Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(361,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.i (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.961 |
Dual form | 980.2.i.k.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.20711 | − | 2.09077i | −0.696923 | − | 1.20711i | −0.969528 | − | 0.244981i | \(-0.921218\pi\) |
0.272605 | − | 0.962126i | \(-0.412115\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.41421 | + | 2.44949i | −0.471405 | + | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.914214 | − | 1.58346i | −0.275646 | − | 0.477432i | 0.694652 | − | 0.719346i | \(-0.255558\pi\) |
−0.970298 | + | 0.241913i | \(0.922225\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.41421 | 1.77898 | 0.889491 | − | 0.456952i | \(-0.151059\pi\) | ||||
0.889491 | + | 0.456952i | \(0.151059\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.79289 | − | 3.10538i | −0.434840 | − | 0.753166i | 0.562442 | − | 0.826837i | \(-0.309862\pi\) |
−0.997283 | + | 0.0736709i | \(0.976529\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.82843 | − | 6.63103i | 0.878301 | − | 1.52126i | 0.0250976 | − | 0.999685i | \(-0.492010\pi\) |
0.853204 | − | 0.521578i | \(-0.174656\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.70711 | + | 2.95680i | −0.355956 | + | 0.616535i | −0.987281 | − | 0.158984i | \(-0.949178\pi\) |
0.631325 | + | 0.775519i | \(0.282511\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.65685 | −0.864756 | −0.432378 | − | 0.901692i | \(-0.642325\pi\) | ||||
−0.432378 | + | 0.901692i | \(0.642325\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.70711 | − | 6.42090i | −0.665816 | − | 1.15323i | −0.979063 | − | 0.203556i | \(-0.934750\pi\) |
0.313247 | − | 0.949672i | \(-0.398583\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.20711 | + | 3.82282i | −0.384208 | + | 0.665468i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.292893 | − | 0.507306i | 0.0481513 | − | 0.0834006i | −0.840945 | − | 0.541120i | \(-0.818000\pi\) |
0.889097 | + | 0.457720i | \(0.151334\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.74264 | − | 13.4106i | −1.23981 | − | 2.14742i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.41421 | 0.533211 | 0.266605 | − | 0.963806i | \(-0.414098\pi\) | ||||
0.266605 | + | 0.963806i | \(0.414098\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.343146 | 0.0523292 | 0.0261646 | − | 0.999658i | \(-0.491671\pi\) | ||||
0.0261646 | + | 0.999658i | \(0.491671\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421 | + | 2.44949i | 0.210819 | + | 0.365148i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.44975 | + | 9.43924i | −0.794927 | + | 1.37685i | 0.127958 | + | 0.991780i | \(0.459158\pi\) |
−0.922885 | + | 0.385075i | \(0.874176\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.32843 | + | 7.49706i | −0.606101 | + | 1.04980i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.12132 | + | 10.6024i | 0.840828 | + | 1.45636i | 0.889196 | + | 0.457527i | \(0.151265\pi\) |
−0.0483676 | + | 0.998830i | \(0.515402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.82843 | −0.246545 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.4853 | −2.44844 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.292893 | − | 0.507306i | −0.0381314 | − | 0.0660456i | 0.846330 | − | 0.532659i | \(-0.178807\pi\) |
−0.884461 | + | 0.466614i | \(0.845474\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.41421 | + | 9.37769i | −0.693219 | + | 1.20069i | 0.277558 | + | 0.960709i | \(0.410475\pi\) |
−0.970777 | + | 0.239982i | \(0.922859\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.20711 | − | 5.55487i | 0.397793 | − | 0.688997i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.53553 | − | 2.65962i | −0.187595 | − | 0.324925i | 0.756853 | − | 0.653586i | \(-0.226736\pi\) |
−0.944448 | + | 0.328661i | \(0.893403\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.24264 | 0.992297 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4853 | −1.24437 | −0.622187 | − | 0.782869i | \(-0.713756\pi\) | ||||
−0.622187 | + | 0.782869i | \(0.713756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.41421 | − | 9.37769i | −0.633686 | − | 1.09758i | −0.986792 | − | 0.161993i | \(-0.948208\pi\) |
0.353106 | − | 0.935583i | \(-0.385125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.20711 | + | 2.09077i | −0.139385 | + | 0.241421i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.57107 | − | 13.1135i | 0.851812 | − | 1.47538i | −0.0277599 | − | 0.999615i | \(-0.508837\pi\) |
0.879572 | − | 0.475766i | \(-0.157829\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.74264 | + | 8.21449i | 0.526960 | + | 0.912722i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.58579 | −0.388933 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.62132 | + | 9.73641i | 0.602669 | + | 1.04385i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.48528 | − | 14.6969i | 0.899438 | − | 1.55787i | 0.0712241 | − | 0.997460i | \(-0.477309\pi\) |
0.828214 | − | 0.560412i | \(-0.189357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.94975 | + | 15.5014i | −0.928046 | + | 1.60742i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.82843 | − | 6.63103i | −0.392788 | − | 0.680329i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.72792 | −0.987721 | −0.493860 | − | 0.869541i | \(-0.664415\pi\) | ||||
−0.493860 | + | 0.869541i | \(0.664415\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.17157 | 0.519763 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.414214 | − | 0.717439i | −0.0412158 | − | 0.0713878i | 0.844682 | − | 0.535269i | \(-0.179790\pi\) |
−0.885897 | + | 0.463881i | \(0.846456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.20711 | + | 3.82282i | −0.217473 | + | 0.376674i | −0.954035 | − | 0.299696i | \(-0.903115\pi\) |
0.736562 | + | 0.676370i | \(0.236448\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.58579 | − | 9.67487i | 0.539998 | − | 0.935305i | −0.458905 | − | 0.888485i | \(-0.651758\pi\) |
0.998903 | − | 0.0468193i | \(-0.0149085\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.50000 | − | 7.79423i | −0.431022 | − | 0.746552i | 0.565940 | − | 0.824447i | \(-0.308513\pi\) |
−0.996962 | + | 0.0778949i | \(0.975180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.41421 | −0.134231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.07107 | 0.853334 | 0.426667 | − | 0.904409i | \(-0.359688\pi\) | ||||
0.426667 | + | 0.904409i | \(0.359688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.70711 | + | 2.95680i | 0.159189 | + | 0.275723i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.07107 | + | 15.7116i | −0.838621 | + | 1.45253i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.82843 | − | 6.63103i | 0.348039 | − | 0.602821i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.12132 | − | 7.13834i | −0.371607 | − | 0.643642i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.10051 | −0.186390 | −0.0931948 | − | 0.995648i | \(-0.529708\pi\) | ||||
