Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5700,2,Mod(1,5700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5700, 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("5700.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5700.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: | \(45.5147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1524.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1140) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.27307\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5700.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.166860 | 0.0630672 | 0.0315336 | − | 0.999503i | \(-0.489961\pi\) | ||||
0.0315336 | + | 0.999503i | \(0.489961\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.71301 | 1.42102 | 0.710512 | − | 0.703685i | \(-0.248463\pi\) | ||||
0.710512 | + | 0.703685i | \(0.248463\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.83314 | −0.508421 | −0.254211 | − | 0.967149i | \(-0.581816\pi\) | ||||
−0.254211 | + | 0.967149i | \(0.581816\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.54615 | 1.10260 | 0.551301 | − | 0.834306i | \(-0.314132\pi\) | ||||
0.551301 | + | 0.834306i | \(0.314132\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.166860 | 0.0364119 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.54615 | 0.947937 | 0.473968 | − | 0.880542i | \(-0.342821\pi\) | ||||
0.473968 | + | 0.880542i | \(0.342821\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.71301 | 1.24657 | 0.623287 | − | 0.781993i | \(-0.285797\pi\) | ||||
0.623287 | + | 0.781993i | \(0.285797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.54615 | −0.457301 | −0.228651 | − | 0.973509i | \(-0.573431\pi\) | ||||
−0.228651 | + | 0.973509i | \(0.573431\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.71301 | 0.820429 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.16686 | −0.356230 | −0.178115 | − | 0.984010i | \(-0.557000\pi\) | ||||
−0.178115 | + | 0.984010i | \(0.557000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.83314 | −0.293537 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7130 | 1.67309 | 0.836545 | − | 0.547898i | \(-0.184572\pi\) | ||||
0.836545 | + | 0.547898i | \(0.184572\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.25915 | −1.41201 | −0.706004 | − | 0.708208i | \(-0.749504\pi\) | ||||
−0.706004 | + | 0.708208i | \(0.749504\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.546146 | −0.0796635 | −0.0398318 | − | 0.999206i | \(-0.512682\pi\) | ||||
−0.0398318 | + | 0.999206i | \(0.512682\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.97216 | −0.996023 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.54615 | 0.636588 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5461 | −1.44862 | −0.724312 | − | 0.689472i | \(-0.757843\pi\) | ||||
−0.724312 | + | 0.689472i | \(0.757843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.42601 | −1.22716 | −0.613581 | − | 0.789632i | \(-0.710272\pi\) | ||||
−0.613581 | + | 0.789632i | \(0.710272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.8799 | 1.64910 | 0.824549 | − | 0.565791i | \(-0.191429\pi\) | ||||
0.824549 | + | 0.565791i | \(0.191429\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.166860 | 0.0210224 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.54615 | 0.547292 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.42601 | −0.643949 | −0.321975 | − | 0.946748i | \(-0.604347\pi\) | ||||
−0.321975 | + | 0.946748i | \(0.604347\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.0923 | −1.76642 | −0.883210 | − | 0.468979i | \(-0.844622\pi\) | ||||
−0.883210 | + | 0.468979i | \(0.844622\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.786413 | 0.0896201 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7597 | 1.54809 | 0.774045 | − | 0.633130i | \(-0.218230\pi\) | ||||
0.774045 | + | 0.633130i | \(0.218230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.9722 | 1.53364 | 0.766822 | − | 0.641860i | \(-0.221837\pi\) | ||||
0.766822 | + | 0.641860i | \(0.221837\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.71301 | 0.719710 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.04557 | 0.640829 | 0.320414 | − | 0.947278i | \(-0.396178\pi\) | ||||
0.320414 | + | 0.947278i | \(0.396178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.305878 | −0.0320647 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.54615 | −0.264023 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.16686 | 0.220011 | 0.110006 | − | 0.993931i | \(-0.464913\pi\) | ||||
0.110006 | + | 0.993931i | \(0.464913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.71301 | 0.473675 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.5183 | −1.64363 | −0.821816 | − | 0.569753i | \(-0.807039\pi\) | ||||
−0.821816 | + | 0.569753i | \(0.807039\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.09229 | 0.501758 | 0.250879 | − | 0.968018i | \(-0.419280\pi\) | ||||
0.250879 | + | 0.968018i | \(0.419280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0000 | 1.54678 | 0.773389 | − | 0.633932i | \(-0.218560\pi\) | ||||
0.773389 | + | 0.633932i | \(0.218560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4260 | 1.47754 | 0.738772 | − | 0.673955i | \(-0.235406\pi\) | ||||
