Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1444,2,Mod(429,1444)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1444, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1444.429");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1444 = 2^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1444.e (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: | \(11.5303980519\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 429.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1444.429 |
Dual form | 1444.2.e.c.653.1 |
$q$-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 \(\left(\mathbb{Z}/1444\mathbb{Z}\right)^\times\).
\(n\) | \(723\) | \(1085\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | − | 1.73205i | 0.577350 | − | 1.00000i | −0.418432 | − | 0.908248i | \(-0.637420\pi\) |
0.995782 | − | 0.0917517i | \(-0.0292466\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.00000 | 1.50756 | 0.753778 | − | 0.657129i | \(-0.228229\pi\) | ||||
0.753778 | + | 0.657129i | \(0.228229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | − | 3.46410i | −0.554700 | − | 0.960769i | −0.997927 | − | 0.0643593i | \(-0.979500\pi\) |
0.443227 | − | 0.896410i | \(-0.353834\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | − | 1.73205i | −0.258199 | − | 0.447214i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | + | 5.19615i | −0.654654 | + | 1.13389i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | − | 6.92820i | −0.834058 | − | 1.44463i | −0.894795 | − | 0.446476i | \(-0.852679\pi\) |
0.0607377 | − | 0.998154i | \(-0.480655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.00000 | − | 8.66025i | 0.870388 | − | 1.50756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.50000 | + | 2.59808i | −0.253546 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0000 | −1.64399 | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.00000 | −1.28103 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | − | 8.66025i | 0.780869 | − | 1.35250i | −0.150567 | − | 0.988600i | \(-0.548110\pi\) |
0.931436 | − | 0.363905i | \(-0.118557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.500000 | + | 0.866025i | 0.0729325 | + | 0.126323i | 0.900185 | − | 0.435507i | \(-0.143431\pi\) |
−0.827253 | + | 0.561830i | \(0.810098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | − | 3.46410i | −0.274721 | − | 0.475831i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
−0.970065 | + | 0.242846i | \(0.921919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.50000 | − | 4.33013i | 0.337100 | − | 0.583874i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.50000 | + | 2.59808i | 0.188982 | + | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | − | 10.3923i | −0.733017 | − | 1.26962i | −0.955588 | − | 0.294706i | \(-0.904778\pi\) |
0.222571 | − | 0.974916i | \(-0.428555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.0000 | −1.92617 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00000 | − | 1.73205i | 0.118678 | − | 0.205557i | −0.800566 | − | 0.599245i | \(-0.795468\pi\) |
0.919244 | + | 0.393688i | \(0.128801\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.50000 | + | 7.79423i | −0.526685 | + | 0.912245i | 0.472831 | + | 0.881153i | \(0.343232\pi\) |
−0.999517 | + | 0.0310925i | \(0.990101\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.00000 | 0.923760 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.0000 | −1.70941 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | − | 6.92820i | 0.450035 | − | 0.779484i | −0.548352 | − | 0.836247i | \(-0.684745\pi\) |
0.998388 | + | 0.0567635i | \(0.0180781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.50000 | − | 2.59808i | −0.162698 | − | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.00000 | −0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | + | 10.3923i | 0.635999 | + | 1.10158i | 0.986303 | + | 0.164946i | \(0.0527450\pi\) |
−0.350304 | + | 0.936636i | \(0.613922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 10.3923i | 0.628971 | + | 1.08941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | + | 6.92820i | −0.414781 | + | 0.718421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | + | 6.92820i | −0.406138 | + | 0.703452i | −0.994453 | − | 0.105180i | \(-0.966458\pi\) |
0.588315 | + | 0.808632i | \(0.299792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.50000 | − | 4.33013i | −0.251259 | − | 0.435194i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.00000 | + | 8.66025i | 0.497519 | + | 0.861727i | 0.999996 | − | 0.00286291i | \(-0.000911295\pi\) |
−0.502477 | + | 0.864590i | \(0.667578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | 0.591198 | 0.295599 | − | 0.955312i | \(-0.404481\pi\) | ||||
0.295599 | + | 0.955312i | \(0.404481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.00000 | + | 5.19615i | 0.292770 | + | 0.507093i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.00000 | −0.193347 | −0.0966736 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966736 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | + | 17.3205i | −0.949158 | + | 1.64399i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | −0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | + | 3.46410i | −0.184900 | + | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.50000 | + | 7.79423i | −0.412514 | + | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.0000 | − | 17.3205i | −0.901670 | − | 1.56174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.00000 | + | 5.19615i | 0.266207 | + | 0.461084i | 0.967879 | − | 0.251416i | \(-0.0808962\pi\) |
−0.701672 | + | 0.712500i | \(0.747563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.00000 | + | 1.73205i | 0.0880451 | + | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50000 | − | 7.79423i | 0.393167 | − | 0.680985i | −0.599699 | − | 0.800226i | \(-0.704713\pi\) |
0.992865 | + | 0.119241i | \(0.0380462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.00000 | − | 3.46410i | 0.172133 | − | 0.298142i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.50000 | + | 9.52628i | 0.469897 | + | 0.813885i | 0.999408 | − | 0.0344182i | \(-0.0109578\pi\) |
−0.529511 | + | 0.848303i | \(0.677624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.50000 | + | 2.59808i | 0.127228 | + | 0.220366i | 0.922602 | − | 0.385754i | \(-0.126059\pi\) |
