Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(1,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.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: | \(5.82109430735\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{36})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 6x^{4} + 9x^{2} - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.96962\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96962 | −1.39273 | −0.696364 | − | 0.717689i | \(-0.745200\pi\) | ||||
−0.696364 | + | 0.717689i | \(0.745200\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.87939 | 0.939693 | ||||||||
\(5\) | 3.70167 | 1.65544 | 0.827718 | − | 0.561145i | \(-0.189639\pi\) | ||||
0.827718 | + | 0.561145i | \(0.189639\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.34730 | −0.887195 | −0.443597 | − | 0.896226i | \(-0.646298\pi\) | ||||
−0.443597 | + | 0.896226i | \(0.646298\pi\) | |||||||
\(8\) | 0.237565 | 0.0839918 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.29086 | −2.30557 | ||||||||
\(11\) | −2.17853 | −0.656850 | −0.328425 | − | 0.944530i | \(-0.606518\pi\) | ||||
−0.328425 | + | 0.944530i | \(0.606518\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.71688 | −1.30823 | −0.654114 | − | 0.756396i | \(-0.726958\pi\) | ||||
−0.654114 | + | 0.756396i | \(0.726958\pi\) | |||||||
\(14\) | 4.62327 | 1.23562 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.22668 | −1.05667 | ||||||||
\(17\) | −2.93512 | −0.711871 | −0.355936 | − | 0.934510i | \(-0.615838\pi\) | ||||
−0.355936 | + | 0.934510i | \(0.615838\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.22668 | −1.42850 | −0.714249 | − | 0.699891i | \(-0.753232\pi\) | ||||
−0.714249 | + | 0.699891i | \(0.753232\pi\) | |||||||
\(20\) | 6.95686 | 1.55560 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.29086 | 0.914814 | ||||||||
\(23\) | 0.519030 | 0.108225 | 0.0541126 | − | 0.998535i | \(-0.482767\pi\) | ||||
0.0541126 | + | 0.998535i | \(0.482767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.70233 | 1.74047 | ||||||||
\(26\) | 9.29044 | 1.82201 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.41147 | −0.833690 | ||||||||
\(29\) | −3.49276 | −0.648588 | −0.324294 | − | 0.945956i | \(-0.605127\pi\) | ||||
−0.324294 | + | 0.945956i | \(0.605127\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.30541 | −0.773274 | −0.386637 | − | 0.922232i | \(-0.626363\pi\) | ||||
−0.386637 | + | 0.922232i | \(0.626363\pi\) | |||||||
\(32\) | 7.84981 | 1.38766 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.78106 | 0.991443 | ||||||||
\(35\) | −8.68891 | −1.46869 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.41147 | 0.396444 | 0.198222 | − | 0.980157i | \(-0.436483\pi\) | ||||
0.198222 | + | 0.980157i | \(0.436483\pi\) | |||||||
\(38\) | 12.2642 | 1.98951 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.879385 | 0.139043 | ||||||||
\(41\) | 2.49860 | 0.390215 | 0.195108 | − | 0.980782i | \(-0.437494\pi\) | ||||
0.195108 | + | 0.980782i | \(0.437494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.06418 | 0.162286 | 0.0811428 | − | 0.996702i | \(-0.474143\pi\) | ||||
0.0811428 | + | 0.996702i | \(0.474143\pi\) | |||||||
\(44\) | −4.09429 | −0.617237 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.02229 | −0.150728 | ||||||||
\(47\) | −0.237565 | −0.0346524 | −0.0173262 | − | 0.999850i | \(-0.505515\pi\) | ||||
−0.0173262 | + | 0.999850i | \(0.505515\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.49020 | −0.212886 | ||||||||
\(50\) | −17.1403 | −2.42400 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.86484 | −1.22933 | ||||||||
\(53\) | 4.66717 | 0.641085 | 0.320543 | − | 0.947234i | \(-0.396135\pi\) | ||||
0.320543 | + | 0.947234i | \(0.396135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.06418 | −1.08737 | ||||||||
\(56\) | −0.557635 | −0.0745171 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.87939 | 0.903308 | ||||||||
\(59\) | −13.3122 | −1.73310 | −0.866549 | − | 0.499092i | \(-0.833667\pi\) | ||||
−0.866549 | + | 0.499092i | \(0.833667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.67499 | −0.470535 | −0.235267 | − | 0.971931i | \(-0.575597\pi\) | ||||
−0.235267 | + | 0.971931i | \(0.575597\pi\) | |||||||
\(62\) | 8.48000 | 1.07696 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.00774 | −0.875968 | ||||||||
\(65\) | −17.4603 | −2.16569 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.2986 | 1.74685 | 0.873426 | − | 0.486957i | \(-0.161893\pi\) | ||||
0.873426 | + | 0.486957i | \(0.161893\pi\) | |||||||
\(68\) | −5.51622 | −0.668940 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 17.1138 | 2.04549 | ||||||||
\(71\) | 1.20307 | 0.142778 | 0.0713891 | − | 0.997449i | \(-0.477257\pi\) | ||||
0.0713891 | + | 0.997449i | \(0.477257\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.68004 | −0.547758 | −0.273879 | − | 0.961764i | \(-0.588307\pi\) | ||||
−0.273879 | + | 0.961764i | \(0.588307\pi\) | |||||||
\(74\) | −4.74968 | −0.552139 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.7023 | −1.34235 | ||||||||
\(77\) | 5.11365 | 0.582754 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8007 | −1.44019 | −0.720093 | − | 0.693877i | \(-0.755901\pi\) | ||||
−0.720093 | + | 0.693877i | \(0.755901\pi\) | |||||||
\(80\) | −15.6458 | −1.74925 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.92127 | −0.543464 | ||||||||
\(83\) | −11.3040 | −1.24077 | −0.620385 | − | 0.784297i | \(-0.713024\pi\) | ||||
−0.620385 | + | 0.784297i | \(0.713024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.8648 | −1.17846 | ||||||||
\(86\) | −2.09602 | −0.226020 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.517541 | −0.0551701 | ||||||||
\(89\) | 0.699287 | 0.0741242 | 0.0370621 | − | 0.999313i | \(-0.488200\pi\) | ||||
0.0370621 | + | 0.999313i | \(0.488200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.0719 | 1.16065 | ||||||||
\(92\) | 0.975457 | 0.101698 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.467911 | 0.0482613 | ||||||||
\(95\) | −23.0491 | −2.36479 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.08647 | −0.719522 | −0.359761 | − | 0.933045i | \(-0.617142\pi\) | ||||
−0.359761 | + | 0.933045i | \(0.617142\pi\) | |||||||
\(98\) | 2.93512 | 0.296492 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 16.3550 | 1.63550 | ||||||||
\(101\) | 4.67712 | 0.465391 | 0.232696 | − | 0.972550i | \(-0.425245\pi\) | ||||
0.232696 | + | 0.972550i | \(0.425245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6236 | −1.34237 | −0.671187 | − | 0.741288i | \(-0.734215\pi\) | ||||
−0.671187 | + | 0.741288i | \(0.734215\pi\) | |||||||
\(104\) | −1.12056 | −0.109880 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.19253 | −0.892858 | ||||||||
\(107\) | 11.6340 | 1.12470 | 0.562350 | − | 0.826900i | \(-0.309898\pi\) | ||||
