Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 115) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.291367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | 3.14073 | 1.81330 | 0.906651 | − | 0.421881i | \(-0.138630\pi\) | ||||
0.906651 | + | 0.421881i | \(0.138630\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.20647 | −0.456004 | −0.228002 | − | 0.973661i | \(-0.573219\pi\) | ||||
−0.228002 | + | 0.973661i | \(0.573219\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.86420 | 2.28807 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.65773 | −1.10285 | −0.551423 | − | 0.834226i | \(-0.685915\pi\) | ||||
−0.551423 | + | 0.834226i | \(0.685915\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.859268 | −0.238318 | −0.119159 | − | 0.992875i | \(-0.538020\pi\) | ||||
−0.119159 | + | 0.992875i | \(0.538020\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.72347 | −1.63068 | −0.815340 | − | 0.578982i | \(-0.803450\pi\) | ||||
−0.815340 | + | 0.578982i | \(0.803450\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.51699 | 0.348022 | 0.174011 | − | 0.984744i | \(-0.444327\pi\) | ||||
0.174011 | + | 0.984744i | \(0.444327\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.78921 | −0.826873 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.1364 | 2.33565 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.548747 | 0.101900 | 0.0509498 | − | 0.998701i | \(-0.483775\pi\) | ||||
0.0509498 | + | 0.998701i | \(0.483775\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.99568 | 1.07686 | 0.538428 | − | 0.842672i | \(-0.319018\pi\) | ||||
0.538428 | + | 0.842672i | \(0.319018\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.4879 | −1.99979 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.04100 | −0.335539 | −0.167770 | − | 0.985826i | \(-0.553656\pi\) | ||||
−0.167770 | + | 0.985826i | \(0.553656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.69873 | −0.432143 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.14998 | −1.11664 | −0.558320 | − | 0.829626i | \(-0.688554\pi\) | ||||
−0.558320 | + | 0.829626i | \(0.688554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0799 | −1.53717 | −0.768587 | − | 0.639745i | \(-0.779040\pi\) | ||||
−0.768587 | + | 0.639745i | \(0.779040\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.17040 | −1.33764 | −0.668820 | − | 0.743424i | \(-0.733200\pi\) | ||||
−0.668820 | + | 0.743424i | \(0.733200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.54442 | −0.792061 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −21.1166 | −2.95692 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.37896 | −0.738857 | −0.369428 | − | 0.929259i | \(-0.620446\pi\) | ||||
−0.369428 | + | 0.929259i | \(0.620446\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.76447 | 0.631070 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.582734 | 0.0758655 | 0.0379327 | − | 0.999280i | \(-0.487923\pi\) | ||||
0.0379327 | + | 0.999280i | \(0.487923\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.83244 | −1.13088 | −0.565439 | − | 0.824790i | \(-0.691293\pi\) | ||||
−0.565439 | + | 0.824790i | \(0.691293\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.28146 | −1.04337 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.20647 | −0.391733 | −0.195866 | − | 0.980631i | \(-0.562752\pi\) | ||||
−0.195866 | + | 0.980631i | \(0.562752\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.14073 | −0.378100 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.5784 | 1.49278 | 0.746391 | − | 0.665507i | \(-0.231785\pi\) | ||||
0.746391 | + | 0.665507i | \(0.231785\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.62597 | −1.00959 | −0.504797 | − | 0.863238i | \(-0.668433\pi\) | ||||
−0.504797 | + | 0.863238i | \(0.668433\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.41294 | 0.502902 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0700619 | −0.00788258 | −0.00394129 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394129 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.5246 | 1.94718 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.74197 | 0.740027 | 0.370014 | − | 0.929026i | \(-0.379353\pi\) | ||||
0.370014 | + | 0.929026i | \(0.379353\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.72347 | 0.184775 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.96393 | 0.526175 | 0.263088 | − | 0.964772i | \(-0.415259\pi\) | ||||
0.263088 | + | 0.964772i | \(0.415259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.03668 | 0.108674 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.8308 | 1.95266 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3380 | −1.15119 | −0.575597 | − | 0.817733i | \(-0.695230\pi\) | ||||
−0.575597 | + | 0.817733i | \(0.695230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25.1074 | −2.52338 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.44693 | 0.342983 | 0.171491 | − | 0.985186i | \(-0.445141\pi\) | ||||
0.171491 | + | 0.985186i | \(0.445141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.13641 | 0.900237 | 0.450119 | − | 0.892969i | \(-0.351382\pi\) | ||||
0.450119 | + | 0.892969i | \(0.351382\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.24539 | 0.893786 | 0.446893 | − | 0.894588i | \(-0.352531\pi\) | ||||
0.446893 | + | 0.894588i | \(0.352531\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.64847 | 0.157895 | 0.0789476 | − | 0.996879i | \(-0.474844\pi\) | ||||
0.0789476 | + | 0.996879i | \(0.474844\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.41025 | −0.608434 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.20647 | −0.113495 | −0.0567477 | − | 0.998389i | \(-0.518073\pi\) | ||||
