Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(2276,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2475.2276");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.7629745003\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2276.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.2276 |
Dual form | 2475.2.f.d.2276.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2475\mathbb{Z}\right)^\times\).
\(n\) | \(551\) | \(2026\) | \(2377\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | 0.353553 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421i | 0.534522i | 0.963624 | + | 0.267261i | \(0.0861187\pi\) | ||||
−0.963624 | + | 0.267261i | \(0.913881\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 1.41421i | 0.904534 | + | 0.426401i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.82843i | − | 0.784465i | −0.919866 | − | 0.392232i | \(-0.871703\pi\) | ||
0.919866 | − | 0.392232i | \(-0.128297\pi\) | |||||||
\(14\) | 1.41421i | 0.377964i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24264i | 0.973329i | 0.873589 | + | 0.486664i | \(0.161786\pi\) | ||||
−0.873589 | + | 0.486664i | \(0.838214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | + | 1.41421i | 0.639602 | + | 0.301511i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 2.82843i | − | 0.554700i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 1.41421i | − | 0.267261i | ||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 4.24264i | 0.688247i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.41421i | 0.215666i | 0.994169 | + | 0.107833i | \(0.0343911\pi\) | ||||
−0.994169 | + | 0.107833i | \(0.965609\pi\) | |||||||
\(44\) | −3.00000 | − | 1.41421i | −0.452267 | − | 0.213201i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.48528i | 1.23771i | 0.785507 | + | 0.618853i | \(0.212402\pi\) | ||||
−0.785507 | + | 0.618853i | \(0.787598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.82843i | 0.392232i | ||||||||
\(53\) | 4.24264i | 0.582772i | 0.956606 | + | 0.291386i | \(0.0941163\pi\) | ||||
−0.956606 | + | 0.291386i | \(0.905884\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 4.24264i | − | 0.566947i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | 8.48528i | 1.10469i | 0.833616 | + | 0.552345i | \(0.186267\pi\) | ||||
−0.833616 | + | 0.552345i | \(0.813733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.48528i | 1.08643i | 0.839594 | + | 0.543214i | \(0.182793\pi\) | ||||
−0.839594 | + | 0.543214i | \(0.817207\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | −2.00000 | −0.242536 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48528i | 1.00702i | 0.863990 | + | 0.503509i | \(0.167958\pi\) | ||||
−0.863990 | + | 0.503509i | \(0.832042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3137i | 1.32417i | 0.749429 | + | 0.662085i | \(0.230328\pi\) | ||||
−0.749429 | + | 0.662085i | \(0.769672\pi\) | |||||||
\(74\) | −6.00000 | −0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.24264i | − | 0.486664i | ||||||
\(77\) | −2.00000 | + | 4.24264i | −0.227921 | + | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7279i | 1.43200i | 0.698099 | + | 0.716002i | \(0.254030\pi\) | ||||
−0.698099 | + | 0.716002i | \(0.745970\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | 14.0000 | 1.53670 | 0.768350 | − | 0.640030i | \(-0.221078\pi\) | ||||
0.768350 | + | 0.640030i | \(0.221078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.41421i | 0.152499i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.00000 | − | 4.24264i | −0.959403 | − | 0.452267i | ||||
\(89\) | − | 7.07107i | − | 0.749532i | −0.927119 | − | 0.374766i | \(-0.877723\pi\) | ||
0.927119 | − | 0.374766i | \(-0.122277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.48528i | 0.875190i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0000 | −1.21842 | −0.609208 | − | 0.793011i | \(-0.708512\pi\) | ||||
−0.609208 | + | 0.793011i | \(0.708512\pi\) | |||||||
\(98\) | 5.00000 | 0.505076 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0000 | 1.18240 | 0.591198 | − | 0.806527i | \(-0.298655\pi\) | ||||
0.591198 | + | 0.806527i | \(0.298655\pi\) | |||||||
\(104\) | 8.48528i | 0.832050i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.24264i | 0.412082i | ||||||||
\(107\) | −14.0000 | −1.35343 | −0.676716 | − | 0.736245i | \(-0.736597\pi\) | ||||
−0.676716 | + | 0.736245i | \(0.736597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.9706i | 1.62549i | 0.582623 | + | 0.812743i | \(0.302026\pi\) | ||||
−0.582623 | + | 0.812743i | \(0.697974\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.41421i | − | 0.133631i | ||||||
\(113\) | − | 12.7279i | − | 1.19734i | −0.800995 | − | 0.598671i | \(-0.795696\pi\) | ||
0.800995 | − | 0.598671i | \(-0.204304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.48528i | 0.781133i | ||||||||
\(119\) | 2.82843i | 0.259281i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | + | 8.48528i | 0.636364 | + | 0.771389i | ||||
\(122\) | 8.48528i | 0.768221i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18.3848i | − | 1.63139i | −0.578486 | − | 0.815693i | \(-0.696356\pi\) | ||
