi\) |
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.41421i | 0.226455i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000i | 0.937043i | 0.883452 | + | 0.468521i | \(0.155213\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24264 | + | 4.24264i | 0.646997 | + | 0.646997i | 0.952266 | − | 0.305269i | \(-0.0987465\pi\) |
−0.305269 | + | 0.952266i | \(0.598747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.48528 | 1.23771 | 0.618853 | − | 0.785507i | \(-0.287598\pi\) | ||||
0.618853 | + | 0.785507i | \(0.287598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.24264 | + | 4.24264i | −0.594089 | + | 0.594089i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | − | 6.00000i | −0.824163 | − | 0.824163i | 0.162539 | − | 0.986702i | \(-0.448032\pi\) |
−0.986702 | + | 0.162539i | \(0.948032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | − | 5.00000i | 0.640184 | − | 0.640184i | −0.310416 | − | 0.950601i | \(-0.600468\pi\) |
0.950601 | + | 0.310416i | \(0.100468\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.41421 | −0.178174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.82843 | + | 2.82843i | −0.345547 | + | 0.345547i | −0.858448 | − | 0.512901i | \(-0.828571\pi\) |
0.512901 | + | 0.858448i | \(0.328571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | + | 6.00000i | 0.722315 | + | 0.722315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.48528i | − | 1.00702i | −0.863990 | − | 0.503509i | \(-0.832042\pi\) | ||
0.863990 | − | 0.503509i | \(-0.167958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.53553 | + | 3.53553i | 0.408248 | + | 0.408248i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.41421 | −0.159111 | −0.0795557 | − | 0.996830i | \(-0.525350\pi\) | ||||
−0.0795557 | + | 0.996830i | \(0.525350\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.48528 | − | 8.48528i | 0.931381 | − | 0.931381i | −0.0664117 | − | 0.997792i | \(-0.521155\pi\) |
0.997792 | + | 0.0664117i | \(0.0211551\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.48528i | 0.909718i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.41421 | − | 1.41421i | −0.148250 | − | 0.148250i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | + | 1.00000i | −0.103695 | + | 0.103695i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0000 | −1.21842 | −0.609208 | − | 0.793011i | \(-0.708512\pi\) | ||||
−0.609208 | + | 0.793011i | \(0.708512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 6.00000i | −0.597022 | − | 0.597022i | 0.342497 | − | 0.939519i | \(-0.388727\pi\) |
−0.939519 | + | 0.342497i | \(0.888727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.89949i | 0.975426i | 0.873004 | + | 0.487713i | \(0.162169\pi\) | ||||
−0.873004 | + | 0.487713i | \(0.837831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.48528 | − | 8.48528i | −0.820303 | − | 0.820303i | 0.165848 | − | 0.986151i | \(-0.446964\pi\) |
−0.986151 | + | 0.165848i | \(0.946964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0000 | + | 13.0000i | −1.24517 | + | 1.24517i | −0.287348 | + | 0.957826i | \(0.592774\pi\) |
−0.957826 | + | 0.287348i | \(0.907226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.07107 | −0.671156 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | − | 1.00000i | −0.0924500 | − | 0.0924500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 8.48528i | − | 0.777844i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.0000i | − | 1.00000i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.24264 | − | 4.24264i | −0.382546 | − | 0.382546i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.89949 | −0.878438 | −0.439219 | − | 0.898380i | \(-0.644745\pi\) | ||||
−0.439219 | + | 0.898380i | \(0.644745\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | −0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.48528 | − | 8.48528i | 0.741362 | − | 0.741362i | −0.231478 | − | 0.972840i | \(-0.574356\pi\) |
0.972840 | + | 0.231478i | \(0.0743560\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | + | 6.00000i | 0.520266 | + | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.0000i | 1.53784i | 0.639343 | + | 0.768922i | \(0.279207\pi\) | ||||
−0.639343 | + | 0.768922i | \(0.720793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.82843 | − | 2.82843i | −0.239904 | − | 0.239904i | 0.576906 | − | 0.816810i | \(-0.304260\pi\) |
−0.816810 | + | 0.576906i | \(0.804260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | + | 6.00000i | −0.505291 | + | 0.505291i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.53553 | + | 3.53553i | −0.291606 | + | 0.291606i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0000 | − | 12.0000i | −0.983078 | − | 0.983078i | 0.0167809 | − | 0.999859i | \(-0.494658\pi\) |
−0.999859 | + | 0.0167809i | \(0.994658\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3848i | 1.49613i | 0.663624 | + | 0.748066i | \(0.269017\pi\) | ||||
−0.663624 | + | 0.748066i | \(0.730983\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | + | 5.00000i | −0.399043 | + | 0.399043i | −0.877896 | − | 0.478852i | \(-0.841053\pi\) |
0.478852 | + | 0.877896i | \(0.341053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.48528 | 0.672927 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | −0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.24264 | − | 4.24264i | 0.332309 | − | 0.332309i | −0.521154 | − | 0.853463i | \(-0.674498\pi\) |
