Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.60231 | −1.13300 | −0.566502 | − | 0.824060i | \(-0.691704\pi\) | ||||
−0.566502 | + | 0.824060i | \(0.691704\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.567397 | 0.283699 | ||||||||
\(5\) | −0.489899 | −0.219090 | −0.109545 | − | 0.993982i | \(-0.534939\pi\) | ||||
−0.109545 | + | 0.993982i | \(0.534939\pi\) | |||||||
\(6\) | 1.60231 | 0.654140 | ||||||||
\(7\) | −0.574101 | −0.216990 | −0.108495 | − | 0.994097i | \(-0.534603\pi\) | ||||
−0.108495 | + | 0.994097i | \(0.534603\pi\) | |||||||
\(8\) | 2.29547 | 0.811573 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.784971 | 0.248230 | ||||||||
\(11\) | −0.698667 | −0.210656 | −0.105328 | − | 0.994438i | \(-0.533589\pi\) | ||||
−0.105328 | + | 0.994438i | \(0.533589\pi\) | |||||||
\(12\) | −0.567397 | −0.163793 | ||||||||
\(13\) | 2.26250 | 0.627504 | 0.313752 | − | 0.949505i | \(-0.398414\pi\) | ||||
0.313752 | + | 0.949505i | \(0.398414\pi\) | |||||||
\(14\) | 0.919888 | 0.245850 | ||||||||
\(15\) | 0.489899 | 0.126492 | ||||||||
\(16\) | −4.81285 | −1.20321 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.60231 | −0.377668 | ||||||||
\(19\) | 1.07352 | 0.246282 | 0.123141 | − | 0.992389i | \(-0.460703\pi\) | ||||
0.123141 | + | 0.992389i | \(0.460703\pi\) | |||||||
\(20\) | −0.277968 | −0.0621554 | ||||||||
\(21\) | 0.574101 | 0.125279 | ||||||||
\(22\) | 1.11948 | 0.238674 | ||||||||
\(23\) | −7.79211 | −1.62477 | −0.812384 | − | 0.583123i | \(-0.801831\pi\) | ||||
−0.812384 | + | 0.583123i | \(0.801831\pi\) | |||||||
\(24\) | −2.29547 | −0.468562 | ||||||||
\(25\) | −4.76000 | −0.952000 | ||||||||
\(26\) | −3.62522 | −0.710965 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.325743 | −0.0615597 | ||||||||
\(29\) | 5.05791 | 0.939231 | 0.469616 | − | 0.882871i | \(-0.344393\pi\) | ||||
0.469616 | + | 0.882871i | \(0.344393\pi\) | |||||||
\(30\) | −0.784971 | −0.143315 | ||||||||
\(31\) | 9.16611 | 1.64628 | 0.823141 | − | 0.567838i | \(-0.192220\pi\) | ||||
0.823141 | + | 0.567838i | \(0.192220\pi\) | |||||||
\(32\) | 3.12074 | 0.551674 | ||||||||
\(33\) | 0.698667 | 0.121622 | ||||||||
\(34\) | 1.60231 | 0.274794 | ||||||||
\(35\) | 0.281252 | 0.0475402 | ||||||||
\(36\) | 0.567397 | 0.0945662 | ||||||||
\(37\) | −0.352965 | −0.0580270 | −0.0290135 | − | 0.999579i | \(-0.509237\pi\) | ||||
−0.0290135 | + | 0.999579i | \(0.509237\pi\) | |||||||
\(38\) | −1.72011 | −0.279039 | ||||||||
\(39\) | −2.26250 | −0.362290 | ||||||||
\(40\) | −1.12455 | −0.177807 | ||||||||
\(41\) | 9.93207 | 1.55113 | 0.775564 | − | 0.631269i | \(-0.217466\pi\) | ||||
0.775564 | + | 0.631269i | \(0.217466\pi\) | |||||||
\(42\) | −0.919888 | −0.141942 | ||||||||
\(43\) | 7.78761 | 1.18760 | 0.593800 | − | 0.804613i | \(-0.297627\pi\) | ||||
0.593800 | + | 0.804613i | \(0.297627\pi\) | |||||||
\(44\) | −0.396422 | −0.0597628 | ||||||||
\(45\) | −0.489899 | −0.0730299 | ||||||||
\(46\) | 12.4854 | 1.84087 | ||||||||
\(47\) | 2.72064 | 0.396847 | 0.198423 | − | 0.980116i | \(-0.436418\pi\) | ||||
0.198423 | + | 0.980116i | \(0.436418\pi\) | |||||||
\(48\) | 4.81285 | 0.694676 | ||||||||
\(49\) | −6.67041 | −0.952915 | ||||||||
\(50\) | 7.62699 | 1.07862 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 1.28373 | 0.178022 | ||||||||
\(53\) | −3.40047 | −0.467091 | −0.233546 | − | 0.972346i | \(-0.575033\pi\) | ||||
−0.233546 | + | 0.972346i | \(0.575033\pi\) | |||||||
\(54\) | 1.60231 | 0.218047 | ||||||||
\(55\) | 0.342277 | 0.0461526 | ||||||||
\(56\) | −1.31783 | −0.176103 | ||||||||
\(57\) | −1.07352 | −0.142191 | ||||||||
\(58\) | −8.10435 | −1.06415 | ||||||||
\(59\) | −6.49490 | −0.845564 | −0.422782 | − | 0.906231i | \(-0.638946\pi\) | ||||
−0.422782 | + | 0.906231i | \(0.638946\pi\) | |||||||
\(60\) | 0.277968 | 0.0358855 | ||||||||
\(61\) | −3.39102 | −0.434176 | −0.217088 | − | 0.976152i | \(-0.569656\pi\) | ||||
−0.217088 | + | 0.976152i | \(0.569656\pi\) | |||||||
\(62\) | −14.6869 | −1.86524 | ||||||||
\(63\) | −0.574101 | −0.0723299 | ||||||||
\(64\) | 4.62532 | 0.578165 | ||||||||
\(65\) | −1.10840 | −0.137480 | ||||||||
\(66\) | −1.11948 | −0.137799 | ||||||||
\(67\) | 3.05135 | 0.372781 | 0.186391 | − | 0.982476i | \(-0.440321\pi\) | ||||
0.186391 | + | 0.982476i | \(0.440321\pi\) | |||||||
\(68\) | −0.567397 | −0.0688070 | ||||||||
\(69\) | 7.79211 | 0.938060 | ||||||||
\(70\) | −0.450653 | −0.0538633 | ||||||||
\(71\) | 3.33996 | 0.396381 | 0.198190 | − | 0.980164i | \(-0.436494\pi\) | ||||
0.198190 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(72\) | 2.29547 | 0.270524 | ||||||||
\(73\) | −6.93796 | −0.812027 | −0.406013 | − | 0.913867i | \(-0.633081\pi\) | ||||
−0.406013 | + | 0.913867i | \(0.633081\pi\) | |||||||
\(74\) | 0.565559 | 0.0657449 | ||||||||
\(75\) | 4.76000 | 0.549637 | ||||||||
\(76\) | 0.609112 | 0.0698700 | ||||||||
\(77\) | 0.401106 | 0.0457102 | ||||||||
\(78\) | 3.62522 | 0.410476 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 2.35782 | 0.263612 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −15.9142 | −1.75743 | ||||||||
\(83\) | −11.1415 | −1.22294 | −0.611471 | − | 0.791267i | \(-0.709422\pi\) | ||||
−0.611471 | + | 0.791267i | \(0.709422\pi\) | |||||||
\(84\) | 0.325743 | 0.0355415 | ||||||||
\(85\) | 0.489899 | 0.0531371 | ||||||||
\(86\) | −12.4782 | −1.34555 | ||||||||
\(87\) | −5.05791 | −0.542265 | ||||||||
\(88\) | −1.60377 | −0.170963 | ||||||||
\(89\) | −6.31600 | −0.669494 | −0.334747 | − | 0.942308i | \(-0.608651\pi\) | ||||
−0.334747 | + | 0.942308i | \(0.608651\pi\) | |||||||
\(90\) | 0.784971 | 0.0827432 | ||||||||
\(91\) | −1.29890 | −0.136162 | ||||||||
\(92\) | −4.42122 | −0.460944 | ||||||||
\(93\) | −9.16611 | −0.950481 | ||||||||
\(94\) | −4.35931 | −0.449629 | ||||||||
\(95\) | −0.525917 | −0.0539579 | ||||||||
\(96\) | −3.12074 | −0.318509 | ||||||||
\(97\) | −1.51033 | −0.153351 | −0.0766754 | − | 0.997056i | \(-0.524431\pi\) | ||||
−0.0766754 | + | 0.997056i | \(0.524431\pi\) | |||||||
\(98\) | 10.6881 | 1.07966 | ||||||||
\(99\) | −0.698667 | −0.0702187 | ||||||||
\(100\) | −2.70081 | −0.270081 | ||||||||
\(101\) | −11.9380 | −1.18787 | −0.593936 | − | 0.804512i | \(-0.702427\pi\) | ||||
−0.593936 | + | 0.804512i | \(0.702427\pi\) | |||||||
\(102\) | −1.60231 | −0.158652 | ||||||||
\(103\) | −7.29866 | −0.719158 | −0.359579 | − | 0.933115i | \(-0.617080\pi\) | ||||
−0.359579 | + | 0.933115i | \(0.617080\pi\) | |||||||
\(104\) | 5.19351 | 0.509265 | ||||||||
\(105\) | −0.281252 | −0.0274474 | ||||||||
\(106\) | 5.44861 | 0.529216 | ||||||||
\(107\) | −10.5574 | −1.02062 | −0.510309 | − | 0.859991i | \(-0.670469\pi\) | ||||
−0.510309 | + | 0.859991i | \(0.670469\pi\) | |||||||
\(108\) | −0.567397 | −0.0545978 | ||||||||
\(109\) | 2.02361 | 0.193827 | 0.0969136 | − | 0.995293i | \(-0.469103\pi\) | ||||
0.0969136 | + | 0.995293i | \(0.469103\pi\) | |||||||
\(110\) | −0.548433 | −0.0522911 | ||||||||
\(111\) | 0.352965 | 0.0335019 | ||||||||
\(112\) | 2.76306 | 0.261085 | ||||||||
\(113\) | 0.257584 | 0.0242315 | 0.0121157 | − | 0.999927i | \(-0.496143\pi\) | ||||
0.0121157 | + | 0.999927i | \(0.496143\pi\) | |||||||