−0.0567477 | + | 0.998389i | \(0.518073\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.89819 | −0.545287 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.11167 | 0.743596 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.37896 | 0.216269 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.4562 | −2.02481 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3542 | 1.36247 | 0.681233 | − | 0.732066i | \(-0.261444\pi\) | ||||
0.681233 | + | 0.732066i | \(0.261444\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −31.6583 | −2.78736 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.0734 | −1.14223 | −0.571113 | − | 0.820872i | \(-0.693488\pi\) | ||||
−0.571113 | + | 0.820872i | \(0.693488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.83021 | −0.158699 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.1840 | 1.12638 | 0.563191 | − | 0.826327i | \(-0.309573\pi\) | ||||
0.563191 | + | 0.826327i | \(0.309573\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1160 | 1.19730 | 0.598652 | − | 0.801010i | \(-0.295703\pi\) | ||||
0.598652 | + | 0.801010i | \(0.295703\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.8018 | −2.42555 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.14297 | 0.262828 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.4136 | −1.43625 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.54442 | −0.536140 | −0.268070 | − | 0.963399i | \(-0.586386\pi\) | ||||
−0.268070 | + | 0.963399i | \(0.586386\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.61672 | −0.212946 | −0.106473 | − | 0.994316i | \(-0.533956\pi\) | ||||
−0.106473 | + | 0.994316i | \(0.533956\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −46.1512 | −3.73110 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.81394 | −0.703429 | −0.351715 | − | 0.936107i | \(-0.614401\pi\) | ||||
−0.351715 | + | 0.936107i | \(0.614401\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.8939 | −1.33977 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.20647 | 0.0950833 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.1747 | −0.796946 | −0.398473 | − | 0.917180i | \(-0.630460\pi\) | ||||
−0.398473 | + | 0.917180i | \(0.630460\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.6647 | −0.980027 | −0.490014 | − | 0.871715i | \(-0.663008\pi\) | ||||
−0.490014 | + | 0.871715i | \(0.663008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2617 | −0.943205 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.4129 | 0.796298 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.6901 | 1.19290 | 0.596448 | − | 0.802652i | \(-0.296578\pi\) | ||||
0.596448 | + | 0.802652i | \(0.296578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.83021 | 0.137567 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.39876 | 0.179292 | 0.0896460 | − | 0.995974i | \(-0.471426\pi\) | ||||
0.0896460 | + | 0.995974i | \(0.471426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.87122 | −0.733722 | −0.366861 | − | 0.930276i | \(-0.619567\pi\) | ||||
−0.366861 | + | 0.930276i | \(0.619567\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27.7403 | −2.05063 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.5926 | 1.79839 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.6422 | −1.06507 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.60617 | 0.695078 | 0.347539 | − | 0.937666i | \(-0.387017\pi\) | ||||
0.347539 | + | 0.937666i | \(0.387017\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.9709 | −1.79745 | −0.898724 | − | 0.438515i | \(-0.855505\pi\) | ||||
−0.898724 | + | 0.438515i | \(0.855505\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.92292 | 0.706979 | 0.353489 | − | 0.935439i | \(-0.384995\pi\) | ||||
0.353489 | + | 0.935439i | \(0.384995\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.01818 | −0.497506 | −0.248753 | − | 0.968567i | \(-0.580021\pi\) | ||||
−0.248753 | + | 0.968567i | \(0.580021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.0707 | −0.710330 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.662047 | −0.0464666 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.86420 | −0.477095 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.54875 | −0.383815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.44693 | −0.512668 | −0.256334 | − | 0.966588i | \(-0.582515\pi\) | ||||
−0.256334 | + | 0.966588i | \(0.582515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 39.5054 | 2.70687 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.23362 | −0.491050 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.0919 | −1.83070 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.77726 | 0.388620 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.2180 | −0.684245 | −0.342123 | − | 0.939655i | \(-0.611146\pi\) | ||||
−0.342123 | + | 0.939655i | \(0.611146\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.83291 | −0.387144 | −0.193572 | − | 0.981086i | \(-0.562007\pi\) | ||||
−0.193572 | + | 0.981086i | \(0.562007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.87061 | 0.387941 | 0.193970 | − | 0.981007i | \(-0.437863\pi\) | ||||
0.193970 | + | 0.981007i | \(0.437863\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.8599 | 0.911913 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.839462 | 0.0549950 | 0.0274975 | − | 0.999622i | \(-0.491246\pi\) | ||||