0.578486 | − | 0.815693i | \(-0.303644\pi\) | |||||||
\(128\) | −3.00000 | −0.265165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0000 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | −0.520266 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | − | 4.24264i | − | 0.362473i | −0.983440 | − | 0.181237i | \(-0.941990\pi\) | ||
0.983440 | − | 0.181237i | \(-0.0580100\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.24264i | 0.359856i | 0.983680 | + | 0.179928i | \(0.0575865\pi\) | ||||
−0.983680 | + | 0.179928i | \(0.942414\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.48528i | 0.712069i | ||||||||
\(143\) | 4.00000 | − | 8.48528i | 0.334497 | − | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.3137i | 0.936329i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | 0.493197 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.24264i | 0.345261i | 0.984987 | + | 0.172631i | \(0.0552267\pi\) | ||||
−0.984987 | + | 0.172631i | \(0.944773\pi\) | |||||||
\(152\) | − | 12.7279i | − | 1.03237i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.00000 | + | 4.24264i | −0.161165 | + | 0.341882i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.0000 | 1.91541 | 0.957704 | − | 0.287754i | \(-0.0929087\pi\) | ||||
0.957704 | + | 0.287754i | \(0.0929087\pi\) | |||||||
\(158\) | 12.7279i | 1.01258i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.0000 | 1.87983 | 0.939913 | − | 0.341415i | \(-0.110906\pi\) | ||||
0.939913 | + | 0.341415i | \(0.110906\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.0000 | 1.08661 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1.41421i | − | 0.107833i | ||||||
\(173\) | −14.0000 | −1.06440 | −0.532200 | − | 0.846619i | \(-0.678635\pi\) | ||||
−0.532200 | + | 0.846619i | \(0.678635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | − | 1.41421i | −0.226134 | − | 0.106600i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 7.07107i | − | 0.529999i | ||||||
\(179\) | − | 5.65685i | − | 0.422813i | −0.977398 | − | 0.211407i | \(-0.932196\pi\) | ||
0.977398 | − | 0.211407i | \(-0.0678044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 4.00000 | 0.296500 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | + | 2.82843i | 0.438763 | + | 0.206835i | ||||
\(188\) | − | 8.48528i | − | 0.618853i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.82843i | 0.204658i | 0.994751 | + | 0.102329i | \(0.0326294\pi\) | ||||
−0.994751 | + | 0.102329i | \(0.967371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 19.7990i | − | 1.42516i | −0.701590 | − | 0.712581i | \(-0.747526\pi\) | ||
0.701590 | − | 0.712581i | \(-0.252474\pi\) | |||||||
\(194\) | −12.0000 | −0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | −0.357143 | ||||||||
\(197\) | 14.0000 | 0.997459 | 0.498729 | − | 0.866758i | \(-0.333800\pi\) | ||||
0.498729 | + | 0.866758i | \(0.333800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.00000 | −0.422159 | ||||||||
\(203\) | − | 8.48528i | − | 0.595550i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.0000 | 0.836080 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.82843i | 0.196116i | ||||||||
\(209\) | −6.00000 | + | 12.7279i | −0.415029 | + | 0.880409i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.24264i | 0.292075i | 0.989279 | + | 0.146038i | \(0.0466521\pi\) | ||||
−0.989279 | + | 0.146038i | \(0.953348\pi\) | |||||||
\(212\) | − | 4.24264i | − | 0.291386i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.0000 | −0.957020 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.9706i | 1.14939i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5.65685i | − | 0.380521i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | 7.07107i | 0.472456i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 12.7279i | − | 0.846649i | ||||||
\(227\) | 2.00000 | 0.132745 | 0.0663723 | − | 0.997795i | \(-0.478857\pi\) | ||||
0.0663723 | + | 0.997795i | \(0.478857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.0000 | 1.18176 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 8.48528i | − | 0.552345i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.82843i | 0.183340i | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.48528i | 0.546585i | 0.961931 | + | 0.273293i | \(0.0881127\pi\) | ||||
−0.961931 | + | 0.273293i | \(0.911887\pi\) | |||||||
\(242\) | 7.00000 | + | 8.48528i | 0.449977 | + | 0.545455i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.48528i | − | 0.543214i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | 0.763542 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 16.9706i | − | 1.07117i | −0.844481 | − | 0.535586i | \(-0.820091\pi\) | ||
0.844481 | − | 0.535586i | \(-0.179909\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 18.3848i | − | 1.15356i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | − | 29.6985i | − | 1.85254i | −0.376860 | − | 0.926270i | \(-0.622996\pi\) | ||