−0.795373 | + | 0.606120i | \(0.792725\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | 0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.0000 | − | 17.3205i | −0.836242 | − | 1.44841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.00000 | − | 3.46410i | 0.164957 | − | 0.285714i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.50000 | − | 12.9904i | 0.614424 | − | 1.06421i | −0.376061 | − | 0.926595i | \(-0.622722\pi\) |
0.990485 | − | 0.137619i | \(-0.0439449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | + | 3.46410i | −0.160644 | + | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00000 | − | 1.73205i | 0.0798087 | − | 0.138233i | −0.823359 | − | 0.567521i | \(-0.807902\pi\) |
0.903167 | + | 0.429289i | \(0.141236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.00000 | −0.634441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | + | 20.7846i | 0.945732 | + | 1.63806i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.00000 | − | 8.66025i | −0.389249 | − | 0.674200i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | − | 5.19615i | −0.232147 | − | 0.402090i | 0.726293 | − | 0.687386i | \(-0.241242\pi\) |
−0.958440 | + | 0.285295i | \(0.907908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.00000 | − | 10.3923i | −0.453557 | − | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.00000 | − | 10.3923i | −0.450988 | − | 0.781133i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.0000 | −1.34538 | −0.672692 | − | 0.739923i | \(-0.734862\pi\) | ||||
−0.672692 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | + | 8.66025i | 0.371647 | + | 0.643712i | 0.989819 | − | 0.142331i | \(-0.0454598\pi\) |
−0.618172 | + | 0.786043i | \(0.712126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.0000 | 1.92198 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.00000 | + | 8.66025i | −0.367607 | + | 0.636715i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.50000 | − | 12.9904i | 0.548454 | − | 0.949951i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.0000 | −0.872872 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.0000 | 1.80894 | 0.904468 | − | 0.426541i | \(-0.140268\pi\) | ||||
0.904468 | + | 0.426541i | \(0.140268\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | − | 10.3923i | 0.431889 | − | 0.748054i | −0.565147 | − | 0.824991i | \(-0.691180\pi\) |
0.997036 | + | 0.0769360i | \(0.0245137\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.00000 | + | 6.92820i | −0.286446 | + | 0.496139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | + | 6.06218i | 0.248108 | + | 0.429736i | 0.963001 | − | 0.269498i | \(-0.0868577\pi\) |
−0.714893 | + | 0.699234i | \(0.753524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.0000 | −1.69283 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000 | + | 5.19615i | 0.210559 | + | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.00000 | − | 8.66025i | −0.349215 | − | 0.604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | + | 6.92820i | −0.278019 | + | 0.481543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000 | − | 15.5885i | 0.619586 | − | 1.07315i | −0.369976 | − | 0.929041i | \(-0.620634\pi\) |
0.989561 | − | 0.144112i | \(-0.0460326\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.00000 | − | 3.46410i | −0.137038 | − | 0.237356i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.500000 | + | 0.866025i | 0.0340997 | + | 0.0590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.00000 | + | 15.5885i | 0.608164 | + | 1.05337i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | − | 1.73205i | 0.0669650 | − | 0.115987i | −0.830599 | − | 0.556871i | \(-0.812002\pi\) |
0.897564 | + | 0.440884i | \(0.145335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | − | 3.46410i | 0.133333 | − | 0.230940i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0000 | 1.12339 | 0.561696 | − | 0.827344i | \(-0.310149\pi\) | ||||
0.561696 | + | 0.827344i | \(0.310149\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.0000 | + | 25.9808i | −0.986928 | + | 1.70941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.50000 | + | 2.59808i | −0.0982683 | + | 0.170206i | −0.910968 | − | 0.412477i | \(-0.864664\pi\) |
0.812700 | + | 0.582683i | \(0.197997\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.00000 | 0.0652328 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.00000 | − | 13.8564i | −0.519656 | − | 0.900070i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.0000 | 1.35838 | 0.679189 | − | 0.733964i | \(-0.262332\pi\) | ||||
0.679189 | + | 0.733964i | \(0.262332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | − | 22.5167i | −0.837404 | − | 1.45043i | −0.892058 | − | 0.451920i | \(-0.850739\pi\) |
0.0546547 | − | 0.998505i | \(-0.482594\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.00000 | − | 8.66025i | −0.320750 | − | 0.555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | + | 20.7846i | −0.760469 | + | 1.31717i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.50000 | − | 9.52628i | −0.347157 | − | 0.601293i | 0.638586 | − | 0.769550i | \(-0.279520\pi\) |
−0.985743 | + | 0.168257i | \(0.946186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0000 | − | 34.6410i | −1.25739 | − | 2.17786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.00000 | −0.375735 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.0000 | + | 27.7128i | 0.998053 | + | 1.72868i | 0.553047 | + | 0.833150i | \(0.313465\pi\) |
0.445005 | + | 0.895528i | \(0.353202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.0000 | 1.86411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | + | 1.73205i | −0.0618984 | + | 0.107211i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5000 | − | 18.1865i | 0.647458 | − | 1.12143i | −0.336270 | − | 0.941766i | \(-0.609166\pi\) |
0.983728 | − | 0.179664i | \(-0.0575011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.0000 | 1.46878 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0000 | + | 20.7846i | −0.731653 | + | 1.26726i | 0.224523 | + | 0.974469i | \(0.427917\pi\) |
−0.956176 | + | 0.292791i | \(0.905416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000 | − | 6.92820i | 0.242983 | − | 0.420858i | −0.718580 | − | 0.695444i | \(-0.755208\pi\) |
0.961563 | + | 0.274586i | \(0.0885408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 24.0000 | 1.45255 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0000 | + | 17.3205i | 0.603023 | + | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | 0.0600842 | 0.0300421 | − | 0.999549i | \(-0.490436\pi\) | ||||