0.562350 | + | 0.826900i | \(0.309898\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.6040 | 1.39881 | 0.699405 | − | 0.714725i | \(-0.253448\pi\) | ||||
0.699405 | + | 0.714725i | \(0.253448\pi\) | |||||||
\(110\) | 15.8833 | 1.51442 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.92127 | 0.937472 | ||||||||
\(113\) | 4.69583 | 0.441746 | 0.220873 | − | 0.975303i | \(-0.429109\pi\) | ||||
0.220873 | + | 0.975303i | \(0.429109\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.92127 | 0.179160 | ||||||||
\(116\) | −6.56423 | −0.609474 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 26.2199 | 2.41374 | ||||||||
\(119\) | 6.88960 | 0.631568 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.25402 | −0.568548 | ||||||||
\(122\) | 7.23832 | 0.655327 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.09152 | −0.726640 | ||||||||
\(125\) | 13.7048 | 1.22579 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.09152 | 0.540535 | 0.270267 | − | 0.962785i | \(-0.412888\pi\) | ||||
0.270267 | + | 0.962785i | \(0.412888\pi\) | |||||||
\(128\) | −1.89706 | −0.167678 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 34.3901 | 3.01621 | ||||||||
\(131\) | 10.3484 | 0.904144 | 0.452072 | − | 0.891981i | \(-0.350685\pi\) | ||||
0.452072 | + | 0.891981i | \(0.350685\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.6159 | 1.26736 | ||||||||
\(134\) | −28.1627 | −2.43289 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.697281 | −0.0597914 | ||||||||
\(137\) | 19.0847 | 1.63051 | 0.815257 | − | 0.579100i | \(-0.196596\pi\) | ||||
0.815257 | + | 0.579100i | \(0.196596\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −23.3037 | −1.97659 | −0.988295 | − | 0.152555i | \(-0.951250\pi\) | ||||
−0.988295 | + | 0.152555i | \(0.951250\pi\) | |||||||
\(140\) | −16.3298 | −1.38012 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.36959 | −0.198851 | ||||||||
\(143\) | 10.2759 | 0.859310 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.9290 | −1.07370 | ||||||||
\(146\) | 9.21789 | 0.762878 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.53209 | 0.372535 | ||||||||
\(149\) | 15.5060 | 1.27030 | 0.635149 | − | 0.772390i | \(-0.280939\pi\) | ||||
0.635149 | + | 0.772390i | \(0.280939\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.90167 | −0.480271 | −0.240136 | − | 0.970739i | \(-0.577192\pi\) | ||||
−0.240136 | + | 0.970739i | \(0.577192\pi\) | |||||||
\(152\) | −1.47924 | −0.119982 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.0719 | −0.811618 | ||||||||
\(155\) | −15.9372 | −1.28011 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.21213 | −0.0967388 | −0.0483694 | − | 0.998830i | \(-0.515402\pi\) | ||||
−0.0483694 | + | 0.998830i | \(0.515402\pi\) | |||||||
\(158\) | 25.2124 | 2.00579 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 29.0574 | 2.29719 | ||||||||
\(161\) | −1.21832 | −0.0960168 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.77332 | 0.217223 | 0.108612 | − | 0.994084i | \(-0.465360\pi\) | ||||
0.108612 | + | 0.994084i | \(0.465360\pi\) | |||||||
\(164\) | 4.69583 | 0.366682 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.2645 | 1.72806 | ||||||||
\(167\) | −3.82807 | −0.296225 | −0.148113 | − | 0.988971i | \(-0.547320\pi\) | ||||
−0.148113 | + | 0.988971i | \(0.547320\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.24897 | 0.711459 | ||||||||
\(170\) | 21.3996 | 1.64127 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | −7.02941 | −0.534436 | −0.267218 | − | 0.963636i | \(-0.586104\pi\) | ||||
−0.267218 | + | 0.963636i | \(0.586104\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.4270 | −1.54413 | ||||||||
\(176\) | 9.20794 | 0.694074 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.37733 | −0.103235 | ||||||||
\(179\) | −14.3854 | −1.07521 | −0.537607 | − | 0.843195i | \(-0.680672\pi\) | ||||
−0.537607 | + | 0.843195i | \(0.680672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.2003 | 0.981169 | 0.490584 | − | 0.871394i | \(-0.336783\pi\) | ||||
0.490584 | + | 0.871394i | \(0.336783\pi\) | |||||||
\(182\) | −21.8074 | −1.61647 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.123303 | 0.00909003 | ||||||||
\(185\) | 8.92647 | 0.656287 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.39424 | 0.467593 | ||||||||
\(188\) | −0.446476 | −0.0325626 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 45.3979 | 3.29351 | ||||||||
\(191\) | 13.4233 | 0.971279 | 0.485639 | − | 0.874159i | \(-0.338587\pi\) | ||||
0.485639 | + | 0.874159i | \(0.338587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0051 | 1.08009 | 0.540044 | − | 0.841637i | \(-0.318408\pi\) | ||||
0.540044 | + | 0.841637i | \(0.318408\pi\) | |||||||
\(194\) | 13.9576 | 1.00210 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.80066 | −0.200047 | ||||||||
\(197\) | −22.3212 | −1.59032 | −0.795158 | − | 0.606402i | \(-0.792612\pi\) | ||||
−0.795158 | + | 0.606402i | \(0.792612\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.10101 | −0.645154 | −0.322577 | − | 0.946543i | \(-0.604549\pi\) | ||||
−0.322577 | + | 0.946543i | \(0.604549\pi\) | |||||||
\(200\) | 2.06737 | 0.146185 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.21213 | −0.648163 | ||||||||
\(203\) | 8.19853 | 0.575424 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.24897 | 0.645976 | ||||||||
\(206\) | 26.8333 | 1.86956 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 19.9368 | 1.38237 | ||||||||
\(209\) | 13.5650 | 0.938310 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.97771 | −0.411523 | −0.205761 | − | 0.978602i | \(-0.565967\pi\) | ||||
−0.205761 | + | 0.978602i | \(0.565967\pi\) | |||||||
\(212\) | 8.77141 | 0.602423 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −22.9145 | −1.56640 | ||||||||
\(215\) | 3.93923 | 0.268653 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.1061 | 0.686045 | ||||||||
\(218\) | −28.7643 | −1.94816 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −15.1557 | −1.02180 | ||||||||
\(221\) | 13.8446 | 0.931290 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.90167 | −0.596100 | −0.298050 | − | 0.954550i | \(-0.596336\pi\) | ||||
−0.298050 | + | 0.954550i | \(0.596336\pi\) | |||||||
\(224\) | −18.4258 | −1.23113 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.24897 | −0.615232 | ||||||||
\(227\) | −10.6685 | −0.708092 | −0.354046 | − | 0.935228i | \(-0.615194\pi\) | ||||
−0.354046 | + | 0.935228i | \(0.615194\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.27126 | −0.546580 | −0.273290 | − | 0.961932i | \(-0.588112\pi\) | ||||
−0.273290 | + | 0.961932i | \(0.588112\pi\) | |||||||
\(230\) | −3.78417 | −0.249521 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.829755 | −0.0544761 | ||||||||
\(233\) | 12.7393 | 0.834579 | 0.417290 | − | 0.908774i | \(-0.362980\pi\) | ||||
0.417290 | + | 0.908774i | \(0.362980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.879385 | −0.0573648 | ||||||||