\(114\) | 1.72011 | 0.161103 | ||||||||
\(115\) | 3.81735 | 0.355970 | ||||||||
\(116\) | 2.86985 | 0.266458 | ||||||||
\(117\) | 2.26250 | 0.209168 | ||||||||
\(118\) | 10.4068 | 0.958028 | ||||||||
\(119\) | 0.574101 | 0.0526278 | ||||||||
\(120\) | 1.12455 | 0.102657 | ||||||||
\(121\) | −10.5119 | −0.955624 | ||||||||
\(122\) | 5.43347 | 0.491923 | ||||||||
\(123\) | −9.93207 | −0.895544 | ||||||||
\(124\) | 5.20082 | 0.467048 | ||||||||
\(125\) | 4.78142 | 0.427663 | ||||||||
\(126\) | 0.919888 | 0.0819501 | ||||||||
\(127\) | 11.9765 | 1.06275 | 0.531373 | − | 0.847138i | \(-0.321676\pi\) | ||||
0.531373 | + | 0.847138i | \(0.321676\pi\) | |||||||
\(128\) | −13.6527 | −1.20674 | ||||||||
\(129\) | −7.78761 | −0.685661 | ||||||||
\(130\) | 1.77600 | 0.155765 | ||||||||
\(131\) | −12.0690 | −1.05448 | −0.527238 | − | 0.849717i | \(-0.676773\pi\) | ||||
−0.527238 | + | 0.849717i | \(0.676773\pi\) | |||||||
\(132\) | 0.396422 | 0.0345041 | ||||||||
\(133\) | −0.616309 | −0.0534408 | ||||||||
\(134\) | −4.88920 | −0.422363 | ||||||||
\(135\) | 0.489899 | 0.0421638 | ||||||||
\(136\) | −2.29547 | −0.196835 | ||||||||
\(137\) | 15.3158 | 1.30852 | 0.654260 | − | 0.756270i | \(-0.272980\pi\) | ||||
0.654260 | + | 0.756270i | \(0.272980\pi\) | |||||||
\(138\) | −12.4854 | −1.06283 | ||||||||
\(139\) | 17.0014 | 1.44204 | 0.721020 | − | 0.692914i | \(-0.243674\pi\) | ||||
0.721020 | + | 0.692914i | \(0.243674\pi\) | |||||||
\(140\) | 0.159581 | 0.0134871 | ||||||||
\(141\) | −2.72064 | −0.229119 | ||||||||
\(142\) | −5.35166 | −0.449101 | ||||||||
\(143\) | −1.58073 | −0.132188 | ||||||||
\(144\) | −4.81285 | −0.401071 | ||||||||
\(145\) | −2.47787 | −0.205776 | ||||||||
\(146\) | 11.1168 | 0.920029 | ||||||||
\(147\) | 6.67041 | 0.550166 | ||||||||
\(148\) | −0.200271 | −0.0164622 | ||||||||
\(149\) | 5.12625 | 0.419958 | 0.209979 | − | 0.977706i | \(-0.432660\pi\) | ||||
0.209979 | + | 0.977706i | \(0.432660\pi\) | |||||||
\(150\) | −7.62699 | −0.622741 | ||||||||
\(151\) | 17.1238 | 1.39352 | 0.696759 | − | 0.717306i | \(-0.254625\pi\) | ||||
0.696759 | + | 0.717306i | \(0.254625\pi\) | |||||||
\(152\) | 2.46424 | 0.199876 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −0.642696 | −0.0517899 | ||||||||
\(155\) | −4.49047 | −0.360683 | ||||||||
\(156\) | −1.28373 | −0.102781 | ||||||||
\(157\) | 6.71405 | 0.535840 | 0.267920 | − | 0.963441i | \(-0.413664\pi\) | ||||
0.267920 | + | 0.963441i | \(0.413664\pi\) | |||||||
\(158\) | −1.60231 | −0.127473 | ||||||||
\(159\) | 3.40047 | 0.269675 | ||||||||
\(160\) | −1.52885 | −0.120866 | ||||||||
\(161\) | 4.47346 | 0.352558 | ||||||||
\(162\) | −1.60231 | −0.125889 | ||||||||
\(163\) | 16.8836 | 1.32243 | 0.661213 | − | 0.750198i | \(-0.270042\pi\) | ||||
0.661213 | + | 0.750198i | \(0.270042\pi\) | |||||||
\(164\) | 5.63543 | 0.440053 | ||||||||
\(165\) | −0.342277 | −0.0266462 | ||||||||
\(166\) | 17.8522 | 1.38560 | ||||||||
\(167\) | 16.1012 | 1.24595 | 0.622974 | − | 0.782242i | \(-0.285924\pi\) | ||||
0.622974 | + | 0.782242i | \(0.285924\pi\) | |||||||
\(168\) | 1.31783 | 0.101673 | ||||||||
\(169\) | −7.88110 | −0.606239 | ||||||||
\(170\) | −0.784971 | −0.0602045 | ||||||||
\(171\) | 1.07352 | 0.0820941 | ||||||||
\(172\) | 4.41867 | 0.336920 | ||||||||
\(173\) | −4.66812 | −0.354911 | −0.177455 | − | 0.984129i | \(-0.556787\pi\) | ||||
−0.177455 | + | 0.984129i | \(0.556787\pi\) | |||||||
\(174\) | 8.10435 | 0.614389 | ||||||||
\(175\) | 2.73272 | 0.206574 | ||||||||
\(176\) | 3.36258 | 0.253464 | ||||||||
\(177\) | 6.49490 | 0.488187 | ||||||||
\(178\) | 10.1202 | 0.758540 | ||||||||
\(179\) | 11.8916 | 0.888817 | 0.444409 | − | 0.895824i | \(-0.353414\pi\) | ||||
0.444409 | + | 0.895824i | \(0.353414\pi\) | |||||||
\(180\) | −0.277968 | −0.0207185 | ||||||||
\(181\) | 10.8727 | 0.808161 | 0.404080 | − | 0.914723i | \(-0.367592\pi\) | ||||
0.404080 | + | 0.914723i | \(0.367592\pi\) | |||||||
\(182\) | 2.08124 | 0.154272 | ||||||||
\(183\) | 3.39102 | 0.250672 | ||||||||
\(184\) | −17.8866 | −1.31862 | ||||||||
\(185\) | 0.172917 | 0.0127131 | ||||||||
\(186\) | 14.6869 | 1.07690 | ||||||||
\(187\) | 0.698667 | 0.0510916 | ||||||||
\(188\) | 1.54368 | 0.112585 | ||||||||
\(189\) | 0.574101 | 0.0417597 | ||||||||
\(190\) | 0.842682 | 0.0611346 | ||||||||
\(191\) | −22.7980 | −1.64960 | −0.824802 | − | 0.565422i | \(-0.808713\pi\) | ||||
−0.824802 | + | 0.565422i | \(0.808713\pi\) | |||||||
\(192\) | −4.62532 | −0.333804 | ||||||||
\(193\) | −0.849871 | −0.0611751 | −0.0305875 | − | 0.999532i | \(-0.509738\pi\) | ||||
−0.0305875 | + | 0.999532i | \(0.509738\pi\) | |||||||
\(194\) | 2.42002 | 0.173747 | ||||||||
\(195\) | 1.10840 | 0.0793739 | ||||||||
\(196\) | −3.78477 | −0.270341 | ||||||||
\(197\) | −25.4230 | −1.81131 | −0.905657 | − | 0.424012i | \(-0.860622\pi\) | ||||
−0.905657 | + | 0.424012i | \(0.860622\pi\) | |||||||
\(198\) | 1.11948 | 0.0795581 | ||||||||
\(199\) | 20.6740 | 1.46554 | 0.732771 | − | 0.680476i | \(-0.238227\pi\) | ||||
0.732771 | + | 0.680476i | \(0.238227\pi\) | |||||||
\(200\) | −10.9265 | −0.772617 | ||||||||
\(201\) | −3.05135 | −0.215225 | ||||||||
\(202\) | 19.1283 | 1.34586 | ||||||||
\(203\) | −2.90375 | −0.203804 | ||||||||
\(204\) | 0.567397 | 0.0397257 | ||||||||
\(205\) | −4.86571 | −0.339836 | ||||||||
\(206\) | 11.6947 | 0.814809 | ||||||||
\(207\) | −7.79211 | −0.541589 | ||||||||
\(208\) | −10.8891 | −0.755022 | ||||||||
\(209\) | −0.750033 | −0.0518809 | ||||||||
\(210\) | 0.450653 | 0.0310980 | ||||||||
\(211\) | −11.5984 | −0.798467 | −0.399233 | − | 0.916849i | \(-0.630724\pi\) | ||||
−0.399233 | + | 0.916849i | \(0.630724\pi\) | |||||||
\(212\) | −1.92942 | −0.132513 | ||||||||
\(213\) | −3.33996 | −0.228850 | ||||||||
\(214\) | 16.9162 | 1.15637 | ||||||||
\(215\) | −3.81515 | −0.260191 | ||||||||
\(216\) | −2.29547 | −0.156187 | ||||||||
\(217\) | −5.26227 | −0.357226 | ||||||||
\(218\) | −3.24246 | −0.219607 | ||||||||
\(219\) | 6.93796 | 0.468824 | ||||||||
\(220\) | 0.194207 | 0.0130934 | ||||||||
\(221\) | −2.26250 | −0.152192 | ||||||||
\(222\) | −0.565559 | −0.0379578 | ||||||||
\(223\) | −9.20846 | −0.616644 | −0.308322 | − | 0.951282i | \(-0.599767\pi\) | ||||
−0.308322 | + | 0.951282i | \(0.599767\pi\) | |||||||
\(224\) | −1.79162 | −0.119708 | ||||||||
\(225\) | −4.76000 | −0.317333 | ||||||||
\(226\) | −0.412730 | −0.0274544 | ||||||||
\(227\) | −13.9762 | −0.927632 | −0.463816 | − | 0.885931i | \(-0.653520\pi\) | ||||
−0.463816 | + | 0.885931i | \(0.653520\pi\) | |||||||
\(228\) | −0.609112 | −0.0403394 | ||||||||
\(229\) | 23.3438 | 1.54260 | 0.771301 | − | 0.636471i | \(-0.219607\pi\) | ||||
0.771301 | + | 0.636471i | \(0.219607\pi\) | |||||||
\(230\) | −6.11658 | −0.403315 | ||||||||
\(231\) | −0.401106 | −0.0263908 | ||||||||
\(232\) | 11.6103 | 0.762254 | ||||||||
\(233\) | 3.44550 | 0.225722 | 0.112861 | − | 0.993611i | \(-0.463999\pi\) | ||||
0.112861 | + | 0.993611i | \(0.463999\pi\) | |||||||
\(234\) | −3.62522 | −0.236988 | ||||||||
\(235\) | −1.33284 | −0.0869450 | ||||||||
\(236\) | −3.68519 | −0.239885 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −0.919888 | −0.0596275 | ||||||||
