Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.75153\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.75153 | 1.23052 | 0.615261 | − | 0.788323i | \(-0.289051\pi\) | ||||
0.615261 | + | 0.788323i | \(0.289051\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.32246 | −1.30327 | −0.651635 | − | 0.758532i | \(-0.725917\pi\) | ||||
−0.651635 | + | 0.758532i | \(0.725917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57093 | 0.435697 | 0.217849 | − | 0.975983i | \(-0.430096\pi\) | ||||
0.217849 | + | 0.975983i | \(0.430096\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.75153 | 0.710443 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.819397 | 0.198733 | 0.0993664 | − | 0.995051i | \(-0.468318\pi\) | ||||
0.0993664 | + | 0.995051i | \(0.468318\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.81940 | 0.646814 | 0.323407 | − | 0.946260i | \(-0.395172\pi\) | ||||
0.323407 | + | 0.946260i | \(0.395172\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.57093 | 0.514186 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.819397 | −0.152158 | −0.0760791 | − | 0.997102i | \(-0.524240\pi\) | ||||
−0.0760791 | + | 0.997102i | \(0.524240\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.32246 | −1.49476 | −0.747379 | − | 0.664398i | \(-0.768688\pi\) | ||||
−0.747379 | + | 0.664398i | \(0.768688\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.32246 | −0.752444 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.75153 | −0.465094 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.68367 | 1.42759 | 0.713793 | − | 0.700357i | \(-0.246976\pi\) | ||||
0.713793 | + | 0.700357i | \(0.246976\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.57093 | 0.251550 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3225 | 1.61210 | 0.806049 | − | 0.591849i | \(-0.201602\pi\) | ||||
0.806049 | + | 0.591849i | \(0.201602\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.429071 | 0.0654328 | 0.0327164 | − | 0.999465i | \(-0.489584\pi\) | ||||
0.0327164 | + | 0.999465i | \(0.489584\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.75153 | 0.410174 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.1480 | 1.48024 | 0.740118 | − | 0.672477i | \(-0.234770\pi\) | ||||
0.740118 | + | 0.672477i | \(0.234770\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.819397 | 0.114738 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.39645 | −1.01598 | −0.507991 | − | 0.861363i | \(-0.669612\pi\) | ||||
−0.507991 | + | 0.861363i | \(0.669612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.8934 | −1.60370 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.81940 | 0.373438 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.39033 | 0.831950 | 0.415975 | − | 0.909376i | \(-0.363440\pi\) | ||||
0.415975 | + | 0.909376i | \(0.363440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4352 | 1.72020 | 0.860101 | − | 0.510125i | \(-0.170401\pi\) | ||||
0.860101 | + | 0.510125i | \(0.170401\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.32246 | 0.536135 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.60967 | 0.196653 | 0.0983265 | − | 0.995154i | \(-0.468651\pi\) | ||||
0.0983265 | + | 0.995154i | \(0.468651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.06786 | 0.245410 | 0.122705 | − | 0.992443i | \(-0.460843\pi\) | ||||
0.122705 | + | 0.992443i | \(0.460843\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.4643 | −1.57588 | −0.787940 | − | 0.615752i | \(-0.788852\pi\) | ||||
−0.787940 | + | 0.615752i | \(0.788852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.57093 | 0.296865 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.32246 | 0.492590 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.81940 | 0.767242 | 0.383621 | − | 0.923491i | \(-0.374677\pi\) | ||||
0.383621 | + | 0.923491i | \(0.374677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.32246 | 0.474452 | 0.237226 | − | 0.971455i | \(-0.423762\pi\) | ||||
0.237226 | + | 0.971455i | \(0.423762\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.25460 | 0.244545 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.819397 | −0.0878485 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.93214 | 0.840805 | 0.420402 | − | 0.907338i | \(-0.361889\pi\) | ||||
0.420402 | + | 0.907338i | \(0.361889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.57093 | −0.164678 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.32246 | −0.862999 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.75766 | 0.795919 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.67754 | 0.170328 | 0.0851641 | − | 0.996367i | \(-0.472859\pi\) | ||||
0.0851641 | + | 0.996367i | \(0.472859\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.32246 | −0.434424 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.39033 | 0.834869 | 0.417434 | − | 0.908707i | \(-0.362929\pi\) | ||||
0.417434 | + | 0.908707i | \(0.362929\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0061 | 1.08447 | 0.542233 | − | 0.840228i | \(-0.317579\pi\) | ||||
0.542233 | + | 0.840228i | \(0.317579\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.75153 | −0.268522 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.29334 | 0.415053 | 0.207527 | − | 0.978229i | \(-0.433459\pi\) | ||||
0.207527 | + | 0.978229i | \(0.433459\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.89339 | −0.564484 | −0.282242 | − | 0.959343i | \(-0.591078\pi\) | ||||
−0.282242 | + | 0.959343i | \(0.591078\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.68367 | 0.824217 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.74540 | 0.352338 | 0.176169 | − | 0.984360i | \(-0.443629\pi\) | ||||
0.176169 | + | 0.984360i | \(0.443629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.75153 | −0.256582 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.57093 | 0.145232 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.819397 | −0.0751140 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.68367 | 0.698515 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3225 | 0.930745 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.68367 | −0.597805 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.07399 | −0.450244 | −0.225122 | − | 0.974331i | \(-0.572278\pi\) | ||||
