Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.44504 | −0.646242 | −0.323121 | − | 0.946358i | \(-0.604732\pi\) | ||||
−0.323121 | + | 0.946358i | \(0.604732\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.44504 | −0.456962 | ||||||||
\(11\) | −3.74094 | −1.12794 | −0.563968 | − | 0.825797i | \(-0.690726\pi\) | ||||
−0.563968 | + | 0.825797i | \(0.690726\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.44504 | 0.373108 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.692021 | 0.167840 | 0.0839199 | − | 0.996473i | \(-0.473256\pi\) | ||||
0.0839199 | + | 0.996473i | \(0.473256\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.753020 | −0.172755 | −0.0863774 | − | 0.996262i | \(-0.527529\pi\) | ||||
−0.0863774 | + | 0.996262i | \(0.527529\pi\) | |||||||
\(20\) | −1.44504 | −0.323121 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −3.74094 | −0.797571 | ||||||||
\(23\) | 1.82908 | 0.381391 | 0.190695 | − | 0.981649i | \(-0.438926\pi\) | ||||
0.190695 | + | 0.981649i | \(0.438926\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.91185 | −0.582371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 6.89977 | 1.28126 | 0.640628 | − | 0.767852i | \(-0.278674\pi\) | ||||
0.640628 | + | 0.767852i | \(0.278674\pi\) | |||||||
\(30\) | 1.44504 | 0.263827 | ||||||||
\(31\) | 0.960771 | 0.172560 | 0.0862798 | − | 0.996271i | \(-0.472502\pi\) | ||||
0.0862798 | + | 0.996271i | \(0.472502\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.74094 | 0.651214 | ||||||||
\(34\) | 0.692021 | 0.118681 | ||||||||
\(35\) | −1.44504 | −0.244257 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.04892 | −0.501239 | −0.250619 | − | 0.968086i | \(-0.580634\pi\) | ||||
−0.250619 | + | 0.968086i | \(0.580634\pi\) | |||||||
\(38\) | −0.753020 | −0.122156 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.44504 | −0.228481 | ||||||||
\(41\) | 1.44504 | 0.225678 | 0.112839 | − | 0.993613i | \(-0.464006\pi\) | ||||
0.112839 | + | 0.993613i | \(0.464006\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 5.82908 | 0.888927 | 0.444464 | − | 0.895797i | \(-0.353394\pi\) | ||||
0.444464 | + | 0.895797i | \(0.353394\pi\) | |||||||
\(44\) | −3.74094 | −0.563968 | ||||||||
\(45\) | −1.44504 | −0.215414 | ||||||||
\(46\) | 1.82908 | 0.269684 | ||||||||
\(47\) | −3.71379 | −0.541712 | −0.270856 | − | 0.962620i | \(-0.587307\pi\) | ||||
−0.270856 | + | 0.962620i | \(0.587307\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.91185 | −0.411798 | ||||||||
\(51\) | −0.692021 | −0.0969024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.57673 | −0.216580 | −0.108290 | − | 0.994119i | \(-0.534538\pi\) | ||||
−0.108290 | + | 0.994119i | \(0.534538\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 5.40581 | 0.728920 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0.753020 | 0.0997400 | ||||||||
\(58\) | 6.89977 | 0.905985 | ||||||||
\(59\) | 6.65279 | 0.866120 | 0.433060 | − | 0.901365i | \(-0.357434\pi\) | ||||
0.433060 | + | 0.901365i | \(0.357434\pi\) | |||||||
\(60\) | 1.44504 | 0.186554 | ||||||||
\(61\) | −7.00000 | −0.896258 | −0.448129 | − | 0.893969i | \(-0.647910\pi\) | ||||
−0.448129 | + | 0.893969i | \(0.647910\pi\) | |||||||
\(62\) | 0.960771 | 0.122018 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.74094 | 0.460478 | ||||||||
\(67\) | −9.11960 | −1.11414 | −0.557069 | − | 0.830467i | \(-0.688074\pi\) | ||||
−0.557069 | + | 0.830467i | \(0.688074\pi\) | |||||||
\(68\) | 0.692021 | 0.0839199 | ||||||||
\(69\) | −1.82908 | −0.220196 | ||||||||
\(70\) | −1.44504 | −0.172716 | ||||||||
\(71\) | 0.219833 | 0.0260893 | 0.0130447 | − | 0.999915i | \(-0.495848\pi\) | ||||
0.0130447 | + | 0.999915i | \(0.495848\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −4.91185 | −0.574889 | −0.287445 | − | 0.957797i | \(-0.592806\pi\) | ||||
−0.287445 | + | 0.957797i | \(0.592806\pi\) | |||||||
\(74\) | −3.04892 | −0.354429 | ||||||||
\(75\) | 2.91185 | 0.336232 | ||||||||
\(76\) | −0.753020 | −0.0863774 | ||||||||
\(77\) | −3.74094 | −0.426320 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.44504 | −0.837633 | −0.418816 | − | 0.908071i | \(-0.637555\pi\) | ||||
−0.418816 | + | 0.908071i | \(0.637555\pi\) | |||||||
\(80\) | −1.44504 | −0.161561 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.44504 | 0.159578 | ||||||||
\(83\) | −8.75302 | −0.960769 | −0.480384 | − | 0.877058i | \(-0.659503\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −1.00000 | −0.108465 | ||||||||
\(86\) | 5.82908 | 0.628566 | ||||||||
\(87\) | −6.89977 | −0.739733 | ||||||||
\(88\) | −3.74094 | −0.398785 | ||||||||
\(89\) | −14.5579 | −1.54314 | −0.771569 | − | 0.636145i | \(-0.780528\pi\) | ||||
−0.771569 | + | 0.636145i | \(0.780528\pi\) | |||||||
\(90\) | −1.44504 | −0.152321 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.82908 | 0.190695 | ||||||||
\(93\) | −0.960771 | −0.0996273 | ||||||||
\(94\) | −3.71379 | −0.383048 | ||||||||
\(95\) | 1.08815 | 0.111641 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.06100 | −0.615401 | −0.307701 | − | 0.951483i | \(-0.599560\pi\) | ||||
−0.307701 | + | 0.951483i | \(0.599560\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −3.74094 | −0.375978 | ||||||||
\(100\) | −2.91185 | −0.291185 | ||||||||
\(101\) | −2.81402 | −0.280005 | −0.140003 | − | 0.990151i | \(-0.544711\pi\) | ||||
−0.140003 | + | 0.990151i | \(0.544711\pi\) | |||||||
\(102\) | −0.692021 | −0.0685203 | ||||||||
\(103\) | −8.23490 | −0.811409 | −0.405704 | − | 0.914004i | \(-0.632974\pi\) | ||||
−0.405704 | + | 0.914004i | \(0.632974\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.44504 | 0.141022 | ||||||||
\(106\) | −1.57673 | −0.153145 | ||||||||
\(107\) | 10.6039 | 1.02512 | 0.512558 | − | 0.858653i | \(-0.328698\pi\) | ||||
0.512558 | + | 0.858653i | \(0.328698\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 8.48858 | 0.813059 | 0.406529 | − | 0.913638i | \(-0.366739\pi\) | ||||
0.406529 | + | 0.913638i | \(0.366739\pi\) | |||||||
\(110\) | 5.40581 | 0.515424 | ||||||||
\(111\) | 3.04892 | 0.289390 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −5.92692 | −0.557558 | −0.278779 | − | 0.960355i | \(-0.589930\pi\) | ||||
−0.278779 | + | 0.960355i | \(0.589930\pi\) | |||||||
\(114\) | 0.753020 | 0.0705268 | ||||||||
\(115\) | −2.64310 | −0.246471 | ||||||||
\(116\) | 6.89977 | 0.640628 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.65279 | 0.612439 | ||||||||
\(119\) | 0.692021 | 0.0634375 | ||||||||
\(120\) | 1.44504 | 0.131914 | ||||||||
\(121\) | 2.99462 | 0.272238 | ||||||||
\(122\) | −7.00000 | −0.633750 | ||||||||
\(123\) | −1.44504 | −0.130295 | ||||||||
\(124\) | 0.960771 | 0.0862798 | ||||||||
\(125\) | 11.4330 | 1.02260 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 9.67994 | 0.858956 | 0.429478 | − | 0.903077i | \(-0.358698\pi\) | ||||
