Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(4409,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.4409");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.d (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: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4409.15 | ||
Root | \(-1.27963 + 1.83372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.4409 |
Dual form | 4410.2.d.a.4409.16 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.22787 | − | 0.191334i | 0.996332 | − | 0.0855670i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.22787 | + | 0.191334i | −0.704513 | + | 0.0605050i | ||||
\(11\) | 2.39690i | 0.722691i | 0.932432 | + | 0.361346i | \(0.117683\pi\) | ||||
−0.932432 | + | 0.361346i | \(0.882317\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.67714 | −1.57455 | −0.787277 | − | 0.616599i | \(-0.788510\pi\) | ||||
−0.787277 | + | 0.616599i | \(0.788510\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.07192i | − | 0.502515i | −0.967920 | − | 0.251258i | \(-0.919156\pi\) | ||
0.967920 | − | 0.251258i | \(-0.0808441\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.91397i | − | 1.35676i | −0.734713 | − | 0.678378i | \(-0.762683\pi\) | ||
0.734713 | − | 0.678378i | \(-0.237317\pi\) | |||||||
\(20\) | 2.22787 | − | 0.191334i | 0.498166 | − | 0.0427835i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.39690i | − | 0.511020i | ||||||
\(23\) | −1.86175 | −0.388203 | −0.194101 | − | 0.980981i | \(-0.562179\pi\) | ||||
−0.194101 | + | 0.980981i | \(0.562179\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.92678 | − | 0.852531i | 0.985357 | − | 0.170506i | ||||
\(26\) | 5.67714 | 1.11338 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.88913i | − | 0.907889i | −0.891030 | − | 0.453944i | \(-0.850016\pi\) | ||
0.891030 | − | 0.453944i | \(-0.149984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.52651i | 0.812986i | 0.913654 | + | 0.406493i | \(0.133248\pi\) | ||||
−0.913654 | + | 0.406493i | \(0.866752\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.07192i | 0.355332i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.96911i | 0.488119i | 0.969760 | + | 0.244059i | \(0.0784792\pi\) | ||||
−0.969760 | + | 0.244059i | \(0.921521\pi\) | |||||||
\(38\) | 5.91397i | 0.959372i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.22787 | + | 0.191334i | −0.352257 | + | 0.0302525i | ||||
\(41\) | −7.04428 | −1.10013 | −0.550066 | − | 0.835121i | \(-0.685397\pi\) | ||||
−0.550066 | + | 0.835121i | \(0.685397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.55956i | 1.30532i | 0.757651 | + | 0.652660i | \(0.226347\pi\) | ||||
−0.757651 | + | 0.652660i | \(0.773653\pi\) | |||||||
\(44\) | 2.39690i | 0.361346i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.86175 | 0.274501 | ||||||||
\(47\) | − | 5.57882i | − | 0.813754i | −0.913483 | − | 0.406877i | \(-0.866618\pi\) | ||
0.913483 | − | 0.406877i | \(-0.133382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.92678 | + | 0.852531i | −0.696752 | + | 0.120566i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.67714 | −0.787277 | ||||||||
\(53\) | −4.19077 | −0.575646 | −0.287823 | − | 0.957684i | \(-0.592932\pi\) | ||||
−0.287823 | + | 0.957684i | \(0.592932\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.458606 | + | 5.33996i | 0.0618385 | + | 0.720041i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.88913i | 0.641974i | ||||||||
\(59\) | 2.00624 | 0.261191 | 0.130595 | − | 0.991436i | \(-0.458311\pi\) | ||||
0.130595 | + | 0.991436i | \(0.458311\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4548i | 1.59467i | 0.603537 | + | 0.797335i | \(0.293758\pi\) | ||||
−0.603537 | + | 0.797335i | \(0.706242\pi\) | |||||||
\(62\) | − | 4.52651i | − | 0.574868i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.6479 | + | 1.08623i | −1.56878 | + | 0.134730i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.62222i | − | 0.931202i | −0.884995 | − | 0.465601i | \(-0.845838\pi\) | ||
0.884995 | − | 0.465601i | \(-0.154162\pi\) | |||||||
\(68\) | − | 2.07192i | − | 0.251258i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.14126i | − | 1.08487i | −0.840099 | − | 0.542434i | \(-0.817503\pi\) | ||
0.840099 | − | 0.542434i | \(-0.182497\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.08235 | −0.126679 | −0.0633395 | − | 0.997992i | \(-0.520175\pi\) | ||||
−0.0633395 | + | 0.997992i | \(0.520175\pi\) | |||||||
\(74\) | − | 2.96911i | − | 0.345152i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.91397i | − | 0.678378i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.7678 | −1.88653 | −0.943265 | − | 0.332042i | \(-0.892263\pi\) | ||||
−0.943265 | + | 0.332042i | \(0.892263\pi\) | |||||||
\(80\) | 2.22787 | − | 0.191334i | 0.249083 | − | 0.0213917i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.04428 | 0.777911 | ||||||||
\(83\) | − | 13.6122i | − | 1.49414i | −0.664747 | − | 0.747068i | \(-0.731461\pi\) | ||
0.664747 | − | 0.747068i | \(-0.268539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.396428 | − | 4.61597i | −0.0429987 | − | 0.500672i | ||||
\(86\) | − | 8.55956i | − | 0.923001i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.39690i | − | 0.255510i | ||||||
\(89\) | −13.2626 | −1.40583 | −0.702916 | − | 0.711273i | \(-0.748119\pi\) | ||||
−0.702916 | + | 0.711273i | \(0.748119\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.86175 | −0.194101 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.57882i | 0.575411i | ||||||||
\(95\) | −1.13154 | − | 13.1755i | −0.116094 | − | 1.35178i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8260 | −1.30229 | −0.651143 | − | 0.758955i | \(-0.725710\pi\) | ||||
−0.651143 | + | 0.758955i | \(0.725710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.92678 | − | 0.852531i | 0.492678 | − | 0.0852531i | ||||
\(101\) | 8.91147 | 0.886724 | 0.443362 | − | 0.896343i | \(-0.353786\pi\) | ||||
0.443362 | + | 0.896343i | \(0.353786\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8198 | −1.06611 | −0.533053 | − | 0.846082i | \(-0.678955\pi\) | ||||
−0.533053 | + | 0.846082i | \(0.678955\pi\) | |||||||
\(104\) | 5.67714 | 0.556689 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.19077 | 0.407043 | ||||||||
\(107\) | −5.57707 | −0.539156 | −0.269578 | − | 0.962979i | \(-0.586884\pi\) | ||||
−0.269578 | + | 0.962979i | \(0.586884\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −0.458606 | − | 5.33996i | −0.0437264 | − | 0.509146i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.5030 | −1.36432 | −0.682161 | − | 0.731202i | \(-0.738960\pi\) | ||||
−0.682161 | + | 0.731202i | \(0.738960\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.14774 | + | 0.356216i | −0.386779 | + | 0.0332173i | ||||
\(116\) | − | 4.88913i | − | 0.453944i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00624 | −0.184690 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.25489 | 0.477717 | ||||||||
