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 | 361.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.361 |
Dual form | 980.2.i.l.961.2 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | −0.272605 | − | 0.962126i | \(-0.587885\pi\) |
0.969528 | − | 0.244981i | \(-0.0787816\pi\) | |||||||
\(4\) | 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 | −0.970298 | − | 0.241913i | \(-0.922225\pi\) |
0.694652 | + | 0.719346i | \(0.255558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.41421 | −1.77898 | −0.889491 | − | 0.456952i | \(-0.848941\pi\) | ||||
−0.889491 | + | 0.456952i | \(0.848941\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.79289 | − | 3.10538i | 0.434840 | − | 0.753166i | −0.562442 | − | 0.826837i | \(-0.690138\pi\) |
0.997283 | + | 0.0736709i | \(0.0234714\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.82843 | − | 6.63103i | −0.878301 | − | 1.52126i | −0.853204 | − | 0.521578i | \(-0.825344\pi\) |
−0.0250976 | − | 0.999685i | \(-0.507990\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.70711 | − | 2.95680i | −0.355956 | − | 0.616535i | 0.631325 | − | 0.775519i | \(-0.282511\pi\) |
−0.987281 | + | 0.158984i | \(0.949178\pi\) | |||||||
\(24\) | 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 | −0.313247 | − | 0.949672i | \(-0.601417\pi\) |
0.979063 | − | 0.203556i | \(-0.0652498\pi\) | |||||||
\(32\) | 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 | 0.889097 | − | 0.457720i | \(-0.151334\pi\) |
−0.840945 | + | 0.541120i | \(0.818000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.74264 | + | 13.4106i | −1.23981 | + | 2.14742i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.41421 | −0.533211 | −0.266605 | − | 0.963806i | \(-0.585902\pi\) | ||||
−0.266605 | + | 0.963806i | \(0.585902\pi\) | |||||||
\(42\) | 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 | 0.922885 | + | 0.385075i | \(0.125824\pi\) |
−0.127958 | + | 0.991780i | \(0.540842\pi\) | |||||||
\(48\) | 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 | −0.0483676 | − | 0.998830i | \(-0.515402\pi\) |
0.889196 | − | 0.457527i | \(-0.151265\pi\) | |||||||
\(54\) | 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 | \(-0.821193\pi\) |
0.884461 | + | 0.466614i | \(0.154526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.41421 | + | 9.37769i | 0.693219 | + | 1.20069i | 0.970777 | + | 0.239982i | \(0.0771415\pi\) |
−0.277558 | + | 0.960709i | \(0.589525\pi\) | |||||||
\(62\) | 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 | −0.944448 | − | 0.328661i | \(-0.893403\pi\) |
0.756853 | + | 0.653586i | \(0.226736\pi\) | |||||||
\(68\) | 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 | −0.353106 | − | 0.935583i | \(-0.614875\pi\) |
0.986792 | − | 0.161993i | \(-0.0517921\pi\) | |||||||
\(74\) | 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 | 0.879572 | + | 0.475766i | \(0.157829\pi\) |
−0.0277599 | + | 0.999615i | \(0.508837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.74264 | − | 8.21449i | 0.526960 | − | 0.912722i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 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 | −0.828214 | − | 0.560412i | \(-0.810643\pi\) |
−0.0712241 | − | 0.997460i | \(-0.522691\pi\) | |||||||
\(90\) | 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 | \(-0.335585\pi\) | ||||
0.493860 | + | 0.869541i | \(0.335585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.17157 | 0.519763 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.414214 | − | 0.717439i | 0.0412158 | − | 0.0713878i | −0.844682 | − | 0.535269i | \(-0.820210\pi\) |
