Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(17,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.s (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: | \(2.87461447277\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.17 |
Dual form | 360.2.s.a.233.1 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −2.12132 | − | 0.707107i | −0.948683 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.65685i | − | 1.70561i | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||
0.522233 | − | 0.852803i | \(-0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 3.00000i | 0.832050 | − | 0.832050i | −0.155747 | − | 0.987797i | \(-0.549778\pi\) |
0.987797 | + | 0.155747i | \(0.0497784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | − | 2.82843i | −0.589768 | − | 0.589768i | 0.347801 | − | 0.937568i | \(-0.386929\pi\) |
−0.937568 | + | 0.347801i | \(0.886929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | + | 3.00000i | 0.800000 | + | 0.600000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.41421 | −0.262613 | −0.131306 | − | 0.991342i | \(-0.541917\pi\) | ||||
−0.131306 | + | 0.991342i | \(0.541917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.00000 | + | 7.00000i | 1.15079 | + | 1.15079i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) |
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.41421i | 0.220863i | 0.993884 | + | 0.110432i | \(0.0352233\pi\) | ||||
−0.993884 | + | 0.110432i | \(0.964777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | − | 4.00000i | 0.609994 | − | 0.609994i | −0.332950 | − | 0.942944i | \(-0.608044\pi\) |
0.942944 | + | 0.332950i | \(0.108044\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | + | 2.82843i | −0.412568 | + | 0.412568i | −0.882632 | − | 0.470064i | \(-0.844231\pi\) |
0.470064 | + | 0.882632i | \(0.344231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 7.00000i | − | 1.00000i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.48528 | + | 8.48528i | 1.16554 | + | 1.16554i | 0.983243 | + | 0.182300i | \(0.0583542\pi\) |
0.182300 | + | 0.983243i | \(0.441646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | + | 12.0000i | −0.539360 | + | 1.61808i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.3137 | 1.47292 | 0.736460 | − | 0.676481i | \(-0.236496\pi\) | ||||
0.736460 | + | 0.676481i | \(0.236496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0000 | −1.53644 | −0.768221 | − | 0.640184i | \(-0.778858\pi\) | ||||
−0.768221 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.48528 | + | 4.24264i | −1.05247 | + | 0.526235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | − | 8.00000i | −0.977356 | − | 0.977356i | 0.0223937 | − | 0.999749i | \(-0.492871\pi\) |
−0.999749 | + | 0.0223937i | \(0.992871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.65685i | − | 0.671345i | −0.941979 | − | 0.335673i | \(-0.891036\pi\) | ||
0.941979 | − | 0.335673i | \(-0.108964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | + | 3.00000i | −0.351123 | + | 0.351123i | −0.860527 | − | 0.509404i | \(-0.829866\pi\) |
0.509404 | + | 0.860527i | \(0.329866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000i | 0.900070i | 0.893011 | + | 0.450035i | \(0.148589\pi\) | ||||
−0.893011 | + | 0.450035i | \(0.851411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.3137 | + | 11.3137i | 1.24184 | + | 1.24184i | 0.959237 | + | 0.282604i | \(0.0911983\pi\) |
0.282604 | + | 0.959237i | \(0.408802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.07107 | 0.749532 | 0.374766 | − | 0.927119i | \(-0.377723\pi\) | ||||
0.374766 | + | 0.927119i | \(0.377723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.82843 | + | 8.48528i | −0.290191 | + | 0.870572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | + | 5.00000i | 0.507673 | + | 0.507673i | 0.913812 | − | 0.406138i | \(-0.133125\pi\) |
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.41421i | − | 0.140720i | −0.997522 | − | 0.0703598i | \(-0.977585\pi\) | ||
0.997522 | − | 0.0703598i | \(-0.0224147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | − | 4.00000i | 0.394132 | − | 0.394132i | −0.482025 | − | 0.876157i | \(-0.660099\pi\) |
0.876157 | + | 0.482025i | \(0.160099\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.3137 | + | 11.3137i | −1.09374 | + | 1.09374i | −0.0986115 | + | 0.995126i | \(0.531440\pi\) |
−0.995126 | + | 0.0986115i | \(0.968560\pi\) | |||||||
\(108\) | 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 | ||||||||
\(113\) | 4.24264 | + | 4.24264i | 0.399114 | + | 0.399114i | 0.877920 | − | 0.478806i | \(-0.158930\pi\) |