\(122\) | − | 12.4548i | − | 1.12760i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.52651i | 0.406493i | ||||||||
\(125\) | 10.8131 | − | 2.84199i | 0.967153 | − | 0.254195i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2462i | 1.70783i | 0.520416 | + | 0.853913i | \(0.325777\pi\) | ||||
−0.520416 | + | 0.853913i | \(0.674223\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.6479 | − | 1.08623i | 1.10929 | − | 0.0952684i | ||||
\(131\) | −4.69940 | −0.410589 | −0.205294 | − | 0.978700i | \(-0.565815\pi\) | ||||
−0.205294 | + | 0.978700i | \(0.565815\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.62222i | 0.658459i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.07192i | 0.177666i | ||||||||
\(137\) | 22.8845 | 1.95515 | 0.977577 | − | 0.210579i | \(-0.0675350\pi\) | ||||
0.977577 | + | 0.210579i | \(0.0675350\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.13862i | − | 0.775127i | −0.921843 | − | 0.387564i | \(-0.873317\pi\) | ||
0.921843 | − | 0.387564i | \(-0.126683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.14126i | 0.767117i | ||||||||
\(143\) | − | 13.6075i | − | 1.13792i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.935455 | − | 10.8923i | −0.0776853 | − | 0.904559i | ||||
\(146\) | 1.08235 | 0.0895756 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.96911i | 0.244059i | ||||||||
\(149\) | 10.4506i | 0.856150i | 0.903743 | + | 0.428075i | \(0.140808\pi\) | ||||
−0.903743 | + | 0.428075i | \(0.859192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7187 | −1.44193 | −0.720965 | − | 0.692971i | \(-0.756301\pi\) | ||||
−0.720965 | + | 0.692971i | \(0.756301\pi\) | |||||||
\(152\) | 5.91397i | 0.479686i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.866074 | + | 10.0845i | 0.0695647 | + | 0.810004i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.08297 | 0.485474 | 0.242737 | − | 0.970092i | \(-0.421955\pi\) | ||||
0.242737 | + | 0.970092i | \(0.421955\pi\) | |||||||
\(158\) | 16.7678 | 1.33398 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.22787 | + | 0.191334i | −0.176128 | + | 0.0151262i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.937339i | − | 0.0734181i | −0.999326 | − | 0.0367090i | \(-0.988313\pi\) | ||
0.999326 | − | 0.0367090i | \(-0.0116875\pi\) | |||||||
\(164\) | −7.04428 | −0.550066 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.6122i | 1.05651i | ||||||||
\(167\) | − | 17.2101i | − | 1.33176i | −0.746060 | − | 0.665879i | \(-0.768057\pi\) | ||
0.746060 | − | 0.665879i | \(-0.231943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.2299 | 1.47922 | ||||||||
\(170\) | 0.396428 | + | 4.61597i | 0.0304047 | + | 0.354029i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.55956i | 0.652660i | ||||||||
\(173\) | 1.97623i | 0.150250i | 0.997174 | + | 0.0751249i | \(0.0239355\pi\) | ||||
−0.997174 | + | 0.0751249i | \(0.976064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.39690i | 0.180673i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.2626 | 0.994073 | ||||||||
\(179\) | − | 0.887342i | − | 0.0663231i | −0.999450 | − | 0.0331615i | \(-0.989442\pi\) | ||
0.999450 | − | 0.0331615i | \(-0.0105576\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.89973i | − | 0.364194i | −0.983281 | − | 0.182097i | \(-0.941712\pi\) | ||
0.983281 | − | 0.182097i | \(-0.0582885\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.86175 | 0.137250 | ||||||||
\(185\) | 0.568090 | + | 6.61478i | 0.0417668 | + | 0.486328i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.96618 | 0.363163 | ||||||||
\(188\) | − | 5.57882i | − | 0.406877i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.13154 | + | 13.1755i | 0.0820905 | + | 0.955853i | ||||
\(191\) | 2.82843i | 0.204658i | 0.994751 | + | 0.102329i | \(0.0326294\pi\) | ||||
−0.994751 | + | 0.102329i | \(0.967371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.4966i | 1.40339i | 0.712476 | + | 0.701697i | \(0.247574\pi\) | ||||
−0.712476 | + | 0.701697i | \(0.752426\pi\) | |||||||
\(194\) | 12.8260 | 0.920855 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.1576 | −1.93490 | −0.967448 | − | 0.253069i | \(-0.918560\pi\) | ||||
−0.967448 | + | 0.253069i | \(0.918560\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.46410i | 0.245564i | 0.992434 | + | 0.122782i | \(0.0391815\pi\) | ||||
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | −4.92678 | + | 0.852531i | −0.348376 | + | 0.0602831i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.91147 | −0.627009 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.6937 | + | 1.34781i | −1.09610 | + | 0.0941349i | ||||
\(206\) | 10.8198 | 0.753850 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.67714 | −0.393639 | ||||||||
\(209\) | 14.1752 | 0.980516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.06071 | −0.279551 | −0.139775 | − | 0.990183i | \(-0.544638\pi\) | ||||
−0.139775 | + | 0.990183i | \(0.544638\pi\) | |||||||
\(212\) | −4.19077 | −0.287823 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.57707 | 0.381241 | ||||||||
\(215\) | 1.63773 | + | 19.0696i | 0.111692 | + | 1.30053i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.458606 | + | 5.33996i | 0.0309192 | + | 0.360020i | ||||
\(221\) | 11.7626i | 0.791238i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1486 | 1.08139 | 0.540696 | − | 0.841218i | \(-0.318161\pi\) | ||||
0.540696 | + | 0.841218i | \(0.318161\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.5030 | 0.964722 | ||||||||
\(227\) | 1.67980i | 0.111492i | 0.998445 | + | 0.0557462i | \(0.0177538\pi\) | ||||
−0.998445 | + | 0.0557462i | \(0.982246\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.6027i | − | 0.832811i | −0.909179 | − | 0.416406i | \(-0.863290\pi\) | ||
0.909179 | − | 0.416406i | \(-0.136710\pi\) | |||||||
\(230\) | 4.14774 | − | 0.356216i | 0.273494 | − | 0.0234882i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.88913i | 0.320987i | ||||||||
\(233\) | −14.5164 | −0.950999 | −0.475499 | − | 0.879716i | \(-0.657733\pi\) | ||||
−0.475499 | + | 0.879716i | \(0.657733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.06742 | − | 12.4289i | −0.0696305 | − | 0.810770i | ||||
\(236\) | 2.00624 | 0.130595 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.207089i | 0.0133955i | 0.999978 | + | 0.00669774i | \(0.00213197\pi\) | ||||
−0.999978 | + | 0.00669774i | \(0.997868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.4405i | − | 0.672530i | −0.941767 | − | 0.336265i | \(-0.890836\pi\) | ||
0.941767 | − | 0.336265i | \(-0.109164\pi\) | |||||||
\(242\) | −5.25489 | −0.337797 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.4548i | 0.797335i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.5744i | 2.13629i | ||||||||
\(248\) | − | 4.52651i | − | 0.287434i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.8131 | + | 2.84199i | −0.683880 | + | 0.179743i | ||||