0.429478 | + | 0.903077i | \(0.358698\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.82908 | −0.513222 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.25236 | 0.196789 | 0.0983946 | − | 0.995147i | \(-0.468629\pi\) | ||||
0.0983946 | + | 0.995147i | \(0.468629\pi\) | |||||||
\(132\) | 3.74094 | 0.325607 | ||||||||
\(133\) | −0.753020 | −0.0652951 | ||||||||
\(134\) | −9.11960 | −0.787814 | ||||||||
\(135\) | 1.44504 | 0.124369 | ||||||||
\(136\) | 0.692021 | 0.0593404 | ||||||||
\(137\) | −12.0489 | −1.02941 | −0.514704 | − | 0.857368i | \(-0.672098\pi\) | ||||
−0.514704 | + | 0.857368i | \(0.672098\pi\) | |||||||
\(138\) | −1.82908 | −0.155702 | ||||||||
\(139\) | −16.6383 | −1.41124 | −0.705622 | − | 0.708589i | \(-0.749332\pi\) | ||||
−0.705622 | + | 0.708589i | \(0.749332\pi\) | |||||||
\(140\) | −1.44504 | −0.122128 | ||||||||
\(141\) | 3.71379 | 0.312758 | ||||||||
\(142\) | 0.219833 | 0.0184479 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −9.97046 | −0.828002 | ||||||||
\(146\) | −4.91185 | −0.406508 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −3.04892 | −0.250619 | ||||||||
\(149\) | 8.35690 | 0.684624 | 0.342312 | − | 0.939586i | \(-0.388790\pi\) | ||||
0.342312 | + | 0.939586i | \(0.388790\pi\) | |||||||
\(150\) | 2.91185 | 0.237752 | ||||||||
\(151\) | −7.63102 | −0.621004 | −0.310502 | − | 0.950573i | \(-0.600497\pi\) | ||||
−0.310502 | + | 0.950573i | \(0.600497\pi\) | |||||||
\(152\) | −0.753020 | −0.0610780 | ||||||||
\(153\) | 0.692021 | 0.0559466 | ||||||||
\(154\) | −3.74094 | −0.301453 | ||||||||
\(155\) | −1.38835 | −0.111515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2935 | 0.981128 | 0.490564 | − | 0.871405i | \(-0.336791\pi\) | ||||
0.490564 | + | 0.871405i | \(0.336791\pi\) | |||||||
\(158\) | −7.44504 | −0.592296 | ||||||||
\(159\) | 1.57673 | 0.125043 | ||||||||
\(160\) | −1.44504 | −0.114241 | ||||||||
\(161\) | 1.82908 | 0.144152 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −15.0151 | −1.17607 | −0.588035 | − | 0.808835i | \(-0.700098\pi\) | ||||
−0.588035 | + | 0.808835i | \(0.700098\pi\) | |||||||
\(164\) | 1.44504 | 0.112839 | ||||||||
\(165\) | −5.40581 | −0.420842 | ||||||||
\(166\) | −8.75302 | −0.679366 | ||||||||
\(167\) | 18.3153 | 1.41728 | 0.708639 | − | 0.705571i | \(-0.249309\pi\) | ||||
0.708639 | + | 0.705571i | \(0.249309\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | −0.753020 | −0.0575849 | ||||||||
\(172\) | 5.82908 | 0.444464 | ||||||||
\(173\) | −16.7875 | −1.27633 | −0.638164 | − | 0.769901i | \(-0.720306\pi\) | ||||
−0.638164 | + | 0.769901i | \(0.720306\pi\) | |||||||
\(174\) | −6.89977 | −0.523070 | ||||||||
\(175\) | −2.91185 | −0.220115 | ||||||||
\(176\) | −3.74094 | −0.281984 | ||||||||
\(177\) | −6.65279 | −0.500055 | ||||||||
\(178\) | −14.5579 | −1.09116 | ||||||||
\(179\) | 4.86725 | 0.363795 | 0.181898 | − | 0.983317i | \(-0.441776\pi\) | ||||
0.181898 | + | 0.983317i | \(0.441776\pi\) | |||||||
\(180\) | −1.44504 | −0.107707 | ||||||||
\(181\) | −13.4644 | −1.00080 | −0.500401 | − | 0.865794i | \(-0.666814\pi\) | ||||
−0.500401 | + | 0.865794i | \(0.666814\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.00000 | 0.517455 | ||||||||
\(184\) | 1.82908 | 0.134842 | ||||||||
\(185\) | 4.40581 | 0.323922 | ||||||||
\(186\) | −0.960771 | −0.0704472 | ||||||||
\(187\) | −2.58881 | −0.189313 | ||||||||
\(188\) | −3.71379 | −0.270856 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 1.08815 | 0.0789424 | ||||||||
\(191\) | −5.26444 | −0.380921 | −0.190461 | − | 0.981695i | \(-0.560998\pi\) | ||||
−0.190461 | + | 0.981695i | \(0.560998\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −22.8713 | −1.64631 | −0.823156 | − | 0.567815i | \(-0.807789\pi\) | ||||
−0.823156 | + | 0.567815i | \(0.807789\pi\) | |||||||
\(194\) | −6.06100 | −0.435154 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 18.8877 | 1.34569 | 0.672846 | − | 0.739782i | \(-0.265072\pi\) | ||||
0.672846 | + | 0.739782i | \(0.265072\pi\) | |||||||
\(198\) | −3.74094 | −0.265857 | ||||||||
\(199\) | −3.36898 | −0.238820 | −0.119410 | − | 0.992845i | \(-0.538100\pi\) | ||||
−0.119410 | + | 0.992845i | \(0.538100\pi\) | |||||||
\(200\) | −2.91185 | −0.205899 | ||||||||
\(201\) | 9.11960 | 0.643247 | ||||||||
\(202\) | −2.81402 | −0.197994 | ||||||||
\(203\) | 6.89977 | 0.484269 | ||||||||
\(204\) | −0.692021 | −0.0484512 | ||||||||
\(205\) | −2.08815 | −0.145842 | ||||||||
\(206\) | −8.23490 | −0.573753 | ||||||||
\(207\) | 1.82908 | 0.127130 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.81700 | 0.194856 | ||||||||
\(210\) | 1.44504 | 0.0997174 | ||||||||
\(211\) | 17.1511 | 1.18073 | 0.590364 | − | 0.807137i | \(-0.298984\pi\) | ||||
0.590364 | + | 0.807137i | \(0.298984\pi\) | |||||||
\(212\) | −1.57673 | −0.108290 | ||||||||
\(213\) | −0.219833 | −0.0150627 | ||||||||
\(214\) | 10.6039 | 0.724866 | ||||||||
\(215\) | −8.42327 | −0.574462 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.960771 | 0.0652214 | ||||||||
\(218\) | 8.48858 | 0.574919 | ||||||||
\(219\) | 4.91185 | 0.331912 | ||||||||
\(220\) | 5.40581 | 0.364460 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.04892 | 0.204630 | ||||||||
\(223\) | −25.0911 | −1.68023 | −0.840113 | − | 0.542411i | \(-0.817512\pi\) | ||||
−0.840113 | + | 0.542411i | \(0.817512\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −2.91185 | −0.194124 | ||||||||
\(226\) | −5.92692 | −0.394253 | ||||||||
\(227\) | 5.84415 | 0.387890 | 0.193945 | − | 0.981012i | \(-0.437872\pi\) | ||||
0.193945 | + | 0.981012i | \(0.437872\pi\) | |||||||
\(228\) | 0.753020 | 0.0498700 | ||||||||
\(229\) | −15.2252 | −1.00611 | −0.503055 | − | 0.864254i | \(-0.667791\pi\) | ||||
−0.503055 | + | 0.864254i | \(0.667791\pi\) | |||||||
\(230\) | −2.64310 | −0.174281 | ||||||||
\(231\) | 3.74094 | 0.246136 | ||||||||
\(232\) | 6.89977 | 0.452992 | ||||||||
\(233\) | −25.2000 | −1.65091 | −0.825453 | − | 0.564471i | \(-0.809080\pi\) | ||||
−0.825453 | + | 0.564471i | \(0.809080\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.36658 | 0.350077 | ||||||||
\(236\) | 6.65279 | 0.433060 | ||||||||
\(237\) | 7.44504 | 0.483607 | ||||||||
\(238\) | 0.692021 | 0.0448571 | ||||||||
\(239\) | 6.71379 | 0.434279 | 0.217140 | − | 0.976141i | \(-0.430327\pi\) | ||||
0.217140 | + | 0.976141i | \(0.430327\pi\) | |||||||
\(240\) | 1.44504 | 0.0932771 | ||||||||
\(241\) | −5.21313 | −0.335807 | −0.167904 | − | 0.985803i | \(-0.553700\pi\) | ||||
−0.167904 | + | 0.985803i | \(0.553700\pi\) | |||||||
\(242\) | 2.99462 | 0.192502 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.00000 | −0.448129 | ||||||||
\(245\) | −1.44504 | −0.0923203 | ||||||||
\(246\) | −1.44504 | −0.0921325 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.960771 | 0.0610090 | ||||||||
\(249\) | 8.75302 | 0.554700 | ||||||||