0.0300421 | + | 0.999549i | \(0.490436\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00000 | + | 3.46410i | 0.119737 | + | 0.207390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0000 | + | 19.0526i | 0.656205 | + | 1.13658i | 0.981590 | + | 0.190999i | \(0.0611727\pi\) |
−0.325385 | + | 0.945582i | \(0.605494\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.50000 | − | 2.59808i | 0.0891657 | − | 0.154440i | −0.817993 | − | 0.575228i | \(-0.804913\pi\) |
0.907159 | + | 0.420789i | \(0.138247\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.0000 | + | 25.9808i | −0.885422 | + | 1.53360i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.00000 | + | 13.8564i | 0.468968 | + | 0.812277i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.00000 | − | 5.19615i | −0.174667 | − | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.0000 | 1.16052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.0000 | + | 27.7128i | −0.925304 | + | 1.60267i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.50000 | − | 2.59808i | 0.0864586 | − | 0.149751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.0000 | 1.14897 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.0000 | 0.744378 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.00000 | − | 10.3923i | 0.342438 | − | 0.593120i | −0.642447 | − | 0.766330i | \(-0.722081\pi\) |
0.984885 | + | 0.173210i | \(0.0554140\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000 | − | 10.3923i | 0.341328 | − | 0.591198i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.00000 | 0.396934 | 0.198467 | − | 0.980108i | \(-0.436404\pi\) | ||||
0.198467 | + | 0.980108i | \(0.436404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | + | 8.66025i | 0.282617 | + | 0.489506i | 0.972028 | − | 0.234863i | \(-0.0754642\pi\) |
−0.689412 | + | 0.724370i | \(0.742131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.00000 | 0.169031 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0000 | + | 25.9808i | 0.842484 | + | 1.45922i | 0.887788 | + | 0.460252i | \(0.152241\pi\) |
−0.0453045 | + | 0.998973i | \(0.514426\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.00000 | − | 8.66025i | −0.279946 | − | 0.484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00000 | + | 3.46410i | −0.111629 | + | 0.193347i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00000 | − | 13.8564i | 0.443760 | − | 0.768615i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.50000 | − | 2.59808i | −0.0826977 | − | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.00000 | + | 8.66025i | 0.273998 | + | 0.474579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.0000 | + | 27.7128i | −0.871576 | + | 1.50961i | −0.0112091 | + | 0.999937i | \(0.503568\pi\) |
−0.860366 | + | 0.509676i | \(0.829765\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.0000 | − | 17.3205i | 0.543125 | − | 0.940721i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.0000 | −1.08306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00000 | + | 13.8564i | −0.430706 | + | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.50000 | + | 16.4545i | −0.509987 | + | 0.883323i | 0.489946 | + | 0.871753i | \(0.337016\pi\) |
−0.999933 | + | 0.0115703i | \(0.996317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.0000 | −0.588817 | −0.294408 | − | 0.955680i | \(-0.595123\pi\) | ||||
−0.294408 | + | 0.955680i | \(0.595123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | − | 13.8564i | −0.427008 | − | 0.739600i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.00000 | − | 1.73205i | −0.0530745 | − | 0.0919277i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.00000 | + | 15.5885i | 0.476331 | + | 0.825029i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.5000 | + | 18.1865i | −0.554169 | + | 0.959849i | 0.443799 | + | 0.896126i | \(0.353630\pi\) |
−0.997968 | + | 0.0637221i | \(0.979703\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.0000 | − | 24.2487i | 0.734809 | − | 1.27273i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.50000 | + | 7.79423i | 0.235541 | + | 0.407969i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | − | 13.8564i | −0.417597 | − | 0.723299i | 0.578101 | − | 0.815966i | \(-0.303794\pi\) |
−0.995697 | + | 0.0926670i | \(0.970461\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.0000 | −0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | + | 10.3923i | 0.311504 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.00000 | 0.207112 | 0.103556 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.00000 | − | 15.5885i | 0.464758 | − | 0.804984i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | + | 6.92820i | −0.206010 | + | 0.356821i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.0000 | 1.54100 | 0.770498 | − | 0.637442i | \(-0.220007\pi\) | ||||
0.770498 | + | 0.637442i | \(0.220007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0000 | 0.614779 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.00000 | − | 3.46410i | 0.102195 | − | 0.177007i | −0.810394 | − | 0.585886i | \(-0.800747\pi\) |
0.912589 | + | 0.408879i | \(0.134080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.50000 | + | 12.9904i | −0.382235 | + | 0.662051i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.00000 | 0.0508329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5000 | + | 18.1865i | 0.532371 | + | 0.922094i | 0.999286 | + | 0.0377914i | \(0.0120322\pi\) |
−0.466915 | + | 0.884302i | \(0.654634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.00000 | − | 15.5885i | −0.453990 | − | 0.786334i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.00000 | − | 6.92820i | −0.201262 | − | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.50000 | + | 4.33013i | −0.125471 | + | 0.217323i | −0.921917 | − | 0.387387i | \(-0.873378\pi\) |
0.796446 | + | 0.604710i | \(0.206711\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.0000 | − | 24.2487i | 0.699127 | − | 1.21092i | −0.269643 | − | 0.962960i | \(-0.586906\pi\) |
0.968770 | − | 0.247962i | \(-0.0797610\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.00000 | + | 13.8564i | 0.398508 | + | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.50000 | − | 9.52628i | −0.273297 | − | 0.473365i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −50.0000 | −2.47841 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | − | 17.3205i | −0.494468 | − | 0.856444i | 0.505511 | − | 0.862820i | \(-0.331304\pi\) |
