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 | 4409.6 | ||
Root | \(-0.442358 + 2.19188i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.4409 |
Dual form | 4410.2.d.a.4409.5 |
$q$-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 | ||||||||
\(5\) | −1.67704 | + | 1.47903i | −0.749996 | + | 0.661443i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.67704 | − | 1.47903i | 0.530327 | − | 0.467711i | ||||
\(11\) | − | 6.33033i | − | 1.90867i | −0.298743 | − | 0.954334i | \(-0.596567\pi\) | ||
0.298743 | − | 0.954334i | \(-0.403433\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.05290 | −0.292021 | −0.146011 | − | 0.989283i | \(-0.546643\pi\) | ||||
−0.146011 | + | 0.989283i | \(0.546643\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.63684i | − | 1.12460i | −0.826934 | − | 0.562299i | \(-0.809917\pi\) | ||
0.826934 | − | 0.562299i | \(-0.190083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.17914i | − | 1.41759i | −0.705414 | − | 0.708795i | \(-0.749239\pi\) | ||
0.705414 | − | 0.708795i | \(-0.250761\pi\) | |||||||
\(20\) | −1.67704 | + | 1.47903i | −0.374998 | + | 0.330721i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.33033i | 1.34963i | ||||||||
\(23\) | −7.04472 | −1.46893 | −0.734463 | − | 0.678649i | \(-0.762566\pi\) | ||||
−0.734463 | + | 0.678649i | \(0.762566\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.624933 | − | 4.96079i | 0.124987 | − | 0.992158i | ||||
\(26\) | 1.05290 | 0.206490 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.98101i | − | 0.553560i | −0.960933 | − | 0.276780i | \(-0.910733\pi\) | ||
0.960933 | − | 0.276780i | \(-0.0892674\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.31561i | 1.13432i | 0.823608 | + | 0.567159i | \(0.191957\pi\) | ||||
−0.823608 | + | 0.567159i | \(0.808043\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.63684i | 0.795211i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.47982i | 0.572078i | 0.958218 | + | 0.286039i | \(0.0923388\pi\) | ||||
−0.958218 | + | 0.286039i | \(0.907661\pi\) | |||||||
\(38\) | 6.17914i | 1.00239i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.67704 | − | 1.47903i | 0.265163 | − | 0.233855i | ||||
\(41\) | −6.97007 | −1.08854 | −0.544271 | − | 0.838909i | \(-0.683194\pi\) | ||||
−0.544271 | + | 0.838909i | \(0.683194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.58650i | − | 0.394437i | −0.980360 | − | 0.197218i | \(-0.936809\pi\) | ||
0.980360 | − | 0.197218i | \(-0.0631908\pi\) | |||||||
\(44\) | − | 6.33033i | − | 0.954334i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.04472 | 1.03869 | ||||||||
\(47\) | 8.15421i | 1.18941i | 0.803942 | + | 0.594707i | \(0.202732\pi\) | ||||
−0.803942 | + | 0.594707i | \(0.797268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.624933 | + | 4.96079i | −0.0883789 | + | 0.701562i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.05290 | −0.146011 | ||||||||
\(53\) | 8.87365 | 1.21889 | 0.609445 | − | 0.792829i | \(-0.291392\pi\) | ||||
0.609445 | + | 0.792829i | \(0.291392\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.36276 | + | 10.6162i | 1.26247 | + | 1.43149i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.98101i | 0.391426i | ||||||||
\(59\) | −0.904592 | −0.117768 | −0.0588839 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588839 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1735i | 1.30258i | 0.758830 | + | 0.651289i | \(0.225771\pi\) | ||||
−0.758830 | + | 0.651289i | \(0.774229\pi\) | |||||||
\(62\) | − | 6.31561i | − | 0.802084i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.76575 | − | 1.55727i | 0.219015 | − | 0.193155i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.83224i | 1.20120i | 0.799550 | + | 0.600600i | \(0.205071\pi\) | ||||
−0.799550 | + | 0.600600i | \(0.794929\pi\) | |||||||
\(68\) | − | 4.63684i | − | 0.562299i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.4282i | − | 1.71232i | −0.516713 | − | 0.856159i | \(-0.672844\pi\) | ||
0.516713 | − | 0.856159i | \(-0.327156\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.36666 | 0.979244 | 0.489622 | − | 0.871935i | \(-0.337135\pi\) | ||||
0.489622 | + | 0.871935i | \(0.337135\pi\) | |||||||
\(74\) | − | 3.47982i | − | 0.404520i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.17914i | − | 0.708795i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.46566 | −0.614934 | −0.307467 | − | 0.951559i | \(-0.599481\pi\) | ||||
−0.307467 | + | 0.951559i | \(0.599481\pi\) | |||||||
\(80\) | −1.67704 | + | 1.47903i | −0.187499 | + | 0.165361i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.97007 | 0.769716 | ||||||||
\(83\) | 14.6297i | 1.60581i | 0.596105 | + | 0.802907i | \(0.296714\pi\) | ||||
−0.596105 | + | 0.802907i | \(0.703286\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.85803 | + | 7.77617i | 0.743858 | + | 0.843444i | ||||
\(86\) | 2.58650i | 0.278909i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.33033i | 0.674816i | ||||||||
\(89\) | −3.83964 | −0.407001 | −0.203500 | − | 0.979075i | \(-0.565232\pi\) | ||||
−0.203500 | + | 0.979075i | \(0.565232\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.04472 | −0.734463 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 8.15421i | − | 0.841043i | ||||||
\(95\) | 9.13913 | + | 10.3627i | 0.937655 | + | 1.06319i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.87891 | 0.596913 | 0.298457 | − | 0.954423i | \(-0.403528\pi\) | ||||
0.298457 | + | 0.954423i | \(0.403528\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.624933 | − | 4.96079i | 0.0624933 | − | 0.496079i | ||||
\(101\) | −6.70816 | −0.667487 | −0.333744 | − | 0.942664i | \(-0.608312\pi\) | ||||
−0.333744 | + | 0.942664i | \(0.608312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.97432 | 0.490135 | 0.245067 | − | 0.969506i | \(-0.421190\pi\) | ||||
0.245067 | + | 0.969506i | \(0.421190\pi\) | |||||||
\(104\) | 1.05290 | 0.103245 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.87365 | −0.861885 | ||||||||
\(107\) | −7.33930 | −0.709517 | −0.354759 | − | 0.934958i | \(-0.615437\pi\) | ||||
−0.354759 | + | 0.934958i | \(0.615437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −9.36276 | − | 10.6162i | −0.892704 | − | 1.01222i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.184551 | −0.0173611 | −0.00868054 | − | 0.999962i | \(-0.502763\pi\) | ||||
−0.00868054 | + | 0.999962i | \(0.502763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.8143 | − | 10.4194i | 1.10169 | − | 0.971610i | ||||
\(116\) | − | 2.98101i | − | 0.276780i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.904592 | 0.0832745 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −29.0731 | −2.64301 | ||||||||
\(122\) | − | 10.1735i | − | 0.921061i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.31561i | 0.567159i | ||||||||
