Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1250,2,Mod(1,1250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1250, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1250.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1250 = 2 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1250.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: | \(9.98130025266\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 50) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1250.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.61803 | −1.51152 | −0.755761 | − | 0.654847i | \(-0.772733\pi\) | ||||
−0.755761 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.61803 | 1.06881 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.236068 | −0.0711772 | −0.0355886 | − | 0.999367i | \(-0.511331\pi\) | ||||
−0.0355886 | + | 0.999367i | \(0.511331\pi\) | |||||||
\(12\) | −2.61803 | −0.755761 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 3.00000 | 0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.85410 | 1.90490 | 0.952450 | − | 0.304696i | \(-0.0985548\pi\) | ||||
0.952450 | + | 0.304696i | \(0.0985548\pi\) | |||||||
\(18\) | −3.85410 | −0.908421 | ||||||||
\(19\) | −0.854102 | −0.195944 | −0.0979722 | − | 0.995189i | \(-0.531236\pi\) | ||||
−0.0979722 | + | 0.995189i | \(0.531236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.85410 | 1.71391 | ||||||||
\(22\) | 0.236068 | 0.0503299 | ||||||||
\(23\) | −6.23607 | −1.30031 | −0.650155 | − | 0.759802i | \(-0.725296\pi\) | ||||
−0.650155 | + | 0.759802i | \(0.725296\pi\) | |||||||
\(24\) | 2.61803 | 0.534404 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −3.00000 | −0.566947 | ||||||||
\(29\) | −0.527864 | −0.0980219 | −0.0490109 | − | 0.998798i | \(-0.515607\pi\) | ||||
−0.0490109 | + | 0.998798i | \(0.515607\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.23607 | 0.760820 | 0.380410 | − | 0.924818i | \(-0.375783\pi\) | ||||
0.380410 | + | 0.924818i | \(0.375783\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.618034 | 0.107586 | ||||||||
\(34\) | −7.85410 | −1.34697 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.85410 | 0.642350 | ||||||||
\(37\) | 7.32624 | 1.20443 | 0.602213 | − | 0.798335i | \(-0.294286\pi\) | ||||
0.602213 | + | 0.798335i | \(0.294286\pi\) | |||||||
\(38\) | 0.854102 | 0.138554 | ||||||||
\(39\) | −2.61803 | −0.419221 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.47214 | −1.16695 | −0.583476 | − | 0.812131i | \(-0.698308\pi\) | ||||
−0.583476 | + | 0.812131i | \(0.698308\pi\) | |||||||
\(42\) | −7.85410 | −1.21191 | ||||||||
\(43\) | −1.76393 | −0.268997 | −0.134499 | − | 0.990914i | \(-0.542942\pi\) | ||||
−0.134499 | + | 0.990914i | \(0.542942\pi\) | |||||||
\(44\) | −0.236068 | −0.0355886 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.23607 | 0.919458 | ||||||||
\(47\) | 5.94427 | 0.867061 | 0.433531 | − | 0.901139i | \(-0.357268\pi\) | ||||
0.433531 | + | 0.901139i | \(0.357268\pi\) | |||||||
\(48\) | −2.61803 | −0.377881 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20.5623 | −2.87930 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 1.52786 | 0.209868 | 0.104934 | − | 0.994479i | \(-0.466537\pi\) | ||||
0.104934 | + | 0.994479i | \(0.466537\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 2.23607 | 0.296174 | ||||||||
\(58\) | 0.527864 | 0.0693119 | ||||||||
\(59\) | 4.47214 | 0.582223 | 0.291111 | − | 0.956689i | \(-0.405975\pi\) | ||||
0.291111 | + | 0.956689i | \(0.405975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.14590 | −0.274754 | −0.137377 | − | 0.990519i | \(-0.543867\pi\) | ||||
−0.137377 | + | 0.990519i | \(0.543867\pi\) | |||||||
\(62\) | −4.23607 | −0.537981 | ||||||||
\(63\) | −11.5623 | −1.45671 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.618034 | −0.0760747 | ||||||||
\(67\) | −5.76393 | −0.704176 | −0.352088 | − | 0.935967i | \(-0.614528\pi\) | ||||
−0.352088 | + | 0.935967i | \(0.614528\pi\) | |||||||
\(68\) | 7.85410 | 0.952450 | ||||||||
\(69\) | 16.3262 | 1.96545 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | −3.85410 | −0.454210 | ||||||||
\(73\) | −5.70820 | −0.668095 | −0.334047 | − | 0.942556i | \(-0.608415\pi\) | ||||
−0.334047 | + | 0.942556i | \(0.608415\pi\) | |||||||
\(74\) | −7.32624 | −0.851658 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.854102 | −0.0979722 | ||||||||
\(77\) | 0.708204 | 0.0807073 | ||||||||
\(78\) | 2.61803 | 0.296434 | ||||||||
\(79\) | −2.76393 | −0.310967 | −0.155483 | − | 0.987839i | \(-0.549693\pi\) | ||||
−0.155483 | + | 0.987839i | \(0.549693\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | 7.47214 | 0.825159 | ||||||||
\(83\) | −13.4721 | −1.47876 | −0.739380 | − | 0.673289i | \(-0.764881\pi\) | ||||
−0.739380 | + | 0.673289i | \(0.764881\pi\) | |||||||
\(84\) | 7.85410 | 0.856953 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.76393 | 0.190210 | ||||||||
\(87\) | 1.38197 | 0.148162 | ||||||||
\(88\) | 0.236068 | 0.0251649 | ||||||||
\(89\) | −4.47214 | −0.474045 | −0.237023 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237023 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | −0.314485 | ||||||||
\(92\) | −6.23607 | −0.650155 | ||||||||
\(93\) | −11.0902 | −1.15000 | ||||||||
\(94\) | −5.94427 | −0.613105 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.61803 | 0.267202 | ||||||||
\(97\) | −10.5623 | −1.07244 | −0.536220 | − | 0.844078i | \(-0.680148\pi\) | ||||
−0.536220 | + | 0.844078i | \(0.680148\pi\) | |||||||
\(98\) | −2.00000 | −0.202031 | ||||||||
\(99\) | −0.909830 | −0.0914414 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.61803 | −0.161000 | −0.0805002 | − | 0.996755i | \(-0.525652\pi\) | ||||
−0.0805002 | + | 0.996755i | \(0.525652\pi\) | |||||||
\(102\) | 20.5623 | 2.03597 | ||||||||
\(103\) | −19.8541 | −1.95628 | −0.978141 | − | 0.207941i | \(-0.933324\pi\) | ||||
−0.978141 | + | 0.207941i | \(0.933324\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.52786 | −0.148399 | ||||||||
\(107\) | 10.0902 | 0.975454 | 0.487727 | − | 0.872996i | \(-0.337826\pi\) | ||||
0.487727 | + | 0.872996i | \(0.337826\pi\) | |||||||
\(108\) | −2.23607 | −0.215166 | ||||||||
\(109\) | −15.0000 | −1.43674 | −0.718370 | − | 0.695662i | \(-0.755111\pi\) | ||||
−0.718370 | + | 0.695662i | \(0.755111\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.1803 | −1.82052 | ||||||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | 8.23607 | 0.774784 | 0.387392 | − | 0.921915i | \(-0.373376\pi\) | ||||
0.387392 | + | 0.921915i | \(0.373376\pi\) | |||||||
\(114\) | −2.23607 | −0.209427 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.527864 | −0.0490109 | ||||||||
\(117\) | 3.85410 | 0.356312 | ||||||||
\(118\) | −4.47214 | −0.411693 | ||||||||
\(119\) | −23.5623 | −2.15995 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9443 | −0.994934 | ||||||||