−0.225122 | + | 0.974331i | \(0.572278\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.429071 | 0.0377776 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.3225 | −1.07662 | −0.538309 | − | 0.842747i | \(-0.680937\pi\) | ||||
−0.538309 | + | 0.842747i | \(0.680937\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.81940 | −0.244473 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.75153 | 0.236814 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.67754 | 0.143322 | 0.0716609 | − | 0.997429i | \(-0.477170\pi\) | ||||
0.0716609 | + | 0.997429i | \(0.477170\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7577 | 0.997272 | 0.498636 | − | 0.866812i | \(-0.333834\pi\) | ||||
0.498636 | + | 0.866812i | \(0.333834\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.1480 | 0.854615 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.79028 | −0.567832 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.25460 | −0.187234 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.496936 | −0.0407106 | −0.0203553 | − | 0.999793i | \(-0.506480\pi\) | ||||
−0.0203553 | + | 0.999793i | \(0.506480\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1480 | 0.825831 | 0.412916 | − | 0.910769i | \(-0.364510\pi\) | ||||
0.412916 | + | 0.910769i | \(0.364510\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.819397 | 0.0662443 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.8995 | −1.83933 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.4256 | 1.55033 | 0.775165 | − | 0.631759i | \(-0.217667\pi\) | ||||
0.775165 | + | 0.631759i | \(0.217667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.39645 | −0.586577 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.25460 | −0.176594 | −0.0882968 | − | 0.996094i | \(-0.528142\pi\) | ||||
−0.0882968 | + | 0.996094i | \(0.528142\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.8934 | −0.925899 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.31633 | 0.411390 | 0.205695 | − | 0.978616i | \(-0.434054\pi\) | ||||
0.205695 | + | 0.978616i | \(0.434054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5322 | −0.810168 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.81940 | 0.215605 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.9613 | 1.51763 | 0.758813 | − | 0.651309i | \(-0.225780\pi\) | ||||
0.758813 | + | 0.651309i | \(0.225780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.57093 | −0.194344 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.39033 | 0.480326 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.02912 | −0.301150 | −0.150575 | − | 0.988599i | \(-0.548113\pi\) | ||||
−0.150575 | + | 0.988599i | \(0.548113\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.955126 | 0.0709939 | 0.0354970 | − | 0.999370i | \(-0.488699\pi\) | ||||
0.0354970 | + | 0.999370i | \(0.488699\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.4352 | 0.993159 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.8934 | 1.75668 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.54181 | −0.259003 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.85814 | −0.640953 | −0.320476 | − | 0.947257i | \(-0.603843\pi\) | ||||
−0.320476 | + | 0.947257i | \(0.603843\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.14186 | 0.658045 | 0.329023 | − | 0.944322i | \(-0.393281\pi\) | ||||
0.329023 | + | 0.944322i | \(0.393281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.32246 | 0.309538 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.21585 | −0.442861 | −0.221431 | − | 0.975176i | \(-0.571073\pi\) | ||||
−0.221431 | + | 0.975176i | \(0.571073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.3965 | −1.51675 | −0.758377 | − | 0.651816i | \(-0.774007\pi\) | ||||
−0.758377 | + | 0.651816i | \(0.774007\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.60967 | 0.113538 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.819397 | 0.0575104 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.4026 | 1.98372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.1867 | −0.842974 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.18060 | −0.356647 | −0.178324 | − | 0.983972i | \(-0.557067\pi\) | ||||
−0.178324 | + | 0.983972i | \(0.557067\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.06786 | 0.141688 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.18060 | 0.0805165 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.32246 | 0.564965 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.4643 | −0.909834 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.28721 | 0.0865874 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0291 | 1.07339 | 0.536695 | − | 0.843777i | \(-0.319673\pi\) | ||||
0.536695 | + | 0.843777i | \(0.319673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.57093 | 0.171395 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2607 | 0.880145 | 0.440073 | − | 0.897962i | \(-0.354953\pi\) | ||||
0.440073 | + | 0.897962i | \(0.354953\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.254596 | −0.0168242 | −0.00841210 | − | 0.999965i | \(-0.502678\pi\) | ||||
−0.00841210 | + | 0.999965i | \(0.502678\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.32246 | 0.284397 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.74540 | 0.245370 | 0.122685 | − | 0.992446i | \(-0.460850\pi\) | ||||
0.122685 | + | 0.992446i | \(0.460850\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.9225 | 1.82146 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.81940 | 0.442967 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.61580 | −0.557310 | −0.278655 | − | 0.960391i | \(-0.589889\pi\) | ||||
−0.278655 | + | 0.960391i | \(0.589889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.683667 | −0.0440389 | −0.0220194 | − | 0.999758i | \(-0.507010\pi\) | ||||
−0.0220194 | + | 0.999758i | \(0.507010\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.75153 | 0.175789 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.42907 | 0.281815 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.32246 | 0.273925 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.5092 | 1.54701 | 0.773503 | − | 0.633792i | \(-0.218503\pi\) | ||||
