Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (of order \(3\), degree \(2\), 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: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.38363328.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 3x^{4} - 2x^{3} - 21x^{2} - 49x + 343 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.247423 - 2.63416i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.361 |
Dual form | 2520.2.bi.o.1801.1 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.40496 | + | 1.10280i | −0.908989 | + | 0.416821i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.90496 | − | 3.29948i | 0.574366 | − | 0.994832i | −0.421744 | − | 0.906715i | \(-0.638582\pi\) |
0.996110 | − | 0.0881168i | \(-0.0280849\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.31507 | 1.19679 | 0.598393 | − | 0.801203i | \(-0.295806\pi\) | ||||
0.598393 | + | 0.801203i | \(0.295806\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.657535 | + | 1.13888i | −0.159476 | + | 0.276220i | −0.934680 | − | 0.355491i | \(-0.884314\pi\) |
0.775204 | + | 0.631711i | \(0.217647\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.81507 | − | 6.60790i | −0.875237 | − | 1.51596i | −0.856510 | − | 0.516131i | \(-0.827372\pi\) |
−0.0187273 | − | 0.999825i | \(-0.505961\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.41011 | + | 5.90649i | 0.711058 | + | 1.23159i | 0.964461 | + | 0.264227i | \(0.0851168\pi\) |
−0.253403 | + | 0.967361i | \(0.581550\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.30476 | 0.799374 | 0.399687 | − | 0.916652i | \(-0.369119\pi\) | ||||
0.399687 | + | 0.916652i | \(0.369119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.747423 | + | 1.29457i | −0.134241 | + | 0.232512i | −0.925307 | − | 0.379218i | \(-0.876193\pi\) |
0.791066 | + | 0.611731i | \(0.209526\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.15754 | − | 1.53135i | −0.364690 | − | 0.258846i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.65238 | − | 8.05816i | −0.764847 | − | 1.32475i | −0.940328 | − | 0.340271i | \(-0.889481\pi\) |
0.175481 | − | 0.984483i | \(-0.443852\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4401 | 1.63046 | 0.815231 | − | 0.579135i | \(-0.196610\pi\) | ||||
0.815231 | + | 0.579135i | \(0.196610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.80992 | −0.733505 | −0.366753 | − | 0.930318i | \(-0.619530\pi\) | ||||
−0.366753 | + | 0.930318i | \(0.619530\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.75258 | − | 3.03555i | −0.255640 | − | 0.442781i | 0.709429 | − | 0.704776i | \(-0.248953\pi\) |
−0.965069 | + | 0.261996i | \(0.915619\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.56765 | − | 5.30439i | 0.652521 | − | 0.757771i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.06765 | + | 7.04537i | −0.558734 | + | 0.967756i | 0.438868 | + | 0.898551i | \(0.355380\pi\) |
−0.997602 | + | 0.0692048i | \(0.977954\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.80992 | 0.513729 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.15238 | − | 7.19214i | 0.540594 | − | 0.936336i | −0.458276 | − | 0.888810i | \(-0.651533\pi\) |
0.998870 | − | 0.0475263i | \(-0.0151338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.31507 | + | 5.74187i | 0.424451 | + | 0.735171i | 0.996369 | − | 0.0851398i | \(-0.0271337\pi\) |
−0.571918 | + | 0.820311i | \(0.693800\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.15754 | + | 3.73696i | 0.267609 | + | 0.463513i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.72003 | − | 13.3715i | 0.943152 | − | 1.63359i | 0.183741 | − | 0.982975i | \(-0.441179\pi\) |
0.759410 | − | 0.650612i | \(-0.225487\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.32538 | 0.513328 | 0.256664 | − | 0.966501i | \(-0.417377\pi\) | ||||
0.256664 | + | 0.966501i | \(0.417377\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.91011 | + | 3.30841i | −0.223562 | + | 0.387220i | −0.955887 | − | 0.293735i | \(-0.905102\pi\) |
0.732325 | + | 0.680955i | \(0.238435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.942661 | + | 10.0359i | −0.107426 | + | 1.14370i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.06249 | + | 1.84029i | 0.119540 | + | 0.207049i | 0.919585 | − | 0.392890i | \(-0.128525\pi\) |
−0.800046 | + | 0.599939i | \(0.795191\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.9349 | 1.20026 | 0.600131 | − | 0.799902i | \(-0.295115\pi\) | ||||
0.600131 | + | 0.799902i | \(0.295115\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.31507 | −0.142639 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.65754 | + | 9.79914i | 0.599698 | + | 1.03871i | 0.992865 | + | 0.119240i | \(0.0380458\pi\) |
−0.393168 | + | 0.919467i | \(0.628621\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3776 | + | 4.75868i | −1.08786 | + | 0.498845i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.81507 | − | 6.60790i | 0.391418 | − | 0.677956i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6301 | 1.07933 | 0.539664 | − | 0.841881i | \(-0.318551\pi\) | ||||
0.539664 | + | 0.841881i | \(0.318551\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.34246 | − | 9.25342i | 0.531595 | − | 0.920750i | −0.467725 | − | 0.883874i | \(-0.654926\pi\) |
0.999320 | − | 0.0368756i | \(-0.0117405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.72003 | + | 16.8356i | 0.957743 | + | 1.65886i | 0.727963 | + | 0.685617i | \(0.240467\pi\) |
0.229780 | + | 0.973243i | \(0.426199\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.15238 | + | 8.92419i | 0.498099 | + | 0.862734i | 0.999998 | − | 0.00219314i | \(-0.000698099\pi\) |
−0.501898 | + | 0.864927i | \(0.667365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.55734 | − | 6.16149i | 0.340731 | − | 0.590164i | −0.643837 | − | 0.765162i | \(-0.722659\pi\) |
