Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1560) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.16053\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.46967 | −1.95068 | −0.975339 | − | 0.220713i | \(-0.929162\pi\) | ||||
−0.975339 | + | 0.220713i | \(0.929162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.49264 | −0.847089 | −0.423544 | − | 0.905875i | \(-0.639214\pi\) | ||||
−0.423544 | + | 0.905875i | \(0.639214\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.21016 | −0.507045 | −0.253522 | − | 0.967330i | \(-0.581589\pi\) | ||||
−0.253522 | + | 0.967330i | \(0.581589\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.14949 | 1.49077 | 0.745386 | − | 0.666633i | \(-0.232265\pi\) | ||||
0.745386 | + | 0.666633i | \(0.232265\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.82843 | 0.896616 | 0.448308 | − | 0.893879i | \(-0.352027\pi\) | ||||
0.448308 | + | 0.893879i | \(0.352027\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.65685 | −1.73442 | −0.867211 | − | 0.497941i | \(-0.834090\pi\) | ||||
−0.867211 | + | 0.497941i | \(0.834090\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.46967 | 1.12622 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.93933 | −1.14082 | −0.570410 | − | 0.821360i | \(-0.693216\pi\) | ||||
−0.570410 | + | 0.821360i | \(0.693216\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.148604 | −0.0232080 | −0.0116040 | − | 0.999933i | \(-0.503694\pi\) | ||||
−0.0116040 | + | 0.999933i | \(0.503694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.03858 | −0.463380 | −0.231690 | − | 0.972790i | \(-0.574425\pi\) | ||||
−0.231690 | + | 0.972790i | \(0.574425\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.79073 | −0.990530 | −0.495265 | − | 0.868742i | \(-0.664929\pi\) | ||||
−0.495265 | + | 0.868742i | \(0.664929\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.49264 | 0.489067 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.70279 | −0.233897 | −0.116948 | − | 0.993138i | \(-0.537311\pi\) | ||||
−0.116948 | + | 0.993138i | \(0.537311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.21016 | 0.292742 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.46967 | −0.842279 | −0.421139 | − | 0.906996i | \(-0.638370\pi\) | ||||
−0.421139 | + | 0.906996i | \(0.638370\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.66421 | 0.341117 | 0.170558 | − | 0.985348i | \(-0.445443\pi\) | ||||
0.170558 | + | 0.985348i | \(0.445443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.82843 | −0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.70279 | 0.941046 | 0.470523 | − | 0.882388i | \(-0.344065\pi\) | ||||
0.470523 | + | 0.882388i | \(0.344065\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.14949 | −0.860697 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0879 | −1.31590 | −0.657948 | − | 0.753063i | \(-0.728575\pi\) | ||||
−0.657948 | + | 0.753063i | \(0.728575\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.76776 | −0.675065 | −0.337533 | − | 0.941314i | \(-0.609592\pi\) | ||||
−0.337533 | + | 0.941314i | \(0.609592\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.2990 | 2.08536 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0239 | −1.12777 | −0.563886 | − | 0.825853i | \(-0.690694\pi\) | ||||
−0.563886 | + | 0.825853i | \(0.690694\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.27171 | 0.249353 | 0.124676 | − | 0.992197i | \(-0.460211\pi\) | ||||
0.124676 | + | 0.992197i | \(0.460211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.82843 | −0.517662 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.21104 | −0.976369 | −0.488184 | − | 0.872741i | \(-0.662341\pi\) | ||||
−0.488184 | + | 0.872741i | \(0.662341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.65685 | 1.00137 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.11091 | 0.823538 | 0.411769 | − | 0.911288i | \(-0.364911\pi\) | ||||
0.411769 | + | 0.911288i | \(0.364911\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.46967 | −0.650226 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.1421 | −1.60620 | −0.803101 | − | 0.595843i | \(-0.796818\pi\) | ||||
−0.803101 | + | 0.595843i | \(0.796818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.5815 | 1.92942 | 0.964709 | − | 0.263318i | \(-0.0848167\pi\) | ||||
0.964709 | + | 0.263318i | \(0.0848167\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.35965 | −0.131442 | −0.0657210 | − | 0.997838i | \(-0.520935\pi\) | ||||
−0.0657210 | + | 0.997838i | \(0.520935\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.49264 | 0.334534 | 0.167267 | − | 0.985912i | \(-0.446506\pi\) | ||||
0.167267 | + | 0.985912i | \(0.446506\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.93933 | 0.658652 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.4320 | 1.16950 | 0.584751 | − | 0.811213i | \(-0.301192\pi\) | ||||
0.584751 | + | 0.811213i | \(0.301192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.87867 | 0.905576 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.8566 | 2.80514 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.148604 | 0.0133991 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.6200 | −1.65226 | −0.826131 | − | 0.563478i | \(-0.809463\pi\) | ||||