−0.0931948 | + | 0.995648i | \(0.529708\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.414214 | − | 0.717439i | −0.0364695 | − | 0.0631670i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.1213 | − | 17.5306i | 0.884304 | − | 1.53166i | 0.0377944 | − | 0.999286i | \(-0.487967\pi\) |
0.846509 | − | 0.532374i | \(-0.178700\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.207107 | + | 0.358719i | −0.0178249 | + | 0.0308737i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4853 | + | 18.1610i | 0.895818 | + | 1.55160i | 0.832789 | + | 0.553591i | \(0.186743\pi\) |
0.0630291 | + | 0.998012i | \(0.479924\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.89949 | 0.500389 | 0.250194 | − | 0.968196i | \(-0.419505\pi\) | ||||
0.250194 | + | 0.968196i | \(0.419505\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.3137 | 2.21601 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.86396 | − | 10.1567i | −0.490369 | − | 0.849344i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.32843 | + | 4.03295i | −0.193365 | + | 0.334919i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.2426 | + | 17.7408i | −0.839110 | + | 1.45338i | 0.0515300 | + | 0.998671i | \(0.483590\pi\) |
−0.890640 | + | 0.454709i | \(0.849743\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.08579 | + | 5.34474i | 0.251118 | + | 0.434949i | 0.963834 | − | 0.266504i | \(-0.0858685\pi\) |
−0.712716 | + | 0.701453i | \(0.752535\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.1421 | 0.819943 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.41421 | −0.595524 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.24264 | + | 5.61642i | 0.258791 | + | 0.448239i | 0.965918 | − | 0.258847i | \(-0.0833426\pi\) |
−0.707127 | + | 0.707086i | \(0.750009\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.7782 | − | 25.5965i | 1.17199 | − | 2.02994i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.77817 | − | 8.27604i | 0.374256 | − | 0.648230i | −0.615960 | − | 0.787778i | \(-0.711232\pi\) |
0.990215 | + | 0.139548i | \(0.0445650\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.20711 | + | 3.82282i | 0.171823 | + | 0.297606i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.414214 | −0.0320528 | −0.0160264 | − | 0.999872i | \(-0.505102\pi\) | ||||
−0.0160264 | + | 0.999872i | \(0.505102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.1421 | 2.16478 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.8284 | + | 18.7554i | 0.828071 | + | 1.43426i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.27817 | − | 10.8741i | 0.477321 | − | 0.826744i | −0.522341 | − | 0.852736i | \(-0.674941\pi\) |
0.999662 | + | 0.0259926i | \(0.00827465\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.707107 | + | 1.22474i | −0.0531494 | + | 0.0920575i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.24264 | + | 9.08052i | 0.391853 | + | 0.678710i | 0.992694 | − | 0.120659i | \(-0.0385007\pi\) |
−0.600841 | + | 0.799369i | \(0.705167\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2426 | 0.761329 | 0.380665 | − | 0.924713i | \(-0.375695\pi\) | ||||
0.380665 | + | 0.924713i | \(0.375695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.1421 | 1.93248 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.292893 | − | 0.507306i | −0.0215339 | − | 0.0372979i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.27817 | + | 5.67796i | −0.239724 | + | 0.415214i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.67157 | + | 4.62730i | −0.193308 | + | 0.334820i | −0.946345 | − | 0.323159i | \(-0.895255\pi\) |
0.753036 | + | 0.657979i | \(0.228588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.82843 | + | 4.89898i | 0.203595 | + | 0.352636i | 0.949684 | − | 0.313210i | \(-0.101404\pi\) |
−0.746089 | + | 0.665846i | \(0.768071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.4853 | −1.10892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.55635 | 0.253379 | 0.126690 | − | 0.991942i | \(-0.459565\pi\) | ||||
0.126690 | + | 0.991942i | \(0.459565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.636039 | + | 1.10165i | 0.0450876 | + | 0.0780940i | 0.887688 | − | 0.460445i | \(-0.152310\pi\) |
−0.842601 | + | 0.538539i | \(0.818977\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.70711 | + | 6.42090i | −0.261479 | + | 0.452895i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.70711 | − | 2.95680i | 0.119230 | − | 0.206512i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.82843 | − | 8.36308i | −0.335599 | − | 0.581274i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.0000 | −0.968400 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.68629 | −0.116089 | −0.0580445 | − | 0.998314i | \(-0.518487\pi\) | ||||
−0.0580445 | + | 0.998314i | \(0.518487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.6569 | + | 21.9223i | 0.867233 | + | 1.50209i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.171573 | − | 0.297173i | 0.0117012 | − | 0.0202670i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.0711 | + | 22.6398i | −0.883261 | + | 1.52985i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.5000 | − | 19.9186i | −0.773574 | − | 1.33987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.92893 | 0.664890 | 0.332445 | − | 0.943123i | \(-0.392126\pi\) | ||||
0.332445 | + | 0.943123i | \(0.392126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.86396 | + | 15.3528i | 0.588322 | + | 1.01900i | 0.994452 | + | 0.105188i | \(0.0335445\pi\) |
−0.406131 | + | 0.913815i | \(0.633122\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.05025 | + | 3.55114i | −0.135485 | + | 0.234666i | −0.925782 | − | 0.378057i | \(-0.876592\pi\) |
0.790298 | + | 0.612723i | \(0.209926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.41421 | − | 12.8418i | 0.485721 | − | 0.841294i | −0.514144 | − | 0.857704i | \(-0.671890\pi\) |
0.999865 | + | 0.0164099i | \(0.00522367\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.44975 | + | 9.43924i | 0.355502 | + | 0.615748i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −36.5563 | −2.37459 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8284 | 1.28259 | 0.641297 | − | 0.767293i | \(-0.278397\pi\) | ||||
0.641297 | + | 0.767293i | \(0.278397\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7782 | − | 23.8645i | −0.887530 | − | 1.53725i | −0.842786 | − | 0.538249i | \(-0.819086\pi\) |
−0.0447444 | − | 0.998998i | \(-0.514247\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.8284 | − | 18.7554i | 0.694644 | − | 1.20316i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.5563 | − | 42.5328i | 1.56248 | − | 2.70630i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.65685 | + | 16.7262i | 0.611978 | + | 1.05998i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9289 | −0.816067 | −0.408033 | − | 0.912967i | \(-0.633785\pi\) | ||||