−0.999980 | + | 0.00637586i | \(0.997970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.0000 | 1.08518 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.00000 | + | 15.5885i | −0.442861 | + | 0.767058i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | + | 10.3923i | −0.294528 | + | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.0000 | −1.75872 | −0.879358 | − | 0.476162i | \(-0.842028\pi\) | ||||
−0.879358 | + | 0.476162i | \(0.842028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | + | 34.6410i | −0.974740 | + | 1.68830i | −0.293951 | + | 0.955820i | \(0.594970\pi\) |
−0.680789 | + | 0.732479i | \(0.738363\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.500000 | − | 0.866025i | 0.0243108 | − | 0.0421076i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.5000 | − | 33.7750i | −0.943671 | − | 1.63449i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −40.0000 | −1.93122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | + | 20.7846i | 0.578020 | + | 1.00116i | 0.995706 | + | 0.0925683i | \(0.0295076\pi\) |
−0.417687 | + | 0.908591i | \(0.637159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.00000 | + | 1.73205i | 0.0480569 | + | 0.0832370i | 0.889053 | − | 0.457804i | \(-0.151364\pi\) |
−0.840996 | + | 0.541041i | \(0.818030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | + | 3.46410i | −0.0958927 | + | 0.166091i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.00000 | − | 1.73205i | 0.0477274 | − | 0.0826663i | −0.841175 | − | 0.540763i | \(-0.818135\pi\) |
0.888902 | + | 0.458097i | \(0.151469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | − | 1.73205i | −0.0476190 | − | 0.0824786i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.50000 | + | 4.33013i | 0.118779 | + | 0.205731i | 0.919284 | − | 0.393595i | \(-0.128769\pi\) |
−0.800505 | + | 0.599326i | \(0.795435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.0000 | − | 25.9808i | −0.709476 | − | 1.22885i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.0000 | −0.755087 | −0.377543 | − | 0.925992i | \(-0.623231\pi\) | ||||
−0.377543 | + | 0.925992i | \(0.623231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.0000 | − | 43.3013i | 1.17720 | − | 2.03898i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.00000 | + | 3.46410i | −0.0939682 | + | 0.162758i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0000 | 0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0000 | −0.608114 | −0.304057 | − | 0.952654i | \(-0.598341\pi\) | ||||
−0.304057 | + | 0.952654i | \(0.598341\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.00000 | − | 10.3923i | 0.280056 | − | 0.485071i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.50000 | − | 16.4545i | 0.442459 | − | 0.766362i | −0.555412 | − | 0.831575i | \(-0.687440\pi\) |
0.997871 | + | 0.0652135i | \(0.0207728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0000 | 0.883005 | 0.441502 | − | 0.897260i | \(-0.354446\pi\) | ||||
0.441502 | + | 0.897260i | \(0.354446\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | + | 6.92820i | 0.185496 | + | 0.321288i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.00000 | −0.231372 | −0.115686 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115686 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.0000 | + | 31.1769i | 0.831163 | + | 1.43962i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00000 | − | 3.46410i | −0.0921551 | − | 0.159617i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.50000 | + | 4.33013i | −0.114950 | + | 0.199099i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | + | 3.46410i | −0.0915737 | + | 0.158610i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.00000 | − | 3.46410i | −0.0913823 | − | 0.158279i | 0.816711 | − | 0.577047i | \(-0.195795\pi\) |
−0.908093 | + | 0.418769i | \(0.862462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | + | 34.6410i | 0.911922 | + | 1.57949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 48.0000 | 2.18408 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.00000 | + | 6.92820i | 0.181631 | + | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.0000 | 1.17817 | 0.589086 | − | 0.808070i | \(-0.299488\pi\) | ||||
0.589086 | + | 0.808070i | \(0.299488\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | + | 6.92820i | −0.180886 | + | 0.313304i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0000 | − | 24.2487i | 0.631811 | − | 1.09433i | −0.355370 | − | 0.934726i | \(-0.615645\pi\) |
0.987181 | − | 0.159603i | \(-0.0510215\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | −0.270226 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.00000 | −0.224733 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.00000 | + | 5.19615i | −0.134568 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.50000 | + | 16.4545i | −0.425278 | + | 0.736604i | −0.996446 | − | 0.0842294i | \(-0.973157\pi\) |
0.571168 | + | 0.820833i | \(0.306490\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.0000 | −0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.0000 | + | 31.1769i | 0.802580 | + | 1.39011i | 0.917912 | + | 0.396783i | \(0.129873\pi\) |
−0.115332 | + | 0.993327i | \(0.536793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.00000 | + | 5.19615i | 0.133235 | + | 0.230769i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5000 | − | 23.3827i | 0.597205 | − | 1.03439i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.00000 | − | 5.19615i | 0.132196 | − | 0.228970i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.50000 | + | 4.33013i | 0.109950 | + | 0.190439i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | − | 10.3923i | −0.263371 | − | 0.456172i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.0000 | −1.40195 | −0.700973 | − | 0.713188i | \(-0.747251\pi\) | ||||
−0.700973 | + | 0.713188i | \(0.747251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0000 | + | 22.5167i | 0.568450 | + | 0.984585i | 0.996719 | + | 0.0809336i | \(0.0257902\pi\) |
