Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(2899,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3450.2899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.d (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: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 690) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2899.4 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.2899 |
Dual form | 3450.2.d.v.2899.1 |
$q$-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 \(\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(1151\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.12311i | 1.18042i | 0.807249 | + | 0.590211i | \(0.200956\pi\) | ||||
−0.807249 | + | 0.590211i | \(0.799044\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.12311 | −0.941652 | −0.470826 | − | 0.882226i | \(-0.656044\pi\) | ||||
−0.470826 | + | 0.882226i | \(0.656044\pi\) | |||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | − 2.00000i | − 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | −3.12311 | −0.834685 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 1.12311i | − 0.272393i | −0.990682 | − | 0.136197i | \(-0.956512\pi\) | ||||
0.990682 | − | 0.136197i | \(-0.0434879\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12311 | −0.681518 | ||||||||
\(22\) | − 3.12311i | − 0.665848i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 3.12311i | − 0.590211i | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 3.12311i | − 0.543663i | ||||||||
\(34\) | 1.12311 | 0.192611 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.12311i | 0.184637i | 0.995730 | + | 0.0923187i | \(0.0294279\pi\) | ||||
−0.995730 | + | 0.0923187i | \(0.970572\pi\) | |||||||
\(38\) | − 4.00000i | − 0.648886i | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | − 3.12311i | − 0.481906i | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 3.12311 | 0.470826 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | − 8.00000i | − 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −2.75379 | −0.393398 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.12311 | 0.157266 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | − 12.2462i | − 1.68215i | −0.540921 | − | 0.841073i | \(-0.681924\pi\) | ||||
0.540921 | − | 0.841073i | \(-0.318076\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.12311 | 0.417343 | ||||||||
\(57\) | − 4.00000i | − 0.529813i | ||||||||
\(58\) | − 2.00000i | − 0.262613i | ||||||||
\(59\) | −2.24621 | −0.292432 | −0.146216 | − | 0.989253i | \(-0.546709\pi\) | ||||
−0.146216 | + | 0.989253i | \(0.546709\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.12311 | 1.16809 | 0.584047 | − | 0.811720i | \(-0.301468\pi\) | ||||
0.584047 | + | 0.811720i | \(0.301468\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 3.12311i | − 0.393474i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.12311 | 0.384428 | ||||||||
\(67\) | − 8.00000i | − 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 1.12311i | 0.136197i | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2462 | −1.21600 | −0.608001 | − | 0.793936i | \(-0.708028\pi\) | ||||
−0.608001 | + | 0.793936i | \(0.708028\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 4.24621i | 0.496981i | 0.968634 | + | 0.248491i | \(0.0799345\pi\) | ||||
−0.968634 | + | 0.248491i | \(0.920065\pi\) | |||||||
\(74\) | −1.12311 | −0.130558 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | − 9.75379i | − 1.11155i | ||||||||
\(78\) | 2.00000i | 0.226455i | ||||||||
\(79\) | −3.12311 | −0.351377 | −0.175688 | − | 0.984446i | \(-0.556215\pi\) | ||||
−0.175688 | + | 0.984446i | \(0.556215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000i | 0.220863i | ||||||||
\(83\) | 13.3693i | 1.46747i | 0.679434 | + | 0.733737i | \(0.262225\pi\) | ||||
−0.679434 | + | 0.733737i | \(0.737775\pi\) | |||||||
\(84\) | 3.12311 | 0.340759 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2.00000i | − 0.214423i | ||||||||
\(88\) | 3.12311i | 0.332924i | ||||||||
\(89\) | 5.12311 | 0.543048 | 0.271524 | − | 0.962432i | \(-0.412472\pi\) | ||||
0.271524 | + | 0.962432i | \(0.412472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.24621 | 0.654781 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − 16.2462i | − 1.64955i | −0.565459 | − | 0.824776i | \(-0.691301\pi\) | ||||
0.565459 | − | 0.824776i | \(-0.308699\pi\) | |||||||
\(98\) | − 2.75379i | − 0.278175i | ||||||||
\(99\) | 3.12311 | 0.313884 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.246211 | 0.0244989 | 0.0122495 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122495 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(102\) | 1.12311i | 0.111204i | ||||||||
\(103\) | 9.36932i | 0.923186i | 0.887092 | + | 0.461593i | \(0.152722\pi\) | ||||
−0.887092 | + | 0.461593i | \(0.847278\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.2462 | 1.18946 | ||||||||
\(107\) | − 13.3693i | − 1.29246i | −0.763142 | − | 0.646230i | \(-0.776345\pi\) | ||||
0.763142 | − | 0.646230i | \(-0.223655\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −2.87689 | −0.275557 | −0.137778 | − | 0.990463i | \(-0.543996\pi\) | ||||
−0.137778 | + | 0.990463i | \(0.543996\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.12311 | −0.106600 | ||||||||
\(112\) | 3.12311i | 0.295106i | ||||||||
\(113\) | 9.12311i | 0.858230i | 0.903250 | + | 0.429115i | \(0.141174\pi\) | ||||
−0.903250 | + | 0.429115i | \(0.858826\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | − 2.24621i | − 0.206781i | ||||||||
\(119\) | 3.50758 | 0.321539 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.24621 | −0.113292 | ||||||||
\(122\) | 9.12311i | 0.825967i | ||||||||
\(123\) | 2.00000i | 0.180334i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.12311 | 0.278228 | ||||||||
\(127\) | − 5.75379i | − 0.510566i | −0.966866 | − | 0.255283i | \(-0.917831\pi\) | ||||
0.966866 | − | 0.255283i | \(-0.0821687\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 3.12311i | 0.271831i | ||||||||
\(133\) | − 12.4924i | − 1.08323i | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.12311 | −0.0963055 | ||||||||
\(137\) | − 10.8769i | − 0.929276i | −0.885501 | − | 0.464638i | \(-0.846184\pi\) | ||||
0.885501 | − | 0.464638i | \(-0.153816\pi\) | |||||||