\(125\) | 6.28913 | + | 9.24375i | 0.562517 | + | 0.826786i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.70276i | 0.594774i | 0.954757 | + | 0.297387i | \(0.0961151\pi\) | ||||
−0.954757 | + | 0.297387i | \(0.903885\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.76575 | + | 1.55727i | −0.154867 | + | 0.136581i | ||||
\(131\) | 4.48232 | 0.391622 | 0.195811 | − | 0.980642i | \(-0.437266\pi\) | ||||
0.195811 | + | 0.980642i | \(0.437266\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 9.83224i | − | 0.849376i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.63684i | 0.397606i | ||||||||
\(137\) | −17.5627 | −1.50049 | −0.750243 | − | 0.661162i | \(-0.770064\pi\) | ||||
−0.750243 | + | 0.661162i | \(0.770064\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.02268i | 0.510837i | 0.966831 | + | 0.255418i | \(0.0822132\pi\) | ||||
−0.966831 | + | 0.255418i | \(0.917787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.4282i | 1.21079i | ||||||||
\(143\) | 6.66519i | 0.557371i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.40901 | + | 4.99928i | 0.366149 | + | 0.415168i | ||||
\(146\) | −8.36666 | −0.692430 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.47982i | 0.286039i | ||||||||
\(149\) | − | 7.00381i | − | 0.573775i | −0.957964 | − | 0.286887i | \(-0.907379\pi\) | ||
0.957964 | − | 0.286887i | \(-0.0926205\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8708 | 1.04741 | 0.523706 | − | 0.851899i | \(-0.324549\pi\) | ||||
0.523706 | + | 0.851899i | \(0.324549\pi\) | |||||||
\(152\) | 6.17914i | 0.501194i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.34099 | − | 10.5915i | −0.750286 | − | 0.850733i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0439 | −0.881396 | −0.440698 | − | 0.897655i | \(-0.645269\pi\) | ||||
−0.440698 | + | 0.897655i | \(0.645269\pi\) | |||||||
\(158\) | 5.46566 | 0.434824 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.67704 | − | 1.47903i | 0.132582 | − | 0.116928i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.24574i | − | 0.567530i | −0.958894 | − | 0.283765i | \(-0.908416\pi\) | ||
0.958894 | − | 0.283765i | \(-0.0915836\pi\) | |||||||
\(164\) | −6.97007 | −0.544271 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 14.6297i | − | 1.13548i | ||||||
\(167\) | 13.8606i | 1.07257i | 0.844038 | + | 0.536283i | \(0.180172\pi\) | ||||
−0.844038 | + | 0.536283i | \(0.819828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8914 | −0.914724 | ||||||||
\(170\) | −6.85803 | − | 7.77617i | −0.525987 | − | 0.596405i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 2.58650i | − | 0.197218i | ||||||
\(173\) | − | 0.958803i | − | 0.0728965i | −0.999336 | − | 0.0364482i | \(-0.988396\pi\) | ||
0.999336 | − | 0.0364482i | \(-0.0116044\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 6.33033i | − | 0.477167i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.83964 | 0.287793 | ||||||||
\(179\) | 23.3862i | 1.74797i | 0.485954 | + | 0.873984i | \(0.338472\pi\) | ||||
−0.485954 | + | 0.873984i | \(0.661528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.2865i | − | 1.43355i | −0.697303 | − | 0.716776i | \(-0.745617\pi\) | ||
0.697303 | − | 0.716776i | \(-0.254383\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.04472 | 0.519344 | ||||||||
\(185\) | −5.14676 | − | 5.83580i | −0.378397 | − | 0.429056i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −29.3527 | −2.14648 | ||||||||
\(188\) | 8.15421i | 0.594707i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.13913 | − | 10.3627i | −0.663022 | − | 0.751787i | ||||
\(191\) | 2.82843i | 0.204658i | 0.994751 | + | 0.102329i | \(0.0326294\pi\) | ||||
−0.994751 | + | 0.102329i | \(0.967371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 8.21725i | − | 0.591490i | −0.955267 | − | 0.295745i | \(-0.904432\pi\) | ||
0.955267 | − | 0.295745i | \(-0.0955679\pi\) | |||||||
\(194\) | −5.87891 | −0.422081 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.51321 | −0.250306 | −0.125153 | − | 0.992137i | \(-0.539942\pi\) | ||||
−0.125153 | + | 0.992137i | \(0.539942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.46410i | − | 0.245564i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) | ||
0.992434 | − | 0.122782i | \(-0.0391815\pi\) | |||||||
\(200\) | −0.624933 | + | 4.96079i | −0.0441895 | + | 0.350781i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.70816 | 0.471985 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6891 | − | 10.3090i | 0.816402 | − | 0.720009i | ||||
\(206\) | −4.97432 | −0.346577 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.05290 | −0.0730053 | ||||||||
\(209\) | −39.1160 | −2.70571 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.96592 | −0.686082 | −0.343041 | − | 0.939320i | \(-0.611457\pi\) | ||||
−0.343041 | + | 0.939320i | \(0.611457\pi\) | |||||||
\(212\) | 8.87365 | 0.609445 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.33930 | 0.501705 | ||||||||
\(215\) | 3.82551 | + | 4.33766i | 0.260897 | + | 0.295826i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.36276 | + | 10.6162i | 0.631237 | + | 0.715746i | ||||
\(221\) | 4.88212i | 0.328407i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1087 | 0.743894 | 0.371947 | − | 0.928254i | \(-0.378690\pi\) | ||||
0.371947 | + | 0.928254i | \(0.378690\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.184551 | 0.0122761 | ||||||||
\(227\) | 23.5238i | 1.56133i | 0.624949 | + | 0.780665i | \(0.285120\pi\) | ||||
−0.624949 | + | 0.780665i | \(0.714880\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.48678i | 0.626904i | 0.949604 | + | 0.313452i | \(0.101485\pi\) | ||||
−0.949604 | + | 0.313452i | \(0.898515\pi\) | |||||||
\(230\) | −11.8143 | + | 10.4194i | −0.779011 | + | 0.687032i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.98101i | 0.195713i | ||||||||
\(233\) | −10.3734 | −0.679583 | −0.339791 | − | 0.940501i | \(-0.610356\pi\) | ||||
−0.339791 | + | 0.940501i | \(0.610356\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0603 | − | 13.6750i | −0.786730 | − | 0.892056i | ||||
\(236\) | −0.904592 | −0.0588839 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.3746i | 0.800444i | 0.916418 | + | 0.400222i | \(0.131067\pi\) | ||||
−0.916418 | + | 0.400222i | \(0.868933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 12.4947i | − | 0.804858i | −0.915451 | − | 0.402429i | \(-0.868166\pi\) | ||
0.915451 | − | 0.402429i | \(-0.131834\pi\) | |||||||
\(242\) | 29.0731 | 1.86889 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.1735i | 0.651289i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.50600i | 0.413967i | ||||||||
\(248\) | − | 6.31561i | − | 0.401042i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.28913 | − | 9.24375i | −0.397759 | − | 0.584626i | ||||
\(251\) | 13.5304 | 0.854034 | 0.427017 | − | 0.904244i | \(-0.359564\pi\) | ||||