\(250\) | 11.4330 | 0.723084 | ||||||||
\(251\) | 9.22952 | 0.582562 | 0.291281 | − | 0.956638i | \(-0.405919\pi\) | ||||
0.291281 | + | 0.956638i | \(0.405919\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −6.84249 | −0.430184 | ||||||||
\(254\) | 9.67994 | 0.607373 | ||||||||
\(255\) | 1.00000 | 0.0626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.51035 | 0.156591 | 0.0782957 | − | 0.996930i | \(-0.475052\pi\) | ||||
0.0782957 | + | 0.996930i | \(0.475052\pi\) | |||||||
\(258\) | −5.82908 | −0.362903 | ||||||||
\(259\) | −3.04892 | −0.189451 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.89977 | 0.427085 | ||||||||
\(262\) | 2.25236 | 0.139151 | ||||||||
\(263\) | 30.1511 | 1.85919 | 0.929597 | − | 0.368577i | \(-0.120155\pi\) | ||||
0.929597 | + | 0.368577i | \(0.120155\pi\) | |||||||
\(264\) | 3.74094 | 0.230239 | ||||||||
\(265\) | 2.27844 | 0.139963 | ||||||||
\(266\) | −0.753020 | −0.0461706 | ||||||||
\(267\) | 14.5579 | 0.890932 | ||||||||
\(268\) | −9.11960 | −0.557069 | ||||||||
\(269\) | −14.6063 | −0.890560 | −0.445280 | − | 0.895391i | \(-0.646896\pi\) | ||||
−0.445280 | + | 0.895391i | \(0.646896\pi\) | |||||||
\(270\) | 1.44504 | 0.0879424 | ||||||||
\(271\) | −22.0978 | −1.34235 | −0.671174 | − | 0.741300i | \(-0.734210\pi\) | ||||
−0.671174 | + | 0.741300i | \(0.734210\pi\) | |||||||
\(272\) | 0.692021 | 0.0419600 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0489 | −0.727902 | ||||||||
\(275\) | 10.8931 | 0.656877 | ||||||||
\(276\) | −1.82908 | −0.110098 | ||||||||
\(277\) | 1.23729 | 0.0743416 | 0.0371708 | − | 0.999309i | \(-0.488165\pi\) | ||||
0.0371708 | + | 0.999309i | \(0.488165\pi\) | |||||||
\(278\) | −16.6383 | −0.997900 | ||||||||
\(279\) | 0.960771 | 0.0575199 | ||||||||
\(280\) | −1.44504 | −0.0863578 | ||||||||
\(281\) | −8.51035 | −0.507685 | −0.253843 | − | 0.967246i | \(-0.581695\pi\) | ||||
−0.253843 | + | 0.967246i | \(0.581695\pi\) | |||||||
\(282\) | 3.71379 | 0.221153 | ||||||||
\(283\) | −16.3002 | −0.968947 | −0.484473 | − | 0.874806i | \(-0.660989\pi\) | ||||
−0.484473 | + | 0.874806i | \(0.660989\pi\) | |||||||
\(284\) | 0.219833 | 0.0130447 | ||||||||
\(285\) | −1.08815 | −0.0644562 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.44504 | 0.0852981 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.5211 | −0.971830 | ||||||||
\(290\) | −9.97046 | −0.585486 | ||||||||
\(291\) | 6.06100 | 0.355302 | ||||||||
\(292\) | −4.91185 | −0.287445 | ||||||||
\(293\) | −29.8853 | −1.74592 | −0.872959 | − | 0.487794i | \(-0.837802\pi\) | ||||
−0.872959 | + | 0.487794i | \(0.837802\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −9.61356 | −0.559723 | ||||||||
\(296\) | −3.04892 | −0.177215 | ||||||||
\(297\) | 3.74094 | 0.217071 | ||||||||
\(298\) | 8.35690 | 0.484102 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.91185 | 0.168116 | ||||||||
\(301\) | 5.82908 | 0.335983 | ||||||||
\(302\) | −7.63102 | −0.439116 | ||||||||
\(303\) | 2.81402 | 0.161661 | ||||||||
\(304\) | −0.753020 | −0.0431887 | ||||||||
\(305\) | 10.1153 | 0.579200 | ||||||||
\(306\) | 0.692021 | 0.0395602 | ||||||||
\(307\) | −24.4547 | −1.39571 | −0.697853 | − | 0.716241i | \(-0.745861\pi\) | ||||
−0.697853 | + | 0.716241i | \(0.745861\pi\) | |||||||
\(308\) | −3.74094 | −0.213160 | ||||||||
\(309\) | 8.23490 | 0.468467 | ||||||||
\(310\) | −1.38835 | −0.0788533 | ||||||||
\(311\) | −22.3177 | −1.26552 | −0.632759 | − | 0.774348i | \(-0.718078\pi\) | ||||
−0.632759 | + | 0.774348i | \(0.718078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.47889 | −0.140115 | −0.0700577 | − | 0.997543i | \(-0.522318\pi\) | ||||
−0.0700577 | + | 0.997543i | \(0.522318\pi\) | |||||||
\(314\) | 12.2935 | 0.693763 | ||||||||
\(315\) | −1.44504 | −0.0814189 | ||||||||
\(316\) | −7.44504 | −0.418816 | ||||||||
\(317\) | −5.65710 | −0.317735 | −0.158867 | − | 0.987300i | \(-0.550784\pi\) | ||||
−0.158867 | + | 0.987300i | \(0.550784\pi\) | |||||||
\(318\) | 1.57673 | 0.0884185 | ||||||||
\(319\) | −25.8116 | −1.44517 | ||||||||
\(320\) | −1.44504 | −0.0807803 | ||||||||
\(321\) | −10.6039 | −0.591851 | ||||||||
\(322\) | 1.82908 | 0.101931 | ||||||||
\(323\) | −0.521106 | −0.0289951 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.0151 | −0.831608 | ||||||||
\(327\) | −8.48858 | −0.469420 | ||||||||
\(328\) | 1.44504 | 0.0797891 | ||||||||
\(329\) | −3.71379 | −0.204748 | ||||||||
\(330\) | −5.40581 | −0.297580 | ||||||||
\(331\) | 23.1879 | 1.27452 | 0.637261 | − | 0.770648i | \(-0.280067\pi\) | ||||
0.637261 | + | 0.770648i | \(0.280067\pi\) | |||||||
\(332\) | −8.75302 | −0.480384 | ||||||||
\(333\) | −3.04892 | −0.167080 | ||||||||
\(334\) | 18.3153 | 1.00217 | ||||||||
\(335\) | 13.1782 | 0.720003 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 10.4873 | 0.571277 | 0.285639 | − | 0.958337i | \(-0.407794\pi\) | ||||
0.285639 | + | 0.958337i | \(0.407794\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.92692 | 0.321906 | ||||||||
\(340\) | −1.00000 | −0.0542326 | ||||||||
\(341\) | −3.59419 | −0.194636 | ||||||||
\(342\) | −0.753020 | −0.0407187 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 5.82908 | 0.314283 | ||||||||
\(345\) | 2.64310 | 0.142300 | ||||||||
\(346\) | −16.7875 | −0.902500 | ||||||||
\(347\) | −5.28514 | −0.283721 | −0.141861 | − | 0.989887i | \(-0.545309\pi\) | ||||
−0.141861 | + | 0.989887i | \(0.545309\pi\) | |||||||
\(348\) | −6.89977 | −0.369867 | ||||||||
\(349\) | 8.19029 | 0.438416 | 0.219208 | − | 0.975678i | \(-0.429653\pi\) | ||||
0.219208 | + | 0.975678i | \(0.429653\pi\) | |||||||
\(350\) | −2.91185 | −0.155645 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.74094 | −0.199393 | ||||||||
\(353\) | 35.9758 | 1.91480 | 0.957400 | − | 0.288764i | \(-0.0932443\pi\) | ||||
0.957400 | + | 0.288764i | \(0.0932443\pi\) | |||||||
\(354\) | −6.65279 | −0.353592 | ||||||||
\(355\) | −0.317667 | −0.0168600 | ||||||||
\(356\) | −14.5579 | −0.771569 | ||||||||
\(357\) | −0.692021 | −0.0366257 | ||||||||
\(358\) | 4.86725 | 0.257242 | ||||||||
\(359\) | −28.7603 | −1.51791 | −0.758956 | − | 0.651142i | \(-0.774290\pi\) | ||||
−0.758956 | + | 0.651142i | \(0.774290\pi\) | |||||||
\(360\) | −1.44504 | −0.0761604 | ||||||||
\(361\) | −18.4330 | −0.970156 | ||||||||
\(362\) | −13.4644 | −0.707674 | ||||||||
\(363\) | −2.99462 | −0.157177 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.09783 | 0.371518 | ||||||||
\(366\) | 7.00000 | 0.365896 | ||||||||
\(367\) | −3.61463 | −0.188682 | −0.0943411 | − | 0.995540i | \(-0.530074\pi\) | ||||
−0.0943411 | + | 0.995540i | \(0.530074\pi\) | |||||||
\(368\) | 1.82908 | 0.0953476 | ||||||||
\(369\) | 1.44504 | 0.0752259 | ||||||||
\(370\) | 4.40581 | 0.229047 | ||||||||
\(371\) | −1.57673 | −0.0818597 | ||||||||
\(372\) | −0.960771 | −0.0498137 | ||||||||
\(373\) | 17.9312 | 0.928444 | 0.464222 | − | 0.885719i | \(-0.346334\pi\) | ||||