−0.478806 | + | 0.877920i | \(0.658930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | + | 8.00000i | 0.373002 | + | 0.746004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −1.90909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.36396 | − | 9.19239i | −0.569210 | − | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000 | + | 12.0000i | 1.06483 | + | 1.06483i | 0.997748 | + | 0.0670802i | \(0.0213683\pi\) |
0.0670802 | + | 0.997748i | \(0.478632\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.65685i | − | 0.494242i | −0.968985 | − | 0.247121i | \(-0.920516\pi\) | ||
0.968985 | − | 0.247121i | \(-0.0794845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.7279 | − | 12.7279i | 1.08742 | − | 1.08742i | 0.0916263 | − | 0.995793i | \(-0.470793\pi\) |
0.995793 | − | 0.0916263i | \(-0.0292065\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.0000i | − | 1.69638i | −0.529694 | − | 0.848189i | \(-0.677693\pi\) | ||
0.529694 | − | 0.848189i | \(-0.322307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.9706 | − | 16.9706i | −1.41915 | − | 1.41915i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.00000 | + | 1.00000i | 0.249136 | + | 0.0830455i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.24264 | −0.347571 | −0.173785 | − | 0.984784i | \(-0.555600\pi\) | ||||
−0.173785 | + | 0.984784i | \(0.555600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.9706 | + | 5.65685i | 1.36311 | + | 0.454369i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | − | 7.00000i | −0.558661 | − | 0.558661i | 0.370265 | − | 0.928926i | \(-0.379267\pi\) |
−0.928926 | + | 0.370265i | \(0.879267\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | − | 12.0000i | 0.939913 | − | 0.939913i | −0.0583818 | − | 0.998294i | \(-0.518594\pi\) |
0.998294 | + | 0.0583818i | \(0.0185941\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.48528 | + | 8.48528i | −0.656611 | + | 0.656611i | −0.954577 | − | 0.297966i | \(-0.903692\pi\) |
0.297966 | + | 0.954577i | \(0.403692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.07107 | − | 7.07107i | −0.537603 | − | 0.537603i | 0.385221 | − | 0.922824i | \(-0.374125\pi\) |
−0.922824 | + | 0.385221i | \(0.874125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.65685 | −0.422813 | −0.211407 | − | 0.977398i | \(-0.567804\pi\) | ||||
−0.211407 | + | 0.977398i | \(0.567804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.00000 | 0.297318 | 0.148659 | − | 0.988889i | \(-0.452504\pi\) | ||||
0.148659 | + | 0.988889i | \(0.452504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.89949 | − | 19.7990i | −0.727825 | − | 1.45565i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.3137i | − | 0.818631i | −0.912393 | − | 0.409316i | \(-0.865768\pi\) | ||
0.912393 | − | 0.409316i | \(-0.134232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000 | − | 5.00000i | 0.359908 | − | 0.359908i | −0.503871 | − | 0.863779i | \(-0.668091\pi\) |
0.863779 | + | 0.503871i | \(0.168091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.7279 | − | 12.7279i | 0.906827 | − | 0.906827i | −0.0891879 | − | 0.996015i | \(-0.528427\pi\) |
0.996015 | + | 0.0891879i | \(0.0284272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000i | 1.70131i | 0.525720 | + | 0.850657i | \(0.323796\pi\) | ||||
−0.525720 | + | 0.850657i | \(0.676204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00000 | − | 3.00000i | 0.0698430 | − | 0.209529i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.6274 | −1.56517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.3137 | + | 5.65685i | −0.771589 | + | 0.385794i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.00000i | − | 0.396491i | −0.980152 | − | 0.198246i | \(-0.936476\pi\) | ||
0.980152 | − | 0.198246i | \(-0.0635244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.65685 | + | 5.65685i | 0.370593 | + | 0.370593i | 0.867693 | − | 0.497100i | \(-0.165602\pi\) |
−0.497100 | + | 0.867693i | \(0.665602\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | − | 4.00000i | 0.521862 | − | 0.260931i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9706 | 1.09773 | 0.548867 | − | 0.835910i | \(-0.315059\pi\) | ||||
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 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 | ||||||||
\(245\) | −4.94975 | + | 14.8492i | −0.316228 | + | 0.948683i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0000 | − | 12.0000i | −0.763542 | − | 0.763542i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.0000 | + | 16.0000i | −1.00591 | + | 1.00591i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.07107 | + | 7.07107i | −0.441081 | + | 0.441081i | −0.892375 | − | 0.451294i | \(-0.850963\pi\) |
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.82843 | − | 2.82843i | −0.174408 | − | 0.174408i | 0.614505 | − | 0.788913i | \(-0.289356\pi\) |