0.984569 | + | 0.174998i | \(0.0559920\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.41011 | + | 5.90649i | −0.317995 | + | 0.550783i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.325379 | − | 3.46410i | 0.0298274 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.75773 | − | 3.04448i | −0.159794 | − | 0.276771i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9452 | 1.50364 | 0.751822 | − | 0.659366i | \(-0.229175\pi\) | ||||
0.751822 | + | 0.659366i | \(0.229175\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.55219 | − | 11.3487i | −0.572467 | − | 0.991542i | −0.996312 | − | 0.0858072i | \(-0.972653\pi\) |
0.423845 | − | 0.905735i | \(-0.360680\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.4623 | + | 11.6844i | 1.42746 | + | 1.01317i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.46745 | − | 11.2020i | 0.552552 | − | 0.957048i | −0.445538 | − | 0.895263i | \(-0.646988\pi\) |
0.998090 | − | 0.0617845i | \(-0.0196791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.7448 | −0.996183 | −0.498091 | − | 0.867125i | \(-0.665966\pi\) | ||||
−0.498091 | + | 0.867125i | \(0.665966\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.22003 | − | 14.2375i | 0.687393 | − | 1.19060i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.15238 | + | 3.72803i | 0.178746 | + | 0.309596i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.00000 | − | 3.46410i | −0.163846 | − | 0.283790i | 0.772399 | − | 0.635138i | \(-0.219057\pi\) |
−0.936245 | + | 0.351348i | \(0.885723\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.315070 | + | 0.545718i | −0.0256401 | + | 0.0444099i | −0.878561 | − | 0.477631i | \(-0.841496\pi\) |
0.852921 | + | 0.522041i | \(0.174829\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.49485 | −0.120069 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.43751 | + | 7.68599i | −0.354152 | + | 0.613409i | −0.986972 | − | 0.160890i | \(-0.948564\pi\) |
0.632821 | + | 0.774298i | \(0.281897\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.7149 | − | 10.4442i | −1.15969 | − | 0.823116i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.00000 | − | 13.8564i | −0.626608 | − | 1.08532i | −0.988227 | − | 0.152992i | \(-0.951109\pi\) |
0.361619 | − | 0.932326i | \(-0.382224\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0599 | −0.933222 | −0.466611 | − | 0.884463i | \(-0.654525\pi\) | ||||
−0.466611 | + | 0.884463i | \(0.654525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.61983 | 0.432295 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.56249 | + | 14.8307i | 0.650994 | + | 1.12756i | 0.982882 | + | 0.184236i | \(0.0589812\pi\) |
−0.331888 | + | 0.943319i | \(0.607685\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.247423 | − | 2.63416i | 0.0187034 | − | 0.199124i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.75258 | + | 9.96376i | −0.429968 | + | 0.744726i | −0.996870 | − | 0.0790591i | \(-0.974808\pi\) |
0.566902 | + | 0.823785i | \(0.308142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.48454 | 0.481992 | 0.240996 | − | 0.970526i | \(-0.422526\pi\) | ||||
0.240996 | + | 0.970526i | \(0.422526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.65238 | − | 8.05816i | 0.342050 | − | 0.592448i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.50515 | + | 4.33905i | 0.183195 | + | 0.317303i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.61983 | − | 11.4659i | −0.478994 | − | 0.829642i | 0.520716 | − | 0.853730i | \(-0.325665\pi\) |
−0.999710 | + | 0.0240878i | \(0.992332\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.73034 | + | 13.3893i | −0.556442 | + | 0.963785i | 0.441348 | + | 0.897336i | \(0.354500\pi\) |
−0.997790 | + | 0.0664495i | \(0.978833\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.4401 | 1.02881 | 0.514406 | − | 0.857547i | \(-0.328013\pi\) | ||||
0.514406 | + | 0.857547i | \(0.328013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.19008 | + | 2.06129i | −0.0843628 | + | 0.146121i | −0.905120 | − | 0.425157i | \(-0.860219\pi\) |
0.820757 | + | 0.571278i | \(0.193552\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.3528 | + | 4.74731i | −0.726622 | + | 0.333196i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.22003 | + | 9.04135i | 0.364583 | + | 0.631476i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.0702 | −2.01083 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1147 | −1.10938 | −0.554690 | − | 0.832057i | \(-0.687163\pi\) | ||||
−0.554690 | + | 0.832057i | \(0.687163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.40496 | − | 4.16551i | −0.164017 | − | 0.284085i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.369859 | − | 3.93766i | 0.0251077 | − | 0.267306i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.83731 | + | 4.91437i | −0.190858 | + | 0.330576i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6095 | 0.844396 | 0.422198 | − | 0.906504i | \(-0.361259\pi\) | ||||
0.422198 | + | 0.906504i | \(0.361259\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.46745 | + | 2.54170i | −0.0973982 | + | 0.168699i | −0.910607 | − | 0.413273i | \(-0.864385\pi\) |
0.813209 | + | 0.581972i | \(0.197719\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.24227 | − | 10.8119i | −0.412501 | − | 0.714472i | 0.582662 | − | 0.812715i | \(-0.302011\pi\) |
−0.995163 | + | 0.0982425i | \(0.968678\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.3151 | − | 21.3303i | −0.806787 | − | 1.39740i | −0.915078 | − | 0.403277i | \(-0.867871\pi\) |
