Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, 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("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56155 | −1.10418 | −0.552092 | − | 0.833783i | \(-0.686170\pi\) | ||||
−0.552092 | + | 0.833783i | \(0.686170\pi\) | |||||||
\(3\) | −2.56155 | −1.47891 | −0.739457 | − | 0.673204i | \(-0.764917\pi\) | ||||
−0.739457 | + | 0.673204i | \(0.764917\pi\) | |||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 4.00000 | 1.63299 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.43845 | 0.862121 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | −1.56155 | −0.493806 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.12311 | −0.324213 | ||||||||
\(13\) | −4.56155 | −1.26515 | −0.632574 | − | 0.774500i | \(-0.718001\pi\) | ||||
−0.632574 | + | 0.774500i | \(0.718001\pi\) | |||||||
\(14\) | −1.56155 | −0.417343 | ||||||||
\(15\) | −2.56155 | −0.661390 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 4.56155 | 1.10634 | 0.553170 | − | 0.833069i | \(-0.313418\pi\) | ||||
0.553170 | + | 0.833069i | \(0.313418\pi\) | |||||||
\(18\) | −5.56155 | −1.31087 | ||||||||
\(19\) | −1.12311 | −0.257658 | −0.128829 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128829 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(20\) | 0.438447 | 0.0980398 | ||||||||
\(21\) | −2.56155 | −0.558977 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.12311 | −1.06824 | −0.534121 | − | 0.845408i | \(-0.679357\pi\) | ||||
−0.534121 | + | 0.845408i | \(0.679357\pi\) | |||||||
\(24\) | −6.24621 | −1.27500 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 7.12311 | 1.39696 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | 0.438447 | 0.0828587 | ||||||||
\(29\) | 5.68466 | 1.05561 | 0.527807 | − | 0.849364i | \(-0.323014\pi\) | ||||
0.527807 | + | 0.849364i | \(0.323014\pi\) | |||||||
\(30\) | 4.00000 | 0.730297 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 2.43845 | 0.431061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.12311 | −1.22160 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.56155 | 0.260259 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 1.75379 | 0.284502 | ||||||||
\(39\) | 11.6847 | 1.87104 | ||||||||
\(40\) | 2.43845 | 0.385552 | ||||||||
\(41\) | 3.12311 | 0.487747 | 0.243874 | − | 0.969807i | \(-0.421582\pi\) | ||||
0.243874 | + | 0.969807i | \(0.421582\pi\) | |||||||
\(42\) | 4.00000 | 0.617213 | ||||||||
\(43\) | −9.12311 | −1.39126 | −0.695630 | − | 0.718400i | \(-0.744875\pi\) | ||||
−0.695630 | + | 0.718400i | \(0.744875\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.56155 | 0.530925 | ||||||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 3.68466 | 0.537463 | 0.268731 | − | 0.963215i | \(-0.413396\pi\) | ||||
0.268731 | + | 0.963215i | \(0.413396\pi\) | |||||||
\(48\) | 12.0000 | 1.73205 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.56155 | −0.220837 | ||||||||
\(51\) | −11.6847 | −1.63618 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | 3.12311 | 0.428992 | 0.214496 | − | 0.976725i | \(-0.431189\pi\) | ||||
0.214496 | + | 0.976725i | \(0.431189\pi\) | |||||||
\(54\) | 2.24621 | 0.305671 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.43845 | 0.325851 | ||||||||
\(57\) | 2.87689 | 0.381054 | ||||||||
\(58\) | −8.87689 | −1.16559 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | −1.12311 | −0.144992 | ||||||||
\(61\) | 9.36932 | 1.19962 | 0.599809 | − | 0.800143i | \(-0.295243\pi\) | ||||
0.599809 | + | 0.800143i | \(0.295243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.56155 | 0.448713 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | −4.56155 | −0.565791 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.24621 | −0.763096 | −0.381548 | − | 0.924349i | \(-0.624609\pi\) | ||||
−0.381548 | + | 0.924349i | \(0.624609\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | 13.1231 | 1.57984 | ||||||||
\(70\) | −1.56155 | −0.186641 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 8.68466 | 1.02350 | ||||||||
\(73\) | −4.24621 | −0.496981 | −0.248491 | − | 0.968634i | \(-0.579935\pi\) | ||||
−0.248491 | + | 0.968634i | \(0.579935\pi\) | |||||||
\(74\) | −9.36932 | −1.08916 | ||||||||
\(75\) | −2.56155 | −0.295783 | ||||||||
\(76\) | −0.492423 | −0.0564847 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −18.2462 | −2.06598 | ||||||||
\(79\) | 6.56155 | 0.738232 | 0.369116 | − | 0.929383i | \(-0.379660\pi\) | ||||
0.369116 | + | 0.929383i | \(0.379660\pi\) | |||||||
\(80\) | −4.68466 | −0.523761 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | −4.87689 | −0.538563 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | −1.12311 | −0.122541 | ||||||||
\(85\) | 4.56155 | 0.494770 | ||||||||
\(86\) | 14.2462 | 1.53621 | ||||||||
\(87\) | −14.5616 | −1.56116 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.12311 | 0.755048 | 0.377524 | − | 0.926000i | \(-0.376776\pi\) | ||||
0.377524 | + | 0.926000i | \(0.376776\pi\) | |||||||
\(90\) | −5.56155 | −0.586239 | ||||||||
\(91\) | −4.56155 | −0.478181 | ||||||||
\(92\) | −2.24621 | −0.234184 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.75379 | −0.593458 | ||||||||
\(95\) | −1.12311 | −0.115228 | ||||||||
\(96\) | −6.24621 | −0.637501 | ||||||||
\(97\) | −14.8078 | −1.50350 | −0.751750 | − | 0.659448i | \(-0.770790\pi\) | ||||
−0.751750 | + | 0.659448i | \(0.770790\pi\) | |||||||
\(98\) | −1.56155 | −0.157741 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.438447 | 0.0438447 | ||||||||
\(101\) | −0.246211 | −0.0244989 | −0.0122495 | − | 0.999925i | \(-0.503899\pi\) | ||||
−0.0122495 | + | 0.999925i | \(0.503899\pi\) | |||||||
\(102\) | 18.2462 | 1.80664 | ||||||||
\(103\) | 1.43845 | 0.141734 | 0.0708672 | − | 0.997486i | \(-0.477423\pi\) | ||||
0.0708672 | + | 0.997486i | \(0.477423\pi\) | |||||||
\(104\) | −11.1231 | −1.09071 | ||||||||
\(105\) | −2.56155 | −0.249982 | ||||||||
\(106\) | −4.87689 | −0.473686 | ||||||||
\(107\) | 11.3693 | 1.09911 | 0.549557 | − | 0.835456i | \(-0.314797\pi\) | ||||
0.549557 | + | 0.835456i | \(0.314797\pi\) | |||||||
\(108\) | −0.630683 | −0.0606875 | ||||||||
\(109\) | −17.6847 | −1.69388 | −0.846942 | − | 0.531686i | \(-0.821559\pi\) | ||||
−0.846942 | + | 0.531686i | \(0.821559\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.3693 | −1.45879 | ||||||||
\(112\) | −4.68466 | −0.442659 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | −4.49242 | −0.420754 | ||||||||
\(115\) | −5.12311 | −0.477732 | ||||||||
\(116\) | 2.49242 | 0.231416 | ||||||||
\(117\) | −16.2462 | −1.50196 | ||||||||
\(118\) | 6.24621 | 0.575010 | ||||||||
\(119\) | 4.56155 | 0.418157 | ||||||||
\(120\) | −6.24621 | −0.570198 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −14.6307 | −1.32460 | ||||||||
\(123\) | −8.00000 | −0.721336 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −5.56155 | −0.495463 | ||||||||
\(127\) | −10.2462 | −0.909204 | −0.454602 | − | 0.890695i | \(-0.650219\pi\) | ||||
