Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9801,2,Mod(1,9801)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9801, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9801.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9801 = 3^{4} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9801.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: | \(78.2613790211\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{18} - 2 x^{17} - 22 x^{16} + 42 x^{15} + 198 x^{14} - 357 x^{13} - 944 x^{12} + 1579 x^{11} + \cdots - 55 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.490494\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9801.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.490494 | 0.346832 | 0.173416 | − | 0.984849i | \(-0.444520\pi\) | ||||
0.173416 | + | 0.984849i | \(0.444520\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.75942 | −0.879708 | ||||||||
\(5\) | −1.70818 | −0.763920 | −0.381960 | − | 0.924179i | \(-0.624751\pi\) | ||||
−0.381960 | + | 0.924179i | \(0.624751\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.41052 | 1.28906 | 0.644528 | − | 0.764581i | \(-0.277054\pi\) | ||||
0.644528 | + | 0.764581i | \(0.277054\pi\) | |||||||
\(8\) | −1.84397 | −0.651942 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.837851 | −0.264952 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.99792 | −1.10882 | −0.554412 | − | 0.832242i | \(-0.687057\pi\) | ||||
−0.554412 | + | 0.832242i | \(0.687057\pi\) | |||||||
\(14\) | 1.67284 | 0.447086 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.61437 | 0.653594 | ||||||||
\(17\) | 3.30458 | 0.801477 | 0.400739 | − | 0.916192i | \(-0.368754\pi\) | ||||
0.400739 | + | 0.916192i | \(0.368754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.41765 | −1.01348 | −0.506739 | − | 0.862099i | \(-0.669149\pi\) | ||||
−0.506739 | + | 0.862099i | \(0.669149\pi\) | |||||||
\(20\) | 3.00539 | 0.672026 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.49201 | −1.56219 | −0.781096 | − | 0.624411i | \(-0.785339\pi\) | ||||
−0.781096 | + | 0.624411i | \(0.785339\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.08213 | −0.416426 | ||||||||
\(26\) | −1.96096 | −0.384575 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.00053 | −1.13399 | ||||||||
\(29\) | −1.69129 | −0.314064 | −0.157032 | − | 0.987593i | \(-0.550193\pi\) | ||||
−0.157032 | + | 0.987593i | \(0.550193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.89852 | −0.700194 | −0.350097 | − | 0.936713i | \(-0.613851\pi\) | ||||
−0.350097 | + | 0.936713i | \(0.613851\pi\) | |||||||
\(32\) | 4.97028 | 0.878629 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.62087 | 0.277978 | ||||||||
\(35\) | −5.82578 | −0.984736 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.06553 | 0.503970 | 0.251985 | − | 0.967731i | \(-0.418917\pi\) | ||||
0.251985 | + | 0.967731i | \(0.418917\pi\) | |||||||
\(38\) | −2.16683 | −0.351506 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.14983 | 0.498032 | ||||||||
\(41\) | −0.390875 | −0.0610444 | −0.0305222 | − | 0.999534i | \(-0.509717\pi\) | ||||
−0.0305222 | + | 0.999534i | \(0.509717\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.61268 | 1.46592 | 0.732960 | − | 0.680272i | \(-0.238138\pi\) | ||||
0.732960 | + | 0.680272i | \(0.238138\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.67479 | −0.541818 | ||||||||
\(47\) | 1.08026 | 0.157572 | 0.0787859 | − | 0.996892i | \(-0.474896\pi\) | ||||
0.0787859 | + | 0.996892i | \(0.474896\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.63167 | 0.661666 | ||||||||
\(50\) | −1.02127 | −0.144430 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.03401 | 0.975442 | ||||||||
\(53\) | 12.5638 | 1.72577 | 0.862884 | − | 0.505402i | \(-0.168656\pi\) | ||||
0.862884 | + | 0.505402i | \(0.168656\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.28890 | −0.840390 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.829567 | −0.108927 | ||||||||
\(59\) | 3.65654 | 0.476041 | 0.238021 | − | 0.971260i | \(-0.423501\pi\) | ||||
0.238021 | + | 0.971260i | \(0.423501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.85318 | −0.493349 | −0.246674 | − | 0.969098i | \(-0.579338\pi\) | ||||
−0.246674 | + | 0.969098i | \(0.579338\pi\) | |||||||
\(62\) | −1.91220 | −0.242849 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.79086 | −0.348857 | ||||||||
\(65\) | 6.82916 | 0.847053 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.10120 | 0.378872 | 0.189436 | − | 0.981893i | \(-0.439334\pi\) | ||||
0.189436 | + | 0.981893i | \(0.439334\pi\) | |||||||
\(68\) | −5.81412 | −0.705066 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.85751 | −0.341538 | ||||||||
\(71\) | −7.01715 | −0.832783 | −0.416391 | − | 0.909186i | \(-0.636705\pi\) | ||||
−0.416391 | + | 0.909186i | \(0.636705\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.0426 | −1.76060 | −0.880302 | − | 0.474413i | \(-0.842660\pi\) | ||||
−0.880302 | + | 0.474413i | \(0.842660\pi\) | |||||||
\(74\) | 1.50362 | 0.174793 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.77248 | 0.891565 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.99913 | −0.449937 | −0.224969 | − | 0.974366i | \(-0.572228\pi\) | ||||
−0.224969 | + | 0.974366i | \(0.572228\pi\) | |||||||
\(80\) | −4.46581 | −0.499293 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.191722 | −0.0211721 | ||||||||
\(83\) | 0.124966 | 0.0137168 | 0.00685839 | − | 0.999976i | \(-0.497817\pi\) | ||||
0.00685839 | + | 0.999976i | \(0.497817\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.64480 | −0.612265 | ||||||||
\(86\) | 4.71496 | 0.508428 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.93327 | 0.840925 | 0.420462 | − | 0.907310i | \(-0.361868\pi\) | ||||
0.420462 | + | 0.907310i | \(0.361868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.6350 | −1.42934 | ||||||||
\(92\) | 13.1816 | 1.37427 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.529860 | 0.0546509 | ||||||||
\(95\) | 7.54613 | 0.774217 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.343160 | 0.0348426 | 0.0174213 | − | 0.999848i | \(-0.494454\pi\) | ||||
0.0174213 | + | 0.999848i | \(0.494454\pi\) | |||||||
\(98\) | 2.27180 | 0.229487 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.66333 | 0.366333 | ||||||||
\(101\) | −7.11558 | −0.708027 | −0.354014 | − | 0.935240i | \(-0.615183\pi\) | ||||
−0.354014 | + | 0.935240i | \(0.615183\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.65429 | −0.163002 | −0.0815009 | − | 0.996673i | \(-0.525971\pi\) | ||||
−0.0815009 | + | 0.996673i | \(0.525971\pi\) | |||||||