0.108291 | − | 0.994119i | \(-0.465462\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.75258 | − | 3.03555i | 0.114326 | − | 0.198018i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.87756 | + | 13.6443i | −0.507438 | + | 0.878909i | 0.492524 | + | 0.870299i | \(0.336074\pi\) |
−0.999963 | + | 0.00861063i | \(0.997259\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.87756 | + | 1.30350i | 0.439391 | + | 0.0832777i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.4623 | − | 28.5135i | −1.04747 | − | 1.81427i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.82022 | 0.556728 | 0.278364 | − | 0.960476i | \(-0.410208\pi\) | ||||
0.278364 | + | 0.960476i | \(0.410208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.9845 | 1.63363 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.46745 | + | 12.9340i | 0.465807 | + | 0.806801i | 0.999238 | − | 0.0390427i | \(-0.0124308\pi\) |
−0.533431 | + | 0.845844i | \(0.679097\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0754 | + | 14.2489i | 1.24742 | + | 0.885382i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.31507 | − | 2.27777i | 0.0810907 | − | 0.140453i | −0.822628 | − | 0.568580i | \(-0.807493\pi\) |
0.903719 | + | 0.428127i | \(0.140826\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.13529 | −0.499747 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.82022 | − | 17.0091i | 0.598750 | − | 1.03706i | −0.394256 | − | 0.919001i | \(-0.628998\pi\) |
0.993006 | − | 0.118064i | \(-0.0376689\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.44006 | − | 12.8866i | −0.451951 | − | 0.782803i | 0.546556 | − | 0.837423i | \(-0.315939\pi\) |
−0.998507 | + | 0.0546200i | \(0.982605\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.90496 | + | 3.29948i | 0.114873 | + | 0.198966i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.41527 | − | 4.18336i | 0.145119 | − | 0.251354i | −0.784298 | − | 0.620384i | \(-0.786977\pi\) |
0.929417 | + | 0.369030i | \(0.120310\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.50515 | 0.567030 | 0.283515 | − | 0.958968i | \(-0.408499\pi\) | ||||
0.283515 | + | 0.958968i | \(0.408499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8553 | − | 23.9981i | 0.823613 | − | 1.42654i | −0.0793609 | − | 0.996846i | \(-0.525288\pi\) |
0.902974 | − | 0.429694i | \(-0.141379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.1079 | + | 11.5133i | −1.48207 | + | 0.679611i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.63529 | + | 13.2247i | 0.449135 | + | 0.777925i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.49485 | 0.145750 | 0.0728752 | − | 0.997341i | \(-0.476783\pi\) | ||||
0.0728752 | + | 0.997341i | \(0.476783\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.30476 | 0.483522 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.7149 | + | 25.4869i | 0.850983 | + | 1.47395i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5676 | − | 5.30439i | 0.666748 | − | 0.305740i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.31507 | + | 5.74187i | −0.189820 | + | 0.328779i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.21070 | 0.0690983 | 0.0345492 | − | 0.999403i | \(-0.489000\pi\) | ||||
0.0345492 | + | 0.999403i | \(0.489000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.6027 | − | 25.2927i | 0.828046 | − | 1.43422i | −0.0715233 | − | 0.997439i | \(-0.522786\pi\) |
0.899569 | − | 0.436778i | \(-0.143881\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.404958 | + | 0.701408i | 0.0228896 | + | 0.0396459i | 0.877243 | − | 0.480046i | \(-0.159380\pi\) |
−0.854354 | + | 0.519692i | \(0.826047\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.14207 | − | 7.17428i | −0.232642 | − | 0.402948i | 0.725943 | − | 0.687755i | \(-0.241404\pi\) |
−0.958585 | + | 0.284807i | \(0.908070\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.20039 | − | 14.2035i | 0.459134 | − | 0.795243i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0342 | 0.558316 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.15754 | + | 3.73696i | −0.119679 | + | 0.207289i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.56249 | + | 5.36763i | 0.416934 | + | 0.295927i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9401 | − | 22.4128i | −0.711250 | − | 1.23192i | −0.964388 | − | 0.264491i | \(-0.914796\pi\) |
0.253138 | − | 0.967430i | \(-0.418537\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.4401 | 0.843580 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.6797 | −1.67123 | −0.835615 | − | 0.549315i | \(-0.814889\pi\) | ||||
−0.835615 | + | 0.549315i | \(0.814889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.84762 | + | 4.93222i | 0.154207 | + | 0.267095i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.13529 | + | 17.7941i | −0.277280 | + | 0.960789i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.1250 | + | 26.1972i | −0.811952 | + | 1.40634i | 0.0995443 | + | 0.995033i | \(0.468262\pi\) |
−0.911496 | + | 0.411309i | \(0.865072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.9897 | 1.44473 | 0.722363 | − | 0.691515i | \(-0.243056\pi\) | ||||
0.722363 | + | 0.691515i | \(0.243056\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.46745 | + | 12.9340i | −0.397452 | + | 0.688408i | −0.993411 | − | 0.114608i | \(-0.963439\pi\) |
0.595959 | + | 0.803015i | \(0.296772\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.16269 | + | 3.74589i | 0.114784 | + | 0.198811i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.84762 | − | 13.5925i | −0.414181 | − | 0.717383i | 0.581161 | − | 0.813789i | \(-0.302599\pi\) |
−0.995342 | + | 0.0964055i | \(0.969265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.6095 | + | 33.9647i | −1.03208 | + | 1.78762i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.82022 | −0.199960 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.1575 | + | 17.5934i | −0.530219 | + | 0.918366i | 0.469159 | + | 0.883113i | \(0.344557\pi\) |