−0.454602 | + | 0.890695i | \(0.650219\pi\) | |||||||
\(128\) | −13.5616 | −1.19868 | ||||||||
\(129\) | 23.3693 | 2.05755 | ||||||||
\(130\) | 7.12311 | 0.624738 | ||||||||
\(131\) | 9.12311 | 0.797089 | 0.398545 | − | 0.917149i | \(-0.369515\pi\) | ||||
0.398545 | + | 0.917149i | \(0.369515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.12311 | −0.0973856 | ||||||||
\(134\) | 9.75379 | 0.842599 | ||||||||
\(135\) | −1.43845 | −0.123802 | ||||||||
\(136\) | 11.1231 | 0.953798 | ||||||||
\(137\) | −8.87689 | −0.758404 | −0.379202 | − | 0.925314i | \(-0.623801\pi\) | ||||
−0.379202 | + | 0.925314i | \(0.623801\pi\) | |||||||
\(138\) | −20.4924 | −1.74443 | ||||||||
\(139\) | 6.87689 | 0.583291 | 0.291645 | − | 0.956527i | \(-0.405797\pi\) | ||||
0.291645 | + | 0.956527i | \(0.405797\pi\) | |||||||
\(140\) | 0.438447 | 0.0370556 | ||||||||
\(141\) | −9.43845 | −0.794861 | ||||||||
\(142\) | −12.4924 | −1.04834 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −16.6847 | −1.39039 | ||||||||
\(145\) | 5.68466 | 0.472085 | ||||||||
\(146\) | 6.63068 | 0.548759 | ||||||||
\(147\) | −2.56155 | −0.211273 | ||||||||
\(148\) | 2.63068 | 0.216241 | ||||||||
\(149\) | 4.24621 | 0.347863 | 0.173932 | − | 0.984758i | \(-0.444353\pi\) | ||||
0.173932 | + | 0.984758i | \(0.444353\pi\) | |||||||
\(150\) | 4.00000 | 0.326599 | ||||||||
\(151\) | −21.9309 | −1.78471 | −0.892354 | − | 0.451335i | \(-0.850948\pi\) | ||||
−0.892354 | + | 0.451335i | \(0.850948\pi\) | |||||||
\(152\) | −2.73863 | −0.222133 | ||||||||
\(153\) | 16.2462 | 1.31343 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.12311 | 0.410177 | ||||||||
\(157\) | 3.75379 | 0.299585 | 0.149792 | − | 0.988717i | \(-0.452139\pi\) | ||||
0.149792 | + | 0.988717i | \(0.452139\pi\) | |||||||
\(158\) | −10.2462 | −0.815145 | ||||||||
\(159\) | −8.00000 | −0.634441 | ||||||||
\(160\) | 2.43845 | 0.192776 | ||||||||
\(161\) | −5.12311 | −0.403757 | ||||||||
\(162\) | 10.9309 | 0.858810 | ||||||||
\(163\) | 1.12311 | 0.0879684 | 0.0439842 | − | 0.999032i | \(-0.485995\pi\) | ||||
0.0439842 | + | 0.999032i | \(0.485995\pi\) | |||||||
\(164\) | 1.36932 | 0.106926 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.24621 | 0.484800 | ||||||||
\(167\) | −21.9309 | −1.69706 | −0.848531 | − | 0.529146i | \(-0.822512\pi\) | ||||
−0.848531 | + | 0.529146i | \(0.822512\pi\) | |||||||
\(168\) | −6.24621 | −0.481906 | ||||||||
\(169\) | 7.80776 | 0.600597 | ||||||||
\(170\) | −7.12311 | −0.546317 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | 8.56155 | 0.650923 | 0.325461 | − | 0.945555i | \(-0.394480\pi\) | ||||
0.325461 | + | 0.945555i | \(0.394480\pi\) | |||||||
\(174\) | 22.7386 | 1.72381 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2462 | 0.770152 | ||||||||
\(178\) | −11.1231 | −0.833712 | ||||||||
\(179\) | 20.0000 | 1.49487 | 0.747435 | − | 0.664335i | \(-0.231285\pi\) | ||||
0.747435 | + | 0.664335i | \(0.231285\pi\) | |||||||
\(180\) | 1.56155 | 0.116391 | ||||||||
\(181\) | 23.6155 | 1.75533 | 0.877664 | − | 0.479276i | \(-0.159101\pi\) | ||||
0.877664 | + | 0.479276i | \(0.159101\pi\) | |||||||
\(182\) | 7.12311 | 0.528000 | ||||||||
\(183\) | −24.0000 | −1.77413 | ||||||||
\(184\) | −12.4924 | −0.920954 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.61553 | 0.117824 | ||||||||
\(189\) | −1.43845 | −0.104632 | ||||||||
\(190\) | 1.75379 | 0.127233 | ||||||||
\(191\) | −9.43845 | −0.682942 | −0.341471 | − | 0.939892i | \(-0.610925\pi\) | ||||
−0.341471 | + | 0.939892i | \(0.610925\pi\) | |||||||
\(192\) | −14.2462 | −1.02813 | ||||||||
\(193\) | 5.36932 | 0.386492 | 0.193246 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193246 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(194\) | 23.1231 | 1.66014 | ||||||||
\(195\) | 11.6847 | 0.836756 | ||||||||
\(196\) | 0.438447 | 0.0313177 | ||||||||
\(197\) | 7.12311 | 0.507500 | 0.253750 | − | 0.967270i | \(-0.418336\pi\) | ||||
0.253750 | + | 0.967270i | \(0.418336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2462 | −1.29344 | −0.646720 | − | 0.762728i | \(-0.723860\pi\) | ||||
−0.646720 | + | 0.762728i | \(0.723860\pi\) | |||||||
\(200\) | 2.43845 | 0.172424 | ||||||||
\(201\) | 16.0000 | 1.12855 | ||||||||
\(202\) | 0.384472 | 0.0270513 | ||||||||
\(203\) | 5.68466 | 0.398985 | ||||||||
\(204\) | −5.12311 | −0.358689 | ||||||||
\(205\) | 3.12311 | 0.218127 | ||||||||
\(206\) | −2.24621 | −0.156501 | ||||||||
\(207\) | −18.2462 | −1.26820 | ||||||||
\(208\) | 21.3693 | 1.48170 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.00000 | 0.276026 | ||||||||
\(211\) | 23.0540 | 1.58710 | 0.793551 | − | 0.608504i | \(-0.208230\pi\) | ||||
0.793551 | + | 0.608504i | \(0.208230\pi\) | |||||||
\(212\) | 1.36932 | 0.0940451 | ||||||||
\(213\) | −20.4924 | −1.40412 | ||||||||
\(214\) | −17.7538 | −1.21362 | ||||||||
\(215\) | −9.12311 | −0.622191 | ||||||||
\(216\) | −3.50758 | −0.238660 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27.6155 | 1.87036 | ||||||||
\(219\) | 10.8769 | 0.734992 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.8078 | −1.39968 | ||||||||
\(222\) | 24.0000 | 1.61077 | ||||||||
\(223\) | −6.56155 | −0.439394 | −0.219697 | − | 0.975568i | \(-0.570507\pi\) | ||||
−0.219697 | + | 0.975568i | \(0.570507\pi\) | |||||||
\(224\) | 2.43845 | 0.162926 | ||||||||
\(225\) | 3.56155 | 0.237437 | ||||||||
\(226\) | 21.8617 | 1.45422 | ||||||||
\(227\) | −23.6847 | −1.57201 | −0.786003 | − | 0.618223i | \(-0.787853\pi\) | ||||
−0.786003 | + | 0.618223i | \(0.787853\pi\) | |||||||
\(228\) | 1.26137 | 0.0835360 | ||||||||
\(229\) | 19.1231 | 1.26369 | 0.631845 | − | 0.775095i | \(-0.282298\pi\) | ||||
0.631845 | + | 0.775095i | \(0.282298\pi\) | |||||||
\(230\) | 8.00000 | 0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.8617 | 0.910068 | ||||||||
\(233\) | 3.12311 | 0.204601 | 0.102301 | − | 0.994754i | \(-0.467380\pi\) | ||||
0.102301 | + | 0.994754i | \(0.467380\pi\) | |||||||
\(234\) | 25.3693 | 1.65844 | ||||||||
\(235\) | 3.68466 | 0.240361 | ||||||||
\(236\) | −1.75379 | −0.114162 | ||||||||
\(237\) | −16.8078 | −1.09178 | ||||||||
\(238\) | −7.12311 | −0.461722 | ||||||||
\(239\) | 0.807764 | 0.0522499 | 0.0261250 | − | 0.999659i | \(-0.491683\pi\) | ||||
0.0261250 | + | 0.999659i | \(0.491683\pi\) | |||||||
\(240\) | 12.0000 | 0.774597 | ||||||||
\(241\) | −12.2462 | −0.788848 | −0.394424 | − | 0.918929i | \(-0.629056\pi\) | ||||
−0.394424 | + | 0.918929i | \(0.629056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462 | 1.42710 | ||||||||
\(244\) | 4.10795 | 0.262985 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 12.4924 | 0.796488 | ||||||||
\(247\) | 5.12311 | 0.325975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.2462 | 0.649327 | ||||||||
\(250\) | −1.56155 | −0.0987613 | ||||||||
\(251\) | −17.1231 | −1.08080 | −0.540400 | − | 0.841408i | \(-0.681727\pi\) | ||||
−0.540400 | + | 0.841408i | \(0.681727\pi\) | |||||||