\(236\) | −25.0187 | −1.62858 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13.5699 | −0.879603 | ||||||||
\(239\) | 15.0156 | 0.971277 | 0.485638 | − | 0.874160i | \(-0.338587\pi\) | ||||
0.485638 | + | 0.874160i | \(0.338587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.795607 | 0.0512496 | 0.0256248 | − | 0.999672i | \(-0.491842\pi\) | ||||
0.0256248 | + | 0.999672i | \(0.491842\pi\) | |||||||
\(242\) | 12.3180 | 0.791832 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.90673 | −0.442158 | ||||||||
\(245\) | −5.51622 | −0.352419 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.3705 | 1.86880 | ||||||||
\(248\) | −1.02281 | −0.0649487 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −26.9932 | −1.70720 | ||||||||
\(251\) | 8.31499 | 0.524837 | 0.262419 | − | 0.964954i | \(-0.415480\pi\) | ||||
0.262419 | + | 0.964954i | \(0.415480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.13072 | −0.0710877 | ||||||||
\(254\) | −11.9980 | −0.752818 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.7520 | 1.10950 | ||||||||
\(257\) | −25.6202 | −1.59815 | −0.799074 | − | 0.601233i | \(-0.794676\pi\) | ||||
−0.799074 | + | 0.601233i | \(0.794676\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.66044 | −0.351723 | ||||||||
\(260\) | −32.8147 | −2.03508 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.3824 | −1.25923 | ||||||||
\(263\) | 28.0650 | 1.73056 | 0.865281 | − | 0.501287i | \(-0.167140\pi\) | ||||
0.865281 | + | 0.501287i | \(0.167140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.2763 | 1.06128 | ||||||||
\(266\) | −28.7876 | −1.76508 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 26.8726 | 1.64150 | ||||||||
\(269\) | −30.1710 | −1.83956 | −0.919778 | − | 0.392439i | \(-0.871631\pi\) | ||||
−0.919778 | + | 0.392439i | \(0.871631\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0000 | −1.15417 | −0.577084 | − | 0.816685i | \(-0.695809\pi\) | ||||
−0.577084 | + | 0.816685i | \(0.695809\pi\) | |||||||
\(272\) | 12.4058 | 0.752213 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −37.5895 | −2.27086 | ||||||||
\(275\) | −18.9583 | −1.14323 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.1215 | 1.26907 | 0.634535 | − | 0.772894i | \(-0.281191\pi\) | ||||
0.634535 | + | 0.772894i | \(0.281191\pi\) | |||||||
\(278\) | 45.8992 | 2.75285 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.06418 | −0.123358 | ||||||||
\(281\) | −1.74730 | −0.104235 | −0.0521175 | − | 0.998641i | \(-0.516597\pi\) | ||||
−0.0521175 | + | 0.998641i | \(0.516597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.28817 | −0.433237 | −0.216618 | − | 0.976256i | \(-0.569503\pi\) | ||||
−0.216618 | + | 0.976256i | \(0.569503\pi\) | |||||||
\(284\) | 2.26103 | 0.134168 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.2395 | −1.19679 | ||||||||
\(287\) | −5.86495 | −0.346197 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.38507 | −0.493239 | ||||||||
\(290\) | 25.4652 | 1.49537 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.79561 | −0.514724 | ||||||||
\(293\) | −15.3509 | −0.896809 | −0.448404 | − | 0.893831i | \(-0.648008\pi\) | ||||
−0.448404 | + | 0.893831i | \(0.648008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −49.2772 | −2.86903 | ||||||||
\(296\) | 0.572881 | 0.0332980 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −30.5408 | −1.76918 | ||||||||
\(299\) | −2.44820 | −0.141583 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.49794 | −0.143979 | ||||||||
\(302\) | 11.6240 | 0.668888 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 26.3182 | 1.50945 | ||||||||
\(305\) | −13.6036 | −0.778940 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.7638 | 0.956762 | 0.478381 | − | 0.878152i | \(-0.341224\pi\) | ||||
0.478381 | + | 0.878152i | \(0.341224\pi\) | |||||||
\(308\) | 9.61051 | 0.547610 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 31.3901 | 1.78284 | ||||||||
\(311\) | 16.0231 | 0.908589 | 0.454295 | − | 0.890852i | \(-0.349891\pi\) | ||||
0.454295 | + | 0.890852i | \(0.349891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.4056 | 1.94472 | 0.972360 | − | 0.233488i | \(-0.0750138\pi\) | ||||
0.972360 | + | 0.233488i | \(0.0750138\pi\) | |||||||
\(314\) | 2.38744 | 0.134731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.0574 | −1.35333 | ||||||||
\(317\) | 16.3111 | 0.916123 | 0.458061 | − | 0.888921i | \(-0.348544\pi\) | ||||
0.458061 | + | 0.888921i | \(0.348544\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.60906 | 0.426026 | ||||||||
\(320\) | −25.9403 | −1.45011 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.39961 | 0.133725 | ||||||||
\(323\) | 18.2761 | 1.01691 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −41.0479 | −2.27693 | ||||||||
\(326\) | −5.46237 | −0.302533 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.593578 | 0.0327749 | ||||||||
\(329\) | 0.557635 | 0.0307434 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.5800 | −1.73579 | −0.867896 | − | 0.496746i | \(-0.834528\pi\) | ||||
−0.867896 | + | 0.496746i | \(0.834528\pi\) | |||||||
\(332\) | −21.2445 | −1.16594 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.53983 | 0.412561 | ||||||||
\(335\) | 52.9286 | 2.89180 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00505 | 0.327116 | 0.163558 | − | 0.986534i | \(-0.447703\pi\) | ||||
0.163558 | + | 0.986534i | \(0.447703\pi\) | |||||||
\(338\) | −18.2169 | −0.990870 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −20.4192 | −1.10739 | ||||||||
\(341\) | 9.37944 | 0.507925 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9290 | 1.07607 | ||||||||
\(344\) | 0.252811 | 0.0136307 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.8452 | 0.744325 | ||||||||
\(347\) | −23.0304 | −1.23634 | −0.618168 | − | 0.786046i | \(-0.712125\pi\) | ||||
−0.618168 | + | 0.786046i | \(0.712125\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5662 | −0.619126 | −0.309563 | − | 0.950879i | \(-0.600183\pi\) | ||||
−0.309563 | + | 0.950879i | \(0.600183\pi\) | |||||||
\(350\) | 40.2332 | 2.15056 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −17.1010 | −0.911487 | ||||||||
\(353\) | 2.13463 | 0.113615 | 0.0568073 | − | 0.998385i | \(-0.481908\pi\) | ||||
0.0568073 | + | 0.998385i | \(0.481908\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.45336 | 0.236360 | ||||||||
\(356\) | 1.31423 | 0.0696540 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 28.3337 | 1.49748 | ||||||||
\(359\) | −24.2235 | −1.27847 | −0.639234 | − | 0.769012i | \(-0.720749\pi\) | ||||
−0.639234 | + | 0.769012i | \(0.720749\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.7716 | 1.04061 | ||||||||
\(362\) | −25.9995 | −1.36650 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20.8084 | 1.09066 | ||||||||
