Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(149,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.u (of order \(6\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.3 | ||
Root | \(0.535233 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.149 |
Dual form | 900.3.u.b.749.3 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.59808 | − | 1.50000i | 0.866025 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.24410 | + | 1.87298i | −0.463443 | + | 0.267569i | −0.713491 | − | 0.700664i | \(-0.752887\pi\) |
0.250048 | + | 0.968234i | \(0.419554\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.1190 | + | 5.84218i | −0.919905 | + | 0.531107i | −0.883605 | − | 0.468234i | \(-0.844891\pi\) |
−0.0362999 | + | 0.999341i | \(0.511557\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.95205 | + | 1.12702i | 0.150158 | + | 0.0866936i | 0.573196 | − | 0.819418i | \(-0.305703\pi\) |
−0.423039 | + | 0.906112i | \(0.639037\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.6844 | 0.687315 | 0.343658 | − | 0.939095i | \(-0.388334\pi\) | ||||
0.343658 | + | 0.939095i | \(0.388334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.7460 | 1.40768 | 0.703841 | − | 0.710357i | \(-0.251467\pi\) | ||||
0.703841 | + | 0.710357i | \(0.251467\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.61895 | + | 9.73231i | −0.267569 | + | 0.463443i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.95231 | − | 17.2379i | 0.432709 | − | 0.749474i | −0.564397 | − | 0.825504i | \(-0.690891\pi\) |
0.997106 | + | 0.0760299i | \(0.0242244\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.0000i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 38.2379 | − | 22.0767i | 1.31855 | − | 0.761264i | 0.335053 | − | 0.942199i | \(-0.391246\pi\) |
0.983495 | + | 0.180935i | \(0.0579124\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.1109 | − | 45.2254i | 0.842287 | − | 1.45888i | −0.0456704 | − | 0.998957i | \(-0.514542\pi\) |
0.887957 | − | 0.459927i | \(-0.152124\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.5265 | + | 30.3569i | −0.531107 | + | 0.919905i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 14.0000i | − | 0.378378i | −0.981941 | − | 0.189189i | \(-0.939414\pi\) | ||
0.981941 | − | 0.189189i | \(-0.0605859\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.76210 | 0.173387 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −22.5000 | − | 12.9904i | −0.548780 | − | 0.316839i | 0.199849 | − | 0.979827i | \(-0.435955\pi\) |
−0.748630 | + | 0.662988i | \(0.769288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.3591 | − | 20.9919i | 0.845560 | − | 0.488184i | −0.0135900 | − | 0.999908i | \(-0.504326\pi\) |
0.859150 | + | 0.511723i | \(0.170993\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22.7367 | − | 39.3810i | −0.483759 | − | 0.837895i | 0.516067 | − | 0.856548i | \(-0.327395\pi\) |
−0.999826 | + | 0.0186534i | \(0.994062\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.4839 | + | 30.2829i | −0.356814 | + | 0.618019i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 30.3569 | − | 17.5265i | 0.595232 | − | 0.343658i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.8323 | 0.204383 | 0.102192 | − | 0.994765i | \(-0.467415\pi\) | ||||
0.102192 | + | 0.994765i | \(0.467415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 69.4881 | − | 40.1190i | 1.21909 | − | 0.703841i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 31.8810 | + | 18.4065i | 0.540357 | + | 0.311975i | 0.745224 | − | 0.666815i | \(-0.232343\pi\) |
−0.204867 | + | 0.978790i | \(0.565676\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22.6190 | + | 39.1772i | 0.370802 | + | 0.642249i | 0.989689 | − | 0.143232i | \(-0.0457494\pi\) |
−0.618887 | + | 0.785480i | \(0.712416\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 33.7137i | 0.535138i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −86.5606 | − | 49.9758i | −1.29195 | − | 0.745907i | −0.312950 | − | 0.949770i | \(-0.601317\pi\) |
−0.979000 | + | 0.203862i | \(0.934651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 59.7138i | − | 0.865418i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 102.603i | 1.44511i | 0.691312 | + | 0.722557i | \(0.257033\pi\) | ||||
−0.691312 | + | 0.722557i | \(0.742967\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.7621i | − | 0.188522i | −0.995548 | − | 0.0942610i | \(-0.969951\pi\) | ||
0.995548 | − | 0.0942610i | \(-0.0300488\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 21.8846 | − | 37.9052i | 0.284216 | − | 0.492276i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 28.3810 | + | 49.1574i | 0.359254 | + | 0.622246i | 0.987836 | − | 0.155497i | \(-0.0496979\pi\) |
−0.628583 | + | 0.777743i | \(0.716365\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −45.0333 | − | 78.0000i | −0.542570 | − | 0.939759i | −0.998756 | − | 0.0498743i | \(-0.984118\pi\) |
0.456185 | − | 0.889885i | \(-0.349215\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 66.2300 | − | 114.714i | 0.761264 | − | 1.31855i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 95.2349i | 1.07005i | 0.844835 | + | 0.535027i | \(0.179699\pi\) | ||||
−0.844835 | + | 0.535027i | \(0.820301\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.44353 | −0.0927861 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 156.665i | − | 1.68457i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 88.0727 | − | 50.8488i | 0.907966 | − | 0.524214i | 0.0281897 | − | 0.999603i | \(-0.491026\pi\) |
0.879776 | + | 0.475388i | \(0.157692\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 105.159i | 1.06221i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −87.7621 | + | 50.6695i | −0.868932 | + | 0.501678i | −0.866993 | − | 0.498320i | \(-0.833950\pi\) |
−0.00193860 | + | 0.999998i | \(0.500617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.1043 | − | 8.14315i | −0.136935 | − | 0.0790597i | 0.429967 | − | 0.902844i | \(-0.358525\pi\) |
−0.566903 | + | 0.823785i | \(0.691858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −84.8705 | −0.793182 | −0.396591 | − | 0.917995i | \(-0.629807\pi\) | ||||
−0.396591 | + | 0.917995i | \(0.629807\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 161.968 | 1.48594 | 0.742971 | − | 0.669323i | \(-0.233416\pi\) | ||||
0.742971 | + | 0.669323i | \(0.233416\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.0000 | − | 36.3731i | −0.189189 | − | 0.327685i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.46410 | + | 6.00000i | −0.0306558 | + | 0.0530973i | −0.880946 | − | 0.473216i | \(-0.843093\pi\) |
