Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + \cdots + 12144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.04519\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.04519 | −0.914636 | −0.457318 | − | 0.889303i | \(-0.651190\pi\) | ||||
−0.457318 | + | 0.889303i | \(0.651190\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.81275 | 0.685154 | 0.342577 | − | 0.939490i | \(-0.388700\pi\) | ||||
0.342577 | + | 0.939490i | \(0.388700\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.62116 | −0.488797 | −0.244398 | − | 0.969675i | \(-0.578590\pi\) | ||||
−0.244398 | + | 0.969675i | \(0.578590\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.43477 | −0.952633 | −0.476316 | − | 0.879274i | \(-0.658028\pi\) | ||||
−0.476316 | + | 0.879274i | \(0.658028\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.04519 | −0.528065 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.77393 | −1.15785 | −0.578924 | − | 0.815381i | \(-0.696527\pi\) | ||||
−0.578924 | + | 0.815381i | \(0.696527\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.04637 | 1.15772 | 0.578859 | − | 0.815428i | \(-0.303498\pi\) | ||||
0.578859 | + | 0.815428i | \(0.303498\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.81275 | 0.395574 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.71784 | 0.775222 | 0.387611 | − | 0.921823i | \(-0.373300\pi\) | ||||
0.387611 | + | 0.921823i | \(0.373300\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.817207 | −0.163441 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.69513 | 1.05756 | 0.528780 | − | 0.848759i | \(-0.322650\pi\) | ||||
0.528780 | + | 0.848759i | \(0.322650\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.23616 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.62116 | −0.282207 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.70741 | −0.626666 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.11506 | −0.347714 | −0.173857 | − | 0.984771i | \(-0.555623\pi\) | ||||
−0.173857 | + | 0.984771i | \(0.555623\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.43477 | −0.550003 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.68365 | 0.419116 | 0.209558 | − | 0.977796i | \(-0.432797\pi\) | ||||
0.209558 | + | 0.977796i | \(0.432797\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.6956 | 1.93606 | 0.968030 | − | 0.250834i | \(-0.0807049\pi\) | ||||
0.968030 | + | 0.250834i | \(0.0807049\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.04519 | −0.304879 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.44574 | −1.23194 | −0.615969 | − | 0.787771i | \(-0.711235\pi\) | ||||
−0.615969 | + | 0.787771i | \(0.711235\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.71395 | −0.530564 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.77393 | −0.668484 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.62431 | −0.360476 | −0.180238 | − | 0.983623i | \(-0.557687\pi\) | ||||
−0.180238 | + | 0.983623i | \(0.557687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.31557 | 0.447071 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.04637 | 0.668409 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.400667 | 0.0521624 | 0.0260812 | − | 0.999660i | \(-0.491697\pi\) | ||||
0.0260812 | + | 0.999660i | \(0.491697\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.131727 | 0.0168660 | 0.00843298 | − | 0.999964i | \(-0.497316\pi\) | ||||
0.00843298 | + | 0.999964i | \(0.497316\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.81275 | 0.228385 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.02474 | 0.871312 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.63043 | 0.810036 | 0.405018 | − | 0.914309i | \(-0.367265\pi\) | ||||
0.405018 | + | 0.914309i | \(0.367265\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.71784 | 0.447575 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.2723 | 1.45646 | 0.728228 | − | 0.685335i | \(-0.240344\pi\) | ||||
0.728228 | + | 0.685335i | \(0.240344\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.2063 | 1.54568 | 0.772840 | − | 0.634601i | \(-0.218836\pi\) | ||||
0.772840 | + | 0.634601i | \(0.218836\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.817207 | −0.0943629 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.93875 | −0.334901 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.93266 | 0.329950 | 0.164975 | − | 0.986298i | \(-0.447246\pi\) | ||||
0.164975 | + | 0.986298i | \(0.447246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.4039 | 1.69080 | 0.845399 | − | 0.534135i | \(-0.179363\pi\) | ||||
0.845399 | + | 0.534135i | \(0.179363\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.76358 | 1.05901 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.69513 | 0.610582 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.43002 | 0.575581 | 0.287791 | − | 0.957693i | \(-0.407079\pi\) | ||||
0.287791 | + | 0.957693i | \(0.407079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.22636 | −0.652700 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.23616 | 0.439269 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.3208 | −1.05889 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.62800 | 0.977575 | 0.488788 | − | 0.872403i | \(-0.337439\pi\) | ||||
0.488788 | + | 0.872403i | \(0.337439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.62116 | −0.162932 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.8915 | −1.18325 | −0.591625 | − | 0.806213i | \(-0.701513\pi\) | ||||
−0.591625 | + | 0.806213i | \(0.701513\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.78324 | 0.668372 | 0.334186 | − | 0.942507i | \(-0.391539\pi\) | ||||
0.334186 | + | 0.942507i | \(0.391539\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.70741 | −0.361806 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.79200 | −0.366586 | −0.183293 | − | 0.983058i | \(-0.558676\pi\) | ||||
−0.183293 | + | 0.983058i | \(0.558676\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8797 | 1.32944 | 0.664719 | − | 0.747093i | \(-0.268551\pi\) | ||||
0.664719 | + | 0.747093i | \(0.268551\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.11506 | −0.200753 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.5403 | −1.83820 | −0.919099 | − | 0.394027i | \(-0.871082\pi\) | ||||