0.376860 | − | 0.926270i | \(-0.377004\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.48528i | − | 0.527250i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.0000 | −1.11204 | ||||||||
\(263\) | −8.00000 | −0.493301 | −0.246651 | − | 0.969104i | \(-0.579330\pi\) | ||||
−0.246651 | + | 0.969104i | \(0.579330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.00000 | −0.367884 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.7279i | 0.776035i | 0.921652 | + | 0.388018i | \(0.126840\pi\) | ||||
−0.921652 | + | 0.388018i | \(0.873160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7279i | 0.773166i | 0.922255 | + | 0.386583i | \(0.126345\pi\) | ||||
−0.922255 | + | 0.386583i | \(0.873655\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 4.24264i | − | 0.256307i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.1127i | 1.86938i | 0.355463 | + | 0.934690i | \(0.384323\pi\) | ||||
−0.355463 | + | 0.934690i | \(0.615677\pi\) | |||||||
\(278\) | 4.24264i | 0.254457i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.41421i | − | 0.0840663i | −0.999116 | − | 0.0420331i | \(-0.986616\pi\) | ||
0.999116 | − | 0.0420331i | \(-0.0133835\pi\) | |||||||
\(284\) | − | 8.48528i | − | 0.503509i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | − | 8.48528i | 0.236525 | − | 0.501745i | ||||
\(287\) | − | 8.48528i | − | 0.500870i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 11.3137i | − | 0.662085i | ||||||
\(293\) | −10.0000 | −0.584206 | −0.292103 | − | 0.956387i | \(-0.594355\pi\) | ||||
−0.292103 | + | 0.956387i | \(0.594355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 18.0000 | 1.04623 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.0000 | −1.04271 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | 4.24264i | 0.244137i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.24264i | − | 0.243332i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.0416i | − | 1.37213i | −0.727541 | − | 0.686064i | \(-0.759337\pi\) | ||
0.727541 | − | 0.686064i | \(-0.240663\pi\) | |||||||
\(308\) | 2.00000 | − | 4.24264i | 0.113961 | − | 0.241747i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.9706i | 0.962312i | 0.876635 | + | 0.481156i | \(0.159783\pi\) | ||||
−0.876635 | + | 0.481156i | \(0.840217\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 24.0000 | 1.35440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 12.7279i | − | 0.716002i | ||||||
\(317\) | − | 21.2132i | − | 1.19145i | −0.803188 | − | 0.595726i | \(-0.796864\pi\) | ||
0.803188 | − | 0.595726i | \(-0.203136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | − | 8.48528i | −1.00781 | − | 0.475085i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.48528i | 0.472134i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.0000 | 1.32924 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.0000 | 0.993884 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | −14.0000 | −0.768350 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.3137i | 0.616297i | 0.951338 | + | 0.308148i | \(0.0997094\pi\) | ||||
−0.951338 | + | 0.308148i | \(0.900291\pi\) | |||||||
\(338\) | 5.00000 | 0.271964 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | − | 4.24264i | − | 0.228748i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.0000 | −0.752645 | ||||||||
\(347\) | 14.0000 | 0.751559 | 0.375780 | − | 0.926709i | \(-0.377375\pi\) | ||||
0.375780 | + | 0.926709i | \(0.377375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.48528i | 0.454207i | 0.973871 | + | 0.227103i | \(0.0729255\pi\) | ||||
−0.973871 | + | 0.227103i | \(0.927074\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.0000 | + | 7.07107i | 0.799503 | + | 0.376889i | ||||
\(353\) | − | 4.24264i | − | 0.225813i | −0.993606 | − | 0.112906i | \(-0.963984\pi\) | ||
0.993606 | − | 0.112906i | \(-0.0360161\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.07107i | 0.374766i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 5.65685i | − | 0.298974i | ||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.00000 | −0.209657 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.0000 | −0.626395 | −0.313197 | − | 0.949688i | \(-0.601400\pi\) | ||||
−0.313197 | + | 0.949688i | \(0.601400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | −0.311504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.6274i | − | 1.17160i | −0.810454 | − | 0.585802i | \(-0.800780\pi\) | ||
0.810454 | − | 0.585802i | \(-0.199220\pi\) | |||||||
\(374\) | 6.00000 | + | 2.82843i | 0.310253 | + | 0.146254i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 25.4558i | − | 1.31278i | ||||||
\(377\) | 16.9706i | 0.874028i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.82843i | 0.144715i | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 19.7990i | − | 1.00774i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.0000 | 0.609208 | ||||||||
\(389\) | 21.2132i | 1.07555i | 0.843088 | + | 0.537776i | \(0.180735\pi\) | ||||