0.0274975 | + | 0.999622i | \(0.491246\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.220046 | −0.0142935 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3296 | 1.37970 | 0.689850 | − | 0.723953i | \(-0.257677\pi\) | ||||
0.689850 | + | 0.723953i | \(0.257677\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.7037 | −1.33364 | −0.666820 | − | 0.745219i | \(-0.732345\pi\) | ||||
−0.666820 | + | 0.745219i | \(0.732345\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.6309 | 1.19517 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.30350 | −0.0829400 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.1747 | 1.34189 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7290 | −1.49776 | −0.748881 | − | 0.662705i | \(-0.769408\pi\) | ||||
−0.748881 | + | 0.662705i | \(0.769408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.65773 | 0.229959 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.2481 | 1.13828 | 0.569142 | − | 0.822239i | \(-0.307275\pi\) | ||||
0.569142 | + | 0.822239i | \(0.307275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.46242 | 0.153007 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.76670 | 0.233153 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.8718 | 1.59532 | 0.797662 | − | 0.603104i | \(-0.206070\pi\) | ||||
0.797662 | + | 0.603104i | \(0.206070\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.5904 | 0.954115 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.34497 | 0.447831 | 0.223915 | − | 0.974609i | \(-0.428116\pi\) | ||||
0.223915 | + | 0.974609i | \(0.428116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.2278 | −1.83621 | −0.918105 | − | 0.396338i | \(-0.870281\pi\) | ||||
−0.918105 | + | 0.396338i | \(0.870281\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.25594 | 0.197059 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.50983 | −0.150801 | −0.0754005 | − | 0.997153i | \(-0.524024\pi\) | ||||
−0.0754005 | + | 0.997153i | \(0.524024\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 41.1555 | 2.46392 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4836 | −0.625400 | −0.312700 | − | 0.949852i | \(-0.601233\pi\) | ||||
−0.312700 | + | 0.949852i | \(0.601233\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.83946 | 0.228232 | 0.114116 | − | 0.993467i | \(-0.463596\pi\) | ||||
0.114116 | + | 0.993467i | \(0.463596\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.62626 | 0.509192 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.2050 | 1.65912 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35.6095 | −2.08746 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.544425 | −0.0318056 | −0.0159028 | − | 0.999874i | \(-0.505062\pi\) | ||||
−0.0159028 | + | 0.999874i | \(0.505062\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −44.3917 | −2.57587 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.859268 | 0.0496927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.1611 | 0.700957 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.8259 | 0.621931 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.1850 | 0.923729 | 0.461865 | − | 0.886950i | \(-0.347181\pi\) | ||||
0.461865 | + | 0.886950i | \(0.347181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.6950 | 1.63240 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.51923 | 0.426376 | 0.213188 | − | 0.977011i | \(-0.431615\pi\) | ||||
0.213188 | + | 0.977011i | \(0.431615\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.2475 | −1.42707 | −0.713536 | − | 0.700619i | \(-0.752907\pi\) | ||||
−0.713536 | + | 0.700619i | \(0.752907\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.4173 | 0.753589 | 0.376794 | − | 0.926297i | \(-0.377026\pi\) | ||||
0.376794 | + | 0.926297i | \(0.377026\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00716 | −0.112380 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.0373 | 1.62070 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.1995 | −0.567513 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.17741 | 0.286312 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.0638 | 0.609969 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.3748 | 1.33976 | 0.669880 | − | 0.742470i | \(-0.266346\pi\) | ||||
0.669880 | + | 0.742470i | \(0.266346\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.0099 | −0.767736 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.2454 | −1.04836 | −0.524182 | − | 0.851607i | \(-0.675629\pi\) | ||||
−0.524182 | + | 0.851607i | \(0.675629\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.78921 | −0.205801 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.9305 | −1.18761 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.1345 | 0.817186 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.51044 | −0.403181 | −0.201591 | − | 0.979470i | \(-0.564611\pi\) | ||||
−0.201591 | + | 0.979470i | \(0.564611\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.3208 | 0.659520 | 0.329760 | − | 0.944065i | \(-0.393032\pi\) | ||||
0.329760 | + | 0.944065i | \(0.393032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.4284 | −0.556628 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7333 | 0.624502 | 0.312251 | − | 0.950000i | \(-0.398917\pi\) | ||||
0.312251 | + | 0.950000i | \(0.398917\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.4766 | 1.34836 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.6879 | 0.986307 | 0.493154 | − | 0.869942i | \(-0.335844\pi\) | ||||
0.493154 | + | 0.869942i | \(0.335844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6987 | −0.878881 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.47167 | 0.392161 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.0103 | −1.20113 | −0.600564 | − | 0.799576i | \(-0.705057\pi\) | ||||