−0.999378 | + | 0.0352528i | \(0.988776\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.01286 | − | 21.4296i | 0.104502 | − | 1.11257i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.40496 | + | 5.89756i | 0.176302 | + | 0.305364i | 0.940611 | − | 0.339486i | \(-0.110253\pi\) |
−0.764309 | + | 0.644850i | \(0.776920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.5754 | 0.956679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.2397 | −1.55331 | −0.776654 | − | 0.629928i | \(-0.783084\pi\) | ||||
−0.776654 | + | 0.629928i | \(0.783084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.06765 | + | 7.04537i | 0.207847 | + | 0.360002i | 0.951036 | − | 0.309080i | \(-0.100021\pi\) |
−0.743189 | + | 0.669082i | \(0.766688\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.16269 | + | 4.20159i | −0.466974 | + | 0.214133i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4675 | + | 25.0584i | −0.733529 | + | 1.27051i | 0.221837 | + | 0.975084i | \(0.428795\pi\) |
−0.955366 | + | 0.295426i | \(0.904539\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.96908 | −0.453586 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.06249 | + | 1.84029i | −0.0534598 | + | 0.0925952i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.214874 | + | 0.372173i | 0.0107842 | + | 0.0186789i | 0.871367 | − | 0.490631i | \(-0.163234\pi\) |
−0.860583 | + | 0.509310i | \(0.829901\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.55219 | + | 2.68846i | 0.0775124 | + | 0.134255i | 0.902176 | − | 0.431368i | \(-0.141969\pi\) |
−0.824664 | + | 0.565623i | \(0.808636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.22518 | + | 5.58618i | −0.160658 | + | 0.278267i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.4504 | −1.75721 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.75773 | − | 9.97268i | 0.284701 | − | 0.493117i | −0.687835 | − | 0.725867i | \(-0.741439\pi\) |
0.972537 | + | 0.232749i | \(0.0747722\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.05479 | + | 21.8760i | −0.101110 | + | 1.07645i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.46745 | + | 9.46990i | 0.268387 | + | 0.464859i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.86471 | 0.481922 | 0.240961 | − | 0.970535i | \(-0.422537\pi\) | ||||
0.240961 | + | 0.970535i | \(0.422537\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.1353 | −1.03007 | −0.515036 | − | 0.857169i | \(-0.672221\pi\) | ||||
−0.515036 | + | 0.857169i | \(0.672221\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.657535 | − | 1.13888i | −0.0318951 | − | 0.0552440i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.3048 | − | 10.1531i | −0.692256 | − | 0.491342i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.0599 | + | 33.0127i | −0.918083 | + | 1.59017i | −0.115758 | + | 0.993277i | \(0.536930\pi\) |
−0.802324 | + | 0.596888i | \(0.796404\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.8099 | 0.807833 | 0.403917 | − | 0.914796i | \(-0.367649\pi\) | ||||
0.403917 | + | 0.914796i | \(0.367649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.0196 | − | 45.0673i | 1.24469 | − | 2.15586i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.50515 | − | 7.80316i | −0.215019 | − | 0.372424i | 0.738259 | − | 0.674517i | \(-0.235648\pi\) |
−0.953279 | + | 0.302093i | \(0.902315\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.30476 | + | 10.9202i | 0.299548 | + | 0.518833i | 0.976033 | − | 0.217624i | \(-0.0698307\pi\) |
−0.676484 | + | 0.736457i | \(0.736497\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.65754 | + | 9.79914i | −0.268193 | + | 0.464524i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.74482 | −0.318308 | −0.159154 | − | 0.987254i | \(-0.550877\pi\) | ||||
−0.159154 | + | 0.987254i | \(0.550877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.8879 | − | 34.4468i | 0.936483 | − | 1.62204i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.30992 | − | 6.60790i | −0.436456 | − | 0.309783i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0454 | − | 29.5235i | −0.797351 | − | 1.38105i | −0.921336 | − | 0.388768i | \(-0.872901\pi\) |
0.123985 | − | 0.992284i | \(-0.460432\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.5857 | −1.47109 | −0.735545 | − | 0.677475i | \(-0.763074\pi\) | ||||
−0.735545 | + | 0.677475i | \(0.763074\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.5857 | −1.42144 | −0.710718 | − | 0.703477i | \(-0.751630\pi\) | ||||
−0.710718 | + | 0.703477i | \(0.751630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.51546 | − | 6.08896i | −0.162676 | − | 0.281763i | 0.773151 | − | 0.634221i | \(-0.218679\pi\) |
−0.935828 | + | 0.352458i | \(0.885346\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.82022 | + | 40.6715i | −0.176402 | + | 1.87804i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.16269 | + | 15.8702i | −0.421301 | + | 0.729715i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.63014 | 0.350095 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.7551 | + | 27.2887i | −0.719870 | + | 1.24685i | 0.241181 | + | 0.970480i | \(0.422465\pi\) |
−0.961051 | + | 0.276371i | \(0.910868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0754 | − | 34.7715i | −0.915357 | − | 1.58545i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.31507 | + | 9.20597i | 0.241345 | + | 0.418022i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0248 | − | 17.3634i | 0.454267 | − | 0.786813i | −0.544379 | − | 0.838839i | \(-0.683235\pi\) |
0.998646 | + | 0.0520264i | \(0.0165680\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.60952 | −0.208025 | −0.104012 | − | 0.994576i | \(-0.533168\pi\) | ||||