0.773503 | + | 0.633792i | \(0.218503\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.32246 | 0.271751 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.25460 | 0.141188 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.7929 | 1.79605 | 0.898026 | − | 0.439942i | \(-0.145001\pi\) | ||||
0.898026 | + | 0.439942i | \(0.145001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.68367 | −0.539577 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.819397 | −0.0507194 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.1929 | −1.43013 | −0.715067 | − | 0.699056i | \(-0.753604\pi\) | ||||
−0.715067 | + | 0.699056i | \(0.753604\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.3516 | −1.25019 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.93214 | 0.485439 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.57093 | 0.583550 | 0.291775 | − | 0.956487i | \(-0.405754\pi\) | ||||
0.291775 | + | 0.956487i | \(0.405754\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1154 | 1.16118 | 0.580588 | − | 0.814198i | \(-0.302823\pi\) | ||||
0.580588 | + | 0.814198i | \(0.302823\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.57093 | −0.0950769 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.1127 | −0.670123 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.84852 | 0.291319 | 0.145660 | − | 0.989335i | \(-0.453470\pi\) | ||||
0.145660 | + | 0.989335i | \(0.453470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.32246 | −0.498253 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.14799 | −0.486068 | −0.243034 | − | 0.970018i | \(-0.578143\pi\) | ||||
−0.243034 | + | 0.970018i | \(0.578143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0291 | −1.19061 | −0.595304 | − | 0.803501i | \(-0.702968\pi\) | ||||
−0.595304 | + | 0.803501i | \(0.702968\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.75766 | 0.459524 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3225 | −0.609316 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3286 | −0.960505 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.67754 | 0.0983391 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.92251 | −0.345997 | −0.172998 | − | 0.984922i | \(-0.555346\pi\) | ||||
−0.172998 | + | 0.984922i | \(0.555346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.5832 | 1.02373 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.32246 | −0.250815 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.57093 | −0.0908492 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.429071 | −0.0247313 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.39033 | 0.482012 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.9674 | 2.11675 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.40608 | −0.194395 | −0.0971976 | − | 0.995265i | \(-0.530988\pi\) | ||||
−0.0971976 | + | 0.995265i | \(0.530988\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.0061 | 0.626117 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.4413 | −1.49935 | −0.749675 | − | 0.661806i | \(-0.769790\pi\) | ||||
−0.749675 | + | 0.661806i | \(0.769790\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.63879 | 0.431770 | 0.215885 | − | 0.976419i | \(-0.430736\pi\) | ||||
0.215885 | + | 0.976419i | \(0.430736\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.75153 | −0.155031 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.75766 | −0.548045 | −0.274022 | − | 0.961723i | \(-0.588354\pi\) | ||||
−0.274022 | + | 0.961723i | \(0.588354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.54181 | 0.198303 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.29334 | 0.239631 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.31020 | 0.128543 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.03875 | 0.224029 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.89339 | −0.325905 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.1480 | −0.559477 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.64492 | −0.255308 | −0.127654 | − | 0.991819i | \(-0.540745\pi\) | ||||
−0.127654 | + | 0.991819i | \(0.540745\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.68367 | 0.475862 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.42907 | 0.241986 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.15148 | 0.171672 | 0.0858362 | − | 0.996309i | \(-0.472644\pi\) | ||||
0.0858362 | + | 0.996309i | \(0.472644\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.74540 | 0.203422 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.9735 | 1.94807 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.75153 | −0.148138 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.6123 | −1.16021 | −0.580105 | − | 0.814542i | \(-0.696988\pi\) | ||||
−0.580105 | + | 0.814542i | \(0.696988\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.60967 | 0.193221 | 0.0966107 | − | 0.995322i | \(-0.469200\pi\) | ||||
0.0966107 | + | 0.995322i | \(0.469200\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57093 | 0.0838500 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.2572 | −1.71688 | −0.858439 | − | 0.512915i | \(-0.828566\pi\) | ||||
−0.858439 | + | 0.512915i | \(0.828566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.68980 | 0.301983 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.819397 | −0.0433671 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.47395 | −0.500016 | −0.250008 | − | 0.968244i | \(-0.580433\pi\) | ||||
−0.250008 | + | 0.968244i | \(0.580433\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0510 | −0.581632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.68367 | 0.403288 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −37.0475 | −1.93915 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.0740 | −0.682457 | −0.341228 | − | 0.939980i | \(-0.610843\pi\) | ||||
−0.341228 | + | 0.939980i | \(0.610843\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.3225 | 0.537366 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.39645 | 0.384005 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.3347 | −1.67423 | −0.837114 | − | 0.547028i | \(-0.815759\pi\) | ||||