\(104\) | 7.37205 | 0.722889 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.16246 | 0.598551 | ||||||||
\(107\) | −3.30683 | −0.319683 | −0.159842 | − | 0.987143i | \(-0.551098\pi\) | ||||
−0.159842 | + | 0.987143i | \(0.551098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.50709 | −0.527484 | −0.263742 | − | 0.964593i | \(-0.584957\pi\) | ||||
−0.263742 | + | 0.964593i | \(0.584957\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.91638 | 0.842519 | ||||||||
\(113\) | 16.4092 | 1.54365 | 0.771825 | − | 0.635835i | \(-0.219344\pi\) | ||||
0.771825 | + | 0.635835i | \(0.219344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.7977 | 1.19339 | ||||||||
\(116\) | 2.97568 | 0.276285 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.79351 | 0.165106 | ||||||||
\(119\) | 11.2703 | 1.03315 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.88996 | −0.171109 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.85911 | 0.615966 | ||||||||
\(125\) | 12.0975 | 1.08204 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.7949 | 0.957894 | 0.478947 | − | 0.877844i | \(-0.341019\pi\) | ||||
0.478947 | + | 0.877844i | \(0.341019\pi\) | |||||||
\(128\) | −11.3095 | −0.999624 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.34966 | 0.293785 | ||||||||
\(131\) | 21.1557 | 1.84838 | 0.924189 | − | 0.381935i | \(-0.124742\pi\) | ||||
0.924189 | + | 0.381935i | \(0.124742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.0665 | −1.30643 | ||||||||
\(134\) | 1.52112 | 0.131405 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.09354 | −0.522517 | ||||||||
\(137\) | −3.20052 | −0.273439 | −0.136720 | − | 0.990610i | \(-0.543656\pi\) | ||||
−0.136720 | + | 0.990610i | \(0.543656\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.9936 | −1.27174 | −0.635872 | − | 0.771794i | \(-0.719360\pi\) | ||||
−0.635872 | + | 0.771794i | \(0.719360\pi\) | |||||||
\(140\) | 10.2500 | 0.866280 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.44187 | −0.288835 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.88902 | 0.239920 | ||||||||
\(146\) | −7.37831 | −0.610633 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.39354 | −0.443346 | ||||||||
\(149\) | −4.05112 | −0.331881 | −0.165940 | − | 0.986136i | \(-0.553066\pi\) | ||||
−0.165940 | + | 0.986136i | \(0.553066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.79399 | −0.634266 | −0.317133 | − | 0.948381i | \(-0.602720\pi\) | ||||
−0.317133 | + | 0.948381i | \(0.602720\pi\) | |||||||
\(152\) | 8.14602 | 0.660729 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.65936 | 0.534892 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.309152 | 0.0246730 | 0.0123365 | − | 0.999924i | \(-0.496073\pi\) | ||||
0.0123365 | + | 0.999924i | \(0.496073\pi\) | |||||||
\(158\) | −1.96155 | −0.156052 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.49011 | −0.671202 | ||||||||
\(161\) | −25.5517 | −2.01375 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.9941 | 0.861125 | 0.430563 | − | 0.902561i | \(-0.358315\pi\) | ||||
0.430563 | + | 0.902561i | \(0.358315\pi\) | |||||||
\(164\) | 0.687711 | 0.0537012 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0612950 | 0.00475741 | ||||||||
\(167\) | 17.5739 | 1.35991 | 0.679953 | − | 0.733255i | \(-0.262000\pi\) | ||||
0.679953 | + | 0.733255i | \(0.262000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.98339 | 0.229492 | ||||||||
\(170\) | −2.76874 | −0.212353 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.9127 | −1.28958 | ||||||||
\(173\) | −12.3657 | −0.940150 | −0.470075 | − | 0.882627i | \(-0.655773\pi\) | ||||
−0.470075 | + | 0.882627i | \(0.655773\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.10116 | −0.536797 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.89122 | 0.291659 | ||||||||
\(179\) | −21.8823 | −1.63556 | −0.817780 | − | 0.575531i | \(-0.804795\pi\) | ||||
−0.817780 | + | 0.575531i | \(0.804795\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.38018 | −0.325576 | −0.162788 | − | 0.986661i | \(-0.552049\pi\) | ||||
−0.162788 | + | 0.986661i | \(0.552049\pi\) | |||||||
\(182\) | −6.68789 | −0.495739 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.8150 | 1.01846 | ||||||||
\(185\) | −5.23647 | −0.384993 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.90062 | −0.138617 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.70133 | 0.268523 | ||||||||
\(191\) | −12.5147 | −0.905534 | −0.452767 | − | 0.891629i | \(-0.649563\pi\) | ||||
−0.452767 | + | 0.891629i | \(0.649563\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.5657 | −0.904500 | −0.452250 | − | 0.891891i | \(-0.649378\pi\) | ||||
−0.452250 | + | 0.891891i | \(0.649378\pi\) | |||||||
\(194\) | 0.168318 | 0.0120845 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.14902 | −0.582073 | ||||||||
\(197\) | 10.3453 | 0.737075 | 0.368538 | − | 0.929613i | \(-0.379859\pi\) | ||||
0.368538 | + | 0.929613i | \(0.379859\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.4773 | 1.87693 | 0.938464 | − | 0.345376i | \(-0.112249\pi\) | ||||
0.938464 | + | 0.345376i | \(0.112249\pi\) | |||||||
\(200\) | 3.83939 | 0.271486 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.49015 | −0.245566 | ||||||||
\(203\) | −5.76818 | −0.404847 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.667683 | 0.0466330 | ||||||||
\(206\) | −0.811418 | −0.0565342 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.4521 | −0.724721 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.28390 | −0.501444 | −0.250722 | − | 0.968059i | \(-0.580668\pi\) | ||||
−0.250722 | + | 0.968059i | \(0.580668\pi\) | |||||||
\(212\) | −22.1049 | −1.51817 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.62198 | −0.110876 | ||||||||
\(215\) | −16.4202 | −1.11985 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.2960 | −0.902590 | ||||||||
\(218\) | −2.70120 | −0.182948 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.2114 | −0.888698 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.5101 | 1.57435 | 0.787175 | − | 0.616730i | \(-0.211543\pi\) | ||||
0.787175 | + | 0.616730i | \(0.211543\pi\) | |||||||
\(224\) | 16.9512 | 1.13260 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.04863 | 0.535387 | ||||||||
\(227\) | 11.9222 | 0.791303 | 0.395652 | − | 0.918401i | \(-0.370519\pi\) | ||||
0.395652 | + | 0.918401i | \(0.370519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.05757 | 0.202050 | 0.101025 | − | 0.994884i | \(-0.467788\pi\) | ||||
0.101025 | + | 0.994884i | \(0.467788\pi\) | |||||||
\(230\) | 6.27719 | 0.413905 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.11869 | 0.204752 | ||||||||