−0.919099 | + | 0.394027i | \(0.871082\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.60367 | −0.709046 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.43477 | −0.317544 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.65393 | −0.793304 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.37185 | −0.761077 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.68365 | 0.241977 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8973 | 1.06413 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.29936 | −0.381507 | −0.190753 | − | 0.981638i | \(-0.561093\pi\) | ||||
−0.190753 | + | 0.981638i | \(0.561093\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.6956 | 1.11778 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.0965 | 1.31898 | 0.659492 | − | 0.751712i | \(-0.270771\pi\) | ||||
0.659492 | + | 0.751712i | \(0.270771\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.14780 | 0.793215 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.04519 | −0.176022 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.35974 | −0.116170 | −0.0580852 | − | 0.998312i | \(-0.518499\pi\) | ||||
−0.0580852 | + | 0.998312i | \(0.518499\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.9242 | −1.68995 | −0.844973 | − | 0.534808i | \(-0.820384\pi\) | ||||
−0.844973 | + | 0.534808i | \(0.820384\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.44574 | −0.711259 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.56829 | 0.465644 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6476 | −0.967282 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.71395 | −0.306321 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.38010 | −0.604601 | −0.302301 | − | 0.953213i | \(-0.597755\pi\) | ||||
−0.302301 | + | 0.953213i | \(0.597755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.5284 | 1.26368 | 0.631841 | − | 0.775098i | \(-0.282300\pi\) | ||||
0.631841 | + | 0.775098i | \(0.282300\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.77393 | −0.385949 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.66373 | −0.695888 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.4332 | 1.55094 | 0.775470 | − | 0.631385i | \(-0.217513\pi\) | ||||
0.775470 | + | 0.631385i | \(0.217513\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.62431 | −0.208121 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.73949 | 0.531147 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.15822 | 0.717327 | 0.358664 | − | 0.933467i | \(-0.383233\pi\) | ||||
0.358664 | + | 0.933467i | \(0.383233\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.31557 | 0.258117 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.20239 | −0.0924912 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.04637 | 0.385906 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.5002 | −1.40655 | −0.703274 | − | 0.710919i | \(-0.748279\pi\) | ||||
−0.703274 | + | 0.710919i | \(0.748279\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.48139 | −0.111982 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.400667 | 0.0301160 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.2383 | 1.43794 | 0.718969 | − | 0.695042i | \(-0.244614\pi\) | ||||
0.718969 | + | 0.695042i | \(0.244614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.1135 | 1.94100 | 0.970501 | − | 0.241098i | \(-0.0775076\pi\) | ||||
0.970501 | + | 0.241098i | \(0.0775076\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.131727 | 0.00973757 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.32569 | 0.318031 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.73929 | 0.565953 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.81275 | 0.131858 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.0096 | −1.88199 | −0.940993 | − | 0.338425i | \(-0.890106\pi\) | ||||
−0.940993 | + | 0.338425i | \(0.890106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.70727 | 0.482800 | 0.241400 | − | 0.970426i | \(-0.422393\pi\) | ||||
0.241400 | + | 0.970426i | \(0.422393\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.02474 | 0.503052 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.2795 | −1.44486 | −0.722429 | − | 0.691445i | \(-0.756974\pi\) | ||||
−0.722429 | + | 0.691445i | \(0.756974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.4915 | −1.45260 | −0.726301 | − | 0.687377i | \(-0.758762\pi\) | ||||
−0.726301 | + | 0.687377i | \(0.758762\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.63043 | 0.467675 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3238 | 0.724591 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.48857 | −0.383339 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.71784 | 0.258407 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.18096 | −0.565889 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.74296 | −0.670733 | −0.335366 | − | 0.942088i | \(-0.608860\pi\) | ||||
−0.335366 | + | 0.942088i | \(0.608860\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.2723 | 0.840885 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.9649 | −1.77079 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.67908 | 0.521290 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.2063 | 0.892398 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3973 | 1.10300 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0423 | 1.27516 | 0.637582 | − | 0.770382i | \(-0.279935\pi\) | ||||
0.637582 | + | 0.770382i | \(0.279935\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.817207 | −0.0544804 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.0274 | 1.59476 | 0.797378 | − | 0.603480i | \(-0.206220\pi\) | ||||
0.797378 | + | 0.603480i | \(0.206220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.6375 | −0.835109 | −0.417555 | − | 0.908652i | \(-0.637113\pi\) | ||||
−0.417555 | + | 0.908652i | \(0.637113\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.93875 | −0.193355 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.0038 | 1.63805 | 0.819027 | − | 0.573754i | \(-0.194514\pi\) | ||||
0.819027 | + | 0.573754i | \(0.194514\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.2731 | 1.12677 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.93266 | 0.190497 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.9032 | 0.834638 | 0.417319 | − | 0.908760i | \(-0.362970\pi\) | ||||