−0.428269 | + | 0.903651i | \(0.640876\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.0000 | −1.04745 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00000 | + | 10.3923i | −0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.0000 | −1.73259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.00000 | + | 1.73205i | −0.0432338 | + | 0.0748831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.0000 | + | 31.1769i | −0.776757 | + | 1.34538i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0000 | 0.430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.50000 | − | 9.52628i | −0.236463 | − | 0.409567i | 0.723234 | − | 0.690604i | \(-0.242655\pi\) |
−0.959697 | + | 0.281037i | \(0.909322\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.0000 | 0.858282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | + | 24.2487i | 0.598597 | + | 1.03680i | 0.993028 | + | 0.117875i | \(0.0376081\pi\) |
−0.394432 | + | 0.918925i | \(0.629059\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.50000 | − | 11.2583i | 0.277413 | − | 0.480494i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.0000 | + | 20.7846i | −0.510292 | + | 0.883852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.0000 | + | 17.3205i | 0.424476 | + | 0.735215i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.500000 | − | 0.866025i | −0.0211857 | − | 0.0366947i | 0.855238 | − | 0.518235i | \(-0.173411\pi\) |
−0.876424 | + | 0.481540i | \(0.840077\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.0000 | − | 25.9808i | −0.633300 | − | 1.09691i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.0000 | −1.77009 | −0.885044 | − | 0.465506i | \(-0.845872\pi\) | ||||
−0.885044 | + | 0.465506i | \(0.845872\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.00000 | − | 8.66025i | 0.210352 | − | 0.364340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.5000 | + | 28.5788i | −0.692935 | + | 1.20020i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.00000 | 0.335377 | 0.167689 | − | 0.985840i | \(-0.446370\pi\) | ||||
0.167689 | + | 0.985840i | \(0.446370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.0000 | − | 43.3013i | 1.04439 | − | 1.80894i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.0000 | − | 27.7128i | 0.667246 | − | 1.15570i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.0000 | −0.541197 | −0.270599 | − | 0.962692i | \(-0.587222\pi\) | ||||
−0.270599 | + | 0.962692i | \(0.587222\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.0000 | − | 20.7846i | −0.498703 | − | 0.863779i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.0000 | 1.49353 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0000 | − | 17.3205i | −0.414158 | − | 0.717342i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | + | 3.46410i | 0.0826898 | + | 0.143223i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.50000 | + | 2.59808i | −0.0619116 | + | 0.107234i | −0.895320 | − | 0.445424i | \(-0.853053\pi\) |
0.833408 | + | 0.552658i | \(0.186386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.00000 | − | 3.46410i | 0.0822690 | − | 0.142494i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.0000 | − | 19.0526i | −0.451716 | − | 0.782395i | 0.546777 | − | 0.837278i | \(-0.315855\pi\) |
−0.998493 | + | 0.0548835i | \(0.982521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.50000 | + | 7.79423i | 0.184482 | + | 0.319532i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.0000 | 0.572982 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.00000 | − | 10.3923i | −0.245153 | − | 0.424618i | 0.717021 | − | 0.697051i | \(-0.245505\pi\) |
−0.962175 | + | 0.272433i | \(0.912172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.00000 | + | 10.3923i | −0.244339 | + | 0.423207i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | − | 12.1244i | 0.284590 | − | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.0000 | −1.29884 | −0.649420 | − | 0.760430i | \(-0.724988\pi\) | ||||
−0.649420 | + | 0.760430i | \(0.724988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0000 | 0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.00000 | − | 3.46410i | 0.0809113 | − | 0.140143i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5000 | − | 40.7032i | 0.949156 | − | 1.64399i | 0.201948 | − | 0.979396i | \(-0.435273\pi\) |
0.747208 | − | 0.664590i | \(-0.231394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.0000 | −0.806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.50000 | − | 7.79423i | −0.181163 | − | 0.313784i | 0.761114 | − | 0.648618i | \(-0.224653\pi\) |
−0.942277 | + | 0.334835i | \(0.891320\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.0000 | − | 27.7128i | −0.642058 | − | 1.11208i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.0000 | − | 31.1769i | −0.721155 | − | 1.24908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.0000 | + | 25.9808i | −0.598089 | + | 1.03592i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.50000 | + | 6.06218i | 0.139333 | + | 0.241331i | 0.927244 | − | 0.374457i | \(-0.122171\pi\) |
−0.787911 | + | 0.615789i | \(0.788838\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.0000 | − | 31.1769i | −0.715436 | − | 1.23917i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.00000 | 0.238103 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | − | 6.92820i | −0.158486 | − | 0.274505i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.00000 | −0.0791188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.50000 | − | 9.52628i | 0.216899 | − | 0.375680i | −0.736959 | − | 0.675937i | \(-0.763739\pi\) |
0.953858 | + | 0.300257i | \(0.0970725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.00000 | 0.0787499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.00000 | −0.275198 | −0.137599 | − | 0.990488i | \(-0.543939\pi\) | ||||
−0.137599 | + | 0.990488i | \(0.543939\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.0000 | − | 25.9808i | 0.588802 | − | 1.01983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0000 | − | 20.7846i | 0.470317 | − | 0.814613i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.0000 | −1.05659 | −0.528296 | − | 0.849060i | \(-0.677169\pi\) | ||||
−0.528296 | + | 0.849060i | \(0.677169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.50000 | − | 7.79423i | −0.175830 | − | 0.304546i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.00000 | 0.351123 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.0000 | − | 29.4449i | −0.662226 | − | 1.14701i | −0.980029 | − | 0.198852i | \(-0.936279\pi\) |