0.853463 | + | 0.521154i | \(0.174498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.9706i | 1.31322i | 0.754230 | + | 0.656611i | \(0.228011\pi\) | ||||
−0.754230 | + | 0.656611i | \(0.771989\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.24264 | + | 4.24264i | 0.324443 | + | 0.324443i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.0000 | + | 12.0000i | −0.912343 | + | 0.912343i | −0.996456 | − | 0.0841131i | \(-0.973194\pi\) |
0.0841131 | + | 0.996456i | \(0.473194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.07107 | −0.534522 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.9706 | − | 16.9706i | 1.26844 | − | 1.26844i | 0.321545 | − | 0.946894i | \(-0.395798\pi\) |
0.946894 | − | 0.321545i | \(-0.104202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0000 | − | 11.0000i | −0.817624 | − | 0.817624i | 0.168140 | − | 0.985763i | \(-0.446224\pi\) |
−0.985763 | + | 0.168140i | \(0.946224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.07107i | 0.522708i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | − | 1.00000i | 0.0727393 | − | 0.0727393i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9706 | −1.22795 | −0.613973 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613973 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | + | 6.00000i | 0.427482 | + | 0.427482i | 0.887770 | − | 0.460288i | \(-0.152254\pi\) |
−0.460288 | + | 0.887770i | \(0.652254\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.89949i | − | 0.701757i | −0.936421 | − | 0.350878i | \(-0.885883\pi\) | ||
0.936421 | − | 0.350878i | \(-0.114117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.00000i | − | 0.282138i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.48528 | − | 8.48528i | −0.595550 | − | 0.595550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.48528 | −0.589768 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.82843 | − | 2.82843i | 0.194717 | − | 0.194717i | −0.603014 | − | 0.797731i | \(-0.706034\pi\) |
0.797731 | + | 0.603014i | \(0.206034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | + | 6.00000i | 0.411113 | + | 0.411113i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.00000i | − | 0.135769i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 6.00000i | 0.403604 | − | 0.403604i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.8701 | 1.79935 | 0.899676 | − | 0.436558i | \(-0.143803\pi\) | ||||
0.899676 | + | 0.436558i | \(0.143803\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.48528 | + | 8.48528i | −0.563188 | + | 0.563188i | −0.930212 | − | 0.367024i | \(-0.880377\pi\) |
0.367024 | + | 0.930212i | \(0.380377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | + | 1.00000i | 0.0660819 | + | 0.0660819i | 0.739375 | − | 0.673293i | \(-0.235121\pi\) |
−0.673293 | + | 0.739375i | \(0.735121\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.00000 | − | 1.00000i | 0.0649570 | − | 0.0649570i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9706 | 1.09773 | 0.548867 | − | 0.835910i | \(-0.315059\pi\) | ||||
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.48528i | 0.539906i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000i | 0.760469i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.9706 | + | 16.9706i | 1.07117 | + | 1.07117i | 0.997265 | + | 0.0739073i | \(0.0235469\pi\) |
0.0739073 | + | 0.997265i | \(0.476453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.07107 | − | 7.07107i | 0.439375 | − | 0.439375i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | − | 6.00000i | −0.371391 | − | 0.371391i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.24264 | − | 4.24264i | −0.259645 | − | 0.259645i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | − | 6.00000i | 0.365826 | − | 0.365826i | −0.500126 | − | 0.865953i | \(-0.666713\pi\) |
0.865953 | + | 0.500126i | \(0.166713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.8701 | −1.63224 | −0.816120 | − | 0.577883i | \(-0.803879\pi\) | ||||
−0.816120 | + | 0.577883i | \(0.803879\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.00000 | 0.121046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | + | 11.0000i | 0.660926 | + | 0.660926i | 0.955598 | − | 0.294672i | \(-0.0952105\pi\) |
−0.294672 | + | 0.955598i | \(0.595211\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.41421i | − | 0.0846668i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.0000i | − | 1.07379i | −0.843649 | − | 0.536895i | \(-0.819597\pi\) | ||
0.843649 | − | 0.536895i | \(-0.180403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.82843 | − | 2.82843i | −0.168133 | − | 0.168133i | 0.618026 | − | 0.786158i | \(-0.287933\pi\) |
−0.786158 | + | 0.618026i | \(0.787933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.48528 | 0.500870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.48528 | − | 8.48528i | 0.497416 | − | 0.497416i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | + | 6.00000i | 0.350524 | + | 0.350524i | 0.860304 | − | 0.509781i | \(-0.170273\pi\) |