0.417319 | + | 0.908760i | \(0.362970\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1834 | −0.655972 | −0.327986 | − | 0.944683i | \(-0.606370\pi\) | ||||
−0.327986 | + | 0.944683i | \(0.606370\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.59572 | 0.485273 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.3331 | −1.10288 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.4039 | 0.976183 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.514670 | 0.0324857 | 0.0162428 | − | 0.999868i | \(-0.494830\pi\) | ||||
0.0162428 | + | 0.999868i | \(0.494830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.02719 | −0.378926 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.76358 | 0.611419 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.3692 | 1.39535 | 0.697677 | − | 0.716412i | \(-0.254217\pi\) | ||||
0.697677 | + | 0.716412i | \(0.254217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.83407 | −0.238237 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.69513 | 0.352520 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.7692 | −0.972368 | −0.486184 | − | 0.873857i | \(-0.661611\pi\) | ||||
−0.486184 | + | 0.873857i | \(0.661611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.36720 | 0.329705 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.43002 | 0.332312 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.4917 | 0.883575 | 0.441788 | − | 0.897120i | \(-0.354345\pi\) | ||||
0.441788 | + | 0.897120i | \(0.354345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.2465 | −1.71585 | −0.857927 | − | 0.513772i | \(-0.828248\pi\) | ||||
−0.857927 | + | 0.513772i | \(0.828248\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.22636 | −0.376836 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.32482 | 0.0798896 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.04261 | −0.302981 | −0.151490 | − | 0.988459i | \(-0.548407\pi\) | ||||
−0.151490 | + | 0.988459i | \(0.548407\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.23616 | 0.253612 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8548 | −1.00547 | −0.502736 | − | 0.864440i | \(-0.667673\pi\) | ||||
−0.502736 | + | 0.864440i | \(0.667673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2569 | 1.38248 | 0.691238 | − | 0.722627i | \(-0.257066\pi\) | ||||
0.691238 | + | 0.722627i | \(0.257066\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.3208 | −0.611350 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.86478 | 0.287159 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.79041 | 0.340612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.62800 | 0.564403 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.38017 | 0.547995 | 0.273998 | − | 0.961730i | \(-0.411654\pi\) | ||||
0.273998 | + | 0.961730i | \(0.411654\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.819440 | −0.0477096 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.62116 | −0.0940690 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.7699 | −0.738502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.0139 | 1.32650 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.8915 | −0.683150 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.269407 | −0.0154262 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.3987 | 1.33543 | 0.667716 | − | 0.744416i | \(-0.267272\pi\) | ||||
0.667716 | + | 0.744416i | \(0.267272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.78324 | 0.385885 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.38962 | −0.248912 | −0.124456 | − | 0.992225i | \(-0.539719\pi\) | ||||
−0.124456 | + | 0.992225i | \(0.539719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.5307 | 1.72570 | 0.862848 | − | 0.505464i | \(-0.168679\pi\) | ||||
0.862848 | + | 0.505464i | \(0.168679\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.70741 | −0.208889 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.0063 | 1.29216 | 0.646082 | − | 0.763268i | \(-0.276406\pi\) | ||||
0.646082 | + | 0.763268i | \(0.276406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.23270 | −0.516932 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.79200 | −0.211649 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.0910 | −1.34046 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.80691 | 0.155700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.8797 | 0.767552 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.3100 | −0.844067 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5613 | 1.18512 | 0.592559 | − | 0.805527i | \(-0.298118\pi\) | ||||
0.592559 | + | 0.805527i | \(0.298118\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.11506 | −0.115905 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.5605 | −0.740888 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.17835 | −0.173136 | −0.0865679 | − | 0.996246i | \(-0.527590\pi\) | ||||
−0.0865679 | + | 0.996246i | \(0.527590\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.5403 | −1.06128 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.86747 | −0.371894 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.4217 | −1.04867 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.60367 | −0.409368 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.98591 | −0.160292 | −0.0801460 | − | 0.996783i | \(-0.525539\pi\) | ||||
−0.0801460 | + | 0.996783i | \(0.525539\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1887 | 1.24126 | 0.620631 | − | 0.784102i | \(-0.286876\pi\) | ||||
0.620631 | + | 0.784102i | \(0.286876\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.43477 | −0.183334 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7847 | 1.10626 | 0.553128 | − | 0.833096i | \(-0.313434\pi\) | ||||
0.553128 | + | 0.833096i | \(0.313434\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.0992 | −1.33213 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.65393 | −0.458014 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.44829 | −0.445884 | −0.222942 | − | 0.974832i | \(-0.571566\pi\) | ||||
−0.222942 | + | 0.974832i | \(0.571566\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.46589 | 0.340310 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.37185 | −0.439408 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.0093 | −1.41373 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.08409 | 0.108789 | 0.0543944 | − | 0.998520i | \(-0.482677\pi\) | ||||