−0.788913 | + | 0.614505i | \(0.789356\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | − | 24.0000i | −0.737154 | − | 1.47431i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.5563 | 0.948487 | 0.474244 | − | 0.880394i | \(-0.342722\pi\) | ||||
0.474244 | + | 0.880394i | \(0.342722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.9706 | − | 22.6274i | 1.02336 | − | 1.36448i | ||||
\(276\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.24264i | 0.253095i | 0.991961 | + | 0.126547i | \(0.0403896\pi\) | ||||
−0.991961 | + | 0.126547i | \(0.959610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.0000 | + | 16.0000i | −0.951101 | + | 0.951101i | −0.998859 | − | 0.0477577i | \(-0.984792\pi\) |
0.0477577 | + | 0.998859i | \(0.484792\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.41421 | − | 1.41421i | −0.0826192 | − | 0.0826192i | 0.664589 | − | 0.747209i | \(-0.268606\pi\) |
−0.747209 | + | 0.664589i | \(0.768606\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0000 | − | 8.00000i | −1.39733 | − | 0.465778i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.9706 | −0.981433 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.4558 | + | 8.48528i | 1.45760 | + | 0.485866i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | − | 20.0000i | −1.14146 | − | 1.14146i | −0.988183 | − | 0.153277i | \(-0.951017\pi\) |
−0.153277 | − | 0.988183i | \(-0.548983\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.2843i | 1.60385i | 0.597422 | + | 0.801927i | \(0.296192\pi\) | ||||
−0.597422 | + | 0.801927i | \(0.703808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.00000 | + | 9.00000i | −0.508710 | + | 0.508710i | −0.914130 | − | 0.405420i | \(-0.867125\pi\) |
0.405420 | + | 0.914130i | \(0.367125\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.82843 | − | 2.82843i | 0.158860 | − | 0.158860i | −0.623201 | − | 0.782062i | \(-0.714168\pi\) |
0.782062 | + | 0.623201i | \(0.214168\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000i | 0.447914i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.0000 | − | 3.00000i | 1.16487 | − | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3137 | + | 22.6274i | 0.618134 | + | 1.23627i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.0000 | + | 15.0000i | 0.817102 | + | 0.817102i | 0.985687 | − | 0.168585i | \(-0.0539198\pi\) |
−0.168585 | + | 0.985687i | \(0.553920\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 45.2548i | 2.45069i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.00000i | 0.214115i | 0.994253 | + | 0.107058i | \(0.0341429\pi\) | ||||
−0.994253 | + | 0.107058i | \(0.965857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.65685 | + | 5.65685i | 0.301084 | + | 0.301084i | 0.841438 | − | 0.540354i | \(-0.181710\pi\) |
−0.540354 | + | 0.841438i | \(0.681710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | + | 12.0000i | −0.212298 | + | 0.636894i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.65685 | 0.298557 | 0.149279 | − | 0.988795i | \(-0.452305\pi\) | ||||
0.149279 | + | 0.988795i | \(0.452305\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.48528 | − | 4.24264i | 0.444140 | − | 0.222070i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | − | 4.00000i | −0.208798 | − | 0.208798i | 0.594958 | − | 0.803757i | \(-0.297169\pi\) |
−0.803757 | + | 0.594958i | \(0.797169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.00000 | + | 3.00000i | −0.155334 | + | 0.155334i | −0.780496 | − | 0.625161i | \(-0.785033\pi\) |
0.625161 | + | 0.780496i | \(0.285033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.24264 | + | 4.24264i | −0.218507 | + | 0.218507i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000i | 0.616399i | 0.951322 | + | 0.308199i | \(0.0997264\pi\) | ||||
−0.951322 | + | 0.308199i | \(0.900274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.48528 | − | 8.48528i | −0.433578 | − | 0.433578i | 0.456266 | − | 0.889843i | \(-0.349187\pi\) |
−0.889843 | + | 0.456266i | \(0.849187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.6985 | −1.50577 | −0.752886 | − | 0.658150i | \(-0.771339\pi\) | ||||
−0.752886 | + | 0.658150i | \(0.771339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.65685 | − | 16.9706i | 0.284627 | − | 0.853882i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.0000 | − | 19.0000i | −0.953583 | − | 0.953583i | 0.0453868 | − | 0.998969i | \(-0.485548\pi\) |
−0.998969 | + | 0.0453868i | \(0.985548\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8701i | 1.34183i | 0.741536 | + | 0.670913i | \(0.234098\pi\) | ||||