−0.826131 | + | 0.563478i | \(0.809463\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.03858 | 0.267532 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.751258 | −0.0656378 | −0.0328189 | − | 0.999461i | \(-0.510448\pi\) | ||||
−0.0328189 | + | 0.999461i | \(0.510448\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.25127 | 0.542054 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.08794 | −0.0929487 | −0.0464743 | − | 0.998919i | \(-0.514799\pi\) | ||||
−0.0464743 | + | 0.998919i | \(0.514799\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.420314 | 0.0356506 | 0.0178253 | − | 0.999841i | \(-0.494326\pi\) | ||||
0.0178253 | + | 0.999841i | \(0.494326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.79073 | 0.571883 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.46967 | −0.541021 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.1265 | −1.15729 | −0.578645 | − | 0.815580i | \(-0.696418\pi\) | ||||
−0.578645 | + | 0.815580i | \(0.696418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.07717 | 0.494553 | 0.247276 | − | 0.968945i | \(-0.420464\pi\) | ||||
0.247276 | + | 0.968945i | \(0.420464\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.49264 | −0.282363 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7266 | 0.935888 | 0.467944 | − | 0.883758i | \(-0.344995\pi\) | ||||
0.467944 | + | 0.883758i | \(0.344995\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.70279 | 0.135040 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.2218 | −1.59370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.31371 | −0.572854 | −0.286427 | − | 0.958102i | \(-0.592468\pi\) | ||||
−0.286427 | + | 0.958102i | \(0.592468\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.0420 | 1.62828 | 0.814139 | − | 0.580670i | \(-0.197209\pi\) | ||||
0.814139 | + | 0.580670i | \(0.197209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.21016 | −0.169015 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.9706 | 1.44231 | 0.721153 | − | 0.692776i | \(-0.243613\pi\) | ||||
0.721153 | + | 0.692776i | \(0.243613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.46967 | 0.486290 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.4099 | 1.52551 | 0.762753 | − | 0.646690i | \(-0.223847\pi\) | ||||
0.762753 | + | 0.646690i | \(0.223847\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8934 | 1.85031 | 0.925156 | − | 0.379588i | \(-0.123934\pi\) | ||||
0.925156 | + | 0.379588i | \(0.123934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.66421 | −0.196944 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.5962 | 1.65240 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843 | 0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9853 | −1.08430 | −0.542148 | − | 0.840283i | \(-0.682389\pi\) | ||||
−0.542148 | + | 0.840283i | \(0.682389\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.7990 | 1.35318 | 0.676590 | − | 0.736360i | \(-0.263457\pi\) | ||||
0.676590 | + | 0.736360i | \(0.263457\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.92857 | −0.137405 | −0.0687023 | − | 0.997637i | \(-0.521886\pi\) | ||||
−0.0687023 | + | 0.997637i | \(0.521886\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0239 | −0.710572 | −0.355286 | − | 0.934758i | \(-0.615617\pi\) | ||||
−0.355286 | + | 0.934758i | \(0.615617\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.70279 | −0.543313 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.6569 | −0.958523 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.14949 | 0.496924 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.2990 | 0.989081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.2751 | 1.39580 | 0.697899 | − | 0.716197i | \(-0.254119\pi\) | ||||
0.697899 | + | 0.716197i | \(0.254119\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.0879 | 0.759733 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.3137 | 1.85418 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.76776 | 0.389749 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.49264 | −0.234940 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.1881 | −1.08403 | −0.542017 | − | 0.840368i | \(-0.682339\pi\) | ||||
−0.542017 | + | 0.840368i | \(0.682339\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.0879 | 1.53240 | 0.766200 | − | 0.642602i | \(-0.222145\pi\) | ||||
0.766200 | + | 0.642602i | \(0.222145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.30886 | −0.284738 | −0.142369 | − | 0.989814i | \(-0.545472\pi\) | ||||
−0.142369 | + | 0.989814i | \(0.545472\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.2990 | −1.20398 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.53857 | 0.100795 | 0.0503977 | − | 0.998729i | \(-0.483951\pi\) | ||||
0.0503977 | + | 0.998729i | \(0.483951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.0239 | 0.651119 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.8514 | −1.15471 | −0.577355 | − | 0.816493i | \(-0.695915\pi\) | ||||
−0.577355 | + | 0.816493i | \(0.695915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.95406 | 0.254703 | 0.127352 | − | 0.991858i | \(-0.459352\pi\) | ||||
0.127352 | + | 0.991858i | \(0.459352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.21016 | −0.140629 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.27171 | −0.143964 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.42284 | 0.216048 | 0.108024 | − | 0.994148i | \(-0.465548\pi\) | ||||