0.885897 | + | 0.463881i | \(0.153544\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.20711 | + | 3.82282i | 0.217473 | + | 0.376674i | 0.954035 | − | 0.299696i | \(-0.0968854\pi\) |
−0.736562 | + | 0.676370i | \(0.763552\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.58579 | + | 9.67487i | 0.539998 | + | 0.935305i | 0.998903 | + | 0.0468193i | \(0.0149085\pi\) |
−0.458905 | + | 0.888485i | \(0.651758\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.50000 | + | 7.79423i | −0.431022 | + | 0.746552i | −0.996962 | − | 0.0778949i | \(-0.975180\pi\) |
0.565940 | + | 0.824447i | \(0.308513\pi\) | |||||||
\(110\) | 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 | −0.846509 | − | 0.532374i | \(-0.821300\pi\) |
−0.0377944 | − | 0.999286i | \(-0.512033\pi\) | |||||||
\(132\) | 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 | 0.0630291 | − | 0.998012i | \(-0.479924\pi\) |
0.832789 | − | 0.553591i | \(-0.186743\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.89949 | −0.500389 | −0.250194 | − | 0.968196i | \(-0.580495\pi\) | ||||
−0.250194 | + | 0.968196i | \(0.580495\pi\) | |||||||
\(140\) | 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 | −0.890640 | − | 0.454709i | \(-0.849743\pi\) |
0.0515300 | − | 0.998671i | \(-0.483590\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.08579 | − | 5.34474i | 0.251118 | − | 0.434949i | −0.712716 | − | 0.701453i | \(-0.752535\pi\) |
0.963834 | + | 0.266504i | \(0.0858685\pi\) | |||||||
\(152\) | 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 | \(-0.916657\pi\) |
0.707127 | + | 0.707086i | \(0.249991\pi\) | |||||||
\(158\) | 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 | 0.990215 | − | 0.139548i | \(-0.0445650\pi\) |
−0.615960 | + | 0.787778i | \(0.711232\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.20711 | − | 3.82282i | 0.171823 | − | 0.297606i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.414214 | 0.0320528 | 0.0160264 | − | 0.999872i | \(-0.494898\pi\) | ||||
0.0160264 | + | 0.999872i | \(0.494898\pi\) | |||||||
\(168\) | 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 | \(-0.325059\pi\) |
−0.999662 | + | 0.0259926i | \(0.991725\pi\) | |||||||
\(174\) | 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 | −0.600841 | − | 0.799369i | \(-0.705167\pi\) |
0.992694 | + | 0.120659i | \(0.0385007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2426 | −0.761329 | −0.380665 | − | 0.924713i | \(-0.624305\pi\) | ||||
−0.380665 | + | 0.924713i | \(0.624305\pi\) | |||||||
\(182\) | 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 | 0.753036 | − | 0.657979i | \(-0.228588\pi\) |
−0.946345 | + | 0.323159i | \(0.895255\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.82843 | − | 4.89898i | 0.203595 | − | 0.352636i | −0.746089 | − | 0.665846i | \(-0.768071\pi\) |
0.949684 | + | 0.313210i | \(0.101404\pi\) | |||||||
\(194\) | 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 | \(-0.847690\pi\) |
0.842601 | + | 0.538539i | \(0.181023\pi\) | |||||||
\(200\) | 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 | \(-0.607874\pi\) | ||||
−0.332445 | + | 0.943123i | \(0.607874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.86396 | + | 15.3528i | −0.588322 | + | 1.01900i | 0.406131 | + | 0.913815i | \(0.366878\pi\) |
−0.994452 | + | 0.105188i | \(0.966456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.05025 | + | 3.55114i | 0.135485 | + | 0.234666i | 0.925782 | − | 0.378057i | \(-0.123408\pi\) |