−0.408033 | + | 0.912967i | \(0.633785\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.24264 | 0.392471 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.32843 | + | 7.49706i | 0.271057 | + | 0.469484i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.89949 | + | 11.9503i | −0.430379 | + | 0.745438i | −0.996906 | − | 0.0786054i | \(-0.974953\pi\) |
0.566527 | + | 0.824043i | \(0.308287\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.58579 | − | 11.4069i | 0.407650 | − | 0.706070i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.00000 | − | 8.66025i | −0.308313 | − | 0.534014i | 0.669680 | − | 0.742650i | \(-0.266431\pi\) |
−0.977993 | + | 0.208635i | \(0.933098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.2426 | 0.752059 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −40.9706 | −2.50736 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.36396 | − | 7.55860i | −0.266075 | − | 0.460856i | 0.701769 | − | 0.712404i | \(-0.252394\pi\) |
−0.967845 | + | 0.251548i | \(0.919060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.48528 | − | 4.30463i | 0.150970 | − | 0.261488i | −0.780614 | − | 0.625013i | \(-0.785094\pi\) |
0.931584 | + | 0.363525i | \(0.118427\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.914214 | + | 1.58346i | −0.0551292 | + | 0.0954865i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.29289 | + | 3.97141i | 0.137767 | + | 0.238619i | 0.926651 | − | 0.375923i | \(-0.122674\pi\) |
−0.788884 | + | 0.614542i | \(0.789341\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.9706 | 1.25547 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00000 | −0.0596550 | −0.0298275 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298275 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6213 | + | 23.5928i | 0.809703 | + | 1.40245i | 0.913069 | + | 0.407804i | \(0.133705\pi\) |
−0.103366 | + | 0.994643i | \(0.532961\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.24264 | + | 16.0087i | −0.547487 | + | 0.948275i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.07107 | − | 3.58719i | 0.121828 | − | 0.211011i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.7426 | + | 20.3389i | 0.688366 | + | 1.19228i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.5858 | −0.676849 | −0.338424 | − | 0.940994i | \(-0.609894\pi\) | ||||
−0.338424 | + | 0.940994i | \(0.609894\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.585786 | −0.0341058 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.378680 | + | 0.655892i | 0.0219732 | + | 0.0380587i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.9497 | + | 18.9655i | −0.633240 | + | 1.09680i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.00000 | + | 1.73205i | −0.0574485 | + | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.41421 | + | 9.37769i | 0.310017 | + | 0.536965i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.41421 | 0.366079 | 0.183039 | − | 0.983106i | \(-0.441406\pi\) | ||||
0.183039 | + | 0.983106i | \(0.441406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.6569 | 0.606247 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.4853 | + | 23.3572i | 0.764680 | + | 1.32446i | 0.940416 | + | 0.340027i | \(0.110436\pi\) |
−0.175735 | + | 0.984437i | \(0.556230\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.27817 | − | 12.6062i | 0.411387 | − | 0.712543i | −0.583655 | − | 0.812002i | \(-0.698378\pi\) |
0.995042 | + | 0.0994591i | \(0.0317112\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.48528 | + | 16.4290i | −0.532746 | + | 0.922744i | 0.466522 | + | 0.884509i | \(0.345507\pi\) |
−0.999269 | + | 0.0382345i | \(0.987827\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.25736 | + | 7.37396i | 0.238366 | + | 0.412863i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.9706 | −1.50535 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.4558 | −1.52768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.20711 | − | 5.55487i | −0.177898 | − | 0.308129i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.8640 | + | 18.8169i | −0.600778 | + | 1.04058i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.414214 | − | 0.717439i | 0.0227672 | − | 0.0394340i | −0.854417 | − | 0.519587i | \(-0.826086\pi\) |
0.877185 | + | 0.480153i | \(0.159419\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.828427 | + | 1.43488i | 0.0453975 | + | 0.0786308i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.07107 | −0.167790 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.72792 | 0.366493 | 0.183247 | − | 0.983067i | \(-0.441339\pi\) | ||||
0.183247 | + | 0.983067i | \(0.441339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.9497 | − | 18.9655i | −0.594709 | − | 1.03007i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.77817 | + | 11.7401i | −0.367059 | + | 0.635764i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.12132 | − | 7.13834i | 0.221884 | − | 0.384315i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.29289 | + | 3.97141i | 0.123089 | + | 0.213196i | 0.920984 | − | 0.389600i | \(-0.127387\pi\) |
−0.797895 | + | 0.602796i | \(0.794053\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000 | 0.963518 | 0.481759 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481759 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.65685 | −0.141812 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.03553 | − | 10.4539i | −0.321239 | − | 0.556402i | 0.659505 | − | 0.751700i | \(-0.270766\pi\) |
−0.980744 | + | 0.195298i | \(0.937433\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.24264 | + | 9.08052i | −0.278250 | + | 0.481944i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.65685 | − | 9.79796i | 0.298557 | − | 0.517116i | −0.677249 | − | 0.735754i | \(-0.736828\pi\) |
0.975806 | + | 0.218638i | \(0.0701613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.8137 | − | 34.3183i | −1.04283 | − | 1.80623i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.4853 | −0.970226 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.8284 | −0.566786 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.86396 | + | 4.96053i | 0.149498 | + | 0.258937i | 0.931042 | − | 0.364912i | \(-0.118901\pi\) |
−0.781544 | + | 0.623850i | \(0.785568\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.82843 | + | 8.36308i | −0.251358 | + | 0.435365i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.242641 | − | 0.420266i | 0.0125635 | − | 0.0217605i | −0.859675 | − | 0.510841i | \(-0.829334\pi\) |
