Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(1,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.a (trivial) |
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: | yes |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.585786 | 0.176621 | 0.0883106 | − | 0.996093i | \(-0.471853\pi\) | ||||
0.0883106 | + | 0.996093i | \(0.471853\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.41421 | 0.342997 | 0.171499 | − | 0.985184i | \(-0.445139\pi\) | ||||
0.171499 | + | 0.985184i | \(0.445139\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.585786 | 0.124890 | ||||||||
\(23\) | 4.82843 | 1.00680 | 0.503398 | − | 0.864054i | \(-0.332083\pi\) | ||||
0.503398 | + | 0.864054i | \(0.332083\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.24264 | 1.53062 | 0.765310 | − | 0.643662i | \(-0.222586\pi\) | ||||
0.765310 | + | 0.643662i | \(0.222586\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 5.07107 | 0.910791 | 0.455395 | − | 0.890289i | \(-0.349498\pi\) | ||||
0.455395 | + | 0.890289i | \(0.349498\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.585786 | 0.101972 | ||||||||
\(34\) | 1.41421 | 0.242536 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.41421 | −0.232495 | −0.116248 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116248 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(38\) | −2.82843 | −0.458831 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −8.82843 | −1.37877 | −0.689384 | − | 0.724396i | \(-0.742119\pi\) | ||||
−0.689384 | + | 0.724396i | \(0.742119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.58579 | 0.699326 | 0.349663 | − | 0.936876i | \(-0.386296\pi\) | ||||
0.349663 | + | 0.936876i | \(0.386296\pi\) | |||||||
\(44\) | 0.585786 | 0.0883106 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 4.82843 | 0.711913 | ||||||||
\(47\) | −9.07107 | −1.32315 | −0.661576 | − | 0.749878i | \(-0.730112\pi\) | ||||
−0.661576 | + | 0.749878i | \(0.730112\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.41421 | 0.198030 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.31371 | −1.27934 | −0.639668 | − | 0.768651i | \(-0.720928\pi\) | ||||
−0.639668 | + | 0.768651i | \(0.720928\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.585786 | 0.0789874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | 8.24264 | 1.08231 | ||||||||
\(59\) | 2.48528 | 0.323556 | 0.161778 | − | 0.986827i | \(-0.448277\pi\) | ||||
0.161778 | + | 0.986827i | \(0.448277\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −11.6569 | −1.49251 | −0.746254 | − | 0.665662i | \(-0.768149\pi\) | ||||
−0.746254 | + | 0.665662i | \(0.768149\pi\) | |||||||
\(62\) | 5.07107 | 0.644026 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.585786 | 0.0721053 | ||||||||
\(67\) | 7.89949 | 0.965077 | 0.482538 | − | 0.875875i | \(-0.339715\pi\) | ||||
0.482538 | + | 0.875875i | \(0.339715\pi\) | |||||||
\(68\) | 1.41421 | 0.171499 | ||||||||
\(69\) | 4.82843 | 0.581274 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.8284 | 1.28510 | 0.642549 | − | 0.766245i | \(-0.277877\pi\) | ||||
0.642549 | + | 0.766245i | \(0.277877\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 7.65685 | 0.896167 | 0.448084 | − | 0.893992i | \(-0.352107\pi\) | ||||
0.448084 | + | 0.893992i | \(0.352107\pi\) | |||||||
\(74\) | −1.41421 | −0.164399 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −2.82843 | −0.324443 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3137 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.82843 | −0.974937 | ||||||||
\(83\) | −5.17157 | −0.567654 | −0.283827 | − | 0.958876i | \(-0.591604\pi\) | ||||
−0.283827 | + | 0.958876i | \(0.591604\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.41421 | 0.153393 | ||||||||
\(86\) | 4.58579 | 0.494498 | ||||||||
\(87\) | 8.24264 | 0.883704 | ||||||||
\(88\) | 0.585786 | 0.0624450 | ||||||||
\(89\) | −6.48528 | −0.687438 | −0.343719 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343719 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.82843 | 0.503398 | ||||||||
\(93\) | 5.07107 | 0.525845 | ||||||||
\(94\) | −9.07107 | −0.935609 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 8.82843 | 0.896391 | 0.448195 | − | 0.893936i | \(-0.352067\pi\) | ||||
0.448195 | + | 0.893936i | \(0.352067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.585786 | 0.0588738 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.34315 | −0.631167 | −0.315583 | − | 0.948898i | \(-0.602200\pi\) | ||||
−0.315583 | + | 0.948898i | \(0.602200\pi\) | |||||||
\(102\) | 1.41421 | 0.140028 | ||||||||
\(103\) | −10.1421 | −0.999334 | −0.499667 | − | 0.866217i | \(-0.666544\pi\) | ||||
−0.499667 | + | 0.866217i | \(0.666544\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.31371 | −0.904627 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 5.31371 | 0.508961 | 0.254480 | − | 0.967078i | \(-0.418096\pi\) | ||||
0.254480 | + | 0.967078i | \(0.418096\pi\) | |||||||
\(110\) | 0.585786 | 0.0558525 | ||||||||
\(111\) | −1.41421 | −0.134231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.31371 | 0.876160 | 0.438080 | − | 0.898936i | \(-0.355659\pi\) | ||||
0.438080 | + | 0.898936i | \(0.355659\pi\) | |||||||
\(114\) | −2.82843 | −0.264906 | ||||||||
\(115\) | 4.82843 | 0.450253 | ||||||||
\(116\) | 8.24264 | 0.765310 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.48528 | 0.228789 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | −11.6569 | −1.05536 | ||||||||
\(123\) | −8.82843 | −0.796032 | ||||||||
\(124\) | 5.07107 | 0.455395 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1421 | −1.25491 | −0.627456 | − | 0.778652i | \(-0.715904\pi\) | ||||
−0.627456 | + | 0.778652i | \(0.715904\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.58579 | 0.403756 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.8284 | −1.47031 | −0.735153 | − | 0.677901i | \(-0.762890\pi\) | ||||
−0.735153 | + | 0.677901i | \(0.762890\pi\) | |||||||
\(132\) | 0.585786 | 0.0509862 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.89949 | 0.682412 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 1.41421 | 0.121268 | ||||||||
\(137\) | −16.0000 | −1.36697 | −0.683486 | − | 0.729964i | \(-0.739537\pi\) | ||||
−0.683486 | + | 0.729964i | \(0.739537\pi\) | |||||||
\(138\) | 4.82843 | 0.411023 | ||||||||
\(139\) | 17.6569 | 1.49763 | 0.748817 | − | 0.662776i | \(-0.230622\pi\) | ||||