−0.790298 | + | 0.612723i | \(0.790074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.41421 | + | 12.8418i | 0.485721 | + | 0.841294i | 0.999865 | − | 0.0164099i | \(-0.00522367\pi\) |
−0.514144 | + | 0.857704i | \(0.671890\pi\) | |||||||
\(234\) | 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 | 0.0447444 | − | 0.998998i | \(-0.485753\pi\) |
0.842786 | − | 0.538249i | \(-0.180914\pi\) | |||||||
\(242\) | 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 | \(-0.366215\pi\) | ||||
0.408033 | + | 0.912967i | \(0.366215\pi\) | |||||||
\(252\) | 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 | \(-0.0250467\pi\) |
−0.566527 | + | 0.824043i | \(0.691713\pi\) | |||||||
\(258\) | 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 | −0.977993 | − | 0.208635i | \(-0.933098\pi\) |
0.669680 | + | 0.742650i | \(0.266431\pi\) | |||||||
\(264\) | 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 | \(-0.747606\pi\) |
0.967845 | + | 0.251548i | \(0.0809396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.48528 | − | 4.30463i | −0.150970 | − | 0.261488i | 0.780614 | − | 0.625013i | \(-0.214906\pi\) |
−0.931584 | + | 0.363525i | \(0.881573\pi\) | |||||||
\(272\) | 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 | −0.788884 | − | 0.614542i | \(-0.789341\pi\) |
0.926651 | + | 0.375923i | \(0.122674\pi\) | |||||||
\(278\) | 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 | 0.103366 | + | 0.994643i | \(0.467039\pi\) |
−0.913069 | + | 0.407804i | \(0.866295\pi\) | |||||||
\(284\) | 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 | \(-0.390106\pi\) | ||||
0.338424 | + | 0.940994i | \(0.390106\pi\) | |||||||
\(294\) | 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 | \(-0.558594\pi\) | ||||
−0.183039 | + | 0.983106i | \(0.558594\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.6569 | 0.606247 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4853 | + | 23.3572i | −0.764680 | + | 1.32446i | 0.175735 | + | 0.984437i | \(0.443770\pi\) |
−0.940416 | + | 0.340027i | \(0.889564\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.27817 | − | 12.6062i | −0.411387 | − | 0.712543i | 0.583655 | − | 0.812002i | \(-0.301622\pi\) |
−0.995042 | + | 0.0994591i | \(0.968289\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.48528 | − | 16.4290i | −0.532746 | − | 0.922744i | −0.999269 | − | 0.0382345i | \(-0.987827\pi\) |
0.466522 | − | 0.884509i | \(-0.345507\pi\) | |||||||
\(318\) | 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 | 0.877185 | − | 0.480153i | \(-0.159419\pi\) |
−0.854417 | + | 0.519587i | \(0.826086\pi\) | |||||||
\(332\) | 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 | −0.797895 | − | 0.602796i | \(-0.794053\pi\) |
0.920984 | + | 0.389600i | \(0.127387\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.65685 | −0.141812 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.03553 | − | 10.4539i | 0.321239 | − | 0.556402i | −0.659505 | − | 0.751700i | \(-0.729234\pi\) |
0.980744 | + | 0.195298i | \(0.0625674\pi\) | |||||||
\(354\) | 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 | 0.975806 | − | 0.218638i | \(-0.0701613\pi\) |
−0.677249 | + | 0.735754i | \(0.736828\pi\) | |||||||
\(360\) | 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 | \(-0.881099\pi\) |
0.781544 | + | 0.623850i | \(0.214432\pi\) | |||||||
\(368\) | 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 | 0.872239 | − | 0.489080i | \(-0.162667\pi\) |
−0.859675 | + | 0.510841i | \(0.829334\pi\) | |||||||
\(374\) | 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 | −0.999630 | − | 0.0272042i | \(-0.991340\pi\) |
0.476255 | − | 0.879307i | \(-0.341994\pi\) | |||||||