0.427017 | + | 0.904244i | \(0.359564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.5954i | 2.80369i | ||||||||
\(254\) | − | 6.70276i | − | 0.420569i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 4.41799i | − | 0.275587i | −0.990461 | − | 0.137793i | \(-0.955999\pi\) | ||
0.990461 | − | 0.137793i | \(-0.0440010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.76575 | − | 1.55727i | 0.109507 | − | 0.0965777i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.48232 | −0.276919 | ||||||||
\(263\) | 6.12635 | 0.377767 | 0.188884 | − | 0.981999i | \(-0.439513\pi\) | ||||
0.188884 | + | 0.981999i | \(0.439513\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.8815 | + | 13.1244i | −0.914162 | + | 0.806226i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.83224i | 0.600600i | ||||||||
\(269\) | −4.18740 | −0.255310 | −0.127655 | − | 0.991819i | \(-0.540745\pi\) | ||||
−0.127655 | + | 0.991819i | \(0.540745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 0.292938i | − | 0.0177947i | −0.999960 | − | 0.00889737i | \(-0.997168\pi\) | ||
0.999960 | − | 0.00889737i | \(-0.00283216\pi\) | |||||||
\(272\) | − | 4.63684i | − | 0.281150i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.5627 | 1.06100 | ||||||||
\(275\) | −31.4035 | − | 3.95604i | −1.89370 | − | 0.238558i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 14.6220i | − | 0.878550i | −0.898353 | − | 0.439275i | \(-0.855235\pi\) | ||
0.898353 | − | 0.439275i | \(-0.144765\pi\) | |||||||
\(278\) | − | 6.02268i | − | 0.361216i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.1691i | − | 1.08388i | −0.840419 | − | 0.541938i | \(-0.817691\pi\) | ||
0.840419 | − | 0.541938i | \(-0.182309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.2133 | −1.26100 | −0.630499 | − | 0.776190i | \(-0.717150\pi\) | ||||
−0.630499 | + | 0.776190i | \(0.717150\pi\) | |||||||
\(284\) | − | 14.4282i | − | 0.856159i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 6.66519i | − | 0.394121i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.50027 | −0.264722 | ||||||||
\(290\) | −4.40901 | − | 4.99928i | −0.258906 | − | 0.293568i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.36666 | 0.489622 | ||||||||
\(293\) | − | 7.64481i | − | 0.446615i | −0.974748 | − | 0.223307i | \(-0.928315\pi\) | ||
0.974748 | − | 0.223307i | \(-0.0716853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.51704 | − | 1.33792i | 0.0883254 | − | 0.0778967i | ||||
\(296\) | − | 3.47982i | − | 0.202260i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.00381i | 0.405720i | ||||||||
\(299\) | 7.41737 | 0.428957 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.8708 | −0.740632 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6.17914i | − | 0.354398i | ||||||
\(305\) | −15.0469 | − | 17.0613i | −0.861581 | − | 0.976927i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.1561 | 0.750859 | 0.375429 | − | 0.926851i | \(-0.377495\pi\) | ||||
0.375429 | + | 0.926851i | \(0.377495\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.34099 | + | 10.5915i | 0.530533 | + | 0.601559i | ||||
\(311\) | 6.26087 | 0.355021 | 0.177511 | − | 0.984119i | \(-0.443196\pi\) | ||||
0.177511 | + | 0.984119i | \(0.443196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4813 | 0.988101 | 0.494051 | − | 0.869433i | \(-0.335516\pi\) | ||||
0.494051 | + | 0.869433i | \(0.335516\pi\) | |||||||
\(314\) | 11.0439 | 0.623241 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.46566 | −0.307467 | ||||||||
\(317\) | 1.53381 | 0.0861474 | 0.0430737 | − | 0.999072i | \(-0.486285\pi\) | ||||
0.0430737 | + | 0.999072i | \(0.486285\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.8708 | −1.05656 | ||||||||
\(320\) | −1.67704 | + | 1.47903i | −0.0937494 | + | 0.0826804i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.6516 | −1.59422 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.657991 | + | 5.22321i | −0.0364988 | + | 0.289731i | ||||
\(326\) | 7.24574i | 0.401305i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.97007 | 0.384858 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.51321 | −0.0831737 | −0.0415869 | − | 0.999135i | \(-0.513241\pi\) | ||||
−0.0415869 | + | 0.999135i | \(0.513241\pi\) | |||||||
\(332\) | 14.6297i | 0.802907i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 13.8606i | − | 0.758419i | ||||||
\(335\) | −14.5422 | − | 16.4891i | −0.794525 | − | 0.900894i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.14064i | 0.171082i | 0.996335 | + | 0.0855408i | \(0.0272618\pi\) | ||||
−0.996335 | + | 0.0855408i | \(0.972738\pi\) | |||||||
\(338\) | 11.8914 | 0.646807 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.85803 | + | 7.77617i | 0.371929 | + | 0.421722i | ||||
\(341\) | 39.9799 | 2.16504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.58650i | 0.139455i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.958803i | 0.0515456i | ||||||||
\(347\) | 27.4052 | 1.47119 | 0.735593 | − | 0.677424i | \(-0.236904\pi\) | ||||
0.735593 | + | 0.677424i | \(0.236904\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5594i | 1.04699i | 0.852028 | + | 0.523496i | \(0.175373\pi\) | ||||
−0.852028 | + | 0.523496i | \(0.824627\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.33033i | 0.337408i | ||||||||
\(353\) | − | 14.8103i | − | 0.788272i | −0.919052 | − | 0.394136i | \(-0.871044\pi\) | ||
0.919052 | − | 0.394136i | \(-0.128956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.3398 | + | 24.1968i | 1.13260 | + | 1.28423i | ||||
\(356\) | −3.83964 | −0.203500 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 23.3862i | − | 1.23600i | ||||||
\(359\) | 16.5690i | 0.874479i | 0.899345 | + | 0.437239i | \(0.144044\pi\) | ||||
−0.899345 | + | 0.437239i | \(0.855956\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.1817 | −1.00956 | ||||||||
\(362\) | 19.2865i | 1.01367i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0312 | + | 12.3746i | −0.734429 | + | 0.647714i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0131 | 0.731478 | 0.365739 | − | 0.930717i | \(-0.380816\pi\) | ||||
0.365739 | + | 0.930717i | \(0.380816\pi\) | |||||||
\(368\) | −7.04472 | −0.367231 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.14676 | + | 5.83580i | 0.267567 | + | 0.303389i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6220i | 0.757098i | 0.925581 | + | 0.378549i | \(0.123577\pi\) | ||||
−0.925581 | + | 0.378549i | \(0.876423\pi\) | |||||||
\(374\) | 29.3527 | 1.51779 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 8.15421i | − | 0.420522i | ||||||
\(377\) | 3.13870i | 0.161651i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.68145 | −0.240470 | −0.120235 | − | 0.992745i | \(-0.538365\pi\) | ||||
−0.120235 | + | 0.992745i | \(0.538365\pi\) | |||||||
