Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3200,2,Mod(2049,3200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3200.2049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3200 = 2^{7} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3200.c (of order \(2\), degree \(1\), not 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: | \(25.5521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2049.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3200.2049 |
Dual form | 3200.2.c.bb.2049.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3200\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1151\) | \(2177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 0.414214i | − 0.239146i | −0.992825 | − | 0.119573i | \(-0.961847\pi\) | ||||
0.992825 | − | 0.119573i | \(-0.0381526\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.82843i | 1.82497i | 0.409106 | + | 0.912487i | \(0.365841\pi\) | ||||
−0.409106 | + | 0.912487i | \(0.634159\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.24264 | −0.977693 | −0.488846 | − | 0.872370i | \(-0.662582\pi\) | ||||
−0.488846 | + | 0.872370i | \(0.662582\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.65685i | − 1.56893i | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
0.620174 | − | 0.784465i | \(-0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.82843i | 1.41360i | 0.707413 | + | 0.706801i | \(0.249862\pi\) | ||||
−0.707413 | + | 0.706801i | \(0.750138\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.41421 | −1.01269 | −0.506345 | − | 0.862331i | \(-0.669004\pi\) | ||||
−0.506345 | + | 0.862331i | \(0.669004\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.828427i | 0.172739i | 0.996263 | + | 0.0863695i | \(0.0275266\pi\) | ||||
−0.996263 | + | 0.0863695i | \(0.972473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2.41421i | − 0.464616i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.82843 | 0.867211 | 0.433606 | − | 0.901103i | \(-0.357241\pi\) | ||||
0.433606 | + | 0.901103i | \(0.357241\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.34315i | 0.233812i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.65685i | 0.601183i | 0.953753 | + | 0.300592i | \(0.0971841\pi\) | ||||
−0.953753 | + | 0.300592i | \(0.902816\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.34315 | −0.375204 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.656854 | −0.102583 | −0.0512917 | − | 0.998684i | \(-0.516334\pi\) | ||||
−0.0512917 | + | 0.998684i | \(0.516334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000i | 1.52499i | 0.646997 | + | 0.762493i | \(0.276025\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.65685i | − 0.241677i | −0.992672 | − | 0.120839i | \(-0.961442\pi\) | ||||
0.992672 | − | 0.120839i | \(-0.0385583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.3137 | −2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.41421 | 0.338058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.65685i | 0.502308i | 0.967947 | + | 0.251154i | \(0.0808100\pi\) | ||||
−0.967947 | + | 0.251154i | \(0.919190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.82843i | 0.242181i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.65685 | −0.996838 | −0.498419 | − | 0.866936i | \(-0.666086\pi\) | ||||
−0.498419 | + | 0.866936i | \(0.666086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.6569i | 1.72060i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2426i | 1.37351i | 0.726890 | + | 0.686754i | \(0.240965\pi\) | ||||
−0.726890 | + | 0.686754i | \(0.759035\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.343146 | 0.0413099 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.65685 | 0.196632 | 0.0983162 | − | 0.995155i | \(-0.468654\pi\) | ||||
0.0983162 | + | 0.995155i | \(0.468654\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.171573i | 0.0200811i | 0.999950 | + | 0.0100405i | \(0.00319606\pi\) | ||||
−0.999950 | + | 0.0100405i | \(0.996804\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 15.6569i | − 1.78426i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.17157 | −0.806865 | −0.403432 | − | 0.915009i | \(-0.632183\pi\) | ||||
−0.403432 | + | 0.915009i | \(0.632183\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.24264i | − 0.794983i | −0.917606 | − | 0.397492i | \(-0.869881\pi\) | ||||
0.917606 | − | 0.397492i | \(-0.130119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 3.31371i | − 0.355267i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8284 | −1.25381 | −0.626905 | − | 0.779095i | \(-0.715679\pi\) | ||||
−0.626905 | + | 0.779095i | \(0.715679\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.3137 | 2.86325 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 2.00000i | − 0.207390i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 5.31371i | − 0.539525i | −0.962927 | − | 0.269763i | \(-0.913055\pi\) | ||||
0.962927 | − | 0.269763i | \(-0.0869453\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.17157 | −0.921778 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.9706 | −1.48963 | −0.744813 | − | 0.667273i | \(-0.767461\pi\) | ||||
−0.744813 | + | 0.667273i | \(0.767461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 9.65685i | − 0.951518i | −0.879576 | − | 0.475759i | \(-0.842173\pi\) | ||||
0.879576 | − | 0.475759i | \(-0.157827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0711i | 1.55365i | 0.629717 | + | 0.776824i | \(0.283171\pi\) | ||||
−0.629717 | + | 0.776824i | \(0.716829\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.343146 | 0.0328674 | 0.0164337 | − | 0.999865i | \(-0.494769\pi\) | ||||