\(122\) | 2.14590 | 0.194280 | ||||||||
\(123\) | 19.5623 | 1.76387 | ||||||||
\(124\) | 4.23607 | 0.380410 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 11.5623 | 1.03005 | ||||||||
\(127\) | −12.4721 | −1.10672 | −0.553362 | − | 0.832941i | \(-0.686655\pi\) | ||||
−0.553362 | + | 0.832941i | \(0.686655\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.61803 | 0.406595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4164 | 0.910086 | 0.455043 | − | 0.890470i | \(-0.349624\pi\) | ||||
0.455043 | + | 0.890470i | \(0.349624\pi\) | |||||||
\(132\) | 0.618034 | 0.0537930 | ||||||||
\(133\) | 2.56231 | 0.222180 | ||||||||
\(134\) | 5.76393 | 0.497928 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.85410 | −0.673484 | ||||||||
\(137\) | −6.09017 | −0.520318 | −0.260159 | − | 0.965566i | \(-0.583775\pi\) | ||||
−0.260159 | + | 0.965566i | \(0.583775\pi\) | |||||||
\(138\) | −16.3262 | −1.38978 | ||||||||
\(139\) | 10.3262 | 0.875860 | 0.437930 | − | 0.899009i | \(-0.355712\pi\) | ||||
0.437930 | + | 0.899009i | \(0.355712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.5623 | −1.31058 | ||||||||
\(142\) | 3.00000 | 0.251754 | ||||||||
\(143\) | −0.236068 | −0.0197410 | ||||||||
\(144\) | 3.85410 | 0.321175 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.70820 | 0.472414 | ||||||||
\(147\) | −5.23607 | −0.431864 | ||||||||
\(148\) | 7.32624 | 0.602213 | ||||||||
\(149\) | −2.23607 | −0.183186 | −0.0915929 | − | 0.995797i | \(-0.529196\pi\) | ||||
−0.0915929 | + | 0.995797i | \(0.529196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.70820 | 0.301769 | 0.150885 | − | 0.988551i | \(-0.451788\pi\) | ||||
0.150885 | + | 0.988551i | \(0.451788\pi\) | |||||||
\(152\) | 0.854102 | 0.0692768 | ||||||||
\(153\) | 30.2705 | 2.44723 | ||||||||
\(154\) | −0.708204 | −0.0570687 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.61803 | −0.209610 | ||||||||
\(157\) | −15.5623 | −1.24201 | −0.621004 | − | 0.783808i | \(-0.713275\pi\) | ||||
−0.621004 | + | 0.783808i | \(0.713275\pi\) | |||||||
\(158\) | 2.76393 | 0.219887 | ||||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.7082 | 1.47441 | ||||||||
\(162\) | 5.70820 | 0.448479 | ||||||||
\(163\) | −4.85410 | −0.380203 | −0.190101 | − | 0.981764i | \(-0.560882\pi\) | ||||
−0.190101 | + | 0.981764i | \(0.560882\pi\) | |||||||
\(164\) | −7.47214 | −0.583476 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.4721 | 1.04564 | ||||||||
\(167\) | 15.6180 | 1.20856 | 0.604280 | − | 0.796772i | \(-0.293461\pi\) | ||||
0.604280 | + | 0.796772i | \(0.293461\pi\) | |||||||
\(168\) | −7.85410 | −0.605957 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.29180 | −0.251730 | ||||||||
\(172\) | −1.76393 | −0.134499 | ||||||||
\(173\) | 3.23607 | 0.246034 | 0.123017 | − | 0.992405i | \(-0.460743\pi\) | ||||
0.123017 | + | 0.992405i | \(0.460743\pi\) | |||||||
\(174\) | −1.38197 | −0.104767 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.236068 | −0.0177943 | ||||||||
\(177\) | −11.7082 | −0.880042 | ||||||||
\(178\) | 4.47214 | 0.335201 | ||||||||
\(179\) | −11.1803 | −0.835658 | −0.417829 | − | 0.908526i | \(-0.637209\pi\) | ||||
−0.417829 | + | 0.908526i | \(0.637209\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.4164 | −1.59187 | −0.795935 | − | 0.605383i | \(-0.793020\pi\) | ||||
−0.795935 | + | 0.605383i | \(0.793020\pi\) | |||||||
\(182\) | 3.00000 | 0.222375 | ||||||||
\(183\) | 5.61803 | 0.415297 | ||||||||
\(184\) | 6.23607 | 0.459729 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.0902 | 0.813171 | ||||||||
\(187\) | −1.85410 | −0.135585 | ||||||||
\(188\) | 5.94427 | 0.433531 | ||||||||
\(189\) | 6.70820 | 0.487950 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.6525 | 1.27729 | 0.638644 | − | 0.769502i | \(-0.279496\pi\) | ||||
0.638644 | + | 0.769502i | \(0.279496\pi\) | |||||||
\(192\) | −2.61803 | −0.188940 | ||||||||
\(193\) | 16.6525 | 1.19867 | 0.599336 | − | 0.800498i | \(-0.295431\pi\) | ||||
0.599336 | + | 0.800498i | \(0.295431\pi\) | |||||||
\(194\) | 10.5623 | 0.758329 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0.909830 | 0.0646588 | ||||||||
\(199\) | −17.5623 | −1.24496 | −0.622479 | − | 0.782636i | \(-0.713875\pi\) | ||||
−0.622479 | + | 0.782636i | \(0.713875\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.0902 | 1.06438 | ||||||||
\(202\) | 1.61803 | 0.113844 | ||||||||
\(203\) | 1.58359 | 0.111146 | ||||||||
\(204\) | −20.5623 | −1.43965 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 19.8541 | 1.38330 | ||||||||
\(207\) | −24.0344 | −1.67051 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 0.201626 | 0.0139468 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2705 | 0.775894 | 0.387947 | − | 0.921682i | \(-0.373184\pi\) | ||||
0.387947 | + | 0.921682i | \(0.373184\pi\) | |||||||
\(212\) | 1.52786 | 0.104934 | ||||||||
\(213\) | 7.85410 | 0.538154 | ||||||||
\(214\) | −10.0902 | −0.689750 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −12.7082 | −0.862689 | ||||||||
\(218\) | 15.0000 | 1.01593 | ||||||||
\(219\) | 14.9443 | 1.00984 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.85410 | 0.528324 | ||||||||
\(222\) | 19.1803 | 1.28730 | ||||||||
\(223\) | −9.00000 | −0.602685 | −0.301342 | − | 0.953516i | \(-0.597435\pi\) | ||||
−0.301342 | + | 0.953516i | \(0.597435\pi\) | |||||||
\(224\) | 3.00000 | 0.200446 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.23607 | −0.547855 | ||||||||
\(227\) | −15.3607 | −1.01952 | −0.509762 | − | 0.860315i | \(-0.670267\pi\) | ||||
−0.509762 | + | 0.860315i | \(0.670267\pi\) | |||||||
\(228\) | 2.23607 | 0.148087 | ||||||||
\(229\) | 17.5623 | 1.16055 | 0.580275 | − | 0.814421i | \(-0.302945\pi\) | ||||
0.580275 | + | 0.814421i | \(0.302945\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.85410 | −0.121991 | ||||||||
\(232\) | 0.527864 | 0.0346560 | ||||||||
\(233\) | 27.7082 | 1.81522 | 0.907612 | − | 0.419809i | \(-0.137903\pi\) | ||||
0.907612 | + | 0.419809i | \(0.137903\pi\) | |||||||
\(234\) | −3.85410 | −0.251951 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.47214 | 0.291111 | ||||||||
\(237\) | 7.23607 | 0.470033 | ||||||||
\(238\) | 23.5623 | 1.52732 | ||||||||
\(239\) | −18.0902 | −1.17016 | −0.585078 | − | 0.810977i | \(-0.698936\pi\) | ||||
−0.585078 | + | 0.810977i | \(0.698936\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3820 | 0.862008 | 0.431004 | − | 0.902350i | \(-0.358159\pi\) | ||||
0.431004 | + | 0.902350i | \(0.358159\pi\) | |||||||
\(242\) | 10.9443 | 0.703524 | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | −2.14590 | −0.137377 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −19.5623 | −1.24725 | ||||||||
\(247\) | −0.854102 | −0.0543452 | ||||||||
\(248\) | −4.23607 | −0.268991 | ||||||||
\(249\) | 35.2705 | 2.23518 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.1803 | 1.46313 | 0.731565 | − | 0.681772i | \(-0.238790\pi\) | ||||