−0.741536 | + | 0.670913i | \(0.765902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.0000 | + | 24.0000i | −1.19553 | + | 1.19553i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.5980 | − | 39.5980i | 1.96280 | − | 1.96280i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0000i | 1.18672i | 0.804936 | + | 0.593362i | \(0.202200\pi\) | ||||
−0.804936 | + | 0.593362i | \(0.797800\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0000 | − | 32.0000i | −0.785409 | − | 1.57082i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.3137 | −0.552711 | −0.276355 | − | 0.961056i | \(-0.589127\pi\) | ||||
−0.276355 | + | 0.961056i | \(0.589127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.0000 | 1.85201 | 0.926003 | − | 0.377515i | \(-0.123221\pi\) | ||||
0.926003 | + | 0.377515i | \(0.123221\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.65685i | 0.272481i | 0.990676 | + | 0.136241i | \(0.0435020\pi\) | ||||
−0.990676 | + | 0.136241i | \(0.956498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0000 | − | 11.0000i | 0.528626 | − | 0.528626i | −0.391536 | − | 0.920163i | \(-0.628056\pi\) |
0.920163 | + | 0.391536i | \(0.128056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.3137 | + | 11.3137i | −0.541208 | + | 0.541208i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.00000i | − | 0.381819i | −0.981608 | − | 0.190910i | \(-0.938856\pi\) | ||
0.981608 | − | 0.190910i | \(-0.0611437\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.3137 | + | 11.3137i | 0.537531 | + | 0.537531i | 0.922803 | − | 0.385272i | \(-0.125893\pi\) |
−0.385272 | + | 0.922803i | \(0.625893\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.0000 | − | 5.00000i | −0.711068 | − | 0.237023i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3848 | 0.867631 | 0.433816 | − | 0.901002i | \(-0.357167\pi\) | ||||
0.433816 | + | 0.901002i | \(0.357167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0000 | − | 23.0000i | −1.07589 | − | 1.07589i | −0.996873 | − | 0.0790217i | \(-0.974820\pi\) |
−0.0790217 | − | 0.996873i | \(-0.525180\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 32.5269i | − | 1.51493i | −0.652876 | − | 0.757465i | \(-0.726438\pi\) | ||
0.652876 | − | 0.757465i | \(-0.273562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | − | 4.00000i | 0.185896 | − | 0.185896i | −0.608023 | − | 0.793919i | \(-0.708037\pi\) |
0.793919 | + | 0.608023i | \(0.208037\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.9706 | + | 16.9706i | −0.785304 | + | 0.785304i | −0.980720 | − | 0.195416i | \(-0.937394\pi\) |
0.195416 | + | 0.980720i | \(0.437394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.6274 | − | 22.6274i | −1.04041 | − | 1.04041i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000 | − | 16.0000i | 0.550598 | − | 0.734130i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.65685 | 0.258468 | 0.129234 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129234 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.0000 | 1.91504 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.07107 | − | 14.1421i | −0.321081 | − | 0.642161i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | + | 12.0000i | 0.543772 | + | 0.543772i | 0.924632 | − | 0.380861i | \(-0.124372\pi\) |
−0.380861 | + | 0.924632i | \(0.624372\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.6274i | − | 1.02116i | −0.859830 | − | 0.510581i | \(-0.829431\pi\) | ||
0.859830 | − | 0.510581i | \(-0.170569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000i | 0.179065i | 0.995984 | + | 0.0895323i | \(0.0285372\pi\) | ||||
−0.995984 | + | 0.0895323i | \(0.971463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.4558 | − | 25.4558i | −1.13502 | − | 1.13502i | −0.989330 | − | 0.145690i | \(-0.953460\pi\) |
−0.145690 | − | 0.989330i | \(-0.546540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.00000 | + | 3.00000i | −0.0444994 | + | 0.133498i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.7279 | 0.564155 | 0.282078 | − | 0.959392i | \(-0.408976\pi\) | ||||
0.282078 | + | 0.959392i | \(0.408976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.3137 | + | 5.65685i | −0.498542 | + | 0.249271i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000 | + | 16.0000i | 0.703679 | + | 0.703679i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.2132i | − | 0.929367i | −0.885477 | − | 0.464684i | \(-0.846168\pi\) | ||
0.885477 | − | 0.464684i | \(-0.153832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0000 | + | 24.0000i | −1.04945 | + | 1.04945i | −0.0507346 | + | 0.998712i | \(0.516156\pi\) |