\(239\) | 19.8842 | 1.28620 | 0.643100 | − | 0.765782i | \(-0.277648\pi\) | ||||
0.643100 | + | 0.765782i | \(0.277648\pi\) | |||||||
\(240\) | −2.35782 | −0.152196 | ||||||||
\(241\) | −7.29299 | −0.469783 | −0.234891 | − | 0.972022i | \(-0.575473\pi\) | ||||
−0.234891 | + | 0.972022i | \(0.575473\pi\) | |||||||
\(242\) | 16.8433 | 1.08273 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.92406 | −0.123175 | ||||||||
\(245\) | 3.26783 | 0.208774 | ||||||||
\(246\) | 15.9142 | 1.01466 | ||||||||
\(247\) | 2.42884 | 0.154543 | ||||||||
\(248\) | 21.0406 | 1.33608 | ||||||||
\(249\) | 11.1415 | 0.706066 | ||||||||
\(250\) | −7.66131 | −0.484544 | ||||||||
\(251\) | −10.1340 | −0.639655 | −0.319828 | − | 0.947476i | \(-0.603625\pi\) | ||||
−0.319828 | + | 0.947476i | \(0.603625\pi\) | |||||||
\(252\) | −0.325743 | −0.0205199 | ||||||||
\(253\) | 5.44409 | 0.342267 | ||||||||
\(254\) | −19.1901 | −1.20410 | ||||||||
\(255\) | −0.489899 | −0.0306787 | ||||||||
\(256\) | 12.6252 | 0.789073 | ||||||||
\(257\) | 11.2550 | 0.702068 | 0.351034 | − | 0.936363i | \(-0.385830\pi\) | ||||
0.351034 | + | 0.936363i | \(0.385830\pi\) | |||||||
\(258\) | 12.4782 | 0.776856 | ||||||||
\(259\) | 0.202637 | 0.0125913 | ||||||||
\(260\) | −0.628901 | −0.0390028 | ||||||||
\(261\) | 5.05791 | 0.313077 | ||||||||
\(262\) | 19.3383 | 1.19473 | ||||||||
\(263\) | 3.88146 | 0.239341 | 0.119670 | − | 0.992814i | \(-0.461816\pi\) | ||||
0.119670 | + | 0.992814i | \(0.461816\pi\) | |||||||
\(264\) | 1.60377 | 0.0987054 | ||||||||
\(265\) | 1.66589 | 0.102335 | ||||||||
\(266\) | 0.987518 | 0.0605486 | ||||||||
\(267\) | 6.31600 | 0.386533 | ||||||||
\(268\) | 1.73132 | 0.105757 | ||||||||
\(269\) | −15.9238 | −0.970893 | −0.485446 | − | 0.874266i | \(-0.661343\pi\) | ||||
−0.485446 | + | 0.874266i | \(0.661343\pi\) | |||||||
\(270\) | −0.784971 | −0.0477718 | ||||||||
\(271\) | 21.9553 | 1.33369 | 0.666845 | − | 0.745197i | \(-0.267644\pi\) | ||||
0.666845 | + | 0.745197i | \(0.267644\pi\) | |||||||
\(272\) | 4.81285 | 0.291822 | ||||||||
\(273\) | 1.29890 | 0.0786132 | ||||||||
\(274\) | −24.5407 | −1.48256 | ||||||||
\(275\) | 3.32566 | 0.200545 | ||||||||
\(276\) | 4.42122 | 0.266126 | ||||||||
\(277\) | 30.3549 | 1.82385 | 0.911925 | − | 0.410357i | \(-0.134596\pi\) | ||||
0.911925 | + | 0.410357i | \(0.134596\pi\) | |||||||
\(278\) | −27.2415 | −1.63384 | ||||||||
\(279\) | 9.16611 | 0.548760 | ||||||||
\(280\) | 0.645606 | 0.0385823 | ||||||||
\(281\) | 8.60041 | 0.513057 | 0.256529 | − | 0.966537i | \(-0.417421\pi\) | ||||
0.256529 | + | 0.966537i | \(0.417421\pi\) | |||||||
\(282\) | 4.35931 | 0.259593 | ||||||||
\(283\) | 28.4638 | 1.69199 | 0.845997 | − | 0.533187i | \(-0.179006\pi\) | ||||
0.845997 | + | 0.533187i | \(0.179006\pi\) | |||||||
\(284\) | 1.89509 | 0.112453 | ||||||||
\(285\) | 0.525917 | 0.0311526 | ||||||||
\(286\) | 2.53283 | 0.149769 | ||||||||
\(287\) | −5.70201 | −0.336579 | ||||||||
\(288\) | 3.12074 | 0.183891 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 3.97031 | 0.233145 | ||||||||
\(291\) | 1.51033 | 0.0885371 | ||||||||
\(292\) | −3.93658 | −0.230371 | ||||||||
\(293\) | 4.49834 | 0.262796 | 0.131398 | − | 0.991330i | \(-0.458053\pi\) | ||||
0.131398 | + | 0.991330i | \(0.458053\pi\) | |||||||
\(294\) | −10.6881 | −0.623340 | ||||||||
\(295\) | 3.18185 | 0.185254 | ||||||||
\(296\) | −0.810221 | −0.0470932 | ||||||||
\(297\) | 0.698667 | 0.0405408 | ||||||||
\(298\) | −8.21383 | −0.475815 | ||||||||
\(299\) | −17.6296 | −1.01955 | ||||||||
\(300\) | 2.70081 | 0.155931 | ||||||||
\(301\) | −4.47087 | −0.257697 | ||||||||
\(302\) | −27.4377 | −1.57886 | ||||||||
\(303\) | 11.9380 | 0.685819 | ||||||||
\(304\) | −5.16670 | −0.296330 | ||||||||
\(305\) | 1.66126 | 0.0951235 | ||||||||
\(306\) | 1.60231 | 0.0915980 | ||||||||
\(307\) | 4.25804 | 0.243019 | 0.121510 | − | 0.992590i | \(-0.461227\pi\) | ||||
0.121510 | + | 0.992590i | \(0.461227\pi\) | |||||||
\(308\) | 0.227586 | 0.0129679 | ||||||||
\(309\) | 7.29866 | 0.415206 | ||||||||
\(310\) | 7.19513 | 0.408656 | ||||||||
\(311\) | 17.9692 | 1.01894 | 0.509469 | − | 0.860489i | \(-0.329842\pi\) | ||||
0.509469 | + | 0.860489i | \(0.329842\pi\) | |||||||
\(312\) | −5.19351 | −0.294024 | ||||||||
\(313\) | 21.7435 | 1.22902 | 0.614508 | − | 0.788910i | \(-0.289354\pi\) | ||||
0.614508 | + | 0.788910i | \(0.289354\pi\) | |||||||
\(314\) | −10.7580 | −0.607109 | ||||||||
\(315\) | 0.281252 | 0.0158467 | ||||||||
\(316\) | 0.567397 | 0.0319186 | ||||||||
\(317\) | −31.0138 | −1.74191 | −0.870955 | − | 0.491363i | \(-0.836499\pi\) | ||||
−0.870955 | + | 0.491363i | \(0.836499\pi\) | |||||||
\(318\) | −5.44861 | −0.305543 | ||||||||
\(319\) | −3.53380 | −0.197855 | ||||||||
\(320\) | −2.26594 | −0.126670 | ||||||||
\(321\) | 10.5574 | 0.589254 | ||||||||
\(322\) | −7.16787 | −0.399450 | ||||||||
\(323\) | −1.07352 | −0.0597323 | ||||||||
\(324\) | 0.567397 | 0.0315221 | ||||||||
\(325\) | −10.7695 | −0.597384 | ||||||||
\(326\) | −27.0528 | −1.49832 | ||||||||
\(327\) | −2.02361 | −0.111906 | ||||||||
\(328\) | 22.7988 | 1.25885 | ||||||||
\(329\) | −1.56192 | −0.0861116 | ||||||||
\(330\) | 0.548433 | 0.0301903 | ||||||||
\(331\) | 35.6022 | 1.95687 | 0.978436 | − | 0.206548i | \(-0.0662231\pi\) | ||||
0.978436 | + | 0.206548i | \(0.0662231\pi\) | |||||||
\(332\) | −6.32167 | −0.346947 | ||||||||
\(333\) | −0.352965 | −0.0193423 | ||||||||
\(334\) | −25.7991 | −1.41166 | ||||||||
\(335\) | −1.49485 | −0.0816725 | ||||||||
\(336\) | −2.76306 | −0.150738 | ||||||||
\(337\) | −10.8761 | −0.592461 | −0.296230 | − | 0.955117i | \(-0.595730\pi\) | ||||
−0.296230 | + | 0.955117i | \(0.595730\pi\) | |||||||
\(338\) | 12.6280 | 0.686871 | ||||||||
\(339\) | −0.257584 | −0.0139901 | ||||||||
\(340\) | 0.277968 | 0.0150749 | ||||||||
\(341\) | −6.40406 | −0.346799 | ||||||||
\(342\) | −1.72011 | −0.0930130 | ||||||||
\(343\) | 7.84820 | 0.423763 | ||||||||
\(344\) | 17.8763 | 0.963823 | ||||||||
\(345\) | −3.81735 | −0.205519 | ||||||||
\(346\) | 7.47978 | 0.402115 | ||||||||
\(347\) | 10.2697 | 0.551304 | 0.275652 | − | 0.961257i | \(-0.411106\pi\) | ||||
0.275652 | + | 0.961257i | \(0.411106\pi\) | |||||||
\(348\) | −2.86985 | −0.153840 | ||||||||
\(349\) | 18.4409 | 0.987120 | 0.493560 | − | 0.869712i | \(-0.335695\pi\) | ||||
0.493560 | + | 0.869712i | \(0.335695\pi\) | |||||||
\(350\) | −4.37866 | −0.234049 | ||||||||
\(351\) | −2.26250 | −0.120763 | ||||||||
\(352\) | −2.18036 | −0.116213 | ||||||||
\(353\) | 5.30021 | 0.282101 | 0.141051 | − | 0.990002i | \(-0.454952\pi\) | ||||
0.141051 | + | 0.990002i | \(0.454952\pi\) | |||||||
\(354\) | −10.4068 | −0.553118 | ||||||||
\(355\) | −1.63625 | −0.0868429 | ||||||||
\(356\) | −3.58368 | −0.189935 | ||||||||
\(357\) | −0.574101 | −0.0303846 | ||||||||
\(358\) | −19.0540 | −1.00703 | ||||||||
\(359\) | 32.2104 | 1.70000 | 0.849999 | − | 0.526784i | \(-0.176602\pi\) | ||||
0.849999 | + | 0.526784i | \(0.176602\pi\) | |||||||
\(360\) | −1.12455 | −0.0592691 | ||||||||
\(361\) | −17.8476 | −0.939345 | ||||||||
\(362\) | −17.4214 | −0.915650 | ||||||||
