Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10000,2,Mod(1,10000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10000, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("10000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 10000.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: | \(79.8504020213\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 200) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10000.1 |
$q$-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 | ||||||||
\(3\) | −2.23607 | −1.29099 | −0.645497 | − | 0.763763i | \(-0.723350\pi\) | ||||
−0.645497 | + | 0.763763i | \(0.723350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.381966 | −0.144370 | −0.0721848 | − | 0.997391i | \(-0.522997\pi\) | ||||
−0.0721848 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | 0.975711 | 0.487856 | − | 0.872924i | \(-0.337779\pi\) | ||||
0.487856 | + | 0.872924i | \(0.337779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.61803 | 1.55816 | 0.779081 | − | 0.626923i | \(-0.215686\pi\) | ||||
0.779081 | + | 0.626923i | \(0.215686\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.763932 | 0.185281 | 0.0926404 | − | 0.995700i | \(-0.470469\pi\) | ||||
0.0926404 | + | 0.995700i | \(0.470469\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.38197 | −1.23471 | −0.617354 | − | 0.786686i | \(-0.711795\pi\) | ||||
−0.617354 | + | 0.786686i | \(0.711795\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.854102 | 0.186380 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.47214 | 0.723990 | 0.361995 | − | 0.932180i | \(-0.382096\pi\) | ||||
0.361995 | + | 0.932180i | \(0.382096\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.61803 | 1.22894 | 0.614469 | − | 0.788941i | \(-0.289370\pi\) | ||||
0.614469 | + | 0.788941i | \(0.289370\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.70820 | −1.56404 | −0.782020 | − | 0.623254i | \(-0.785810\pi\) | ||||
−0.782020 | + | 0.623254i | \(0.785810\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.23607 | −1.25964 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.76393 | −0.618787 | −0.309393 | − | 0.950934i | \(-0.600126\pi\) | ||||
−0.309393 | + | 0.950934i | \(0.600126\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.5623 | −2.01158 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.70820 | −1.20382 | −0.601910 | − | 0.798564i | \(-0.705593\pi\) | ||||
−0.601910 | + | 0.798564i | \(0.705593\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.61803 | −1.00924 | −0.504620 | − | 0.863341i | \(-0.668368\pi\) | ||||
−0.504620 | + | 0.863341i | \(0.668368\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.85410 | −0.999774 | −0.499887 | − | 0.866091i | \(-0.666625\pi\) | ||||
−0.499887 | + | 0.866091i | \(0.666625\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.85410 | −0.979157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.70820 | −0.239196 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.94427 | −1.36595 | −0.682975 | − | 0.730441i | \(-0.739314\pi\) | ||||
−0.682975 | + | 0.730441i | \(0.739314\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0344 | 1.59400 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.61803 | −0.601217 | −0.300608 | − | 0.953748i | \(-0.597190\pi\) | ||||
−0.300608 | + | 0.953748i | \(0.597190\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.18034 | 1.17542 | 0.587711 | − | 0.809071i | \(-0.300029\pi\) | ||||
0.587711 | + | 0.809071i | \(0.300029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.763932 | −0.0962464 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.291796 | −0.0356486 | −0.0178243 | − | 0.999841i | \(-0.505674\pi\) | ||||
−0.0178243 | + | 0.999841i | \(0.505674\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.76393 | −0.934668 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.38197 | 0.757400 | 0.378700 | − | 0.925519i | \(-0.376371\pi\) | ||||
0.378700 | + | 0.925519i | \(0.376371\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0000 | 1.28745 | 0.643726 | − | 0.765256i | \(-0.277388\pi\) | ||||
0.643726 | + | 0.765256i | \(0.277388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.23607 | −0.140863 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3262 | −1.16179 | −0.580896 | − | 0.813978i | \(-0.697298\pi\) | ||||
−0.580896 | + | 0.813978i | \(0.697298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.4721 | 1.47876 | 0.739380 | − | 0.673289i | \(-0.235119\pi\) | ||||
0.739380 | + | 0.673289i | \(0.235119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.7984 | −1.58655 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.00000 | 0.423999 | 0.212000 | − | 0.977270i | \(-0.432002\pi\) | ||||
0.212000 | + | 0.977270i | \(0.432002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.14590 | −0.224951 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.4721 | 2.01917 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.2705 | 1.85509 | 0.927545 | − | 0.373712i | \(-0.121915\pi\) | ||||
0.927545 | + | 0.373712i | \(0.121915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.47214 | 0.650474 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.0557281 | −0.00554515 | −0.00277258 | − | 0.999996i | \(-0.500883\pi\) | ||||
−0.00277258 | + | 0.999996i | \(0.500883\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.85410 | 0.970954 | 0.485477 | − | 0.874250i | \(-0.338646\pi\) | ||||
0.485477 | + | 0.874250i | \(0.338646\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.29180 | −0.318230 | −0.159115 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159115 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9443 | −1.43140 | −0.715701 | − | 0.698407i | \(-0.753893\pi\) | ||||