\(365\) | −17.3240 | −0.906778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.83481 | −0.147976 | −0.0739879 | − | 0.997259i | \(-0.523573\pi\) | ||||
−0.0739879 | + | 0.997259i | \(0.523573\pi\) | |||||||
\(368\) | −2.19377 | −0.114358 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17.5817 | −0.914030 | ||||||||
\(371\) | −10.9552 | −0.568767 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.8334 | −1.49294 | −0.746468 | − | 0.665421i | \(-0.768252\pi\) | ||||
−0.746468 | + | 0.665421i | \(0.768252\pi\) | |||||||
\(374\) | −12.5942 | −0.651230 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0564370 | −0.00291052 | ||||||||
\(377\) | 16.4749 | 0.848501 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.1985 | 1.65393 | 0.826963 | − | 0.562256i | \(-0.190066\pi\) | ||||
0.826963 | + | 0.562256i | \(0.190066\pi\) | |||||||
\(380\) | −43.3181 | −2.22217 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.4388 | −1.35273 | ||||||||
\(383\) | −0.672250 | −0.0343504 | −0.0171752 | − | 0.999852i | \(-0.505467\pi\) | ||||
−0.0171752 | + | 0.999852i | \(0.505467\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.9290 | 0.964712 | ||||||||
\(386\) | −29.5542 | −1.50427 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.3182 | −0.676129 | ||||||||
\(389\) | 4.25930 | 0.215955 | 0.107978 | − | 0.994153i | \(-0.465563\pi\) | ||||
0.107978 | + | 0.994153i | \(0.465563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.52341 | −0.0770424 | ||||||||
\(392\) | −0.354019 | −0.0178807 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 43.9641 | 2.21488 | ||||||||
\(395\) | −47.3838 | −2.38414 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.86484 | −0.444913 | −0.222457 | − | 0.974943i | \(-0.571408\pi\) | ||||
−0.222457 | + | 0.974943i | \(0.571408\pi\) | |||||||
\(398\) | 17.9255 | 0.898524 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −36.7820 | −1.83910 | ||||||||
\(401\) | −37.0839 | −1.85188 | −0.925941 | − | 0.377667i | \(-0.876726\pi\) | ||||
−0.925941 | + | 0.377667i | \(0.876726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.3081 | 1.01162 | ||||||||
\(404\) | 8.79012 | 0.437325 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.1480 | −0.801410 | ||||||||
\(407\) | −5.25346 | −0.260404 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.38919 | −0.167584 | −0.0837922 | − | 0.996483i | \(-0.526703\pi\) | ||||
−0.0837922 | + | 0.996483i | \(0.526703\pi\) | |||||||
\(410\) | −18.2169 | −0.899669 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −25.6040 | −1.26142 | ||||||||
\(413\) | 31.2476 | 1.53760 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.8435 | −2.05402 | ||||||||
\(416\) | −37.0266 | −1.81538 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −26.7178 | −1.30681 | ||||||||
\(419\) | 20.6564 | 1.00913 | 0.504565 | − | 0.863374i | \(-0.331653\pi\) | ||||
0.504565 | + | 0.863374i | \(0.331653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.5330 | 1.34188 | 0.670939 | − | 0.741513i | \(-0.265891\pi\) | ||||
0.670939 | + | 0.741513i | \(0.265891\pi\) | |||||||
\(422\) | 11.7738 | 0.573139 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.10876 | 0.0538459 | ||||||||
\(425\) | −25.5424 | −1.23899 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.62630 | 0.417456 | ||||||||
\(428\) | 21.8647 | 1.05687 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.75877 | −0.374161 | ||||||||
\(431\) | 2.58110 | 0.124327 | 0.0621636 | − | 0.998066i | \(-0.480200\pi\) | ||||
0.0621636 | + | 0.998066i | \(0.480200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.0137 | −1.29820 | −0.649098 | − | 0.760704i | \(-0.724854\pi\) | ||||
−0.649098 | + | 0.760704i | \(0.724854\pi\) | |||||||
\(434\) | −19.9051 | −0.955474 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.4466 | 1.31445 | ||||||||
\(437\) | −3.23183 | −0.154599 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.7101 | 0.558891 | 0.279446 | − | 0.960162i | \(-0.409849\pi\) | ||||
0.279446 | + | 0.960162i | \(0.409849\pi\) | |||||||
\(440\) | −1.91576 | −0.0913305 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −27.2686 | −1.29703 | ||||||||
\(443\) | −2.08077 | −0.0988606 | −0.0494303 | − | 0.998778i | \(-0.515741\pi\) | ||||
−0.0494303 | + | 0.998778i | \(0.515741\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.58853 | 0.122708 | ||||||||
\(446\) | 17.5329 | 0.830206 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.4492 | 0.777154 | ||||||||
\(449\) | −10.5508 | −0.497924 | −0.248962 | − | 0.968513i | \(-0.580089\pi\) | ||||
−0.248962 | + | 0.968513i | \(0.580089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.44326 | −0.256313 | ||||||||
\(452\) | 8.82526 | 0.415106 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.0128 | 0.986179 | ||||||||
\(455\) | 40.9845 | 1.92139 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.90941 | −0.369987 | −0.184993 | − | 0.982740i | \(-0.559226\pi\) | ||||
−0.184993 | + | 0.982740i | \(0.559226\pi\) | |||||||
\(458\) | 16.2912 | 0.761238 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.61081 | 0.168355 | ||||||||
\(461\) | 39.0928 | 1.82073 | 0.910366 | − | 0.413804i | \(-0.135800\pi\) | ||||
0.910366 | + | 0.413804i | \(0.135800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.6928 | 1.10110 | 0.550550 | − | 0.834802i | \(-0.314418\pi\) | ||||
0.550550 | + | 0.834802i | \(0.314418\pi\) | |||||||
\(464\) | 14.7628 | 0.685344 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.0915 | −1.16234 | ||||||||
\(467\) | 34.7152 | 1.60643 | 0.803214 | − | 0.595691i | \(-0.203122\pi\) | ||||
0.803214 | + | 0.595691i | \(0.203122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.5631 | −1.54980 | ||||||||
\(470\) | 1.73205 | 0.0798935 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.16250 | −0.145566 | ||||||||
\(473\) | −2.31834 | −0.106597 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −54.1867 | −2.48625 | ||||||||
\(476\) | 12.9482 | 0.593480 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −29.5749 | −1.35272 | ||||||||
\(479\) | 6.48173 | 0.296158 | 0.148079 | − | 0.988976i | \(-0.452691\pi\) | ||||
0.148079 | + | 0.988976i | \(0.452691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.3746 | −0.518639 | ||||||||
\(482\) | −1.56704 | −0.0713767 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.7537 | −0.534260 | ||||||||
\(485\) | −26.2317 | −1.19112 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.9828 | 0.905505 | 0.452753 | − | 0.891636i | \(-0.350442\pi\) | ||||
0.452753 | + | 0.891636i | \(0.350442\pi\) | |||||||
\(488\) | −0.873048 | −0.0395210 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.8648 | 0.490823 | ||||||||
\(491\) | 26.2271 | 1.18361 | 0.591806 | − | 0.806081i | \(-0.298415\pi\) | ||||
0.591806 | + | 0.806081i | \(0.298415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.2517 | 0.461711 | ||||||||