\(363\) | 10.5119 | 0.551730 | ||||||||
\(364\) | −0.736994 | −0.0386290 | ||||||||
\(365\) | 3.39890 | 0.177907 | ||||||||
\(366\) | −5.43347 | −0.284012 | ||||||||
\(367\) | −27.3496 | −1.42764 | −0.713818 | − | 0.700331i | \(-0.753036\pi\) | ||||
−0.713818 | + | 0.700331i | \(0.753036\pi\) | |||||||
\(368\) | 37.5023 | 1.95494 | ||||||||
\(369\) | 9.93207 | 0.517043 | ||||||||
\(370\) | −0.277067 | −0.0144040 | ||||||||
\(371\) | 1.95222 | 0.101354 | ||||||||
\(372\) | −5.20082 | −0.269650 | ||||||||
\(373\) | −20.7592 | −1.07487 | −0.537435 | − | 0.843305i | \(-0.680607\pi\) | ||||
−0.537435 | + | 0.843305i | \(0.680607\pi\) | |||||||
\(374\) | −1.11948 | −0.0578870 | ||||||||
\(375\) | −4.78142 | −0.246911 | ||||||||
\(376\) | 6.24516 | 0.322070 | ||||||||
\(377\) | 11.4435 | 0.589371 | ||||||||
\(378\) | −0.919888 | −0.0473139 | ||||||||
\(379\) | 25.8674 | 1.32872 | 0.664359 | − | 0.747414i | \(-0.268705\pi\) | ||||
0.664359 | + | 0.747414i | \(0.268705\pi\) | |||||||
\(380\) | −0.298404 | −0.0153078 | ||||||||
\(381\) | −11.9765 | −0.613576 | ||||||||
\(382\) | 36.5294 | 1.86901 | ||||||||
\(383\) | 32.3795 | 1.65451 | 0.827257 | − | 0.561824i | \(-0.189900\pi\) | ||||
0.827257 | + | 0.561824i | \(0.189900\pi\) | |||||||
\(384\) | 13.6527 | 0.696710 | ||||||||
\(385\) | −0.196501 | −0.0100146 | ||||||||
\(386\) | 1.36176 | 0.0693116 | ||||||||
\(387\) | 7.78761 | 0.395866 | ||||||||
\(388\) | −0.856957 | −0.0435054 | ||||||||
\(389\) | −0.907985 | −0.0460367 | −0.0230183 | − | 0.999735i | \(-0.507328\pi\) | ||||
−0.0230183 | + | 0.999735i | \(0.507328\pi\) | |||||||
\(390\) | −1.77600 | −0.0899310 | ||||||||
\(391\) | 7.79211 | 0.394064 | ||||||||
\(392\) | −15.3117 | −0.773360 | ||||||||
\(393\) | 12.0690 | 0.608803 | ||||||||
\(394\) | 40.7355 | 2.05223 | ||||||||
\(395\) | −0.489899 | −0.0246495 | ||||||||
\(396\) | −0.396422 | −0.0199209 | ||||||||
\(397\) | −18.5764 | −0.932323 | −0.466161 | − | 0.884700i | \(-0.654363\pi\) | ||||
−0.466161 | + | 0.884700i | \(0.654363\pi\) | |||||||
\(398\) | −33.1262 | −1.66046 | ||||||||
\(399\) | 0.616309 | 0.0308540 | ||||||||
\(400\) | 22.9092 | 1.14546 | ||||||||
\(401\) | 0.0418962 | 0.00209219 | 0.00104610 | − | 0.999999i | \(-0.499667\pi\) | ||||
0.00104610 | + | 0.999999i | \(0.499667\pi\) | |||||||
\(402\) | 4.88920 | 0.243851 | ||||||||
\(403\) | 20.7383 | 1.03305 | ||||||||
\(404\) | −6.77357 | −0.336998 | ||||||||
\(405\) | −0.489899 | −0.0243433 | ||||||||
\(406\) | 4.65271 | 0.230910 | ||||||||
\(407\) | 0.246605 | 0.0122238 | ||||||||
\(408\) | 2.29547 | 0.113643 | ||||||||
\(409\) | 27.7478 | 1.37204 | 0.686019 | − | 0.727583i | \(-0.259356\pi\) | ||||
0.686019 | + | 0.727583i | \(0.259356\pi\) | |||||||
\(410\) | 7.79638 | 0.385036 | ||||||||
\(411\) | −15.3158 | −0.755474 | ||||||||
\(412\) | −4.14124 | −0.204024 | ||||||||
\(413\) | 3.72873 | 0.183479 | ||||||||
\(414\) | 12.4854 | 0.613623 | ||||||||
\(415\) | 5.45823 | 0.267934 | ||||||||
\(416\) | 7.06066 | 0.346177 | ||||||||
\(417\) | −17.0014 | −0.832562 | ||||||||
\(418\) | 1.20179 | 0.0587813 | ||||||||
\(419\) | 16.1724 | 0.790074 | 0.395037 | − | 0.918665i | \(-0.370732\pi\) | ||||
0.395037 | + | 0.918665i | \(0.370732\pi\) | |||||||
\(420\) | −0.159581 | −0.00778678 | ||||||||
\(421\) | 16.4390 | 0.801190 | 0.400595 | − | 0.916255i | \(-0.368803\pi\) | ||||
0.400595 | + | 0.916255i | \(0.368803\pi\) | |||||||
\(422\) | 18.5842 | 0.904666 | ||||||||
\(423\) | 2.72064 | 0.132282 | ||||||||
\(424\) | −7.80570 | −0.379078 | ||||||||
\(425\) | 4.76000 | 0.230894 | ||||||||
\(426\) | 5.35166 | 0.259289 | ||||||||
\(427\) | 1.94679 | 0.0942117 | ||||||||
\(428\) | −5.99022 | −0.289548 | ||||||||
\(429\) | 1.58073 | 0.0763185 | ||||||||
\(430\) | 6.11305 | 0.294797 | ||||||||
\(431\) | −16.5452 | −0.796956 | −0.398478 | − | 0.917178i | \(-0.630462\pi\) | ||||
−0.398478 | + | 0.917178i | \(0.630462\pi\) | |||||||
\(432\) | 4.81285 | 0.231559 | ||||||||
\(433\) | 2.68854 | 0.129203 | 0.0646016 | − | 0.997911i | \(-0.479422\pi\) | ||||
0.0646016 | + | 0.997911i | \(0.479422\pi\) | |||||||
\(434\) | 8.43179 | 0.404739 | ||||||||
\(435\) | 2.47787 | 0.118805 | ||||||||
\(436\) | 1.14819 | 0.0549885 | ||||||||
\(437\) | −8.36499 | −0.400152 | ||||||||
\(438\) | −11.1168 | −0.531179 | ||||||||
\(439\) | −39.4729 | −1.88394 | −0.941970 | − | 0.335696i | \(-0.891028\pi\) | ||||
−0.941970 | + | 0.335696i | \(0.891028\pi\) | |||||||
\(440\) | 0.785687 | 0.0374562 | ||||||||
\(441\) | −6.67041 | −0.317638 | ||||||||
\(442\) | 3.62522 | 0.172434 | ||||||||
\(443\) | 8.90882 | 0.423271 | 0.211635 | − | 0.977349i | \(-0.432121\pi\) | ||||
0.211635 | + | 0.977349i | \(0.432121\pi\) | |||||||
\(444\) | 0.200271 | 0.00950445 | ||||||||
\(445\) | 3.09420 | 0.146679 | ||||||||
\(446\) | 14.7548 | 0.698660 | ||||||||
\(447\) | −5.12625 | −0.242463 | ||||||||
\(448\) | −2.65540 | −0.125456 | ||||||||
\(449\) | 6.53782 | 0.308539 | 0.154269 | − | 0.988029i | \(-0.450698\pi\) | ||||
0.154269 | + | 0.988029i | \(0.450698\pi\) | |||||||
\(450\) | 7.62699 | 0.359540 | ||||||||
\(451\) | −6.93921 | −0.326755 | ||||||||
\(452\) | 0.146153 | 0.00687444 | ||||||||
\(453\) | −17.1238 | −0.804547 | ||||||||
\(454\) | 22.3942 | 1.05101 | ||||||||
\(455\) | 0.636332 | 0.0298317 | ||||||||
\(456\) | −2.46424 | −0.115398 | ||||||||
\(457\) | −3.87714 | −0.181365 | −0.0906824 | − | 0.995880i | \(-0.528905\pi\) | ||||
−0.0906824 | + | 0.995880i | \(0.528905\pi\) | |||||||
\(458\) | −37.4040 | −1.74777 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 2.16595 | 0.100988 | ||||||||
\(461\) | 4.35167 | 0.202678 | 0.101339 | − | 0.994852i | \(-0.467687\pi\) | ||||
0.101339 | + | 0.994852i | \(0.467687\pi\) | |||||||
\(462\) | 0.642696 | 0.0299009 | ||||||||
\(463\) | 30.2355 | 1.40516 | 0.702582 | − | 0.711603i | \(-0.252030\pi\) | ||||
0.702582 | + | 0.711603i | \(0.252030\pi\) | |||||||
\(464\) | −24.3430 | −1.13010 | ||||||||
\(465\) | 4.49047 | 0.208241 | ||||||||
\(466\) | −5.52075 | −0.255744 | ||||||||
\(467\) | 34.5291 | 1.59781 | 0.798907 | − | 0.601454i | \(-0.205412\pi\) | ||||
0.798907 | + | 0.601454i | \(0.205412\pi\) | |||||||
\(468\) | 1.28373 | 0.0593407 | ||||||||
\(469\) | −1.75178 | −0.0808897 | ||||||||
\(470\) | 2.13563 | 0.0985090 | ||||||||
\(471\) | −6.71405 | −0.309367 | ||||||||
\(472\) | −14.9089 | −0.686237 | ||||||||
\(473\) | −5.44095 | −0.250175 | ||||||||
\(474\) | 1.60231 | 0.0735965 | ||||||||
\(475\) | −5.10995 | −0.234461 | ||||||||
\(476\) | 0.325743 | 0.0149304 | ||||||||
\(477\) | −3.40047 | −0.155697 | ||||||||
\(478\) | −31.8606 | −1.45727 | ||||||||
\(479\) | −19.6477 | −0.897728 | −0.448864 | − | 0.893600i | \(-0.648171\pi\) | ||||
−0.448864 | + | 0.893600i | \(0.648171\pi\) | |||||||
\(480\) | 1.52885 | 0.0697820 | ||||||||
\(481\) | −0.798582 | −0.0364122 | ||||||||
\(482\) | 11.6856 | 0.532266 | ||||||||
\(483\) | −4.47346 | −0.203549 | ||||||||
\(484\) | −5.96440 | −0.271109 | ||||||||
\(485\) | 0.739910 | 0.0335976 | ||||||||
\(486\) | 1.60231 | 0.0726823 | ||||||||
\(487\) | 21.2907 | 0.964775 | 0.482387 | − | 0.875958i | \(-0.339770\pi\) | ||||
0.482387 | + | 0.875958i | \(0.339770\pi\) | |||||||