0.738772 | + | 0.673955i | \(0.235406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.16686 | −0.205669 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.8799 | −1.39978 | −0.699890 | − | 0.714251i | \(-0.746768\pi\) | ||||
−0.699890 | + | 0.714251i | \(0.746768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.83314 | −0.169474 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.758571 | 0.0695381 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.2124 | 1.01931 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.7130 | 0.965959 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.25915 | −0.815223 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1390 | 1.23533 | 0.617666 | − | 0.786441i | \(-0.288078\pi\) | ||||
0.617666 | + | 0.786441i | \(0.288078\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.166860 | 0.0144686 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.42601 | 0.799504 | 0.399752 | − | 0.916623i | \(-0.369096\pi\) | ||||
0.399752 | + | 0.916623i | \(0.369096\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.546146 | −0.0459938 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.63960 | −0.722480 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.97216 | −0.575054 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.0923 | −1.23641 | −0.618204 | − | 0.786017i | \(-0.712140\pi\) | ||||
−0.618204 | + | 0.786017i | \(0.712140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2136 | 0.912549 | 0.456274 | − | 0.889839i | \(-0.349184\pi\) | ||||
0.456274 | + | 0.889839i | \(0.349184\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.54615 | 0.367534 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.7586 | 1.17786 | 0.588931 | − | 0.808183i | \(-0.299549\pi\) | ||||
0.588931 | + | 0.808183i | \(0.299549\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.5461 | −0.836364 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.758571 | 0.0597838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.49942 | 0.274096 | 0.137048 | − | 0.990564i | \(-0.456239\pi\) | ||||
0.137048 | + | 0.990564i | \(0.456239\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.21243 | −0.480732 | −0.240366 | − | 0.970682i | \(-0.577267\pi\) | ||||
−0.240366 | + | 0.970682i | \(0.577267\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.63960 | −0.741508 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.12013 | 0.0851622 | 0.0425811 | − | 0.999093i | \(-0.486442\pi\) | ||||
0.0425811 | + | 0.999093i | \(0.486442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.42601 | −0.708502 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.6663 | −0.871979 | −0.435989 | − | 0.899952i | \(-0.643601\pi\) | ||||
−0.435989 | + | 0.899952i | \(0.643601\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.66628 | 0.718489 | 0.359244 | − | 0.933243i | \(-0.383034\pi\) | ||||
0.359244 | + | 0.933243i | \(0.383034\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8799 | 0.952107 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.4260 | 1.56683 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.166860 | 0.0121373 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.04673 | 0.0757385 | 0.0378692 | − | 0.999283i | \(-0.487943\pi\) | ||||
0.0378692 | + | 0.999283i | \(0.487943\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.9254 | 0.786430 | 0.393215 | − | 0.919447i | \(-0.371363\pi\) | ||||
0.393215 | + | 0.919447i | \(0.371363\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4539 | 0.816053 | 0.408027 | − | 0.912970i | \(-0.366217\pi\) | ||||
0.408027 | + | 0.912970i | \(0.366217\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.7586 | −1.75509 | −0.877544 | − | 0.479496i | \(-0.840820\pi\) | ||||
−0.877544 | + | 0.479496i | \(0.840820\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.12013 | 0.0786180 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.54615 | 0.315979 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.71301 | 0.326005 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4249 | 1.13073 | 0.565367 | − | 0.824840i | \(-0.308735\pi\) | ||||
0.565367 | + | 0.824840i | \(0.308735\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.42601 | −0.371784 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.424850 | −0.0288407 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.0923 | −1.01984 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.33372 | −0.560587 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.09229 | 0.341005 | 0.170503 | − | 0.985357i | \(-0.445461\pi\) | ||||
0.170503 | + | 0.985357i | \(0.445461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.6396 | 1.63539 | 0.817694 | − | 0.575653i | \(-0.195252\pi\) | ||||
0.817694 | + | 0.575653i | \(0.195252\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.78757 | −0.514617 | −0.257309 | − | 0.966329i | \(-0.582836\pi\) | ||||
−0.257309 | + | 0.966329i | \(0.582836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.786413 | 0.0517422 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.9443 | 1.69967 | 0.849834 | − | 0.527050i | \(-0.176702\pi\) | ||||
0.849834 | + | 0.527050i | \(0.176702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.7597 | 0.893791 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.3793 | −1.05949 | −0.529744 | − | 0.848158i | \(-0.677712\pi\) | ||||