−0.715701 | + | 0.698407i | \(0.753893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.41641 | 0.798850 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.56231 | 0.899546 | 0.449773 | − | 0.893143i | \(-0.351505\pi\) | ||||
0.449773 | + | 0.893143i | \(0.351505\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.2361 | 1.03877 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.291796 | −0.0267489 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.2361 | 1.55412 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4721 | −1.46167 | −0.730833 | − | 0.682556i | \(-0.760868\pi\) | ||||
−0.730833 | + | 0.682556i | \(0.760868\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.7984 | 1.30292 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.0902 | −0.881582 | −0.440791 | − | 0.897610i | \(-0.645302\pi\) | ||||
−0.440791 | + | 0.897610i | \(0.645302\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.05573 | 0.178254 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000 | 0.427179 | 0.213589 | − | 0.976924i | \(-0.431485\pi\) | ||||
0.213589 | + | 0.976924i | \(0.431485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.2361 | −1.20749 | −0.603744 | − | 0.797178i | \(-0.706325\pi\) | ||||
−0.603744 | + | 0.797178i | \(0.706325\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.3262 | 1.29070 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.1803 | 1.52032 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.3262 | 1.26409 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.41641 | 0.689499 | 0.344749 | − | 0.938695i | \(-0.387964\pi\) | ||||
0.344749 | + | 0.938695i | \(0.387964\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.61803 | −0.213053 | −0.106526 | − | 0.994310i | \(-0.533973\pi\) | ||||
−0.106526 | + | 0.994310i | \(0.533973\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.52786 | 0.123520 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.236068 | −0.0188403 | −0.00942014 | − | 0.999956i | \(-0.502999\pi\) | ||||
−0.00942014 | + | 0.999956i | \(0.502999\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.2361 | 1.76343 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.32624 | −0.104522 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.18034 | 0.562408 | 0.281204 | − | 0.959648i | \(-0.409266\pi\) | ||||
0.281204 | + | 0.959648i | \(0.409266\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.0344 | −0.776488 | −0.388244 | − | 0.921557i | \(-0.626918\pi\) | ||||
−0.388244 | + | 0.921557i | \(0.626918\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.5623 | 1.42787 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.7639 | −0.823138 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4721 | 1.17632 | 0.588162 | − | 0.808743i | \(-0.299852\pi\) | ||||
0.588162 | + | 0.808743i | \(0.299852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3262 | 0.776168 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.7082 | −1.24883 | −0.624415 | − | 0.781093i | \(-0.714663\pi\) | ||||
−0.624415 | + | 0.781093i | \(0.714663\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.7082 | −1.61356 | −0.806779 | − | 0.590853i | \(-0.798791\pi\) | ||||
−0.806779 | + | 0.590853i | \(0.798791\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.5279 | −1.51746 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.47214 | 0.180780 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.854102 | −0.0621268 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7082 | 0.991891 | 0.495945 | − | 0.868354i | \(-0.334822\pi\) | ||||
0.495945 | + | 0.868354i | \(0.334822\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.70820 | 0.410886 | 0.205443 | − | 0.978669i | \(-0.434137\pi\) | ||||
0.205443 | + | 0.978669i | \(0.434137\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.2361 | −1.37051 | −0.685257 | − | 0.728302i | \(-0.740310\pi\) | ||||
−0.685257 | + | 0.728302i | \(0.740310\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.6180 | −0.823581 | −0.411790 | − | 0.911279i | \(-0.635096\pi\) | ||||
−0.411790 | + | 0.911279i | \(0.635096\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.652476 | 0.0460221 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.52786 | −0.177421 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.94427 | 0.482660 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.4164 | −1.20472 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.05573 | −0.141522 | −0.0707611 | − | 0.997493i | \(-0.522543\pi\) | ||||
−0.0707611 | + | 0.997493i | \(0.522543\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.2705 | −0.977799 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.32624 | 0.225800 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.5967 | −1.66209 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.29180 | 0.288697 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.70820 | 0.516180 | 0.258090 | − | 0.966121i | \(-0.416907\pi\) | ||||
0.258090 | + | 0.966121i | \(0.416907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.5967 | −1.56617 | −0.783086 | − | 0.621914i | \(-0.786355\pi\) | ||||
−0.783086 | + | 0.621914i | \(0.786355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.18034 | −0.144081 | −0.0720405 | − | 0.997402i | \(-0.522951\pi\) | ||||
−0.0720405 | + | 0.997402i | \(0.522951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.76393 | 0.181853 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.0902 | 1.49987 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.7639 | 1.14905 | 0.574527 | − | 0.818486i | \(-0.305186\pi\) | ||||