−0.600564 | + | 0.799576i | \(0.705057\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −49.0789 | −2.55495 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.48956 | 0.336921 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.7402 | −1.85056 | −0.925278 | − | 0.379290i | \(-0.876168\pi\) | ||||
−0.925278 | + | 0.379290i | \(0.876168\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.471520 | −0.0242845 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.65178 | −0.495779 | −0.247889 | − | 0.968788i | \(-0.579737\pi\) | ||||
−0.247889 | + | 0.968788i | \(0.579737\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 48.2235 | 2.47056 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.0954 | −1.28232 | −0.641158 | − | 0.767409i | \(-0.721546\pi\) | ||||
−0.641158 | + | 0.767409i | \(0.721546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −69.1906 | −3.51715 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.8259 | 0.853106 | 0.426553 | − | 0.904462i | \(-0.359728\pi\) | ||||
0.426553 | + | 0.904462i | \(0.359728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.72347 | 0.340020 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −41.0599 | −2.07120 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.8080 | −1.39564 | −0.697822 | − | 0.716272i | \(-0.745847\pi\) | ||||
−0.697822 | + | 0.716272i | \(0.745847\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.74820 | −0.287770 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.46483 | 0.0731500 | 0.0365750 | − | 0.999331i | \(-0.488355\pi\) | ||||
0.0365750 | + | 0.999331i | \(0.488355\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.15189 | −0.256634 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.46544 | 0.370048 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.514906 | 0.0254605 | 0.0127302 | − | 0.999919i | \(-0.495948\pi\) | ||||
0.0127302 | + | 0.999919i | \(0.495948\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.4073 | 2.04247 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.703052 | −0.0345949 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 44.3346 | 2.17107 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.65387 | 0.471622 | 0.235811 | − | 0.971799i | \(-0.424225\pi\) | ||||
0.235811 | + | 0.971799i | \(0.424225\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.2788 | 0.695905 | 0.347952 | − | 0.937512i | \(-0.386877\pi\) | ||||
0.347952 | + | 0.937512i | \(0.386877\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −62.9474 | −3.06061 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.6561 | 0.515685 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.87122 | 0.476587 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.71198 | −0.275136 | −0.137568 | − | 0.990492i | \(-0.543929\pi\) | ||||
−0.137568 | + | 0.990492i | \(0.543929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3302 | 1.45758 | 0.728789 | − | 0.684738i | \(-0.240083\pi\) | ||||
0.728789 | + | 0.684738i | \(0.240083\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.51699 | −0.0725676 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7579 | 0.942994 | 0.471497 | − | 0.881868i | \(-0.343714\pi\) | ||||
0.471497 | + | 0.881868i | \(0.343714\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −38.0580 | −1.81229 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.0643 | 0.763236 | 0.381618 | − | 0.924320i | \(-0.375367\pi\) | ||||
0.381618 | + | 0.924320i | \(0.375367\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.5543 | −0.972184 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.5881 | 1.34916 | 0.674579 | − | 0.738203i | \(-0.264325\pi\) | ||||
0.674579 | + | 0.738203i | \(0.264325\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.1527 | 1.23148 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.21842 | −0.386135 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.1209 | −0.473437 | −0.236718 | − | 0.971578i | \(-0.576072\pi\) | ||||
−0.236718 | + | 0.971578i | \(0.576072\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −81.5987 | −3.80870 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.6931 | 0.730901 | 0.365450 | − | 0.930831i | \(-0.380915\pi\) | ||||
0.365450 | + | 0.930831i | \(0.380915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9124 | 0.600089 | 0.300044 | − | 0.953925i | \(-0.402999\pi\) | ||||
0.300044 | + | 0.953925i | \(0.402999\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.10196 | −0.328640 | −0.164320 | − | 0.986407i | \(-0.552543\pi\) | ||||
−0.164320 | + | 0.986407i | \(0.552543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.86852 | 0.178632 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.6822 | −1.27553 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.8696 | 1.69527 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −36.9222 | −1.69055 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.7758 | −0.766506 | −0.383253 | − | 0.923643i | \(-0.625196\pi\) | ||||
−0.383253 | + | 0.923643i | \(0.625196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.75377 | 0.0799650 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.78921 | 0.172415 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.02488 | 0.318328 | 0.159164 | − | 0.987252i | \(-0.449120\pi\) | ||||
0.159164 | + | 0.987252i | \(0.449120\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.9561 | −1.44510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.1500 | −0.503192 | −0.251596 | − | 0.967832i | \(-0.580955\pi\) | ||||