0.108024 | + | 0.994148i | \(0.465548\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −46.2548 | −2.90802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.14772 | 0.196349 | 0.0981746 | − | 0.995169i | \(-0.468700\pi\) | ||||
0.0981746 | + | 0.995169i | \(0.468700\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.6274 | 1.21959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.82843 | 0.298872 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.7144 | −0.845669 | −0.422835 | − | 0.906207i | \(-0.638965\pi\) | ||||
−0.422835 | + | 0.906207i | \(0.638965\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.21104 | 0.563707 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.84316 | 0.600148 | 0.300074 | − | 0.953916i | \(-0.402989\pi\) | ||||
0.300074 | + | 0.953916i | \(0.402989\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.86216 | −0.173864 | −0.0869320 | − | 0.996214i | \(-0.527706\pi\) | ||||
−0.0869320 | + | 0.996214i | \(0.527706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.82843 | 0.171184 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.24389 | −0.375159 | −0.187580 | − | 0.982249i | \(-0.560064\pi\) | ||||
−0.187580 | + | 0.982249i | \(0.560064\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.65685 | −0.578141 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.3869 | −1.87239 | −0.936193 | − | 0.351486i | \(-0.885677\pi\) | ||||
−0.936193 | + | 0.351486i | \(0.885677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.56496 | −0.152471 | −0.0762354 | − | 0.997090i | \(-0.524290\pi\) | ||||
−0.0762354 | + | 0.997090i | \(0.524290\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.420314 | 0.0248104 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.80150 | −0.282441 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.11091 | −0.475470 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.834895 | 0.0487751 | 0.0243875 | − | 0.999703i | \(-0.492236\pi\) | ||||
0.0243875 | + | 0.999703i | \(0.492236\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.46967 | 0.375408 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.14949 | 0.413466 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.59441 | 0.495374 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.1421 | 0.927341 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.7556 | 1.01336 | 0.506682 | − | 0.862133i | \(-0.330872\pi\) | ||||
0.506682 | + | 0.862133i | \(0.330872\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.5815 | −1.11395 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.35965 | −0.0770985 | −0.0385493 | − | 0.999257i | \(-0.512274\pi\) | ||||
−0.0385493 | + | 0.999257i | \(0.512274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.75611 | 0.438401 | 0.219201 | − | 0.975680i | \(-0.429655\pi\) | ||||
0.219201 | + | 0.975680i | \(0.429655\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.38514 | 0.527122 | 0.263561 | − | 0.964643i | \(-0.415103\pi\) | ||||
0.263561 | + | 0.964643i | \(0.415103\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −31.2383 | −1.74901 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.35965 | 0.0758881 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.71927 | 0.429512 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.49264 | −0.193143 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.2071 | 1.05892 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.0576 | 0.882605 | 0.441303 | − | 0.897358i | \(-0.354517\pi\) | ||||
0.441303 | + | 0.897358i | \(0.354517\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.93933 | −0.380273 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0698 | −0.603011 | −0.301506 | − | 0.953464i | \(-0.597489\pi\) | ||||
−0.301506 | + | 0.953464i | \(0.597489\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.4320 | −0.675212 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 62.4766 | 3.38330 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.6127 | −1.58969 | −0.794846 | − | 0.606811i | \(-0.792449\pi\) | ||||
−0.794846 | + | 0.606811i | \(0.792449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1183 | 0.916319 | 0.458160 | − | 0.888870i | \(-0.348509\pi\) | ||||
0.458160 | + | 0.888870i | \(0.348509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.3245 | −0.975313 | −0.487657 | − | 0.873035i | \(-0.662148\pi\) | ||||
−0.487657 | + | 0.873035i | \(0.662148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.87867 | −0.522834 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.1356 | 1.43216 | 0.716082 | − | 0.698016i | \(-0.245933\pi\) | ||||
0.716082 | + | 0.698016i | \(0.245933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.1152 | −0.742906 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.8566 | −1.61955 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1855 | 0.792679 | 0.396340 | − | 0.918104i | \(-0.370280\pi\) | ||||
0.396340 | + | 0.918104i | \(0.370280\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.148604 | −0.00773599 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.81623 | 0.250046 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.1776 | −1.14831 | −0.574157 | − | 0.818745i | \(-0.694670\pi\) | ||||
−0.574157 | + | 0.818745i | \(0.694670\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.82843 | 0.248677 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7604 | 0.758191 | 0.379096 | − | 0.925358i | \(-0.376235\pi\) | ||||
