Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2112,2,Mod(1,2112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2112, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2112.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2112 = 2^{6} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2112.a (trivial) |
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: | yes |
Analytic conductor: | \(16.8644049069\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1056) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2112.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.23607 | 0.552786 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.23607 | −1.22312 | −0.611559 | − | 0.791199i | \(-0.709457\pi\) | ||||
−0.611559 | + | 0.791199i | \(0.709457\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.23607 | −1.45222 | −0.726112 | − | 0.687576i | \(-0.758675\pi\) | ||||
−0.726112 | + | 0.687576i | \(0.758675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.23607 | 0.319151 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.47214 | 1.48481 | 0.742405 | − | 0.669951i | \(-0.233685\pi\) | ||||
0.742405 | + | 0.669951i | \(0.233685\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.70820 | 1.19024 | 0.595121 | − | 0.803636i | \(-0.297104\pi\) | ||||
0.595121 | + | 0.803636i | \(0.297104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.47214 | −1.57324 | −0.786618 | − | 0.617440i | \(-0.788170\pi\) | ||||
−0.786618 | + | 0.617440i | \(0.788170\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.23607 | −0.838442 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9443 | 1.70921 | 0.854604 | − | 0.519280i | \(-0.173800\pi\) | ||||
0.854604 | + | 0.519280i | \(0.173800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.9443 | −1.97398 | −0.986991 | − | 0.160773i | \(-0.948601\pi\) | ||||
−0.986991 | + | 0.160773i | \(0.948601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.23607 | 0.184262 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.70820 | −0.832627 | −0.416314 | − | 0.909221i | \(-0.636678\pi\) | ||||
−0.416314 | + | 0.909221i | \(0.636678\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.47214 | −0.626224 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.76393 | −0.929098 | −0.464549 | − | 0.885548i | \(-0.653783\pi\) | ||||
−0.464549 | + | 0.885548i | \(0.653783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.23607 | −0.166671 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.47214 | 0.857255 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.52786 | −0.719667 | −0.359833 | − | 0.933017i | \(-0.617166\pi\) | ||||
−0.359833 | + | 0.933017i | \(0.617166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.7082 | −1.49908 | −0.749541 | − | 0.661958i | \(-0.769726\pi\) | ||||
−0.749541 | + | 0.661958i | \(0.769726\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.23607 | −0.407706 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.47214 | −0.802770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.70820 | 0.687187 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.70820 | 0.677439 | 0.338720 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338720 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.47214 | −0.400928 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.23607 | 0.368784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.70820 | −0.192188 | −0.0960940 | − | 0.995372i | \(-0.530635\pi\) | ||||
−0.0960940 | + | 0.995372i | \(0.530635\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.94427 | 0.542704 | 0.271352 | − | 0.962480i | \(-0.412529\pi\) | ||||
0.271352 | + | 0.962480i | \(0.412529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.52786 | −0.599581 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.47214 | −0.908308 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.9443 | 1.77624 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.00000 | 0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.47214 | −0.860215 | −0.430108 | − | 0.902778i | \(-0.641524\pi\) | ||||
−0.430108 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.52786 | −0.351036 | −0.175518 | − | 0.984476i | \(-0.556160\pi\) | ||||
−0.175518 | + | 0.984476i | \(0.556160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.47214 | 0.637719 | 0.318859 | − | 0.947802i | \(-0.396700\pi\) | ||||
0.318859 | + | 0.947802i | \(0.396700\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.00000 | −0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.9443 | −1.63806 | −0.819032 | − | 0.573747i | \(-0.805489\pi\) | ||||
−0.819032 | + | 0.573747i | \(0.805489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.6525 | 1.97815 | 0.989074 | − | 0.147418i | \(-0.0470964\pi\) | ||||
0.989074 | + | 0.147418i | \(0.0470964\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.94427 | 0.653262 | 0.326631 | − | 0.945152i | \(-0.394087\pi\) | ||||
0.326631 | + | 0.945152i | \(0.394087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.05573 | 0.657950 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.23607 | −0.484075 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.4721 | 1.32666 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.9443 | 0.986812 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.18034 | 0.725888 | 0.362944 | − | 0.931811i | \(-0.381772\pi\) | ||||
0.362944 | + | 0.931811i | \(0.381772\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.9443 | −1.13968 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0000 | −1.39793 | −0.698963 | − | 0.715158i | \(-0.746355\pi\) | ||||