−0.998712 | + | 0.0507346i | \(0.983844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.24264 | + | 4.24264i | 0.183769 | + | 0.183769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.0000 | − | 16.0000i | 1.38348 | − | 0.691740i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −39.5980 | −1.70561 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | −0.171973 | −0.0859867 | − | 0.996296i | \(-0.527404\pi\) | ||||
−0.0859867 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.82843 | + | 8.48528i | −0.121157 | + | 0.363470i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | + | 12.0000i | 0.513083 | + | 0.513083i | 0.915470 | − | 0.402387i | \(-0.131819\pi\) |
−0.402387 | + | 0.915470i | \(0.631819\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.65685i | 0.240990i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.48528 | − | 8.48528i | 0.359533 | − | 0.359533i | −0.504108 | − | 0.863641i | \(-0.668179\pi\) |
0.863641 | + | 0.504108i | \(0.168179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 24.0000i | − | 1.01509i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.65685 | + | 5.65685i | 0.238408 | + | 0.238408i | 0.816191 | − | 0.577783i | \(-0.196082\pi\) |
−0.577783 | + | 0.816191i | \(0.696082\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | − | 12.0000i | −0.252422 | − | 0.504844i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.3553 | −1.48217 | −0.741086 | − | 0.671410i | \(-0.765689\pi\) | ||||
−0.741086 | + | 0.671410i | \(0.765689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.82843 | − | 19.7990i | −0.117954 | − | 0.825675i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.00000 | − | 9.00000i | −0.374675 | − | 0.374675i | 0.494502 | − | 0.869177i | \(-0.335351\pi\) |
−0.869177 | + | 0.494502i | \(0.835351\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.0000 | − | 48.0000i | 1.98796 | − | 1.98796i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.65685 | + | 5.65685i | −0.233483 | + | 0.233483i | −0.814145 | − | 0.580662i | \(-0.802794\pi\) |
0.580662 | + | 0.814145i | \(0.302794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0000i | 1.31854i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.3848 | − | 18.3848i | −0.754972 | − | 0.754972i | 0.220430 | − | 0.975403i | \(-0.429254\pi\) |
−0.975403 | + | 0.220430i | \(0.929254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.2843 | 1.15566 | 0.577832 | − | 0.816156i | \(-0.303899\pi\) | ||||
0.577832 | + | 0.816156i | \(0.303899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.0000 | −1.30531 | −0.652654 | − | 0.757656i | \(-0.726344\pi\) | ||||
−0.652654 | + | 0.757656i | \(0.726344\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 44.5477 | + | 14.8492i | 1.81112 | + | 0.603708i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | + | 8.00000i | 0.324710 | + | 0.324710i | 0.850571 | − | 0.525861i | \(-0.176257\pi\) |
−0.525861 | + | 0.850571i | \(0.676257\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.9706i | 0.686555i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.0000 | − | 15.0000i | 0.605844 | − | 0.605844i | −0.336013 | − | 0.941857i | \(-0.609079\pi\) |
0.941857 | + | 0.336013i | \(0.109079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.9706 | − | 16.9706i | 0.683209 | − | 0.683209i | −0.277513 | − | 0.960722i | \(-0.589510\pi\) |
0.960722 | + | 0.277513i | \(0.0895101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000i | 0.482321i | 0.970485 | + | 0.241160i | \(0.0775280\pi\) | ||||
−0.970485 | + | 0.241160i | \(0.922472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.9706 | − | 33.9411i | −0.673456 | − | 1.34691i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.0000 | − | 21.0000i | −0.832050 | − | 0.832050i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 26.8701i | − | 1.06130i | −0.847590 | − | 0.530652i | \(-0.821947\pi\) | ||
0.847590 | − | 0.530652i | \(-0.178053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.0000 | + | 28.0000i | −1.10421 | + | 1.10421i | −0.110316 | + | 0.993897i | \(0.535186\pi\) |
−0.993897 | + | 0.110316i | \(0.964814\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.7990 | − | 19.7990i | 0.778379 | − | 0.778379i | −0.201176 | − | 0.979555i | \(-0.564476\pi\) |
0.979555 | + | 0.201176i | \(0.0644765\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 64.0000i | − | 2.51222i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.4558 | − | 25.4558i | −0.996164 | − | 0.996164i | 0.00382851 | − | 0.999993i | \(-0.498781\pi\) |
−0.999993 | + | 0.00382851i | \(0.998781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | + | 12.0000i | −0.156293 | + | 0.468879i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.9411 | −1.32216 | −0.661079 | − | 0.750316i | \(-0.729901\pi\) | ||||