0.379096 | + | 0.925358i | \(0.376235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.6200 | 0.953934 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.33238 | 0.476862 | 0.238431 | − | 0.971159i | \(-0.423367\pi\) | ||||
0.238431 | + | 0.971159i | \(0.423367\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.03858 | −0.154460 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.09618 | −0.156982 | −0.0784912 | − | 0.996915i | \(-0.525010\pi\) | ||||
−0.0784912 | + | 0.996915i | \(0.525010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.9706 | −1.26282 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.751258 | 0.0378960 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.26777 | −0.364759 | −0.182379 | − | 0.983228i | \(-0.558380\pi\) | ||||
−0.182379 | + | 0.983228i | \(0.558380\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.25127 | −0.312955 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.40164 | −0.419558 | −0.209779 | − | 0.977749i | \(-0.567274\pi\) | ||||
−0.209779 | + | 0.977749i | \(0.567274\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.65685 | −0.481042 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.8952 | 2.22537 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5815 | 0.572666 | 0.286333 | − | 0.958130i | \(-0.407564\pi\) | ||||
0.286333 | + | 0.958130i | \(0.407564\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.08794 | 0.0536639 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.2990 | 0.900434 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.420314 | −0.0205829 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.7071 | −1.20702 | −0.603510 | − | 0.797355i | \(-0.706232\pi\) | ||||
−0.603510 | + | 0.797355i | \(0.706232\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.7769 | −1.01260 | −0.506302 | − | 0.862356i | \(-0.668988\pi\) | ||||
−0.506302 | + | 0.862356i | \(0.668988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.79073 | −0.330177 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.53552 | −0.364669 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.46967 | 0.312358 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.6694 | 0.802936 | 0.401468 | − | 0.915873i | \(-0.368500\pi\) | ||||
0.401468 | + | 0.915873i | \(0.368500\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.8860 | −0.619263 | −0.309631 | − | 0.950857i | \(-0.600206\pi\) | ||||
−0.309631 | + | 0.950857i | \(0.600206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.8015 | −0.755888 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.1924 | 1.77510 | 0.887548 | − | 0.460716i | \(-0.152407\pi\) | ||||
0.887548 | + | 0.460716i | \(0.152407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.0693 | 1.57117 | 0.785584 | − | 0.618755i | \(-0.212363\pi\) | ||||
0.785584 | + | 0.618755i | \(0.212363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.1265 | 0.668161 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.7448 | −0.507078 | −0.253539 | − | 0.967325i | \(-0.581595\pi\) | ||||
−0.253539 | + | 0.967325i | \(0.581595\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.961416 | 0.0452713 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.07717 | −0.285530 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.9419 | 1.02640 | 0.513198 | − | 0.858270i | \(-0.328460\pi\) | ||||
0.513198 | + | 0.858270i | \(0.328460\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.49264 | 0.163022 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0034 | 1.02480 | 0.512401 | − | 0.858747i | \(-0.328756\pi\) | ||||
0.512401 | + | 0.858747i | \(0.328756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0208 | 1.48813 | 0.744066 | − | 0.668106i | \(-0.232895\pi\) | ||||
0.744066 | + | 0.668106i | \(0.232895\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.3596 | 1.17350 | 0.586752 | − | 0.809767i | \(-0.300406\pi\) | ||||
0.586752 | + | 0.809767i | \(0.300406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.7868 | −1.00602 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.7266 | −0.540335 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.6586 | 0.903905 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.70279 | −0.0779655 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.46231 | 0.432344 | 0.216172 | − | 0.976355i | \(-0.430643\pi\) | ||||
0.216172 | + | 0.976355i | \(0.430643\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.93933 | −0.316406 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.2218 | 0.920124 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.3327 | −1.01199 | −0.505996 | − | 0.862536i | \(-0.668875\pi\) | ||||
−0.505996 | + | 0.862536i | \(0.668875\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.31371 | 0.330737 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.8762 | 1.34829 | 0.674146 | − | 0.738598i | \(-0.264512\pi\) | ||||
0.674146 | + | 0.738598i | \(0.264512\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.8639 | −0.759513 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.3614 | 1.40675 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7145 | −1.10637 | −0.553186 | − | 0.833058i | \(-0.686588\pi\) | ||||