0.872239 | + | 0.489080i | \(0.162667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.20711 | + | 2.09077i | 0.0623347 | + | 0.107967i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.8701 | −1.53839 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0000 | 0.719132 | 0.359566 | − | 0.933120i | \(-0.382925\pi\) | ||||
0.359566 | + | 0.933120i | \(0.382925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.53553 | + | 4.39167i | 0.129899 | + | 0.224992i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.2426 | − | 17.7408i | 0.523374 | − | 0.906511i | −0.476255 | − | 0.879307i | \(-0.658006\pi\) |
0.999630 | − | 0.0272042i | \(-0.00866044\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.485281 | + | 0.840532i | −0.0246682 | + | 0.0427266i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.57107 | + | 13.1135i | 0.383868 | + | 0.664880i | 0.991611 | − | 0.129254i | \(-0.0412583\pi\) |
−0.607743 | + | 0.794134i | \(0.707925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.2426 | 0.619137 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −48.8701 | −2.46517 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.57107 | − | 13.1135i | −0.380942 | − | 0.659810i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.79289 | + | 10.0336i | −0.290737 | + | 0.503571i | −0.973984 | − | 0.226616i | \(-0.927234\pi\) |
0.683247 | + | 0.730187i | \(0.260567\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.74264 | + | 15.1427i | −0.436587 | + | 0.756190i | −0.997424 | − | 0.0717360i | \(-0.977146\pi\) |
0.560837 | + | 0.827926i | \(0.310479\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.7782 | − | 41.1850i | −1.18448 | − | 2.05157i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.48528 | 0.471327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.07107 | −0.0530909 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5858 | − | 23.5313i | −0.671774 | − | 1.16355i | −0.977401 | − | 0.211395i | \(-0.932199\pi\) |
0.305627 | − | 0.952151i | \(-0.401134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.3137 | − | 43.8446i | 1.24863 | − | 2.16270i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | + | 6.92820i | −0.196352 | + | 0.340092i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.12132 | − | 12.3345i | −0.348733 | − | 0.604023i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.5563 | 1.05310 | 0.526548 | − | 0.850145i | \(-0.323486\pi\) | ||||
0.526548 | + | 0.850145i | \(0.323486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31371 | −0.112763 | −0.0563816 | − | 0.998409i | \(-0.517956\pi\) | ||||
−0.0563816 | + | 0.998409i | \(0.517956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.4142 | − | 26.6982i | −0.749465 | − | 1.29811i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.79289 | + | 3.10538i | −0.0869681 | + | 0.150633i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.1569 | + | 24.5204i | −0.683499 | + | 1.18386i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.08579 | + | 3.61269i | 0.100469 | + | 0.174017i | 0.911878 | − | 0.410462i | \(-0.134632\pi\) |
−0.811409 | + | 0.584479i | \(0.801299\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.2843 | 1.64760 | 0.823798 | − | 0.566883i | \(-0.191851\pi\) | ||||
0.823798 | + | 0.566883i | \(0.191851\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.2426 | 0.539043 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.0711 | + | 22.6398i | 0.625274 | + | 1.08301i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.87868 | + | 13.6463i | −0.376029 | + | 0.651301i | −0.990480 | − | 0.137653i | \(-0.956044\pi\) |
0.614452 | + | 0.788955i | \(0.289377\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.72792 | + | 13.3852i | −0.367165 | + | 0.635948i | −0.989121 | − | 0.147104i | \(-0.953005\pi\) |
0.621956 | + | 0.783052i | \(0.286338\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.48528 | − | 14.6969i | −0.402241 | − | 0.696702i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 49.4558 | 2.33918 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.1716 | 0.857570 | 0.428785 | − | 0.903407i | \(-0.358942\pi\) | ||||
0.428785 | + | 0.903407i | \(0.358942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.12132 | − | 5.40629i | −0.146977 | − | 0.254572i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.44975 | − | 12.9033i | 0.350020 | − | 0.606252i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.464466 | − | 0.804479i | 0.0217268 | − | 0.0376319i | −0.854958 | − | 0.518698i | \(-0.826417\pi\) |
0.876684 | + | 0.481066i | \(0.159750\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.742641 | + | 1.28629i | 0.0346635 | + | 0.0600389i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.6569 | 1.56756 | 0.783778 | − | 0.621041i | \(-0.213290\pi\) | ||||
0.783778 | + | 0.621041i | \(0.213290\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.4558 | 1.74072 | 0.870360 | − | 0.492415i | \(-0.163886\pi\) | ||||
0.870360 | + | 0.492415i | \(0.163886\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.94975 | + | 15.5014i | 0.415035 | + | 0.718861i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.44975 | − | 16.3674i | 0.437282 | − | 0.757395i | −0.560197 | − | 0.828360i | \(-0.689274\pi\) |
0.997479 | + | 0.0709647i | \(0.0226078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.82843 | − | 13.5592i | 0.360715 | − | 0.624777i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.313708 | − | 0.543359i | −0.0144243 | − | 0.0249837i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.65685 | −0.351321 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.6274 | −1.58548 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.29289 | − | 5.70346i | −0.150456 | − | 0.260598i | 0.780939 | − | 0.624607i | \(-0.214741\pi\) |
−0.931395 | + | 0.364010i | \(0.881408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.87868 | − | 3.25397i | 0.0856604 | − | 0.148368i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.86396 | + | 8.42463i | −0.220861 | + | 0.382543i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.29289 | + | 3.97141i | 0.103901 | + | 0.179962i | 0.913289 | − | 0.407313i | \(-0.133534\pi\) |
−0.809388 | + | 0.587275i | \(0.800201\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.0711 | −1.04331 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.2843 | −1.77287 | −0.886437 | − | 0.462849i | \(-0.846827\pi\) | ||||
−0.886437 | + | 0.462849i | \(0.846827\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.34924 | + | 14.4613i | 0.376031 | + | 0.651305i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.58579 | − | 4.47871i | 0.116222 | − | 0.201303i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.8137 | + | 27.3901i | −0.707919 | + | 1.22615i | 0.257709 | + | 0.966223i | \(0.417032\pi\) |
−0.965628 | + | 0.259929i | \(0.916301\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.500000 | + | 0.866025i | 0.0223384 | + | 0.0386912i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.04163 | −0.403146 | −0.201573 | − | 0.979473i | \(-0.564605\pi\) | ||||