0.317803 | − | 0.948157i | \(-0.397055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.00000 | + | 13.8564i | 0.311164 | + | 0.538952i | 0.978615 | − | 0.205702i | \(-0.0659478\pi\) |
−0.667451 | + | 0.744654i | \(0.732615\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.0000 | + | 20.7846i | −0.466041 | + | 0.807207i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | + | 13.8564i | −0.309761 | + | 0.536522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.00000 | − | 3.46410i | −0.0773245 | − | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.5000 | + | 56.2917i | 1.25465 | + | 2.17312i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.00000 | + | 13.8564i | 0.307920 | + | 0.533333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.00000 | 0.0768662 | 0.0384331 | − | 0.999261i | \(-0.487763\pi\) | ||||
0.0384331 | + | 0.999261i | \(0.487763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | − | 20.7846i | 0.460518 | − | 0.797640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.00000 | + | 6.92820i | −0.153280 | + | 0.265489i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.0000 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.0000 | 0.420288 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.0000 | − | 29.4449i | 0.648590 | − | 1.12339i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.00000 | + | 13.8564i | −0.304776 | + | 0.527887i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.0000 | −1.25538 | −0.627690 | − | 0.778464i | \(-0.715999\pi\) | ||||
−0.627690 | + | 0.778464i | \(0.715999\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.50000 | + | 12.9904i | 0.284901 | + | 0.493464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.00000 | 0.113796 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.0000 | − | 25.9808i | −0.568166 | − | 0.984092i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.00000 | + | 5.19615i | 0.113470 | + | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.00000 | − | 8.66025i | 0.188847 | − | 0.327093i | −0.756019 | − | 0.654550i | \(-0.772858\pi\) |
0.944866 | + | 0.327457i | \(0.106192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.00000 | − | 1.73205i | 0.0376622 | − | 0.0652328i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.0000 | − | 25.9808i | −0.564133 | − | 0.977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.00000 | + | 5.19615i | 0.112667 | + | 0.195146i | 0.916845 | − | 0.399244i | \(-0.130727\pi\) |
−0.804178 | + | 0.594389i | \(0.797394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.0000 | + | 27.7128i | 0.599205 | + | 1.03785i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.0000 | −0.747958 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.0000 | − | 36.3731i | 0.784259 | − | 1.35838i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.50000 | + | 11.2583i | −0.242409 | + | 0.419865i | −0.961400 | − | 0.275155i | \(-0.911271\pi\) |
0.718991 | + | 0.695019i | \(0.244604\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.0000 | −0.670355 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −52.0000 | −1.93390 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | − | 6.92820i | 0.148556 | − | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.50000 | + | 6.06218i | −0.129808 | + | 0.224834i | −0.923602 | − | 0.383353i | \(-0.874769\pi\) |
0.793794 | + | 0.608186i | \(0.208103\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.50000 | + | 2.59808i | 0.0554795 | + | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.00000 | −0.221615 | −0.110808 | − | 0.993842i | \(-0.535344\pi\) | ||||
−0.110808 | + | 0.993842i | \(0.535344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.00000 | − | 3.46410i | −0.0737711 | − | 0.127775i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.0000 | − | 51.9615i | −1.10506 | − | 1.91403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.5000 | − | 37.2391i | 0.790890 | − | 1.36986i | −0.134526 | − | 0.990910i | \(-0.542951\pi\) |
0.925416 | − | 0.378952i | \(-0.123715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.0000 | + | 34.6410i | −0.733729 | + | 1.27086i | 0.221550 | + | 0.975149i | \(0.428888\pi\) |
−0.955279 | + | 0.295707i | \(0.904445\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.50000 | − | 12.9904i | −0.274779 | − | 0.475931i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | + | 10.3923i | 0.219529 | + | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000 | 0.219235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.00000 | − | 13.8564i | −0.291924 | − | 0.505627i | 0.682341 | − | 0.731034i | \(-0.260962\pi\) |
−0.974265 | + | 0.225407i | \(0.927629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.0000 | −0.801725 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.00000 | + | 1.73205i | −0.0363937 | + | 0.0630358i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.50000 | − | 4.33013i | 0.0908640 | − | 0.157381i | −0.817011 | − | 0.576622i | \(-0.804370\pi\) |
0.907875 | + | 0.419241i | \(0.137704\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −80.0000 | −2.90382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.00000 | 0.326250 | 0.163125 | − | 0.986605i | \(-0.447843\pi\) | ||||
0.163125 | + | 0.986605i | \(0.447843\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.50000 | + | 2.59808i | −0.0542326 | + | 0.0939336i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.0000 | −0.866590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.5000 | − | 26.8468i | −0.558944 | − | 0.968120i | −0.997585 | − | 0.0694574i | \(-0.977873\pi\) |
0.438641 | − | 0.898663i | \(-0.355460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 64.0000 | 2.30490 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.00000 | + | 15.5885i | 0.323708 | + | 0.560678i | 0.981250 | − | 0.192740i | \(-0.0617373\pi\) |
−0.657542 | + | 0.753418i | \(0.728404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | − | 13.8564i | −0.287368 | − | 0.497737i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.0000 | − | 51.9615i | 1.07624 | − | 1.86411i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.00000 | − | 8.66025i | 0.178914 | − | 0.309888i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.00000 | − | 6.92820i | −0.142948 | − | 0.247594i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.00000 | − | 1.73205i | −0.0356915 | − | 0.0618195i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.00000 | −0.142585 | −0.0712923 | − | 0.997455i | \(-0.522712\pi\) | ||||