0.748817 | + | 0.662776i | \(0.230622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.07107 | −0.763922 | ||||||||
\(142\) | 10.8284 | 0.908701 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.24264 | 0.684514 | ||||||||
\(146\) | 7.65685 | 0.633686 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.41421 | −0.116248 | ||||||||
\(149\) | −13.8995 | −1.13869 | −0.569345 | − | 0.822098i | \(-0.692803\pi\) | ||||
−0.569345 | + | 0.822098i | \(0.692803\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 17.7990 | 1.44846 | 0.724231 | − | 0.689558i | \(-0.242195\pi\) | ||||
0.724231 | + | 0.689558i | \(0.242195\pi\) | |||||||
\(152\) | −2.82843 | −0.229416 | ||||||||
\(153\) | 1.41421 | 0.114332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.07107 | 0.407318 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.343146 | 0.0273860 | 0.0136930 | − | 0.999906i | \(-0.495641\pi\) | ||||
0.0136930 | + | 0.999906i | \(0.495641\pi\) | |||||||
\(158\) | −11.3137 | −0.900070 | ||||||||
\(159\) | −9.31371 | −0.738625 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 14.7279 | 1.15358 | 0.576790 | − | 0.816893i | \(-0.304305\pi\) | ||||
0.576790 | + | 0.816893i | \(0.304305\pi\) | |||||||
\(164\) | −8.82843 | −0.689384 | ||||||||
\(165\) | 0.585786 | 0.0456034 | ||||||||
\(166\) | −5.17157 | −0.401392 | ||||||||
\(167\) | 1.07107 | 0.0828817 | 0.0414409 | − | 0.999141i | \(-0.486805\pi\) | ||||
0.0414409 | + | 0.999141i | \(0.486805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 1.41421 | 0.108465 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 4.58579 | 0.349663 | ||||||||
\(173\) | 18.4853 | 1.40541 | 0.702705 | − | 0.711481i | \(-0.251975\pi\) | ||||
0.702705 | + | 0.711481i | \(0.251975\pi\) | |||||||
\(174\) | 8.24264 | 0.624873 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.585786 | 0.0441553 | ||||||||
\(177\) | 2.48528 | 0.186805 | ||||||||
\(178\) | −6.48528 | −0.486092 | ||||||||
\(179\) | 0.585786 | 0.0437837 | 0.0218919 | − | 0.999760i | \(-0.493031\pi\) | ||||
0.0218919 | + | 0.999760i | \(0.493031\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −8.82843 | −0.656212 | −0.328106 | − | 0.944641i | \(-0.606410\pi\) | ||||
−0.328106 | + | 0.944641i | \(0.606410\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.6569 | −0.861699 | ||||||||
\(184\) | 4.82843 | 0.355956 | ||||||||
\(185\) | −1.41421 | −0.103975 | ||||||||
\(186\) | 5.07107 | 0.371829 | ||||||||
\(187\) | 0.828427 | 0.0605806 | ||||||||
\(188\) | −9.07107 | −0.661576 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.82843 | −0.205196 | ||||||||
\(191\) | −11.3137 | −0.818631 | −0.409316 | − | 0.912393i | \(-0.634232\pi\) | ||||
−0.409316 | + | 0.912393i | \(0.634232\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −21.7990 | −1.56913 | −0.784563 | − | 0.620049i | \(-0.787113\pi\) | ||||
−0.784563 | + | 0.620049i | \(0.787113\pi\) | |||||||
\(194\) | 8.82843 | 0.633844 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.8284 | −1.48396 | −0.741982 | − | 0.670420i | \(-0.766114\pi\) | ||||
−0.741982 | + | 0.670420i | \(0.766114\pi\) | |||||||
\(198\) | 0.585786 | 0.0416300 | ||||||||
\(199\) | 2.92893 | 0.207626 | 0.103813 | − | 0.994597i | \(-0.466896\pi\) | ||||
0.103813 | + | 0.994597i | \(0.466896\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 7.89949 | 0.557187 | ||||||||
\(202\) | −6.34315 | −0.446302 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.41421 | 0.0990148 | ||||||||
\(205\) | −8.82843 | −0.616604 | ||||||||
\(206\) | −10.1421 | −0.706636 | ||||||||
\(207\) | 4.82843 | 0.335599 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.65685 | −0.114607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.65685 | −0.114063 | −0.0570313 | − | 0.998372i | \(-0.518163\pi\) | ||||
−0.0570313 | + | 0.998372i | \(0.518163\pi\) | |||||||
\(212\) | −9.31371 | −0.639668 | ||||||||
\(213\) | 10.8284 | 0.741952 | ||||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | 4.58579 | 0.312748 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.31371 | 0.359890 | ||||||||
\(219\) | 7.65685 | 0.517402 | ||||||||
\(220\) | 0.585786 | 0.0394937 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.41421 | −0.0949158 | ||||||||
\(223\) | 17.6569 | 1.18239 | 0.591195 | − | 0.806529i | \(-0.298656\pi\) | ||||
0.591195 | + | 0.806529i | \(0.298656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 9.31371 | 0.619539 | ||||||||
\(227\) | −13.6569 | −0.906437 | −0.453219 | − | 0.891399i | \(-0.649724\pi\) | ||||
−0.453219 | + | 0.891399i | \(0.649724\pi\) | |||||||
\(228\) | −2.82843 | −0.187317 | ||||||||
\(229\) | 25.7990 | 1.70485 | 0.852423 | − | 0.522853i | \(-0.175132\pi\) | ||||
0.852423 | + | 0.522853i | \(0.175132\pi\) | |||||||
\(230\) | 4.82843 | 0.318377 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.24264 | 0.541156 | ||||||||
\(233\) | 6.97056 | 0.456657 | 0.228328 | − | 0.973584i | \(-0.426674\pi\) | ||||
0.228328 | + | 0.973584i | \(0.426674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.07107 | −0.591731 | ||||||||
\(236\) | 2.48528 | 0.161778 | ||||||||
\(237\) | −11.3137 | −0.734904 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.3137 | 1.50804 | 0.754019 | − | 0.656852i | \(-0.228113\pi\) | ||||
0.754019 | + | 0.656852i | \(0.228113\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −16.2426 | −1.04628 | −0.523140 | − | 0.852247i | \(-0.675240\pi\) | ||||
−0.523140 | + | 0.852247i | \(0.675240\pi\) | |||||||
\(242\) | −10.6569 | −0.685049 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.6569 | −0.746254 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.82843 | −0.562880 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.07107 | 0.322013 | ||||||||
\(249\) | −5.17157 | −0.327735 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −17.6569 | −1.11449 | −0.557245 | − | 0.830348i | \(-0.688142\pi\) | ||||
−0.557245 | + | 0.830348i | \(0.688142\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.82843 | 0.177822 | ||||||||
\(254\) | −14.1421 | −0.887357 | ||||||||
\(255\) | 1.41421 | 0.0885615 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.89949 | 0.118487 | 0.0592436 | − | 0.998244i | \(-0.481131\pi\) | ||||
0.0592436 | + | 0.998244i | \(0.481131\pi\) | |||||||
\(258\) | 4.58579 | 0.285499 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.24264 | 0.510207 | ||||||||