\(138\) | 1.00000i | 0.0851257i | ||||||||
\(139\) | −16.4924 | −1.39887 | −0.699435 | − | 0.714697i | \(-0.746565\pi\) | ||||
−0.699435 | + | 0.714697i | \(0.746565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | − 10.2462i | − 0.859843i | ||||||||
\(143\) | 6.24621i | 0.522334i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.24621 | −0.351419 | ||||||||
\(147\) | − 2.75379i | − 0.227129i | ||||||||
\(148\) | − 1.12311i | − 0.0923187i | ||||||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.24621 | 0.508309 | 0.254155 | − | 0.967164i | \(-0.418203\pi\) | ||||
0.254155 | + | 0.967164i | \(0.418203\pi\) | |||||||
\(152\) | 4.00000i | 0.324443i | ||||||||
\(153\) | 1.12311i | 0.0907977i | ||||||||
\(154\) | 9.75379 | 0.785983 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | 9.12311i | 0.728103i | 0.931379 | + | 0.364052i | \(0.118607\pi\) | ||||
−0.931379 | + | 0.364052i | \(0.881393\pi\) | |||||||
\(158\) | − 3.12311i | − 0.248461i | ||||||||
\(159\) | 12.2462 | 0.971188 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.12311 | 0.246135 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 12.0000i | 0.939913i | 0.882690 | + | 0.469956i | \(0.155730\pi\) | ||||
−0.882690 | + | 0.469956i | \(0.844270\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.3693 | −1.03766 | ||||||||
\(167\) | − 8.00000i | − 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 3.12311i | 0.240953i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 20.2462i | − 1.53929i | −0.638471 | − | 0.769645i | \(-0.720433\pi\) | ||||
0.638471 | − | 0.769645i | \(-0.279567\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.12311 | −0.235413 | ||||||||
\(177\) | − 2.24621i | − 0.168836i | ||||||||
\(178\) | 5.12311i | 0.383993i | ||||||||
\(179\) | 8.49242 | 0.634753 | 0.317377 | − | 0.948300i | \(-0.397198\pi\) | ||||
0.317377 | + | 0.948300i | \(0.397198\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.8769 | 0.808473 | 0.404237 | − | 0.914654i | \(-0.367537\pi\) | ||||
0.404237 | + | 0.914654i | \(0.367537\pi\) | |||||||
\(182\) | 6.24621i | 0.463000i | ||||||||
\(183\) | 9.12311i | 0.674399i | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.50758i | 0.256499i | ||||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | 3.12311 | 0.227173 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4924 | 0.903920 | 0.451960 | − | 0.892038i | \(-0.350725\pi\) | ||||
0.451960 | + | 0.892038i | \(0.350725\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | − 8.24621i | − 0.593575i | −0.954944 | − | 0.296788i | \(-0.904085\pi\) | ||||
0.954944 | − | 0.296788i | \(-0.0959153\pi\) | |||||||
\(194\) | 16.2462 | 1.16641 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.75379 | 0.196699 | ||||||||
\(197\) | − 10.0000i | − 0.712470i | −0.934396 | − | 0.356235i | \(-0.884060\pi\) | ||||
0.934396 | − | 0.356235i | \(-0.115940\pi\) | |||||||
\(198\) | 3.12311i | 0.221949i | ||||||||
\(199\) | −19.1231 | −1.35560 | −0.677801 | − | 0.735246i | \(-0.737067\pi\) | ||||
−0.677801 | + | 0.735246i | \(0.737067\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 0.246211i | 0.0173234i | ||||||||
\(203\) | − 6.24621i | − 0.438398i | ||||||||
\(204\) | −1.12311 | −0.0786331 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.36932 | −0.652791 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | − 2.00000i | − 0.138675i | ||||||||
\(209\) | 12.4924 | 0.864119 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.4924 | −1.13539 | −0.567693 | − | 0.823241i | \(-0.692164\pi\) | ||||
−0.567693 | + | 0.823241i | \(0.692164\pi\) | |||||||
\(212\) | 12.2462i | 0.841073i | ||||||||
\(213\) | − 10.2462i | − 0.702059i | ||||||||
\(214\) | 13.3693 | 0.913908 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 2.87689i | − 0.194848i | ||||||||
\(219\) | −4.24621 | −0.286932 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.24621 | −0.151097 | ||||||||
\(222\) | − 1.12311i | − 0.0753779i | ||||||||
\(223\) | 10.2462i | 0.686137i | 0.939310 | + | 0.343069i | \(0.111466\pi\) | ||||
−0.939310 | + | 0.343069i | \(0.888534\pi\) | |||||||
\(224\) | −3.12311 | −0.208671 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.12311 | −0.606860 | ||||||||
\(227\) | − 5.36932i | − 0.356374i | −0.983997 | − | 0.178187i | \(-0.942977\pi\) | ||||
0.983997 | − | 0.178187i | \(-0.0570232\pi\) | |||||||
\(228\) | 4.00000i | 0.264906i | ||||||||
\(229\) | −23.3693 | −1.54429 | −0.772144 | − | 0.635448i | \(-0.780816\pi\) | ||||
−0.772144 | + | 0.635448i | \(0.780816\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.75379 | 0.641752 | ||||||||
\(232\) | 2.00000i | 0.131306i | ||||||||
\(233\) | − 28.7386i | − 1.88273i | −0.337389 | − | 0.941365i | \(-0.609544\pi\) | ||||
0.337389 | − | 0.941365i | \(-0.390456\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.24621 | 0.146216 | ||||||||
\(237\) | − 3.12311i | − 0.202868i | ||||||||
\(238\) | 3.50758i | 0.227362i | ||||||||
\(239\) | 18.2462 | 1.18025 | 0.590125 | − | 0.807312i | \(-0.299079\pi\) | ||||
0.590125 | + | 0.807312i | \(0.299079\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.4924 | 1.96419 | 0.982095 | − | 0.188387i | \(-0.0603260\pi\) | ||||
0.982095 | + | 0.188387i | \(0.0603260\pi\) | |||||||
\(242\) | − 1.24621i | − 0.0801095i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −9.12311 | −0.584047 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 8.00000i | 0.509028i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.3693 | −0.847246 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.3693 | 1.09634 | 0.548171 | − | 0.836366i | \(-0.315324\pi\) | ||||
0.548171 | + | 0.836366i | \(0.315324\pi\) | |||||||
\(252\) | 3.12311i | 0.196737i | ||||||||
\(253\) | 3.12311i | 0.196348i | ||||||||
\(254\) | 5.75379 | 0.361025 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.24621i | 0.514385i | 0.966360 | + | 0.257192i | \(0.0827974\pi\) | ||||
−0.966360 | + | 0.257192i | \(0.917203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.50758 | −0.217950 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | − 4.00000i | − 0.247121i | ||||||||
\(263\) | 6.24621i | 0.385158i | 0.981281 | + | 0.192579i | \(0.0616851\pi\) | ||||
−0.981281 | + | 0.192579i | \(0.938315\pi\) | |||||||