−0.0712923 | + | 0.997455i | \(0.522712\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.0000 | − | 36.3731i | −0.747620 | − | 1.29492i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.0000 | −1.06668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.0000 | − | 45.0333i | 0.923287 | − | 1.59918i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.00000 | + | 6.92820i | −0.141865 | + | 0.245718i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000 | 0.425062 | 0.212531 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212531 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.00000 | 0.106132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | − | 10.3923i | 0.212000 | − | 0.367194i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.5000 | + | 38.9711i | −0.794008 | + | 1.37526i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.0000 | 0.845889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.0000 | + | 41.5692i | 0.844840 | + | 1.46331i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.0000 | 1.37117 | 0.685583 | − | 0.727994i | \(-0.259547\pi\) | ||||
0.685583 | + | 0.727994i | \(0.259547\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.00000 | − | 13.8564i | −0.280572 | − | 0.485965i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.00000 | − | 10.3923i | 0.209657 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.5000 | − | 38.9711i | −0.785255 | − | 1.36010i | −0.928846 | − | 0.370465i | \(-0.879198\pi\) |
0.143591 | − | 0.989637i | \(-0.454135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.5000 | − | 45.8993i | −0.923732 | − | 1.59995i | −0.793588 | − | 0.608456i | \(-0.791789\pi\) |
−0.130144 | − | 0.991495i | \(-0.541544\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 40.0000 | 1.39262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.0000 | − | 24.2487i | −0.486828 | − | 0.843210i | 0.513058 | − | 0.858354i | \(-0.328513\pi\) |
−0.999885 | + | 0.0151439i | \(0.995179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.0000 | 1.66711 | 0.833554 | − | 0.552437i | \(-0.186302\pi\) | ||||
0.833554 | + | 0.552437i | \(0.186302\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.00000 | − | 1.73205i | 0.0346896 | − | 0.0600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.00000 | − | 5.19615i | 0.103944 | − | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | −0.207639 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0000 | −0.553041 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.00000 | + | 8.66025i | −0.172619 | + | 0.298985i | −0.939335 | − | 0.343002i | \(-0.888556\pi\) |
0.766716 | + | 0.641987i | \(0.221890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 44.0000 | 1.51544 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.50000 | + | 2.59808i | 0.0516016 | + | 0.0893765i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −42.0000 | −1.44314 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.00000 | − | 5.19615i | −0.102960 | − | 0.178331i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.0000 | + | 69.2820i | 1.37118 | + | 2.37496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.0000 | + | 36.3731i | −0.719026 | + | 1.24539i | 0.242360 | + | 0.970186i | \(0.422079\pi\) |
−0.961386 | + | 0.275204i | \(0.911255\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | − | 15.5885i | 0.307434 | − | 0.532492i | −0.670366 | − | 0.742030i | \(-0.733863\pi\) |
0.977800 | + | 0.209539i | \(0.0671963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.500000 | − | 0.866025i | −0.0170598 | − | 0.0295484i | 0.857369 | − | 0.514701i | \(-0.172097\pi\) |
−0.874429 | + | 0.485153i | \(0.838764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30.0000 | + | 51.9615i | 1.02240 | + | 1.77084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.00000 | −0.204242 | −0.102121 | − | 0.994772i | \(-0.532563\pi\) | ||||
−0.102121 | + | 0.994772i | \(0.532563\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.00000 | − | 5.19615i | −0.102003 | − | 0.176674i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.0000 | 0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.0000 | − | 34.6410i | 0.678454 | − | 1.17512i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | + | 41.5692i | −0.813209 | + | 1.40852i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.00000 | 0.270759 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.0000 | −0.912767 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.0000 | − | 29.4449i | 0.574049 | − | 0.994282i | −0.422095 | − | 0.906552i | \(-0.638705\pi\) |
0.996144 | − | 0.0877308i | \(-0.0279615\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0000 | − | 20.7846i | 0.404750 | − | 0.701047i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.0000 | −1.71823 | −0.859117 | − | 0.511780i | \(-0.828986\pi\) | ||||
−0.859117 | + | 0.511780i | \(0.828986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.500000 | − | 0.866025i | −0.0168263 | − | 0.0291441i | 0.857490 | − | 0.514501i | \(-0.172023\pi\) |
−0.874316 | + | 0.485357i | \(0.838690\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0000 | −0.403376 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.0000 | + | 19.0526i | 0.369344 | + | 0.639722i | 0.989463 | − | 0.144785i | \(-0.0462491\pi\) |
−0.620119 | + | 0.784508i | \(0.712916\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.00000 | − | 15.5885i | −0.301850 | − | 0.522820i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.5000 | − | 47.6314i | 0.921285 | − | 1.59571i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.00000 | + | 15.5885i | −0.300837 | + | 0.521065i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.0000 | + | 55.4256i | 1.06845 | + | 1.85061i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00000 | + | 6.92820i | 0.133407 | + | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.00000 | − | 5.19615i | −0.0998337 | − | 0.172917i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0000 | 0.332411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.0000 | + | 34.6410i | −0.664089 | + | 1.15024i | 0.315442 | + | 0.948945i | \(0.397847\pi\) |
−0.979531 | + | 0.201291i | \(0.935486\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.00000 | − | 8.66025i | 0.165840 | − | 0.287242i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.0000 | 0.596367 | 0.298183 | − | 0.954509i | \(-0.403619\pi\) | ||||