−0.661079 | + | 0.750316i | \(0.729901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0000 | −0.777910 | −0.388955 | − | 0.921257i | \(-0.627164\pi\) | ||||
−0.388955 | + | 0.921257i | \(0.627164\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000 | + | 4.00000i | 0.154881 | + | 0.154881i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 67.8823i | 2.62057i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0000 | + | 19.0000i | −0.732396 | + | 0.732396i | −0.971094 | − | 0.238698i | \(-0.923279\pi\) |
0.238698 | + | 0.971094i | \(0.423279\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.7990 | + | 19.7990i | −0.760937 | + | 0.760937i | −0.976492 | − | 0.215555i | \(-0.930844\pi\) |
0.215555 | + | 0.976492i | \(0.430844\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.9411 | + | 33.9411i | 1.29872 | + | 1.29872i | 0.929237 | + | 0.369484i | \(0.120466\pi\) |
0.369484 | + | 0.929237i | \(0.379534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.0000 | + | 18.0000i | −1.37549 | + | 0.687745i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 50.9117 | 1.93958 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.1421 | + | 42.4264i | −0.536442 | + | 1.60933i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.5269i | − | 1.22852i | −0.789102 | − | 0.614262i | \(-0.789454\pi\) | ||
0.789102 | − | 0.614262i | \(-0.210546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.0000 | − | 28.0000i | 1.05604 | − | 1.05604i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000i | 0.225335i | 0.993633 | + | 0.112667i | \(0.0359394\pi\) | ||||
−0.993633 | + | 0.112667i | \(0.964061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.6274 | + | 22.6274i | 0.847403 | + | 0.847403i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | + | 48.0000i | 0.897549 | + | 1.79510i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.6274 | 0.843860 | 0.421930 | − | 0.906628i | \(-0.361353\pi\) | ||||
0.421930 | + | 0.906628i | \(0.361353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.65685 | − | 4.24264i | −0.210090 | − | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.0000 | + | 12.0000i | 0.445055 | + | 0.445055i | 0.893707 | − | 0.448651i | \(-0.148096\pi\) |
−0.448651 | + | 0.893707i | \(0.648096\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0000 | − | 23.0000i | 0.849524 | − | 0.849524i | −0.140549 | − | 0.990074i | \(-0.544887\pi\) |
0.990074 | + | 0.140549i | \(0.0448868\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −45.2548 | + | 45.2548i | −1.66698 | + | 1.66698i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000i | 0.147142i | 0.997290 | + | 0.0735712i | \(0.0234396\pi\) | ||||
−0.997290 | + | 0.0735712i | \(0.976560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.4558 | + | 25.4558i | 0.933884 | + | 0.933884i | 0.997946 | − | 0.0640616i | \(-0.0204054\pi\) |
−0.0640616 | + | 0.997946i | \(0.520405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | + | 3.00000i | 0.329734 | + | 0.109911i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.9706 | − | 5.65685i | −0.617622 | − | 0.205874i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.00000 | − | 3.00000i | −0.109037 | − | 0.109037i | 0.650484 | − | 0.759520i | \(-0.274566\pi\) |
−0.759520 | + | 0.650484i | \(0.774566\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.41421i | 0.0512652i | 0.999671 | + | 0.0256326i | \(0.00816000\pi\) | ||||
−0.999671 | + | 0.0256326i | \(0.991840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.9411 | − | 33.9411i | 1.22554 | − | 1.22554i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.0000i | 1.44244i | 0.692708 | + | 0.721218i | \(0.256418\pi\) | ||||
−0.692708 | + | 0.721218i | \(0.743582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.1421 | + | 14.1421i | 0.508657 | + | 0.508657i | 0.914114 | − | 0.405457i | \(-0.132888\pi\) |
−0.405457 | + | 0.914114i | \(0.632888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.0000 | − | 24.0000i | −1.14947 | − | 0.862105i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.65685 | 0.202678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.89949 | + | 19.7990i | 0.353328 | + | 0.706656i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.0000 | + | 24.0000i | 0.855508 | + | 0.855508i | 0.990805 | − | 0.135297i | \(-0.0431990\pi\) |
−0.135297 | + | 0.990805i | \(0.543199\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0000 | + | 36.0000i | −1.27840 | + | 1.27840i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.6985 | + | 29.6985i | −1.05197 | + | 1.05197i | −0.0534012 | + | 0.998573i | \(0.517006\pi\) |
−0.998573 | + | 0.0534012i | \(0.982994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.9706 | + | 16.9706i | 0.598878 | + | 0.598878i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.5269 | 1.14359 | 0.571793 | − | 0.820398i | \(-0.306248\pi\) | ||||