−0.843088 | + | 0.537776i | \(0.819265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −15.0000 | −0.757614 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.0000 | 0.705310 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00000 | 0.301131 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(398\) | 20.0000 | 1.00251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8701i | 1.34183i | 0.741536 | + | 0.670913i | \(0.234098\pi\) | ||||
−0.741536 | + | 0.670913i | \(0.765902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 8.48528i | − | 0.421117i | ||||||
\(407\) | −18.0000 | − | 8.48528i | −0.892227 | − | 0.420600i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.48528i | − | 0.419570i | −0.977748 | − | 0.209785i | \(-0.932724\pi\) | ||
0.977748 | − | 0.209785i | \(-0.0672764\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.0000 | −0.591198 | ||||||||
\(413\) | −12.0000 | −0.590481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 14.1421i | − | 0.693375i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.00000 | + | 12.7279i | −0.293470 | + | 0.622543i | ||||
\(419\) | − | 39.5980i | − | 1.93449i | −0.253849 | − | 0.967244i | \(-0.581697\pi\) | ||
0.253849 | − | 0.967244i | \(-0.418303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.0000 | 1.16969 | 0.584844 | − | 0.811146i | \(-0.301156\pi\) | ||||
0.584844 | + | 0.811146i | \(0.301156\pi\) | |||||||
\(422\) | 4.24264i | 0.206529i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 12.7279i | − | 0.618123i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0000 | −0.580721 | ||||||||
\(428\) | 14.0000 | 0.676716 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.0000 | 0.867029 | 0.433515 | − | 0.901146i | \(-0.357273\pi\) | ||||
0.433515 | + | 0.901146i | \(0.357273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0000 | 0.865025 | 0.432512 | − | 0.901628i | \(-0.357627\pi\) | ||||
0.432512 | + | 0.901628i | \(0.357627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 16.9706i | − | 0.812743i | ||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 38.1838i | − | 1.82241i | −0.411951 | − | 0.911206i | \(-0.635153\pi\) | ||
0.411951 | − | 0.911206i | \(-0.364847\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 5.65685i | − | 0.269069i | ||||||
\(443\) | − | 25.4558i | − | 1.20944i | −0.796437 | − | 0.604722i | \(-0.793284\pi\) | ||
0.796437 | − | 0.604722i | \(-0.206716\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.0000 | −1.13643 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.89949i | 0.467707i | ||||||||
\(449\) | − | 32.5269i | − | 1.53504i | −0.641025 | − | 0.767520i | \(-0.721491\pi\) | ||
0.641025 | − | 0.767520i | \(-0.278509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | − | 8.48528i | −0.847587 | − | 0.399556i | ||||
\(452\) | 12.7279i | 0.598671i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.00000 | 0.0938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 28.2843i | − | 1.32308i | −0.749909 | − | 0.661541i | \(-0.769903\pi\) | ||
0.749909 | − | 0.661541i | \(-0.230097\pi\) | |||||||
\(458\) | 14.0000 | 0.654177 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000 | 1.11537 | 0.557687 | − | 0.830051i | \(-0.311689\pi\) | ||||
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.0000 | −0.463241 | ||||||||
\(467\) | 8.48528i | 0.392652i | 0.980539 | + | 0.196326i | \(0.0629011\pi\) | ||||
−0.980539 | + | 0.196326i | \(0.937099\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 25.4558i | − | 1.17170i | ||||||
\(473\) | −2.00000 | + | 4.24264i | −0.0919601 | + | 0.195077i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 2.82843i | − | 0.129641i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.00000 | 0.274434 | ||||||||
\(479\) | 6.00000 | 0.274147 | 0.137073 | − | 0.990561i | \(-0.456230\pi\) | ||||
0.137073 | + | 0.990561i | \(0.456230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9706i | 0.773791i | ||||||||
\(482\) | 8.48528i | 0.386494i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | − | 8.48528i | −0.318182 | − | 0.385695i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | 0.543772 | 0.271886 | − | 0.962329i | \(-0.412353\pi\) | ||||
0.271886 | + | 0.962329i | \(0.412353\pi\) | |||||||
\(488\) | − | 25.4558i | − | 1.15233i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | −0.540453 | ||||||||
\(494\) | 12.0000 | 0.539906 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.0000 | −1.43252 | −0.716258 | − | 0.697835i | \(-0.754147\pi\) | ||||
−0.716258 | + | 0.697835i | \(0.754147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 16.9706i | − | 0.757433i | ||||||
\(503\) | 16.0000 | 0.713405 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.3848i | 0.815693i | ||||||||
\(509\) | 4.24264i | 0.188052i | 0.995570 | + | 0.0940259i | \(0.0299736\pi\) | ||||
−0.995570 | + | 0.0940259i | \(0.970026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 29.6985i | − | 1.30994i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | + | 25.4558i | −0.527759 | + | 1.11955i | ||||
\(518\) | − | 8.48528i | − | 0.372822i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.07107i | − | 0.309789i | −0.987931 | − | 0.154895i | \(-0.950496\pi\) | ||