\(488\) | −7.78400 | −0.352365 | ||||||||
\(489\) | −16.8836 | −0.763504 | ||||||||
\(490\) | −5.23608 | −0.236542 | ||||||||
\(491\) | −32.7613 | −1.47850 | −0.739248 | − | 0.673433i | \(-0.764819\pi\) | ||||
−0.739248 | + | 0.673433i | \(0.764819\pi\) | |||||||
\(492\) | −5.63543 | −0.254065 | ||||||||
\(493\) | −5.05791 | −0.227797 | ||||||||
\(494\) | −3.89175 | −0.175098 | ||||||||
\(495\) | 0.342277 | 0.0153842 | ||||||||
\(496\) | −44.1151 | −1.98083 | ||||||||
\(497\) | −1.91748 | −0.0860106 | ||||||||
\(498\) | −17.8522 | −0.799976 | ||||||||
\(499\) | −3.55771 | −0.159265 | −0.0796326 | − | 0.996824i | \(-0.525375\pi\) | ||||
−0.0796326 | + | 0.996824i | \(0.525375\pi\) | |||||||
\(500\) | 2.71296 | 0.121327 | ||||||||
\(501\) | −16.1012 | −0.719349 | ||||||||
\(502\) | 16.2379 | 0.724732 | ||||||||
\(503\) | −36.8868 | −1.64470 | −0.822350 | − | 0.568981i | \(-0.807338\pi\) | ||||
−0.822350 | + | 0.568981i | \(0.807338\pi\) | |||||||
\(504\) | −1.31783 | −0.0587010 | ||||||||
\(505\) | 5.84841 | 0.260251 | ||||||||
\(506\) | −8.72313 | −0.387790 | ||||||||
\(507\) | 7.88110 | 0.350012 | ||||||||
\(508\) | 6.79545 | 0.301499 | ||||||||
\(509\) | 34.0191 | 1.50787 | 0.753936 | − | 0.656948i | \(-0.228153\pi\) | ||||
0.753936 | + | 0.656948i | \(0.228153\pi\) | |||||||
\(510\) | 0.784971 | 0.0347591 | ||||||||
\(511\) | 3.98309 | 0.176201 | ||||||||
\(512\) | 7.07591 | 0.312714 | ||||||||
\(513\) | −1.07352 | −0.0473971 | ||||||||
\(514\) | −18.0340 | −0.795447 | ||||||||
\(515\) | 3.57561 | 0.157560 | ||||||||
\(516\) | −4.41867 | −0.194521 | ||||||||
\(517\) | −1.90082 | −0.0835982 | ||||||||
\(518\) | −0.324688 | −0.0142660 | ||||||||
\(519\) | 4.66812 | 0.204908 | ||||||||
\(520\) | −2.54430 | −0.111575 | ||||||||
\(521\) | −12.6791 | −0.555482 | −0.277741 | − | 0.960656i | \(-0.589586\pi\) | ||||
−0.277741 | + | 0.960656i | \(0.589586\pi\) | |||||||
\(522\) | −8.10435 | −0.354718 | ||||||||
\(523\) | −14.3810 | −0.628839 | −0.314420 | − | 0.949284i | \(-0.601810\pi\) | ||||
−0.314420 | + | 0.949284i | \(0.601810\pi\) | |||||||
\(524\) | −6.84794 | −0.299154 | ||||||||
\(525\) | −2.73272 | −0.119266 | ||||||||
\(526\) | −6.21929 | −0.271174 | ||||||||
\(527\) | −9.16611 | −0.399282 | ||||||||
\(528\) | −3.36258 | −0.146338 | ||||||||
\(529\) | 37.7170 | 1.63987 | ||||||||
\(530\) | −2.66927 | −0.115946 | ||||||||
\(531\) | −6.49490 | −0.281855 | ||||||||
\(532\) | −0.349692 | −0.0151611 | ||||||||
\(533\) | 22.4713 | 0.973339 | ||||||||
\(534\) | −10.1202 | −0.437943 | ||||||||
\(535\) | 5.17205 | 0.223607 | ||||||||
\(536\) | 7.00428 | 0.302539 | ||||||||
\(537\) | −11.8916 | −0.513159 | ||||||||
\(538\) | 25.5149 | 1.10003 | ||||||||
\(539\) | 4.66040 | 0.200737 | ||||||||
\(540\) | 0.277968 | 0.0119618 | ||||||||
\(541\) | −2.38103 | −0.102368 | −0.0511842 | − | 0.998689i | \(-0.516300\pi\) | ||||
−0.0511842 | + | 0.998689i | \(0.516300\pi\) | |||||||
\(542\) | −35.1792 | −1.51108 | ||||||||
\(543\) | −10.8727 | −0.466592 | ||||||||
\(544\) | −3.12074 | −0.133800 | ||||||||
\(545\) | −0.991368 | −0.0424655 | ||||||||
\(546\) | −2.08124 | −0.0890690 | ||||||||
\(547\) | −18.1173 | −0.774640 | −0.387320 | − | 0.921945i | \(-0.626599\pi\) | ||||
−0.387320 | + | 0.921945i | \(0.626599\pi\) | |||||||
\(548\) | 8.69016 | 0.371225 | ||||||||
\(549\) | −3.39102 | −0.144725 | ||||||||
\(550\) | −5.32873 | −0.227218 | ||||||||
\(551\) | 5.42977 | 0.231316 | ||||||||
\(552\) | 17.8866 | 0.761304 | ||||||||
\(553\) | −0.574101 | −0.0244133 | ||||||||
\(554\) | −48.6380 | −2.06643 | ||||||||
\(555\) | −0.172917 | −0.00733993 | ||||||||
\(556\) | 9.64654 | 0.409105 | ||||||||
\(557\) | 31.9345 | 1.35311 | 0.676555 | − | 0.736392i | \(-0.263472\pi\) | ||||
0.676555 | + | 0.736392i | \(0.263472\pi\) | |||||||
\(558\) | −14.6869 | −0.621748 | ||||||||
\(559\) | 17.6195 | 0.745223 | ||||||||
\(560\) | −1.35362 | −0.0572011 | ||||||||
\(561\) | −0.698667 | −0.0294978 | ||||||||
\(562\) | −13.7805 | −0.581296 | ||||||||
\(563\) | 12.1716 | 0.512970 | 0.256485 | − | 0.966548i | \(-0.417436\pi\) | ||||
0.256485 | + | 0.966548i | \(0.417436\pi\) | |||||||
\(564\) | −1.54368 | −0.0650008 | ||||||||
\(565\) | −0.126190 | −0.00530887 | ||||||||
\(566\) | −45.6078 | −1.91704 | ||||||||
\(567\) | −0.574101 | −0.0241100 | ||||||||
\(568\) | 7.66680 | 0.321692 | ||||||||
\(569\) | −1.16814 | −0.0489710 | −0.0244855 | − | 0.999700i | \(-0.507795\pi\) | ||||
−0.0244855 | + | 0.999700i | \(0.507795\pi\) | |||||||
\(570\) | −0.842682 | −0.0352961 | ||||||||
\(571\) | −4.92214 | −0.205985 | −0.102993 | − | 0.994682i | \(-0.532842\pi\) | ||||
−0.102993 | + | 0.994682i | \(0.532842\pi\) | |||||||
\(572\) | −0.896904 | −0.0375014 | ||||||||
\(573\) | 22.7980 | 0.952399 | ||||||||
\(574\) | 9.13639 | 0.381345 | ||||||||
\(575\) | 37.0904 | 1.54678 | ||||||||
\(576\) | 4.62532 | 0.192722 | ||||||||
\(577\) | −2.56160 | −0.106641 | −0.0533205 | − | 0.998577i | \(-0.516980\pi\) | ||||
−0.0533205 | + | 0.998577i | \(0.516980\pi\) | |||||||
\(578\) | −1.60231 | −0.0666473 | ||||||||
\(579\) | 0.849871 | 0.0353194 | ||||||||
\(580\) | −1.40594 | −0.0583783 | ||||||||
\(581\) | 6.39637 | 0.265366 | ||||||||
\(582\) | −2.42002 | −0.100313 | ||||||||
\(583\) | 2.37580 | 0.0983956 | ||||||||
\(584\) | −15.9259 | −0.659018 | ||||||||
\(585\) | −1.10840 | −0.0458266 | ||||||||
\(586\) | −7.20773 | −0.297749 | ||||||||
\(587\) | 29.4450 | 1.21533 | 0.607663 | − | 0.794195i | \(-0.292107\pi\) | ||||
0.607663 | + | 0.794195i | \(0.292107\pi\) | |||||||
\(588\) | 3.78477 | 0.156081 | ||||||||
\(589\) | 9.84000 | 0.405450 | ||||||||
\(590\) | −5.09831 | −0.209894 | ||||||||
\(591\) | 25.4230 | 1.04576 | ||||||||
\(592\) | 1.69877 | 0.0698189 | ||||||||
\(593\) | −2.63492 | −0.108203 | −0.0541015 | − | 0.998535i | \(-0.517229\pi\) | ||||
−0.0541015 | + | 0.998535i | \(0.517229\pi\) | |||||||
\(594\) | −1.11948 | −0.0459329 | ||||||||
\(595\) | −0.281252 | −0.0115302 | ||||||||
\(596\) | 2.90862 | 0.119142 | ||||||||
\(597\) | −20.6740 | −0.846131 | ||||||||
\(598\) | 28.2481 | 1.15515 | ||||||||
\(599\) | 11.2767 | 0.460754 | 0.230377 | − | 0.973101i | \(-0.426004\pi\) | ||||
0.230377 | + | 0.973101i | \(0.426004\pi\) | |||||||
\(600\) | 10.9265 | 0.446071 | ||||||||
\(601\) | −17.2047 | −0.701793 | −0.350896 | − | 0.936414i | \(-0.614123\pi\) | ||||
−0.350896 | + | 0.936414i | \(0.614123\pi\) | |||||||
\(602\) | 7.16373 | 0.291972 | ||||||||
\(603\) | 3.05135 | 0.124260 | ||||||||
\(604\) | 9.71601 | 0.395339 | ||||||||
\(605\) | 5.14976 | 0.209367 | ||||||||
\(606\) | −19.1283 | −0.777035 | ||||||||
\(607\) | −4.81057 | −0.195255 | −0.0976275 | − | 0.995223i | \(-0.531125\pi\) | ||||
−0.0976275 | + | 0.995223i | \(0.531125\pi\) | |||||||
\(608\) | 3.35017 | 0.135867 | ||||||||
\(609\) | 2.90375 | 0.117666 | ||||||||
\(610\) | −2.66185 | −0.107775 | ||||||||
\(611\) | 6.15545 | 0.249023 | ||||||||
\(612\) | −0.567397 | −0.0229357 | ||||||||
\(613\) | 35.0556 | 1.41588 | 0.707941 | − | 0.706272i | \(-0.249624\pi\) | ||||
0.707941 | + | 0.706272i | \(0.249624\pi\) | |||||||
\(614\) | −6.82270 | −0.275342 | ||||||||