0.571793 | + | 0.820398i | \(0.306248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.9411 | + | 16.9706i | −1.18891 | + | 0.594453i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | − | 16.0000i | −0.559769 | − | 0.559769i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 18.3848i | − | 0.641633i | −0.947141 | − | 0.320817i | \(-0.896043\pi\) | ||
0.947141 | − | 0.320817i | \(-0.103957\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.0000 | + | 32.0000i | −1.11545 | + | 1.11545i | −0.123049 | + | 0.992401i | \(0.539267\pi\) |
−0.992401 | + | 0.123049i | \(0.960733\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.9706 | + | 16.9706i | −0.590124 | + | 0.590124i | −0.937665 | − | 0.347541i | \(-0.887017\pi\) |
0.347541 | + | 0.937665i | \(0.387017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 28.0000i | − | 0.972480i | −0.873825 | − | 0.486240i | \(-0.838368\pi\) | ||
0.873825 | − | 0.486240i | \(-0.161632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.0000 | − | 12.0000i | 0.830554 | − | 0.415277i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.65685 | −0.195296 | −0.0976481 | − | 0.995221i | \(-0.531132\pi\) | ||||
−0.0976481 | + | 0.995221i | \(0.531132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0000 | −0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.53553 | + | 10.6066i | −0.121626 | + | 0.364878i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 39.5980i | − | 1.35740i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.00000 | − | 9.00000i | 0.308154 | − | 0.308154i | −0.536039 | − | 0.844193i | \(-0.680080\pi\) |
0.844193 | + | 0.536039i | \(0.180080\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.9411 | − | 33.9411i | 1.15941 | − | 1.15941i | 0.174803 | − | 0.984603i | \(-0.444071\pi\) |
0.984603 | − | 0.174803i | \(-0.0559290\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 28.0000i | − | 0.955348i | −0.878537 | − | 0.477674i | \(-0.841480\pi\) | ||
0.878537 | − | 0.477674i | \(-0.158520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.4558 | + | 25.4558i | 0.866527 | + | 0.866527i | 0.992086 | − | 0.125559i | \(-0.0400725\pi\) |
−0.125559 | + | 0.992086i | \(0.540072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.0000 | + | 20.0000i | 0.340010 | + | 0.680020i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.2548 | 1.53517 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.0000 | −1.62642 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.0000 | + | 15.0000i | 0.506514 | + | 0.506514i | 0.913455 | − | 0.406941i | \(-0.133404\pi\) |
−0.406941 | + | 0.913455i | \(0.633404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.41421i | − | 0.0476461i | −0.999716 | − | 0.0238230i | \(-0.992416\pi\) | ||
0.999716 | − | 0.0238230i | \(-0.00758382\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0000 | − | 12.0000i | 0.403832 | − | 0.403832i | −0.475749 | − | 0.879581i | \(-0.657823\pi\) |
0.879581 | + | 0.475749i | \(0.157823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.1127 | + | 31.1127i | −1.04466 | + | 1.04466i | −0.0457073 | + | 0.998955i | \(0.514554\pi\) |
−0.998955 | + | 0.0457073i | \(0.985446\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.3137 | + | 11.3137i | 0.378599 | + | 0.378599i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | + | 4.00000i | 0.401116 | + | 0.133705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.3137 | 0.377333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.48528 | − | 2.82843i | −0.282060 | − | 0.0940201i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.00000 | − | 8.00000i | −0.265636 | − | 0.265636i | 0.561703 | − | 0.827339i | \(-0.310146\pi\) |
−0.827339 | + | 0.561703i | \(0.810146\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28.2843i | − | 0.937100i | −0.883437 | − | 0.468550i | \(-0.844777\pi\) | ||
0.883437 | − | 0.468550i | \(-0.155223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 64.0000 | − | 64.0000i | 2.11809 | − | 2.11809i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 32.0000i | − | 1.05558i | −0.849374 | − | 0.527791i | \(-0.823020\pi\) | ||
0.849374 | − | 0.527791i | \(-0.176980\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.9706 | − | 16.9706i | −0.558593 | − | 0.558593i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.00000 | + | 49.0000i | 0.230159 | + | 1.61111i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.5563 | −0.510387 | −0.255194 | − | 0.966890i | \(-0.582139\pi\) | ||||