0.464222 | + | 0.885719i | \(0.346334\pi\) | |||||||
\(374\) | −2.58881 | −0.133864 | ||||||||
\(375\) | −11.4330 | −0.590396 | ||||||||
\(376\) | −3.71379 | −0.191524 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 22.2338 | 1.14208 | 0.571038 | − | 0.820924i | \(-0.306541\pi\) | ||||
0.571038 | + | 0.820924i | \(0.306541\pi\) | |||||||
\(380\) | 1.08815 | 0.0558207 | ||||||||
\(381\) | −9.67994 | −0.495918 | ||||||||
\(382\) | −5.26444 | −0.269352 | ||||||||
\(383\) | −25.4330 | −1.29956 | −0.649782 | − | 0.760121i | \(-0.725140\pi\) | ||||
−0.649782 | + | 0.760121i | \(0.725140\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 5.40581 | 0.275506 | ||||||||
\(386\) | −22.8713 | −1.16412 | ||||||||
\(387\) | 5.82908 | 0.296309 | ||||||||
\(388\) | −6.06100 | −0.307701 | ||||||||
\(389\) | −14.9855 | −0.759796 | −0.379898 | − | 0.925028i | \(-0.624041\pi\) | ||||
−0.379898 | + | 0.925028i | \(0.624041\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.26577 | 0.0640125 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −2.25236 | −0.113616 | ||||||||
\(394\) | 18.8877 | 0.951548 | ||||||||
\(395\) | 10.7584 | 0.541314 | ||||||||
\(396\) | −3.74094 | −0.187989 | ||||||||
\(397\) | −11.8358 | −0.594021 | −0.297011 | − | 0.954874i | \(-0.595990\pi\) | ||||
−0.297011 | + | 0.954874i | \(0.595990\pi\) | |||||||
\(398\) | −3.36898 | −0.168872 | ||||||||
\(399\) | 0.753020 | 0.0376982 | ||||||||
\(400\) | −2.91185 | −0.145593 | ||||||||
\(401\) | 11.6256 | 0.580557 | 0.290279 | − | 0.956942i | \(-0.406252\pi\) | ||||
0.290279 | + | 0.956942i | \(0.406252\pi\) | |||||||
\(402\) | 9.11960 | 0.454845 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.81402 | −0.140003 | ||||||||
\(405\) | −1.44504 | −0.0718047 | ||||||||
\(406\) | 6.89977 | 0.342430 | ||||||||
\(407\) | 11.4058 | 0.565365 | ||||||||
\(408\) | −0.692021 | −0.0342602 | ||||||||
\(409\) | −8.09485 | −0.400265 | −0.200132 | − | 0.979769i | \(-0.564137\pi\) | ||||
−0.200132 | + | 0.979769i | \(0.564137\pi\) | |||||||
\(410\) | −2.08815 | −0.103126 | ||||||||
\(411\) | 12.0489 | 0.594329 | ||||||||
\(412\) | −8.23490 | −0.405704 | ||||||||
\(413\) | 6.65279 | 0.327363 | ||||||||
\(414\) | 1.82908 | 0.0898946 | ||||||||
\(415\) | 12.6485 | 0.620890 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.6383 | 0.814782 | ||||||||
\(418\) | 2.81700 | 0.137784 | ||||||||
\(419\) | −5.80087 | −0.283391 | −0.141696 | − | 0.989910i | \(-0.545255\pi\) | ||||
−0.141696 | + | 0.989910i | \(0.545255\pi\) | |||||||
\(420\) | 1.44504 | 0.0705108 | ||||||||
\(421\) | 21.9909 | 1.07177 | 0.535885 | − | 0.844291i | \(-0.319978\pi\) | ||||
0.535885 | + | 0.844291i | \(0.319978\pi\) | |||||||
\(422\) | 17.1511 | 0.834901 | ||||||||
\(423\) | −3.71379 | −0.180571 | ||||||||
\(424\) | −1.57673 | −0.0765727 | ||||||||
\(425\) | −2.01507 | −0.0977450 | ||||||||
\(426\) | −0.219833 | −0.0106509 | ||||||||
\(427\) | −7.00000 | −0.338754 | ||||||||
\(428\) | 10.6039 | 0.512558 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.42327 | −0.406206 | ||||||||
\(431\) | 3.34242 | 0.160999 | 0.0804994 | − | 0.996755i | \(-0.474348\pi\) | ||||
0.0804994 | + | 0.996755i | \(0.474348\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 14.0344 | 0.674452 | 0.337226 | − | 0.941424i | \(-0.390511\pi\) | ||||
0.337226 | + | 0.941424i | \(0.390511\pi\) | |||||||
\(434\) | 0.960771 | 0.0461185 | ||||||||
\(435\) | 9.97046 | 0.478047 | ||||||||
\(436\) | 8.48858 | 0.406529 | ||||||||
\(437\) | −1.37734 | −0.0658870 | ||||||||
\(438\) | 4.91185 | 0.234697 | ||||||||
\(439\) | 25.7735 | 1.23010 | 0.615050 | − | 0.788488i | \(-0.289136\pi\) | ||||
0.615050 | + | 0.788488i | \(0.289136\pi\) | |||||||
\(440\) | 5.40581 | 0.257712 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.53558 | 0.263003 | 0.131502 | − | 0.991316i | \(-0.458020\pi\) | ||||
0.131502 | + | 0.991316i | \(0.458020\pi\) | |||||||
\(444\) | 3.04892 | 0.144695 | ||||||||
\(445\) | 21.0368 | 0.997242 | ||||||||
\(446\) | −25.0911 | −1.18810 | ||||||||
\(447\) | −8.35690 | −0.395268 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −21.0616 | −0.993958 | −0.496979 | − | 0.867763i | \(-0.665557\pi\) | ||||
−0.496979 | + | 0.867763i | \(0.665557\pi\) | |||||||
\(450\) | −2.91185 | −0.137266 | ||||||||
\(451\) | −5.40581 | −0.254550 | ||||||||
\(452\) | −5.92692 | −0.278779 | ||||||||
\(453\) | 7.63102 | 0.358537 | ||||||||
\(454\) | 5.84415 | 0.274280 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.753020 | 0.0352634 | ||||||||
\(457\) | −39.7506 | −1.85946 | −0.929728 | − | 0.368247i | \(-0.879958\pi\) | ||||
−0.929728 | + | 0.368247i | \(0.879958\pi\) | |||||||
\(458\) | −15.2252 | −0.711427 | ||||||||
\(459\) | −0.692021 | −0.0323008 | ||||||||
\(460\) | −2.64310 | −0.123235 | ||||||||
\(461\) | −18.7851 | −0.874908 | −0.437454 | − | 0.899241i | \(-0.644120\pi\) | ||||
−0.437454 | + | 0.899241i | \(0.644120\pi\) | |||||||
\(462\) | 3.74094 | 0.174044 | ||||||||
\(463\) | −30.6504 | −1.42444 | −0.712222 | − | 0.701954i | \(-0.752311\pi\) | ||||
−0.712222 | + | 0.701954i | \(0.752311\pi\) | |||||||
\(464\) | 6.89977 | 0.320314 | ||||||||
\(465\) | 1.38835 | 0.0643834 | ||||||||
\(466\) | −25.2000 | −1.16737 | ||||||||
\(467\) | 1.57673 | 0.0729623 | 0.0364811 | − | 0.999334i | \(-0.488385\pi\) | ||||
0.0364811 | + | 0.999334i | \(0.488385\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.11960 | −0.421104 | ||||||||
\(470\) | 5.36658 | 0.247542 | ||||||||
\(471\) | −12.2935 | −0.566455 | ||||||||
\(472\) | 6.65279 | 0.306220 | ||||||||
\(473\) | −21.8062 | −1.00265 | ||||||||
\(474\) | 7.44504 | 0.341962 | ||||||||
\(475\) | 2.19269 | 0.100607 | ||||||||
\(476\) | 0.692021 | 0.0317188 | ||||||||
\(477\) | −1.57673 | −0.0721934 | ||||||||
\(478\) | 6.71379 | 0.307082 | ||||||||
\(479\) | 23.5907 | 1.07789 | 0.538944 | − | 0.842342i | \(-0.318823\pi\) | ||||
0.538944 | + | 0.842342i | \(0.318823\pi\) | |||||||
\(480\) | 1.44504 | 0.0659568 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5.21313 | −0.237451 | ||||||||
\(483\) | −1.82908 | −0.0832262 | ||||||||
\(484\) | 2.99462 | 0.136119 | ||||||||
\(485\) | 8.75840 | 0.397698 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −4.42460 | −0.200498 | −0.100249 | − | 0.994962i | \(-0.531964\pi\) | ||||
−0.100249 | + | 0.994962i | \(0.531964\pi\) | |||||||
\(488\) | −7.00000 | −0.316875 | ||||||||
\(489\) | 15.0151 | 0.679005 | ||||||||
\(490\) | −1.44504 | −0.0652803 | ||||||||
\(491\) | 4.27652 | 0.192997 | 0.0964983 | − | 0.995333i | \(-0.469236\pi\) | ||||
0.0964983 | + | 0.995333i | \(0.469236\pi\) | |||||||
\(492\) | −1.44504 | −0.0651475 | ||||||||
\(493\) | 4.77479 | 0.215046 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.40581 | 0.242973 | ||||||||
\(496\) | 0.960771 | 0.0431399 | ||||||||
\(497\) | 0.219833 | 0.00986084 | ||||||||