−0.104012 | + | 0.994576i | \(0.533168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.83053 | + | 4.90263i | −0.127481 | + | 0.220803i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.4024 | + | 4.77004i | −0.466609 | + | 0.213966i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1327 | − | 36.6029i | −0.946029 | − | 1.63857i | −0.753677 | − | 0.657245i | \(-0.771722\pi\) |
−0.192352 | − | 0.981326i | \(-0.561611\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.61983 | −0.250576 | −0.125288 | − | 0.992120i | \(-0.539985\pi\) | ||||
−0.125288 | + | 0.992120i | \(0.539985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.6849 | 0.475473 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.5650 | − | 25.2274i | −0.645584 | − | 1.11818i | −0.984166 | − | 0.177248i | \(-0.943281\pi\) |
0.338582 | − | 0.940937i | \(-0.390053\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.945211 | − | 10.0631i | 0.0418137 | − | 0.445164i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.72003 | + | 16.8356i | −0.428316 | + | 0.741864i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.3543 | −0.587323 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.68748 | + | 13.3151i | −0.336795 | + | 0.583345i | −0.983828 | − | 0.179116i | \(-0.942676\pi\) |
0.647033 | + | 0.762462i | \(0.276009\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.59504 | + | 4.49474i | 0.113473 | + | 0.196541i | 0.917168 | − | 0.398500i | \(-0.130469\pi\) |
−0.803695 | + | 0.595041i | \(0.797136\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.982914 | − | 1.70246i | −0.0428164 | − | 0.0741602i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7577 | + | 20.3650i | −0.511206 | + | 0.885434i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45.0496 | 1.95131 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.15238 | + | 8.92419i | −0.222757 | + | 0.385826i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.80059 | − | 25.1755i | −0.379068 | − | 1.08439i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.24227 | − | 3.88372i | −0.0964027 | − | 0.166974i | 0.813790 | − | 0.581158i | \(-0.197400\pi\) |
−0.910193 | + | 0.414184i | \(0.864067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.11468 | 0.304759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.650757 | −0.0278244 | −0.0139122 | − | 0.999903i | \(-0.504429\pi\) | ||||
−0.0139122 | + | 0.999903i | \(0.504429\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.4230 | − | 28.4454i | −0.699642 | − | 1.21182i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.58473 | − | 3.25410i | −0.194963 | − | 0.138379i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5077 | − | 30.3242i | 0.741825 | − | 1.28488i | −0.209838 | − | 0.977736i | \(-0.567294\pi\) |
0.951663 | − | 0.307143i | \(-0.0993730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.7551 | −0.877848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6301 | + | 27.0722i | −0.658732 | + | 1.14096i | 0.322212 | + | 0.946667i | \(0.395574\pi\) |
−0.980944 | + | 0.194290i | \(0.937760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | + | 5.19615i | 0.126211 | + | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.779971 | − | 1.35095i | −0.0326981 | − | 0.0566348i | 0.849213 | − | 0.528050i | \(-0.177077\pi\) |
−0.881911 | + | 0.471415i | \(0.843743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.57796 | − | 7.92925i | 0.191581 | − | 0.331829i | −0.754193 | − | 0.656653i | \(-0.771972\pi\) |
0.945775 | + | 0.324824i | \(0.105305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.82022 | −0.284423 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.415266 | − | 0.719262i | 0.0172878 | − | 0.0299433i | −0.857252 | − | 0.514897i | \(-0.827830\pi\) |
0.874540 | + | 0.484954i | \(0.161164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.2980 | + | 12.0591i | −1.09102 | + | 0.500294i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.4974 | + | 26.8423i | 0.641837 | + | 1.11169i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.0651 | 0.951998 | 0.475999 | − | 0.879446i | \(-0.342087\pi\) | ||||
0.475999 | + | 0.879446i | \(0.342087\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4059 | 0.469971 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.7928 | − | 20.4258i | −0.484273 | − | 0.838786i | 0.515563 | − | 0.856851i | \(-0.327583\pi\) |
−0.999837 | + | 0.0180652i | \(0.994249\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.16269 | − | 1.45026i | 0.129658 | − | 0.0594551i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.190084 | + | 0.329235i | −0.00776661 | + | 0.0134522i | −0.869883 | − | 0.493259i | \(-0.835806\pi\) |
0.862116 | + | 0.506711i | \(0.169139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.10437 | −0.249002 | −0.124501 | − | 0.992219i | \(-0.539733\pi\) | ||||
−0.124501 | + | 0.992219i | \(0.539733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.75773 | − | 3.04448i | 0.0714619 | − | 0.123776i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.71748 | + | 8.17091i | 0.191477 | + | 0.331647i | 0.945740 | − | 0.324925i | \(-0.105339\pi\) |
−0.754263 | + | 0.656572i | \(0.772006\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.56249 | − | 13.0986i | −0.305946 | − | 0.529914i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.0676 | + | 20.9018i | −0.487408 | + | 0.844215i | −0.999895 | − | 0.0144798i | \(-0.995391\pi\) |
0.512487 | + | 0.858695i | \(0.328724\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.8595 | −1.48391 | −0.741954 | − | 0.670451i | \(-0.766101\pi\) | ||||
−0.741954 | + | 0.670451i | \(0.766101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0650 | + | 27.8255i | −0.645709 | + | 1.11840i | 0.338429 | + | 0.940992i | \(0.390105\pi\) |