−0.255194 | + | 0.966890i | \(0.582139\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.0000 | −0.917663 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.00000 | + | 5.00000i | 0.163343 | + | 0.163343i | 0.784046 | − | 0.620703i | \(-0.213153\pi\) |
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 12.7279i | − | 0.414918i | −0.978244 | − | 0.207459i | \(-0.933481\pi\) | ||
0.978244 | − | 0.207459i | \(-0.0665194\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.00000 | − | 4.00000i | 0.130258 | − | 0.130258i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.3137 | − | 11.3137i | 0.367646 | − | 0.367646i | −0.498972 | − | 0.866618i | \(-0.666289\pi\) |
0.866618 | + | 0.498972i | \(0.166289\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0000i | 0.584305i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.2132 | − | 21.2132i | −0.687163 | − | 0.687163i | 0.274441 | − | 0.961604i | \(-0.411507\pi\) |
−0.961604 | + | 0.274441i | \(0.911507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | + | 24.0000i | −0.258874 | + | 0.776622i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.1421 | + | 7.07107i | −0.455251 | + | 0.227626i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0000 | + | 24.0000i | 0.771788 | + | 0.771788i | 0.978419 | − | 0.206631i | \(-0.0662500\pi\) |
−0.206631 | + | 0.978419i | \(0.566250\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.6274i | 0.726148i | 0.931760 | + | 0.363074i | \(0.118273\pi\) | ||||
−0.931760 | + | 0.363074i | \(0.881727\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.9411 | + | 33.9411i | −1.08587 | + | 1.08587i | −0.0899242 | + | 0.995949i | \(0.528662\pi\) |
−0.995949 | + | 0.0899242i | \(0.971338\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 40.0000i | − | 1.27841i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.4558 | − | 25.4558i | −0.811915 | − | 0.811915i | 0.173006 | − | 0.984921i | \(-0.444652\pi\) |
−0.984921 | + | 0.173006i | \(0.944652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | + | 18.0000i | −1.14706 | + | 0.573528i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.6274 | −0.719510 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.9706 | − | 50.9117i | 0.538003 | − | 1.61401i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.00000 | + | 3.00000i | 0.0950110 | + | 0.0950110i | 0.753015 | − | 0.658004i | \(-0.228599\pi\) |
−0.658004 | + | 0.753015i | \(0.728599\pi\) | |||||||
\(998\) | 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 | 360.2.s.a.17.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 360.2.s.a.17.2 | yes | 4 | |
4.3 | odd | 2 | 720.2.w.c.17.1 | 4 | |||
5.2 | odd | 4 | 1800.2.s.b.593.1 | 4 | |||
5.3 | odd | 4 | inner | 360.2.s.a.233.2 | yes | 4 | |
5.4 | even | 2 | 1800.2.s.b.1457.1 | 4 | |||
8.3 | odd | 2 | 2880.2.w.f.2177.2 | 4 | |||
8.5 | even | 2 | 2880.2.w.e.2177.2 | 4 | |||
12.11 | even | 2 | 720.2.w.c.17.2 | 4 | |||
15.2 | even | 4 | 1800.2.s.b.593.2 | 4 | |||
15.8 | even | 4 | inner | 360.2.s.a.233.1 | yes | 4 | |
15.14 | odd | 2 | 1800.2.s.b.1457.2 | 4 | |||
20.3 | even | 4 | 720.2.w.c.593.2 | 4 | |||
20.7 | even | 4 | 3600.2.w.d.593.2 | 4 | |||
20.19 | odd | 2 | 3600.2.w.d.1457.2 | 4 | |||
24.5 | odd | 2 | 2880.2.w.e.2177.1 | 4 | |||
24.11 | even | 2 | 2880.2.w.f.2177.1 | 4 | |||
40.3 | even | 4 | 2880.2.w.f.2753.1 | 4 | |||
40.13 | odd | 4 | 2880.2.w.e.2753.1 | 4 | |||
60.23 | odd | 4 | 720.2.w.c.593.1 | 4 | |||
60.47 | odd | 4 | 3600.2.w.d.593.1 | 4 | |||
60.59 | even | 2 | 3600.2.w.d.1457.1 | 4 | |||
120.53 | even | 4 | 2880.2.w.e.2753.2 | 4 | |||
120.83 | odd | 4 | 2880.2.w.f.2753.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.s.a.17.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
360.2.s.a.17.2 | yes | 4 | 3.2 | odd | 2 | inner | |
360.2.s.a.233.1 | yes | 4 | 15.8 | even | 4 | inner | |
360.2.s.a.233.2 | yes | 4 | 5.3 | odd | 4 | inner | |
720.2.w.c.17.1 | 4 | 4.3 | odd | 2 | |||
720.2.w.c.17.2 | 4 | 12.11 | even | 2 | |||
720.2.w.c.593.1 | 4 | 60.23 | odd | 4 | |||
720.2.w.c.593.2 | 4 | 20.3 | even | 4 | |||
1800.2.s.b.593.1 | 4 | 5.2 | odd | 4 | |||
1800.2.s.b.593.2 | 4 | 15.2 | even | 4 | |||
1800.2.s.b.1457.1 | 4 | 5.4 | even | 2 | |||
1800.2.s.b.1457.2 | 4 | 15.14 | odd | 2 | |||
2880.2.w.e.2177.1 | 4 | 24.5 | odd | 2 | |||
2880.2.w.e.2177.2 | 4 | 8.5 | even | 2 | |||
2880.2.w.e.2753.1 | 4 | 40.13 | odd | 4 | |||
2880.2.w.e.2753.2 | 4 | 120.53 | even | 4 | |||
2880.2.w.f.2177.1 | 4 | 24.11 | even | 2 | |||
2880.2.w.f.2177.2 | 4 | 8.3 | odd | 2 | |||
2880.2.w.f.2753.1 | 4 | 40.3 | even | 4 | |||
2880.2.w.f.2753.2 | 4 | 120.83 | odd | 4 | |||
3600.2.w.d.593.1 | 4 | 60.47 | odd | 4 | |||
3600.2.w.d.593.2 | 4 | 20.7 | even | 4 | |||
3600.2.w.d.1457.1 | 4 | 60.59 | even | 2 | |||
3600.2.w.d.1457.2 | 4 | 20.19 | odd | 2 |