Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, 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("525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(4.19214610612\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30278 | −1.62831 | −0.814154 | − | 0.580649i | \(-0.802799\pi\) | ||||
−0.814154 | + | 0.580649i | \(0.802799\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.30278 | 1.65139 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.30278 | 0.940104 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | −3.30278 | −0.953429 | ||||||||
\(13\) | 2.60555 | 0.722650 | 0.361325 | − | 0.932440i | \(-0.382325\pi\) | ||||
0.361325 | + | 0.932440i | \(0.382325\pi\) | |||||||
\(14\) | 2.30278 | 0.615443 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.302776 | 0.0756939 | ||||||||
\(17\) | −4.60555 | −1.11701 | −0.558505 | − | 0.829501i | \(-0.688625\pi\) | ||||
−0.558505 | + | 0.829501i | \(0.688625\pi\) | |||||||
\(18\) | −2.30278 | −0.542769 | ||||||||
\(19\) | 6.60555 | 1.51542 | 0.757709 | − | 0.652593i | \(-0.226319\pi\) | ||||
0.757709 | + | 0.652593i | \(0.226319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 6.90833 | 1.47286 | ||||||||
\(23\) | 6.21110 | 1.29510 | 0.647552 | − | 0.762021i | \(-0.275793\pi\) | ||||
0.647552 | + | 0.762021i | \(0.275793\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.00000 | −1.17670 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.30278 | −0.624166 | ||||||||
\(29\) | −7.60555 | −1.41232 | −0.706158 | − | 0.708055i | \(-0.749573\pi\) | ||||
−0.706158 | + | 0.708055i | \(0.749573\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.21110 | −1.29515 | −0.647576 | − | 0.762001i | \(-0.724217\pi\) | ||||
−0.647576 | + | 0.762001i | \(0.724217\pi\) | |||||||
\(32\) | 5.30278 | 0.937407 | ||||||||
\(33\) | 3.00000 | 0.522233 | ||||||||
\(34\) | 10.6056 | 1.81884 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.30278 | 0.550463 | ||||||||
\(37\) | 4.21110 | 0.692301 | 0.346150 | − | 0.938179i | \(-0.387489\pi\) | ||||
0.346150 | + | 0.938179i | \(0.387489\pi\) | |||||||
\(38\) | −15.2111 | −2.46757 | ||||||||
\(39\) | −2.60555 | −0.417222 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | −2.30278 | −0.355326 | ||||||||
\(43\) | −9.60555 | −1.46483 | −0.732416 | − | 0.680857i | \(-0.761608\pi\) | ||||
−0.732416 | + | 0.680857i | \(0.761608\pi\) | |||||||
\(44\) | −9.90833 | −1.49374 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.3028 | −2.10883 | ||||||||
\(47\) | −10.6056 | −1.54698 | −0.773489 | − | 0.633809i | \(-0.781490\pi\) | ||||
−0.773489 | + | 0.633809i | \(0.781490\pi\) | |||||||
\(48\) | −0.302776 | −0.0437019 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.60555 | 0.644906 | ||||||||
\(52\) | 8.60555 | 1.19338 | ||||||||
\(53\) | −3.21110 | −0.441079 | −0.220539 | − | 0.975378i | \(-0.570782\pi\) | ||||
−0.220539 | + | 0.975378i | \(0.570782\pi\) | |||||||
\(54\) | 2.30278 | 0.313368 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | −6.60555 | −0.874927 | ||||||||
\(58\) | 17.5139 | 2.29968 | ||||||||
\(59\) | −10.6056 | −1.38073 | −0.690363 | − | 0.723464i | \(-0.742549\pi\) | ||||
−0.690363 | + | 0.723464i | \(0.742549\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.21110 | −0.155066 | −0.0775329 | − | 0.996990i | \(-0.524704\pi\) | ||||
−0.0775329 | + | 0.996990i | \(0.524704\pi\) | |||||||
\(62\) | 16.6056 | 2.10891 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −12.8167 | −1.60208 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.90833 | −0.850356 | ||||||||
\(67\) | −15.6056 | −1.90652 | −0.953261 | − | 0.302149i | \(-0.902296\pi\) | ||||
−0.953261 | + | 0.302149i | \(0.902296\pi\) | |||||||
\(68\) | −15.2111 | −1.84462 | ||||||||
\(69\) | −6.21110 | −0.747729 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | −0.605551 | −0.0708744 | −0.0354372 | − | 0.999372i | \(-0.511282\pi\) | ||||
−0.0354372 | + | 0.999372i | \(0.511282\pi\) | |||||||
\(74\) | −9.69722 | −1.12728 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 21.8167 | 2.50254 | ||||||||
\(77\) | 3.00000 | 0.341882 | ||||||||
\(78\) | 6.00000 | 0.679366 | ||||||||
\(79\) | −14.8167 | −1.66700 | −0.833502 | − | 0.552517i | \(-0.813668\pi\) | ||||
−0.833502 | + | 0.552517i | \(0.813668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.21110 | 0.352464 | 0.176232 | − | 0.984349i | \(-0.443609\pi\) | ||||
0.176232 | + | 0.984349i | \(0.443609\pi\) | |||||||
\(84\) | 3.30278 | 0.360362 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 22.1194 | 2.38520 | ||||||||
\(87\) | 7.60555 | 0.815401 | ||||||||
\(88\) | 9.00000 | 0.959403 | ||||||||
\(89\) | 7.81665 | 0.828564 | 0.414282 | − | 0.910149i | \(-0.364033\pi\) | ||||
0.414282 | + | 0.910149i | \(0.364033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.60555 | −0.273136 | ||||||||
\(92\) | 20.5139 | 2.13872 | ||||||||
\(93\) | 7.21110 | 0.747757 | ||||||||
\(94\) | 24.4222 | 2.51896 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.30278 | −0.541212 | ||||||||
\(97\) | 0.788897 | 0.0801004 | 0.0400502 | − | 0.999198i | \(-0.487248\pi\) | ||||
0.0400502 | + | 0.999198i | \(0.487248\pi\) | |||||||
\(98\) | −2.30278 | −0.232615 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.6056 | 1.65231 | 0.826157 | − | 0.563440i | \(-0.190522\pi\) | ||||
0.826157 | + | 0.563440i | \(0.190522\pi\) | |||||||
\(102\) | −10.6056 | −1.05011 | ||||||||
\(103\) | −3.81665 | −0.376066 | −0.188033 | − | 0.982163i | \(-0.560211\pi\) | ||||
−0.188033 | + | 0.982163i | \(0.560211\pi\) | |||||||
\(104\) | −7.81665 | −0.766486 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.39445 | 0.718212 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −3.30278 | −0.317810 | ||||||||
\(109\) | 2.21110 | 0.211785 | 0.105893 | − | 0.994378i | \(-0.466230\pi\) | ||||
0.105893 | + | 0.994378i | \(0.466230\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.21110 | −0.399700 | ||||||||
\(112\) | −0.302776 | −0.0286096 | ||||||||
\(113\) | 10.8167 | 1.01755 | 0.508773 | − | 0.860901i | \(-0.330099\pi\) | ||||
0.508773 | + | 0.860901i | \(0.330099\pi\) | |||||||
\(114\) | 15.2111 | 1.42465 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −25.1194 | −2.33228 | ||||||||
\(117\) | 2.60555 | 0.240883 | ||||||||
\(118\) | 24.4222 | 2.24825 | ||||||||
\(119\) | 4.60555 | 0.422190 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 2.78890 | 0.252495 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −23.8167 | −2.13880 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.30278 | 0.205148 | ||||||||