\(264\) | −3.12311 | −0.192214 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.4924 | 0.765960 | ||||||||
\(267\) | 5.12311i | 0.313529i | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | −0.246211 | −0.0150118 | −0.00750588 | − | 0.999972i | \(-0.502389\pi\) | ||||
−0.00750588 | + | 0.999972i | \(0.502389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.24621 | −0.379430 | −0.189715 | − | 0.981839i | \(-0.560756\pi\) | ||||
−0.189715 | + | 0.981839i | \(0.560756\pi\) | |||||||
\(272\) | − 1.12311i | − 0.0680983i | ||||||||
\(273\) | 6.24621i | 0.378038i | ||||||||
\(274\) | 10.8769 | 0.657097 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 3.75379i | 0.225543i | 0.993621 | + | 0.112772i | \(0.0359729\pi\) | ||||
−0.993621 | + | 0.112772i | \(0.964027\pi\) | |||||||
\(278\) | − 16.4924i | − 0.989150i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.1231 | −1.26010 | −0.630049 | − | 0.776555i | \(-0.716965\pi\) | ||||
−0.630049 | + | 0.776555i | \(0.716965\pi\) | |||||||
\(282\) | 8.00000i | 0.476393i | ||||||||
\(283\) | − 14.2462i | − 0.846849i | −0.905931 | − | 0.423425i | \(-0.860828\pi\) | ||||
0.905931 | − | 0.423425i | \(-0.139172\pi\) | |||||||
\(284\) | 10.2462 | 0.608001 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.24621 | −0.369346 | ||||||||
\(287\) | 6.24621i | 0.368702i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | 15.7386 | 0.925802 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.2462 | 0.952370 | ||||||||
\(292\) | − 4.24621i | − 0.248491i | ||||||||
\(293\) | − 28.2462i | − 1.65016i | −0.565015 | − | 0.825081i | \(-0.691130\pi\) | ||||
0.565015 | − | 0.825081i | \(-0.308870\pi\) | |||||||
\(294\) | 2.75379 | 0.160604 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.12311 | 0.0652792 | ||||||||
\(297\) | 3.12311i | 0.181221i | ||||||||
\(298\) | 10.0000i | 0.579284i | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.24621i | 0.359429i | ||||||||
\(303\) | 0.246211i | 0.0141445i | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.12311 | −0.0642037 | ||||||||
\(307\) | − 32.4924i | − 1.85444i | −0.374516 | − | 0.927220i | \(-0.622191\pi\) | ||||
0.374516 | − | 0.927220i | \(-0.377809\pi\) | |||||||
\(308\) | 9.75379i | 0.555774i | ||||||||
\(309\) | −9.36932 | −0.533002 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.7386 | −1.28939 | −0.644695 | − | 0.764440i | \(-0.723016\pi\) | ||||
−0.644695 | + | 0.764440i | \(0.723016\pi\) | |||||||
\(312\) | − 2.00000i | − 0.113228i | ||||||||
\(313\) | 22.4924i | 1.27135i | 0.771958 | + | 0.635673i | \(0.219278\pi\) | ||||
−0.771958 | + | 0.635673i | \(0.780722\pi\) | |||||||
\(314\) | −9.12311 | −0.514847 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.12311 | 0.175688 | ||||||||
\(317\) | − 28.7386i | − 1.61412i | −0.590468 | − | 0.807061i | \(-0.701057\pi\) | ||||
0.590468 | − | 0.807061i | \(-0.298943\pi\) | |||||||
\(318\) | 12.2462i | 0.686733i | ||||||||
\(319\) | 6.24621 | 0.349721 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.3693 | 0.746203 | ||||||||
\(322\) | 3.12311i | 0.174044i | ||||||||
\(323\) | 4.49242i | 0.249965i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | − 2.87689i | − 0.159093i | ||||||||
\(328\) | − 2.00000i | − 0.110432i | ||||||||
\(329\) | 24.9848 | 1.37746 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.492423 | 0.0270660 | 0.0135330 | − | 0.999908i | \(-0.495692\pi\) | ||||
0.0135330 | + | 0.999908i | \(0.495692\pi\) | |||||||
\(332\) | − 13.3693i | − 0.733737i | ||||||||
\(333\) | − 1.12311i | − 0.0615458i | ||||||||
\(334\) | 8.00000 | 0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.12311 | −0.170379 | ||||||||
\(337\) | 26.4924i | 1.44313i | 0.692345 | + | 0.721567i | \(0.256578\pi\) | ||||
−0.692345 | + | 0.721567i | \(0.743422\pi\) | |||||||
\(338\) | 9.00000i | 0.489535i | ||||||||
\(339\) | −9.12311 | −0.495499 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.00000i | 0.216295i | ||||||||
\(343\) | 13.2614i | 0.716046i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.2462 | 1.08844 | ||||||||
\(347\) | 14.7386i | 0.791211i | 0.918420 | + | 0.395606i | \(0.129465\pi\) | ||||
−0.918420 | + | 0.395606i | \(0.870535\pi\) | |||||||
\(348\) | 2.00000i | 0.107211i | ||||||||
\(349\) | −24.7386 | −1.32423 | −0.662114 | − | 0.749403i | \(-0.730341\pi\) | ||||
−0.662114 | + | 0.749403i | \(0.730341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | − 3.12311i | − 0.166462i | ||||||||
\(353\) | 14.0000i | 0.745145i | 0.928003 | + | 0.372572i | \(0.121524\pi\) | ||||
−0.928003 | + | 0.372572i | \(0.878476\pi\) | |||||||
\(354\) | 2.24621 | 0.119385 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.12311 | −0.271524 | ||||||||
\(357\) | 3.50758i | 0.185641i | ||||||||
\(358\) | 8.49242i | 0.448838i | ||||||||
\(359\) | −20.4924 | −1.08155 | −0.540774 | − | 0.841168i | \(-0.681869\pi\) | ||||
−0.540774 | + | 0.841168i | \(0.681869\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 10.8769i | 0.571677i | ||||||||
\(363\) | − 1.24621i | − 0.0654091i | ||||||||
\(364\) | −6.24621 | −0.327390 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.12311 | −0.476872 | ||||||||
\(367\) | 4.87689i | 0.254572i | 0.991866 | + | 0.127286i | \(0.0406266\pi\) | ||||
−0.991866 | + | 0.127286i | \(0.959373\pi\) | |||||||
\(368\) | − 1.00000i | − 0.0521286i | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 38.2462 | 1.98564 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3693i | 0.588681i | 0.955701 | + | 0.294340i | \(0.0951000\pi\) | ||||
−0.955701 | + | 0.294340i | \(0.904900\pi\) | |||||||
\(374\) | −3.50758 | −0.181373 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | 4.00000i | 0.206010i | ||||||||
\(378\) | 3.12311i | 0.160635i | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.75379 | 0.294776 | ||||||||
\(382\) | 12.4924i | 0.639168i | ||||||||
\(383\) | − 30.2462i | − 1.54551i | −0.634705 | − | 0.772755i | \(-0.718878\pi\) | ||||
0.634705 | − | 0.772755i | \(-0.281122\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.24621 | 0.419721 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.2462i | 0.824776i | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.12311 | −0.0567979 | ||||||||