\(384\) | 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 | −0.607743 | − | 0.794134i | \(-0.707925\pi\) |
0.991611 | + | 0.129254i | \(0.0412583\pi\) | |||||||
\(390\) | 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 | \(-0.0727662\pi\) |
−0.683247 | + | 0.730187i | \(0.739433\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.74264 | − | 15.1427i | −0.436587 | − | 0.756190i | 0.560837 | − | 0.827926i | \(-0.310479\pi\) |
−0.997424 | + | 0.0717360i | \(0.977146\pi\) | |||||||
\(402\) | 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 | −0.305627 | − | 0.952151i | \(-0.598866\pi\) |
0.977401 | − | 0.211395i | \(-0.0678007\pi\) | |||||||
\(410\) | 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 | \(-0.676514\pi\) | ||||
−0.526548 | + | 0.850145i | \(0.676514\pi\) | |||||||
\(420\) | 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 | −0.811409 | − | 0.584479i | \(-0.801299\pi\) |
0.911878 | + | 0.410462i | \(0.134632\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.2843 | −1.64760 | −0.823798 | − | 0.566883i | \(-0.808149\pi\) | ||||
−0.823798 | + | 0.566883i | \(0.808149\pi\) | |||||||
\(434\) | 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 | \(-0.0439560\pi\) |
−0.614452 | + | 0.788955i | \(0.710623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.72792 | − | 13.3852i | −0.367165 | − | 0.635948i | 0.621956 | − | 0.783052i | \(-0.286338\pi\) |
−0.989121 | + | 0.147104i | \(0.953005\pi\) | |||||||
\(444\) | 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 | 0.876684 | − | 0.481066i | \(-0.159750\pi\) |
−0.854958 | + | 0.518698i | \(0.826417\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.742641 | − | 1.28629i | 0.0346635 | − | 0.0600389i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.6569 | −1.56756 | −0.783778 | − | 0.621041i | \(-0.786710\pi\) | ||||
−0.783778 | + | 0.621041i | \(0.786710\pi\) | |||||||
\(462\) | 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 | \(-0.310726\pi\) |
−0.997479 | + | 0.0709647i | \(0.977392\pi\) | |||||||
\(468\) | 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 | \(-0.785259\pi\) |
0.931395 | + | 0.364010i | \(0.118592\pi\) | |||||||
\(480\) | 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 | −0.809388 | − | 0.587275i | \(-0.800201\pi\) |
0.913289 | + | 0.407313i | \(0.133534\pi\) | |||||||
\(488\) | 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 | −0.965628 | − | 0.259929i | \(-0.916301\pi\) |
0.257709 | − | 0.966223i | \(-0.417032\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.500000 | − | 0.866025i | 0.0223384 | − | 0.0386912i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.04163 | 0.403146 | 0.201573 | − | 0.979473i | \(-0.435395\pi\) | ||||
0.201573 | + | 0.979473i | \(0.435395\pi\) | |||||||
\(504\) | 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 | \(-0.320192\pi\) |
−0.999148 | + | 0.0412743i | \(0.986858\pi\) | |||||||
\(510\) | 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 | −0.342828 | − | 0.939398i | \(-0.611385\pi\) |
0.984957 | − | 0.172801i | \(-0.0552818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.0711 | + | 26.1039i | 0.659012 | + | 1.14144i | 0.980872 | + | 0.194655i | \(0.0623586\pi\) |
−0.321860 | + | 0.946787i | \(0.604308\pi\) | |||||||
\(524\) | 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 | 0.991950 | − | 0.126633i | \(-0.0404171\pi\) |
−0.605642 | + | 0.795737i | \(0.707084\pi\) | |||||||
\(542\) | 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 | 0.303169 | + | 0.952937i | \(0.401955\pi\) |
−0.976852 | + | 0.213917i | \(0.931378\pi\) | |||||||