−0.509781 | + | 0.860304i | \(0.670273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.48528 | − | 8.48528i | −0.490716 | − | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | − | 6.00000i | 0.345834 | − | 0.345834i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.48528 | 0.487467 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.1421 | + | 14.1421i | −0.807134 | + | 0.807134i | −0.984199 | − | 0.177065i | \(-0.943340\pi\) |
0.177065 | + | 0.984199i | \(0.443340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00000 | − | 7.00000i | −0.398216 | − | 0.398216i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.9706i | − | 0.962312i | −0.876635 | − | 0.481156i | \(-0.840217\pi\) | ||
0.876635 | − | 0.481156i | \(-0.159783\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0000i | 0.565233i | 0.959233 | + | 0.282617i | \(0.0912024\pi\) | ||||
−0.959233 | + | 0.282617i | \(0.908798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00000 | + | 6.00000i | −0.336994 | + | 0.336994i | −0.855235 | − | 0.518241i | \(-0.826587\pi\) |
0.518241 | + | 0.855235i | \(0.326587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.4558 | + | 25.4558i | −1.41640 | + | 1.41640i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.00000 | − | 5.00000i | −0.277350 | − | 0.277350i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 18.3848i | − | 1.01668i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 12.0000i | − | 0.661581i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.7990 | + | 19.7990i | 1.08825 | + | 1.08825i | 0.995709 | + | 0.0925421i | \(0.0294993\pi\) |
0.0925421 | + | 0.995709i | \(0.470501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.00000 | − | 5.00000i | 0.273998 | − | 0.273998i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.0000 | 1.30736 | 0.653682 | − | 0.756770i | \(-0.273224\pi\) | ||||
0.653682 | + | 0.756770i | \(0.273224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.24264 | + | 4.24264i | −0.230429 | + | 0.230429i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.48528 | + | 8.48528i | 0.455514 | + | 0.455514i | 0.897180 | − | 0.441666i | \(-0.145612\pi\) |
−0.441666 | + | 0.897180i | \(0.645612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0000 | − | 19.0000i | 1.01705 | − | 1.01705i | 0.0171945 | − | 0.999852i | \(-0.494527\pi\) |
0.999852 | − | 0.0171945i | \(-0.00547346\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41421 | 0.0754851 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.00000 | + | 6.00000i | 0.317554 | + | 0.317554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.4558i | 1.34351i | 0.740774 | + | 0.671754i | \(0.234459\pi\) | ||||
−0.740774 | + | 0.671754i | \(0.765541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 17.0000i | − | 0.894737i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.77817 | + | 7.77817i | 0.408248 | + | 0.408248i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.5269 | 1.69789 | 0.848945 | − | 0.528480i | \(-0.177238\pi\) | ||||
0.848945 | + | 0.528480i | \(0.177238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.48528 | + | 8.48528i | −0.440534 | + | 0.440534i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.00000 | − | 5.00000i | −0.258890 | − | 0.258890i | 0.565712 | − | 0.824603i | \(-0.308601\pi\) |
−0.824603 | + | 0.565712i | \(0.808601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.2132 | − | 21.2132i | −1.08965 | − | 1.08965i | −0.995564 | − | 0.0940849i | \(-0.970007\pi\) |
−0.0940849 | − | 0.995564i | \(-0.529993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.00000 | − | 7.00000i | 0.358621 | − | 0.358621i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.9411 | −1.73431 | −0.867155 | − | 0.498038i | \(-0.834054\pi\) | ||||
−0.867155 | + | 0.498038i | \(0.834054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.24264 | − | 4.24264i | 0.215666 | − | 0.215666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0000 | + | 12.0000i | 0.608424 | + | 0.608424i | 0.942534 | − | 0.334110i | \(-0.108436\pi\) |
−0.334110 | + | 0.942534i | \(0.608436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 50.9117i | − | 2.57471i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000i | 0.605320i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.00000 | + | 7.00000i | −0.351320 | + | 0.351320i | −0.860601 | − | 0.509281i | \(-0.829912\pi\) |
0.509281 | + | 0.860601i | \(0.329912\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.48528 | −0.424795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.41421 | − | 1.41421i | 0.0704470 | − | 0.0704470i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.7279 | − | 12.7279i | −0.627822 | − | 0.627822i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.00000 | 0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.4558 | + | 25.4558i | −1.24360 | + | 1.24360i | −0.285102 | + | 0.958497i | \(0.592028\pi\) |
−0.958497 | + | 0.285102i | \(0.907972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | − | 11.0000i | −0.536107 | − | 0.536107i | 0.386276 | − | 0.922383i | \(-0.373761\pi\) |
−0.922383 | + | 0.386276i | \(0.873761\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 8.48528i | − | 0.412568i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 30.0000i | − | 1.45521i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.07107 | − | 7.07107i | −0.342193 | − | 0.342193i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.48528 | 0.408722 | 0.204361 | − | 0.978896i | \(-0.434488\pi\) | ||||