−0.251596 | + | 0.967832i | \(0.580955\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.68948 | −0.166166 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.1755 | −0.680714 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.8347 | −0.664091 | −0.332046 | − | 0.943263i | \(-0.607739\pi\) | ||||
−0.332046 | + | 0.943263i | \(0.607739\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.7766 | −1.77709 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.10196 | −0.138310 | −0.0691548 | − | 0.997606i | \(-0.522030\pi\) | ||||
−0.0691548 | + | 0.997606i | \(0.522030\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −38.5106 | −1.71032 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.3353 | −0.989993 | −0.494996 | − | 0.868895i | \(-0.664831\pi\) | ||||
−0.494996 | + | 0.868895i | \(0.664831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.4070 | 0.460378 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.4109 | 0.812859 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.5428 | 1.47521 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 49.2784 | 2.16308 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.2147 | −0.622758 | −0.311379 | − | 0.950286i | \(-0.600791\pi\) | ||||
−0.311379 | + | 0.950286i | \(0.600791\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.09494 | 0.179059 | 0.0895297 | − | 0.995984i | \(-0.471464\pi\) | ||||
0.0895297 | + | 0.995984i | \(0.471464\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −40.3117 | −1.75601 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.14375 | 0.266115 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.53387 | 0.325111 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.2800 | 0.873521 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.6902 | 1.44846 | 0.724228 | − | 0.689560i | \(-0.242196\pi\) | ||||
0.724228 | + | 0.689560i | \(0.242196\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −31.0028 | −1.33046 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.9358 | −1.40823 | −0.704117 | − | 0.710084i | \(-0.748657\pi\) | ||||
−0.704117 | + | 0.710084i | \(0.748657\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −60.6277 | −2.58753 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.832445 | 0.0354633 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0845278 | 0.00359449 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.8337 | −0.882751 | −0.441375 | − | 0.897323i | \(-0.645509\pi\) | ||||
−0.441375 | + | 0.897323i | \(0.645509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.66135 | 0.366336 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 77.2387 | 3.26102 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.4368 | −1.28276 | −0.641380 | − | 0.767223i | \(-0.721638\pi\) | ||||
−0.641380 | + | 0.767223i | \(0.721638\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.1430 | −0.887921 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.4801 | 1.65509 | 0.827545 | − | 0.561399i | \(-0.189737\pi\) | ||||
0.827545 | + | 0.561399i | \(0.189737\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.0301 | −1.13118 | −0.565588 | − | 0.824688i | \(-0.691351\pi\) | ||||
−0.565588 | + | 0.824688i | \(0.691351\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.1704 | 1.26039 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.68818 | 0.195171 | 0.0975857 | − | 0.995227i | \(-0.468888\pi\) | ||||
0.0975857 | + | 0.995227i | \(0.468888\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −78.4270 | −3.25932 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.13400 | −0.337455 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.6747 | 0.814845 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.61718 | −0.396944 | −0.198472 | − | 0.980107i | \(-0.563598\pi\) | ||||
−0.198472 | + | 0.980107i | \(0.563598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.09541 | 0.374770 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.1652 | 1.28197 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.68902 | 0.356815 | 0.178408 | − | 0.983957i | \(-0.442905\pi\) | ||||
0.178408 | + | 0.983957i | \(0.442905\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.0422 | −0.902128 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.7581 | −0.480421 | −0.240211 | − | 0.970721i | \(-0.577217\pi\) | ||||
−0.240211 | + | 0.970721i | \(0.577217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.9388 | 1.54756 | 0.773778 | − | 0.633457i | \(-0.218365\pi\) | ||||
0.773778 | + | 0.633457i | \(0.218365\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.0099 | −0.896311 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.01418 | −0.365874 | −0.182937 | − | 0.983125i | \(-0.558560\pi\) | ||||
−0.182937 | + | 0.983125i | \(0.558560\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.07931 | −0.0842580 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.87983 | 0.318784 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.5846 | 1.71997 | 0.859987 | − | 0.510316i | \(-0.170472\pi\) | ||||
0.859987 | + | 0.510316i | \(0.170472\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6190 | −0.508020 | −0.254010 | − | 0.967202i | \(-0.581750\pi\) | ||||
−0.254010 | + | 0.967202i | \(0.581750\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.0638 | 1.04759 | 0.523796 | − | 0.851844i | \(-0.324515\pi\) | ||||
0.523796 | + | 0.851844i | \(0.324515\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.1364 | −0.487017 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.98884 | −0.239938 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.4271 | −0.695972 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.7226 | 0.547157 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.1083 | 1.83554 | 0.917771 | − | 0.397110i | \(-0.129987\pi\) | ||||