\(127\) | −12.8167 | −1.13729 | −0.568647 | − | 0.822582i | \(-0.692533\pi\) | ||||
−0.568647 | + | 0.822582i | \(0.692533\pi\) | |||||||
\(128\) | 18.9083 | 1.67128 | ||||||||
\(129\) | 9.60555 | 0.845722 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.39445 | −0.646056 | −0.323028 | − | 0.946389i | \(-0.604701\pi\) | ||||
−0.323028 | + | 0.946389i | \(0.604701\pi\) | |||||||
\(132\) | 9.90833 | 0.862409 | ||||||||
\(133\) | −6.60555 | −0.572774 | ||||||||
\(134\) | 35.9361 | 3.10440 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.8167 | 1.18477 | ||||||||
\(137\) | 3.21110 | 0.274343 | 0.137172 | − | 0.990547i | \(-0.456199\pi\) | ||||
0.137172 | + | 0.990547i | \(0.456199\pi\) | |||||||
\(138\) | 14.3028 | 1.21753 | ||||||||
\(139\) | 19.0278 | 1.61391 | 0.806957 | − | 0.590611i | \(-0.201113\pi\) | ||||
0.806957 | + | 0.590611i | \(0.201113\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.6056 | 0.893149 | ||||||||
\(142\) | 6.90833 | 0.579734 | ||||||||
\(143\) | −7.81665 | −0.653661 | ||||||||
\(144\) | 0.302776 | 0.0252313 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.39445 | 0.115405 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 13.9083 | 1.14326 | ||||||||
\(149\) | −16.3944 | −1.34309 | −0.671543 | − | 0.740966i | \(-0.734368\pi\) | ||||
−0.671543 | + | 0.740966i | \(0.734368\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.81665 | 0.554731 | 0.277366 | − | 0.960764i | \(-0.410539\pi\) | ||||
0.277366 | + | 0.960764i | \(0.410539\pi\) | |||||||
\(152\) | −19.8167 | −1.60734 | ||||||||
\(153\) | −4.60555 | −0.372337 | ||||||||
\(154\) | −6.90833 | −0.556689 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.60555 | −0.688996 | ||||||||
\(157\) | −14.4222 | −1.15102 | −0.575509 | − | 0.817796i | \(-0.695196\pi\) | ||||
−0.575509 | + | 0.817796i | \(0.695196\pi\) | |||||||
\(158\) | 34.1194 | 2.71440 | ||||||||
\(159\) | 3.21110 | 0.254657 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.21110 | −0.489503 | ||||||||
\(162\) | −2.30278 | −0.180923 | ||||||||
\(163\) | −17.2111 | −1.34808 | −0.674039 | − | 0.738696i | \(-0.735442\pi\) | ||||
−0.674039 | + | 0.738696i | \(0.735442\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.39445 | −0.573921 | ||||||||
\(167\) | 17.0278 | 1.31765 | 0.658824 | − | 0.752297i | \(-0.271054\pi\) | ||||
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(168\) | −3.00000 | −0.231455 | ||||||||
\(169\) | −6.21110 | −0.477777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.60555 | 0.505139 | ||||||||
\(172\) | −31.7250 | −2.41901 | ||||||||
\(173\) | 7.81665 | 0.594289 | 0.297145 | − | 0.954832i | \(-0.403966\pi\) | ||||
0.297145 | + | 0.954832i | \(0.403966\pi\) | |||||||
\(174\) | −17.5139 | −1.32772 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.908327 | −0.0684677 | ||||||||
\(177\) | 10.6056 | 0.797162 | ||||||||
\(178\) | −18.0000 | −1.34916 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.6056 | 0.936963 | 0.468482 | − | 0.883473i | \(-0.344801\pi\) | ||||
0.468482 | + | 0.883473i | \(0.344801\pi\) | |||||||
\(182\) | 6.00000 | 0.444750 | ||||||||
\(183\) | 1.21110 | 0.0895273 | ||||||||
\(184\) | −18.6333 | −1.37367 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −16.6056 | −1.21758 | ||||||||
\(187\) | 13.8167 | 1.01037 | ||||||||
\(188\) | −35.0278 | −2.55466 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.78890 | −0.201798 | −0.100899 | − | 0.994897i | \(-0.532172\pi\) | ||||
−0.100899 | + | 0.994897i | \(0.532172\pi\) | |||||||
\(192\) | 12.8167 | 0.924962 | ||||||||
\(193\) | −8.21110 | −0.591048 | −0.295524 | − | 0.955335i | \(-0.595494\pi\) | ||||
−0.295524 | + | 0.955335i | \(0.595494\pi\) | |||||||
\(194\) | −1.81665 | −0.130428 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.30278 | 0.235913 | ||||||||
\(197\) | −16.8167 | −1.19814 | −0.599068 | − | 0.800698i | \(-0.704462\pi\) | ||||
−0.599068 | + | 0.800698i | \(0.704462\pi\) | |||||||
\(198\) | 6.90833 | 0.490953 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.6056 | 1.10073 | ||||||||
\(202\) | −38.2389 | −2.69048 | ||||||||
\(203\) | 7.60555 | 0.533805 | ||||||||
\(204\) | 15.2111 | 1.06499 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.78890 | 0.612352 | ||||||||
\(207\) | 6.21110 | 0.431701 | ||||||||
\(208\) | 0.788897 | 0.0547002 | ||||||||
\(209\) | −19.8167 | −1.37075 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.4222 | 1.81898 | 0.909490 | − | 0.415726i | \(-0.136473\pi\) | ||||
0.909490 | + | 0.415726i | \(0.136473\pi\) | |||||||
\(212\) | −10.6056 | −0.728392 | ||||||||
\(213\) | 3.00000 | 0.205557 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.00000 | 0.204124 | ||||||||
\(217\) | 7.21110 | 0.489522 | ||||||||
\(218\) | −5.09167 | −0.344852 | ||||||||
\(219\) | 0.605551 | 0.0409194 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 9.69722 | 0.650835 | ||||||||
\(223\) | −15.3944 | −1.03089 | −0.515444 | − | 0.856923i | \(-0.672373\pi\) | ||||
−0.515444 | + | 0.856923i | \(0.672373\pi\) | |||||||
\(224\) | −5.30278 | −0.354307 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.9083 | −1.65688 | ||||||||
\(227\) | −22.6056 | −1.50038 | −0.750192 | − | 0.661221i | \(-0.770039\pi\) | ||||
−0.750192 | + | 0.661221i | \(0.770039\pi\) | |||||||
\(228\) | −21.8167 | −1.44484 | ||||||||
\(229\) | −7.21110 | −0.476523 | −0.238262 | − | 0.971201i | \(-0.576578\pi\) | ||||
−0.238262 | + | 0.971201i | \(0.576578\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | −0.197386 | ||||||||
\(232\) | 22.8167 | 1.49799 | ||||||||
\(233\) | 1.18335 | 0.0775236 | 0.0387618 | − | 0.999248i | \(-0.487659\pi\) | ||||
0.0387618 | + | 0.999248i | \(0.487659\pi\) | |||||||
\(234\) | −6.00000 | −0.392232 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −35.0278 | −2.28011 | ||||||||
\(237\) | 14.8167 | 0.962445 | ||||||||
\(238\) | −10.6056 | −0.687456 | ||||||||
\(239\) | 14.7889 | 0.956614 | 0.478307 | − | 0.878193i | \(-0.341251\pi\) | ||||
0.478307 | + | 0.878193i | \(0.341251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.39445 | 0.605150 | 0.302575 | − | 0.953126i | \(-0.402154\pi\) | ||||
0.302575 | + | 0.953126i | \(0.402154\pi\) | |||||||
\(242\) | 4.60555 | 0.296056 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.2111 | 1.09512 | ||||||||
\(248\) | 21.6333 | 1.37372 | ||||||||
\(249\) | −3.21110 | −0.203495 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.8167 | −0.872099 | −0.436050 | − | 0.899923i | \(-0.643623\pi\) | ||||
−0.436050 | + | 0.899923i | \(0.643623\pi\) | |||||||
\(252\) | −3.30278 | −0.208055 | ||||||||
\(253\) | −18.6333 | −1.17147 | ||||||||