0.574527 | + | 0.818486i | \(0.305186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.52786 | 0.162834 | 0.0814170 | − | 0.996680i | \(-0.474055\pi\) | ||||
0.0814170 | + | 0.996680i | \(0.474055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.8885 | 1.14755 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.2361 | −1.92387 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.1246 | −1.90907 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.9443 | 1.63759 | 0.818794 | − | 0.574087i | \(-0.194643\pi\) | ||||
0.818794 | + | 0.574087i | \(0.194643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.2361 | 0.706406 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.38197 | −0.0862047 | −0.0431023 | − | 0.999071i | \(-0.513724\pi\) | ||||
−0.0431023 | + | 0.999071i | \(0.513724\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.43769 | 0.0893340 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.2361 | 0.819292 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.14590 | 0.440635 | 0.220317 | − | 0.975428i | \(-0.429291\pi\) | ||||
0.220317 | + | 0.975428i | \(0.429291\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.94427 | −0.547381 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.7082 | −1.68940 | −0.844700 | − | 0.535241i | \(-0.820221\pi\) | ||||
−0.844700 | + | 0.535241i | \(0.820221\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.94427 | 0.300343 | 0.150172 | − | 0.988660i | \(-0.452017\pi\) | ||||
0.150172 | + | 0.988660i | \(0.452017\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.79837 | 0.290411 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.18034 | −0.0709198 | −0.0354599 | − | 0.999371i | \(-0.511290\pi\) | ||||
−0.0354599 | + | 0.999371i | \(0.511290\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.4164 | −1.04269 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8541 | 0.945776 | 0.472888 | − | 0.881122i | \(-0.343211\pi\) | ||||
0.472888 | + | 0.881122i | \(0.343211\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.2705 | −1.56162 | −0.780810 | − | 0.624769i | \(-0.785193\pi\) | ||||
−0.780810 | + | 0.624769i | \(0.785193\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.94427 | 0.173795 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −40.8541 | −2.39491 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.47214 | −0.494947 | −0.247474 | − | 0.968895i | \(-0.579600\pi\) | ||||
−0.247474 | + | 0.968895i | \(0.579600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.23607 | 0.419879 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.5066 | 1.12809 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.52786 | 0.145704 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.124612 | 0.00715876 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2361 | −0.869568 | −0.434784 | − | 0.900535i | \(-0.643175\pi\) | ||||
−0.434784 | + | 0.900535i | \(0.643175\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.0344 | −1.25350 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0902 | 0.912390 | 0.456195 | − | 0.889880i | \(-0.349212\pi\) | ||||
0.456195 | + | 0.889880i | \(0.349212\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.70820 | −0.435693 | −0.217847 | − | 0.975983i | \(-0.569903\pi\) | ||||
−0.217847 | + | 0.975983i | \(0.569903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.76393 | −0.548397 | −0.274199 | − | 0.961673i | \(-0.588413\pi\) | ||||
−0.274199 | + | 0.961673i | \(0.588413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.4164 | 1.19909 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.36068 | 0.410833 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.11146 | −0.228768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 33.4164 | 1.84793 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.61803 | 0.144337 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0689 | 1.43288 | 0.716438 | − | 0.697651i | \(-0.245771\pi\) | ||||
0.716438 | + | 0.697651i | \(0.245771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.52786 | −0.412524 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.09017 | 0.113859 | 0.0569294 | − | 0.998378i | \(-0.481869\pi\) | ||||
0.0569294 | + | 0.998378i | \(0.481869\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.3820 | −1.16131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.1803 | −1.52605 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.29180 | 0.285730 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.145898 | −0.00783222 | −0.00391611 | − | 0.999992i | \(-0.501247\pi\) | ||||
−0.00391611 | + | 0.999992i | \(0.501247\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.1246 | −0.809602 | −0.404801 | − | 0.914405i | \(-0.632659\pi\) | ||||
−0.404801 | + | 0.914405i | \(0.632659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.5623 | 0.670526 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.43769 | −0.502318 | −0.251159 | − | 0.967946i | \(-0.580812\pi\) | ||||
−0.251159 | + | 0.967946i | \(0.580812\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.652476 | 0.0345327 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.27051 | 0.436501 | 0.218250 | − | 0.975893i | \(-0.429965\pi\) | ||||
0.218250 | + | 0.975893i | \(0.429965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.96556 | 0.524503 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.18034 | 0.0619518 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2705 | 0.744915 | 0.372457 | − | 0.928049i | \(-0.378515\pi\) | ||||