−0.529744 | + | 0.848158i | \(0.677712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.83314 | −0.116640 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.9722 | 0.885450 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.4716 | −1.35527 | −0.677637 | − | 0.735397i | \(-0.736996\pi\) | ||||
−0.677637 | + | 0.735397i | \(0.736996\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.4260 | 1.34704 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.9722 | 0.996316 | 0.498158 | − | 0.867086i | \(-0.334010\pi\) | ||||
0.498158 | + | 0.867086i | \(0.334010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.361563 | −0.0224664 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.71301 | 0.415525 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.3047 | −1.06705 | −0.533527 | − | 0.845783i | \(-0.679134\pi\) | ||||
−0.533527 | + | 0.845783i | \(0.679134\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.04557 | 0.369983 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.04673 | −0.429646 | −0.214823 | − | 0.976653i | \(-0.568918\pi\) | ||||
−0.214823 | + | 0.976653i | \(0.568918\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6663 | 0.708676 | 0.354338 | − | 0.935117i | \(-0.384706\pi\) | ||||
0.354338 | + | 0.935117i | \(0.384706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.305878 | −0.0185126 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.9443 | −1.79918 | −0.899590 | − | 0.436736i | \(-0.856134\pi\) | ||||
−0.899590 | + | 0.436736i | \(0.856134\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.54615 | −0.152434 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1390 | 1.44001 | 0.720007 | − | 0.693967i | \(-0.244139\pi\) | ||||
0.720007 | + | 0.693967i | \(0.244139\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.92543 | −0.292786 | −0.146393 | − | 0.989226i | \(-0.546766\pi\) | ||||
−0.146393 | + | 0.989226i | \(0.546766\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.78757 | 0.105517 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.66744 | 0.215732 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.16686 | 0.127024 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.12013 | −0.532804 | −0.266402 | − | 0.963862i | \(-0.585835\pi\) | ||||
−0.266402 | + | 0.963862i | \(0.585835\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.71301 | 0.273476 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.33372 | −0.481951 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.54498 | −0.0890514 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.5183 | −0.948952 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.75857 | 0.499878 | 0.249939 | − | 0.968262i | \(-0.419589\pi\) | ||||
0.249939 | + | 0.968262i | \(0.419589\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.09229 | 0.289690 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.04673 | 0.0593544 | 0.0296772 | − | 0.999560i | \(-0.490552\pi\) | ||||
0.0296772 | + | 0.999560i | \(0.490552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.6663 | 1.22465 | 0.612325 | − | 0.790606i | \(-0.290234\pi\) | ||||
0.612325 | + | 0.790606i | \(0.290234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.5461 | 0.816993 | 0.408496 | − | 0.912760i | \(-0.366053\pi\) | ||||
0.408496 | + | 0.912760i | \(0.366053\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.6384 | 1.77141 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.0000 | 0.893033 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.54615 | 0.252954 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.4260 | 0.853060 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.0911300 | −0.00502416 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.21359 | 0.396495 | 0.198247 | − | 0.980152i | \(-0.436475\pi\) | ||||
0.198247 | + | 0.980152i | \(0.436475\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.16686 | −0.118743 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.59171 | 0.141179 | 0.0705897 | − | 0.997505i | \(-0.477512\pi\) | ||||
0.0705897 | + | 0.997505i | \(0.477512\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.8799 | −0.808163 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.33140 | −0.125884 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.54498 | 0.190305 | 0.0951524 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951524 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.8520 | −1.54441 | −0.772207 | − | 0.635371i | \(-0.780847\pi\) | ||||
−0.772207 | + | 0.635371i | \(0.780847\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.83314 | −0.0978458 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.8520 | −1.10984 | −0.554921 | − | 0.831903i | \(-0.687251\pi\) | ||||
−0.554921 | + | 0.831903i | \(0.687251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.758571 | 0.0401478 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4727 | −0.552730 | −0.276365 | − | 0.961053i | \(-0.589130\pi\) | ||||
−0.276365 | + | 0.961053i | \(0.589130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.2124 | 0.588500 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.40713 | −0.125651 | −0.0628255 | − | 0.998025i | \(-0.520011\pi\) | ||||
−0.0628255 | + | 0.998025i | \(0.520011\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.7130 | 0.557697 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.75973 | −0.0913608 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.2592 | 1.61854 | 0.809269 | − | 0.587439i | \(-0.199864\pi\) | ||||