0.987931 | − | 0.154895i | \(-0.0495038\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.07107i | 0.309196i | 0.987977 | + | 0.154598i | \(0.0494083\pi\) | ||||
−0.987977 | + | 0.154598i | \(0.950592\pi\) | |||||||
\(524\) | 18.0000 | 0.786334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00000 | −0.348817 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.00000 | 0.260133 | ||||||||
\(533\) | 16.9706i | 0.735077i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.7279i | 0.548740i | ||||||||
\(539\) | 15.0000 | + | 7.07107i | 0.646096 | + | 0.304572i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.9411i | 1.45924i | 0.683851 | + | 0.729621i | \(0.260304\pi\) | ||||
−0.683851 | + | 0.729621i | \(0.739696\pi\) | |||||||
\(542\) | 12.7279i | 0.546711i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.0000 | 0.428746 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.89949i | 0.423272i | 0.977349 | + | 0.211636i | \(0.0678791\pi\) | ||||
−0.977349 | + | 0.211636i | \(0.932121\pi\) | |||||||
\(548\) | 4.24264i | 0.181237i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 25.4558i | − | 1.08446i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.0000 | −0.765438 | ||||||||
\(554\) | 31.1127i | 1.32185i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 4.24264i | − | 0.179928i | ||||||
\(557\) | 34.0000 | 1.44063 | 0.720313 | − | 0.693649i | \(-0.243998\pi\) | ||||
0.720313 | + | 0.693649i | \(0.243998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 1.41421i | − | 0.0594438i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 25.4558i | − | 1.06810i | ||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.24264i | 0.177549i | 0.996052 | + | 0.0887745i | \(0.0282950\pi\) | ||||
−0.996052 | + | 0.0887745i | \(0.971705\pi\) | |||||||
\(572\) | −4.00000 | + | 8.48528i | −0.167248 | + | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 8.48528i | − | 0.354169i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | −13.0000 | −0.540729 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.7990i | 0.821401i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | + | 12.7279i | −0.248495 | + | 0.527137i | ||||
\(584\) | − | 33.9411i | − | 1.40449i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.0000 | −0.413096 | ||||||||
\(587\) | 42.4264i | 1.75113i | 0.483105 | + | 0.875563i | \(0.339509\pi\) | ||||
−0.483105 | + | 0.875563i | \(0.660491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000 | 0.246598 | ||||||||
\(593\) | 2.00000 | 0.0821302 | 0.0410651 | − | 0.999156i | \(-0.486925\pi\) | ||||
0.0410651 | + | 0.999156i | \(0.486925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3137i | 0.462266i | 0.972922 | + | 0.231133i | \(0.0742432\pi\) | ||||
−0.972922 | + | 0.231133i | \(0.925757\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 33.9411i | − | 1.38449i | −0.721664 | − | 0.692244i | \(-0.756622\pi\) | ||
0.721664 | − | 0.692244i | \(-0.243378\pi\) | |||||||
\(602\) | −2.00000 | −0.0815139 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 4.24264i | − | 0.172631i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.5269i | 1.32023i | 0.751166 | + | 0.660113i | \(0.229492\pi\) | ||||
−0.751166 | + | 0.660113i | \(0.770508\pi\) | |||||||
\(608\) | 21.2132i | 0.860309i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 28.2843i | − | 1.14239i | −0.820814 | − | 0.571195i | \(-0.806480\pi\) | ||
0.820814 | − | 0.571195i | \(-0.193520\pi\) | |||||||
\(614\) | − | 24.0416i | − | 0.970241i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.00000 | − | 12.7279i | 0.241747 | − | 0.512823i | ||||
\(617\) | 4.24264i | 0.170802i | 0.996347 | + | 0.0854011i | \(0.0272172\pi\) | ||||
−0.996347 | + | 0.0854011i | \(0.972783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.9706i | 0.680458i | ||||||||
\(623\) | 10.0000 | 0.400642 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.00000 | −0.239808 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −24.0000 | −0.957704 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | − | 38.1838i | − | 1.51887i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 21.2132i | − | 0.842484i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 14.1421i | − | 0.560332i | ||||||
\(638\) | −18.0000 | − | 8.48528i | −0.712627 | − | 0.335936i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 15.5563i | − | 0.614439i | −0.951639 | − | 0.307219i | \(-0.900601\pi\) | ||
0.951639 | − | 0.307219i | \(-0.0993986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0000 | −0.473234 | −0.236617 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.48528i | 0.333849i | ||||||||
\(647\) | 16.9706i | 0.667182i | 0.942718 | + | 0.333591i | \(0.108260\pi\) | ||||
−0.942718 | + | 0.333591i | \(0.891740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | + | 25.4558i | −0.471041 | + | 0.999229i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.0000 | −0.939913 | ||||||||
\(653\) | 29.6985i | 1.16219i | 0.813835 | + | 0.581096i | \(0.197376\pi\) | ||||