0.0164337 | + | 0.999865i | \(0.494769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.51472 | 0.143771 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.6569i | 1.37880i | 0.724380 | + | 0.689400i | \(0.242126\pi\) | ||||
−0.724380 | + | 0.689400i | \(0.757874\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 16.0000i | − 1.47920i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −28.1421 | −2.57979 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.485281 | −0.0441165 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.272078i | 0.0245324i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.14214i | 0.722498i | 0.932469 | + | 0.361249i | \(0.117650\pi\) | ||||
−0.932469 | + | 0.361249i | \(0.882350\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.14214 | 0.364695 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3137 | −1.51271 | −0.756353 | − | 0.654164i | \(-0.773021\pi\) | ||||
−0.756353 | + | 0.654164i | \(0.773021\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 21.3137i | − 1.84813i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000i | 0.427179i | 0.976924 | + | 0.213589i | \(0.0685155\pi\) | ||||
−0.976924 | + | 0.213589i | \(0.931485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.89949 | 0.754845 | 0.377423 | − | 0.926041i | \(-0.376810\pi\) | ||||
0.377423 | + | 0.926041i | \(0.376810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.686292 | −0.0577962 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.3431i | 1.53393i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.75736i | 0.557338i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.3137 | 1.58224 | 0.791120 | − | 0.611661i | \(-0.209498\pi\) | ||||
0.791120 | + | 0.611661i | \(0.209498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4853 | −0.853280 | −0.426640 | − | 0.904422i | \(-0.640303\pi\) | ||||
−0.426640 | + | 0.904422i | \(0.640303\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.4853i | 1.33276i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.34315i | 0.665856i | 0.942952 | + | 0.332928i | \(0.108037\pi\) | ||||
−0.942952 | + | 0.332928i | \(0.891963\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.51472 | 0.120125 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.72792i | 0.448645i | 0.974515 | + | 0.224323i | \(0.0720170\pi\) | ||||
−0.974515 | + | 0.224323i | \(0.927983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.6569i | 1.05680i | 0.848996 | + | 0.528400i | \(0.177208\pi\) | ||||
−0.848996 | + | 0.528400i | \(0.822792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.0000 | −1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.4853 | −0.954773 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.65685i | 0.125968i | 0.998015 | + | 0.0629841i | \(0.0200618\pi\) | ||||
−0.998015 | + | 0.0629841i | \(0.979938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.17157i | 0.238390i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.4142 | −1.82480 | −0.912402 | − | 0.409295i | \(-0.865775\pi\) | ||||
−0.912402 | + | 0.409295i | \(0.865775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.34315 | −0.322823 | −0.161412 | − | 0.986887i | \(-0.551605\pi\) | ||||
−0.161412 | + | 0.986887i | \(0.551605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.48528i | 0.183717i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 18.8995i | − 1.38207i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.6569 | 0.847911 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.4853 | 1.33755 | 0.668774 | − | 0.743466i | \(-0.266819\pi\) | ||||
0.668774 | + | 0.743466i | \(0.266819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 13.8284i | − 0.995392i | −0.867352 | − | 0.497696i | \(-0.834180\pi\) | ||||
0.867352 | − | 0.497696i | \(-0.165820\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3.65685i | − 0.260540i | −0.991479 | − | 0.130270i | \(-0.958416\pi\) | ||||
0.991479 | − | 0.130270i | \(-0.0415844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.3431 | −1.01676 | −0.508379 | − | 0.861133i | \(-0.669755\pi\) | ||||
−0.508379 | + | 0.861133i | \(0.669755\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.65685 | 0.328469 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 38.6274i | 2.71111i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.34315i | 0.162860i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.3137 | 0.990100 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.89949 | 0.612666 | 0.306333 | − | 0.951924i | \(-0.400898\pi\) | ||||
0.306333 | + | 0.951924i | \(0.400898\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 0.686292i | − 0.0470239i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.3137i | 1.58264i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0710678 | 0.00480232 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.9706 | 2.21784 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.34315i | 0.156909i | 0.996918 | + | 0.0784543i | \(0.0249985\pi\) | ||||
−0.996918 | + | 0.0784543i | \(0.975002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.31371i | − 0.0871939i | −0.999049 | − | 0.0435969i | \(-0.986118\pi\) | ||||
0.999049 | − | 0.0435969i | \(-0.0138817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.3137 | 1.54061 | 0.770307 | − | 0.637674i | \(-0.220103\pi\) | ||||
0.770307 | + | 0.637674i | \(0.220103\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.48528 | −0.426700 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.31371i | 0.610161i | 0.952327 | + | 0.305081i | \(0.0986834\pi\) | ||||
−0.952327 | + | 0.305081i | \(0.901317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.97056i | 0.192959i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.6274 | 1.72238 | 0.861192 | − | 0.508279i | \(-0.169718\pi\) | ||||