\(252\) | 1.56155 | 0.0983686 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.0000 | 1.00393 | ||||||||
\(255\) | −11.6847 | −0.731722 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | 22.4924 | 1.40304 | 0.701519 | − | 0.712650i | \(-0.252505\pi\) | ||||
0.701519 | + | 0.712650i | \(0.252505\pi\) | |||||||
\(258\) | −36.4924 | −2.27192 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 20.2462 | 1.25321 | ||||||||
\(262\) | −14.2462 | −0.880134 | ||||||||
\(263\) | 21.1231 | 1.30251 | 0.651253 | − | 0.758860i | \(-0.274244\pi\) | ||||
0.651253 | + | 0.758860i | \(0.274244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.12311 | 0.191851 | ||||||||
\(266\) | 1.75379 | 0.107532 | ||||||||
\(267\) | −18.2462 | −1.11665 | ||||||||
\(268\) | −2.73863 | −0.167289 | ||||||||
\(269\) | 28.7386 | 1.75223 | 0.876113 | − | 0.482106i | \(-0.160128\pi\) | ||||
0.876113 | + | 0.482106i | \(0.160128\pi\) | |||||||
\(270\) | 2.24621 | 0.136700 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | −21.3693 | −1.29571 | ||||||||
\(273\) | 11.6847 | 0.707188 | ||||||||
\(274\) | 13.8617 | 0.837418 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.75379 | 0.346337 | ||||||||
\(277\) | −16.2462 | −0.976140 | −0.488070 | − | 0.872804i | \(-0.662299\pi\) | ||||
−0.488070 | + | 0.872804i | \(0.662299\pi\) | |||||||
\(278\) | −10.7386 | −0.644060 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.43845 | 0.145725 | ||||||||
\(281\) | −16.5616 | −0.987979 | −0.493990 | − | 0.869468i | \(-0.664462\pi\) | ||||
−0.493990 | + | 0.869468i | \(0.664462\pi\) | |||||||
\(282\) | 14.7386 | 0.877673 | ||||||||
\(283\) | 23.6847 | 1.40791 | 0.703953 | − | 0.710246i | \(-0.251416\pi\) | ||||
0.703953 | + | 0.710246i | \(0.251416\pi\) | |||||||
\(284\) | 3.50758 | 0.208136 | ||||||||
\(285\) | 2.87689 | 0.170413 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.12311 | 0.184351 | ||||||||
\(288\) | 8.68466 | 0.511748 | ||||||||
\(289\) | 3.80776 | 0.223986 | ||||||||
\(290\) | −8.87689 | −0.521269 | ||||||||
\(291\) | 37.9309 | 2.22355 | ||||||||
\(292\) | −1.86174 | −0.108950 | ||||||||
\(293\) | −9.68466 | −0.565784 | −0.282892 | − | 0.959152i | \(-0.591294\pi\) | ||||
−0.282892 | + | 0.959152i | \(0.591294\pi\) | |||||||
\(294\) | 4.00000 | 0.233285 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 14.6307 | 0.850391 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.63068 | −0.384105 | ||||||||
\(299\) | 23.3693 | 1.35148 | ||||||||
\(300\) | −1.12311 | −0.0648425 | ||||||||
\(301\) | −9.12311 | −0.525847 | ||||||||
\(302\) | 34.2462 | 1.97065 | ||||||||
\(303\) | 0.630683 | 0.0362318 | ||||||||
\(304\) | 5.26137 | 0.301760 | ||||||||
\(305\) | 9.36932 | 0.536486 | ||||||||
\(306\) | −25.3693 | −1.45027 | ||||||||
\(307\) | 31.6847 | 1.80834 | 0.904169 | − | 0.427174i | \(-0.140491\pi\) | ||||
0.904169 | + | 0.427174i | \(0.140491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.68466 | −0.209613 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.61553 | −0.545247 | −0.272623 | − | 0.962121i | \(-0.587891\pi\) | ||||
−0.272623 | + | 0.962121i | \(0.587891\pi\) | |||||||
\(312\) | 28.4924 | 1.61307 | ||||||||
\(313\) | 31.3002 | 1.76919 | 0.884596 | − | 0.466359i | \(-0.154434\pi\) | ||||
0.884596 | + | 0.466359i | \(0.154434\pi\) | |||||||
\(314\) | −5.86174 | −0.330797 | ||||||||
\(315\) | 3.56155 | 0.200671 | ||||||||
\(316\) | 2.87689 | 0.161838 | ||||||||
\(317\) | −22.4924 | −1.26330 | −0.631650 | − | 0.775254i | \(-0.717622\pi\) | ||||
−0.631650 | + | 0.775254i | \(0.717622\pi\) | |||||||
\(318\) | 12.4924 | 0.700540 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 5.56155 | 0.310900 | ||||||||
\(321\) | −29.1231 | −1.62549 | ||||||||
\(322\) | 8.00000 | 0.445823 | ||||||||
\(323\) | −5.12311 | −0.285057 | ||||||||
\(324\) | −3.06913 | −0.170507 | ||||||||
\(325\) | −4.56155 | −0.253029 | ||||||||
\(326\) | −1.75379 | −0.0971334 | ||||||||
\(327\) | 45.3002 | 2.50511 | ||||||||
\(328\) | 7.61553 | 0.420497 | ||||||||
\(329\) | 3.68466 | 0.203142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | −1.75379 | −0.0962517 | ||||||||
\(333\) | 21.3693 | 1.17103 | ||||||||
\(334\) | 34.2462 | 1.87387 | ||||||||
\(335\) | −6.24621 | −0.341267 | ||||||||
\(336\) | 12.0000 | 0.654654 | ||||||||
\(337\) | 34.4924 | 1.87892 | 0.939461 | − | 0.342656i | \(-0.111326\pi\) | ||||
0.939461 | + | 0.342656i | \(0.111326\pi\) | |||||||
\(338\) | −12.1922 | −0.663170 | ||||||||
\(339\) | 35.8617 | 1.94774 | ||||||||
\(340\) | 2.00000 | 0.108465 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.24621 | 0.337756 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −22.2462 | −1.19944 | ||||||||
\(345\) | 13.1231 | 0.706524 | ||||||||
\(346\) | −13.3693 | −0.718739 | ||||||||
\(347\) | 1.12311 | 0.0602915 | 0.0301457 | − | 0.999546i | \(-0.490403\pi\) | ||||
0.0301457 | + | 0.999546i | \(0.490403\pi\) | |||||||
\(348\) | −6.38447 | −0.342244 | ||||||||
\(349\) | 22.4924 | 1.20399 | 0.601996 | − | 0.798499i | \(-0.294372\pi\) | ||||
0.601996 | + | 0.798499i | \(0.294372\pi\) | |||||||
\(350\) | −1.56155 | −0.0834685 | ||||||||
\(351\) | 6.56155 | 0.350230 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.8078 | −0.788138 | −0.394069 | − | 0.919081i | \(-0.628933\pi\) | ||||
−0.394069 | + | 0.919081i | \(0.628933\pi\) | |||||||
\(354\) | −16.0000 | −0.850390 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 3.12311 | 0.165524 | ||||||||
\(357\) | −11.6847 | −0.618418 | ||||||||
\(358\) | −31.2311 | −1.65061 | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 8.68466 | 0.457722 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | −36.8769 | −1.93821 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | −4.24621 | −0.222257 | ||||||||
\(366\) | 37.4773 | 1.95897 | ||||||||
\(367\) | 3.68466 | 0.192338 | 0.0961688 | − | 0.995365i | \(-0.469341\pi\) | ||||
0.0961688 | + | 0.995365i | \(0.469341\pi\) | |||||||
\(368\) | 24.0000 | 1.25109 | ||||||||
\(369\) | 11.1231 | 0.579046 | ||||||||
\(370\) | −9.36932 | −0.487088 | ||||||||
\(371\) | 3.12311 | 0.162144 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.3693 | −1.52069 | −0.760343 | − | 0.649522i | \(-0.774969\pi\) | ||||
−0.760343 | + | 0.649522i | \(0.774969\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.56155 | −0.132278 | ||||||||
\(376\) | 8.98485 | 0.463358 | ||||||||
\(377\) | −25.9309 | −1.33551 | ||||||||
\(378\) | 2.24621 | 0.115533 | ||||||||
\(379\) | 16.4924 | 0.847159 | 0.423579 | − | 0.905859i | \(-0.360773\pi\) | ||||
0.423579 | + | 0.905859i | \(0.360773\pi\) | |||||||
\(380\) | −0.492423 | −0.0252607 | ||||||||
\(381\) | 26.2462 | 1.34463 | ||||||||
\(382\) | 14.7386 | 0.754094 | ||||||||
\(383\) | −10.2462 | −0.523557 | −0.261778 | − | 0.965128i | \(-0.584309\pi\) | ||||
−0.261778 | + | 0.965128i | \(0.584309\pi\) | |||||||
\(384\) | 34.7386 | 1.77275 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.38447 | −0.426758 | ||||||||
\(387\) | −32.4924 | −1.65168 | ||||||||
\(388\) | −6.49242 | −0.329603 | ||||||||