0.372457 | + | 0.928049i | \(0.378515\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.4164 | −0.802546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.79837 | 0.197202 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.90983 | 0.254221 | 0.127111 | − | 0.991889i | \(-0.459430\pi\) | ||||
0.127111 | + | 0.991889i | \(0.459430\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.1803 | 1.91488 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.00000 | 0.256833 | 0.128416 | − | 0.991720i | \(-0.459011\pi\) | ||||
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.8328 | 1.88700 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.2361 | −0.931820 | −0.465910 | − | 0.884832i | \(-0.654273\pi\) | ||||
−0.465910 | + | 0.884832i | \(0.654273\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.2361 | −0.672827 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.4164 | 0.730941 | 0.365470 | − | 0.930823i | \(-0.380908\pi\) | ||||
0.365470 | + | 0.930823i | \(0.380908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.65248 | 0.134141 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.5623 | 1.13812 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.90983 | 0.447172 | 0.223586 | − | 0.974684i | \(-0.428224\pi\) | ||||
0.223586 | + | 0.974684i | \(0.428224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.59675 | −0.230125 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.5967 | 0.629052 | 0.314526 | − | 0.949249i | \(-0.398155\pi\) | ||||
0.314526 | + | 0.949249i | \(0.398155\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48.9230 | −2.43703 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.1803 | −0.603757 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.4721 | −1.45730 | −0.728652 | − | 0.684884i | \(-0.759853\pi\) | ||||
−0.728652 | + | 0.684884i | \(0.759853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.1803 | −0.551485 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.76393 | 0.0867974 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.8328 | 1.55886 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.1246 | 0.690032 | 0.345016 | − | 0.938597i | \(-0.387873\pi\) | ||||
0.345016 | + | 0.938597i | \(0.387873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.9443 | −0.630865 | −0.315433 | − | 0.948948i | \(-0.602150\pi\) | ||||
−0.315433 | + | 0.948948i | \(0.602150\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.7082 | −0.666516 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.50658 | −0.169695 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −40.6525 | −1.96272 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.7082 | −0.804806 | −0.402403 | − | 0.915463i | \(-0.631825\pi\) | ||||
−0.402403 | + | 0.915463i | \(0.631825\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.2705 | −1.50276 | −0.751382 | − | 0.659867i | \(-0.770613\pi\) | ||||
−0.751382 | + | 0.659867i | \(0.770613\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.6869 | −0.893917 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.79837 | 0.372196 | 0.186098 | − | 0.982531i | \(-0.440416\pi\) | ||||
0.186098 | + | 0.982531i | \(0.440416\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.7082 | −0.652772 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.6525 | 1.88395 | 0.941973 | − | 0.335689i | \(-0.108969\pi\) | ||||
0.941973 | + | 0.335689i | \(0.108969\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.8197 | −0.890139 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.0902 | −1.65601 | −0.828004 | − | 0.560723i | \(-0.810523\pi\) | ||||
−0.828004 | + | 0.560723i | \(0.810523\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.9443 | −1.17458 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.85410 | 0.275050 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.47214 | 0.209198 | 0.104599 | − | 0.994514i | \(-0.466644\pi\) | ||||
0.104599 | + | 0.994514i | \(0.466644\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.70820 | 0.0797321 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.7082 | −1.61652 | −0.808261 | − | 0.588824i | \(-0.799591\pi\) | ||||
−0.808261 | + | 0.588824i | \(0.799591\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.94427 | −0.0903580 | −0.0451790 | − | 0.998979i | \(-0.514386\pi\) | ||||
−0.0451790 | + | 0.998979i | \(0.514386\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.2705 | −1.21565 | −0.607827 | − | 0.794069i | \(-0.707959\pi\) | ||||
−0.607827 | + | 0.794069i | \(0.707959\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.111456 | 0.00514657 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.527864 | 0.0243227 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.4164 | −0.984727 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.8885 | −0.910634 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.6180 | −1.12483 | −0.562413 | − | 0.826856i | \(-0.690127\pi\) | ||||
−0.562413 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.1459 | −0.964170 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.96556 | 0.134938 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.2918 | 0.602309 | 0.301154 | − | 0.953575i | \(-0.402628\pi\) | ||||
0.301154 | + | 0.953575i | \(0.402628\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0557 | −0.726065 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.23607 | −0.371689 | −0.185844 | − | 0.982579i | \(-0.559502\pi\) | ||||
−0.185844 | + | 0.982579i | \(0.559502\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.05573 | 0.227699 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.43769 | −0.109346 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.43769 | −0.422489 | −0.211245 | − | 0.977433i | \(-0.567752\pi\) | ||||