−0.837114 | + | 0.547028i | \(0.815759\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.68367 | −0.345143 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.28721 | −0.0662949 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7285 | 0.602455 | 0.301227 | − | 0.953552i | \(-0.402604\pi\) | ||||
0.301227 | + | 0.953552i | \(0.402604\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.07399 | −0.259949 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.3286 | −0.987645 | −0.493822 | − | 0.869563i | \(-0.664401\pi\) | ||||
−0.493822 | + | 0.869563i | \(0.664401\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.8934 | 0.606143 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.429071 | 0.0218109 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.7480 | −1.60969 | −0.804845 | − | 0.593486i | \(-0.797751\pi\) | ||||
−0.804845 | + | 0.593486i | \(0.797751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.819397 | −0.0414387 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.3225 | −0.621586 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.7638 | 0.944109 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.7868 | −1.29420 | −0.647101 | − | 0.762405i | \(-0.724019\pi\) | ||||
−0.647101 | + | 0.762405i | \(0.724019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.81940 | −0.141146 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.7480 | 0.786419 | 0.393210 | − | 0.919449i | \(-0.371365\pi\) | ||||
0.393210 | + | 0.919449i | \(0.371365\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.0740 | −0.651262 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.75153 | 0.136725 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.5348 | −1.86053 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.96125 | −0.195871 | −0.0979357 | − | 0.995193i | \(-0.531224\pi\) | ||||
−0.0979357 | + | 0.995193i | \(0.531224\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.67754 | 0.0827469 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.39033 | −0.314447 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.8934 | 0.583824 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.7577 | 0.575775 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.7515 | 0.818366 | 0.409183 | − | 0.912452i | \(-0.365814\pi\) | ||||
0.409183 | + | 0.912452i | \(0.365814\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.77802 | −0.135392 | −0.0676962 | − | 0.997706i | \(-0.521565\pi\) | ||||
−0.0676962 | + | 0.997706i | \(0.521565\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.1480 | 0.493412 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.10661 | 0.102186 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.4352 | −0.650175 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.79028 | −0.327838 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.58319 | −0.461606 | −0.230803 | − | 0.973001i | \(-0.574135\pi\) | ||||
−0.230803 | + | 0.973001i | \(0.574135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.4317 | 1.27023 | 0.635113 | − | 0.772419i | \(-0.280953\pi\) | ||||
0.635113 | + | 0.772419i | \(0.280953\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.25460 | −0.108100 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.81940 | −0.134870 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.6898 | 1.03520 | 0.517599 | − | 0.855623i | \(-0.326826\pi\) | ||||
0.517599 | + | 0.855623i | \(0.326826\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.00613 | −0.332871 | −0.166436 | − | 0.986052i | \(-0.553226\pi\) | ||||
−0.166436 | + | 0.986052i | \(0.553226\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.8255 | 1.03463 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.496936 | −0.0235043 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5322 | 0.921781 | 0.460890 | − | 0.887457i | \(-0.347530\pi\) | ||||
0.460890 | + | 0.887457i | \(0.347530\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.6184 | −2.10100 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.1480 | 0.476794 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.32246 | −0.202640 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.4026 | −1.79640 | −0.898199 | − | 0.439590i | \(-0.855124\pi\) | ||||
−0.898199 | + | 0.439590i | \(0.855124\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.819397 | 0.0382462 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.6740 | 1.42863 | 0.714316 | − | 0.699823i | \(-0.246738\pi\) | ||||
0.714316 | + | 0.699823i | \(0.246738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.8960 | −1.85413 | −0.927063 | − | 0.374907i | \(-0.877675\pi\) | ||||
−0.927063 | + | 0.374907i | \(0.877675\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −22.8995 | −1.06194 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.671411 | 0.0310692 | 0.0155346 | − | 0.999879i | \(-0.495055\pi\) | ||||
0.0155346 | + | 0.999879i | \(0.495055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.60967 | −0.0743279 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.4256 | 0.895083 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.85464 | −0.0852766 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.24847 | 0.332583 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.39645 | −0.338660 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.9091 | −0.772599 | −0.386299 | − | 0.922373i | \(-0.626247\pi\) | ||||
−0.386299 | + | 0.922373i | \(0.626247\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.6414 | 0.621995 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.61580 | 0.209593 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.03875 | 0.0923844 | 0.0461922 | − | 0.998933i | \(-0.485291\pi\) | ||||
0.0461922 | + | 0.998933i | \(0.485291\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.25460 | −0.101956 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.7250 | 0.574273 | 0.287137 | − | 0.957890i | \(-0.407297\pi\) | ||||