\(389\) | 3.93087 | 0.199303 | 0.0996515 | − | 0.995022i | \(-0.468227\pi\) | ||||
0.0996515 | + | 0.995022i | \(0.468227\pi\) | |||||||
\(390\) | −18.2462 | −0.923933 | ||||||||
\(391\) | −23.3693 | −1.18184 | ||||||||
\(392\) | 2.43845 | 0.123160 | ||||||||
\(393\) | −23.3693 | −1.17883 | ||||||||
\(394\) | −11.1231 | −0.560374 | ||||||||
\(395\) | 6.56155 | 0.330148 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.4384 | 1.17634 | 0.588171 | − | 0.808737i | \(-0.299848\pi\) | ||||
0.588171 | + | 0.808737i | \(0.299848\pi\) | |||||||
\(398\) | 28.4924 | 1.42820 | ||||||||
\(399\) | 2.87689 | 0.144025 | ||||||||
\(400\) | −4.68466 | −0.234233 | ||||||||
\(401\) | 27.4384 | 1.37021 | 0.685105 | − | 0.728444i | \(-0.259756\pi\) | ||||
0.685105 | + | 0.728444i | \(0.259756\pi\) | |||||||
\(402\) | −24.9848 | −1.24613 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.107951 | −0.00537074 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | −8.87689 | −0.440553 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −28.4924 | −1.41059 | ||||||||
\(409\) | 26.4924 | 1.30997 | 0.654983 | − | 0.755644i | \(-0.272676\pi\) | ||||
0.654983 | + | 0.755644i | \(0.272676\pi\) | |||||||
\(410\) | −4.87689 | −0.240853 | ||||||||
\(411\) | 22.7386 | 1.12161 | ||||||||
\(412\) | 0.630683 | 0.0310715 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 28.4924 | 1.40033 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | −11.1231 | −0.545355 | ||||||||
\(417\) | −17.6155 | −0.862636 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.75379 | 0.476504 | 0.238252 | − | 0.971203i | \(-0.423426\pi\) | ||||
0.238252 | + | 0.971203i | \(0.423426\pi\) | |||||||
\(420\) | −1.12311 | −0.0548019 | ||||||||
\(421\) | 9.68466 | 0.472001 | 0.236001 | − | 0.971753i | \(-0.424163\pi\) | ||||
0.236001 | + | 0.971753i | \(0.424163\pi\) | |||||||
\(422\) | −36.0000 | −1.75245 | ||||||||
\(423\) | 13.1231 | 0.638067 | ||||||||
\(424\) | 7.61553 | 0.369843 | ||||||||
\(425\) | 4.56155 | 0.221268 | ||||||||
\(426\) | 32.0000 | 1.55041 | ||||||||
\(427\) | 9.36932 | 0.453413 | ||||||||
\(428\) | 4.98485 | 0.240952 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.2462 | 0.687013 | ||||||||
\(431\) | −0.807764 | −0.0389086 | −0.0194543 | − | 0.999811i | \(-0.506193\pi\) | ||||
−0.0194543 | + | 0.999811i | \(0.506193\pi\) | |||||||
\(432\) | 6.73863 | 0.324213 | ||||||||
\(433\) | −8.24621 | −0.396288 | −0.198144 | − | 0.980173i | \(-0.563491\pi\) | ||||
−0.198144 | + | 0.980173i | \(0.563491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.5616 | −0.698173 | ||||||||
\(436\) | −7.75379 | −0.371339 | ||||||||
\(437\) | 5.75379 | 0.275241 | ||||||||
\(438\) | −16.9848 | −0.811567 | ||||||||
\(439\) | 15.3693 | 0.733537 | 0.366769 | − | 0.930312i | \(-0.380464\pi\) | ||||
0.366769 | + | 0.930312i | \(0.380464\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.56155 | 0.169598 | ||||||||
\(442\) | 32.4924 | 1.54551 | ||||||||
\(443\) | −27.3693 | −1.30036 | −0.650178 | − | 0.759782i | \(-0.725306\pi\) | ||||
−0.650178 | + | 0.759782i | \(0.725306\pi\) | |||||||
\(444\) | −6.73863 | −0.319801 | ||||||||
\(445\) | 7.12311 | 0.337668 | ||||||||
\(446\) | 10.2462 | 0.485172 | ||||||||
\(447\) | −10.8769 | −0.514459 | ||||||||
\(448\) | 5.56155 | 0.262759 | ||||||||
\(449\) | 18.8078 | 0.887593 | 0.443797 | − | 0.896128i | \(-0.353631\pi\) | ||||
0.443797 | + | 0.896128i | \(0.353631\pi\) | |||||||
\(450\) | −5.56155 | −0.262174 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.13826 | −0.288719 | ||||||||
\(453\) | 56.1771 | 2.63943 | ||||||||
\(454\) | 36.9848 | 1.73578 | ||||||||
\(455\) | −4.56155 | −0.213849 | ||||||||
\(456\) | 7.01515 | 0.328515 | ||||||||
\(457\) | 8.87689 | 0.415244 | 0.207622 | − | 0.978209i | \(-0.433428\pi\) | ||||
0.207622 | + | 0.978209i | \(0.433428\pi\) | |||||||
\(458\) | −29.8617 | −1.39535 | ||||||||
\(459\) | −6.56155 | −0.306267 | ||||||||
\(460\) | −2.24621 | −0.104730 | ||||||||
\(461\) | 4.87689 | 0.227140 | 0.113570 | − | 0.993530i | \(-0.463771\pi\) | ||||
0.113570 | + | 0.993530i | \(0.463771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4924 | −0.952364 | −0.476182 | − | 0.879347i | \(-0.657980\pi\) | ||||
−0.476182 | + | 0.879347i | \(0.657980\pi\) | |||||||
\(464\) | −26.6307 | −1.23630 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.87689 | −0.225918 | ||||||||
\(467\) | 26.5616 | 1.22912 | 0.614561 | − | 0.788869i | \(-0.289333\pi\) | ||||
0.614561 | + | 0.788869i | \(0.289333\pi\) | |||||||
\(468\) | −7.12311 | −0.329266 | ||||||||
\(469\) | −6.24621 | −0.288423 | ||||||||
\(470\) | −5.75379 | −0.265402 | ||||||||
\(471\) | −9.61553 | −0.443060 | ||||||||
\(472\) | −9.75379 | −0.448955 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 26.2462 | 1.20553 | ||||||||
\(475\) | −1.12311 | −0.0515316 | ||||||||
\(476\) | 2.00000 | 0.0916698 | ||||||||
\(477\) | 11.1231 | 0.509292 | ||||||||
\(478\) | −1.26137 | −0.0576935 | ||||||||
\(479\) | −13.1231 | −0.599610 | −0.299805 | − | 0.954001i | \(-0.596922\pi\) | ||||
−0.299805 | + | 0.954001i | \(0.596922\pi\) | |||||||
\(480\) | −6.24621 | −0.285099 | ||||||||
\(481\) | −27.3693 | −1.24793 | ||||||||
\(482\) | 19.1231 | 0.871034 | ||||||||
\(483\) | 13.1231 | 0.597122 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.8078 | −0.672386 | ||||||||
\(486\) | −34.7386 | −1.57578 | ||||||||
\(487\) | 5.12311 | 0.232150 | 0.116075 | − | 0.993240i | \(-0.462969\pi\) | ||||
0.116075 | + | 0.993240i | \(0.462969\pi\) | |||||||
\(488\) | 22.8466 | 1.03422 | ||||||||
\(489\) | −2.87689 | −0.130098 | ||||||||
\(490\) | −1.56155 | −0.0705438 | ||||||||
\(491\) | −4.17708 | −0.188509 | −0.0942545 | − | 0.995548i | \(-0.530047\pi\) | ||||
−0.0942545 | + | 0.995548i | \(0.530047\pi\) | |||||||
\(492\) | −3.50758 | −0.158134 | ||||||||
\(493\) | 25.9309 | 1.16787 | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | −16.0000 | −0.716977 | ||||||||
\(499\) | −4.17708 | −0.186992 | −0.0934959 | − | 0.995620i | \(-0.529804\pi\) | ||||
−0.0934959 | + | 0.995620i | \(0.529804\pi\) | |||||||
\(500\) | 0.438447 | 0.0196080 | ||||||||
\(501\) | 56.1771 | 2.50981 | ||||||||
\(502\) | 26.7386 | 1.19340 | ||||||||
\(503\) | −10.0691 | −0.448960 | −0.224480 | − | 0.974479i | \(-0.572068\pi\) | ||||
−0.224480 | + | 0.974479i | \(0.572068\pi\) | |||||||
\(504\) | 8.68466 | 0.386845 | ||||||||
\(505\) | −0.246211 | −0.0109563 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.0000 | −0.888231 | ||||||||
\(508\) | −4.49242 | −0.199319 | ||||||||
\(509\) | −28.2462 | −1.25199 | −0.625996 | − | 0.779827i | \(-0.715307\pi\) | ||||
−0.625996 | + | 0.779827i | \(0.715307\pi\) | |||||||
\(510\) | 18.2462 | 0.807956 | ||||||||
\(511\) | −4.24621 | −0.187841 | ||||||||
\(512\) | 11.4233 | 0.504843 | ||||||||
\(513\) | 1.61553 | 0.0713273 | ||||||||
\(514\) | −35.1231 | −1.54921 | ||||||||
\(515\) | 1.43845 | 0.0633856 | ||||||||