0.850290 | + | 0.526314i | \(0.176426\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.5685 | − | 10.1431i | 0.150158 | − | 0.0866936i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −37.9052 | + | 21.8846i | −0.318532 | + | 0.183904i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.76210 | − | 13.4444i | 0.0641496 | − | 0.111110i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −77.9423 | −0.633677 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 225.903i | 1.77877i | 0.457163 | + | 0.889383i | \(0.348865\pi\) | ||||
−0.457163 | + | 0.889383i | \(0.651135\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 62.9758 | − | 109.077i | 0.488184 | − | 0.845560i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −81.7137 | − | 47.1774i | −0.623769 | − | 0.360133i | 0.154566 | − | 0.987982i | \(-0.450602\pi\) |
−0.778335 | + | 0.627849i | \(0.783935\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −86.7667 | + | 50.0948i | −0.652381 | + | 0.376652i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −103.689 | − | 179.595i | −0.756855 | − | 1.31091i | −0.944447 | − | 0.328664i | \(-0.893402\pi\) |
0.187592 | − | 0.982247i | \(-0.439932\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3569 | − | 28.3309i | 0.117675 | − | 0.203819i | −0.801171 | − | 0.598436i | \(-0.795789\pi\) |
0.918846 | + | 0.394616i | \(0.129123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −118.143 | − | 68.2100i | −0.837895 | − | 0.483759i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −26.3369 | −0.184174 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 104.903i | 0.713627i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.3327 | − | 10.5844i | −0.123038 | − | 0.0710360i | 0.437218 | − | 0.899356i | \(-0.355964\pi\) |
−0.560256 | + | 0.828320i | \(0.689297\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 137.714 | + | 238.527i | 0.912011 | + | 1.57965i | 0.811219 | + | 0.584742i | \(0.198804\pi\) |
0.100792 | + | 0.994908i | \(0.467862\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 52.5796 | − | 91.0706i | 0.343658 | − | 0.595232i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 155.829 | + | 89.9677i | 0.992539 | + | 0.573043i | 0.906032 | − | 0.423208i | \(-0.139096\pi\) |
0.0865070 | + | 0.996251i | \(0.472430\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.1431 | − | 16.2485i | 0.177001 | − | 0.102192i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 74.5620i | 0.463118i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 264.411i | − | 1.62216i | −0.584939 | − | 0.811078i | \(-0.698881\pi\) | ||
0.584939 | − | 0.811078i | \(-0.301119\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 86.3267 | − | 149.522i | 0.516926 | − | 0.895342i | −0.482881 | − | 0.875686i | \(-0.660410\pi\) |
0.999807 | − | 0.0196561i | \(-0.00625713\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −81.9597 | − | 141.958i | −0.484968 | − | 0.839990i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 120.357 | − | 208.464i | 0.703841 | − | 1.21909i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 147.168 | + | 254.903i | 0.850685 | + | 1.47343i | 0.880591 | + | 0.473876i | \(0.157146\pi\) |
−0.0299069 | + | 0.999553i | \(0.509521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 110.439 | 0.623950 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 64.1138i | − | 0.358178i | −0.983833 | − | 0.179089i | \(-0.942685\pi\) | ||
0.983833 | − | 0.179089i | \(-0.0573150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 291.206 | 1.60887 | 0.804435 | − | 0.594040i | \(-0.202468\pi\) | ||||
0.804435 | + | 0.594040i | \(0.202468\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 117.532 | + | 67.8569i | 0.642249 | + | 0.370802i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −118.233 | + | 68.2621i | −0.632264 | + | 0.365038i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 50.5706 | + | 87.5908i | 0.267569 | + | 0.463443i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8085 | − | 7.97231i | 0.0722956 | − | 0.0417399i | −0.463416 | − | 0.886141i | \(-0.653377\pi\) |
0.535712 | + | 0.844401i | \(0.320043\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 211.928 | + | 122.357i | 1.09807 | + | 0.633973i | 0.935714 | − | 0.352758i | \(-0.114756\pi\) |
0.162360 | + | 0.986732i | \(0.448090\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −210.374 | −1.06789 | −0.533945 | − | 0.845519i | \(-0.679291\pi\) | ||||
−0.533945 | + | 0.845519i | \(0.679291\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 102.730 | 0.516230 | 0.258115 | − | 0.966114i | \(-0.416899\pi\) | ||||
0.258115 | + | 0.966114i | \(0.416899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −299.855 | −1.49181 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −82.6984 | + | 143.238i | −0.407381 | + | 0.705605i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −89.5708 | − | 155.141i | −0.432709 | − | 0.749474i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −270.641 | + | 156.255i | −1.29493 | + | 0.747630i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 113.984 | − | 197.426i | 0.540208 | − | 0.935668i | −0.458684 | − | 0.888600i | \(-0.651679\pi\) |
0.998892 | − | 0.0470680i | \(-0.0149877\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 153.905 | + | 266.571i | 0.722557 | + | 1.25150i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 195.621i | 0.901479i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.6431 | − | 35.7550i | −0.0942610 | − | 0.163265i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.8085 | + | 13.1685i | 0.103206 | + | 0.0595858i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −241.935 | + | 139.681i | −1.08491 | + | 0.626374i | −0.932217 | − | 0.361899i | \(-0.882128\pi\) |
−0.152695 | + | 0.988273i | \(0.548795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −124.282 | − | 215.262i | −0.547496 | − | 0.948291i | −0.998445 | − | 0.0557415i | \(-0.982248\pi\) |
0.450949 | − | 0.892550i | \(-0.351086\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 78.8891 | − | 136.640i | 0.344494 | − | 0.596681i | −0.640768 | − | 0.767735i | \(-0.721384\pi\) |
0.985262 | + | 0.171054i | \(0.0547172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 131.308i | − | 0.568431i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 332.854 | 1.42856 | 0.714279 | − | 0.699861i | \(-0.246755\pi\) | ||||
0.714279 | + | 0.699861i | \(0.246755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 147.472 | + | 85.1431i | 0.622246 | + | 0.359254i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −207.714 | − | 119.924i | −0.869095 | − | 0.501772i | −0.00204759 | − | 0.999998i | \(-0.500652\pi\) |
−0.867047 | + | 0.498226i | \(0.833985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 94.7540 | + | 164.119i | 0.393170 | + | 0.680991i | 0.992866 | − | 0.119237i | \(-0.0380450\pi\) |