\(392\) | 2.75379i | 0.139087i | ||||||||
\(393\) | − 4.00000i | − 0.201773i | ||||||||
\(394\) | 10.0000 | 0.503793 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.12311 | −0.156942 | ||||||||
\(397\) | − 1.50758i | − 0.0756631i | −0.999284 | − | 0.0378316i | \(-0.987955\pi\) | ||||
0.999284 | − | 0.0378316i | \(-0.0120450\pi\) | |||||||
\(398\) | − 19.1231i | − 0.958555i | ||||||||
\(399\) | 12.4924 | 0.625403 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.36932 | 0.368006 | 0.184003 | − | 0.982926i | \(-0.441094\pi\) | ||||
0.184003 | + | 0.982926i | \(0.441094\pi\) | |||||||
\(402\) | 8.00000i | 0.399004i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.246211 | −0.0122495 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.24621 | 0.309994 | ||||||||
\(407\) | − 3.50758i | − 0.173864i | ||||||||
\(408\) | − 1.12311i | − 0.0556020i | ||||||||
\(409\) | −0.246211 | −0.0121744 | −0.00608718 | − | 0.999981i | \(-0.501938\pi\) | ||||
−0.00608718 | + | 0.999981i | \(0.501938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.8769 | 0.536518 | ||||||||
\(412\) | − 9.36932i | − 0.461593i | ||||||||
\(413\) | − 7.01515i | − 0.345193i | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | − 16.4924i | − 0.807637i | ||||||||
\(418\) | 12.4924i | 0.611024i | ||||||||
\(419\) | −39.6155 | −1.93535 | −0.967673 | − | 0.252210i | \(-0.918843\pi\) | ||||
−0.967673 | + | 0.252210i | \(0.918843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.3693 | −0.554107 | −0.277053 | − | 0.960855i | \(-0.589358\pi\) | ||||
−0.277053 | + | 0.960855i | \(0.589358\pi\) | |||||||
\(422\) | − 16.4924i | − 0.802839i | ||||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | −12.2462 | −0.594729 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.2462 | 0.496431 | ||||||||
\(427\) | 28.4924i | 1.37884i | ||||||||
\(428\) | 13.3693i | 0.646230i | ||||||||
\(429\) | −6.24621 | −0.301570 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.75379 | 0.469823 | 0.234912 | − | 0.972017i | \(-0.424520\pi\) | ||||
0.234912 | + | 0.972017i | \(0.424520\pi\) | |||||||
\(432\) | − 1.00000i | − 0.0481125i | ||||||||
\(433\) | 22.4924i | 1.08092i | 0.841371 | + | 0.540458i | \(0.181749\pi\) | ||||
−0.841371 | + | 0.540458i | \(0.818251\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.87689 | 0.137778 | ||||||||
\(437\) | 4.00000i | 0.191346i | ||||||||
\(438\) | − 4.24621i | − 0.202892i | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.75379 | 0.131133 | ||||||||
\(442\) | − 2.24621i | − 0.106841i | ||||||||
\(443\) | − 8.49242i | − 0.403487i | −0.979438 | − | 0.201744i | \(-0.935339\pi\) | ||||
0.979438 | − | 0.201744i | \(-0.0646608\pi\) | |||||||
\(444\) | 1.12311 | 0.0533002 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.2462 | −0.485172 | ||||||||
\(447\) | 10.0000i | 0.472984i | ||||||||
\(448\) | − 3.12311i | − 0.147553i | ||||||||
\(449\) | −22.4924 | −1.06148 | −0.530742 | − | 0.847534i | \(-0.678087\pi\) | ||||
−0.530742 | + | 0.847534i | \(0.678087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.24621 | −0.294123 | ||||||||
\(452\) | − 9.12311i | − 0.429115i | ||||||||
\(453\) | 6.24621i | 0.293473i | ||||||||
\(454\) | 5.36932 | 0.251995 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | 16.7386i | 0.783000i | 0.920178 | + | 0.391500i | \(0.128044\pi\) | ||||
−0.920178 | + | 0.391500i | \(0.871956\pi\) | |||||||
\(458\) | − 23.3693i | − 1.09198i | ||||||||
\(459\) | −1.12311 | −0.0524221 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.7386 | −0.779596 | −0.389798 | − | 0.920900i | \(-0.627455\pi\) | ||||
−0.389798 | + | 0.920900i | \(0.627455\pi\) | |||||||
\(462\) | 9.75379i | 0.453787i | ||||||||
\(463\) | 36.0000i | 1.67306i | 0.547920 | + | 0.836531i | \(0.315420\pi\) | ||||
−0.547920 | + | 0.836531i | \(0.684580\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.7386 | 1.33129 | ||||||||
\(467\) | 21.3693i | 0.988854i | 0.869219 | + | 0.494427i | \(0.164622\pi\) | ||||
−0.869219 | + | 0.494427i | \(0.835378\pi\) | |||||||
\(468\) | − 2.00000i | − 0.0924500i | ||||||||
\(469\) | 24.9848 | 1.15369 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.12311 | −0.420371 | ||||||||
\(472\) | 2.24621i | 0.103390i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.12311 | 0.143449 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.50758 | −0.160770 | ||||||||
\(477\) | 12.2462i | 0.560715i | ||||||||
\(478\) | 18.2462i | 0.834562i | ||||||||
\(479\) | −12.4924 | −0.570793 | −0.285397 | − | 0.958409i | \(-0.592125\pi\) | ||||
−0.285397 | + | 0.958409i | \(0.592125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.24621 | 0.102418 | ||||||||
\(482\) | 30.4924i | 1.38889i | ||||||||
\(483\) | 3.12311i | 0.142106i | ||||||||
\(484\) | 1.24621 | 0.0566460 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 7.50758i | 0.340201i | 0.985427 | + | 0.170100i | \(0.0544092\pi\) | ||||
−0.985427 | + | 0.170100i | \(0.945591\pi\) | |||||||
\(488\) | − 9.12311i | − 0.412984i | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | − 2.00000i | − 0.0901670i | ||||||||
\(493\) | 2.24621i | 0.101164i | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 32.0000i | − 1.43540i | ||||||||
\(498\) | − 13.3693i | − 0.599093i | ||||||||
\(499\) | −36.9848 | −1.65567 | −0.827835 | − | 0.560972i | \(-0.810427\pi\) | ||||
−0.827835 | + | 0.560972i | \(0.810427\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000 | 0.357414 | ||||||||
\(502\) | 17.3693i | 0.775231i | ||||||||
\(503\) | − 42.7386i | − 1.90562i | −0.303565 | − | 0.952811i | \(-0.598177\pi\) | ||||
0.303565 | − | 0.952811i | \(-0.401823\pi\) | |||||||
\(504\) | −3.12311 | −0.139114 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.12311 | −0.138839 | ||||||||
\(507\) | 9.00000i | 0.399704i | ||||||||
\(508\) | 5.75379i | 0.255283i | ||||||||
\(509\) | −34.0000 | −1.50702 | −0.753512 | − | 0.657434i | \(-0.771642\pi\) | ||||
−0.753512 | + | 0.657434i | \(0.771642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.2614 | −0.586648 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 4.00000i | 0.176604i | ||||||||
\(514\) | −8.24621 | −0.363725 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.9848i | 1.09883i | ||||||||
\(518\) | − 3.50758i | − 0.154114i | ||||||||