−0.201573 | + | 0.979473i | \(0.564605\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.828427 | −0.0368645 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.9706 | − | 58.8387i | −1.50869 | − | 2.61312i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.4645 | − | 18.1250i | 0.463829 | − | 0.803376i | −0.535319 | − | 0.844650i | \(-0.679808\pi\) |
0.999148 | + | 0.0412743i | \(0.0131418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.58579 | + | 2.74666i | −0.0700142 | + | 0.121268i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.20711 | + | 3.82282i | 0.0972567 | + | 0.168454i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.9289 | 0.876473 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.3137 | −1.33062 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.6569 | − | 25.3864i | −0.642128 | − | 1.11220i | −0.984957 | − | 0.172801i | \(-0.944718\pi\) |
0.342828 | − | 0.939398i | \(-0.388615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0711 | + | 26.1039i | −0.659012 | + | 1.14144i | 0.321860 | + | 0.946787i | \(0.395692\pi\) |
−0.980872 | + | 0.194655i | \(0.937641\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.2929 | + | 23.0240i | −0.579048 | + | 1.00294i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.67157 | + | 9.82345i | 0.246590 | + | 0.427107i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.65685 | 0.0719014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.8995 | 0.948572 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.58579 | − | 9.67487i | −0.241495 | − | 0.418281i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.6569 | − | 21.9223i | 0.546184 | − | 0.946018i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.98528 | − | 15.5630i | 0.386307 | − | 0.669104i | −0.605642 | − | 0.795737i | \(-0.707084\pi\) |
0.991950 | + | 0.126633i | \(0.0404171\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.3640 | − | 21.4150i | −0.530588 | − | 0.919006i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.00000 | −0.385518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4853 | 1.04692 | 0.523458 | − | 0.852052i | \(-0.324642\pi\) | ||||
0.523458 | + | 0.852052i | \(0.324642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.3137 | − | 26.5241i | −0.653573 | − | 1.13202i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.8284 | + | 30.8797i | −0.759517 | + | 1.31552i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.707107 | + | 1.22474i | −0.0300150 | + | 0.0519875i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.8995 | − | 27.5387i | −0.673683 | − | 1.16685i | −0.976852 | − | 0.213917i | \(-0.931378\pi\) |
0.303169 | − | 0.952937i | \(-0.401955\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.20101 | 0.0930928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8284 | 0.668277 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.3137 | − | 21.3280i | −0.518961 | − | 0.898867i | −0.999757 | − | 0.0220344i | \(-0.992986\pi\) |
0.480796 | − | 0.876832i | \(-0.340348\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.53553 | − | 7.85578i | 0.190811 | − | 0.330495i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.89949 | + | 6.75412i | −0.163475 | + | 0.283148i | −0.936113 | − | 0.351700i | \(-0.885604\pi\) |
0.772637 | + | 0.634848i | \(0.218937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.414214 | + | 0.717439i | 0.0173343 | + | 0.0300239i | 0.874562 | − | 0.484913i | \(-0.161149\pi\) |
−0.857228 | + | 0.514937i | \(0.827815\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8995 | 0.538884 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.41421 | 0.142383 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.0355339 | − | 0.0615465i | −0.00147930 | − | 0.00256222i | 0.865285 | − | 0.501281i | \(-0.167138\pi\) |
−0.866764 | + | 0.498718i | \(0.833804\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.82843 | − | 11.8272i | 0.283780 | − | 0.491521i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.1924 | − | 19.3858i | 0.463541 | − | 0.802877i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.07107 | + | 15.7116i | 0.375042 | + | 0.649593i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.1716 | −1.03894 | −0.519471 | − | 0.854488i | \(-0.673871\pi\) | ||||
−0.519471 | + | 0.854488i | \(0.673871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.7696 | −2.33915 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.29289 | − | 7.43551i | −0.176586 | − | 0.305856i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.86396 | − | 6.69258i | 0.158674 | − | 0.274831i | −0.775717 | − | 0.631081i | \(-0.782611\pi\) |
0.934391 | + | 0.356250i | \(0.115945\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.53553 | − | 2.65962i | 0.0628452 | − | 0.108851i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.3995 | − | 23.2086i | −0.547489 | − | 0.948278i | −0.998446 | − | 0.0557324i | \(-0.982251\pi\) |
0.450957 | − | 0.892546i | \(-0.351083\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.3431 | 1.15614 | 0.578071 | − | 0.815987i | \(-0.303806\pi\) | ||||
0.578071 | + | 0.815987i | \(0.303806\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.68629 | 0.353733 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.82843 | − | 6.63103i | −0.155648 | − | 0.269590i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0355 | + | 24.3103i | −0.569685 | + | 0.986723i | 0.426912 | + | 0.904293i | \(0.359601\pi\) |
−0.996597 | + | 0.0824298i | \(0.973732\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.9558 | + | 60.5453i | −1.41416 | + | 2.44940i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.34315 | + | 16.1828i | 0.377366 | + | 0.653617i | 0.990678 | − | 0.136223i | \(-0.0434965\pi\) |
−0.613312 | + | 0.789841i | \(0.710163\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.24264 | −0.332375 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.8701 | −0.518129 | −0.259065 | − | 0.965860i | \(-0.583414\pi\) | ||||
−0.259065 | + | 0.965860i | \(0.583414\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.4350 | + | 37.1266i | 0.861547 | + | 1.49224i | 0.870436 | + | 0.492282i | \(0.163837\pi\) |
−0.00888927 | + | 0.999960i | \(0.502830\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.707107 | − | 1.22474i | 0.0283752 | − | 0.0491473i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.8995 | + | 29.2708i | 0.674901 | + | 1.16896i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.10051 | −0.0837526 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5147 | −0.896297 | −0.448148 | − | 0.893959i | \(-0.647916\pi\) | ||||