\(254\) | 29.5139 | 1.85187 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.9083 | −1.11927 | ||||||||
\(257\) | 21.6333 | 1.34945 | 0.674724 | − | 0.738070i | \(-0.264263\pi\) | ||||
0.674724 | + | 0.738070i | \(0.264263\pi\) | |||||||
\(258\) | −22.1194 | −1.37710 | ||||||||
\(259\) | −4.21110 | −0.261665 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.60555 | −0.470772 | ||||||||
\(262\) | 17.0278 | 1.05198 | ||||||||
\(263\) | 5.78890 | 0.356959 | 0.178479 | − | 0.983944i | \(-0.442882\pi\) | ||||
0.178479 | + | 0.983944i | \(0.442882\pi\) | |||||||
\(264\) | −9.00000 | −0.553912 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.2111 | 0.932653 | ||||||||
\(267\) | −7.81665 | −0.478371 | ||||||||
\(268\) | −51.5416 | −3.14841 | ||||||||
\(269\) | −3.21110 | −0.195784 | −0.0978922 | − | 0.995197i | \(-0.531210\pi\) | ||||
−0.0978922 | + | 0.995197i | \(0.531210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.6056 | −1.61617 | −0.808086 | − | 0.589064i | \(-0.799496\pi\) | ||||
−0.808086 | + | 0.589064i | \(0.799496\pi\) | |||||||
\(272\) | −1.39445 | −0.0845509 | ||||||||
\(273\) | 2.60555 | 0.157695 | ||||||||
\(274\) | −7.39445 | −0.446715 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −20.5139 | −1.23479 | ||||||||
\(277\) | 10.0000 | 0.600842 | 0.300421 | − | 0.953807i | \(-0.402873\pi\) | ||||
0.300421 | + | 0.953807i | \(0.402873\pi\) | |||||||
\(278\) | −43.8167 | −2.62795 | ||||||||
\(279\) | −7.21110 | −0.431717 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.18335 | −0.0705925 | −0.0352963 | − | 0.999377i | \(-0.511237\pi\) | ||||
−0.0352963 | + | 0.999377i | \(0.511237\pi\) | |||||||
\(282\) | −24.4222 | −1.45432 | ||||||||
\(283\) | 13.6333 | 0.810416 | 0.405208 | − | 0.914225i | \(-0.367199\pi\) | ||||
0.405208 | + | 0.914225i | \(0.367199\pi\) | |||||||
\(284\) | −9.90833 | −0.587951 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.0000 | 1.06436 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.30278 | 0.312469 | ||||||||
\(289\) | 4.21110 | 0.247712 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.788897 | −0.0462460 | ||||||||
\(292\) | −2.00000 | −0.117041 | ||||||||
\(293\) | −10.6056 | −0.619583 | −0.309791 | − | 0.950805i | \(-0.600259\pi\) | ||||
−0.309791 | + | 0.950805i | \(0.600259\pi\) | |||||||
\(294\) | 2.30278 | 0.134301 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.6333 | −0.734296 | ||||||||
\(297\) | 3.00000 | 0.174078 | ||||||||
\(298\) | 37.7527 | 2.18696 | ||||||||
\(299\) | 16.1833 | 0.935907 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.60555 | 0.553655 | ||||||||
\(302\) | −15.6972 | −0.903274 | ||||||||
\(303\) | −16.6056 | −0.953964 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.6056 | 0.606279 | ||||||||
\(307\) | 8.60555 | 0.491145 | 0.245572 | − | 0.969378i | \(-0.421024\pi\) | ||||
0.245572 | + | 0.969378i | \(0.421024\pi\) | |||||||
\(308\) | 9.90833 | 0.564579 | ||||||||
\(309\) | 3.81665 | 0.217122 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.8167 | 0.783471 | 0.391735 | − | 0.920078i | \(-0.371875\pi\) | ||||
0.391735 | + | 0.920078i | \(0.371875\pi\) | |||||||
\(312\) | 7.81665 | 0.442531 | ||||||||
\(313\) | 23.8167 | 1.34620 | 0.673098 | − | 0.739553i | \(-0.264963\pi\) | ||||
0.673098 | + | 0.739553i | \(0.264963\pi\) | |||||||
\(314\) | 33.2111 | 1.87421 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −48.9361 | −2.75287 | ||||||||
\(317\) | 16.3944 | 0.920804 | 0.460402 | − | 0.887711i | \(-0.347705\pi\) | ||||
0.460402 | + | 0.887711i | \(0.347705\pi\) | |||||||
\(318\) | −7.39445 | −0.414660 | ||||||||
\(319\) | 22.8167 | 1.27749 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.3028 | 0.797063 | ||||||||
\(323\) | −30.4222 | −1.69274 | ||||||||
\(324\) | 3.30278 | 0.183488 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 39.6333 | 2.19509 | ||||||||
\(327\) | −2.21110 | −0.122274 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.6056 | 0.584703 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.2389 | −1.16739 | −0.583697 | − | 0.811972i | \(-0.698394\pi\) | ||||
−0.583697 | + | 0.811972i | \(0.698394\pi\) | |||||||
\(332\) | 10.6056 | 0.582055 | ||||||||
\(333\) | 4.21110 | 0.230767 | ||||||||
\(334\) | −39.2111 | −2.14554 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.302776 | 0.0165178 | ||||||||
\(337\) | 7.21110 | 0.392814 | 0.196407 | − | 0.980522i | \(-0.437073\pi\) | ||||
0.196407 | + | 0.980522i | \(0.437073\pi\) | |||||||
\(338\) | 14.3028 | 0.777968 | ||||||||
\(339\) | −10.8167 | −0.587480 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.6333 | 1.17151 | ||||||||
\(342\) | −15.2111 | −0.822522 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 28.8167 | 1.55369 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | −30.2111 | −1.62182 | −0.810908 | − | 0.585173i | \(-0.801027\pi\) | ||||
−0.810908 | + | 0.585173i | \(0.801027\pi\) | |||||||
\(348\) | 25.1194 | 1.34654 | ||||||||
\(349\) | 31.4500 | 1.68348 | 0.841739 | − | 0.539885i | \(-0.181532\pi\) | ||||
0.841739 | + | 0.539885i | \(0.181532\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.60555 | −0.139074 | ||||||||
\(352\) | −15.9083 | −0.847917 | ||||||||
\(353\) | 30.0000 | 1.59674 | 0.798369 | − | 0.602168i | \(-0.205696\pi\) | ||||
0.798369 | + | 0.602168i | \(0.205696\pi\) | |||||||
\(354\) | −24.4222 | −1.29803 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 25.8167 | 1.36828 | ||||||||
\(357\) | −4.60555 | −0.243752 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.6333 | 1.30010 | 0.650048 | − | 0.759893i | \(-0.274749\pi\) | ||||
0.650048 | + | 0.759893i | \(0.274749\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.6333 | 1.29649 | ||||||||
\(362\) | −29.0278 | −1.52567 | ||||||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | −8.60555 | −0.451053 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.78890 | −0.145778 | ||||||||
\(367\) | −14.4222 | −0.752833 | −0.376416 | − | 0.926451i | \(-0.622844\pi\) | ||||
−0.376416 | + | 0.926451i | \(0.622844\pi\) | |||||||
\(368\) | 1.88057 | 0.0980315 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.21110 | 0.166712 | ||||||||
\(372\) | 23.8167 | 1.23484 | ||||||||
\(373\) | 1.00000 | 0.0517780 | 0.0258890 | − | 0.999665i | \(-0.491758\pi\) | ||||
0.0258890 | + | 0.999665i | \(0.491758\pi\) | |||||||
\(374\) | −31.8167 | −1.64520 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31.8167 | 1.64082 | ||||||||
\(377\) | −19.8167 | −1.02061 | ||||||||
\(378\) | −2.30278 | −0.118442 | ||||||||
\(379\) | −14.8167 | −0.761080 | −0.380540 | − | 0.924764i | \(-0.624262\pi\) | ||||