\(516\) | 10.2462 | 0.451064 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −9.36932 | −0.411664 | ||||||||
\(519\) | −21.9309 | −0.962658 | ||||||||
\(520\) | −11.1231 | −0.487780 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | −31.6155 | −1.38377 | ||||||||
\(523\) | −7.50758 | −0.328283 | −0.164142 | − | 0.986437i | \(-0.552485\pi\) | ||||
−0.164142 | + | 0.986437i | \(0.552485\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | −2.56155 | −0.111795 | ||||||||
\(526\) | −32.9848 | −1.43821 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | −4.87689 | −0.211839 | ||||||||
\(531\) | −14.2462 | −0.618233 | ||||||||
\(532\) | −0.492423 | −0.0213492 | ||||||||
\(533\) | −14.2462 | −0.617072 | ||||||||
\(534\) | 28.4924 | 1.23299 | ||||||||
\(535\) | 11.3693 | 0.491538 | ||||||||
\(536\) | −15.2311 | −0.657881 | ||||||||
\(537\) | −51.2311 | −2.21078 | ||||||||
\(538\) | −44.8769 | −1.93478 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.630683 | −0.0271403 | ||||||||
\(541\) | 17.1922 | 0.739152 | 0.369576 | − | 0.929201i | \(-0.379503\pi\) | ||||
0.369576 | + | 0.929201i | \(0.379503\pi\) | |||||||
\(542\) | −24.9848 | −1.07319 | ||||||||
\(543\) | −60.4924 | −2.59598 | ||||||||
\(544\) | 11.1231 | 0.476899 | ||||||||
\(545\) | −17.6847 | −0.757528 | ||||||||
\(546\) | −18.2462 | −0.780866 | ||||||||
\(547\) | −14.2462 | −0.609124 | −0.304562 | − | 0.952493i | \(-0.598510\pi\) | ||||
−0.304562 | + | 0.952493i | \(0.598510\pi\) | |||||||
\(548\) | −3.89205 | −0.166260 | ||||||||
\(549\) | 33.3693 | 1.42417 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.38447 | −0.271988 | ||||||||
\(552\) | 32.0000 | 1.36201 | ||||||||
\(553\) | 6.56155 | 0.279026 | ||||||||
\(554\) | 25.3693 | 1.07784 | ||||||||
\(555\) | −15.3693 | −0.652391 | ||||||||
\(556\) | 3.01515 | 0.127871 | ||||||||
\(557\) | 4.87689 | 0.206641 | 0.103320 | − | 0.994648i | \(-0.467053\pi\) | ||||
0.103320 | + | 0.994648i | \(0.467053\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.6155 | 1.76015 | ||||||||
\(560\) | −4.68466 | −0.197963 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.8617 | 1.09091 | ||||||||
\(563\) | 28.0000 | 1.18006 | 0.590030 | − | 0.807382i | \(-0.299116\pi\) | ||||
0.590030 | + | 0.807382i | \(0.299116\pi\) | |||||||
\(564\) | −4.13826 | −0.174252 | ||||||||
\(565\) | −14.0000 | −0.588984 | ||||||||
\(566\) | −36.9848 | −1.55459 | ||||||||
\(567\) | −7.00000 | −0.293972 | ||||||||
\(568\) | 19.5076 | 0.818520 | ||||||||
\(569\) | −34.9848 | −1.46664 | −0.733320 | − | 0.679883i | \(-0.762031\pi\) | ||||
−0.733320 | + | 0.679883i | \(0.762031\pi\) | |||||||
\(570\) | −4.49242 | −0.188167 | ||||||||
\(571\) | −7.50758 | −0.314182 | −0.157091 | − | 0.987584i | \(-0.550212\pi\) | ||||
−0.157091 | + | 0.987584i | \(0.550212\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.1771 | 1.01001 | ||||||||
\(574\) | −4.87689 | −0.203558 | ||||||||
\(575\) | −5.12311 | −0.213648 | ||||||||
\(576\) | 19.8078 | 0.825324 | ||||||||
\(577\) | 13.0540 | 0.543444 | 0.271722 | − | 0.962376i | \(-0.412407\pi\) | ||||
0.271722 | + | 0.962376i | \(0.412407\pi\) | |||||||
\(578\) | −5.94602 | −0.247322 | ||||||||
\(579\) | −13.7538 | −0.571588 | ||||||||
\(580\) | 2.49242 | 0.103492 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | −59.2311 | −2.45521 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.3542 | −0.428458 | ||||||||
\(585\) | −16.2462 | −0.671698 | ||||||||
\(586\) | 15.1231 | 0.624730 | ||||||||
\(587\) | −9.75379 | −0.402582 | −0.201291 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(588\) | −1.12311 | −0.0463161 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 6.24621 | 0.257152 | ||||||||
\(591\) | −18.2462 | −0.750549 | ||||||||
\(592\) | −28.1080 | −1.15523 | ||||||||
\(593\) | 23.4384 | 0.962502 | 0.481251 | − | 0.876583i | \(-0.340183\pi\) | ||||
0.481251 | + | 0.876583i | \(0.340183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.56155 | 0.187005 | ||||||||
\(596\) | 1.86174 | 0.0762598 | ||||||||
\(597\) | 46.7386 | 1.91288 | ||||||||
\(598\) | −36.4924 | −1.49229 | ||||||||
\(599\) | 8.80776 | 0.359875 | 0.179938 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179938 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(600\) | −6.24621 | −0.255001 | ||||||||
\(601\) | 26.4924 | 1.08065 | 0.540324 | − | 0.841457i | \(-0.318302\pi\) | ||||
0.540324 | + | 0.841457i | \(0.318302\pi\) | |||||||
\(602\) | 14.2462 | 0.580632 | ||||||||
\(603\) | −22.2462 | −0.905936 | ||||||||
\(604\) | −9.61553 | −0.391250 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.984845 | −0.0400066 | ||||||||
\(607\) | 4.94602 | 0.200753 | 0.100376 | − | 0.994950i | \(-0.467995\pi\) | ||||
0.100376 | + | 0.994950i | \(0.467995\pi\) | |||||||
\(608\) | −2.73863 | −0.111066 | ||||||||
\(609\) | −14.5616 | −0.590064 | ||||||||
\(610\) | −14.6307 | −0.592379 | ||||||||
\(611\) | −16.8078 | −0.679969 | ||||||||
\(612\) | 7.12311 | 0.287934 | ||||||||
\(613\) | 8.73863 | 0.352950 | 0.176475 | − | 0.984305i | \(-0.443531\pi\) | ||||
0.176475 | + | 0.984305i | \(0.443531\pi\) | |||||||
\(614\) | −49.4773 | −1.99674 | ||||||||
\(615\) | −8.00000 | −0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.7538 | 0.634224 | 0.317112 | − | 0.948388i | \(-0.397287\pi\) | ||||
0.317112 | + | 0.948388i | \(0.397287\pi\) | |||||||
\(618\) | 5.75379 | 0.231451 | ||||||||
\(619\) | −42.1080 | −1.69246 | −0.846231 | − | 0.532817i | \(-0.821134\pi\) | ||||
−0.846231 | + | 0.532817i | \(0.821134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.36932 | 0.295720 | ||||||||
\(622\) | 15.0152 | 0.602053 | ||||||||
\(623\) | 7.12311 | 0.285381 | ||||||||
\(624\) | −54.7386 | −2.19130 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −48.8769 | −1.95351 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.64584 | 0.0656761 | ||||||||
\(629\) | 27.3693 | 1.09129 | ||||||||
\(630\) | −5.56155 | −0.221578 | ||||||||
\(631\) | 8.80776 | 0.350632 | 0.175316 | − | 0.984512i | \(-0.443905\pi\) | ||||
0.175316 | + | 0.984512i | \(0.443905\pi\) | |||||||
\(632\) | 16.0000 | 0.636446 | ||||||||
\(633\) | −59.0540 | −2.34718 | ||||||||
\(634\) | 35.1231 | 1.39492 | ||||||||
\(635\) | −10.2462 | −0.406608 | ||||||||
\(636\) | −3.50758 | −0.139084 | ||||||||
\(637\) | −4.56155 | −0.180735 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.4924 | 1.12714 | ||||||||
\(640\) | −13.5616 | −0.536067 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 45.4773 | 1.79484 | ||||||||
\(643\) | −2.56155 | −0.101018 | −0.0505089 | − | 0.998724i | \(-0.516084\pi\) | ||||
−0.0505089 | + | 0.998724i | \(0.516084\pi\) | |||||||
\(644\) | −2.24621 | −0.0885131 | ||||||||
\(645\) | 23.3693 | 0.920166 | ||||||||
\(646\) | 8.00000 | 0.314756 | ||||||||
\(647\) | 3.50758 | 0.137897 | 0.0689486 | − | 0.997620i | \(-0.478036\pi\) | ||||
0.0689486 | + | 0.997620i | \(0.478036\pi\) | |||||||
\(648\) | −17.0691 | −0.670539 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 7.12311 | 0.279391 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.492423 | 0.0192848 | ||||||||