\(494\) | −57.8486 | −2.60273 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.1976 | 0.817096 | ||||||||
\(497\) | −2.82396 | −0.126672 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.31727 | 0.282800 | 0.141400 | − | 0.989953i | \(-0.454840\pi\) | ||||
0.141400 | + | 0.989953i | \(0.454840\pi\) | |||||||
\(500\) | 25.7566 | 1.15187 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.3773 | −0.730956 | ||||||||
\(503\) | 21.8261 | 0.973179 | 0.486589 | − | 0.873631i | \(-0.338241\pi\) | ||||
0.486589 | + | 0.873631i | \(0.338241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.3131 | 0.770425 | ||||||||
\(506\) | 2.22708 | 0.0990059 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.4483 | 0.507937 | ||||||||
\(509\) | −29.0931 | −1.28953 | −0.644765 | − | 0.764381i | \(-0.723045\pi\) | ||||
−0.644765 | + | 0.764381i | \(0.723045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.9855 | 0.485968 | ||||||||
\(512\) | −31.1704 | −1.37755 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 50.4620 | 2.22579 | ||||||||
\(515\) | −50.4301 | −2.22221 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.517541 | 0.0227614 | ||||||||
\(518\) | 11.1489 | 0.489855 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.14796 | −0.181900 | ||||||||
\(521\) | 13.6949 | 0.599982 | 0.299991 | − | 0.953942i | \(-0.403016\pi\) | ||||
0.299991 | + | 0.953942i | \(0.403016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.1506 | 0.575038 | 0.287519 | − | 0.957775i | \(-0.407170\pi\) | ||||
0.287519 | + | 0.957775i | \(0.407170\pi\) | |||||||
\(524\) | 19.4486 | 0.849618 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −55.2772 | −2.41020 | ||||||||
\(527\) | 12.6369 | 0.550472 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7306 | −0.988287 | ||||||||
\(530\) | −34.0277 | −1.47807 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 27.4688 | 1.19093 | ||||||||
\(533\) | −11.7856 | −0.510490 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.0651 | 1.86187 | ||||||||
\(536\) | 3.39684 | 0.146721 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 59.4252 | 2.56200 | ||||||||
\(539\) | 3.24644 | 0.139834 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.26083 | 0.269174 | 0.134587 | − | 0.990902i | \(-0.457029\pi\) | ||||
0.134587 | + | 0.990902i | \(0.457029\pi\) | |||||||
\(542\) | 37.4227 | 1.60744 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −23.0401 | −0.987838 | ||||||||
\(545\) | 54.0592 | 2.31564 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.3783 | −1.34164 | −0.670819 | − | 0.741621i | \(-0.734057\pi\) | ||||
−0.670819 | + | 0.741621i | \(0.734057\pi\) | |||||||
\(548\) | 35.8674 | 1.53218 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 37.3405 | 1.59220 | ||||||||
\(551\) | 21.7483 | 0.926508 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.0469 | 1.27773 | ||||||||
\(554\) | −41.6013 | −1.76747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −43.7965 | −1.85739 | ||||||||
\(557\) | 43.4392 | 1.84058 | 0.920290 | − | 0.391237i | \(-0.127953\pi\) | ||||
0.920290 | + | 0.391237i | \(0.127953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.01960 | −0.212306 | ||||||||
\(560\) | 36.7252 | 1.55192 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.44150 | 0.145171 | ||||||||
\(563\) | 32.0176 | 1.34938 | 0.674691 | − | 0.738100i | \(-0.264277\pi\) | ||||
0.674691 | + | 0.738100i | \(0.264277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.3824 | 0.731282 | ||||||||
\(566\) | 14.3549 | 0.603381 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.285807 | 0.0119922 | ||||||||
\(569\) | 6.77194 | 0.283895 | 0.141947 | − | 0.989874i | \(-0.454664\pi\) | ||||
0.141947 | + | 0.989874i | \(0.454664\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.1530 | −0.885226 | −0.442613 | − | 0.896713i | \(-0.645948\pi\) | ||||
−0.442613 | + | 0.896713i | \(0.645948\pi\) | |||||||
\(572\) | 19.3123 | 0.807487 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.5517 | 0.482158 | ||||||||
\(575\) | 4.51677 | 0.188362 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9162 | 0.496079 | 0.248039 | − | 0.968750i | \(-0.420214\pi\) | ||||
0.248039 | + | 0.968750i | \(0.420214\pi\) | |||||||
\(578\) | 16.5154 | 0.686948 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −24.2986 | −1.00894 | ||||||||
\(581\) | 26.5337 | 1.10081 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.1676 | −0.421097 | ||||||||
\(584\) | −1.11181 | −0.0460072 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.2354 | 1.24901 | ||||||||
\(587\) | 0.129862 | 0.00535996 | 0.00267998 | − | 0.999996i | \(-0.499147\pi\) | ||||
0.00267998 | + | 0.999996i | \(0.499147\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.8084 | 1.10462 | ||||||||
\(590\) | 97.0572 | 3.99578 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.1925 | −0.418911 | ||||||||
\(593\) | −26.2622 | −1.07846 | −0.539230 | − | 0.842158i | \(-0.681285\pi\) | ||||
−0.539230 | + | 0.842158i | \(0.681285\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.5030 | 1.04552 | ||||||||
\(596\) | 29.1417 | 1.19369 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.82201 | 0.197187 | ||||||||
\(599\) | −27.5952 | −1.12751 | −0.563754 | − | 0.825943i | \(-0.690643\pi\) | ||||
−0.563754 | + | 0.825943i | \(0.690643\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.33275 | 0.0543639 | 0.0271820 | − | 0.999631i | \(-0.491347\pi\) | ||||
0.0271820 | + | 0.999631i | \(0.491347\pi\) | |||||||
\(602\) | 4.91998 | 0.200524 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.0915 | −0.451308 | ||||||||
\(605\) | −23.1503 | −0.941194 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.5645 | −0.509977 | −0.254988 | − | 0.966944i | \(-0.582072\pi\) | ||||
−0.254988 | + | 0.966944i | \(0.582072\pi\) | |||||||
\(608\) | −48.8783 | −1.98228 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.7939 | 1.08485 | ||||||||
\(611\) | 1.12056 | 0.0453332 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.9982 | −0.565384 | −0.282692 | − | 0.959211i | \(-0.591227\pi\) | ||||
−0.282692 | + | 0.959211i | \(0.591227\pi\) | |||||||
\(614\) | −33.0183 | −1.33251 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.21482 | 0.0489466 | ||||||||
\(617\) | −24.0467 | −0.968084 | −0.484042 | − | 0.875045i | \(-0.660832\pi\) | ||||
−0.484042 | + | 0.875045i | \(0.660832\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.87164 | 0.276195 | 0.138097 | − | 0.990419i | \(-0.455901\pi\) | ||||
0.138097 | + | 0.990419i | \(0.455901\pi\) | |||||||
\(620\) | −29.9521 | −1.20291 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.5594 | −1.26542 | ||||||||
\(623\) | −1.64143 | −0.0657626 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.21894 | 0.288758 | ||||||||
\(626\) | −67.7658 | −2.70847 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.27807 | −0.0909047 | ||||||||