\(233\) | 24.5314 | 1.60710 | 0.803552 | − | 0.595235i | \(-0.202941\pi\) | ||||
0.803552 | + | 0.595235i | \(0.202941\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.84527 | −0.120372 | ||||||||
\(236\) | −6.43338 | −0.418777 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.52803 | 0.358329 | ||||||||
\(239\) | 6.95063 | 0.449599 | 0.224799 | − | 0.974405i | \(-0.427827\pi\) | ||||
0.224799 | + | 0.974405i | \(0.427827\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.77059 | −0.500547 | −0.250274 | − | 0.968175i | \(-0.580521\pi\) | ||||
−0.250274 | + | 0.968175i | \(0.580521\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.77934 | 0.434003 | ||||||||
\(245\) | −7.91170 | −0.505460 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.6614 | 1.12377 | ||||||||
\(248\) | 7.18875 | 0.456486 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.93377 | 0.375284 | ||||||||
\(251\) | −0.327168 | −0.0206506 | −0.0103253 | − | 0.999947i | \(-0.503287\pi\) | ||||
−0.0103253 | + | 0.999947i | \(0.503287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 5.29484 | 0.332228 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.0344986 | 0.00215616 | ||||||||
\(257\) | 13.7292 | 0.856402 | 0.428201 | − | 0.903684i | \(-0.359148\pi\) | ||||
0.428201 | + | 0.903684i | \(0.359148\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.4551 | 0.649645 | ||||||||
\(260\) | −12.0153 | −0.745159 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.3767 | 0.641076 | ||||||||
\(263\) | 16.8542 | 1.03927 | 0.519637 | − | 0.854387i | \(-0.326067\pi\) | ||||
0.519637 | + | 0.854387i | \(0.326067\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.4612 | −1.31835 | ||||||||
\(266\) | −7.39003 | −0.453112 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.45630 | −0.333297 | ||||||||
\(269\) | −12.3974 | −0.755882 | −0.377941 | − | 0.925830i | \(-0.623368\pi\) | ||||
−0.377941 | + | 0.925830i | \(0.623368\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.2695 | 1.17054 | 0.585269 | − | 0.810839i | \(-0.300989\pi\) | ||||
0.585269 | + | 0.810839i | \(0.300989\pi\) | |||||||
\(272\) | 8.63940 | 0.523840 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.56984 | −0.0948374 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3511 | 0.621936 | 0.310968 | − | 0.950420i | \(-0.399347\pi\) | ||||
0.310968 | + | 0.950420i | \(0.399347\pi\) | |||||||
\(278\) | −7.35429 | −0.441081 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.7426 | 0.641991 | ||||||||
\(281\) | 16.4358 | 0.980478 | 0.490239 | − | 0.871588i | \(-0.336910\pi\) | ||||
0.490239 | + | 0.871588i | \(0.336910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.26495 | −0.0751937 | −0.0375968 | − | 0.999293i | \(-0.511970\pi\) | ||||
−0.0375968 | + | 0.999293i | \(0.511970\pi\) | |||||||
\(284\) | 12.3461 | 0.732605 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.33309 | −0.0786896 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.07978 | −0.357634 | ||||||||
\(290\) | 1.41705 | 0.0832119 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26.4662 | 1.54882 | ||||||||
\(293\) | 24.0874 | 1.40720 | 0.703601 | − | 0.710596i | \(-0.251574\pi\) | ||||
0.703601 | + | 0.710596i | \(0.251574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.24602 | −0.363658 | ||||||||
\(296\) | −5.65274 | −0.328559 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.98705 | −0.115107 | ||||||||
\(299\) | 29.9525 | 1.73220 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.7843 | 1.88965 | ||||||||
\(302\) | −3.82290 | −0.219983 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.5494 | −0.662403 | ||||||||
\(305\) | 6.58191 | 0.376879 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2949 | 0.930001 | 0.465001 | − | 0.885310i | \(-0.346054\pi\) | ||||
0.465001 | + | 0.885310i | \(0.346054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.26637 | 0.185518 | ||||||||
\(311\) | −21.3713 | −1.21185 | −0.605926 | − | 0.795521i | \(-0.707197\pi\) | ||||
−0.605926 | + | 0.795521i | \(0.707197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.11613 | 0.176134 | 0.0880669 | − | 0.996115i | \(-0.471931\pi\) | ||||
0.0880669 | + | 0.996115i | \(0.471931\pi\) | |||||||
\(314\) | 0.151637 | 0.00855738 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.03613 | 0.395813 | ||||||||
\(317\) | 18.2648 | 1.02586 | 0.512928 | − | 0.858432i | \(-0.328561\pi\) | ||||
0.512928 | + | 0.858432i | \(0.328561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.76728 | 0.266499 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.5329 | −0.698434 | ||||||||
\(323\) | −14.5985 | −0.812280 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.32420 | 0.461744 | ||||||||
\(326\) | 5.39254 | 0.298665 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.720761 | 0.0397974 | ||||||||
\(329\) | 3.68425 | 0.203119 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.76616 | 0.207007 | 0.103503 | − | 0.994629i | \(-0.466995\pi\) | ||||
0.103503 | + | 0.994629i | \(0.466995\pi\) | |||||||
\(332\) | −0.219867 | −0.0120668 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.61988 | 0.471659 | ||||||||
\(335\) | −5.29740 | −0.289428 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.96618 | 0.324998 | 0.162499 | − | 0.986709i | \(-0.448045\pi\) | ||||
0.162499 | + | 0.986709i | \(0.448045\pi\) | |||||||
\(338\) | 1.46334 | 0.0795950 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.93155 | 0.538614 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.07726 | −0.436131 | ||||||||
\(344\) | −17.7255 | −0.955695 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.06532 | −0.326074 | ||||||||
\(347\) | −24.3493 | −1.30714 | −0.653570 | − | 0.756866i | \(-0.726730\pi\) | ||||
−0.653570 | + | 0.756866i | \(0.726730\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7418 | 0.896166 | 0.448083 | − | 0.893992i | \(-0.352107\pi\) | ||||
0.448083 | + | 0.893992i | \(0.352107\pi\) | |||||||
\(350\) | −3.48307 | −0.186178 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.03132 | 0.427464 | 0.213732 | − | 0.976892i | \(-0.431438\pi\) | ||||
0.213732 | + | 0.976892i | \(0.431438\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.9865 | 0.636179 | ||||||||
\(356\) | −13.9579 | −0.739768 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.7331 | −0.567264 | ||||||||
\(359\) | 28.8250 | 1.52133 | 0.760663 | − | 0.649147i | \(-0.224874\pi\) | ||||
0.760663 | + | 0.649147i | \(0.224874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.515640 | 0.0271390 | ||||||||