−0.813835 | + | 0.581096i | \(0.802624\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.00000 | 0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0000 | −0.467809 | ||||||||
\(659\) | 6.00000 | 0.233727 | 0.116863 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116863 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 12.0000 | 0.466393 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −42.0000 | −1.62992 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 8.00000 | 0.309529 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | + | 25.4558i | −0.463255 | + | 0.982712i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.7696i | 1.41736i | 0.705529 | + | 0.708681i | \(0.250709\pi\) | ||||
−0.705529 | + | 0.708681i | \(0.749291\pi\) | |||||||
\(674\) | 11.3137i | 0.435788i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | 46.0000 | 1.76792 | 0.883962 | − | 0.467559i | \(-0.154866\pi\) | ||||
0.883962 | + | 0.467559i | \(0.154866\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 16.9706i | − | 0.651270i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.9411i | 1.29872i | 0.760481 | + | 0.649361i | \(0.224963\pi\) | ||||
−0.760481 | + | 0.649361i | \(0.775037\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.9706i | 0.647939i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 1.41421i | − | 0.0539164i | ||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 14.0000 | 0.532200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.0000 | 0.531433 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0000 | −0.454532 | ||||||||
\(698\) | 8.48528i | 0.321173i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 25.4558i | − | 0.960085i | ||||||
\(704\) | 21.0000 | + | 9.89949i | 0.791467 | + | 0.373101i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 4.24264i | − | 0.159674i | ||||||
\(707\) | − | 8.48528i | − | 0.319122i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.0000 | −1.12667 | −0.563337 | − | 0.826227i | \(-0.690483\pi\) | ||||
−0.563337 | + | 0.826227i | \(0.690483\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 21.2132i | 0.794998i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.65685i | 0.211407i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.0000 | 0.895672 | ||||||||
\(719\) | 31.1127i | 1.16031i | 0.814507 | + | 0.580154i | \(0.197008\pi\) | ||||
−0.814507 | + | 0.580154i | \(0.802992\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.9706i | 0.632017i | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.0000 | −1.78022 | −0.890111 | − | 0.455744i | \(-0.849373\pi\) | ||||
−0.890111 | + | 0.455744i | \(0.849373\pi\) | |||||||
\(728\) | −12.0000 | −0.444750 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.82843i | 0.104613i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.1127i | − | 1.14917i | −0.818444 | − | 0.574587i | \(-0.805163\pi\) | ||
0.818444 | − | 0.574587i | \(-0.194837\pi\) | |||||||
\(734\) | −12.0000 | −0.442928 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 46.6690i | − | 1.71675i | −0.513024 | − | 0.858374i | \(-0.671475\pi\) | ||
0.513024 | − | 0.858374i | \(-0.328525\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.00000 | −0.220267 | ||||||||
\(743\) | 10.0000 | 0.366864 | 0.183432 | − | 0.983032i | \(-0.441279\pi\) | ||||
0.183432 | + | 0.983032i | \(0.441279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 22.6274i | − | 0.828449i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.00000 | − | 2.82843i | −0.219382 | − | 0.103418i | ||||
\(749\) | − | 19.7990i | − | 0.723439i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | −0.145962 | −0.0729810 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729810 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(752\) | − | 8.48528i | − | 0.309426i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.9706i | 0.618031i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | −16.0000 | −0.581146 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | −0.652499 | −0.326250 | − | 0.945284i | \(-0.605785\pi\) | ||||
−0.326250 | + | 0.945284i | \(0.605785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.0000 | −0.868858 | ||||||||
\(764\) | − | 2.82843i | − | 0.102329i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000 | 0.866590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.7990i | 0.712581i | ||||||||
\(773\) | 4.24264i | 0.152597i | 0.997085 | + | 0.0762986i | \(0.0243102\pi\) | ||||
−0.997085 | + | 0.0762986i | \(0.975690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36.0000 | 1.29232 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.2132i | 0.760530i | ||||||||
\(779\) | − | 25.4558i | − | 0.912050i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | + | 25.4558i | −0.429394 | + | 0.910882i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.00000 | −0.178571 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9.89949i | − | 0.352879i | −0.984311 | − | 0.176439i | \(-0.943542\pi\) | ||
0.984311 | − | 0.176439i | \(-0.0564580\pi\) | |||||||