−0.211245 | + | 0.977433i | \(0.567752\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.4377 | 1.00244 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.8885 | −0.886786 | −0.443393 | − | 0.896327i | \(-0.646225\pi\) | ||||
−0.443393 | + | 0.896327i | \(0.646225\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −41.5066 | −1.84337 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.9098 | 0.882488 | 0.441244 | − | 0.897387i | \(-0.354537\pi\) | ||||
0.441244 | + | 0.897387i | \(0.354537\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.20163 | −0.185869 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.0344 | −0.531334 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.1803 | −0.975490 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34.5967 | −1.51863 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.4164 | −0.806837 | −0.403419 | − | 0.915015i | \(-0.632178\pi\) | ||||
−0.403419 | + | 0.915015i | \(0.632178\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.6180 | 0.901564 | 0.450782 | − | 0.892634i | \(-0.351145\pi\) | ||||
0.450782 | + | 0.892634i | \(0.351145\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.65248 | −0.289786 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9443 | −0.475838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.23607 | −0.400811 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.3050 | −1.87575 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 37.3607 | 1.61223 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.1803 | −0.955375 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.6525 | −0.973906 | −0.486953 | − | 0.873428i | \(-0.661892\pi\) | ||||
−0.486953 | + | 0.873428i | \(0.661892\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 48.5410 | 2.08309 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.3607 | 1.51191 | 0.755957 | − | 0.654622i | \(-0.227172\pi\) | ||||
0.755957 | + | 0.654622i | \(0.227172\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.3607 | 0.783615 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.6180 | −1.51738 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.94427 | 0.167728 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.1803 | −1.27878 | −0.639391 | − | 0.768882i | \(-0.720813\pi\) | ||||
−0.639391 | + | 0.768882i | \(0.720813\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.1803 | −1.57256 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.52786 | −0.233387 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.0344 | −1.30795 | −0.653973 | − | 0.756518i | \(-0.726899\pi\) | ||||
−0.653973 | + | 0.756518i | \(0.726899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.20163 | 0.176452 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.52786 | 0.357507 | 0.178753 | − | 0.983894i | \(-0.442794\pi\) | ||||
0.178753 | + | 0.983894i | \(0.442794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.3050 | −1.26822 | −0.634111 | − | 0.773242i | \(-0.718634\pi\) | ||||
−0.634111 | + | 0.773242i | \(0.718634\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.6525 | −1.28053 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.8885 | −0.827971 | −0.413985 | − | 0.910283i | \(-0.635864\pi\) | ||||
−0.413985 | + | 0.910283i | \(0.635864\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.7639 | −0.530451 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.14590 | −0.213488 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.1803 | −1.33277 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.5279 | 0.929824 | 0.464912 | − | 0.885357i | \(-0.346086\pi\) | ||||
0.464912 | + | 0.885357i | \(0.346086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 46.8673 | 1.93113 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 43.0132 | 1.76932 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.562306 | −0.0230911 | −0.0115456 | − | 0.999933i | \(-0.503675\pi\) | ||||
−0.0115456 | + | 0.999933i | \(0.503675\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.9787 | 1.06324 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.18034 | −0.293381 | −0.146690 | − | 0.989182i | \(-0.546862\pi\) | ||||
−0.146690 | + | 0.989182i | \(0.546862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.5623 | −1.73615 | −0.868076 | − | 0.496431i | \(-0.834644\pi\) | ||||
−0.868076 | + | 0.496431i | \(0.834644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.583592 | −0.0237657 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.2705 | 1.30982 | 0.654910 | − | 0.755707i | \(-0.272707\pi\) | ||||
0.654910 | + | 0.755707i | \(0.272707\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.65248 | 0.229050 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.5066 | −1.55781 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.0344 | 0.768794 | 0.384397 | − | 0.923168i | \(-0.374409\pi\) | ||||
0.384397 | + | 0.923168i | \(0.374409\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.5967 | −0.748677 | −0.374338 | − | 0.927292i | \(-0.622130\pi\) | ||||
−0.374338 | + | 0.927292i | \(0.622130\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.2918 | 1.09695 | 0.548475 | − | 0.836167i | \(-0.315209\pi\) | ||||
0.548475 | + | 0.836167i | \(0.315209\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.76393 | 0.311556 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.52786 | −0.0612126 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 38.9443 | 1.55528 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.87539 | −0.114649 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.8328 | 1.82458 | 0.912288 | − | 0.409550i | \(-0.134314\pi\) | ||||