0.917771 | + | 0.397110i | \(0.129987\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.3888 | −0.929622 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.76415 | 0.188762 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 86.3407 | 3.41559 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.3319 | 0.763563 | 0.381781 | − | 0.924253i | \(-0.375311\pi\) | ||||
0.381781 | + | 0.924253i | \(0.375311\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.27891 | 0.0898713 | 0.0449356 | − | 0.998990i | \(-0.485692\pi\) | ||||
0.0449356 | + | 0.998990i | \(0.485692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.5054 | 1.86763 | 0.933815 | − | 0.357755i | \(-0.116458\pi\) | ||||
0.933815 | + | 0.357755i | \(0.116458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.13148 | −0.0836679 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.7189 | −0.890422 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.73226 | −0.106921 | −0.0534607 | − | 0.998570i | \(-0.517025\pi\) | ||||
−0.0534607 | + | 0.998570i | \(0.517025\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −59.2104 | −2.31002 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.1375 | 0.472809 | 0.236405 | − | 0.971655i | \(-0.424031\pi\) | ||||
0.236405 | + | 0.971655i | \(0.424031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.1992 | 1.60246 | 0.801232 | − | 0.598354i | \(-0.204178\pi\) | ||||
0.801232 | + | 0.598354i | \(0.204178\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.1448 | 0.704686 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.548747 | −0.0212476 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.0919 | −1.24074 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.3067 | 1.24718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.2175 | −0.933516 | −0.466758 | − | 0.884385i | \(-0.654578\pi\) | ||||
−0.466758 | + | 0.884385i | \(0.654578\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.1512 | −1.85060 | −0.925300 | − | 0.379235i | \(-0.876187\pi\) | ||||
−0.925300 | + | 0.379235i | \(0.876187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.6789 | 0.524949 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.3196 | −0.702008 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1351 | 0.464337 | 0.232169 | − | 0.972676i | \(-0.425418\pi\) | ||||
0.232169 | + | 0.972676i | \(0.425418\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.4380 | 0.703454 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.62197 | 0.176083 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8289 | 0.526076 | 0.263038 | − | 0.964785i | \(-0.415275\pi\) | ||||
0.263038 | + | 0.964785i | \(0.415275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 30.2913 | 1.15067 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.0727 | 1.82088 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.63653 | 0.0997226 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.2263 | −0.575089 | −0.287544 | − | 0.957767i | \(-0.592839\pi\) | ||||
−0.287544 | + | 0.957767i | \(0.592839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.09619 | −0.116775 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.15863 | −0.156401 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.2317 | 0.572037 | 0.286019 | − | 0.958224i | \(-0.407668\pi\) | ||||
0.286019 | + | 0.958224i | \(0.407668\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.480919 | −0.0180359 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.99568 | −0.224540 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 66.9907 | 2.50181 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.58943 | −0.171157 | −0.0855784 | − | 0.996331i | \(-0.527274\pi\) | ||||
−0.0855784 | + | 0.996331i | \(0.527274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.0228 | −0.410511 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −65.0246 | −2.41829 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.2414 | 0.787800 | 0.393900 | − | 0.919153i | \(-0.371126\pi\) | ||||
0.393900 | + | 0.919153i | \(0.371126\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.94082 | 0.220030 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 67.7720 | 2.50664 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.5297 | −1.49700 | −0.748499 | − | 0.663136i | \(-0.769225\pi\) | ||||
−0.748499 | + | 0.663136i | \(0.769225\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.7284 | 0.432021 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.6476 | −1.12739 | −0.563695 | − | 0.825983i | \(-0.690621\pi\) | ||||
−0.563695 | + | 0.825983i | \(0.690621\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.09396 | −0.150395 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.01357 | 0.0371844 | 0.0185922 | − | 0.999827i | \(-0.494082\pi\) | ||||
0.0185922 | + | 0.999827i | \(0.494082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 46.2782 | 1.69323 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.1543 | −0.407569 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.0644 | 0.768652 | 0.384326 | − | 0.923197i | \(-0.374434\pi\) | ||||
0.384326 | + | 0.923197i | \(0.374434\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −74.5264 | −2.71589 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.2109 | 0.480160 | 0.240080 | − | 0.970753i | \(-0.422826\pi\) | ||||