\(262\) | −16.8284 | −1.03966 | ||||||||
\(263\) | −21.7990 | −1.34418 | −0.672092 | − | 0.740468i | \(-0.734604\pi\) | ||||
−0.672092 | + | 0.740468i | \(0.734604\pi\) | |||||||
\(264\) | 0.585786 | 0.0360527 | ||||||||
\(265\) | −9.31371 | −0.572137 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.48528 | −0.396893 | ||||||||
\(268\) | 7.89949 | 0.482538 | ||||||||
\(269\) | 7.65685 | 0.466847 | 0.233423 | − | 0.972375i | \(-0.425007\pi\) | ||||
0.233423 | + | 0.972375i | \(0.425007\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −14.2426 | −0.865179 | −0.432589 | − | 0.901591i | \(-0.642400\pi\) | ||||
−0.432589 | + | 0.901591i | \(0.642400\pi\) | |||||||
\(272\) | 1.41421 | 0.0857493 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.0000 | −0.966595 | ||||||||
\(275\) | 0.585786 | 0.0353243 | ||||||||
\(276\) | 4.82843 | 0.290637 | ||||||||
\(277\) | 21.8995 | 1.31581 | 0.657907 | − | 0.753100i | \(-0.271442\pi\) | ||||
0.657907 | + | 0.753100i | \(0.271442\pi\) | |||||||
\(278\) | 17.6569 | 1.05899 | ||||||||
\(279\) | 5.07107 | 0.303597 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5147 | −0.806221 | −0.403110 | − | 0.915151i | \(-0.632071\pi\) | ||||
−0.403110 | + | 0.915151i | \(0.632071\pi\) | |||||||
\(282\) | −9.07107 | −0.540174 | ||||||||
\(283\) | 30.4853 | 1.81216 | 0.906081 | − | 0.423104i | \(-0.139060\pi\) | ||||
0.906081 | + | 0.423104i | \(0.139060\pi\) | |||||||
\(284\) | 10.8284 | 0.642549 | ||||||||
\(285\) | −2.82843 | −0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | 8.24264 | 0.484025 | ||||||||
\(291\) | 8.82843 | 0.517532 | ||||||||
\(292\) | 7.65685 | 0.448084 | ||||||||
\(293\) | −28.6274 | −1.67243 | −0.836216 | − | 0.548401i | \(-0.815237\pi\) | ||||
−0.836216 | + | 0.548401i | \(0.815237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.48528 | 0.144699 | ||||||||
\(296\) | −1.41421 | −0.0821995 | ||||||||
\(297\) | 0.585786 | 0.0339908 | ||||||||
\(298\) | −13.8995 | −0.805176 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.7990 | 1.02422 | ||||||||
\(303\) | −6.34315 | −0.364404 | ||||||||
\(304\) | −2.82843 | −0.162221 | ||||||||
\(305\) | −11.6569 | −0.667470 | ||||||||
\(306\) | 1.41421 | 0.0808452 | ||||||||
\(307\) | −7.31371 | −0.417415 | −0.208708 | − | 0.977978i | \(-0.566926\pi\) | ||||
−0.208708 | + | 0.977978i | \(0.566926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.1421 | −0.576966 | ||||||||
\(310\) | 5.07107 | 0.288017 | ||||||||
\(311\) | −29.1716 | −1.65417 | −0.827084 | − | 0.562078i | \(-0.810002\pi\) | ||||
−0.827084 | + | 0.562078i | \(0.810002\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.8284 | 1.62948 | 0.814740 | − | 0.579827i | \(-0.196880\pi\) | ||||
0.814740 | + | 0.579827i | \(0.196880\pi\) | |||||||
\(314\) | 0.343146 | 0.0193648 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3137 | −0.636446 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | −9.31371 | −0.522287 | ||||||||
\(319\) | 4.82843 | 0.270340 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | −0.222566 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.7279 | 0.815704 | ||||||||
\(327\) | 5.31371 | 0.293849 | ||||||||
\(328\) | −8.82843 | −0.487468 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.585786 | 0.0322465 | ||||||||
\(331\) | −18.6274 | −1.02386 | −0.511928 | − | 0.859029i | \(-0.671068\pi\) | ||||
−0.511928 | + | 0.859029i | \(0.671068\pi\) | |||||||
\(332\) | −5.17157 | −0.283827 | ||||||||
\(333\) | −1.41421 | −0.0774984 | ||||||||
\(334\) | 1.07107 | 0.0586062 | ||||||||
\(335\) | 7.89949 | 0.431596 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.17157 | −0.172767 | −0.0863833 | − | 0.996262i | \(-0.527531\pi\) | ||||
−0.0863833 | + | 0.996262i | \(0.527531\pi\) | |||||||
\(338\) | −13.0000 | −0.707107 | ||||||||
\(339\) | 9.31371 | 0.505851 | ||||||||
\(340\) | 1.41421 | 0.0766965 | ||||||||
\(341\) | 2.97056 | 0.160865 | ||||||||
\(342\) | −2.82843 | −0.152944 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.58579 | 0.247249 | ||||||||
\(345\) | 4.82843 | 0.259954 | ||||||||
\(346\) | 18.4853 | 0.993775 | ||||||||
\(347\) | 1.65685 | 0.0889446 | 0.0444723 | − | 0.999011i | \(-0.485839\pi\) | ||||
0.0444723 | + | 0.999011i | \(0.485839\pi\) | |||||||
\(348\) | 8.24264 | 0.441852 | ||||||||
\(349\) | −5.79899 | −0.310413 | −0.155206 | − | 0.987882i | \(-0.549604\pi\) | ||||
−0.155206 | + | 0.987882i | \(0.549604\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.585786 | 0.0312225 | ||||||||
\(353\) | −0.727922 | −0.0387434 | −0.0193717 | − | 0.999812i | \(-0.506167\pi\) | ||||
−0.0193717 | + | 0.999812i | \(0.506167\pi\) | |||||||
\(354\) | 2.48528 | 0.132091 | ||||||||
\(355\) | 10.8284 | 0.574713 | ||||||||
\(356\) | −6.48528 | −0.343719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.585786 | 0.0309598 | ||||||||
\(359\) | 18.8284 | 0.993726 | 0.496863 | − | 0.867829i | \(-0.334485\pi\) | ||||
0.496863 | + | 0.867829i | \(0.334485\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −8.82843 | −0.464012 | ||||||||
\(363\) | −10.6569 | −0.559340 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.65685 | 0.400778 | ||||||||
\(366\) | −11.6569 | −0.609314 | ||||||||
\(367\) | 16.4853 | 0.860525 | 0.430262 | − | 0.902704i | \(-0.358421\pi\) | ||||
0.430262 | + | 0.902704i | \(0.358421\pi\) | |||||||
\(368\) | 4.82843 | 0.251699 | ||||||||
\(369\) | −8.82843 | −0.459590 | ||||||||
\(370\) | −1.41421 | −0.0735215 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.07107 | 0.262923 | ||||||||
\(373\) | 11.0711 | 0.573238 | 0.286619 | − | 0.958045i | \(-0.407469\pi\) | ||||
0.286619 | + | 0.958045i | \(0.407469\pi\) | |||||||
\(374\) | 0.828427 | 0.0428369 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −9.07107 | −0.467805 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.4853 | −1.25772 | −0.628862 | − | 0.777517i | \(-0.716479\pi\) | ||||
−0.628862 | + | 0.777517i | \(0.716479\pi\) | |||||||
\(380\) | −2.82843 | −0.145095 | ||||||||
\(381\) | −14.1421 | −0.724524 | ||||||||
\(382\) | −11.3137 | −0.578860 | ||||||||
\(383\) | 15.8995 | 0.812426 | 0.406213 | − | 0.913778i | \(-0.366849\pi\) | ||||
0.406213 | + | 0.913778i | \(0.366849\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.7990 | −1.10954 | ||||||||
\(387\) | 4.58579 | 0.233109 | ||||||||
\(388\) | 8.82843 | 0.448195 | ||||||||