−0.599696 | + | 0.800228i | \(0.704712\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −210.444 | − | 121.500i | −0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 52.2095 | + | 30.1431i | 0.211374 | + | 0.122037i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −234.000 | − | 135.100i | −0.939759 | − | 0.542570i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 447.114i | 1.78133i | 0.454661 | + | 0.890664i | \(0.349760\pi\) | ||||
−0.454661 | + | 0.890664i | \(0.650240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 232.573i | 0.919259i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −223.613 | + | 387.308i | −0.870088 | + | 1.50704i | −0.00818336 | + | 0.999967i | \(0.502605\pi\) |
−0.861905 | + | 0.507070i | \(0.830728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.2218 | + | 45.4174i | 0.101242 | + | 0.175357i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 397.380i | − | 1.52253i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −177.273 | − | 307.046i | −0.674043 | − | 1.16748i | −0.976748 | − | 0.214392i | \(-0.931223\pi\) |
0.302705 | − | 0.953084i | \(-0.402110\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 142.852 | + | 247.427i | 0.535027 | + | 0.926694i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 227.367i | 0.845229i | 0.906310 | + | 0.422614i | \(0.138888\pi\) | ||||
−0.906310 | + | 0.422614i | \(0.861112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 228.573 | 0.843441 | 0.421721 | − | 0.906726i | \(-0.361426\pi\) | ||||
0.421721 | + | 0.906726i | \(0.361426\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.9369 | + | 12.6653i | −0.0803551 | + | 0.0463930i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −381.435 | + | 220.222i | −1.37702 | + | 0.795024i | −0.991800 | − | 0.127799i | \(-0.959209\pi\) |
−0.385223 | + | 0.922824i | \(0.625875\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −234.998 | − | 407.028i | −0.842287 | − | 1.45888i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −272.190 | + | 157.149i | −0.968646 | + | 0.559248i | −0.898823 | − | 0.438311i | \(-0.855577\pi\) |
−0.0698227 | + | 0.997559i | \(0.522243\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −232.067 | − | 133.984i | −0.820024 | − | 0.473441i | 0.0304006 | − | 0.999538i | \(-0.490322\pi\) |
−0.850425 | + | 0.526097i | \(0.823655\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 97.3231 | 0.339105 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −152.476 | −0.527598 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 152.546 | − | 264.218i | 0.524214 | − | 0.907966i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −155.033 | + | 268.524i | −0.529121 | + | 0.916465i | 0.470302 | + | 0.882506i | \(0.344145\pi\) |
−0.999423 | + | 0.0339593i | \(0.989188\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 157.739 | + | 273.212i | 0.531107 | + | 0.919905i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 38.8548 | − | 22.4328i | 0.129949 | − | 0.0750262i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −78.6351 | + | 136.200i | −0.261246 | + | 0.452492i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −152.008 | + | 263.286i | −0.501678 | + | 0.868932i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 495.952i | 1.61548i | 0.589541 | + | 0.807739i | \(0.299309\pi\) | ||||
−0.589541 | + | 0.807739i | \(0.700691\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −48.8589 | −0.158119 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −195.762 | − | 113.023i | −0.629460 | − | 0.363419i | 0.151083 | − | 0.988521i | \(-0.451724\pi\) |
−0.780543 | + | 0.625102i | \(0.785057\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 283.326 | − | 163.579i | 0.905196 | − | 0.522615i | 0.0263139 | − | 0.999654i | \(-0.491623\pi\) |
0.878882 | + | 0.477038i | \(0.158290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.09616 | + | 7.09475i | 0.0129216 | + | 0.0223809i | 0.872414 | − | 0.488768i | \(-0.162553\pi\) |
−0.859492 | + | 0.511149i | \(0.829220\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −257.952 | + | 446.785i | −0.808626 | + | 1.40058i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −220.500 | + | 127.306i | −0.686916 | + | 0.396591i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 312.509 | 0.967521 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 420.805 | − | 242.952i | 1.28686 | − | 0.742971i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 147.520 | + | 85.1708i | 0.448389 | + | 0.258878i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −138.903 | − | 240.587i | −0.419647 | − | 0.726850i | 0.576257 | − | 0.817269i | \(-0.304513\pi\) |
−0.995904 | + | 0.0904186i | \(0.971180\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −109.119 | − | 63.0000i | −0.327685 | − | 0.189189i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 48.3473 | + | 27.9133i | 0.143464 | + | 0.0828288i | 0.570014 | − | 0.821635i | \(-0.306938\pi\) |
−0.426550 | + | 0.904464i | \(0.640271\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.7846i | 0.0613115i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 610.178i | 1.78938i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 314.540i | − | 0.917027i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −254.102 | + | 440.117i | −0.732281 | + | 1.26835i | 0.223625 | + | 0.974675i | \(0.428211\pi\) |
−0.955906 | + | 0.293673i | \(0.905122\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 69.2379 | + | 119.924i | 0.198389 | + | 0.343621i | 0.948006 | − | 0.318251i | \(-0.103096\pi\) |
−0.749617 | + | 0.661872i | \(0.769762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 30.4294 | − | 52.7054i | 0.0866936 | − | 0.150158i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −288.027 | − | 498.877i | −0.815940 | − | 1.41325i | −0.908651 | − | 0.417556i | \(-0.862887\pi\) |
0.0927114 | − | 0.995693i | \(-0.470447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −65.6538 | + | 113.716i | −0.183904 | + | 0.318532i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 267.888i | − | 0.746207i | −0.927790 | − | 0.373103i | \(-0.878294\pi\) | ||
0.927790 | − | 0.373103i | \(-0.121706\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 354.347 | 0.981570 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 46.5726i | − | 0.128299i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −52.3736 | + | 30.2379i | −0.142707 | + | 0.0823921i | −0.569654 | − | 0.821885i | \(-0.692923\pi\) |
0.426946 | + | 0.904277i | \(0.359589\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −202.500 | + | 116.913i | −0.548780 | + | 0.316839i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.1411 | + | 20.2887i | −0.0947199 | + | 0.0546866i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 187.501 | + | 108.254i | 0.502685 | + | 0.290225i | 0.729822 | − | 0.683638i | \(-0.239603\pi\) |