0.731565 | + | 0.681772i | \(0.238790\pi\) | |||||||
\(252\) | −11.5623 | −0.728357 | ||||||||
\(253\) | 1.47214 | 0.0925524 | ||||||||
\(254\) | 12.4721 | 0.782571 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.7426 | −1.04438 | −0.522189 | − | 0.852830i | \(-0.674884\pi\) | ||||
−0.522189 | + | 0.852830i | \(0.674884\pi\) | |||||||
\(258\) | −4.61803 | −0.287506 | ||||||||
\(259\) | −21.9787 | −1.36569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.03444 | −0.125929 | ||||||||
\(262\) | −10.4164 | −0.643528 | ||||||||
\(263\) | 2.38197 | 0.146878 | 0.0734392 | − | 0.997300i | \(-0.476603\pi\) | ||||
0.0734392 | + | 0.997300i | \(0.476603\pi\) | |||||||
\(264\) | −0.618034 | −0.0380374 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.56231 | −0.157105 | ||||||||
\(267\) | 11.7082 | 0.716530 | ||||||||
\(268\) | −5.76393 | −0.352088 | ||||||||
\(269\) | 13.0902 | 0.798122 | 0.399061 | − | 0.916924i | \(-0.369336\pi\) | ||||
0.399061 | + | 0.916924i | \(0.369336\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.50658 | −0.577483 | −0.288742 | − | 0.957407i | \(-0.593237\pi\) | ||||
−0.288742 | + | 0.957407i | \(0.593237\pi\) | |||||||
\(272\) | 7.85410 | 0.476225 | ||||||||
\(273\) | 7.85410 | 0.475352 | ||||||||
\(274\) | 6.09017 | 0.367921 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 16.3262 | 0.982724 | ||||||||
\(277\) | 13.7082 | 0.823646 | 0.411823 | − | 0.911264i | \(-0.364892\pi\) | ||||
0.411823 | + | 0.911264i | \(0.364892\pi\) | |||||||
\(278\) | −10.3262 | −0.619327 | ||||||||
\(279\) | 16.3262 | 0.977426 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.1803 | −1.14420 | −0.572102 | − | 0.820183i | \(-0.693872\pi\) | ||||
−0.572102 | + | 0.820183i | \(0.693872\pi\) | |||||||
\(282\) | 15.5623 | 0.926722 | ||||||||
\(283\) | −25.7082 | −1.52819 | −0.764097 | − | 0.645101i | \(-0.776815\pi\) | ||||
−0.764097 | + | 0.645101i | \(0.776815\pi\) | |||||||
\(284\) | −3.00000 | −0.178017 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.236068 | 0.0139590 | ||||||||
\(287\) | 22.4164 | 1.32320 | ||||||||
\(288\) | −3.85410 | −0.227105 | ||||||||
\(289\) | 44.6869 | 2.62864 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 27.6525 | 1.62102 | ||||||||
\(292\) | −5.70820 | −0.334047 | ||||||||
\(293\) | −11.5623 | −0.675477 | −0.337739 | − | 0.941240i | \(-0.609662\pi\) | ||||
−0.337739 | + | 0.941240i | \(0.609662\pi\) | |||||||
\(294\) | 5.23607 | 0.305374 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.32624 | −0.425829 | ||||||||
\(297\) | 0.527864 | 0.0306298 | ||||||||
\(298\) | 2.23607 | 0.129532 | ||||||||
\(299\) | −6.23607 | −0.360641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.29180 | 0.305014 | ||||||||
\(302\) | −3.70820 | −0.213383 | ||||||||
\(303\) | 4.23607 | 0.243356 | ||||||||
\(304\) | −0.854102 | −0.0489861 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −30.2705 | −1.73045 | ||||||||
\(307\) | 17.1246 | 0.977353 | 0.488677 | − | 0.872465i | \(-0.337480\pi\) | ||||
0.488677 | + | 0.872465i | \(0.337480\pi\) | |||||||
\(308\) | 0.708204 | 0.0403537 | ||||||||
\(309\) | 51.9787 | 2.95697 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.0902 | −1.19591 | −0.597957 | − | 0.801528i | \(-0.704021\pi\) | ||||
−0.597957 | + | 0.801528i | \(0.704021\pi\) | |||||||
\(312\) | 2.61803 | 0.148217 | ||||||||
\(313\) | 3.56231 | 0.201353 | 0.100677 | − | 0.994919i | \(-0.467899\pi\) | ||||
0.100677 | + | 0.994919i | \(0.467899\pi\) | |||||||
\(314\) | 15.5623 | 0.878232 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.76393 | −0.155483 | ||||||||
\(317\) | 10.6180 | 0.596368 | 0.298184 | − | 0.954508i | \(-0.403619\pi\) | ||||
0.298184 | + | 0.954508i | \(0.403619\pi\) | |||||||
\(318\) | 4.00000 | 0.224309 | ||||||||
\(319\) | 0.124612 | 0.00697692 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.4164 | −1.47442 | ||||||||
\(322\) | −18.7082 | −1.04257 | ||||||||
\(323\) | −6.70820 | −0.373254 | ||||||||
\(324\) | −5.70820 | −0.317122 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.85410 | 0.268844 | ||||||||
\(327\) | 39.2705 | 2.17166 | ||||||||
\(328\) | 7.47214 | 0.412580 | ||||||||
\(329\) | −17.8328 | −0.983155 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.56231 | 0.250767 | 0.125384 | − | 0.992108i | \(-0.459984\pi\) | ||||
0.125384 | + | 0.992108i | \(0.459984\pi\) | |||||||
\(332\) | −13.4721 | −0.739380 | ||||||||
\(333\) | 28.2361 | 1.54733 | ||||||||
\(334\) | −15.6180 | −0.854581 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.85410 | 0.428476 | ||||||||
\(337\) | −31.4164 | −1.71136 | −0.855680 | − | 0.517505i | \(-0.826861\pi\) | ||||
−0.855680 | + | 0.517505i | \(0.826861\pi\) | |||||||
\(338\) | 12.0000 | 0.652714 | ||||||||
\(339\) | −21.5623 | −1.17110 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.00000 | −0.0541530 | ||||||||
\(342\) | 3.29180 | 0.178000 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 1.76393 | 0.0951048 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.23607 | −0.173972 | ||||||||
\(347\) | −9.90983 | −0.531988 | −0.265994 | − | 0.963975i | \(-0.585700\pi\) | ||||
−0.265994 | + | 0.963975i | \(0.585700\pi\) | |||||||
\(348\) | 1.38197 | 0.0740812 | ||||||||
\(349\) | −22.2361 | −1.19027 | −0.595135 | − | 0.803626i | \(-0.702901\pi\) | ||||
−0.595135 | + | 0.803626i | \(0.702901\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.23607 | −0.119352 | ||||||||
\(352\) | 0.236068 | 0.0125825 | ||||||||
\(353\) | −16.7639 | −0.892254 | −0.446127 | − | 0.894970i | \(-0.647197\pi\) | ||||
−0.446127 | + | 0.894970i | \(0.647197\pi\) | |||||||
\(354\) | 11.7082 | 0.622284 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.47214 | −0.237023 | ||||||||
\(357\) | 61.6869 | 3.26482 | ||||||||
\(358\) | 11.1803 | 0.590899 | ||||||||
\(359\) | 3.09017 | 0.163093 | 0.0815465 | − | 0.996670i | \(-0.474014\pi\) | ||||
0.0815465 | + | 0.996670i | \(0.474014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2705 | −0.961606 | ||||||||
\(362\) | 21.4164 | 1.12562 | ||||||||
\(363\) | 28.6525 | 1.50386 | ||||||||
\(364\) | −3.00000 | −0.157243 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.61803 | −0.293659 | ||||||||
\(367\) | −31.5410 | −1.64643 | −0.823214 | − | 0.567731i | \(-0.807821\pi\) | ||||
−0.823214 | + | 0.567731i | \(0.807821\pi\) | |||||||
\(368\) | −6.23607 | −0.325078 | ||||||||
\(369\) | −28.7984 | −1.49918 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.58359 | −0.237968 | ||||||||
\(372\) | −11.0902 | −0.574999 | ||||||||
\(373\) | −16.2361 | −0.840672 | −0.420336 | − | 0.907369i | \(-0.638088\pi\) | ||||
−0.420336 | + | 0.907369i | \(0.638088\pi\) | |||||||
\(374\) | 1.85410 | 0.0958733 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.94427 | −0.306552 | ||||||||
\(377\) | −0.527864 | −0.0271864 | ||||||||
\(378\) | −6.70820 | −0.345033 | ||||||||