−0.553186 | + | 0.833058i | \(0.686588\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.0420 | −0.940087 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.2267 | −0.768099 | −0.384049 | − | 0.923313i | \(-0.625471\pi\) | ||||
−0.384049 | + | 0.923313i | \(0.625471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.1430 | 1.15877 | 0.579384 | − | 0.815055i | \(-0.303293\pi\) | ||||
0.579384 | + | 0.815055i | \(0.303293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.3137 | 0.721675 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.21016 | 0.0975808 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.9338 | 1.93220 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.9706 | −0.832715 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.0165 | −1.44648 | −0.723240 | − | 0.690597i | \(-0.757348\pi\) | ||||
−0.723240 | + | 0.690597i | \(0.757348\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.2751 | 1.41129 | 0.705646 | − | 0.708564i | \(-0.250657\pi\) | ||||
0.705646 | + | 0.708564i | \(0.250657\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.7279 | 1.46921 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.1152 | 1.22240 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.46967 | −0.280760 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.148604 | −0.00643674 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.4099 | −0.880752 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.46967 | −0.278668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.21193 | −0.0950983 | −0.0475491 | − | 0.998869i | \(-0.515141\pi\) | ||||
−0.0475491 | + | 0.998869i | \(0.515141\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.8934 | −1.06828 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4822 | −1.34608 | −0.673041 | − | 0.739605i | \(-0.735012\pi\) | ||||
−0.673041 | + | 0.739605i | \(0.735012\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.66421 | 0.113706 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.6716 | −0.454625 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.3517 | 1.20564 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.1209 | −1.48812 | −0.744061 | − | 0.668112i | \(-0.767103\pi\) | ||||
−0.744061 | + | 0.668112i | \(0.767103\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.03858 | −0.128518 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5962 | −0.954012 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.3467 | −1.27896 | −0.639480 | − | 0.768808i | \(-0.720850\pi\) | ||||
−0.639480 | + | 0.768808i | \(0.720850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.82843 | −0.118783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.8327 | 1.29257 | 0.646287 | − | 0.763094i | \(-0.276321\pi\) | ||||
0.646287 | + | 0.763094i | \(0.276321\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.1832 | 0.886490 | 0.443245 | − | 0.896400i | \(-0.353827\pi\) | ||||
0.443245 | + | 0.896400i | \(0.353827\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.9853 | 0.626019 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.6594 | 0.943322 | 0.471661 | − | 0.881780i | \(-0.343655\pi\) | ||||
0.471661 | + | 0.881780i | \(0.343655\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.7990 | −0.781259 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.42537 | −0.266569 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.0165 | 0.456257 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.6529 | −0.563515 | −0.281758 | − | 0.959486i | \(-0.590917\pi\) | ||||
−0.281758 | + | 0.959486i | \(0.590917\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.3432 | 0.879430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.92857 | 0.0793306 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.7448 | −0.769756 | −0.384878 | − | 0.922967i | \(-0.625757\pi\) | ||||
−0.384878 | + | 0.922967i | \(0.625757\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.0239 | 0.410249 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −48.7885 | −1.99345 | −0.996723 | − | 0.0808922i | \(-0.974223\pi\) | ||||
−0.996723 | + | 0.0808922i | \(0.974223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.5870 | 0.676599 | 0.338300 | − | 0.941038i | \(-0.390148\pi\) | ||||
0.338300 | + | 0.941038i | \(0.390148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.70279 | 0.313682 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.0642 | 1.17968 | 0.589840 | − | 0.807520i | \(-0.299191\pi\) | ||||
0.589840 | + | 0.807520i | \(0.299191\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.6569 | 0.553404 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.79073 | −0.274723 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.3926 | 0.904430 | 0.452215 | − | 0.891909i | \(-0.350634\pi\) | ||||
0.452215 | + | 0.891909i | \(0.350634\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.63136 | −0.0656760 | −0.0328380 | − | 0.999461i | \(-0.510455\pi\) | ||||
−0.0328380 | + | 0.999461i | \(0.510455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.4485 | −1.50518 | −0.752591 | − | 0.658489i | \(-0.771196\pi\) | ||||
−0.752591 | + | 0.658489i | \(0.771196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.14949 | −0.286899 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.0528 | 1.04378 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.2990 | −0.571046 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.2366 | 0.966375 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.7193 | 0.426728 | 0.213364 | − | 0.976973i | \(-0.431558\pi\) | ||||