−0.227137 | + | 0.973863i | \(0.572936\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 99.5231 | 0.263987 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −285.254 | −0.752649 | −0.376325 | − | 0.926488i | \(-0.622812\pi\) | ||||
−0.376325 | + | 0.926488i | \(0.622812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 338.855 | + | 586.914i | 0.889383 | + | 1.54046i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −81.7905 | + | 141.665i | −0.213552 | + | 0.369883i | −0.952824 | − | 0.303524i | \(-0.901837\pi\) |
0.739272 | + | 0.673407i | \(0.235170\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 377.855i | − | 0.976369i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −250.760 | + | 144.776i | −0.644627 | + | 0.372176i | −0.786395 | − | 0.617724i | \(-0.788055\pi\) |
0.141767 | + | 0.989900i | \(0.454721\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 116.286 | − | 201.414i | 0.297407 | − | 0.515125i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −283.065 | −0.720266 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 66.5081i | 0.167527i | 0.996486 | + | 0.0837633i | \(0.0266940\pi\) | ||||
−0.996486 | + | 0.0837633i | \(0.973306\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −150.284 | + | 260.300i | −0.376652 | + | 0.652381i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −392.165 | − | 226.417i | −0.977968 | − | 0.564630i | −0.0763122 | − | 0.997084i | \(-0.524315\pi\) |
−0.901656 | + | 0.432454i | \(0.857648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 101.940 | − | 58.8548i | 0.252952 | − | 0.146042i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 81.7905 | + | 141.665i | 0.200959 | + | 0.348072i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 150.435 | − | 260.562i | 0.367813 | − | 0.637071i | −0.621410 | − | 0.783485i | \(-0.713440\pi\) |
0.989223 | + | 0.146415i | \(0.0467734\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −538.784 | − | 311.067i | −1.31091 | − | 0.756855i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −137.901 | −0.333900 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 98.1411i | − | 0.235350i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −103.524 | − | 59.7697i | −0.247074 | − | 0.142649i | 0.371349 | − | 0.928493i | \(-0.378895\pi\) |
−0.618424 | + | 0.785845i | \(0.712229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 81.1431 | + | 140.544i | 0.192739 | + | 0.333834i | 0.946157 | − | 0.323708i | \(-0.104930\pi\) |
−0.753418 | + | 0.657542i | \(0.771596\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −409.260 | −0.967517 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −146.756 | − | 84.7298i | −0.343692 | − | 0.198431i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −68.4254 | + | 39.5054i | −0.159500 | + | 0.0920872i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 499.815i | − | 1.15966i | −0.814736 | − | 0.579832i | \(-0.803118\pi\) | ||
0.814736 | − | 0.579832i | \(-0.196882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 739.883i | 1.70874i | 0.519668 | + | 0.854368i | \(0.326056\pi\) | ||||
−0.519668 | + | 0.854368i | \(0.673944\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 266.184 | − | 461.044i | 0.609117 | − | 1.05502i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 124.333 | + | 215.350i | 0.283218 | + | 0.490548i | 0.972175 | − | 0.234254i | \(-0.0752647\pi\) |
−0.688958 | + | 0.724802i | \(0.741931\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 157.355 | + | 272.547i | 0.356814 | + | 0.618019i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −45.5432 | − | 78.8831i | −0.102806 | − | 0.178066i | 0.810034 | − | 0.586384i | \(-0.199449\pi\) |
−0.912840 | + | 0.408318i | \(0.866116\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −63.5062 | −0.142072 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 93.6705i | 0.208620i | 0.994545 | + | 0.104310i | \(0.0332634\pi\) | ||||
−0.994545 | + | 0.104310i | \(0.966737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 303.569 | 0.673101 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 715.581 | + | 413.141i | 1.57965 | + | 0.912011i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −349.005 | + | 201.498i | −0.763686 | + | 0.440915i | −0.830618 | − | 0.556843i | \(-0.812012\pi\) |
0.0669313 | + | 0.997758i | \(0.478679\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 315.478i | − | 0.687315i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −57.9496 | + | 33.4572i | −0.125704 | + | 0.0725752i | −0.561533 | − | 0.827454i | \(-0.689788\pi\) |
0.435829 | + | 0.900029i | \(0.356455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −153.824 | − | 88.8105i | −0.332234 | − | 0.191815i | 0.324599 | − | 0.945852i | \(-0.394771\pi\) |
−0.656832 | + | 0.754037i | \(0.728104\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −620.647 | −1.32901 | −0.664504 | − | 0.747285i | \(-0.731357\pi\) | ||||
−0.664504 | + | 0.747285i | \(0.731357\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 374.415 | 0.798327 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 539.806 | 1.14609 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −245.277 | + | 424.833i | −0.518557 | + | 0.898166i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 48.7454 | − | 84.4294i | 0.102192 | − | 0.177001i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −146.044 | + | 84.3187i | −0.304894 | + | 0.176031i | −0.644639 | − | 0.764487i | \(-0.722992\pi\) |
0.339745 | + | 0.940517i | \(0.389659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7782 | − | 27.3287i | 0.0328030 | − | 0.0568164i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 111.843 | + | 193.718i | 0.231559 | + | 0.401072i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 401.935i | − | 0.825330i | −0.910883 | − | 0.412665i | \(-0.864598\pi\) | ||
0.910883 | − | 0.412665i | \(-0.135402\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −396.617 | − | 686.961i | −0.811078 | − | 1.40483i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −307.833 | − | 177.727i | −0.626950 | − | 0.361970i | 0.152620 | − | 0.988285i | \(-0.451229\pi\) |
−0.779570 | + | 0.626315i | \(0.784562\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 446.785 | − | 257.952i | 0.906258 | − | 0.523228i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −192.174 | − | 332.855i | −0.386668 | − | 0.669728i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.30845 | + | 14.3907i | −0.0166502 | + | 0.0288390i | −0.874230 | − | 0.485511i | \(-0.838634\pi\) |
0.857580 | + | 0.514350i | \(0.171967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 517.960i | − | 1.03385i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 362.522 | 0.720721 | 0.360360 | − | 0.932813i | \(-0.382654\pi\) | ||||