0.204361 | + | 0.978896i | \(0.434488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0000 | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.0000 | + | 36.0000i | 1.72211 | + | 1.72211i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.07107i | − | 0.337484i | −0.985660 | − | 0.168742i | \(-0.946030\pi\) | ||
0.985660 | − | 0.168742i | \(-0.0539704\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 5.00000i | − | 0.238095i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.48528 | + | 8.48528i | 0.403148 | + | 0.403148i | 0.879341 | − | 0.476193i | \(-0.157984\pi\) |
−0.476193 | + | 0.879341i | \(0.657984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.9706 | 0.802680 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.0000 | − | 13.0000i | −0.610793 | − | 0.610793i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.0000i | 0.561336i | 0.959805 | + | 0.280668i | \(0.0905560\pi\) | ||||
−0.959805 | + | 0.280668i | \(0.909444\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.24264 | + | 4.24264i | 0.198030 | + | 0.198030i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0000 | − | 24.0000i | 1.11779 | − | 1.11779i | 0.125726 | − | 0.992065i | \(-0.459874\pi\) |
0.992065 | − | 0.125726i | \(-0.0401262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.07107 | −0.328620 | −0.164310 | − | 0.986409i | \(-0.552540\pi\) | ||||
−0.164310 | + | 0.986409i | \(0.552540\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.48528 | + | 8.48528i | −0.392652 | + | 0.392652i | −0.875632 | − | 0.482980i | \(-0.839555\pi\) |
0.482980 | + | 0.875632i | \(0.339555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | + | 4.00000i | 0.184703 | + | 0.184703i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.07107i | − | 0.325818i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.2132 | + | 21.2132i | 0.973329 | + | 0.973329i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | + | 6.00000i | −0.274721 | + | 0.274721i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.48528 | 0.387702 | 0.193851 | − | 0.981031i | \(-0.437902\pi\) | ||||
0.193851 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0000 | 0.455961 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.48528 | − | 8.48528i | 0.386094 | − | 0.386094i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3848i | 0.833094i | 0.909114 | + | 0.416547i | \(0.136760\pi\) | ||||
−0.909114 | + | 0.416547i | \(0.863240\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000i | 0.271329i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9706 | + | 16.9706i | 0.765871 | + | 0.765871i | 0.977377 | − | 0.211506i | \(-0.0678368\pi\) |
−0.211506 | + | 0.977377i | \(0.567837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.0000 | − | 36.0000i | 1.62136 | − | 1.62136i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.82843 | + | 2.82843i | −0.126618 | + | 0.126618i | −0.767576 | − | 0.640958i | \(-0.778537\pi\) |
0.640958 | + | 0.767576i | \(0.278537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.0000 | − | 12.0000i | −0.536120 | − | 0.536120i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.48528i | − | 0.378340i | −0.981944 | − | 0.189170i | \(-0.939420\pi\) | ||
0.981944 | − | 0.189170i | \(-0.0605797\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.77817 | − | 7.77817i | −0.345441 | − | 0.345441i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.0000 | + | 18.0000i | −0.797836 | + | 0.797836i | −0.982754 | − | 0.184918i | \(-0.940798\pi\) |
0.184918 | + | 0.982754i | \(0.440798\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.00000 | −0.264906 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 16.9706i | − | 0.744925i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 30.0000i | − | 1.31432i | −0.753749 | − | 0.657162i | \(-0.771757\pi\) | ||
0.753749 | − | 0.657162i | \(-0.228243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.7279 | − | 12.7279i | −0.556553 | − | 0.556553i | 0.371771 | − | 0.928324i | \(-0.378751\pi\) |
−0.928324 | + | 0.371771i | \(0.878751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.00000 | − | 5.00000i | 0.218218 | − | 0.218218i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.48528 | 0.369625 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.0000 | −2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | + | 6.00000i | 0.259889 | + | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.0000i | 1.03568i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.0000 | + | 25.0000i | −1.07483 | + | 1.07483i | −0.0778705 | + | 0.996963i | \(0.524812\pi\) |
−0.996963 | + | 0.0778705i | \(0.975188\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.5563 | 0.667587 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.7279 | − | 12.7279i | 0.544207 | − | 0.544207i | −0.380553 | − | 0.924759i | \(-0.624266\pi\) |
0.924759 | + | 0.380553i | \(0.124266\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.00000 | − | 5.00000i | −0.213395 | − | 0.213395i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.9117i | 2.16891i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000i | 0.0850487i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0000 | + | 12.0000i | −0.508456 | + | 0.508456i | −0.914052 | − | 0.405596i | \(-0.867064\pi\) |