0.861192 | + | 0.508279i | \(0.169718\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.17157 | 0.268715 | 0.134357 | − | 0.990933i | \(-0.457103\pi\) | ||||
0.134357 | + | 0.990933i | \(0.457103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 10.3431i | − 0.663513i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.9706i | 1.58884i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.00000 | −0.190117 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.2426 | 1.08835 | 0.544173 | − | 0.838973i | \(-0.316844\pi\) | ||||
0.544173 | + | 0.838973i | \(0.316844\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.68629i | − 0.168886i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.3137i | 1.08000i | 0.841665 | + | 0.540000i | \(0.181576\pi\) | ||||
−0.841665 | + | 0.540000i | \(0.818424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.6569 | −1.09714 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.6274 | 1.40060 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 6.48528i | − 0.399900i | −0.979806 | − | 0.199950i | \(-0.935922\pi\) | ||||
0.979806 | − | 0.199950i | \(-0.0640779\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.89949i | 0.299844i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.6569 | −1.07656 | −0.538279 | − | 0.842767i | \(-0.680925\pi\) | ||||
−0.538279 | + | 0.842767i | \(0.680925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.8284 | 1.50822 | 0.754110 | − | 0.656748i | \(-0.228069\pi\) | ||||
0.754110 | + | 0.656748i | \(0.228069\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 11.3137i | − 0.684737i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.65685i | − 0.0995507i | −0.998760 | − | 0.0497754i | \(-0.984149\pi\) | ||||
0.998760 | − | 0.0497754i | \(-0.0158505\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.6569 | 0.817614 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6274 | 1.46915 | 0.734574 | − | 0.678528i | \(-0.237382\pi\) | ||||
0.734574 | + | 0.678528i | \(0.237382\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.7279i | 0.934928i | 0.884012 | + | 0.467464i | \(0.154832\pi\) | ||||
−0.884012 | + | 0.467464i | \(0.845168\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3.17157i | − 0.187212i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9706 | −0.998268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.20101 | −0.129025 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.31371i | 0.310430i | 0.987881 | + | 0.155215i | \(0.0496071\pi\) | ||||
−0.987881 | + | 0.155215i | \(0.950393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.82843i | 0.454251i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.68629 | 0.271015 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −48.2843 | −2.78306 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.20101i | 0.356239i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5.24264i | − 0.299213i | −0.988746 | − | 0.149607i | \(-0.952199\pi\) | ||||
0.988746 | − | 0.149607i | \(-0.0478007\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.51472 | −0.312711 | −0.156356 | − | 0.987701i | \(-0.549975\pi\) | ||||
−0.156356 | + | 0.987701i | \(0.549975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 10.0000i | − 0.565233i | −0.959233 | − | 0.282617i | \(-0.908798\pi\) | ||||
0.959233 | − | 0.282617i | \(-0.0912024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.6569i | 0.767045i | 0.923531 | + | 0.383523i | \(0.125289\pi\) | ||||
−0.923531 | + | 0.383523i | \(0.874711\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.9411 | −1.45242 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.65685 | 0.371549 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 25.7279i | − 1.43154i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 0.142136i | − 0.00786012i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.10051 | 0.170419 | 0.0852096 | − | 0.996363i | \(-0.472844\pi\) | ||||
0.0852096 | + | 0.996363i | \(0.472844\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.3431i | 0.566801i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 18.6569i | − 1.01630i | −0.861268 | − | 0.508152i | \(-0.830329\pi\) | ||||
0.861268 | − | 0.508152i | \(-0.169671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.07107 | 0.329735 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.6569 | −0.847866 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 44.9706i | − 2.42818i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 0.899495i | − 0.0482874i | −0.999708 | − | 0.0241437i | \(-0.992314\pi\) | ||||
0.999708 | − | 0.0241437i | \(-0.00768593\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.68629 | 0.357909 | 0.178954 | − | 0.983857i | \(-0.442729\pi\) | ||||
0.178954 | + | 0.983857i | \(0.442729\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.6569 | −0.728949 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.6274i | 1.73658i | 0.496055 | + | 0.868291i | \(0.334781\pi\) | ||||
−0.496055 | + | 0.868291i | \(0.665219\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.6569i | 0.616946i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.17157 | −0.167389 | −0.0836946 | − | 0.996491i | \(-0.526672\pi\) | ||||
−0.0836946 | + | 0.996491i | \(0.526672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.485281 | 0.0255411 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.201010i | 0.0105503i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 32.9706i | − 1.72105i | −0.509409 | − | 0.860525i | \(-0.670136\pi\) | ||||