\(629\) | −7.07797 | −0.282217 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.3773 | −1.40835 | −0.704175 | − | 0.710027i | \(-0.748683\pi\) | ||||
−0.704175 | + | 0.710027i | \(0.748683\pi\) | |||||||
\(632\) | −3.04098 | −0.120964 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −32.1266 | −1.27591 | ||||||||
\(635\) | 22.5488 | 0.894821 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.02910 | 0.278503 | ||||||||
\(638\) | −14.9869 | −0.593338 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.02229 | −0.277580 | ||||||||
\(641\) | 19.1737 | 0.757314 | 0.378657 | − | 0.925537i | \(-0.376386\pi\) | ||||
0.378657 | + | 0.925537i | \(0.376386\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.3764 | 0.764130 | 0.382065 | − | 0.924135i | \(-0.375213\pi\) | ||||
0.382065 | + | 0.924135i | \(0.375213\pi\) | |||||||
\(644\) | −2.28969 | −0.0902263 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −35.9968 | −1.41628 | ||||||||
\(647\) | −8.77141 | −0.344840 | −0.172420 | − | 0.985024i | \(-0.555159\pi\) | ||||
−0.172420 | + | 0.985024i | \(0.555159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.0009 | 1.13839 | ||||||||
\(650\) | 80.8485 | 3.17114 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.21213 | 0.204123 | ||||||||
\(653\) | −32.8094 | −1.28393 | −0.641965 | − | 0.766734i | \(-0.721881\pi\) | ||||
−0.641965 | + | 0.766734i | \(0.721881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.3063 | 1.49675 | ||||||||
\(656\) | −10.5608 | −0.412329 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.09833 | −0.0428172 | ||||||||
\(659\) | −18.6516 | −0.726563 | −0.363282 | − | 0.931679i | \(-0.618344\pi\) | ||||
−0.363282 | + | 0.931679i | \(0.618344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.4074 | 1.41608 | 0.708041 | − | 0.706171i | \(-0.249579\pi\) | ||||
0.708041 | + | 0.706171i | \(0.249579\pi\) | |||||||
\(662\) | 62.2004 | 2.41749 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.68542 | −0.104215 | ||||||||
\(665\) | 54.1031 | 2.09803 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.81284 | −0.0701936 | ||||||||
\(668\) | −7.19442 | −0.278361 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −104.249 | −4.02749 | ||||||||
\(671\) | 8.00607 | 0.309071 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.3901 | 1.51838 | 0.759189 | − | 0.650871i | \(-0.225596\pi\) | ||||
0.759189 | + | 0.650871i | \(0.225596\pi\) | |||||||
\(674\) | −11.8276 | −0.455584 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.3824 | 0.668553 | ||||||||
\(677\) | −31.6754 | −1.21738 | −0.608692 | − | 0.793406i | \(-0.708306\pi\) | ||||
−0.608692 | + | 0.793406i | \(0.708306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.6340 | 0.638356 | ||||||||
\(680\) | −2.58110 | −0.0989807 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −18.4739 | −0.707402 | ||||||||
\(683\) | 29.0656 | 1.11217 | 0.556083 | − | 0.831127i | \(-0.312304\pi\) | ||||
0.556083 | + | 0.831127i | \(0.312304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 70.6451 | 2.69921 | ||||||||
\(686\) | −39.2525 | −1.49867 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.49794 | −0.171482 | ||||||||
\(689\) | −22.0145 | −0.838685 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.35740 | 0.203805 | 0.101903 | − | 0.994794i | \(-0.467507\pi\) | ||||
0.101903 | + | 0.994794i | \(0.467507\pi\) | |||||||
\(692\) | −13.2110 | −0.502206 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 45.3610 | 1.72188 | ||||||||
\(695\) | −86.2623 | −3.27212 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.33368 | −0.277783 | ||||||||
\(698\) | 22.7810 | 0.862275 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −38.3901 | −1.45101 | ||||||||
\(701\) | 25.6536 | 0.968922 | 0.484461 | − | 0.874813i | \(-0.339016\pi\) | ||||
0.484461 | + | 0.874813i | \(0.339016\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.0155 | −0.566320 | ||||||||
\(704\) | 15.2665 | 0.575380 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.20439 | −0.158234 | ||||||||
\(707\) | −10.9786 | −0.412893 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.69047 | −0.176154 | −0.0880772 | − | 0.996114i | \(-0.528072\pi\) | ||||
−0.0880772 | + | 0.996114i | \(0.528072\pi\) | |||||||
\(710\) | −8.77141 | −0.329185 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.166126 | 0.00622583 | ||||||||
\(713\) | −2.23463 | −0.0836877 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.0378 | 1.42253 | ||||||||
\(716\) | −27.0357 | −1.01037 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 47.7110 | 1.78056 | ||||||||
\(719\) | −39.0669 | −1.45695 | −0.728476 | − | 0.685072i | \(-0.759771\pi\) | ||||
−0.728476 | + | 0.685072i | \(0.759771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.9786 | 1.19095 | ||||||||
\(722\) | −38.9424 | −1.44929 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24.8084 | 0.921997 | ||||||||
\(725\) | −30.3951 | −1.12885 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.8253 | −0.401489 | −0.200744 | − | 0.979644i | \(-0.564336\pi\) | ||||
−0.200744 | + | 0.979644i | \(0.564336\pi\) | |||||||
\(728\) | 2.63030 | 0.0974853 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 34.1215 | 1.26290 | ||||||||
\(731\) | −3.12349 | −0.115526 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.41241 | −0.126040 | −0.0630201 | − | 0.998012i | \(-0.520073\pi\) | ||||
−0.0630201 | + | 0.998012i | \(0.520073\pi\) | |||||||
\(734\) | 5.58348 | 0.206090 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.07428 | 0.150180 | ||||||||
\(737\) | −31.1499 | −1.14742 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.3010 | 0.967497 | 0.483748 | − | 0.875207i | \(-0.339275\pi\) | ||||
0.483748 | + | 0.875207i | \(0.339275\pi\) | |||||||
\(740\) | 16.7763 | 0.616708 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21.5776 | 0.792139 | ||||||||
\(743\) | −28.9439 | −1.06185 | −0.530924 | − | 0.847419i | \(-0.678155\pi\) | ||||
−0.530924 | + | 0.847419i | \(0.678155\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 57.3979 | 2.10289 | ||||||||
\(746\) | 56.7907 | 2.07925 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.0172 | 0.439394 | ||||||||
\(749\) | −27.3084 | −0.997827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.4483 | −0.709679 | −0.354839 | − | 0.934927i | \(-0.615464\pi\) | ||||
−0.354839 | + | 0.934927i | \(0.615464\pi\) | |||||||
\(752\) | 1.00411 | 0.0366161 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −32.4492 | −1.18173 | ||||||||
\(755\) | −21.8460 | −0.795058 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.59627 | 0.239745 | 0.119873 | − | 0.992789i | \(-0.461751\pi\) | ||||
0.119873 | + | 0.992789i | \(0.461751\pi\) | |||||||
\(758\) | −63.4187 | −2.30347 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.47565 | −0.198623 | ||||||||
\(761\) | −10.3297 | −0.374451 | −0.187226 | − | 0.982317i | \(-0.559950\pi\) | ||||