0.213364 | + | 0.976973i | \(0.431558\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.2751 | −0.805864 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.0879 | −0.438632 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.0183 | −1.22515 | −0.612574 | − | 0.790413i | \(-0.709866\pi\) | ||||
−0.612574 | + | 0.790413i | \(0.709866\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4515 | −0.491041 | −0.245520 | − | 0.969391i | \(-0.578959\pi\) | ||||
−0.245520 | + | 0.969391i | \(0.578959\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.6538 | 1.63758 | 0.818790 | − | 0.574093i | \(-0.194645\pi\) | ||||
0.818790 | + | 0.574093i | \(0.194645\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.8566 | 1.64301 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.3137 | −1.07051 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.83095 | 0.149917 | 0.0749584 | − | 0.997187i | \(-0.476118\pi\) | ||||
0.0749584 | + | 0.997187i | \(0.476118\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.76776 | −0.225022 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.8926 | −1.63191 | −0.815953 | − | 0.578119i | \(-0.803787\pi\) | ||||
−0.815953 | + | 0.578119i | \(0.803787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.8523 | 1.58897 | 0.794485 | − | 0.607284i | \(-0.207741\pi\) | ||||
0.794485 | + | 0.607284i | \(0.207741\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.49264 | 0.135643 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.5208 | 1.33665 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.1881 | 0.625867 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.2365 | −0.665409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.2401 | 1.74388 | 0.871939 | − | 0.489615i | \(-0.162863\pi\) | ||||
0.871939 | + | 0.489615i | \(0.162863\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.58146 | 0.137647 | 0.0688233 | − | 0.997629i | \(-0.478076\pi\) | ||||
0.0688233 | + | 0.997629i | \(0.478076\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.9411 | −0.880399 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.0879 | −0.884732 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.8402 | −1.71576 | −0.857882 | − | 0.513848i | \(-0.828220\pi\) | ||||
−0.857882 | + | 0.513848i | \(0.828220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.30886 | 0.164393 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.70279 | −0.0648712 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.2891 | 0.695750 | 0.347875 | − | 0.937541i | \(-0.386903\pi\) | ||||
0.347875 | + | 0.937541i | \(0.386903\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.2990 | 0.695121 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.519018 | 0.0196592 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.53857 | −0.0581942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0667 | 1.36222 | 0.681111 | − | 0.732180i | \(-0.261497\pi\) | ||||
0.681111 | + | 0.732180i | \(0.261497\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3370 | 0.578447 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.6569 | 1.71710 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.7769 | −0.442291 | −0.221146 | − | 0.975241i | \(-0.570980\pi\) | ||||
−0.221146 | + | 0.975241i | \(0.570980\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.0239 | −0.375924 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −69.0416 | −2.58563 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.8514 | 0.666673 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.7261 | −1.74259 | −0.871295 | − | 0.490759i | \(-0.836719\pi\) | ||||
−0.871295 | + | 0.490759i | \(0.836719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.3847 | −2.06264 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.95406 | −0.147053 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.8038 | −1.40207 | −0.701033 | − | 0.713129i | \(-0.747277\pi\) | ||||
−0.701033 | + | 0.713129i | \(0.747277\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.6127 | 0.392524 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.9411 | 0.773477 | 0.386739 | − | 0.922189i | \(-0.373602\pi\) | ||||
0.386739 | + | 0.922189i | \(0.373602\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −49.8345 | −1.83568 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.5012 | 1.15879 | 0.579396 | − | 0.815046i | \(-0.303289\pi\) | ||||
0.579396 | + | 0.815046i | \(0.303289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.21016 | 0.0811922 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.96483 | −0.108769 | −0.0543845 | − | 0.998520i | \(-0.517320\pi\) | ||||
−0.0543845 | + | 0.998520i | \(0.517320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.27171 | 0.0831176 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.84566 | 0.140517 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0295 | 0.365980 | 0.182990 | − | 0.983115i | \(-0.441422\pi\) | ||||
0.182990 | + | 0.983115i | \(0.441422\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.42284 | −0.124735 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.4731 | 1.32564 | 0.662818 | − | 0.748780i | \(-0.269360\pi\) | ||||