\(362\) | −2.14845 | −0.112920 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 23.9896 | 1.25740 | ||||||||
\(365\) | 25.6954 | 1.34496 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.3434 | 1.16632 | 0.583158 | − | 0.812359i | \(-0.301817\pi\) | ||||
0.583158 | + | 0.812359i | \(0.301817\pi\) | |||||||
\(368\) | −19.5869 | −1.02104 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.56845 | −0.133528 | ||||||||
\(371\) | 42.8491 | 2.22461 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.07872 | 0.366522 | 0.183261 | − | 0.983064i | \(-0.441335\pi\) | ||||
0.183261 | + | 0.983064i | \(0.441335\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.99196 | −0.102728 | ||||||||
\(377\) | 6.76164 | 0.348242 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.3461 | −1.25057 | −0.625287 | − | 0.780394i | \(-0.715018\pi\) | ||||
−0.625287 | + | 0.780394i | \(0.715018\pi\) | |||||||
\(380\) | −13.2768 | −0.681084 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.13840 | −0.314068 | ||||||||
\(383\) | 17.6379 | 0.901254 | 0.450627 | − | 0.892712i | \(-0.351200\pi\) | ||||
0.450627 | + | 0.892712i | \(0.351200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.16341 | −0.313709 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.603760 | −0.0306513 | ||||||||
\(389\) | 17.8830 | 0.906704 | 0.453352 | − | 0.891332i | \(-0.350228\pi\) | ||||
0.453352 | + | 0.891332i | \(0.350228\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.7579 | −1.25206 | ||||||||
\(392\) | −8.54066 | −0.431368 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.07433 | 0.255641 | ||||||||
\(395\) | 6.83122 | 0.343716 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.9395 | −1.10111 | −0.550556 | − | 0.834798i | \(-0.685584\pi\) | ||||
−0.550556 | + | 0.834798i | \(0.685584\pi\) | |||||||
\(398\) | 12.9870 | 0.650978 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.44347 | −0.272174 | ||||||||
\(401\) | −5.40756 | −0.270041 | −0.135020 | − | 0.990843i | \(-0.543110\pi\) | ||||
−0.135020 | + | 0.990843i | \(0.543110\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.5860 | 0.776392 | ||||||||
\(404\) | 12.5193 | 0.622857 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.82926 | −0.140414 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.6201 | 1.16794 | 0.583970 | − | 0.811775i | \(-0.301498\pi\) | ||||
0.583970 | + | 0.811775i | \(0.301498\pi\) | |||||||
\(410\) | 0.327495 | 0.0161738 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.91058 | 0.143394 | ||||||||
\(413\) | 12.4707 | 0.613644 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.213464 | −0.0104785 | ||||||||
\(416\) | −19.8708 | −0.974245 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.1313 | 0.885773 | 0.442886 | − | 0.896578i | \(-0.353955\pi\) | ||||
0.442886 | + | 0.896578i | \(0.353955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.8122 | −0.624428 | −0.312214 | − | 0.950012i | \(-0.601071\pi\) | ||||
−0.312214 | + | 0.950012i | \(0.601071\pi\) | |||||||
\(422\) | −3.57271 | −0.173917 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −23.1672 | −1.12510 | ||||||||
\(425\) | −6.88056 | −0.333756 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.1413 | −0.635954 | ||||||||
\(428\) | 5.81809 | 0.281228 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.05399 | −0.388398 | ||||||||
\(431\) | 6.57916 | 0.316907 | 0.158453 | − | 0.987366i | \(-0.449349\pi\) | ||||
0.158453 | + | 0.987366i | \(0.449349\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.9978 | 0.672690 | 0.336345 | − | 0.941739i | \(-0.390809\pi\) | ||||
0.336345 | + | 0.941739i | \(0.390809\pi\) | |||||||
\(434\) | −6.52160 | −0.313047 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.68927 | 0.464032 | ||||||||
\(437\) | 33.0971 | 1.58325 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.1782 | 1.20169 | 0.600846 | − | 0.799365i | \(-0.294831\pi\) | ||||
0.600846 | + | 0.799365i | \(0.294831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.48013 | −0.308228 | ||||||||
\(443\) | −26.8225 | −1.27437 | −0.637187 | − | 0.770709i | \(-0.719902\pi\) | ||||
−0.637187 | + | 0.770709i | \(0.719902\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.5514 | −0.642399 | ||||||||
\(446\) | 11.5315 | 0.546034 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.51829 | −0.449697 | ||||||||
\(449\) | −14.1758 | −0.668999 | −0.334499 | − | 0.942396i | \(-0.608567\pi\) | ||||
−0.334499 | + | 0.942396i | \(0.608567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −28.8706 | −1.35796 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.84776 | 0.274449 | ||||||||
\(455\) | 23.2910 | 1.09190 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6413 | 1.15267 | 0.576335 | − | 0.817213i | \(-0.304482\pi\) | ||||
0.576335 | + | 0.817213i | \(0.304482\pi\) | |||||||
\(458\) | 1.49972 | 0.0700773 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −22.5164 | −1.04983 | ||||||||
\(461\) | 26.2454 | 1.22237 | 0.611185 | − | 0.791488i | \(-0.290693\pi\) | ||||
0.611185 | + | 0.791488i | \(0.290693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6922 | 0.589855 | 0.294928 | − | 0.955520i | \(-0.404704\pi\) | ||||
0.294928 | + | 0.955520i | \(0.404704\pi\) | |||||||
\(464\) | −4.42166 | −0.205270 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0325 | 0.557394 | ||||||||
\(467\) | 27.7040 | 1.28199 | 0.640994 | − | 0.767546i | \(-0.278522\pi\) | ||||
0.640994 | + | 0.767546i | \(0.278522\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.5767 | 0.488387 | ||||||||
\(470\) | −0.905095 | −0.0417489 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.74256 | −0.310351 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.19813 | 0.422039 | ||||||||
\(476\) | −19.8292 | −0.908870 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.40924 | 0.155935 | ||||||||
\(479\) | 15.6222 | 0.713797 | 0.356898 | − | 0.934143i | \(-0.383834\pi\) | ||||
0.356898 | + | 0.934143i | \(0.383834\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.2557 | −0.558814 | ||||||||
\(482\) | −3.81143 | −0.173606 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.586177 | −0.0266169 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.9270 | 1.22018 | 0.610090 | − | 0.792332i | \(-0.291133\pi\) | ||||
0.610090 | + | 0.792332i | \(0.291133\pi\) | |||||||
\(488\) | 7.10514 | 0.321635 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.88064 | −0.175310 | ||||||||
\(491\) | −38.9997 | −1.76003 | −0.880017 | − | 0.474942i | \(-0.842469\pi\) | ||||
−0.880017 | + | 0.474942i | \(0.842469\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.58899 | −0.251715 | ||||||||