0.240080 | + | 0.970753i | \(0.422826\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.4879 | 0.416986 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.9759 | −0.434125 | −0.217063 | − | 0.976158i | \(-0.569648\pi\) | ||||
−0.217063 | + | 0.976158i | \(0.569648\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.98884 | −0.0720008 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.500724 | −0.0180801 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.6569 | 1.43006 | 0.715031 | − | 0.699092i | \(-0.246412\pi\) | ||||
0.715031 | + | 0.699092i | \(0.246412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 57.3123 | 2.06405 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.0305 | −0.576575 | −0.288288 | − | 0.957544i | \(-0.593086\pi\) | ||||
−0.288288 | + | 0.957544i | \(0.593086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.73379 | 0.277448 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.8465 | −0.388615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46.0084 | −1.64631 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.65981 | 0.238002 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.0352 | −1.39145 | −0.695727 | − | 0.718306i | \(-0.744918\pi\) | ||||
−0.695727 | + | 0.718306i | \(0.744918\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 81.2565 | 2.89281 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.45558 | 0.0517543 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.58944 | 0.269509 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.37687 | 0.119615 | 0.0598074 | − | 0.998210i | \(-0.480951\pi\) | ||||
0.0598074 | + | 0.998210i | \(0.480951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.6569 | 2.18126 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.0734 | 1.20392 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.5514 | 1.11343 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.0686 | 0.812053 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.3406 | −1.73472 | −0.867361 | − | 0.497680i | \(-0.834186\pi\) | ||||
−0.867361 | + | 0.497680i | \(0.834186\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.3582 | −0.644645 | −0.322322 | − | 0.946630i | \(-0.604463\pi\) | ||||
−0.322322 | + | 0.946630i | \(0.604463\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −94.9375 | −3.32960 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.2912 | −0.534971 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.11600 | 0.248653 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.4610 | 0.679192 | 0.339596 | − | 0.940571i | \(-0.389710\pi\) | ||||
0.339596 | + | 0.940571i | \(0.389710\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.2973 | −1.64868 | −0.824341 | − | 0.566094i | \(-0.808454\pi\) | ||||
−0.824341 | + | 0.566094i | \(0.808454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.2901 | 0.914197 | 0.457098 | − | 0.889416i | \(-0.348889\pi\) | ||||
0.457098 | + | 0.889416i | \(0.348889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0140 | −0.695116 | −0.347558 | − | 0.937658i | \(-0.612989\pi\) | ||||
−0.347558 | + | 0.937658i | \(0.612989\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.88270 | −0.273448 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.2778 | 1.29160 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 72.7660 | 2.51516 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.7210 | 1.40585 | 0.702923 | − | 0.711266i | \(-0.251878\pi\) | ||||
0.702923 | + | 0.711266i | \(0.251878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6989 | −0.989616 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.9262 | −1.13404 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.87015 | −0.0986194 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.0587 | 0.413854 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.04100 | 0.0699647 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.34390 | −0.182972 | −0.0914858 | − | 0.995806i | \(-0.529162\pi\) | ||||
−0.0914858 | + | 0.995806i | \(0.529162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.4603 | −1.65537 | −0.827686 | − | 0.561192i | \(-0.810343\pi\) | ||||
−0.827686 | + | 0.561192i | \(0.810343\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.3123 | 1.75075 | 0.875377 | − | 0.483440i | \(-0.160613\pi\) | ||||
0.875377 | + | 0.483440i | \(0.160613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.0928 | 0.923319 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.5507 | 0.835714 | 0.417857 | − | 0.908513i | \(-0.362781\pi\) | ||||
0.417857 | + | 0.908513i | \(0.362781\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 88.5843 | 3.00848 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.256267 | 0.00869327 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.75522 | 0.0933570 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −77.8260 | −2.63401 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.1400 | −1.01776 | −0.508878 | − | 0.860838i | \(-0.669940\pi\) | ||||
−0.508878 | + | 0.860838i | \(0.669940\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.70989 | −0.0576732 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.4729 | 1.22880 | 0.614401 | − | 0.788994i | \(-0.289398\pi\) | ||||
0.614401 | + | 0.788994i | \(0.289398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.17426 | −0.0731696 | −0.0365848 | − | 0.999331i | \(-0.511648\pi\) | ||||
−0.0365848 | + | 0.999331i | \(0.511648\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.1463 | −0.542139 | −0.271069 | − | 0.962560i | \(-0.587377\pi\) | ||||