\(615\) | 4.86571 | 0.196205 | ||||||||
\(616\) | 0.920728 | 0.0370972 | ||||||||
\(617\) | 37.0697 | 1.49237 | 0.746184 | − | 0.665739i | \(-0.231884\pi\) | ||||
0.746184 | + | 0.665739i | \(0.231884\pi\) | |||||||
\(618\) | −11.6947 | −0.470430 | ||||||||
\(619\) | −34.6064 | −1.39095 | −0.695474 | − | 0.718551i | \(-0.744805\pi\) | ||||
−0.695474 | + | 0.718551i | \(0.744805\pi\) | |||||||
\(620\) | −2.54788 | −0.102325 | ||||||||
\(621\) | 7.79211 | 0.312687 | ||||||||
\(622\) | −28.7922 | −1.15446 | ||||||||
\(623\) | 3.62602 | 0.145273 | ||||||||
\(624\) | 10.8891 | 0.435912 | ||||||||
\(625\) | 21.4576 | 0.858303 | ||||||||
\(626\) | −34.8399 | −1.39248 | ||||||||
\(627\) | 0.750033 | 0.0299534 | ||||||||
\(628\) | 3.80953 | 0.152017 | ||||||||
\(629\) | 0.352965 | 0.0140736 | ||||||||
\(630\) | −0.450653 | −0.0179544 | ||||||||
\(631\) | 45.6281 | 1.81643 | 0.908214 | − | 0.418506i | \(-0.137446\pi\) | ||||
0.908214 | + | 0.418506i | \(0.137446\pi\) | |||||||
\(632\) | 2.29547 | 0.0913090 | ||||||||
\(633\) | 11.5984 | 0.460995 | ||||||||
\(634\) | 49.6938 | 1.97359 | ||||||||
\(635\) | −5.86730 | −0.232837 | ||||||||
\(636\) | 1.92942 | 0.0765064 | ||||||||
\(637\) | −15.0918 | −0.597958 | ||||||||
\(638\) | 5.66224 | 0.224170 | ||||||||
\(639\) | 3.33996 | 0.132127 | ||||||||
\(640\) | 6.68844 | 0.264384 | ||||||||
\(641\) | 14.8843 | 0.587895 | 0.293948 | − | 0.955822i | \(-0.405031\pi\) | ||||
0.293948 | + | 0.955822i | \(0.405031\pi\) | |||||||
\(642\) | −16.9162 | −0.667628 | ||||||||
\(643\) | −10.4041 | −0.410298 | −0.205149 | − | 0.978731i | \(-0.565768\pi\) | ||||
−0.205149 | + | 0.978731i | \(0.565768\pi\) | |||||||
\(644\) | 2.53823 | 0.100020 | ||||||||
\(645\) | 3.81515 | 0.150221 | ||||||||
\(646\) | 1.72011 | 0.0676769 | ||||||||
\(647\) | −24.1055 | −0.947686 | −0.473843 | − | 0.880609i | \(-0.657133\pi\) | ||||
−0.473843 | + | 0.880609i | \(0.657133\pi\) | |||||||
\(648\) | 2.29547 | 0.0901747 | ||||||||
\(649\) | 4.53778 | 0.178123 | ||||||||
\(650\) | 17.2561 | 0.676838 | ||||||||
\(651\) | 5.26227 | 0.206245 | ||||||||
\(652\) | 9.57971 | 0.375171 | ||||||||
\(653\) | 21.4039 | 0.837599 | 0.418799 | − | 0.908079i | \(-0.362451\pi\) | ||||
0.418799 | + | 0.908079i | \(0.362451\pi\) | |||||||
\(654\) | 3.24246 | 0.126790 | ||||||||
\(655\) | 5.91262 | 0.231025 | ||||||||
\(656\) | −47.8016 | −1.86634 | ||||||||
\(657\) | −6.93796 | −0.270676 | ||||||||
\(658\) | 2.50269 | 0.0975648 | ||||||||
\(659\) | 18.7219 | 0.729300 | 0.364650 | − | 0.931145i | \(-0.381189\pi\) | ||||
0.364650 | + | 0.931145i | \(0.381189\pi\) | |||||||
\(660\) | −0.194207 | −0.00755949 | ||||||||
\(661\) | 33.8495 | 1.31659 | 0.658297 | − | 0.752758i | \(-0.271277\pi\) | ||||
0.658297 | + | 0.752758i | \(0.271277\pi\) | |||||||
\(662\) | −57.0457 | −2.21715 | ||||||||
\(663\) | 2.26250 | 0.0878682 | ||||||||
\(664\) | −25.5751 | −0.992506 | ||||||||
\(665\) | 0.301929 | 0.0117083 | ||||||||
\(666\) | 0.565559 | 0.0219150 | ||||||||
\(667\) | −39.4118 | −1.52603 | ||||||||
\(668\) | 9.13578 | 0.353474 | ||||||||
\(669\) | 9.20846 | 0.356019 | ||||||||
\(670\) | 2.39522 | 0.0925353 | ||||||||
\(671\) | 2.36920 | 0.0914618 | ||||||||
\(672\) | 1.79162 | 0.0691132 | ||||||||
\(673\) | −27.9586 | −1.07773 | −0.538863 | − | 0.842393i | \(-0.681146\pi\) | ||||
−0.538863 | + | 0.842393i | \(0.681146\pi\) | |||||||
\(674\) | 17.4269 | 0.671260 | ||||||||
\(675\) | 4.76000 | 0.183212 | ||||||||
\(676\) | −4.47171 | −0.171989 | ||||||||
\(677\) | −23.1635 | −0.890246 | −0.445123 | − | 0.895469i | \(-0.646840\pi\) | ||||
−0.445123 | + | 0.895469i | \(0.646840\pi\) | |||||||
\(678\) | 0.412730 | 0.0158508 | ||||||||
\(679\) | 0.867082 | 0.0332755 | ||||||||
\(680\) | 1.12455 | 0.0431246 | ||||||||
\(681\) | 13.9762 | 0.535569 | ||||||||
\(682\) | 10.2613 | 0.392925 | ||||||||
\(683\) | −5.61775 | −0.214957 | −0.107479 | − | 0.994207i | \(-0.534278\pi\) | ||||
−0.107479 | + | 0.994207i | \(0.534278\pi\) | |||||||
\(684\) | 0.609112 | 0.0232900 | ||||||||
\(685\) | −7.50322 | −0.286683 | ||||||||
\(686\) | −12.5752 | −0.480125 | ||||||||
\(687\) | −23.3438 | −0.890621 | ||||||||
\(688\) | −37.4806 | −1.42894 | ||||||||
\(689\) | −7.69357 | −0.293102 | ||||||||
\(690\) | 6.11658 | 0.232854 | ||||||||
\(691\) | 18.5513 | 0.705725 | 0.352862 | − | 0.935675i | \(-0.385208\pi\) | ||||
0.352862 | + | 0.935675i | \(0.385208\pi\) | |||||||
\(692\) | −2.64868 | −0.100688 | ||||||||
\(693\) | 0.401106 | 0.0152367 | ||||||||
\(694\) | −16.4552 | −0.624630 | ||||||||
\(695\) | −8.32898 | −0.315936 | ||||||||
\(696\) | −11.6103 | −0.440088 | ||||||||
\(697\) | −9.93207 | −0.376204 | ||||||||
\(698\) | −29.5481 | −1.11841 | ||||||||
\(699\) | −3.44550 | −0.130321 | ||||||||
\(700\) | 1.55054 | 0.0586048 | ||||||||
\(701\) | 11.7218 | 0.442728 | 0.221364 | − | 0.975191i | \(-0.428949\pi\) | ||||
0.221364 | + | 0.975191i | \(0.428949\pi\) | |||||||
\(702\) | 3.62522 | 0.136825 | ||||||||
\(703\) | −0.378915 | −0.0142910 | ||||||||
\(704\) | −3.23156 | −0.121794 | ||||||||
\(705\) | 1.33284 | 0.0501977 | ||||||||
\(706\) | −8.49257 | −0.319622 | ||||||||
\(707\) | 6.85360 | 0.257756 | ||||||||
\(708\) | 3.68519 | 0.138498 | ||||||||
\(709\) | 18.9333 | 0.711054 | 0.355527 | − | 0.934666i | \(-0.384301\pi\) | ||||
0.355527 | + | 0.934666i | \(0.384301\pi\) | |||||||
\(710\) | 2.62177 | 0.0983934 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −14.4982 | −0.543343 | ||||||||
\(713\) | −71.4233 | −2.67482 | ||||||||
\(714\) | 0.919888 | 0.0344259 | ||||||||
\(715\) | 0.774401 | 0.0289609 | ||||||||
\(716\) | 6.74724 | 0.252156 | ||||||||
\(717\) | −19.8842 | −0.742588 | ||||||||
\(718\) | −51.6110 | −1.92611 | ||||||||
\(719\) | 11.4781 | 0.428061 | 0.214030 | − | 0.976827i | \(-0.431341\pi\) | ||||
0.214030 | + | 0.976827i | \(0.431341\pi\) | |||||||
\(720\) | 2.35782 | 0.0878706 | ||||||||
\(721\) | 4.19017 | 0.156050 | ||||||||
\(722\) | 28.5973 | 1.06428 | ||||||||
\(723\) | 7.29299 | 0.271229 | ||||||||
\(724\) | 6.16913 | 0.229274 | ||||||||
\(725\) | −24.0757 | −0.894148 | ||||||||
\(726\) | −16.8433 | −0.625112 | ||||||||
\(727\) | 38.8740 | 1.44176 | 0.720879 | − | 0.693061i | \(-0.243738\pi\) | ||||
0.720879 | + | 0.693061i | \(0.243738\pi\) | |||||||
\(728\) | −2.98160 | −0.110505 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.44609 | −0.201569 | ||||||||
\(731\) | −7.78761 | −0.288035 | ||||||||
\(732\) | 1.92406 | 0.0711151 | ||||||||
\(733\) | −15.8870 | −0.586800 | −0.293400 | − | 0.955990i | \(-0.594787\pi\) | ||||
−0.293400 | + | 0.955990i | \(0.594787\pi\) | |||||||
\(734\) | 43.8225 | 1.61752 | ||||||||
\(735\) | −3.26783 | −0.120536 | ||||||||
\(736\) | −24.3171 | −0.896341 | ||||||||
\(737\) | −2.13188 | −0.0785286 | ||||||||
\(738\) | −15.9142 | −0.585812 | ||||||||
\(739\) | 25.8495 | 0.950889 | 0.475445 | − | 0.879746i | \(-0.342287\pi\) | ||||
0.475445 | + | 0.879746i | \(0.342287\pi\) | |||||||
\(740\) | 0.0981127 | 0.00360670 | ||||||||
\(741\) | −2.42884 | −0.0892256 | ||||||||
\(742\) | −3.12805 | −0.114835 | ||||||||
\(743\) | 35.0359 | 1.28534 | 0.642671 | − | 0.766142i | \(-0.277826\pi\) | ||||