\(251\) | −28.6464 | −1.80815 | −0.904074 | − | 0.427377i | \(-0.859438\pi\) | ||||
−0.904074 | + | 0.427377i | \(0.859438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.46243i | − | 0.280551i | ||||||
\(254\) | − | 19.2462i | − | 1.20762i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 24.9190i | − | 1.55440i | −0.629251 | − | 0.777202i | \(-0.716638\pi\) | ||
0.629251 | − | 0.777202i | \(-0.283362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −12.6479 | + | 1.08623i | −0.784390 | + | 0.0673649i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.69940 | 0.290330 | ||||||||
\(263\) | 19.1908 | 1.18335 | 0.591677 | − | 0.806175i | \(-0.298466\pi\) | ||||
0.591677 | + | 0.806175i | \(0.298466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.33647 | + | 0.801834i | −0.573535 | + | 0.0492563i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 7.62222i | − | 0.465601i | ||||||
\(269\) | 4.85489 | 0.296008 | 0.148004 | − | 0.988987i | \(-0.452715\pi\) | ||||
0.148004 | + | 0.988987i | \(0.452715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.6651i | − | 0.830098i | −0.909799 | − | 0.415049i | \(-0.863764\pi\) | ||
0.909799 | − | 0.415049i | \(-0.136236\pi\) | |||||||
\(272\) | − | 2.07192i | − | 0.125629i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.8845 | −1.38250 | ||||||||
\(275\) | 2.04343 | + | 11.8090i | 0.123223 | + | 0.712109i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.1298i | − | 0.728810i | −0.931241 | − | 0.364405i | \(-0.881272\pi\) | ||
0.931241 | − | 0.364405i | \(-0.118728\pi\) | |||||||
\(278\) | 9.13862i | 0.548098i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 32.6206i | − | 1.94598i | −0.230839 | − | 0.972992i | \(-0.574147\pi\) | ||
0.230839 | − | 0.972992i | \(-0.425853\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6609 | −0.752612 | −0.376306 | − | 0.926495i | \(-0.622806\pi\) | ||||
−0.376306 | + | 0.926495i | \(0.622806\pi\) | |||||||
\(284\) | − | 9.14126i | − | 0.542434i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.6075i | 0.804628i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.7071 | 0.747478 | ||||||||
\(290\) | 0.935455 | + | 10.8923i | 0.0549318 | + | 0.639620i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.08235 | −0.0633395 | ||||||||
\(293\) | − | 25.1151i | − | 1.46724i | −0.679559 | − | 0.733621i | \(-0.737829\pi\) | ||
0.679559 | − | 0.733621i | \(-0.262171\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.46965 | − | 0.383862i | 0.260233 | − | 0.0223493i | ||||
\(296\) | − | 2.96911i | − | 0.172576i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 10.4506i | − | 0.605390i | ||||||
\(299\) | 10.5694 | 0.611246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.7187 | 1.01960 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 5.91397i | − | 0.339189i | ||||||
\(305\) | 2.38302 | + | 27.7476i | 0.136451 | + | 1.58882i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.5674 | −1.05970 | −0.529849 | − | 0.848092i | \(-0.677751\pi\) | ||||
−0.529849 | + | 0.848092i | \(0.677751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.866074 | − | 10.0845i | −0.0491897 | − | 0.572760i | ||||
\(311\) | −12.4366 | −0.705216 | −0.352608 | − | 0.935771i | \(-0.614705\pi\) | ||||
−0.352608 | + | 0.935771i | \(0.614705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4135 | 0.701653 | 0.350826 | − | 0.936441i | \(-0.385901\pi\) | ||||
0.350826 | + | 0.936441i | \(0.385901\pi\) | |||||||
\(314\) | −6.08297 | −0.343282 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.7678 | −0.943265 | ||||||||
\(317\) | 24.6464 | 1.38428 | 0.692141 | − | 0.721763i | \(-0.256668\pi\) | ||||
0.692141 | + | 0.721763i | \(0.256668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7187 | 0.656123 | ||||||||
\(320\) | 2.22787 | − | 0.191334i | 0.124542 | − | 0.0106959i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.2533 | −0.681791 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.9700 | + | 4.83994i | −1.55150 | + | 0.268471i | ||||
\(326\) | 0.937339i | 0.0519144i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.04428 | 0.388955 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.1576 | −1.38278 | −0.691392 | − | 0.722479i | \(-0.743002\pi\) | ||||
−0.691392 | + | 0.722479i | \(0.743002\pi\) | |||||||
\(332\) | − | 13.6122i | − | 0.747068i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.2101i | 0.941694i | ||||||||
\(335\) | −1.45839 | − | 16.9813i | −0.0796801 | − | 0.927787i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4214i | 0.785584i | 0.919627 | + | 0.392792i | \(0.128491\pi\) | ||||
−0.919627 | + | 0.392792i | \(0.871509\pi\) | |||||||
\(338\) | −19.2299 | −1.04597 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.396428 | − | 4.61597i | −0.0214994 | − | 0.250336i | ||||
\(341\) | −10.8496 | −0.587538 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 8.55956i | − | 0.461500i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 1.97623i | − | 0.106243i | ||||||
\(347\) | −14.4866 | −0.777680 | −0.388840 | − | 0.921305i | \(-0.627124\pi\) | ||||
−0.388840 | + | 0.921305i | \(0.627124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.12483i | 0.113739i | 0.998382 | + | 0.0568697i | \(0.0181119\pi\) | ||||
−0.998382 | + | 0.0568697i | \(0.981888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 2.39690i | − | 0.127755i | ||||||
\(353\) | − | 14.5267i | − | 0.773178i | −0.922252 | − | 0.386589i | \(-0.873653\pi\) | ||
0.922252 | − | 0.386589i | \(-0.126347\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.74903 | − | 20.3655i | −0.0928288 | − | 1.08089i | ||||
\(356\) | −13.2626 | −0.702916 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.887342i | 0.0468975i | ||||||||
\(359\) | − | 3.94970i | − | 0.208457i | −0.994553 | − | 0.104228i | \(-0.966763\pi\) | ||
0.994553 | − | 0.104228i | \(-0.0332373\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.9750 | −0.840789 | ||||||||
\(362\) | 4.89973i | 0.257524i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.41132 | + | 0.207089i | −0.126214 | + | 0.0108395i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.6927 | 1.44555 | 0.722775 | − | 0.691084i | \(-0.242866\pi\) | ||||
0.722775 | + | 0.691084i | \(0.242866\pi\) | |||||||
\(368\) | −1.86175 | −0.0970506 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.568090 | − | 6.61478i | −0.0295336 | − | 0.343886i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1298i | 0.628058i | 0.949413 | + | 0.314029i | \(0.101679\pi\) | ||||
−0.949413 | + | 0.314029i | \(0.898321\pi\) | |||||||
\(374\) | −4.96618 | −0.256795 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.57882i | 0.287706i | ||||||||
\(377\) | 27.7563i | 1.42952i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.6821 | −0.959636 | −0.479818 | − | 0.877368i | \(-0.659297\pi\) | ||||