\(380\) | 9.13913 | + | 10.3627i | 0.468828 | + | 0.531593i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 2.82843i | − | 0.144715i | ||||||
\(383\) | 11.6724i | 0.596433i | 0.954498 | + | 0.298216i | \(0.0963917\pi\) | ||||
−0.954498 | + | 0.298216i | \(0.903608\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.21725i | 0.418247i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.87891 | 0.298457 | ||||||||
\(389\) | 13.1004i | 0.664214i | 0.943242 | + | 0.332107i | \(0.107760\pi\) | ||||
−0.943242 | + | 0.332107i | \(0.892240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.6652i | 1.65195i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.51321 | 0.176993 | ||||||||
\(395\) | 9.16613 | − | 8.08388i | 0.461198 | − | 0.406744i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.6804 | −1.53981 | −0.769903 | − | 0.638161i | \(-0.779696\pi\) | ||||
−0.769903 | + | 0.638161i | \(0.779696\pi\) | |||||||
\(398\) | 3.46410i | 0.173640i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.624933 | − | 4.96079i | 0.0312467 | − | 0.248040i | ||||
\(401\) | − | 7.94533i | − | 0.396771i | −0.980124 | − | 0.198385i | \(-0.936430\pi\) | ||
0.980124 | − | 0.198385i | \(-0.0635697\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.64969i | − | 0.331245i | ||||||
\(404\) | −6.70816 | −0.333744 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.0284 | 1.09191 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.8323i | 1.96958i | 0.173754 | + | 0.984789i | \(0.444410\pi\) | ||||
−0.173754 | + | 0.984789i | \(0.555590\pi\) | |||||||
\(410\) | −11.6891 | + | 10.3090i | −0.577283 | + | 0.509123i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.97432 | 0.245067 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.6377 | − | 24.5345i | −1.06215 | − | 1.20435i | ||||
\(416\) | 1.05290 | 0.0516226 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 39.1160 | 1.91323 | ||||||||
\(419\) | 11.0357 | 0.539131 | 0.269566 | − | 0.962982i | \(-0.413120\pi\) | ||||
0.269566 | + | 0.962982i | \(0.413120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.78421 | −0.379379 | −0.189690 | − | 0.981844i | \(-0.560748\pi\) | ||||
−0.189690 | + | 0.981844i | \(0.560748\pi\) | |||||||
\(422\) | 9.96592 | 0.485134 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.87365 | −0.430942 | ||||||||
\(425\) | −23.0024 | − | 2.89772i | −1.11578 | − | 0.140560i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.33930 | −0.354759 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.82551 | − | 4.33766i | −0.184482 | − | 0.209181i | ||||
\(431\) | − | 10.2338i | − | 0.492945i | −0.969150 | − | 0.246472i | \(-0.920729\pi\) | ||
0.969150 | − | 0.246472i | \(-0.0792714\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −40.3902 | −1.94103 | −0.970513 | − | 0.241047i | \(-0.922509\pi\) | ||||
−0.970513 | + | 0.241047i | \(0.922509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 43.5303i | 2.08234i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9709i | 0.619065i | 0.950889 | + | 0.309533i | \(0.100173\pi\) | ||||
−0.950889 | + | 0.309533i | \(0.899827\pi\) | |||||||
\(440\) | −9.36276 | − | 10.6162i | −0.446352 | − | 0.506109i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 4.88212i | − | 0.232219i | ||||||
\(443\) | 8.65502 | 0.411212 | 0.205606 | − | 0.978635i | \(-0.434083\pi\) | ||||
0.205606 | + | 0.978635i | \(0.434083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.43923 | − | 5.67894i | 0.305249 | − | 0.269208i | ||||
\(446\) | −11.1087 | −0.526012 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 25.4407i | − | 1.20062i | −0.799768 | − | 0.600310i | \(-0.795044\pi\) | ||
0.799768 | − | 0.600310i | \(-0.204956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.1229i | 2.07767i | ||||||||
\(452\) | −0.184551 | −0.00868054 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 23.5238i | − | 1.10403i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.5395i | 1.42858i | 0.699851 | + | 0.714289i | \(0.253250\pi\) | ||||
−0.699851 | + | 0.714289i | \(0.746750\pi\) | |||||||
\(458\) | − | 9.48678i | − | 0.443288i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.8143 | − | 10.4194i | 0.550844 | − | 0.485805i | ||||
\(461\) | 15.6680 | 0.729734 | 0.364867 | − | 0.931060i | \(-0.381114\pi\) | ||||
0.364867 | + | 0.931060i | \(0.381114\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 32.0462i | − | 1.48931i | −0.667448 | − | 0.744656i | \(-0.732613\pi\) | ||
0.667448 | − | 0.744656i | \(-0.267387\pi\) | |||||||
\(464\) | − | 2.98101i | − | 0.138390i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.3734 | 0.480538 | ||||||||
\(467\) | 0.699158i | 0.0323532i | 0.999869 | + | 0.0161766i | \(0.00514940\pi\) | ||||
−0.999869 | + | 0.0161766i | \(0.994851\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12.0603 | + | 13.6750i | 0.556302 | + | 0.630779i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.904592 | 0.0416372 | ||||||||
\(473\) | −16.3734 | −0.752849 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −30.6534 | − | 3.86155i | −1.40647 | − | 0.177180i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 12.3746i | − | 0.565999i | ||||||
\(479\) | −8.54561 | −0.390459 | −0.195229 | − | 0.980758i | \(-0.562545\pi\) | ||||
−0.195229 | + | 0.980758i | \(0.562545\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3.66389i | − | 0.167059i | ||||||
\(482\) | 12.4947i | 0.569120i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −29.0731 | −1.32151 | ||||||||
\(485\) | −9.85918 | + | 8.69510i | −0.447682 | + | 0.394824i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.8178i | − | 1.07929i | −0.841894 | − | 0.539643i | \(-0.818559\pi\) | ||
0.841894 | − | 0.539643i | \(-0.181441\pi\) | |||||||
\(488\) | − | 10.1735i | − | 0.460531i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.9104i | − | 0.582638i | −0.956626 | − | 0.291319i | \(-0.905906\pi\) | ||
0.956626 | − | 0.291319i | \(-0.0940941\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.8225 | −0.622533 | ||||||||
\(494\) | − | 6.50600i | − | 0.292719i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.31561i | 0.283579i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.3365 | −0.731321 | −0.365660 | − | 0.930748i | \(-0.619157\pi\) | ||||
−0.365660 | + | 0.930748i | \(0.619157\pi\) | |||||||
\(500\) | 6.28913 | + | 9.24375i | 0.281258 | + | 0.413393i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.5304 | −0.603893 | ||||||||
\(503\) | 28.3413i | 1.26368i | 0.775100 | + | 0.631838i | \(0.217699\pi\) | ||||
−0.775100 | + | 0.631838i | \(0.782301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.2499 | − | 9.92158i | 0.500613 | − | 0.441505i | ||||
\(506\) | − | 44.5954i | − | 1.98251i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.70276i | 0.297387i | ||||||||
\(509\) | −2.37821 | −0.105412 | −0.0527062 | − | 0.998610i | \(-0.516785\pi\) | ||||