0.287137 | + | 0.957890i | \(0.407297\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.671411 | −0.0302388 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.8934 | −0.534568 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.06786 | −0.0927564 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.9056 | −0.980631 | −0.490316 | − | 0.871545i | \(-0.663119\pi\) | ||||
−0.490316 | + | 0.871545i | \(0.663119\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.31633 | 0.237516 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.9770 | 0.846143 | 0.423072 | − | 0.906096i | \(-0.360952\pi\) | ||||
0.423072 | + | 0.906096i | \(0.360952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.0862 | 1.02732 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.5322 | −0.467751 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.5214 | 1.79608 | 0.898041 | − | 0.439912i | \(-0.144990\pi\) | ||||
0.898041 | + | 0.439912i | \(0.144990\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.4643 | 0.595626 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.81940 | 0.124479 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.2837 | 1.33446 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.8643 | −1.92915 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.9613 | 0.876202 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.71629 | 0.162813 | 0.0814067 | − | 0.996681i | \(-0.474059\pi\) | ||||
0.0814067 | + | 0.996681i | \(0.474059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.3551 | −0.496523 | −0.248261 | − | 0.968693i | \(-0.579859\pi\) | ||||
−0.248261 | + | 0.968693i | \(0.579859\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.57093 | −0.112205 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.81940 | −0.297058 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.39033 | 0.277317 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.2159 | 0.702386 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.8133 | 0.510732 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.02912 | −0.173869 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.32246 | −0.186182 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.5092 | −1.31169 | −0.655846 | − | 0.754894i | \(-0.727688\pi\) | ||||
−0.655846 | + | 0.754894i | \(0.727688\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.955126 | 0.0409884 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.2159 | −0.694611 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.6802 | 1.35455 | 0.677273 | − | 0.735732i | \(-0.263162\pi\) | ||||
0.677273 | + | 0.735732i | \(0.263162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.4352 | 0.573400 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.31020 | −0.0984180 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.81940 | −0.289990 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 23.8934 | 1.01422 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.4194 | 0.695714 | 0.347857 | − | 0.937548i | \(-0.386909\pi\) | ||||
0.347857 | + | 0.937548i | \(0.386909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.674040 | 0.0285089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.54181 | −0.149535 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.5648 | −0.529543 | −0.264772 | − | 0.964311i | \(-0.585297\pi\) | ||||
−0.264772 | + | 0.964311i | \(0.585297\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3056 | 0.433560 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.9286 | 1.38044 | 0.690220 | − | 0.723599i | \(-0.257514\pi\) | ||||
0.690220 | + | 0.723599i | \(0.257514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.7542 | 1.87290 | 0.936452 | − | 0.350797i | \(-0.114089\pi\) | ||||
0.936452 | + | 0.350797i | \(0.114089\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.85814 | −0.370054 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.57093 | −0.107215 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.14186 | 0.379923 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.32246 | −0.179326 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.9709 | 1.32410 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.32246 | 0.178712 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.2342 | 1.70192 | 0.850960 | − | 0.525231i | \(-0.176021\pi\) | ||||
0.850960 | + | 0.525231i | \(0.176021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.4643 | −0.966830 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.21585 | −0.255686 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.4256 | 1.61901 | 0.809507 | − | 0.587110i | \(-0.199734\pi\) | ||||
0.809507 | + | 0.587110i | \(0.199734\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.25460 | −0.0924294 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.3965 | −0.875699 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.293342 | −0.0119856 | −0.00599282 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599282 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4739 | 0.468032 | 0.234016 | − | 0.972233i | \(-0.424813\pi\) | ||||
0.234016 | + | 0.972233i | \(0.424813\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.60967 | 0.0655510 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.1419 | 0.859539 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.72504 | −0.354139 | −0.177069 | − | 0.984198i | \(-0.556662\pi\) | ||||
−0.177069 | + | 0.984198i | \(0.556662\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.819397 | 0.0332036 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.9418 | 0.644935 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.1154 | −1.49908 | −0.749538 | − | 0.661962i | \(-0.769724\pi\) | ||||
−0.749538 | + | 0.661962i | \(0.769724\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.4026 | 1.14530 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.3516 | −0.899841 | −0.449920 | − | 0.893069i | \(-0.648548\pi\) | ||||
−0.449920 | + | 0.893069i | \(0.648548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.2342 | 1.33580 | 0.667898 | − | 0.744253i | \(-0.267194\pi\) | ||||