\(558\) | 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 | −0.480796 | − | 0.876832i | \(-0.659652\pi\) |
0.999757 | − | 0.0220344i | \(-0.00701433\pi\) | |||||||
\(564\) | 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 | 0.772637 | − | 0.634848i | \(-0.218937\pi\) |
−0.936113 | + | 0.351700i | \(0.885604\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.414214 | − | 0.717439i | 0.0173343 | − | 0.0300239i | −0.857228 | − | 0.514937i | \(-0.827815\pi\) |
0.874562 | + | 0.484913i | \(0.161149\pi\) | |||||||
\(572\) | 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 | \(-0.832862\pi\) |
0.866764 | + | 0.498718i | \(0.166196\pi\) | |||||||
\(578\) | 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 | \(-0.326129\pi\) | ||||
0.519471 | + | 0.854488i | \(0.326129\pi\) | |||||||
\(588\) | 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 | \(-0.217389\pi\) |
−0.934391 | + | 0.356250i | \(0.884055\pi\) | |||||||
\(594\) | 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 | 0.450957 | + | 0.892546i | \(0.351083\pi\) |
−0.998446 | + | 0.0557324i | \(0.982251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.3431 | −1.15614 | −0.578071 | − | 0.815987i | \(-0.696194\pi\) | ||||
−0.578071 | + | 0.815987i | \(0.696194\pi\) | |||||||
\(602\) | 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 | 0.996597 | + | 0.0824298i | \(0.0262680\pi\) |
−0.426912 | + | 0.904293i | \(0.640399\pi\) | |||||||
\(608\) | 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 | −0.613312 | − | 0.789841i | \(-0.710163\pi\) |
0.990678 | + | 0.136223i | \(0.0434965\pi\) | |||||||
\(614\) | 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 | 0.00888927 | + | 0.999960i | \(0.497170\pi\) |
−0.870436 | + | 0.492282i | \(0.836163\pi\) | |||||||
\(620\) | 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 | −0.982420 | − | 0.186687i | \(-0.940225\pi\) |
0.652885 | + | 0.757457i | \(0.273558\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.2132 | 1.50698 | 0.753491 | − | 0.657458i | \(-0.228368\pi\) | ||||
0.753491 | + | 0.657458i | \(0.228368\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.828427 | −0.0326193 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.5563 | + | 23.4803i | −0.532955 | + | 0.923105i | 0.466304 | + | 0.884624i | \(0.345585\pi\) |
−0.999259 | + | 0.0384809i | \(0.987748\pi\) | |||||||
\(648\) | 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 | 0.709891 | + | 0.704312i | \(0.248744\pi\) |
0.255006 | + | 0.966939i | \(0.417922\pi\) | |||||||
\(654\) | 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 | \(-0.869675\pi\) |
0.803426 | + | 0.595404i | \(0.203008\pi\) | |||||||
\(662\) | 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 | −0.972941 | − | 0.231052i | \(-0.925783\pi\) |
0.286374 | − | 0.958118i | \(-0.407550\pi\) | |||||||
\(678\) | 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 | −0.481044 | − | 0.876696i | \(-0.659742\pi\) |
0.999763 | − | 0.0217518i | \(-0.00692435\pi\) | |||||||
\(684\) | 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 | \(-0.0392632\pi\) |
−0.602754 | + | 0.797927i | \(0.705930\pi\) | |||||||
\(692\) | 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 | 0.930965 | + | 0.365108i | \(0.118968\pi\) |
−0.149290 | + | 0.988793i | \(0.547699\pi\) | |||||||
\(710\) | 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 | \(-0.0173599\pi\) |
−0.546464 | + | 0.837482i | \(0.684027\pi\) | |||||||
\(720\) | 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 | \(-0.391672\pi\) | ||||