\(494\) | 8.66283 | 0.389759 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.1922 | −0.457642 | ||||||||
\(497\) | −23.9322 | −1.07350 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.0351 | −1.07596 | −0.537980 | − | 0.842958i | \(-0.680812\pi\) | ||||
−0.537980 | + | 0.842958i | \(0.680812\pi\) | |||||||
\(500\) | −21.2846 | −0.951876 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.160474 | −0.00716229 | ||||||||
\(503\) | 23.9865 | 1.06950 | 0.534752 | − | 0.845009i | \(-0.320405\pi\) | ||||
0.534752 | + | 0.845009i | \(0.320405\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1547 | 0.540876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.9927 | −0.842667 | ||||||||
\(509\) | −3.69886 | −0.163949 | −0.0819746 | − | 0.996634i | \(-0.526123\pi\) | ||||
−0.0819746 | + | 0.996634i | \(0.526123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −51.3032 | −2.26952 | ||||||||
\(512\) | 22.6358 | 1.00037 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.73407 | 0.297027 | ||||||||
\(515\) | 2.82582 | 0.124520 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5.12814 | 0.225318 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.5928 | −0.552230 | ||||||||
\(521\) | 6.41318 | 0.280966 | 0.140483 | − | 0.990083i | \(-0.455134\pi\) | ||||
0.140483 | + | 0.990083i | \(0.455134\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.73856 | −0.119749 | −0.0598745 | − | 0.998206i | \(-0.519070\pi\) | ||||
−0.0598745 | + | 0.998206i | \(0.519070\pi\) | |||||||
\(524\) | −37.2216 | −1.62603 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.26688 | 0.360453 | ||||||||
\(527\) | −12.8829 | −0.561190 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.1302 | 1.44044 | ||||||||
\(530\) | −10.5266 | −0.457245 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.5082 | 1.14928 | ||||||||
\(533\) | 1.56269 | 0.0676875 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.64865 | 0.244213 | ||||||||
\(536\) | −5.71852 | −0.247003 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.08085 | −0.262164 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.9037 | 0.898719 | 0.449359 | − | 0.893351i | \(-0.351652\pi\) | ||||
0.449359 | + | 0.893351i | \(0.351652\pi\) | |||||||
\(542\) | 9.45157 | 0.405980 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.4247 | 0.704201 | ||||||||
\(545\) | 9.40709 | 0.402956 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.8764 | −1.79050 | −0.895252 | − | 0.445560i | \(-0.853004\pi\) | ||||
−0.895252 | + | 0.445560i | \(0.853004\pi\) | |||||||
\(548\) | 5.63105 | 0.240547 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.47152 | 0.318298 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.6391 | −0.579995 | ||||||||
\(554\) | 5.07714 | 0.215707 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26.3801 | 1.11876 | ||||||||
\(557\) | 12.5244 | 0.530675 | 0.265337 | − | 0.964156i | \(-0.414517\pi\) | ||||
0.265337 | + | 0.964156i | \(0.414517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.4308 | −1.62545 | ||||||||
\(560\) | −15.2308 | −0.643617 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.06166 | 0.340061 | ||||||||
\(563\) | 14.5087 | 0.611470 | 0.305735 | − | 0.952117i | \(-0.401098\pi\) | ||||
0.305735 | + | 0.952117i | \(0.401098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.0299 | −1.17923 | ||||||||
\(566\) | −0.620452 | −0.0260796 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.9394 | 0.542926 | ||||||||
\(569\) | 27.9724 | 1.17266 | 0.586332 | − | 0.810071i | \(-0.300571\pi\) | ||||
0.586332 | + | 0.810071i | \(0.300571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.04886 | 0.378683 | 0.189341 | − | 0.981911i | \(-0.439365\pi\) | ||||
0.189341 | + | 0.981911i | \(0.439365\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.653871 | −0.0272921 | ||||||||
\(575\) | 15.5993 | 0.650538 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.3471 | 1.59641 | 0.798204 | − | 0.602387i | \(-0.205783\pi\) | ||||
0.798204 | + | 0.602387i | \(0.205783\pi\) | |||||||
\(578\) | −2.98210 | −0.124039 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.08299 | −0.211060 | ||||||||
\(581\) | 0.426199 | 0.0176817 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 27.7381 | 1.14781 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.8147 | 0.488062 | ||||||||
\(587\) | 0.722617 | 0.0298256 | 0.0149128 | − | 0.999889i | \(-0.495253\pi\) | ||||
0.0149128 | + | 0.999889i | \(0.495253\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.2223 | 0.709632 | ||||||||
\(590\) | −3.06364 | −0.126128 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.01444 | 0.329391 | ||||||||
\(593\) | 39.6596 | 1.62863 | 0.814313 | − | 0.580426i | \(-0.197114\pi\) | ||||
0.814313 | + | 0.580426i | \(0.197114\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.2517 | −0.789244 | ||||||||
\(596\) | 7.12761 | 0.291958 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.6915 | 0.600781 | ||||||||
\(599\) | 20.3768 | 0.832573 | 0.416287 | − | 0.909233i | \(-0.363331\pi\) | ||||
0.416287 | + | 0.909233i | \(0.363331\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −48.3717 | −1.97312 | −0.986562 | − | 0.163389i | \(-0.947757\pi\) | ||||
−0.986562 | + | 0.163389i | \(0.947757\pi\) | |||||||
\(602\) | 16.0805 | 0.655392 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.7129 | 0.557968 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.7023 | −0.799691 | −0.399845 | − | 0.916583i | \(-0.630936\pi\) | ||||
−0.399845 | + | 0.916583i | \(0.630936\pi\) | |||||||
\(608\) | −21.9569 | −0.890472 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.22839 | 0.130714 | ||||||||
\(611\) | −4.31879 | −0.174720 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.71781 | 0.230940 | 0.115470 | − | 0.993311i | \(-0.463163\pi\) | ||||
0.115470 | + | 0.993311i | \(0.463163\pi\) | |||||||
\(614\) | 7.99257 | 0.322554 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.10692 | −0.245855 | −0.122928 | − | 0.992416i | \(-0.539228\pi\) | ||||
−0.122928 | + | 0.992416i | \(0.539228\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.77973 | −0.0715335 | −0.0357668 | − | 0.999360i | \(-0.511387\pi\) | ||||
−0.0357668 | + | 0.999360i | \(0.511387\pi\) | |||||||
\(620\) | −11.7166 | −0.470549 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.4825 | −0.420309 | ||||||||
\(623\) | 27.0566 | 1.08400 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.2541 | −0.410163 | ||||||||
\(626\) | 1.52844 | 0.0610888 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.543927 | −0.0217050 | ||||||||