\(379\) | 0.527864 | 0.0271146 | 0.0135573 | − | 0.999908i | \(-0.495684\pi\) | ||||
0.0135573 | + | 0.999908i | \(0.495684\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.6525 | 1.67284 | ||||||||
\(382\) | −17.6525 | −0.903179 | ||||||||
\(383\) | −4.32624 | −0.221060 | −0.110530 | − | 0.993873i | \(-0.535255\pi\) | ||||
−0.110530 | + | 0.993873i | \(0.535255\pi\) | |||||||
\(384\) | 2.61803 | 0.133601 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.6525 | −0.847589 | ||||||||
\(387\) | −6.79837 | −0.345581 | ||||||||
\(388\) | −10.5623 | −0.536220 | ||||||||
\(389\) | −33.2148 | −1.68406 | −0.842028 | − | 0.539434i | \(-0.818638\pi\) | ||||
−0.842028 | + | 0.539434i | \(0.818638\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −48.9787 | −2.47696 | ||||||||
\(392\) | −2.00000 | −0.101015 | ||||||||
\(393\) | −27.2705 | −1.37562 | ||||||||
\(394\) | −12.0000 | −0.604551 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.909830 | −0.0457207 | ||||||||
\(397\) | −5.76393 | −0.289283 | −0.144642 | − | 0.989484i | \(-0.546203\pi\) | ||||
−0.144642 | + | 0.989484i | \(0.546203\pi\) | |||||||
\(398\) | 17.5623 | 0.880319 | ||||||||
\(399\) | −6.70820 | −0.335830 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.18034 | 0.408507 | 0.204253 | − | 0.978918i | \(-0.434523\pi\) | ||||
0.204253 | + | 0.978918i | \(0.434523\pi\) | |||||||
\(402\) | −15.0902 | −0.752629 | ||||||||
\(403\) | 4.23607 | 0.211014 | ||||||||
\(404\) | −1.61803 | −0.0805002 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.58359 | −0.0785924 | ||||||||
\(407\) | −1.72949 | −0.0857276 | ||||||||
\(408\) | 20.5623 | 1.01799 | ||||||||
\(409\) | 6.70820 | 0.331699 | 0.165850 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165850 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.9443 | 0.786473 | ||||||||
\(412\) | −19.8541 | −0.978141 | ||||||||
\(413\) | −13.4164 | −0.660178 | ||||||||
\(414\) | 24.0344 | 1.18123 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −27.0344 | −1.32388 | ||||||||
\(418\) | −0.201626 | −0.00986186 | ||||||||
\(419\) | 27.2361 | 1.33057 | 0.665284 | − | 0.746590i | \(-0.268310\pi\) | ||||
0.665284 | + | 0.746590i | \(0.268310\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2705 | −0.598028 | −0.299014 | − | 0.954249i | \(-0.596658\pi\) | ||||
−0.299014 | + | 0.954249i | \(0.596658\pi\) | |||||||
\(422\) | −11.2705 | −0.548640 | ||||||||
\(423\) | 22.9098 | 1.11391 | ||||||||
\(424\) | −1.52786 | −0.0741996 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.85410 | −0.380532 | ||||||||
\(427\) | 6.43769 | 0.311542 | ||||||||
\(428\) | 10.0902 | 0.487727 | ||||||||
\(429\) | 0.618034 | 0.0298390 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.0689 | −1.54470 | −0.772352 | − | 0.635195i | \(-0.780920\pi\) | ||||
−0.772352 | + | 0.635195i | \(0.780920\pi\) | |||||||
\(432\) | −2.23607 | −0.107583 | ||||||||
\(433\) | 23.3607 | 1.12264 | 0.561321 | − | 0.827598i | \(-0.310293\pi\) | ||||
0.561321 | + | 0.827598i | \(0.310293\pi\) | |||||||
\(434\) | 12.7082 | 0.610013 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.0000 | −0.718370 | ||||||||
\(437\) | 5.32624 | 0.254789 | ||||||||
\(438\) | −14.9443 | −0.714065 | ||||||||
\(439\) | −5.65248 | −0.269778 | −0.134889 | − | 0.990861i | \(-0.543068\pi\) | ||||
−0.134889 | + | 0.990861i | \(0.543068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.70820 | 0.367057 | ||||||||
\(442\) | −7.85410 | −0.373582 | ||||||||
\(443\) | −7.41641 | −0.352364 | −0.176182 | − | 0.984358i | \(-0.556375\pi\) | ||||
−0.176182 | + | 0.984358i | \(0.556375\pi\) | |||||||
\(444\) | −19.1803 | −0.910259 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.00000 | 0.426162 | ||||||||
\(447\) | 5.85410 | 0.276890 | ||||||||
\(448\) | −3.00000 | −0.141737 | ||||||||
\(449\) | 13.9443 | 0.658071 | 0.329035 | − | 0.944318i | \(-0.393276\pi\) | ||||
0.329035 | + | 0.944318i | \(0.393276\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.76393 | 0.0830603 | ||||||||
\(452\) | 8.23607 | 0.387392 | ||||||||
\(453\) | −9.70820 | −0.456131 | ||||||||
\(454\) | 15.3607 | 0.720912 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.23607 | −0.104713 | ||||||||
\(457\) | −11.2148 | −0.524605 | −0.262303 | − | 0.964986i | \(-0.584482\pi\) | ||||
−0.262303 | + | 0.964986i | \(0.584482\pi\) | |||||||
\(458\) | −17.5623 | −0.820633 | ||||||||
\(459\) | −17.5623 | −0.819738 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.1803 | 1.31249 | 0.656245 | − | 0.754548i | \(-0.272144\pi\) | ||||
0.656245 | + | 0.754548i | \(0.272144\pi\) | |||||||
\(462\) | 1.85410 | 0.0862606 | ||||||||
\(463\) | 11.9787 | 0.556698 | 0.278349 | − | 0.960480i | \(-0.410213\pi\) | ||||
0.278349 | + | 0.960480i | \(0.410213\pi\) | |||||||
\(464\) | −0.527864 | −0.0245055 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.7082 | −1.28356 | ||||||||
\(467\) | 3.18034 | 0.147169 | 0.0735843 | − | 0.997289i | \(-0.476556\pi\) | ||||
0.0735843 | + | 0.997289i | \(0.476556\pi\) | |||||||
\(468\) | 3.85410 | 0.178156 | ||||||||
\(469\) | 17.2918 | 0.798461 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.7426 | 1.87732 | ||||||||
\(472\) | −4.47214 | −0.205847 | ||||||||
\(473\) | 0.416408 | 0.0191465 | ||||||||
\(474\) | −7.23607 | −0.332364 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −23.5623 | −1.07998 | ||||||||
\(477\) | 5.88854 | 0.269618 | ||||||||
\(478\) | 18.0902 | 0.827425 | ||||||||
\(479\) | −39.7984 | −1.81843 | −0.909217 | − | 0.416322i | \(-0.863319\pi\) | ||||
−0.909217 | + | 0.416322i | \(0.863319\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.32624 | 0.334048 | ||||||||
\(482\) | −13.3820 | −0.609532 | ||||||||
\(483\) | −48.9787 | −2.22861 | ||||||||
\(484\) | −10.9443 | −0.497467 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −21.6525 | −0.982176 | ||||||||
\(487\) | −18.1246 | −0.821305 | −0.410652 | − | 0.911792i | \(-0.634699\pi\) | ||||
−0.410652 | + | 0.911792i | \(0.634699\pi\) | |||||||
\(488\) | 2.14590 | 0.0971402 | ||||||||
\(489\) | 12.7082 | 0.574685 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.7639 | 0.666287 | 0.333143 | − | 0.942876i | \(-0.391891\pi\) | ||||
0.333143 | + | 0.942876i | \(0.391891\pi\) | |||||||
\(492\) | 19.5623 | 0.881937 | ||||||||
\(493\) | −4.14590 | −0.186722 | ||||||||
\(494\) | 0.854102 | 0.0384279 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.23607 | 0.190205 | ||||||||
\(497\) | 9.00000 | 0.403705 | ||||||||
\(498\) | −35.2705 | −1.58051 | ||||||||
\(499\) | 40.8541 | 1.82888 | 0.914440 | − | 0.404721i | \(-0.132631\pi\) | ||||
0.914440 | + | 0.404721i | \(0.132631\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −40.8885 | −1.82677 | ||||||||
\(502\) | −23.1803 | −1.03459 | ||||||||
\(503\) | 7.50658 | 0.334702 | 0.167351 | − | 0.985897i | \(-0.446479\pi\) | ||||
0.167351 | + | 0.985897i | \(0.446479\pi\) | |||||||