0.809269 | + | 0.587439i | \(0.199864\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.3059 | −0.633785 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6384 | −0.597826 | −0.298913 | − | 0.954280i | \(-0.596624\pi\) | ||||
−0.298913 | + | 0.954280i | \(0.596624\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.0923 | −1.28216 | −0.641078 | − | 0.767476i | \(-0.721513\pi\) | ||||
−0.641078 | + | 0.767476i | \(0.721513\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.25915 | −0.470669 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.7597 | 0.596242 | 0.298121 | − | 0.954528i | \(-0.403640\pi\) | ||||
0.298121 | + | 0.954528i | \(0.403640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.6674 | 1.04520 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.1390 | 0.713219 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.5195 | −1.28079 | −0.640393 | − | 0.768048i | \(-0.721228\pi\) | ||||
−0.640393 | + | 0.768048i | \(0.721228\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.166860 | 0.00835346 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.194703 | 0.00972298 | 0.00486149 | − | 0.999988i | \(-0.498453\pi\) | ||||
0.00486149 | + | 0.999988i | \(0.498453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.66744 | 0.232502 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2124 | −0.506211 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.6106 | 1.46415 | 0.732075 | − | 0.681224i | \(-0.238552\pi\) | ||||
0.732075 | + | 0.681224i | \(0.238552\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.57283 | −0.0773937 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.42601 | 0.461594 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.95443 | −0.193187 | −0.0965934 | − | 0.995324i | \(-0.530795\pi\) | ||||
−0.0965934 | + | 0.995324i | \(0.530795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.546146 | −0.0265545 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.14914 | 0.104004 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.63960 | −0.417124 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.8509 | −1.43787 | −0.718933 | − | 0.695080i | \(-0.755369\pi\) | ||||
−0.718933 | + | 0.695080i | \(0.755369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.07457 | −0.243868 | −0.121934 | − | 0.992538i | \(-0.538910\pi\) | ||||
−0.121934 | + | 0.992538i | \(0.538910\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.54615 | 0.217472 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.8520 | −1.66340 | −0.831698 | − | 0.555228i | \(-0.812631\pi\) | ||||
−0.831698 | + | 0.555228i | \(0.812631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.97216 | −0.332008 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.8787 | −0.754420 | −0.377210 | − | 0.926128i | \(-0.623117\pi\) | ||||
−0.377210 | + | 0.926128i | \(0.623117\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.0923 | −0.713841 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.8053 | 0.557126 | 0.278563 | − | 0.960418i | \(-0.410142\pi\) | ||||
0.278563 | + | 0.960418i | \(0.410142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 50.4905 | 2.37750 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.2136 | 0.526860 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.4260 | 1.65716 | 0.828579 | − | 0.559871i | \(-0.189149\pi\) | ||||
0.828579 | + | 0.559871i | \(0.189149\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.54615 | 0.212196 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6674 | −0.496832 | −0.248416 | − | 0.968653i | \(-0.579910\pi\) | ||||
−0.248416 | + | 0.968653i | \(0.579910\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.9266 | −0.647224 | −0.323612 | − | 0.946190i | \(-0.604897\pi\) | ||||
−0.323612 | + | 0.946190i | \(0.604897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.30588 | −0.106703 | −0.0533517 | − | 0.998576i | \(-0.516990\pi\) | ||||
−0.0533517 | + | 0.998576i | \(0.516990\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.7586 | 0.680039 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −43.6384 | −2.00650 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.5461 | −0.482875 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.13902 | 0.0977342 | 0.0488671 | − | 0.998805i | \(-0.484439\pi\) | ||||
0.0488671 | + | 0.998805i | \(0.484439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.97216 | 0.181115 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.758571 | 0.0345162 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.09113 | 0.366644 | 0.183322 | − | 0.983053i | \(-0.441315\pi\) | ||||
0.183322 | + | 0.983053i | \(0.441315\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.49942 | 0.158249 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.37929 | 0.197634 | 0.0988172 | − | 0.995106i | \(-0.468494\pi\) | ||||
0.0988172 | + | 0.995106i | \(0.468494\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.5183 | 1.37448 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.905386 | −0.0406121 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0935 | −0.451845 | −0.225923 | − | 0.974145i | \(-0.572540\pi\) | ||||