\(653\) | 49.2311 | 1.92656 | 0.963280 | − | 0.268499i | \(-0.0865275\pi\) | ||||
0.963280 | + | 0.268499i | \(0.0865275\pi\) | |||||||
\(654\) | −70.7386 | −2.76610 | ||||||||
\(655\) | 9.12311 | 0.356469 | ||||||||
\(656\) | −14.6307 | −0.571232 | ||||||||
\(657\) | −15.1231 | −0.590009 | ||||||||
\(658\) | −5.75379 | −0.224306 | ||||||||
\(659\) | 36.1771 | 1.40926 | 0.704629 | − | 0.709575i | \(-0.251113\pi\) | ||||
0.704629 | + | 0.709575i | \(0.251113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.12311 | 0.121475 | 0.0607374 | − | 0.998154i | \(-0.480655\pi\) | ||||
0.0607374 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(662\) | −18.7386 | −0.728298 | ||||||||
\(663\) | 53.3002 | 2.07001 | ||||||||
\(664\) | −9.75379 | −0.378520 | ||||||||
\(665\) | −1.12311 | −0.0435522 | ||||||||
\(666\) | −33.3693 | −1.29303 | ||||||||
\(667\) | −29.1231 | −1.12765 | ||||||||
\(668\) | −9.61553 | −0.372036 | ||||||||
\(669\) | 16.8078 | 0.649826 | ||||||||
\(670\) | 9.75379 | 0.376822 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −6.24621 | −0.240953 | ||||||||
\(673\) | 25.8617 | 0.996897 | 0.498448 | − | 0.866919i | \(-0.333903\pi\) | ||||
0.498448 | + | 0.866919i | \(0.333903\pi\) | |||||||
\(674\) | −53.8617 | −2.07468 | ||||||||
\(675\) | −1.43845 | −0.0553659 | ||||||||
\(676\) | 3.42329 | 0.131665 | ||||||||
\(677\) | 23.9309 | 0.919738 | 0.459869 | − | 0.887987i | \(-0.347896\pi\) | ||||
0.459869 | + | 0.887987i | \(0.347896\pi\) | |||||||
\(678\) | −56.0000 | −2.15067 | ||||||||
\(679\) | −14.8078 | −0.568270 | ||||||||
\(680\) | 11.1231 | 0.426552 | ||||||||
\(681\) | 60.6695 | 2.32486 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.7386 | 1.63535 | 0.817674 | − | 0.575681i | \(-0.195263\pi\) | ||||
0.817674 | + | 0.575681i | \(0.195263\pi\) | |||||||
\(684\) | −1.75379 | −0.0670578 | ||||||||
\(685\) | −8.87689 | −0.339169 | ||||||||
\(686\) | −1.56155 | −0.0596204 | ||||||||
\(687\) | −48.9848 | −1.86889 | ||||||||
\(688\) | 42.7386 | 1.62940 | ||||||||
\(689\) | −14.2462 | −0.542737 | ||||||||
\(690\) | −20.4924 | −0.780133 | ||||||||
\(691\) | 8.49242 | 0.323067 | 0.161533 | − | 0.986867i | \(-0.448356\pi\) | ||||
0.161533 | + | 0.986867i | \(0.448356\pi\) | |||||||
\(692\) | 3.75379 | 0.142698 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.75379 | −0.0665729 | ||||||||
\(695\) | 6.87689 | 0.260855 | ||||||||
\(696\) | −35.5076 | −1.34591 | ||||||||
\(697\) | 14.2462 | 0.539614 | ||||||||
\(698\) | −35.1231 | −1.32943 | ||||||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | 0.438447 | 0.0165717 | ||||||||
\(701\) | −0.0691303 | −0.00261102 | −0.00130551 | − | 0.999999i | \(-0.500416\pi\) | ||||
−0.00130551 | + | 0.999999i | \(0.500416\pi\) | |||||||
\(702\) | −10.2462 | −0.386718 | ||||||||
\(703\) | −6.73863 | −0.254152 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.43845 | −0.355472 | ||||||||
\(706\) | 23.1231 | 0.870250 | ||||||||
\(707\) | −0.246211 | −0.00925973 | ||||||||
\(708\) | 4.49242 | 0.168836 | ||||||||
\(709\) | −18.1771 | −0.682655 | −0.341327 | − | 0.939945i | \(-0.610876\pi\) | ||||
−0.341327 | + | 0.939945i | \(0.610876\pi\) | |||||||
\(710\) | −12.4924 | −0.468832 | ||||||||
\(711\) | 23.3693 | 0.876418 | ||||||||
\(712\) | 17.3693 | 0.650943 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 18.2462 | 0.682847 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.76894 | 0.327711 | ||||||||
\(717\) | −2.06913 | −0.0772731 | ||||||||
\(718\) | 12.4924 | 0.466213 | ||||||||
\(719\) | 49.6155 | 1.85035 | 0.925173 | − | 0.379544i | \(-0.123919\pi\) | ||||
0.925173 | + | 0.379544i | \(0.123919\pi\) | |||||||
\(720\) | −16.6847 | −0.621801 | ||||||||
\(721\) | 1.43845 | 0.0535706 | ||||||||
\(722\) | 27.6998 | 1.03088 | ||||||||
\(723\) | 31.3693 | 1.16664 | ||||||||
\(724\) | 10.3542 | 0.384809 | ||||||||
\(725\) | 5.68466 | 0.211123 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5076 | 0.723496 | 0.361748 | − | 0.932276i | \(-0.382180\pi\) | ||||
0.361748 | + | 0.932276i | \(0.382180\pi\) | |||||||
\(728\) | −11.1231 | −0.412250 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 6.63068 | 0.245413 | ||||||||
\(731\) | −41.6155 | −1.53921 | ||||||||
\(732\) | −10.5227 | −0.388931 | ||||||||
\(733\) | 5.68466 | 0.209968 | 0.104984 | − | 0.994474i | \(-0.466521\pi\) | ||||
0.104984 | + | 0.994474i | \(0.466521\pi\) | |||||||
\(734\) | −5.75379 | −0.212376 | ||||||||
\(735\) | −2.56155 | −0.0944843 | ||||||||
\(736\) | −12.4924 | −0.460477 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −17.3693 | −0.639373 | ||||||||
\(739\) | −6.06913 | −0.223257 | −0.111628 | − | 0.993750i | \(-0.535607\pi\) | ||||
−0.111628 | + | 0.993750i | \(0.535607\pi\) | |||||||
\(740\) | 2.63068 | 0.0967058 | ||||||||
\(741\) | −13.1231 | −0.482089 | ||||||||
\(742\) | −4.87689 | −0.179036 | ||||||||
\(743\) | −32.9848 | −1.21010 | −0.605048 | − | 0.796189i | \(-0.706846\pi\) | ||||
−0.605048 | + | 0.796189i | \(0.706846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.24621 | 0.155569 | ||||||||
\(746\) | 45.8617 | 1.67912 | ||||||||
\(747\) | −14.2462 | −0.521242 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.3693 | 0.415426 | ||||||||
\(750\) | 4.00000 | 0.146059 | ||||||||
\(751\) | 45.9309 | 1.67604 | 0.838021 | − | 0.545639i | \(-0.183713\pi\) | ||||
0.838021 | + | 0.545639i | \(0.183713\pi\) | |||||||
\(752\) | −17.2614 | −0.629457 | ||||||||
\(753\) | 43.8617 | 1.59841 | ||||||||
\(754\) | 40.4924 | 1.47465 | ||||||||
\(755\) | −21.9309 | −0.798146 | ||||||||
\(756\) | −0.630683 | −0.0229377 | ||||||||
\(757\) | 14.6307 | 0.531761 | 0.265881 | − | 0.964006i | \(-0.414337\pi\) | ||||
0.265881 | + | 0.964006i | \(0.414337\pi\) | |||||||
\(758\) | −25.7538 | −0.935420 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.73863 | −0.0993407 | ||||||||
\(761\) | −31.7538 | −1.15107 | −0.575537 | − | 0.817776i | \(-0.695207\pi\) | ||||
−0.575537 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(762\) | −40.9848 | −1.48472 | ||||||||
\(763\) | −17.6847 | −0.640228 | ||||||||
\(764\) | −4.13826 | −0.149717 | ||||||||
\(765\) | 16.2462 | 0.587383 | ||||||||
\(766\) | 16.0000 | 0.578103 | ||||||||
\(767\) | 18.2462 | 0.658833 | ||||||||
\(768\) | −25.7538 | −0.929310 | ||||||||
\(769\) | 9.50758 | 0.342852 | 0.171426 | − | 0.985197i | \(-0.445163\pi\) | ||||
0.171426 | + | 0.985197i | \(0.445163\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −57.6155 | −2.07497 | ||||||||
\(772\) | 2.35416 | 0.0847281 | ||||||||
\(773\) | 8.06913 | 0.290226 | 0.145113 | − | 0.989415i | \(-0.453645\pi\) | ||||
0.145113 | + | 0.989415i | \(0.453645\pi\) | |||||||
\(774\) | 50.7386 | 1.82376 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −36.1080 | −1.29620 | ||||||||
\(777\) | −15.3693 | −0.551371 | ||||||||
\(778\) | −6.13826 | −0.220067 | ||||||||
\(779\) | −3.50758 | −0.125672 | ||||||||