0.360360 | + | 0.932813i | \(0.382654\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −425.875 | − | 245.879i | −0.839990 | − | 0.484968i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 578.286 | + | 333.874i | 1.13612 | + | 0.655941i | 0.945467 | − | 0.325717i | \(-0.105606\pi\) |
0.190655 | + | 0.981657i | \(0.438939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.7762 | + | 44.6457i | 0.0504426 | + | 0.0873692i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 722.141i | − | 1.40768i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 460.142 | + | 265.663i | 0.890024 | + | 0.513855i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 764.710 | + | 441.505i | 1.47343 | + | 0.850685i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 676.352i | 1.29818i | 0.760712 | + | 0.649090i | \(0.224850\pi\) | ||||
−0.760712 | + | 0.649090i | \(0.775150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 189.427i | 0.362194i | 0.983465 | + | 0.181097i | \(0.0579648\pi\) | ||||
−0.983465 | + | 0.181097i | \(0.942035\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 305.089 | − | 528.429i | 0.578916 | − | 1.00271i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 66.4032 | + | 115.014i | 0.125526 | + | 0.217417i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 286.929 | − | 165.659i | 0.540357 | − | 0.311975i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.2808 | − | 50.7157i | −0.0549357 | − | 0.0951515i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −96.1707 | − | 166.573i | −0.179089 | − | 0.310191i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 408.575i | − | 0.758025i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −590.629 | −1.09174 | −0.545868 | − | 0.837871i | \(-0.683800\pi\) | ||||
−0.545868 | + | 0.837871i | \(0.683800\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 756.574 | − | 436.808i | 1.39332 | − | 0.804435i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 683.783 | − | 394.782i | 1.25006 | − | 0.721722i | 0.278939 | − | 0.960309i | \(-0.410017\pi\) |
0.971121 | + | 0.238586i | \(0.0766840\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 407.141 | 0.741605 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1022.71 | − | 590.462i | 1.85610 | − | 1.07162i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −184.142 | − | 106.314i | −0.332987 | − | 0.192250i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1004.69 | 1.80376 | 0.901880 | − | 0.431987i | \(-0.142187\pi\) | ||||
0.901880 | + | 0.431987i | \(0.142187\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 94.6330 | 0.169290 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −204.786 | + | 354.700i | −0.365038 | + | 0.632264i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 157.603 | − | 272.976i | 0.279934 | − | 0.484859i | −0.691434 | − | 0.722439i | \(-0.743021\pi\) |
0.971368 | + | 0.237580i | \(0.0763542\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 262.772 | + | 151.712i | 0.463443 | + | 0.267569i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 823.923 | − | 475.692i | 1.44802 | − | 0.836015i | 0.449656 | − | 0.893202i | \(-0.351546\pi\) |
0.998363 | + | 0.0571870i | \(0.0182131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −229.183 | + | 396.957i | −0.401372 | + | 0.695197i | −0.993892 | − | 0.110359i | \(-0.964800\pi\) |
0.592520 | + | 0.805556i | \(0.298133\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.9169 | − | 41.4254i | 0.0417399 | − | 0.0722956i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 991.190i | − | 1.71783i | −0.512116 | − | 0.858916i | \(-0.671138\pi\) | ||
0.512116 | − | 0.858916i | \(-0.328862\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 734.141 | 1.26795 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 292.185 | + | 168.693i | 0.502901 | + | 0.290350i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −109.612 | + | 63.2843i | −0.188013 | + | 0.108549i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −83.6483 | − | 144.883i | −0.142501 | − | 0.246820i | 0.785937 | − | 0.618307i | \(-0.212181\pi\) |
−0.928438 | + | 0.371488i | \(0.878848\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 698.361 | − | 1209.60i | 1.18567 | − | 2.05364i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −546.569 | + | 315.561i | −0.924820 | + | 0.533945i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 868.330 | 1.46430 | 0.732150 | − | 0.681143i | \(-0.238517\pi\) | ||||
0.732150 | + | 0.681143i | \(0.238517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 266.900 | − | 154.095i | 0.447069 | − | 0.258115i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 170.335 | + | 98.3428i | 0.284365 | + | 0.164178i | 0.635398 | − | 0.772185i | \(-0.280836\pi\) |
−0.351033 | + | 0.936363i | \(0.614169\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −332.181 | − | 575.355i | −0.552715 | − | 0.957330i | −0.998077 | − | 0.0619795i | \(-0.980259\pi\) |
0.445363 | − | 0.895350i | \(-0.353075\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −779.046 | + | 449.782i | −1.29195 | + | 0.745907i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −64.4979 | − | 37.2379i | −0.106257 | − | 0.0613474i | 0.445930 | − | 0.895068i | \(-0.352873\pi\) |
−0.552187 | + | 0.833720i | \(0.686206\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 496.191i | 0.814763i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 102.498i | − | 0.167755i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 304.569i | − | 0.496849i | −0.968651 | − | 0.248425i | \(-0.920087\pi\) | ||
0.968651 | − | 0.248425i | \(-0.0799128\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −470.744 | + | 815.353i | −0.762956 | + | 1.32148i | 0.178364 | + | 0.983965i | \(0.442920\pi\) |
−0.941320 | + | 0.337515i | \(0.890414\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −117.736 | − | 203.924i | −0.190203 | − | 0.329442i | 0.755114 | − | 0.655593i | \(-0.227581\pi\) |
−0.945318 | + | 0.326151i | \(0.894248\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −465.423 | − | 268.712i | −0.749474 | − | 0.432709i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −178.373 | − | 308.952i | −0.286313 | − | 0.495909i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −468.764 | + | 811.923i | −0.747630 | + | 1.29493i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 163.581i | − | 0.260065i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −832.125 | −1.31874 | −0.659370 | − | 0.751819i | \(-0.729177\pi\) | ||||
−0.659370 | + | 0.751819i | \(0.729177\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 683.903i | − | 1.08042i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −68.2588 | + | 39.4092i | −0.107157 | + | 0.0618669i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 799.712 | + | 461.714i | 1.25150 | + | 0.722557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 913.355 | − | 527.326i | 1.42489 | − | 0.822661i | 0.428179 | − | 0.903694i | \(-0.359155\pi\) |