0.333792 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(728\) | 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 | 0.999387 | + | 0.0349962i | \(0.0111419\pi\) |
−0.469386 | + | 0.882993i | \(0.655525\pi\) | |||||||
\(734\) | 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 | −0.939065 | − | 0.343738i | \(-0.888307\pi\) |
0.767219 | + | 0.641385i | \(0.221640\pi\) | |||||||
\(740\) | 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 | 0.999985 | − | 0.00551611i | \(-0.00175584\pi\) |
−0.504769 | + | 0.863254i | \(0.668423\pi\) | |||||||
\(752\) | 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 | 0.987138 | + | 0.159868i | \(0.0511070\pi\) |
−0.355119 | + | 0.934821i | \(0.615560\pi\) | |||||||
\(762\) | 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 | \(-0.499184\pi\) | ||||
0.00256277 | + | 0.999997i | \(0.499184\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.3137 | 1.19976 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.13604 | + | 15.8241i | −0.328600 | + | 0.569153i | −0.982234 | − | 0.187658i | \(-0.939910\pi\) |
0.653634 | + | 0.756811i | \(0.273244\pi\) | |||||||
\(774\) | 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 | \(-0.938921\pi\) |
0.655982 | + | 0.754777i | \(0.272255\pi\) | |||||||
\(788\) | 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 | \(-0.507808\pi\) | ||||
−0.0245256 | + | 0.999699i | \(0.507808\pi\) | |||||||
\(798\) | 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 | 0.264890 | + | 0.964279i | \(0.414664\pi\) |
−0.967535 | + | 0.252738i | \(0.918669\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.5563 | −0.405798 | −0.202899 | − | 0.979200i | \(-0.565036\pi\) | ||||
−0.202899 | + | 0.979200i | \(0.565036\pi\) | |||||||
\(812\) | 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 | −0.954328 | − | 0.298762i | \(-0.903426\pi\) |
0.218429 | − | 0.975853i | \(-0.429907\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.2635 | − | 24.7050i | 0.497193 | − | 0.861163i | −0.502802 | − | 0.864402i | \(-0.667697\pi\) |
0.999995 | + | 0.00323843i | \(0.00103082\pi\) | |||||||
\(824\) | 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 | \(-0.848418\pi\) |
0.841367 | + | 0.540464i | \(0.181751\pi\) | |||||||
\(830\) | 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 | \(-0.420125\pi\) | ||||
0.248309 | + | 0.968681i | \(0.420125\pi\) | |||||||
\(840\) | 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 | \(-0.648568\pi\) | ||||
−0.449978 | + | 0.893040i | \(0.648568\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.6569 | 0.740649 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.58579 | + | 13.1390i | −0.259126 | + | 0.448819i | −0.966008 | − | 0.258513i | \(-0.916768\pi\) |
0.706882 | + | 0.707331i | \(0.250101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.72792 | + | 4.72490i | 0.0930755 | + | 0.161211i | 0.908804 | − | 0.417224i | \(-0.136997\pi\) |
−0.815728 | + | 0.578435i | \(0.803664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.1213 | + | 24.4588i | 0.480695 | + | 0.832589i | 0.999755 | − | 0.0221495i | \(-0.00705097\pi\) |
−0.519059 | + | 0.854738i | \(0.673718\pi\) | |||||||
\(864\) | 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 | −0.997281 | − | 0.0736948i | \(-0.976521\pi\) |
0.434819 | − | 0.900518i | \(-0.356812\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.9853 | − | 24.2232i | 0.471712 | − | 0.817029i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.284271 | −0.00957734 | −0.00478867 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478867 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(882\) | 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 | \(-0.284776\pi\) |