\(498\) | 8.75302 | 0.392232 | ||||||||
\(499\) | −5.35152 | −0.239567 | −0.119783 | − | 0.992800i | \(-0.538220\pi\) | ||||
−0.119783 | + | 0.992800i | \(0.538220\pi\) | |||||||
\(500\) | 11.4330 | 0.511298 | ||||||||
\(501\) | −18.3153 | −0.818266 | ||||||||
\(502\) | 9.22952 | 0.411934 | ||||||||
\(503\) | 12.1806 | 0.543106 | 0.271553 | − | 0.962423i | \(-0.412463\pi\) | ||||
0.271553 | + | 0.962423i | \(0.412463\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 4.06638 | 0.180951 | ||||||||
\(506\) | −6.84249 | −0.304186 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.67994 | 0.429478 | ||||||||
\(509\) | 16.4698 | 0.730011 | 0.365005 | − | 0.931005i | \(-0.381067\pi\) | ||||
0.365005 | + | 0.931005i | \(0.381067\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | −4.91185 | −0.217288 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.753020 | 0.0332467 | ||||||||
\(514\) | 2.51035 | 0.110727 | ||||||||
\(515\) | 11.8998 | 0.524367 | ||||||||
\(516\) | −5.82908 | −0.256611 | ||||||||
\(517\) | 13.8931 | 0.611016 | ||||||||
\(518\) | −3.04892 | −0.133962 | ||||||||
\(519\) | 16.7875 | 0.736888 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.89440 | 0.0829950 | 0.0414975 | − | 0.999139i | \(-0.486787\pi\) | ||||
0.0414975 | + | 0.999139i | \(0.486787\pi\) | |||||||
\(522\) | 6.89977 | 0.301995 | ||||||||
\(523\) | 31.7211 | 1.38707 | 0.693533 | − | 0.720425i | \(-0.256053\pi\) | ||||
0.693533 | + | 0.720425i | \(0.256053\pi\) | |||||||
\(524\) | 2.25236 | 0.0983946 | ||||||||
\(525\) | 2.91185 | 0.127084 | ||||||||
\(526\) | 30.1511 | 1.31465 | ||||||||
\(527\) | 0.664874 | 0.0289624 | ||||||||
\(528\) | 3.74094 | 0.162803 | ||||||||
\(529\) | −19.6544 | −0.854541 | ||||||||
\(530\) | 2.27844 | 0.0989690 | ||||||||
\(531\) | 6.65279 | 0.288707 | ||||||||
\(532\) | −0.753020 | −0.0326476 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14.5579 | 0.629984 | ||||||||
\(535\) | −15.3230 | −0.662473 | ||||||||
\(536\) | −9.11960 | −0.393907 | ||||||||
\(537\) | −4.86725 | −0.210037 | ||||||||
\(538\) | −14.6063 | −0.629721 | ||||||||
\(539\) | −3.74094 | −0.161134 | ||||||||
\(540\) | 1.44504 | 0.0621847 | ||||||||
\(541\) | −7.16362 | −0.307988 | −0.153994 | − | 0.988072i | \(-0.549214\pi\) | ||||
−0.153994 | + | 0.988072i | \(0.549214\pi\) | |||||||
\(542\) | −22.0978 | −0.949183 | ||||||||
\(543\) | 13.4644 | 0.577814 | ||||||||
\(544\) | 0.692021 | 0.0296702 | ||||||||
\(545\) | −12.2664 | −0.525433 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.7754 | −1.05932 | −0.529659 | − | 0.848210i | \(-0.677680\pi\) | ||||
−0.529659 | + | 0.848210i | \(0.677680\pi\) | |||||||
\(548\) | −12.0489 | −0.514704 | ||||||||
\(549\) | −7.00000 | −0.298753 | ||||||||
\(550\) | 10.8931 | 0.464482 | ||||||||
\(551\) | −5.19567 | −0.221343 | ||||||||
\(552\) | −1.82908 | −0.0778510 | ||||||||
\(553\) | −7.44504 | −0.316595 | ||||||||
\(554\) | 1.23729 | 0.0525675 | ||||||||
\(555\) | −4.40581 | −0.187016 | ||||||||
\(556\) | −16.6383 | −0.705622 | ||||||||
\(557\) | 29.2653 | 1.24001 | 0.620005 | − | 0.784598i | \(-0.287131\pi\) | ||||
0.620005 | + | 0.784598i | \(0.287131\pi\) | |||||||
\(558\) | 0.960771 | 0.0406727 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.44504 | −0.0610642 | ||||||||
\(561\) | 2.58881 | 0.109300 | ||||||||
\(562\) | −8.51035 | −0.358988 | ||||||||
\(563\) | −7.93230 | −0.334306 | −0.167153 | − | 0.985931i | \(-0.553457\pi\) | ||||
−0.167153 | + | 0.985931i | \(0.553457\pi\) | |||||||
\(564\) | 3.71379 | 0.156379 | ||||||||
\(565\) | 8.56465 | 0.360317 | ||||||||
\(566\) | −16.3002 | −0.685149 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0.219833 | 0.00922397 | ||||||||
\(569\) | 40.7942 | 1.71018 | 0.855090 | − | 0.518479i | \(-0.173502\pi\) | ||||
0.855090 | + | 0.518479i | \(0.173502\pi\) | |||||||
\(570\) | −1.08815 | −0.0455774 | ||||||||
\(571\) | 31.7289 | 1.32781 | 0.663906 | − | 0.747816i | \(-0.268898\pi\) | ||||
0.663906 | + | 0.747816i | \(0.268898\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.26444 | 0.219925 | ||||||||
\(574\) | 1.44504 | 0.0603149 | ||||||||
\(575\) | −5.32603 | −0.222111 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 3.88471 | 0.161722 | 0.0808612 | − | 0.996725i | \(-0.474233\pi\) | ||||
0.0808612 | + | 0.996725i | \(0.474233\pi\) | |||||||
\(578\) | −16.5211 | −0.687187 | ||||||||
\(579\) | 22.8713 | 0.950499 | ||||||||
\(580\) | −9.97046 | −0.414001 | ||||||||
\(581\) | −8.75302 | −0.363136 | ||||||||
\(582\) | 6.06100 | 0.251236 | ||||||||
\(583\) | 5.89844 | 0.244289 | ||||||||
\(584\) | −4.91185 | −0.203254 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.8853 | −1.23455 | ||||||||
\(587\) | −19.2446 | −0.794309 | −0.397155 | − | 0.917752i | \(-0.630002\pi\) | ||||
−0.397155 | + | 0.917752i | \(0.630002\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −0.723480 | −0.0298105 | ||||||||
\(590\) | −9.61356 | −0.395784 | ||||||||
\(591\) | −18.8877 | −0.776936 | ||||||||
\(592\) | −3.04892 | −0.125310 | ||||||||
\(593\) | −8.85086 | −0.363461 | −0.181731 | − | 0.983348i | \(-0.558170\pi\) | ||||
−0.181731 | + | 0.983348i | \(0.558170\pi\) | |||||||
\(594\) | 3.74094 | 0.153493 | ||||||||
\(595\) | −1.00000 | −0.0409960 | ||||||||
\(596\) | 8.35690 | 0.342312 | ||||||||
\(597\) | 3.36898 | 0.137883 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.2174 | 0.989498 | 0.494749 | − | 0.869036i | \(-0.335260\pi\) | ||||
0.494749 | + | 0.869036i | \(0.335260\pi\) | |||||||
\(600\) | 2.91185 | 0.118876 | ||||||||
\(601\) | −13.3575 | −0.544863 | −0.272432 | − | 0.962175i | \(-0.587828\pi\) | ||||
−0.272432 | + | 0.962175i | \(0.587828\pi\) | |||||||
\(602\) | 5.82908 | 0.237576 | ||||||||
\(603\) | −9.11960 | −0.371379 | ||||||||
\(604\) | −7.63102 | −0.310502 | ||||||||
\(605\) | −4.32736 | −0.175932 | ||||||||
\(606\) | 2.81402 | 0.114312 | ||||||||
\(607\) | −0.568959 | −0.0230933 | −0.0115467 | − | 0.999933i | \(-0.503675\pi\) | ||||
−0.0115467 | + | 0.999933i | \(0.503675\pi\) | |||||||
\(608\) | −0.753020 | −0.0305390 | ||||||||
\(609\) | −6.89977 | −0.279593 | ||||||||
\(610\) | 10.1153 | 0.409556 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.692021 | 0.0279733 | ||||||||
\(613\) | 21.1008 | 0.852254 | 0.426127 | − | 0.904663i | \(-0.359878\pi\) | ||||
0.426127 | + | 0.904663i | \(0.359878\pi\) | |||||||
\(614\) | −24.4547 | −0.986913 | ||||||||
\(615\) | 2.08815 | 0.0842022 | ||||||||
\(616\) | −3.74094 | −0.150727 | ||||||||
\(617\) | −15.9705 | −0.642947 | −0.321473 | − | 0.946919i | \(-0.604178\pi\) | ||||
−0.321473 | + | 0.946919i | \(0.604178\pi\) | |||||||
\(618\) | 8.23490 | 0.331256 | ||||||||
\(619\) | −37.9657 | −1.52597 | −0.762985 | − | 0.646417i | \(-0.776267\pi\) | ||||
−0.762985 | + | 0.646417i | \(0.776267\pi\) | |||||||
\(620\) | −1.38835 | −0.0557577 | ||||||||