0.912288 | + | 0.409550i | \(0.134314\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.59675 | 0.182704 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.5066 | −1.52569 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.7639 | 0.504933 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.4508 | 1.51872 | 0.759359 | − | 0.650672i | \(-0.225513\pi\) | ||||
0.759359 | + | 0.650672i | \(0.225513\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.9443 | −1.45694 | −0.728470 | − | 0.685078i | \(-0.759768\pi\) | ||||
−0.728470 | + | 0.685078i | \(0.759768\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.65248 | −0.340164 | −0.170082 | − | 0.985430i | \(-0.554403\pi\) | ||||
−0.170082 | + | 0.985430i | \(0.554403\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.9443 | −0.586614 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.43769 | −0.291506 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.50658 | −0.293755 | −0.146878 | − | 0.989155i | \(-0.546922\pi\) | ||||
−0.146878 | + | 0.989155i | \(0.546922\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.0000 | 0.858302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.8885 | −1.39802 | −0.699010 | − | 0.715112i | \(-0.746376\pi\) | ||||
−0.699010 | + | 0.715112i | \(0.746376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.4377 | −0.561561 | −0.280781 | − | 0.959772i | \(-0.590593\pi\) | ||||
−0.280781 | + | 0.959772i | \(0.590593\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.59675 | −0.372707 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.9787 | 0.889739 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.2361 | −0.666385 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.7082 | 1.14687 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.12461 | 0.274634 | 0.137317 | − | 0.990527i | \(-0.456152\pi\) | ||||
0.137317 | + | 0.990527i | \(0.456152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.14590 | −0.0440404 | −0.0220202 | − | 0.999758i | \(-0.507010\pi\) | ||||
−0.0220202 | + | 0.999758i | \(0.507010\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.97871 | −0.267818 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 52.7639 | 2.02192 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.29180 | 0.279013 | 0.139506 | − | 0.990221i | \(-0.455448\pi\) | ||||
0.139506 | + | 0.990221i | \(0.455448\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.87539 | 0.186008 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −55.8673 | −2.12837 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.1459 | 1.52722 | 0.763611 | − | 0.645677i | \(-0.223425\pi\) | ||||
0.763611 | + | 0.645677i | \(0.223425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.47214 | −0.0939087 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.88854 | −0.223045 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.4164 | −0.507455 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.1803 | −0.762201 | −0.381100 | − | 0.924534i | \(-0.624455\pi\) | ||||
−0.381100 | + | 0.924534i | \(0.624455\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.2574 | 0.764021 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0212862 | 0.000800551 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5967 | 0.473081 | 0.236540 | − | 0.971622i | \(-0.423986\pi\) | ||||
0.236540 | + | 0.971622i | \(0.423986\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.6525 | −0.774528 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.2361 | −1.13235 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.7214 | −1.48342 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.3050 | −0.906422 | −0.453211 | − | 0.891403i | \(-0.649722\pi\) | ||||
−0.453211 | + | 0.891403i | \(0.649722\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.76393 | −0.140176 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.65248 | −0.210218 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.32624 | 0.160451 | 0.0802256 | − | 0.996777i | \(-0.474436\pi\) | ||||
0.0802256 | + | 0.996777i | \(0.474436\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.05573 | −0.186993 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.14590 | 0.153132 | 0.0765661 | − | 0.997065i | \(-0.475604\pi\) | ||||
0.0765661 | + | 0.997065i | \(0.475604\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.944272 | −0.0347827 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.32624 | 0.159143 | 0.0795716 | − | 0.996829i | \(-0.474645\pi\) | ||||
0.0795716 | + | 0.996829i | \(0.474645\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 67.6099 | 2.48371 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.2492 | −1.25648 | −0.628241 | − | 0.778019i | \(-0.716225\pi\) | ||||
−0.628241 | + | 0.778019i | \(0.716225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.9443 | 0.985839 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.25735 | 0.0459427 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.2361 | 1.32227 | 0.661136 | − | 0.750266i | \(-0.270074\pi\) | ||||
0.661136 | + | 0.750266i | \(0.270074\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −58.0132 | −2.11412 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0000 | 0.545184 | 0.272592 | − | 0.962130i | \(-0.412119\pi\) | ||||
0.272592 | + | 0.962130i | \(0.412119\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.1246 | −0.911966 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.8541 | −1.15471 | −0.577355 | − | 0.816493i | \(-0.695915\pi\) | ||||