0.667898 | + | 0.744253i | \(0.267194\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.93214 | −0.317794 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2450 | −1.24980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.1867 | −0.486691 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.11537 | 0.283708 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.60005 | 0.143316 | 0.0716578 | − | 0.997429i | \(-0.477171\pi\) | ||||
0.0716578 | + | 0.997429i | \(0.477171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.18060 | −0.205910 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.9613 | −0.554035 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.57093 | 0.0622425 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.06786 | 0.0818035 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.7250 | −0.897585 | −0.448793 | − | 0.893636i | \(-0.648146\pi\) | ||||
−0.448793 | + | 0.893636i | \(0.648146\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.9505 | 1.69380 | 0.846902 | − | 0.531750i | \(-0.178465\pi\) | ||||
0.846902 | + | 0.531750i | \(0.178465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.18060 | 0.0464862 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2607 | −0.678589 | −0.339295 | − | 0.940680i | \(-0.610188\pi\) | ||||
−0.339295 | + | 0.940680i | \(0.610188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.6219 | −1.08426 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.32246 | 0.326183 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.7638 | 0.969082 | 0.484541 | − | 0.874769i | \(-0.338987\pi\) | ||||
0.484541 | + | 0.874769i | \(0.338987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.9056 | −1.32480 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.4643 | −0.525293 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.2388 | 0.515712 | 0.257856 | − | 0.966183i | \(-0.416984\pi\) | ||||
0.257856 | + | 0.966183i | \(0.416984\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.6837 | 0.960083 | 0.480042 | − | 0.877246i | \(-0.340622\pi\) | ||||
0.480042 | + | 0.877246i | \(0.340622\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.28721 | 0.0499912 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.75766 | −0.300829 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.819397 | 0.0317272 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0291 | 0.619722 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −58.0731 | −2.24189 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.4000 | −0.709266 | −0.354633 | − | 0.935006i | \(-0.615394\pi\) | ||||
−0.354633 | + | 0.935006i | \(0.615394\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.57093 | 0.0989551 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.1506 | −1.85058 | −0.925289 | − | 0.379262i | \(-0.876178\pi\) | ||||
−0.925289 | + | 0.379262i | \(0.876178\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.67754 | −0.0643780 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.2607 | 0.508152 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0510 | 1.37945 | 0.689727 | − | 0.724070i | \(-0.257731\pi\) | ||||
0.689727 | + | 0.724070i | \(0.257731\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.61580 | 0.176361 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.254596 | −0.00971345 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.6193 | −0.442660 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0088 | 0.723127 | 0.361564 | − | 0.932347i | \(-0.382243\pi\) | ||||
0.361564 | + | 0.932347i | \(0.382243\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.32246 | 0.164197 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.3516 | 1.22717 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.45819 | 0.320377 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.74540 | 0.141664 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.60967 | −0.287413 | −0.143707 | − | 0.989620i | \(-0.545902\pi\) | ||||
−0.143707 | + | 0.989620i | \(0.545902\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.4827 | 0.923383 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27.9225 | 1.05162 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.39033 | −0.315551 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.2933 | −1.28791 | −0.643957 | − | 0.765062i | \(-0.722708\pi\) | ||||
−0.643957 | + | 0.765062i | \(0.722708\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.81940 | 0.255747 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.32246 | 0.311679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.6837 | −0.698730 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.61580 | −0.321763 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.807140 | −0.0301012 | −0.0150506 | − | 0.999887i | \(-0.504791\pi\) | ||||
−0.0150506 | + | 0.999887i | \(0.504791\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.0061 | −0.409890 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.683667 | −0.0254259 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.10661 | −0.0782375 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.37457 | −0.199332 | −0.0996659 | − | 0.995021i | \(-0.531777\pi\) | ||||
−0.0996659 | + | 0.995021i | \(0.531777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.351580 | 0.0130036 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.7093 | −1.39282 | −0.696412 | − | 0.717642i | \(-0.745221\pi\) | ||||
−0.696412 | + | 0.717642i | \(0.745221\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.75153 | 0.101492 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.95776 | −0.256292 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.18060 | −0.190572 | −0.0952858 | − | 0.995450i | \(-0.530376\pi\) | ||||
−0.0952858 | + | 0.995450i | \(0.530376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.42907 | 0.162706 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.8343 | 1.20457 | 0.602287 | − | 0.798280i | \(-0.294256\pi\) | ||||
0.602287 | + | 0.798280i | \(0.294256\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.36733 | −0.0500953 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.32246 | 0.158151 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.29334 | −0.156875 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.8282 | −0.796521 | −0.398260 | − | 0.917272i | \(-0.630386\pi\) | ||||