0.996711 | + | 0.0810330i | \(0.0258219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −854.928 | − | 493.593i | −1.32959 | − | 0.767640i | −0.344356 | − | 0.938839i | \(-0.611903\pi\) |
−0.985236 | + | 0.171199i | \(0.945236\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 75.6097 | 0.116862 | 0.0584310 | − | 0.998291i | \(-0.481390\pi\) | ||||
0.0584310 | + | 0.998291i | \(0.481390\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −430.137 | −0.662769 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 293.431 | + | 508.238i | 0.450740 | + | 0.780704i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −623.510 | + | 1079.95i | −0.954840 | + | 1.65383i | −0.220105 | + | 0.975476i | \(0.570640\pi\) |
−0.734734 | + | 0.678355i | \(0.762693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −107.265 | − | 61.9294i | −0.163265 | − | 0.0942610i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −544.851 | + | 314.570i | −0.826784 | + | 0.477344i | −0.852750 | − | 0.522319i | \(-0.825067\pi\) |
0.0259662 | + | 0.999663i | \(0.491734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −323.282 | + | 559.941i | −0.489080 | + | 0.847112i | −0.999921 | − | 0.0125632i | \(-0.996001\pi\) |
0.510841 | + | 0.859675i | \(0.329334\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 79.0108 | 0.119172 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 878.855i | − | 1.31762i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −419.044 | + | 725.806i | −0.626374 | + | 1.08491i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −457.760 | − | 264.288i | −0.682206 | − | 0.393872i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 79.5905 | − | 45.9516i | 0.118262 | − | 0.0682788i | −0.439702 | − | 0.898144i | \(-0.644916\pi\) |
0.557964 | + | 0.829865i | \(0.311583\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −365.763 | − | 633.520i | −0.540270 | − | 0.935776i | −0.998888 | − | 0.0471421i | \(-0.984989\pi\) |
0.458618 | − | 0.888634i | \(-0.348345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −190.478 | + | 329.917i | −0.280527 | + | 0.485887i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −645.786 | − | 372.845i | −0.948291 | − | 0.547496i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 682.177 | 0.998794 | 0.499397 | − | 0.866373i | \(-0.333555\pi\) | ||||
0.499397 | + | 0.866373i | \(0.333555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 473.335i | − | 0.688988i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.1452 | + | 12.2082i | 0.0306897 | + | 0.0177187i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 210.331 | + | 364.303i | 0.304386 | + | 0.527212i | 0.977124 | − | 0.212669i | \(-0.0682155\pi\) |
−0.672739 | + | 0.739880i | \(0.734882\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −196.961 | − | 341.147i | −0.284216 | − | 0.492276i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −262.898 | − | 151.784i | −0.377185 | − | 0.217768i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 864.780 | − | 499.281i | 1.23717 | − | 0.714279i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 70.8185i | 0.101025i | 0.998723 | + | 0.0505125i | \(0.0160855\pi\) | ||||
−0.998723 | + | 0.0505125i | \(0.983915\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 374.444i | − | 0.532637i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 189.806 | − | 328.754i | 0.268467 | − | 0.464998i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 399.696 | + | 692.293i | 0.563745 | + | 0.976436i | 0.997165 | + | 0.0752436i | \(0.0239734\pi\) |
−0.433420 | + | 0.901192i | \(0.642693\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 510.859 | 0.718508 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −519.727 | − | 900.194i | −0.728930 | − | 1.26254i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −719.541 | −1.00354 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 368.675i | 0.512761i | 0.966576 | + | 0.256381i | \(0.0825300\pi\) | ||||
−0.966576 | + | 0.256381i | \(0.917470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 61.0079 | 0.0846157 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 492.356 | + | 284.262i | 0.680991 | + | 0.393170i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 784.783 | − | 453.095i | 1.07948 | − | 0.623239i | 0.148725 | − | 0.988879i | \(-0.452483\pi\) |
0.930757 | + | 0.365640i | \(0.119150\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 424.833 | − | 245.277i | 0.581166 | − | 0.335537i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −87.9190 | − | 50.7601i | −0.119944 | − | 0.0692497i | 0.438828 | − | 0.898571i | \(-0.355394\pi\) |
−0.558772 | + | 0.829322i | \(0.688727\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1167.87 | 1.58463 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −557.665 | −0.754622 | −0.377311 | − | 0.926087i | \(-0.623151\pi\) | ||||
−0.377311 | + | 0.926087i | \(0.623151\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 180.859 | 0.244074 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 178.289 | − | 308.806i | 0.239959 | − | 0.415621i | −0.720743 | − | 0.693202i | \(-0.756199\pi\) |
0.960702 | + | 0.277581i | \(0.0895327\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −810.600 | −1.08514 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 275.329 | − | 158.961i | 0.367595 | − | 0.212231i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −244.810 | + | 424.024i | −0.325979 | + | 0.564613i | −0.981710 | − | 0.190382i | \(-0.939027\pi\) |
0.655731 | + | 0.754995i | \(0.272361\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 670.670 | + | 1161.63i | 0.890664 | + | 1.54268i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 198.379i | − | 0.262059i | −0.991378 | − | 0.131030i | \(-0.958172\pi\) | ||
0.991378 | − | 0.131030i | \(-0.0418283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 348.859 | + | 604.241i | 0.459630 | + | 0.796102i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.6653 | − | 17.7046i | −0.0402961 | − | 0.0232649i | 0.479717 | − | 0.877423i | \(-0.340739\pi\) |
−0.520013 | + | 0.854159i | \(0.674073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −525.440 | + | 303.363i | −0.688650 | + | 0.397592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 41.4889 | + | 71.8609i | 0.0540925 | + | 0.0936909i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −114.552 | + | 198.411i | −0.148963 | + | 0.258011i | −0.930844 | − | 0.365416i | \(-0.880927\pi\) |