0.509409 | − | 0.860525i | \(-0.329864\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.85786 | −0.0967166 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.6569 | −0.916698 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6863i | 0.553315i | 0.960969 | + | 0.276658i | \(0.0892268\pi\) | ||||
−0.960969 | + | 0.276658i | \(0.910773\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 45.2548i | − 2.33074i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.89949 | −0.148937 | −0.0744685 | − | 0.997223i | \(-0.523726\pi\) | ||||
−0.0744685 | + | 0.997223i | \(0.523726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.37258 | 0.172783 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.4558i | 1.19854i | 0.800548 | + | 0.599269i | \(0.204542\pi\) | ||||
−0.800548 | + | 0.599269i | \(0.795458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.2843i | 1.43777i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.3137 | −0.877840 | −0.438920 | − | 0.898526i | \(-0.644639\pi\) | ||||
−0.438920 | + | 0.898526i | \(0.644639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.82843 | −0.244184 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.17157i | 0.361758i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 31.3137i | − 1.57159i | −0.618487 | − | 0.785795i | \(-0.712254\pi\) | ||||
0.618487 | − | 0.785795i | \(-0.287746\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.82843 | −0.441974 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.4558 | −1.52089 | −0.760446 | − | 0.649401i | \(-0.775020\pi\) | ||||
−0.760446 | + | 0.649401i | \(0.775020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 27.3137i | − 1.36059i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 11.8579i | − 0.587773i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.9706 | 1.38306 | 0.691528 | − | 0.722350i | \(-0.256938\pi\) | ||||
0.691528 | + | 0.722350i | \(0.256938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.07107 | 0.102158 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 36.9706i | − 1.81920i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 3.68629i | − 0.180518i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.5563 | 1.19966 | 0.599828 | − | 0.800129i | \(-0.295236\pi\) | ||||
0.599828 | + | 0.800129i | \(0.295236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | 0.194948 | 0.0974740 | − | 0.995238i | \(-0.468924\pi\) | ||||
0.0974740 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 4.68629i | − 0.227855i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 28.9706i | − 1.40198i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.59798 | 0.366834 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.1421 | −0.777539 | −0.388770 | − | 0.921335i | \(-0.627100\pi\) | ||||
−0.388770 | + | 0.921335i | \(0.627100\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 16.1716i | − 0.777156i | −0.921416 | − | 0.388578i | \(-0.872966\pi\) | ||||
0.921416 | − | 0.388578i | \(-0.127034\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.65685i | − 0.174931i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.3137 | −1.11270 | −0.556351 | − | 0.830947i | \(-0.687799\pi\) | ||||
−0.556351 | + | 0.830947i | \(0.687799\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.1421 | −2.19724 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8.55635i | − 0.406524i | −0.979124 | − | 0.203262i | \(-0.934846\pi\) | ||||
0.979124 | − | 0.203262i | \(-0.0651544\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 8.00000i | − 0.378387i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.4558 | −0.776599 | −0.388300 | − | 0.921533i | \(-0.626937\pi\) | ||||
−0.388300 | + | 0.921533i | \(0.626937\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.12994 | 0.100295 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.34315i | 0.204059i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 28.6569i | − 1.34051i | −0.742130 | − | 0.670256i | \(-0.766184\pi\) | ||||
0.742130 | − | 0.670256i | \(-0.233816\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.0711 | 0.656781 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.65685 | 0.263466 | 0.131733 | − | 0.991285i | \(-0.457946\pi\) | ||||
0.131733 | + | 0.991285i | \(0.457946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.9706i | 0.974585i | 0.873239 | + | 0.487292i | \(0.162015\pi\) | ||||
−0.873239 | + | 0.487292i | \(0.837985\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3137i | 0.616085i | 0.951373 | + | 0.308042i | \(0.0996739\pi\) | ||||
−0.951373 | + | 0.308042i | \(0.900326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.2843 | −2.50661 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.45584 | 0.159237 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 32.4264i | − 1.49097i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3431i | 0.473580i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.8284 | 1.86550 | 0.932749 | − | 0.360526i | \(-0.117403\pi\) | ||||
0.932749 | + | 0.360526i | \(0.117403\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.6863 | 0.943214 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.65685i | 0.0753895i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 37.1127i | − 1.68174i | −0.541240 | − | 0.840868i | \(-0.682045\pi\) | ||||
0.541240 | − | 0.840868i | \(-0.317955\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.37258 | 0.107292 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.6274 | 1.29194 | 0.645969 | − | 0.763364i | \(-0.276454\pi\) | ||||