−0.448148 | + | 0.893959i | \(0.647916\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.03553 | + | 3.52565i | 0.0809052 | + | 0.140132i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.05025 | + | 1.81909i | −0.0416780 | + | 0.0721884i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.8284 | − | 25.6836i | 0.586604 | − | 1.01603i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.34315 | − | 14.4508i | −0.329534 | − | 0.570770i | 0.652885 | − | 0.757457i | \(-0.273558\pi\) |
−0.982420 | + | 0.186687i | \(0.940225\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.2132 | −1.50698 | −0.753491 | − | 0.657458i | \(-0.771632\pi\) | ||||
−0.753491 | + | 0.657458i | \(0.771632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.828427 | −0.0326193 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.5563 | + | 23.4803i | 0.532955 | + | 0.923105i | 0.999259 | + | 0.0384809i | \(0.0122519\pi\) |
−0.466304 | + | 0.884624i | \(0.654415\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.535534 | + | 0.927572i | −0.0210215 | + | 0.0364104i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.6569 | − | 42.7069i | 0.964897 | − | 1.67125i | 0.255006 | − | 0.966939i | \(-0.417922\pi\) |
0.709891 | − | 0.704312i | \(-0.248744\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.1213 | − | 17.5306i | −0.395473 | − | 0.684979i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.6274 | 1.19489 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.34315 | −0.363957 | −0.181979 | − | 0.983302i | \(-0.558250\pi\) | ||||
−0.181979 | + | 0.983302i | \(0.558250\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.92893 | + | 5.07306i | 0.113922 | + | 0.197319i | 0.917348 | − | 0.398085i | \(-0.130325\pi\) |
−0.803426 | + | 0.595404i | \(0.796992\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.7635 | + | 48.0877i | −1.07824 | + | 1.86757i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.94975 | − | 13.7694i | 0.307815 | − | 0.533152i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.9853 | − | 20.7591i | −0.463378 | − | 0.802594i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.7990 | 0.764332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.4853 | −1.71478 | −0.857391 | − | 0.514666i | \(-0.827916\pi\) | ||||
−0.857391 | + | 0.514666i | \(0.827916\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.207107 | + | 0.358719i | 0.00797154 | + | 0.0138071i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.8640 | − | 30.9413i | 0.686568 | − | 1.18917i | −0.286374 | − | 0.958118i | \(-0.592450\pi\) |
0.972941 | − | 0.231052i | \(-0.0742168\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.3995 | − | 37.0650i | 0.820030 | − | 1.42033i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.5563 | + | 23.4803i | 0.518719 | + | 0.898448i | 0.999763 | + | 0.0217518i | \(0.00692435\pi\) |
−0.481044 | + | 0.876696i | \(0.659742\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.9706 | 0.801244 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.89949 | 0.377689 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.2635 | + | 68.0063i | 1.49582 | + | 2.59083i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.2426 | + | 17.7408i | −0.389648 | + | 0.674891i | −0.992402 | − | 0.123036i | \(-0.960737\pi\) |
0.602754 | + | 0.797927i | \(0.294070\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.94975 | − | 5.10911i | 0.111890 | − | 0.193800i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.12132 | − | 10.6024i | −0.231862 | − | 0.401596i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −35.7990 | −1.35404 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4853 | 0.660410 | 0.330205 | − | 0.943909i | \(-0.392882\pi\) | ||||
0.330205 | + | 0.943909i | \(0.392882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.24264 | − | 3.88437i | −0.0845828 | − | 0.146502i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.1569 | − | 22.7883i | 0.495516 | − | 0.858259i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.8137 | − | 36.0504i | 0.781675 | − | 1.35390i | −0.149290 | − | 0.988793i | \(-0.547699\pi\) |
0.930965 | − | 0.365108i | \(-0.118968\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.4142 | + | 37.0905i | 0.803096 | + | 1.39100i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.3137 | 0.948006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.7279 | −0.438599 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.9350 | − | 41.4567i | −0.893870 | − | 1.54823i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.1213 | + | 20.9947i | −0.452049 | + | 0.782972i | −0.998513 | − | 0.0545107i | \(-0.982640\pi\) |
0.546464 | + | 0.837482i | \(0.315973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −33.2635 | + | 57.6140i | −1.23708 | + | 2.14269i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.32843 | + | 4.03295i | 0.0864756 | + | 0.149780i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0000 | −0.667583 | −0.333792 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.615224 | − | 1.06560i | −0.0227549 | − | 0.0394126i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.3492 | + | 24.8536i | −0.530001 | + | 0.917989i | 0.469386 | + | 0.882993i | \(0.344475\pi\) |
−0.999387 | + | 0.0349962i | \(0.988858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.80761 | + | 4.86293i | −0.103420 | + | 0.179128i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.67157 | − | 8.09140i | −0.171847 | − | 0.297647i | 0.767219 | − | 0.641385i | \(-0.221640\pi\) |
−0.939065 | + | 0.343738i | \(0.888307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −118.569 | −4.35572 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.0711 | −0.846395 | −0.423198 | − | 0.906037i | \(-0.639092\pi\) | ||||
−0.423198 | + | 0.906037i | \(0.639092\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.2426 | + | 17.7408i | 0.375261 | + | 0.649972i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.3137 | − | 19.5959i | 0.413947 | − | 0.716977i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.5711 | − | 23.5058i | 0.495215 | − | 0.857738i | −0.504769 | − | 0.863254i | \(-0.668423\pi\) |
0.999985 | + | 0.00551611i | \(0.00175584\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.6066 | + | 27.0314i | 0.568736 | + | 0.985080i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.17157 | 0.224607 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.8284 | 1.55663 | 0.778313 | − | 0.627877i | \(-0.216076\pi\) | ||||
0.778313 | + | 0.627877i | \(0.216076\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.53553 | − | 13.0519i | −0.273523 | − | 0.473755i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.4350 | + | 30.1984i | −0.632019 | + | 1.09469i | 0.355119 | + | 0.934821i | \(0.384440\pi\) |