0.0543944 | + | 0.998520i | \(0.482677\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.68365 | 0.139705 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.75721 | −0.246982 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.7296 | −0.918005 | −0.459002 | − | 0.888435i | \(-0.651793\pi\) | ||||
−0.459002 | + | 0.888435i | \(0.651793\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.8973 | 0.614373 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.5614 | −1.00747 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.5594 | −1.05607 | −0.528034 | − | 0.849223i | \(-0.677071\pi\) | ||||
−0.528034 | + | 0.849223i | \(0.677071\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.29936 | −0.220263 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.1341 | −1.02880 | −0.514401 | − | 0.857550i | \(-0.671986\pi\) | ||||
−0.514401 | + | 0.857550i | \(0.671986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.01029 | 0.306313 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.6956 | 0.645353 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.1426 | −1.52829 | −0.764146 | − | 0.645043i | \(-0.776839\pi\) | ||||
−0.764146 | + | 0.645043i | \(0.776839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.7487 | −0.897590 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.0965 | 0.761516 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.99784 | −0.301784 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.2249 | 0.764116 | 0.382058 | − | 0.924138i | \(-0.375215\pi\) | ||||
0.382058 | + | 0.924138i | \(0.375215\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.14780 | 0.457963 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.0171 | 0.550166 | 0.275083 | − | 0.961421i | \(-0.411295\pi\) | ||||
0.275083 | + | 0.961421i | \(0.411295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5502 | −0.724797 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.04519 | −0.101626 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.42884 | 0.169961 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1892 | 0.899400 | 0.449700 | − | 0.893180i | \(-0.351531\pi\) | ||||
0.449700 | + | 0.893180i | \(0.351531\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.35974 | −0.0670710 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.726308 | 0.0357393 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.5039 | −1.54646 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.9242 | −0.975691 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.1465 | −0.935370 | −0.467685 | − | 0.883895i | \(-0.654912\pi\) | ||||
−0.467685 | + | 0.883895i | \(0.654912\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.1391 | 1.66384 | 0.831918 | − | 0.554899i | \(-0.187243\pi\) | ||||
0.831918 | + | 0.554899i | \(0.187243\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.44574 | −0.410646 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.90129 | 0.189240 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.238788 | 0.0115558 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.56829 | 0.268840 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.9439 | −1.82769 | −0.913846 | − | 0.406061i | \(-0.866902\pi\) | ||||
−0.913846 | + | 0.406061i | \(0.866902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0410 | 1.49174 | 0.745869 | − | 0.666093i | \(-0.232035\pi\) | ||||
0.745869 | + | 0.666093i | \(0.232035\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.6476 | −0.558460 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.7616 | 0.897488 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8058 | −0.658915 | −0.329458 | − | 0.944170i | \(-0.606866\pi\) | ||||
−0.329458 | + | 0.944170i | \(0.606866\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.71395 | −0.176855 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.9941 | 1.33004 | 0.665021 | − | 0.746825i | \(-0.268423\pi\) | ||||
0.665021 | + | 0.746825i | \(0.268423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.1054 | −0.526447 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.38010 | −0.349067 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.3679 | 0.819644 | 0.409822 | − | 0.912166i | \(-0.365591\pi\) | ||||
0.409822 | + | 0.912166i | \(0.365591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.35062 | −0.204863 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.5284 | 0.729587 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.7341 | 0.596983 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −41.6155 | −1.94669 | −0.973345 | − | 0.229347i | \(-0.926341\pi\) | ||||
−0.973345 | + | 0.229347i | \(0.926341\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.77393 | −0.222828 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.29941 | −0.200243 | −0.100122 | − | 0.994975i | \(-0.531923\pi\) | ||||
−0.100122 | + | 0.994975i | \(0.531923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.3526 | −1.73592 | −0.867960 | − | 0.496634i | \(-0.834569\pi\) | ||||
−0.867960 | + | 0.496634i | \(0.834569\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.66373 | −0.401771 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.1745 | 1.30376 | 0.651881 | − | 0.758321i | \(-0.273980\pi\) | ||||
0.651881 | + | 0.758321i | \(0.273980\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0193 | 0.554999 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.4332 | 0.895435 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.5815 | −0.946340 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.12393 | −0.189219 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.62431 | −0.120159 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.39801 | −0.429406 | −0.214703 | − | 0.976679i | \(-0.568878\pi\) | ||||
−0.214703 | + | 0.976679i | \(0.568878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.26473 | 0.331243 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.73949 | 0.306658 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.6911 | −0.894125 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5408 | 0.477650 | 0.238825 | − | 0.971063i | \(-0.423238\pi\) | ||||