−0.0527062 | + | 0.998610i | \(0.516785\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.41799i | 0.194869i | ||||||||
\(515\) | −8.34214 | + | 7.35718i | −0.367599 | + | 0.324196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.6189 | 2.27020 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.76575 | + | 1.55727i | −0.0774334 | + | 0.0682907i | ||||
\(521\) | 8.28370 | 0.362915 | 0.181458 | − | 0.983399i | \(-0.441918\pi\) | ||||
0.181458 | + | 0.983399i | \(0.441918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.8616 | −1.83048 | −0.915239 | − | 0.402910i | \(-0.867999\pi\) | ||||
−0.915239 | + | 0.402910i | \(0.867999\pi\) | |||||||
\(524\) | 4.48232 | 0.195811 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.12635 | −0.267122 | ||||||||
\(527\) | 29.2845 | 1.27565 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.6281 | 1.15774 | ||||||||
\(530\) | 14.8815 | − | 13.1244i | 0.646410 | − | 0.570088i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.33877 | 0.317877 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.3083 | − | 10.8551i | 0.532135 | − | 0.469305i | ||||
\(536\) | − | 9.83224i | − | 0.424688i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.18740 | 0.180531 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.9304 | 1.97470 | 0.987352 | − | 0.158543i | \(-0.0506796\pi\) | ||||
0.987352 | + | 0.158543i | \(0.0506796\pi\) | |||||||
\(542\) | 0.292938i | 0.0125828i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.63684i | 0.198803i | ||||||||
\(545\) | −3.35408 | + | 2.95806i | −0.143673 | + | 0.126709i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.88688i | 0.208948i | 0.994528 | + | 0.104474i | \(0.0333159\pi\) | ||||
−0.994528 | + | 0.104474i | \(0.966684\pi\) | |||||||
\(548\) | −17.5627 | −0.750243 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 31.4035 | + | 3.95604i | 1.33905 | + | 0.168686i | ||||
\(551\) | −18.4201 | −0.784722 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.6220i | 0.621229i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.02268i | 0.255418i | ||||||||
\(557\) | −29.3677 | −1.24435 | −0.622175 | − | 0.782878i | \(-0.713751\pi\) | ||||
−0.622175 | + | 0.782878i | \(0.713751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.72332i | 0.115184i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.1691i | 0.766415i | ||||||||
\(563\) | 2.73921i | 0.115444i | 0.998333 | + | 0.0577220i | \(0.0183837\pi\) | ||||
−0.998333 | + | 0.0577220i | \(0.981616\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.309499 | − | 0.272956i | 0.0130207 | − | 0.0114834i | ||||
\(566\) | 21.2133 | 0.891660 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.4282i | 0.605396i | ||||||||
\(569\) | 0.922450i | 0.0386711i | 0.999813 | + | 0.0193356i | \(0.00615508\pi\) | ||||
−0.999813 | + | 0.0193356i | \(0.993845\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.5523 | −1.02748 | −0.513740 | − | 0.857946i | \(-0.671740\pi\) | ||||
−0.513740 | + | 0.857946i | \(0.671740\pi\) | |||||||
\(572\) | 6.66519i | 0.278686i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.40248 | + | 34.9474i | −0.183596 | + | 1.45741i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.1333 | −1.12958 | −0.564788 | − | 0.825236i | \(-0.691042\pi\) | ||||
−0.564788 | + | 0.825236i | \(0.691042\pi\) | |||||||
\(578\) | 4.50027 | 0.187186 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.40901 | + | 4.99928i | 0.183074 | + | 0.207584i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 56.1731i | − | 2.32645i | ||||||
\(584\) | −8.36666 | −0.346215 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.64481i | 0.315804i | ||||||||
\(587\) | − | 8.71353i | − | 0.359646i | −0.983699 | − | 0.179823i | \(-0.942448\pi\) | ||
0.983699 | − | 0.179823i | \(-0.0575525\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39.0250 | 1.60800 | ||||||||
\(590\) | −1.51704 | + | 1.33792i | −0.0624555 | + | 0.0550813i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.47982i | 0.143020i | ||||||||
\(593\) | 18.2686i | 0.750203i | 0.926984 | + | 0.375102i | \(0.122392\pi\) | ||||
−0.926984 | + | 0.375102i | \(0.877608\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 7.00381i | − | 0.286887i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.41737 | −0.303319 | ||||||||
\(599\) | − | 11.4844i | − | 0.469239i | −0.972087 | − | 0.234619i | \(-0.924616\pi\) | ||
0.972087 | − | 0.234619i | \(-0.0753844\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.4022i | − | 1.40329i | −0.712525 | − | 0.701647i | \(-0.752448\pi\) | ||
0.712525 | − | 0.701647i | \(-0.247552\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.8708 | 0.523706 | ||||||||
\(605\) | 48.7568 | − | 43.0001i | 1.98225 | − | 1.74820i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.5128 | −1.84731 | −0.923653 | − | 0.383229i | \(-0.874812\pi\) | ||||
−0.923653 | + | 0.383229i | \(0.874812\pi\) | |||||||
\(608\) | 6.17914i | 0.250597i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.0469 | + | 17.0613i | 0.609229 | + | 0.690792i | ||||
\(611\) | − | 8.58555i | − | 0.347334i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.7041i | 0.472724i | 0.971665 | + | 0.236362i | \(0.0759552\pi\) | ||||
−0.971665 | + | 0.236362i | \(0.924045\pi\) | |||||||
\(614\) | −13.1561 | −0.530937 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0582 | 0.968547 | 0.484273 | − | 0.874917i | \(-0.339084\pi\) | ||||
0.484273 | + | 0.874917i | \(0.339084\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.84278i | 0.154454i | 0.997014 | + | 0.0772271i | \(0.0246067\pi\) | ||||
−0.997014 | + | 0.0772271i | \(0.975393\pi\) | |||||||
\(620\) | −9.34099 | − | 10.5915i | −0.375143 | − | 0.425367i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.26087 | −0.251038 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2189 | − | 6.20033i | −0.968757 | − | 0.248013i | ||||
\(626\) | −17.4813 | −0.698693 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0439 | −0.440698 | ||||||||
\(629\) | 16.1353 | 0.643358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4387 | −1.01270 | −0.506349 | − | 0.862328i | \(-0.669005\pi\) | ||||
−0.506349 | + | 0.862328i | \(0.669005\pi\) | |||||||
\(632\) | 5.46566 | 0.217412 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.53381 | −0.0609154 | ||||||||
\(635\) | −9.91359 | − | 11.2408i | −0.393409 | − | 0.446078i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.8708 | 0.747102 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.67704 | − | 1.47903i | 0.0662909 | − | 0.0584638i | ||||
\(641\) | 39.5346i | 1.56152i | 0.624829 | + | 0.780762i | \(0.285169\pi\) | ||||
−0.624829 | + | 0.780762i | \(0.714831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.2816 | −0.484341 | −0.242170 | − | 0.970234i | \(-0.577859\pi\) | ||||