−0.987138 | + | 0.159868i | \(0.948893\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.07107 | − | 8.78335i | 0.183345 | − | 0.317563i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.87868 | − | 3.25397i | −0.0678352 | − | 0.117494i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.142136 | −0.00512554 | −0.00256277 | − | 0.999997i | \(-0.500816\pi\) | ||||
−0.00256277 | + | 0.999997i | \(0.500816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.3137 | 1.19976 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.13604 | + | 15.8241i | 0.328600 | + | 0.569153i | 0.982234 | − | 0.187658i | \(-0.0600897\pi\) |
−0.653634 | + | 0.756811i | \(0.726756\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.70711 | + | 6.42090i | −0.133163 | + | 0.230645i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.0711 | − | 22.6398i | 0.468320 | − | 0.811153i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.58579 | + | 16.6031i | 0.343006 | + | 0.594105i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.92893 | 0.0689344 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.48528 | 0.231470 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.13604 | + | 15.8241i | 0.325665 | + | 0.564068i | 0.981647 | − | 0.190709i | \(-0.0610786\pi\) |
−0.655982 | + | 0.754777i | \(0.727745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.0711 | + | 20.9077i | −0.429741 | + | 0.744334i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.7279 | + | 60.1505i | −1.23322 | + | 2.13601i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.7782 | − | 25.5965i | −0.524128 | − | 0.907816i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.38478 | 0.0490513 | 0.0245256 | − | 0.999699i | \(-0.492192\pi\) | ||||
0.0245256 | + | 0.999699i | \(0.492192\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.0833 | 1.38267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.0000 | + | 41.5692i | 0.847998 | + | 1.46878i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.89949 | + | 17.1464i | −0.349346 | + | 0.605084i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.5355 | + | 18.2481i | −0.370868 | + | 0.642363i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.9853 | − | 34.6155i | −0.702645 | − | 1.21702i | −0.967535 | − | 0.252738i | \(-0.918669\pi\) |
0.264890 | − | 0.964279i | \(-0.414664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.5563 | 0.405798 | 0.202899 | − | 0.979200i | \(-0.434964\pi\) | ||||
0.202899 | + | 0.979200i | \(0.434964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | −0.420858 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.77817 | − | 8.27604i | −0.167372 | − | 0.289897i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.31371 | − | 2.27541i | 0.0459608 | − | 0.0796065i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0858 | + | 36.5217i | −0.735899 | + | 1.27461i | 0.218429 | + | 0.975853i | \(0.429907\pi\) |
−0.954328 | + | 0.298762i | \(0.903426\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.2635 | + | 24.7050i | 0.497193 | + | 0.861163i | 0.999995 | − | 0.00323843i | \(-0.00103082\pi\) |
−0.502802 | + | 0.864402i | \(0.667697\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.41421 | 0.153683 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.0416 | 1.32284 | 0.661419 | − | 0.750017i | \(-0.269955\pi\) | ||||
0.661419 | + | 0.750017i | \(0.269955\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.36396 | + | 2.36245i | 0.0473723 | + | 0.0820513i | 0.888739 | − | 0.458413i | \(-0.151582\pi\) |
−0.841367 | + | 0.540464i | \(0.818249\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.53553 | − | 9.58783i | 0.192026 | − | 0.332598i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.207107 | + | 0.358719i | −0.00716723 | + | 0.0124140i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.53553 | + | 2.65962i | 0.0530758 | + | 0.0919300i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.3848 | −0.496618 | −0.248309 | − | 0.968681i | \(-0.579875\pi\) | ||||
−0.248309 | + | 0.968681i | \(0.579875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.31371 | −0.252197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.20711 | + | 2.09077i | 0.0415750 | + | 0.0720100i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.0711 | − | 24.3718i | 0.484059 | − | 0.838416i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.8848 | − | 56.9581i | 1.12860 | − | 1.95480i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.00000 | + | 1.73205i | 0.0342796 | + | 0.0593739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.2843 | 0.899956 | 0.449978 | − | 0.893040i | \(-0.351432\pi\) | ||||
0.449978 | + | 0.893040i | \(0.351432\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.6569 | 0.740649 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.58579 | + | 13.1390i | 0.259126 | + | 0.448819i | 0.966008 | − | 0.258513i | \(-0.0832323\pi\) |
−0.706882 | + | 0.707331i | \(0.749899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.72792 | + | 4.72490i | −0.0930755 | + | 0.161211i | −0.908804 | − | 0.417224i | \(-0.863003\pi\) |
0.815728 | + | 0.578435i | \(0.196336\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.1213 | − | 24.4588i | 0.480695 | − | 0.832589i | −0.519059 | − | 0.854738i | \(-0.673718\pi\) |
0.999755 | + | 0.0221495i | \(0.00705097\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.27817 | − | 10.8741i | −0.213464 | − | 0.369731i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.0000 | −0.339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.6863 | −0.939193 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.84924 | − | 17.0594i | −0.333729 | − | 0.578035i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.7574 | − | 23.8284i | 0.465616 | − | 0.806471i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.6569 | + | 28.8505i | −0.562462 | + | 0.974213i | 0.434819 | + | 0.900518i | \(0.356812\pi\) |
−0.997281 | + | 0.0736948i | \(0.976521\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.9853 | + | 24.2232i | 0.471712 | + | 0.817029i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.284271 | 0.00957734 | 0.00478867 | − | 0.999989i | \(-0.498476\pi\) | ||||
0.00478867 | + | 0.999989i | \(0.498476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.1127 | 1.85469 | 0.927345 | − | 0.374208i | \(-0.122085\pi\) | ||||
0.927345 | + | 0.374208i | \(0.122085\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.707107 | + | 1.22474i | 0.0237691 | + | 0.0411693i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.7990 | − | 18.7044i | 0.362595 | − | 0.628032i | −0.625792 | − | 0.779990i | \(-0.715224\pi\) |