0.238825 | + | 0.971063i | \(0.423238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.15822 | 0.414149 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3694 | −0.648482 | −0.324241 | − | 0.945975i | \(-0.605109\pi\) | ||||
−0.324241 | + | 0.945975i | \(0.605109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.1882 | −1.22449 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.31557 | 0.149024 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.2466 | 0.997896 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.1966 | −1.30702 | −0.653511 | − | 0.756917i | \(-0.726704\pi\) | ||||
−0.653511 | + | 0.756917i | \(0.726704\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.1817 | 1.07821 | 0.539104 | − | 0.842239i | \(-0.318763\pi\) | ||||
0.539104 | + | 0.842239i | \(0.318763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.3204 | 1.08224 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.20239 | −0.0533998 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.3635 | −1.47881 | −0.739405 | − | 0.673260i | \(-0.764893\pi\) | ||||
−0.739405 | + | 0.673260i | \(0.764893\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.9397 | 1.05903 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.04637 | 0.222803 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.8730 | −0.611317 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6919 | 0.602167 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.5002 | −0.812071 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.496462 | −0.0217504 | −0.0108752 | − | 0.999941i | \(-0.503462\pi\) | ||||
−0.0108752 | + | 0.999941i | \(0.503462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.9410 | −1.04687 | −0.523434 | − | 0.852066i | \(-0.675349\pi\) | ||||
−0.523434 | + | 0.852066i | \(0.675349\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.48139 | −0.0646531 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.2231 | −0.880932 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.17770 | −0.399030 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.400667 | 0.0173875 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.21772 | −0.399264 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.75535 | 0.335293 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.2383 | 0.830194 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.02089 | 0.259338 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0931 | −0.820876 | −0.410438 | − | 0.911889i | \(-0.634624\pi\) | ||||
−0.410438 | + | 0.911889i | \(0.634624\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.1135 | 1.12064 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.3867 | −1.21595 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.49603 | 0.192236 | 0.0961181 | − | 0.995370i | \(-0.469357\pi\) | ||||
0.0961181 | + | 0.995370i | \(0.469357\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.131727 | 0.00562199 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.7398 | 1.22436 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.31617 | 0.226066 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.32569 | 0.183615 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.0454 | −1.27306 | −0.636532 | − | 0.771250i | \(-0.719632\pi\) | ||||
−0.636532 | + | 0.771250i | \(0.719632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −43.6064 | −1.84435 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.73929 | 0.326753 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.3325 | −1.36265 | −0.681326 | − | 0.731980i | \(-0.738597\pi\) | ||||
−0.681326 | + | 0.731980i | \(0.738597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.9636 | 1.68128 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.81275 | 0.0761282 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.1979 | 0.846738 | 0.423369 | − | 0.905957i | \(-0.360847\pi\) | ||||
0.423369 | + | 0.905957i | \(0.360847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.2137 | 1.38995 | 0.694976 | − | 0.719033i | \(-0.255415\pi\) | ||||
0.694976 | + | 0.719033i | \(0.255415\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.0096 | −1.08657 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.03824 | −0.126703 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.6552 | −1.44271 | −0.721356 | − | 0.692564i | \(-0.756481\pi\) | ||||
−0.721356 | + | 0.692564i | \(0.756481\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.70727 | 0.278745 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.9234 | 1.15846 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.25441 | 0.176200 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.02474 | 0.290437 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.82995 | 0.158079 | 0.0790394 | − | 0.996871i | \(-0.474815\pi\) | ||||
0.0790394 | + | 0.996871i | \(0.474815\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.3772 | 0.880833 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.2795 | −0.834189 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.3949 | −0.878581 | −0.439291 | − | 0.898345i | \(-0.644770\pi\) | ||||
−0.439291 | + | 0.898345i | \(0.644770\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.6989 | 0.725584 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.4915 | −0.838660 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.79373 | 0.359302 | 0.179651 | − | 0.983730i | \(-0.442503\pi\) | ||||
0.179651 | + | 0.983730i | \(0.442503\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.891749 | −0.0363752 | −0.0181876 | − | 0.999835i | \(-0.505790\pi\) | ||||
−0.0181876 | + | 0.999835i | \(0.505790\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.63043 | 0.270012 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.1220 | 0.696109 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.2852 | −0.823353 | −0.411676 | − | 0.911330i | \(-0.635057\pi\) | ||||
−0.411676 | + | 0.911330i | \(0.635057\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.3238 | 0.418343 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.0091 | 1.17358 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.1524 | 0.450441 | 0.225221 | − | 0.974308i | \(-0.427690\pi\) | ||||
0.225221 | + | 0.974308i | \(0.427690\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.48857 | −0.221321 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.1142 | −1.33313 | −0.666564 | − | 0.745447i | \(-0.732236\pi\) | ||||