−0.242170 | + | 0.970234i | \(0.577859\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.6516 | 1.12728 | ||||||||
\(647\) | 13.3894i | 0.526392i | 0.964742 | + | 0.263196i | \(0.0847766\pi\) | ||||
−0.964742 | + | 0.263196i | \(0.915223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.72637i | 0.224780i | ||||||||
\(650\) | 0.657991 | − | 5.22321i | 0.0258085 | − | 0.204871i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 7.24574i | − | 0.283765i | ||||||
\(653\) | −49.5777 | −1.94012 | −0.970062 | − | 0.242857i | \(-0.921915\pi\) | ||||
−0.970062 | + | 0.242857i | \(0.921915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.51704 | + | 6.62949i | −0.293715 | + | 0.259036i | ||||
\(656\) | −6.97007 | −0.272136 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.7622i | 1.58787i | 0.608002 | + | 0.793936i | \(0.291971\pi\) | ||||
−0.608002 | + | 0.793936i | \(0.708029\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 35.7556i | − | 1.39073i | −0.718657 | − | 0.695365i | \(-0.755243\pi\) | ||
0.718657 | − | 0.695365i | \(-0.244757\pi\) | |||||||
\(662\) | 1.51321 | 0.0588127 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.6297i | − | 0.567741i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.0004i | 0.813139i | ||||||||
\(668\) | 13.8606i | 0.536283i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.5422 | + | 16.4891i | 0.561814 | + | 0.637028i | ||||
\(671\) | 64.4014 | 2.48619 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 35.1987i | − | 1.35681i | −0.734687 | − | 0.678406i | \(-0.762671\pi\) | ||
0.734687 | − | 0.678406i | \(-0.237329\pi\) | |||||||
\(674\) | − | 3.14064i | − | 0.120973i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.8914 | −0.457362 | ||||||||
\(677\) | 38.4422i | 1.47745i | 0.674005 | + | 0.738727i | \(0.264573\pi\) | ||||
−0.674005 | + | 0.738727i | \(0.735427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.85803 | − | 7.77617i | −0.262993 | − | 0.298202i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −39.9799 | −1.53091 | ||||||||
\(683\) | −38.4023 | −1.46942 | −0.734712 | − | 0.678379i | \(-0.762683\pi\) | ||||
−0.734712 | + | 0.678379i | \(0.762683\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.4534 | − | 25.9758i | 1.12536 | − | 0.992486i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 2.58650i | − | 0.0986092i | ||||||
\(689\) | −9.34304 | −0.355942 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.3469i | − | 0.774033i | −0.922073 | − | 0.387016i | \(-0.873506\pi\) | ||
0.922073 | − | 0.387016i | \(-0.126494\pi\) | |||||||
\(692\) | − | 0.958803i | − | 0.0364482i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.4052 | −1.04029 | ||||||||
\(695\) | −8.90772 | − | 10.1003i | −0.337889 | − | 0.383125i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.3191i | 1.22417i | ||||||||
\(698\) | − | 19.5594i | − | 0.740335i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.98574i | − | 0.263848i | −0.991260 | − | 0.131924i | \(-0.957885\pi\) | ||
0.991260 | − | 0.131924i | \(-0.0421154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.5023 | 0.810973 | ||||||||
\(704\) | − | 6.33033i | − | 0.238583i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.8103i | 0.557393i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0270 | 0.451682 | 0.225841 | − | 0.974164i | \(-0.427487\pi\) | ||||
0.225841 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(710\) | −21.3398 | − | 24.1968i | −0.800869 | − | 0.908088i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.83964 | 0.143896 | ||||||||
\(713\) | − | 44.4917i | − | 1.66623i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.85803 | − | 11.1778i | −0.368669 | − | 0.418026i | ||||
\(716\) | 23.3862i | 0.873984i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 16.5690i | − | 0.618350i | ||||||
\(719\) | 1.67139 | 0.0623323 | 0.0311661 | − | 0.999514i | \(-0.490078\pi\) | ||||
0.0311661 | + | 0.999514i | \(0.490078\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19.1817 | 0.713869 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 19.2865i | − | 0.716776i | ||||||
\(725\) | −14.7882 | − | 1.86294i | −0.549220 | − | 0.0691877i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.5043 | −1.57640 | −0.788198 | − | 0.615422i | \(-0.788986\pi\) | ||||
−0.788198 | + | 0.615422i | \(0.788986\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.0312 | − | 12.3746i | 0.519319 | − | 0.458003i | ||||
\(731\) | −11.9932 | −0.443583 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.8759 | 1.17736 | 0.588681 | − | 0.808365i | \(-0.299647\pi\) | ||||
0.588681 | + | 0.808365i | \(0.299647\pi\) | |||||||
\(734\) | −14.0131 | −0.517233 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.04472 | 0.259672 | ||||||||
\(737\) | 62.2414 | 2.29269 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.4186 | 0.603969 | 0.301985 | − | 0.953313i | \(-0.402351\pi\) | ||||
0.301985 | + | 0.953313i | \(0.402351\pi\) | |||||||
\(740\) | −5.14676 | − | 5.83580i | −0.189199 | − | 0.214528i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.52385 | 0.165964 | 0.0829821 | − | 0.996551i | \(-0.473556\pi\) | ||||
0.0829821 | + | 0.996551i | \(0.473556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.3589 | + | 11.7457i | 0.379519 | + | 0.430328i | ||||
\(746\) | − | 14.6220i | − | 0.535349i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.3527 | −1.07324 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3975 | −0.634844 | −0.317422 | − | 0.948284i | \(-0.602817\pi\) | ||||
−0.317422 | + | 0.948284i | \(0.602817\pi\) | |||||||
\(752\) | 8.15421i | 0.297354i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 3.13870i | − | 0.114305i | ||||||
\(755\) | −21.5849 | + | 19.0363i | −0.785554 | + | 0.692803i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.25454i | 0.190980i | 0.995430 | + | 0.0954898i | \(0.0304417\pi\) | ||||
−0.995430 | + | 0.0954898i | \(0.969558\pi\) | |||||||
\(758\) | 4.68145 | 0.170038 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.13913 | − | 10.3627i | −0.331511 | − | 0.375893i | ||||
\(761\) | 14.6280 | 0.530266 | 0.265133 | − | 0.964212i | \(-0.414584\pi\) | ||||
0.265133 | + | 0.964212i | \(0.414584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.82843i | 0.102329i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 11.6724i | − | 0.421742i | ||||||
\(767\) | 0.952443 | 0.0343907 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 12.4548i | − | 0.449131i | −0.974459 | − | 0.224566i | \(-0.927904\pi\) | ||
0.974459 | − | 0.224566i | \(-0.0720963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 8.21725i | − | 0.295745i | ||||||
\(773\) | 8.30576i | 0.298737i | 0.988782 | + | 0.149369i | \(0.0477241\pi\) | ||||
−0.988782 | + | 0.149369i | \(0.952276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.3304 | + | 3.94684i | 1.12542 | + | 0.141775i | ||||