−0.380540 | + | 0.924764i | \(0.624262\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.8167 | 0.656617 | ||||||||
\(382\) | 6.42221 | 0.328589 | ||||||||
\(383\) | 26.2389 | 1.34074 | 0.670372 | − | 0.742026i | \(-0.266135\pi\) | ||||
0.670372 | + | 0.742026i | \(0.266135\pi\) | |||||||
\(384\) | −18.9083 | −0.964912 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.9083 | 0.962408 | ||||||||
\(387\) | −9.60555 | −0.488278 | ||||||||
\(388\) | 2.60555 | 0.132277 | ||||||||
\(389\) | −28.8167 | −1.46106 | −0.730531 | − | 0.682879i | \(-0.760727\pi\) | ||||
−0.730531 | + | 0.682879i | \(0.760727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.6056 | −1.44664 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | 7.39445 | 0.373001 | ||||||||
\(394\) | 38.7250 | 1.95094 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.90833 | −0.497912 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | −18.4222 | −0.923422 | ||||||||
\(399\) | 6.60555 | 0.330691 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.8167 | −0.839784 | −0.419892 | − | 0.907574i | \(-0.637932\pi\) | ||||
−0.419892 | + | 0.907574i | \(0.637932\pi\) | |||||||
\(402\) | −35.9361 | −1.79233 | ||||||||
\(403\) | −18.7889 | −0.935942 | ||||||||
\(404\) | 54.8444 | 2.72861 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.5139 | −0.869199 | ||||||||
\(407\) | −12.6333 | −0.626210 | ||||||||
\(408\) | −13.8167 | −0.684026 | ||||||||
\(409\) | −11.8167 | −0.584296 | −0.292148 | − | 0.956373i | \(-0.594370\pi\) | ||||
−0.292148 | + | 0.956373i | \(0.594370\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.21110 | −0.158392 | ||||||||
\(412\) | −12.6056 | −0.621031 | ||||||||
\(413\) | 10.6056 | 0.521865 | ||||||||
\(414\) | −14.3028 | −0.702943 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 13.8167 | 0.677417 | ||||||||
\(417\) | −19.0278 | −0.931793 | ||||||||
\(418\) | 45.6333 | 2.23200 | ||||||||
\(419\) | 6.00000 | 0.293119 | 0.146560 | − | 0.989202i | \(-0.453180\pi\) | ||||
0.146560 | + | 0.989202i | \(0.453180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.2111 | −0.497659 | −0.248829 | − | 0.968547i | \(-0.580046\pi\) | ||||
−0.248829 | + | 0.968547i | \(0.580046\pi\) | |||||||
\(422\) | −60.8444 | −2.96186 | ||||||||
\(423\) | −10.6056 | −0.515660 | ||||||||
\(424\) | 9.63331 | 0.467835 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.90833 | −0.334710 | ||||||||
\(427\) | 1.21110 | 0.0586094 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.81665 | 0.377392 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.57779 | 0.268673 | 0.134336 | − | 0.990936i | \(-0.457110\pi\) | ||||
0.134336 | + | 0.990936i | \(0.457110\pi\) | |||||||
\(432\) | −0.302776 | −0.0145673 | ||||||||
\(433\) | 37.2111 | 1.78825 | 0.894126 | − | 0.447816i | \(-0.147798\pi\) | ||||
0.894126 | + | 0.447816i | \(0.147798\pi\) | |||||||
\(434\) | −16.6056 | −0.797092 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.30278 | 0.349740 | ||||||||
\(437\) | 41.0278 | 1.96262 | ||||||||
\(438\) | −1.39445 | −0.0666293 | ||||||||
\(439\) | 6.60555 | 0.315266 | 0.157633 | − | 0.987498i | \(-0.449614\pi\) | ||||
0.157633 | + | 0.987498i | \(0.449614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 27.6333 | 1.31438 | ||||||||
\(443\) | −15.6333 | −0.742761 | −0.371380 | − | 0.928481i | \(-0.621115\pi\) | ||||
−0.371380 | + | 0.928481i | \(0.621115\pi\) | |||||||
\(444\) | −13.9083 | −0.660060 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 35.4500 | 1.67860 | ||||||||
\(447\) | 16.3944 | 0.775431 | ||||||||
\(448\) | 12.8167 | 0.605530 | ||||||||
\(449\) | −34.8167 | −1.64310 | −0.821550 | − | 0.570137i | \(-0.806890\pi\) | ||||
−0.821550 | + | 0.570137i | \(0.806890\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 35.7250 | 1.68036 | ||||||||
\(453\) | −6.81665 | −0.320274 | ||||||||
\(454\) | 52.0555 | 2.44309 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 19.8167 | 0.928000 | ||||||||
\(457\) | 3.78890 | 0.177237 | 0.0886186 | − | 0.996066i | \(-0.471755\pi\) | ||||
0.0886186 | + | 0.996066i | \(0.471755\pi\) | |||||||
\(458\) | 16.6056 | 0.775926 | ||||||||
\(459\) | 4.60555 | 0.214969 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.2389 | −1.22207 | −0.611033 | − | 0.791605i | \(-0.709246\pi\) | ||||
−0.611033 | + | 0.791605i | \(0.709246\pi\) | |||||||
\(462\) | 6.90833 | 0.321404 | ||||||||
\(463\) | −17.2111 | −0.799868 | −0.399934 | − | 0.916544i | \(-0.630967\pi\) | ||||
−0.399934 | + | 0.916544i | \(0.630967\pi\) | |||||||
\(464\) | −2.30278 | −0.106904 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.72498 | −0.126232 | ||||||||
\(467\) | 0.422205 | 0.0195373 | 0.00976866 | − | 0.999952i | \(-0.496890\pi\) | ||||
0.00976866 | + | 0.999952i | \(0.496890\pi\) | |||||||
\(468\) | 8.60555 | 0.397792 | ||||||||
\(469\) | 15.6056 | 0.720597 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4222 | 0.664540 | ||||||||
\(472\) | 31.8167 | 1.46448 | ||||||||
\(473\) | 28.8167 | 1.32499 | ||||||||
\(474\) | −34.1194 | −1.56716 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 15.2111 | 0.697200 | ||||||||
\(477\) | −3.21110 | −0.147026 | ||||||||
\(478\) | −34.0555 | −1.55766 | ||||||||
\(479\) | 34.6056 | 1.58117 | 0.790584 | − | 0.612354i | \(-0.209777\pi\) | ||||
0.790584 | + | 0.612354i | \(0.209777\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.9722 | 0.500291 | ||||||||
\(482\) | −21.6333 | −0.985370 | ||||||||
\(483\) | 6.21110 | 0.282615 | ||||||||
\(484\) | −6.60555 | −0.300252 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.30278 | 0.104456 | ||||||||
\(487\) | 20.8167 | 0.943293 | 0.471646 | − | 0.881788i | \(-0.343660\pi\) | ||||
0.471646 | + | 0.881788i | \(0.343660\pi\) | |||||||
\(488\) | 3.63331 | 0.164472 | ||||||||
\(489\) | 17.2111 | 0.778313 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.00000 | −0.135388 | −0.0676941 | − | 0.997706i | \(-0.521564\pi\) | ||||
−0.0676941 | + | 0.997706i | \(0.521564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.0278 | 1.57757 | ||||||||
\(494\) | −39.6333 | −1.78319 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.18335 | −0.0980351 | ||||||||
\(497\) | 3.00000 | 0.134568 | ||||||||
\(498\) | 7.39445 | 0.331353 | ||||||||
\(499\) | −28.0000 | −1.25345 | −0.626726 | − | 0.779240i | \(-0.715605\pi\) | ||||
−0.626726 | + | 0.779240i | \(0.715605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.0278 | −0.760744 | ||||||||
\(502\) | 31.8167 | 1.42005 | ||||||||
\(503\) | 8.78890 | 0.391878 | 0.195939 | − | 0.980616i | \(-0.437225\pi\) | ||||