−0.479818 | + | 0.877368i | \(0.659297\pi\) | |||||||
\(380\) | −1.13154 | − | 13.1755i | −0.0580468 | − | 0.675890i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 2.82843i | − | 0.144715i | ||||||
\(383\) | 11.0293i | 0.563569i | 0.959478 | + | 0.281784i | \(0.0909263\pi\) | ||||
−0.959478 | + | 0.281784i | \(0.909074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 19.4966i | − | 0.992349i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.8260 | −0.651143 | ||||||||
\(389\) | 34.3710i | 1.74268i | 0.490679 | + | 0.871341i | \(0.336749\pi\) | ||||
−0.490679 | + | 0.871341i | \(0.663251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.85741i | 0.195078i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 27.1576 | 1.36818 | ||||||||
\(395\) | −37.3565 | + | 3.20825i | −1.87961 | + | 0.161425i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.0107 | 1.55638 | 0.778191 | − | 0.628027i | \(-0.216137\pi\) | ||||
0.778191 | + | 0.628027i | \(0.216137\pi\) | |||||||
\(398\) | − | 3.46410i | − | 0.173640i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.92678 | − | 0.852531i | 0.246339 | − | 0.0426266i | ||||
\(401\) | − | 9.47745i | − | 0.473281i | −0.971597 | − | 0.236641i | \(-0.923954\pi\) | ||
0.971597 | − | 0.236641i | \(-0.0760464\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 25.6976i | − | 1.28009i | ||||||
\(404\) | 8.91147 | 0.443362 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.11665 | −0.352759 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.47784i | − | 0.468649i | −0.972158 | − | 0.234324i | \(-0.924712\pi\) | ||
0.972158 | − | 0.234324i | \(-0.0752878\pi\) | |||||||
\(410\) | 15.6937 | − | 1.34781i | 0.775058 | − | 0.0665634i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.8198 | −0.533053 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.60448 | − | 30.3262i | −0.127849 | − | 1.48866i | ||||
\(416\) | 5.67714 | 0.278345 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.1752 | −0.693330 | ||||||||
\(419\) | 2.54445 | 0.124305 | 0.0621523 | − | 0.998067i | \(-0.480204\pi\) | ||||
0.0621523 | + | 0.998067i | \(0.480204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.08573 | −0.247863 | −0.123932 | − | 0.992291i | \(-0.539550\pi\) | ||||
−0.123932 | + | 0.992291i | \(0.539550\pi\) | |||||||
\(422\) | 4.06071 | 0.197672 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.19077 | 0.203522 | ||||||||
\(425\) | −1.76638 | − | 10.2079i | −0.0856820 | − | 0.495157i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.57707 | −0.269578 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.63773 | − | 19.0696i | −0.0789784 | − | 0.919616i | ||||
\(431\) | − | 13.2980i | − | 0.640544i | −0.947326 | − | 0.320272i | \(-0.896226\pi\) | ||
0.947326 | − | 0.320272i | \(-0.103774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.7895 | −0.614626 | −0.307313 | − | 0.951608i | \(-0.599430\pi\) | ||||
−0.307313 | + | 0.951608i | \(0.599430\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 11.0103i | 0.526696i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.373212i | 0.0178125i | 0.999960 | + | 0.00890623i | \(0.00283498\pi\) | ||||
−0.999960 | + | 0.00890623i | \(0.997165\pi\) | |||||||
\(440\) | −0.458606 | − | 5.33996i | −0.0218632 | − | 0.254573i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 11.7626i | − | 0.559490i | ||||||
\(443\) | −24.6330 | −1.17035 | −0.585175 | − | 0.810907i | \(-0.698974\pi\) | ||||
−0.585175 | + | 0.810907i | \(0.698974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.5473 | + | 2.53758i | −1.40068 | + | 0.120293i | ||||
\(446\) | −16.1486 | −0.764660 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.6223i | 1.91708i | 0.284950 | + | 0.958542i | \(0.408023\pi\) | ||||
−0.284950 | + | 0.958542i | \(0.591977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.8844i | − | 0.795056i | ||||||
\(452\) | −14.5030 | −0.682161 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 1.67980i | − | 0.0788370i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 0.990551i | − | 0.0463360i | −0.999732 | − | 0.0231680i | \(-0.992625\pi\) | ||
0.999732 | − | 0.0231680i | \(-0.00737527\pi\) | |||||||
\(458\) | 12.6027i | 0.588886i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.14774 | + | 0.356216i | −0.193389 | + | 0.0166087i | ||||
\(461\) | 20.7397 | 0.965945 | 0.482972 | − | 0.875636i | \(-0.339557\pi\) | ||||
0.482972 | + | 0.875636i | \(0.339557\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.46421i | − | 0.0680476i | −0.999421 | − | 0.0340238i | \(-0.989168\pi\) | ||
0.999421 | − | 0.0340238i | \(-0.0108322\pi\) | |||||||
\(464\) | − | 4.88913i | − | 0.226972i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.5164 | 0.672458 | ||||||||
\(467\) | − | 36.2680i | − | 1.67828i | −0.543912 | − | 0.839142i | \(-0.683057\pi\) | ||
0.543912 | − | 0.839142i | \(-0.316943\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.06742 | + | 12.4289i | 0.0492362 | + | 0.573301i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00624 | −0.0923449 | ||||||||
\(473\) | −20.5164 | −0.943343 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.04184 | − | 29.1368i | −0.231336 | − | 1.33689i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 0.207089i | − | 0.00947203i | ||||||
\(479\) | −10.3258 | −0.471796 | −0.235898 | − | 0.971778i | \(-0.575803\pi\) | ||||
−0.235898 | + | 0.971778i | \(0.575803\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 16.8560i | − | 0.768569i | ||||||
\(482\) | 10.4405i | 0.475551i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.25489 | 0.238859 | ||||||||
\(485\) | −28.5747 | + | 2.45405i | −1.29751 | + | 0.111433i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.3291i | 0.921198i | 0.887608 | + | 0.460599i | \(0.152365\pi\) | ||||
−0.887608 | + | 0.460599i | \(0.847635\pi\) | |||||||
\(488\) | − | 12.4548i | − | 0.563801i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.6034i | 1.56163i | 0.624764 | + | 0.780814i | \(0.285195\pi\) | ||||
−0.624764 | + | 0.780814i | \(0.714805\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.1299 | −0.456228 | ||||||||
\(494\) | − | 33.5744i | − | 1.51058i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.52651i | 0.203247i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.95089 | 0.132100 | 0.0660501 | − | 0.997816i | \(-0.478960\pi\) | ||||
0.0660501 | + | 0.997816i | \(0.478960\pi\) | |||||||
\(500\) | 10.8131 | − | 2.84199i | 0.483577 | − | 0.127097i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.6464 | 1.27855 | ||||||||
\(503\) | 31.8907i | 1.42193i | 0.703225 | + | 0.710967i | \(0.251742\pi\) | ||||
−0.703225 | + | 0.710967i | \(0.748258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.8536 | − | 1.70506i | 0.883472 | − | 0.0758743i | ||||
\(506\) | 4.46243i | 0.198379i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.2462i | 0.853913i | ||||||||