−0.577355 | + | 0.816493i | \(0.695915\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.70820 | 0.206651 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.9443 | −0.936793 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.4721 | 1.74795 | 0.873975 | − | 0.485971i | \(-0.161534\pi\) | ||||
0.873975 | + | 0.485971i | \(0.161534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.09017 | 0.111290 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.3262 | 1.52237 | 0.761184 | − | 0.648535i | \(-0.224618\pi\) | ||||
0.761184 | + | 0.648535i | \(0.224618\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.21478 | −0.115330 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41.4853 | 1.48636 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.6525 | 0.739004 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.7984 | 0.528851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.7082 | −1.55803 | −0.779015 | − | 0.627006i | \(-0.784280\pi\) | ||||
−0.779015 | + | 0.627006i | \(0.784280\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.9787 | −0.568857 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.65248 | −0.129867 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51.5755 | 1.83150 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.7082 | −0.662679 | −0.331339 | − | 0.943512i | \(-0.607500\pi\) | ||||
−0.331339 | + | 0.943512i | \(0.607500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.23607 | −0.185239 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.00000 | 0.282666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.5967 | 1.25618 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 61.9574 | 2.18100 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.7984 | 1.11797 | 0.558986 | − | 0.829177i | \(-0.311191\pi\) | ||||
0.558986 | + | 0.829177i | \(0.311191\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.639320 | 0.0224496 | 0.0112248 | − | 0.999937i | \(-0.496427\pi\) | ||||
0.0112248 | + | 0.999937i | \(0.496427\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.0557 | −0.387741 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.6180 | 1.24612 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.29180 | −0.149967 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.14590 | −0.249394 | −0.124697 | − | 0.992195i | \(-0.539796\pi\) | ||||
−0.124697 | + | 0.992195i | \(0.539796\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.5967 | −1.24082 | −0.620412 | − | 0.784276i | \(-0.713035\pi\) | ||||
−0.620412 | + | 0.784276i | \(0.713035\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.1459 | −0.909182 | −0.454591 | − | 0.890700i | \(-0.650215\pi\) | ||||
−0.454591 | + | 0.890700i | \(0.650215\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.5623 | −0.853084 | −0.426542 | − | 0.904468i | \(-0.640268\pi\) | ||||
−0.426542 | + | 0.904468i | \(0.640268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.63932 | 0.0915570 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.23607 | −0.181419 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.4721 | −0.673055 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.7984 | −0.510897 | −0.255448 | − | 0.966823i | \(-0.582223\pi\) | ||||
−0.255448 | + | 0.966823i | \(0.582223\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.7984 | 0.510289 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.4508 | −1.22099 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.201626 | 0.00692796 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 58.7426 | 2.01604 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.0689 | −0.447996 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.4164 | −0.733284 | −0.366642 | − | 0.930362i | \(-0.619493\pi\) | ||||
−0.366642 | + | 0.930362i | \(0.619493\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.85410 | −0.336610 | −0.168305 | − | 0.985735i | \(-0.553829\pi\) | ||||
−0.168305 | + | 0.985735i | \(0.553829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5967 | 0.634513 | 0.317256 | − | 0.948340i | \(-0.397238\pi\) | ||||
0.317256 | + | 0.948340i | \(0.397238\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.58359 | −0.224368 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.5066 | −0.834214 | −0.417107 | − | 0.908857i | \(-0.636956\pi\) | ||||
−0.417107 | + | 0.908857i | \(0.636956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 36.7082 | 1.24668 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.4164 | −1.13357 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.63932 | −0.0555462 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.5410 | 1.23673 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.34752 | 0.113038 | 0.0565189 | − | 0.998402i | \(-0.482000\pi\) | ||||
0.0565189 | + | 0.998402i | \(0.482000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.9443 | 0.638974 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.5836 | −0.558715 | −0.279358 | − | 0.960187i | \(-0.590122\pi\) | ||||
−0.279358 | + | 0.960187i | \(0.590122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5279 | −0.724470 | −0.362235 | − | 0.932087i | \(-0.617986\pi\) | ||||
−0.362235 | + | 0.932087i | \(0.617986\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.8885 | 1.27217 | 0.636086 | − | 0.771618i | \(-0.280552\pi\) | ||||