−0.398260 | + | 0.917272i | \(0.630386\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.5092 | 0.893165 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.9225 | 1.01620 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.9613 | −1.45242 | −0.726208 | − | 0.687475i | \(-0.758719\pi\) | ||||
−0.726208 | + | 0.687475i | \(0.758719\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.32246 | 0.156895 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.3735 | 0.666038 | 0.333019 | − | 0.942920i | \(-0.391933\pi\) | ||||
0.333019 | + | 0.942920i | \(0.391933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.89339 | 0.213355 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.25460 | 0.0815151 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.0387 | 0.362478 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.7154 | −1.90097 | −0.950483 | − | 0.310776i | \(-0.899411\pi\) | ||||
−0.950483 | + | 0.310776i | \(0.899411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.7929 | 1.03695 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.9083 | −1.14766 | −0.573830 | − | 0.818974i | \(-0.694543\pi\) | ||||
−0.573830 | + | 0.818974i | \(0.694543\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.3965 | −0.768583 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.68367 | −0.311525 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.1031 | 1.04273 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.93826 | −0.319836 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.819397 | −0.0292828 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.4501 | 1.90772 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.11887 | −0.218114 | −0.109057 | − | 0.994035i | \(-0.534783\pi\) | ||||
−0.109057 | + | 0.994035i | \(0.534783\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.1929 | −0.825688 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.74540 | −0.133171 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.1057 | 0.749487 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.3516 | −0.721796 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.7868 | −1.48016 | −0.740082 | − | 0.672517i | \(-0.765213\pi\) | ||||
−0.740082 | + | 0.672517i | \(0.765213\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.31523 | 0.294172 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.93214 | 0.280268 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 58.1990 | 2.05380 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.75153 | 0.0969788 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.57093 | 0.336913 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.1322 | 0.813286 | 0.406643 | − | 0.913587i | \(-0.366699\pi\) | ||||
0.406643 | + | 0.913587i | \(0.366699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.8255 | −1.04732 | −0.523658 | − | 0.851929i | \(-0.675433\pi\) | ||||
−0.523658 | + | 0.851929i | \(0.675433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.1154 | 0.670405 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.20359 | −0.217302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.20972 | 0.0423228 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.57093 | −0.0548927 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.7929 | −1.00488 | −0.502440 | − | 0.864612i | \(-0.667564\pi\) | ||||
−0.502440 | + | 0.864612i | \(0.667564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.67404 | −0.302358 | −0.151179 | − | 0.988506i | \(-0.548307\pi\) | ||||
−0.151179 | + | 0.988506i | \(0.548307\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.1127 | −0.386896 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.89952 | 0.100826 | 0.0504131 | − | 0.998728i | \(-0.483946\pi\) | ||||
0.0504131 | + | 0.998728i | \(0.483946\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.7021 | 1.44837 | 0.724186 | − | 0.689605i | \(-0.242216\pi\) | ||||
0.724186 | + | 0.689605i | \(0.242216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.84852 | 0.168193 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.819397 | 0.0283904 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.6281 | 0.506225 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.32246 | −0.287666 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.3577 | 0.668302 | 0.334151 | − | 0.942520i | \(-0.391550\pi\) | ||||
0.334151 | + | 0.942520i | \(0.391550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3286 | −0.976848 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.14799 | −0.280632 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.9796 | −0.996930 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.68367 | −0.264014 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.0291 | −0.687398 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.68367 | −0.297672 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.56830 | −0.0536975 | −0.0268488 | − | 0.999640i | \(-0.508547\pi\) | ||||
−0.0268488 | + | 0.999640i | \(0.508547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.75766 | 0.265306 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.1602 | 1.44017 | 0.720083 | − | 0.693888i | \(-0.244104\pi\) | ||||
0.720083 | + | 0.693888i | \(0.244104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.94089 | −0.305059 | −0.152530 | − | 0.988299i | \(-0.548742\pi\) | ||||
−0.152530 | + | 0.988299i | \(0.548742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.3225 | −0.351789 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.5153 | 1.61744 | 0.808720 | − | 0.588194i | \(-0.200161\pi\) | ||||
0.808720 | + | 0.588194i | \(0.200161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.9240 | 1.86747 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.3286 | −0.554548 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.4766 | −0.999924 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.52868 | 0.0856812 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.67754 | 0.0567761 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.68367 | 0.225949 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.2307 | −1.35850 | −0.679248 | − | 0.733909i | \(-0.737694\pi\) | ||||