−0.271069 | + | 0.962560i | \(0.587377\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.5244 | −0.621290 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −64.1003 | −2.14744 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.9114 | −0.465528 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.69873 | 0.0901080 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.29011 | 0.109731 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.1652 | 1.20484 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 38.1949 | 1.27105 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.74475 | −0.157547 | −0.0787734 | − | 0.996893i | \(-0.525100\pi\) | ||||
−0.0787734 | + | 0.996893i | \(0.525100\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.6604 | 0.784767 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.8650 | −1.28765 | −0.643827 | − | 0.765171i | \(-0.722654\pi\) | ||||
−0.643827 | + | 0.765171i | \(0.722654\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.6603 | −0.816136 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.7727 | 0.520859 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.5516 | −1.33767 | −0.668837 | − | 0.743409i | \(-0.733207\pi\) | ||||
−0.668837 | + | 0.743409i | \(0.733207\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 50.8329 | 1.67500 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.8082 | −0.355757 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 62.7141 | 2.05980 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.4994 | 0.639755 | 0.319878 | − | 0.947459i | \(-0.396358\pi\) | ||||
0.319878 | + | 0.947459i | \(0.396358\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.41086 | −0.275655 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.6159 | 0.773149 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.9361 | 0.814626 | 0.407313 | − | 0.913289i | \(-0.366466\pi\) | ||||
0.407313 | + | 0.913289i | \(0.366466\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −79.2956 | −2.58771 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.9160 | −1.36642 | −0.683211 | − | 0.730221i | \(-0.739417\pi\) | ||||
−0.683211 | + | 0.730221i | \(0.739417\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.14998 | 0.232836 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.3006 | −0.952141 | −0.476070 | − | 0.879407i | \(-0.657939\pi\) | ||||
−0.476070 | + | 0.879407i | \(0.657939\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.41202 | 0.240604 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.1400 | 1.36648 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.9759 | 0.809048 | 0.404524 | − | 0.914527i | \(-0.367437\pi\) | ||||
0.404524 | + | 0.914527i | \(0.367437\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.30397 | −0.203778 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.9061 | −0.513635 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.94816 | 0.159618 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 63.4622 | 2.04504 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.405142 | 0.0130285 | 0.00651424 | − | 0.999979i | \(-0.497926\pi\) | ||||
0.00651424 | + | 0.999979i | \(0.497926\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.0338 | −1.02907 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.8032 | −1.24525 | −0.622627 | − | 0.782519i | \(-0.713935\pi\) | ||||
−0.622627 | + | 0.782519i | \(0.713935\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.0306 | −0.545975 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.9940 | 1.27952 | 0.639760 | − | 0.768575i | \(-0.279034\pi\) | ||||
0.639760 | + | 0.768575i | \(0.279034\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.1567 | −0.580290 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3155 | 0.361275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.3563 | 0.681160 | 0.340580 | − | 0.940216i | \(-0.389377\pi\) | ||||
0.340580 | + | 0.940216i | \(0.389377\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 34.7485 | 1.10606 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.0799 | 0.320523 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.39444 | −0.139594 | −0.0697970 | − | 0.997561i | \(-0.522235\pi\) | ||||
−0.0697970 | + | 0.997561i | \(0.522235\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 76.5547 | 2.42939 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.9420 | −0.916603 | −0.458302 | − | 0.888797i | \(-0.651542\pi\) | ||||
−0.458302 | + | 0.888797i | \(0.651542\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.7705 | −0.783703 |
(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 | 9200.2.a.cq.1.4 | 4 | ||
4.3 | odd | 2 | 575.2.a.i.1.2 | 4 | |||
5.2 | odd | 4 | 1840.2.e.d.369.1 | 8 | |||
5.3 | odd | 4 | 1840.2.e.d.369.8 | 8 | |||
5.4 | even | 2 | 9200.2.a.ck.1.1 | 4 | |||
12.11 | even | 2 | 5175.2.a.bv.1.3 | 4 | |||
20.3 | even | 4 | 115.2.b.b.24.5 | yes | 8 | ||
20.7 | even | 4 | 115.2.b.b.24.4 | ✓ | 8 | ||
20.19 | odd | 2 | 575.2.a.j.1.3 | 4 | |||
60.23 | odd | 4 | 1035.2.b.e.829.4 | 8 | |||
60.47 | odd | 4 | 1035.2.b.e.829.5 | 8 | |||
60.59 | even | 2 | 5175.2.a.bw.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.b.b.24.4 | ✓ | 8 | 20.7 | even | 4 | ||
115.2.b.b.24.5 | yes | 8 | 20.3 | even | 4 | ||
575.2.a.i.1.2 | 4 | 4.3 | odd | 2 | |||
575.2.a.j.1.3 | 4 | 20.19 | odd | 2 | |||
1035.2.b.e.829.4 | 8 | 60.23 | odd | 4 | |||
1035.2.b.e.829.5 | 8 | 60.47 | odd | 4 | |||
1840.2.e.d.369.1 | 8 | 5.2 | odd | 4 | |||
1840.2.e.d.369.8 | 8 | 5.3 | odd | 4 | |||
5175.2.a.bv.1.3 | 4 | 12.11 | even | 2 | |||
5175.2.a.bw.1.2 | 4 | 60.59 | even | 2 | |||
9200.2.a.ck.1.1 | 4 | 5.4 | even | 2 | |||
9200.2.a.cq.1.4 | 4 | 1.1 | even | 1 | trivial |