\(509\) | 0.842398 | 0.0373386 | 0.0186693 | − | 0.999826i | \(-0.494057\pi\) | ||||
0.0186693 | + | 0.999826i | \(0.494057\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.9190i | 1.09913i | ||||||||
\(515\) | −24.1050 | + | 2.07019i | −1.06220 | + | 0.0912234i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3718 | 0.588093 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.6479 | − | 1.08623i | 0.554647 | − | 0.0476342i | ||||
\(521\) | −5.62999 | −0.246654 | −0.123327 | − | 0.992366i | \(-0.539356\pi\) | ||||
−0.123327 | + | 0.992366i | \(0.539356\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.8380 | −0.780001 | −0.390000 | − | 0.920815i | \(-0.627525\pi\) | ||||
−0.390000 | + | 0.920815i | \(0.627525\pi\) | |||||||
\(524\) | −4.69940 | −0.205294 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1908 | −0.836757 | ||||||||
\(527\) | 9.37859 | 0.408538 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.5339 | −0.849299 | ||||||||
\(530\) | 9.33647 | − | 0.801834i | 0.405550 | − | 0.0348295i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.9913 | 1.73222 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.4250 | + | 1.06708i | −0.537179 | + | 0.0461339i | ||||
\(536\) | 7.62222i | 0.329230i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.85489 | −0.209309 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.4241 | −1.09307 | −0.546533 | − | 0.837438i | \(-0.684053\pi\) | ||||
−0.546533 | + | 0.837438i | \(0.684053\pi\) | |||||||
\(542\) | 13.6651i | 0.586968i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.07192i | 0.0888330i | ||||||||
\(545\) | 4.45573 | − | 0.382667i | 0.190863 | − | 0.0163917i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.1182i | − | 0.518138i | −0.965859 | − | 0.259069i | \(-0.916584\pi\) | ||
0.965859 | − | 0.259069i | \(-0.0834158\pi\) | |||||||
\(548\) | 22.8845 | 0.977577 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.04343 | − | 11.8090i | −0.0871321 | − | 0.503537i | ||||
\(551\) | −28.9141 | −1.23178 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.1298i | 0.515346i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9.13862i | − | 0.387564i | ||||||
\(557\) | 1.53957 | 0.0652338 | 0.0326169 | − | 0.999468i | \(-0.489616\pi\) | ||||
0.0326169 | + | 0.999468i | \(0.489616\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 48.5938i | − | 2.05530i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 32.6206i | 1.37602i | ||||||||
\(563\) | 22.4644i | 0.946762i | 0.880858 | + | 0.473381i | \(0.156967\pi\) | ||||
−0.880858 | + | 0.473381i | \(0.843033\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.3106 | + | 2.77490i | −1.35932 | + | 0.116741i | ||||
\(566\) | 12.6609 | 0.532177 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.14126i | 0.383559i | ||||||||
\(569\) | 10.8058i | 0.453003i | 0.974011 | + | 0.226501i | \(0.0727288\pi\) | ||||
−0.974011 | + | 0.226501i | \(0.927271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.96338 | −0.333257 | −0.166629 | − | 0.986020i | \(-0.553288\pi\) | ||||
−0.166629 | + | 0.986020i | \(0.553288\pi\) | |||||||
\(572\) | − | 13.6075i | − | 0.568958i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.17246 | + | 1.58720i | −0.382518 | + | 0.0661910i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.5928 | 1.02381 | 0.511906 | − | 0.859041i | \(-0.328939\pi\) | ||||
0.511906 | + | 0.859041i | \(0.328939\pi\) | |||||||
\(578\) | −12.7071 | −0.528547 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.935455 | − | 10.8923i | −0.0388426 | − | 0.452280i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 10.0448i | − | 0.416014i | ||||||
\(584\) | 1.08235 | 0.0447878 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.1151i | 1.03750i | ||||||||
\(587\) | 12.8469i | 0.530248i | 0.964214 | + | 0.265124i | \(0.0854129\pi\) | ||||
−0.964214 | + | 0.265124i | \(0.914587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.7696 | 1.10302 | ||||||||
\(590\) | −4.46965 | + | 0.383862i | −0.184012 | + | 0.0158033i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.96911i | 0.122030i | ||||||||
\(593\) | 17.1631i | 0.704804i | 0.935849 | + | 0.352402i | \(0.114635\pi\) | ||||
−0.935849 | + | 0.352402i | \(0.885365\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.4506i | 0.428075i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.5694 | −0.432216 | ||||||||
\(599\) | 19.6083i | 0.801174i | 0.916259 | + | 0.400587i | \(0.131194\pi\) | ||||
−0.916259 | + | 0.400587i | \(0.868806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.2340i | 1.15169i | 0.817560 | + | 0.575844i | \(0.195326\pi\) | ||||
−0.817560 | + | 0.575844i | \(0.804674\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.7187 | −0.720965 | ||||||||
\(605\) | 11.7072 | − | 1.00544i | 0.475965 | − | 0.0408768i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.65314 | −0.391809 | −0.195904 | − | 0.980623i | \(-0.562764\pi\) | ||||
−0.195904 | + | 0.980623i | \(0.562764\pi\) | |||||||
\(608\) | 5.91397i | 0.239843i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.38302 | − | 27.7476i | −0.0964855 | − | 1.12347i | ||||
\(611\) | 31.6717i | 1.28130i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.05588i | − | 0.365764i | −0.983135 | − | 0.182882i | \(-0.941457\pi\) | ||
0.983135 | − | 0.182882i | \(-0.0585426\pi\) | |||||||
\(614\) | 18.5674 | 0.749320 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.3122 | 1.01903 | 0.509515 | − | 0.860462i | \(-0.329825\pi\) | ||||
0.509515 | + | 0.860462i | \(0.329825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 38.8711i | − | 1.56236i | −0.624305 | − | 0.781181i | \(-0.714618\pi\) | ||
0.624305 | − | 0.781181i | \(-0.285382\pi\) | |||||||
\(620\) | 0.866074 | + | 10.0845i | 0.0347824 | + | 0.405002i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.4366 | 0.498663 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5464 | − | 8.40047i | 0.941855 | − | 0.336019i | ||||
\(626\) | −12.4135 | −0.496143 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.08297 | 0.242737 | ||||||||
\(629\) | 6.15177 | 0.245287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.8670 | −0.950129 | −0.475065 | − | 0.879951i | \(-0.657575\pi\) | ||||
−0.475065 | + | 0.879951i | \(0.657575\pi\) | |||||||
\(632\) | 16.7678 | 0.666989 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −24.6464 | −0.978834 | ||||||||
\(635\) | 3.68245 | + | 42.8780i | 0.146133 | + | 1.70156i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.7187 | −0.463949 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.22787 | + | 0.191334i | −0.0880642 | + | 0.00756312i | ||||
\(641\) | − | 34.8796i | − | 1.37766i | −0.724923 | − | 0.688830i | \(-0.758124\pi\) | ||
0.724923 | − | 0.688830i | \(-0.241876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.25944 | −0.246848 | −0.123424 | − | 0.992354i | \(-0.539388\pi\) | ||||