0.405596 | + | 0.914052i | \(0.367064\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.48528 | 0.358889 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.41421i | 0.0593914i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.0000i | 0.754599i | 0.926091 | + | 0.377300i | \(0.123147\pi\) | ||||
−0.926091 | + | 0.377300i | \(0.876853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.82843 | + | 2.82843i | 0.118366 | + | 0.118366i | 0.763809 | − | 0.645443i | \(-0.223327\pi\) |
−0.645443 | + | 0.763809i | \(0.723327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | − | 12.0000i | 0.501307 | − | 0.501307i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −42.4264 | −1.76930 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.0000 | 1.49870 | 0.749350 | − | 0.662174i | \(-0.230366\pi\) | ||||
0.749350 | + | 0.662174i | \(0.230366\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.89949 | − | 9.89949i | 0.411409 | − | 0.411409i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | − | 12.0000i | −0.497844 | − | 0.497844i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | + | 6.00000i | −0.247226 | + | 0.247226i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.48528 | −0.349038 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.00000 | + | 7.00000i | 0.286491 | + | 0.286491i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.4558i | 1.04010i | 0.854137 | + | 0.520049i | \(0.174086\pi\) | ||||
−0.854137 | + | 0.520049i | \(0.825914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.0000i | 0.489490i | 0.969587 | + | 0.244745i | \(0.0787043\pi\) | ||||
−0.969587 | + | 0.244745i | \(0.921296\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.82843 | + | 2.82843i | 0.115182 | + | 0.115182i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0416 | 0.975820 | 0.487910 | − | 0.872894i | \(-0.337759\pi\) | ||||
0.487910 | + | 0.872894i | \(0.337759\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0000 | 0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.48528 | − | 8.48528i | 0.343278 | − | 0.343278i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | − | 19.0000i | −0.767403 | − | 0.767403i | 0.210246 | − | 0.977649i | \(-0.432574\pi\) |
−0.977649 | + | 0.210246i | \(0.932574\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.00000i | − | 0.241551i | −0.992680 | − | 0.120775i | \(-0.961462\pi\) | ||
0.992680 | − | 0.120775i | \(-0.0385381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.7990 | + | 19.7990i | 0.795789 | + | 0.795789i | 0.982428 | − | 0.186640i | \(-0.0597597\pi\) |
−0.186640 | + | 0.982428i | \(0.559760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.00000 | − | 6.00000i | 0.240772 | − | 0.240772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.48528 | 0.339956 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.0000 | + | 30.0000i | 1.19618 | + | 1.19618i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18.3848i | − | 0.731886i | −0.930637 | − | 0.365943i | \(-0.880746\pi\) | ||
0.930637 | − | 0.365943i | \(-0.119254\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.00000i | 0.158986i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00000 | − | 5.00000i | 0.198107 | − | 0.198107i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.48528 | −0.335673 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.0000 | −1.65890 | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.7279 | − | 12.7279i | 0.501940 | − | 0.501940i | −0.410100 | − | 0.912040i | \(-0.634506\pi\) |
0.912040 | + | 0.410100i | \(0.134506\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.48528i | 0.333591i | 0.985992 | + | 0.166795i | \(0.0533419\pi\) | ||||
−0.985992 | + | 0.166795i | \(0.946658\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.41421 | + | 1.41421i | 0.0554274 | + | 0.0554274i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.0000 | + | 12.0000i | −0.469596 | + | 0.469596i | −0.901784 | − | 0.432187i | \(-0.857742\pi\) |
0.432187 | + | 0.901784i | \(0.357742\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 7.00000i | −0.272268 | − | 0.272268i | 0.557744 | − | 0.830013i | \(-0.311667\pi\) |
−0.830013 | + | 0.557744i | \(0.811667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.48528i | 0.329541i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.9117 | − | 50.9117i | −1.97131 | − | 1.97131i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.0000 | + | 19.0000i | −0.734582 | + | 0.734582i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.0000 | −0.925132 | −0.462566 | − | 0.886585i | \(-0.653071\pi\) | ||||
−0.462566 | + | 0.886585i | \(0.653071\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.53553 | − | 3.53553i | 0.136083 | − | 0.136083i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.9706i | 0.651270i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 12.0000i | − | 0.459841i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.4558 | − | 25.4558i | −0.974041 | − | 0.974041i | 0.0256307 | − | 0.999671i | \(-0.491841\pi\) |