\(629\) | 10.1303 | 0.403920 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.8407 | −1.78508 | −0.892541 | − | 0.450966i | \(-0.851079\pi\) | ||||
−0.892541 | + | 0.450966i | \(0.851079\pi\) | |||||||
\(632\) | 7.37428 | 0.293333 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.95880 | 0.355799 | ||||||||
\(635\) | −18.4396 | −0.731754 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.5170 | −0.733672 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19.3185 | 0.763633 | ||||||||
\(641\) | 27.0096 | 1.06681 | 0.533407 | − | 0.845859i | \(-0.320912\pi\) | ||||
0.533407 | + | 0.845859i | \(0.320912\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.5574 | −1.28394 | −0.641969 | − | 0.766731i | \(-0.721882\pi\) | ||||
−0.641969 | + | 0.766731i | \(0.721882\pi\) | |||||||
\(644\) | 44.9560 | 1.77152 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.16046 | −0.281724 | ||||||||
\(647\) | 31.4833 | 1.23774 | 0.618868 | − | 0.785495i | \(-0.287592\pi\) | ||||
0.618868 | + | 0.785495i | \(0.287592\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.08297 | 0.160147 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.3432 | −0.757538 | ||||||||
\(653\) | 4.65977 | 0.182351 | 0.0911755 | − | 0.995835i | \(-0.470938\pi\) | ||||
0.0911755 | + | 0.995835i | \(0.470938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.1376 | −1.41201 | ||||||||
\(656\) | −1.02189 | −0.0398982 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.80710 | 0.0704481 | ||||||||
\(659\) | 32.0418 | 1.24817 | 0.624086 | − | 0.781355i | \(-0.285471\pi\) | ||||
0.624086 | + | 0.781355i | \(0.285471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.7054 | −1.58325 | −0.791627 | − | 0.611004i | \(-0.790766\pi\) | ||||
−0.791627 | + | 0.611004i | \(0.790766\pi\) | |||||||
\(662\) | 1.84728 | 0.0717965 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.230433 | −0.00894255 | ||||||||
\(665\) | 25.7362 | 0.998009 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.6712 | 0.490629 | ||||||||
\(668\) | −30.9197 | −1.19632 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.59834 | −0.100383 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.7635 | −1.45568 | −0.727838 | − | 0.685749i | \(-0.759475\pi\) | ||||
−0.727838 | + | 0.685749i | \(0.759475\pi\) | |||||||
\(674\) | 2.92637 | 0.112720 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.24903 | −0.201886 | ||||||||
\(677\) | −18.9007 | −0.726412 | −0.363206 | − | 0.931709i | \(-0.618318\pi\) | ||||
−0.363206 | + | 0.931709i | \(0.618318\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.17035 | 0.0449140 | ||||||||
\(680\) | 10.4088 | 0.399161 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.1053 | −1.19021 | −0.595105 | − | 0.803648i | \(-0.702890\pi\) | ||||
−0.595105 | + | 0.803648i | \(0.702890\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.46706 | 0.208886 | ||||||||
\(686\) | −3.96185 | −0.151264 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25.1312 | 0.958116 | ||||||||
\(689\) | −50.2290 | −1.91357 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.2114 | 0.844962 | 0.422481 | − | 0.906372i | \(-0.361159\pi\) | ||||
0.422481 | + | 0.906372i | \(0.361159\pi\) | |||||||
\(692\) | 21.7565 | 0.827057 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.9432 | −0.453358 | ||||||||
\(695\) | 25.6118 | 0.971511 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.29167 | −0.0489257 | ||||||||
\(698\) | 8.21174 | 0.310819 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.4939 | 0.472224 | ||||||||
\(701\) | 29.9457 | 1.13103 | 0.565517 | − | 0.824736i | \(-0.308677\pi\) | ||||
0.565517 | + | 0.824736i | \(0.308677\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.5424 | −0.510763 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.93931 | 0.148258 | ||||||||
\(707\) | −24.2679 | −0.912687 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.2057 | 0.646175 | 0.323087 | − | 0.946369i | \(-0.395279\pi\) | ||||
0.323087 | + | 0.946369i | \(0.395279\pi\) | |||||||
\(710\) | 5.87932 | 0.220647 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.6287 | −0.548234 | ||||||||
\(713\) | 29.2077 | 1.09384 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 38.5001 | 1.43881 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.1385 | 0.527644 | ||||||||
\(719\) | −4.72508 | −0.176216 | −0.0881079 | − | 0.996111i | \(-0.528082\pi\) | ||||
−0.0881079 | + | 0.996111i | \(0.528082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.64199 | −0.210119 | ||||||||
\(722\) | 0.252919 | 0.00941265 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.70655 | 0.286412 | ||||||||
\(725\) | 3.52148 | 0.130785 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.20088 | 0.192890 | 0.0964450 | − | 0.995338i | \(-0.469253\pi\) | ||||
0.0964450 | + | 0.995338i | \(0.469253\pi\) | |||||||
\(728\) | 25.1426 | 0.931845 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.6035 | 0.466475 | ||||||||
\(731\) | 31.7658 | 1.17490 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.0632 | −1.81219 | −0.906095 | − | 0.423075i | \(-0.860951\pi\) | ||||
−0.906095 | + | 0.423075i | \(0.860951\pi\) | |||||||
\(734\) | 10.9593 | 0.404515 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.2374 | −1.37259 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.5942 | −0.573641 | −0.286821 | − | 0.957984i | \(-0.592598\pi\) | ||||
−0.286821 | + | 0.957984i | \(0.592598\pi\) | |||||||
\(740\) | 9.21312 | 0.338681 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21.0172 | 0.771566 | ||||||||
\(743\) | −11.1344 | −0.408483 | −0.204242 | − | 0.978921i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978921i | \(0.565473\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.92004 | 0.253530 | ||||||||
\(746\) | 3.47207 | 0.127122 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.2780 | −0.412090 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.08520 | −0.295033 | −0.147517 | − | 0.989060i | \(-0.547128\pi\) | ||||
−0.147517 | + | 0.989060i | \(0.547128\pi\) | |||||||
\(752\) | 2.82420 | 0.102988 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.31654 | 0.120781 | ||||||||
\(755\) | 13.3135 | 0.484528 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.8616 | 1.08534 | 0.542669 | − | 0.839947i | \(-0.317414\pi\) | ||||
0.542669 | + | 0.839947i | \(0.317414\pi\) | |||||||
\(758\) | −11.9416 | −0.433739 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.9148 | −0.504744 | ||||||||
\(761\) | −34.8926 | −1.26486 | −0.632428 | − | 0.774619i | \(-0.717941\pi\) | ||||
−0.632428 | + | 0.774619i | \(0.717941\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.7821 | −0.679957 | ||||||||