\(780\) | 5.12311 | 0.183437 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 36.4924 | 1.30497 | ||||||||
\(783\) | −8.17708 | −0.292225 | ||||||||
\(784\) | −4.68466 | −0.167309 | ||||||||
\(785\) | 3.75379 | 0.133978 | ||||||||
\(786\) | 36.4924 | 1.30164 | ||||||||
\(787\) | 3.82292 | 0.136272 | 0.0681362 | − | 0.997676i | \(-0.478295\pi\) | ||||
0.0681362 | + | 0.997676i | \(0.478295\pi\) | |||||||
\(788\) | 3.12311 | 0.111256 | ||||||||
\(789\) | −54.1080 | −1.92629 | ||||||||
\(790\) | −10.2462 | −0.364544 | ||||||||
\(791\) | −14.0000 | −0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.7386 | −1.51769 | ||||||||
\(794\) | −36.6004 | −1.29890 | ||||||||
\(795\) | −8.00000 | −0.283731 | ||||||||
\(796\) | −8.00000 | −0.283552 | ||||||||
\(797\) | −13.0540 | −0.462396 | −0.231198 | − | 0.972907i | \(-0.574264\pi\) | ||||
−0.231198 | + | 0.972907i | \(0.574264\pi\) | |||||||
\(798\) | −4.49242 | −0.159030 | ||||||||
\(799\) | 16.8078 | 0.594616 | ||||||||
\(800\) | 2.43845 | 0.0862121 | ||||||||
\(801\) | 25.3693 | 0.896381 | ||||||||
\(802\) | −42.8466 | −1.51297 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 7.01515 | 0.247405 | ||||||||
\(805\) | −5.12311 | −0.180566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −73.6155 | −2.59139 | ||||||||
\(808\) | −0.600373 | −0.0211211 | ||||||||
\(809\) | 53.5464 | 1.88259 | 0.941296 | − | 0.337584i | \(-0.109610\pi\) | ||||
0.941296 | + | 0.337584i | \(0.109610\pi\) | |||||||
\(810\) | 10.9309 | 0.384072 | ||||||||
\(811\) | 21.6155 | 0.759024 | 0.379512 | − | 0.925187i | \(-0.376092\pi\) | ||||
0.379512 | + | 0.925187i | \(0.376092\pi\) | |||||||
\(812\) | 2.49242 | 0.0874669 | ||||||||
\(813\) | −40.9848 | −1.43740 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.12311 | 0.0393407 | ||||||||
\(816\) | 54.7386 | 1.91624 | ||||||||
\(817\) | 10.2462 | 0.358470 | ||||||||
\(818\) | −41.3693 | −1.44644 | ||||||||
\(819\) | −16.2462 | −0.567689 | ||||||||
\(820\) | 1.36932 | 0.0478186 | ||||||||
\(821\) | −40.4233 | −1.41078 | −0.705391 | − | 0.708818i | \(-0.749229\pi\) | ||||
−0.705391 | + | 0.708818i | \(0.749229\pi\) | |||||||
\(822\) | −35.5076 | −1.23847 | ||||||||
\(823\) | −3.50758 | −0.122266 | −0.0611332 | − | 0.998130i | \(-0.519471\pi\) | ||||
−0.0611332 | + | 0.998130i | \(0.519471\pi\) | |||||||
\(824\) | 3.50758 | 0.122192 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.24621 | 0.217333 | ||||||||
\(827\) | −19.3693 | −0.673537 | −0.336769 | − | 0.941587i | \(-0.609334\pi\) | ||||
−0.336769 | + | 0.941587i | \(0.609334\pi\) | |||||||
\(828\) | −8.00000 | −0.278019 | ||||||||
\(829\) | 43.1231 | 1.49773 | 0.748864 | − | 0.662724i | \(-0.230600\pi\) | ||||
0.748864 | + | 0.662724i | \(0.230600\pi\) | |||||||
\(830\) | 6.24621 | 0.216809 | ||||||||
\(831\) | 41.6155 | 1.44363 | ||||||||
\(832\) | −25.3693 | −0.879523 | ||||||||
\(833\) | 4.56155 | 0.158048 | ||||||||
\(834\) | 27.5076 | 0.952510 | ||||||||
\(835\) | −21.9309 | −0.758949 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.2311 | −0.526148 | ||||||||
\(839\) | −37.1231 | −1.28163 | −0.640816 | − | 0.767695i | \(-0.721404\pi\) | ||||
−0.640816 | + | 0.767695i | \(0.721404\pi\) | |||||||
\(840\) | −6.24621 | −0.215515 | ||||||||
\(841\) | 3.31534 | 0.114322 | ||||||||
\(842\) | −15.1231 | −0.521177 | ||||||||
\(843\) | 42.4233 | 1.46114 | ||||||||
\(844\) | 10.1080 | 0.347930 | ||||||||
\(845\) | 7.80776 | 0.268595 | ||||||||
\(846\) | −20.4924 | −0.704544 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.6307 | −0.502420 | ||||||||
\(849\) | −60.6695 | −2.08217 | ||||||||
\(850\) | −7.12311 | −0.244321 | ||||||||
\(851\) | −30.7386 | −1.05371 | ||||||||
\(852\) | −8.98485 | −0.307816 | ||||||||
\(853\) | 56.7386 | 1.94269 | 0.971347 | − | 0.237666i | \(-0.0763824\pi\) | ||||
0.971347 | + | 0.237666i | \(0.0763824\pi\) | |||||||
\(854\) | −14.6307 | −0.500652 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 27.7235 | 0.947569 | ||||||||
\(857\) | 32.2462 | 1.10151 | 0.550755 | − | 0.834667i | \(-0.314340\pi\) | ||||
0.550755 | + | 0.834667i | \(0.314340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4924 | 0.562714 | 0.281357 | − | 0.959603i | \(-0.409215\pi\) | ||||
0.281357 | + | 0.959603i | \(0.409215\pi\) | |||||||
\(860\) | −4.00000 | −0.136399 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | 1.26137 | 0.0429623 | ||||||||
\(863\) | −42.2462 | −1.43808 | −0.719039 | − | 0.694970i | \(-0.755418\pi\) | ||||
−0.719039 | + | 0.694970i | \(0.755418\pi\) | |||||||
\(864\) | −3.50758 | −0.119330 | ||||||||
\(865\) | 8.56155 | 0.291102 | ||||||||
\(866\) | 12.8769 | 0.437575 | ||||||||
\(867\) | −9.75379 | −0.331256 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 22.7386 | 0.770912 | ||||||||
\(871\) | 28.4924 | 0.965429 | ||||||||
\(872\) | −43.1231 | −1.46033 | ||||||||
\(873\) | −52.7386 | −1.78493 | ||||||||
\(874\) | −8.98485 | −0.303917 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 4.76894 | 0.161128 | ||||||||
\(877\) | 23.7538 | 0.802108 | 0.401054 | − | 0.916054i | \(-0.368644\pi\) | ||||
0.401054 | + | 0.916054i | \(0.368644\pi\) | |||||||
\(878\) | −24.0000 | −0.809961 | ||||||||
\(879\) | 24.8078 | 0.836745 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.8617 | 1.54512 | 0.772561 | − | 0.634941i | \(-0.218976\pi\) | ||||
0.772561 | + | 0.634941i | \(0.218976\pi\) | |||||||
\(882\) | −5.56155 | −0.187267 | ||||||||
\(883\) | 24.4924 | 0.824236 | 0.412118 | − | 0.911131i | \(-0.364789\pi\) | ||||
0.412118 | + | 0.911131i | \(0.364789\pi\) | |||||||
\(884\) | −9.12311 | −0.306843 | ||||||||
\(885\) | 10.2462 | 0.344423 | ||||||||
\(886\) | 42.7386 | 1.43583 | ||||||||
\(887\) | 12.4924 | 0.419454 | 0.209727 | − | 0.977760i | \(-0.432742\pi\) | ||||
0.209727 | + | 0.977760i | \(0.432742\pi\) | |||||||
\(888\) | −37.4773 | −1.25765 | ||||||||
\(889\) | −10.2462 | −0.343647 | ||||||||
\(890\) | −11.1231 | −0.372847 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.87689 | −0.0963255 | ||||||||
\(893\) | −4.13826 | −0.138482 | ||||||||
\(894\) | 16.9848 | 0.568058 | ||||||||
\(895\) | 20.0000 | 0.668526 | ||||||||
\(896\) | −13.5616 | −0.453060 | ||||||||
\(897\) | −59.8617 | −1.99873 | ||||||||
\(898\) | −29.3693 | −0.980067 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.56155 | 0.0520518 | ||||||||
\(901\) | 14.2462 | 0.474610 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.3693 | 0.777682 | ||||||||
\(904\) | −34.1383 | −1.13542 | ||||||||
\(905\) | 23.6155 | 0.785007 | ||||||||
\(906\) | −87.7235 | −2.91442 | ||||||||
\(907\) | 50.1080 | 1.66381 | 0.831904 | − | 0.554920i | \(-0.187251\pi\) | ||||
0.831904 | + | 0.554920i | \(0.187251\pi\) | |||||||
\(908\) | −10.3845 | −0.344621 | ||||||||
\(909\) | −0.876894 | −0.0290848 | ||||||||
\(910\) | 7.12311 | 0.236129 | ||||||||
\(911\) | 4.49242 | 0.148841 | 0.0744203 | − | 0.997227i | \(-0.476289\pi\) | ||||
0.0744203 | + | 0.997227i | \(0.476289\pi\) | |||||||