−0.999671 | + | 0.0256307i | \(0.991841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.41421 | −0.0539556 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.6985 | − | 29.6985i | 1.12978 | − | 1.12978i | 0.139572 | − | 0.990212i | \(-0.455427\pi\) |
0.990212 | − | 0.139572i | \(-0.0445726\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.0000i | 1.36360i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.24264 | − | 4.24264i | −0.160471 | − | 0.160471i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | + | 18.0000i | −0.679851 | + | 0.679851i | −0.959966 | − | 0.280116i | \(-0.909627\pi\) |
0.280116 | + | 0.959966i | \(0.409627\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.4264 | −1.60014 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.48528 | + | 8.48528i | −0.319122 | + | 0.319122i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00000 | − | 1.00000i | −0.0375558 | − | 0.0375558i | 0.688080 | − | 0.725635i | \(-0.258454\pi\) |
−0.725635 | + | 0.688080i | \(0.758454\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.41421i | 0.0530372i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.0000i | − | 0.449404i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.0000 | + | 12.0000i | −0.448148 | + | 0.448148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.48528 | −0.316448 | −0.158224 | − | 0.987403i | \(-0.550577\pi\) | ||||
−0.158224 | + | 0.987403i | \(0.550577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0000 | 0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.07107 | − | 7.07107i | 0.262976 | − | 0.262976i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.0000 | − | 30.0000i | −1.11417 | − | 1.11417i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.5269i | 1.20636i | 0.797606 | + | 0.603178i | \(0.206099\pi\) | ||||
−0.797606 | + | 0.603178i | \(0.793901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.4558 | + | 25.4558i | 0.941518 | + | 0.941518i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.0000 | + | 35.0000i | −1.29275 | + | 1.29275i | −0.359678 | + | 0.933076i | \(0.617113\pi\) |
−0.933076 | + | 0.359678i | \(0.882887\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1421 | − | 14.1421i | 0.520227 | − | 0.520227i | −0.397413 | − | 0.917640i | \(-0.630092\pi\) |
0.917640 | + | 0.397413i | \(0.130092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | − | 6.00000i | −0.220416 | − | 0.220416i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.9706i | 0.622590i | 0.950313 | + | 0.311295i | \(0.100763\pi\) | ||||
−0.950313 | + | 0.311295i | \(0.899237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.48528 | − | 8.48528i | −0.310460 | − | 0.310460i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | + | 12.0000i | −0.438470 | + | 0.438470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.4975 | −1.80619 | −0.903094 | − | 0.429442i | \(-0.858710\pi\) | ||||
−0.903094 | + | 0.429442i | \(0.858710\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.0000 | −0.874609 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.00000 | + | 1.00000i | 0.0363456 | + | 0.0363456i | 0.725046 | − | 0.688700i | \(-0.241818\pi\) |
−0.688700 | + | 0.725046i | \(0.741818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.00000i | − | 0.217500i | −0.994069 | − | 0.108750i | \(-0.965315\pi\) | ||
0.994069 | − | 0.108750i | \(-0.0346848\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.3848 | + | 18.3848i | 0.665574 | + | 0.665574i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.24264 | − | 4.24264i | 0.152795 | − | 0.152795i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0000 | − | 18.0000i | −0.647415 | − | 0.647415i | 0.304953 | − | 0.952368i | \(-0.401359\pi\) |
−0.952368 | + | 0.304953i | \(0.901359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.07107i | − | 0.254000i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.0000i | 0.358748i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.4558 | − | 25.4558i | −0.912050 | − | 0.912050i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.48528 | 0.303239 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.7279 | + | 12.7279i | −0.453701 | + | 0.453701i | −0.896581 | − | 0.442880i | \(-0.853957\pi\) |
0.442880 | + | 0.896581i | \(0.353957\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.48528i | − | 0.301702i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.0000i | − | 0.355110i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000 | − | 12.0000i | 0.425062 | − | 0.425062i | −0.461880 | − | 0.886942i | \(-0.652825\pi\) |
0.886942 | + | 0.461880i | \(0.152825\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.9117 | 1.80113 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.48528i | 0.298696i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000i | 0.632846i | 0.948618 | + | 0.316423i | \(0.102482\pi\) | ||||
−0.948618 | + | 0.316423i | \(0.897518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.24264 | − | 4.24264i | −0.148979 | − | 0.148979i | 0.628683 | − | 0.777662i | \(-0.283594\pi\) |