−0.679248 | + | 0.733909i | \(0.737694\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.92251 | −0.199761 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.70316 | −0.225835 | −0.112918 | − | 0.993604i | \(-0.536020\pi\) | ||||
−0.112918 | + | 0.993604i | \(0.536020\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.2802 | 0.918052 | 0.459026 | − | 0.888423i | \(-0.348198\pi\) | ||||
0.459026 | + | 0.888423i | \(0.348198\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.5832 | 0.591052 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.2933 | 0.547077 | 0.273538 | − | 0.961861i | \(-0.411806\pi\) | ||||
0.273538 | + | 0.961861i | \(0.411806\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.07399 | 0.170176 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.32246 | −0.144808 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.6112 | 0.957437 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.0862 | −0.370572 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.57093 | −0.0524518 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.81940 | 0.227440 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.06063 | −0.201909 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.429071 | −0.0142786 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.62806 | 0.0873597 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.80977 | −0.292524 | −0.146262 | − | 0.989246i | \(-0.546724\pi\) | ||||
−0.146262 | + | 0.989246i | \(0.546724\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.39033 | 0.278290 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4440 | 1.00865 | 0.504327 | − | 0.863513i | \(-0.331741\pi\) | ||||
0.504327 | + | 0.863513i | \(0.331741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.6837 | −0.618339 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.9674 | 1.22210 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.3225 | 0.406924 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.6184 | 0.944035 | 0.472017 | − | 0.881589i | \(-0.343526\pi\) | ||||
0.472017 | + | 0.881589i | \(0.343526\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.40608 | −0.112234 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.24847 | 0.106925 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.3251 | 0.734044 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.0061 | 0.361489 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.7117 | 1.30290 | 0.651449 | − | 0.758692i | \(-0.274161\pi\) | ||||
0.651449 | + | 0.758692i | \(0.274161\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.81940 | 0.0924020 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.4413 | −0.865650 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.74540 | −0.318709 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.1867 | 1.24751 | 0.623753 | − | 0.781621i | \(-0.285607\pi\) | ||||
0.623753 | + | 0.781621i | \(0.285607\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.63879 | 0.249283 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.2246 | 1.08309 | 0.541546 | − | 0.840671i | \(-0.317839\pi\) | ||||
0.541546 | + | 0.840671i | \(0.317839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3225 | −0.336146 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.75153 | −0.0895073 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.19397 | 0.266268 | 0.133134 | − | 0.991098i | \(-0.457496\pi\) | ||||
0.133134 | + | 0.991098i | \(0.457496\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.1515 | −0.686606 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.75766 | −0.316414 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.7710 | 0.413694 | 0.206847 | − | 0.978373i | \(-0.433680\pi\) | ||||
0.206847 | + | 0.978373i | \(0.433680\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.3735 | −0.788707 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.54181 | 0.114490 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.67754 | −0.0541706 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.2634 | 1.23430 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.29334 | 0.138351 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.1541 | 0.809740 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.3673 | 1.20165 | 0.600826 | − | 0.799380i | \(-0.294838\pi\) | ||||
0.600826 | + | 0.799380i | \(0.294838\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.31020 | 0.0742145 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.0088 | −1.12348 | −0.561742 | − | 0.827312i | \(-0.689869\pi\) | ||||
−0.561742 | + | 0.827312i | \(0.689869\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.7577 | −0.376933 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.03875 | 0.129343 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.2995 | 0.681430 | 0.340715 | − | 0.940167i | \(-0.389331\pi\) | ||||
0.340715 | + | 0.940167i | \(0.389331\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.2863 | −1.09580 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.89339 | −0.188161 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.4122 | 0.587258 | 0.293629 | − | 0.955919i | \(-0.405137\pi\) | ||||
0.293629 | + | 0.955919i | \(0.405137\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.1031 | −0.544950 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.1480 | −0.323014 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.429071 | −0.0136437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.3700 | 1.82242 | 0.911208 | − | 0.411945i | \(-0.135151\pi\) | ||||
0.911208 | + | 0.411945i | \(0.135151\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.64492 | −0.147402 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −58.8730 | −1.86640 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.5939 | −0.588875 | −0.294438 | − | 0.955671i | \(-0.595132\pi\) | ||||
−0.294438 | + | 0.955671i | \(0.595132\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.68367 | 0.274739 |
(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 | 7728.2.a.by.1.3 | 3 | ||
4.3 | odd | 2 | 3864.2.a.n.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.n.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
7728.2.a.by.1.3 | 3 | 1.1 | even | 1 | trivial |