\(776\) | −5.87891 | −0.211041 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 13.1004i | − | 0.469670i | ||||||
\(779\) | 43.0690i | 1.54311i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −91.3356 | −3.26824 | ||||||||
\(782\) | − | 32.6652i | − | 1.16811i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.5210 | − | 16.3342i | 0.661043 | − | 0.582993i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.6071 | −1.80395 | −0.901975 | − | 0.431788i | \(-0.857883\pi\) | ||||
−0.901975 | + | 0.431788i | \(0.857883\pi\) | |||||||
\(788\) | −3.51321 | −0.125153 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.16613 | + | 8.08388i | −0.326116 | + | 0.287611i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.7116i | − | 0.380380i | ||||||
\(794\) | 30.6804 | 1.08881 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 3.46410i | − | 0.122782i | ||||||
\(797\) | − | 36.6354i | − | 1.29769i | −0.760920 | − | 0.648846i | \(-0.775252\pi\) | ||
0.760920 | − | 0.648846i | \(-0.224748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.8098 | 1.33761 | ||||||||
\(800\) | −0.624933 | + | 4.96079i | −0.0220947 | + | 0.175390i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.94533i | 0.280559i | ||||||||
\(803\) | − | 52.9638i | − | 1.86905i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.64969i | 0.234225i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.70816 | 0.235992 | ||||||||
\(809\) | 43.5386i | 1.53074i | 0.643593 | + | 0.765368i | \(0.277443\pi\) | ||||
−0.643593 | + | 0.765368i | \(0.722557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.8915i | 0.487795i | 0.969801 | + | 0.243897i | \(0.0784260\pi\) | ||||
−0.969801 | + | 0.243897i | \(0.921574\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.0284 | −0.772095 | ||||||||
\(815\) | 10.7167 | + | 12.1514i | 0.375389 | + | 0.425645i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.9823 | −0.559150 | ||||||||
\(818\) | − | 39.8323i | − | 1.39270i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.6891 | − | 10.3090i | 0.408201 | − | 0.360004i | ||||
\(821\) | 9.54514i | 0.333128i | 0.986031 | + | 0.166564i | \(0.0532672\pi\) | ||||
−0.986031 | + | 0.166564i | \(0.946733\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.7960i | 0.376323i | 0.982138 | + | 0.188162i | \(0.0602529\pi\) | ||||
−0.982138 | + | 0.188162i | \(0.939747\pi\) | |||||||
\(824\) | −4.97432 | −0.173289 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.5599 | −0.367204 | −0.183602 | − | 0.983001i | \(-0.558776\pi\) | ||||
−0.183602 | + | 0.983001i | \(0.558776\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 35.4826i | − | 1.23236i | −0.787605 | − | 0.616181i | \(-0.788679\pi\) | ||
0.787605 | − | 0.616181i | \(-0.211321\pi\) | |||||||
\(830\) | 21.6377 | + | 24.5345i | 0.751056 | + | 0.851606i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.05290 | −0.0365027 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.5003 | − | 23.2448i | −0.709441 | − | 0.804420i | ||||
\(836\) | −39.1160 | −1.35285 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.0357 | −0.381223 | ||||||||
\(839\) | −32.5932 | −1.12524 | −0.562621 | − | 0.826715i | \(-0.690207\pi\) | ||||
−0.562621 | + | 0.826715i | \(0.690207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.1136 | 0.693571 | ||||||||
\(842\) | 7.78421 | 0.268262 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.96592 | −0.343041 | ||||||||
\(845\) | 19.9424 | − | 17.5878i | 0.686039 | − | 0.605037i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.87365 | 0.304722 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 23.0024 | + | 2.89772i | 0.788975 | + | 0.0993908i | ||||
\(851\) | − | 24.5143i | − | 0.840340i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2310 | 0.692695 | 0.346347 | − | 0.938106i | \(-0.387422\pi\) | ||||
0.346347 | + | 0.938106i | \(0.387422\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.33930 | 0.250852 | ||||||||
\(857\) | − | 44.9710i | − | 1.53618i | −0.640341 | − | 0.768091i | \(-0.721207\pi\) | ||
0.640341 | − | 0.768091i | \(-0.278793\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.7042i | 1.49117i | 0.666411 | + | 0.745585i | \(0.267830\pi\) | ||||
−0.666411 | + | 0.745585i | \(0.732170\pi\) | |||||||
\(860\) | 3.82551 | + | 4.33766i | 0.130449 | + | 0.147913i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.2338i | 0.348565i | ||||||||
\(863\) | 35.6382 | 1.21314 | 0.606569 | − | 0.795031i | \(-0.292546\pi\) | ||||
0.606569 | + | 0.795031i | \(0.292546\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.41810 | + | 1.60795i | 0.0482168 | + | 0.0546720i | ||||
\(866\) | 40.3902 | 1.37251 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.5994i | 1.17371i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.3523i | − | 0.350776i | ||||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 43.5303i | − | 1.47243i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.4906i | 1.23220i | 0.787668 | + | 0.616100i | \(0.211288\pi\) | ||||
−0.787668 | + | 0.616100i | \(0.788712\pi\) | |||||||
\(878\) | − | 12.9709i | − | 0.437745i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.36276 | + | 10.6162i | 0.315619 | + | 0.357873i | ||||
\(881\) | 0.487935 | 0.0164390 | 0.00821948 | − | 0.999966i | \(-0.497384\pi\) | ||||
0.00821948 | + | 0.999966i | \(0.497384\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.26720i | − | 0.210908i | −0.994424 | − | 0.105454i | \(-0.966370\pi\) | ||
0.994424 | − | 0.105454i | \(-0.0336296\pi\) | |||||||
\(884\) | 4.88212i | 0.164203i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.65502 | −0.290771 | ||||||||
\(887\) | 56.9197i | 1.91118i | 0.294706 | + | 0.955588i | \(0.404778\pi\) | ||||
−0.294706 | + | 0.955588i | \(0.595222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.43923 | + | 5.67894i | −0.215843 | + | 0.190359i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.1087 | 0.371947 | ||||||||
\(893\) | 50.3860 | 1.68610 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.5890 | − | 39.2197i | −1.15618 | − | 1.31097i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.4407i | 0.848966i | ||||||||
\(899\) | 18.8269 | 0.627913 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 41.1457i | − | 1.37076i | ||||||
\(902\) | − | 44.1229i | − | 1.46913i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.184551 | 0.00613807 | ||||||||
\(905\) | 28.5253 | + | 32.3442i | 0.948213 | + | 1.07516i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6606i | 0.553207i | 0.960984 | + | 0.276603i | \(0.0892088\pi\) | ||||
−0.960984 | + | 0.276603i | \(0.910791\pi\) | |||||||
\(908\) | 23.5238i | 0.780665i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.02653i | 0.265931i | 0.991121 | + | 0.132965i | \(0.0424499\pi\) | ||||