\(389\) | 27.0711 | 1.37256 | 0.686279 | − | 0.727339i | \(-0.259243\pi\) | ||||
0.686279 | + | 0.727339i | \(0.259243\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.82843 | 0.345328 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.8284 | −0.848882 | ||||||||
\(394\) | −20.8284 | −1.04932 | ||||||||
\(395\) | −11.3137 | −0.569254 | ||||||||
\(396\) | 0.585786 | 0.0294369 | ||||||||
\(397\) | 20.6274 | 1.03526 | 0.517630 | − | 0.855604i | \(-0.326814\pi\) | ||||
0.517630 | + | 0.855604i | \(0.326814\pi\) | |||||||
\(398\) | 2.92893 | 0.146814 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −25.3137 | −1.26411 | −0.632053 | − | 0.774925i | \(-0.717788\pi\) | ||||
−0.632053 | + | 0.774925i | \(0.717788\pi\) | |||||||
\(402\) | 7.89949 | 0.393991 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.34315 | −0.315583 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.828427 | −0.0410636 | ||||||||
\(408\) | 1.41421 | 0.0700140 | ||||||||
\(409\) | −18.3848 | −0.909069 | −0.454534 | − | 0.890729i | \(-0.650194\pi\) | ||||
−0.454534 | + | 0.890729i | \(0.650194\pi\) | |||||||
\(410\) | −8.82843 | −0.436005 | ||||||||
\(411\) | −16.0000 | −0.789222 | ||||||||
\(412\) | −10.1421 | −0.499667 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.82843 | 0.237304 | ||||||||
\(415\) | −5.17157 | −0.253863 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.6569 | 0.864660 | ||||||||
\(418\) | −1.65685 | −0.0810394 | ||||||||
\(419\) | −17.6569 | −0.862594 | −0.431297 | − | 0.902210i | \(-0.641944\pi\) | ||||
−0.431297 | + | 0.902210i | \(0.641944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6274 | 0.810371 | 0.405185 | − | 0.914235i | \(-0.367207\pi\) | ||||
0.405185 | + | 0.914235i | \(0.367207\pi\) | |||||||
\(422\) | −1.65685 | −0.0806544 | ||||||||
\(423\) | −9.07107 | −0.441050 | ||||||||
\(424\) | −9.31371 | −0.452314 | ||||||||
\(425\) | 1.41421 | 0.0685994 | ||||||||
\(426\) | 10.8284 | 0.524639 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.58579 | 0.221146 | ||||||||
\(431\) | 14.1421 | 0.681203 | 0.340601 | − | 0.940208i | \(-0.389369\pi\) | ||||
0.340601 | + | 0.940208i | \(0.389369\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 8.82843 | 0.424267 | 0.212134 | − | 0.977241i | \(-0.431959\pi\) | ||||
0.212134 | + | 0.977241i | \(0.431959\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.24264 | 0.395204 | ||||||||
\(436\) | 5.31371 | 0.254480 | ||||||||
\(437\) | −13.6569 | −0.653296 | ||||||||
\(438\) | 7.65685 | 0.365859 | ||||||||
\(439\) | 33.5563 | 1.60156 | 0.800779 | − | 0.598960i | \(-0.204419\pi\) | ||||
0.800779 | + | 0.598960i | \(0.204419\pi\) | |||||||
\(440\) | 0.585786 | 0.0279263 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.6569 | 0.648857 | 0.324428 | − | 0.945910i | \(-0.394828\pi\) | ||||
0.324428 | + | 0.945910i | \(0.394828\pi\) | |||||||
\(444\) | −1.41421 | −0.0671156 | ||||||||
\(445\) | −6.48528 | −0.307432 | ||||||||
\(446\) | 17.6569 | 0.836076 | ||||||||
\(447\) | −13.8995 | −0.657424 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.1127 | −1.18514 | −0.592571 | − | 0.805518i | \(-0.701887\pi\) | ||||
−0.592571 | + | 0.805518i | \(0.701887\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −5.17157 | −0.243520 | ||||||||
\(452\) | 9.31371 | 0.438080 | ||||||||
\(453\) | 17.7990 | 0.836269 | ||||||||
\(454\) | −13.6569 | −0.640948 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.82843 | −0.132453 | ||||||||
\(457\) | −9.79899 | −0.458377 | −0.229189 | − | 0.973382i | \(-0.573607\pi\) | ||||
−0.229189 | + | 0.973382i | \(0.573607\pi\) | |||||||
\(458\) | 25.7990 | 1.20551 | ||||||||
\(459\) | 1.41421 | 0.0660098 | ||||||||
\(460\) | 4.82843 | 0.225127 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.6569 | 1.56417 | 0.782083 | − | 0.623174i | \(-0.214157\pi\) | ||||
0.782083 | + | 0.623174i | \(0.214157\pi\) | |||||||
\(464\) | 8.24264 | 0.382655 | ||||||||
\(465\) | 5.07107 | 0.235165 | ||||||||
\(466\) | 6.97056 | 0.322905 | ||||||||
\(467\) | −20.4853 | −0.947946 | −0.473973 | − | 0.880539i | \(-0.657181\pi\) | ||||
−0.473973 | + | 0.880539i | \(0.657181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.07107 | −0.418417 | ||||||||
\(471\) | 0.343146 | 0.0158113 | ||||||||
\(472\) | 2.48528 | 0.114394 | ||||||||
\(473\) | 2.68629 | 0.123516 | ||||||||
\(474\) | −11.3137 | −0.519656 | ||||||||
\(475\) | −2.82843 | −0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.31371 | −0.426445 | ||||||||
\(478\) | 23.3137 | 1.06634 | ||||||||
\(479\) | 16.4853 | 0.753232 | 0.376616 | − | 0.926370i | \(-0.377088\pi\) | ||||
0.376616 | + | 0.926370i | \(0.377088\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16.2426 | −0.739832 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.6569 | −0.484402 | ||||||||
\(485\) | 8.82843 | 0.400878 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 24.4853 | 1.10953 | 0.554767 | − | 0.832006i | \(-0.312807\pi\) | ||||
0.554767 | + | 0.832006i | \(0.312807\pi\) | |||||||
\(488\) | −11.6569 | −0.527681 | ||||||||
\(489\) | 14.7279 | 0.666020 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.8995 | 0.537017 | 0.268508 | − | 0.963277i | \(-0.413469\pi\) | ||||
0.268508 | + | 0.963277i | \(0.413469\pi\) | |||||||
\(492\) | −8.82843 | −0.398016 | ||||||||
\(493\) | 11.6569 | 0.524998 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.585786 | 0.0263291 | ||||||||
\(496\) | 5.07107 | 0.227698 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.17157 | −0.231744 | ||||||||
\(499\) | 15.7990 | 0.707260 | 0.353630 | − | 0.935385i | \(-0.384947\pi\) | ||||
0.353630 | + | 0.935385i | \(0.384947\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 1.07107 | 0.0478518 | ||||||||
\(502\) | −17.6569 | −0.788064 | ||||||||
\(503\) | 23.8995 | 1.06563 | 0.532813 | − | 0.846233i | \(-0.321135\pi\) | ||||
0.532813 | + | 0.846233i | \(0.321135\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.34315 | −0.282266 | ||||||||
\(506\) | 2.82843 | 0.125739 | ||||||||
\(507\) | −13.0000 | −0.577350 | ||||||||
\(508\) | −14.1421 | −0.627456 | ||||||||
\(509\) | −18.3431 | −0.813046 | −0.406523 | − | 0.913641i | \(-0.633259\pi\) | ||||
−0.406523 | + | 0.913641i | \(0.633259\pi\) | |||||||
\(510\) | 1.41421 | 0.0626224 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.82843 | −0.124878 | ||||||||
\(514\) | 1.89949 | 0.0837831 | ||||||||