−0.984137 | + | 0.177408i | \(0.943229\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.4127 | − | 17.3274i | −0.978073 | − | 0.694206i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.2364 | 0.487898 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2912 | 0.887399 | 0.443699 | − | 0.896176i | \(-0.353666\pi\) | ||||
0.443699 | + | 0.896176i | \(0.353666\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.47261 | + | 14.6750i | 0.336225 | + | 0.582359i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.7097 | − | 22.8888i | 0.780928 | − | 0.906889i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0196 | + | 29.4789i | −0.672235 | + | 1.16435i | 0.305034 | + | 0.952342i | \(0.401332\pi\) |
−0.977269 | + | 0.212004i | \(0.932001\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.4297 | 1.43665 | 0.718325 | − | 0.695708i | \(-0.244909\pi\) | ||||
0.718325 | + | 0.695708i | \(0.244909\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.0196 | + | 19.0866i | −0.433227 | + | 0.750371i | −0.997149 | − | 0.0754573i | \(-0.975958\pi\) |
0.563922 | + | 0.825828i | \(0.309292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.8202 | − | 27.4014i | −0.620998 | − | 1.07560i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.79028 | − | 8.29701i | −0.187458 | − | 0.324687i | 0.756944 | − | 0.653480i | \(-0.226692\pi\) |
−0.944402 | + | 0.328793i | \(0.893358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.55219 | − | 11.3487i | 0.256015 | − | 0.443431i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.2603 | 0.984001 | 0.492000 | − | 0.870595i | \(-0.336266\pi\) | ||||
0.492000 | + | 0.870595i | \(0.336266\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8827 | − | 22.3135i | 0.501080 | − | 0.867895i | −0.498920 | − | 0.866648i | \(-0.666270\pi\) |
0.999999 | − | 0.00124712i | \(-0.000396971\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.88787 | + | 20.0990i | −0.0732085 | + | 0.779405i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6797 | + | 25.4260i | 0.568401 | + | 0.984500i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.2603 | 0.975162 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.82022 | −0.224353 | −0.112177 | − | 0.993688i | \(-0.535782\pi\) | ||||
−0.112177 | + | 0.993688i | \(0.535782\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.05056 | + | 15.6760i | 0.347841 | + | 0.602479i | 0.985866 | − | 0.167537i | \(-0.0535815\pi\) |
−0.638024 | + | 0.770016i | \(0.720248\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.5650 | + | 11.7230i | −0.981096 | + | 0.449886i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.65754 | + | 8.06709i | −0.178216 | + | 0.308679i | −0.941269 | − | 0.337656i | \(-0.890366\pi\) |
0.763054 | + | 0.646335i | \(0.223699\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9349 | 0.494217 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.5522 | + | 30.4013i | −0.668685 | + | 1.15820i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1875 | + | 33.2337i | 0.729926 | + | 1.26427i | 0.956914 | + | 0.290372i | \(0.0937789\pi\) |
−0.226988 | + | 0.973898i | \(0.572888\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.87241 | − | 10.1713i | −0.222753 | − | 0.385820i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.86471 | + | 11.8900i | −0.260019 | + | 0.450367i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.575352 | −0.0217307 | −0.0108654 | − | 0.999941i | \(-0.503459\pi\) | ||||
−0.0108654 | + | 0.999941i | \(0.503459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.4983 | + | 61.4849i | −1.33884 | + | 2.31895i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.64370 | + | 28.1458i | −0.0994265 | + | 1.05853i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.3151 | − | 19.5983i | −0.424946 | − | 0.736029i | 0.571469 | − | 0.820624i | \(-0.306374\pi\) |
−0.996415 | + | 0.0845949i | \(0.973040\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.1952 | −0.381813 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.4401 | 0.614823 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.3151 | + | 17.8662i | 0.384687 | + | 0.666298i | 0.991726 | − | 0.128375i | \(-0.0409760\pi\) |
−0.607039 | + | 0.794672i | \(0.707643\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41.9426 | − | 29.7696i | −1.56202 | − | 1.10868i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.15238 | + | 3.72803i | −0.0799374 | + | 0.138456i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.27384 | 0.232684 | 0.116342 | − | 0.993209i | \(-0.462883\pi\) | ||||
0.116342 | + | 0.993209i | \(0.462883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.16269 | − | 5.47794i | 0.116976 | − | 0.202609i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.33731 | − | 5.78039i | −0.123266 | − | 0.213504i | 0.797788 | − | 0.602939i | \(-0.206004\pi\) |
−0.921054 | + | 0.389435i | \(0.872670\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.4127 | − | 50.9442i | −1.08343 | − | 1.87655i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.13014 | + | 8.88566i | −0.188715 | + | 0.326864i | −0.944822 | − | 0.327584i | \(-0.893766\pi\) |
0.756107 | + | 0.654448i | \(0.227099\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.85115 | 0.0679121 | 0.0339560 | − | 0.999423i | \(-0.489189\pi\) | ||||
0.0339560 | + | 0.999423i | \(0.489189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | − | 3.46410i | 0.0732743 | − | 0.126915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.2329 | − | 15.7802i | −0.812372 | − | 0.576597i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.68233 | − | 13.3062i | −0.280332 | − | 0.485549i | 0.691134 | − | 0.722726i | \(-0.257111\pi\) |