−0.666564 | + | 0.745447i | \(0.732236\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.3281 | −0.977828 | −0.488914 | − | 0.872332i | \(-0.662607\pi\) | ||||
−0.488914 | + | 0.872332i | \(0.662607\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.71784 | 0.149192 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.84326 | 0.394362 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.2461 | −0.809846 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.18096 | −0.326716 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0971 | 0.402599 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.3393 | −0.809693 | −0.404846 | − | 0.914385i | \(-0.632675\pi\) | ||||
−0.404846 | + | 0.914385i | \(0.632675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.74296 | −0.387248 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.79300 | 0.348940 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.7565 | 0.505433 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.2723 | 0.485485 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8194 | −0.506338 | −0.253169 | − | 0.967422i | \(-0.581473\pi\) | ||||
−0.253169 | + | 0.967422i | \(0.581473\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.5937 | −0.457211 | −0.228605 | − | 0.973519i | \(-0.573417\pi\) | ||||
−0.228605 | + | 0.973519i | \(0.573417\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.9649 | −1.02237 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.44127 | 0.135290 | 0.0676452 | − | 0.997709i | \(-0.478451\pi\) | ||||
0.0676452 | + | 0.997709i | \(0.478451\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.649544 | −0.0254968 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.67908 | 0.300967 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.9286 | 0.936400 | 0.468200 | − | 0.883622i | \(-0.344903\pi\) | ||||
0.468200 | + | 0.883622i | \(0.344903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.8751 | −1.20639 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.2063 | 0.515226 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.8812 | 0.813417 | 0.406708 | − | 0.913558i | \(-0.366677\pi\) | ||||
0.406708 | + | 0.913558i | \(0.366677\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.7368 | 1.15663 | 0.578314 | − | 0.815814i | \(-0.303711\pi\) | ||||
0.578314 | + | 0.815814i | \(0.303711\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.3973 | 0.636820 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.7090 | −0.725503 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.1736 | 0.819844 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.0423 | 0.736217 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.213551 | −0.00824403 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.94319 | 0.190546 | 0.0952730 | − | 0.995451i | \(-0.469628\pi\) | ||||
0.0952730 | + | 0.995451i | \(0.469628\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.817207 | −0.0314543 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.2784 | 0.548764 | 0.274382 | − | 0.961621i | \(-0.411527\pi\) | ||||
0.274382 | + | 0.961621i | \(0.411527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4531 | 0.669789 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0274 | 0.920733 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.5913 | 0.902694 | 0.451347 | − | 0.892348i | \(-0.350944\pi\) | ||||
0.451347 | + | 0.892348i | \(0.350944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.78092 | 0.106254 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.6375 | −0.482151 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.01388 | 0.343402 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.3287 | 0.887467 | 0.443733 | − | 0.896159i | \(-0.353654\pi\) | ||||
0.443733 | + | 0.896159i | \(0.353654\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.93875 | −0.111634 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 40.7487 | 1.54569 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.8116 | −0.485273 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.0038 | 0.945731 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0234 | 1.13397 | 0.566984 | − | 0.823729i | \(-0.308110\pi\) | ||||
0.566984 | + | 0.823729i | \(0.308110\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6734 | −0.402554 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.2731 | 0.650543 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.5563 | −0.810709 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.6410 | −0.587410 | −0.293705 | − | 0.955896i | \(-0.594888\pi\) | ||||
−0.293705 | + | 0.955896i | \(0.594888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.93266 | 0.109983 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.7493 | 0.589817 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.3882 | −0.425895 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.9032 | 0.481878 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.66277 | 0.323067 | 0.161533 | − | 0.986867i | \(-0.448356\pi\) | ||||
0.161533 | + | 0.986867i | \(0.448356\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.2963 | 0.457938 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.1834 | −0.378726 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.65410 | −0.172849 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.1368 | 0.895183 | 0.447592 | − | 0.894238i | \(-0.352282\pi\) | ||||
0.447592 | + | 0.894238i | \(0.352282\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −60.6079 | −2.24166 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.9993 | −1.44047 | −0.720235 | − | 0.693730i | \(-0.755966\pi\) | ||||
−0.720235 | + | 0.693730i | \(0.755966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.59572 | 0.280172 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.7490 | −0.395943 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.1884 | −1.11050 | −0.555250 | − | 0.831684i | \(-0.687377\pi\) | ||||
−0.555250 | + | 0.831684i | \(0.687377\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.3331 | −0.636748 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.1790 | 0.373432 | 0.186716 | − | 0.982414i | \(-0.440216\pi\) | ||||