\(504\) | 11.5623 | 0.515026 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.47214 | −0.0654444 | ||||||||
\(507\) | 31.4164 | 1.39525 | ||||||||
\(508\) | −12.4721 | −0.553362 | ||||||||
\(509\) | −13.0902 | −0.580212 | −0.290106 | − | 0.956995i | \(-0.593690\pi\) | ||||
−0.290106 | + | 0.956995i | \(0.593690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.1246 | 0.757548 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.90983 | 0.0843211 | ||||||||
\(514\) | 16.7426 | 0.738486 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.61803 | 0.203298 | ||||||||
\(517\) | −1.40325 | −0.0617150 | ||||||||
\(518\) | 21.9787 | 0.965689 | ||||||||
\(519\) | −8.47214 | −0.371885 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.4508 | 1.42170 | 0.710849 | − | 0.703345i | \(-0.248311\pi\) | ||||
0.710849 | + | 0.703345i | \(0.248311\pi\) | |||||||
\(522\) | 2.03444 | 0.0890451 | ||||||||
\(523\) | 26.6525 | 1.16543 | 0.582716 | − | 0.812676i | \(-0.301990\pi\) | ||||
0.582716 | + | 0.812676i | \(0.301990\pi\) | |||||||
\(524\) | 10.4164 | 0.455043 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.38197 | −0.103859 | ||||||||
\(527\) | 33.2705 | 1.44929 | ||||||||
\(528\) | 0.618034 | 0.0268965 | ||||||||
\(529\) | 15.8885 | 0.690806 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.2361 | 0.747982 | ||||||||
\(532\) | 2.56231 | 0.111090 | ||||||||
\(533\) | −7.47214 | −0.323654 | ||||||||
\(534\) | −11.7082 | −0.506664 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.76393 | 0.248964 | ||||||||
\(537\) | 29.2705 | 1.26312 | ||||||||
\(538\) | −13.0902 | −0.564357 | ||||||||
\(539\) | −0.472136 | −0.0203363 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.7082 | 1.23426 | 0.617131 | − | 0.786860i | \(-0.288295\pi\) | ||||
0.617131 | + | 0.786860i | \(0.288295\pi\) | |||||||
\(542\) | 9.50658 | 0.408342 | ||||||||
\(543\) | 56.0689 | 2.40615 | ||||||||
\(544\) | −7.85410 | −0.336742 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.85410 | −0.336125 | ||||||||
\(547\) | 10.6180 | 0.453994 | 0.226997 | − | 0.973895i | \(-0.427109\pi\) | ||||
0.226997 | + | 0.973895i | \(0.427109\pi\) | |||||||
\(548\) | −6.09017 | −0.260159 | ||||||||
\(549\) | −8.27051 | −0.352977 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.450850 | 0.0192068 | ||||||||
\(552\) | −16.3262 | −0.694891 | ||||||||
\(553\) | 8.29180 | 0.352603 | ||||||||
\(554\) | −13.7082 | −0.582406 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.3262 | 0.437930 | ||||||||
\(557\) | −10.8885 | −0.461362 | −0.230681 | − | 0.973029i | \(-0.574095\pi\) | ||||
−0.230681 | + | 0.973029i | \(0.574095\pi\) | |||||||
\(558\) | −16.3262 | −0.691145 | ||||||||
\(559\) | −1.76393 | −0.0746064 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.85410 | 0.204940 | ||||||||
\(562\) | 19.1803 | 0.809074 | ||||||||
\(563\) | −34.8541 | −1.46893 | −0.734463 | − | 0.678649i | \(-0.762566\pi\) | ||||
−0.734463 | + | 0.678649i | \(0.762566\pi\) | |||||||
\(564\) | −15.5623 | −0.655291 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.7082 | 1.08060 | ||||||||
\(567\) | 17.1246 | 0.719166 | ||||||||
\(568\) | 3.00000 | 0.125877 | ||||||||
\(569\) | 22.2361 | 0.932184 | 0.466092 | − | 0.884736i | \(-0.345661\pi\) | ||||
0.466092 | + | 0.884736i | \(0.345661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.67376 | 0.0700448 | 0.0350224 | − | 0.999387i | \(-0.488850\pi\) | ||||
0.0350224 | + | 0.999387i | \(0.488850\pi\) | |||||||
\(572\) | −0.236068 | −0.00987050 | ||||||||
\(573\) | −46.2148 | −1.93065 | ||||||||
\(574\) | −22.4164 | −0.935643 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.85410 | 0.160588 | ||||||||
\(577\) | −43.0000 | −1.79011 | −0.895057 | − | 0.445952i | \(-0.852865\pi\) | ||||
−0.895057 | + | 0.445952i | \(0.852865\pi\) | |||||||
\(578\) | −44.6869 | −1.85873 | ||||||||
\(579\) | −43.5967 | −1.81182 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.4164 | 1.67676 | ||||||||
\(582\) | −27.6525 | −1.14623 | ||||||||
\(583\) | −0.360680 | −0.0149378 | ||||||||
\(584\) | 5.70820 | 0.236207 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.5623 | 0.477634 | ||||||||
\(587\) | −11.8197 | −0.487850 | −0.243925 | − | 0.969794i | \(-0.578435\pi\) | ||||
−0.243925 | + | 0.969794i | \(0.578435\pi\) | |||||||
\(588\) | −5.23607 | −0.215932 | ||||||||
\(589\) | −3.61803 | −0.149078 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.4164 | −1.29230 | ||||||||
\(592\) | 7.32624 | 0.301107 | ||||||||
\(593\) | −47.0132 | −1.93060 | −0.965299 | − | 0.261145i | \(-0.915900\pi\) | ||||
−0.965299 | + | 0.261145i | \(0.915900\pi\) | |||||||
\(594\) | −0.527864 | −0.0216585 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.23607 | −0.0915929 | ||||||||
\(597\) | 45.9787 | 1.88178 | ||||||||
\(598\) | 6.23607 | 0.255012 | ||||||||
\(599\) | −8.94427 | −0.365453 | −0.182727 | − | 0.983164i | \(-0.558492\pi\) | ||||
−0.182727 | + | 0.983164i | \(0.558492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.8328 | −0.605043 | −0.302522 | − | 0.953143i | \(-0.597828\pi\) | ||||
−0.302522 | + | 0.953143i | \(0.597828\pi\) | |||||||
\(602\) | −5.29180 | −0.215678 | ||||||||
\(603\) | −22.2148 | −0.904656 | ||||||||
\(604\) | 3.70820 | 0.150885 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.23607 | −0.172078 | ||||||||
\(607\) | −27.1459 | −1.10182 | −0.550909 | − | 0.834565i | \(-0.685719\pi\) | ||||
−0.550909 | + | 0.834565i | \(0.685719\pi\) | |||||||
\(608\) | 0.854102 | 0.0346384 | ||||||||
\(609\) | −4.14590 | −0.168000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.94427 | 0.240480 | ||||||||
\(612\) | 30.2705 | 1.22361 | ||||||||
\(613\) | −41.5623 | −1.67869 | −0.839343 | − | 0.543602i | \(-0.817060\pi\) | ||||
−0.839343 | + | 0.543602i | \(0.817060\pi\) | |||||||
\(614\) | −17.1246 | −0.691093 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.708204 | −0.0285343 | ||||||||
\(617\) | −30.3607 | −1.22227 | −0.611137 | − | 0.791524i | \(-0.709288\pi\) | ||||
−0.611137 | + | 0.791524i | \(0.709288\pi\) | |||||||
\(618\) | −51.9787 | −2.09089 | ||||||||
\(619\) | −46.9574 | −1.88738 | −0.943689 | − | 0.330833i | \(-0.892670\pi\) | ||||
−0.943689 | + | 0.330833i | \(0.892670\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.9443 | 0.559564 | ||||||||
\(622\) | 21.0902 | 0.845639 | ||||||||
\(623\) | 13.4164 | 0.537517 | ||||||||
\(624\) | −2.61803 | −0.104805 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.56231 | −0.142378 | ||||||||
\(627\) | −0.527864 | −0.0210809 | ||||||||
\(628\) | −15.5623 | −0.621004 | ||||||||
\(629\) | 57.5410 | 2.29431 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.83282 | 0.351629 | 0.175814 | − | 0.984423i | \(-0.443744\pi\) | ||||
0.175814 | + | 0.984423i | \(0.443744\pi\) | |||||||
\(632\) | 2.76393 | 0.109943 | ||||||||
\(633\) | −29.5066 | −1.17278 | ||||||||