−0.187226 | + | 0.982317i | \(0.559950\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.2799 | −1.24102 | ||||||||
\(764\) | 25.2276 | 0.912703 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.32407 | 0.0478407 | ||||||||
\(767\) | 62.7920 | 2.26729 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.8590 | 1.61766 | 0.808828 | − | 0.588046i | \(-0.200102\pi\) | ||||
0.808828 | + | 0.588046i | \(0.200102\pi\) | |||||||
\(770\) | −37.2829 | −1.34358 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.2003 | 1.01495 | ||||||||
\(773\) | −42.9355 | −1.54428 | −0.772141 | − | 0.635452i | \(-0.780814\pi\) | ||||
−0.772141 | + | 0.635452i | \(0.780814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.4671 | −1.34586 | ||||||||
\(776\) | −1.68349 | −0.0604339 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.38919 | −0.300767 | ||||||||
\(779\) | −15.5580 | −0.557422 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.62092 | −0.0937839 | ||||||||
\(782\) | 3.00054 | 0.107299 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.29860 | 0.224950 | ||||||||
\(785\) | −4.48691 | −0.160145 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.477407 | 0.0170177 | 0.00850885 | − | 0.999964i | \(-0.497292\pi\) | ||||
0.00850885 | + | 0.999964i | \(0.497292\pi\) | |||||||
\(788\) | −41.9501 | −1.49441 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 93.3278 | 3.32045 | ||||||||
\(791\) | −11.0225 | −0.391915 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.3345 | 0.615566 | ||||||||
\(794\) | 17.4603 | 0.619644 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.1043 | −0.606246 | ||||||||
\(797\) | −11.4690 | −0.406252 | −0.203126 | − | 0.979153i | \(-0.565110\pi\) | ||||
−0.203126 | + | 0.979153i | \(0.565110\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.697281 | 0.0246680 | ||||||||
\(800\) | 68.3116 | 2.41518 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 73.0411 | 2.57917 | ||||||||
\(803\) | 10.1956 | 0.359795 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.50980 | −0.158950 | ||||||||
\(806\) | −39.9991 | −1.40891 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.11112 | 0.0390890 | ||||||||
\(809\) | −42.7873 | −1.50432 | −0.752161 | − | 0.658979i | \(-0.770988\pi\) | ||||
−0.752161 | + | 0.658979i | \(0.770988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.2098 | −1.09592 | −0.547962 | − | 0.836503i | \(-0.684596\pi\) | ||||
−0.547962 | + | 0.836503i | \(0.684596\pi\) | |||||||
\(812\) | 15.4082 | 0.540722 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.3473 | 0.362673 | ||||||||
\(815\) | 10.2659 | 0.359599 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.62630 | −0.231825 | ||||||||
\(818\) | 6.67539 | 0.233400 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.3824 | 0.607019 | ||||||||
\(821\) | −27.2511 | −0.951070 | −0.475535 | − | 0.879697i | \(-0.657745\pi\) | ||||
−0.475535 | + | 0.879697i | \(0.657745\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.4406 | −0.503367 | −0.251683 | − | 0.967810i | \(-0.580984\pi\) | ||||
−0.251683 | + | 0.967810i | \(0.580984\pi\) | |||||||
\(824\) | −3.23649 | −0.112748 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −61.5458 | −2.14145 | ||||||||
\(827\) | −7.02757 | −0.244373 | −0.122186 | − | 0.992507i | \(-0.538991\pi\) | ||||
−0.122186 | + | 0.992507i | \(0.538991\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.0806 | −1.46152 | −0.730760 | − | 0.682635i | \(-0.760834\pi\) | ||||
−0.730760 | + | 0.682635i | \(0.760834\pi\) | |||||||
\(830\) | 82.4156 | 2.86069 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 33.0547 | 1.14596 | ||||||||
\(833\) | 4.37392 | 0.151547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.1702 | −0.490382 | ||||||||
\(836\) | 25.4938 | 0.881723 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −40.6851 | −1.40544 | ||||||||
\(839\) | 39.9213 | 1.37824 | 0.689118 | − | 0.724649i | \(-0.257998\pi\) | ||||
0.689118 | + | 0.724649i | \(0.257998\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.8007 | −0.579333 | ||||||||
\(842\) | −54.2295 | −1.86887 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.2344 | −0.386705 | ||||||||
\(845\) | 34.2366 | 1.17777 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.6800 | 0.504412 | ||||||||
\(848\) | −19.7266 | −0.677416 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 50.3087 | 1.72557 | ||||||||
\(851\) | 1.25163 | 0.0429052 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.4810 | −0.803975 | −0.401988 | − | 0.915645i | \(-0.631680\pi\) | ||||
−0.401988 | + | 0.915645i | \(0.631680\pi\) | |||||||
\(854\) | −16.9905 | −0.581402 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.76382 | 0.0944655 | ||||||||
\(857\) | 8.03472 | 0.274461 | 0.137230 | − | 0.990539i | \(-0.456180\pi\) | ||||
0.137230 | + | 0.990539i | \(0.456180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.2959 | −0.828966 | −0.414483 | − | 0.910057i | \(-0.636038\pi\) | ||||
−0.414483 | + | 0.910057i | \(0.636038\pi\) | |||||||
\(860\) | 7.40333 | 0.252452 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.08378 | −0.173154 | ||||||||
\(863\) | −10.2828 | −0.350029 | −0.175015 | − | 0.984566i | \(-0.555997\pi\) | ||||
−0.175015 | + | 0.984566i | \(0.555997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.0205 | −0.884725 | ||||||||
\(866\) | 53.2067 | 1.80804 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.9932 | 0.644671 | ||||||||
\(869\) | 27.8866 | 0.945987 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −67.4448 | −2.28528 | ||||||||
\(872\) | 3.46940 | 0.117489 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.36547 | 0.215315 | ||||||||
\(875\) | −32.1692 | −1.08752 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.2276 | −0.885644 | −0.442822 | − | 0.896610i | \(-0.646023\pi\) | ||||
−0.442822 | + | 0.896610i | \(0.646023\pi\) | |||||||
\(878\) | −23.0643 | −0.778384 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 34.0847 | 1.14900 | ||||||||
\(881\) | −39.2326 | −1.32178 | −0.660890 | − | 0.750483i | \(-0.729821\pi\) | ||||
−0.660890 | + | 0.750483i | \(0.729821\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.79830 | 0.262434 | 0.131217 | − | 0.991354i | \(-0.458112\pi\) | ||||
0.131217 | + | 0.991354i | \(0.458112\pi\) | |||||||
\(884\) | 26.0194 | 0.875126 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.09833 | 0.137686 | ||||||||
\(887\) | −22.8571 | −0.767465 | −0.383732 | − | 0.923444i | \(-0.625361\pi\) | ||||
−0.383732 | + | 0.923444i | \(0.625361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.2986 | −0.479560 | ||||||||
\(890\) | −5.09840 | −0.170899 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.7297 | −0.560151 | ||||||||
\(893\) | 1.47924 | 0.0495009 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −53.2499 | −1.77995 | ||||||||