\(621\) | −1.82908 | −0.0733986 | ||||||||
\(622\) | −22.3177 | −0.894857 | ||||||||
\(623\) | −14.5579 | −0.583252 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.96184 | −0.0784735 | ||||||||
\(626\) | −2.47889 | −0.0990765 | ||||||||
\(627\) | −2.81700 | −0.112500 | ||||||||
\(628\) | 12.2935 | 0.490564 | ||||||||
\(629\) | −2.10992 | −0.0841279 | ||||||||
\(630\) | −1.44504 | −0.0575718 | ||||||||
\(631\) | −16.2054 | −0.645125 | −0.322563 | − | 0.946548i | \(-0.604544\pi\) | ||||
−0.322563 | + | 0.946548i | \(0.604544\pi\) | |||||||
\(632\) | −7.44504 | −0.296148 | ||||||||
\(633\) | −17.1511 | −0.681694 | ||||||||
\(634\) | −5.65710 | −0.224672 | ||||||||
\(635\) | −13.9879 | −0.555094 | ||||||||
\(636\) | 1.57673 | 0.0625213 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.8116 | −1.02189 | ||||||||
\(639\) | 0.219833 | 0.00869644 | ||||||||
\(640\) | −1.44504 | −0.0571203 | ||||||||
\(641\) | −33.1879 | −1.31084 | −0.655422 | − | 0.755263i | \(-0.727509\pi\) | ||||
−0.655422 | + | 0.755263i | \(0.727509\pi\) | |||||||
\(642\) | −10.6039 | −0.418502 | ||||||||
\(643\) | −9.71486 | −0.383117 | −0.191558 | − | 0.981481i | \(-0.561354\pi\) | ||||
−0.191558 | + | 0.981481i | \(0.561354\pi\) | |||||||
\(644\) | 1.82908 | 0.0720760 | ||||||||
\(645\) | 8.42327 | 0.331666 | ||||||||
\(646\) | −0.521106 | −0.0205027 | ||||||||
\(647\) | −15.5066 | −0.609629 | −0.304814 | − | 0.952412i | \(-0.598594\pi\) | ||||
−0.304814 | + | 0.952412i | \(0.598594\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −24.8877 | −0.976927 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.960771 | −0.0376556 | ||||||||
\(652\) | −15.0151 | −0.588035 | ||||||||
\(653\) | −4.37627 | −0.171257 | −0.0856284 | − | 0.996327i | \(-0.527290\pi\) | ||||
−0.0856284 | + | 0.996327i | \(0.527290\pi\) | |||||||
\(654\) | −8.48858 | −0.331930 | ||||||||
\(655\) | −3.25475 | −0.127174 | ||||||||
\(656\) | 1.44504 | 0.0564194 | ||||||||
\(657\) | −4.91185 | −0.191630 | ||||||||
\(658\) | −3.71379 | −0.144779 | ||||||||
\(659\) | 24.9638 | 0.972450 | 0.486225 | − | 0.873834i | \(-0.338374\pi\) | ||||
0.486225 | + | 0.873834i | \(0.338374\pi\) | |||||||
\(660\) | −5.40581 | −0.210421 | ||||||||
\(661\) | −20.2252 | −0.786669 | −0.393335 | − | 0.919395i | \(-0.628679\pi\) | ||||
−0.393335 | + | 0.919395i | \(0.628679\pi\) | |||||||
\(662\) | 23.1879 | 0.901223 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.75302 | −0.339683 | ||||||||
\(665\) | 1.08815 | 0.0421965 | ||||||||
\(666\) | −3.04892 | −0.118143 | ||||||||
\(667\) | 12.6203 | 0.488659 | ||||||||
\(668\) | 18.3153 | 0.708639 | ||||||||
\(669\) | 25.0911 | 0.970079 | ||||||||
\(670\) | 13.1782 | 0.509119 | ||||||||
\(671\) | 26.1866 | 1.01092 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 26.9119 | 1.03738 | 0.518688 | − | 0.854964i | \(-0.326421\pi\) | ||||
0.518688 | + | 0.854964i | \(0.326421\pi\) | |||||||
\(674\) | 10.4873 | 0.403954 | ||||||||
\(675\) | 2.91185 | 0.112077 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.9571 | 1.42037 | 0.710187 | − | 0.704013i | \(-0.248610\pi\) | ||||
0.710187 | + | 0.704013i | \(0.248610\pi\) | |||||||
\(678\) | 5.92692 | 0.227622 | ||||||||
\(679\) | −6.06100 | −0.232600 | ||||||||
\(680\) | −1.00000 | −0.0383482 | ||||||||
\(681\) | −5.84415 | −0.223948 | ||||||||
\(682\) | −3.59419 | −0.137629 | ||||||||
\(683\) | 4.53212 | 0.173417 | 0.0867084 | − | 0.996234i | \(-0.472365\pi\) | ||||
0.0867084 | + | 0.996234i | \(0.472365\pi\) | |||||||
\(684\) | −0.753020 | −0.0287925 | ||||||||
\(685\) | 17.4112 | 0.665247 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 15.2252 | 0.580878 | ||||||||
\(688\) | 5.82908 | 0.222232 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 2.64310 | 0.100621 | ||||||||
\(691\) | −24.7670 | −0.942182 | −0.471091 | − | 0.882085i | \(-0.656140\pi\) | ||||
−0.471091 | + | 0.882085i | \(0.656140\pi\) | |||||||
\(692\) | −16.7875 | −0.638164 | ||||||||
\(693\) | −3.74094 | −0.142107 | ||||||||
\(694\) | −5.28514 | −0.200621 | ||||||||
\(695\) | 24.0431 | 0.912005 | ||||||||
\(696\) | −6.89977 | −0.261535 | ||||||||
\(697\) | 1.00000 | 0.0378777 | ||||||||
\(698\) | 8.19029 | 0.310007 | ||||||||
\(699\) | 25.2000 | 0.953151 | ||||||||
\(700\) | −2.91185 | −0.110058 | ||||||||
\(701\) | 38.2965 | 1.44644 | 0.723219 | − | 0.690619i | \(-0.242662\pi\) | ||||
0.723219 | + | 0.690619i | \(0.242662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.29590 | 0.0865914 | ||||||||
\(704\) | −3.74094 | −0.140992 | ||||||||
\(705\) | −5.36658 | −0.202117 | ||||||||
\(706\) | 35.9758 | 1.35397 | ||||||||
\(707\) | −2.81402 | −0.105832 | ||||||||
\(708\) | −6.65279 | −0.250027 | ||||||||
\(709\) | −44.3256 | −1.66468 | −0.832341 | − | 0.554265i | \(-0.813000\pi\) | ||||
−0.832341 | + | 0.554265i | \(0.813000\pi\) | |||||||
\(710\) | −0.317667 | −0.0119218 | ||||||||
\(711\) | −7.44504 | −0.279211 | ||||||||
\(712\) | −14.5579 | −0.545582 | ||||||||
\(713\) | 1.75733 | 0.0658126 | ||||||||
\(714\) | −0.692021 | −0.0258983 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.86725 | 0.181898 | ||||||||
\(717\) | −6.71379 | −0.250731 | ||||||||
\(718\) | −28.7603 | −1.07333 | ||||||||
\(719\) | −24.5773 | −0.916579 | −0.458290 | − | 0.888803i | \(-0.651538\pi\) | ||||
−0.458290 | + | 0.888803i | \(0.651538\pi\) | |||||||
\(720\) | −1.44504 | −0.0538535 | ||||||||
\(721\) | −8.23490 | −0.306684 | ||||||||
\(722\) | −18.4330 | −0.686004 | ||||||||
\(723\) | 5.21313 | 0.193878 | ||||||||
\(724\) | −13.4644 | −0.500401 | ||||||||
\(725\) | −20.0911 | −0.746166 | ||||||||
\(726\) | −2.99462 | −0.111141 | ||||||||
\(727\) | 38.8280 | 1.44005 | 0.720026 | − | 0.693947i | \(-0.244130\pi\) | ||||
0.720026 | + | 0.693947i | \(0.244130\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.09783 | 0.262703 | ||||||||
\(731\) | 4.03385 | 0.149197 | ||||||||
\(732\) | 7.00000 | 0.258727 | ||||||||
\(733\) | 21.6142 | 0.798337 | 0.399169 | − | 0.916878i | \(-0.369299\pi\) | ||||
0.399169 | + | 0.916878i | \(0.369299\pi\) | |||||||
\(734\) | −3.61463 | −0.133418 | ||||||||
\(735\) | 1.44504 | 0.0533012 | ||||||||
\(736\) | 1.82908 | 0.0674210 | ||||||||
\(737\) | 34.1159 | 1.25667 | ||||||||
\(738\) | 1.44504 | 0.0531927 | ||||||||
\(739\) | −13.4644 | −0.495297 | −0.247648 | − | 0.968850i | \(-0.579658\pi\) | ||||
−0.247648 | + | 0.968850i | \(0.579658\pi\) | |||||||
\(740\) | 4.40581 | 0.161961 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.57673 | −0.0578835 | ||||||||
\(743\) | 3.90887 | 0.143403 | 0.0717013 | − | 0.997426i | \(-0.477157\pi\) | ||||
0.0717013 | + | 0.997426i | \(0.477157\pi\) | |||||||
\(744\) | −0.960771 | −0.0352236 | ||||||||
\(745\) | −12.0761 | −0.442433 | ||||||||
\(746\) | 17.9312 | 0.656509 | ||||||||
\(747\) | −8.75302 | −0.320256 | ||||||||
\(748\) | −2.58881 | −0.0946563 | ||||||||