−0.971466 | + | 0.237177i | \(0.923778\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.630141 | −0.0229332 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.0206 | 1.16381 | 0.581905 | − | 0.813257i | \(-0.302308\pi\) | ||||
0.581905 | + | 0.813257i | \(0.302308\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.70457 | + | 13.3447i | 0.279290 | + | 0.483745i | 0.971209 | − | 0.238231i | \(-0.0765675\pi\) |
−0.691918 | + | 0.721976i | \(0.743234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.76033 | + | 18.7412i | −0.0637284 | + | 0.678476i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.9178 | − | 31.0346i | 0.646975 | − | 1.12059i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.2500 | 1.41539 | 0.707695 | − | 0.706518i | \(-0.249735\pi\) | ||||
0.707695 | + | 0.706518i | \(0.249735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0196 | − | 19.0866i | 0.396349 | − | 0.686496i | −0.596924 | − | 0.802298i | \(-0.703610\pi\) |
0.993272 | + | 0.115802i | \(0.0369438\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.747423 | − | 1.29457i | −0.0268482 | − | 0.0465025i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.8296 | − | 68.9868i | −1.42704 | − | 2.47171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.23967 | − | 14.2715i | 0.294838 | − | 0.510675i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.87501 | −0.316763 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.4401 | + | 42.3314i | −0.871194 | + | 1.50895i | −0.0104313 | + | 0.999946i | \(0.503320\pi\) |
−0.860763 | + | 0.509007i | \(0.830013\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.4297 | + | 6.61682i | −0.513063 | + | 0.235267i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.3048 | + | 24.7766i | 0.507977 | + | 0.879842i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.1746 | −0.997994 | −0.498997 | − | 0.866604i | \(-0.666298\pi\) | ||||
−0.498997 | + | 0.866604i | \(0.666298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.60952 | 0.163073 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.27737 | + | 12.6048i | 0.256813 | + | 0.444813i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.68748 | − | 17.9655i | 0.0594759 | − | 0.633202i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.1275 | − | 46.9863i | 0.953753 | − | 1.65195i | 0.216558 | − | 0.976270i | \(-0.430517\pi\) |
0.737195 | − | 0.675680i | \(-0.236150\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5258 | −0.474954 | −0.237477 | − | 0.971393i | \(-0.576320\pi\) | ||||
−0.237477 | + | 0.971393i | \(0.576320\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | − | 13.8564i | 0.280228 | − | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.3502 | + | 31.7834i | 0.641991 | + | 1.11196i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.85793 | − | 10.1462i | −0.204443 | − | 0.354106i | 0.745512 | − | 0.666492i | \(-0.232205\pi\) |
−0.949955 | + | 0.312386i | \(0.898872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.50515 | − | 14.7314i | 0.296471 | − | 0.513503i | −0.678855 | − | 0.734272i | \(-0.737524\pi\) |
0.975326 | + | 0.220769i | \(0.0708568\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.3905 | −0.882913 | −0.441457 | − | 0.897283i | \(-0.645538\pi\) | ||||
−0.441457 | + | 0.897283i | \(0.645538\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.6275 | − | 46.1202i | 0.924813 | − | 1.60182i | 0.132950 | − | 0.991123i | \(-0.457555\pi\) |
0.791862 | − | 0.610700i | \(-0.209112\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.03770 | + | 8.68985i | 0.105250 | + | 0.301085i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.02994 | − | 10.4442i | −0.208675 | − | 0.361435i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.6952 | 0.818050 | 0.409025 | − | 0.912523i | \(-0.365869\pi\) | ||||
0.409025 | + | 0.912523i | \(0.365869\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.4690 | −0.361001 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.80992 | + | 4.86692i | 0.0966641 | + | 0.167427i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.58473 | + | 5.38341i | 0.260615 | + | 0.184976i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.7303 | − | 54.9585i | 1.08770 | − | 1.88395i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.5238 | 0.771201 | 0.385600 | − | 0.922666i | \(-0.373994\pi\) | ||||
0.385600 | + | 0.922666i | \(0.373994\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.7380 | − | 39.3834i | 0.776717 | − | 1.34531i | −0.157108 | − | 0.987581i | \(-0.550217\pi\) |
0.933825 | − | 0.357731i | \(-0.116450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.7345 | + | 35.9132i | 0.707452 | + | 1.22534i | 0.965799 | + | 0.259291i | \(0.0834890\pi\) |
−0.258347 | + | 0.966052i | \(0.583178\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.8331 | + | 37.8160i | 0.743207 | + | 1.28727i | 0.951028 | + | 0.309105i | \(0.100029\pi\) |
−0.207821 | + | 0.978167i | \(0.566637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.56249 | + | 14.8307i | −0.291134 | + | 0.504258i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.09602 | 0.274639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3125 | − | 57.6989i | 1.12875 | − | 1.95505i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.40496 | − | 1.10280i | 0.0813024 | − | 0.0372816i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.7423 | − | 35.9267i | −0.700417 | − | 1.21316i | −0.968320 | − | 0.249712i | \(-0.919664\pi\) |
0.267904 | − | 0.963446i | \(-0.413669\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0154 | −0.438500 | −0.219250 | − | 0.975669i | \(-0.570361\pi\) | ||||
−0.219250 | + | 0.975669i | \(0.570361\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.2996 | 0.750440 | 0.375220 | − | 0.926936i | \(-0.377567\pi\) | ||||