−0.123424 | + | 0.992354i | \(0.539388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.2533 | 0.482099 | ||||||||
\(647\) | − | 37.5022i | − | 1.47436i | −0.675695 | − | 0.737181i | \(-0.736156\pi\) | ||
0.675695 | − | 0.737181i | \(-0.263844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.80876i | 0.188760i | ||||||||
\(650\) | 27.9700 | − | 4.83994i | 1.09707 | − | 0.189838i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 0.937339i | − | 0.0367090i | ||||||
\(653\) | 26.4516 | 1.03513 | 0.517565 | − | 0.855644i | \(-0.326839\pi\) | ||||
0.517565 | + | 0.855644i | \(0.326839\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.4696 | + | 0.899153i | −0.409083 | + | 0.0351328i | ||||
\(656\) | −7.04428 | −0.275033 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 19.9524i | − | 0.777234i | −0.921399 | − | 0.388617i | \(-0.872953\pi\) | ||
0.921399 | − | 0.388617i | \(-0.127047\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 5.44098i | − | 0.211630i | −0.994386 | − | 0.105815i | \(-0.966255\pi\) | ||
0.994386 | − | 0.105815i | \(-0.0337451\pi\) | |||||||
\(662\) | 25.1576 | 0.977776 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.6122i | 0.528257i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.10236i | 0.352445i | ||||||||
\(668\) | − | 17.2101i | − | 0.665879i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.45839 | + | 16.9813i | 0.0563424 | + | 0.656044i | ||||
\(671\) | −29.8528 | −1.15245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.50635i | − | 0.327896i | −0.986469 | − | 0.163948i | \(-0.947577\pi\) | ||
0.986469 | − | 0.163948i | \(-0.0524228\pi\) | |||||||
\(674\) | − | 14.4214i | − | 0.555492i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.2299 | 0.739611 | ||||||||
\(677\) | 5.08639i | 0.195486i | 0.995212 | + | 0.0977430i | \(0.0311623\pi\) | ||||
−0.995212 | + | 0.0977430i | \(0.968838\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.396428 | + | 4.61597i | 0.0152023 | + | 0.177014i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.8496 | 0.415452 | ||||||||
\(683\) | 21.0145 | 0.804099 | 0.402050 | − | 0.915618i | \(-0.368298\pi\) | ||||
0.402050 | + | 0.915618i | \(0.368298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.9836 | − | 4.37857i | 1.94798 | − | 0.167297i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.55956i | 0.326330i | ||||||||
\(689\) | 23.7916 | 0.906386 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 24.9095i | − | 0.947604i | −0.880631 | − | 0.473802i | \(-0.842881\pi\) | ||
0.880631 | − | 0.473802i | \(-0.157119\pi\) | |||||||
\(692\) | 1.97623i | 0.0751249i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.4866 | 0.549903 | ||||||||
\(695\) | −1.74852 | − | 20.3596i | −0.0663253 | − | 0.772285i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5952i | 0.552833i | ||||||||
\(698\) | − | 2.12483i | − | 0.0804259i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 22.5321i | − | 0.851025i | −0.904953 | − | 0.425512i | \(-0.860094\pi\) | ||
0.904953 | − | 0.425512i | \(-0.139906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.5592 | 0.662258 | ||||||||
\(704\) | 2.39690i | 0.0903364i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.5267i | 0.546719i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.9009 | 0.935172 | 0.467586 | − | 0.883948i | \(-0.345124\pi\) | ||||
0.467586 | + | 0.883948i | \(0.345124\pi\) | |||||||
\(710\) | 1.74903 | + | 20.3655i | 0.0656399 | + | 0.764304i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.2626 | 0.497037 | ||||||||
\(713\) | − | 8.42726i | − | 0.315603i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.60357 | − | 30.3157i | −0.0973681 | − | 1.13374i | ||||
\(716\) | − | 0.887342i | − | 0.0331615i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.94970i | 0.147401i | ||||||||
\(719\) | −39.8483 | −1.48609 | −0.743045 | − | 0.669241i | \(-0.766619\pi\) | ||||
−0.743045 | + | 0.669241i | \(0.766619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.9750 | 0.594527 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 4.89973i | − | 0.182097i | ||||||
\(725\) | −4.16814 | − | 24.0877i | −0.154801 | − | 0.894594i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.124004 | 0.00459906 | 0.00229953 | − | 0.999997i | \(-0.499268\pi\) | ||||
0.00229953 | + | 0.999997i | \(0.499268\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.41132 | − | 0.207089i | 0.0892471 | − | 0.00766471i | ||||
\(731\) | 17.7348 | 0.655943 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.5478 | −1.05444 | −0.527218 | − | 0.849730i | \(-0.676765\pi\) | ||||
−0.527218 | + | 0.849730i | \(0.676765\pi\) | |||||||
\(734\) | −27.6927 | −1.02216 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.86175 | 0.0686252 | ||||||||
\(737\) | 18.2697 | 0.672972 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0361 | −0.700256 | −0.350128 | − | 0.936702i | \(-0.613862\pi\) | ||||
−0.350128 | + | 0.936702i | \(0.613862\pi\) | |||||||
\(740\) | 0.568090 | + | 6.61478i | 0.0208834 | + | 0.243164i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.0800 | 0.626605 | 0.313303 | − | 0.949653i | \(-0.398565\pi\) | ||||
0.313303 | + | 0.949653i | \(0.398565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.99956 | + | 23.2826i | 0.0732582 | + | 0.853010i | ||||
\(746\) | − | 12.1298i | − | 0.444104i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.96618 | 0.181582 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8893 | −0.616298 | −0.308149 | − | 0.951338i | \(-0.599709\pi\) | ||||
−0.308149 | + | 0.951338i | \(0.599709\pi\) | |||||||
\(752\) | − | 5.57882i | − | 0.203439i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 27.7563i | − | 1.01082i | ||||||
\(755\) | −39.4750 | + | 3.39019i | −1.43664 | + | 0.123382i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.4057i | 1.21415i | 0.794644 | + | 0.607076i | \(0.207658\pi\) | ||||
−0.794644 | + | 0.607076i | \(0.792342\pi\) | |||||||
\(758\) | 18.6821 | 0.678565 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.13154 | + | 13.1755i | 0.0410453 | + | 0.477927i | ||||
\(761\) | −32.6148 | −1.18229 | −0.591143 | − | 0.806566i | \(-0.701323\pi\) | ||||
−0.591143 | + | 0.806566i | \(0.701323\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.82843i | 0.102329i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 11.0293i | − | 0.398503i | ||||||
\(767\) | −11.3897 | −0.411259 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4396i | 0.809192i | 0.914495 | + | 0.404596i | \(0.132588\pi\) | ||||
−0.914495 | + | 0.404596i | \(0.867412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.4966i | 0.701697i | ||||||||
\(773\) | 39.8331i | 1.43270i | 0.697743 | + | 0.716348i | \(0.254188\pi\) | ||||
−0.697743 | + | 0.716348i | \(0.745812\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.85900 | + | 22.3012i | 0.138619 | + | 0.801081i | ||||