−0.988387 | + | 0.151957i | \(0.951442\pi\) | |||||||
\(888\) | 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 | −0.260273 | − | 0.965535i | \(-0.583813\pi\) |
0.966314 | − | 0.257365i | \(-0.0828541\pi\) | |||||||
\(908\) | 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 | 0.994841 | + | 0.101446i | \(0.0323471\pi\) |
−0.409565 | + | 0.912281i | \(0.634320\pi\) | |||||||
\(920\) | 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 | −0.939425 | − | 0.342755i | \(-0.888640\pi\) |
0.172878 | − | 0.984943i | \(-0.444693\pi\) | |||||||
\(930\) | 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 | \(-0.593513\pi\) | ||||
−0.289573 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.1421 | −1.14682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.00000 | + | 3.46410i | −0.0651981 | + | 0.112926i | −0.896782 | − | 0.442473i | \(-0.854101\pi\) |
0.831584 | + | 0.555399i | \(0.187435\pi\) | |||||||
\(942\) | 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 | 0.705771 | − | 0.708440i | \(-0.250601\pi\) |
−0.966413 | + | 0.256996i | \(0.917267\pi\) | |||||||
\(948\) | 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 | 0.974254 | + | 0.225455i | \(0.0723870\pi\) |
−0.291877 | + | 0.956456i | \(0.594280\pi\) | |||||||
\(972\) | 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 | −0.980942 | − | 0.194300i | \(-0.937756\pi\) |
0.658740 | + | 0.752371i | \(0.271090\pi\) | |||||||
\(978\) | 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 | −0.347755 | − | 0.937585i | \(-0.613056\pi\) |
0.985850 | − | 0.167628i | \(-0.0536108\pi\) | |||||||
\(984\) | 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 | −0.886570 | − | 0.462594i | \(-0.846919\pi\) |
0.843904 | + | 0.536495i | \(0.180252\pi\) | |||||||
\(992\) | 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 | −0.411699 | − | 0.911320i | \(-0.635064\pi\) |
0.995076 | − | 0.0991186i | \(-0.0316023\pi\) | |||||||
\(998\) | 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.l.361.2 | 4 | ||
7.2 | even | 3 | inner | 980.2.i.l.961.2 | 4 | ||
7.3 | odd | 6 | 980.2.a.k.1.2 | yes | 2 | ||
7.4 | even | 3 | 980.2.a.j.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | 980.2.i.k.961.1 | 4 | |||
7.6 | odd | 2 | 980.2.i.k.361.1 | 4 | |||
21.11 | odd | 6 | 8820.2.a.bg.1.1 | 2 | |||
21.17 | even | 6 | 8820.2.a.bl.1.1 | 2 | |||
28.3 | even | 6 | 3920.2.a.bo.1.1 | 2 | |||
28.11 | odd | 6 | 3920.2.a.bx.1.2 | 2 | |||
35.3 | even | 12 | 4900.2.e.r.2549.4 | 4 | |||
35.4 | even | 6 | 4900.2.a.z.1.2 | 2 | |||
35.17 | even | 12 | 4900.2.e.r.2549.1 | 4 | |||
35.18 | odd | 12 | 4900.2.e.q.2549.1 | 4 | |||
35.24 | odd | 6 | 4900.2.a.x.1.1 | 2 | |||
35.32 | odd | 12 | 4900.2.e.q.2549.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.a.j.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
980.2.a.k.1.2 | yes | 2 | 7.3 | odd | 6 | ||
980.2.i.k.361.1 | 4 | 7.6 | odd | 2 | |||
980.2.i.k.961.1 | 4 | 7.5 | odd | 6 | |||
980.2.i.l.361.2 | 4 | 1.1 | even | 1 | trivial | ||
980.2.i.l.961.2 | 4 | 7.2 | even | 3 | inner | ||
3920.2.a.bo.1.1 | 2 | 28.3 | even | 6 | |||
3920.2.a.bx.1.2 | 2 | 28.11 | odd | 6 | |||
4900.2.a.x.1.1 | 2 | 35.24 | odd | 6 | |||
4900.2.a.z.1.2 | 2 | 35.4 | even | 6 | |||
4900.2.e.q.2549.1 | 4 | 35.18 | odd | 12 | |||
4900.2.e.q.2549.4 | 4 | 35.32 | odd | 12 | |||
4900.2.e.r.2549.1 | 4 | 35.17 | even | 12 | |||
4900.2.e.r.2549.4 | 4 | 35.3 | even | 12 | |||
8820.2.a.bg.1.1 | 2 | 21.11 | odd | 6 | |||
8820.2.a.bl.1.1 | 2 | 21.17 | even | 6 |