\(519\) | 20.2462 | 0.888710 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.1231 | 0.750177 | 0.375088 | − | 0.926989i | \(-0.377612\pi\) | ||||
0.375088 | + | 0.926989i | \(0.377612\pi\) | |||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | − 4.49242i | − 0.196440i | −0.995165 | − | 0.0982200i | \(-0.968685\pi\) | ||||
0.995165 | − | 0.0982200i | \(-0.0313149\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.24621 | −0.272348 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | − 3.12311i | − 0.135916i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.24621 | 0.0974773 | ||||||||
\(532\) | 12.4924i | 0.541615i | ||||||||
\(533\) | − 4.00000i | − 0.173259i | ||||||||
\(534\) | −5.12311 | −0.221698 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | 8.49242i | 0.366475i | ||||||||
\(538\) | − 0.246211i | − 0.0106149i | ||||||||
\(539\) | 8.60037 | 0.370444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.2462 | −1.38637 | −0.693186 | − | 0.720758i | \(-0.743794\pi\) | ||||
−0.693186 | + | 0.720758i | \(0.743794\pi\) | |||||||
\(542\) | − 6.24621i | − 0.268298i | ||||||||
\(543\) | 10.8769i | 0.466772i | ||||||||
\(544\) | 1.12311 | 0.0481528 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.24621 | −0.267313 | ||||||||
\(547\) | − 32.4924i | − 1.38928i | −0.719360 | − | 0.694638i | \(-0.755565\pi\) | ||||
0.719360 | − | 0.694638i | \(-0.244435\pi\) | |||||||
\(548\) | 10.8769i | 0.464638i | ||||||||
\(549\) | −9.12311 | −0.389365 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.00000 | 0.340811 | ||||||||
\(552\) | − 1.00000i | − 0.0425628i | ||||||||
\(553\) | − 9.75379i | − 0.414773i | ||||||||
\(554\) | −3.75379 | −0.159483 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4924 | 0.699435 | ||||||||
\(557\) | − 2.00000i | − 0.0847427i | −0.999102 | − | 0.0423714i | \(-0.986509\pi\) | ||||
0.999102 | − | 0.0423714i | \(-0.0134913\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.50758 | −0.148090 | ||||||||
\(562\) | − 21.1231i | − 0.891024i | ||||||||
\(563\) | 13.3693i | 0.563450i | 0.959495 | + | 0.281725i | \(0.0909065\pi\) | ||||
−0.959495 | + | 0.281725i | \(0.909093\pi\) | |||||||
\(564\) | −8.00000 | −0.336861 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.2462 | 0.598813 | ||||||||
\(567\) | 3.12311i | 0.131158i | ||||||||
\(568\) | 10.2462i | 0.429921i | ||||||||
\(569\) | −18.8769 | −0.791361 | −0.395680 | − | 0.918388i | \(-0.629491\pi\) | ||||
−0.395680 | + | 0.918388i | \(0.629491\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.7386 | −0.616793 | −0.308396 | − | 0.951258i | \(-0.599792\pi\) | ||||
−0.308396 | + | 0.951258i | \(0.599792\pi\) | |||||||
\(572\) | − 6.24621i | − 0.261167i | ||||||||
\(573\) | 12.4924i | 0.521878i | ||||||||
\(574\) | −6.24621 | −0.260712 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 18.4924i | − 0.769850i | −0.922948 | − | 0.384925i | \(-0.874227\pi\) | ||||
0.922948 | − | 0.384925i | \(-0.125773\pi\) | |||||||
\(578\) | 15.7386i | 0.654641i | ||||||||
\(579\) | 8.24621 | 0.342701 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −41.7538 | −1.73224 | ||||||||
\(582\) | 16.2462i | 0.673427i | ||||||||
\(583\) | 38.2462i | 1.58400i | ||||||||
\(584\) | 4.24621 | 0.175709 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.2462 | 1.16684 | ||||||||
\(587\) | − 26.2462i | − 1.08330i | −0.840605 | − | 0.541649i | \(-0.817800\pi\) | ||||
0.840605 | − | 0.541649i | \(-0.182200\pi\) | |||||||
\(588\) | 2.75379i | 0.113564i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 1.12311i | 0.0461594i | ||||||||
\(593\) | − 24.2462i | − 0.995673i | −0.867271 | − | 0.497836i | \(-0.834128\pi\) | ||||
0.867271 | − | 0.497836i | \(-0.165872\pi\) | |||||||
\(594\) | −3.12311 | −0.128143 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | − 19.1231i | − 0.782657i | ||||||||
\(598\) | − 2.00000i | − 0.0817861i | ||||||||
\(599\) | −10.2462 | −0.418649 | −0.209324 | − | 0.977846i | \(-0.567126\pi\) | ||||
−0.209324 | + | 0.977846i | \(0.567126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | −6.24621 | −0.254155 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.246211 | −0.0100016 | ||||||||
\(607\) | − 22.7386i | − 0.922933i | −0.887158 | − | 0.461466i | \(-0.847324\pi\) | ||||
0.887158 | − | 0.461466i | \(-0.152676\pi\) | |||||||
\(608\) | − 4.00000i | − 0.162221i | ||||||||
\(609\) | 6.24621 | 0.253109 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.0000 | −0.647291 | ||||||||
\(612\) | − 1.12311i | − 0.0453989i | ||||||||
\(613\) | − 34.8769i | − 1.40866i | −0.709870 | − | 0.704332i | \(-0.751247\pi\) | ||||
0.709870 | − | 0.704332i | \(-0.248753\pi\) | |||||||
\(614\) | 32.4924 | 1.31129 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.75379 | −0.392991 | ||||||||
\(617\) | − 34.1080i | − 1.37313i | −0.727066 | − | 0.686567i | \(-0.759117\pi\) | ||||
0.727066 | − | 0.686567i | \(-0.240883\pi\) | |||||||
\(618\) | − 9.36932i | − 0.376889i | ||||||||
\(619\) | 36.0000 | 1.44696 | 0.723481 | − | 0.690344i | \(-0.242541\pi\) | ||||
0.723481 | + | 0.690344i | \(0.242541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | − 22.7386i | − 0.911736i | ||||||||
\(623\) | 16.0000i | 0.641026i | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.4924 | −0.898978 | ||||||||
\(627\) | 12.4924i | 0.498899i | ||||||||
\(628\) | − 9.12311i | − 0.364052i | ||||||||
\(629\) | 1.26137 | 0.0502940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.6307 | −0.582438 | −0.291219 | − | 0.956656i | \(-0.594061\pi\) | ||||
−0.291219 | + | 0.956656i | \(0.594061\pi\) | |||||||
\(632\) | 3.12311i | 0.124230i | ||||||||
\(633\) | − 16.4924i | − 0.655515i | ||||||||
\(634\) | 28.7386 | 1.14136 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.2462 | −0.485594 | ||||||||
\(637\) | 5.50758i | 0.218218i | ||||||||
\(638\) | 6.24621i | 0.247290i | ||||||||
\(639\) | 10.2462 | 0.405334 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.3693 | 0.607052 | 0.303526 | − | 0.952823i | \(-0.401836\pi\) | ||||
0.303526 | + | 0.952823i | \(0.401836\pi\) | |||||||
\(642\) | 13.3693i | 0.527645i | ||||||||
\(643\) | − 3.50758i | − 0.138325i | −0.997605 | − | 0.0691627i | \(-0.977967\pi\) | ||||