0.988387 | + | 0.151957i | \(0.0485576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.67157 | − | 15.0196i | 0.290509 | − | 0.503176i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.7279 | + | 72.2749i | 1.39637 | + | 2.41859i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.4853 | 0.350484 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 52.8701 | 1.76528 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.2635 | + | 29.9012i | 0.575768 | + | 0.997260i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.9497 | − | 38.0181i | 0.731252 | − | 1.26657i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.12132 | − | 8.87039i | 0.170238 | − | 0.294862i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.2635 | + | 36.8294i | 0.706041 | + | 1.22290i | 0.966314 | + | 0.257365i | \(0.0828541\pi\) |
−0.260273 | + | 0.965535i | \(0.583813\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.34315 | 0.0777172 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5980 | 0.781836 | 0.390918 | − | 0.920426i | \(-0.372158\pi\) | ||||
0.390918 | + | 0.920426i | \(0.372158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.31371 | + | 12.6677i | 0.242048 | + | 0.419240i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.0711 | − | 22.6398i | 0.432116 | − | 0.748447i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.7426 | − | 30.7312i | 0.585276 | − | 1.01373i | −0.409565 | − | 0.912281i | \(-0.634320\pi\) |
0.994841 | − | 0.101446i | \(-0.0323471\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.74264 | − | 13.4106i | −0.255129 | − | 0.441896i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −67.2548 | −2.21372 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.585786 | −0.0192605 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.24264 | − | 10.8126i | −0.205035 | − | 0.355131i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3640 | − | 40.4676i | 0.766547 | − | 1.32770i | −0.172878 | − | 0.984943i | \(-0.555307\pi\) |
0.939425 | − | 0.342755i | \(-0.111360\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.5563 | − | 56.3893i | 1.06585 | − | 1.84610i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.27817 | + | 5.67796i | 0.107208 | + | 0.185689i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7279 | 0.579146 | 0.289573 | − | 0.957156i | \(-0.406487\pi\) | ||||
0.289573 | + | 0.957156i | \(0.406487\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.1421 | −1.14682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.00000 | + | 3.46410i | 0.0651981 | + | 0.112926i | 0.896782 | − | 0.442473i | \(-0.145899\pi\) |
−0.831584 | + | 0.555399i | \(0.812565\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.82843 | + | 10.0951i | −0.189800 | + | 0.328743i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.02082 | + | 13.8925i | −0.260641 | + | 0.451444i | −0.966413 | − | 0.256996i | \(-0.917267\pi\) |
0.705771 | + | 0.708440i | \(0.250601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.7279 | − | 60.1505i | −1.12732 | − | 1.95257i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.7990 | 1.48513 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.8701 | 0.481688 | 0.240844 | − | 0.970564i | \(-0.422576\pi\) | ||||
0.240844 | + | 0.970564i | \(0.422576\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.67157 | + | 4.62730i | 0.0864501 | + | 0.149736i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.2782 | − | 17.8023i | 0.332246 | − | 0.575467i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.9853 | + | 20.7591i | −0.386622 | + | 0.669649i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.7990 | + | 27.3647i | 0.509115 | + | 0.881814i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.65685 | 0.182101 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.4558 | 1.39745 | 0.698723 | − | 0.715392i | \(-0.253752\pi\) | ||||
0.698723 | + | 0.715392i | \(0.253752\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.1421 | + | 57.4039i | 1.06468 | + | 1.84408i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.2635 | + | 36.8294i | −0.682377 | + | 1.18191i | 0.291877 | + | 0.956456i | \(0.405720\pi\) |
−0.974254 | + | 0.225455i | \(0.927613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.74264 | + | 13.4106i | −0.247963 | + | 0.429484i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.0711 | − | 17.4436i | −0.322202 | − | 0.558070i | 0.658740 | − | 0.752371i | \(-0.271090\pi\) |
−0.980942 | + | 0.194300i | \(0.937756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.0294 | −0.991705 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.4558 | 0.812743 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.0061 | − | 34.6516i | −0.638095 | − | 1.10521i | −0.985850 | − | 0.167628i | \(-0.946389\pi\) |
0.347755 | − | 0.937585i | \(-0.386944\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.77817 | − | 3.07989i | 0.0566574 | − | 0.0981334i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.585786 | + | 1.01461i | −0.0186269 | + | 0.0322628i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.34315 | − | 2.32640i | −0.0426664 | − | 0.0739004i | 0.843904 | − | 0.536495i | \(-0.180252\pi\) |
−0.886570 | + | 0.462594i | \(0.846919\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.00000 | −0.0634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.27208 | 0.0403276 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.4203 | − | 31.9049i | −0.583377 | − | 1.01044i | −0.995076 | − | 0.0991186i | \(-0.968398\pi\) |
0.411699 | − | 0.911320i | \(-0.364936\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.121320 | + | 0.210133i | −0.00383841 | + | 0.00664831i |
(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 | 980.2.i.k.961.1 | 4 | ||
7.2 | even | 3 | 980.2.a.k.1.2 | yes | 2 | ||
7.3 | odd | 6 | 980.2.i.l.361.2 | 4 | |||
7.4 | even | 3 | inner | 980.2.i.k.361.1 | 4 | ||
7.5 | odd | 6 | 980.2.a.j.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 980.2.i.l.961.2 | 4 | |||
21.2 | odd | 6 | 8820.2.a.bl.1.1 | 2 | |||
21.5 | even | 6 | 8820.2.a.bg.1.1 | 2 | |||
28.19 | even | 6 | 3920.2.a.bx.1.2 | 2 | |||
28.23 | odd | 6 | 3920.2.a.bo.1.1 | 2 | |||
35.2 | odd | 12 | 4900.2.e.r.2549.1 | 4 | |||
35.9 | even | 6 | 4900.2.a.x.1.1 | 2 | |||
35.12 | even | 12 | 4900.2.e.q.2549.4 | 4 | |||
35.19 | odd | 6 | 4900.2.a.z.1.2 | 2 | |||
35.23 | odd | 12 | 4900.2.e.r.2549.4 | 4 | |||
35.33 | even | 12 | 4900.2.e.q.2549.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.a.j.1.1 | ✓ | 2 | 7.5 | odd | 6 | ||
980.2.a.k.1.2 | yes | 2 | 7.2 | even | 3 | ||
980.2.i.k.361.1 | 4 | 7.4 | even | 3 | inner | ||
980.2.i.k.961.1 | 4 | 1.1 | even | 1 | trivial | ||
980.2.i.l.361.2 | 4 | 7.3 | odd | 6 | |||
980.2.i.l.961.2 | 4 | 7.6 | odd | 2 | |||
3920.2.a.bo.1.1 | 2 | 28.23 | odd | 6 | |||
3920.2.a.bx.1.2 | 2 | 28.19 | even | 6 | |||
4900.2.a.x.1.1 | 2 | 35.9 | even | 6 | |||
4900.2.a.z.1.2 | 2 | 35.19 | odd | 6 | |||
4900.2.e.q.2549.1 | 4 | 35.33 | even | 12 | |||
4900.2.e.q.2549.4 | 4 | 35.12 | even | 12 | |||
4900.2.e.r.2549.1 | 4 | 35.2 | odd | 12 | |||
4900.2.e.r.2549.4 | 4 | 35.23 | odd | 12 | |||
8820.2.a.bg.1.1 | 2 | 21.5 | even | 6 | |||
8820.2.a.bl.1.1 | 2 | 21.2 | odd | 6 |