−0.777662 | + | 0.628683i | \(0.783594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.0000 | − | 19.0000i | 0.666359 | − | 0.666359i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0000 | −1.25948 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.41421 | + | 1.41421i | −0.0494166 | + | 0.0494166i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | + | 6.00000i | 0.209401 | + | 0.209401i | 0.804013 | − | 0.594612i | \(-0.202694\pi\) |
−0.594612 | + | 0.804013i | \(0.702694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.5269i | 1.13382i | 0.823781 | + | 0.566908i | \(0.191861\pi\) | ||||
−0.823781 | + | 0.566908i | \(0.808139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.48528 | − | 8.48528i | −0.295062 | − | 0.295062i | 0.544014 | − | 0.839076i | \(-0.316904\pi\) |
−0.839076 | + | 0.544014i | \(0.816904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0000 | + | 11.0000i | −0.382046 | + | 0.382046i | −0.871839 | − | 0.489793i | \(-0.837072\pi\) |
0.489793 | + | 0.871839i | \(0.337072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.5563 | −0.539644 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.0000 | 1.03944 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00000 | + | 1.00000i | 0.0345651 | + | 0.0345651i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 25.4558i | − | 0.878833i | −0.898283 | − | 0.439417i | \(-0.855185\pi\) | ||
0.898283 | − | 0.439417i | \(-0.144815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 43.0000i | − | 1.48276i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.7279 | + | 12.7279i | 0.438373 | + | 0.438373i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.5563 | −0.534522 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.4264 | − | 42.4264i | 1.45436 | − | 1.45436i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.0000 | + | 31.0000i | 1.06142 | + | 1.06142i | 0.997986 | + | 0.0634337i | \(0.0202051\pi\) |
0.0634337 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.0000i | 1.43469i | 0.696717 | + | 0.717346i | \(0.254643\pi\) | ||||
−0.696717 | + | 0.717346i | \(0.745357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.24264 | + | 4.24264i | 0.144757 | + | 0.144757i | 0.775771 | − | 0.631014i | \(-0.217361\pi\) |
−0.631014 | + | 0.775771i | \(0.717361\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | + | 6.00000i | −0.204479 | + | 0.204479i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.4350 | + | 13.4350i | −0.456278 | + | 0.456278i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.65685i | 0.191675i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0000i | 0.406138i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.00000 | + | 5.00000i | −0.168838 | + | 0.168838i | −0.786468 | − | 0.617630i | \(-0.788093\pi\) |
0.617630 | + | 0.786468i | \(0.288093\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.48528 | −0.286201 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.2132 | + | 21.2132i | −0.713881 | + | 0.713881i | −0.967345 | − | 0.253464i | \(-0.918430\pi\) |
0.253464 | + | 0.967345i | \(0.418430\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9706i | 0.569816i | 0.958555 | + | 0.284908i | \(0.0919630\pi\) | ||||
−0.958555 | + | 0.284908i | \(0.908037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.0000i | 0.469545i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.0000 | + | 36.0000i | −1.20469 | + | 1.20469i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.48528 | − | 8.48528i | 0.283000 | − | 0.283000i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | − | 36.0000i | −1.19933 | − | 1.19933i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.48528i | 0.282372i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.24264 | − | 4.24264i | −0.140875 | − | 0.140875i | 0.633153 | − | 0.774027i | \(-0.281761\pi\) |
−0.774027 | + | 0.633153i | \(0.781761\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | + | 6.00000i | −0.199007 | + | 0.199007i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9706 | −0.562260 | −0.281130 | − | 0.959670i | \(-0.590709\pi\) | ||||
−0.281130 | + | 0.959670i | \(0.590709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.0000 | − | 12.0000i | −0.396275 | − | 0.396275i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.41421i | − | 0.0466506i | −0.999728 | − | 0.0233253i | \(-0.992575\pi\) | ||
0.999728 | − | 0.0233253i | \(-0.00742535\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 20.0000i | − | 0.659022i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.48528 | − | 8.48528i | −0.279296 | − | 0.279296i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.0000 | − | 25.0000i | 0.821995 | − | 0.821995i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.89949 | 0.325142 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00000 | 0.196854 | 0.0984268 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984268 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.2132 | + | 21.2132i | −0.695235 | + | 0.695235i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.0000 | + | 12.0000i | 0.392862 | + | 0.392862i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.00000i | − | 0.0653372i | −0.999466 | − | 0.0326686i | \(-0.989599\pi\) | ||
0.999466 | − | 0.0326686i | \(-0.0104006\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.07107 | − | 7.07107i | −0.230756 | − | 0.230756i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.0000 | − | 36.0000i | 1.17357 | − | 1.17357i | 0.192213 | − | 0.981353i | \(-0.438433\pi\) |