−0.698963 | + | 0.715158i | \(0.746355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.9443 | −1.81610 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.23607 | 0.106384 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.52786 | −0.643149 | −0.321574 | − | 0.946884i | \(-0.604212\pi\) | ||||
−0.321574 | + | 0.946884i | \(0.604212\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.52786 | 0.129592 | 0.0647959 | − | 0.997899i | \(-0.479360\pi\) | ||||
0.0647959 | + | 0.997899i | \(0.479360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.70820 | −0.480717 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.23607 | 0.437862 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4721 | −0.869664 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.47214 | 0.286377 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.00000 | −0.163846 | −0.0819232 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819232 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2361 | 0.914378 | 0.457189 | − | 0.889369i | \(-0.348856\pi\) | ||||
0.457189 | + | 0.889369i | \(0.348856\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.47214 | −0.361551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4721 | 1.31462 | 0.657310 | − | 0.753620i | \(-0.271694\pi\) | ||||
0.657310 | + | 0.753620i | \(0.271694\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.76393 | −0.536415 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.4721 | −1.45581 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.0000 | 1.56652 | 0.783260 | − | 0.621694i | \(-0.213555\pi\) | ||||
0.783260 | + | 0.621694i | \(0.213555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.23607 | −0.0962278 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.3607 | −1.88509 | −0.942543 | − | 0.334085i | \(-0.891573\pi\) | ||||
−0.942543 | + | 0.334085i | \(0.891573\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.47214 | 0.494937 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.52786 | 0.572333 | 0.286166 | − | 0.958180i | \(-0.407619\pi\) | ||||
0.286166 | + | 0.958180i | \(0.407619\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2361 | 0.849367 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.52786 | −0.415500 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.4721 | −0.782724 | −0.391362 | − | 0.920237i | \(-0.627996\pi\) | ||||
−0.391362 | + | 0.920237i | \(0.627996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.47214 | 0.629729 | 0.314864 | − | 0.949137i | \(-0.398041\pi\) | ||||
0.314864 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.7082 | −0.865495 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.41641 | −0.545265 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.47214 | 0.327035 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.23607 | −0.235389 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.23607 | 0.523584 | 0.261792 | − | 0.965124i | \(-0.415687\pi\) | ||||
0.261792 | + | 0.965124i | \(0.415687\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.52786 | −0.541868 | −0.270934 | − | 0.962598i | \(-0.587332\pi\) | ||||
−0.270934 | + | 0.962598i | \(0.587332\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.47214 | −0.463479 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.41641 | −0.385903 | −0.192952 | − | 0.981208i | \(-0.561806\pi\) | ||||
−0.192952 | + | 0.981208i | \(0.561806\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.41641 | 0.242183 | 0.121091 | − | 0.992641i | \(-0.461361\pi\) | ||||
0.121091 | + | 0.992641i | \(0.461361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 27.4164 | 1.92425 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5279 | 0.944827 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.70820 | 0.396748 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.47214 | −0.447687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.05573 | 0.210365 | 0.105182 | − | 0.994453i | \(-0.466457\pi\) | ||||
0.105182 | + | 0.994453i | \(0.466457\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.70820 | 0.391120 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.0000 | −1.09119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.4164 | 1.57516 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.47214 | −0.231476 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.41641 | −0.622254 | −0.311127 | − | 0.950368i | \(-0.600706\pi\) | ||||
−0.311127 | + | 0.950368i | \(0.600706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.23607 | 0.212918 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.00000 | −0.131024 | −0.0655122 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655122 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.05573 | −0.460265 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.70820 | −0.110960 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.5279 | 1.13378 | 0.566892 | − | 0.823792i | \(-0.308146\pi\) | ||||
0.566892 | + | 0.823792i | \(0.308146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3607 | 1.18272 | 0.591358 | − | 0.806409i | \(-0.298592\pi\) | ||||
0.591358 | + | 0.806409i | \(0.298592\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.29180 | 0.274193 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −33.8885 | −2.15628 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.94427 | 0.313331 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.3607 | −1.28515 | −0.642577 | − | 0.766221i | \(-0.722135\pi\) | ||||
−0.642577 | + | 0.766221i | \(0.722135\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.70820 | −0.358872 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.52786 | −0.346168 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.4164 | 1.20648 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.47214 | −0.524412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.36068 | −0.513592 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.00000 | 0.122398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.29180 | 0.261675 | 0.130838 | − | 0.991404i | \(-0.458233\pi\) | ||||