0.186716 | + | 0.982414i | \(0.440216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.0937 | 0.552990 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.4039 | 0.563599 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.87394 | −0.251168 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.6388 | 0.534179 | 0.267089 | − | 0.963672i | \(-0.413938\pi\) | ||||
0.267089 | + | 0.963672i | \(0.413938\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.514670 | 0.0187556 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.7584 | −1.15581 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.6501 | −1.47745 | −0.738727 | − | 0.674004i | \(-0.764573\pi\) | ||||
−0.738727 | + | 0.674004i | \(0.764573\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.02719 | −0.218773 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.7343 | −1.22287 | −0.611434 | − | 0.791295i | \(-0.709407\pi\) | ||||
−0.611434 | + | 0.791295i | \(0.709407\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.1605 | 0.910870 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.76358 | 0.353003 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.37620 | −0.0496916 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.28736 | −0.334911 | −0.167455 | − | 0.985880i | \(-0.553555\pi\) | ||||
−0.167455 | + | 0.985880i | \(0.553555\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.3692 | 0.805608 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.0520 | −0.829122 | −0.414561 | − | 0.910021i | \(-0.636065\pi\) | ||||
−0.414561 | + | 0.910021i | \(0.636065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.46181 | −0.124352 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.83407 | −0.137546 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.5427 | 0.485218 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.8953 | −0.711911 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.69513 | 0.203527 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.7446 | −1.41854 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.4746 | 0.587255 | 0.293627 | − | 0.955920i | \(-0.405137\pi\) | ||||
0.293627 | + | 0.955920i | \(0.405137\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.7692 | −0.561397 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.4216 | −1.25945 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.452453 | −0.0160671 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.36720 | 0.190355 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.0201 | −1.55927 | −0.779636 | − | 0.626233i | \(-0.784596\pi\) | ||||
−0.779636 | + | 0.626233i | \(0.784596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.3194 | 1.42640 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.43002 | 0.191860 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.4095 | −0.755523 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.7835 | −0.485806 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.4917 | 0.510132 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.92181 | 0.102726 | 0.0513628 | − | 0.998680i | \(-0.483644\pi\) | ||||
0.0513628 | + | 0.998680i | \(0.483644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.6747 | −0.796217 | −0.398109 | − | 0.917338i | \(-0.630333\pi\) | ||||
−0.398109 | + | 0.917338i | \(0.630333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.2465 | −0.990649 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.7303 | −0.656093 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 64.0667 | 2.24141 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.22636 | −0.217567 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1758 | 0.390038 | 0.195019 | − | 0.980799i | \(-0.437523\pi\) | ||||
0.195019 | + | 0.980799i | \(0.437523\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.9066 | 0.519613 | 0.259806 | − | 0.965661i | \(-0.416341\pi\) | ||||
0.259806 | + | 0.965661i | \(0.416341\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.32482 | 0.0461243 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.7483 | −0.373754 | −0.186877 | − | 0.982383i | \(-0.559837\pi\) | ||||
−0.186877 | + | 0.982383i | \(0.559837\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.3443 | 1.47068 | 0.735339 | − | 0.677700i | \(-0.237023\pi\) | ||||
0.735339 | + | 0.677700i | \(0.237023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.04261 | −0.174926 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.7301 | 0.614313 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.04519 | 0.0707766 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.23616 | 0.146423 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.10935 | −0.314490 | −0.157245 | − | 0.987560i | \(-0.550261\pi\) | ||||
−0.157245 | + | 0.987560i | \(0.550261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.43453 | 0.118432 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.8548 | −0.580510 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.45911 | 0.0845958 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.1760 | −0.521455 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.2569 | 0.798173 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.86344 | −0.269555 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.1422 | −0.689656 | −0.344828 | − | 0.938666i | \(-0.612063\pi\) | ||||
−0.344828 | + | 0.938666i | \(0.612063\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.3208 | −0.352963 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.3338 | 0.421316 | 0.210658 | − | 0.977560i | \(-0.432439\pi\) | ||||
0.210658 | + | 0.977560i | \(0.432439\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.6878 | 1.28589 | 0.642945 | − | 0.765912i | \(-0.277712\pi\) | ||||
0.642945 | + | 0.765912i | \(0.277712\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.86478 | 0.165791 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.5076 | −0.630005 | −0.315003 | − | 0.949091i | \(-0.602005\pi\) | ||||
−0.315003 | + | 0.949091i | \(0.602005\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.8365 | 1.28648 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.79041 | 0.196653 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.75430 | −0.161278 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.7740 | −0.771667 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.62800 | 0.325858 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.5668 | 0.729090 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.78287 | −0.0939710 | −0.0469855 | − | 0.998896i | \(-0.514961\pi\) | ||||