0.195939 | + | 0.980616i | \(0.437225\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 42.9083 | 1.90751 | ||||||||
\(507\) | 6.21110 | 0.275845 | ||||||||
\(508\) | −42.3305 | −1.87811 | ||||||||
\(509\) | 1.39445 | 0.0618079 | 0.0309039 | − | 0.999522i | \(-0.490161\pi\) | ||||
0.0309039 | + | 0.999522i | \(0.490161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.605551 | 0.0267880 | ||||||||
\(512\) | 3.42221 | 0.151242 | ||||||||
\(513\) | −6.60555 | −0.291642 | ||||||||
\(514\) | −49.8167 | −2.19732 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 31.7250 | 1.39661 | ||||||||
\(517\) | 31.8167 | 1.39929 | ||||||||
\(518\) | 9.69722 | 0.426072 | ||||||||
\(519\) | −7.81665 | −0.343113 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.4222 | −1.59569 | −0.797843 | − | 0.602865i | \(-0.794026\pi\) | ||||
−0.797843 | + | 0.602865i | \(0.794026\pi\) | |||||||
\(522\) | 17.5139 | 0.766562 | ||||||||
\(523\) | 16.0000 | 0.699631 | 0.349816 | − | 0.936819i | \(-0.386244\pi\) | ||||
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(524\) | −24.4222 | −1.06689 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.3305 | −0.581239 | ||||||||
\(527\) | 33.2111 | 1.44670 | ||||||||
\(528\) | 0.908327 | 0.0395299 | ||||||||
\(529\) | 15.5778 | 0.677295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.6056 | −0.460242 | ||||||||
\(532\) | −21.8167 | −0.945872 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 18.0000 | 0.778936 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 46.8167 | 2.02217 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.39445 | 0.318797 | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.4222 | −1.35095 | −0.675473 | − | 0.737385i | \(-0.736061\pi\) | ||||
−0.675473 | + | 0.737385i | \(0.736061\pi\) | |||||||
\(542\) | 61.2666 | 2.63163 | ||||||||
\(543\) | −12.6056 | −0.540956 | ||||||||
\(544\) | −24.4222 | −1.04709 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.00000 | −0.256776 | ||||||||
\(547\) | 29.6056 | 1.26584 | 0.632921 | − | 0.774216i | \(-0.281856\pi\) | ||||
0.632921 | + | 0.774216i | \(0.281856\pi\) | |||||||
\(548\) | 10.6056 | 0.453047 | ||||||||
\(549\) | −1.21110 | −0.0516886 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −50.2389 | −2.14025 | ||||||||
\(552\) | 18.6333 | 0.793086 | ||||||||
\(553\) | 14.8167 | 0.630068 | ||||||||
\(554\) | −23.0278 | −0.978356 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 62.8444 | 2.66520 | ||||||||
\(557\) | −11.2389 | −0.476206 | −0.238103 | − | 0.971240i | \(-0.576526\pi\) | ||||
−0.238103 | + | 0.971240i | \(0.576526\pi\) | |||||||
\(558\) | 16.6056 | 0.702969 | ||||||||
\(559\) | −25.0278 | −1.05856 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.8167 | −0.583340 | ||||||||
\(562\) | 2.72498 | 0.114946 | ||||||||
\(563\) | −15.2111 | −0.641072 | −0.320536 | − | 0.947236i | \(-0.603863\pi\) | ||||
−0.320536 | + | 0.947236i | \(0.603863\pi\) | |||||||
\(564\) | 35.0278 | 1.47493 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −31.3944 | −1.31961 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 9.00000 | 0.377632 | ||||||||
\(569\) | −1.18335 | −0.0496085 | −0.0248042 | − | 0.999692i | \(-0.507896\pi\) | ||||
−0.0248042 | + | 0.999692i | \(0.507896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.60555 | −0.234585 | −0.117293 | − | 0.993097i | \(-0.537422\pi\) | ||||
−0.117293 | + | 0.993097i | \(0.537422\pi\) | |||||||
\(572\) | −25.8167 | −1.07945 | ||||||||
\(573\) | 2.78890 | 0.116508 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.8167 | −0.534027 | ||||||||
\(577\) | −30.6056 | −1.27413 | −0.637063 | − | 0.770812i | \(-0.719851\pi\) | ||||
−0.637063 | + | 0.770812i | \(0.719851\pi\) | |||||||
\(578\) | −9.69722 | −0.403351 | ||||||||
\(579\) | 8.21110 | 0.341242 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.21110 | −0.133219 | ||||||||
\(582\) | 1.81665 | 0.0753027 | ||||||||
\(583\) | 9.63331 | 0.398971 | ||||||||
\(584\) | 1.81665 | 0.0751737 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.4222 | 1.00887 | ||||||||
\(587\) | −37.8167 | −1.56086 | −0.780430 | − | 0.625243i | \(-0.785000\pi\) | ||||
−0.780430 | + | 0.625243i | \(0.785000\pi\) | |||||||
\(588\) | −3.30278 | −0.136204 | ||||||||
\(589\) | −47.6333 | −1.96270 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.8167 | 0.691745 | ||||||||
\(592\) | 1.27502 | 0.0524030 | ||||||||
\(593\) | −27.6333 | −1.13476 | −0.567382 | − | 0.823455i | \(-0.692044\pi\) | ||||
−0.567382 | + | 0.823455i | \(0.692044\pi\) | |||||||
\(594\) | −6.90833 | −0.283452 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −54.1472 | −2.21796 | ||||||||
\(597\) | −8.00000 | −0.327418 | ||||||||
\(598\) | −37.2666 | −1.52395 | ||||||||
\(599\) | 5.78890 | 0.236528 | 0.118264 | − | 0.992982i | \(-0.462267\pi\) | ||||
0.118264 | + | 0.992982i | \(0.462267\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2111 | 0.702056 | 0.351028 | − | 0.936365i | \(-0.385832\pi\) | ||||
0.351028 | + | 0.936365i | \(0.385832\pi\) | |||||||
\(602\) | −22.1194 | −0.901521 | ||||||||
\(603\) | −15.6056 | −0.635507 | ||||||||
\(604\) | 22.5139 | 0.916077 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 38.2389 | 1.55335 | ||||||||
\(607\) | 23.8167 | 0.966688 | 0.483344 | − | 0.875430i | \(-0.339422\pi\) | ||||
0.483344 | + | 0.875430i | \(0.339422\pi\) | |||||||
\(608\) | 35.0278 | 1.42056 | ||||||||
\(609\) | −7.60555 | −0.308192 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.6333 | −1.11792 | ||||||||
\(612\) | −15.2111 | −0.614872 | ||||||||
\(613\) | 49.4222 | 1.99614 | 0.998072 | − | 0.0620663i | \(-0.0197690\pi\) | ||||
0.998072 | + | 0.0620663i | \(0.0197690\pi\) | |||||||
\(614\) | −19.8167 | −0.799735 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.00000 | −0.362620 | ||||||||
\(617\) | −22.8167 | −0.918564 | −0.459282 | − | 0.888291i | \(-0.651893\pi\) | ||||
−0.459282 | + | 0.888291i | \(0.651893\pi\) | |||||||
\(618\) | −8.78890 | −0.353541 | ||||||||
\(619\) | −2.60555 | −0.104726 | −0.0523630 | − | 0.998628i | \(-0.516675\pi\) | ||||
−0.0523630 | + | 0.998628i | \(0.516675\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.21110 | −0.249243 | ||||||||
\(622\) | −31.8167 | −1.27573 | ||||||||
\(623\) | −7.81665 | −0.313168 | ||||||||
\(624\) | −0.788897 | −0.0315812 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −54.8444 | −2.19202 | ||||||||
\(627\) | 19.8167 | 0.791401 | ||||||||
\(628\) | −47.6333 | −1.90078 | ||||||||
\(629\) | −19.3944 | −0.773307 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0278 | 0.876911 | 0.438456 | − | 0.898753i | \(-0.355526\pi\) | ||||