0.662818 | + | 0.748780i | \(0.269360\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 46.2548 | 1.67894 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.88085 | −0.358181 | −0.179090 | − | 0.983833i | \(-0.557315\pi\) | ||||
−0.179090 | + | 0.983833i | \(0.557315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.87867 | −0.357632 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.46967 | −0.233606 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.6274 | 1.17657 | 0.588287 | − | 0.808652i | \(-0.299802\pi\) | ||||
0.588287 | + | 0.808652i | \(0.299802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.14772 | −0.113362 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.2950 | 1.59318 | 0.796591 | − | 0.604519i | \(-0.206635\pi\) | ||||
0.796591 | + | 0.604519i | \(0.206635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.6274 | −0.704129 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.328437 | 0.0117675 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 71.7352 | 2.56689 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.82843 | −0.172554 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.0068 | −0.855751 | −0.427875 | − | 0.903838i | \(-0.640738\pi\) | ||||
−0.427875 | + | 0.903838i | \(0.640738\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.7144 | 0.488247 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.1629 | −1.25025 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.66421 | 0.0946088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.4271 | −1.50285 | −0.751423 | − | 0.659821i | \(-0.770632\pi\) | ||||
−0.751423 | + | 0.659821i | \(0.770632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7175 | 0.839066 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.21104 | −0.325456 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.3155 | 1.31683 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.84316 | −0.346495 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.0495 | −0.423637 | −0.211819 | − | 0.977309i | \(-0.567939\pi\) | ||||
−0.211819 | + | 0.977309i | \(0.567939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.5619 | −1.21363 | −0.606816 | − | 0.794842i | \(-0.707554\pi\) | ||||
−0.606816 | + | 0.794842i | \(0.707554\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.86216 | 0.100380 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.71575 | 0.234954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.92119 | −0.0670500 | −0.0335250 | − | 0.999438i | \(-0.510673\pi\) | ||||
−0.0335250 | + | 0.999438i | \(0.510673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.9246 | 1.28711 | 0.643556 | − | 0.765399i | \(-0.277458\pi\) | ||||
0.643556 | + | 0.765399i | \(0.277458\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.9501 | −0.728507 | −0.364254 | − | 0.931300i | \(-0.618676\pi\) | ||||
−0.364254 | + | 0.931300i | \(0.618676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.55255 | −0.123385 | −0.0616926 | − | 0.998095i | \(-0.519650\pi\) | ||||
−0.0616926 | + | 0.998095i | \(0.519650\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.24389 | 0.216598 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.49264 | −0.121013 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.65685 | 0.333790 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.2768 | −0.423841 | −0.211920 | − | 0.977287i | \(-0.567972\pi\) | ||||
−0.211920 | + | 0.977287i | \(0.567972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.3869 | 1.08102 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −87.2756 | −2.99882 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.56496 | 0.0880291 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −49.6127 | −1.70070 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6734 | 0.365449 | 0.182724 | − | 0.983164i | \(-0.441508\pi\) | ||||
0.182724 | + | 0.983164i | \(0.441508\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −54.5324 | −1.86279 | −0.931396 | − | 0.364006i | \(-0.881409\pi\) | ||||
−0.931396 | + | 0.364006i | \(0.881409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.6218 | −1.55660 | −0.778298 | − | 0.627894i | \(-0.783917\pi\) | ||||
−0.778298 | + | 0.627894i | \(0.783917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.420314 | −0.0143243 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.1798 | 0.618849 | 0.309424 | − | 0.950924i | \(-0.399864\pi\) | ||||
0.309424 | + | 0.950924i | \(0.399864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.80150 | 0.163067 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.8510 | 2.19992 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.70279 | 0.260999 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.11091 | 0.274513 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1611 | 0.782096 | 0.391048 | − | 0.920370i | \(-0.372113\pi\) | ||||
0.391048 | + | 0.920370i | \(0.372113\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.834895 | −0.0281603 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.7358 | 0.563843 | 0.281921 | − | 0.959438i | \(-0.409028\pi\) | ||||
0.281921 | + | 0.959438i | \(0.409028\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.3959 | −0.686377 | −0.343189 | − | 0.939267i | \(-0.611507\pi\) | ||||
−0.343189 | + | 0.939267i | \(0.611507\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −58.7395 | −1.97228 | −0.986140 | − | 0.165912i | \(-0.946943\pi\) | ||||