\(515\) | −10.1421 | −0.446916 | ||||||||
\(516\) | 4.58579 | 0.201878 | ||||||||
\(517\) | −5.31371 | −0.233697 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.4853 | 0.811414 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.1421 | −0.531957 | −0.265978 | − | 0.963979i | \(-0.585695\pi\) | ||||
−0.265978 | + | 0.963979i | \(0.585695\pi\) | |||||||
\(522\) | 8.24264 | 0.360771 | ||||||||
\(523\) | −21.1127 | −0.923194 | −0.461597 | − | 0.887090i | \(-0.652723\pi\) | ||||
−0.461597 | + | 0.887090i | \(0.652723\pi\) | |||||||
\(524\) | −16.8284 | −0.735153 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.7990 | −0.950481 | ||||||||
\(527\) | 7.17157 | 0.312399 | ||||||||
\(528\) | 0.585786 | 0.0254931 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | −9.31371 | −0.404562 | ||||||||
\(531\) | 2.48528 | 0.107852 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.48528 | −0.280646 | ||||||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | 7.89949 | 0.341206 | ||||||||
\(537\) | 0.585786 | 0.0252786 | ||||||||
\(538\) | 7.65685 | 0.330110 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −2.48528 | −0.106851 | −0.0534253 | − | 0.998572i | \(-0.517014\pi\) | ||||
−0.0534253 | + | 0.998572i | \(0.517014\pi\) | |||||||
\(542\) | −14.2426 | −0.611774 | ||||||||
\(543\) | −8.82843 | −0.378864 | ||||||||
\(544\) | 1.41421 | 0.0606339 | ||||||||
\(545\) | 5.31371 | 0.227614 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.4142 | 1.17215 | 0.586074 | − | 0.810258i | \(-0.300673\pi\) | ||||
0.586074 | + | 0.810258i | \(0.300673\pi\) | |||||||
\(548\) | −16.0000 | −0.683486 | ||||||||
\(549\) | −11.6569 | −0.497502 | ||||||||
\(550\) | 0.585786 | 0.0249780 | ||||||||
\(551\) | −23.3137 | −0.993197 | ||||||||
\(552\) | 4.82843 | 0.205512 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.8995 | 0.930420 | ||||||||
\(555\) | −1.41421 | −0.0600300 | ||||||||
\(556\) | 17.6569 | 0.748817 | ||||||||
\(557\) | 12.6274 | 0.535041 | 0.267520 | − | 0.963552i | \(-0.413796\pi\) | ||||
0.267520 | + | 0.963552i | \(0.413796\pi\) | |||||||
\(558\) | 5.07107 | 0.214675 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.828427 | 0.0349762 | ||||||||
\(562\) | −13.5147 | −0.570084 | ||||||||
\(563\) | −26.1421 | −1.10176 | −0.550880 | − | 0.834585i | \(-0.685708\pi\) | ||||
−0.550880 | + | 0.834585i | \(0.685708\pi\) | |||||||
\(564\) | −9.07107 | −0.381961 | ||||||||
\(565\) | 9.31371 | 0.391831 | ||||||||
\(566\) | 30.4853 | 1.28139 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.8284 | 0.454351 | ||||||||
\(569\) | 34.9706 | 1.46604 | 0.733021 | − | 0.680206i | \(-0.238110\pi\) | ||||
0.733021 | + | 0.680206i | \(0.238110\pi\) | |||||||
\(570\) | −2.82843 | −0.118470 | ||||||||
\(571\) | 4.68629 | 0.196115 | 0.0980576 | − | 0.995181i | \(-0.468737\pi\) | ||||
0.0980576 | + | 0.995181i | \(0.468737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.3137 | −0.472637 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.82843 | 0.201359 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −12.1421 | −0.505484 | −0.252742 | − | 0.967534i | \(-0.581332\pi\) | ||||
−0.252742 | + | 0.967534i | \(0.581332\pi\) | |||||||
\(578\) | −15.0000 | −0.623918 | ||||||||
\(579\) | −21.7990 | −0.905935 | ||||||||
\(580\) | 8.24264 | 0.342257 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.82843 | 0.365950 | ||||||||
\(583\) | −5.45584 | −0.225958 | ||||||||
\(584\) | 7.65685 | 0.316843 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.6274 | −1.18259 | ||||||||
\(587\) | 19.7990 | 0.817192 | 0.408596 | − | 0.912715i | \(-0.366019\pi\) | ||||
0.408596 | + | 0.912715i | \(0.366019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.3431 | −0.590999 | ||||||||
\(590\) | 2.48528 | 0.102317 | ||||||||
\(591\) | −20.8284 | −0.856767 | ||||||||
\(592\) | −1.41421 | −0.0581238 | ||||||||
\(593\) | 37.2132 | 1.52816 | 0.764082 | − | 0.645120i | \(-0.223192\pi\) | ||||
0.764082 | + | 0.645120i | \(0.223192\pi\) | |||||||
\(594\) | 0.585786 | 0.0240351 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.8995 | −0.569345 | ||||||||
\(597\) | 2.92893 | 0.119873 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.68629 | 0.191477 | 0.0957383 | − | 0.995407i | \(-0.469479\pi\) | ||||
0.0957383 | + | 0.995407i | \(0.469479\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 42.1838 | 1.72071 | 0.860356 | − | 0.509694i | \(-0.170241\pi\) | ||||
0.860356 | + | 0.509694i | \(0.170241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.89949 | 0.321692 | ||||||||
\(604\) | 17.7990 | 0.724231 | ||||||||
\(605\) | −10.6569 | −0.433263 | ||||||||
\(606\) | −6.34315 | −0.257673 | ||||||||
\(607\) | −4.97056 | −0.201749 | −0.100874 | − | 0.994899i | \(-0.532164\pi\) | ||||
−0.100874 | + | 0.994899i | \(0.532164\pi\) | |||||||
\(608\) | −2.82843 | −0.114708 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.6569 | −0.471972 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.41421 | 0.0571662 | ||||||||
\(613\) | −5.21320 | −0.210559 | −0.105280 | − | 0.994443i | \(-0.533574\pi\) | ||||
−0.105280 | + | 0.994443i | \(0.533574\pi\) | |||||||
\(614\) | −7.31371 | −0.295157 | ||||||||
\(615\) | −8.82843 | −0.355997 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.2843 | −1.78282 | −0.891409 | − | 0.453200i | \(-0.850282\pi\) | ||||
−0.891409 | + | 0.453200i | \(0.850282\pi\) | |||||||
\(618\) | −10.1421 | −0.407977 | ||||||||
\(619\) | 1.85786 | 0.0746739 | 0.0373369 | − | 0.999303i | \(-0.488113\pi\) | ||||
0.0373369 | + | 0.999303i | \(0.488113\pi\) | |||||||
\(620\) | 5.07107 | 0.203659 | ||||||||
\(621\) | 4.82843 | 0.193758 | ||||||||
\(622\) | −29.1716 | −1.16967 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 28.8284 | 1.15222 | ||||||||
\(627\) | −1.65685 | −0.0661684 | ||||||||
\(628\) | 0.343146 | 0.0136930 | ||||||||
\(629\) | −2.00000 | −0.0797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.8284 | 0.988404 | 0.494202 | − | 0.869347i | \(-0.335460\pi\) | ||||
0.494202 | + | 0.869347i | \(0.335460\pi\) | |||||||
\(632\) | −11.3137 | −0.450035 | ||||||||
\(633\) | −1.65685 | −0.0658540 | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −14.1421 | −0.561214 | ||||||||
\(636\) | −9.31371 | −0.369313 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.82843 | 0.191159 | ||||||||
\(639\) | 10.8284 | 0.428366 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | −4.00000 | −0.157867 | ||||||||