0.438456 | + | 0.898753i | \(0.355526\pi\) | |||||||
\(632\) | 44.4500 | 1.76812 | ||||||||
\(633\) | −26.4222 | −1.05019 | ||||||||
\(634\) | −37.7527 | −1.49935 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.6056 | 0.420537 | ||||||||
\(637\) | 2.60555 | 0.103236 | ||||||||
\(638\) | −52.5416 | −2.08014 | ||||||||
\(639\) | −3.00000 | −0.118678 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.8167 | 0.901204 | 0.450602 | − | 0.892725i | \(-0.351209\pi\) | ||||
0.450602 | + | 0.892725i | \(0.351209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.4222 | −1.51522 | −0.757612 | − | 0.652705i | \(-0.773634\pi\) | ||||
−0.757612 | + | 0.652705i | \(0.773634\pi\) | |||||||
\(644\) | −20.5139 | −0.808360 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 70.0555 | 2.75630 | ||||||||
\(647\) | −6.00000 | −0.235884 | −0.117942 | − | 0.993020i | \(-0.537630\pi\) | ||||
−0.117942 | + | 0.993020i | \(0.537630\pi\) | |||||||
\(648\) | −3.00000 | −0.117851 | ||||||||
\(649\) | 31.8167 | 1.24891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.21110 | −0.282625 | ||||||||
\(652\) | −56.8444 | −2.22620 | ||||||||
\(653\) | 3.21110 | 0.125660 | 0.0628301 | − | 0.998024i | \(-0.479987\pi\) | ||||
0.0628301 | + | 0.998024i | \(0.479987\pi\) | |||||||
\(654\) | 5.09167 | 0.199100 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.605551 | −0.0236248 | ||||||||
\(658\) | −24.4222 | −0.952077 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.1833 | −0.785041 | −0.392521 | − | 0.919743i | \(-0.628397\pi\) | ||||
−0.392521 | + | 0.919743i | \(0.628397\pi\) | |||||||
\(662\) | 48.9083 | 1.90088 | ||||||||
\(663\) | 12.0000 | 0.466041 | ||||||||
\(664\) | −9.63331 | −0.373845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.69722 | −0.375760 | ||||||||
\(667\) | −47.2389 | −1.82910 | ||||||||
\(668\) | 56.2389 | 2.17595 | ||||||||
\(669\) | 15.3944 | 0.595184 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.63331 | 0.140262 | ||||||||
\(672\) | 5.30278 | 0.204559 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | −16.6056 | −0.639622 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.5139 | −0.788995 | ||||||||
\(677\) | 8.78890 | 0.337785 | 0.168892 | − | 0.985634i | \(-0.445981\pi\) | ||||
0.168892 | + | 0.985634i | \(0.445981\pi\) | |||||||
\(678\) | 24.9083 | 0.956599 | ||||||||
\(679\) | −0.788897 | −0.0302751 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.6056 | 0.866247 | ||||||||
\(682\) | −49.8167 | −1.90758 | ||||||||
\(683\) | 18.6333 | 0.712984 | 0.356492 | − | 0.934298i | \(-0.383973\pi\) | ||||
0.356492 | + | 0.934298i | \(0.383973\pi\) | |||||||
\(684\) | 21.8167 | 0.834181 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.30278 | 0.0879204 | ||||||||
\(687\) | 7.21110 | 0.275121 | ||||||||
\(688\) | −2.90833 | −0.110879 | ||||||||
\(689\) | −8.36669 | −0.318746 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.2111 | 1.56774 | 0.783872 | − | 0.620922i | \(-0.213242\pi\) | ||||
0.783872 | + | 0.620922i | \(0.213242\pi\) | |||||||
\(692\) | 25.8167 | 0.981402 | ||||||||
\(693\) | 3.00000 | 0.113961 | ||||||||
\(694\) | 69.5694 | 2.64082 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −22.8167 | −0.864863 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −72.4222 | −2.74122 | ||||||||
\(699\) | −1.18335 | −0.0447583 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.7889 | −0.785186 | −0.392593 | − | 0.919712i | \(-0.628422\pi\) | ||||
−0.392593 | + | 0.919712i | \(0.628422\pi\) | |||||||
\(702\) | 6.00000 | 0.226455 | ||||||||
\(703\) | 27.8167 | 1.04912 | ||||||||
\(704\) | 38.4500 | 1.44914 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −69.0833 | −2.59998 | ||||||||
\(707\) | −16.6056 | −0.624516 | ||||||||
\(708\) | 35.0278 | 1.31642 | ||||||||
\(709\) | −34.8444 | −1.30861 | −0.654305 | − | 0.756231i | \(-0.727039\pi\) | ||||
−0.654305 | + | 0.756231i | \(0.727039\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.8167 | −0.555668 | ||||||||
\(712\) | −23.4500 | −0.878824 | ||||||||
\(713\) | −44.7889 | −1.67736 | ||||||||
\(714\) | 10.6056 | 0.396903 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.7889 | −0.552301 | ||||||||
\(718\) | −56.7250 | −2.11696 | ||||||||
\(719\) | 26.7889 | 0.999057 | 0.499529 | − | 0.866297i | \(-0.333507\pi\) | ||||
0.499529 | + | 0.866297i | \(0.333507\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.81665 | 0.142140 | ||||||||
\(722\) | −56.7250 | −2.11109 | ||||||||
\(723\) | −9.39445 | −0.349383 | ||||||||
\(724\) | 41.6333 | 1.54729 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.60555 | −0.170928 | ||||||||
\(727\) | 23.3944 | 0.867652 | 0.433826 | − | 0.900997i | \(-0.357163\pi\) | ||||
0.433826 | + | 0.900997i | \(0.357163\pi\) | |||||||
\(728\) | 7.81665 | 0.289704 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44.2389 | 1.63623 | ||||||||
\(732\) | 4.00000 | 0.147844 | ||||||||
\(733\) | −20.0000 | −0.738717 | −0.369358 | − | 0.929287i | \(-0.620423\pi\) | ||||
−0.369358 | + | 0.929287i | \(0.620423\pi\) | |||||||
\(734\) | 33.2111 | 1.22584 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 32.9361 | 1.21404 | ||||||||
\(737\) | 46.8167 | 1.72451 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.18335 | 0.117101 | 0.0585506 | − | 0.998284i | \(-0.481352\pi\) | ||||
0.0585506 | + | 0.998284i | \(0.481352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.2111 | −0.632266 | ||||||||
\(742\) | −7.39445 | −0.271459 | ||||||||
\(743\) | 27.6333 | 1.01377 | 0.506884 | − | 0.862014i | \(-0.330797\pi\) | ||||
0.506884 | + | 0.862014i | \(0.330797\pi\) | |||||||
\(744\) | −21.6333 | −0.793116 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.30278 | −0.0843106 | ||||||||
\(747\) | 3.21110 | 0.117488 | ||||||||
\(748\) | 45.6333 | 1.66852 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.366692 | −0.0133808 | −0.00669040 | − | 0.999978i | \(-0.502130\pi\) | ||||
−0.00669040 | + | 0.999978i | \(0.502130\pi\) | |||||||
\(752\) | −3.21110 | −0.117097 | ||||||||
\(753\) | 13.8167 | 0.503507 | ||||||||
\(754\) | 45.6333 | 1.66187 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.30278 | 0.120121 | ||||||||
\(757\) | −41.0000 | −1.49017 | −0.745085 | − | 0.666969i | \(-0.767591\pi\) | ||||
−0.745085 | + | 0.666969i | \(0.767591\pi\) | |||||||
\(758\) | 34.1194 | 1.23927 | ||||||||
\(759\) | 18.6333 | 0.676346 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.6333 | −1.00171 | −0.500853 | − | 0.865532i | \(-0.666980\pi\) | ||||
−0.500853 | + | 0.865532i | \(0.666980\pi\) | |||||||