0.645969 | + | 0.763364i | \(0.276454\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.6274i | 2.09999i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000i | 0.358849i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.65685 | 0.252730 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.9706i | 0.756680i | 0.925667 | + | 0.378340i | \(0.123505\pi\) | ||||
−0.925667 | + | 0.378340i | \(0.876495\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.87006i | 0.349522i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | 0.620539 | 0.310270 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310270 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.828427 | −0.0366475 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.6569i | 0.470512i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.37258i | 0.236286i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.686292 | 0.0301249 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.31371 | −0.276609 | −0.138304 | − | 0.990390i | \(-0.544165\pi\) | ||||
−0.138304 | + | 0.990390i | \(0.544165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 22.4142i | − 0.980105i | −0.871693 | − | 0.490053i | \(-0.836978\pi\) | ||||
0.871693 | − | 0.490053i | \(-0.163022\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.1421i | 1.22589i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3137 | 0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.6569 | −0.939827 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.71573i | 0.160946i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.1127i | 0.436395i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 52.8995 | 2.27854 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.34315 | 0.272713 | 0.136357 | − | 0.990660i | \(-0.456461\pi\) | ||||
0.136357 | + | 0.990660i | \(0.456461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.79899i | 0.0772020i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 16.5563i | − 0.707898i | −0.935265 | − | 0.353949i | \(-0.884839\pi\) | ||||
0.935265 | − | 0.353949i | \(-0.115161\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.9706 | −0.724286 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.3137 | −1.50441 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 34.6274i | − 1.47251i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 37.6569i | − 1.59557i | −0.602941 | − | 0.797786i | \(-0.706004\pi\) | ||||
0.602941 | − | 0.797786i | \(-0.293996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 56.5685 | 2.39259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.82843 | −0.330516 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.9706i | 1.13667i | 0.822796 | + | 0.568337i | \(0.192413\pi\) | ||||
−0.822796 | + | 0.568337i | \(0.807587\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.1421i | 1.51783i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.68629 | 0.154537 | 0.0772687 | − | 0.997010i | \(-0.475380\pi\) | ||||
0.0772687 | + | 0.997010i | \(0.475380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.9411 | −1.50409 | −0.752045 | − | 0.659112i | \(-0.770932\pi\) | ||||
−0.752045 | + | 0.659112i | \(0.770932\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 7.65685i | − 0.319870i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2843i | 0.636293i | 0.948042 | + | 0.318146i | \(0.103060\pi\) | ||||
−0.948042 | + | 0.318146i | \(0.896940\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.72792 | −0.238044 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.9706 | 1.45082 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 11.8579i | − 0.491103i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 14.0711i | − 0.580775i | −0.956909 | − | 0.290388i | \(-0.906216\pi\) | ||||
0.956909 | − | 0.290388i | \(-0.0937842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.3137 | −0.878216 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.51472 | −0.0623072 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 7.00000i | − 0.287456i | −0.989617 | − | 0.143728i | \(-0.954091\pi\) | ||||
0.989617 | − | 0.143728i | \(-0.0459090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.94113i | 0.243154i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.7696 | 1.91095 | 0.955476 | − | 0.295069i | \(-0.0953425\pi\) | ||||
0.955476 | + | 0.295069i | \(0.0953425\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.85786 | 0.279738 | 0.139869 | − | 0.990170i | \(-0.455332\pi\) | ||||
0.139869 | + | 0.990170i | \(0.455332\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.7990i | 1.29495i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 36.0000i | − 1.46119i | −0.682808 | − | 0.730597i | \(-0.739242\pi\) | ||||
0.682808 | − | 0.730597i | \(-0.260758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.0000 | 0.648353 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.37258 | −0.379174 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.3137i | 1.18397i | 0.805949 | + | 0.591985i | \(0.201655\pi\) | ||||
−0.805949 | + | 0.591985i | \(0.798345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.31371 | −0.374350 | −0.187175 | − | 0.982327i | \(-0.559933\pi\) | ||||
−0.187175 | + | 0.982327i | \(0.559933\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | 0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 57.1127i | − 2.28817i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 5.92893i | − 0.236779i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.3137 | −0.849833 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.1421 | 1.75727 | 0.878635 | − | 0.477493i | \(-0.158455\pi\) | ||||
0.878635 | + | 0.477493i | \(0.158455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 3.68629i | − 0.146517i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 92.2843i | 3.65644i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.68629 | 0.185387 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.6863 | −0.896055 | −0.448027 | − | 0.894020i | \(-0.647873\pi\) | ||||