0.781882 | + | 0.623427i | \(0.214260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1341.68i | 1.74018i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −905.388 | −1.17126 | −0.585632 | − | 0.810577i | \(-0.699154\pi\) | ||||
−0.585632 | + | 0.810577i | \(0.699154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 136.252 | + | 78.6653i | 0.175357 | + | 0.101242i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −601.784 | − | 347.440i | −0.772509 | − | 0.446008i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −599.425 | − | 1038.24i | −0.767510 | − | 1.32937i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −596.070 | − | 1032.42i | −0.761264 | − | 1.31855i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −128.423 | − | 74.1452i | −0.163181 | − | 0.0942125i | 0.416186 | − | 0.909280i | \(-0.363367\pi\) |
−0.579366 | + | 0.815067i | \(0.696700\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −921.139 | − | 531.820i | −1.16748 | − | 0.674043i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 25.9528i | − | 0.0328101i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 101.968i | 0.128585i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 122.864 | − | 212.806i | 0.154158 | − | 0.267009i | −0.778594 | − | 0.627528i | \(-0.784067\pi\) |
0.932752 | + | 0.360518i | \(0.117400\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −265.663 | − | 460.142i | −0.332495 | − | 0.575898i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 742.282 | + | 428.557i | 0.926694 | + | 0.535027i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 80.4006 | + | 139.258i | 0.100125 | + | 0.173422i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 341.050 | + | 590.716i | 0.422614 | + | 0.731990i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1551.44i | 1.91773i | 0.283865 | + | 0.958864i | \(0.408383\pi\) | ||||
−0.283865 | + | 0.958864i | \(0.591617\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −439.512 | −0.541939 | −0.270969 | − | 0.962588i | \(-0.587344\pi\) | ||||
−0.270969 | + | 0.962588i | \(0.587344\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 593.849 | − | 342.859i | 0.730442 | − | 0.421721i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 972.459 | − | 561.450i | 1.19028 | − | 0.687209i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −37.9959 | + | 65.8108i | −0.0463930 | + | 0.0803551i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 942.187 | − | 543.972i | 1.14761 | − | 0.662573i | 0.199306 | − | 0.979937i | \(-0.436131\pi\) |
0.948304 | + | 0.317365i | \(0.102798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 812.709 | + | 469.218i | 0.987496 | + | 0.570131i | 0.904525 | − | 0.426421i | \(-0.140226\pi\) |
0.0829708 | + | 0.996552i | \(0.473559\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 615.395 | 0.744129 | 0.372065 | − | 0.928207i | \(-0.378650\pi\) | ||||
0.372065 | + | 0.928207i | \(0.378650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 559.230 | 0.674583 | 0.337292 | − | 0.941400i | \(-0.390489\pi\) | ||||
0.337292 | + | 0.941400i | \(0.390489\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −660.665 | + | 1144.31i | −0.795024 | + | 1.37702i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −204.288 | + | 353.837i | −0.245243 | + | 0.424774i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1221.09 | − | 704.994i | −1.45888 | − | 0.842287i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 914.135 | − | 527.776i | 1.08955 | − | 0.629054i | 0.156096 | − | 0.987742i | \(-0.450109\pi\) |
0.933457 | + | 0.358688i | \(0.116776\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 554.258 | − | 960.003i | 0.659046 | − | 1.14150i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −471.446 | + | 816.569i | −0.559248 | + | 0.968646i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 58.1531i | 0.0686578i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −803.903 | −0.946882 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −241.331 | − | 139.332i | −0.283585 | − | 0.163728i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −79.5941 | + | 45.9536i | −0.0933107 | + | 0.0538730i | −0.545929 | − | 0.837831i | \(-0.683823\pi\) |
0.452619 | + | 0.891704i | \(0.350490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 589.498 | + | 1021.04i | 0.687862 | + | 1.19141i | 0.972528 | + | 0.232785i | \(0.0747840\pi\) |
−0.284666 | + | 0.958627i | \(0.591883\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −669.784 | + | 1160.10i | −0.779726 | + | 1.35052i | 0.152374 | + | 0.988323i | \(0.451308\pi\) |
−0.932100 | + | 0.362201i | \(0.882025\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 252.853 | − | 145.985i | 0.293673 | − | 0.169552i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1332.42 | 1.54393 | 0.771967 | − | 0.635663i | \(-0.219273\pi\) | ||||
0.771967 | + | 0.635663i | \(0.219273\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −396.144 | + | 228.714i | −0.456913 | + | 0.263799i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −574.373 | − | 331.614i | −0.660958 | − | 0.381605i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −112.647 | − | 195.111i | −0.129331 | − | 0.224007i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 915.278i | − | 1.04843i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −556.537 | − | 321.317i | −0.634591 | − | 0.366381i | 0.147937 | − | 0.988997i | \(-0.452737\pi\) |
−0.782528 | + | 0.622615i | \(0.786070\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 930.195i | 1.05824i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 983.693i | − | 1.11656i | −0.829651 | − | 0.558282i | \(-0.811461\pi\) | ||
0.829651 | − | 0.558282i | \(-0.188539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 197.540i | 0.223715i | 0.993724 | + | 0.111857i | \(0.0356800\pi\) | ||||
−0.993724 | + | 0.111857i | \(0.964320\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −655.920 | + | 1136.09i | −0.739481 | + | 1.28082i | 0.213248 | + | 0.976998i | \(0.431596\pi\) |
−0.952729 | + | 0.303821i | \(0.901738\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −423.113 | − | 732.853i | −0.475943 | − | 0.824357i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 819.635 | + | 473.216i | 0.919905 | + | 0.531107i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −608.114 | − | 1053.28i | −0.680979 | − | 1.17949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 67.2985 | − | 116.564i | 0.0750262 | − | 0.129949i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2305.76i | − | 2.56481i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 126.569 | 0.140476 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 471.810i | 0.522492i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1499.08 | + | 865.496i | −1.65279 | + | 0.954240i | −0.676876 | + | 0.736097i | \(0.736667\pi\) |