\(643\) | 48.4264 | 1.90975 | 0.954876 | − | 0.297006i | \(-0.0959882\pi\) | ||||
0.954876 | + | 0.297006i | \(0.0959882\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.58579 | 0.180565 | ||||||||
\(646\) | −4.00000 | −0.157378 | ||||||||
\(647\) | 33.0711 | 1.30016 | 0.650079 | − | 0.759867i | \(-0.274736\pi\) | ||||
0.650079 | + | 0.759867i | \(0.274736\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 1.45584 | 0.0571469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.7279 | 0.576790 | ||||||||
\(653\) | 32.8284 | 1.28468 | 0.642338 | − | 0.766422i | \(-0.277965\pi\) | ||||
0.642338 | + | 0.766422i | \(0.277965\pi\) | |||||||
\(654\) | 5.31371 | 0.207782 | ||||||||
\(655\) | −16.8284 | −0.657541 | ||||||||
\(656\) | −8.82843 | −0.344692 | ||||||||
\(657\) | 7.65685 | 0.298722 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.1005 | 0.783005 | 0.391502 | − | 0.920177i | \(-0.371956\pi\) | ||||
0.391502 | + | 0.920177i | \(0.371956\pi\) | |||||||
\(660\) | 0.585786 | 0.0228017 | ||||||||
\(661\) | −27.6569 | −1.07573 | −0.537863 | − | 0.843032i | \(-0.680768\pi\) | ||||
−0.537863 | + | 0.843032i | \(0.680768\pi\) | |||||||
\(662\) | −18.6274 | −0.723975 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.17157 | −0.200696 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.41421 | −0.0547997 | ||||||||
\(667\) | 39.7990 | 1.54102 | ||||||||
\(668\) | 1.07107 | 0.0414409 | ||||||||
\(669\) | 17.6569 | 0.682653 | ||||||||
\(670\) | 7.89949 | 0.305184 | ||||||||
\(671\) | −6.82843 | −0.263609 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.5980 | 1.60348 | 0.801742 | − | 0.597670i | \(-0.203907\pi\) | ||||
0.801742 | + | 0.597670i | \(0.203907\pi\) | |||||||
\(674\) | −3.17157 | −0.122164 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 11.1716 | 0.429358 | 0.214679 | − | 0.976685i | \(-0.431129\pi\) | ||||
0.214679 | + | 0.976685i | \(0.431129\pi\) | |||||||
\(678\) | 9.31371 | 0.357691 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.41421 | 0.0542326 | ||||||||
\(681\) | −13.6569 | −0.523332 | ||||||||
\(682\) | 2.97056 | 0.113749 | ||||||||
\(683\) | 31.7990 | 1.21675 | 0.608377 | − | 0.793648i | \(-0.291821\pi\) | ||||
0.608377 | + | 0.793648i | \(0.291821\pi\) | |||||||
\(684\) | −2.82843 | −0.108148 | ||||||||
\(685\) | −16.0000 | −0.611329 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.7990 | 0.984293 | ||||||||
\(688\) | 4.58579 | 0.174831 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.82843 | 0.183815 | ||||||||
\(691\) | −12.2843 | −0.467316 | −0.233658 | − | 0.972319i | \(-0.575070\pi\) | ||||
−0.233658 | + | 0.972319i | \(0.575070\pi\) | |||||||
\(692\) | 18.4853 | 0.702705 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.65685 | 0.0628933 | ||||||||
\(695\) | 17.6569 | 0.669763 | ||||||||
\(696\) | 8.24264 | 0.312436 | ||||||||
\(697\) | −12.4853 | −0.472914 | ||||||||
\(698\) | −5.79899 | −0.219495 | ||||||||
\(699\) | 6.97056 | 0.263651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.5563 | −0.436477 | −0.218239 | − | 0.975895i | \(-0.570031\pi\) | ||||
−0.218239 | + | 0.975895i | \(0.570031\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0.585786 | 0.0220777 | ||||||||
\(705\) | −9.07107 | −0.341636 | ||||||||
\(706\) | −0.727922 | −0.0273957 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.48528 | 0.0934026 | ||||||||
\(709\) | −45.1127 | −1.69424 | −0.847121 | − | 0.531399i | \(-0.821666\pi\) | ||||
−0.847121 | + | 0.531399i | \(0.821666\pi\) | |||||||
\(710\) | 10.8284 | 0.406384 | ||||||||
\(711\) | −11.3137 | −0.424297 | ||||||||
\(712\) | −6.48528 | −0.243046 | ||||||||
\(713\) | 24.4853 | 0.916981 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.585786 | 0.0218919 | ||||||||
\(717\) | 23.3137 | 0.870666 | ||||||||
\(718\) | 18.8284 | 0.702671 | ||||||||
\(719\) | −12.2843 | −0.458126 | −0.229063 | − | 0.973412i | \(-0.573566\pi\) | ||||
−0.229063 | + | 0.973412i | \(0.573566\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.0000 | −0.409378 | ||||||||
\(723\) | −16.2426 | −0.604070 | ||||||||
\(724\) | −8.82843 | −0.328106 | ||||||||
\(725\) | 8.24264 | 0.306124 | ||||||||
\(726\) | −10.6569 | −0.395513 | ||||||||
\(727\) | 45.6569 | 1.69332 | 0.846659 | − | 0.532135i | \(-0.178610\pi\) | ||||
0.846659 | + | 0.532135i | \(0.178610\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.65685 | 0.283393 | ||||||||
\(731\) | 6.48528 | 0.239867 | ||||||||
\(732\) | −11.6569 | −0.430850 | ||||||||
\(733\) | −15.9411 | −0.588799 | −0.294399 | − | 0.955682i | \(-0.595120\pi\) | ||||
−0.294399 | + | 0.955682i | \(0.595120\pi\) | |||||||
\(734\) | 16.4853 | 0.608483 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.82843 | 0.177978 | ||||||||
\(737\) | 4.62742 | 0.170453 | ||||||||
\(738\) | −8.82843 | −0.324979 | ||||||||
\(739\) | −43.1127 | −1.58593 | −0.792963 | − | 0.609270i | \(-0.791463\pi\) | ||||
−0.792963 | + | 0.609270i | \(0.791463\pi\) | |||||||
\(740\) | −1.41421 | −0.0519875 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.65685 | 0.207530 | 0.103765 | − | 0.994602i | \(-0.466911\pi\) | ||||
0.103765 | + | 0.994602i | \(0.466911\pi\) | |||||||
\(744\) | 5.07107 | 0.185914 | ||||||||
\(745\) | −13.8995 | −0.509238 | ||||||||
\(746\) | 11.0711 | 0.405341 | ||||||||
\(747\) | −5.17157 | −0.189218 | ||||||||
\(748\) | 0.828427 | 0.0302903 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 25.5147 | 0.931045 | 0.465523 | − | 0.885036i | \(-0.345866\pi\) | ||||
0.465523 | + | 0.885036i | \(0.345866\pi\) | |||||||
\(752\) | −9.07107 | −0.330788 | ||||||||
\(753\) | −17.6569 | −0.643452 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.7990 | 0.647772 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.7574 | 0.863476 | 0.431738 | − | 0.901999i | \(-0.357901\pi\) | ||||
0.431738 | + | 0.901999i | \(0.357901\pi\) | |||||||
\(758\) | −24.4853 | −0.889345 | ||||||||
\(759\) | 2.82843 | 0.102665 | ||||||||
\(760\) | −2.82843 | −0.102598 | ||||||||
\(761\) | −18.9706 | −0.687682 | −0.343841 | − | 0.939028i | \(-0.611728\pi\) | ||||
−0.343841 | + | 0.939028i | \(0.611728\pi\) | |||||||
\(762\) | −14.1421 | −0.512316 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −11.3137 | −0.409316 | ||||||||
\(765\) | 1.41421 | 0.0511310 | ||||||||