\(634\) | −10.6180 | −0.421696 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | −0.124612 | −0.00493343 | ||||||||
\(639\) | −11.5623 | −0.457398 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.3607 | 0.567213 | 0.283606 | − | 0.958941i | \(-0.408469\pi\) | ||||
0.283606 | + | 0.958941i | \(0.408469\pi\) | |||||||
\(642\) | 26.4164 | 1.04257 | ||||||||
\(643\) | −36.2361 | −1.42901 | −0.714506 | − | 0.699630i | \(-0.753348\pi\) | ||||
−0.714506 | + | 0.699630i | \(0.753348\pi\) | |||||||
\(644\) | 18.7082 | 0.737207 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.70820 | 0.263931 | ||||||||
\(647\) | 7.65248 | 0.300850 | 0.150425 | − | 0.988621i | \(-0.451936\pi\) | ||||
0.150425 | + | 0.988621i | \(0.451936\pi\) | |||||||
\(648\) | 5.70820 | 0.224239 | ||||||||
\(649\) | −1.05573 | −0.0414410 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.2705 | 1.30397 | ||||||||
\(652\) | −4.85410 | −0.190101 | ||||||||
\(653\) | 40.5967 | 1.58867 | 0.794337 | − | 0.607478i | \(-0.207819\pi\) | ||||
0.794337 | + | 0.607478i | \(0.207819\pi\) | |||||||
\(654\) | −39.2705 | −1.53560 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.47214 | −0.291738 | ||||||||
\(657\) | −22.0000 | −0.858302 | ||||||||
\(658\) | 17.8328 | 0.695196 | ||||||||
\(659\) | 5.65248 | 0.220189 | 0.110095 | − | 0.993921i | \(-0.464885\pi\) | ||||
0.110095 | + | 0.993921i | \(0.464885\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.27051 | 0.243895 | 0.121947 | − | 0.992537i | \(-0.461086\pi\) | ||||
0.121947 | + | 0.992537i | \(0.461086\pi\) | |||||||
\(662\) | −4.56231 | −0.177319 | ||||||||
\(663\) | −20.5623 | −0.798574 | ||||||||
\(664\) | 13.4721 | 0.522820 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −28.2361 | −1.09413 | ||||||||
\(667\) | 3.29180 | 0.127459 | ||||||||
\(668\) | 15.6180 | 0.604280 | ||||||||
\(669\) | 23.5623 | 0.910971 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.506578 | 0.0195562 | ||||||||
\(672\) | −7.85410 | −0.302979 | ||||||||
\(673\) | −1.23607 | −0.0476469 | −0.0238235 | − | 0.999716i | \(-0.507584\pi\) | ||||
−0.0238235 | + | 0.999716i | \(0.507584\pi\) | |||||||
\(674\) | 31.4164 | 1.21011 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | 10.6180 | 0.408084 | 0.204042 | − | 0.978962i | \(-0.434592\pi\) | ||||
0.204042 | + | 0.978962i | \(0.434592\pi\) | |||||||
\(678\) | 21.5623 | 0.828095 | ||||||||
\(679\) | 31.6869 | 1.21603 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 40.2148 | 1.54103 | ||||||||
\(682\) | 1.00000 | 0.0382920 | ||||||||
\(683\) | 33.3607 | 1.27651 | 0.638255 | − | 0.769825i | \(-0.279656\pi\) | ||||
0.638255 | + | 0.769825i | \(0.279656\pi\) | |||||||
\(684\) | −3.29180 | −0.125865 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.0000 | −0.572703 | ||||||||
\(687\) | −45.9787 | −1.75420 | ||||||||
\(688\) | −1.76393 | −0.0672493 | ||||||||
\(689\) | 1.52786 | 0.0582070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.27051 | 0.0483325 | 0.0241662 | − | 0.999708i | \(-0.492307\pi\) | ||||
0.0241662 | + | 0.999708i | \(0.492307\pi\) | |||||||
\(692\) | 3.23607 | 0.123017 | ||||||||
\(693\) | 2.72949 | 0.103685 | ||||||||
\(694\) | 9.90983 | 0.376172 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.38197 | −0.0523833 | ||||||||
\(697\) | −58.6869 | −2.22293 | ||||||||
\(698\) | 22.2361 | 0.841648 | ||||||||
\(699\) | −72.5410 | −2.74375 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.18034 | −0.157889 | −0.0789446 | − | 0.996879i | \(-0.525155\pi\) | ||||
−0.0789446 | + | 0.996879i | \(0.525155\pi\) | |||||||
\(702\) | 2.23607 | 0.0843949 | ||||||||
\(703\) | −6.25735 | −0.236001 | ||||||||
\(704\) | −0.236068 | −0.00889715 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.7639 | 0.630919 | ||||||||
\(707\) | 4.85410 | 0.182557 | ||||||||
\(708\) | −11.7082 | −0.440021 | ||||||||
\(709\) | 7.76393 | 0.291581 | 0.145790 | − | 0.989316i | \(-0.453428\pi\) | ||||
0.145790 | + | 0.989316i | \(0.453428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.6525 | −0.399499 | ||||||||
\(712\) | 4.47214 | 0.167600 | ||||||||
\(713\) | −26.4164 | −0.989302 | ||||||||
\(714\) | −61.6869 | −2.30857 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.1803 | −0.417829 | ||||||||
\(717\) | 47.3607 | 1.76872 | ||||||||
\(718\) | −3.09017 | −0.115324 | ||||||||
\(719\) | −26.5066 | −0.988529 | −0.494264 | − | 0.869312i | \(-0.664562\pi\) | ||||
−0.494264 | + | 0.869312i | \(0.664562\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 59.5623 | 2.21822 | ||||||||
\(722\) | 18.2705 | 0.679958 | ||||||||
\(723\) | −35.0344 | −1.30294 | ||||||||
\(724\) | −21.4164 | −0.795935 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −28.6525 | −1.06339 | ||||||||
\(727\) | −28.6525 | −1.06266 | −0.531331 | − | 0.847164i | \(-0.678308\pi\) | ||||
−0.531331 | + | 0.847164i | \(0.678308\pi\) | |||||||
\(728\) | 3.00000 | 0.111187 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.8541 | −0.512412 | ||||||||
\(732\) | 5.61803 | 0.207649 | ||||||||
\(733\) | −39.7771 | −1.46920 | −0.734600 | − | 0.678500i | \(-0.762630\pi\) | ||||
−0.734600 | + | 0.678500i | \(0.762630\pi\) | |||||||
\(734\) | 31.5410 | 1.16420 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.23607 | 0.229865 | ||||||||
\(737\) | 1.36068 | 0.0501213 | ||||||||
\(738\) | 28.7984 | 1.06008 | ||||||||
\(739\) | 30.0000 | 1.10357 | 0.551784 | − | 0.833987i | \(-0.313947\pi\) | ||||
0.551784 | + | 0.833987i | \(0.313947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.23607 | 0.0821440 | ||||||||
\(742\) | 4.58359 | 0.168269 | ||||||||
\(743\) | −18.2705 | −0.670280 | −0.335140 | − | 0.942168i | \(-0.608784\pi\) | ||||
−0.335140 | + | 0.942168i | \(0.608784\pi\) | |||||||
\(744\) | 11.0902 | 0.406585 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.2361 | 0.594445 | ||||||||
\(747\) | −51.9230 | −1.89976 | ||||||||
\(748\) | −1.85410 | −0.0677927 | ||||||||
\(749\) | −30.2705 | −1.10606 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.14590 | 0.0418144 | 0.0209072 | − | 0.999781i | \(-0.493345\pi\) | ||||
0.0209072 | + | 0.999781i | \(0.493345\pi\) | |||||||
\(752\) | 5.94427 | 0.216765 | ||||||||
\(753\) | −60.6869 | −2.21155 | ||||||||
\(754\) | 0.527864 | 0.0192237 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.70820 | 0.243975 | ||||||||
\(757\) | 10.4164 | 0.378591 | 0.189295 | − | 0.981920i | \(-0.439380\pi\) | ||||
0.189295 | + | 0.981920i | \(0.439380\pi\) | |||||||
\(758\) | −0.527864 | −0.0191729 | ||||||||
\(759\) | −3.85410 | −0.139895 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.9230 | −1.37471 | −0.687354 | − | 0.726323i | \(-0.741228\pi\) | ||||
−0.687354 | + | 0.726323i | \(0.741228\pi\) | |||||||
\(762\) | −32.6525 | −1.18287 | ||||||||
\(763\) | 45.0000 | 1.62911 | ||||||||
\(764\) | 17.6525 | 0.638644 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.32624 | 0.156313 | ||||||||