−0.225923 | + | 0.974145i | \(0.572540\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.21243 | −0.277551 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.21243 | 0.366174 | 0.183087 | − | 0.983097i | \(-0.441391\pi\) | ||||
0.183087 | + | 0.983097i | \(0.441391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.63960 | −0.428110 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.8065 | 1.45412 | 0.727060 | − | 0.686574i | \(-0.240886\pi\) | ||||
0.727060 | + | 0.686574i | \(0.240886\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.51830 | −0.111403 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.57399 | −0.113204 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.12013 | 0.0491684 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.62071 | −0.421491 | −0.210746 | − | 0.977541i | \(-0.567589\pi\) | ||||
−0.210746 | + | 0.977541i | \(0.567589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.6106 | 1.38223 | 0.691117 | − | 0.722743i | \(-0.257119\pi\) | ||||
0.691117 | + | 0.722743i | \(0.257119\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.5751 | −0.504221 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.33256 | −0.101416 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.42601 | −0.409054 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.6384 | −0.850635 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.6663 | −0.503437 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −32.8598 | −1.41537 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.1846 | −1.38372 | −0.691862 | − | 0.722030i | \(-0.743209\pi\) | ||||
−0.691862 | + | 0.722030i | \(0.743209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.66628 | 0.414820 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.4260 | −1.42919 | −0.714597 | − | 0.699537i | \(-0.753390\pi\) | ||||
−0.714597 | + | 0.699537i | \(0.753390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.8799 | 0.549699 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.71301 | 0.285984 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.29595 | 0.0976338 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.2769 | −1.07102 | −0.535508 | − | 0.844530i | \(-0.679880\pi\) | ||||
−0.535508 | + | 0.844530i | \(0.679880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.9733 | 0.717895 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.4260 | 0.904607 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.6396 | 1.37560 | 0.687798 | − | 0.725903i | \(-0.258578\pi\) | ||||
0.687798 | + | 0.725903i | \(0.258578\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.166860 | 0.00700747 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.6207 | 1.07408 | 0.537038 | − | 0.843558i | \(-0.319543\pi\) | ||||
0.537038 | + | 0.843558i | \(0.319543\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.1857 | −1.13769 | −0.568844 | − | 0.822445i | \(-0.692609\pi\) | ||||
−0.568844 | + | 0.822445i | \(0.692609\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.04673 | 0.0437276 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.51830 | −0.188099 | −0.0940497 | − | 0.995568i | \(-0.529981\pi\) | ||||
−0.0940497 | + | 0.995568i | \(0.529981\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.9254 | 0.454045 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.33140 | 0.0967227 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.7040 | −2.05853 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.9733 | −1.11331 | −0.556654 | − | 0.830744i | \(-0.687915\pi\) | ||||
−0.556654 | + | 0.830744i | \(0.687915\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.54615 | −0.104912 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4539 | 0.471149 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.09229 | 0.291246 | 0.145623 | − | 0.989340i | \(-0.453481\pi\) | ||||
0.145623 | + | 0.989340i | \(0.453481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.7586 | −1.01330 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.85202 | −0.279966 | −0.139983 | − | 0.990154i | \(-0.544705\pi\) | ||||
−0.139983 | + | 0.990154i | \(0.544705\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.8509 | −1.29922 | −0.649612 | − | 0.760266i | \(-0.725069\pi\) | ||||
−0.649612 | + | 0.760266i | \(0.725069\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.3703 | −1.67917 | −0.839585 | − | 0.543229i | \(-0.817202\pi\) | ||||
−0.839585 | + | 0.543229i | \(0.817202\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.12013 | 0.0453901 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00116 | 0.0405027 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.66628 | −0.228859 | −0.114429 | − | 0.993431i | \(-0.536504\pi\) | ||||
−0.114429 | + | 0.993431i | \(0.536504\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.7307 | 1.23717 | 0.618586 | − | 0.785717i | \(-0.287706\pi\) | ||||
0.618586 | + | 0.785717i | \(0.287706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.99884 | 0.120533 | 0.0602667 | − | 0.998182i | \(-0.480805\pi\) | ||||
0.0602667 | + | 0.998182i | \(0.480805\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.54615 | 0.182431 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.00876 | 0.0404153 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.71301 | 0.188219 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.85086 | −0.392780 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.5171 | 1.01582 | 0.507911 | − | 0.861410i | \(-0.330418\pi\) | ||||