0.642671 | + | 0.766142i | \(0.277826\pi\) | |||||||
\(744\) | −21.0406 | −0.771384 | ||||||||
\(745\) | −2.51134 | −0.0920086 | ||||||||
\(746\) | 33.2626 | 1.21783 | ||||||||
\(747\) | −11.1415 | −0.407647 | ||||||||
\(748\) | 0.396422 | 0.0144946 | ||||||||
\(749\) | 6.06099 | 0.221464 | ||||||||
\(750\) | 7.66131 | 0.279752 | ||||||||
\(751\) | 22.2508 | 0.811944 | 0.405972 | − | 0.913885i | \(-0.366933\pi\) | ||||
0.405972 | + | 0.913885i | \(0.366933\pi\) | |||||||
\(752\) | −13.0941 | −0.477491 | ||||||||
\(753\) | 10.1340 | 0.369305 | ||||||||
\(754\) | −18.3361 | −0.667760 | ||||||||
\(755\) | −8.38895 | −0.305305 | ||||||||
\(756\) | 0.325743 | 0.0118472 | ||||||||
\(757\) | −54.7133 | −1.98859 | −0.994295 | − | 0.106669i | \(-0.965981\pi\) | ||||
−0.994295 | + | 0.106669i | \(0.965981\pi\) | |||||||
\(758\) | −41.4475 | −1.50544 | ||||||||
\(759\) | −5.44409 | −0.197608 | ||||||||
\(760\) | −1.20723 | −0.0437908 | ||||||||
\(761\) | 22.0158 | 0.798073 | 0.399036 | − | 0.916935i | \(-0.369345\pi\) | ||||
0.399036 | + | 0.916935i | \(0.369345\pi\) | |||||||
\(762\) | 19.1901 | 0.695185 | ||||||||
\(763\) | −1.16176 | −0.0420585 | ||||||||
\(764\) | −12.9355 | −0.467990 | ||||||||
\(765\) | 0.489899 | 0.0177124 | ||||||||
\(766\) | −51.8819 | −1.87457 | ||||||||
\(767\) | −14.6947 | −0.530595 | ||||||||
\(768\) | −12.6252 | −0.455572 | ||||||||
\(769\) | 18.0810 | 0.652017 | 0.326008 | − | 0.945367i | \(-0.394296\pi\) | ||||
0.326008 | + | 0.945367i | \(0.394296\pi\) | |||||||
\(770\) | 0.314856 | 0.0113466 | ||||||||
\(771\) | −11.2550 | −0.405339 | ||||||||
\(772\) | −0.482214 | −0.0173553 | ||||||||
\(773\) | 12.6102 | 0.453557 | 0.226779 | − | 0.973946i | \(-0.427181\pi\) | ||||
0.226779 | + | 0.973946i | \(0.427181\pi\) | |||||||
\(774\) | −12.4782 | −0.448518 | ||||||||
\(775\) | −43.6306 | −1.56726 | ||||||||
\(776\) | −3.46692 | −0.124455 | ||||||||
\(777\) | −0.202637 | −0.00726958 | ||||||||
\(778\) | 1.45487 | 0.0521597 | ||||||||
\(779\) | 10.6623 | 0.382016 | ||||||||
\(780\) | 0.628901 | 0.0225183 | ||||||||
\(781\) | −2.33352 | −0.0835000 | ||||||||
\(782\) | −12.4854 | −0.446476 | ||||||||
\(783\) | −5.05791 | −0.180755 | ||||||||
\(784\) | 32.1037 | 1.14656 | ||||||||
\(785\) | −3.28921 | −0.117397 | ||||||||
\(786\) | −19.3383 | −0.689776 | ||||||||
\(787\) | 52.8292 | 1.88316 | 0.941578 | − | 0.336795i | \(-0.109343\pi\) | ||||
0.941578 | + | 0.336795i | \(0.109343\pi\) | |||||||
\(788\) | −14.4249 | −0.513867 | ||||||||
\(789\) | −3.88146 | −0.138183 | ||||||||
\(790\) | 0.784971 | 0.0279280 | ||||||||
\(791\) | −0.147879 | −0.00525798 | ||||||||
\(792\) | −1.60377 | −0.0569876 | ||||||||
\(793\) | −7.67218 | −0.272447 | ||||||||
\(794\) | 29.7652 | 1.05633 | ||||||||
\(795\) | −1.66589 | −0.0590831 | ||||||||
\(796\) | 11.7304 | 0.415772 | ||||||||
\(797\) | −25.2909 | −0.895850 | −0.447925 | − | 0.894071i | \(-0.647837\pi\) | ||||
−0.447925 | + | 0.894071i | \(0.647837\pi\) | |||||||
\(798\) | −0.987518 | −0.0349578 | ||||||||
\(799\) | −2.72064 | −0.0962494 | ||||||||
\(800\) | −14.8547 | −0.525193 | ||||||||
\(801\) | −6.31600 | −0.223165 | ||||||||
\(802\) | −0.0671306 | −0.00237047 | ||||||||
\(803\) | 4.84732 | 0.171058 | ||||||||
\(804\) | −1.73132 | −0.0610591 | ||||||||
\(805\) | −2.19155 | −0.0772418 | ||||||||
\(806\) | −33.2292 | −1.17045 | ||||||||
\(807\) | 15.9238 | 0.560545 | ||||||||
\(808\) | −27.4033 | −0.964045 | ||||||||
\(809\) | 15.4002 | 0.541443 | 0.270722 | − | 0.962658i | \(-0.412738\pi\) | ||||
0.270722 | + | 0.962658i | \(0.412738\pi\) | |||||||
\(810\) | 0.784971 | 0.0275811 | ||||||||
\(811\) | −35.8840 | −1.26006 | −0.630029 | − | 0.776572i | \(-0.716957\pi\) | ||||
−0.630029 | + | 0.776572i | \(0.716957\pi\) | |||||||
\(812\) | −1.64758 | −0.0578188 | ||||||||
\(813\) | −21.9553 | −0.770006 | ||||||||
\(814\) | −0.395138 | −0.0138496 | ||||||||
\(815\) | −8.27128 | −0.289730 | ||||||||
\(816\) | −4.81285 | −0.168484 | ||||||||
\(817\) | 8.36015 | 0.292485 | ||||||||
\(818\) | −44.4605 | −1.55453 | ||||||||
\(819\) | −1.29890 | −0.0453873 | ||||||||
\(820\) | −2.76079 | −0.0964110 | ||||||||
\(821\) | −13.1523 | −0.459020 | −0.229510 | − | 0.973306i | \(-0.573712\pi\) | ||||
−0.229510 | + | 0.973306i | \(0.573712\pi\) | |||||||
\(822\) | 24.5407 | 0.855956 | ||||||||
\(823\) | −16.0495 | −0.559449 | −0.279724 | − | 0.960080i | \(-0.590243\pi\) | ||||
−0.279724 | + | 0.960080i | \(0.590243\pi\) | |||||||
\(824\) | −16.7539 | −0.583649 | ||||||||
\(825\) | −3.32566 | −0.115784 | ||||||||
\(826\) | −5.97458 | −0.207882 | ||||||||
\(827\) | −21.4115 | −0.744552 | −0.372276 | − | 0.928122i | \(-0.621423\pi\) | ||||
−0.372276 | + | 0.928122i | \(0.621423\pi\) | |||||||
\(828\) | −4.42122 | −0.153648 | ||||||||
\(829\) | 45.1129 | 1.56684 | 0.783418 | − | 0.621495i | \(-0.213474\pi\) | ||||
0.783418 | + | 0.621495i | \(0.213474\pi\) | |||||||
\(830\) | −8.74578 | −0.303570 | ||||||||
\(831\) | −30.3549 | −1.05300 | ||||||||
\(832\) | 10.4648 | 0.362801 | ||||||||
\(833\) | 6.67041 | 0.231116 | ||||||||
\(834\) | 27.2415 | 0.943296 | ||||||||
\(835\) | −7.88797 | −0.272975 | ||||||||
\(836\) | −0.425567 | −0.0147185 | ||||||||
\(837\) | −9.16611 | −0.316827 | ||||||||
\(838\) | −25.9132 | −0.895157 | ||||||||
\(839\) | 18.0718 | 0.623909 | 0.311954 | − | 0.950097i | \(-0.399016\pi\) | ||||
0.311954 | + | 0.950097i | \(0.399016\pi\) | |||||||
\(840\) | −0.645606 | −0.0222755 | ||||||||
\(841\) | −3.41751 | −0.117845 | ||||||||
\(842\) | −26.3404 | −0.907752 | ||||||||
\(843\) | −8.60041 | −0.296214 | ||||||||
\(844\) | −6.58090 | −0.226524 | ||||||||
\(845\) | 3.86095 | 0.132821 | ||||||||
\(846\) | −4.35931 | −0.149876 | ||||||||
\(847\) | 6.03487 | 0.207361 | ||||||||
\(848\) | 16.3660 | 0.562010 | ||||||||
\(849\) | −28.4638 | −0.976874 | ||||||||
\(850\) | −7.62699 | −0.261604 | ||||||||
\(851\) | 2.75034 | 0.0942805 | ||||||||
\(852\) | −1.89509 | −0.0649245 | ||||||||
\(853\) | −47.8982 | −1.64000 | −0.820002 | − | 0.572361i | \(-0.806028\pi\) | ||||
−0.820002 | + | 0.572361i | \(0.806028\pi\) | |||||||
\(854\) | −3.11936 | −0.106742 | ||||||||
\(855\) | −0.525917 | −0.0179860 | ||||||||
\(856\) | −24.2341 | −0.828306 | ||||||||
\(857\) | −22.5706 | −0.770997 | −0.385499 | − | 0.922708i | \(-0.625971\pi\) | ||||
−0.385499 | + | 0.922708i | \(0.625971\pi\) | |||||||
\(858\) | −2.53283 | −0.0864692 | ||||||||
\(859\) | 4.34984 | 0.148415 | 0.0742073 | − | 0.997243i | \(-0.476357\pi\) | ||||
0.0742073 | + | 0.997243i | \(0.476357\pi\) | |||||||
\(860\) | −2.16470 | −0.0738157 | ||||||||
\(861\) | 5.70201 | 0.194324 | ||||||||
\(862\) | 26.5106 | 0.902955 | ||||||||
\(863\) | −24.4102 | −0.830932 | −0.415466 | − | 0.909609i | \(-0.636381\pi\) | ||||
−0.415466 | + | 0.909609i | \(0.636381\pi\) | |||||||
\(864\) | −3.12074 | −0.106170 | ||||||||
\(865\) | 2.28691 | 0.0777573 | ||||||||
\(866\) | −4.30788 | −0.146388 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −2.98580 | −0.101345 | ||||||||
\(869\) | −0.698667 | −0.0237007 | ||||||||
\(870\) | −3.97031 | −0.134606 | ||||||||
\(871\) | 6.90366 | 0.233922 | ||||||||
\(872\) | 4.64515 | 0.157305 | ||||||||