0.997605 | − | 0.0691627i | \(-0.0220328\pi\) | |||||||
\(644\) | −3.12311 | −0.123068 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.49242 | −0.176752 | ||||||||
\(647\) | 44.4924i | 1.74918i | 0.484865 | + | 0.874589i | \(0.338869\pi\) | ||||
−0.484865 | + | 0.874589i | \(0.661131\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 7.01515 | 0.275369 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 12.0000i | − 0.469956i | ||||||||
\(653\) | 22.4924i | 0.880197i | 0.897950 | + | 0.440098i | \(0.145056\pi\) | ||||
−0.897950 | + | 0.440098i | \(0.854944\pi\) | |||||||
\(654\) | 2.87689 | 0.112495 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | − 4.24621i | − 0.165660i | ||||||||
\(658\) | 24.9848i | 0.974011i | ||||||||
\(659\) | −17.3693 | −0.676613 | −0.338306 | − | 0.941036i | \(-0.609854\pi\) | ||||
−0.338306 | + | 0.941036i | \(0.609854\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.8617 | −0.928114 | −0.464057 | − | 0.885805i | \(-0.653607\pi\) | ||||
−0.464057 | + | 0.885805i | \(0.653607\pi\) | |||||||
\(662\) | 0.492423i | 0.0191385i | ||||||||
\(663\) | − 2.24621i | − 0.0872356i | ||||||||
\(664\) | 13.3693 | 0.518830 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.12311 | 0.0435195 | ||||||||
\(667\) | 2.00000i | 0.0774403i | ||||||||
\(668\) | 8.00000i | 0.309529i | ||||||||
\(669\) | −10.2462 | −0.396141 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.4924 | −1.09994 | ||||||||
\(672\) | − 3.12311i | − 0.120476i | ||||||||
\(673\) | − 18.9848i | − 0.731812i | −0.930652 | − | 0.365906i | \(-0.880759\pi\) | ||||
0.930652 | − | 0.365906i | \(-0.119241\pi\) | |||||||
\(674\) | −26.4924 | −1.02045 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | − 13.5076i | − 0.519138i | −0.965725 | − | 0.259569i | \(-0.916419\pi\) | ||||
0.965725 | − | 0.259569i | \(-0.0835806\pi\) | |||||||
\(678\) | − 9.12311i | − 0.350371i | ||||||||
\(679\) | 50.7386 | 1.94717 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.36932 | 0.205753 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 34.2462i | − 1.31039i | −0.755458 | − | 0.655197i | \(-0.772585\pi\) | ||||
0.755458 | − | 0.655197i | \(-0.227415\pi\) | |||||||
\(684\) | −4.00000 | −0.152944 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.2614 | −0.506321 | ||||||||
\(687\) | − 23.3693i | − 0.891595i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.4924 | −0.933087 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | 20.2462i | 0.769645i | ||||||||
\(693\) | 9.75379i | 0.370516i | ||||||||
\(694\) | −14.7386 | −0.559471 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.00000 | −0.0758098 | ||||||||
\(697\) | − 2.24621i | − 0.0850813i | ||||||||
\(698\) | − 24.7386i | − 0.936371i | ||||||||
\(699\) | 28.7386 | 1.08699 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.7538 | −0.746090 | −0.373045 | − | 0.927813i | \(-0.621686\pi\) | ||||
−0.373045 | + | 0.927813i | \(0.621686\pi\) | |||||||
\(702\) | − 2.00000i | − 0.0754851i | ||||||||
\(703\) | − 4.49242i | − 0.169435i | ||||||||
\(704\) | 3.12311 | 0.117706 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.0000 | −0.526897 | ||||||||
\(707\) | 0.768944i | 0.0289191i | ||||||||
\(708\) | 2.24621i | 0.0844178i | ||||||||
\(709\) | 11.3693 | 0.426984 | 0.213492 | − | 0.976945i | \(-0.431516\pi\) | ||||
0.213492 | + | 0.976945i | \(0.431516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.12311 | 0.117126 | ||||||||
\(712\) | − 5.12311i | − 0.191997i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −3.50758 | −0.131268 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.49242 | −0.317377 | ||||||||
\(717\) | 18.2462i | 0.681417i | ||||||||
\(718\) | − 20.4924i | − 0.764770i | ||||||||
\(719\) | 26.2462 | 0.978819 | 0.489409 | − | 0.872054i | \(-0.337212\pi\) | ||||
0.489409 | + | 0.872054i | \(0.337212\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.2614 | −1.08975 | ||||||||
\(722\) | − 3.00000i | − 0.111648i | ||||||||
\(723\) | 30.4924i | 1.13403i | ||||||||
\(724\) | −10.8769 | −0.404237 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.24621 | 0.0462512 | ||||||||
\(727\) | − 29.8617i | − 1.10751i | −0.832679 | − | 0.553755i | \(-0.813194\pi\) | ||||
0.832679 | − | 0.553755i | \(-0.186806\pi\) | |||||||
\(728\) | − 6.24621i | − 0.231500i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − 9.12311i | − 0.337200i | ||||||||
\(733\) | − 43.8617i | − 1.62007i | −0.586381 | − | 0.810035i | \(-0.699448\pi\) | ||||
0.586381 | − | 0.810035i | \(-0.300552\pi\) | |||||||
\(734\) | −4.87689 | −0.180009 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 24.9848i | 0.920329i | ||||||||
\(738\) | − 2.00000i | − 0.0736210i | ||||||||
\(739\) | −7.50758 | −0.276171 | −0.138085 | − | 0.990420i | \(-0.544095\pi\) | ||||
−0.138085 | + | 0.990420i | \(0.544095\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | 38.2462i | 1.40406i | ||||||||
\(743\) | − 34.7386i | − 1.27444i | −0.770683 | − | 0.637218i | \(-0.780085\pi\) | ||||
0.770683 | − | 0.637218i | \(-0.219915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.3693 | −0.416260 | ||||||||
\(747\) | − 13.3693i | − 0.489158i | ||||||||
\(748\) | − 3.50758i | − 0.128250i | ||||||||
\(749\) | 41.7538 | 1.52565 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8617 | −0.505822 | −0.252911 | − | 0.967490i | \(-0.581388\pi\) | ||||
−0.252911 | + | 0.967490i | \(0.581388\pi\) | |||||||
\(752\) | − 8.00000i | − 0.291730i | ||||||||
\(753\) | 17.3693i | 0.632973i | ||||||||
\(754\) | −4.00000 | −0.145671 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.12311 | −0.113586 | ||||||||
\(757\) | − 47.8617i | − 1.73956i | −0.493436 | − | 0.869782i | \(-0.664259\pi\) | ||||
0.493436 | − | 0.869782i | \(-0.335741\pi\) | |||||||
\(758\) | − 4.00000i | − 0.145287i | ||||||||
\(759\) | −3.12311 | −0.113362 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.7538 | −1.15107 | −0.575537 | − | 0.817776i | \(-0.695207\pi\) | ||||
−0.575537 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(762\) | 5.75379i | 0.208438i | ||||||||
\(763\) | − 8.98485i | − 0.325273i | ||||||||
\(764\) | −12.4924 | −0.451960 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.2462 | 1.09284 | ||||||||