0.636086 | + | 0.771618i | \(0.280552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.29180 | 0.211020 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.5967 | −1.19254 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.8885 | 1.23443 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −43.6180 | −1.45636 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57.6312 | −1.92211 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.59675 | −0.253084 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.65248 | −0.188103 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.8197 | −0.359261 | −0.179630 | − | 0.983734i | \(-0.557490\pi\) | ||||
−0.179630 | + | 0.983734i | \(0.557490\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.111456 | −0.00369677 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.3607 | 0.575185 | 0.287592 | − | 0.957753i | \(-0.407145\pi\) | ||||
0.287592 | + | 0.957753i | \(0.407145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.5967 | 1.44284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.85410 | 0.127274 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.5623 | −0.513353 | −0.256677 | − | 0.966497i | \(-0.582628\pi\) | ||||
−0.256677 | + | 0.966497i | \(0.582628\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.0689 | 1.12261 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.8541 | 1.18015 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.7082 | 0.647302 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 58.5623 | 1.92137 | 0.960683 | − | 0.277646i | \(-0.0895542\pi\) | ||||
0.960683 | + | 0.277646i | \(0.0895542\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.8885 | 1.20897 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −35.9787 | −1.17789 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.437694 | 0.0142988 | 0.00714942 | − | 0.999974i | \(-0.497724\pi\) | ||||
0.00714942 | + | 0.999974i | \(0.497724\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.2361 | 0.562478 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0557 | −0.979789 | −0.489894 | − | 0.871782i | \(-0.662965\pi\) | ||||
−0.489894 | + | 0.871782i | \(0.662965\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.7639 | −0.871554 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.0132 | −0.682836 | −0.341418 | − | 0.939912i | \(-0.610907\pi\) | ||||
−0.341418 | + | 0.939912i | \(0.610907\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61.7984 | 2.00606 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.8328 | 0.707978 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.21478 | 0.298496 | 0.149248 | − | 0.988800i | \(-0.452315\pi\) | ||||
0.149248 | + | 0.988800i | \(0.452315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.8885 | −1.54802 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.90983 | −0.0616716 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.8328 | 1.44622 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.58359 | −0.212153 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.47214 | 0.272446 | 0.136223 | − | 0.990678i | \(-0.456504\pi\) | ||||
0.136223 | + | 0.990678i | \(0.456504\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.19350 | 0.295338 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.5623 | −1.52635 | −0.763174 | − | 0.646194i | \(-0.776360\pi\) | ||||
−0.763174 | + | 0.646194i | \(0.776360\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.43769 | 0.174324 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.29180 | −0.169300 | −0.0846498 | − | 0.996411i | \(-0.526977\pi\) | ||||
−0.0846498 | + | 0.996411i | \(0.526977\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.9443 | 0.413701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.8885 | −0.954268 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.7984 | 0.663365 | 0.331683 | − | 0.943391i | \(-0.392384\pi\) | ||||
0.331683 | + | 0.943391i | \(0.392384\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.85410 | −0.186338 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.9787 | −0.730681 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.8197 | 0.915487 | 0.457743 | − | 0.889084i | \(-0.348658\pi\) | ||||
0.457743 | + | 0.889084i | \(0.348658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −58.2918 | −1.84983 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.4721 | −1.50346 | −0.751729 | − | 0.659472i | \(-0.770780\pi\) | ||||
−0.751729 | + | 0.659472i | \(0.770780\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.41641 | −0.266283 |
(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 | 10000.2.a.g.1.1 | 2 | ||
4.3 | odd | 2 | 5000.2.a.c.1.2 | 2 | |||
5.4 | even | 2 | 10000.2.a.i.1.2 | 2 | |||
20.19 | odd | 2 | 5000.2.a.a.1.1 | 2 | |||
25.6 | even | 5 | 400.2.u.a.161.1 | 4 | |||
25.21 | even | 5 | 400.2.u.a.241.1 | 4 | |||
100.3 | even | 20 | 1000.2.q.a.49.1 | 8 | |||
100.19 | odd | 10 | 1000.2.m.a.801.1 | 4 | |||
100.31 | odd | 10 | 200.2.m.a.161.1 | yes | 4 | ||
100.47 | even | 20 | 1000.2.q.a.49.2 | 8 | |||
100.67 | even | 20 | 1000.2.q.a.449.1 | 8 | |||
100.71 | odd | 10 | 200.2.m.a.41.1 | ✓ | 4 | ||
100.79 | odd | 10 | 1000.2.m.a.201.1 | 4 | |||
100.83 | even | 20 | 1000.2.q.a.449.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.m.a.41.1 | ✓ | 4 | 100.71 | odd | 10 | ||
200.2.m.a.161.1 | yes | 4 | 100.31 | odd | 10 | ||
400.2.u.a.161.1 | 4 | 25.6 | even | 5 | |||
400.2.u.a.241.1 | 4 | 25.21 | even | 5 | |||
1000.2.m.a.201.1 | 4 | 100.79 | odd | 10 | |||
1000.2.m.a.801.1 | 4 | 100.19 | odd | 10 | |||
1000.2.q.a.49.1 | 8 | 100.3 | even | 20 | |||
1000.2.q.a.49.2 | 8 | 100.47 | even | 20 | |||
1000.2.q.a.449.1 | 8 | 100.67 | even | 20 | |||
1000.2.q.a.449.2 | 8 | 100.83 | even | 20 | |||
5000.2.a.a.1.1 | 2 | 20.19 | odd | 2 | |||
5000.2.a.c.1.2 | 2 | 4.3 | odd | 2 | |||
10000.2.a.g.1.1 | 2 | 1.1 | even | 1 | trivial | ||
10000.2.a.i.1.2 | 2 | 5.4 | even | 2 |