0.130838 | + | 0.991404i | \(0.458233\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7639 | 0.775354 | 0.387677 | − | 0.921795i | \(-0.373278\pi\) | ||||
0.387677 | + | 0.921795i | \(0.373278\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.9443 | 1.02551 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.47214 | 0.209378 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.23607 | 0.0742681 | 0.0371341 | − | 0.999310i | \(-0.488177\pi\) | ||||
0.0371341 | + | 0.999310i | \(0.488177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.3607 | −0.856686 | −0.428343 | − | 0.903616i | \(-0.640903\pi\) | ||||
−0.428343 | + | 0.903616i | \(0.640903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.9443 | 1.24501 | 0.622504 | − | 0.782617i | \(-0.286115\pi\) | ||||
0.622504 | + | 0.782617i | \(0.286115\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −35.4164 | −2.09056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.47214 | −0.496645 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.88854 | 0.460854 | 0.230427 | − | 0.973090i | \(-0.425988\pi\) | ||||
0.230427 | + | 0.973090i | \(0.425988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.83282 | −0.397822 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.8885 | −1.72850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.8885 | 2.41442 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.52786 | −0.202670 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.4721 | −0.828672 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.4721 | −1.73914 | −0.869568 | − | 0.493813i | \(-0.835603\pi\) | ||||
−0.869568 | + | 0.493813i | \(0.835603\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.47214 | 0.368187 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.29180 | −0.129956 | −0.0649779 | − | 0.997887i | \(-0.520698\pi\) | ||||
−0.0649779 | + | 0.997887i | \(0.520698\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.8885 | −0.898074 | −0.449037 | − | 0.893513i | \(-0.648233\pi\) | ||||
−0.449037 | + | 0.893513i | \(0.648233\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.00000 | −0.225374 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.70820 | 0.432936 | 0.216468 | − | 0.976290i | \(-0.430546\pi\) | ||||
0.216468 | + | 0.976290i | \(0.430546\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.47214 | 0.474349 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.9443 | −0.945737 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.9443 | −1.61050 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.1803 | 1.00846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.6525 | 1.14208 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.4721 | 1.01840 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9443 | −0.931341 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.88854 | 0.540269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.9443 | −1.46775 | −0.733874 | − | 0.679286i | \(-0.762290\pi\) | ||||
−0.733874 | + | 0.679286i | \(0.762290\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.94427 | 0.377161 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4164 | 0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.05573 | 0.379868 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.8885 | −0.960307 | −0.480154 | − | 0.877184i | \(-0.659419\pi\) | ||||
−0.480154 | + | 0.877184i | \(0.659419\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.2918 | −0.872080 | −0.436040 | − | 0.899927i | \(-0.643619\pi\) | ||||
−0.436040 | + | 0.899927i | \(0.643619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.23607 | −0.279481 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.8328 | 1.32172 | 0.660859 | − | 0.750510i | \(-0.270192\pi\) | ||||
0.660859 | + | 0.750510i | \(0.270192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.05573 | 0.374479 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.4721 | 0.765947 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.4164 | 0.602535 | 0.301267 | − | 0.953540i | \(-0.402590\pi\) | ||||
0.301267 | + | 0.953540i | \(0.402590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.41641 | −0.388193 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.9443 | 1.92848 | 0.964238 | − | 0.265039i | \(-0.0853849\pi\) | ||||
0.964238 | + | 0.265039i | \(0.0853849\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.9443 | 0.569736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.8885 | 1.13640 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.1803 | −0.941342 | −0.470671 | − | 0.882309i | \(-0.655988\pi\) | ||||
−0.470671 | + | 0.882309i | \(0.655988\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.4721 | −0.540779 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 44.3607 | 2.28469 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.8885 | 1.53527 | 0.767636 | − | 0.640886i | \(-0.221433\pi\) | ||||
0.767636 | + | 0.640886i | \(0.221433\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.18034 | 0.419092 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.0689 | −1.53645 | −0.768224 | − | 0.640181i | \(-0.778859\pi\) | ||||
−0.768224 | + | 0.640181i | \(0.778859\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.9443 | −0.657994 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.7082 | −1.40486 | −0.702431 | − | 0.711752i | \(-0.747902\pi\) | ||||
−0.702431 | + | 0.711752i | \(0.747902\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.5279 | −1.29100 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.0000 | −0.807093 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.11146 | −0.106239 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.3607 | −0.720742 | −0.360371 | − | 0.932809i | \(-0.617350\pi\) | ||||