\(762\) | −29.5139 | −1.06917 | ||||||||
\(763\) | −2.21110 | −0.0800473 | ||||||||
\(764\) | −9.21110 | −0.333246 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −60.4222 | −2.18314 | ||||||||
\(767\) | −27.6333 | −0.997781 | ||||||||
\(768\) | 17.9083 | 0.646211 | ||||||||
\(769\) | −31.6333 | −1.14073 | −0.570363 | − | 0.821393i | \(-0.693198\pi\) | ||||
−0.570363 | + | 0.821393i | \(0.693198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.6333 | −0.779105 | ||||||||
\(772\) | −27.1194 | −0.976050 | ||||||||
\(773\) | −6.00000 | −0.215805 | −0.107903 | − | 0.994161i | \(-0.534413\pi\) | ||||
−0.107903 | + | 0.994161i | \(0.534413\pi\) | |||||||
\(774\) | 22.1194 | 0.795066 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.36669 | −0.0849593 | ||||||||
\(777\) | 4.21110 | 0.151072 | ||||||||
\(778\) | 66.3583 | 2.37906 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | 0.322045 | ||||||||
\(782\) | 65.8722 | 2.35558 | ||||||||
\(783\) | 7.60555 | 0.271800 | ||||||||
\(784\) | 0.302776 | 0.0108134 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.0278 | −0.607360 | ||||||||
\(787\) | −28.2389 | −1.00661 | −0.503303 | − | 0.864110i | \(-0.667882\pi\) | ||||
−0.503303 | + | 0.864110i | \(0.667882\pi\) | |||||||
\(788\) | −55.5416 | −1.97859 | ||||||||
\(789\) | −5.78890 | −0.206090 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.8167 | −0.384596 | ||||||||
\(792\) | 9.00000 | 0.319801 | ||||||||
\(793\) | −3.15559 | −0.112058 | ||||||||
\(794\) | 4.60555 | 0.163445 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.4222 | 0.936510 | ||||||||
\(797\) | 29.4500 | 1.04317 | 0.521586 | − | 0.853199i | \(-0.325341\pi\) | ||||
0.521586 | + | 0.853199i | \(0.325341\pi\) | |||||||
\(798\) | −15.2111 | −0.538467 | ||||||||
\(799\) | 48.8444 | 1.72799 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.81665 | 0.276188 | ||||||||
\(802\) | 38.7250 | 1.36743 | ||||||||
\(803\) | 1.81665 | 0.0641083 | ||||||||
\(804\) | 51.5416 | 1.81773 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 43.2666 | 1.52400 | ||||||||
\(807\) | 3.21110 | 0.113036 | ||||||||
\(808\) | −49.8167 | −1.75254 | ||||||||
\(809\) | 32.4500 | 1.14088 | 0.570440 | − | 0.821339i | \(-0.306773\pi\) | ||||
0.570440 | + | 0.821339i | \(0.306773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.8444 | 0.521258 | 0.260629 | − | 0.965439i | \(-0.416070\pi\) | ||||
0.260629 | + | 0.965439i | \(0.416070\pi\) | |||||||
\(812\) | 25.1194 | 0.881519 | ||||||||
\(813\) | 26.6056 | 0.933097 | ||||||||
\(814\) | 29.0917 | 1.01966 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.39445 | 0.0488155 | ||||||||
\(817\) | −63.4500 | −2.21983 | ||||||||
\(818\) | 27.2111 | 0.951414 | ||||||||
\(819\) | −2.60555 | −0.0910453 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.2666 | 1.71942 | 0.859708 | − | 0.510785i | \(-0.170645\pi\) | ||||
0.859708 | + | 0.510785i | \(0.170645\pi\) | |||||||
\(822\) | 7.39445 | 0.257911 | ||||||||
\(823\) | −24.8167 | −0.865054 | −0.432527 | − | 0.901621i | \(-0.642378\pi\) | ||||
−0.432527 | + | 0.901621i | \(0.642378\pi\) | |||||||
\(824\) | 11.4500 | 0.398878 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.4222 | −0.849757 | ||||||||
\(827\) | 30.6333 | 1.06522 | 0.532612 | − | 0.846359i | \(-0.321210\pi\) | ||||
0.532612 | + | 0.846359i | \(0.321210\pi\) | |||||||
\(828\) | 20.5139 | 0.712907 | ||||||||
\(829\) | −0.238859 | −0.00829591 | −0.00414796 | − | 0.999991i | \(-0.501320\pi\) | ||||
−0.00414796 | + | 0.999991i | \(0.501320\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | −0.346896 | ||||||||
\(832\) | −33.3944 | −1.15774 | ||||||||
\(833\) | −4.60555 | −0.159573 | ||||||||
\(834\) | 43.8167 | 1.51725 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −65.4500 | −2.26363 | ||||||||
\(837\) | 7.21110 | 0.249252 | ||||||||
\(838\) | −13.8167 | −0.477288 | ||||||||
\(839\) | −22.1833 | −0.765854 | −0.382927 | − | 0.923779i | \(-0.625084\pi\) | ||||
−0.382927 | + | 0.923779i | \(0.625084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8444 | 0.994635 | ||||||||
\(842\) | 23.5139 | 0.810342 | ||||||||
\(843\) | 1.18335 | 0.0407566 | ||||||||
\(844\) | 87.2666 | 3.00384 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 24.4222 | 0.839653 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | −0.972244 | −0.0333870 | ||||||||
\(849\) | −13.6333 | −0.467894 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.1556 | 0.896602 | ||||||||
\(852\) | 9.90833 | 0.339454 | ||||||||
\(853\) | 6.78890 | 0.232447 | 0.116224 | − | 0.993223i | \(-0.462921\pi\) | ||||
0.116224 | + | 0.993223i | \(0.462921\pi\) | |||||||
\(854\) | −2.78890 | −0.0954341 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.6333 | −0.943936 | −0.471968 | − | 0.881616i | \(-0.656456\pi\) | ||||
−0.471968 | + | 0.881616i | \(0.656456\pi\) | |||||||
\(858\) | −18.0000 | −0.614510 | ||||||||
\(859\) | −49.6333 | −1.69347 | −0.846733 | − | 0.532018i | \(-0.821434\pi\) | ||||
−0.846733 | + | 0.532018i | \(0.821434\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.8444 | −0.437482 | ||||||||
\(863\) | −5.36669 | −0.182684 | −0.0913422 | − | 0.995820i | \(-0.529116\pi\) | ||||
−0.0913422 | + | 0.995820i | \(0.529116\pi\) | |||||||
\(864\) | −5.30278 | −0.180404 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −85.6888 | −2.91182 | ||||||||
\(867\) | −4.21110 | −0.143017 | ||||||||
\(868\) | 23.8167 | 0.808390 | ||||||||
\(869\) | 44.4500 | 1.50786 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.6611 | −1.37775 | ||||||||
\(872\) | −6.63331 | −0.224632 | ||||||||
\(873\) | 0.788897 | 0.0267001 | ||||||||
\(874\) | −94.4777 | −3.19576 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | 22.0000 | 0.742887 | 0.371444 | − | 0.928456i | \(-0.378863\pi\) | ||||
0.371444 | + | 0.928456i | \(0.378863\pi\) | |||||||
\(878\) | −15.2111 | −0.513350 | ||||||||
\(879\) | 10.6056 | 0.357716 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.6333 | 1.13313 | 0.566567 | − | 0.824015i | \(-0.308271\pi\) | ||||
0.566567 | + | 0.824015i | \(0.308271\pi\) | |||||||
\(882\) | −2.30278 | −0.0775385 | ||||||||
\(883\) | −15.6056 | −0.525169 | −0.262584 | − | 0.964909i | \(-0.584575\pi\) | ||||
−0.262584 | + | 0.964909i | \(0.584575\pi\) | |||||||
\(884\) | −39.6333 | −1.33301 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.0000 | 1.20944 | ||||||||
\(887\) | 14.7889 | 0.496563 | 0.248281 | − | 0.968688i | \(-0.420134\pi\) | ||||
0.248281 | + | 0.968688i | \(0.420134\pi\) | |||||||
\(888\) | 12.6333 | 0.423946 | ||||||||