\(764\) | 22.0186 | 0.796606 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.65128 | 0.312583 | ||||||||
\(767\) | −14.6186 | −0.527846 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.60723 | −0.202202 | −0.101101 | − | 0.994876i | \(-0.532237\pi\) | ||||
−0.101101 | + | 0.994876i | \(0.532237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.1083 | 0.795696 | ||||||||
\(773\) | 10.8401 | 0.389893 | 0.194946 | − | 0.980814i | \(-0.437547\pi\) | ||||
0.194946 | + | 0.980814i | \(0.437547\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.11722 | 0.291579 | ||||||||
\(776\) | −0.632776 | −0.0227153 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.77150 | 0.314473 | ||||||||
\(779\) | 1.72675 | 0.0618672 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −12.1436 | −0.434255 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.1089 | 0.432461 | ||||||||
\(785\) | −0.528086 | −0.0188482 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.47643 | −0.0882752 | −0.0441376 | − | 0.999025i | \(-0.514054\pi\) | ||||
−0.0441376 | + | 0.999025i | \(0.514054\pi\) | |||||||
\(788\) | −18.2018 | −0.648411 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.35067 | 0.119212 | ||||||||
\(791\) | 55.9640 | 1.98985 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.4047 | 0.547037 | ||||||||
\(794\) | −10.7612 | −0.381900 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −46.5846 | −1.65115 | ||||||||
\(797\) | 9.67969 | 0.342872 | 0.171436 | − | 0.985195i | \(-0.445159\pi\) | ||||
0.171436 | + | 0.985195i | \(0.445159\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.56980 | 0.126290 | ||||||||
\(800\) | −10.3488 | −0.365884 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.65237 | −0.0936586 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 43.6468 | 1.53835 | ||||||||
\(806\) | 7.64482 | 0.269277 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.1209 | 0.461593 | ||||||||
\(809\) | 7.86532 | 0.276530 | 0.138265 | − | 0.990395i | \(-0.455847\pi\) | ||||
0.138265 | + | 0.990395i | \(0.455847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.5047 | 1.38720 | 0.693599 | − | 0.720361i | \(-0.256024\pi\) | ||||
0.693599 | + | 0.720361i | \(0.256024\pi\) | |||||||
\(812\) | 10.1486 | 0.356147 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.7799 | −0.657831 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.4655 | −1.48568 | ||||||||
\(818\) | 11.5855 | 0.405079 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.17473 | −0.0410234 | ||||||||
\(821\) | 3.35362 | 0.117042 | 0.0585211 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585211 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.1018 | 0.561274 | 0.280637 | − | 0.959814i | \(-0.409454\pi\) | ||||
0.280637 | + | 0.959814i | \(0.409454\pi\) | |||||||
\(824\) | 3.05046 | 0.106268 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.11681 | 0.212831 | ||||||||
\(827\) | −15.2905 | −0.531702 | −0.265851 | − | 0.964014i | \(-0.585653\pi\) | ||||
−0.265851 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.1463 | −1.46380 | −0.731901 | − | 0.681411i | \(-0.761367\pi\) | ||||
−0.731901 | + | 0.681411i | \(0.761367\pi\) | |||||||
\(830\) | −0.104703 | −0.00363428 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.1576 | 0.386822 | ||||||||
\(833\) | 15.3057 | 0.530311 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.0193 | −1.03886 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.89330 | 0.307214 | ||||||||
\(839\) | −2.64739 | −0.0913981 | −0.0456990 | − | 0.998955i | \(-0.514552\pi\) | ||||
−0.0456990 | + | 0.998955i | \(0.514552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.1395 | −0.901364 | ||||||||
\(842\) | −6.28431 | −0.216572 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.8154 | 0.441125 | ||||||||
\(845\) | −5.09616 | −0.175313 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 32.8464 | 1.12795 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.37487 | −0.115757 | ||||||||
\(851\) | −22.9670 | −0.787298 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.27037 | 0.317411 | 0.158706 | − | 0.987326i | \(-0.449268\pi\) | ||||
0.158706 | + | 0.987326i | \(0.449268\pi\) | |||||||
\(854\) | −6.44575 | −0.220569 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.09770 | 0.208415 | ||||||||
\(857\) | 20.5356 | 0.701483 | 0.350742 | − | 0.936472i | \(-0.385930\pi\) | ||||
0.350742 | + | 0.936472i | \(0.385930\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.0278 | 1.22925 | 0.614626 | − | 0.788819i | \(-0.289307\pi\) | ||||
0.614626 | + | 0.788819i | \(0.289307\pi\) | |||||||
\(860\) | 28.8899 | 0.985137 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.22704 | 0.109913 | ||||||||
\(863\) | −4.31646 | −0.146934 | −0.0734670 | − | 0.997298i | \(-0.523406\pi\) | ||||
−0.0734670 | + | 0.997298i | \(0.523406\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.1229 | 0.718199 | ||||||||
\(866\) | 6.86583 | 0.233310 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23.3932 | 0.794015 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.3984 | −0.420102 | ||||||||
\(872\) | 10.1549 | 0.343889 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.2339 | 0.549121 | ||||||||
\(875\) | 41.2589 | 1.39481 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.1160 | 1.05071 | 0.525356 | − | 0.850882i | \(-0.323932\pi\) | ||||
0.525356 | + | 0.850882i | \(0.323932\pi\) | |||||||
\(878\) | 12.3498 | 0.416785 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.9267 | −1.47993 | −0.739964 | − | 0.672647i | \(-0.765157\pi\) | ||||
−0.739964 | + | 0.672647i | \(0.765157\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.87946 | −0.197860 | −0.0989298 | − | 0.995094i | \(-0.531542\pi\) | ||||
−0.0989298 | + | 0.995094i | \(0.531542\pi\) | |||||||
\(884\) | 23.2444 | 0.781794 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.1563 | −0.441993 | ||||||||
\(887\) | 7.69510 | 0.258376 | 0.129188 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129188 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.8163 | 1.23478 | ||||||||
\(890\) | −6.64689 | −0.222804 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −41.3640 | −1.38497 | ||||||||
\(893\) | −4.77220 | −0.159696 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.3788 | 1.24944 | ||||||||
\(896\) | −38.5711 | −1.28857 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.95316 | −0.232030 | ||||||||
\(899\) | 6.59352 | 0.219906 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.5180 | 1.38316 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.2581 | −1.00637 | ||||||||