−0.360371 | + | 0.932809i | \(0.617350\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.9443 | −1.04853 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4164 | 0.669983 | 0.334992 | − | 0.942221i | \(-0.391266\pi\) | ||||
0.334992 | + | 0.942221i | \(0.391266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.23607 | 0.0614207 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.4721 | 1.60564 | 0.802822 | − | 0.596219i | \(-0.203331\pi\) | ||||
0.802822 | + | 0.596219i | \(0.203331\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.52786 | −0.371322 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.8885 | 0.880238 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.11146 | 0.300000 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.52786 | 0.0748198 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.41641 | 0.362315 | 0.181158 | − | 0.983454i | \(-0.442016\pi\) | ||||
0.181158 | + | 0.983454i | \(0.442016\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.70820 | −0.277542 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.5279 | 0.753212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.8885 | 1.83356 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.23607 | 0.252800 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.0557 | −0.917882 | −0.458941 | − | 0.888467i | \(-0.651771\pi\) | ||||
−0.458941 | + | 0.888467i | \(0.651771\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.8328 | −1.77007 | −0.885036 | − | 0.465522i | \(-0.845866\pi\) | ||||
−0.885036 | + | 0.465522i | \(0.845866\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4721 | −0.502100 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.9443 | 1.76728 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.2361 | 1.29991 | 0.649953 | − | 0.759974i | \(-0.274788\pi\) | ||||
0.649953 | + | 0.759974i | \(0.274788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47214 | 0.165340 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.5279 | 1.40291 | 0.701456 | − | 0.712713i | \(-0.252534\pi\) | ||||
0.701456 | + | 0.712713i | \(0.252534\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.47214 | 0.117190 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.00000 | −0.0945968 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5279 | 0.544034 | 0.272017 | − | 0.962293i | \(-0.412309\pi\) | ||||
0.272017 | + | 0.962293i | \(0.412309\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.9443 | −0.515346 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.2361 | 0.527917 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.9443 | 0.981883 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.3050 | 1.46438 | 0.732192 | − | 0.681098i | \(-0.238497\pi\) | ||||
0.732192 | + | 0.681098i | \(0.238497\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.47214 | −0.208741 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.9443 | 0.882323 | 0.441161 | − | 0.897428i | \(-0.354567\pi\) | ||||
0.441161 | + | 0.897428i | \(0.354567\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.4721 | −0.672577 | −0.336289 | − | 0.941759i | \(-0.609172\pi\) | ||||
−0.336289 | + | 0.941759i | \(0.609172\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.05573 | 0.326500 | 0.163250 | − | 0.986585i | \(-0.447802\pi\) | ||||
0.163250 | + | 0.986585i | \(0.447802\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.8885 | −1.19542 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.4721 | 0.758996 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.9443 | 0.595178 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.4721 | −1.03109 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.76393 | −0.309699 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.0000 | −1.46212 | −0.731059 | − | 0.682315i | \(-0.760973\pi\) | ||||
−0.731059 | + | 0.682315i | \(0.760973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.4164 | 1.43246 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.4721 | −0.840511 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.4721 | −0.475515 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.52786 | −0.0692341 | −0.0346171 | − | 0.999401i | \(-0.511021\pi\) | ||||
−0.0346171 | + | 0.999401i | \(0.511021\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.0000 | 0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.8885 | 1.34885 | 0.674426 | − | 0.738343i | \(-0.264391\pi\) | ||||
0.674426 | + | 0.738343i | \(0.264391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.8885 | 1.70641 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.23607 | −0.0555571 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.4721 | −0.828589 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9443 | 0.758530 | 0.379265 | − | 0.925288i | \(-0.376177\pi\) | ||||
0.379265 | + | 0.925288i | \(0.376177\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.3607 | −1.08835 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.4164 | 0.865735 | 0.432867 | − | 0.901458i | \(-0.357502\pi\) | ||||
0.432867 | + | 0.901458i | \(0.357502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.36068 | −0.194048 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.4164 | 0.640255 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.65248 | −0.383514 | −0.191757 | − | 0.981442i | \(-0.561419\pi\) | ||||
−0.191757 | + | 0.981442i | \(0.561419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.4164 | 0.858931 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.47214 | 0.285752 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.70820 | 0.251047 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.52786 | 0.330437 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.4721 | 0.721657 | 0.360829 | − | 0.932632i | \(-0.382494\pi\) | ||||