−0.448027 | + | 0.894020i | \(0.647873\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 37.3137i | − 1.47151i | −0.677248 | − | 0.735755i | \(-0.736828\pi\) | ||||
0.677248 | − | 0.735755i | \(-0.263172\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 5.65685i | − 0.222394i | −0.993798 | − | 0.111197i | \(-0.964532\pi\) | ||||
0.993798 | − | 0.111197i | \(-0.0354684\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.8284 | 0.974601 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.65685 | 0.378482 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 6.00000i | − 0.234798i | −0.993085 | − | 0.117399i | \(-0.962544\pi\) | ||||
0.993085 | − | 0.117399i | \(-0.0374557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.485281i | 0.0189326i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.1838 | −0.981020 | −0.490510 | − | 0.871435i | \(-0.663190\pi\) | ||||
−0.490510 | + | 0.871435i | \(0.663190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.6569 | −0.686772 | −0.343386 | − | 0.939194i | \(-0.611574\pi\) | ||||
−0.343386 | + | 0.939194i | \(0.611574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 13.6569i | − 0.530388i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.62742i | 0.256615i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.970563 | 0.0375241 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.4558 | 0.751085 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 2.68629i | − 0.103549i | −0.998659 | − | 0.0517745i | \(-0.983512\pi\) | ||||
0.998659 | − | 0.0517745i | \(-0.0164877\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 51.3137i | 1.97215i | 0.166313 | + | 0.986073i | \(0.446814\pi\) | ||||
−0.166313 | + | 0.986073i | \(0.553186\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.6569 | 0.984620 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.544156 | −0.0208521 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 42.6985i | − 1.63381i | −0.576771 | − | 0.816906i | \(-0.695687\pi\) | ||||
0.576771 | − | 0.816906i | \(-0.304313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 9.65685i | − 0.368432i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.6863 | 0.788085 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.21320 | −0.236361 | −0.118181 | − | 0.992992i | \(-0.537706\pi\) | ||||
−0.118181 | + | 0.992992i | \(0.537706\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 44.2843i | − 1.68222i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 3.82843i | − 0.145012i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.85786 | 0.145918 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.6863 | 0.932388 | 0.466194 | − | 0.884682i | \(-0.345625\pi\) | ||||
0.466194 | + | 0.884682i | \(0.345625\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 16.1421i | − 0.608812i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 72.2843i | − 2.71853i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.9411 | 1.72536 | 0.862678 | − | 0.505754i | \(-0.168786\pi\) | ||||
0.862678 | + | 0.505754i | \(0.168786\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.2843 | −0.760720 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000i | 0.149801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 11.0294i | − 0.411902i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.4558 | −1.02393 | −0.511965 | − | 0.859006i | \(-0.671082\pi\) | ||||
−0.511965 | + | 0.859006i | \(0.671082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.6274 | 1.73650 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.72792i | − 0.0642621i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 32.0000i | − 1.18681i | −0.804902 | − | 0.593407i | \(-0.797782\pi\) | ||||
0.804902 | − | 0.593407i | \(-0.202218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.1716 | 0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −58.2843 | −2.15572 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.6569i | 1.39089i | 0.718580 | + | 0.695444i | \(0.244792\pi\) | ||||
−0.718580 | + | 0.695444i | \(0.755208\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 36.4558i | − 1.34287i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.6274 | −0.611649 | −0.305825 | − | 0.952088i | \(-0.598932\pi\) | ||||
−0.305825 | + | 0.952088i | \(0.598932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.3431 | 0.379965 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 13.7990i | − 0.506236i | −0.967435 | − | 0.253118i | \(-0.918544\pi\) | ||||
0.967435 | − | 0.253118i | \(-0.0814561\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 20.4853i | − 0.749517i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −77.5980 | −2.83537 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.6274 | 0.387800 | 0.193900 | − | 0.981021i | \(-0.437886\pi\) | ||||
0.193900 | + | 0.981021i | \(0.437886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 7.14214i | − 0.260274i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.3431i | 0.521310i | 0.965432 | + | 0.260655i | \(0.0839386\pi\) | ||||
−0.965432 | + | 0.260655i | \(0.916061\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.11270 | −0.0403884 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.2843 | 0.626554 | 0.313277 | − | 0.949662i | \(-0.398573\pi\) | ||||
0.313277 | + | 0.949662i | \(0.398573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.65685i | 0.0599822i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.3137i | 1.56397i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.1127 | 1.01377 | 0.506885 | − | 0.862014i | \(-0.330797\pi\) | ||||