\(905\) | 7.48212 | 0.248714 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.9906 | −0.630571 | −0.315285 | − | 0.948997i | \(-0.602100\pi\) | ||||
−0.315285 | + | 0.948997i | \(0.602100\pi\) | |||||||
\(908\) | −20.9761 | −0.696116 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.4241 | 0.378705 | ||||||||
\(911\) | −50.0353 | −1.65774 | −0.828871 | − | 0.559439i | \(-0.811017\pi\) | ||||
−0.828871 | + | 0.559439i | \(0.811017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 12.0864 | 0.399783 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.37954 | −0.177745 | ||||||||
\(917\) | 72.1519 | 2.38266 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.07419 | 0.101408 | 0.0507042 | − | 0.998714i | \(-0.483853\pi\) | ||||
0.0507042 | + | 0.998714i | \(0.483853\pi\) | |||||||
\(920\) | −23.5985 | −0.778021 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.8732 | 0.423956 | ||||||||
\(923\) | 28.0540 | 0.923410 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.38283 | −0.209866 | ||||||||
\(926\) | 6.22544 | 0.204581 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.40617 | −0.275946 | ||||||||
\(929\) | 0.905574 | 0.0297109 | 0.0148555 | − | 0.999890i | \(-0.495271\pi\) | ||||
0.0148555 | + | 0.999890i | \(0.495271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.4611 | −0.670585 | ||||||||
\(932\) | −43.1609 | −1.41378 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.5887 | 0.444634 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.0542 | −0.720481 | −0.360240 | − | 0.932860i | \(-0.617305\pi\) | ||||
−0.360240 | + | 0.932860i | \(0.617305\pi\) | |||||||
\(938\) | 5.18781 | 0.169388 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.24660 | 0.105892 | ||||||||
\(941\) | −5.46092 | −0.178021 | −0.0890105 | − | 0.996031i | \(-0.528370\pi\) | ||||
−0.0890105 | + | 0.996031i | \(0.528370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.92844 | 0.0953630 | ||||||||
\(944\) | 9.55957 | 0.311138 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.4406 | −1.05418 | −0.527089 | − | 0.849810i | \(-0.676717\pi\) | ||||
−0.527089 | + | 0.849810i | \(0.676717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.1392 | 1.95220 | ||||||||
\(950\) | 4.51163 | 0.146377 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20.7822 | −0.673554 | ||||||||
\(953\) | 53.8088 | 1.74304 | 0.871518 | − | 0.490363i | \(-0.163136\pi\) | ||||
0.871518 | + | 0.490363i | \(0.163136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.3774 | 0.691756 | ||||||||
\(956\) | −12.2290 | −0.395516 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.66260 | 0.247567 | ||||||||
\(959\) | −10.9155 | −0.352479 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.8016 | −0.509728 | ||||||||
\(962\) | −6.01137 | −0.193814 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.6717 | 0.440335 | ||||||||
\(965\) | 21.4645 | 0.690966 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.8151 | −0.926630 | −0.463315 | − | 0.886194i | \(-0.653340\pi\) | ||||
−0.463315 | + | 0.886194i | \(0.653340\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.287516 | −0.00923160 | ||||||||
\(971\) | −5.39405 | −0.173103 | −0.0865517 | − | 0.996247i | \(-0.527585\pi\) | ||||
−0.0865517 | + | 0.996247i | \(0.527585\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.1362 | −1.63935 | ||||||||
\(974\) | 13.2075 | 0.423197 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0736 | −0.322450 | ||||||||
\(977\) | 3.31236 | 0.105972 | 0.0529859 | − | 0.998595i | \(-0.483126\pi\) | ||||
0.0529859 | + | 0.998595i | \(0.483126\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 13.9200 | 0.444657 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.1291 | −0.610435 | ||||||||
\(983\) | −33.8721 | −1.08035 | −0.540176 | − | 0.841552i | \(-0.681643\pi\) | ||||
−0.540176 | + | 0.841552i | \(0.681643\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.6717 | −0.563067 | ||||||||
\(986\) | −2.74137 | −0.0873029 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.0738 | −0.988589 | ||||||||
\(989\) | −72.0183 | −2.29005 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.66640 | 0.275297 | 0.137649 | − | 0.990481i | \(-0.456046\pi\) | ||||
0.137649 | + | 0.990481i | \(0.456046\pi\) | |||||||
\(992\) | −19.3767 | −0.615211 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.7386 | −0.372325 | ||||||||
\(995\) | −45.2280 | −1.43382 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.2654 | −0.958515 | −0.479258 | − | 0.877674i | \(-0.659094\pi\) | ||||
−0.479258 | + | 0.877674i | \(0.659094\pi\) | |||||||
\(998\) | −11.7891 | −0.373177 | ||||||||
\(999\) | 0 | 0 |
(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 | 9801.2.a.cp.1.10 | 18 | ||
3.2 | odd | 2 | 9801.2.a.cm.1.9 | 18 | |||
9.2 | odd | 6 | 1089.2.e.p.364.10 | 36 | |||
9.5 | odd | 6 | 1089.2.e.p.727.10 | 36 | |||
11.5 | even | 5 | 891.2.f.e.487.5 | 36 | |||
11.9 | even | 5 | 891.2.f.e.730.5 | 36 | |||
11.10 | odd | 2 | 9801.2.a.cn.1.9 | 18 | |||
33.5 | odd | 10 | 891.2.f.f.487.5 | 36 | |||
33.20 | odd | 10 | 891.2.f.f.730.5 | 36 | |||
33.32 | even | 2 | 9801.2.a.co.1.10 | 18 | |||
99.5 | odd | 30 | 99.2.m.b.25.5 | yes | 72 | ||
99.16 | even | 15 | 297.2.n.b.91.5 | 72 | |||
99.20 | odd | 30 | 99.2.m.b.4.5 | ✓ | 72 | ||
99.31 | even | 15 | 297.2.n.b.235.5 | 72 | |||
99.32 | even | 6 | 1089.2.e.o.727.9 | 36 | |||
99.38 | odd | 30 | 99.2.m.b.58.5 | yes | 72 | ||
99.49 | even | 15 | 297.2.n.b.289.5 | 72 | |||
99.65 | even | 6 | 1089.2.e.o.364.9 | 36 | |||
99.86 | odd | 30 | 99.2.m.b.70.5 | yes | 72 | ||
99.97 | even | 15 | 297.2.n.b.37.5 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.4.5 | ✓ | 72 | 99.20 | odd | 30 | ||
99.2.m.b.25.5 | yes | 72 | 99.5 | odd | 30 | ||
99.2.m.b.58.5 | yes | 72 | 99.38 | odd | 30 | ||
99.2.m.b.70.5 | yes | 72 | 99.86 | odd | 30 | ||
297.2.n.b.37.5 | 72 | 99.97 | even | 15 | |||
297.2.n.b.91.5 | 72 | 99.16 | even | 15 | |||
297.2.n.b.235.5 | 72 | 99.31 | even | 15 | |||
297.2.n.b.289.5 | 72 | 99.49 | even | 15 | |||
891.2.f.e.487.5 | 36 | 11.5 | even | 5 | |||
891.2.f.e.730.5 | 36 | 11.9 | even | 5 | |||
891.2.f.f.487.5 | 36 | 33.5 | odd | 10 | |||
891.2.f.f.730.5 | 36 | 33.20 | odd | 10 | |||
1089.2.e.o.364.9 | 36 | 99.65 | even | 6 | |||
1089.2.e.o.727.9 | 36 | 99.32 | even | 6 | |||
1089.2.e.p.364.10 | 36 | 9.2 | odd | 6 | |||
1089.2.e.p.727.10 | 36 | 9.5 | odd | 6 | |||
9801.2.a.cm.1.9 | 18 | 3.2 | odd | 2 | |||
9801.2.a.cn.1.9 | 18 | 11.10 | odd | 2 | |||
9801.2.a.co.1.10 | 18 | 33.32 | even | 2 | |||
9801.2.a.cp.1.10 | 18 | 1.1 | even | 1 | trivial |