0.360829 | + | 0.932632i | \(0.382494\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.88854 | −0.432396 | −0.216198 | − | 0.976350i | \(-0.569366\pi\) | ||||
−0.216198 | + | 0.976350i | \(0.569366\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.2361 | 0.490382 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.58359 | 0.416678 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.52786 | −0.239889 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −57.3050 | −2.48215 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.9443 | −0.905500 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.4721 | −0.451906 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.47214 | −0.149555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.29180 | −0.356492 | −0.178246 | − | 0.983986i | \(-0.557042\pi\) | ||||
−0.178246 | + | 0.983986i | \(0.557042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.47214 | 0.363574 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.5279 | 1.09349 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.41641 | −0.146075 | −0.0730375 | − | 0.997329i | \(-0.523269\pi\) | ||||
−0.0730375 | + | 0.997329i | \(0.523269\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.7082 | −0.499694 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54.8328 | −2.33596 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.52786 | 0.235069 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.41641 | −0.314809 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8885 | 1.35116 | 0.675580 | − | 0.737286i | \(-0.263893\pi\) | ||||
0.675580 | + | 0.737286i | \(0.263893\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 67.7771 | 2.86667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.47214 | 0.188814 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.05573 | 0.297363 | 0.148682 | − | 0.988885i | \(-0.452497\pi\) | ||||
0.148682 | + | 0.988885i | \(0.452497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.58359 | 0.361114 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.23607 | −0.135902 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.5279 | 0.818651 | 0.409325 | − | 0.912389i | \(-0.365764\pi\) | ||||
0.409325 | + | 0.912389i | \(0.365764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.5836 | −0.526607 | −0.263303 | − | 0.964713i | \(-0.584812\pi\) | ||||
−0.263303 | + | 0.964713i | \(0.584812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.23607 | 0.302291 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.8197 | −0.826537 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.4164 | 0.725055 | 0.362527 | − | 0.931973i | \(-0.381914\pi\) | ||||
0.362527 | + | 0.931973i | \(0.381914\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.52786 | −0.312847 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.0000 | −0.663792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.76393 | 0.280133 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.47214 | −0.267590 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.583592 | −0.0240874 | −0.0120437 | − | 0.999927i | \(-0.503834\pi\) | ||||
−0.0120437 | + | 0.999927i | \(0.503834\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.41641 | −0.222801 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.52786 | 0.144872 | 0.0724360 | − | 0.997373i | \(-0.476923\pi\) | ||||
0.0724360 | + | 0.997373i | \(0.476923\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.8885 | 0.733359 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.41641 | 0.139824 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.0689 | −1.55545 | −0.777726 | − | 0.628603i | \(-0.783627\pi\) | ||||
−0.777726 | + | 0.628603i | \(0.783627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.88854 | −0.321780 | −0.160890 | − | 0.986972i | \(-0.551437\pi\) | ||||
−0.160890 | + | 0.986972i | \(0.551437\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.23607 | 0.0502533 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.87539 | −0.116708 | −0.0583542 | − | 0.998296i | \(-0.518585\pi\) | ||||
−0.0583542 | + | 0.998296i | \(0.518585\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.4164 | 1.11097 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.8885 | 1.20916 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.8197 | −1.04285 | −0.521423 | − | 0.853298i | \(-0.674599\pi\) | ||||
−0.521423 | + | 0.853298i | \(0.674599\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.5279 | 0.545496 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.8885 | −0.961717 | −0.480858 | − | 0.876798i | \(-0.659675\pi\) | ||||
−0.480858 | + | 0.876798i | \(0.659675\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.7771 | −1.11646 | −0.558228 | − | 0.829688i | \(-0.688518\pi\) | ||||
−0.558228 | + | 0.829688i | \(0.688518\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.70820 | 0.229062 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.47214 | −0.259301 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.47214 | −0.258472 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.8328 | 1.06989 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.05573 | 0.121454 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.1115 | 0.401261 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.1803 | −0.720331 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.70820 | 0.225813 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.2492 | −1.58975 | −0.794874 | − | 0.606774i | \(-0.792463\pi\) | ||||