\(788\) | −14.0000 | −0.498729 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0000 | 0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | 0.852265 | ||||||||
\(794\) | 6.00000 | 0.212932 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | 29.6985i | 1.05197i | 0.850493 | + | 0.525987i | \(0.176304\pi\) | ||||
−0.850493 | + | 0.525987i | \(0.823696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.9706i | 0.600375i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.8701i | 0.948815i | ||||||||
\(803\) | −16.0000 | + | 33.9411i | −0.564628 | + | 1.19776i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.0000 | 0.633238 | ||||||||
\(809\) | 6.00000 | 0.210949 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 46.6690i | − | 1.63877i | −0.573242 | − | 0.819386i | \(-0.694315\pi\) | ||
0.573242 | − | 0.819386i | \(-0.305685\pi\) | |||||||
\(812\) | 8.48528i | 0.297775i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18.0000 | − | 8.48528i | −0.630900 | − | 0.297409i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.00000 | −0.209913 | ||||||||
\(818\) | − | 8.48528i | − | 0.296681i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.0000 | −0.836587 | −0.418294 | − | 0.908312i | \(-0.637372\pi\) | ||||
−0.418294 | + | 0.908312i | \(0.637372\pi\) | |||||||
\(824\) | −36.0000 | −1.25412 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.0000 | −0.417533 | ||||||||
\(827\) | −34.0000 | −1.18230 | −0.591148 | − | 0.806563i | \(-0.701325\pi\) | ||||
−0.591148 | + | 0.806563i | \(0.701325\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.00000 | −0.208389 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 19.7990i | − | 0.686406i | ||||||
\(833\) | 10.0000 | 0.346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.00000 | − | 12.7279i | 0.207514 | − | 0.440204i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 39.5980i | − | 1.36789i | ||||||
\(839\) | − | 50.9117i | − | 1.75767i | −0.477129 | − | 0.878833i | \(-0.658323\pi\) | ||
0.477129 | − | 0.878833i | \(-0.341677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 24.0000 | 0.827095 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 4.24264i | − | 0.146038i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.0000 | + | 9.89949i | −0.412325 | + | 0.340151i | ||||
\(848\) | − | 4.24264i | − | 0.145693i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.2843i | 0.968435i | 0.874948 | + | 0.484218i | \(0.160896\pi\) | ||||
−0.874948 | + | 0.484218i | \(0.839104\pi\) | |||||||
\(854\) | −12.0000 | −0.410632 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.0000 | 1.43553 | ||||||||
\(857\) | −26.0000 | −0.888143 | −0.444072 | − | 0.895991i | \(-0.646466\pi\) | ||||
−0.444072 | + | 0.895991i | \(0.646466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.0000 | 1.63774 | 0.818869 | − | 0.573980i | \(-0.194601\pi\) | ||||
0.818869 | + | 0.573980i | \(0.194601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | 0.613082 | ||||||||
\(863\) | − | 33.9411i | − | 1.15537i | −0.816260 | − | 0.577685i | \(-0.803956\pi\) | ||
0.816260 | − | 0.577685i | \(-0.196044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.0000 | 0.611665 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.0000 | + | 38.1838i | −0.610608 | + | 1.29530i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 50.9117i | − | 1.72409i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3137i | 0.382037i | 0.981586 | + | 0.191018i | \(0.0611790\pi\) | ||||
−0.981586 | + | 0.191018i | \(0.938821\pi\) | |||||||
\(878\) | − | 38.1838i | − | 1.28864i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 21.2132i | − | 0.714691i | −0.933972 | − | 0.357345i | \(-0.883682\pi\) | ||
0.933972 | − | 0.357345i | \(-0.116318\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 5.65685i | 0.190261i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 25.4558i | − | 0.855206i | ||||||
\(887\) | 2.00000 | 0.0671534 | 0.0335767 | − | 0.999436i | \(-0.489310\pi\) | ||||
0.0335767 | + | 0.999436i | \(0.489310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.0000 | 0.872012 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.0000 | 0.803579 | ||||||||
\(893\) | −36.0000 | −1.20469 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 4.24264i | − | 0.141737i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 32.5269i | − | 1.08544i | ||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.48528i | 0.282686i | ||||||||
\(902\) | −18.0000 | − | 8.48528i | −0.599334 | − | 0.282529i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38.1838i | 1.26997i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.0000 | 0.398453 | 0.199227 | − | 0.979953i | \(-0.436157\pi\) | ||||
0.199227 | + | 0.979953i | \(0.436157\pi\) | |||||||
\(908\) | −2.00000 | −0.0663723 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.82843i | − | 0.0937100i | −0.998902 | − | 0.0468550i | \(-0.985080\pi\) | ||
0.998902 | − | 0.0468550i | \(-0.0149199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.0000 | + | 19.7990i | 1.39000 | + | 0.655251i | ||||
\(914\) | − | 28.2843i | − | 0.935561i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0000 | −0.462573 | ||||||||