\(776\) | 12.8260 | 0.460428 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 34.3710i | − | 1.23226i | ||||||
\(779\) | 41.6596i | 1.49261i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.9106 | 0.784024 | ||||||||
\(782\) | − | 3.85741i | − | 0.137941i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.5521 | − | 1.16388i | 0.483694 | − | 0.0415405i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.7330 | 0.596466 | 0.298233 | − | 0.954493i | \(-0.403603\pi\) | ||||
0.298233 | + | 0.954493i | \(0.403603\pi\) | |||||||
\(788\) | −27.1576 | −0.967448 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 37.3565 | − | 3.20825i | 1.32909 | − | 0.114144i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 70.7074i | − | 2.51090i | ||||||
\(794\) | −31.0107 | −1.10053 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.46410i | 0.122782i | ||||||||
\(797\) | 2.68812i | 0.0952182i | 0.998866 | + | 0.0476091i | \(0.0151602\pi\) | ||||
−0.998866 | + | 0.0476091i | \(0.984840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.5589 | −0.408924 | ||||||||
\(800\) | −4.92678 | + | 0.852531i | −0.174188 | + | 0.0301415i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.47745i | 0.334660i | ||||||||
\(803\) | − | 2.59427i | − | 0.0915498i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.6976i | 0.905161i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.91147 | −0.313504 | ||||||||
\(809\) | 31.4325i | 1.10511i | 0.833477 | + | 0.552554i | \(0.186347\pi\) | ||||
−0.833477 | + | 0.552554i | \(0.813653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.3830i | 1.73407i | 0.498246 | + | 0.867036i | \(0.333978\pi\) | ||||
−0.498246 | + | 0.867036i | \(0.666022\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.11665 | 0.249438 | ||||||||
\(815\) | −0.179344 | − | 2.08827i | −0.00628216 | − | 0.0731488i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.6209 | 1.77100 | ||||||||
\(818\) | 9.47784i | 0.331385i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.6937 | + | 1.34781i | −0.548048 | + | 0.0470675i | ||||
\(821\) | − | 44.7263i | − | 1.56096i | −0.625181 | − | 0.780480i | \(-0.714975\pi\) | ||
0.625181 | − | 0.780480i | \(-0.285025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.1414i | 0.458081i | 0.973417 | + | 0.229041i | \(0.0735589\pi\) | ||||
−0.973417 | + | 0.229041i | \(0.926441\pi\) | |||||||
\(824\) | 10.8198 | 0.376925 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.4125 | 1.64869 | 0.824346 | − | 0.566086i | \(-0.191543\pi\) | ||||
0.824346 | + | 0.566086i | \(0.191543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.21588i | − | 0.285349i | −0.989770 | − | 0.142675i | \(-0.954430\pi\) | ||
0.989770 | − | 0.142675i | \(-0.0455703\pi\) | |||||||
\(830\) | 2.60448 | + | 30.3262i | 0.0904027 | + | 1.05264i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.67714 | −0.196819 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.29287 | − | 38.3418i | −0.113954 | − | 1.32687i | ||||
\(836\) | 14.1752 | 0.490258 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.54445 | −0.0878967 | ||||||||
\(839\) | 17.6943 | 0.610875 | 0.305437 | − | 0.952212i | \(-0.401197\pi\) | ||||
0.305437 | + | 0.952212i | \(0.401197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.09640 | 0.175738 | ||||||||
\(842\) | 5.08573 | 0.175266 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.06071 | −0.139775 | ||||||||
\(845\) | 42.8416 | − | 3.67932i | 1.47380 | − | 0.126572i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.19077 | −0.143912 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.76638 | + | 10.2079i | 0.0605863 | + | 0.350129i | ||||
\(851\) | − | 5.52775i | − | 0.189489i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.1129 | 1.37344 | 0.686720 | − | 0.726922i | \(-0.259050\pi\) | ||||
0.686720 | + | 0.726922i | \(0.259050\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.57707 | 0.190620 | ||||||||
\(857\) | − | 44.1308i | − | 1.50748i | −0.657173 | − | 0.753740i | \(-0.728248\pi\) | ||
0.657173 | − | 0.753740i | \(-0.271752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 14.3575i | − | 0.489870i | −0.969539 | − | 0.244935i | \(-0.921233\pi\) | ||
0.969539 | − | 0.244935i | \(-0.0787667\pi\) | |||||||
\(860\) | 1.63773 | + | 19.0696i | 0.0558461 | + | 0.650266i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.2980i | 0.452933i | ||||||||
\(863\) | 12.8029 | 0.435814 | 0.217907 | − | 0.975970i | \(-0.430077\pi\) | ||||
0.217907 | + | 0.975970i | \(0.430077\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.378119 | + | 4.40277i | 0.0128564 | + | 0.149699i | ||||
\(866\) | 12.7895 | 0.434606 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 40.1908i | − | 1.36338i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.2724i | 1.46623i | ||||||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 11.0103i | − | 0.372431i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 58.2720i | 1.96771i | 0.178980 | + | 0.983853i | \(0.442720\pi\) | ||||
−0.178980 | + | 0.983853i | \(0.557280\pi\) | |||||||
\(878\) | − | 0.373212i | − | 0.0125953i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.458606 | + | 5.33996i | 0.0154596 | + | 0.180010i | ||||
\(881\) | −1.80667 | −0.0608682 | −0.0304341 | − | 0.999537i | \(-0.509689\pi\) | ||||
−0.0304341 | + | 0.999537i | \(0.509689\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.8997i | − | 0.467761i | −0.972265 | − | 0.233881i | \(-0.924858\pi\) | ||
0.972265 | − | 0.233881i | \(-0.0751425\pi\) | |||||||
\(884\) | 11.7626i | 0.395619i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.6330 | 0.827562 | ||||||||
\(887\) | − | 26.4918i | − | 0.889508i | −0.895653 | − | 0.444754i | \(-0.853291\pi\) | ||
0.895653 | − | 0.444754i | \(-0.146709\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 29.5473 | − | 2.53758i | 0.990427 | − | 0.0850598i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.1486 | 0.540696 | ||||||||
\(893\) | −32.9929 | −1.10407 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.169778 | − | 1.97688i | −0.00567506 | − | 0.0660798i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 40.6223i | − | 1.35558i | ||||||
\(899\) | 22.1307 | 0.738101 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.68295i | 0.289271i | ||||||||
\(902\) | 16.8844i | 0.562189i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.5030 | 0.482361 | ||||||||
\(905\) | −0.937482 | − | 10.9159i | −0.0311630 | − | 0.362858i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.7300i | 1.21960i | 0.792556 | + | 0.609800i | \(0.208750\pi\) | ||||
−0.792556 | + | 0.609800i | \(0.791250\pi\) | |||||||
\(908\) | 1.67980i | 0.0557462i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 39.8018i | − | 1.31869i | −0.751839 | − | 0.659347i | \(-0.770833\pi\) | ||