\(766\) | 15.8995 | 0.574472 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −30.5858 | −1.10295 | −0.551476 | − | 0.834191i | \(-0.685935\pi\) | ||||
−0.551476 | + | 0.834191i | \(0.685935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.89949 | 0.0684086 | ||||||||
\(772\) | −21.7990 | −0.784563 | ||||||||
\(773\) | 28.3431 | 1.01943 | 0.509716 | − | 0.860343i | \(-0.329750\pi\) | ||||
0.509716 | + | 0.860343i | \(0.329750\pi\) | |||||||
\(774\) | 4.58579 | 0.164833 | ||||||||
\(775\) | 5.07107 | 0.182158 | ||||||||
\(776\) | 8.82843 | 0.316922 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.0711 | 0.970545 | ||||||||
\(779\) | 24.9706 | 0.894663 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.34315 | 0.226976 | ||||||||
\(782\) | 6.82843 | 0.244184 | ||||||||
\(783\) | 8.24264 | 0.294568 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.343146 | 0.0122474 | ||||||||
\(786\) | −16.8284 | −0.600250 | ||||||||
\(787\) | 28.9706 | 1.03269 | 0.516345 | − | 0.856381i | \(-0.327292\pi\) | ||||
0.516345 | + | 0.856381i | \(0.327292\pi\) | |||||||
\(788\) | −20.8284 | −0.741982 | ||||||||
\(789\) | −21.7990 | −0.776065 | ||||||||
\(790\) | −11.3137 | −0.402524 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.585786 | 0.0208150 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 20.6274 | 0.732040 | ||||||||
\(795\) | −9.31371 | −0.330323 | ||||||||
\(796\) | 2.92893 | 0.103813 | ||||||||
\(797\) | 26.4853 | 0.938157 | 0.469078 | − | 0.883157i | \(-0.344586\pi\) | ||||
0.469078 | + | 0.883157i | \(0.344586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.8284 | −0.453837 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −6.48528 | −0.229146 | ||||||||
\(802\) | −25.3137 | −0.893858 | ||||||||
\(803\) | 4.48528 | 0.158282 | ||||||||
\(804\) | 7.89949 | 0.278594 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.65685 | 0.269534 | ||||||||
\(808\) | −6.34315 | −0.223151 | ||||||||
\(809\) | 25.1127 | 0.882915 | 0.441458 | − | 0.897282i | \(-0.354462\pi\) | ||||
0.441458 | + | 0.897282i | \(0.354462\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −3.02944 | −0.106378 | −0.0531890 | − | 0.998584i | \(-0.516939\pi\) | ||||
−0.0531890 | + | 0.998584i | \(0.516939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.2426 | −0.499511 | ||||||||
\(814\) | −0.828427 | −0.0290364 | ||||||||
\(815\) | 14.7279 | 0.515897 | ||||||||
\(816\) | 1.41421 | 0.0495074 | ||||||||
\(817\) | −12.9706 | −0.453783 | ||||||||
\(818\) | −18.3848 | −0.642809 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.82843 | −0.308302 | ||||||||
\(821\) | −4.44365 | −0.155084 | −0.0775422 | − | 0.996989i | \(-0.524707\pi\) | ||||
−0.0775422 | + | 0.996989i | \(0.524707\pi\) | |||||||
\(822\) | −16.0000 | −0.558064 | ||||||||
\(823\) | 16.2843 | 0.567634 | 0.283817 | − | 0.958878i | \(-0.408399\pi\) | ||||
0.283817 | + | 0.958878i | \(0.408399\pi\) | |||||||
\(824\) | −10.1421 | −0.353318 | ||||||||
\(825\) | 0.585786 | 0.0203945 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.1127 | −0.386426 | −0.193213 | − | 0.981157i | \(-0.561891\pi\) | ||||
−0.193213 | + | 0.981157i | \(0.561891\pi\) | |||||||
\(828\) | 4.82843 | 0.167799 | ||||||||
\(829\) | −45.3137 | −1.57381 | −0.786905 | − | 0.617074i | \(-0.788318\pi\) | ||||
−0.786905 | + | 0.617074i | \(0.788318\pi\) | |||||||
\(830\) | −5.17157 | −0.179508 | ||||||||
\(831\) | 21.8995 | 0.759685 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 17.6569 | 0.611407 | ||||||||
\(835\) | 1.07107 | 0.0370658 | ||||||||
\(836\) | −1.65685 | −0.0573035 | ||||||||
\(837\) | 5.07107 | 0.175282 | ||||||||
\(838\) | −17.6569 | −0.609946 | ||||||||
\(839\) | 5.17157 | 0.178543 | 0.0892713 | − | 0.996007i | \(-0.471546\pi\) | ||||
0.0892713 | + | 0.996007i | \(0.471546\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.9411 | 1.34280 | ||||||||
\(842\) | 16.6274 | 0.573019 | ||||||||
\(843\) | −13.5147 | −0.465472 | ||||||||
\(844\) | −1.65685 | −0.0570313 | ||||||||
\(845\) | −13.0000 | −0.447214 | ||||||||
\(846\) | −9.07107 | −0.311870 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.31371 | −0.319834 | ||||||||
\(849\) | 30.4853 | 1.04625 | ||||||||
\(850\) | 1.41421 | 0.0485071 | ||||||||
\(851\) | −6.82843 | −0.234075 | ||||||||
\(852\) | 10.8284 | 0.370976 | ||||||||
\(853\) | 6.68629 | 0.228934 | 0.114467 | − | 0.993427i | \(-0.463484\pi\) | ||||
0.114467 | + | 0.993427i | \(0.463484\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.82843 | −0.0967302 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 27.2721 | 0.931596 | 0.465798 | − | 0.884891i | \(-0.345767\pi\) | ||||
0.465798 | + | 0.884891i | \(0.345767\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.9706 | 0.579028 | 0.289514 | − | 0.957174i | \(-0.406506\pi\) | ||||
0.289514 | + | 0.957174i | \(0.406506\pi\) | |||||||
\(860\) | 4.58579 | 0.156374 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.1421 | 0.481683 | ||||||||
\(863\) | −0.970563 | −0.0330383 | −0.0165192 | − | 0.999864i | \(-0.505258\pi\) | ||||
−0.0165192 | + | 0.999864i | \(0.505258\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 18.4853 | 0.628518 | ||||||||
\(866\) | 8.82843 | 0.300002 | ||||||||
\(867\) | −15.0000 | −0.509427 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.62742 | −0.224820 | ||||||||
\(870\) | 8.24264 | 0.279452 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.31371 | 0.179945 | ||||||||
\(873\) | 8.82843 | 0.298797 | ||||||||
\(874\) | −13.6569 | −0.461950 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.65685 | 0.258701 | ||||||||
\(877\) | 21.4142 | 0.723107 | 0.361553 | − | 0.932351i | \(-0.382247\pi\) | ||||
0.361553 | + | 0.932351i | \(0.382247\pi\) | |||||||
\(878\) | 33.5563 | 1.13247 | ||||||||
\(879\) | −28.6274 | −0.965579 | ||||||||
\(880\) | 0.585786 | 0.0197469 | ||||||||
\(881\) | 31.6569 | 1.06655 | 0.533273 | − | 0.845943i | \(-0.320962\pi\) | ||||
0.533273 | + | 0.845943i | \(0.320962\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.0416 | −0.337928 | −0.168964 | − | 0.985622i | \(-0.554042\pi\) | ||||
−0.168964 | + | 0.985622i | \(0.554042\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.48528 | 0.0835418 | ||||||||
\(886\) | 13.6569 | 0.458811 | ||||||||
\(887\) | −23.6985 | −0.795717 | −0.397859 | − | 0.917447i | \(-0.630247\pi\) | ||||
−0.397859 | + | 0.917447i | \(0.630247\pi\) | |||||||