\(767\) | 4.49242i | 0.162212i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −28.7386 | −1.03634 | −0.518171 | − | 0.855277i | \(-0.673387\pi\) | ||||
−0.518171 | + | 0.855277i | \(0.673387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.24621 | −0.296980 | ||||||||
\(772\) | 8.24621i | 0.296788i | ||||||||
\(773\) | 19.7538i | 0.710494i | 0.934772 | + | 0.355247i | \(0.115603\pi\) | ||||
−0.934772 | + | 0.355247i | \(0.884397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.2462 | −0.583205 | ||||||||
\(777\) | − 3.50758i | − 0.125834i | ||||||||
\(778\) | 18.0000i | 0.645331i | ||||||||
\(779\) | −8.00000 | −0.286630 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0000 | 1.14505 | ||||||||
\(782\) | − 1.12311i | − 0.0401622i | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | −2.75379 | −0.0983496 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.00000 | 0.142675 | ||||||||
\(787\) | 48.0000i | 1.71102i | 0.517790 | + | 0.855508i | \(0.326755\pi\) | ||||
−0.517790 | + | 0.855508i | \(0.673245\pi\) | |||||||
\(788\) | 10.0000i | 0.356235i | ||||||||
\(789\) | −6.24621 | −0.222371 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.4924 | −1.01307 | ||||||||
\(792\) | − 3.12311i | − 0.110975i | ||||||||
\(793\) | − 18.2462i | − 0.647942i | ||||||||
\(794\) | 1.50758 | 0.0535019 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.1231 | 0.677801 | ||||||||
\(797\) | 10.4924i | 0.371661i | 0.982582 | + | 0.185830i | \(0.0594975\pi\) | ||||
−0.982582 | + | 0.185830i | \(0.940503\pi\) | |||||||
\(798\) | 12.4924i | 0.442227i | ||||||||
\(799\) | −8.98485 | −0.317861 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.12311 | −0.181016 | ||||||||
\(802\) | 7.36932i | 0.260220i | ||||||||
\(803\) | − 13.2614i | − 0.467983i | ||||||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 0.246211i | − 0.00866705i | ||||||||
\(808\) | − 0.246211i | − 0.00866168i | ||||||||
\(809\) | 12.2462 | 0.430554 | 0.215277 | − | 0.976553i | \(-0.430935\pi\) | ||||
0.215277 | + | 0.976553i | \(0.430935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.0000 | −1.26413 | −0.632065 | − | 0.774915i | \(-0.717793\pi\) | ||||
−0.632065 | + | 0.774915i | \(0.717793\pi\) | |||||||
\(812\) | 6.24621i | 0.219199i | ||||||||
\(813\) | − 6.24621i | − 0.219064i | ||||||||
\(814\) | 3.50758 | 0.122941 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.12311 | 0.0393166 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − 0.246211i | − 0.00860857i | ||||||||
\(819\) | −6.24621 | −0.218260 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.2462 | −1.26500 | −0.632501 | − | 0.774560i | \(-0.717971\pi\) | ||||
−0.632501 | + | 0.774560i | \(0.717971\pi\) | |||||||
\(822\) | 10.8769i | 0.379375i | ||||||||
\(823\) | 4.00000i | 0.139431i | 0.997567 | + | 0.0697156i | \(0.0222092\pi\) | ||||
−0.997567 | + | 0.0697156i | \(0.977791\pi\) | |||||||
\(824\) | 9.36932 | 0.326396 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.01515 | 0.244088 | ||||||||
\(827\) | 8.87689i | 0.308680i | 0.988018 | + | 0.154340i | \(0.0493251\pi\) | ||||
−0.988018 | + | 0.154340i | \(0.950675\pi\) | |||||||
\(828\) | − 1.00000i | − 0.0347524i | ||||||||
\(829\) | −15.7538 | −0.547152 | −0.273576 | − | 0.961850i | \(-0.588206\pi\) | ||||
−0.273576 | + | 0.961850i | \(0.588206\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.75379 | −0.130217 | ||||||||
\(832\) | 2.00000i | 0.0693375i | ||||||||
\(833\) | 3.09280i | 0.107159i | ||||||||
\(834\) | 16.4924 | 0.571086 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.4924 | −0.432059 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 39.6155i | − 1.36850i | ||||||||
\(839\) | 9.75379 | 0.336738 | 0.168369 | − | 0.985724i | \(-0.446150\pi\) | ||||
0.168369 | + | 0.985724i | \(0.446150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | − 11.3693i | − 0.391813i | ||||||||
\(843\) | − 21.1231i | − 0.727518i | ||||||||
\(844\) | 16.4924 | 0.567693 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | − 3.89205i | − 0.133732i | ||||||||
\(848\) | − 12.2462i | − 0.420537i | ||||||||
\(849\) | 14.2462 | 0.488929 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.12311 | 0.0384996 | ||||||||
\(852\) | 10.2462i | 0.351029i | ||||||||
\(853\) | 6.00000i | 0.205436i | 0.994711 | + | 0.102718i | \(0.0327539\pi\) | ||||
−0.994711 | + | 0.102718i | \(0.967246\pi\) | |||||||
\(854\) | −28.4924 | −0.974991 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.3693 | −0.456954 | ||||||||
\(857\) | − 24.7386i | − 0.845056i | −0.906350 | − | 0.422528i | \(-0.861143\pi\) | ||||
0.906350 | − | 0.422528i | \(-0.138857\pi\) | |||||||
\(858\) | − 6.24621i | − 0.213242i | ||||||||
\(859\) | −15.5076 | −0.529112 | −0.264556 | − | 0.964370i | \(-0.585225\pi\) | ||||
−0.264556 | + | 0.964370i | \(0.585225\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.24621 | −0.212870 | ||||||||
\(862\) | 9.75379i | 0.332215i | ||||||||
\(863\) | 16.9848i | 0.578171i | 0.957303 | + | 0.289085i | \(0.0933512\pi\) | ||||
−0.957303 | + | 0.289085i | \(0.906649\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −22.4924 | −0.764324 | ||||||||
\(867\) | 15.7386i | 0.534512i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.75379 | 0.330875 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | 2.87689i | 0.0974239i | ||||||||
\(873\) | 16.2462i | 0.549851i | ||||||||
\(874\) | −4.00000 | −0.135302 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.24621 | 0.143466 | ||||||||
\(877\) | 52.7386i | 1.78086i | 0.455123 | + | 0.890429i | \(0.349595\pi\) | ||||
−0.455123 | + | 0.890429i | \(0.650405\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.2462 | 0.952721 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.61553 | −0.323955 | −0.161978 | − | 0.986794i | \(-0.551787\pi\) | ||||
−0.161978 | + | 0.986794i | \(0.551787\pi\) | |||||||
\(882\) | 2.75379i | 0.0927249i | ||||||||
\(883\) | − 44.9848i | − 1.51386i | −0.653496 | − | 0.756930i | \(-0.726698\pi\) | ||||
0.653496 | − | 0.756930i | \(-0.273302\pi\) | |||||||
\(884\) | 2.24621 | 0.0755483 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.49242 | 0.285309 | ||||||||
\(887\) | 19.5076i | 0.655000i | 0.944851 | + | 0.327500i | \(0.106206\pi\) | ||||
−0.944851 | + | 0.327500i | \(0.893794\pi\) | |||||||