0.507911 | + | 0.861410i | \(0.330418\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.4249 | 0.652829 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.7809 | 0.506399 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.42601 | −0.214650 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.13902 | −0.163481 | −0.0817407 | − | 0.996654i | \(-0.526048\pi\) | ||||
−0.0817407 | + | 0.996654i | \(0.526048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.2603 | −1.03561 | −0.517803 | − | 0.855500i | \(-0.673250\pi\) | ||||
−0.517803 | + | 0.855500i | \(0.673250\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.3970 | 0.880517 | 0.440259 | − | 0.897871i | \(-0.354887\pi\) | ||||
0.440259 | + | 0.897871i | \(0.354887\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −44.4249 | −1.74383 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.424850 | −0.0166512 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.6384 | −0.533713 | −0.266857 | − | 0.963736i | \(-0.585985\pi\) | ||||
−0.266857 | + | 0.963736i | \(0.585985\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.0923 | −0.588806 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.0923 | −0.510003 | −0.255002 | − | 0.966941i | \(-0.582076\pi\) | ||||
−0.255002 | + | 0.966941i | \(0.582076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5183 | −0.798070 | −0.399035 | − | 0.916936i | \(-0.630655\pi\) | ||||
−0.399035 | + | 0.916936i | \(0.630655\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.33372 | −0.323655 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.5183 | 1.18167 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.09229 | 0.196879 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 60.7029 | 2.34341 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.16686 | 0.0835263 | 0.0417632 | − | 0.999128i | \(-0.486703\pi\) | ||||
0.0417632 | + | 0.999128i | \(0.486703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.3036 | 0.857195 | 0.428598 | − | 0.903495i | \(-0.359008\pi\) | ||||
0.428598 | + | 0.903495i | \(0.359008\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.361563 | 0.0138755 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.6396 | 0.944191 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.33256 | −0.280573 | −0.140286 | − | 0.990111i | \(-0.544802\pi\) | ||||
−0.140286 | + | 0.990111i | \(0.544802\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.78757 | −0.297115 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.3326 | 0.736512 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.333720 | 0.0126953 | 0.00634766 | − | 0.999980i | \(-0.497979\pi\) | ||||
0.00634766 | + | 0.999980i | \(0.497979\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.786413 | 0.0298734 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.7029 | 1.84475 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.9443 | 0.981304 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.7597 | 0.746315 | 0.373157 | − | 0.927768i | \(-0.378275\pi\) | ||||
0.373157 | + | 0.927768i | \(0.378275\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.16686 | −0.0817247 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.75625 | −0.103659 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.3970 | 1.14158 | 0.570792 | − | 0.821095i | \(-0.306636\pi\) | ||||
0.570792 | + | 0.821095i | \(0.306636\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.7597 | 0.516030 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.5751 | −0.433493 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.3793 | −0.611696 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.1390 | −1.27317 | −0.636585 | − | 0.771206i | \(-0.719654\pi\) | ||||
−0.636585 | + | 0.771206i | \(0.719654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.849701 | 0.0316445 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.00000 | −0.0743808 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.2592 | −1.53022 | −0.765109 | − | 0.643901i | \(-0.777315\pi\) | ||||
−0.765109 | + | 0.643901i | \(0.777315\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.0935 | −1.55688 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.09229 | −0.114216 | −0.0571082 | − | 0.998368i | \(-0.518188\pi\) | ||||
−0.0571082 | + | 0.998368i | \(0.518188\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.5195 | −0.570893 | −0.285446 | − | 0.958395i | \(-0.592142\pi\) | ||||
−0.285446 | + | 0.958395i | \(0.592142\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.83314 | −0.0673421 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.4272 | −0.969519 | −0.484759 | − | 0.874647i | \(-0.661093\pi\) | ||||
−0.484759 | + | 0.874647i | \(0.661093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.9722 | 0.511215 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.66976 | 0.0975510 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.3059 | 1.47078 | 0.735391 | − | 0.677643i | \(-0.236998\pi\) | ||||
0.735391 | + | 0.677643i | \(0.236998\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.4716 | −0.782468 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.573988 | −0.0208620 | −0.0104310 | − | 0.999946i | \(-0.503320\pi\) | ||||