\(896\) | 4.45297 | 0.148763 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.7811 | 0.693473 | ||||||||
\(899\) | 15.0377 | 0.501537 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.6987 | −0.456370 | ||||||||
\(902\) | 10.7211 | 0.356974 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.11556 | 0.0371031 | ||||||||
\(905\) | 48.8630 | 1.62426 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.8485 | −1.25674 | −0.628370 | − | 0.777915i | \(-0.716278\pi\) | ||||
−0.628370 | + | 0.777915i | \(0.716278\pi\) | |||||||
\(908\) | −20.0502 | −0.665388 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −80.7238 | −2.67597 | ||||||||
\(911\) | −52.7045 | −1.74618 | −0.873089 | − | 0.487561i | \(-0.837887\pi\) | ||||
−0.873089 | + | 0.487561i | \(0.837887\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.6260 | 0.815001 | ||||||||
\(914\) | 15.5785 | 0.515291 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.5449 | −0.513617 | ||||||||
\(917\) | −24.2908 | −0.802152 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.1052 | −1.61983 | −0.809916 | − | 0.586545i | \(-0.800488\pi\) | ||||
−0.809916 | + | 0.586545i | \(0.800488\pi\) | |||||||
\(920\) | 0.456427 | 0.0150480 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −76.9977 | −2.53579 | ||||||||
\(923\) | −5.67474 | −0.186786 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.9855 | 0.689997 | ||||||||
\(926\) | −46.6658 | −1.53353 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −27.4175 | −0.900022 | ||||||||
\(929\) | −17.9507 | −0.588943 | −0.294472 | − | 0.955660i | \(-0.595144\pi\) | ||||
−0.294472 | + | 0.955660i | \(0.595144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.27900 | 0.304107 | ||||||||
\(932\) | 23.9420 | 0.784248 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −68.3756 | −2.23732 | ||||||||
\(935\) | 23.6693 | 0.774070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.7980 | −0.973457 | −0.486729 | − | 0.873553i | \(-0.661810\pi\) | ||||
−0.486729 | + | 0.873553i | \(0.661810\pi\) | |||||||
\(938\) | 66.1063 | 2.15845 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.65270 | −0.0539052 | ||||||||
\(941\) | 30.0112 | 0.978339 | 0.489169 | − | 0.872189i | \(-0.337300\pi\) | ||||
0.489169 | + | 0.872189i | \(0.337300\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.29685 | 0.0422311 | ||||||||
\(944\) | 56.2663 | 1.83131 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.56624 | 0.148461 | ||||||||
\(947\) | −45.6013 | −1.48184 | −0.740922 | − | 0.671591i | \(-0.765611\pi\) | ||||
−0.740922 | + | 0.671591i | \(0.765611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.0752 | 0.716592 | ||||||||
\(950\) | 106.727 | 3.46268 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.63673 | 0.0530466 | ||||||||
\(953\) | 13.1957 | 0.427451 | 0.213726 | − | 0.976894i | \(-0.431440\pi\) | ||||
0.213726 | + | 0.976894i | \(0.431440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 49.6887 | 1.60789 | ||||||||
\(956\) | 28.2201 | 0.912702 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.7665 | −0.412467 | ||||||||
\(959\) | −44.7974 | −1.44658 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.4635 | −0.402047 | ||||||||
\(962\) | 22.4037 | 0.722323 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.49525 | 0.0481588 | ||||||||
\(965\) | 55.5437 | 1.78801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.1548 | −0.648133 | −0.324067 | − | 0.946034i | \(-0.605050\pi\) | ||||
−0.324067 | + | 0.946034i | \(0.605050\pi\) | |||||||
\(968\) | −1.48574 | −0.0477533 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 51.6664 | 1.65891 | ||||||||
\(971\) | 26.5839 | 0.853118 | 0.426559 | − | 0.904460i | \(-0.359726\pi\) | ||||
0.426559 | + | 0.904460i | \(0.359726\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 54.7006 | 1.75362 | ||||||||
\(974\) | −39.3584 | −1.26112 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.5330 | 0.497200 | ||||||||
\(977\) | −14.4041 | −0.460828 | −0.230414 | − | 0.973093i | \(-0.574008\pi\) | ||||
−0.230414 | + | 0.973093i | \(0.574008\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.52341 | −0.0486885 | ||||||||
\(980\) | −10.3671 | −0.331165 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −51.6573 | −1.64845 | ||||||||
\(983\) | 42.9881 | 1.37111 | 0.685554 | − | 0.728022i | \(-0.259560\pi\) | ||||
0.685554 | + | 0.728022i | \(0.259560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −82.6255 | −2.63267 | ||||||||
\(986\) | −20.1918 | −0.643039 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 55.1985 | 1.75610 | ||||||||
\(989\) | 0.552340 | 0.0175634 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.5794 | −0.494895 | −0.247447 | − | 0.968901i | \(-0.579592\pi\) | ||||
−0.247447 | + | 0.968901i | \(0.579592\pi\) | |||||||
\(992\) | −33.7966 | −1.07304 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.56212 | 0.176420 | ||||||||
\(995\) | −33.6889 | −1.06801 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.6186 | 1.28640 | 0.643201 | − | 0.765697i | \(-0.277606\pi\) | ||||
0.643201 | + | 0.765697i | \(0.277606\pi\) | |||||||
\(998\) | −12.4426 | −0.393863 | ||||||||
\(999\) | 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 | 729.2.a.c.1.1 | ✓ | 6 | |
3.2 | odd | 2 | inner | 729.2.a.c.1.6 | yes | 6 | |
9.2 | odd | 6 | 729.2.c.c.244.1 | 12 | |||
9.4 | even | 3 | 729.2.c.c.487.6 | 12 | |||
9.5 | odd | 6 | 729.2.c.c.487.1 | 12 | |||
9.7 | even | 3 | 729.2.c.c.244.6 | 12 | |||
27.2 | odd | 18 | 729.2.e.r.568.1 | 12 | |||
27.4 | even | 9 | 729.2.e.q.406.1 | 12 | |||
27.5 | odd | 18 | 729.2.e.m.649.2 | 12 | |||
27.7 | even | 9 | 729.2.e.q.325.1 | 12 | |||
27.11 | odd | 18 | 729.2.e.m.82.2 | 12 | |||
27.13 | even | 9 | 729.2.e.r.163.2 | 12 | |||
27.14 | odd | 18 | 729.2.e.r.163.1 | 12 | |||
27.16 | even | 9 | 729.2.e.m.82.1 | 12 | |||
27.20 | odd | 18 | 729.2.e.q.325.2 | 12 | |||
27.22 | even | 9 | 729.2.e.m.649.1 | 12 | |||
27.23 | odd | 18 | 729.2.e.q.406.2 | 12 | |||
27.25 | even | 9 | 729.2.e.r.568.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
729.2.a.c.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
729.2.a.c.1.6 | yes | 6 | 3.2 | odd | 2 | inner | |
729.2.c.c.244.1 | 12 | 9.2 | odd | 6 | |||
729.2.c.c.244.6 | 12 | 9.7 | even | 3 | |||
729.2.c.c.487.1 | 12 | 9.5 | odd | 6 | |||
729.2.c.c.487.6 | 12 | 9.4 | even | 3 | |||
729.2.e.m.82.1 | 12 | 27.16 | even | 9 | |||
729.2.e.m.82.2 | 12 | 27.11 | odd | 18 | |||
729.2.e.m.649.1 | 12 | 27.22 | even | 9 | |||
729.2.e.m.649.2 | 12 | 27.5 | odd | 18 | |||
729.2.e.q.325.1 | 12 | 27.7 | even | 9 | |||
729.2.e.q.325.2 | 12 | 27.20 | odd | 18 | |||
729.2.e.q.406.1 | 12 | 27.4 | even | 9 | |||
729.2.e.q.406.2 | 12 | 27.23 | odd | 18 | |||
729.2.e.r.163.1 | 12 | 27.14 | odd | 18 | |||
729.2.e.r.163.2 | 12 | 27.13 | even | 9 | |||
729.2.e.r.568.1 | 12 | 27.2 | odd | 18 | |||
729.2.e.r.568.2 | 12 | 27.25 | even | 9 |