0.751839 | − | 0.659347i | \(-0.229167\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.6271 | 1.07980 | ||||||||
\(914\) | 0.990551i | 0.0327645i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 12.6027i | − | 0.416406i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −60.3383 | −1.99038 | −0.995189 | − | 0.0979740i | \(-0.968764\pi\) | ||||
−0.995189 | + | 0.0979740i | \(0.968764\pi\) | |||||||
\(920\) | 4.14774 | − | 0.356216i | 0.136747 | − | 0.0117441i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.7397 | −0.683026 | ||||||||
\(923\) | 51.8962i | 1.70818i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.53126 | + | 14.6282i | 0.0832273 | + | 0.480971i | ||||
\(926\) | 1.46421i | 0.0481169i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.88913i | 0.160494i | ||||||||
\(929\) | 44.3497 | 1.45507 | 0.727533 | − | 0.686072i | \(-0.240667\pi\) | ||||
0.727533 | + | 0.686072i | \(0.240667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.5164 | −0.475499 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36.2680i | 1.18673i | ||||||||
\(935\) | 11.0640 | − | 0.950198i | 0.361831 | − | 0.0310748i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.54073 | −0.0830021 | −0.0415010 | − | 0.999138i | \(-0.513214\pi\) | ||||
−0.0415010 | + | 0.999138i | \(0.513214\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.06742 | − | 12.4289i | −0.0348152 | − | 0.405385i | ||||
\(941\) | −33.8977 | −1.10503 | −0.552516 | − | 0.833502i | \(-0.686332\pi\) | ||||
−0.552516 | + | 0.833502i | \(0.686332\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.1147 | 0.427074 | ||||||||
\(944\) | 2.00624 | 0.0652977 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.5164 | 0.667045 | ||||||||
\(947\) | 49.5089 | 1.60882 | 0.804411 | − | 0.594073i | \(-0.202481\pi\) | ||||
0.804411 | + | 0.594073i | \(0.202481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.14463 | 0.199463 | ||||||||
\(950\) | 5.04184 | + | 29.1368i | 0.163579 | + | 0.945323i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.0625 | 0.552709 | 0.276355 | − | 0.961056i | \(-0.410874\pi\) | ||||
0.276355 | + | 0.961056i | \(0.410874\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.541173 | + | 6.30136i | 0.0175119 | + | 0.203907i | ||||
\(956\) | 0.207089i | 0.00669774i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.3258 | 0.333610 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.5107 | 0.339054 | ||||||||
\(962\) | 16.8560i | 0.543461i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 10.4405i | − | 0.336265i | ||||||
\(965\) | 3.73035 | + | 43.4357i | 0.120084 | + | 1.39825i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 49.6639i | − | 1.59708i | −0.601940 | − | 0.798541i | \(-0.705606\pi\) | ||
0.601940 | − | 0.798541i | \(-0.294394\pi\) | |||||||
\(968\) | −5.25489 | −0.168899 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 28.5747 | − | 2.45405i | 0.917478 | − | 0.0787948i | ||||
\(971\) | 28.5859 | 0.917366 | 0.458683 | − | 0.888600i | \(-0.348321\pi\) | ||||
0.458683 | + | 0.888600i | \(0.348321\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 20.3291i | − | 0.651386i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.4548i | 0.398668i | ||||||||
\(977\) | 27.7205 | 0.886859 | 0.443429 | − | 0.896309i | \(-0.353762\pi\) | ||||
0.443429 | + | 0.896309i | \(0.353762\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.7890i | − | 1.01598i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 34.6034i | − | 1.10424i | ||||||
\(983\) | 42.8268i | 1.36596i | 0.730436 | + | 0.682982i | \(0.239317\pi\) | ||||
−0.730436 | + | 0.682982i | \(0.760683\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −60.5034 | + | 5.19615i | −1.92780 | + | 0.165563i | ||||
\(986\) | 10.1299 | 0.322602 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.5744i | 1.06814i | ||||||||
\(989\) | − | 15.9358i | − | 0.506729i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.7446 | 1.35783 | 0.678914 | − | 0.734218i | \(-0.262451\pi\) | ||||
0.678914 | + | 0.734218i | \(0.262451\pi\) | |||||||
\(992\) | − | 4.52651i | − | 0.143717i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.662799 | + | 7.71756i | 0.0210121 | + | 0.244663i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.8719 | 1.04106 | 0.520531 | − | 0.853843i | \(-0.325734\pi\) | ||||
0.520531 | + | 0.853843i | \(0.325734\pi\) | |||||||
\(998\) | −2.95089 | −0.0934089 | ||||||||
\(999\) | 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 | 4410.2.d.a.4409.15 | 16 | ||
3.2 | odd | 2 | 4410.2.d.b.4409.2 | 16 | |||
5.4 | even | 2 | 4410.2.d.b.4409.16 | 16 | |||
7.2 | even | 3 | 630.2.bo.b.269.2 | yes | 16 | ||
7.3 | odd | 6 | 630.2.bo.b.89.5 | yes | 16 | ||
7.6 | odd | 2 | inner | 4410.2.d.a.4409.2 | 16 | ||
15.14 | odd | 2 | inner | 4410.2.d.a.4409.1 | 16 | ||
21.2 | odd | 6 | 630.2.bo.a.269.7 | yes | 16 | ||
21.17 | even | 6 | 630.2.bo.a.89.4 | ✓ | 16 | ||
21.20 | even | 2 | 4410.2.d.b.4409.15 | 16 | |||
35.2 | odd | 12 | 3150.2.bf.f.1151.1 | 32 | |||
35.3 | even | 12 | 3150.2.bf.f.1601.2 | 32 | |||
35.9 | even | 6 | 630.2.bo.a.269.4 | yes | 16 | ||
35.17 | even | 12 | 3150.2.bf.f.1601.11 | 32 | |||
35.23 | odd | 12 | 3150.2.bf.f.1151.12 | 32 | |||
35.24 | odd | 6 | 630.2.bo.a.89.7 | yes | 16 | ||
35.34 | odd | 2 | 4410.2.d.b.4409.1 | 16 | |||
105.2 | even | 12 | 3150.2.bf.f.1151.11 | 32 | |||
105.17 | odd | 12 | 3150.2.bf.f.1601.1 | 32 | |||
105.23 | even | 12 | 3150.2.bf.f.1151.2 | 32 | |||
105.38 | odd | 12 | 3150.2.bf.f.1601.12 | 32 | |||
105.44 | odd | 6 | 630.2.bo.b.269.5 | yes | 16 | ||
105.59 | even | 6 | 630.2.bo.b.89.2 | yes | 16 | ||
105.104 | even | 2 | inner | 4410.2.d.a.4409.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.4 | ✓ | 16 | 21.17 | even | 6 | ||
630.2.bo.a.89.7 | yes | 16 | 35.24 | odd | 6 | ||
630.2.bo.a.269.4 | yes | 16 | 35.9 | even | 6 | ||
630.2.bo.a.269.7 | yes | 16 | 21.2 | odd | 6 | ||
630.2.bo.b.89.2 | yes | 16 | 105.59 | even | 6 | ||
630.2.bo.b.89.5 | yes | 16 | 7.3 | odd | 6 | ||
630.2.bo.b.269.2 | yes | 16 | 7.2 | even | 3 | ||
630.2.bo.b.269.5 | yes | 16 | 105.44 | odd | 6 | ||
3150.2.bf.f.1151.1 | 32 | 35.2 | odd | 12 | |||
3150.2.bf.f.1151.2 | 32 | 105.23 | even | 12 | |||
3150.2.bf.f.1151.11 | 32 | 105.2 | even | 12 | |||
3150.2.bf.f.1151.12 | 32 | 35.23 | odd | 12 | |||
3150.2.bf.f.1601.1 | 32 | 105.17 | odd | 12 | |||
3150.2.bf.f.1601.2 | 32 | 35.3 | even | 12 | |||
3150.2.bf.f.1601.11 | 32 | 35.17 | even | 12 | |||
3150.2.bf.f.1601.12 | 32 | 105.38 | odd | 12 | |||
4410.2.d.a.4409.1 | 16 | 15.14 | odd | 2 | inner | ||
4410.2.d.a.4409.2 | 16 | 7.6 | odd | 2 | inner | ||
4410.2.d.a.4409.15 | 16 | 1.1 | even | 1 | trivial | ||
4410.2.d.a.4409.16 | 16 | 105.104 | even | 2 | inner | ||
4410.2.d.b.4409.1 | 16 | 35.34 | odd | 2 | |||
4410.2.d.b.4409.2 | 16 | 3.2 | odd | 2 | |||
4410.2.d.b.4409.15 | 16 | 21.20 | even | 2 | |||
4410.2.d.b.4409.16 | 16 | 5.4 | even | 2 |