\(767\) | 4.47214 | 0.161479 | ||||||||
\(768\) | −2.61803 | −0.0944702 | ||||||||
\(769\) | −23.4164 | −0.844417 | −0.422209 | − | 0.906499i | \(-0.638745\pi\) | ||||
−0.422209 | + | 0.906499i | \(0.638745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.8328 | 1.57860 | ||||||||
\(772\) | 16.6525 | 0.599336 | ||||||||
\(773\) | 6.20163 | 0.223057 | 0.111528 | − | 0.993761i | \(-0.464425\pi\) | ||||
0.111528 | + | 0.993761i | \(0.464425\pi\) | |||||||
\(774\) | 6.79837 | 0.244363 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.5623 | 0.379165 | ||||||||
\(777\) | 57.5410 | 2.06427 | ||||||||
\(778\) | 33.2148 | 1.19081 | ||||||||
\(779\) | 6.38197 | 0.228658 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.708204 | 0.0253415 | ||||||||
\(782\) | 48.9787 | 1.75148 | ||||||||
\(783\) | 1.18034 | 0.0421819 | ||||||||
\(784\) | 2.00000 | 0.0714286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27.2705 | 0.972707 | ||||||||
\(787\) | 15.4164 | 0.549536 | 0.274768 | − | 0.961511i | \(-0.411399\pi\) | ||||
0.274768 | + | 0.961511i | \(0.411399\pi\) | |||||||
\(788\) | 12.0000 | 0.427482 | ||||||||
\(789\) | −6.23607 | −0.222010 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.7082 | −0.878523 | ||||||||
\(792\) | 0.909830 | 0.0323294 | ||||||||
\(793\) | −2.14590 | −0.0762031 | ||||||||
\(794\) | 5.76393 | 0.204554 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.5623 | −0.622479 | ||||||||
\(797\) | 3.38197 | 0.119795 | 0.0598977 | − | 0.998205i | \(-0.480923\pi\) | ||||
0.0598977 | + | 0.998205i | \(0.480923\pi\) | |||||||
\(798\) | 6.70820 | 0.237468 | ||||||||
\(799\) | 46.6869 | 1.65166 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.2361 | −0.609007 | ||||||||
\(802\) | −8.18034 | −0.288858 | ||||||||
\(803\) | 1.34752 | 0.0475531 | ||||||||
\(804\) | 15.0902 | 0.532189 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.23607 | −0.149209 | ||||||||
\(807\) | −34.2705 | −1.20638 | ||||||||
\(808\) | 1.61803 | 0.0569222 | ||||||||
\(809\) | 2.23607 | 0.0786160 | 0.0393080 | − | 0.999227i | \(-0.487485\pi\) | ||||
0.0393080 | + | 0.999227i | \(0.487485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.0557 | 0.809596 | 0.404798 | − | 0.914406i | \(-0.367342\pi\) | ||||
0.404798 | + | 0.914406i | \(0.367342\pi\) | |||||||
\(812\) | 1.58359 | 0.0555732 | ||||||||
\(813\) | 24.8885 | 0.872879 | ||||||||
\(814\) | 1.72949 | 0.0606186 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.5623 | −0.719825 | ||||||||
\(817\) | 1.50658 | 0.0527085 | ||||||||
\(818\) | −6.70820 | −0.234547 | ||||||||
\(819\) | −11.5623 | −0.404020 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.1591 | −1.05256 | −0.526279 | − | 0.850312i | \(-0.676413\pi\) | ||||
−0.526279 | + | 0.850312i | \(0.676413\pi\) | |||||||
\(822\) | −15.9443 | −0.556120 | ||||||||
\(823\) | 32.8328 | 1.14448 | 0.572240 | − | 0.820086i | \(-0.306075\pi\) | ||||
0.572240 | + | 0.820086i | \(0.306075\pi\) | |||||||
\(824\) | 19.8541 | 0.691650 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.4164 | 0.466817 | ||||||||
\(827\) | 24.0344 | 0.835759 | 0.417880 | − | 0.908502i | \(-0.362773\pi\) | ||||
0.417880 | + | 0.908502i | \(0.362773\pi\) | |||||||
\(828\) | −24.0344 | −0.835255 | ||||||||
\(829\) | 26.5836 | 0.923286 | 0.461643 | − | 0.887066i | \(-0.347260\pi\) | ||||
0.461643 | + | 0.887066i | \(0.347260\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.8885 | −1.24496 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 15.7082 | 0.544257 | ||||||||
\(834\) | 27.0344 | 0.936126 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.201626 | 0.00697339 | ||||||||
\(837\) | −9.47214 | −0.327405 | ||||||||
\(838\) | −27.2361 | −0.940854 | ||||||||
\(839\) | 25.2492 | 0.871700 | 0.435850 | − | 0.900019i | \(-0.356448\pi\) | ||||
0.435850 | + | 0.900019i | \(0.356448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7214 | −0.990392 | ||||||||
\(842\) | 12.2705 | 0.422870 | ||||||||
\(843\) | 50.2148 | 1.72949 | ||||||||
\(844\) | 11.2705 | 0.387947 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −22.9098 | −0.787656 | ||||||||
\(847\) | 32.8328 | 1.12815 | ||||||||
\(848\) | 1.52786 | 0.0524671 | ||||||||
\(849\) | 67.3050 | 2.30990 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45.6869 | −1.56613 | ||||||||
\(852\) | 7.85410 | 0.269077 | ||||||||
\(853\) | −24.8541 | −0.850988 | −0.425494 | − | 0.904961i | \(-0.639900\pi\) | ||||
−0.425494 | + | 0.904961i | \(0.639900\pi\) | |||||||
\(854\) | −6.43769 | −0.220293 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0902 | −0.344875 | ||||||||
\(857\) | 35.3394 | 1.20717 | 0.603585 | − | 0.797298i | \(-0.293738\pi\) | ||||
0.603585 | + | 0.797298i | \(0.293738\pi\) | |||||||
\(858\) | −0.618034 | −0.0210993 | ||||||||
\(859\) | −39.3951 | −1.34414 | −0.672072 | − | 0.740486i | \(-0.734596\pi\) | ||||
−0.672072 | + | 0.740486i | \(0.734596\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −58.6869 | −2.00004 | ||||||||
\(862\) | 32.0689 | 1.09227 | ||||||||
\(863\) | −6.76393 | −0.230247 | −0.115123 | − | 0.993351i | \(-0.536726\pi\) | ||||
−0.115123 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(864\) | 2.23607 | 0.0760726 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.3607 | −0.793828 | ||||||||
\(867\) | −116.992 | −3.97325 | ||||||||
\(868\) | −12.7082 | −0.431345 | ||||||||
\(869\) | 0.652476 | 0.0221337 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.76393 | −0.195303 | ||||||||
\(872\) | 15.0000 | 0.507964 | ||||||||
\(873\) | −40.7082 | −1.37776 | ||||||||
\(874\) | −5.32624 | −0.180163 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.9443 | 0.504920 | ||||||||
\(877\) | 24.5623 | 0.829410 | 0.414705 | − | 0.909956i | \(-0.363885\pi\) | ||||
0.414705 | + | 0.909956i | \(0.363885\pi\) | |||||||
\(878\) | 5.65248 | 0.190762 | ||||||||
\(879\) | 30.2705 | 1.02100 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.8197 | 0.532978 | 0.266489 | − | 0.963838i | \(-0.414136\pi\) | ||||
0.266489 | + | 0.963838i | \(0.414136\pi\) | |||||||
\(882\) | −7.70820 | −0.259549 | ||||||||
\(883\) | 18.6869 | 0.628865 | 0.314432 | − | 0.949280i | \(-0.398186\pi\) | ||||
0.314432 | + | 0.949280i | \(0.398186\pi\) | |||||||
\(884\) | 7.85410 | 0.264162 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.41641 | 0.249159 | ||||||||
\(887\) | 10.8197 | 0.363289 | 0.181644 | − | 0.983364i | \(-0.441858\pi\) | ||||
0.181644 | + | 0.983364i | \(0.441858\pi\) | |||||||
\(888\) | 19.1803 | 0.643650 | ||||||||
\(889\) | 37.4164 | 1.25491 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.34752 | 0.0451438 | ||||||||
\(892\) | −9.00000 | −0.301342 | ||||||||
\(893\) | −5.07701 | −0.169896 | ||||||||
\(894\) | −5.85410 | −0.195790 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | 16.3262 | 0.545117 | ||||||||
\(898\) | −13.9443 | −0.465326 | ||||||||