0.506885 | + | 0.862014i | \(0.330797\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.17157 | 0.258278 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.31371i | 0.119186i | 0.998223 | + | 0.0595929i | \(0.0189803\pi\) | ||||
−0.998223 | + | 0.0595929i | \(0.981020\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.31371i | 0.262378i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.89949 | 0.103885 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.37258 | −0.192246 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 19.3137i | − 0.690216i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 28.6274i | − 1.02046i | −0.860039 | − | 0.510229i | \(-0.829561\pi\) | ||||
0.860039 | − | 0.510229i | \(-0.170439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.68629 | −0.0956345 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −70.7696 | −2.51628 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.9411i | 1.20528i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.0000i | 1.48772i | 0.668338 | + | 0.743858i | \(0.267006\pi\) | ||||
−0.668338 | + | 0.743858i | \(0.732994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.65685 | 0.341635 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.4558 | −1.18210 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 0.556349i | − 0.0196331i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.31371i | 0.257455i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.62742 | 0.162691 | 0.0813457 | − | 0.996686i | \(-0.474078\pi\) | ||||
0.0813457 | + | 0.996686i | \(0.474078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.9411 | 1.12160 | 0.560802 | − | 0.827950i | \(-0.310493\pi\) | ||||
0.560802 | + | 0.827950i | \(0.310493\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 10.2843i | − 0.360685i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 44.1421i | − 1.54434i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 77.2548 | 2.69950 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.62742 | −0.161498 | −0.0807490 | − | 0.996734i | \(-0.525731\pi\) | ||||
−0.0807490 | + | 0.996734i | \(0.525731\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.9706i | 0.730988i | 0.930814 | + | 0.365494i | \(0.119100\pi\) | ||||
−0.930814 | + | 0.365494i | \(0.880900\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.9289i | 1.17982i | 0.807467 | + | 0.589912i | \(0.200838\pi\) | ||||
−0.807467 | + | 0.589912i | \(0.799162\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0000 | 0.694629 | 0.347314 | − | 0.937749i | \(-0.387094\pi\) | ||||
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.686292 | −0.0238072 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 95.0833i | − 3.29444i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 11.6569i | − 0.402920i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.00000 | −0.138095 | −0.0690477 | − | 0.997613i | \(-0.521996\pi\) | ||||
−0.0690477 | + | 0.997613i | \(0.521996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 10.2010i | − 0.351341i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.34315i | − 0.0805114i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.51472 | 0.223585 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.02944 | −0.103848 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.6274i | 0.980184i | 0.871671 | + | 0.490092i | \(0.163037\pi\) | ||||
−0.871671 | + | 0.490092i | \(0.836963\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 11.0000i | − 0.375753i | −0.982193 | − | 0.187876i | \(-0.939840\pi\) | ||||
0.982193 | − | 0.187876i | \(-0.0601604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.7868 | −0.402160 | −0.201080 | − | 0.979575i | \(-0.564445\pi\) | ||||
−0.201080 | + | 0.979575i | \(0.564445\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.31371 | −0.0447711 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 4.00000i | − 0.136162i | −0.997680 | − | 0.0680808i | \(-0.978312\pi\) | ||||
0.997680 | − | 0.0680808i | \(-0.0216876\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.02944i | 0.238732i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.2548 | 0.788866 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.5980 | 2.15494 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 15.0294i | − 0.508669i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 37.6569i | − 1.27158i | −0.771861 | − | 0.635791i | \(-0.780674\pi\) | ||||
0.771861 | − | 0.635791i | \(-0.219326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.20101 | 0.0742382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.3137 | −1.25713 | −0.628565 | − | 0.777757i | \(-0.716358\pi\) | ||||
−0.628565 | + | 0.777757i | \(0.716358\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 34.7574i | − 1.16968i | −0.811149 | − | 0.584839i | \(-0.801158\pi\) | ||||
0.811149 | − | 0.584839i | \(-0.198842\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 33.6569i | − 1.13009i | −0.825061 | − | 0.565043i | \(-0.808859\pi\) | ||||
0.825061 | − | 0.565043i | \(-0.191141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39.3137 | −1.31854 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.2721 | −0.813145 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.31371i | 0.244744i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1.94113i | − 0.0648123i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.6274 | 1.28830 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.3137 | −0.710063 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.0000i | 0.665558i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 22.6863i | − 0.753286i | −0.926359 | − | 0.376643i | \(-0.877078\pi\) | ||||