\(749\) | 10.6039 | 0.387457 | ||||||||
\(750\) | −11.4330 | −0.417473 | ||||||||
\(751\) | 45.2922 | 1.65273 | 0.826367 | − | 0.563131i | \(-0.190403\pi\) | ||||
0.826367 | + | 0.563131i | \(0.190403\pi\) | |||||||
\(752\) | −3.71379 | −0.135428 | ||||||||
\(753\) | −9.22952 | −0.336342 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.0271 | 0.401319 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 23.6872 | 0.860927 | 0.430464 | − | 0.902608i | \(-0.358350\pi\) | ||||
0.430464 | + | 0.902608i | \(0.358350\pi\) | |||||||
\(758\) | 22.2338 | 0.807569 | ||||||||
\(759\) | 6.84249 | 0.248367 | ||||||||
\(760\) | 1.08815 | 0.0394712 | ||||||||
\(761\) | 9.25667 | 0.335554 | 0.167777 | − | 0.985825i | \(-0.446341\pi\) | ||||
0.167777 | + | 0.985825i | \(0.446341\pi\) | |||||||
\(762\) | −9.67994 | −0.350667 | ||||||||
\(763\) | 8.48858 | 0.307307 | ||||||||
\(764\) | −5.26444 | −0.190461 | ||||||||
\(765\) | −1.00000 | −0.0361551 | ||||||||
\(766\) | −25.4330 | −0.918930 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −36.1390 | −1.30321 | −0.651603 | − | 0.758561i | \(-0.725903\pi\) | ||||
−0.651603 | + | 0.758561i | \(0.725903\pi\) | |||||||
\(770\) | 5.40581 | 0.194812 | ||||||||
\(771\) | −2.51035 | −0.0904081 | ||||||||
\(772\) | −22.8713 | −0.823156 | ||||||||
\(773\) | 14.6552 | 0.527110 | 0.263555 | − | 0.964644i | \(-0.415105\pi\) | ||||
0.263555 | + | 0.964644i | \(0.415105\pi\) | |||||||
\(774\) | 5.82908 | 0.209522 | ||||||||
\(775\) | −2.79763 | −0.100494 | ||||||||
\(776\) | −6.06100 | −0.217577 | ||||||||
\(777\) | 3.04892 | 0.109379 | ||||||||
\(778\) | −14.9855 | −0.537257 | ||||||||
\(779\) | −1.08815 | −0.0389869 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.822380 | −0.0294271 | ||||||||
\(782\) | 1.26577 | 0.0452637 | ||||||||
\(783\) | −6.89977 | −0.246578 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −17.7646 | −0.634047 | ||||||||
\(786\) | −2.25236 | −0.0803389 | ||||||||
\(787\) | 11.7724 | 0.419641 | 0.209820 | − | 0.977740i | \(-0.432712\pi\) | ||||
0.209820 | + | 0.977740i | \(0.432712\pi\) | |||||||
\(788\) | 18.8877 | 0.672846 | ||||||||
\(789\) | −30.1511 | −1.07341 | ||||||||
\(790\) | 10.7584 | 0.382767 | ||||||||
\(791\) | −5.92692 | −0.210737 | ||||||||
\(792\) | −3.74094 | −0.132928 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −11.8358 | −0.420036 | ||||||||
\(795\) | −2.27844 | −0.0808079 | ||||||||
\(796\) | −3.36898 | −0.119410 | ||||||||
\(797\) | 40.0431 | 1.41840 | 0.709199 | − | 0.705008i | \(-0.249057\pi\) | ||||
0.709199 | + | 0.705008i | \(0.249057\pi\) | |||||||
\(798\) | 0.753020 | 0.0266566 | ||||||||
\(799\) | −2.57002 | −0.0909209 | ||||||||
\(800\) | −2.91185 | −0.102950 | ||||||||
\(801\) | −14.5579 | −0.514380 | ||||||||
\(802\) | 11.6256 | 0.410516 | ||||||||
\(803\) | 18.3749 | 0.648438 | ||||||||
\(804\) | 9.11960 | 0.321624 | ||||||||
\(805\) | −2.64310 | −0.0931572 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.6063 | 0.514165 | ||||||||
\(808\) | −2.81402 | −0.0989969 | ||||||||
\(809\) | 41.8243 | 1.47046 | 0.735232 | − | 0.677816i | \(-0.237073\pi\) | ||||
0.735232 | + | 0.677816i | \(0.237073\pi\) | |||||||
\(810\) | −1.44504 | −0.0507736 | ||||||||
\(811\) | 9.53212 | 0.334718 | 0.167359 | − | 0.985896i | \(-0.446476\pi\) | ||||
0.167359 | + | 0.985896i | \(0.446476\pi\) | |||||||
\(812\) | 6.89977 | 0.242135 | ||||||||
\(813\) | 22.0978 | 0.775005 | ||||||||
\(814\) | 11.4058 | 0.399774 | ||||||||
\(815\) | 21.6974 | 0.760027 | ||||||||
\(816\) | −0.692021 | −0.0242256 | ||||||||
\(817\) | −4.38942 | −0.153566 | ||||||||
\(818\) | −8.09485 | −0.283030 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.08815 | −0.0729212 | ||||||||
\(821\) | 0.509025 | 0.0177651 | 0.00888254 | − | 0.999961i | \(-0.497173\pi\) | ||||
0.00888254 | + | 0.999961i | \(0.497173\pi\) | |||||||
\(822\) | 12.0489 | 0.420254 | ||||||||
\(823\) | 35.4233 | 1.23478 | 0.617389 | − | 0.786658i | \(-0.288191\pi\) | ||||
0.617389 | + | 0.786658i | \(0.288191\pi\) | |||||||
\(824\) | −8.23490 | −0.286876 | ||||||||
\(825\) | −10.8931 | −0.379248 | ||||||||
\(826\) | 6.65279 | 0.231480 | ||||||||
\(827\) | −31.6547 | −1.10074 | −0.550371 | − | 0.834920i | \(-0.685514\pi\) | ||||
−0.550371 | + | 0.834920i | \(0.685514\pi\) | |||||||
\(828\) | 1.82908 | 0.0635651 | ||||||||
\(829\) | −32.3026 | −1.12192 | −0.560958 | − | 0.827844i | \(-0.689567\pi\) | ||||
−0.560958 | + | 0.827844i | \(0.689567\pi\) | |||||||
\(830\) | 12.6485 | 0.439035 | ||||||||
\(831\) | −1.23729 | −0.0429211 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.692021 | 0.0239771 | ||||||||
\(834\) | 16.6383 | 0.576138 | ||||||||
\(835\) | −26.4663 | −0.915905 | ||||||||
\(836\) | 2.81700 | 0.0974281 | ||||||||
\(837\) | −0.960771 | −0.0332091 | ||||||||
\(838\) | −5.80087 | −0.200388 | ||||||||
\(839\) | 19.4896 | 0.672857 | 0.336429 | − | 0.941709i | \(-0.390781\pi\) | ||||
0.336429 | + | 0.941709i | \(0.390781\pi\) | |||||||
\(840\) | 1.44504 | 0.0498587 | ||||||||
\(841\) | 18.6069 | 0.641616 | ||||||||
\(842\) | 21.9909 | 0.757857 | ||||||||
\(843\) | 8.51035 | 0.293112 | ||||||||
\(844\) | 17.1511 | 0.590364 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.71379 | −0.127683 | ||||||||
\(847\) | 2.99462 | 0.102896 | ||||||||
\(848\) | −1.57673 | −0.0541451 | ||||||||
\(849\) | 16.3002 | 0.559422 | ||||||||
\(850\) | −2.01507 | −0.0691162 | ||||||||
\(851\) | −5.57673 | −0.191168 | ||||||||
\(852\) | −0.219833 | −0.00753134 | ||||||||
\(853\) | −6.02177 | −0.206181 | −0.103091 | − | 0.994672i | \(-0.532873\pi\) | ||||
−0.103091 | + | 0.994672i | \(0.532873\pi\) | |||||||
\(854\) | −7.00000 | −0.239535 | ||||||||
\(855\) | 1.08815 | 0.0372138 | ||||||||
\(856\) | 10.6039 | 0.362433 | ||||||||
\(857\) | −41.1172 | −1.40454 | −0.702269 | − | 0.711912i | \(-0.747829\pi\) | ||||
−0.702269 | + | 0.711912i | \(0.747829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.3666 | 1.82084 | 0.910422 | − | 0.413680i | \(-0.135757\pi\) | ||||
0.910422 | + | 0.413680i | \(0.135757\pi\) | |||||||
\(860\) | −8.42327 | −0.287231 | ||||||||
\(861\) | −1.44504 | −0.0492469 | ||||||||
\(862\) | 3.34242 | 0.113843 | ||||||||
\(863\) | −27.5056 | −0.936300 | −0.468150 | − | 0.883649i | \(-0.655079\pi\) | ||||
−0.468150 | + | 0.883649i | \(0.655079\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 24.2586 | 0.824817 | ||||||||
\(866\) | 14.0344 | 0.476910 | ||||||||
\(867\) | 16.5211 | 0.561086 | ||||||||
\(868\) | 0.960771 | 0.0326107 | ||||||||
\(869\) | 27.8514 | 0.944796 | ||||||||
\(870\) | 9.97046 | 0.338030 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.48858 | 0.287460 | ||||||||
\(873\) | −6.06100 | −0.205134 | ||||||||
\(874\) | −1.37734 | −0.0465892 | ||||||||
\(875\) | 11.4330 | 0.386505 | ||||||||
\(876\) | 4.91185 | 0.165956 | ||||||||