0.375220 | + | 0.926936i | \(0.377567\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.7722 | − | 23.8542i | −0.462426 | − | 0.800945i | 0.536656 | − | 0.843801i | \(-0.319687\pi\) |
−0.999081 | + | 0.0428566i | \(0.986354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.7525 | + | 18.6872i | −1.36680 | + | 0.626750i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.3724 | + | 23.1617i | −0.447491 | + | 0.775077i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.5052 | −0.384575 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.21748 | + | 5.57284i | −0.107309 | + | 0.185864i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.34924 | − | 9.26516i | −0.178209 | − | 0.308667i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.24227 | + | 5.61577i | 0.107777 | + | 0.186675i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.1601 | + | 27.9901i | −0.536587 | + | 0.929396i | 0.462498 | + | 0.886620i | \(0.346953\pi\) |
−0.999085 | + | 0.0427753i | \(0.986380\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.55474 | 0.0846422 | 0.0423211 | − | 0.999104i | \(-0.486525\pi\) | ||||
0.0423211 | + | 0.999104i | \(0.486525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.8305 | − | 36.0795i | 0.689390 | − | 1.19406i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.2731 | + | 20.0674i | 0.933661 | + | 0.662684i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.5573 | + | 35.6064i | 0.678124 | + | 1.17455i | 0.975545 | + | 0.219799i | \(0.0705401\pi\) |
−0.297421 | + | 0.954746i | \(0.596127\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.6643 | 0.614343 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.30476 | 0.305939 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.10535 | − | 1.91452i | −0.0362654 | − | 0.0628134i | 0.847323 | − | 0.531078i | \(-0.178213\pi\) |
−0.883588 | + | 0.468264i | \(0.844879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −52.4768 | − | 9.94590i | −1.71986 | − | 0.325964i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.50515 | + | 4.33905i | −0.0819273 | + | 0.141902i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.7003 | −1.59097 | −0.795485 | − | 0.605973i | \(-0.792784\pi\) | ||||
−0.795485 | + | 0.605973i | \(0.792784\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.9075 | + | 24.0885i | −0.453372 | + | 0.785263i | −0.998593 | − | 0.0530292i | \(-0.983112\pi\) |
0.545221 | + | 0.838292i | \(0.316446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.6018 | + | 61.6641i | 1.15935 | + | 2.00806i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.9520 | − | 32.8258i | −0.615857 | − | 1.06670i | −0.990234 | − | 0.139419i | \(-0.955477\pi\) |
0.374377 | − | 0.927277i | \(-0.377857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.24227 | + | 14.2760i | −0.267555 | + | 0.463419i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.9110 | 0.450623 | 0.225311 | − | 0.974287i | \(-0.427660\pi\) | ||||
0.225311 | + | 0.974287i | \(0.427660\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.61983 | − | 11.4659i | 0.214213 | − | 0.371027i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.20039 | + | 34.0726i | −0.103346 | + | 1.10026i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.3827 | + | 24.9116i | 0.463959 | + | 0.803600i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.4607 | −0.497697 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.80992 | 0.154676 | 0.0773382 | − | 0.997005i | \(-0.475358\pi\) | ||||
0.0773382 | + | 0.997005i | \(0.475358\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.25773 | + | 3.91051i | 0.0724540 | + | 0.125494i | 0.899976 | − | 0.435939i | \(-0.143584\pi\) |
−0.827522 | + | 0.561433i | \(0.810250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.2458 | − | 12.9522i | 0.905519 | − | 0.415229i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.5480 | + | 37.3222i | −0.689380 | + | 1.19404i | 0.282658 | + | 0.959221i | \(0.408784\pi\) |
−0.972039 | + | 0.234821i | \(0.924550\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.1095 | 1.37778 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.57958 | − | 13.1282i | 0.241751 | − | 0.418725i | −0.719462 | − | 0.694532i | \(-0.755612\pi\) |
0.961213 | + | 0.275807i | \(0.0889449\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.22003 | + | 12.5055i | 0.230049 | + | 0.398457i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.4024 | − | 28.4097i | −0.521565 | − | 0.903376i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.68233 | − | 13.3062i | 0.244037 | − | 0.422685i | −0.717823 | − | 0.696225i | \(-0.754861\pi\) |
0.961860 | + | 0.273541i | \(0.0881948\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.38017 | −0.0754564 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.4153 | + | 38.8244i | −0.709899 | + | 1.22958i | 0.254996 | + | 0.966942i | \(0.417926\pi\) |
−0.964894 | + | 0.262638i | \(0.915407\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2520.2.bi.o.361.1 | 6 | ||
3.2 | odd | 2 | 840.2.bg.i.361.1 | yes | 6 | ||
7.2 | even | 3 | inner | 2520.2.bi.o.1801.1 | 6 | ||
12.11 | even | 2 | 1680.2.bg.u.1201.3 | 6 | |||
21.2 | odd | 6 | 840.2.bg.i.121.1 | ✓ | 6 | ||
21.11 | odd | 6 | 5880.2.a.bw.1.3 | 3 | |||
21.17 | even | 6 | 5880.2.a.bt.1.3 | 3 | |||
84.23 | even | 6 | 1680.2.bg.u.961.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.bg.i.121.1 | ✓ | 6 | 21.2 | odd | 6 | ||
840.2.bg.i.361.1 | yes | 6 | 3.2 | odd | 2 | ||
1680.2.bg.u.961.3 | 6 | 84.23 | even | 6 | |||
1680.2.bg.u.1201.3 | 6 | 12.11 | even | 2 | |||
2520.2.bi.o.361.1 | 6 | 1.1 | even | 1 | trivial | ||
2520.2.bi.o.1801.1 | 6 | 7.2 | even | 3 | inner | ||
5880.2.a.bt.1.3 | 3 | 21.17 | even | 6 | |||
5880.2.a.bw.1.3 | 3 | 21.11 | odd | 6 |