\(888\) | 1.12311i | 0.0376890i | ||||||||
\(889\) | 17.9697 | 0.602684 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.12311 | −0.104628 | ||||||||
\(892\) | − 10.2462i | − 0.343069i | ||||||||
\(893\) | 32.0000i | 1.07084i | ||||||||
\(894\) | −10.0000 | −0.334450 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.12311 | 0.104336 | ||||||||
\(897\) | − 2.00000i | − 0.0667781i | ||||||||
\(898\) | − 22.4924i | − 0.750582i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.7538 | −0.458205 | ||||||||
\(902\) | − 6.24621i | − 0.207976i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.12311 | 0.303430 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.24621 | −0.207516 | ||||||||
\(907\) | 54.2462i | 1.80122i | 0.434632 | + | 0.900608i | \(0.356878\pi\) | ||||
−0.434632 | + | 0.900608i | \(0.643122\pi\) | |||||||
\(908\) | 5.36932i | 0.178187i | ||||||||
\(909\) | −0.246211 | −0.00816631 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.2462 | −1.00210 | −0.501051 | − | 0.865418i | \(-0.667053\pi\) | ||||
−0.501051 | + | 0.865418i | \(0.667053\pi\) | |||||||
\(912\) | − 4.00000i | − 0.132453i | ||||||||
\(913\) | − 41.7538i | − 1.38185i | ||||||||
\(914\) | −16.7386 | −0.553665 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.3693 | 0.772144 | ||||||||
\(917\) | − 12.4924i | − 0.412536i | ||||||||
\(918\) | − 1.12311i | − 0.0370680i | ||||||||
\(919\) | −19.1231 | −0.630813 | −0.315407 | − | 0.948957i | \(-0.602141\pi\) | ||||
−0.315407 | + | 0.948957i | \(0.602141\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.4924 | 1.07066 | ||||||||
\(922\) | − 16.7386i | − 0.551258i | ||||||||
\(923\) | 20.4924i | 0.674516i | ||||||||
\(924\) | −9.75379 | −0.320876 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −36.0000 | −1.18303 | ||||||||
\(927\) | − 9.36932i | − 0.307729i | ||||||||
\(928\) | − 2.00000i | − 0.0656532i | ||||||||
\(929\) | −34.9848 | −1.14782 | −0.573908 | − | 0.818920i | \(-0.694573\pi\) | ||||
−0.573908 | + | 0.818920i | \(0.694573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.0152 | 0.361007 | ||||||||
\(932\) | 28.7386i | 0.941365i | ||||||||
\(933\) | − 22.7386i | − 0.744429i | ||||||||
\(934\) | −21.3693 | −0.699225 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | 32.7386i | 1.06952i | 0.845003 | + | 0.534762i | \(0.179599\pi\) | ||||
−0.845003 | + | 0.534762i | \(0.820401\pi\) | |||||||
\(938\) | 24.9848i | 0.815784i | ||||||||
\(939\) | −22.4924 | −0.734012 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.4924 | 0.863628 | 0.431814 | − | 0.901963i | \(-0.357874\pi\) | ||||
0.431814 | + | 0.901963i | \(0.357874\pi\) | |||||||
\(942\) | − 9.12311i | − 0.297247i | ||||||||
\(943\) | − 2.00000i | − 0.0651290i | ||||||||
\(944\) | −2.24621 | −0.0731079 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.75379i | 0.186973i | 0.995621 | + | 0.0934865i | \(0.0298012\pi\) | ||||
−0.995621 | + | 0.0934865i | \(0.970199\pi\) | |||||||
\(948\) | 3.12311i | 0.101434i | ||||||||
\(949\) | 8.49242 | 0.275676 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.7386 | 0.931914 | ||||||||
\(952\) | − 3.50758i | − 0.113681i | ||||||||
\(953\) | − 23.8617i | − 0.772958i | −0.922298 | − | 0.386479i | \(-0.873691\pi\) | ||||
0.922298 | − | 0.386479i | \(-0.126309\pi\) | |||||||
\(954\) | −12.2462 | −0.396486 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.2462 | −0.590125 | ||||||||
\(957\) | 6.24621i | 0.201911i | ||||||||
\(958\) | − 12.4924i | − 0.403612i | ||||||||
\(959\) | 33.9697 | 1.09694 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 2.24621i | 0.0724208i | ||||||||
\(963\) | 13.3693i | 0.430820i | ||||||||
\(964\) | −30.4924 | −0.982095 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.12311 | −0.100484 | ||||||||
\(967\) | 60.9848i | 1.96114i | 0.196168 | + | 0.980570i | \(0.437150\pi\) | ||||
−0.196168 | + | 0.980570i | \(0.562850\pi\) | |||||||
\(968\) | 1.24621i | 0.0400547i | ||||||||
\(969\) | −4.49242 | −0.144317 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.1231 | 1.38389 | 0.691943 | − | 0.721952i | \(-0.256755\pi\) | ||||
0.691943 | + | 0.721952i | \(0.256755\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | − 51.5076i | − 1.65126i | ||||||||
\(974\) | −7.50758 | −0.240558 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.12311 | 0.292023 | ||||||||
\(977\) | − 35.8617i | − 1.14732i | −0.819094 | − | 0.573659i | \(-0.805523\pi\) | ||||
0.819094 | − | 0.573659i | \(-0.194477\pi\) | |||||||
\(978\) | − 12.0000i | − 0.383718i | ||||||||
\(979\) | −16.0000 | −0.511362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.87689 | 0.0918522 | ||||||||
\(982\) | − 12.0000i | − 0.382935i | ||||||||
\(983\) | 9.75379i | 0.311098i | 0.987828 | + | 0.155549i | \(0.0497146\pi\) | ||||
−0.987828 | + | 0.155549i | \(0.950285\pi\) | |||||||
\(984\) | 2.00000 | 0.0637577 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.24621 | −0.0715339 | ||||||||
\(987\) | 24.9848i | 0.795276i | ||||||||
\(988\) | − 8.00000i | − 0.254514i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.4773 | 1.95289 | 0.976445 | − | 0.215767i | \(-0.0692252\pi\) | ||||
0.976445 | + | 0.215767i | \(0.0692252\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.492423i | 0.0156266i | ||||||||
\(994\) | 32.0000 | 1.01498 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.3693 | 0.423623 | ||||||||
\(997\) | 3.75379i | 0.118884i | 0.998232 | + | 0.0594418i | \(0.0189321\pi\) | ||||
−0.998232 | + | 0.0594418i | \(0.981068\pi\) | |||||||
\(998\) | − 36.9848i | − 1.17073i | ||||||||
\(999\) | 1.12311 | 0.0355335 |
(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 | 3450.2.d.v.2899.4 | 4 | ||
5.2 | odd | 4 | 3450.2.a.bi.1.1 | 2 | |||
5.3 | odd | 4 | 690.2.a.l.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 3450.2.d.v.2899.1 | 4 | ||
15.8 | even | 4 | 2070.2.a.t.1.2 | 2 | |||
20.3 | even | 4 | 5520.2.a.bs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.a.l.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
2070.2.a.t.1.2 | 2 | 15.8 | even | 4 | |||
3450.2.a.bi.1.1 | 2 | 5.2 | odd | 4 | |||
3450.2.d.v.2899.1 | 4 | 5.4 | even | 2 | inner | ||
3450.2.d.v.2899.4 | 4 | 1.1 | even | 1 | trivial | ||
5520.2.a.bs.1.1 | 2 | 20.3 | even | 4 |