0.981353 | − | 0.192213i | \(-0.0615665\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.9117 | 1.65791 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.9706 | − | 16.9706i | 0.551469 | − | 0.551469i | −0.375396 | − | 0.926865i | \(-0.622493\pi\) |
0.926865 | + | 0.375396i | \(0.122493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 8.48528i | − | 0.275154i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000i | 0.194359i | 0.995267 | + | 0.0971795i | \(0.0309821\pi\) | ||||
−0.995267 | + | 0.0971795i | \(0.969018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.4558 | 0.822012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0000 | −0.935484 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.48528 | + | 8.48528i | −0.273434 | + | 0.273434i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 41.0122i | − | 1.31886i | −0.751765 | − | 0.659432i | \(-0.770797\pi\) | ||
0.751765 | − | 0.659432i | \(-0.229203\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 36.0000i | − | 1.15649i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.4264 | + | 42.4264i | 1.36153 | + | 1.36153i | 0.871971 | + | 0.489557i | \(0.162841\pi\) |
0.489557 | + | 0.871971i | \(0.337159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.00000 | + | 4.00000i | −0.128234 | + | 0.128234i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.07107 | 0.226455 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.00000 | −0.191957 | −0.0959785 | − | 0.995383i | \(-0.530598\pi\) | ||||
−0.0959785 | + | 0.995383i | \(0.530598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.0000 | + | 13.0000i | 0.415058 | + | 0.415058i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 33.9411i | − | 1.08255i | −0.840844 | − | 0.541277i | \(-0.817941\pi\) | ||
0.840844 | − | 0.541277i | \(-0.182059\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.48528 | + | 8.48528i | 0.270089 | + | 0.270089i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.0000 | − | 36.0000i | 1.14473 | − | 1.14473i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.3259 | −1.66219 | −0.831094 | − | 0.556133i | \(-0.812285\pi\) | ||||
−0.831094 | + | 0.556133i | \(0.812285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.0000 | −0.888553 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.0000 | + | 41.0000i | 1.29848 | + | 1.29848i | 0.929394 | + | 0.369089i | \(0.120330\pi\) |
0.369089 | + | 0.929394i | \(0.379670\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.07107i | 0.223719i |
(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 | 768.2.j.c.193.1 | yes | 4 | |
3.2 | odd | 2 | 2304.2.k.c.1729.1 | 4 | |||
4.3 | odd | 2 | inner | 768.2.j.c.193.2 | yes | 4 | |
8.3 | odd | 2 | 768.2.j.b.193.1 | ✓ | 4 | ||
8.5 | even | 2 | 768.2.j.b.193.2 | yes | 4 | ||
12.11 | even | 2 | 2304.2.k.c.1729.2 | 4 | |||
16.3 | odd | 4 | inner | 768.2.j.c.577.2 | yes | 4 | |
16.5 | even | 4 | 768.2.j.b.577.2 | yes | 4 | ||
16.11 | odd | 4 | 768.2.j.b.577.1 | yes | 4 | ||
16.13 | even | 4 | inner | 768.2.j.c.577.1 | yes | 4 | |
24.5 | odd | 2 | 2304.2.k.b.1729.1 | 4 | |||
24.11 | even | 2 | 2304.2.k.b.1729.2 | 4 | |||
32.3 | odd | 8 | 3072.2.a.g.1.2 | 2 | |||
32.5 | even | 8 | 3072.2.d.a.1537.2 | 4 | |||
32.11 | odd | 8 | 3072.2.d.a.1537.1 | 4 | |||
32.13 | even | 8 | 3072.2.a.g.1.1 | 2 | |||
32.19 | odd | 8 | 3072.2.a.a.1.2 | 2 | |||
32.21 | even | 8 | 3072.2.d.a.1537.4 | 4 | |||
32.27 | odd | 8 | 3072.2.d.a.1537.3 | 4 | |||
32.29 | even | 8 | 3072.2.a.a.1.1 | 2 | |||
48.5 | odd | 4 | 2304.2.k.b.577.2 | 4 | |||
48.11 | even | 4 | 2304.2.k.b.577.1 | 4 | |||
48.29 | odd | 4 | 2304.2.k.c.577.2 | 4 | |||
48.35 | even | 4 | 2304.2.k.c.577.1 | 4 | |||
96.29 | odd | 8 | 9216.2.a.o.1.1 | 2 | |||
96.35 | even | 8 | 9216.2.a.n.1.2 | 2 | |||
96.77 | odd | 8 | 9216.2.a.n.1.1 | 2 | |||
96.83 | even | 8 | 9216.2.a.o.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.b.193.1 | ✓ | 4 | 8.3 | odd | 2 | ||
768.2.j.b.193.2 | yes | 4 | 8.5 | even | 2 | ||
768.2.j.b.577.1 | yes | 4 | 16.11 | odd | 4 | ||
768.2.j.b.577.2 | yes | 4 | 16.5 | even | 4 | ||
768.2.j.c.193.1 | yes | 4 | 1.1 | even | 1 | trivial | |
768.2.j.c.193.2 | yes | 4 | 4.3 | odd | 2 | inner | |
768.2.j.c.577.1 | yes | 4 | 16.13 | even | 4 | inner | |
768.2.j.c.577.2 | yes | 4 | 16.3 | odd | 4 | inner | |
2304.2.k.b.577.1 | 4 | 48.11 | even | 4 | |||
2304.2.k.b.577.2 | 4 | 48.5 | odd | 4 | |||
2304.2.k.b.1729.1 | 4 | 24.5 | odd | 2 | |||
2304.2.k.b.1729.2 | 4 | 24.11 | even | 2 | |||
2304.2.k.c.577.1 | 4 | 48.35 | even | 4 | |||
2304.2.k.c.577.2 | 4 | 48.29 | odd | 4 | |||
2304.2.k.c.1729.1 | 4 | 3.2 | odd | 2 | |||
2304.2.k.c.1729.2 | 4 | 12.11 | even | 2 | |||
3072.2.a.a.1.1 | 2 | 32.29 | even | 8 | |||
3072.2.a.a.1.2 | 2 | 32.19 | odd | 8 | |||
3072.2.a.g.1.1 | 2 | 32.13 | even | 8 | |||
3072.2.a.g.1.2 | 2 | 32.3 | odd | 8 | |||
3072.2.d.a.1537.1 | 4 | 32.11 | odd | 8 | |||
3072.2.d.a.1537.2 | 4 | 32.5 | even | 8 | |||
3072.2.d.a.1537.3 | 4 | 32.27 | odd | 8 | |||
3072.2.d.a.1537.4 | 4 | 32.21 | even | 8 | |||
9216.2.a.n.1.1 | 2 | 96.77 | odd | 8 | |||
9216.2.a.n.1.2 | 2 | 96.35 | even | 8 | |||
9216.2.a.o.1.1 | 2 | 96.29 | odd | 8 | |||
9216.2.a.o.1.2 | 2 | 96.83 | even | 8 |