\(877\) | 11.8092 | 0.398769 | 0.199385 | − | 0.979921i | \(-0.436106\pi\) | ||||
0.199385 | + | 0.979921i | \(0.436106\pi\) | |||||||
\(878\) | 25.7735 | 0.869812 | ||||||||
\(879\) | 29.8853 | 1.00801 | ||||||||
\(880\) | 5.40581 | 0.182230 | ||||||||
\(881\) | −35.6848 | −1.20225 | −0.601126 | − | 0.799154i | \(-0.705281\pi\) | ||||
−0.601126 | + | 0.799154i | \(0.705281\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 18.0718 | 0.608163 | 0.304081 | − | 0.952646i | \(-0.401650\pi\) | ||||
0.304081 | + | 0.952646i | \(0.401650\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.61356 | 0.323156 | ||||||||
\(886\) | 5.53558 | 0.185971 | ||||||||
\(887\) | −36.9922 | −1.24208 | −0.621039 | − | 0.783780i | \(-0.713289\pi\) | ||||
−0.621039 | + | 0.783780i | \(0.713289\pi\) | |||||||
\(888\) | 3.04892 | 0.102315 | ||||||||
\(889\) | 9.67994 | 0.324655 | ||||||||
\(890\) | 21.0368 | 0.705156 | ||||||||
\(891\) | −3.74094 | −0.125326 | ||||||||
\(892\) | −25.0911 | −0.840113 | ||||||||
\(893\) | 2.79656 | 0.0935833 | ||||||||
\(894\) | −8.35690 | −0.279496 | ||||||||
\(895\) | −7.03338 | −0.235100 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.0616 | −0.702834 | ||||||||
\(899\) | 6.62910 | 0.221093 | ||||||||
\(900\) | −2.91185 | −0.0970618 | ||||||||
\(901\) | −1.09113 | −0.0363508 | ||||||||
\(902\) | −5.40581 | −0.179994 | ||||||||
\(903\) | −5.82908 | −0.193980 | ||||||||
\(904\) | −5.92692 | −0.197126 | ||||||||
\(905\) | 19.4566 | 0.646761 | ||||||||
\(906\) | 7.63102 | 0.253524 | ||||||||
\(907\) | 24.4902 | 0.813185 | 0.406593 | − | 0.913610i | \(-0.366717\pi\) | ||||
0.406593 | + | 0.913610i | \(0.366717\pi\) | |||||||
\(908\) | 5.84415 | 0.193945 | ||||||||
\(909\) | −2.81402 | −0.0933351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.8407 | 0.988666 | 0.494333 | − | 0.869273i | \(-0.335412\pi\) | ||||
0.494333 | + | 0.869273i | \(0.335412\pi\) | |||||||
\(912\) | 0.753020 | 0.0249350 | ||||||||
\(913\) | 32.7445 | 1.08369 | ||||||||
\(914\) | −39.7506 | −1.31483 | ||||||||
\(915\) | −10.1153 | −0.334401 | ||||||||
\(916\) | −15.2252 | −0.503055 | ||||||||
\(917\) | 2.25236 | 0.0743794 | ||||||||
\(918\) | −0.692021 | −0.0228401 | ||||||||
\(919\) | 44.0756 | 1.45392 | 0.726960 | − | 0.686680i | \(-0.240933\pi\) | ||||
0.726960 | + | 0.686680i | \(0.240933\pi\) | |||||||
\(920\) | −2.64310 | −0.0871406 | ||||||||
\(921\) | 24.4547 | 0.805811 | ||||||||
\(922\) | −18.7851 | −0.618653 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.74094 | 0.123068 | ||||||||
\(925\) | 8.87800 | 0.291907 | ||||||||
\(926\) | −30.6504 | −1.00723 | ||||||||
\(927\) | −8.23490 | −0.270470 | ||||||||
\(928\) | 6.89977 | 0.226496 | ||||||||
\(929\) | 2.83340 | 0.0929607 | 0.0464804 | − | 0.998919i | \(-0.485200\pi\) | ||||
0.0464804 | + | 0.998919i | \(0.485200\pi\) | |||||||
\(930\) | 1.38835 | 0.0455259 | ||||||||
\(931\) | −0.753020 | −0.0246792 | ||||||||
\(932\) | −25.2000 | −0.825453 | ||||||||
\(933\) | 22.3177 | 0.730648 | ||||||||
\(934\) | 1.57673 | 0.0515921 | ||||||||
\(935\) | 3.74094 | 0.122342 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.3129 | −1.31696 | −0.658482 | − | 0.752596i | \(-0.728801\pi\) | ||||
−0.658482 | + | 0.752596i | \(0.728801\pi\) | |||||||
\(938\) | −9.11960 | −0.297766 | ||||||||
\(939\) | 2.47889 | 0.0808956 | ||||||||
\(940\) | 5.36658 | 0.175039 | ||||||||
\(941\) | 54.3223 | 1.77086 | 0.885428 | − | 0.464776i | \(-0.153865\pi\) | ||||
0.885428 | + | 0.464776i | \(0.153865\pi\) | |||||||
\(942\) | −12.2935 | −0.400544 | ||||||||
\(943\) | 2.64310 | 0.0860713 | ||||||||
\(944\) | 6.65279 | 0.216530 | ||||||||
\(945\) | 1.44504 | 0.0470072 | ||||||||
\(946\) | −21.8062 | −0.708982 | ||||||||
\(947\) | 50.8980 | 1.65396 | 0.826981 | − | 0.562230i | \(-0.190056\pi\) | ||||
0.826981 | + | 0.562230i | \(0.190056\pi\) | |||||||
\(948\) | 7.44504 | 0.241804 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.19269 | 0.0711401 | ||||||||
\(951\) | 5.65710 | 0.183444 | ||||||||
\(952\) | 0.692021 | 0.0224285 | ||||||||
\(953\) | −4.62266 | −0.149743 | −0.0748714 | − | 0.997193i | \(-0.523855\pi\) | ||||
−0.0748714 | + | 0.997193i | \(0.523855\pi\) | |||||||
\(954\) | −1.57673 | −0.0510485 | ||||||||
\(955\) | 7.60733 | 0.246168 | ||||||||
\(956\) | 6.71379 | 0.217140 | ||||||||
\(957\) | 25.8116 | 0.834371 | ||||||||
\(958\) | 23.5907 | 0.762182 | ||||||||
\(959\) | −12.0489 | −0.389080 | ||||||||
\(960\) | 1.44504 | 0.0466385 | ||||||||
\(961\) | −30.0769 | −0.970223 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.6039 | 0.341705 | ||||||||
\(964\) | −5.21313 | −0.167904 | ||||||||
\(965\) | 33.0500 | 1.06392 | ||||||||
\(966\) | −1.82908 | −0.0588498 | ||||||||
\(967\) | 52.9235 | 1.70190 | 0.850952 | − | 0.525244i | \(-0.176026\pi\) | ||||
0.850952 | + | 0.525244i | \(0.176026\pi\) | |||||||
\(968\) | 2.99462 | 0.0962508 | ||||||||
\(969\) | 0.521106 | 0.0167403 | ||||||||
\(970\) | 8.75840 | 0.281215 | ||||||||
\(971\) | 2.78256 | 0.0892966 | 0.0446483 | − | 0.999003i | \(-0.485783\pi\) | ||||
0.0446483 | + | 0.999003i | \(0.485783\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −16.6383 | −0.533400 | ||||||||
\(974\) | −4.42460 | −0.141773 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.00000 | −0.224065 | ||||||||
\(977\) | −12.0922 | −0.386864 | −0.193432 | − | 0.981114i | \(-0.561962\pi\) | ||||
−0.193432 | + | 0.981114i | \(0.561962\pi\) | |||||||
\(978\) | 15.0151 | 0.480129 | ||||||||
\(979\) | 54.4604 | 1.74056 | ||||||||
\(980\) | −1.44504 | −0.0461602 | ||||||||
\(981\) | 8.48858 | 0.271020 | ||||||||
\(982\) | 4.27652 | 0.136469 | ||||||||
\(983\) | −22.9474 | −0.731907 | −0.365954 | − | 0.930633i | \(-0.619257\pi\) | ||||
−0.365954 | + | 0.930633i | \(0.619257\pi\) | |||||||
\(984\) | −1.44504 | −0.0460663 | ||||||||
\(985\) | −27.2935 | −0.869643 | ||||||||
\(986\) | 4.77479 | 0.152060 | ||||||||
\(987\) | 3.71379 | 0.118211 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.6619 | 0.339028 | ||||||||
\(990\) | 5.40581 | 0.171808 | ||||||||
\(991\) | −1.44876 | −0.0460215 | −0.0230107 | − | 0.999735i | \(-0.507325\pi\) | ||||
−0.0230107 | + | 0.999735i | \(0.507325\pi\) | |||||||
\(992\) | 0.960771 | 0.0305045 | ||||||||
\(993\) | −23.1879 | −0.735846 | ||||||||
\(994\) | 0.219833 | 0.00697266 | ||||||||
\(995\) | 4.86831 | 0.154336 | ||||||||
\(996\) | 8.75302 | 0.277350 | ||||||||
\(997\) | 39.6491 | 1.25570 | 0.627849 | − | 0.778335i | \(-0.283935\pi\) | ||||
0.627849 | + | 0.778335i | \(0.283935\pi\) | |||||||
\(998\) | −5.35152 | −0.169399 | ||||||||
\(999\) | 3.04892 | 0.0964635 |
(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 | 7098.2.a.ch.1.2 | yes | 3 | |
13.12 | even | 2 | 7098.2.a.ce.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.ce.1.2 | ✓ | 3 | 13.12 | even | 2 | ||
7098.2.a.ch.1.2 | yes | 3 | 1.1 | even | 1 | trivial |