−0.0469855 | + | 0.998896i | \(0.514961\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.38017 | 0.316385 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.2793 | −1.66026 | −0.830131 | − | 0.557568i | \(-0.811735\pi\) | ||||
−0.830131 | + | 0.557568i | \(0.811735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.1741 | −0.746219 | −0.373110 | − | 0.927787i | \(-0.621708\pi\) | ||||
−0.373110 | + | 0.927787i | \(0.621708\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.819440 | −0.0275452 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.7418 | −0.394250 | −0.197125 | − | 0.980378i | \(-0.563160\pi\) | ||||
−0.197125 | + | 0.980378i | \(0.563160\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.79365 | −0.261391 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.62116 | −0.0543108 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42.6204 | −1.42624 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.3459 | −1.31519 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.7699 | −0.426374 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.1255 | 0.804629 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.5283 | 0.417377 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.0139 | 0.765855 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −53.4070 | −1.77531 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.7655 | −0.921938 | −0.460969 | − | 0.887416i | \(-0.652498\pi\) | ||||
−0.460969 | + | 0.887416i | \(0.652498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.8915 | −0.394417 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.1106 | −1.29579 | −0.647896 | − | 0.761729i | \(-0.724351\pi\) | ||||
−0.647896 | + | 0.761729i | \(0.724351\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.9721 | −0.826457 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.269407 | −0.00890633 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.3661 | 0.903707 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.66627 | 0.153926 | 0.0769630 | − | 0.997034i | \(-0.475478\pi\) | ||||
0.0769630 | + | 0.997034i | \(0.475478\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.3987 | 0.771012 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.1525 | −1.38747 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.72844 | 0.0568308 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.78324 | 0.222791 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.00389 | 0.0657454 | 0.0328727 | − | 0.999460i | \(-0.489534\pi\) | ||||
0.0328727 | + | 0.999460i | \(0.489534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.7420 | −0.614243 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.38962 | −0.143710 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.8283 | −0.517641 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.0177 | 1.33999 | 0.669994 | − | 0.742366i | \(-0.266297\pi\) | ||||
0.669994 | + | 0.742366i | \(0.266297\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.5307 | 0.996331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.9672 | −0.944302 | −0.472151 | − | 0.881518i | \(-0.656522\pi\) | ||||
−0.472151 | + | 0.881518i | \(0.656522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.97738 | 0.324908 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.70741 | −0.120602 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56.9248 | 1.84981 | 0.924905 | − | 0.380199i | \(-0.124145\pi\) | ||||
0.924905 | + | 0.380199i | \(0.124145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.3605 | −1.47246 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.0063 | 0.746031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.31738 | 0.204640 | 0.102320 | − | 0.994752i | \(-0.467373\pi\) | ||||
0.102320 | + | 0.994752i | \(0.467373\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53.1945 | 1.72133 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.23270 | −0.298451 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.46486 | −0.0795946 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0550 | −0.421129 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.79200 | −0.122195 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.7176 | −0.441586 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.63830 | 0.117000 | 0.0585000 | − | 0.998287i | \(-0.481368\pi\) | ||||
0.0585000 | + | 0.998287i | \(0.481368\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0910 | −0.773916 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.4885 | −1.81280 | −0.906402 | − | 0.422417i | \(-0.861182\pi\) | ||||
−0.906402 | + | 0.422417i | \(0.861182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.1175 | −1.15787 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.80691 | 0.0898932 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.4542 | 0.942322 | 0.471161 | − | 0.882047i | \(-0.343835\pi\) | ||||
0.471161 | + | 0.882047i | \(0.343835\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.80292 | −0.281342 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.8797 | 0.443146 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44.6845 | 1.42521 | 0.712607 | − | 0.701564i | \(-0.247514\pi\) | ||||
0.712607 | + | 0.701564i | \(0.247514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.4755 | 1.32152 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.3100 | −0.487322 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.2001 | 1.50088 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.8233 | 1.70975 | 0.854877 | − | 0.518831i | \(-0.173633\pi\) | ||||
0.854877 | + | 0.518831i | \(0.173633\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.5613 | 0.684229 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.9089 | 1.32860 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.4015 | 1.02617 | 0.513083 | − | 0.858339i | \(-0.328503\pi\) | ||||
0.513083 | + | 0.858339i | \(0.328503\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.11506 | −0.0669175 |
(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 | 4008.2.a.m.1.5 | ✓ | 13 | |
4.3 | odd | 2 | 8016.2.a.bg.1.5 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.5 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8016.2.a.bg.1.5 | 13 | 4.3 | odd | 2 |