−0.794874 | + | 0.606774i | \(0.792463\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.0557 | 1.06697 | 0.533487 | − | 0.845808i | \(-0.320881\pi\) | ||||
0.533487 | + | 0.845808i | \(0.320881\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.0000 | −0.629999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.6525 | 1.67684 | 0.838421 | − | 0.545023i | \(-0.183479\pi\) | ||||
0.838421 | + | 0.545023i | \(0.183479\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.52786 | 0.216988 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.1246 | −1.53106 | −0.765532 | − | 0.643398i | \(-0.777524\pi\) | ||||
−0.765532 | + | 0.643398i | \(0.777524\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.7771 | −0.772755 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −48.9443 | −1.90660 | −0.953299 | − | 0.302028i | \(-0.902336\pi\) | ||||
−0.953299 | + | 0.302028i | \(0.902336\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.52786 | −0.292800 | −0.146400 | − | 0.989225i | \(-0.546769\pi\) | ||||
−0.146400 | + | 0.989225i | \(0.546769\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.4164 | 0.909418 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −25.8885 | −1.00391 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.3607 | −1.87253 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.7082 | 0.451990 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.4721 | 0.634954 | 0.317477 | − | 0.948266i | \(-0.397164\pi\) | ||||
0.317477 | + | 0.948266i | \(0.397164\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.47214 | −0.133643 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.52786 | 0.289319 | 0.144660 | − | 0.989481i | \(-0.453791\pi\) | ||||
0.144660 | + | 0.989481i | \(0.453791\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.4164 | 1.05215 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.00000 | −0.153280 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.4164 | −0.589892 | −0.294946 | − | 0.955514i | \(-0.595302\pi\) | ||||
−0.294946 | + | 0.955514i | \(0.595302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.30495 | −0.355524 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.41641 | −0.359258 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.4164 | 1.34926 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.23607 | 0.122928 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.88854 | 0.0716366 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −48.9443 | −1.85390 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.00000 | −0.0756469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.8328 | −0.635767 | −0.317883 | − | 0.948130i | \(-0.602972\pi\) | ||||
−0.317883 | + | 0.948130i | \(0.602972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.8328 | −1.46461 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.05573 | −0.265734 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4164 | 0.429358 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3607 | 0.389103 | 0.194552 | − | 0.980892i | \(-0.437675\pi\) | ||||
0.194552 | + | 0.980892i | \(0.437675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.70820 | −0.0640627 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.47214 | 0.242044 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.5279 | 0.654590 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.0689 | −1.41973 | −0.709865 | − | 0.704338i | \(-0.751244\pi\) | ||||
−0.709865 | + | 0.704338i | \(0.751244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.9443 | −0.780005 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.3607 | 0.682841 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.4164 | 1.09250 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.4164 | −1.01682 | −0.508409 | − | 0.861116i | \(-0.669766\pi\) | ||||
−0.508409 | + | 0.861116i | \(0.669766\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 57.8885 | 2.14109 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.1246 | −1.14961 | −0.574807 | − | 0.818289i | \(-0.694923\pi\) | ||||
−0.574807 | + | 0.818289i | \(0.694923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.29180 | 0.158305 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.00000 | −0.294684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.88854 | 0.363756 | 0.181878 | − | 0.983321i | \(-0.441782\pi\) | ||||
0.181878 | + | 0.983321i | \(0.441782\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.8885 | −1.24493 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.3050 | 1.36859 | 0.684293 | − | 0.729207i | \(-0.260111\pi\) | ||||
0.684293 | + | 0.729207i | \(0.260111\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.47214 | −0.0905721 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.94427 | 0.180901 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.8328 | 2.00355 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.8885 | −1.23661 | −0.618305 | − | 0.785938i | \(-0.712180\pi\) | ||||
−0.618305 | + | 0.785938i | \(0.712180\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.3607 | −0.741984 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.8885 | 0.505456 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.9443 | 1.41545 | 0.707727 | − | 0.706486i | \(-0.249721\pi\) | ||||
0.707727 | + | 0.706486i | \(0.249721\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.70820 | −0.207195 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.5836 | −0.673655 | −0.336827 | − | 0.941566i | \(-0.609354\pi\) | ||||
−0.336827 | + | 0.941566i | \(0.609354\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −66.8328 | −2.41951 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.52786 | −0.199860 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.9443 | 1.04512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.4721 | 0.882488 | 0.441244 | − | 0.897387i | \(-0.354537\pi\) | ||||