−0.986140 | + | 0.165912i | \(0.946943\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 52.6654 | 1.76634 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.46967 | −0.216742 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.0086 | 0.502243 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.14949 | −0.238715 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.6274 | −1.55511 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.94723 | 0.198131 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.59441 | −0.286004 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.9853 | 0.597192 | 0.298596 | − | 0.954380i | \(-0.403482\pi\) | ||||
0.298596 | + | 0.954380i | \(0.403482\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.1421 | −0.535401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.0269 | 1.82312 | 0.911561 | − | 0.411165i | \(-0.134878\pi\) | ||||
0.911561 | + | 0.411165i | \(0.134878\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.6972 | −0.486407 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.12488 | 0.0701697 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00913 | 0.0332880 | 0.0166440 | − | 0.999861i | \(-0.494702\pi\) | ||||
0.0166440 | + | 0.999861i | \(0.494702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.7556 | −0.585066 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.0879 | −0.364964 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.5815 | 0.643139 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.1407 | −0.759222 | −0.379611 | − | 0.925146i | \(-0.623942\pi\) | ||||
−0.379611 | + | 0.925146i | \(0.623942\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.21016 | −0.0724350 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.35965 | 0.0445128 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.72667 | 0.285088 | 0.142544 | − | 0.989788i | \(-0.454472\pi\) | ||||
0.142544 | + | 0.989788i | \(0.454472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.75611 | −0.253111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.24965 | 0.171134 | 0.0855668 | − | 0.996332i | \(-0.472730\pi\) | ||||
0.0855668 | + | 0.996332i | \(0.472730\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.06244 | −0.0345978 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.0420 | 0.553791 | 0.276895 | − | 0.960900i | \(-0.410694\pi\) | ||||
0.276895 | + | 0.960900i | \(0.410694\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.76776 | −0.187229 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.38514 | −0.304334 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.16243 | −0.167227 | −0.0836137 | − | 0.996498i | \(-0.526646\pi\) | ||||
−0.0836137 | + | 0.996498i | \(0.526646\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 31.2383 | 1.00979 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.07715 | 0.0993663 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.2548 | 2.00822 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.35965 | −0.0438140 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.3657 | −1.29807 | −0.649037 | − | 0.760757i | \(-0.724828\pi\) | ||||
−0.649037 | + | 0.760757i | \(0.724828\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.71927 | −0.247979 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.2322 | −0.649283 | −0.324642 | − | 0.945837i | \(-0.605244\pi\) | ||||
−0.324642 | + | 0.945837i | \(0.605244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.18883 | −0.0381121 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.4034 | 0.972691 | 0.486346 | − | 0.873766i | \(-0.338330\pi\) | ||||
0.486346 | + | 0.873766i | \(0.338330\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 59.5924 | 1.90458 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.49264 | 0.111511 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.4250 | 1.60831 | 0.804153 | − | 0.594422i | \(-0.202619\pi\) | ||||
0.804153 | + | 0.594422i | \(0.202619\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.2071 | −0.611368 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.7243 | −0.690793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.1005 | 1.71856 | 0.859279 | − | 0.511507i | \(-0.170913\pi\) | ||||
0.859279 | + | 0.511507i | \(0.170913\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.0576 | −0.509572 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.3921 | −1.24756 | −0.623780 | − | 0.781600i | \(-0.714404\pi\) | ||||
−0.623780 | + | 0.781600i | \(0.714404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.93933 | 0.219551 |
(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 | 7800.2.a.bv.1.1 | 4 | ||
5.2 | odd | 4 | 1560.2.l.e.1249.8 | yes | 8 | ||
5.3 | odd | 4 | 1560.2.l.e.1249.4 | ✓ | 8 | ||
5.4 | even | 2 | 7800.2.a.bw.1.3 | 4 | |||
15.2 | even | 4 | 4680.2.l.f.2809.1 | 8 | |||
15.8 | even | 4 | 4680.2.l.f.2809.2 | 8 | |||
20.3 | even | 4 | 3120.2.l.o.1249.8 | 8 | |||
20.7 | even | 4 | 3120.2.l.o.1249.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.e.1249.4 | ✓ | 8 | 5.3 | odd | 4 | ||
1560.2.l.e.1249.8 | yes | 8 | 5.2 | odd | 4 | ||
3120.2.l.o.1249.4 | 8 | 20.7 | even | 4 | |||
3120.2.l.o.1249.8 | 8 | 20.3 | even | 4 | |||
4680.2.l.f.2809.1 | 8 | 15.2 | even | 4 | |||
4680.2.l.f.2809.2 | 8 | 15.8 | even | 4 | |||
7800.2.a.bv.1.1 | 4 | 1.1 | even | 1 | trivial | ||
7800.2.a.bw.1.3 | 4 | 5.4 | even | 2 |