0.298183 | + | 0.954509i | \(0.403619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −60.0000 | −1.98571 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.0000 | − | 22.5167i | 0.429767 | − | 0.744378i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.5000 | + | 23.3827i | −0.445809 | + | 0.772164i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0000 | −0.923635 | −0.461817 | − | 0.886975i | \(-0.652802\pi\) | ||||
−0.461817 | + | 0.886975i | \(0.652802\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | − | 20.7846i | −0.395413 | − | 0.684876i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.00000 | −0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0000 | − | 34.6410i | −0.657596 | − | 1.13899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.00000 | − | 5.19615i | −0.0985329 | − | 0.170664i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.00000 | + | 12.1244i | −0.229663 | + | 0.397787i | −0.957708 | − | 0.287742i | \(-0.907096\pi\) |
0.728046 | + | 0.685529i | \(0.240429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.00000 | − | 12.1244i | 0.229170 | − | 0.396934i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.50000 | − | 12.9904i | −0.245276 | − | 0.424831i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.5000 | + | 26.8468i | 0.506363 | + | 0.877046i | 0.999973 | + | 0.00736293i | \(0.00234371\pi\) |
−0.493610 | + | 0.869683i | \(0.664323\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.0000 | 0.652675 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.0000 | − | 22.5167i | −0.423788 | − | 0.734022i | 0.572518 | − | 0.819892i | \(-0.305966\pi\) |
−0.996306 | + | 0.0858697i | \(0.972633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −80.0000 | −2.60516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.00000 | + | 10.3923i | −0.195180 | + | 0.338062i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.00000 | − | 10.3923i | 0.194974 | − | 0.337705i | −0.751918 | − | 0.659256i | \(-0.770871\pi\) |
0.946892 | + | 0.321552i | \(0.104204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.0000 | 1.16861 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 60.0000 | 1.94563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.00000 | + | 13.8564i | −0.259145 | + | 0.448853i | −0.966013 | − | 0.258493i | \(-0.916774\pi\) |
0.706868 | + | 0.707346i | \(0.250108\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.5000 | − | 21.6506i | 0.404491 | − | 0.700598i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.0000 | −0.646508 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.5000 | − | 28.5788i | −0.532813 | − | 0.922859i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.00000 | + | 1.73205i | 0.0322245 | + | 0.0558146i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.00000 | − | 10.3923i | −0.193147 | − | 0.334540i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0000 | + | 41.5692i | −0.771788 | + | 1.33678i | 0.164794 | + | 0.986328i | \(0.447304\pi\) |
−0.936582 | + | 0.350448i | \(0.886029\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.0000 | − | 17.3205i | 0.320915 | − | 0.555842i | −0.659762 | − | 0.751475i | \(-0.729343\pi\) |
0.980677 | + | 0.195633i | \(0.0626762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.50000 | − | 7.79423i | −0.144263 | − | 0.249871i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.0000 | − | 27.7128i | −0.512410 | − | 0.887520i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.0000 | −1.79160 | −0.895799 | − | 0.444459i | \(-0.853396\pi\) | ||||
−0.895799 | + | 0.444459i | \(0.853396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.0000 | + | 51.9615i | 0.958804 | + | 1.66070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.00000 | + | 10.3923i | −0.191370 | + | 0.331463i | −0.945705 | − | 0.325027i | \(-0.894626\pi\) |
0.754334 | + | 0.656490i | \(0.227960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.00000 | − | 1.73205i | 0.0318626 | − | 0.0551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.00000 | −0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.0000 | + | 32.9090i | −0.603555 | + | 1.04539i | 0.388723 | + | 0.921355i | \(0.372916\pi\) |
−0.992278 | + | 0.124033i | \(0.960417\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.00000 | − | 6.92820i | 0.126936 | − | 0.219860i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.00000 | 0.221915 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.5000 | − | 32.0429i | −0.585901 | − | 1.01481i | −0.994762 | − | 0.102214i | \(-0.967407\pi\) |
0.408862 | − | 0.912596i | \(-0.365926\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.0000 | −1.26554 |
(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 | 1444.2.e.c.429.1 | 2 | ||
19.7 | even | 3 | inner | 1444.2.e.c.653.1 | 2 | ||
19.8 | odd | 6 | 76.2.a.a.1.1 | ✓ | 1 | ||
19.11 | even | 3 | 1444.2.a.a.1.1 | 1 | |||
19.12 | odd | 6 | 1444.2.e.a.653.1 | 2 | |||
19.18 | odd | 2 | 1444.2.e.a.429.1 | 2 | |||
57.8 | even | 6 | 684.2.a.b.1.1 | 1 | |||
76.11 | odd | 6 | 5776.2.a.p.1.1 | 1 | |||
76.27 | even | 6 | 304.2.a.a.1.1 | 1 | |||
95.8 | even | 12 | 1900.2.c.b.1749.2 | 2 | |||
95.27 | even | 12 | 1900.2.c.b.1749.1 | 2 | |||
95.84 | odd | 6 | 1900.2.a.b.1.1 | 1 | |||
133.27 | even | 6 | 3724.2.a.a.1.1 | 1 | |||
152.27 | even | 6 | 1216.2.a.q.1.1 | 1 | |||
152.141 | odd | 6 | 1216.2.a.c.1.1 | 1 | |||
209.65 | even | 6 | 9196.2.a.f.1.1 | 1 | |||
228.179 | odd | 6 | 2736.2.a.q.1.1 | 1 | |||
380.179 | even | 6 | 7600.2.a.p.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.2.a.a.1.1 | ✓ | 1 | 19.8 | odd | 6 | ||
304.2.a.a.1.1 | 1 | 76.27 | even | 6 | |||
684.2.a.b.1.1 | 1 | 57.8 | even | 6 | |||
1216.2.a.c.1.1 | 1 | 152.141 | odd | 6 | |||
1216.2.a.q.1.1 | 1 | 152.27 | even | 6 | |||
1444.2.a.a.1.1 | 1 | 19.11 | even | 3 | |||
1444.2.e.a.429.1 | 2 | 19.18 | odd | 2 | |||
1444.2.e.a.653.1 | 2 | 19.12 | odd | 6 | |||
1444.2.e.c.429.1 | 2 | 1.1 | even | 1 | trivial | ||
1444.2.e.c.653.1 | 2 | 19.7 | even | 3 | inner | ||
1900.2.a.b.1.1 | 1 | 95.84 | odd | 6 | |||
1900.2.c.b.1749.1 | 2 | 95.27 | even | 12 | |||
1900.2.c.b.1749.2 | 2 | 95.8 | even | 12 | |||
2736.2.a.q.1.1 | 1 | 228.179 | odd | 6 | |||
3724.2.a.a.1.1 | 1 | 133.27 | even | 6 | |||
5776.2.a.p.1.1 | 1 | 76.11 | odd | 6 | |||
7600.2.a.p.1.1 | 1 | 380.179 | even | 6 | |||
9196.2.a.f.1.1 | 1 | 209.65 | even | 6 |