0.441244 | + | 0.897387i | \(0.354537\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.81966 | −0.353189 | −0.176594 | − | 0.984284i | \(-0.556508\pi\) | ||||
−0.176594 | + | 0.984284i | \(0.556508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.4164 | 0.696560 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 70.8328 | 2.53785 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.70820 | −0.204256 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.47214 | −0.302769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.3607 | 0.726704 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.8328 | −0.813902 | −0.406951 | − | 0.913450i | \(-0.633408\pi\) | ||||
−0.406951 | + | 0.913450i | \(0.633408\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.0000 | 0.569615 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.4721 | −0.799017 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 61.3050 | 2.17700 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.36068 | −0.296523 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.12461 | 0.110679 | 0.0553397 | − | 0.998468i | \(-0.482376\pi\) | ||||
0.0553397 | + | 0.998468i | \(0.482376\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.5279 | 0.903111 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.00000 | 0.211735 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.8328 | −0.804751 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.29180 | 0.151078 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.8885 | 0.558611 | 0.279306 | − | 0.960202i | \(-0.409896\pi\) | ||||
0.279306 | + | 0.960202i | \(0.409896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.8885 | −1.47091 | −0.735453 | − | 0.677576i | \(-0.763031\pi\) | ||||
−0.735453 | + | 0.677576i | \(0.763031\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.7639 | 0.447651 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.7214 | 0.865951 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −83.7771 | −2.93099 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.9443 | 0.592081 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.3607 | −1.75760 | −0.878800 | − | 0.477190i | \(-0.841655\pi\) | ||||
−0.878800 | + | 0.477190i | \(0.841655\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.8885 | 0.902418 | 0.451209 | − | 0.892418i | \(-0.350993\pi\) | ||||
0.451209 | + | 0.892418i | \(0.350993\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.47214 | 0.120884 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.7771 | 0.687717 | 0.343858 | − | 0.939022i | \(-0.388266\pi\) | ||||
0.343858 | + | 0.939022i | \(0.388266\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.11146 | 0.281723 | 0.140861 | − | 0.990029i | \(-0.455013\pi\) | ||||
0.140861 | + | 0.990029i | \(0.455013\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.23607 | 0.0428787 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.5279 | −0.538009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.1115 | −1.04205 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.2361 | 0.802198 | 0.401099 | − | 0.916035i | \(-0.368628\pi\) | ||||
0.401099 | + | 0.916035i | \(0.368628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.3607 | −0.494608 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.8197 | 0.613015 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.23607 | −0.111193 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.9443 | 0.718806 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.2492 | −1.17405 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.9017 | 1.87980 | 0.939899 | − | 0.341452i | \(-0.110919\pi\) | ||||
0.939899 | + | 0.341452i | \(0.110919\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.00000 | 0.273594 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.1115 | −0.550357 | −0.275178 | − | 0.961393i | \(-0.588737\pi\) | ||||
−0.275178 | + | 0.961393i | \(0.588737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.8885 | 1.01978 | 0.509892 | − | 0.860238i | \(-0.329685\pi\) | ||||
0.509892 | + | 0.860238i | \(0.329685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −35.4164 | −1.20699 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.7639 | −0.570651 | −0.285325 | − | 0.958431i | \(-0.592102\pi\) | ||||
−0.285325 | + | 0.958431i | \(0.592102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.30495 | 0.316378 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.00000 | 0.101885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.70820 | 0.0579468 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.8885 | −1.41934 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.47214 | −0.286738 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.8885 | 1.14564 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.2361 | −0.987232 | −0.493616 | − | 0.869680i | \(-0.664325\pi\) | ||||
−0.493616 | + | 0.869680i | \(0.664325\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.88854 | 0.266074 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.9443 | −1.44683 | −0.723415 | − | 0.690414i | \(-0.757428\pi\) | ||||
−0.723415 | + | 0.690414i | \(0.757428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.7214 | 1.37038 | 0.685191 | − | 0.728363i | \(-0.259719\pi\) | ||||
0.685191 | + | 0.728363i | \(0.259719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.83282 | −0.229683 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.3607 | 0.817952 | 0.408976 | − | 0.912545i | \(-0.365886\pi\) | ||||