−0.975917 | + | 0.218143i | \(0.930000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 912.050i | 1.00336i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 210.720 | − | 121.659i | 0.231306 | − | 0.133545i | −0.379868 | − | 0.925041i | \(-0.624031\pi\) |
0.611174 | + | 0.791496i | \(0.290697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 911.380 | + | 526.185i | 0.998225 | + | 0.576326i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 353.450 | 0.385442 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −449.145 | −0.488733 | −0.244366 | − | 0.969683i | \(-0.578580\pi\) | ||||
−0.244366 | + | 0.969683i | \(0.578580\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 743.927 | + | 1288.52i | 0.807739 | + | 1.39904i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −115.635 | + | 200.286i | −0.125282 | + | 0.216995i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −126.939 | + | 73.2883i | −0.136935 | + | 0.0790597i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.2420 | − | 26.1205i | 0.0486997 | − | 0.0281168i | −0.475452 | − | 0.879741i | \(-0.657716\pi\) |
0.524152 | + | 0.851625i | \(0.324382\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −467.623 | + | 809.947i | −0.502280 | + | 0.869975i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −678.140 | −0.726838 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 196.798i | − | 0.210030i | −0.994471 | − | 0.105015i | \(-0.966511\pi\) | ||
0.994471 | − | 0.105015i | \(-0.0334891\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 490.736 | − | 849.979i | 0.522615 | − | 0.905196i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −822.375 | − | 474.798i | −0.873937 | − | 0.504568i | −0.00528258 | − | 0.999986i | \(-0.501682\pi\) |
−0.868655 | + | 0.495418i | \(0.835015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −447.854 | + | 258.569i | −0.474924 | + | 0.274198i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 814.378 | + | 1410.54i | 0.859956 | + | 1.48949i | 0.871970 | + | 0.489559i | \(0.162842\pi\) |
−0.0120142 | + | 0.999928i | \(0.503824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.5101 | − | 26.8643i | 0.0163436 | − | 0.0283080i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.2843 | + | 12.2885i | 0.0223809 | + | 0.0129216i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −789.836 | −0.828789 | −0.414395 | − | 0.910097i | \(-0.636007\pi\) | ||||
−0.414395 | + | 0.910097i | \(0.636007\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1547.71i | 1.61725i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 672.756 | + | 388.416i | 0.701518 | + | 0.405022i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −883.056 | − | 1529.50i | −0.918893 | − | 1.59157i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −381.917 | + | 661.500i | −0.396591 | + | 0.686916i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 456.689 | + | 263.669i | 0.472274 | + | 0.272667i | 0.717191 | − | 0.696877i | \(-0.245427\pi\) |
−0.244917 | + | 0.969544i | \(0.578761\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 811.923 | − | 468.764i | 0.837898 | − | 0.483761i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 179.700i | 0.185067i | 0.995710 | + | 0.0925337i | \(0.0294966\pi\) | ||||
−0.995710 | + | 0.0925337i | \(0.970503\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 122.544i | 0.125945i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −463.376 | + | 802.591i | −0.474284 | + | 0.821485i | −0.999566 | − | 0.0294434i | \(-0.990627\pi\) |
0.525282 | + | 0.850928i | \(0.323960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −556.379 | − | 963.677i | −0.568314 | − | 0.984348i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 728.855 | − | 1262.41i | 0.742971 | − | 1.28686i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 282.492 | + | 489.290i | 0.287377 | + | 0.497752i | 0.973183 | − | 0.230033i | \(-0.0738833\pi\) |
−0.685806 | + | 0.727785i | \(0.740550\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 511.025 | 0.517755 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 835.673i | − | 0.844967i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1815.42 | −1.83191 | −0.915953 | − | 0.401285i | \(-0.868564\pi\) | ||||
−0.915953 | + | 0.401285i | \(0.868564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −721.762 | − | 416.710i | −0.726850 | − | 0.419647i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −590.961 | + | 341.192i | −0.592739 | + | 0.342218i | −0.766180 | − | 0.642626i | \(-0.777845\pi\) |
0.173441 | + | 0.984844i | \(0.444512\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −378.000 | −0.378378 |
(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 | 900.3.u.b.149.3 | 8 | ||
3.2 | odd | 2 | 2700.3.u.a.449.2 | 8 | |||
5.2 | odd | 4 | 180.3.o.a.41.1 | ✓ | 4 | ||
5.3 | odd | 4 | 900.3.p.b.401.2 | 4 | |||
5.4 | even | 2 | inner | 900.3.u.b.149.2 | 8 | ||
9.2 | odd | 6 | inner | 900.3.u.b.749.2 | 8 | ||
9.7 | even | 3 | 2700.3.u.a.2249.3 | 8 | |||
15.2 | even | 4 | 540.3.o.a.341.2 | 4 | |||
15.8 | even | 4 | 2700.3.p.a.2501.2 | 4 | |||
15.14 | odd | 2 | 2700.3.u.a.449.3 | 8 | |||
20.7 | even | 4 | 720.3.bs.a.401.1 | 4 | |||
45.2 | even | 12 | 180.3.o.a.101.1 | yes | 4 | ||
45.7 | odd | 12 | 540.3.o.a.521.2 | 4 | |||
45.22 | odd | 12 | 1620.3.g.a.161.4 | 4 | |||
45.29 | odd | 6 | inner | 900.3.u.b.749.3 | 8 | ||
45.32 | even | 12 | 1620.3.g.a.161.2 | 4 | |||
45.34 | even | 6 | 2700.3.u.a.2249.2 | 8 | |||
45.38 | even | 12 | 900.3.p.b.101.2 | 4 | |||
45.43 | odd | 12 | 2700.3.p.a.1601.2 | 4 | |||
60.47 | odd | 4 | 2160.3.bs.a.881.2 | 4 | |||
180.7 | even | 12 | 2160.3.bs.a.1601.2 | 4 | |||
180.47 | odd | 12 | 720.3.bs.a.641.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.o.a.41.1 | ✓ | 4 | 5.2 | odd | 4 | ||
180.3.o.a.101.1 | yes | 4 | 45.2 | even | 12 | ||
540.3.o.a.341.2 | 4 | 15.2 | even | 4 | |||
540.3.o.a.521.2 | 4 | 45.7 | odd | 12 | |||
720.3.bs.a.401.1 | 4 | 20.7 | even | 4 | |||
720.3.bs.a.641.1 | 4 | 180.47 | odd | 12 | |||
900.3.p.b.101.2 | 4 | 45.38 | even | 12 | |||
900.3.p.b.401.2 | 4 | 5.3 | odd | 4 | |||
900.3.u.b.149.2 | 8 | 5.4 | even | 2 | inner | ||
900.3.u.b.149.3 | 8 | 1.1 | even | 1 | trivial | ||
900.3.u.b.749.2 | 8 | 9.2 | odd | 6 | inner | ||
900.3.u.b.749.3 | 8 | 45.29 | odd | 6 | inner | ||
1620.3.g.a.161.2 | 4 | 45.32 | even | 12 | |||
1620.3.g.a.161.4 | 4 | 45.22 | odd | 12 | |||
2160.3.bs.a.881.2 | 4 | 60.47 | odd | 4 | |||
2160.3.bs.a.1601.2 | 4 | 180.7 | even | 12 | |||
2700.3.p.a.1601.2 | 4 | 45.43 | odd | 12 | |||
2700.3.p.a.2501.2 | 4 | 15.8 | even | 4 | |||
2700.3.u.a.449.2 | 8 | 3.2 | odd | 2 | |||
2700.3.u.a.449.3 | 8 | 15.14 | odd | 2 | |||
2700.3.u.a.2249.2 | 8 | 45.34 | even | 6 | |||
2700.3.u.a.2249.3 | 8 | 9.7 | even | 3 |