\(888\) | −1.41421 | −0.0474579 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.48528 | −0.217387 | ||||||||
\(891\) | 0.585786 | 0.0196246 | ||||||||
\(892\) | 17.6569 | 0.591195 | ||||||||
\(893\) | 25.6569 | 0.858574 | ||||||||
\(894\) | −13.8995 | −0.464869 | ||||||||
\(895\) | 0.585786 | 0.0195807 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.1127 | −0.838022 | ||||||||
\(899\) | 41.7990 | 1.39407 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −13.1716 | −0.438809 | ||||||||
\(902\) | −5.17157 | −0.172195 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.31371 | 0.309769 | ||||||||
\(905\) | −8.82843 | −0.293467 | ||||||||
\(906\) | 17.7990 | 0.591332 | ||||||||
\(907\) | 43.2132 | 1.43487 | 0.717435 | − | 0.696625i | \(-0.245316\pi\) | ||||
0.717435 | + | 0.696625i | \(0.245316\pi\) | |||||||
\(908\) | −13.6569 | −0.453219 | ||||||||
\(909\) | −6.34315 | −0.210389 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.65685 | 0.187420 | 0.0937100 | − | 0.995600i | \(-0.470127\pi\) | ||||
0.0937100 | + | 0.995600i | \(0.470127\pi\) | |||||||
\(912\) | −2.82843 | −0.0936586 | ||||||||
\(913\) | −3.02944 | −0.100260 | ||||||||
\(914\) | −9.79899 | −0.324122 | ||||||||
\(915\) | −11.6569 | −0.385364 | ||||||||
\(916\) | 25.7990 | 0.852423 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.41421 | 0.0466760 | ||||||||
\(919\) | 26.7696 | 0.883046 | 0.441523 | − | 0.897250i | \(-0.354438\pi\) | ||||
0.441523 | + | 0.897250i | \(0.354438\pi\) | |||||||
\(920\) | 4.82843 | 0.159189 | ||||||||
\(921\) | −7.31371 | −0.240995 | ||||||||
\(922\) | −14.0000 | −0.461065 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.41421 | −0.0464991 | ||||||||
\(926\) | 33.6569 | 1.10603 | ||||||||
\(927\) | −10.1421 | −0.333111 | ||||||||
\(928\) | 8.24264 | 0.270578 | ||||||||
\(929\) | −11.6569 | −0.382449 | −0.191224 | − | 0.981546i | \(-0.561246\pi\) | ||||
−0.191224 | + | 0.981546i | \(0.561246\pi\) | |||||||
\(930\) | 5.07107 | 0.166287 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.97056 | 0.228328 | ||||||||
\(933\) | −29.1716 | −0.955034 | ||||||||
\(934\) | −20.4853 | −0.670299 | ||||||||
\(935\) | 0.828427 | 0.0270925 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.0294 | −0.556327 | −0.278164 | − | 0.960534i | \(-0.589726\pi\) | ||||
−0.278164 | + | 0.960534i | \(0.589726\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.8284 | 0.940780 | ||||||||
\(940\) | −9.07107 | −0.295866 | ||||||||
\(941\) | 36.2843 | 1.18283 | 0.591417 | − | 0.806366i | \(-0.298569\pi\) | ||||
0.591417 | + | 0.806366i | \(0.298569\pi\) | |||||||
\(942\) | 0.343146 | 0.0111803 | ||||||||
\(943\) | −42.6274 | −1.38814 | ||||||||
\(944\) | 2.48528 | 0.0808890 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.68629 | 0.0873389 | ||||||||
\(947\) | 36.4853 | 1.18561 | 0.592806 | − | 0.805345i | \(-0.298020\pi\) | ||||
0.592806 | + | 0.805345i | \(0.298020\pi\) | |||||||
\(948\) | −11.3137 | −0.367452 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.82843 | −0.0917663 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.5980 | −0.764414 | −0.382207 | − | 0.924077i | \(-0.624836\pi\) | ||||
−0.382207 | + | 0.924077i | \(0.624836\pi\) | |||||||
\(954\) | −9.31371 | −0.301542 | ||||||||
\(955\) | −11.3137 | −0.366103 | ||||||||
\(956\) | 23.3137 | 0.754019 | ||||||||
\(957\) | 4.82843 | 0.156081 | ||||||||
\(958\) | 16.4853 | 0.532615 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −5.28427 | −0.170460 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | −16.2426 | −0.523140 | ||||||||
\(965\) | −21.7990 | −0.701734 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.2843 | −1.42409 | −0.712043 | − | 0.702136i | \(-0.752230\pi\) | ||||
−0.712043 | + | 0.702136i | \(0.752230\pi\) | |||||||
\(968\) | −10.6569 | −0.342524 | ||||||||
\(969\) | −4.00000 | −0.128499 | ||||||||
\(970\) | 8.82843 | 0.283464 | ||||||||
\(971\) | 44.9706 | 1.44317 | 0.721587 | − | 0.692324i | \(-0.243413\pi\) | ||||
0.721587 | + | 0.692324i | \(0.243413\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 24.4853 | 0.784559 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.6569 | −0.373127 | ||||||||
\(977\) | 5.31371 | 0.170001 | 0.0850003 | − | 0.996381i | \(-0.472911\pi\) | ||||
0.0850003 | + | 0.996381i | \(0.472911\pi\) | |||||||
\(978\) | 14.7279 | 0.470947 | ||||||||
\(979\) | −3.79899 | −0.121416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.31371 | 0.169654 | ||||||||
\(982\) | 11.8995 | 0.379728 | ||||||||
\(983\) | −16.8701 | −0.538071 | −0.269036 | − | 0.963130i | \(-0.586705\pi\) | ||||
−0.269036 | + | 0.963130i | \(0.586705\pi\) | |||||||
\(984\) | −8.82843 | −0.281440 | ||||||||
\(985\) | −20.8284 | −0.663649 | ||||||||
\(986\) | 11.6569 | 0.371230 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.1421 | 0.704079 | ||||||||
\(990\) | 0.585786 | 0.0186175 | ||||||||
\(991\) | 20.8284 | 0.661637 | 0.330818 | − | 0.943694i | \(-0.392675\pi\) | ||||
0.330818 | + | 0.943694i | \(0.392675\pi\) | |||||||
\(992\) | 5.07107 | 0.161007 | ||||||||
\(993\) | −18.6274 | −0.591123 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.92893 | 0.0928534 | ||||||||
\(996\) | −5.17157 | −0.163868 | ||||||||
\(997\) | −2.68629 | −0.0850757 | −0.0425379 | − | 0.999095i | \(-0.513544\pi\) | ||||
−0.0425379 | + | 0.999095i | \(0.513544\pi\) | |||||||
\(998\) | 15.7990 | 0.500108 | ||||||||
\(999\) | −1.41421 | −0.0447437 |
(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 | 1470.2.a.v.1.1 | yes | 2 | |
3.2 | odd | 2 | 4410.2.a.bn.1.2 | 2 | |||
5.4 | even | 2 | 7350.2.a.dd.1.1 | 2 | |||
7.2 | even | 3 | 1470.2.i.u.361.2 | 4 | |||
7.3 | odd | 6 | 1470.2.i.v.961.2 | 4 | |||
7.4 | even | 3 | 1470.2.i.u.961.2 | 4 | |||
7.5 | odd | 6 | 1470.2.i.v.361.2 | 4 | |||
7.6 | odd | 2 | 1470.2.a.u.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 4410.2.a.br.1.2 | 2 | |||
35.34 | odd | 2 | 7350.2.a.df.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.a.u.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
1470.2.a.v.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1470.2.i.u.361.2 | 4 | 7.2 | even | 3 | |||
1470.2.i.u.961.2 | 4 | 7.4 | even | 3 | |||
1470.2.i.v.361.2 | 4 | 7.5 | odd | 6 | |||
1470.2.i.v.961.2 | 4 | 7.3 | odd | 6 | |||
4410.2.a.bn.1.2 | 2 | 3.2 | odd | 2 | |||
4410.2.a.br.1.2 | 2 | 21.20 | even | 2 | |||
7350.2.a.dd.1.1 | 2 | 5.4 | even | 2 | |||
7350.2.a.df.1.1 | 2 | 35.34 | odd | 2 |