0.926359 | − | 0.376643i | \(-0.122922\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −42.3431 | −1.40443 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.2843 | −0.672048 | −0.336024 | − | 0.941853i | \(-0.609082\pi\) | ||||
−0.336024 | + | 0.941853i | \(0.609082\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.4853i | 0.777249i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 83.5980i | − 2.76065i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.8284 | 1.47875 | 0.739377 | − | 0.673292i | \(-0.235120\pi\) | ||||
0.739377 | + | 0.673292i | \(0.235120\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.17157 | −0.0715558 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 9.37258i | − 0.308502i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 27.3137i | − 0.897100i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.6274 | 1.46418 | 0.732089 | − | 0.681209i | \(-0.238545\pi\) | ||||
0.732089 | + | 0.681209i | \(0.238545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 72.0122 | 2.36010 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.28427i | 0.0747837i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 42.1127i | − 1.37576i | −0.725824 | − | 0.687881i | \(-0.758541\pi\) | ||||
0.725824 | − | 0.687881i | \(-0.241459\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.14214 | −0.135173 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.02944 | −0.229153 | −0.114577 | − | 0.993414i | \(-0.536551\pi\) | ||||
−0.114577 | + | 0.993414i | \(0.536551\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 0.544156i | − 0.0177202i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.5980i | 1.48174i | 0.671651 | + | 0.740868i | \(0.265585\pi\) | ||||
−0.671651 | + | 0.740868i | \(0.734415\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.970563 | 0.0315058 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.65685 | 0.183436 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.3137i | 0.334094i | 0.985949 | + | 0.167047i | \(0.0534231\pi\) | ||||
−0.985949 | + | 0.167047i | \(0.946577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.7452i | 0.347342i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.1421 | −0.779590 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.68629 | −0.247945 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.4558i | 1.46479i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.62742i | 0.0844920i | 0.999107 | + | 0.0422460i | \(0.0134513\pi\) | ||||
−0.999107 | + | 0.0422460i | \(0.986549\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.6569 | −0.342347 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.1005 | 0.741330 | 0.370665 | − | 0.928767i | \(-0.379130\pi\) | ||||
0.370665 | + | 0.928767i | \(0.379130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.9706i | 1.37757i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.1127i | 1.21933i | 0.792658 | + | 0.609667i | \(0.208697\pi\) | ||||
−0.792658 | + | 0.609667i | \(0.791303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.3553 | 1.22584 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.970563 | 0.0309877 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 5.79899i | − 0.184959i | −0.995715 | − | 0.0924795i | \(-0.970521\pi\) | ||||
0.995715 | − | 0.0924795i | \(-0.0294793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 3.31371i | − 0.105477i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.28427 | −0.263425 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.0833 | −1.08269 | −0.541345 | − | 0.840800i | \(-0.682085\pi\) | ||||
−0.541345 | + | 0.840800i | \(0.682085\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 1.28427i | − 0.0407551i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 16.9706i | − 0.537463i | −0.963215 | − | 0.268732i | \(-0.913396\pi\) | ||||
0.963215 | − | 0.268732i | \(-0.0866045\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.82843 | 0.279319 |
(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 | 3200.2.c.bb.2049.2 | 4 | ||
4.3 | odd | 2 | 3200.2.c.z.2049.3 | 4 | |||
5.2 | odd | 4 | 3200.2.a.bj.1.1 | yes | 2 | ||
5.3 | odd | 4 | 3200.2.a.bh.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 3200.2.c.bb.2049.3 | 4 | ||
8.3 | odd | 2 | 3200.2.c.ba.2049.2 | 4 | |||
8.5 | even | 2 | 3200.2.c.y.2049.3 | 4 | |||
20.3 | even | 4 | 3200.2.a.bi.1.1 | yes | 2 | ||
20.7 | even | 4 | 3200.2.a.bg.1.2 | yes | 2 | ||
20.19 | odd | 2 | 3200.2.c.z.2049.2 | 4 | |||
40.3 | even | 4 | 3200.2.a.bd.1.2 | yes | 2 | ||
40.13 | odd | 4 | 3200.2.a.bm.1.1 | yes | 2 | ||
40.19 | odd | 2 | 3200.2.c.ba.2049.3 | 4 | |||
40.27 | even | 4 | 3200.2.a.bn.1.1 | yes | 2 | ||
40.29 | even | 2 | 3200.2.c.y.2049.2 | 4 | |||
40.37 | odd | 4 | 3200.2.a.bc.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3200.2.a.bc.1.2 | ✓ | 2 | 40.37 | odd | 4 | ||
3200.2.a.bd.1.2 | yes | 2 | 40.3 | even | 4 | ||
3200.2.a.bg.1.2 | yes | 2 | 20.7 | even | 4 | ||
3200.2.a.bh.1.2 | yes | 2 | 5.3 | odd | 4 | ||
3200.2.a.bi.1.1 | yes | 2 | 20.3 | even | 4 | ||
3200.2.a.bj.1.1 | yes | 2 | 5.2 | odd | 4 | ||
3200.2.a.bm.1.1 | yes | 2 | 40.13 | odd | 4 | ||
3200.2.a.bn.1.1 | yes | 2 | 40.27 | even | 4 | ||
3200.2.c.y.2049.2 | 4 | 40.29 | even | 2 | |||
3200.2.c.y.2049.3 | 4 | 8.5 | even | 2 | |||
3200.2.c.z.2049.2 | 4 | 20.19 | odd | 2 | |||
3200.2.c.z.2049.3 | 4 | 4.3 | odd | 2 | |||
3200.2.c.ba.2049.2 | 4 | 8.3 | odd | 2 | |||
3200.2.c.ba.2049.3 | 4 | 40.19 | odd | 2 | |||
3200.2.c.bb.2049.2 | 4 | 1.1 | even | 1 | trivial | ||
3200.2.c.bb.2049.3 | 4 | 5.4 | even | 2 | inner |