−0.991121 | + | 0.132965i | \(0.957550\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 92.6106 | 3.06496 | ||||||||
\(914\) | − | 30.5395i | − | 1.01016i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.48678i | 0.313452i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.7147 | 0.452405 | 0.226202 | − | 0.974080i | \(-0.427369\pi\) | ||||
0.226202 | + | 0.974080i | \(0.427369\pi\) | |||||||
\(920\) | −11.8143 | + | 10.4194i | −0.389505 | + | 0.343516i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.6680 | −0.516000 | ||||||||
\(923\) | 15.1915i | 0.500033i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.2626 | + | 2.17465i | 0.567592 | + | 0.0715022i | ||||
\(926\) | 32.0462i | 1.05310i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.98101i | 0.0978566i | ||||||||
\(929\) | 45.8959 | 1.50580 | 0.752898 | − | 0.658137i | \(-0.228655\pi\) | ||||
0.752898 | + | 0.658137i | \(0.228655\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.3734 | −0.339791 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 0.699158i | − | 0.0228772i | ||||||
\(935\) | 49.2257 | − | 43.4136i | 1.60985 | − | 1.41978i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.17552 | −0.201746 | −0.100873 | − | 0.994899i | \(-0.532164\pi\) | ||||
−0.100873 | + | 0.994899i | \(0.532164\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0603 | − | 13.6750i | −0.393365 | − | 0.446028i | ||||
\(941\) | −33.4096 | −1.08912 | −0.544560 | − | 0.838722i | \(-0.683304\pi\) | ||||
−0.544560 | + | 0.838722i | \(0.683304\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49.1022 | 1.59899 | ||||||||
\(944\) | −0.904592 | −0.0294420 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.3734 | 0.532345 | ||||||||
\(947\) | 6.55365 | 0.212965 | 0.106483 | − | 0.994315i | \(-0.466041\pi\) | ||||
0.106483 | + | 0.994315i | \(0.466041\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.80924 | −0.285960 | ||||||||
\(950\) | 30.6534 | + | 3.86155i | 0.994528 | + | 0.125285i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.5253 | 1.50710 | 0.753551 | − | 0.657389i | \(-0.228339\pi\) | ||||
0.753551 | + | 0.657389i | \(0.228339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.18333 | − | 4.74339i | −0.135369 | − | 0.153492i | ||||
\(956\) | 12.3746i | 0.400222i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.54561 | 0.276096 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.88697 | −0.286677 | ||||||||
\(962\) | 3.66389i | 0.118129i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 12.4947i | − | 0.402429i | ||||||
\(965\) | 12.1536 | + | 13.7807i | 0.391237 | + | 0.443615i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.93169i | 0.190750i | 0.995441 | + | 0.0953752i | \(0.0304051\pi\) | ||||
−0.995441 | + | 0.0953752i | \(0.969595\pi\) | |||||||
\(968\) | 29.0731 | 0.934445 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.85918 | − | 8.69510i | 0.316559 | − | 0.279183i | ||||
\(971\) | −0.340138 | −0.0109155 | −0.00545777 | − | 0.999985i | \(-0.501737\pi\) | ||||
−0.00545777 | + | 0.999985i | \(0.501737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.8178i | 0.763171i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.1735i | 0.325644i | ||||||||
\(977\) | 20.6886 | 0.661886 | 0.330943 | − | 0.943651i | \(-0.392633\pi\) | ||||
0.330943 | + | 0.943651i | \(0.392633\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.3062i | 0.776829i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.9104i | 0.411987i | ||||||||
\(983\) | − | 21.2258i | − | 0.676997i | −0.940967 | − | 0.338499i | \(-0.890081\pi\) | ||
0.940967 | − | 0.338499i | \(-0.109919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.89180 | − | 5.19615i | 0.187728 | − | 0.165563i | ||||
\(986\) | 13.8225 | 0.440197 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.50600i | 0.206983i | ||||||||
\(989\) | 18.2211i | 0.579398i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.2067 | 1.84900 | 0.924499 | − | 0.381184i | \(-0.124484\pi\) | ||||
0.924499 | + | 0.381184i | \(0.124484\pi\) | |||||||
\(992\) | − | 6.31561i | − | 0.200521i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.12351 | + | 5.80944i | 0.162426 | + | 0.184172i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.2832 | −1.21244 | −0.606220 | − | 0.795297i | \(-0.707315\pi\) | ||||
−0.606220 | + | 0.795297i | \(0.707315\pi\) | |||||||
\(998\) | 16.3365 | 0.517122 | ||||||||
\(999\) | 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.4409.6 | 16 | ||
3.2 | odd | 2 | 4410.2.d.b.4409.11 | 16 | |||
5.4 | even | 2 | 4410.2.d.b.4409.5 | 16 | |||
7.4 | even | 3 | 630.2.bo.b.89.3 | yes | 16 | ||
7.5 | odd | 6 | 630.2.bo.b.269.1 | yes | 16 | ||
7.6 | odd | 2 | inner | 4410.2.d.a.4409.11 | 16 | ||
15.14 | odd | 2 | inner | 4410.2.d.a.4409.12 | 16 | ||
21.5 | even | 6 | 630.2.bo.a.269.8 | yes | 16 | ||
21.11 | odd | 6 | 630.2.bo.a.89.6 | ✓ | 16 | ||
21.20 | even | 2 | 4410.2.d.b.4409.6 | 16 | |||
35.4 | even | 6 | 630.2.bo.a.89.8 | yes | 16 | ||
35.12 | even | 12 | 3150.2.bf.f.1151.4 | 32 | |||
35.18 | odd | 12 | 3150.2.bf.f.1601.3 | 32 | |||
35.19 | odd | 6 | 630.2.bo.a.269.6 | yes | 16 | ||
35.32 | odd | 12 | 3150.2.bf.f.1601.16 | 32 | |||
35.33 | even | 12 | 3150.2.bf.f.1151.13 | 32 | |||
35.34 | odd | 2 | 4410.2.d.b.4409.12 | 16 | |||
105.32 | even | 12 | 3150.2.bf.f.1601.4 | 32 | |||
105.47 | odd | 12 | 3150.2.bf.f.1151.14 | 32 | |||
105.53 | even | 12 | 3150.2.bf.f.1601.15 | 32 | |||
105.68 | odd | 12 | 3150.2.bf.f.1151.3 | 32 | |||
105.74 | odd | 6 | 630.2.bo.b.89.1 | yes | 16 | ||
105.89 | even | 6 | 630.2.bo.b.269.3 | yes | 16 | ||
105.104 | even | 2 | inner | 4410.2.d.a.4409.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.6 | ✓ | 16 | 21.11 | odd | 6 | ||
630.2.bo.a.89.8 | yes | 16 | 35.4 | even | 6 | ||
630.2.bo.a.269.6 | yes | 16 | 35.19 | odd | 6 | ||
630.2.bo.a.269.8 | yes | 16 | 21.5 | even | 6 | ||
630.2.bo.b.89.1 | yes | 16 | 105.74 | odd | 6 | ||
630.2.bo.b.89.3 | yes | 16 | 7.4 | even | 3 | ||
630.2.bo.b.269.1 | yes | 16 | 7.5 | odd | 6 | ||
630.2.bo.b.269.3 | yes | 16 | 105.89 | even | 6 | ||
3150.2.bf.f.1151.3 | 32 | 105.68 | odd | 12 | |||
3150.2.bf.f.1151.4 | 32 | 35.12 | even | 12 | |||
3150.2.bf.f.1151.13 | 32 | 35.33 | even | 12 | |||
3150.2.bf.f.1151.14 | 32 | 105.47 | odd | 12 | |||
3150.2.bf.f.1601.3 | 32 | 35.18 | odd | 12 | |||
3150.2.bf.f.1601.4 | 32 | 105.32 | even | 12 | |||
3150.2.bf.f.1601.15 | 32 | 105.53 | even | 12 | |||
3150.2.bf.f.1601.16 | 32 | 35.32 | odd | 12 | |||
4410.2.d.a.4409.5 | 16 | 105.104 | even | 2 | inner | ||
4410.2.d.a.4409.6 | 16 | 1.1 | even | 1 | trivial | ||
4410.2.d.a.4409.11 | 16 | 7.6 | odd | 2 | inner | ||
4410.2.d.a.4409.12 | 16 | 15.14 | odd | 2 | inner | ||
4410.2.d.b.4409.5 | 16 | 5.4 | even | 2 | |||
4410.2.d.b.4409.6 | 16 | 21.20 | even | 2 | |||
4410.2.d.b.4409.11 | 16 | 3.2 | odd | 2 | |||
4410.2.d.b.4409.12 | 16 | 35.34 | odd | 2 |