0.408976 | + | 0.912545i | \(0.365886\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.4721 | −0.887847 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.9443 | −1.23629 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.9443 | −0.432679 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.8885 | −0.997949 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.2492 | 1.00775 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 41.8885 | 1.39396 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.4721 | 0.348106 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.05573 | −0.101464 | −0.0507319 | − | 0.998712i | \(-0.516155\pi\) | ||||
−0.0507319 | + | 0.998712i | \(0.516155\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.52786 | −0.117012 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.1803 | −0.668604 | −0.334302 | − | 0.942466i | \(-0.608501\pi\) | ||||
−0.334302 | + | 0.942466i | \(0.608501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.94427 | −0.163632 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.4721 | −0.478434 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 51.7771 | 1.70983 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.2918 | −0.471443 | −0.235721 | − | 0.971821i | \(-0.575745\pi\) | ||||
−0.235721 | + | 0.971821i | \(0.575745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.4721 | −1.00409 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.8885 | −0.983793 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.8328 | 0.684979 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.47214 | 0.212573 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.3607 | −1.25857 | −0.629287 | − | 0.777173i | \(-0.716653\pi\) | ||||
−0.629287 | + | 0.777173i | \(0.716653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.4721 | 0.736495 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.29180 | −0.0750300 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.52786 | 0.180780 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.8885 | 0.911079 | 0.455540 | − | 0.890216i | \(-0.349446\pi\) | ||||
0.455540 | + | 0.890216i | \(0.349446\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.8885 | −0.518503 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.41641 | −0.176570 | −0.0882849 | − | 0.996095i | \(-0.528139\pi\) | ||||
−0.0882849 | + | 0.996095i | \(0.528139\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 62.4721 | 2.03437 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.00000 | −0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.7214 | −1.19328 | −0.596642 | − | 0.802508i | \(-0.703499\pi\) | ||||
−0.596642 | + | 0.802508i | \(0.703499\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.4164 | 1.01982 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.70820 | 0.249956 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.8885 | 1.03297 | 0.516486 | − | 0.856296i | \(-0.327240\pi\) | ||||
0.516486 | + | 0.856296i | \(0.327240\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.94427 | 0.289430 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.47214 | 0.273865 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.3607 | 0.786647 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.9443 | −0.546022 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.30495 | −0.299537 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.8754 | −0.606992 | −0.303496 | − | 0.952833i | \(-0.598154\pi\) | ||||
−0.303496 | + | 0.952833i | \(0.598154\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.9443 | −0.929824 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.3607 | 1.42360 | 0.711801 | − | 0.702381i | \(-0.247880\pi\) | ||||
0.711801 | + | 0.702381i | \(0.247880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.94427 | −0.158506 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.1803 | 0.582237 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.5279 | −0.752723 | −0.376362 | − | 0.926473i | \(-0.622825\pi\) | ||||
−0.376362 | + | 0.926473i | \(0.622825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.00000 | −0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.6525 | 0.659383 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.9574 | −1.52960 | −0.764802 | − | 0.644265i | \(-0.777163\pi\) | ||||
−0.764802 | + | 0.644265i | \(0.777163\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.69505 | −0.213322 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.4721 | 0.587975 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −73.8885 | −2.34952 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.8885 | −0.822377 | −0.411188 | − | 0.911550i | \(-0.634886\pi\) | ||||
−0.411188 | + | 0.911550i | \(0.634886\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.9443 | −0.537710 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.22291 | 0.133875 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.7082 | 1.25757 | 0.628786 | − | 0.777579i | \(-0.283552\pi\) | ||||
0.628786 | + | 0.777579i | \(0.283552\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.00000 | −0.189832 |
(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 | 2112.2.a.bf.1.2 | 2 | ||
3.2 | odd | 2 | 6336.2.a.cs.1.1 | 2 | |||
4.3 | odd | 2 | 2112.2.a.be.1.2 | 2 | |||
8.3 | odd | 2 | 1056.2.a.l.1.1 | yes | 2 | ||
8.5 | even | 2 | 1056.2.a.k.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 6336.2.a.ct.1.1 | 2 | |||
24.5 | odd | 2 | 3168.2.a.be.1.2 | 2 | |||
24.11 | even | 2 | 3168.2.a.bf.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1056.2.a.k.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
1056.2.a.l.1.1 | yes | 2 | 8.3 | odd | 2 | ||
2112.2.a.be.1.2 | 2 | 4.3 | odd | 2 | |||
2112.2.a.bf.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3168.2.a.be.1.2 | 2 | 24.5 | odd | 2 | |||
3168.2.a.bf.1.2 | 2 | 24.11 | even | 2 | |||
6336.2.a.cs.1.1 | 2 | 3.2 | odd | 2 | |||
6336.2.a.ct.1.1 | 2 | 12.11 | even | 2 |