−0.0104310 | + | 0.999946i | \(0.503320\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.4260 | 0.777715 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.7597 | −1.58629 | −0.793145 | − | 0.609033i | \(-0.791558\pi\) | ||||
−0.793145 | + | 0.609033i | \(0.791558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.57399 | 0.0931846 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.2792 | 0.623916 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.3326 | 0.480784 | 0.240392 | − | 0.970676i | \(-0.422724\pi\) | ||||
0.240392 | + | 0.970676i | \(0.422724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.9722 | 0.575223 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.2136 | 1.12267 | 0.561337 | − | 0.827587i | \(-0.310287\pi\) | ||||
0.561337 | + | 0.827587i | \(0.310287\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.361563 | −0.0129710 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.7130 | 0.383833 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.5728 | −0.915068 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.71301 | 0.239903 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.2780 | 1.72093 | 0.860463 | − | 0.509513i | \(-0.170174\pi\) | ||||
0.860463 | + | 0.509513i | \(0.170174\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.3047 | −0.616064 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.48286 | −0.0882803 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.6106 | −0.838437 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.0644 | −0.604454 | −0.302227 | − | 0.953236i | \(-0.597730\pi\) | ||||
−0.302227 | + | 0.953236i | \(0.597730\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.48286 | −0.0878372 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.04557 | 0.213610 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −71.1301 | −2.51013 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.04673 | −0.248057 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.75973 | −0.132185 | −0.0660926 | − | 0.997813i | \(-0.521053\pi\) | ||||
−0.0660926 | + | 0.997813i | \(0.521053\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.33488 | −0.187333 | −0.0936665 | − | 0.995604i | \(-0.529859\pi\) | ||||
−0.0936665 | + | 0.995604i | \(0.529859\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.6663 | 0.409154 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.25915 | −0.323937 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.305878 | −0.0106882 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.42601 | 0.259170 | 0.129585 | − | 0.991568i | \(-0.458636\pi\) | ||||
0.129585 | + | 0.991568i | \(0.458636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.6852 | 1.06962 | 0.534809 | − | 0.844973i | \(-0.320384\pi\) | ||||
0.534809 | + | 0.844973i | \(0.320384\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.8242 | −1.07186 | −0.535931 | − | 0.844262i | \(-0.680039\pi\) | ||||
−0.535931 | + | 0.844262i | \(0.680039\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5183 | 0.712630 | 0.356315 | − | 0.934366i | \(-0.384033\pi\) | ||||
0.356315 | + | 0.934366i | \(0.384033\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.9443 | −1.03876 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.6964 | −1.09822 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.54615 | −0.0880077 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.9432 | 1.06828 | 0.534138 | − | 0.845397i | \(-0.320636\pi\) | ||||
0.534138 | + | 0.845397i | \(0.320636\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.0644 | 0.553947 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.1390 | 0.831392 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.87091 | 0.0642852 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.92543 | −0.169040 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.85086 | −0.337683 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.4260 | 1.07601 | 0.538003 | − | 0.842943i | \(-0.319179\pi\) | ||||
0.538003 | + | 0.842943i | \(0.319179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.6941 | 0.399464 | 0.199732 | − | 0.979851i | \(-0.435993\pi\) | ||||
0.199732 | + | 0.979851i | \(0.435993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.1289 | −1.30094 | −0.650471 | − | 0.759531i | \(-0.725428\pi\) | ||||
−0.650471 | + | 0.759531i | \(0.725428\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.78757 | 0.0609204 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.0000 | −1.49778 | −0.748889 | − | 0.662696i | \(-0.769412\pi\) | ||||
−0.748889 | + | 0.662696i | \(0.769412\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.66744 | 0.124553 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.8497 | 2.19988 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.16686 | 0.0733371 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.8697 | −0.772256 | −0.386128 | − | 0.922445i | \(-0.626188\pi\) | ||||
−0.386128 | + | 0.922445i | \(0.626188\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.12013 | −0.307614 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −58.2780 | −1.96344 | −0.981718 | − | 0.190339i | \(-0.939041\pi\) | ||||
−0.981718 | + | 0.190339i | \(0.939041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.31484 | 0.0442478 | 0.0221239 | − | 0.999755i | \(-0.492957\pi\) | ||||