\(917\) | − | 25.4558i | − | 0.840626i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 12.7279i | − | 0.419855i | −0.977717 | − | 0.209928i | \(-0.932677\pi\) | ||
0.977717 | − | 0.209928i | \(-0.0673229\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.0000 | 0.592798 | ||||||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24.0000 | 0.788689 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −30.0000 | −0.984798 | ||||||||
\(929\) | 55.1543i | 1.80955i | 0.425885 | + | 0.904777i | \(0.359963\pi\) | ||||
−0.425885 | + | 0.904777i | \(0.640037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.2132i | 0.695235i | ||||||||
\(932\) | 10.0000 | 0.327561 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.48528i | 0.277647i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.82843i | 0.0924007i | 0.998932 | + | 0.0462003i | \(0.0147113\pi\) | ||||
−0.998932 | + | 0.0462003i | \(0.985289\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 8.48528i | − | 0.276172i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.00000 | + | 4.24264i | −0.0650256 | + | 0.137940i | ||||
\(947\) | − | 33.9411i | − | 1.10294i | −0.834195 | − | 0.551469i | \(-0.814067\pi\) | ||
0.834195 | − | 0.551469i | \(-0.185933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.0000 | 1.03876 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 8.48528i | − | 0.275010i | ||||||
\(953\) | 46.0000 | 1.49009 | 0.745043 | − | 0.667016i | \(-0.232429\pi\) | ||||
0.745043 | + | 0.667016i | \(0.232429\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.00000 | −0.194054 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.00000 | 0.193851 | ||||||||
\(959\) | 6.00000 | 0.193750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 16.9706i | 0.547153i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 8.48528i | − | 0.273293i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52.3259i | − | 1.68269i | −0.540500 | − | 0.841344i | \(-0.681765\pi\) | ||
0.540500 | − | 0.841344i | \(-0.318235\pi\) | |||||||
\(968\) | −21.0000 | − | 25.4558i | −0.674966 | − | 0.818182i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 19.7990i | − | 0.635380i | −0.948195 | − | 0.317690i | \(-0.897093\pi\) | ||
0.948195 | − | 0.317690i | \(-0.102907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.00000 | −0.192351 | ||||||||
\(974\) | 12.0000 | 0.384505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 8.48528i | − | 0.271607i | ||||||
\(977\) | 38.1838i | 1.22161i | 0.791782 | + | 0.610803i | \(0.209153\pi\) | ||||
−0.791782 | + | 0.610803i | \(0.790847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0000 | − | 21.2132i | 0.319601 | − | 0.677977i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −36.0000 | −1.14881 | ||||||||
\(983\) | − | 50.9117i | − | 1.62383i | −0.583775 | − | 0.811915i | \(-0.698425\pi\) | ||
0.583775 | − | 0.811915i | \(-0.301575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.0000 | −0.381771 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0000 | −0.381193 | −0.190596 | − | 0.981669i | \(-0.561042\pi\) | ||||
−0.190596 | + | 0.981669i | \(0.561042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.0000 | −0.380617 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 39.5980i | − | 1.25408i | −0.778987 | − | 0.627040i | \(-0.784266\pi\) | ||
0.778987 | − | 0.627040i | \(-0.215734\pi\) | |||||||
\(998\) | −32.0000 | −1.01294 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2475.2.f.d.2276.2 | 2 | ||
3.2 | odd | 2 | 2475.2.f.a.2276.2 | 2 | |||
5.2 | odd | 4 | 495.2.d.b.494.4 | yes | 4 | ||
5.3 | odd | 4 | 495.2.d.b.494.1 | yes | 4 | ||
5.4 | even | 2 | 2475.2.f.b.2276.1 | 2 | |||
11.10 | odd | 2 | 2475.2.f.a.2276.1 | 2 | |||
15.2 | even | 4 | 495.2.d.a.494.1 | ✓ | 4 | ||
15.8 | even | 4 | 495.2.d.a.494.4 | yes | 4 | ||
15.14 | odd | 2 | 2475.2.f.c.2276.1 | 2 | |||
33.32 | even | 2 | inner | 2475.2.f.d.2276.1 | 2 | ||
55.32 | even | 4 | 495.2.d.a.494.2 | yes | 4 | ||
55.43 | even | 4 | 495.2.d.a.494.3 | yes | 4 | ||
55.54 | odd | 2 | 2475.2.f.c.2276.2 | 2 | |||
165.32 | odd | 4 | 495.2.d.b.494.3 | yes | 4 | ||
165.98 | odd | 4 | 495.2.d.b.494.2 | yes | 4 | ||
165.164 | even | 2 | 2475.2.f.b.2276.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.d.a.494.1 | ✓ | 4 | 15.2 | even | 4 | ||
495.2.d.a.494.2 | yes | 4 | 55.32 | even | 4 | ||
495.2.d.a.494.3 | yes | 4 | 55.43 | even | 4 | ||
495.2.d.a.494.4 | yes | 4 | 15.8 | even | 4 | ||
495.2.d.b.494.1 | yes | 4 | 5.3 | odd | 4 | ||
495.2.d.b.494.2 | yes | 4 | 165.98 | odd | 4 | ||
495.2.d.b.494.3 | yes | 4 | 165.32 | odd | 4 | ||
495.2.d.b.494.4 | yes | 4 | 5.2 | odd | 4 | ||
2475.2.f.a.2276.1 | 2 | 11.10 | odd | 2 | |||
2475.2.f.a.2276.2 | 2 | 3.2 | odd | 2 | |||
2475.2.f.b.2276.1 | 2 | 5.4 | even | 2 | |||
2475.2.f.b.2276.2 | 2 | 165.164 | even | 2 | |||
2475.2.f.c.2276.1 | 2 | 15.14 | odd | 2 | |||
2475.2.f.c.2276.2 | 2 | 55.54 | odd | 2 | |||
2475.2.f.d.2276.1 | 2 | 33.32 | even | 2 | inner | ||
2475.2.f.d.2276.2 | 2 | 1.1 | even | 1 | trivial |