\(912\) | −13.4773 | −0.446277 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −13.8617 | −0.458506 | ||||||||
\(915\) | −24.0000 | −0.793416 | ||||||||
\(916\) | 8.38447 | 0.277031 | ||||||||
\(917\) | 9.12311 | 0.301271 | ||||||||
\(918\) | 10.2462 | 0.338175 | ||||||||
\(919\) | 13.3002 | 0.438733 | 0.219366 | − | 0.975643i | \(-0.429601\pi\) | ||||
0.219366 | + | 0.975643i | \(0.429601\pi\) | |||||||
\(920\) | −12.4924 | −0.411863 | ||||||||
\(921\) | −81.1619 | −2.67438 | ||||||||
\(922\) | −7.61553 | −0.250804 | ||||||||
\(923\) | −36.4924 | −1.20116 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 32.0000 | 1.05159 | ||||||||
\(927\) | 5.12311 | 0.168265 | ||||||||
\(928\) | 13.8617 | 0.455034 | ||||||||
\(929\) | −52.1080 | −1.70961 | −0.854803 | − | 0.518952i | \(-0.826322\pi\) | ||||
−0.854803 | + | 0.518952i | \(0.826322\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.12311 | −0.0368083 | ||||||||
\(932\) | 1.36932 | 0.0448535 | ||||||||
\(933\) | 24.6307 | 0.806372 | ||||||||
\(934\) | −41.4773 | −1.35718 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −39.6155 | −1.29487 | ||||||||
\(937\) | −22.6695 | −0.740580 | −0.370290 | − | 0.928916i | \(-0.620742\pi\) | ||||
−0.370290 | + | 0.928916i | \(0.620742\pi\) | |||||||
\(938\) | 9.75379 | 0.318472 | ||||||||
\(939\) | −80.1771 | −2.61648 | ||||||||
\(940\) | 1.61553 | 0.0526927 | ||||||||
\(941\) | 13.8617 | 0.451880 | 0.225940 | − | 0.974141i | \(-0.427455\pi\) | ||||
0.225940 | + | 0.974141i | \(0.427455\pi\) | |||||||
\(942\) | 15.0152 | 0.489220 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 18.7386 | 0.609891 | ||||||||
\(945\) | −1.43845 | −0.0467927 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.00000 | 0.129983 | 0.0649913 | − | 0.997886i | \(-0.479298\pi\) | ||||
0.0649913 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(948\) | −7.36932 | −0.239344 | ||||||||
\(949\) | 19.3693 | 0.628755 | ||||||||
\(950\) | 1.75379 | 0.0569004 | ||||||||
\(951\) | 57.6155 | 1.86831 | ||||||||
\(952\) | 11.1231 | 0.360502 | ||||||||
\(953\) | 24.8769 | 0.805842 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(954\) | −17.3693 | −0.562352 | ||||||||
\(955\) | −9.43845 | −0.305421 | ||||||||
\(956\) | 0.354162 | 0.0114544 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.4924 | 0.662080 | ||||||||
\(959\) | −8.87689 | −0.286650 | ||||||||
\(960\) | −14.2462 | −0.459794 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 42.7386 | 1.37795 | ||||||||
\(963\) | 40.4924 | 1.30485 | ||||||||
\(964\) | −5.36932 | −0.172934 | ||||||||
\(965\) | 5.36932 | 0.172844 | ||||||||
\(966\) | −20.4924 | −0.659333 | ||||||||
\(967\) | 26.8769 | 0.864303 | 0.432151 | − | 0.901801i | \(-0.357755\pi\) | ||||
0.432151 | + | 0.901801i | \(0.357755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.1231 | 0.421575 | ||||||||
\(970\) | 23.1231 | 0.742438 | ||||||||
\(971\) | −49.4773 | −1.58780 | −0.793901 | − | 0.608048i | \(-0.791953\pi\) | ||||
−0.793901 | + | 0.608048i | \(0.791953\pi\) | |||||||
\(972\) | 9.75379 | 0.312853 | ||||||||
\(973\) | 6.87689 | 0.220463 | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 11.6847 | 0.374209 | ||||||||
\(976\) | −43.8920 | −1.40495 | ||||||||
\(977\) | −49.2311 | −1.57504 | −0.787521 | − | 0.616288i | \(-0.788636\pi\) | ||||
−0.787521 | + | 0.616288i | \(0.788636\pi\) | |||||||
\(978\) | 4.49242 | 0.143652 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.438447 | 0.0140057 | ||||||||
\(981\) | −62.9848 | −2.01095 | ||||||||
\(982\) | 6.52273 | 0.208149 | ||||||||
\(983\) | −10.4233 | −0.332451 | −0.166226 | − | 0.986088i | \(-0.553158\pi\) | ||||
−0.166226 | + | 0.986088i | \(0.553158\pi\) | |||||||
\(984\) | −19.5076 | −0.621879 | ||||||||
\(985\) | 7.12311 | 0.226961 | ||||||||
\(986\) | −40.4924 | −1.28954 | ||||||||
\(987\) | −9.43845 | −0.300429 | ||||||||
\(988\) | 2.24621 | 0.0714615 | ||||||||
\(989\) | 46.7386 | 1.48620 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4924 | −0.650963 | −0.325482 | − | 0.945548i | \(-0.605526\pi\) | ||||
−0.325482 | + | 0.945548i | \(0.605526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.7386 | −0.975461 | ||||||||
\(994\) | −12.4924 | −0.396236 | ||||||||
\(995\) | −18.2462 | −0.578444 | ||||||||
\(996\) | 4.49242 | 0.142348 | ||||||||
\(997\) | −9.68466 | −0.306716 | −0.153358 | − | 0.988171i | \(-0.549009\pi\) | ||||
−0.153358 | + | 0.988171i | \(0.549009\pi\) | |||||||
\(998\) | 6.52273 | 0.206473 | ||||||||
\(999\) | −8.63068 | −0.273063 |
(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 | 4235.2.a.m.1.1 | 2 | ||
11.10 | odd | 2 | 35.2.a.b.1.2 | ✓ | 2 | ||
33.32 | even | 2 | 315.2.a.e.1.1 | 2 | |||
44.43 | even | 2 | 560.2.a.i.1.2 | 2 | |||
55.32 | even | 4 | 175.2.b.b.99.3 | 4 | |||
55.43 | even | 4 | 175.2.b.b.99.2 | 4 | |||
55.54 | odd | 2 | 175.2.a.f.1.1 | 2 | |||
77.10 | even | 6 | 245.2.e.h.226.1 | 4 | |||
77.32 | odd | 6 | 245.2.e.i.226.1 | 4 | |||
77.54 | even | 6 | 245.2.e.h.116.1 | 4 | |||
77.65 | odd | 6 | 245.2.e.i.116.1 | 4 | |||
77.76 | even | 2 | 245.2.a.d.1.2 | 2 | |||
88.21 | odd | 2 | 2240.2.a.bh.1.2 | 2 | |||
88.43 | even | 2 | 2240.2.a.bd.1.1 | 2 | |||
132.131 | odd | 2 | 5040.2.a.bt.1.2 | 2 | |||
143.142 | odd | 2 | 5915.2.a.l.1.1 | 2 | |||
165.32 | odd | 4 | 1575.2.d.e.1324.2 | 4 | |||
165.98 | odd | 4 | 1575.2.d.e.1324.3 | 4 | |||
165.164 | even | 2 | 1575.2.a.p.1.2 | 2 | |||
220.43 | odd | 4 | 2800.2.g.t.449.4 | 4 | |||
220.87 | odd | 4 | 2800.2.g.t.449.1 | 4 | |||
220.219 | even | 2 | 2800.2.a.bi.1.1 | 2 | |||
231.230 | odd | 2 | 2205.2.a.x.1.1 | 2 | |||
308.307 | odd | 2 | 3920.2.a.bs.1.1 | 2 | |||
385.153 | odd | 4 | 1225.2.b.f.99.2 | 4 | |||
385.307 | odd | 4 | 1225.2.b.f.99.3 | 4 | |||
385.384 | even | 2 | 1225.2.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.a.b.1.2 | ✓ | 2 | 11.10 | odd | 2 | ||
175.2.a.f.1.1 | 2 | 55.54 | odd | 2 | |||
175.2.b.b.99.2 | 4 | 55.43 | even | 4 | |||
175.2.b.b.99.3 | 4 | 55.32 | even | 4 | |||
245.2.a.d.1.2 | 2 | 77.76 | even | 2 | |||
245.2.e.h.116.1 | 4 | 77.54 | even | 6 | |||
245.2.e.h.226.1 | 4 | 77.10 | even | 6 | |||
245.2.e.i.116.1 | 4 | 77.65 | odd | 6 | |||
245.2.e.i.226.1 | 4 | 77.32 | odd | 6 | |||
315.2.a.e.1.1 | 2 | 33.32 | even | 2 | |||
560.2.a.i.1.2 | 2 | 44.43 | even | 2 | |||
1225.2.a.s.1.1 | 2 | 385.384 | even | 2 | |||
1225.2.b.f.99.2 | 4 | 385.153 | odd | 4 | |||
1225.2.b.f.99.3 | 4 | 385.307 | odd | 4 | |||
1575.2.a.p.1.2 | 2 | 165.164 | even | 2 | |||
1575.2.d.e.1324.2 | 4 | 165.32 | odd | 4 | |||
1575.2.d.e.1324.3 | 4 | 165.98 | odd | 4 | |||
2205.2.a.x.1.1 | 2 | 231.230 | odd | 2 | |||
2240.2.a.bd.1.1 | 2 | 88.43 | even | 2 | |||
2240.2.a.bh.1.2 | 2 | 88.21 | odd | 2 | |||
2800.2.a.bi.1.1 | 2 | 220.219 | even | 2 | |||
2800.2.g.t.449.1 | 4 | 220.87 | odd | 4 | |||
2800.2.g.t.449.4 | 4 | 220.43 | odd | 4 | |||
3920.2.a.bs.1.1 | 2 | 308.307 | odd | 2 | |||
4235.2.a.m.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5040.2.a.bt.1.2 | 2 | 132.131 | odd | 2 | |||
5915.2.a.l.1.1 | 2 | 143.142 | odd | 2 |