0.0221239 | + | 0.999755i | \(0.492957\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.1846 | −0.341965 | −0.170982 | − | 0.985274i | \(-0.554694\pi\) | ||||
−0.170982 | + | 0.985274i | \(0.554694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.667441 | −0.0223853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.71301 | 0.157892 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.546146 | −0.0182761 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.33372 | −0.278255 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.0923 | −0.570060 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.9443 | −1.59726 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.54498 | −0.0514139 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.0354 | 1.46217 | 0.731086 | − | 0.682285i | \(-0.239014\pi\) | ||||
0.731086 | + | 0.682285i | \(0.239014\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.5183 | −0.547878 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.4249 | −1.20681 | −0.603405 | − | 0.797435i | \(-0.706190\pi\) | ||||
−0.603405 | + | 0.797435i | \(0.706190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 65.8509 | 2.17935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.35924 | 0.0779090 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.75973 | −0.189996 | −0.0949980 | − | 0.995477i | \(-0.530284\pi\) | ||||
−0.0949980 | + | 0.995477i | \(0.530284\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.75857 | 0.288605 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.94664 | 0.327398 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.09229 | 0.167253 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.7586 | 1.66533 | 0.832667 | − | 0.553774i | \(-0.186813\pi\) | ||||
0.832667 | + | 0.553774i | \(0.186813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.97216 | −0.228503 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.04673 | 0.0342683 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.2780 | 1.25049 | 0.625244 | − | 0.780429i | \(-0.284999\pi\) | ||||
0.625244 | + | 0.780429i | \(0.284999\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.6663 | 0.707052 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.6573 | 0.999400 | 0.499700 | − | 0.866199i | \(-0.333444\pi\) | ||||
0.499700 | + | 0.866199i | \(0.333444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48.7029 | 1.58598 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.1201 | −0.361356 | −0.180678 | − | 0.983542i | \(-0.557829\pi\) | ||||
−0.180678 | + | 0.983542i | \(0.557829\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.6663 | 0.898085 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.5461 | 0.471691 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.6373 | 0.992439 | 0.496219 | − | 0.868197i | \(-0.334721\pi\) | ||||
0.496219 | + | 0.868197i | \(0.334721\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 31.6384 | 1.02273 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.00116 | 0.0323292 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.5171 | −0.790876 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.0000 | 0.515593 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.6863 | −0.375807 | −0.187903 | − | 0.982188i | \(-0.560169\pi\) | ||||
−0.187903 | + | 0.982188i | \(0.560169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.54615 | 0.146043 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.2769 | 0.490258 | 0.245129 | − | 0.969490i | \(-0.421170\pi\) | ||||
0.245129 | + | 0.969490i | \(0.421170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.57283 | 0.0504225 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.97332 | 0.159111 | 0.0795553 | − | 0.996830i | \(-0.474650\pi\) | ||||
0.0795553 | + | 0.996830i | \(0.474650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.4928 | 0.910633 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.4260 | 0.492515 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.9722 | −0.892173 | −0.446087 | − | 0.894990i | \(-0.647183\pi\) | ||||
−0.446087 | + | 0.894990i | \(0.647183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.0911300 | −0.00290070 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.0935 | −1.33849 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.8520 | −1.10711 | −0.553556 | − | 0.832812i | \(-0.686729\pi\) | ||||
−0.553556 | + | 0.832812i | \(0.686729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.21359 | 0.228916 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.6106 | −1.19114 | −0.595570 | − | 0.803304i | \(-0.703074\pi\) | ||||
−0.595570 | + | 0.803304i | \(0.703074\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.16686 | −0.0685564 |
(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 | 5700.2.a.z.1.2 | 3 | ||
5.2 | odd | 4 | 5700.2.f.p.3649.2 | 6 | |||
5.3 | odd | 4 | 5700.2.f.p.3649.5 | 6 | |||
5.4 | even | 2 | 1140.2.a.f.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 3420.2.a.k.1.2 | 3 | |||
20.19 | odd | 2 | 4560.2.a.bu.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.a.f.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
3420.2.a.k.1.2 | 3 | 15.14 | odd | 2 | |||
4560.2.a.bu.1.2 | 3 | 20.19 | odd | 2 | |||
5700.2.a.z.1.2 | 3 | 1.1 | even | 1 | trivial | ||
5700.2.f.p.3649.2 | 6 | 5.2 | odd | 4 | |||
5700.2.f.p.3649.5 | 6 | 5.3 | odd | 4 |