\(899\) | −2.23607 | −0.0745770 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −1.76393 | −0.0587325 | ||||||||
\(903\) | −13.8541 | −0.461036 | ||||||||
\(904\) | −8.23607 | −0.273928 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.70820 | 0.322533 | ||||||||
\(907\) | 23.3820 | 0.776385 | 0.388193 | − | 0.921578i | \(-0.373099\pi\) | ||||
0.388193 | + | 0.921578i | \(0.373099\pi\) | |||||||
\(908\) | −15.3607 | −0.509762 | ||||||||
\(909\) | −6.23607 | −0.206837 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.4164 | 0.345111 | 0.172555 | − | 0.985000i | \(-0.444798\pi\) | ||||
0.172555 | + | 0.985000i | \(0.444798\pi\) | |||||||
\(912\) | 2.23607 | 0.0740436 | ||||||||
\(913\) | 3.18034 | 0.105254 | ||||||||
\(914\) | 11.2148 | 0.370952 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.5623 | 0.580275 | ||||||||
\(917\) | −31.2492 | −1.03194 | ||||||||
\(918\) | 17.5623 | 0.579642 | ||||||||
\(919\) | 25.6525 | 0.846197 | 0.423099 | − | 0.906084i | \(-0.360942\pi\) | ||||
0.423099 | + | 0.906084i | \(0.360942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −44.8328 | −1.47729 | ||||||||
\(922\) | −28.1803 | −0.928070 | ||||||||
\(923\) | −3.00000 | −0.0987462 | ||||||||
\(924\) | −1.85410 | −0.0609955 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.9787 | −0.393645 | ||||||||
\(927\) | −76.5197 | −2.51324 | ||||||||
\(928\) | 0.527864 | 0.0173280 | ||||||||
\(929\) | −17.1115 | −0.561409 | −0.280704 | − | 0.959794i | \(-0.590568\pi\) | ||||
−0.280704 | + | 0.959794i | \(0.590568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.70820 | −0.0559841 | ||||||||
\(932\) | 27.7082 | 0.907612 | ||||||||
\(933\) | 55.2148 | 1.80765 | ||||||||
\(934\) | −3.18034 | −0.104064 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.85410 | −0.125975 | ||||||||
\(937\) | −22.9230 | −0.748861 | −0.374431 | − | 0.927255i | \(-0.622162\pi\) | ||||
−0.374431 | + | 0.927255i | \(0.622162\pi\) | |||||||
\(938\) | −17.2918 | −0.564597 | ||||||||
\(939\) | −9.32624 | −0.304350 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6180 | −0.378737 | −0.189369 | − | 0.981906i | \(-0.560644\pi\) | ||||
−0.189369 | + | 0.981906i | \(0.560644\pi\) | |||||||
\(942\) | −40.7426 | −1.32747 | ||||||||
\(943\) | 46.5967 | 1.51740 | ||||||||
\(944\) | 4.47214 | 0.145556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.416408 | −0.0135386 | ||||||||
\(947\) | −41.6180 | −1.35240 | −0.676202 | − | 0.736716i | \(-0.736375\pi\) | ||||
−0.676202 | + | 0.736716i | \(0.736375\pi\) | |||||||
\(948\) | 7.23607 | 0.235017 | ||||||||
\(949\) | −5.70820 | −0.185296 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.7984 | −0.901424 | ||||||||
\(952\) | 23.5623 | 0.763659 | ||||||||
\(953\) | 42.3820 | 1.37289 | 0.686443 | − | 0.727183i | \(-0.259171\pi\) | ||||
0.686443 | + | 0.727183i | \(0.259171\pi\) | |||||||
\(954\) | −5.88854 | −0.190649 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.0902 | −0.585078 | ||||||||
\(957\) | −0.326238 | −0.0105458 | ||||||||
\(958\) | 39.7984 | 1.28583 | ||||||||
\(959\) | 18.2705 | 0.589986 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0557 | −0.421153 | ||||||||
\(962\) | −7.32624 | −0.236207 | ||||||||
\(963\) | 38.8885 | 1.25317 | ||||||||
\(964\) | 13.3820 | 0.431004 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 48.9787 | 1.57586 | ||||||||
\(967\) | 27.1246 | 0.872269 | 0.436134 | − | 0.899882i | \(-0.356347\pi\) | ||||
0.436134 | + | 0.899882i | \(0.356347\pi\) | |||||||
\(968\) | 10.9443 | 0.351762 | ||||||||
\(969\) | 17.5623 | 0.564183 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.0689 | −1.67097 | −0.835485 | − | 0.549513i | \(-0.814813\pi\) | ||||
−0.835485 | + | 0.549513i | \(0.814813\pi\) | |||||||
\(972\) | 21.6525 | 0.694503 | ||||||||
\(973\) | −30.9787 | −0.993132 | ||||||||
\(974\) | 18.1246 | 0.580750 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.14590 | −0.0686885 | ||||||||
\(977\) | −26.0132 | −0.832235 | −0.416117 | − | 0.909311i | \(-0.636609\pi\) | ||||
−0.416117 | + | 0.909311i | \(0.636609\pi\) | |||||||
\(978\) | −12.7082 | −0.406364 | ||||||||
\(979\) | 1.05573 | 0.0337412 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −57.8115 | −1.84578 | ||||||||
\(982\) | −14.7639 | −0.471136 | ||||||||
\(983\) | −46.4853 | −1.48265 | −0.741325 | − | 0.671146i | \(-0.765802\pi\) | ||||
−0.741325 | + | 0.671146i | \(0.765802\pi\) | |||||||
\(984\) | −19.5623 | −0.623624 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.14590 | 0.132032 | ||||||||
\(987\) | 46.6869 | 1.48606 | ||||||||
\(988\) | −0.854102 | −0.0271726 | ||||||||
\(989\) | 11.0000 | 0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.4508 | 1.66616 | 0.833078 | − | 0.553155i | \(-0.186576\pi\) | ||||
0.833078 | + | 0.553155i | \(0.186576\pi\) | |||||||
\(992\) | −4.23607 | −0.134495 | ||||||||
\(993\) | −11.9443 | −0.379040 | ||||||||
\(994\) | −9.00000 | −0.285463 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 35.2705 | 1.11759 | ||||||||
\(997\) | −53.2492 | −1.68642 | −0.843210 | − | 0.537584i | \(-0.819337\pi\) | ||||
−0.843210 | + | 0.537584i | \(0.819337\pi\) | |||||||
\(998\) | −40.8541 | −1.29321 | ||||||||
\(999\) | −16.3820 | −0.518302 |
(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 | 1250.2.a.a.1.1 | 2 | ||
4.3 | odd | 2 | 10000.2.a.n.1.2 | 2 | |||
5.2 | odd | 4 | 1250.2.b.b.1249.2 | 4 | |||
5.3 | odd | 4 | 1250.2.b.b.1249.3 | 4 | |||
5.4 | even | 2 | 1250.2.a.d.1.2 | 2 | |||
20.19 | odd | 2 | 10000.2.a.a.1.1 | 2 | |||
25.3 | odd | 20 | 250.2.e.b.49.2 | 8 | |||
25.4 | even | 10 | 250.2.d.a.201.1 | 4 | |||
25.6 | even | 5 | 50.2.d.a.11.1 | ✓ | 4 | ||
25.8 | odd | 20 | 250.2.e.b.199.1 | 8 | |||
25.17 | odd | 20 | 250.2.e.b.199.2 | 8 | |||
25.19 | even | 10 | 250.2.d.a.51.1 | 4 | |||
25.21 | even | 5 | 50.2.d.a.41.1 | yes | 4 | ||
25.22 | odd | 20 | 250.2.e.b.49.1 | 8 | |||
75.56 | odd | 10 | 450.2.h.a.361.1 | 4 | |||
75.71 | odd | 10 | 450.2.h.a.91.1 | 4 | |||
100.31 | odd | 10 | 400.2.u.c.161.1 | 4 | |||
100.71 | odd | 10 | 400.2.u.c.241.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.a.11.1 | ✓ | 4 | 25.6 | even | 5 | ||
50.2.d.a.41.1 | yes | 4 | 25.21 | even | 5 | ||
250.2.d.a.51.1 | 4 | 25.19 | even | 10 | |||
250.2.d.a.201.1 | 4 | 25.4 | even | 10 | |||
250.2.e.b.49.1 | 8 | 25.22 | odd | 20 | |||
250.2.e.b.49.2 | 8 | 25.3 | odd | 20 | |||
250.2.e.b.199.1 | 8 | 25.8 | odd | 20 | |||
250.2.e.b.199.2 | 8 | 25.17 | odd | 20 | |||
400.2.u.c.161.1 | 4 | 100.31 | odd | 10 | |||
400.2.u.c.241.1 | 4 | 100.71 | odd | 10 | |||
450.2.h.a.91.1 | 4 | 75.71 | odd | 10 | |||
450.2.h.a.361.1 | 4 | 75.56 | odd | 10 | |||
1250.2.a.a.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1250.2.a.d.1.2 | 2 | 5.4 | even | 2 | |||
1250.2.b.b.1249.2 | 4 | 5.2 | odd | 4 | |||
1250.2.b.b.1249.3 | 4 | 5.3 | odd | 4 | |||
10000.2.a.a.1.1 | 2 | 20.19 | odd | 2 | |||
10000.2.a.n.1.2 | 2 | 4.3 | odd | 2 |