\(889\) | 12.8167 | 0.429857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | −50.8444 | −1.70240 | ||||||||
\(893\) | −70.0555 | −2.34432 | ||||||||
\(894\) | −37.7527 | −1.26264 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18.9083 | −0.631683 | ||||||||
\(897\) | −16.1833 | −0.540346 | ||||||||
\(898\) | 80.1749 | 2.67547 | ||||||||
\(899\) | 54.8444 | 1.82916 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.7889 | 0.492690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.60555 | −0.319653 | ||||||||
\(904\) | −32.4500 | −1.07927 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 15.6972 | 0.521505 | ||||||||
\(907\) | 13.2111 | 0.438667 | 0.219334 | − | 0.975650i | \(-0.429612\pi\) | ||||
0.219334 | + | 0.975650i | \(0.429612\pi\) | |||||||
\(908\) | −74.6611 | −2.47771 | ||||||||
\(909\) | 16.6056 | 0.550771 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0000 | 0.496972 | 0.248486 | − | 0.968635i | \(-0.420067\pi\) | ||||
0.248486 | + | 0.968635i | \(0.420067\pi\) | |||||||
\(912\) | −2.00000 | −0.0662266 | ||||||||
\(913\) | −9.63331 | −0.318816 | ||||||||
\(914\) | −8.72498 | −0.288597 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.8167 | −0.786924 | ||||||||
\(917\) | 7.39445 | 0.244186 | ||||||||
\(918\) | −10.6056 | −0.350035 | ||||||||
\(919\) | −17.6056 | −0.580754 | −0.290377 | − | 0.956912i | \(-0.593781\pi\) | ||||
−0.290377 | + | 0.956912i | \(0.593781\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.60555 | −0.283563 | ||||||||
\(922\) | 60.4222 | 1.98990 | ||||||||
\(923\) | −7.81665 | −0.257288 | ||||||||
\(924\) | −9.90833 | −0.325960 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 39.6333 | 1.30243 | ||||||||
\(927\) | −3.81665 | −0.125355 | ||||||||
\(928\) | −40.3305 | −1.32391 | ||||||||
\(929\) | −20.2389 | −0.664015 | −0.332008 | − | 0.943277i | \(-0.607726\pi\) | ||||
−0.332008 | + | 0.943277i | \(0.607726\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.60555 | 0.216488 | ||||||||
\(932\) | 3.90833 | 0.128022 | ||||||||
\(933\) | −13.8167 | −0.452337 | ||||||||
\(934\) | −0.972244 | −0.0318128 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.81665 | −0.255495 | ||||||||
\(937\) | 56.4777 | 1.84505 | 0.922523 | − | 0.385941i | \(-0.126123\pi\) | ||||
0.922523 | + | 0.385941i | \(0.126123\pi\) | |||||||
\(938\) | −35.9361 | −1.17335 | ||||||||
\(939\) | −23.8167 | −0.777227 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.00000 | 0.195594 | 0.0977972 | − | 0.995206i | \(-0.468820\pi\) | ||||
0.0977972 | + | 0.995206i | \(0.468820\pi\) | |||||||
\(942\) | −33.2111 | −1.08208 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −3.21110 | −0.104512 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −66.3583 | −2.15749 | ||||||||
\(947\) | 0.844410 | 0.0274396 | 0.0137198 | − | 0.999906i | \(-0.495633\pi\) | ||||
0.0137198 | + | 0.999906i | \(0.495633\pi\) | |||||||
\(948\) | 48.9361 | 1.58937 | ||||||||
\(949\) | −1.57779 | −0.0512174 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.3944 | −0.531626 | ||||||||
\(952\) | −13.8167 | −0.447800 | ||||||||
\(953\) | 13.6056 | 0.440727 | 0.220364 | − | 0.975418i | \(-0.429276\pi\) | ||||
0.220364 | + | 0.975418i | \(0.429276\pi\) | |||||||
\(954\) | 7.39445 | 0.239404 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 48.8444 | 1.57974 | ||||||||
\(957\) | −22.8167 | −0.737558 | ||||||||
\(958\) | −79.6888 | −2.57463 | ||||||||
\(959\) | −3.21110 | −0.103692 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.0000 | 0.677419 | ||||||||
\(962\) | −25.2666 | −0.814628 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31.0278 | 0.999337 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.3028 | −0.460184 | ||||||||
\(967\) | 40.8444 | 1.31347 | 0.656734 | − | 0.754122i | \(-0.271937\pi\) | ||||
0.656734 | + | 0.754122i | \(0.271937\pi\) | |||||||
\(968\) | 6.00000 | 0.192847 | ||||||||
\(969\) | 30.4222 | 0.977302 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.8722 | 1.72884 | 0.864420 | − | 0.502770i | \(-0.167686\pi\) | ||||
0.864420 | + | 0.502770i | \(0.167686\pi\) | |||||||
\(972\) | −3.30278 | −0.105937 | ||||||||
\(973\) | −19.0278 | −0.610002 | ||||||||
\(974\) | −47.9361 | −1.53597 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.366692 | −0.0117375 | ||||||||
\(977\) | 2.02776 | 0.0648737 | 0.0324368 | − | 0.999474i | \(-0.489673\pi\) | ||||
0.0324368 | + | 0.999474i | \(0.489673\pi\) | |||||||
\(978\) | −39.6333 | −1.26733 | ||||||||
\(979\) | −23.4500 | −0.749464 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.21110 | 0.0705951 | ||||||||
\(982\) | 6.90833 | 0.220454 | ||||||||
\(983\) | −40.0555 | −1.27757 | −0.638786 | − | 0.769384i | \(-0.720563\pi\) | ||||
−0.638786 | + | 0.769384i | \(0.720563\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −80.6611 | −2.56877 | ||||||||
\(987\) | −10.6056 | −0.337578 | ||||||||
\(988\) | 56.8444 | 1.80846 | ||||||||
\(989\) | −59.6611 | −1.89711 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.0278 | 1.46212 | 0.731060 | − | 0.682313i | \(-0.239026\pi\) | ||||
0.731060 | + | 0.682313i | \(0.239026\pi\) | |||||||
\(992\) | −38.2389 | −1.21408 | ||||||||
\(993\) | 21.2389 | 0.673995 | ||||||||
\(994\) | −6.90833 | −0.219119 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.6056 | −0.336050 | ||||||||
\(997\) | 15.4500 | 0.489305 | 0.244653 | − | 0.969611i | \(-0.421326\pi\) | ||||
0.244653 | + | 0.969611i | \(0.421326\pi\) | |||||||
\(998\) | 64.4777 | 2.04101 | ||||||||
\(999\) | −4.21110 | −0.133233 |
(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 | 525.2.a.f.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1575.2.a.t.1.2 | 2 | |||
4.3 | odd | 2 | 8400.2.a.df.1.2 | 2 | |||
5.2 | odd | 4 | 525.2.d.d.274.1 | 4 | |||
5.3 | odd | 4 | 525.2.d.d.274.4 | 4 | |||
5.4 | even | 2 | 525.2.a.h.1.2 | yes | 2 | ||
7.6 | odd | 2 | 3675.2.a.w.1.1 | 2 | |||
15.2 | even | 4 | 1575.2.d.g.1324.4 | 4 | |||
15.8 | even | 4 | 1575.2.d.g.1324.1 | 4 | |||
15.14 | odd | 2 | 1575.2.a.o.1.1 | 2 | |||
20.19 | odd | 2 | 8400.2.a.cw.1.1 | 2 | |||
35.34 | odd | 2 | 3675.2.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
525.2.a.h.1.2 | yes | 2 | 5.4 | even | 2 | ||
525.2.d.d.274.1 | 4 | 5.2 | odd | 4 | |||
525.2.d.d.274.4 | 4 | 5.3 | odd | 4 | |||
1575.2.a.o.1.1 | 2 | 15.14 | odd | 2 | |||
1575.2.a.t.1.2 | 2 | 3.2 | odd | 2 | |||
1575.2.d.g.1324.1 | 4 | 15.8 | even | 4 | |||
1575.2.d.g.1324.4 | 4 | 15.2 | even | 4 | |||
3675.2.a.w.1.1 | 2 | 7.6 | odd | 2 | |||
3675.2.a.bb.1.2 | 2 | 35.34 | odd | 2 | |||
8400.2.a.cw.1.1 | 2 | 20.19 | odd | 2 | |||
8400.2.a.df.1.2 | 2 | 4.3 | odd | 2 |