\(873\) | −1.51033 | −0.0511169 | ||||||||
\(874\) | 13.4033 | 0.453374 | ||||||||
\(875\) | −2.74502 | −0.0927985 | ||||||||
\(876\) | 3.93658 | 0.133005 | ||||||||
\(877\) | −15.6442 | −0.528267 | −0.264134 | − | 0.964486i | \(-0.585086\pi\) | ||||
−0.264134 | + | 0.964486i | \(0.585086\pi\) | |||||||
\(878\) | 63.2479 | 2.13451 | ||||||||
\(879\) | −4.49834 | −0.151725 | ||||||||
\(880\) | −1.64733 | −0.0555314 | ||||||||
\(881\) | −22.8745 | −0.770661 | −0.385331 | − | 0.922779i | \(-0.625913\pi\) | ||||
−0.385331 | + | 0.922779i | \(0.625913\pi\) | |||||||
\(882\) | 10.6881 | 0.359886 | ||||||||
\(883\) | 8.88893 | 0.299136 | 0.149568 | − | 0.988751i | \(-0.452212\pi\) | ||||
0.149568 | + | 0.988751i | \(0.452212\pi\) | |||||||
\(884\) | −1.28373 | −0.0431767 | ||||||||
\(885\) | −3.18185 | −0.106957 | ||||||||
\(886\) | −14.2747 | −0.479568 | ||||||||
\(887\) | 14.3487 | 0.481781 | 0.240890 | − | 0.970552i | \(-0.422561\pi\) | ||||
0.240890 | + | 0.970552i | \(0.422561\pi\) | |||||||
\(888\) | 0.810221 | 0.0271892 | ||||||||
\(889\) | −6.87574 | −0.230605 | ||||||||
\(890\) | −4.95787 | −0.166188 | ||||||||
\(891\) | −0.698667 | −0.0234062 | ||||||||
\(892\) | −5.22485 | −0.174941 | ||||||||
\(893\) | 2.92066 | 0.0977363 | ||||||||
\(894\) | 8.21383 | 0.274712 | ||||||||
\(895\) | −5.82567 | −0.194731 | ||||||||
\(896\) | 7.83801 | 0.261850 | ||||||||
\(897\) | 17.6296 | 0.588637 | ||||||||
\(898\) | −10.4756 | −0.349576 | ||||||||
\(899\) | 46.3614 | 1.54624 | ||||||||
\(900\) | −2.70081 | −0.0900270 | ||||||||
\(901\) | 3.40047 | 0.113286 | ||||||||
\(902\) | 11.1188 | 0.370214 | ||||||||
\(903\) | 4.47087 | 0.148781 | ||||||||
\(904\) | 0.591278 | 0.0196656 | ||||||||
\(905\) | −5.32653 | −0.177060 | ||||||||
\(906\) | 27.4377 | 0.911556 | ||||||||
\(907\) | −10.9434 | −0.363369 | −0.181685 | − | 0.983357i | \(-0.558155\pi\) | ||||
−0.181685 | + | 0.983357i | \(0.558155\pi\) | |||||||
\(908\) | −7.93005 | −0.263168 | ||||||||
\(909\) | −11.9380 | −0.395958 | ||||||||
\(910\) | −1.01960 | −0.0337994 | ||||||||
\(911\) | 14.6004 | 0.483733 | 0.241867 | − | 0.970309i | \(-0.422240\pi\) | ||||
0.241867 | + | 0.970309i | \(0.422240\pi\) | |||||||
\(912\) | 5.16670 | 0.171086 | ||||||||
\(913\) | 7.78423 | 0.257620 | ||||||||
\(914\) | 6.21237 | 0.205487 | ||||||||
\(915\) | −1.66126 | −0.0549196 | ||||||||
\(916\) | 13.2452 | 0.437634 | ||||||||
\(917\) | 6.92885 | 0.228811 | ||||||||
\(918\) | −1.60231 | −0.0528841 | ||||||||
\(919\) | −7.97809 | −0.263173 | −0.131586 | − | 0.991305i | \(-0.542007\pi\) | ||||
−0.131586 | + | 0.991305i | \(0.542007\pi\) | |||||||
\(920\) | 8.76263 | 0.288895 | ||||||||
\(921\) | −4.25804 | −0.140307 | ||||||||
\(922\) | −6.97273 | −0.229635 | ||||||||
\(923\) | 7.55666 | 0.248731 | ||||||||
\(924\) | −0.227586 | −0.00748703 | ||||||||
\(925\) | 1.68011 | 0.0552417 | ||||||||
\(926\) | −48.4467 | −1.59206 | ||||||||
\(927\) | −7.29866 | −0.239719 | ||||||||
\(928\) | 15.7844 | 0.518149 | ||||||||
\(929\) | 15.7669 | 0.517294 | 0.258647 | − | 0.965972i | \(-0.416723\pi\) | ||||
0.258647 | + | 0.965972i | \(0.416723\pi\) | |||||||
\(930\) | −7.19513 | −0.235937 | ||||||||
\(931\) | −7.16082 | −0.234686 | ||||||||
\(932\) | 1.95496 | 0.0640370 | ||||||||
\(933\) | −17.9692 | −0.588284 | ||||||||
\(934\) | −55.3263 | −1.81033 | ||||||||
\(935\) | −0.342277 | −0.0111936 | ||||||||
\(936\) | 5.19351 | 0.169755 | ||||||||
\(937\) | 15.6047 | 0.509783 | 0.254891 | − | 0.966970i | \(-0.417960\pi\) | ||||
0.254891 | + | 0.966970i | \(0.417960\pi\) | |||||||
\(938\) | 2.80689 | 0.0916484 | ||||||||
\(939\) | −21.7435 | −0.709573 | ||||||||
\(940\) | −0.756250 | −0.0246662 | ||||||||
\(941\) | 3.36836 | 0.109806 | 0.0549028 | − | 0.998492i | \(-0.482515\pi\) | ||||
0.0549028 | + | 0.998492i | \(0.482515\pi\) | |||||||
\(942\) | 10.7580 | 0.350514 | ||||||||
\(943\) | −77.3918 | −2.52022 | ||||||||
\(944\) | 31.2590 | 1.01739 | ||||||||
\(945\) | −0.281252 | −0.00914912 | ||||||||
\(946\) | 8.71808 | 0.283449 | ||||||||
\(947\) | 44.4132 | 1.44323 | 0.721617 | − | 0.692293i | \(-0.243399\pi\) | ||||
0.721617 | + | 0.692293i | \(0.243399\pi\) | |||||||
\(948\) | −0.567397 | −0.0184282 | ||||||||
\(949\) | −15.6971 | −0.509550 | ||||||||
\(950\) | 8.18773 | 0.265645 | ||||||||
\(951\) | 31.0138 | 1.00569 | ||||||||
\(952\) | 1.31783 | 0.0427112 | ||||||||
\(953\) | −10.0975 | −0.327091 | −0.163545 | − | 0.986536i | \(-0.552293\pi\) | ||||
−0.163545 | + | 0.986536i | \(0.552293\pi\) | |||||||
\(954\) | 5.44861 | 0.176405 | ||||||||
\(955\) | 11.1687 | 0.361411 | ||||||||
\(956\) | 11.2822 | 0.364893 | ||||||||
\(957\) | 3.53380 | 0.114232 | ||||||||
\(958\) | 31.4818 | 1.01713 | ||||||||
\(959\) | −8.79284 | −0.283935 | ||||||||
\(960\) | 2.26594 | 0.0731330 | ||||||||
\(961\) | 53.0175 | 1.71024 | ||||||||
\(962\) | 1.27958 | 0.0412552 | ||||||||
\(963\) | −10.5574 | −0.340206 | ||||||||
\(964\) | −4.13802 | −0.133277 | ||||||||
\(965\) | 0.416351 | 0.0134028 | ||||||||
\(966\) | 7.16787 | 0.230622 | ||||||||
\(967\) | 13.9841 | 0.449699 | 0.224849 | − | 0.974394i | \(-0.427811\pi\) | ||||
0.224849 | + | 0.974394i | \(0.427811\pi\) | |||||||
\(968\) | −24.1297 | −0.775558 | ||||||||
\(969\) | 1.07352 | 0.0344864 | ||||||||
\(970\) | −1.18556 | −0.0380662 | ||||||||
\(971\) | −36.0761 | −1.15774 | −0.578869 | − | 0.815421i | \(-0.696506\pi\) | ||||
−0.578869 | + | 0.815421i | \(0.696506\pi\) | |||||||
\(972\) | −0.567397 | −0.0181993 | ||||||||
\(973\) | −9.76052 | −0.312908 | ||||||||
\(974\) | −34.1143 | −1.09309 | ||||||||
\(975\) | 10.7695 | 0.344900 | ||||||||
\(976\) | 16.3205 | 0.522406 | ||||||||
\(977\) | 25.5124 | 0.816215 | 0.408107 | − | 0.912934i | \(-0.366189\pi\) | ||||
0.408107 | + | 0.912934i | \(0.366189\pi\) | |||||||
\(978\) | 27.0528 | 0.865053 | ||||||||
\(979\) | 4.41278 | 0.141033 | ||||||||
\(980\) | 1.85416 | 0.0592289 | ||||||||
\(981\) | 2.02361 | 0.0646090 | ||||||||
\(982\) | 52.4937 | 1.67514 | ||||||||
\(983\) | 0.556483 | 0.0177490 | 0.00887452 | − | 0.999961i | \(-0.497175\pi\) | ||||
0.00887452 | + | 0.999961i | \(0.497175\pi\) | |||||||
\(984\) | −22.7988 | −0.726799 | ||||||||
\(985\) | 12.4547 | 0.396840 | ||||||||
\(986\) | 8.10435 | 0.258095 | ||||||||
\(987\) | 1.56192 | 0.0497166 | ||||||||
\(988\) | 1.37812 | 0.0438437 | ||||||||
\(989\) | −60.6819 | −1.92957 | ||||||||
\(990\) | −0.548433 | −0.0174304 | ||||||||
\(991\) | −35.4825 | −1.12714 | −0.563569 | − | 0.826069i | \(-0.690572\pi\) | ||||
−0.563569 | + | 0.826069i | \(0.690572\pi\) | |||||||
\(992\) | 28.6050 | 0.908210 | ||||||||
\(993\) | −35.6022 | −1.12980 | ||||||||
\(994\) | 3.07239 | 0.0974503 | ||||||||
\(995\) | −10.1282 | −0.321085 | ||||||||
\(996\) | 6.32167 | 0.200310 | ||||||||
\(997\) | 17.0977 | 0.541489 | 0.270744 | − | 0.962651i | \(-0.412730\pi\) | ||||
0.270744 | + | 0.962651i | \(0.412730\pi\) | |||||||
\(998\) | 5.70056 | 0.180448 | ||||||||
\(999\) | 0.352965 | 0.0111673 |
(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 | 4029.2.a.l.1.10 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.10 | ✓ | 32 | 1.1 | even | 1 | trivial |